1,1,192,0,0.414636," ","integrate(x^3*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, b^{5} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(384 \, c^{5} x^{4} + 48 \, b c^{4} x^{3} - 56 \, b^{2} c^{3} x^{2} + 70 \, b^{3} c^{2} x - 105 \, b^{4} c\right)} \sqrt{c x^{2} + b x}}{3840 \, c^{5}}, -\frac{105 \, b^{5} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(384 \, c^{5} x^{4} + 48 \, b c^{4} x^{3} - 56 \, b^{2} c^{3} x^{2} + 70 \, b^{3} c^{2} x - 105 \, b^{4} c\right)} \sqrt{c x^{2} + b x}}{1920 \, c^{5}}\right]"," ",0,"[1/3840*(105*b^5*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(384*c^5*x^4 + 48*b*c^4*x^3 - 56*b^2*c^3*x^2 + 70*b^3*c^2*x - 105*b^4*c)*sqrt(c*x^2 + b*x))/c^5, -1/1920*(105*b^5*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (384*c^5*x^4 + 48*b*c^4*x^3 - 56*b^2*c^3*x^2 + 70*b^3*c^2*x - 105*b^4*c)*sqrt(c*x^2 + b*x))/c^5]","A",0
2,1,169,0,0.406138," ","integrate(x^2*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, b^{4} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(48 \, c^{4} x^{3} + 8 \, b c^{3} x^{2} - 10 \, b^{2} c^{2} x + 15 \, b^{3} c\right)} \sqrt{c x^{2} + b x}}{384 \, c^{4}}, \frac{15 \, b^{4} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(48 \, c^{4} x^{3} + 8 \, b c^{3} x^{2} - 10 \, b^{2} c^{2} x + 15 \, b^{3} c\right)} \sqrt{c x^{2} + b x}}{192 \, c^{4}}\right]"," ",0,"[1/384*(15*b^4*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(48*c^4*x^3 + 8*b*c^3*x^2 - 10*b^2*c^2*x + 15*b^3*c)*sqrt(c*x^2 + b*x))/c^4, 1/192*(15*b^4*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (48*c^4*x^3 + 8*b*c^3*x^2 - 10*b^2*c^2*x + 15*b^3*c)*sqrt(c*x^2 + b*x))/c^4]","A",0
3,1,148,0,0.420423," ","integrate(x*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, b^{3} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(8 \, c^{3} x^{2} + 2 \, b c^{2} x - 3 \, b^{2} c\right)} \sqrt{c x^{2} + b x}}{48 \, c^{3}}, -\frac{3 \, b^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(8 \, c^{3} x^{2} + 2 \, b c^{2} x - 3 \, b^{2} c\right)} \sqrt{c x^{2} + b x}}{24 \, c^{3}}\right]"," ",0,"[1/48*(3*b^3*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(8*c^3*x^2 + 2*b*c^2*x - 3*b^2*c)*sqrt(c*x^2 + b*x))/c^3, -1/24*(3*b^3*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (8*c^3*x^2 + 2*b*c^2*x - 3*b^2*c)*sqrt(c*x^2 + b*x))/c^3]","A",0
4,1,121,0,0.419667," ","integrate((c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{b^{2} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(2 \, c^{2} x + b c\right)} \sqrt{c x^{2} + b x}}{8 \, c^{2}}, \frac{b^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(2 \, c^{2} x + b c\right)} \sqrt{c x^{2} + b x}}{4 \, c^{2}}\right]"," ",0,"[1/8*(b^2*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(2*c^2*x + b*c)*sqrt(c*x^2 + b*x))/c^2, 1/4*(b^2*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (2*c^2*x + b*c)*sqrt(c*x^2 + b*x))/c^2]","A",0
5,1,100,0,0.419223," ","integrate((c*x^2+b*x)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, \sqrt{c x^{2} + b x} c}{2 \, c}, -\frac{b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - \sqrt{c x^{2} + b x} c}{c}\right]"," ",0,"[1/2*(b*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*sqrt(c*x^2 + b*x)*c)/c, -(b*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - sqrt(c*x^2 + b*x)*c)/c]","A",0
6,1,95,0,0.415161," ","integrate((c*x^2+b*x)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{\sqrt{c} x \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, \sqrt{c x^{2} + b x}}{x}, -\frac{2 \, {\left(\sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + \sqrt{c x^{2} + b x}\right)}}{x}\right]"," ",0,"[(sqrt(c)*x*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*sqrt(c*x^2 + b*x))/x, -2*(sqrt(-c)*x*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + sqrt(c*x^2 + b*x))/x]","A",0
7,1,24,0,0.406914," ","integrate((c*x^2+b*x)^(1/2)/x^3,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x} {\left(c x + b\right)}}{3 \, b x^{2}}"," ",0,"-2/3*sqrt(c*x^2 + b*x)*(c*x + b)/(b*x^2)","A",0
8,1,38,0,0.385581," ","integrate((c*x^2+b*x)^(1/2)/x^4,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, c^{2} x^{2} - b c x - 3 \, b^{2}\right)} \sqrt{c x^{2} + b x}}{15 \, b^{2} x^{3}}"," ",0,"2/15*(2*c^2*x^2 - b*c*x - 3*b^2)*sqrt(c*x^2 + b*x)/(b^2*x^3)","A",0
9,1,49,0,0.389845," ","integrate((c*x^2+b*x)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, c^{3} x^{3} - 4 \, b c^{2} x^{2} + 3 \, b^{2} c x + 15 \, b^{3}\right)} \sqrt{c x^{2} + b x}}{105 \, b^{3} x^{4}}"," ",0,"-2/105*(8*c^3*x^3 - 4*b*c^2*x^2 + 3*b^2*c*x + 15*b^3)*sqrt(c*x^2 + b*x)/(b^3*x^4)","A",0
10,1,60,0,0.385960," ","integrate((c*x^2+b*x)^(1/2)/x^6,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{4} x^{4} - 8 \, b c^{3} x^{3} + 6 \, b^{2} c^{2} x^{2} - 5 \, b^{3} c x - 35 \, b^{4}\right)} \sqrt{c x^{2} + b x}}{315 \, b^{4} x^{5}}"," ",0,"2/315*(16*c^4*x^4 - 8*b*c^3*x^3 + 6*b^2*c^2*x^2 - 5*b^3*c*x - 35*b^4)*sqrt(c*x^2 + b*x)/(b^4*x^5)","A",0
11,1,71,0,0.393259," ","integrate((c*x^2+b*x)^(1/2)/x^7,x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, c^{5} x^{5} - 64 \, b c^{4} x^{4} + 48 \, b^{2} c^{3} x^{3} - 40 \, b^{3} c^{2} x^{2} + 35 \, b^{4} c x + 315 \, b^{5}\right)} \sqrt{c x^{2} + b x}}{3465 \, b^{5} x^{6}}"," ",0,"-2/3465*(128*c^5*x^5 - 64*b*c^4*x^4 + 48*b^2*c^3*x^3 - 40*b^3*c^2*x^2 + 35*b^4*c*x + 315*b^5)*sqrt(c*x^2 + b*x)/(b^5*x^6)","A",0
12,1,214,0,0.416646," ","integrate(x^2*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, b^{6} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(1280 \, c^{6} x^{5} + 1664 \, b c^{5} x^{4} + 48 \, b^{2} c^{4} x^{3} - 56 \, b^{3} c^{3} x^{2} + 70 \, b^{4} c^{2} x - 105 \, b^{5} c\right)} \sqrt{c x^{2} + b x}}{15360 \, c^{5}}, -\frac{105 \, b^{6} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(1280 \, c^{6} x^{5} + 1664 \, b c^{5} x^{4} + 48 \, b^{2} c^{4} x^{3} - 56 \, b^{3} c^{3} x^{2} + 70 \, b^{4} c^{2} x - 105 \, b^{5} c\right)} \sqrt{c x^{2} + b x}}{7680 \, c^{5}}\right]"," ",0,"[1/15360*(105*b^6*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(1280*c^6*x^5 + 1664*b*c^5*x^4 + 48*b^2*c^4*x^3 - 56*b^3*c^3*x^2 + 70*b^4*c^2*x - 105*b^5*c)*sqrt(c*x^2 + b*x))/c^5, -1/7680*(105*b^6*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (1280*c^6*x^5 + 1664*b*c^5*x^4 + 48*b^2*c^4*x^3 - 56*b^3*c^3*x^2 + 70*b^4*c^2*x - 105*b^5*c)*sqrt(c*x^2 + b*x))/c^5]","A",0
13,1,191,0,0.423472," ","integrate(x*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, b^{5} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(128 \, c^{5} x^{4} + 176 \, b c^{4} x^{3} + 8 \, b^{2} c^{3} x^{2} - 10 \, b^{3} c^{2} x + 15 \, b^{4} c\right)} \sqrt{c x^{2} + b x}}{1280 \, c^{4}}, \frac{15 \, b^{5} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(128 \, c^{5} x^{4} + 176 \, b c^{4} x^{3} + 8 \, b^{2} c^{3} x^{2} - 10 \, b^{3} c^{2} x + 15 \, b^{4} c\right)} \sqrt{c x^{2} + b x}}{640 \, c^{4}}\right]"," ",0,"[1/1280*(15*b^5*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(128*c^5*x^4 + 176*b*c^4*x^3 + 8*b^2*c^3*x^2 - 10*b^3*c^2*x + 15*b^4*c)*sqrt(c*x^2 + b*x))/c^4, 1/640*(15*b^5*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (128*c^5*x^4 + 176*b*c^4*x^3 + 8*b^2*c^3*x^2 - 10*b^3*c^2*x + 15*b^4*c)*sqrt(c*x^2 + b*x))/c^4]","A",0
14,1,170,0,0.422585," ","integrate((c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, b^{4} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(16 \, c^{4} x^{3} + 24 \, b c^{3} x^{2} + 2 \, b^{2} c^{2} x - 3 \, b^{3} c\right)} \sqrt{c x^{2} + b x}}{128 \, c^{3}}, -\frac{3 \, b^{4} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(16 \, c^{4} x^{3} + 24 \, b c^{3} x^{2} + 2 \, b^{2} c^{2} x - 3 \, b^{3} c\right)} \sqrt{c x^{2} + b x}}{64 \, c^{3}}\right]"," ",0,"[1/128*(3*b^4*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(16*c^4*x^3 + 24*b*c^3*x^2 + 2*b^2*c^2*x - 3*b^3*c)*sqrt(c*x^2 + b*x))/c^3, -1/64*(3*b^4*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (16*c^4*x^3 + 24*b*c^3*x^2 + 2*b^2*c^2*x - 3*b^3*c)*sqrt(c*x^2 + b*x))/c^3]","A",0
15,1,147,0,0.418059," ","integrate((c*x^2+b*x)^(3/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, b^{3} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(8 \, c^{3} x^{2} + 14 \, b c^{2} x + 3 \, b^{2} c\right)} \sqrt{c x^{2} + b x}}{48 \, c^{2}}, \frac{3 \, b^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, c^{3} x^{2} + 14 \, b c^{2} x + 3 \, b^{2} c\right)} \sqrt{c x^{2} + b x}}{24 \, c^{2}}\right]"," ",0,"[1/48*(3*b^3*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(8*c^3*x^2 + 14*b*c^2*x + 3*b^2*c)*sqrt(c*x^2 + b*x))/c^2, 1/24*(3*b^3*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*c^3*x^2 + 14*b*c^2*x + 3*b^2*c)*sqrt(c*x^2 + b*x))/c^2]","A",0
16,1,126,0,0.419246," ","integrate((c*x^2+b*x)^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, b^{2} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(2 \, c^{2} x + 5 \, b c\right)} \sqrt{c x^{2} + b x}}{8 \, c}, -\frac{3 \, b^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(2 \, c^{2} x + 5 \, b c\right)} \sqrt{c x^{2} + b x}}{4 \, c}\right]"," ",0,"[1/8*(3*b^2*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(2*c^2*x + 5*b*c)*sqrt(c*x^2 + b*x))/c, -1/4*(3*b^2*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (2*c^2*x + 5*b*c)*sqrt(c*x^2 + b*x))/c]","A",0
17,1,116,0,0.401783," ","integrate((c*x^2+b*x)^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, b \sqrt{c} x \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, \sqrt{c x^{2} + b x} {\left(c x - 2 \, b\right)}}{2 \, x}, -\frac{3 \, b \sqrt{-c} x \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - \sqrt{c x^{2} + b x} {\left(c x - 2 \, b\right)}}{x}\right]"," ",0,"[1/2*(3*b*sqrt(c)*x*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*sqrt(c*x^2 + b*x)*(c*x - 2*b))/x, -(3*b*sqrt(-c)*x*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - sqrt(c*x^2 + b*x)*(c*x - 2*b))/x]","A",0
18,1,116,0,0.414182," ","integrate((c*x^2+b*x)^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, c^{\frac{3}{2}} x^{2} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, \sqrt{c x^{2} + b x} {\left(4 \, c x + b\right)}}{3 \, x^{2}}, -\frac{2 \, {\left(3 \, \sqrt{-c} c x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + \sqrt{c x^{2} + b x} {\left(4 \, c x + b\right)}\right)}}{3 \, x^{2}}\right]"," ",0,"[1/3*(3*c^(3/2)*x^2*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*sqrt(c*x^2 + b*x)*(4*c*x + b))/x^2, -2/3*(3*sqrt(-c)*c*x^2*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + sqrt(c*x^2 + b*x)*(4*c*x + b))/x^2]","A",0
19,1,35,0,0.389206," ","integrate((c*x^2+b*x)^(3/2)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(c^{2} x^{2} + 2 \, b c x + b^{2}\right)} \sqrt{c x^{2} + b x}}{5 \, b x^{3}}"," ",0,"-2/5*(c^2*x^2 + 2*b*c*x + b^2)*sqrt(c*x^2 + b*x)/(b*x^3)","A",0
20,1,49,0,0.399316," ","integrate((c*x^2+b*x)^(3/2)/x^6,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, c^{3} x^{3} - b c^{2} x^{2} - 8 \, b^{2} c x - 5 \, b^{3}\right)} \sqrt{c x^{2} + b x}}{35 \, b^{2} x^{4}}"," ",0,"2/35*(2*c^3*x^3 - b*c^2*x^2 - 8*b^2*c*x - 5*b^3)*sqrt(c*x^2 + b*x)/(b^2*x^4)","A",0
21,1,60,0,0.385274," ","integrate((c*x^2+b*x)^(3/2)/x^7,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, c^{4} x^{4} - 4 \, b c^{3} x^{3} + 3 \, b^{2} c^{2} x^{2} + 50 \, b^{3} c x + 35 \, b^{4}\right)} \sqrt{c x^{2} + b x}}{315 \, b^{3} x^{5}}"," ",0,"-2/315*(8*c^4*x^4 - 4*b*c^3*x^3 + 3*b^2*c^2*x^2 + 50*b^3*c*x + 35*b^4)*sqrt(c*x^2 + b*x)/(b^3*x^5)","A",0
22,1,71,0,0.405232," ","integrate((c*x^2+b*x)^(3/2)/x^8,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{5} x^{5} - 8 \, b c^{4} x^{4} + 6 \, b^{2} c^{3} x^{3} - 5 \, b^{3} c^{2} x^{2} - 140 \, b^{4} c x - 105 \, b^{5}\right)} \sqrt{c x^{2} + b x}}{1155 \, b^{4} x^{6}}"," ",0,"2/1155*(16*c^5*x^5 - 8*b*c^4*x^4 + 6*b^2*c^3*x^3 - 5*b^3*c^2*x^2 - 140*b^4*c*x - 105*b^5)*sqrt(c*x^2 + b*x)/(b^4*x^6)","A",0
23,1,82,0,0.385507," ","integrate((c*x^2+b*x)^(3/2)/x^9,x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, c^{6} x^{6} - 64 \, b c^{5} x^{5} + 48 \, b^{2} c^{4} x^{4} - 40 \, b^{3} c^{3} x^{3} + 35 \, b^{4} c^{2} x^{2} + 1470 \, b^{5} c x + 1155 \, b^{6}\right)} \sqrt{c x^{2} + b x}}{15015 \, b^{5} x^{7}}"," ",0,"-2/15015*(128*c^6*x^6 - 64*b*c^5*x^5 + 48*b^2*c^4*x^4 - 40*b^3*c^3*x^3 + 35*b^4*c^2*x^2 + 1470*b^5*c*x + 1155*b^6)*sqrt(c*x^2 + b*x)/(b^5*x^7)","A",0
24,1,257,0,0.424589," ","integrate(x^2*(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, a^{8} \sqrt{b} \log\left(2 \, b x + a - 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) + 2 \, {\left(14336 \, b^{8} x^{7} + 33792 \, a b^{7} x^{6} + 20736 \, a^{2} b^{6} x^{5} + 128 \, a^{3} b^{5} x^{4} - 144 \, a^{4} b^{4} x^{3} + 168 \, a^{5} b^{3} x^{2} - 210 \, a^{6} b^{2} x + 315 \, a^{7} b\right)} \sqrt{b x^{2} + a x}}{229376 \, b^{6}}, \frac{315 \, a^{8} \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) + {\left(14336 \, b^{8} x^{7} + 33792 \, a b^{7} x^{6} + 20736 \, a^{2} b^{6} x^{5} + 128 \, a^{3} b^{5} x^{4} - 144 \, a^{4} b^{4} x^{3} + 168 \, a^{5} b^{3} x^{2} - 210 \, a^{6} b^{2} x + 315 \, a^{7} b\right)} \sqrt{b x^{2} + a x}}{114688 \, b^{6}}\right]"," ",0,"[1/229376*(315*a^8*sqrt(b)*log(2*b*x + a - 2*sqrt(b*x^2 + a*x)*sqrt(b)) + 2*(14336*b^8*x^7 + 33792*a*b^7*x^6 + 20736*a^2*b^6*x^5 + 128*a^3*b^5*x^4 - 144*a^4*b^4*x^3 + 168*a^5*b^3*x^2 - 210*a^6*b^2*x + 315*a^7*b)*sqrt(b*x^2 + a*x))/b^6, 1/114688*(315*a^8*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) + (14336*b^8*x^7 + 33792*a*b^7*x^6 + 20736*a^2*b^6*x^5 + 128*a^3*b^5*x^4 - 144*a^4*b^4*x^3 + 168*a^5*b^3*x^2 - 210*a^6*b^2*x + 315*a^7*b)*sqrt(b*x^2 + a*x))/b^6]","A",0
25,1,236,0,0.413095," ","integrate(x*(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, a^{7} \sqrt{b} \log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) + 2 \, {\left(3072 \, b^{7} x^{6} + 7424 \, a b^{6} x^{5} + 4736 \, a^{2} b^{5} x^{4} + 48 \, a^{3} b^{4} x^{3} - 56 \, a^{4} b^{3} x^{2} + 70 \, a^{5} b^{2} x - 105 \, a^{6} b\right)} \sqrt{b x^{2} + a x}}{43008 \, b^{5}}, -\frac{105 \, a^{7} \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) - {\left(3072 \, b^{7} x^{6} + 7424 \, a b^{6} x^{5} + 4736 \, a^{2} b^{5} x^{4} + 48 \, a^{3} b^{4} x^{3} - 56 \, a^{4} b^{3} x^{2} + 70 \, a^{5} b^{2} x - 105 \, a^{6} b\right)} \sqrt{b x^{2} + a x}}{21504 \, b^{5}}\right]"," ",0,"[1/43008*(105*a^7*sqrt(b)*log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b)) + 2*(3072*b^7*x^6 + 7424*a*b^6*x^5 + 4736*a^2*b^5*x^4 + 48*a^3*b^4*x^3 - 56*a^4*b^3*x^2 + 70*a^5*b^2*x - 105*a^6*b)*sqrt(b*x^2 + a*x))/b^5, -1/21504*(105*a^7*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) - (3072*b^7*x^6 + 7424*a*b^6*x^5 + 4736*a^2*b^5*x^4 + 48*a^3*b^4*x^3 - 56*a^4*b^3*x^2 + 70*a^5*b^2*x - 105*a^6*b)*sqrt(b*x^2 + a*x))/b^5]","A",0
26,1,213,0,0.406942," ","integrate((b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{6} \sqrt{b} \log\left(2 \, b x + a - 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) + 2 \, {\left(256 \, b^{6} x^{5} + 640 \, a b^{5} x^{4} + 432 \, a^{2} b^{4} x^{3} + 8 \, a^{3} b^{3} x^{2} - 10 \, a^{4} b^{2} x + 15 \, a^{5} b\right)} \sqrt{b x^{2} + a x}}{3072 \, b^{4}}, \frac{15 \, a^{6} \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) + {\left(256 \, b^{6} x^{5} + 640 \, a b^{5} x^{4} + 432 \, a^{2} b^{4} x^{3} + 8 \, a^{3} b^{3} x^{2} - 10 \, a^{4} b^{2} x + 15 \, a^{5} b\right)} \sqrt{b x^{2} + a x}}{1536 \, b^{4}}\right]"," ",0,"[1/3072*(15*a^6*sqrt(b)*log(2*b*x + a - 2*sqrt(b*x^2 + a*x)*sqrt(b)) + 2*(256*b^6*x^5 + 640*a*b^5*x^4 + 432*a^2*b^4*x^3 + 8*a^3*b^3*x^2 - 10*a^4*b^2*x + 15*a^5*b)*sqrt(b*x^2 + a*x))/b^4, 1/1536*(15*a^6*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) + (256*b^6*x^5 + 640*a*b^5*x^4 + 432*a^2*b^4*x^3 + 8*a^3*b^3*x^2 - 10*a^4*b^2*x + 15*a^5*b)*sqrt(b*x^2 + a*x))/b^4]","A",0
27,1,192,0,0.417840," ","integrate((b*x^2+a*x)^(5/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, a^{5} \sqrt{b} \log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) + 2 \, {\left(128 \, b^{5} x^{4} + 336 \, a b^{4} x^{3} + 248 \, a^{2} b^{3} x^{2} + 10 \, a^{3} b^{2} x - 15 \, a^{4} b\right)} \sqrt{b x^{2} + a x}}{1280 \, b^{3}}, -\frac{15 \, a^{5} \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) - {\left(128 \, b^{5} x^{4} + 336 \, a b^{4} x^{3} + 248 \, a^{2} b^{3} x^{2} + 10 \, a^{3} b^{2} x - 15 \, a^{4} b\right)} \sqrt{b x^{2} + a x}}{640 \, b^{3}}\right]"," ",0,"[1/1280*(15*a^5*sqrt(b)*log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b)) + 2*(128*b^5*x^4 + 336*a*b^4*x^3 + 248*a^2*b^3*x^2 + 10*a^3*b^2*x - 15*a^4*b)*sqrt(b*x^2 + a*x))/b^3, -1/640*(15*a^5*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) - (128*b^5*x^4 + 336*a*b^4*x^3 + 248*a^2*b^3*x^2 + 10*a^3*b^2*x - 15*a^4*b)*sqrt(b*x^2 + a*x))/b^3]","A",0
28,1,169,0,0.419403," ","integrate((b*x^2+a*x)^(5/2)/x^2,x, algorithm=""fricas"")","\left[\frac{15 \, a^{4} \sqrt{b} \log\left(2 \, b x + a - 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) + 2 \, {\left(48 \, b^{4} x^{3} + 136 \, a b^{3} x^{2} + 118 \, a^{2} b^{2} x + 15 \, a^{3} b\right)} \sqrt{b x^{2} + a x}}{384 \, b^{2}}, \frac{15 \, a^{4} \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) + {\left(48 \, b^{4} x^{3} + 136 \, a b^{3} x^{2} + 118 \, a^{2} b^{2} x + 15 \, a^{3} b\right)} \sqrt{b x^{2} + a x}}{192 \, b^{2}}\right]"," ",0,"[1/384*(15*a^4*sqrt(b)*log(2*b*x + a - 2*sqrt(b*x^2 + a*x)*sqrt(b)) + 2*(48*b^4*x^3 + 136*a*b^3*x^2 + 118*a^2*b^2*x + 15*a^3*b)*sqrt(b*x^2 + a*x))/b^2, 1/192*(15*a^4*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) + (48*b^4*x^3 + 136*a*b^3*x^2 + 118*a^2*b^2*x + 15*a^3*b)*sqrt(b*x^2 + a*x))/b^2]","A",0
29,1,148,0,0.419583," ","integrate((b*x^2+a*x)^(5/2)/x^3,x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} \log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) + 2 \, {\left(8 \, b^{3} x^{2} + 26 \, a b^{2} x + 33 \, a^{2} b\right)} \sqrt{b x^{2} + a x}}{48 \, b}, -\frac{15 \, a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) - {\left(8 \, b^{3} x^{2} + 26 \, a b^{2} x + 33 \, a^{2} b\right)} \sqrt{b x^{2} + a x}}{24 \, b}\right]"," ",0,"[1/48*(15*a^3*sqrt(b)*log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b)) + 2*(8*b^3*x^2 + 26*a*b^2*x + 33*a^2*b)*sqrt(b*x^2 + a*x))/b, -1/24*(15*a^3*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) - (8*b^3*x^2 + 26*a*b^2*x + 33*a^2*b)*sqrt(b*x^2 + a*x))/b]","A",0
30,1,144,0,0.424829," ","integrate((b*x^2+a*x)^(5/2)/x^4,x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} \sqrt{b} x \log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) + 2 \, {\left(2 \, b^{2} x^{2} + 9 \, a b x - 8 \, a^{2}\right)} \sqrt{b x^{2} + a x}}{8 \, x}, -\frac{15 \, a^{2} \sqrt{-b} x \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) - {\left(2 \, b^{2} x^{2} + 9 \, a b x - 8 \, a^{2}\right)} \sqrt{b x^{2} + a x}}{4 \, x}\right]"," ",0,"[1/8*(15*a^2*sqrt(b)*x*log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b)) + 2*(2*b^2*x^2 + 9*a*b*x - 8*a^2)*sqrt(b*x^2 + a*x))/x, -1/4*(15*a^2*sqrt(-b)*x*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) - (2*b^2*x^2 + 9*a*b*x - 8*a^2)*sqrt(b*x^2 + a*x))/x]","A",0
31,1,145,0,0.407045," ","integrate((b*x^2+a*x)^(5/2)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, a b^{\frac{3}{2}} x^{2} \log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) + 2 \, {\left(3 \, b^{2} x^{2} - 14 \, a b x - 2 \, a^{2}\right)} \sqrt{b x^{2} + a x}}{6 \, x^{2}}, -\frac{15 \, a \sqrt{-b} b x^{2} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) - {\left(3 \, b^{2} x^{2} - 14 \, a b x - 2 \, a^{2}\right)} \sqrt{b x^{2} + a x}}{3 \, x^{2}}\right]"," ",0,"[1/6*(15*a*b^(3/2)*x^2*log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b)) + 2*(3*b^2*x^2 - 14*a*b*x - 2*a^2)*sqrt(b*x^2 + a*x))/x^2, -1/3*(15*a*sqrt(-b)*b*x^2*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) - (3*b^2*x^2 - 14*a*b*x - 2*a^2)*sqrt(b*x^2 + a*x))/x^2]","A",0
32,1,144,0,0.412147," ","integrate((b*x^2+a*x)^(5/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, b^{\frac{5}{2}} x^{3} \log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) - 2 \, {\left(23 \, b^{2} x^{2} + 11 \, a b x + 3 \, a^{2}\right)} \sqrt{b x^{2} + a x}}{15 \, x^{3}}, -\frac{2 \, {\left(15 \, \sqrt{-b} b^{2} x^{3} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) + {\left(23 \, b^{2} x^{2} + 11 \, a b x + 3 \, a^{2}\right)} \sqrt{b x^{2} + a x}\right)}}{15 \, x^{3}}\right]"," ",0,"[1/15*(15*b^(5/2)*x^3*log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b)) - 2*(23*b^2*x^2 + 11*a*b*x + 3*a^2)*sqrt(b*x^2 + a*x))/x^3, -2/15*(15*sqrt(-b)*b^2*x^3*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) + (23*b^2*x^2 + 11*a*b*x + 3*a^2)*sqrt(b*x^2 + a*x))/x^3]","A",0
33,1,46,0,0.399680," ","integrate((b*x^2+a*x)^(5/2)/x^7,x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} \sqrt{b x^{2} + a x}}{7 \, a x^{4}}"," ",0,"-2/7*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*sqrt(b*x^2 + a*x)/(a*x^4)","B",0
34,1,60,0,0.399907," ","integrate((b*x^2+a*x)^(5/2)/x^8,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b^{4} x^{4} - a b^{3} x^{3} - 15 \, a^{2} b^{2} x^{2} - 19 \, a^{3} b x - 7 \, a^{4}\right)} \sqrt{b x^{2} + a x}}{63 \, a^{2} x^{5}}"," ",0,"2/63*(2*b^4*x^4 - a*b^3*x^3 - 15*a^2*b^2*x^2 - 19*a^3*b*x - 7*a^4)*sqrt(b*x^2 + a*x)/(a^2*x^5)","A",0
35,1,71,0,0.401947," ","integrate((b*x^2+a*x)^(5/2)/x^9,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, b^{5} x^{5} - 4 \, a b^{4} x^{4} + 3 \, a^{2} b^{3} x^{3} + 113 \, a^{3} b^{2} x^{2} + 161 \, a^{4} b x + 63 \, a^{5}\right)} \sqrt{b x^{2} + a x}}{693 \, a^{3} x^{6}}"," ",0,"-2/693*(8*b^5*x^5 - 4*a*b^4*x^4 + 3*a^2*b^3*x^3 + 113*a^3*b^2*x^2 + 161*a^4*b*x + 63*a^5)*sqrt(b*x^2 + a*x)/(a^3*x^6)","A",0
36,1,82,0,0.400814," ","integrate((b*x^2+a*x)^(5/2)/x^10,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, b^{6} x^{6} - 8 \, a b^{5} x^{5} + 6 \, a^{2} b^{4} x^{4} - 5 \, a^{3} b^{3} x^{3} - 371 \, a^{4} b^{2} x^{2} - 567 \, a^{5} b x - 231 \, a^{6}\right)} \sqrt{b x^{2} + a x}}{3003 \, a^{4} x^{7}}"," ",0,"2/3003*(16*b^6*x^6 - 8*a*b^5*x^5 + 6*a^2*b^4*x^4 - 5*a^3*b^3*x^3 - 371*a^4*b^2*x^2 - 567*a^5*b*x - 231*a^6)*sqrt(b*x^2 + a*x)/(a^4*x^7)","A",0
37,1,93,0,0.392204," ","integrate((b*x^2+a*x)^(5/2)/x^11,x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, b^{7} x^{7} - 64 \, a b^{6} x^{6} + 48 \, a^{2} b^{5} x^{5} - 40 \, a^{3} b^{4} x^{4} + 35 \, a^{4} b^{3} x^{3} + 4473 \, a^{5} b^{2} x^{2} + 7161 \, a^{6} b x + 3003 \, a^{7}\right)} \sqrt{b x^{2} + a x}}{45045 \, a^{5} x^{8}}"," ",0,"-2/45045*(128*b^7*x^7 - 64*a*b^6*x^6 + 48*a^2*b^5*x^5 - 40*a^3*b^4*x^4 + 35*a^4*b^3*x^3 + 4473*a^5*b^2*x^2 + 7161*a^6*b*x + 3003*a^7)*sqrt(b*x^2 + a*x)/(a^5*x^8)","A",0
38,1,104,0,0.391015," ","integrate((b*x^2+a*x)^(5/2)/x^12,x, algorithm=""fricas"")","\frac{2 \, {\left(256 \, b^{8} x^{8} - 128 \, a b^{7} x^{7} + 96 \, a^{2} b^{6} x^{6} - 80 \, a^{3} b^{5} x^{5} + 70 \, a^{4} b^{4} x^{4} - 63 \, a^{5} b^{3} x^{3} - 12705 \, a^{6} b^{2} x^{2} - 21021 \, a^{7} b x - 9009 \, a^{8}\right)} \sqrt{b x^{2} + a x}}{153153 \, a^{6} x^{9}}"," ",0,"2/153153*(256*b^8*x^8 - 128*a*b^7*x^7 + 96*a^2*b^6*x^6 - 80*a^3*b^5*x^5 + 70*a^4*b^4*x^4 - 63*a^5*b^3*x^3 - 12705*a^6*b^2*x^2 - 21021*a^7*b*x - 9009*a^8)*sqrt(b*x^2 + a*x)/(a^6*x^9)","A",0
39,1,42,0,0.400179," ","integrate(x*(-x^2+2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(2 \, x^{2} - x - 3\right)} \sqrt{-x^{2} + 2 \, x} - \arctan\left(\frac{\sqrt{-x^{2} + 2 \, x}}{x}\right)"," ",0,"1/6*(2*x^2 - x - 3)*sqrt(-x^2 + 2*x) - arctan(sqrt(-x^2 + 2*x)/x)","A",0
40,1,43,0,0.395007," ","integrate(x*(-4*x^2+3*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{384} \, {\left(128 \, x^{2} - 24 \, x - 27\right)} \sqrt{-4 \, x^{2} + 3 \, x} - \frac{27}{256} \, \arctan\left(\frac{\sqrt{-4 \, x^{2} + 3 \, x}}{2 \, x}\right)"," ",0,"1/384*(128*x^2 - 24*x - 27)*sqrt(-4*x^2 + 3*x) - 27/256*arctan(1/2*sqrt(-4*x^2 + 3*x)/x)","A",0
41,1,37,0,0.390079," ","integrate(x*(x^2+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{24} \, {\left(8 \, x^{2} + 2 \, x - 3\right)} \sqrt{x^{2} + x} - \frac{1}{16} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x} - 1\right)"," ",0,"1/24*(8*x^2 + 2*x - 3)*sqrt(x^2 + x) - 1/16*log(-2*x + 2*sqrt(x^2 + x) - 1)","A",0
42,1,170,0,0.406898," ","integrate(x^4/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, b^{4} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(48 \, c^{4} x^{3} - 56 \, b c^{3} x^{2} + 70 \, b^{2} c^{2} x - 105 \, b^{3} c\right)} \sqrt{c x^{2} + b x}}{384 \, c^{5}}, -\frac{105 \, b^{4} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(48 \, c^{4} x^{3} - 56 \, b c^{3} x^{2} + 70 \, b^{2} c^{2} x - 105 \, b^{3} c\right)} \sqrt{c x^{2} + b x}}{192 \, c^{5}}\right]"," ",0,"[1/384*(105*b^4*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(48*c^4*x^3 - 56*b*c^3*x^2 + 70*b^2*c^2*x - 105*b^3*c)*sqrt(c*x^2 + b*x))/c^5, -1/192*(105*b^4*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (48*c^4*x^3 - 56*b*c^3*x^2 + 70*b^2*c^2*x - 105*b^3*c)*sqrt(c*x^2 + b*x))/c^5]","A",0
43,1,147,0,0.399692," ","integrate(x^3/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, b^{3} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(8 \, c^{3} x^{2} - 10 \, b c^{2} x + 15 \, b^{2} c\right)} \sqrt{c x^{2} + b x}}{48 \, c^{4}}, \frac{15 \, b^{3} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, c^{3} x^{2} - 10 \, b c^{2} x + 15 \, b^{2} c\right)} \sqrt{c x^{2} + b x}}{24 \, c^{4}}\right]"," ",0,"[1/48*(15*b^3*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(8*c^3*x^2 - 10*b*c^2*x + 15*b^2*c)*sqrt(c*x^2 + b*x))/c^4, 1/24*(15*b^3*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*c^3*x^2 - 10*b*c^2*x + 15*b^2*c)*sqrt(c*x^2 + b*x))/c^4]","A",0
44,1,126,0,0.403769," ","integrate(x^2/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, b^{2} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(2 \, c^{2} x - 3 \, b c\right)} \sqrt{c x^{2} + b x}}{8 \, c^{3}}, -\frac{3 \, b^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(2 \, c^{2} x - 3 \, b c\right)} \sqrt{c x^{2} + b x}}{4 \, c^{3}}\right]"," ",0,"[1/8*(3*b^2*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(2*c^2*x - 3*b*c)*sqrt(c*x^2 + b*x))/c^3, -1/4*(3*b^2*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (2*c^2*x - 3*b*c)*sqrt(c*x^2 + b*x))/c^3]","A",0
45,1,98,0,0.400451," ","integrate(x/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, \sqrt{c x^{2} + b x} c}{2 \, c^{2}}, \frac{b \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + \sqrt{c x^{2} + b x} c}{c^{2}}\right]"," ",0,"[1/2*(b*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*sqrt(c*x^2 + b*x)*c)/c^2, (b*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + sqrt(c*x^2 + b*x)*c)/c^2]","A",0
46,1,62,0,0.424567," ","integrate(1/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right)}{\sqrt{c}}, -\frac{2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right)}{c}\right]"," ",0,"[log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c))/sqrt(c), -2*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x))/c]","A",0
47,1,19,0,0.394545," ","integrate(1/x/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x}}{b x}"," ",0,"-2*sqrt(c*x^2 + b*x)/(b*x)","A",0
48,1,27,0,0.400472," ","integrate(1/x^2/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{2} + b x} {\left(2 \, c x - b\right)}}{3 \, b^{2} x^{2}}"," ",0,"2/3*sqrt(c*x^2 + b*x)*(2*c*x - b)/(b^2*x^2)","A",0
49,1,38,0,0.408620," ","integrate(1/x^3/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, c^{2} x^{2} - 4 \, b c x + 3 \, b^{2}\right)} \sqrt{c x^{2} + b x}}{15 \, b^{3} x^{3}}"," ",0,"-2/15*(8*c^2*x^2 - 4*b*c*x + 3*b^2)*sqrt(c*x^2 + b*x)/(b^3*x^3)","A",0
50,1,49,0,0.420762," ","integrate(1/x^4/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{3} x^{3} - 8 \, b c^{2} x^{2} + 6 \, b^{2} c x - 5 \, b^{3}\right)} \sqrt{c x^{2} + b x}}{35 \, b^{4} x^{4}}"," ",0,"2/35*(16*c^3*x^3 - 8*b*c^2*x^2 + 6*b^2*c*x - 5*b^3)*sqrt(c*x^2 + b*x)/(b^4*x^4)","A",0
51,1,60,0,0.406687," ","integrate(1/x^5/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, c^{4} x^{4} - 64 \, b c^{3} x^{3} + 48 \, b^{2} c^{2} x^{2} - 40 \, b^{3} c x + 35 \, b^{4}\right)} \sqrt{c x^{2} + b x}}{315 \, b^{5} x^{5}}"," ",0,"-2/315*(128*c^4*x^4 - 64*b*c^3*x^3 + 48*b^2*c^2*x^2 - 40*b^3*c*x + 35*b^4)*sqrt(c*x^2 + b*x)/(b^5*x^5)","A",0
52,1,182,0,0.429600," ","integrate(x^4/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} c x + b^{3}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(2 \, c^{3} x^{2} - 5 \, b c^{2} x - 15 \, b^{2} c\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c^{5} x + b c^{4}\right)}}, -\frac{15 \, {\left(b^{2} c x + b^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(2 \, c^{3} x^{2} - 5 \, b c^{2} x - 15 \, b^{2} c\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c^{5} x + b c^{4}\right)}}\right]"," ",0,"[1/8*(15*(b^2*c*x + b^3)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(2*c^3*x^2 - 5*b*c^2*x - 15*b^2*c)*sqrt(c*x^2 + b*x))/(c^5*x + b*c^4), -1/4*(15*(b^2*c*x + b^3)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (2*c^3*x^2 - 5*b*c^2*x - 15*b^2*c)*sqrt(c*x^2 + b*x))/(c^5*x + b*c^4)]","A",0
53,1,152,0,0.414909," ","integrate(x^3/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b c x + b^{2}\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(c^{2} x + 3 \, b c\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(c^{4} x + b c^{3}\right)}}, \frac{3 \, {\left(b c x + b^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(c^{2} x + 3 \, b c\right)} \sqrt{c x^{2} + b x}}{c^{4} x + b c^{3}}\right]"," ",0,"[1/2*(3*(b*c*x + b^2)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(c^2*x + 3*b*c)*sqrt(c*x^2 + b*x))/(c^4*x + b*c^3), (3*(b*c*x + b^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (c^2*x + 3*b*c)*sqrt(c*x^2 + b*x))/(c^4*x + b*c^3)]","A",0
54,1,126,0,0.419647," ","integrate(x^2/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(c x + b\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, \sqrt{c x^{2} + b x} c}{c^{3} x + b c^{2}}, -\frac{2 \, {\left({\left(c x + b\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + \sqrt{c x^{2} + b x} c\right)}}{c^{3} x + b c^{2}}\right]"," ",0,"[((c*x + b)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*sqrt(c*x^2 + b*x)*c)/(c^3*x + b*c^2), -2*((c*x + b)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + sqrt(c*x^2 + b*x)*c)/(c^3*x + b*c^2)]","A",0
55,1,23,0,0.401559," ","integrate(x/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{2} + b x}}{b c x + b^{2}}"," ",0,"2*sqrt(c*x^2 + b*x)/(b*c*x + b^2)","A",0
56,1,35,0,0.393613," ","integrate(1/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x} {\left(2 \, c x + b\right)}}{b^{2} c x^{2} + b^{3} x}"," ",0,"-2*sqrt(c*x^2 + b*x)*(2*c*x + b)/(b^2*c*x^2 + b^3*x)","A",0
57,1,50,0,0.416869," ","integrate(1/x/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{2} x^{2} + 4 \, b c x - b^{2}\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{3} c x^{3} + b^{4} x^{2}\right)}}"," ",0,"2/3*(8*c^2*x^2 + 4*b*c*x - b^2)*sqrt(c*x^2 + b*x)/(b^3*c*x^3 + b^4*x^2)","A",0
58,1,59,0,0.399769," ","integrate(1/x^2/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(16 \, c^{3} x^{3} + 8 \, b c^{2} x^{2} - 2 \, b^{2} c x + b^{3}\right)} \sqrt{c x^{2} + b x}}{5 \, {\left(b^{4} c x^{4} + b^{5} x^{3}\right)}}"," ",0,"-2/5*(16*c^3*x^3 + 8*b*c^2*x^2 - 2*b^2*c*x + b^3)*sqrt(c*x^2 + b*x)/(b^4*c*x^4 + b^5*x^3)","A",0
59,1,72,0,0.409300," ","integrate(1/x^3/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, c^{4} x^{4} + 64 \, b c^{3} x^{3} - 16 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x - 5 \, b^{4}\right)} \sqrt{c x^{2} + b x}}{35 \, {\left(b^{5} c x^{5} + b^{6} x^{4}\right)}}"," ",0,"2/35*(128*c^4*x^4 + 64*b*c^3*x^3 - 16*b^2*c^2*x^2 + 8*b^3*c*x - 5*b^4)*sqrt(c*x^2 + b*x)/(b^5*c*x^5 + b^6*x^4)","A",0
60,1,248,0,0.428362," ","integrate(x^6/(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{2} b^{2} x^{2} + 2 \, a^{3} b x + a^{4}\right)} \sqrt{b} \log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) + 2 \, {\left(6 \, b^{4} x^{3} - 21 \, a b^{3} x^{2} - 140 \, a^{2} b^{2} x - 105 \, a^{3} b\right)} \sqrt{b x^{2} + a x}}{24 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}, -\frac{105 \, {\left(a^{2} b^{2} x^{2} + 2 \, a^{3} b x + a^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) - {\left(6 \, b^{4} x^{3} - 21 \, a b^{3} x^{2} - 140 \, a^{2} b^{2} x - 105 \, a^{3} b\right)} \sqrt{b x^{2} + a x}}{12 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}\right]"," ",0,"[1/24*(105*(a^2*b^2*x^2 + 2*a^3*b*x + a^4)*sqrt(b)*log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b)) + 2*(6*b^4*x^3 - 21*a*b^3*x^2 - 140*a^2*b^2*x - 105*a^3*b)*sqrt(b*x^2 + a*x))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5), -1/12*(105*(a^2*b^2*x^2 + 2*a^3*b*x + a^4)*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) - (6*b^4*x^3 - 21*a*b^3*x^2 - 140*a^2*b^2*x - 105*a^3*b)*sqrt(b*x^2 + a*x))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)]","A",0
61,1,221,0,0.458091," ","integrate(x^5/(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right)} \sqrt{b} \log\left(2 \, b x + a - 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) + 2 \, {\left(3 \, b^{3} x^{2} + 20 \, a b^{2} x + 15 \, a^{2} b\right)} \sqrt{b x^{2} + a x}}{6 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, \frac{15 \, {\left(a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) + {\left(3 \, b^{3} x^{2} + 20 \, a b^{2} x + 15 \, a^{2} b\right)} \sqrt{b x^{2} + a x}}{3 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[1/6*(15*(a*b^2*x^2 + 2*a^2*b*x + a^3)*sqrt(b)*log(2*b*x + a - 2*sqrt(b*x^2 + a*x)*sqrt(b)) + 2*(3*b^3*x^2 + 20*a*b^2*x + 15*a^2*b)*sqrt(b*x^2 + a*x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), 1/3*(15*(a*b^2*x^2 + 2*a^2*b*x + a^3)*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) + (3*b^3*x^2 + 20*a*b^2*x + 15*a^2*b)*sqrt(b*x^2 + a*x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
62,1,193,0,0.425597," ","integrate(x^4/(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{b} \log\left(2 \, b x + a + 2 \, \sqrt{b x^{2} + a x} \sqrt{b}\right) - 2 \, {\left(4 \, b^{2} x + 3 \, a b\right)} \sqrt{b x^{2} + a x}}{3 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}, -\frac{2 \, {\left(3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x^{2} + a x} \sqrt{-b}}{b x}\right) + {\left(4 \, b^{2} x + 3 \, a b\right)} \sqrt{b x^{2} + a x}\right)}}{3 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}\right]"," ",0,"[1/3*(3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(b)*log(2*b*x + a + 2*sqrt(b*x^2 + a*x)*sqrt(b)) - 2*(4*b^2*x + 3*a*b)*sqrt(b*x^2 + a*x))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3), -2/3*(3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(-b)*arctan(sqrt(b*x^2 + a*x)*sqrt(-b)/(b*x)) + (4*b^2*x + 3*a*b)*sqrt(b*x^2 + a*x))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)]","A",0
63,1,35,0,0.411315," ","integrate(x^3/(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x^{2} + a x} x}{3 \, {\left(a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right)}}"," ",0,"2/3*sqrt(b*x^2 + a*x)*x/(a*b^2*x^2 + 2*a^2*b*x + a^3)","A",0
64,1,44,0,0.407620," ","integrate(x^2/(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x^{2} + a x} {\left(2 \, b x + 3 \, a\right)}}{3 \, {\left(a^{2} b^{2} x^{2} + 2 \, a^{3} b x + a^{4}\right)}}"," ",0,"2/3*sqrt(b*x^2 + a*x)*(2*b*x + 3*a)/(a^2*b^2*x^2 + 2*a^3*b*x + a^4)","A",0
65,1,59,0,0.412458," ","integrate(x/(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, b^{2} x^{2} + 12 \, a b x + 3 \, a^{2}\right)} \sqrt{b x^{2} + a x}}{3 \, {\left(a^{3} b^{2} x^{3} + 2 \, a^{4} b x^{2} + a^{5} x\right)}}"," ",0,"-2/3*(8*b^2*x^2 + 12*a*b*x + 3*a^2)*sqrt(b*x^2 + a*x)/(a^3*b^2*x^3 + 2*a^4*b*x^2 + a^5*x)","A",0
66,1,72,0,0.405637," ","integrate(1/(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, b^{3} x^{3} + 24 \, a b^{2} x^{2} + 6 \, a^{2} b x - a^{3}\right)} \sqrt{b x^{2} + a x}}{3 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}"," ",0,"2/3*(16*b^3*x^3 + 24*a*b^2*x^2 + 6*a^2*b*x - a^3)*sqrt(b*x^2 + a*x)/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2)","A",0
67,1,83,0,0.413166," ","integrate(1/x/(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, b^{4} x^{4} + 192 \, a b^{3} x^{3} + 48 \, a^{2} b^{2} x^{2} - 8 \, a^{3} b x + 3 \, a^{4}\right)} \sqrt{b x^{2} + a x}}{15 \, {\left(a^{5} b^{2} x^{5} + 2 \, a^{6} b x^{4} + a^{7} x^{3}\right)}}"," ",0,"-2/15*(128*b^4*x^4 + 192*a*b^3*x^3 + 48*a^2*b^2*x^2 - 8*a^3*b*x + 3*a^4)*sqrt(b*x^2 + a*x)/(a^5*b^2*x^5 + 2*a^6*b*x^4 + a^7*x^3)","A",0
68,1,94,0,0.410331," ","integrate(1/x^2/(b*x^2+a*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(256 \, b^{5} x^{5} + 384 \, a b^{4} x^{4} + 96 \, a^{2} b^{3} x^{3} - 16 \, a^{3} b^{2} x^{2} + 6 \, a^{4} b x - 3 \, a^{5}\right)} \sqrt{b x^{2} + a x}}{21 \, {\left(a^{6} b^{2} x^{6} + 2 \, a^{7} b x^{5} + a^{8} x^{4}\right)}}"," ",0,"2/21*(256*b^5*x^5 + 384*a*b^4*x^4 + 96*a^2*b^3*x^3 - 16*a^3*b^2*x^2 + 6*a^4*b*x - 3*a^5)*sqrt(b*x^2 + a*x)/(a^6*b^2*x^6 + 2*a^7*b*x^5 + a^8*x^4)","A",0
69,1,32,0,0.408710," ","integrate(x/(-x^2+4*x)^(1/2),x, algorithm=""fricas"")","-\sqrt{-x^{2} + 4 \, x} - 4 \, \arctan\left(\frac{\sqrt{-x^{2} + 4 \, x}}{x}\right)"," ",0,"-sqrt(-x^2 + 4*x) - 4*arctan(sqrt(-x^2 + 4*x)/x)","A",0
70,1,27,0,0.404059," ","integrate(x/(x^2-4*x)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} - 4 \, x} - 2 \, \log\left(-x + \sqrt{x^{2} - 4 \, x} + 2\right)"," ",0,"sqrt(x^2 - 4*x) - 2*log(-x + sqrt(x^2 - 4*x) + 2)","A",0
71,1,35,0,0.390031," ","integrate(x^2/(-x^2+2*x)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-x^{2} + 2 \, x} {\left(x + 3\right)} - 3 \, \arctan\left(\frac{\sqrt{-x^{2} + 2 \, x}}{x}\right)"," ",0,"-1/2*sqrt(-x^2 + 2*x)*(x + 3) - 3*arctan(sqrt(-x^2 + 2*x)/x)","A",0
72,1,71,0,0.386270," ","integrate(x^(7/2)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, c^{5} x^{5} + 35 \, b c^{4} x^{4} - 40 \, b^{2} c^{3} x^{3} + 48 \, b^{3} c^{2} x^{2} - 64 \, b^{4} c x + 128 \, b^{5}\right)} \sqrt{c x^{2} + b x}}{3465 \, c^{5} \sqrt{x}}"," ",0,"2/3465*(315*c^5*x^5 + 35*b*c^4*x^4 - 40*b^2*c^3*x^3 + 48*b^3*c^2*x^2 - 64*b^4*c*x + 128*b^5)*sqrt(c*x^2 + b*x)/(c^5*sqrt(x))","A",0
73,1,60,0,0.392944," ","integrate(x^(5/2)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{4} x^{4} + 5 \, b c^{3} x^{3} - 6 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x - 16 \, b^{4}\right)} \sqrt{c x^{2} + b x}}{315 \, c^{4} \sqrt{x}}"," ",0,"2/315*(35*c^4*x^4 + 5*b*c^3*x^3 - 6*b^2*c^2*x^2 + 8*b^3*c*x - 16*b^4)*sqrt(c*x^2 + b*x)/(c^4*sqrt(x))","A",0
74,1,49,0,0.382572," ","integrate(x^(3/2)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c^{3} x^{3} + 3 \, b c^{2} x^{2} - 4 \, b^{2} c x + 8 \, b^{3}\right)} \sqrt{c x^{2} + b x}}{105 \, c^{3} \sqrt{x}}"," ",0,"2/105*(15*c^3*x^3 + 3*b*c^2*x^2 - 4*b^2*c*x + 8*b^3)*sqrt(c*x^2 + b*x)/(c^3*sqrt(x))","A",0
75,1,37,0,0.412455," ","integrate(x^(1/2)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} x^{2} + b c x - 2 \, b^{2}\right)} \sqrt{c x^{2} + b x}}{15 \, c^{2} \sqrt{x}}"," ",0,"2/15*(3*c^2*x^2 + b*c*x - 2*b^2)*sqrt(c*x^2 + b*x)/(c^2*sqrt(x))","A",0
76,1,24,0,0.384981," ","integrate((c*x^2+b*x)^(1/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{2} + b x} {\left(c x + b\right)}}{3 \, c \sqrt{x}}"," ",0,"2/3*sqrt(c*x^2 + b*x)*(c*x + b)/(c*sqrt(x))","A",0
77,1,111,0,0.425814," ","integrate((c*x^2+b*x)^(1/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} x \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, \sqrt{c x^{2} + b x} \sqrt{x}}{x}, \frac{2 \, {\left(\sqrt{-b} x \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + \sqrt{c x^{2} + b x} \sqrt{x}\right)}}{x}\right]"," ",0,"[(sqrt(b)*x*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*sqrt(c*x^2 + b*x)*sqrt(x))/x, 2*(sqrt(-b)*x*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + sqrt(c*x^2 + b*x)*sqrt(x))/x]","A",0
78,1,126,0,0.419282," ","integrate((c*x^2+b*x)^(1/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} c x^{2} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, \sqrt{c x^{2} + b x} b \sqrt{x}}{2 \, b x^{2}}, \frac{\sqrt{-b} c x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - \sqrt{c x^{2} + b x} b \sqrt{x}}{b x^{2}}\right]"," ",0,"[1/2*(sqrt(b)*c*x^2*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*sqrt(c*x^2 + b*x)*b*sqrt(x))/(b*x^2), (sqrt(-b)*c*x^2*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - sqrt(c*x^2 + b*x)*b*sqrt(x))/(b*x^2)]","A",0
79,1,148,0,0.412610," ","integrate((c*x^2+b*x)^(1/2)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} c^{2} x^{3} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, {\left(b c x + 2 \, b^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{8 \, b^{2} x^{3}}, -\frac{\sqrt{-b} c^{2} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(b c x + 2 \, b^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{4 \, b^{2} x^{3}}\right]"," ",0,"[1/8*(sqrt(b)*c^2*x^3*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*(b*c*x + 2*b^2)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*x^3), -1/4*(sqrt(-b)*c^2*x^3*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (b*c*x + 2*b^2)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*x^3)]","A",0
80,1,174,0,0.418268," ","integrate((c*x^2+b*x)^(1/2)/x^(9/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{3} x^{4} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(3 \, b c^{2} x^{2} - 2 \, b^{2} c x - 8 \, b^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{48 \, b^{3} x^{4}}, \frac{3 \, \sqrt{-b} c^{3} x^{4} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(3 \, b c^{2} x^{2} - 2 \, b^{2} c x - 8 \, b^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, b^{3} x^{4}}\right]"," ",0,"[1/48*(3*sqrt(b)*c^3*x^4*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(3*b*c^2*x^2 - 2*b^2*c*x - 8*b^3)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^4), 1/24*(3*sqrt(-b)*c^3*x^4*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (3*b*c^2*x^2 - 2*b^2*c*x - 8*b^3)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^4)]","A",0
81,1,196,0,0.422574," ","integrate((c*x^2+b*x)^(1/2)/x^(11/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{b} c^{4} x^{5} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, {\left(15 \, b c^{3} x^{3} - 10 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x + 48 \, b^{4}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{384 \, b^{4} x^{5}}, -\frac{15 \, \sqrt{-b} c^{4} x^{5} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(15 \, b c^{3} x^{3} - 10 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x + 48 \, b^{4}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{192 \, b^{4} x^{5}}\right]"," ",0,"[1/384*(15*sqrt(b)*c^4*x^5*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*(15*b*c^3*x^3 - 10*b^2*c^2*x^2 + 8*b^3*c*x + 48*b^4)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*x^5), -1/192*(15*sqrt(-b)*c^4*x^5*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (15*b*c^3*x^3 - 10*b^2*c^2*x^2 + 8*b^3*c*x + 48*b^4)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*x^5)]","A",0
82,1,93,0,0.392840," ","integrate(x^(7/2)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, c^{7} x^{7} + 3696 \, b c^{6} x^{6} + 63 \, b^{2} c^{5} x^{5} - 70 \, b^{3} c^{4} x^{4} + 80 \, b^{4} c^{3} x^{3} - 96 \, b^{5} c^{2} x^{2} + 128 \, b^{6} c x - 256 \, b^{7}\right)} \sqrt{c x^{2} + b x}}{45045 \, c^{6} \sqrt{x}}"," ",0,"2/45045*(3003*c^7*x^7 + 3696*b*c^6*x^6 + 63*b^2*c^5*x^5 - 70*b^3*c^4*x^4 + 80*b^4*c^3*x^3 - 96*b^5*c^2*x^2 + 128*b^6*c*x - 256*b^7)*sqrt(c*x^2 + b*x)/(c^6*sqrt(x))","A",0
83,1,82,0,0.398594," ","integrate(x^(5/2)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, c^{6} x^{6} + 1470 \, b c^{5} x^{5} + 35 \, b^{2} c^{4} x^{4} - 40 \, b^{3} c^{3} x^{3} + 48 \, b^{4} c^{2} x^{2} - 64 \, b^{5} c x + 128 \, b^{6}\right)} \sqrt{c x^{2} + b x}}{15015 \, c^{5} \sqrt{x}}"," ",0,"2/15015*(1155*c^6*x^6 + 1470*b*c^5*x^5 + 35*b^2*c^4*x^4 - 40*b^3*c^3*x^3 + 48*b^4*c^2*x^2 - 64*b^5*c*x + 128*b^6)*sqrt(c*x^2 + b*x)/(c^5*sqrt(x))","A",0
84,1,71,0,0.411599," ","integrate(x^(3/2)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, c^{5} x^{5} + 140 \, b c^{4} x^{4} + 5 \, b^{2} c^{3} x^{3} - 6 \, b^{3} c^{2} x^{2} + 8 \, b^{4} c x - 16 \, b^{5}\right)} \sqrt{c x^{2} + b x}}{1155 \, c^{4} \sqrt{x}}"," ",0,"2/1155*(105*c^5*x^5 + 140*b*c^4*x^4 + 5*b^2*c^3*x^3 - 6*b^3*c^2*x^2 + 8*b^4*c*x - 16*b^5)*sqrt(c*x^2 + b*x)/(c^4*sqrt(x))","A",0
85,1,60,0,0.387400," ","integrate(x^(1/2)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{4} x^{4} + 50 \, b c^{3} x^{3} + 3 \, b^{2} c^{2} x^{2} - 4 \, b^{3} c x + 8 \, b^{4}\right)} \sqrt{c x^{2} + b x}}{315 \, c^{3} \sqrt{x}}"," ",0,"2/315*(35*c^4*x^4 + 50*b*c^3*x^3 + 3*b^2*c^2*x^2 - 4*b^3*c*x + 8*b^4)*sqrt(c*x^2 + b*x)/(c^3*sqrt(x))","A",0
86,1,48,0,0.389235," ","integrate((c*x^2+b*x)^(3/2)/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{3} x^{3} + 8 \, b c^{2} x^{2} + b^{2} c x - 2 \, b^{3}\right)} \sqrt{c x^{2} + b x}}{35 \, c^{2} \sqrt{x}}"," ",0,"2/35*(5*c^3*x^3 + 8*b*c^2*x^2 + b^2*c*x - 2*b^3)*sqrt(c*x^2 + b*x)/(c^2*sqrt(x))","A",0
87,1,35,0,0.385269," ","integrate((c*x^2+b*x)^(3/2)/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{2} x^{2} + 2 \, b c x + b^{2}\right)} \sqrt{c x^{2} + b x}}{5 \, c \sqrt{x}}"," ",0,"2/5*(c^2*x^2 + 2*b*c*x + b^2)*sqrt(c*x^2 + b*x)/(c*sqrt(x))","A",0
88,1,129,0,0.410815," ","integrate((c*x^2+b*x)^(3/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, b^{\frac{3}{2}} x \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, \sqrt{c x^{2} + b x} {\left(c x + 4 \, b\right)} \sqrt{x}}{3 \, x}, \frac{2 \, {\left(3 \, \sqrt{-b} b x \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + \sqrt{c x^{2} + b x} {\left(c x + 4 \, b\right)} \sqrt{x}\right)}}{3 \, x}\right]"," ",0,"[1/3*(3*b^(3/2)*x*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*sqrt(c*x^2 + b*x)*(c*x + 4*b)*sqrt(x))/x, 2/3*(3*sqrt(-b)*b*x*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + sqrt(c*x^2 + b*x)*(c*x + 4*b)*sqrt(x))/x]","A",0
89,1,135,0,0.421039," ","integrate((c*x^2+b*x)^(3/2)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c x^{2} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, \sqrt{c x^{2} + b x} {\left(2 \, c x - b\right)} \sqrt{x}}{2 \, x^{2}}, \frac{3 \, \sqrt{-b} c x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + \sqrt{c x^{2} + b x} {\left(2 \, c x - b\right)} \sqrt{x}}{x^{2}}\right]"," ",0,"[1/2*(3*sqrt(b)*c*x^2*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*sqrt(c*x^2 + b*x)*(2*c*x - b)*sqrt(x))/x^2, (3*sqrt(-b)*c*x^2*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + sqrt(c*x^2 + b*x)*(2*c*x - b)*sqrt(x))/x^2]","A",0
90,1,153,0,0.404984," ","integrate((c*x^2+b*x)^(3/2)/x^(9/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{2} x^{3} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, {\left(5 \, b c x + 2 \, b^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{8 \, b x^{3}}, \frac{3 \, \sqrt{-b} c^{2} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) - {\left(5 \, b c x + 2 \, b^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{4 \, b x^{3}}\right]"," ",0,"[1/8*(3*sqrt(b)*c^2*x^3*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*(5*b*c*x + 2*b^2)*sqrt(c*x^2 + b*x)*sqrt(x))/(b*x^3), 1/4*(3*sqrt(-b)*c^2*x^3*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) - (5*b*c*x + 2*b^2)*sqrt(c*x^2 + b*x)*sqrt(x))/(b*x^3)]","A",0
91,1,174,0,0.417935," ","integrate((c*x^2+b*x)^(3/2)/x^(11/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{3} x^{4} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, {\left(3 \, b c^{2} x^{2} + 14 \, b^{2} c x + 8 \, b^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{48 \, b^{2} x^{4}}, -\frac{3 \, \sqrt{-b} c^{3} x^{4} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(3 \, b c^{2} x^{2} + 14 \, b^{2} c x + 8 \, b^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, b^{2} x^{4}}\right]"," ",0,"[1/48*(3*sqrt(b)*c^3*x^4*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*(3*b*c^2*x^2 + 14*b^2*c*x + 8*b^3)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*x^4), -1/24*(3*sqrt(-b)*c^3*x^4*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (3*b*c^2*x^2 + 14*b^2*c*x + 8*b^3)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^2*x^4)]","A",0
92,1,196,0,0.426361," ","integrate((c*x^2+b*x)^(3/2)/x^(13/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{4} x^{5} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(3 \, b c^{3} x^{3} - 2 \, b^{2} c^{2} x^{2} - 24 \, b^{3} c x - 16 \, b^{4}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{128 \, b^{3} x^{5}}, \frac{3 \, \sqrt{-b} c^{4} x^{5} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(3 \, b c^{3} x^{3} - 2 \, b^{2} c^{2} x^{2} - 24 \, b^{3} c x - 16 \, b^{4}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{64 \, b^{3} x^{5}}\right]"," ",0,"[1/128*(3*sqrt(b)*c^4*x^5*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(3*b*c^3*x^3 - 2*b^2*c^2*x^2 - 24*b^3*c*x - 16*b^4)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^5), 1/64*(3*sqrt(-b)*c^4*x^5*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (3*b*c^3*x^3 - 2*b^2*c^2*x^2 - 24*b^3*c*x - 16*b^4)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^5)]","A",0
93,1,218,0,0.434822," ","integrate((c*x^2+b*x)^(3/2)/x^(15/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{b} c^{5} x^{6} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, {\left(15 \, b c^{4} x^{4} - 10 \, b^{2} c^{3} x^{3} + 8 \, b^{3} c^{2} x^{2} + 176 \, b^{4} c x + 128 \, b^{5}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{1280 \, b^{4} x^{6}}, -\frac{15 \, \sqrt{-b} c^{5} x^{6} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(15 \, b c^{4} x^{4} - 10 \, b^{2} c^{3} x^{3} + 8 \, b^{3} c^{2} x^{2} + 176 \, b^{4} c x + 128 \, b^{5}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{640 \, b^{4} x^{6}}\right]"," ",0,"[1/1280*(15*sqrt(b)*c^5*x^6*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*(15*b*c^4*x^4 - 10*b^2*c^3*x^3 + 8*b^3*c^2*x^2 + 176*b^4*c*x + 128*b^5)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*x^6), -1/640*(15*sqrt(-b)*c^5*x^6*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (15*b*c^4*x^4 - 10*b^2*c^3*x^3 + 8*b^3*c^2*x^2 + 176*b^4*c*x + 128*b^5)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*x^6)]","A",0
94,1,49,0,0.381598," ","integrate(x^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{3} x^{3} - 6 \, b c^{2} x^{2} + 8 \, b^{2} c x - 16 \, b^{3}\right)} \sqrt{c x^{2} + b x}}{35 \, c^{4} \sqrt{x}}"," ",0,"2/35*(5*c^3*x^3 - 6*b*c^2*x^2 + 8*b^2*c*x - 16*b^3)*sqrt(c*x^2 + b*x)/(c^4*sqrt(x))","A",0
95,1,38,0,0.382024," ","integrate(x^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} x^{2} - 4 \, b c x + 8 \, b^{2}\right)} \sqrt{c x^{2} + b x}}{15 \, c^{3} \sqrt{x}}"," ",0,"2/15*(3*c^2*x^2 - 4*b*c*x + 8*b^2)*sqrt(c*x^2 + b*x)/(c^3*sqrt(x))","A",0
96,1,26,0,0.406633," ","integrate(x^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{2} + b x} {\left(c x - 2 \, b\right)}}{3 \, c^{2} \sqrt{x}}"," ",0,"2/3*sqrt(c*x^2 + b*x)*(c*x - 2*b)/(c^2*sqrt(x))","A",0
97,1,19,0,0.380844," ","integrate(x^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{2} + b x}}{c \sqrt{x}}"," ",0,"2*sqrt(c*x^2 + b*x)/(c*sqrt(x))","A",0
98,1,71,0,0.406007," ","integrate(1/x^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right)}{\sqrt{b}}, \frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right)}{b}\right]"," ",0,"[log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2)/sqrt(b), 2*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x))/b]","A",0
99,1,126,0,0.404304," ","integrate(1/x^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} c x^{2} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, \sqrt{c x^{2} + b x} b \sqrt{x}}{2 \, b^{2} x^{2}}, -\frac{\sqrt{-b} c x^{2} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + \sqrt{c x^{2} + b x} b \sqrt{x}}{b^{2} x^{2}}\right]"," ",0,"[1/2*(sqrt(b)*c*x^2*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*sqrt(c*x^2 + b*x)*b*sqrt(x))/(b^2*x^2), -(sqrt(-b)*c*x^2*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + sqrt(c*x^2 + b*x)*b*sqrt(x))/(b^2*x^2)]","A",0
100,1,152,0,0.430076," ","integrate(1/x^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{b} c^{2} x^{3} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(3 \, b c x - 2 \, b^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{8 \, b^{3} x^{3}}, \frac{3 \, \sqrt{-b} c^{2} x^{3} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(3 \, b c x - 2 \, b^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{4 \, b^{3} x^{3}}\right]"," ",0,"[1/8*(3*sqrt(b)*c^2*x^3*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(3*b*c*x - 2*b^2)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^3), 1/4*(3*sqrt(-b)*c^2*x^3*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (3*b*c*x - 2*b^2)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*x^3)]","A",0
101,1,174,0,0.425754," ","integrate(1/x^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{b} c^{3} x^{4} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, {\left(15 \, b c^{2} x^{2} - 10 \, b^{2} c x + 8 \, b^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{48 \, b^{4} x^{4}}, -\frac{15 \, \sqrt{-b} c^{3} x^{4} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(15 \, b c^{2} x^{2} - 10 \, b^{2} c x + 8 \, b^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, b^{4} x^{4}}\right]"," ",0,"[1/48*(15*sqrt(b)*c^3*x^4*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*(15*b*c^2*x^2 - 10*b^2*c*x + 8*b^3)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*x^4), -1/24*(15*sqrt(-b)*c^3*x^4*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (15*b*c^2*x^2 - 10*b^2*c*x + 8*b^3)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*x^4)]","A",0
102,1,84,0,0.383758," ","integrate(x^(13/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, c^{5} x^{5} - 10 \, b c^{4} x^{4} + 16 \, b^{2} c^{3} x^{3} - 32 \, b^{3} c^{2} x^{2} + 128 \, b^{4} c x + 256 \, b^{5}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{63 \, {\left(c^{7} x^{2} + b c^{6} x\right)}}"," ",0,"2/63*(7*c^5*x^5 - 10*b*c^4*x^4 + 16*b^2*c^3*x^3 - 32*b^3*c^2*x^2 + 128*b^4*c*x + 256*b^5)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^7*x^2 + b*c^6*x)","A",0
103,1,73,0,0.398127," ","integrate(x^(11/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{4} x^{4} - 8 \, b c^{3} x^{3} + 16 \, b^{2} c^{2} x^{2} - 64 \, b^{3} c x - 128 \, b^{4}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{35 \, {\left(c^{6} x^{2} + b c^{5} x\right)}}"," ",0,"2/35*(5*c^4*x^4 - 8*b*c^3*x^3 + 16*b^2*c^2*x^2 - 64*b^3*c*x - 128*b^4)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^6*x^2 + b*c^5*x)","A",0
104,1,61,0,0.400974," ","integrate(x^(9/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{3} x^{3} - 2 \, b c^{2} x^{2} + 8 \, b^{2} c x + 16 \, b^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{5 \, {\left(c^{5} x^{2} + b c^{4} x\right)}}"," ",0,"2/5*(c^3*x^3 - 2*b*c^2*x^2 + 8*b^2*c*x + 16*b^3)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^5*x^2 + b*c^4*x)","A",0
105,1,50,0,0.395249," ","integrate(x^(7/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{2} x^{2} - 4 \, b c x - 8 \, b^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{3 \, {\left(c^{4} x^{2} + b c^{3} x\right)}}"," ",0,"2/3*(c^2*x^2 - 4*b*c*x - 8*b^2)*sqrt(c*x^2 + b*x)*sqrt(x)/(c^4*x^2 + b*c^3*x)","A",0
106,1,39,0,0.392786," ","integrate(x^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{2} + b x} {\left(c x + 2 \, b\right)} \sqrt{x}}{c^{3} x^{2} + b c^{2} x}"," ",0,"2*sqrt(c*x^2 + b*x)*(c*x + 2*b)*sqrt(x)/(c^3*x^2 + b*c^2*x)","A",0
107,1,30,0,0.396307," ","integrate(x^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x} \sqrt{x}}{c^{2} x^{2} + b c x}"," ",0,"-2*sqrt(c*x^2 + b*x)*sqrt(x)/(c^2*x^2 + b*c*x)","A",0
108,1,155,0,0.414384," ","integrate(x^(1/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(c x^{2} + b x\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, \sqrt{c x^{2} + b x} b \sqrt{x}}{b^{2} c x^{2} + b^{3} x}, \frac{2 \, {\left({\left(c x^{2} + b x\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + \sqrt{c x^{2} + b x} b \sqrt{x}\right)}}{b^{2} c x^{2} + b^{3} x}\right]"," ",0,"[((c*x^2 + b*x)*sqrt(b)*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*sqrt(c*x^2 + b*x)*b*sqrt(x))/(b^2*c*x^2 + b^3*x), 2*((c*x^2 + b*x)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + sqrt(c*x^2 + b*x)*b*sqrt(x))/(b^2*c*x^2 + b^3*x)]","A",0
109,1,188,0,0.416837," ","integrate(1/x^(1/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} x^{3} + b c x^{2}\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, {\left(3 \, b c x + b^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{2 \, {\left(b^{3} c x^{3} + b^{4} x^{2}\right)}}, -\frac{3 \, {\left(c^{2} x^{3} + b c x^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(3 \, b c x + b^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{b^{3} c x^{3} + b^{4} x^{2}}\right]"," ",0,"[1/2*(3*(c^2*x^3 + b*c*x^2)*sqrt(b)*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*(3*b*c*x + b^2)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*c*x^3 + b^4*x^2), -(3*(c^2*x^3 + b*c*x^2)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (3*b*c*x + b^2)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^3*c*x^3 + b^4*x^2)]","A",0
110,1,218,0,0.412549," ","integrate(1/x^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{3} x^{4} + b c^{2} x^{3}\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x - 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) + 2 \, {\left(15 \, b c^{2} x^{2} + 5 \, b^{2} c x - 2 \, b^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{8 \, {\left(b^{4} c x^{4} + b^{5} x^{3}\right)}}, \frac{15 \, {\left(c^{3} x^{4} + b c^{2} x^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(15 \, b c^{2} x^{2} + 5 \, b^{2} c x - 2 \, b^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{4 \, {\left(b^{4} c x^{4} + b^{5} x^{3}\right)}}\right]"," ",0,"[1/8*(15*(c^3*x^4 + b*c^2*x^3)*sqrt(b)*log(-(c*x^2 + 2*b*x - 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) + 2*(15*b*c^2*x^2 + 5*b^2*c*x - 2*b^3)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*c*x^4 + b^5*x^3), 1/4*(15*(c^3*x^4 + b*c^2*x^3)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (15*b*c^2*x^2 + 5*b^2*c*x - 2*b^3)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^4*c*x^4 + b^5*x^3)]","A",0
111,1,240,0,0.419273," ","integrate(1/x^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(c^{4} x^{5} + b c^{3} x^{4}\right)} \sqrt{b} \log\left(-\frac{c x^{2} + 2 \, b x + 2 \, \sqrt{c x^{2} + b x} \sqrt{b} \sqrt{x}}{x^{2}}\right) - 2 \, {\left(105 \, b c^{3} x^{3} + 35 \, b^{2} c^{2} x^{2} - 14 \, b^{3} c x + 8 \, b^{4}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{48 \, {\left(b^{5} c x^{5} + b^{6} x^{4}\right)}}, -\frac{105 \, {\left(c^{4} x^{5} + b c^{3} x^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b} \sqrt{x}}{\sqrt{c x^{2} + b x}}\right) + {\left(105 \, b c^{3} x^{3} + 35 \, b^{2} c^{2} x^{2} - 14 \, b^{3} c x + 8 \, b^{4}\right)} \sqrt{c x^{2} + b x} \sqrt{x}}{24 \, {\left(b^{5} c x^{5} + b^{6} x^{4}\right)}}\right]"," ",0,"[1/48*(105*(c^4*x^5 + b*c^3*x^4)*sqrt(b)*log(-(c*x^2 + 2*b*x + 2*sqrt(c*x^2 + b*x)*sqrt(b)*sqrt(x))/x^2) - 2*(105*b*c^3*x^3 + 35*b^2*c^2*x^2 - 14*b^3*c*x + 8*b^4)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^5*c*x^5 + b^6*x^4), -1/24*(105*(c^4*x^5 + b*c^3*x^4)*sqrt(-b)*arctan(sqrt(-b)*sqrt(x)/sqrt(c*x^2 + b*x)) + (105*b*c^3*x^3 + 35*b^2*c^2*x^2 - 14*b^3*c*x + 8*b^4)*sqrt(c*x^2 + b*x)*sqrt(x))/(b^5*c*x^5 + b^6*x^4)]","A",0
112,1,161,0,0.404812," ","integrate((d*x)^m*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{{\left({\left(c^{3} m^{3} + 15 \, c^{3} m^{2} + 74 \, c^{3} m + 120 \, c^{3}\right)} x^{7} + 3 \, {\left(b c^{2} m^{3} + 16 \, b c^{2} m^{2} + 83 \, b c^{2} m + 140 \, b c^{2}\right)} x^{6} + 3 \, {\left(b^{2} c m^{3} + 17 \, b^{2} c m^{2} + 94 \, b^{2} c m + 168 \, b^{2} c\right)} x^{5} + {\left(b^{3} m^{3} + 18 \, b^{3} m^{2} + 107 \, b^{3} m + 210 \, b^{3}\right)} x^{4}\right)} \left(d x\right)^{m}}{m^{4} + 22 \, m^{3} + 179 \, m^{2} + 638 \, m + 840}"," ",0,"((c^3*m^3 + 15*c^3*m^2 + 74*c^3*m + 120*c^3)*x^7 + 3*(b*c^2*m^3 + 16*b*c^2*m^2 + 83*b*c^2*m + 140*b*c^2)*x^6 + 3*(b^2*c*m^3 + 17*b^2*c*m^2 + 94*b^2*c*m + 168*b^2*c)*x^5 + (b^3*m^3 + 18*b^3*m^2 + 107*b^3*m + 210*b^3)*x^4)*(d*x)^m/(m^4 + 22*m^3 + 179*m^2 + 638*m + 840)","A",0
113,1,89,0,0.416872," ","integrate((d*x)^m*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{{\left({\left(c^{2} m^{2} + 7 \, c^{2} m + 12 \, c^{2}\right)} x^{5} + 2 \, {\left(b c m^{2} + 8 \, b c m + 15 \, b c\right)} x^{4} + {\left(b^{2} m^{2} + 9 \, b^{2} m + 20 \, b^{2}\right)} x^{3}\right)} \left(d x\right)^{m}}{m^{3} + 12 \, m^{2} + 47 \, m + 60}"," ",0,"((c^2*m^2 + 7*c^2*m + 12*c^2)*x^5 + 2*(b*c*m^2 + 8*b*c*m + 15*b*c)*x^4 + (b^2*m^2 + 9*b^2*m + 20*b^2)*x^3)*(d*x)^m/(m^3 + 12*m^2 + 47*m + 60)","A",0
114,1,39,0,0.409489," ","integrate((d*x)^m*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{{\left({\left(c m + 2 \, c\right)} x^{3} + {\left(b m + 3 \, b\right)} x^{2}\right)} \left(d x\right)^{m}}{m^{2} + 5 \, m + 6}"," ",0,"((c*m + 2*c)*x^3 + (b*m + 3*b)*x^2)*(d*x)^m/(m^2 + 5*m + 6)","A",0
115,0,0,0,0.412203," ","integrate((d*x)^m/(c*x^2+b*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{c x^{2} + b x}, x\right)"," ",0,"integral((d*x)^m/(c*x^2 + b*x), x)","F",0
116,0,0,0,0.411280," ","integrate((d*x)^m/(c*x^2+b*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral((d*x)^m/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
117,0,0,0,0.425443," ","integrate((d*x)^m/(c*x^2+b*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral((d*x)^m/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
118,0,0,0,0.418886," ","integrate((d*x)^m*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}\right)} \sqrt{c x^{2} + b x} \left(d x\right)^{m}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + b^2*x^2)*sqrt(c*x^2 + b*x)*(d*x)^m, x)","F",0
119,0,0,0,0.402027," ","integrate((d*x)^m*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x\right)}^{\frac{3}{2}} \left(d x\right)^{m}, x\right)"," ",0,"integral((c*x^2 + b*x)^(3/2)*(d*x)^m, x)","F",0
120,0,0,0,0.409828," ","integrate((d*x)^m*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x} \left(d x\right)^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(d*x)^m, x)","F",0
121,0,0,0,0.415890," ","integrate((d*x)^m/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{\sqrt{c x^{2} + b x}}, x\right)"," ",0,"integral((d*x)^m/sqrt(c*x^2 + b*x), x)","F",0
122,0,0,0,0.422565," ","integrate((d*x)^m/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \left(d x\right)^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(d*x)^m/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
123,0,0,0,0.419306," ","integrate((d*x)^m/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \left(d x\right)^{m}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(d*x)^m/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
124,0,0,0,0.417371," ","integrate((d*x)^m*(c*x^2+b*x)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x\right)}^{p} \left(d x\right)^{m}, x\right)"," ",0,"integral((c*x^2 + b*x)^p*(d*x)^m, x)","F",0
125,0,0,0,0.416843," ","integrate(x^3*(c*x^2+b*x)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x\right)}^{p} x^{3}, x\right)"," ",0,"integral((c*x^2 + b*x)^p*x^3, x)","F",0
126,0,0,0,0.416137," ","integrate(x^2*(c*x^2+b*x)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x\right)}^{p} x^{2}, x\right)"," ",0,"integral((c*x^2 + b*x)^p*x^2, x)","F",0
127,0,0,0,0.415170," ","integrate(x*(c*x^2+b*x)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x\right)}^{p} x, x\right)"," ",0,"integral((c*x^2 + b*x)^p*x, x)","F",0
128,0,0,0,0.418157," ","integrate((c*x^2+b*x)^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x\right)}^{p}}{x}, x\right)"," ",0,"integral((c*x^2 + b*x)^p/x, x)","F",0
129,0,0,0,0.421462," ","integrate((c*x^2+b*x)^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x)^p/x^2, x)","F",0
130,0,0,0,0.416498," ","integrate((c*x^2+b*x)^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((c*x^2 + b*x)^p/x^3, x)","F",0
131,0,0,0,0.423258," ","integrate((d*x)^(5/2)*(c*x^2+b*x)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x} {\left(c x^{2} + b x\right)}^{p} d^{2} x^{2}, x\right)"," ",0,"integral(sqrt(d*x)*(c*x^2 + b*x)^p*d^2*x^2, x)","F",0
132,0,0,0,0.420964," ","integrate((d*x)^(3/2)*(c*x^2+b*x)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x} {\left(c x^{2} + b x\right)}^{p} d x, x\right)"," ",0,"integral(sqrt(d*x)*(c*x^2 + b*x)^p*d*x, x)","F",0
133,0,0,0,0.426888," ","integrate((d*x)^(1/2)*(c*x^2+b*x)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x} {\left(c x^{2} + b x\right)}^{p}, x\right)"," ",0,"integral(sqrt(d*x)*(c*x^2 + b*x)^p, x)","F",0
134,0,0,0,0.415420," ","integrate((c*x^2+b*x)^p/(d*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x} {\left(c x^{2} + b x\right)}^{p}}{d x}, x\right)"," ",0,"integral(sqrt(d*x)*(c*x^2 + b*x)^p/(d*x), x)","F",0
135,0,0,0,0.418775," ","integrate((c*x^2+b*x)^p/(d*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x} {\left(c x^{2} + b x\right)}^{p}}{d^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(d*x)*(c*x^2 + b*x)^p/(d^2*x^2), x)","F",0
136,0,0,0,0.435344," ","integrate((c*x^2+b*x)^p/(d*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x} {\left(c x^{2} + b x\right)}^{p}}{d^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(d*x)*(c*x^2 + b*x)^p/(d^3*x^3), x)","F",0
137,1,13,0,0.390108," ","integrate(x^4*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, b x^{6} + \frac{1}{5} \, a x^{5}"," ",0,"1/6*b*x^6 + 1/5*a*x^5","A",0
138,1,13,0,0.392458," ","integrate(x^3*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, b x^{5} + \frac{1}{4} \, a x^{4}"," ",0,"1/5*b*x^5 + 1/4*a*x^4","A",0
139,1,13,0,0.406474," ","integrate(x^2*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3}"," ",0,"1/4*b*x^4 + 1/3*a*x^3","A",0
140,1,13,0,0.397161," ","integrate(x*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, b x^{3} + \frac{1}{2} \, a x^{2}"," ",0,"1/3*b*x^3 + 1/2*a*x^2","A",0
141,1,10,0,0.395175," ","integrate(((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, b x^{2} + a x"," ",0,"1/2*b*x^2 + a*x","A",0
142,1,8,0,0.403728," ","integrate(((b*x+a)^2)^(1/2)/x,x, algorithm=""fricas"")","b x + a \log\left(x\right)"," ",0,"b*x + a*log(x)","A",0
143,1,13,0,0.400053," ","integrate(((b*x+a)^2)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{b x \log\left(x\right) - a}{x}"," ",0,"(b*x*log(x) - a)/x","A",0
144,1,11,0,0.412992," ","integrate(((b*x+a)^2)^(1/2)/x^3,x, algorithm=""fricas"")","-\frac{2 \, b x + a}{2 \, x^{2}}"," ",0,"-1/2*(2*b*x + a)/x^2","A",0
145,1,13,0,0.400048," ","integrate(((b*x+a)^2)^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{3 \, b x + 2 \, a}{6 \, x^{3}}"," ",0,"-1/6*(3*b*x + 2*a)/x^3","A",0
146,1,13,0,0.389343," ","integrate(((b*x+a)^2)^(1/2)/x^5,x, algorithm=""fricas"")","-\frac{4 \, b x + 3 \, a}{12 \, x^{4}}"," ",0,"-1/12*(4*b*x + 3*a)/x^4","A",0
147,1,13,0,0.391356," ","integrate(((b*x+a)^2)^(1/2)/x^6,x, algorithm=""fricas"")","-\frac{5 \, b x + 4 \, a}{20 \, x^{5}}"," ",0,"-1/20*(5*b*x + 4*a)/x^5","A",0
148,1,35,0,0.392136," ","integrate(x^5*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{9} \, b^{3} x^{9} + \frac{3}{8} \, a b^{2} x^{8} + \frac{3}{7} \, a^{2} b x^{7} + \frac{1}{6} \, a^{3} x^{6}"," ",0,"1/9*b^3*x^9 + 3/8*a*b^2*x^8 + 3/7*a^2*b*x^7 + 1/6*a^3*x^6","A",0
149,1,35,0,0.393066," ","integrate(x^4*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{8} \, b^{3} x^{8} + \frac{3}{7} \, a b^{2} x^{7} + \frac{1}{2} \, a^{2} b x^{6} + \frac{1}{5} \, a^{3} x^{5}"," ",0,"1/8*b^3*x^8 + 3/7*a*b^2*x^7 + 1/2*a^2*b*x^6 + 1/5*a^3*x^5","A",0
150,1,35,0,0.389690," ","integrate(x^3*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{7} \, b^{3} x^{7} + \frac{1}{2} \, a b^{2} x^{6} + \frac{3}{5} \, a^{2} b x^{5} + \frac{1}{4} \, a^{3} x^{4}"," ",0,"1/7*b^3*x^7 + 1/2*a*b^2*x^6 + 3/5*a^2*b*x^5 + 1/4*a^3*x^4","A",0
151,1,35,0,0.396356," ","integrate(x^2*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{6} \, b^{3} x^{6} + \frac{3}{5} \, a b^{2} x^{5} + \frac{3}{4} \, a^{2} b x^{4} + \frac{1}{3} \, a^{3} x^{3}"," ",0,"1/6*b^3*x^6 + 3/5*a*b^2*x^5 + 3/4*a^2*b*x^4 + 1/3*a^3*x^3","A",0
152,1,34,0,0.390005," ","integrate(x*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{5} \, b^{3} x^{5} + \frac{3}{4} \, a b^{2} x^{4} + a^{2} b x^{3} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"1/5*b^3*x^5 + 3/4*a*b^2*x^4 + a^2*b*x^3 + 1/2*a^3*x^2","A",0
153,1,31,0,0.395652," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{4} \, b^{3} x^{4} + a b^{2} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} x"," ",0,"1/4*b^3*x^4 + a*b^2*x^3 + 3/2*a^2*b*x^2 + a^3*x","A",0
154,1,31,0,0.401741," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x,x, algorithm=""fricas"")","\frac{1}{3} \, b^{3} x^{3} + \frac{3}{2} \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3} \log\left(x\right)"," ",0,"1/3*b^3*x^3 + 3/2*a*b^2*x^2 + 3*a^2*b*x + a^3*log(x)","A",0
155,1,36,0,0.403731," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^2,x, algorithm=""fricas"")","\frac{b^{3} x^{3} + 6 \, a b^{2} x^{2} + 6 \, a^{2} b x \log\left(x\right) - 2 \, a^{3}}{2 \, x}"," ",0,"1/2*(b^3*x^3 + 6*a*b^2*x^2 + 6*a^2*b*x*log(x) - 2*a^3)/x","A",0
156,1,37,0,0.410179," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} \log\left(x\right) - 6 \, a^{2} b x - a^{3}}{2 \, x^{2}}"," ",0,"1/2*(2*b^3*x^3 + 6*a*b^2*x^2*log(x) - 6*a^2*b*x - a^3)/x^2","A",0
157,1,37,0,0.390585," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^4,x, algorithm=""fricas"")","\frac{6 \, b^{3} x^{3} \log\left(x\right) - 18 \, a b^{2} x^{2} - 9 \, a^{2} b x - 2 \, a^{3}}{6 \, x^{3}}"," ",0,"1/6*(6*b^3*x^3*log(x) - 18*a*b^2*x^2 - 9*a^2*b*x - 2*a^3)/x^3","A",0
158,1,33,0,0.383658," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^5,x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}}"," ",0,"-1/4*(4*b^3*x^3 + 6*a*b^2*x^2 + 4*a^2*b*x + a^3)/x^4","A",0
159,1,35,0,0.393127," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^6,x, algorithm=""fricas"")","-\frac{10 \, b^{3} x^{3} + 20 \, a b^{2} x^{2} + 15 \, a^{2} b x + 4 \, a^{3}}{20 \, x^{5}}"," ",0,"-1/20*(10*b^3*x^3 + 20*a*b^2*x^2 + 15*a^2*b*x + 4*a^3)/x^5","A",0
160,1,35,0,0.393124," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^7,x, algorithm=""fricas"")","-\frac{20 \, b^{3} x^{3} + 45 \, a b^{2} x^{2} + 36 \, a^{2} b x + 10 \, a^{3}}{60 \, x^{6}}"," ",0,"-1/60*(20*b^3*x^3 + 45*a*b^2*x^2 + 36*a^2*b*x + 10*a^3)/x^6","A",0
161,1,35,0,0.389236," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^8,x, algorithm=""fricas"")","-\frac{35 \, b^{3} x^{3} + 84 \, a b^{2} x^{2} + 70 \, a^{2} b x + 20 \, a^{3}}{140 \, x^{7}}"," ",0,"-1/140*(35*b^3*x^3 + 84*a*b^2*x^2 + 70*a^2*b*x + 20*a^3)/x^7","A",0
162,1,35,0,0.399729," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/x^9,x, algorithm=""fricas"")","-\frac{56 \, b^{3} x^{3} + 140 \, a b^{2} x^{2} + 120 \, a^{2} b x + 35 \, a^{3}}{280 \, x^{8}}"," ",0,"-1/280*(56*b^3*x^3 + 140*a*b^2*x^2 + 120*a^2*b*x + 35*a^3)/x^8","A",0
163,1,57,0,0.392973," ","integrate(x^5*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{11} \, b^{5} x^{11} + \frac{1}{2} \, a b^{4} x^{10} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{5}{4} \, a^{3} b^{2} x^{8} + \frac{5}{7} \, a^{4} b x^{7} + \frac{1}{6} \, a^{5} x^{6}"," ",0,"1/11*b^5*x^11 + 1/2*a*b^4*x^10 + 10/9*a^2*b^3*x^9 + 5/4*a^3*b^2*x^8 + 5/7*a^4*b*x^7 + 1/6*a^5*x^6","A",0
164,1,57,0,0.398791," ","integrate(x^4*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{10} \, b^{5} x^{10} + \frac{5}{9} \, a b^{4} x^{9} + \frac{5}{4} \, a^{2} b^{3} x^{8} + \frac{10}{7} \, a^{3} b^{2} x^{7} + \frac{5}{6} \, a^{4} b x^{6} + \frac{1}{5} \, a^{5} x^{5}"," ",0,"1/10*b^5*x^10 + 5/9*a*b^4*x^9 + 5/4*a^2*b^3*x^8 + 10/7*a^3*b^2*x^7 + 5/6*a^4*b*x^6 + 1/5*a^5*x^5","A",0
165,1,56,0,0.398164," ","integrate(x^3*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{9} \, b^{5} x^{9} + \frac{5}{8} \, a b^{4} x^{8} + \frac{10}{7} \, a^{2} b^{3} x^{7} + \frac{5}{3} \, a^{3} b^{2} x^{6} + a^{4} b x^{5} + \frac{1}{4} \, a^{5} x^{4}"," ",0,"1/9*b^5*x^9 + 5/8*a*b^4*x^8 + 10/7*a^2*b^3*x^7 + 5/3*a^3*b^2*x^6 + a^4*b*x^5 + 1/4*a^5*x^4","A",0
166,1,57,0,0.396857," ","integrate(x^2*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{8} \, b^{5} x^{8} + \frac{5}{7} \, a b^{4} x^{7} + \frac{5}{3} \, a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{5} + \frac{5}{4} \, a^{4} b x^{4} + \frac{1}{3} \, a^{5} x^{3}"," ",0,"1/8*b^5*x^8 + 5/7*a*b^4*x^7 + 5/3*a^2*b^3*x^6 + 2*a^3*b^2*x^5 + 5/4*a^4*b*x^4 + 1/3*a^5*x^3","A",0
167,1,57,0,0.392329," ","integrate(x*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{7} \, b^{5} x^{7} + \frac{5}{6} \, a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{5} + \frac{5}{2} \, a^{3} b^{2} x^{4} + \frac{5}{3} \, a^{4} b x^{3} + \frac{1}{2} \, a^{5} x^{2}"," ",0,"1/7*b^5*x^7 + 5/6*a*b^4*x^6 + 2*a^2*b^3*x^5 + 5/2*a^3*b^2*x^4 + 5/3*a^4*b*x^3 + 1/2*a^5*x^2","A",0
168,1,53,0,0.388605," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{6} \, b^{5} x^{6} + a b^{4} x^{5} + \frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{10}{3} \, a^{3} b^{2} x^{3} + \frac{5}{2} \, a^{4} b x^{2} + a^{5} x"," ",0,"1/6*b^5*x^6 + a*b^4*x^5 + 5/2*a^2*b^3*x^4 + 10/3*a^3*b^2*x^3 + 5/2*a^4*b*x^2 + a^5*x","A",0
169,1,53,0,0.393047," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x,x, algorithm=""fricas"")","\frac{1}{5} \, b^{5} x^{5} + \frac{5}{4} \, a b^{4} x^{4} + \frac{10}{3} \, a^{2} b^{3} x^{3} + 5 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5} \log\left(x\right)"," ",0,"1/5*b^5*x^5 + 5/4*a*b^4*x^4 + 10/3*a^2*b^3*x^3 + 5*a^3*b^2*x^2 + 5*a^4*b*x + a^5*log(x)","A",0
170,1,59,0,0.400883," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^2,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{5} + 20 \, a b^{4} x^{4} + 60 \, a^{2} b^{3} x^{3} + 120 \, a^{3} b^{2} x^{2} + 60 \, a^{4} b x \log\left(x\right) - 12 \, a^{5}}{12 \, x}"," ",0,"1/12*(3*b^5*x^5 + 20*a*b^4*x^4 + 60*a^2*b^3*x^3 + 120*a^3*b^2*x^2 + 60*a^4*b*x*log(x) - 12*a^5)/x","A",0
171,1,59,0,0.403545," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^3,x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 60 \, a^{2} b^{3} x^{3} + 60 \, a^{3} b^{2} x^{2} \log\left(x\right) - 30 \, a^{4} b x - 3 \, a^{5}}{6 \, x^{2}}"," ",0,"1/6*(2*b^5*x^5 + 15*a*b^4*x^4 + 60*a^2*b^3*x^3 + 60*a^3*b^2*x^2*log(x) - 30*a^4*b*x - 3*a^5)/x^2","A",0
172,1,59,0,0.404458," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{5} + 30 \, a b^{4} x^{4} + 60 \, a^{2} b^{3} x^{3} \log\left(x\right) - 60 \, a^{3} b^{2} x^{2} - 15 \, a^{4} b x - 2 \, a^{5}}{6 \, x^{3}}"," ",0,"1/6*(3*b^5*x^5 + 30*a*b^4*x^4 + 60*a^2*b^3*x^3*log(x) - 60*a^3*b^2*x^2 - 15*a^4*b*x - 2*a^5)/x^3","A",0
173,1,59,0,0.401719," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^5,x, algorithm=""fricas"")","\frac{12 \, b^{5} x^{5} + 60 \, a b^{4} x^{4} \log\left(x\right) - 120 \, a^{2} b^{3} x^{3} - 60 \, a^{3} b^{2} x^{2} - 20 \, a^{4} b x - 3 \, a^{5}}{12 \, x^{4}}"," ",0,"1/12*(12*b^5*x^5 + 60*a*b^4*x^4*log(x) - 120*a^2*b^3*x^3 - 60*a^3*b^2*x^2 - 20*a^4*b*x - 3*a^5)/x^4","A",0
174,1,59,0,0.404144," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^6,x, algorithm=""fricas"")","\frac{60 \, b^{5} x^{5} \log\left(x\right) - 300 \, a b^{4} x^{4} - 300 \, a^{2} b^{3} x^{3} - 200 \, a^{3} b^{2} x^{2} - 75 \, a^{4} b x - 12 \, a^{5}}{60 \, x^{5}}"," ",0,"1/60*(60*b^5*x^5*log(x) - 300*a*b^4*x^4 - 300*a^2*b^3*x^3 - 200*a^3*b^2*x^2 - 75*a^4*b*x - 12*a^5)/x^5","A",0
175,1,55,0,0.406416," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^7,x, algorithm=""fricas"")","-\frac{6 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 20 \, a^{2} b^{3} x^{3} + 15 \, a^{3} b^{2} x^{2} + 6 \, a^{4} b x + a^{5}}{6 \, x^{6}}"," ",0,"-1/6*(6*b^5*x^5 + 15*a*b^4*x^4 + 20*a^2*b^3*x^3 + 15*a^3*b^2*x^2 + 6*a^4*b*x + a^5)/x^6","B",0
176,1,57,0,0.382294," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^8,x, algorithm=""fricas"")","-\frac{21 \, b^{5} x^{5} + 70 \, a b^{4} x^{4} + 105 \, a^{2} b^{3} x^{3} + 84 \, a^{3} b^{2} x^{2} + 35 \, a^{4} b x + 6 \, a^{5}}{42 \, x^{7}}"," ",0,"-1/42*(21*b^5*x^5 + 70*a*b^4*x^4 + 105*a^2*b^3*x^3 + 84*a^3*b^2*x^2 + 35*a^4*b*x + 6*a^5)/x^7","A",0
177,1,57,0,0.402717," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^9,x, algorithm=""fricas"")","-\frac{56 \, b^{5} x^{5} + 210 \, a b^{4} x^{4} + 336 \, a^{2} b^{3} x^{3} + 280 \, a^{3} b^{2} x^{2} + 120 \, a^{4} b x + 21 \, a^{5}}{168 \, x^{8}}"," ",0,"-1/168*(56*b^5*x^5 + 210*a*b^4*x^4 + 336*a^2*b^3*x^3 + 280*a^3*b^2*x^2 + 120*a^4*b*x + 21*a^5)/x^8","A",0
178,1,57,0,0.391020," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^10,x, algorithm=""fricas"")","-\frac{126 \, b^{5} x^{5} + 504 \, a b^{4} x^{4} + 840 \, a^{2} b^{3} x^{3} + 720 \, a^{3} b^{2} x^{2} + 315 \, a^{4} b x + 56 \, a^{5}}{504 \, x^{9}}"," ",0,"-1/504*(126*b^5*x^5 + 504*a*b^4*x^4 + 840*a^2*b^3*x^3 + 720*a^3*b^2*x^2 + 315*a^4*b*x + 56*a^5)/x^9","A",0
179,1,57,0,0.393392," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^11,x, algorithm=""fricas"")","-\frac{252 \, b^{5} x^{5} + 1050 \, a b^{4} x^{4} + 1800 \, a^{2} b^{3} x^{3} + 1575 \, a^{3} b^{2} x^{2} + 700 \, a^{4} b x + 126 \, a^{5}}{1260 \, x^{10}}"," ",0,"-1/1260*(252*b^5*x^5 + 1050*a*b^4*x^4 + 1800*a^2*b^3*x^3 + 1575*a^3*b^2*x^2 + 700*a^4*b*x + 126*a^5)/x^10","A",0
180,1,57,0,0.408958," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/x^12,x, algorithm=""fricas"")","-\frac{462 \, b^{5} x^{5} + 1980 \, a b^{4} x^{4} + 3465 \, a^{2} b^{3} x^{3} + 3080 \, a^{3} b^{2} x^{2} + 1386 \, a^{4} b x + 252 \, a^{5}}{2772 \, x^{11}}"," ",0,"-1/2772*(462*b^5*x^5 + 1980*a*b^4*x^4 + 3465*a^2*b^3*x^3 + 3080*a^3*b^2*x^2 + 1386*a^4*b*x + 252*a^5)/x^11","A",0
181,1,52,0,0.412145," ","integrate(x^4/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{4} - 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} - 12 \, a^{3} b x + 12 \, a^{4} \log\left(b x + a\right)}{12 \, b^{5}}"," ",0,"1/12*(3*b^4*x^4 - 4*a*b^3*x^3 + 6*a^2*b^2*x^2 - 12*a^3*b*x + 12*a^4*log(b*x + a))/b^5","A",0
182,1,41,0,0.397497," ","integrate(x^3/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} - 3 \, a b^{2} x^{2} + 6 \, a^{2} b x - 6 \, a^{3} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*b^3*x^3 - 3*a*b^2*x^2 + 6*a^2*b*x - 6*a^3*log(b*x + a))/b^4","A",0
183,1,29,0,0.385630," ","integrate(x^2/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b^{2} x^{2} - 2 \, a b x + 2 \, a^{2} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(b^2*x^2 - 2*a*b*x + 2*a^2*log(b*x + a))/b^3","A",0
184,1,17,0,0.399141," ","integrate(x/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b x - a \log\left(b x + a\right)}{b^{2}}"," ",0,"(b*x - a*log(b*x + a))/b^2","A",0
185,1,10,0,0.385545," ","integrate(1/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(b x + a\right)}{b}"," ",0,"log(b*x + a)/b","A",0
186,1,16,0,0.393528," ","integrate(1/x/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{\log\left(b x + a\right) - \log\left(x\right)}{a}"," ",0,"-(log(b*x + a) - log(x))/a","A",0
187,1,26,0,0.406182," ","integrate(1/x^2/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b x \log\left(b x + a\right) - b x \log\left(x\right) - a}{a^{2} x}"," ",0,"(b*x*log(b*x + a) - b*x*log(x) - a)/(a^2*x)","A",0
188,1,41,0,0.400656," ","integrate(1/x^3/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, b^{2} x^{2} \log\left(b x + a\right) - 2 \, b^{2} x^{2} \log\left(x\right) - 2 \, a b x + a^{2}}{2 \, a^{3} x^{2}}"," ",0,"-1/2*(2*b^2*x^2*log(b*x + a) - 2*b^2*x^2*log(x) - 2*a*b*x + a^2)/(a^3*x^2)","A",0
189,1,54,0,0.399134," ","integrate(1/x^4/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{6 \, b^{3} x^{3} \log\left(b x + a\right) - 6 \, b^{3} x^{3} \log\left(x\right) - 6 \, a b^{2} x^{2} + 3 \, a^{2} b x - 2 \, a^{3}}{6 \, a^{4} x^{3}}"," ",0,"1/6*(6*b^3*x^3*log(b*x + a) - 6*b^3*x^3*log(x) - 6*a*b^2*x^2 + 3*a^2*b*x - 2*a^3)/(a^4*x^3)","A",0
190,1,95,0,0.401546," ","integrate(x^4/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{b^{4} x^{4} - 4 \, a b^{3} x^{3} - 11 \, a^{2} b^{2} x^{2} + 2 \, a^{3} b x + 7 \, a^{4} + 12 \, {\left(a^{2} b^{2} x^{2} + 2 \, a^{3} b x + a^{4}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"1/2*(b^4*x^4 - 4*a*b^3*x^3 - 11*a^2*b^2*x^2 + 2*a^3*b*x + 7*a^4 + 12*(a^2*b^2*x^2 + 2*a^3*b*x + a^4)*log(b*x + a))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","A",0
191,1,83,0,0.400614," ","integrate(x^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} + 4 \, a b^{2} x^{2} - 4 \, a^{2} b x - 5 \, a^{3} - 6 \, {\left(a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/2*(2*b^3*x^3 + 4*a*b^2*x^2 - 4*a^2*b*x - 5*a^3 - 6*(a*b^2*x^2 + 2*a^2*b*x + a^3)*log(b*x + a))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","A",0
192,1,61,0,0.397901," ","integrate(x^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{4 \, a b x + 3 \, a^{2} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"1/2*(4*a*b*x + 3*a^2 + 2*(b^2*x^2 + 2*a*b*x + a^2)*log(b*x + a))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
193,1,32,0,0.392569," ","integrate(x/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, b x + a}{2 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-1/2*(2*b*x + a)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
194,1,24,0,0.387307," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"-1/2/(b^3*x^2 + 2*a*b^2*x + a^2*b)","A",0
195,1,80,0,0.413909," ","integrate(1/x/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, a b x + 3 \, a^{2} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{2} x^{2} + 2 \, a^{4} b x + a^{5}\right)}}"," ",0,"1/2*(2*a*b*x + 3*a^2 - 2*(b^2*x^2 + 2*a*b*x + a^2)*log(b*x + a) + 2*(b^2*x^2 + 2*a*b*x + a^2)*log(x))/(a^3*b^2*x^2 + 2*a^4*b*x + a^5)","A",0
196,1,109,0,0.407428," ","integrate(1/x^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{6 \, a b^{2} x^{2} + 9 \, a^{2} b x + 2 \, a^{3} - 6 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + a^{2} b x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + a^{2} b x\right)} \log\left(x\right)}{2 \, {\left(a^{4} b^{2} x^{3} + 2 \, a^{5} b x^{2} + a^{6} x\right)}}"," ",0,"-1/2*(6*a*b^2*x^2 + 9*a^2*b*x + 2*a^3 - 6*(b^3*x^3 + 2*a*b^2*x^2 + a^2*b*x)*log(b*x + a) + 6*(b^3*x^3 + 2*a*b^2*x^2 + a^2*b*x)*log(x))/(a^4*b^2*x^3 + 2*a^5*b*x^2 + a^6*x)","A",0
197,1,130,0,0.391539," ","integrate(1/x^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{12 \, a b^{3} x^{3} + 18 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x - a^{4} - 12 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{3} + a^{2} b^{2} x^{2}\right)} \log\left(b x + a\right) + 12 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{3} + a^{2} b^{2} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{5} b^{2} x^{4} + 2 \, a^{6} b x^{3} + a^{7} x^{2}\right)}}"," ",0,"1/2*(12*a*b^3*x^3 + 18*a^2*b^2*x^2 + 4*a^3*b*x - a^4 - 12*(b^4*x^4 + 2*a*b^3*x^3 + a^2*b^2*x^2)*log(b*x + a) + 12*(b^4*x^4 + 2*a*b^3*x^3 + a^2*b^2*x^2)*log(x))/(a^5*b^2*x^4 + 2*a^6*b*x^3 + a^7*x^2)","A",0
198,1,162,0,0.407448," ","integrate(x^6/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, b^{6} x^{6} - 12 \, a b^{5} x^{5} - 68 \, a^{2} b^{4} x^{4} - 32 \, a^{3} b^{3} x^{3} + 132 \, a^{4} b^{2} x^{2} + 168 \, a^{5} b x + 57 \, a^{6} + 60 \, {\left(a^{2} b^{4} x^{4} + 4 \, a^{3} b^{3} x^{3} + 6 \, a^{4} b^{2} x^{2} + 4 \, a^{5} b x + a^{6}\right)} \log\left(b x + a\right)}{4 \, {\left(b^{11} x^{4} + 4 \, a b^{10} x^{3} + 6 \, a^{2} b^{9} x^{2} + 4 \, a^{3} b^{8} x + a^{4} b^{7}\right)}}"," ",0,"1/4*(2*b^6*x^6 - 12*a*b^5*x^5 - 68*a^2*b^4*x^4 - 32*a^3*b^3*x^3 + 132*a^4*b^2*x^2 + 168*a^5*b*x + 57*a^6 + 60*(a^2*b^4*x^4 + 4*a^3*b^3*x^3 + 6*a^4*b^2*x^2 + 4*a^5*b*x + a^6)*log(b*x + a))/(b^11*x^4 + 4*a*b^10*x^3 + 6*a^2*b^9*x^2 + 4*a^3*b^8*x + a^4*b^7)","A",0
199,1,149,0,0.421344," ","integrate(x^5/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{12 \, b^{5} x^{5} + 48 \, a b^{4} x^{4} - 48 \, a^{2} b^{3} x^{3} - 252 \, a^{3} b^{2} x^{2} - 248 \, a^{4} b x - 77 \, a^{5} - 60 \, {\left(a b^{4} x^{4} + 4 \, a^{2} b^{3} x^{3} + 6 \, a^{3} b^{2} x^{2} + 4 \, a^{4} b x + a^{5}\right)} \log\left(b x + a\right)}{12 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}"," ",0,"1/12*(12*b^5*x^5 + 48*a*b^4*x^4 - 48*a^2*b^3*x^3 - 252*a^3*b^2*x^2 - 248*a^4*b*x - 77*a^5 - 60*(a*b^4*x^4 + 4*a^2*b^3*x^3 + 6*a^3*b^2*x^2 + 4*a^4*b*x + a^5)*log(b*x + a))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6)","A",0
200,1,127,0,0.423228," ","integrate(x^4/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{48 \, a b^{3} x^{3} + 108 \, a^{2} b^{2} x^{2} + 88 \, a^{3} b x + 25 \, a^{4} + 12 \, {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} \log\left(b x + a\right)}{12 \, {\left(b^{9} x^{4} + 4 \, a b^{8} x^{3} + 6 \, a^{2} b^{7} x^{2} + 4 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}"," ",0,"1/12*(48*a*b^3*x^3 + 108*a^2*b^2*x^2 + 88*a^3*b*x + 25*a^4 + 12*(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*log(b*x + a))/(b^9*x^4 + 4*a*b^8*x^3 + 6*a^2*b^7*x^2 + 4*a^3*b^6*x + a^4*b^5)","A",0
201,1,76,0,0.415062," ","integrate(x^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, {\left(b^{8} x^{4} + 4 \, a b^{7} x^{3} + 6 \, a^{2} b^{6} x^{2} + 4 \, a^{3} b^{5} x + a^{4} b^{4}\right)}}"," ",0,"-1/4*(4*b^3*x^3 + 6*a*b^2*x^2 + 4*a^2*b*x + a^3)/(b^8*x^4 + 4*a*b^7*x^3 + 6*a^2*b^6*x^2 + 4*a^3*b^5*x + a^4*b^4)","B",0
202,1,65,0,0.398550," ","integrate(x^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{6 \, b^{2} x^{2} + 4 \, a b x + a^{2}}{12 \, {\left(b^{7} x^{4} + 4 \, a b^{6} x^{3} + 6 \, a^{2} b^{5} x^{2} + 4 \, a^{3} b^{4} x + a^{4} b^{3}\right)}}"," ",0,"-1/12*(6*b^2*x^2 + 4*a*b*x + a^2)/(b^7*x^4 + 4*a*b^6*x^3 + 6*a^2*b^5*x^2 + 4*a^3*b^4*x + a^4*b^3)","A",0
203,1,54,0,0.418651," ","integrate(x/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, b x + a}{12 \, {\left(b^{6} x^{4} + 4 \, a b^{5} x^{3} + 6 \, a^{2} b^{4} x^{2} + 4 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}"," ",0,"-1/12*(4*b*x + a)/(b^6*x^4 + 4*a*b^5*x^3 + 6*a^2*b^4*x^2 + 4*a^3*b^3*x + a^4*b^2)","A",0
204,1,46,0,0.401682," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}}"," ",0,"-1/4/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b)","A",0
205,1,168,0,0.417729," ","integrate(1/x/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{12 \, a b^{3} x^{3} + 42 \, a^{2} b^{2} x^{2} + 52 \, a^{3} b x + 25 \, a^{4} - 12 \, {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} \log\left(b x + a\right) + 12 \, {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} \log\left(x\right)}{12 \, {\left(a^{5} b^{4} x^{4} + 4 \, a^{6} b^{3} x^{3} + 6 \, a^{7} b^{2} x^{2} + 4 \, a^{8} b x + a^{9}\right)}}"," ",0,"1/12*(12*a*b^3*x^3 + 42*a^2*b^2*x^2 + 52*a^3*b*x + 25*a^4 - 12*(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*log(b*x + a) + 12*(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*log(x))/(a^5*b^4*x^4 + 4*a^6*b^3*x^3 + 6*a^7*b^2*x^2 + 4*a^8*b*x + a^9)","A",0
206,1,197,0,0.425809," ","integrate(1/x^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{60 \, a b^{4} x^{4} + 210 \, a^{2} b^{3} x^{3} + 260 \, a^{3} b^{2} x^{2} + 125 \, a^{4} b x + 12 \, a^{5} - 60 \, {\left(b^{5} x^{5} + 4 \, a b^{4} x^{4} + 6 \, a^{2} b^{3} x^{3} + 4 \, a^{3} b^{2} x^{2} + a^{4} b x\right)} \log\left(b x + a\right) + 60 \, {\left(b^{5} x^{5} + 4 \, a b^{4} x^{4} + 6 \, a^{2} b^{3} x^{3} + 4 \, a^{3} b^{2} x^{2} + a^{4} b x\right)} \log\left(x\right)}{12 \, {\left(a^{6} b^{4} x^{5} + 4 \, a^{7} b^{3} x^{4} + 6 \, a^{8} b^{2} x^{3} + 4 \, a^{9} b x^{2} + a^{10} x\right)}}"," ",0,"-1/12*(60*a*b^4*x^4 + 210*a^2*b^3*x^3 + 260*a^3*b^2*x^2 + 125*a^4*b*x + 12*a^5 - 60*(b^5*x^5 + 4*a*b^4*x^4 + 6*a^2*b^3*x^3 + 4*a^3*b^2*x^2 + a^4*b*x)*log(b*x + a) + 60*(b^5*x^5 + 4*a*b^4*x^4 + 6*a^2*b^3*x^3 + 4*a^3*b^2*x^2 + a^4*b*x)*log(x))/(a^6*b^4*x^5 + 4*a^7*b^3*x^4 + 6*a^8*b^2*x^3 + 4*a^9*b*x^2 + a^10*x)","A",0
207,1,218,0,0.414956," ","integrate(1/x^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{60 \, a b^{5} x^{5} + 210 \, a^{2} b^{4} x^{4} + 260 \, a^{3} b^{3} x^{3} + 125 \, a^{4} b^{2} x^{2} + 12 \, a^{5} b x - 2 \, a^{6} - 60 \, {\left(b^{6} x^{6} + 4 \, a b^{5} x^{5} + 6 \, a^{2} b^{4} x^{4} + 4 \, a^{3} b^{3} x^{3} + a^{4} b^{2} x^{2}\right)} \log\left(b x + a\right) + 60 \, {\left(b^{6} x^{6} + 4 \, a b^{5} x^{5} + 6 \, a^{2} b^{4} x^{4} + 4 \, a^{3} b^{3} x^{3} + a^{4} b^{2} x^{2}\right)} \log\left(x\right)}{4 \, {\left(a^{7} b^{4} x^{6} + 4 \, a^{8} b^{3} x^{5} + 6 \, a^{9} b^{2} x^{4} + 4 \, a^{10} b x^{3} + a^{11} x^{2}\right)}}"," ",0,"1/4*(60*a*b^5*x^5 + 210*a^2*b^4*x^4 + 260*a^3*b^3*x^3 + 125*a^4*b^2*x^2 + 12*a^5*b*x - 2*a^6 - 60*(b^6*x^6 + 4*a*b^5*x^5 + 6*a^2*b^4*x^4 + 4*a^3*b^3*x^3 + a^4*b^2*x^2)*log(b*x + a) + 60*(b^6*x^6 + 4*a*b^5*x^5 + 6*a^2*b^4*x^4 + 4*a^3*b^3*x^3 + a^4*b^2*x^2)*log(x))/(a^7*b^4*x^6 + 4*a^8*b^3*x^5 + 6*a^9*b^2*x^4 + 4*a^10*b*x^3 + a^11*x^2)","A",0
208,1,31,0,0.422910," ","integrate(x*(4*x^2+12*x+9)^(5/2),x, algorithm=""fricas"")","\frac{32}{7} \, x^{7} + 40 \, x^{6} + 144 \, x^{5} + 270 \, x^{4} + 270 \, x^{3} + \frac{243}{2} \, x^{2}"," ",0,"32/7*x^7 + 40*x^6 + 144*x^5 + 270*x^4 + 270*x^3 + 243/2*x^2","A",0
209,1,21,0,0.406145," ","integrate(x*(4*x^2+12*x+9)^(3/2),x, algorithm=""fricas"")","\frac{8}{5} \, x^{5} + 9 \, x^{4} + 18 \, x^{3} + \frac{27}{2} \, x^{2}"," ",0,"8/5*x^5 + 9*x^4 + 18*x^3 + 27/2*x^2","A",0
210,1,11,0,0.409168," ","integrate(x*(4*x^2+12*x+9)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, x^{3} + \frac{3}{2} \, x^{2}"," ",0,"2/3*x^3 + 3/2*x^2","A",0
211,1,12,0,0.403881," ","integrate(x/(4*x^2+12*x+9)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, x - \frac{3}{4} \, \log\left(2 \, x + 3\right)"," ",0,"1/2*x - 3/4*log(2*x + 3)","A",0
212,1,19,0,0.399099," ","integrate(x/(4*x^2+12*x+9)^(3/2),x, algorithm=""fricas"")","-\frac{4 \, x + 3}{8 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"-1/8*(4*x + 3)/(4*x^2 + 12*x + 9)","A",0
213,1,29,0,0.399304," ","integrate(x/(4*x^2+12*x+9)^(5/2),x, algorithm=""fricas"")","-\frac{8 \, x + 3}{48 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"-1/48*(8*x + 3)/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
214,1,39,0,0.396127," ","integrate(x/(4*x^2+12*x+9)^(7/2),x, algorithm=""fricas"")","-\frac{4 \, x + 1}{40 \, {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)}}"," ",0,"-1/40*(4*x + 1)/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)","A",0
215,1,12,0,0.431320," ","integrate(x/((2+3*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, x - \frac{2}{9} \, \log\left(3 \, x + 2\right)"," ",0,"1/3*x - 2/9*log(3*x + 2)","A",0
216,1,12,0,0.403183," ","integrate(x/((-2+3*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, x + \frac{2}{9} \, \log\left(3 \, x - 2\right)"," ",0,"1/3*x + 2/9*log(3*x - 2)","A",0
217,1,10,0,0.419218," ","integrate(x/(-(-2+3*x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} i \, x - \frac{2}{9} i \, \log\left(x - \frac{2}{3}\right)"," ",0,"-1/3*I*x - 2/9*I*log(x - 2/3)","C",0
218,1,10,0,0.413527," ","integrate(x/(-(2+3*x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{3} i \, x + \frac{2}{9} i \, \log\left(x + \frac{2}{3}\right)"," ",0,"-1/3*I*x + 2/9*I*log(x + 2/3)","C",0
219,1,10,0,0.392629," ","integrate((1+x)/(x^2+2*x),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(x^{2} + 2 \, x\right)"," ",0,"1/2*log(x^2 + 2*x)","A",0
220,1,10,0,0.397545," ","integrate((2*b*x+a)/(b*x^2+a*x),x, algorithm=""fricas"")","\log\left(b x^{2} + a x\right)"," ",0,"log(b*x^2 + a*x)","A",0
221,1,100,0,0.351322," ","integrate((e*x+d)^4*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{4} c + \frac{2}{3} x^{6} e^{3} d c + \frac{1}{6} x^{6} e^{4} b + \frac{6}{5} x^{5} e^{2} d^{2} c + \frac{4}{5} x^{5} e^{3} d b + x^{4} e d^{3} c + \frac{3}{2} x^{4} e^{2} d^{2} b + \frac{1}{3} x^{3} d^{4} c + \frac{4}{3} x^{3} e d^{3} b + \frac{1}{2} x^{2} d^{4} b"," ",0,"1/7*x^7*e^4*c + 2/3*x^6*e^3*d*c + 1/6*x^6*e^4*b + 6/5*x^5*e^2*d^2*c + 4/5*x^5*e^3*d*b + x^4*e*d^3*c + 3/2*x^4*e^2*d^2*b + 1/3*x^3*d^4*c + 4/3*x^3*e*d^3*b + 1/2*x^2*d^4*b","A",0
222,1,76,0,0.349330," ","integrate((e*x+d)^3*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{3} c + \frac{3}{5} x^{5} e^{2} d c + \frac{1}{5} x^{5} e^{3} b + \frac{3}{4} x^{4} e d^{2} c + \frac{3}{4} x^{4} e^{2} d b + \frac{1}{3} x^{3} d^{3} c + x^{3} e d^{2} b + \frac{1}{2} x^{2} d^{3} b"," ",0,"1/6*x^6*e^3*c + 3/5*x^5*e^2*d*c + 1/5*x^5*e^3*b + 3/4*x^4*e*d^2*c + 3/4*x^4*e^2*d*b + 1/3*x^3*d^3*c + x^3*e*d^2*b + 1/2*x^2*d^3*b","A",0
223,1,53,0,0.363672," ","integrate((e*x+d)^2*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e^{2} c + \frac{1}{2} x^{4} e d c + \frac{1}{4} x^{4} e^{2} b + \frac{1}{3} x^{3} d^{2} c + \frac{2}{3} x^{3} e d b + \frac{1}{2} x^{2} d^{2} b"," ",0,"1/5*x^5*e^2*c + 1/2*x^4*e*d*c + 1/4*x^4*e^2*b + 1/3*x^3*d^2*c + 2/3*x^3*e*d*b + 1/2*x^2*d^2*b","A",0
224,1,29,0,0.358552," ","integrate((e*x+d)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{1}{4} x^{4} e c + \frac{1}{3} x^{3} d c + \frac{1}{3} x^{3} e b + \frac{1}{2} x^{2} d b"," ",0,"1/4*x^4*e*c + 1/3*x^3*d*c + 1/3*x^3*e*b + 1/2*x^2*d*b","A",0
225,1,13,0,0.357547," ","integrate(c*x^2+b*x,x, algorithm=""fricas"")","\frac{1}{3} x^{3} c + \frac{1}{2} x^{2} b"," ",0,"1/3*x^3*c + 1/2*x^2*b","A",0
226,1,47,0,0.401666," ","integrate((c*x^2+b*x)/(e*x+d),x, algorithm=""fricas"")","\frac{c e^{2} x^{2} - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, {\left(c d^{2} - b d e\right)} \log\left(e x + d\right)}{2 \, e^{3}}"," ",0,"1/2*(c*e^2*x^2 - 2*(c*d*e - b*e^2)*x + 2*(c*d^2 - b*d*e)*log(e*x + d))/e^3","A",0
227,1,72,0,0.393260," ","integrate((c*x^2+b*x)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{c e^{2} x^{2} + c d e x - c d^{2} + b d e - {\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \log\left(e x + d\right)}{e^{4} x + d e^{3}}"," ",0,"(c*e^2*x^2 + c*d*e*x - c*d^2 + b*d*e - (2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*log(e*x + d))/(e^4*x + d*e^3)","A",0
228,1,81,0,0.388691," ","integrate((c*x^2+b*x)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{3 \, c d^{2} - b d e + 2 \, {\left(2 \, c d e - b e^{2}\right)} x + 2 \, {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"1/2*(3*c*d^2 - b*d*e + 2*(2*c*d*e - b*e^2)*x + 2*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*log(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
229,1,71,0,0.395480," ","integrate((c*x^2+b*x)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{6 \, c e^{2} x^{2} + 2 \, c d^{2} + b d e + 3 \, {\left(2 \, c d e + b e^{2}\right)} x}{6 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/6*(6*c*e^2*x^2 + 2*c*d^2 + b*d*e + 3*(2*c*d*e + b*e^2)*x)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
230,1,80,0,0.396479," ","integrate((c*x^2+b*x)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{6 \, c e^{2} x^{2} + c d^{2} + b d e + 4 \, {\left(c d e + b e^{2}\right)} x}{12 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/12*(6*c*e^2*x^2 + c*d^2 + b*d*e + 4*(c*d*e + b*e^2)*x)/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)","A",0
231,1,175,0,0.360211," ","integrate((e*x+d)^4*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{4} c^{2} + \frac{1}{2} x^{8} e^{3} d c^{2} + \frac{1}{4} x^{8} e^{4} c b + \frac{6}{7} x^{7} e^{2} d^{2} c^{2} + \frac{8}{7} x^{7} e^{3} d c b + \frac{1}{7} x^{7} e^{4} b^{2} + \frac{2}{3} x^{6} e d^{3} c^{2} + 2 x^{6} e^{2} d^{2} c b + \frac{2}{3} x^{6} e^{3} d b^{2} + \frac{1}{5} x^{5} d^{4} c^{2} + \frac{8}{5} x^{5} e d^{3} c b + \frac{6}{5} x^{5} e^{2} d^{2} b^{2} + \frac{1}{2} x^{4} d^{4} c b + x^{4} e d^{3} b^{2} + \frac{1}{3} x^{3} d^{4} b^{2}"," ",0,"1/9*x^9*e^4*c^2 + 1/2*x^8*e^3*d*c^2 + 1/4*x^8*e^4*c*b + 6/7*x^7*e^2*d^2*c^2 + 8/7*x^7*e^3*d*c*b + 1/7*x^7*e^4*b^2 + 2/3*x^6*e*d^3*c^2 + 2*x^6*e^2*d^2*c*b + 2/3*x^6*e^3*d*b^2 + 1/5*x^5*d^4*c^2 + 8/5*x^5*e*d^3*c*b + 6/5*x^5*e^2*d^2*b^2 + 1/2*x^4*d^4*c*b + x^4*e*d^3*b^2 + 1/3*x^3*d^4*b^2","A",0
232,1,134,0,0.363038," ","integrate((e*x+d)^3*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{3} c^{2} + \frac{3}{7} x^{7} e^{2} d c^{2} + \frac{2}{7} x^{7} e^{3} c b + \frac{1}{2} x^{6} e d^{2} c^{2} + x^{6} e^{2} d c b + \frac{1}{6} x^{6} e^{3} b^{2} + \frac{1}{5} x^{5} d^{3} c^{2} + \frac{6}{5} x^{5} e d^{2} c b + \frac{3}{5} x^{5} e^{2} d b^{2} + \frac{1}{2} x^{4} d^{3} c b + \frac{3}{4} x^{4} e d^{2} b^{2} + \frac{1}{3} x^{3} d^{3} b^{2}"," ",0,"1/8*x^8*e^3*c^2 + 3/7*x^7*e^2*d*c^2 + 2/7*x^7*e^3*c*b + 1/2*x^6*e*d^2*c^2 + x^6*e^2*d*c*b + 1/6*x^6*e^3*b^2 + 1/5*x^5*d^3*c^2 + 6/5*x^5*e*d^2*c*b + 3/5*x^5*e^2*d*b^2 + 1/2*x^4*d^3*c*b + 3/4*x^4*e*d^2*b^2 + 1/3*x^3*d^3*b^2","A",0
233,1,94,0,0.357796," ","integrate((e*x+d)^2*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{2} c^{2} + \frac{1}{3} x^{6} e d c^{2} + \frac{1}{3} x^{6} e^{2} c b + \frac{1}{5} x^{5} d^{2} c^{2} + \frac{4}{5} x^{5} e d c b + \frac{1}{5} x^{5} e^{2} b^{2} + \frac{1}{2} x^{4} d^{2} c b + \frac{1}{2} x^{4} e d b^{2} + \frac{1}{3} x^{3} d^{2} b^{2}"," ",0,"1/7*x^7*e^2*c^2 + 1/3*x^6*e*d*c^2 + 1/3*x^6*e^2*c*b + 1/5*x^5*d^2*c^2 + 4/5*x^5*e*d*c*b + 1/5*x^5*e^2*b^2 + 1/2*x^4*d^2*c*b + 1/2*x^4*e*d*b^2 + 1/3*x^3*d^2*b^2","A",0
234,1,53,0,0.361096," ","integrate((e*x+d)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} e c^{2} + \frac{1}{5} x^{5} d c^{2} + \frac{2}{5} x^{5} e c b + \frac{1}{2} x^{4} d c b + \frac{1}{4} x^{4} e b^{2} + \frac{1}{3} x^{3} d b^{2}"," ",0,"1/6*x^6*e*c^2 + 1/5*x^5*d*c^2 + 2/5*x^5*e*c*b + 1/2*x^4*d*c*b + 1/4*x^4*e*b^2 + 1/3*x^3*d*b^2","A",0
235,1,24,0,0.357127," ","integrate((c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{1}{5} x^{5} c^{2} + \frac{1}{2} x^{4} c b + \frac{1}{3} x^{3} b^{2}"," ",0,"1/5*x^5*c^2 + 1/2*x^4*c*b + 1/3*x^3*b^2","A",0
236,1,133,0,0.405723," ","integrate((c*x^2+b*x)^2/(e*x+d),x, algorithm=""fricas"")","\frac{3 \, c^{2} e^{4} x^{4} - 4 \, {\left(c^{2} d e^{3} - 2 \, b c e^{4}\right)} x^{3} + 6 \, {\left(c^{2} d^{2} e^{2} - 2 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} - 12 \, {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x + 12 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} \log\left(e x + d\right)}{12 \, e^{5}}"," ",0,"1/12*(3*c^2*e^4*x^4 - 4*(c^2*d*e^3 - 2*b*c*e^4)*x^3 + 6*(c^2*d^2*e^2 - 2*b*c*d*e^3 + b^2*e^4)*x^2 - 12*(c^2*d^3*e - 2*b*c*d^2*e^2 + b^2*d*e^3)*x + 12*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*log(e*x + d))/e^5","A",0
237,1,203,0,0.416039," ","integrate((c*x^2+b*x)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{c^{2} e^{4} x^{4} - 3 \, c^{2} d^{4} + 6 \, b c d^{3} e - 3 \, b^{2} d^{2} e^{2} - {\left(2 \, c^{2} d e^{3} - 3 \, b c e^{4}\right)} x^{3} + 3 \, {\left(2 \, c^{2} d^{2} e^{2} - 3 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 3 \, {\left(3 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x - 6 \, {\left(2 \, c^{2} d^{4} - 3 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"1/3*(c^2*e^4*x^4 - 3*c^2*d^4 + 6*b*c*d^3*e - 3*b^2*d^2*e^2 - (2*c^2*d*e^3 - 3*b*c*e^4)*x^3 + 3*(2*c^2*d^2*e^2 - 3*b*c*d*e^3 + b^2*e^4)*x^2 + 3*(3*c^2*d^3*e - 4*b*c*d^2*e^2 + b^2*d*e^3)*x - 6*(2*c^2*d^4 - 3*b*c*d^3*e + b^2*d^2*e^2 + (2*c^2*d^3*e - 3*b*c*d^2*e^2 + b^2*d*e^3)*x)*log(e*x + d))/(e^6*x + d*e^5)","A",0
238,1,238,0,0.399587," ","integrate((c*x^2+b*x)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{c^{2} e^{4} x^{4} + 7 \, c^{2} d^{4} - 10 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} - 4 \, {\left(c^{2} d e^{3} - b c e^{4}\right)} x^{3} - {\left(11 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3}\right)} x^{2} + 2 \, {\left(c^{2} d^{3} e - 4 \, b c d^{2} e^{2} + 2 \, b^{2} d e^{3}\right)} x + 2 \, {\left(6 \, c^{2} d^{4} - 6 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(6 \, c^{2} d^{2} e^{2} - 6 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 2 \, {\left(6 \, c^{2} d^{3} e - 6 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"1/2*(c^2*e^4*x^4 + 7*c^2*d^4 - 10*b*c*d^3*e + 3*b^2*d^2*e^2 - 4*(c^2*d*e^3 - b*c*e^4)*x^3 - (11*c^2*d^2*e^2 - 8*b*c*d*e^3)*x^2 + 2*(c^2*d^3*e - 4*b*c*d^2*e^2 + 2*b^2*d*e^3)*x + 2*(6*c^2*d^4 - 6*b*c*d^3*e + b^2*d^2*e^2 + (6*c^2*d^2*e^2 - 6*b*c*d*e^3 + b^2*e^4)*x^2 + 2*(6*c^2*d^3*e - 6*b*c*d^2*e^2 + b^2*d*e^3)*x)*log(e*x + d))/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","B",0
239,1,245,0,0.391322," ","integrate((c*x^2+b*x)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, c^{2} e^{4} x^{4} + 9 \, c^{2} d e^{3} x^{3} - 13 \, c^{2} d^{4} + 11 \, b c d^{3} e - b^{2} d^{2} e^{2} - 3 \, {\left(3 \, c^{2} d^{2} e^{2} - 6 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} - 3 \, {\left(9 \, c^{2} d^{3} e - 9 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x - 6 \, {\left(2 \, c^{2} d^{4} - b c d^{3} e + {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} x^{3} + 3 \, {\left(2 \, c^{2} d^{2} e^{2} - b c d e^{3}\right)} x^{2} + 3 \, {\left(2 \, c^{2} d^{3} e - b c d^{2} e^{2}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"1/3*(3*c^2*e^4*x^4 + 9*c^2*d*e^3*x^3 - 13*c^2*d^4 + 11*b*c*d^3*e - b^2*d^2*e^2 - 3*(3*c^2*d^2*e^2 - 6*b*c*d*e^3 + b^2*e^4)*x^2 - 3*(9*c^2*d^3*e - 9*b*c*d^2*e^2 + b^2*d*e^3)*x - 6*(2*c^2*d^4 - b*c*d^3*e + (2*c^2*d*e^3 - b*c*e^4)*x^3 + 3*(2*c^2*d^2*e^2 - b*c*d*e^3)*x^2 + 3*(2*c^2*d^3*e - b*c*d^2*e^2)*x)*log(e*x + d))/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","B",0
240,1,225,0,0.407438," ","integrate((c*x^2+b*x)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{25 \, c^{2} d^{4} - 6 \, b c d^{3} e - b^{2} d^{2} e^{2} + 24 \, {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} x^{3} + 6 \, {\left(18 \, c^{2} d^{2} e^{2} - 6 \, b c d e^{3} - b^{2} e^{4}\right)} x^{2} + 4 \, {\left(22 \, c^{2} d^{3} e - 6 \, b c d^{2} e^{2} - b^{2} d e^{3}\right)} x + 12 \, {\left(c^{2} e^{4} x^{4} + 4 \, c^{2} d e^{3} x^{3} + 6 \, c^{2} d^{2} e^{2} x^{2} + 4 \, c^{2} d^{3} e x + c^{2} d^{4}\right)} \log\left(e x + d\right)}{12 \, {\left(e^{9} x^{4} + 4 \, d e^{8} x^{3} + 6 \, d^{2} e^{7} x^{2} + 4 \, d^{3} e^{6} x + d^{4} e^{5}\right)}}"," ",0,"1/12*(25*c^2*d^4 - 6*b*c*d^3*e - b^2*d^2*e^2 + 24*(2*c^2*d*e^3 - b*c*e^4)*x^3 + 6*(18*c^2*d^2*e^2 - 6*b*c*d*e^3 - b^2*e^4)*x^2 + 4*(22*c^2*d^3*e - 6*b*c*d^2*e^2 - b^2*d*e^3)*x + 12*(c^2*e^4*x^4 + 4*c^2*d*e^3*x^3 + 6*c^2*d^2*e^2*x^2 + 4*c^2*d^3*e*x + c^2*d^4)*log(e*x + d))/(e^9*x^4 + 4*d*e^8*x^3 + 6*d^2*e^7*x^2 + 4*d^3*e^6*x + d^4*e^5)","A",0
241,1,181,0,0.408885," ","integrate((c*x^2+b*x)^2/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{30 \, c^{2} e^{4} x^{4} + 6 \, c^{2} d^{4} + 3 \, b c d^{3} e + b^{2} d^{2} e^{2} + 30 \, {\left(2 \, c^{2} d e^{3} + b c e^{4}\right)} x^{3} + 10 \, {\left(6 \, c^{2} d^{2} e^{2} + 3 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 5 \, {\left(6 \, c^{2} d^{3} e + 3 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x}{30 \, {\left(e^{10} x^{5} + 5 \, d e^{9} x^{4} + 10 \, d^{2} e^{8} x^{3} + 10 \, d^{3} e^{7} x^{2} + 5 \, d^{4} e^{6} x + d^{5} e^{5}\right)}}"," ",0,"-1/30*(30*c^2*e^4*x^4 + 6*c^2*d^4 + 3*b*c*d^3*e + b^2*d^2*e^2 + 30*(2*c^2*d*e^3 + b*c*e^4)*x^3 + 10*(6*c^2*d^2*e^2 + 3*b*c*d*e^3 + b^2*e^4)*x^2 + 5*(6*c^2*d^3*e + 3*b*c*d^2*e^2 + b^2*d*e^3)*x)/(e^10*x^5 + 5*d*e^9*x^4 + 10*d^2*e^8*x^3 + 10*d^3*e^7*x^2 + 5*d^4*e^6*x + d^5*e^5)","A",0
242,1,191,0,0.391208," ","integrate((c*x^2+b*x)^2/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{30 \, c^{2} e^{4} x^{4} + 2 \, c^{2} d^{4} + 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + 40 \, {\left(c^{2} d e^{3} + b c e^{4}\right)} x^{3} + 15 \, {\left(2 \, c^{2} d^{2} e^{2} + 2 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 6 \, {\left(2 \, c^{2} d^{3} e + 2 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x}{60 \, {\left(e^{11} x^{6} + 6 \, d e^{10} x^{5} + 15 \, d^{2} e^{9} x^{4} + 20 \, d^{3} e^{8} x^{3} + 15 \, d^{4} e^{7} x^{2} + 6 \, d^{5} e^{6} x + d^{6} e^{5}\right)}}"," ",0,"-1/60*(30*c^2*e^4*x^4 + 2*c^2*d^4 + 2*b*c*d^3*e + b^2*d^2*e^2 + 40*(c^2*d*e^3 + b*c*e^4)*x^3 + 15*(2*c^2*d^2*e^2 + 2*b*c*d*e^3 + b^2*e^4)*x^2 + 6*(2*c^2*d^3*e + 2*b*c*d^2*e^2 + b^2*d*e^3)*x)/(e^11*x^6 + 6*d*e^10*x^5 + 15*d^2*e^9*x^4 + 20*d^3*e^8*x^3 + 15*d^4*e^7*x^2 + 6*d^5*e^6*x + d^6*e^5)","A",0
243,1,207,0,0.391940," ","integrate((c*x^2+b*x)^2/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{70 \, c^{2} e^{4} x^{4} + 2 \, c^{2} d^{4} + 3 \, b c d^{3} e + 2 \, b^{2} d^{2} e^{2} + 35 \, {\left(2 \, c^{2} d e^{3} + 3 \, b c e^{4}\right)} x^{3} + 21 \, {\left(2 \, c^{2} d^{2} e^{2} + 3 \, b c d e^{3} + 2 \, b^{2} e^{4}\right)} x^{2} + 7 \, {\left(2 \, c^{2} d^{3} e + 3 \, b c d^{2} e^{2} + 2 \, b^{2} d e^{3}\right)} x}{210 \, {\left(e^{12} x^{7} + 7 \, d e^{11} x^{6} + 21 \, d^{2} e^{10} x^{5} + 35 \, d^{3} e^{9} x^{4} + 35 \, d^{4} e^{8} x^{3} + 21 \, d^{5} e^{7} x^{2} + 7 \, d^{6} e^{6} x + d^{7} e^{5}\right)}}"," ",0,"-1/210*(70*c^2*e^4*x^4 + 2*c^2*d^4 + 3*b*c*d^3*e + 2*b^2*d^2*e^2 + 35*(2*c^2*d*e^3 + 3*b*c*e^4)*x^3 + 21*(2*c^2*d^2*e^2 + 3*b*c*d*e^3 + 2*b^2*e^4)*x^2 + 7*(2*c^2*d^3*e + 3*b*c*d^2*e^2 + 2*b^2*d*e^3)*x)/(e^12*x^7 + 7*d*e^11*x^6 + 21*d^2*e^10*x^5 + 35*d^3*e^9*x^4 + 35*d^4*e^8*x^3 + 21*d^5*e^7*x^2 + 7*d^6*e^6*x + d^7*e^5)","A",0
244,1,250,0,0.347266," ","integrate((e*x+d)^4*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{4} c^{3} + \frac{2}{5} x^{10} e^{3} d c^{3} + \frac{3}{10} x^{10} e^{4} c^{2} b + \frac{2}{3} x^{9} e^{2} d^{2} c^{3} + \frac{4}{3} x^{9} e^{3} d c^{2} b + \frac{1}{3} x^{9} e^{4} c b^{2} + \frac{1}{2} x^{8} e d^{3} c^{3} + \frac{9}{4} x^{8} e^{2} d^{2} c^{2} b + \frac{3}{2} x^{8} e^{3} d c b^{2} + \frac{1}{8} x^{8} e^{4} b^{3} + \frac{1}{7} x^{7} d^{4} c^{3} + \frac{12}{7} x^{7} e d^{3} c^{2} b + \frac{18}{7} x^{7} e^{2} d^{2} c b^{2} + \frac{4}{7} x^{7} e^{3} d b^{3} + \frac{1}{2} x^{6} d^{4} c^{2} b + 2 x^{6} e d^{3} c b^{2} + x^{6} e^{2} d^{2} b^{3} + \frac{3}{5} x^{5} d^{4} c b^{2} + \frac{4}{5} x^{5} e d^{3} b^{3} + \frac{1}{4} x^{4} d^{4} b^{3}"," ",0,"1/11*x^11*e^4*c^3 + 2/5*x^10*e^3*d*c^3 + 3/10*x^10*e^4*c^2*b + 2/3*x^9*e^2*d^2*c^3 + 4/3*x^9*e^3*d*c^2*b + 1/3*x^9*e^4*c*b^2 + 1/2*x^8*e*d^3*c^3 + 9/4*x^8*e^2*d^2*c^2*b + 3/2*x^8*e^3*d*c*b^2 + 1/8*x^8*e^4*b^3 + 1/7*x^7*d^4*c^3 + 12/7*x^7*e*d^3*c^2*b + 18/7*x^7*e^2*d^2*c*b^2 + 4/7*x^7*e^3*d*b^3 + 1/2*x^6*d^4*c^2*b + 2*x^6*e*d^3*c*b^2 + x^6*e^2*d^2*b^3 + 3/5*x^5*d^4*c*b^2 + 4/5*x^5*e*d^3*b^3 + 1/4*x^4*d^4*b^3","A",0
245,1,193,0,0.362563," ","integrate((e*x+d)^3*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{3} c^{3} + \frac{1}{3} x^{9} e^{2} d c^{3} + \frac{1}{3} x^{9} e^{3} c^{2} b + \frac{3}{8} x^{8} e d^{2} c^{3} + \frac{9}{8} x^{8} e^{2} d c^{2} b + \frac{3}{8} x^{8} e^{3} c b^{2} + \frac{1}{7} x^{7} d^{3} c^{3} + \frac{9}{7} x^{7} e d^{2} c^{2} b + \frac{9}{7} x^{7} e^{2} d c b^{2} + \frac{1}{7} x^{7} e^{3} b^{3} + \frac{1}{2} x^{6} d^{3} c^{2} b + \frac{3}{2} x^{6} e d^{2} c b^{2} + \frac{1}{2} x^{6} e^{2} d b^{3} + \frac{3}{5} x^{5} d^{3} c b^{2} + \frac{3}{5} x^{5} e d^{2} b^{3} + \frac{1}{4} x^{4} d^{3} b^{3}"," ",0,"1/10*x^10*e^3*c^3 + 1/3*x^9*e^2*d*c^3 + 1/3*x^9*e^3*c^2*b + 3/8*x^8*e*d^2*c^3 + 9/8*x^8*e^2*d*c^2*b + 3/8*x^8*e^3*c*b^2 + 1/7*x^7*d^3*c^3 + 9/7*x^7*e*d^2*c^2*b + 9/7*x^7*e^2*d*c*b^2 + 1/7*x^7*e^3*b^3 + 1/2*x^6*d^3*c^2*b + 3/2*x^6*e*d^2*c*b^2 + 1/2*x^6*e^2*d*b^3 + 3/5*x^5*d^3*c*b^2 + 3/5*x^5*e*d^2*b^3 + 1/4*x^4*d^3*b^3","A",0
246,1,134,0,0.340805," ","integrate((e*x+d)^2*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{2} c^{3} + \frac{1}{4} x^{8} e d c^{3} + \frac{3}{8} x^{8} e^{2} c^{2} b + \frac{1}{7} x^{7} d^{2} c^{3} + \frac{6}{7} x^{7} e d c^{2} b + \frac{3}{7} x^{7} e^{2} c b^{2} + \frac{1}{2} x^{6} d^{2} c^{2} b + x^{6} e d c b^{2} + \frac{1}{6} x^{6} e^{2} b^{3} + \frac{3}{5} x^{5} d^{2} c b^{2} + \frac{2}{5} x^{5} e d b^{3} + \frac{1}{4} x^{4} d^{2} b^{3}"," ",0,"1/9*x^9*e^2*c^3 + 1/4*x^8*e*d*c^3 + 3/8*x^8*e^2*c^2*b + 1/7*x^7*d^2*c^3 + 6/7*x^7*e*d*c^2*b + 3/7*x^7*e^2*c*b^2 + 1/2*x^6*d^2*c^2*b + x^6*e*d*c*b^2 + 1/6*x^6*e^2*b^3 + 3/5*x^5*d^2*c*b^2 + 2/5*x^5*e*d*b^3 + 1/4*x^4*d^2*b^3","A",0
247,1,77,0,0.366166," ","integrate((e*x+d)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e c^{3} + \frac{1}{7} x^{7} d c^{3} + \frac{3}{7} x^{7} e c^{2} b + \frac{1}{2} x^{6} d c^{2} b + \frac{1}{2} x^{6} e c b^{2} + \frac{3}{5} x^{5} d c b^{2} + \frac{1}{5} x^{5} e b^{3} + \frac{1}{4} x^{4} d b^{3}"," ",0,"1/8*x^8*e*c^3 + 1/7*x^7*d*c^3 + 3/7*x^7*e*c^2*b + 1/2*x^6*d*c^2*b + 1/2*x^6*e*c*b^2 + 3/5*x^5*d*c*b^2 + 1/5*x^5*e*b^3 + 1/4*x^4*d*b^3","A",0
248,1,35,0,0.341761," ","integrate((c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{1}{7} x^{7} c^{3} + \frac{1}{2} x^{6} c^{2} b + \frac{3}{5} x^{5} c b^{2} + \frac{1}{4} x^{4} b^{3}"," ",0,"1/7*x^7*c^3 + 1/2*x^6*c^2*b + 3/5*x^5*c*b^2 + 1/4*x^4*b^3","A",0
249,1,266,0,0.406729," ","integrate((c*x^2+b*x)^3/(e*x+d),x, algorithm=""fricas"")","\frac{10 \, c^{3} e^{6} x^{6} - 12 \, {\left(c^{3} d e^{5} - 3 \, b c^{2} e^{6}\right)} x^{5} + 15 \, {\left(c^{3} d^{2} e^{4} - 3 \, b c^{2} d e^{5} + 3 \, b^{2} c e^{6}\right)} x^{4} - 20 \, {\left(c^{3} d^{3} e^{3} - 3 \, b c^{2} d^{2} e^{4} + 3 \, b^{2} c d e^{5} - b^{3} e^{6}\right)} x^{3} + 30 \, {\left(c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} + 3 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2} - 60 \, {\left(c^{3} d^{5} e - 3 \, b c^{2} d^{4} e^{2} + 3 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} x + 60 \, {\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)} \log\left(e x + d\right)}{60 \, e^{7}}"," ",0,"1/60*(10*c^3*e^6*x^6 - 12*(c^3*d*e^5 - 3*b*c^2*e^6)*x^5 + 15*(c^3*d^2*e^4 - 3*b*c^2*d*e^5 + 3*b^2*c*e^6)*x^4 - 20*(c^3*d^3*e^3 - 3*b*c^2*d^2*e^4 + 3*b^2*c*d*e^5 - b^3*e^6)*x^3 + 30*(c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 + 3*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2 - 60*(c^3*d^5*e - 3*b*c^2*d^4*e^2 + 3*b^2*c*d^3*e^3 - b^3*d^2*e^4)*x + 60*(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)*log(e*x + d))/e^7","A",0
250,1,370,0,0.405315," ","integrate((c*x^2+b*x)^3/(e*x+d)^2,x, algorithm=""fricas"")","\frac{4 \, c^{3} e^{6} x^{6} - 20 \, c^{3} d^{6} + 60 \, b c^{2} d^{5} e - 60 \, b^{2} c d^{4} e^{2} + 20 \, b^{3} d^{3} e^{3} - 3 \, {\left(2 \, c^{3} d e^{5} - 5 \, b c^{2} e^{6}\right)} x^{5} + 5 \, {\left(2 \, c^{3} d^{2} e^{4} - 5 \, b c^{2} d e^{5} + 4 \, b^{2} c e^{6}\right)} x^{4} - 10 \, {\left(2 \, c^{3} d^{3} e^{3} - 5 \, b c^{2} d^{2} e^{4} + 4 \, b^{2} c d e^{5} - b^{3} e^{6}\right)} x^{3} + 30 \, {\left(2 \, c^{3} d^{4} e^{2} - 5 \, b c^{2} d^{3} e^{3} + 4 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2} + 20 \, {\left(5 \, c^{3} d^{5} e - 12 \, b c^{2} d^{4} e^{2} + 9 \, b^{2} c d^{3} e^{3} - 2 \, b^{3} d^{2} e^{4}\right)} x - 60 \, {\left(2 \, c^{3} d^{6} - 5 \, b c^{2} d^{5} e + 4 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3} + {\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)} \log\left(e x + d\right)}{20 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"1/20*(4*c^3*e^6*x^6 - 20*c^3*d^6 + 60*b*c^2*d^5*e - 60*b^2*c*d^4*e^2 + 20*b^3*d^3*e^3 - 3*(2*c^3*d*e^5 - 5*b*c^2*e^6)*x^5 + 5*(2*c^3*d^2*e^4 - 5*b*c^2*d*e^5 + 4*b^2*c*e^6)*x^4 - 10*(2*c^3*d^3*e^3 - 5*b*c^2*d^2*e^4 + 4*b^2*c*d*e^5 - b^3*e^6)*x^3 + 30*(2*c^3*d^4*e^2 - 5*b*c^2*d^3*e^3 + 4*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2 + 20*(5*c^3*d^5*e - 12*b*c^2*d^4*e^2 + 9*b^2*c*d^3*e^3 - 2*b^3*d^2*e^4)*x - 60*(2*c^3*d^6 - 5*b*c^2*d^5*e + 4*b^2*c*d^4*e^2 - b^3*d^3*e^3 + (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)*log(e*x + d))/(e^8*x + d*e^7)","B",0
251,1,428,0,0.404918," ","integrate((c*x^2+b*x)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{c^{3} e^{6} x^{6} + 22 \, c^{3} d^{6} - 54 \, b c^{2} d^{5} e + 42 \, b^{2} c d^{4} e^{2} - 10 \, b^{3} d^{3} e^{3} - 2 \, {\left(c^{3} d e^{5} - 2 \, b c^{2} e^{6}\right)} x^{5} + {\left(5 \, c^{3} d^{2} e^{4} - 10 \, b c^{2} d e^{5} + 6 \, b^{2} c e^{6}\right)} x^{4} - 4 \, {\left(5 \, c^{3} d^{3} e^{3} - 10 \, b c^{2} d^{2} e^{4} + 6 \, b^{2} c d e^{5} - b^{3} e^{6}\right)} x^{3} - 2 \, {\left(34 \, c^{3} d^{4} e^{2} - 63 \, b c^{2} d^{3} e^{3} + 33 \, b^{2} c d^{2} e^{4} - 4 \, b^{3} d e^{5}\right)} x^{2} - 4 \, {\left(4 \, c^{3} d^{5} e - 3 \, b c^{2} d^{4} e^{2} - 3 \, b^{2} c d^{3} e^{3} + 2 \, b^{3} d^{2} e^{4}\right)} x + 12 \, {\left(5 \, c^{3} d^{6} - 10 \, b c^{2} d^{5} e + 6 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3} + {\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} + 2 \, {\left(5 \, c^{3} d^{5} e - 10 \, b c^{2} d^{4} e^{2} + 6 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"1/4*(c^3*e^6*x^6 + 22*c^3*d^6 - 54*b*c^2*d^5*e + 42*b^2*c*d^4*e^2 - 10*b^3*d^3*e^3 - 2*(c^3*d*e^5 - 2*b*c^2*e^6)*x^5 + (5*c^3*d^2*e^4 - 10*b*c^2*d*e^5 + 6*b^2*c*e^6)*x^4 - 4*(5*c^3*d^3*e^3 - 10*b*c^2*d^2*e^4 + 6*b^2*c*d*e^5 - b^3*e^6)*x^3 - 2*(34*c^3*d^4*e^2 - 63*b*c^2*d^3*e^3 + 33*b^2*c*d^2*e^4 - 4*b^3*d*e^5)*x^2 - 4*(4*c^3*d^5*e - 3*b*c^2*d^4*e^2 - 3*b^2*c*d^3*e^3 + 2*b^3*d^2*e^4)*x + 12*(5*c^3*d^6 - 10*b*c^2*d^5*e + 6*b^2*c*d^4*e^2 - b^3*d^3*e^3 + (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 + 2*(5*c^3*d^5*e - 10*b*c^2*d^4*e^2 + 6*b^2*c*d^3*e^3 - b^3*d^2*e^4)*x)*log(e*x + d))/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","B",0
252,1,480,0,0.400120," ","integrate((c*x^2+b*x)^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{2 \, c^{3} e^{6} x^{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} - 3 \, {\left(2 \, c^{3} d e^{5} - 3 \, b c^{2} e^{6}\right)} x^{5} + 3 \, {\left(10 \, c^{3} d^{2} e^{4} - 15 \, b c^{2} d e^{5} + 6 \, b^{2} c e^{6}\right)} x^{4} + {\left(146 \, c^{3} d^{3} e^{3} - 189 \, b c^{2} d^{2} e^{4} + 54 \, b^{2} c d e^{5}\right)} x^{3} + 3 \, {\left(26 \, c^{3} d^{4} e^{2} - 9 \, b c^{2} d^{3} e^{3} - 18 \, b^{2} c d^{2} e^{4} + 6 \, b^{3} d e^{5}\right)} x^{2} - 3 \, {\left(34 \, c^{3} d^{5} e - 81 \, b c^{2} d^{4} e^{2} + 54 \, b^{2} c d^{3} e^{3} - 9 \, b^{3} d^{2} e^{4}\right)} x - 6 \, {\left(20 \, c^{3} d^{6} - 30 \, b c^{2} d^{5} e + 12 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3} + {\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)} x^{3} + 3 \, {\left(20 \, c^{3} d^{4} e^{2} - 30 \, b c^{2} d^{3} e^{3} + 12 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(20 \, c^{3} d^{5} e - 30 \, b c^{2} d^{4} e^{2} + 12 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"1/6*(2*c^3*e^6*x^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 - 3*(2*c^3*d*e^5 - 3*b*c^2*e^6)*x^5 + 3*(10*c^3*d^2*e^4 - 15*b*c^2*d*e^5 + 6*b^2*c*e^6)*x^4 + (146*c^3*d^3*e^3 - 189*b*c^2*d^2*e^4 + 54*b^2*c*d*e^5)*x^3 + 3*(26*c^3*d^4*e^2 - 9*b*c^2*d^3*e^3 - 18*b^2*c*d^2*e^4 + 6*b^3*d*e^5)*x^2 - 3*(34*c^3*d^5*e - 81*b*c^2*d^4*e^2 + 54*b^2*c*d^3*e^3 - 9*b^3*d^2*e^4)*x - 6*(20*c^3*d^6 - 30*b*c^2*d^5*e + 12*b^2*c*d^4*e^2 - b^3*d^3*e^3 + (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)*x^3 + 3*(20*c^3*d^4*e^2 - 30*b*c^2*d^3*e^3 + 12*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2 + 3*(20*c^3*d^5*e - 30*b*c^2*d^4*e^2 + 12*b^2*c*d^3*e^3 - b^3*d^2*e^4)*x)*log(e*x + d))/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","B",0
253,1,481,0,0.400167," ","integrate((c*x^2+b*x)^3/(e*x+d)^5,x, algorithm=""fricas"")","\frac{2 \, c^{3} e^{6} x^{6} + 57 \, c^{3} d^{6} - 77 \, b c^{2} d^{5} e + 25 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3} - 12 \, {\left(c^{3} d e^{5} - b c^{2} e^{6}\right)} x^{5} - 4 \, {\left(17 \, c^{3} d^{2} e^{4} - 12 \, b c^{2} d e^{5}\right)} x^{4} - 4 \, {\left(8 \, c^{3} d^{3} e^{3} + 12 \, b c^{2} d^{2} e^{4} - 12 \, b^{2} c d e^{5} + b^{3} e^{6}\right)} x^{3} + 6 \, {\left(22 \, c^{3} d^{4} e^{2} - 42 \, b c^{2} d^{3} e^{3} + 18 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2} + 4 \, {\left(42 \, c^{3} d^{5} e - 62 \, b c^{2} d^{4} e^{2} + 22 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} x + 12 \, {\left(5 \, c^{3} d^{6} - 5 \, b c^{2} d^{5} e + b^{2} c d^{4} e^{2} + {\left(5 \, c^{3} d^{2} e^{4} - 5 \, b c^{2} d e^{5} + b^{2} c e^{6}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{3} - 5 \, b c^{2} d^{2} e^{4} + b^{2} c d e^{5}\right)} x^{3} + 6 \, {\left(5 \, c^{3} d^{4} e^{2} - 5 \, b c^{2} d^{3} e^{3} + b^{2} c d^{2} e^{4}\right)} x^{2} + 4 \, {\left(5 \, c^{3} d^{5} e - 5 \, b c^{2} d^{4} e^{2} + b^{2} c d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(e^{11} x^{4} + 4 \, d e^{10} x^{3} + 6 \, d^{2} e^{9} x^{2} + 4 \, d^{3} e^{8} x + d^{4} e^{7}\right)}}"," ",0,"1/4*(2*c^3*e^6*x^6 + 57*c^3*d^6 - 77*b*c^2*d^5*e + 25*b^2*c*d^4*e^2 - b^3*d^3*e^3 - 12*(c^3*d*e^5 - b*c^2*e^6)*x^5 - 4*(17*c^3*d^2*e^4 - 12*b*c^2*d*e^5)*x^4 - 4*(8*c^3*d^3*e^3 + 12*b*c^2*d^2*e^4 - 12*b^2*c*d*e^5 + b^3*e^6)*x^3 + 6*(22*c^3*d^4*e^2 - 42*b*c^2*d^3*e^3 + 18*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2 + 4*(42*c^3*d^5*e - 62*b*c^2*d^4*e^2 + 22*b^2*c*d^3*e^3 - b^3*d^2*e^4)*x + 12*(5*c^3*d^6 - 5*b*c^2*d^5*e + b^2*c*d^4*e^2 + (5*c^3*d^2*e^4 - 5*b*c^2*d*e^5 + b^2*c*e^6)*x^4 + 4*(5*c^3*d^3*e^3 - 5*b*c^2*d^2*e^4 + b^2*c*d*e^5)*x^3 + 6*(5*c^3*d^4*e^2 - 5*b*c^2*d^3*e^3 + b^2*c*d^2*e^4)*x^2 + 4*(5*c^3*d^5*e - 5*b*c^2*d^4*e^2 + b^2*c*d^3*e^3)*x)*log(e*x + d))/(e^11*x^4 + 4*d*e^10*x^3 + 6*d^2*e^9*x^2 + 4*d^3*e^8*x + d^4*e^7)","B",0
254,1,462,0,0.408333," ","integrate((c*x^2+b*x)^3/(e*x+d)^6,x, algorithm=""fricas"")","\frac{20 \, c^{3} e^{6} x^{6} + 100 \, c^{3} d e^{5} x^{5} - 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} - 20 \, {\left(5 \, c^{3} d^{2} e^{4} - 15 \, b c^{2} d e^{5} + 3 \, b^{2} c e^{6}\right)} x^{4} - 10 \, {\left(80 \, 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(120 \, 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(150 \, 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 - 60 \, {\left(2 \, c^{3} d^{6} - b c^{2} d^{5} e + {\left(2 \, c^{3} d e^{5} - b c^{2} e^{6}\right)} x^{5} + 5 \, {\left(2 \, c^{3} d^{2} e^{4} - b c^{2} d e^{5}\right)} x^{4} + 10 \, {\left(2 \, c^{3} d^{3} e^{3} - b c^{2} d^{2} e^{4}\right)} x^{3} + 10 \, {\left(2 \, c^{3} d^{4} e^{2} - b c^{2} d^{3} e^{3}\right)} x^{2} + 5 \, {\left(2 \, c^{3} d^{5} e - b c^{2} d^{4} e^{2}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{12} x^{5} + 5 \, d e^{11} x^{4} + 10 \, d^{2} e^{10} x^{3} + 10 \, d^{3} e^{9} x^{2} + 5 \, d^{4} e^{8} x + d^{5} e^{7}\right)}}"," ",0,"1/20*(20*c^3*e^6*x^6 + 100*c^3*d*e^5*x^5 - 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 - 20*(5*c^3*d^2*e^4 - 15*b*c^2*d*e^5 + 3*b^2*c*e^6)*x^4 - 10*(80*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*(120*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*(150*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 - 60*(2*c^3*d^6 - b*c^2*d^5*e + (2*c^3*d*e^5 - b*c^2*e^6)*x^5 + 5*(2*c^3*d^2*e^4 - b*c^2*d*e^5)*x^4 + 10*(2*c^3*d^3*e^3 - b*c^2*d^2*e^4)*x^3 + 10*(2*c^3*d^4*e^2 - b*c^2*d^3*e^3)*x^2 + 5*(2*c^3*d^5*e - b*c^2*d^4*e^2)*x)*log(e*x + d))/(e^12*x^5 + 5*d*e^11*x^4 + 10*d^2*e^10*x^3 + 10*d^3*e^9*x^2 + 5*d^4*e^8*x + d^5*e^7)","B",0
255,1,407,0,0.404510," ","integrate((c*x^2+b*x)^3/(e*x+d)^7,x, algorithm=""fricas"")","\frac{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} + 180 \, {\left(2 \, c^{3} d e^{5} - b c^{2} e^{6}\right)} x^{5} + 90 \, {\left(15 \, c^{3} d^{2} e^{4} - 5 \, b c^{2} d e^{5} - b^{2} c e^{6}\right)} x^{4} + 20 \, {\left(110 \, c^{3} d^{3} e^{3} - 30 \, b c^{2} d^{2} e^{4} - 6 \, b^{2} c d e^{5} - b^{3} e^{6}\right)} x^{3} + 15 \, {\left(125 \, c^{3} d^{4} e^{2} - 30 \, b c^{2} d^{3} e^{3} - 6 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2} + 6 \, {\left(137 \, c^{3} d^{5} e - 30 \, b c^{2} d^{4} e^{2} - 6 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} x + 60 \, {\left(c^{3} e^{6} x^{6} + 6 \, c^{3} d e^{5} x^{5} + 15 \, c^{3} d^{2} e^{4} x^{4} + 20 \, c^{3} d^{3} e^{3} x^{3} + 15 \, c^{3} d^{4} e^{2} x^{2} + 6 \, c^{3} d^{5} e x + c^{3} d^{6}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{13} x^{6} + 6 \, d e^{12} x^{5} + 15 \, d^{2} e^{11} x^{4} + 20 \, d^{3} e^{10} x^{3} + 15 \, d^{4} e^{9} x^{2} + 6 \, d^{5} e^{8} x + d^{6} e^{7}\right)}}"," ",0,"1/60*(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 + 180*(2*c^3*d*e^5 - b*c^2*e^6)*x^5 + 90*(15*c^3*d^2*e^4 - 5*b*c^2*d*e^5 - b^2*c*e^6)*x^4 + 20*(110*c^3*d^3*e^3 - 30*b*c^2*d^2*e^4 - 6*b^2*c*d*e^5 - b^3*e^6)*x^3 + 15*(125*c^3*d^4*e^2 - 30*b*c^2*d^3*e^3 - 6*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2 + 6*(137*c^3*d^5*e - 30*b*c^2*d^4*e^2 - 6*b^2*c*d^3*e^3 - b^3*d^2*e^4)*x + 60*(c^3*e^6*x^6 + 6*c^3*d*e^5*x^5 + 15*c^3*d^2*e^4*x^4 + 20*c^3*d^3*e^3*x^3 + 15*c^3*d^4*e^2*x^2 + 6*c^3*d^5*e*x + c^3*d^6)*log(e*x + d))/(e^13*x^6 + 6*d*e^12*x^5 + 15*d^2*e^11*x^4 + 20*d^3*e^10*x^3 + 15*d^4*e^9*x^2 + 6*d^5*e^8*x + d^6*e^7)","A",0
256,1,334,0,0.390569," ","integrate((c*x^2+b*x)^3/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{140 \, c^{3} e^{6} x^{6} + 20 \, c^{3} d^{6} + 10 \, b c^{2} d^{5} e + 4 \, b^{2} c d^{4} e^{2} + b^{3} d^{3} e^{3} + 210 \, {\left(2 \, c^{3} d e^{5} + b c^{2} e^{6}\right)} x^{5} + 70 \, {\left(10 \, c^{3} d^{2} e^{4} + 5 \, b c^{2} d e^{5} + 2 \, b^{2} c e^{6}\right)} x^{4} + 35 \, {\left(20 \, c^{3} d^{3} e^{3} + 10 \, b c^{2} d^{2} e^{4} + 4 \, b^{2} c d e^{5} + b^{3} e^{6}\right)} x^{3} + 21 \, {\left(20 \, c^{3} d^{4} e^{2} + 10 \, b c^{2} d^{3} e^{3} + 4 \, b^{2} c d^{2} e^{4} + b^{3} d e^{5}\right)} x^{2} + 7 \, {\left(20 \, c^{3} d^{5} e + 10 \, b c^{2} d^{4} e^{2} + 4 \, b^{2} c d^{3} e^{3} + b^{3} d^{2} e^{4}\right)} x}{140 \, {\left(e^{14} x^{7} + 7 \, d e^{13} x^{6} + 21 \, d^{2} e^{12} x^{5} + 35 \, d^{3} e^{11} x^{4} + 35 \, d^{4} e^{10} x^{3} + 21 \, d^{5} e^{9} x^{2} + 7 \, d^{6} e^{8} x + d^{7} e^{7}\right)}}"," ",0,"-1/140*(140*c^3*e^6*x^6 + 20*c^3*d^6 + 10*b*c^2*d^5*e + 4*b^2*c*d^4*e^2 + b^3*d^3*e^3 + 210*(2*c^3*d*e^5 + b*c^2*e^6)*x^5 + 70*(10*c^3*d^2*e^4 + 5*b*c^2*d*e^5 + 2*b^2*c*e^6)*x^4 + 35*(20*c^3*d^3*e^3 + 10*b*c^2*d^2*e^4 + 4*b^2*c*d*e^5 + b^3*e^6)*x^3 + 21*(20*c^3*d^4*e^2 + 10*b*c^2*d^3*e^3 + 4*b^2*c*d^2*e^4 + b^3*d*e^5)*x^2 + 7*(20*c^3*d^5*e + 10*b*c^2*d^4*e^2 + 4*b^2*c*d^3*e^3 + b^3*d^2*e^4)*x)/(e^14*x^7 + 7*d*e^13*x^6 + 21*d^2*e^12*x^5 + 35*d^3*e^11*x^4 + 35*d^4*e^10*x^3 + 21*d^5*e^9*x^2 + 7*d^6*e^8*x + d^7*e^7)","A",0
257,1,344,0,0.403070," ","integrate((c*x^2+b*x)^3/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{140 \, c^{3} e^{6} x^{6} + 5 \, c^{3} d^{6} + 5 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} + b^{3} d^{3} e^{3} + 280 \, {\left(c^{3} d e^{5} + b c^{2} e^{6}\right)} x^{5} + 70 \, {\left(5 \, c^{3} d^{2} e^{4} + 5 \, b c^{2} d e^{5} + 3 \, b^{2} c e^{6}\right)} x^{4} + 56 \, {\left(5 \, c^{3} d^{3} e^{3} + 5 \, b c^{2} d^{2} e^{4} + 3 \, b^{2} c d e^{5} + b^{3} e^{6}\right)} x^{3} + 28 \, {\left(5 \, c^{3} d^{4} e^{2} + 5 \, b c^{2} d^{3} e^{3} + 3 \, b^{2} c d^{2} e^{4} + b^{3} d e^{5}\right)} x^{2} + 8 \, {\left(5 \, c^{3} d^{5} e + 5 \, b c^{2} d^{4} e^{2} + 3 \, b^{2} c d^{3} e^{3} + b^{3} d^{2} e^{4}\right)} x}{280 \, {\left(e^{15} x^{8} + 8 \, d e^{14} x^{7} + 28 \, d^{2} e^{13} x^{6} + 56 \, d^{3} e^{12} x^{5} + 70 \, d^{4} e^{11} x^{4} + 56 \, d^{5} e^{10} x^{3} + 28 \, d^{6} e^{9} x^{2} + 8 \, d^{7} e^{8} x + d^{8} e^{7}\right)}}"," ",0,"-1/280*(140*c^3*e^6*x^6 + 5*c^3*d^6 + 5*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 + b^3*d^3*e^3 + 280*(c^3*d*e^5 + b*c^2*e^6)*x^5 + 70*(5*c^3*d^2*e^4 + 5*b*c^2*d*e^5 + 3*b^2*c*e^6)*x^4 + 56*(5*c^3*d^3*e^3 + 5*b*c^2*d^2*e^4 + 3*b^2*c*d*e^5 + b^3*e^6)*x^3 + 28*(5*c^3*d^4*e^2 + 5*b*c^2*d^3*e^3 + 3*b^2*c*d^2*e^4 + b^3*d*e^5)*x^2 + 8*(5*c^3*d^5*e + 5*b*c^2*d^4*e^2 + 3*b^2*c*d^3*e^3 + b^3*d^2*e^4)*x)/(e^15*x^8 + 8*d*e^14*x^7 + 28*d^2*e^13*x^6 + 56*d^3*e^12*x^5 + 70*d^4*e^11*x^4 + 56*d^5*e^10*x^3 + 28*d^6*e^9*x^2 + 8*d^7*e^8*x + d^8*e^7)","A",0
258,1,361,0,0.403728," ","integrate((c*x^2+b*x)^3/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{840 \, c^{3} e^{6} x^{6} + 10 \, c^{3} d^{6} + 15 \, b c^{2} d^{5} e + 12 \, b^{2} c d^{4} e^{2} + 5 \, b^{3} d^{3} e^{3} + 630 \, {\left(2 \, c^{3} d e^{5} + 3 \, b c^{2} e^{6}\right)} x^{5} + 126 \, {\left(10 \, c^{3} d^{2} e^{4} + 15 \, b c^{2} d e^{5} + 12 \, b^{2} c e^{6}\right)} x^{4} + 84 \, {\left(10 \, c^{3} d^{3} e^{3} + 15 \, b c^{2} d^{2} e^{4} + 12 \, b^{2} c d e^{5} + 5 \, b^{3} e^{6}\right)} x^{3} + 36 \, {\left(10 \, c^{3} d^{4} e^{2} + 15 \, b c^{2} d^{3} e^{3} + 12 \, b^{2} c d^{2} e^{4} + 5 \, b^{3} d e^{5}\right)} x^{2} + 9 \, {\left(10 \, c^{3} d^{5} e + 15 \, b c^{2} d^{4} e^{2} + 12 \, b^{2} c d^{3} e^{3} + 5 \, b^{3} d^{2} e^{4}\right)} x}{2520 \, {\left(e^{16} x^{9} + 9 \, d e^{15} x^{8} + 36 \, d^{2} e^{14} x^{7} + 84 \, d^{3} e^{13} x^{6} + 126 \, d^{4} e^{12} x^{5} + 126 \, d^{5} e^{11} x^{4} + 84 \, d^{6} e^{10} x^{3} + 36 \, d^{7} e^{9} x^{2} + 9 \, d^{8} e^{8} x + d^{9} e^{7}\right)}}"," ",0,"-1/2520*(840*c^3*e^6*x^6 + 10*c^3*d^6 + 15*b*c^2*d^5*e + 12*b^2*c*d^4*e^2 + 5*b^3*d^3*e^3 + 630*(2*c^3*d*e^5 + 3*b*c^2*e^6)*x^5 + 126*(10*c^3*d^2*e^4 + 15*b*c^2*d*e^5 + 12*b^2*c*e^6)*x^4 + 84*(10*c^3*d^3*e^3 + 15*b*c^2*d^2*e^4 + 12*b^2*c*d*e^5 + 5*b^3*e^6)*x^3 + 36*(10*c^3*d^4*e^2 + 15*b*c^2*d^3*e^3 + 12*b^2*c*d^2*e^4 + 5*b^3*d*e^5)*x^2 + 9*(10*c^3*d^5*e + 15*b*c^2*d^4*e^2 + 12*b^2*c*d^3*e^3 + 5*b^3*d^2*e^4)*x)/(e^16*x^9 + 9*d*e^15*x^8 + 36*d^2*e^14*x^7 + 84*d^3*e^13*x^6 + 126*d^4*e^12*x^5 + 126*d^5*e^11*x^4 + 84*d^6*e^10*x^3 + 36*d^7*e^9*x^2 + 9*d^8*e^8*x + d^9*e^7)","A",0
259,1,151,0,0.426033," ","integrate((e*x+d)^4/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, b c^{3} e^{4} x^{3} + 6 \, c^{4} d^{4} \log\left(x\right) + 3 \, {\left(4 \, b c^{3} d e^{3} - b^{2} c^{2} e^{4}\right)} x^{2} + 6 \, {\left(6 \, b c^{3} d^{2} e^{2} - 4 \, b^{2} c^{2} d e^{3} + b^{3} c e^{4}\right)} x - 6 \, {\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(c x + b\right)}{6 \, b c^{4}}"," ",0,"1/6*(2*b*c^3*e^4*x^3 + 6*c^4*d^4*log(x) + 3*(4*b*c^3*d*e^3 - b^2*c^2*e^4)*x^2 + 6*(6*b*c^3*d^2*e^2 - 4*b^2*c^2*d*e^3 + b^3*c*e^4)*x - 6*(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(c*x + b))/(b*c^4)","A",0
260,1,97,0,0.396795," ","integrate((e*x+d)^3/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{b c^{2} e^{3} x^{2} + 2 \, c^{3} d^{3} \log\left(x\right) + 2 \, {\left(3 \, b c^{2} d e^{2} - b^{2} c e^{3}\right)} x - 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)} \log\left(c x + b\right)}{2 \, b c^{3}}"," ",0,"1/2*(b*c^2*e^3*x^2 + 2*c^3*d^3*log(x) + 2*(3*b*c^2*d*e^2 - b^2*c*e^3)*x - 2*(c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - b^3*e^3)*log(c*x + b))/(b*c^3)","A",0
261,1,53,0,0.409976," ","integrate((e*x+d)^2/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{b c e^{2} x + c^{2} d^{2} \log\left(x\right) - {\left(c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}\right)} \log\left(c x + b\right)}{b c^{2}}"," ",0,"(b*c*e^2*x + c^2*d^2*log(x) - (c^2*d^2 - 2*b*c*d*e + b^2*e^2)*log(c*x + b))/(b*c^2)","A",0
262,1,29,0,0.413289," ","integrate((e*x+d)/(c*x^2+b*x),x, algorithm=""fricas"")","\frac{c d \log\left(x\right) - {\left(c d - b e\right)} \log\left(c x + b\right)}{b c}"," ",0,"(c*d*log(x) - (c*d - b*e)*log(c*x + b))/(b*c)","A",0
263,1,16,0,0.425636," ","integrate(1/(c*x^2+b*x),x, algorithm=""fricas"")","-\frac{\log\left(c x + b\right) - \log\left(x\right)}{b}"," ",0,"-(log(c*x + b) - log(x))/b","A",0
264,1,50,0,0.518071," ","integrate(1/(e*x+d)/(c*x^2+b*x),x, algorithm=""fricas"")","-\frac{c d \log\left(c x + b\right) - b e \log\left(e x + d\right) - {\left(c d - b e\right)} \log\left(x\right)}{b c d^{2} - b^{2} d e}"," ",0,"-(c*d*log(c*x + b) - b*e*log(e*x + d) - (c*d - b*e)*log(x))/(b*c*d^2 - b^2*d*e)","A",0
265,1,207,0,1.152012," ","integrate(1/(e*x+d)^2/(c*x^2+b*x),x, algorithm=""fricas"")","-\frac{b c d^{2} e - b^{2} d e^{2} + {\left(c^{2} d^{2} e x + c^{2} d^{3}\right)} \log\left(c x + b\right) - {\left(2 \, b c d^{2} e - b^{2} d e^{2} + {\left(2 \, b c d e^{2} - b^{2} e^{3}\right)} x\right)} \log\left(e x + d\right) - {\left(c^{2} d^{3} - 2 \, b c d^{2} e + b^{2} d e^{2} + {\left(c^{2} d^{2} e - 2 \, b c d e^{2} + b^{2} e^{3}\right)} x\right)} \log\left(x\right)}{b c^{2} d^{5} - 2 \, b^{2} c d^{4} e + b^{3} d^{3} e^{2} + {\left(b c^{2} d^{4} e - 2 \, b^{2} c d^{3} e^{2} + b^{3} d^{2} e^{3}\right)} x}"," ",0,"-(b*c*d^2*e - b^2*d*e^2 + (c^2*d^2*e*x + c^2*d^3)*log(c*x + b) - (2*b*c*d^2*e - b^2*d*e^2 + (2*b*c*d*e^2 - b^2*e^3)*x)*log(e*x + d) - (c^2*d^3 - 2*b*c*d^2*e + b^2*d*e^2 + (c^2*d^2*e - 2*b*c*d*e^2 + b^2*e^3)*x)*log(x))/(b*c^2*d^5 - 2*b^2*c*d^4*e + b^3*d^3*e^2 + (b*c^2*d^4*e - 2*b^2*c*d^3*e^2 + b^3*d^2*e^3)*x)","B",0
266,1,506,0,7.414050," ","integrate(1/(e*x+d)^3/(c*x^2+b*x),x, algorithm=""fricas"")","-\frac{5 \, b c^{2} d^{4} e - 8 \, b^{2} c d^{3} e^{2} + 3 \, b^{3} d^{2} e^{3} + 2 \, {\left(2 \, b c^{2} d^{3} e^{2} - 3 \, b^{2} c d^{2} e^{3} + b^{3} d e^{4}\right)} x + 2 \, {\left(c^{3} d^{3} e^{2} x^{2} + 2 \, c^{3} d^{4} e x + c^{3} d^{5}\right)} \log\left(c x + b\right) - 2 \, {\left(3 \, b c^{2} d^{4} e - 3 \, b^{2} c d^{3} e^{2} + b^{3} d^{2} e^{3} + {\left(3 \, b c^{2} d^{2} e^{3} - 3 \, b^{2} c d e^{4} + b^{3} e^{5}\right)} x^{2} + 2 \, {\left(3 \, b c^{2} d^{3} e^{2} - 3 \, b^{2} c d^{2} e^{3} + b^{3} d e^{4}\right)} x\right)} \log\left(e x + d\right) - 2 \, {\left(c^{3} d^{5} - 3 \, b c^{2} d^{4} e + 3 \, b^{2} c d^{3} e^{2} - b^{3} d^{2} e^{3} + {\left(c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, b^{2} c d e^{4} - b^{3} e^{5}\right)} x^{2} + 2 \, {\left(c^{3} d^{4} e - 3 \, b c^{2} d^{3} e^{2} + 3 \, b^{2} c d^{2} e^{3} - b^{3} d e^{4}\right)} x\right)} \log\left(x\right)}{2 \, {\left(b c^{3} d^{8} - 3 \, b^{2} c^{2} d^{7} e + 3 \, b^{3} c d^{6} e^{2} - b^{4} d^{5} e^{3} + {\left(b c^{3} d^{6} e^{2} - 3 \, b^{2} c^{2} d^{5} e^{3} + 3 \, b^{3} c d^{4} e^{4} - b^{4} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(b c^{3} d^{7} e - 3 \, b^{2} c^{2} d^{6} e^{2} + 3 \, b^{3} c d^{5} e^{3} - b^{4} d^{4} e^{4}\right)} x\right)}}"," ",0,"-1/2*(5*b*c^2*d^4*e - 8*b^2*c*d^3*e^2 + 3*b^3*d^2*e^3 + 2*(2*b*c^2*d^3*e^2 - 3*b^2*c*d^2*e^3 + b^3*d*e^4)*x + 2*(c^3*d^3*e^2*x^2 + 2*c^3*d^4*e*x + c^3*d^5)*log(c*x + b) - 2*(3*b*c^2*d^4*e - 3*b^2*c*d^3*e^2 + b^3*d^2*e^3 + (3*b*c^2*d^2*e^3 - 3*b^2*c*d*e^4 + b^3*e^5)*x^2 + 2*(3*b*c^2*d^3*e^2 - 3*b^2*c*d^2*e^3 + b^3*d*e^4)*x)*log(e*x + d) - 2*(c^3*d^5 - 3*b*c^2*d^4*e + 3*b^2*c*d^3*e^2 - b^3*d^2*e^3 + (c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*b^2*c*d*e^4 - b^3*e^5)*x^2 + 2*(c^3*d^4*e - 3*b*c^2*d^3*e^2 + 3*b^2*c*d^2*e^3 - b^3*d*e^4)*x)*log(x))/(b*c^3*d^8 - 3*b^2*c^2*d^7*e + 3*b^3*c*d^6*e^2 - b^4*d^5*e^3 + (b*c^3*d^6*e^2 - 3*b^2*c^2*d^5*e^3 + 3*b^3*c*d^4*e^4 - b^4*d^3*e^5)*x^2 + 2*(b*c^3*d^7*e - 3*b^2*c^2*d^6*e^2 + 3*b^3*c*d^5*e^3 - b^4*d^4*e^4)*x)","B",0
267,1,349,0,0.424104," ","integrate((e*x+d)^5/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{b^{3} c^{3} e^{5} x^{4} - 2 \, b^{2} c^{4} d^{5} + {\left(10 \, b^{3} c^{3} d e^{4} - 3 \, b^{4} c^{2} e^{5}\right)} x^{3} + 2 \, {\left(5 \, b^{4} c^{2} d e^{4} - 2 \, b^{5} c e^{5}\right)} x^{2} - 2 \, {\left(2 \, b c^{5} d^{5} - 5 \, b^{2} c^{4} d^{4} e + 10 \, b^{3} c^{3} d^{3} e^{2} - 10 \, b^{4} c^{2} d^{2} e^{3} + 5 \, b^{5} c d e^{4} - b^{6} e^{5}\right)} x + 2 \, {\left({\left(2 \, c^{6} d^{5} - 5 \, b c^{5} d^{4} e + 10 \, b^{3} c^{3} d^{2} e^{3} - 10 \, b^{4} c^{2} d e^{4} + 3 \, b^{5} c e^{5}\right)} x^{2} + {\left(2 \, b c^{5} d^{5} - 5 \, b^{2} c^{4} d^{4} e + 10 \, b^{4} c^{2} d^{2} e^{3} - 10 \, b^{5} c d e^{4} + 3 \, b^{6} e^{5}\right)} x\right)} \log\left(c x + b\right) - 2 \, {\left({\left(2 \, c^{6} d^{5} - 5 \, b c^{5} d^{4} e\right)} x^{2} + {\left(2 \, b c^{5} d^{5} - 5 \, b^{2} c^{4} d^{4} e\right)} x\right)} \log\left(x\right)}{2 \, {\left(b^{3} c^{5} x^{2} + b^{4} c^{4} x\right)}}"," ",0,"1/2*(b^3*c^3*e^5*x^4 - 2*b^2*c^4*d^5 + (10*b^3*c^3*d*e^4 - 3*b^4*c^2*e^5)*x^3 + 2*(5*b^4*c^2*d*e^4 - 2*b^5*c*e^5)*x^2 - 2*(2*b*c^5*d^5 - 5*b^2*c^4*d^4*e + 10*b^3*c^3*d^3*e^2 - 10*b^4*c^2*d^2*e^3 + 5*b^5*c*d*e^4 - b^6*e^5)*x + 2*((2*c^6*d^5 - 5*b*c^5*d^4*e + 10*b^3*c^3*d^2*e^3 - 10*b^4*c^2*d*e^4 + 3*b^5*c*e^5)*x^2 + (2*b*c^5*d^5 - 5*b^2*c^4*d^4*e + 10*b^4*c^2*d^2*e^3 - 10*b^5*c*d*e^4 + 3*b^6*e^5)*x)*log(c*x + b) - 2*((2*c^6*d^5 - 5*b*c^5*d^4*e)*x^2 + (2*b*c^5*d^5 - 5*b^2*c^4*d^4*e)*x)*log(x))/(b^3*c^5*x^2 + b^4*c^4*x)","B",0
268,1,257,0,0.424172," ","integrate((e*x+d)^4/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{b^{3} c^{2} e^{4} x^{3} + b^{4} c e^{4} x^{2} - b^{2} c^{3} d^{4} - {\left(2 \, b c^{4} d^{4} - 4 \, b^{2} c^{3} d^{3} e + 6 \, b^{3} c^{2} d^{2} e^{2} - 4 \, b^{4} c d e^{3} + b^{5} e^{4}\right)} x + 2 \, {\left({\left(c^{5} d^{4} - 2 \, b c^{4} d^{3} e + 2 \, b^{3} c^{2} d e^{3} - b^{4} c e^{4}\right)} x^{2} + {\left(b c^{4} d^{4} - 2 \, b^{2} c^{3} d^{3} e + 2 \, b^{4} c d e^{3} - b^{5} e^{4}\right)} x\right)} \log\left(c x + b\right) - 2 \, {\left({\left(c^{5} d^{4} - 2 \, b c^{4} d^{3} e\right)} x^{2} + {\left(b c^{4} d^{4} - 2 \, b^{2} c^{3} d^{3} e\right)} x\right)} \log\left(x\right)}{b^{3} c^{4} x^{2} + b^{4} c^{3} x}"," ",0,"(b^3*c^2*e^4*x^3 + b^4*c*e^4*x^2 - b^2*c^3*d^4 - (2*b*c^4*d^4 - 4*b^2*c^3*d^3*e + 6*b^3*c^2*d^2*e^2 - 4*b^4*c*d*e^3 + b^5*e^4)*x + 2*((c^5*d^4 - 2*b*c^4*d^3*e + 2*b^3*c^2*d*e^3 - b^4*c*e^4)*x^2 + (b*c^4*d^4 - 2*b^2*c^3*d^3*e + 2*b^4*c*d*e^3 - b^5*e^4)*x)*log(c*x + b) - 2*((c^5*d^4 - 2*b*c^4*d^3*e)*x^2 + (b*c^4*d^4 - 2*b^2*c^3*d^3*e)*x)*log(x))/(b^3*c^4*x^2 + b^4*c^3*x)","B",0
269,1,198,0,0.421228," ","integrate((e*x+d)^3/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} d^{3} + {\left(2 \, 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)} x - {\left({\left(2 \, c^{4} d^{3} - 3 \, b c^{3} d^{2} e + b^{3} c e^{3}\right)} x^{2} + {\left(2 \, b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e + b^{4} e^{3}\right)} x\right)} \log\left(c x + b\right) + {\left({\left(2 \, c^{4} d^{3} - 3 \, b c^{3} d^{2} e\right)} x^{2} + {\left(2 \, b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e\right)} x\right)} \log\left(x\right)}{b^{3} c^{3} x^{2} + b^{4} c^{2} x}"," ",0,"-(b^2*c^2*d^3 + (2*b*c^3*d^3 - 3*b^2*c^2*d^2*e + 3*b^3*c*d*e^2 - b^4*e^3)*x - ((2*c^4*d^3 - 3*b*c^3*d^2*e + b^3*c*e^3)*x^2 + (2*b*c^3*d^3 - 3*b^2*c^2*d^2*e + b^4*e^3)*x)*log(c*x + b) + ((2*c^4*d^3 - 3*b*c^3*d^2*e)*x^2 + (2*b*c^3*d^3 - 3*b^2*c^2*d^2*e)*x)*log(x))/(b^3*c^3*x^2 + b^4*c^2*x)","B",0
270,1,149,0,0.423096," ","integrate((e*x+d)^2/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{b^{2} c d^{2} + {\left(2 \, b c^{2} d^{2} - 2 \, b^{2} c d e + b^{3} e^{2}\right)} x - 2 \, {\left({\left(c^{3} d^{2} - b c^{2} d e\right)} x^{2} + {\left(b c^{2} d^{2} - b^{2} c d e\right)} x\right)} \log\left(c x + b\right) + 2 \, {\left({\left(c^{3} d^{2} - b c^{2} d e\right)} x^{2} + {\left(b c^{2} d^{2} - b^{2} c d e\right)} x\right)} \log\left(x\right)}{b^{3} c^{2} x^{2} + b^{4} c x}"," ",0,"-(b^2*c*d^2 + (2*b*c^2*d^2 - 2*b^2*c*d*e + b^3*e^2)*x - 2*((c^3*d^2 - b*c^2*d*e)*x^2 + (b*c^2*d^2 - b^2*c*d*e)*x)*log(c*x + b) + 2*((c^3*d^2 - b*c^2*d*e)*x^2 + (b*c^2*d^2 - b^2*c*d*e)*x)*log(x))/(b^3*c^2*x^2 + b^4*c*x)","B",0
271,1,111,0,0.419991," ","integrate((e*x+d)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{b^{2} d + {\left(2 \, b c d - b^{2} e\right)} x - {\left({\left(2 \, c^{2} d - b c e\right)} x^{2} + {\left(2 \, b c d - b^{2} e\right)} x\right)} \log\left(c x + b\right) + {\left({\left(2 \, c^{2} d - b c e\right)} x^{2} + {\left(2 \, b c d - b^{2} e\right)} x\right)} \log\left(x\right)}{b^{3} c x^{2} + b^{4} x}"," ",0,"-(b^2*d + (2*b*c*d - b^2*e)*x - ((2*c^2*d - b*c*e)*x^2 + (2*b*c*d - b^2*e)*x)*log(c*x + b) + ((2*c^2*d - b*c*e)*x^2 + (2*b*c*d - b^2*e)*x)*log(x))/(b^3*c*x^2 + b^4*x)","A",0
272,1,63,0,0.400826," ","integrate(1/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{2 \, b c x + b^{2} - 2 \, {\left(c^{2} x^{2} + b c x\right)} \log\left(c x + b\right) + 2 \, {\left(c^{2} x^{2} + b c x\right)} \log\left(x\right)}{b^{3} c x^{2} + b^{4} x}"," ",0,"-(2*b*c*x + b^2 - 2*(c^2*x^2 + b*c*x)*log(c*x + b) + 2*(c^2*x^2 + b*c*x)*log(x))/(b^3*c*x^2 + b^4*x)","A",0
273,1,288,0,4.277083," ","integrate(1/(e*x+d)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} d^{3} - 2 \, b^{3} c d^{2} e + b^{4} d e^{2} + {\left(2 \, b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e + b^{3} c d e^{2}\right)} x - {\left({\left(2 \, c^{4} d^{3} - 3 \, b c^{3} d^{2} e\right)} x^{2} + {\left(2 \, b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e\right)} x\right)} \log\left(c x + b\right) - {\left(b^{3} c e^{3} x^{2} + b^{4} e^{3} x\right)} \log\left(e x + d\right) + {\left({\left(2 \, c^{4} d^{3} - 3 \, b c^{3} d^{2} e + b^{3} c e^{3}\right)} x^{2} + {\left(2 \, b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e + b^{4} e^{3}\right)} x\right)} \log\left(x\right)}{{\left(b^{3} c^{3} d^{4} - 2 \, b^{4} c^{2} d^{3} e + b^{5} c d^{2} e^{2}\right)} x^{2} + {\left(b^{4} c^{2} d^{4} - 2 \, b^{5} c d^{3} e + b^{6} d^{2} e^{2}\right)} x}"," ",0,"-(b^2*c^2*d^3 - 2*b^3*c*d^2*e + b^4*d*e^2 + (2*b*c^3*d^3 - 3*b^2*c^2*d^2*e + b^3*c*d*e^2)*x - ((2*c^4*d^3 - 3*b*c^3*d^2*e)*x^2 + (2*b*c^3*d^3 - 3*b^2*c^2*d^2*e)*x)*log(c*x + b) - (b^3*c*e^3*x^2 + b^4*e^3*x)*log(e*x + d) + ((2*c^4*d^3 - 3*b*c^3*d^2*e + b^3*c*e^3)*x^2 + (2*b*c^3*d^3 - 3*b^2*c^2*d^2*e + b^4*e^3)*x)*log(x))/((b^3*c^3*d^4 - 2*b^4*c^2*d^3*e + b^5*c*d^2*e^2)*x^2 + (b^4*c^2*d^4 - 2*b^5*c*d^3*e + b^6*d^2*e^2)*x)","B",0
274,1,653,0,13.611937," ","integrate(1/(e*x+d)^2/(c*x^2+b*x)^2,x, algorithm=""fricas"")","-\frac{b^{2} c^{3} d^{5} - 3 \, b^{3} c^{2} d^{4} e + 3 \, b^{4} c d^{3} e^{2} - b^{5} d^{2} e^{3} + 2 \, {\left(b c^{4} d^{4} e - 2 \, b^{2} c^{3} d^{3} e^{2} + 2 \, b^{3} c^{2} d^{2} e^{3} - b^{4} c d e^{4}\right)} x^{2} + {\left(2 \, b c^{4} d^{5} - 3 \, b^{2} c^{3} d^{4} e + 3 \, b^{4} c d^{2} e^{3} - 2 \, b^{5} d e^{4}\right)} x - 2 \, {\left({\left(c^{5} d^{4} e - 2 \, b c^{4} d^{3} e^{2}\right)} x^{3} + {\left(c^{5} d^{5} - b c^{4} d^{4} e - 2 \, b^{2} c^{3} d^{3} e^{2}\right)} x^{2} + {\left(b c^{4} d^{5} - 2 \, b^{2} c^{3} d^{4} e\right)} x\right)} \log\left(c x + b\right) - 2 \, {\left({\left(2 \, b^{3} c^{2} d e^{4} - b^{4} c e^{5}\right)} x^{3} + {\left(2 \, b^{3} c^{2} d^{2} e^{3} + b^{4} c d e^{4} - b^{5} e^{5}\right)} x^{2} + {\left(2 \, b^{4} c d^{2} e^{3} - b^{5} d e^{4}\right)} x\right)} \log\left(e x + d\right) + 2 \, {\left({\left(c^{5} d^{4} e - 2 \, b c^{4} d^{3} e^{2} + 2 \, b^{3} c^{2} d e^{4} - b^{4} c e^{5}\right)} x^{3} + {\left(c^{5} d^{5} - b c^{4} d^{4} e - 2 \, b^{2} c^{3} d^{3} e^{2} + 2 \, b^{3} c^{2} d^{2} e^{3} + b^{4} c d e^{4} - b^{5} e^{5}\right)} x^{2} + {\left(b c^{4} d^{5} - 2 \, b^{2} c^{3} d^{4} e + 2 \, b^{4} c d^{2} e^{3} - b^{5} d e^{4}\right)} x\right)} \log\left(x\right)}{{\left(b^{3} c^{4} d^{6} e - 3 \, b^{4} c^{3} d^{5} e^{2} + 3 \, b^{5} c^{2} d^{4} e^{3} - b^{6} c d^{3} e^{4}\right)} x^{3} + {\left(b^{3} c^{4} d^{7} - 2 \, b^{4} c^{3} d^{6} e + 2 \, b^{6} c d^{4} e^{3} - b^{7} d^{3} e^{4}\right)} x^{2} + {\left(b^{4} c^{3} d^{7} - 3 \, b^{5} c^{2} d^{6} e + 3 \, b^{6} c d^{5} e^{2} - b^{7} d^{4} e^{3}\right)} x}"," ",0,"-(b^2*c^3*d^5 - 3*b^3*c^2*d^4*e + 3*b^4*c*d^3*e^2 - b^5*d^2*e^3 + 2*(b*c^4*d^4*e - 2*b^2*c^3*d^3*e^2 + 2*b^3*c^2*d^2*e^3 - b^4*c*d*e^4)*x^2 + (2*b*c^4*d^5 - 3*b^2*c^3*d^4*e + 3*b^4*c*d^2*e^3 - 2*b^5*d*e^4)*x - 2*((c^5*d^4*e - 2*b*c^4*d^3*e^2)*x^3 + (c^5*d^5 - b*c^4*d^4*e - 2*b^2*c^3*d^3*e^2)*x^2 + (b*c^4*d^5 - 2*b^2*c^3*d^4*e)*x)*log(c*x + b) - 2*((2*b^3*c^2*d*e^4 - b^4*c*e^5)*x^3 + (2*b^3*c^2*d^2*e^3 + b^4*c*d*e^4 - b^5*e^5)*x^2 + (2*b^4*c*d^2*e^3 - b^5*d*e^4)*x)*log(e*x + d) + 2*((c^5*d^4*e - 2*b*c^4*d^3*e^2 + 2*b^3*c^2*d*e^4 - b^4*c*e^5)*x^3 + (c^5*d^5 - b*c^4*d^4*e - 2*b^2*c^3*d^3*e^2 + 2*b^3*c^2*d^2*e^3 + b^4*c*d*e^4 - b^5*e^5)*x^2 + (b*c^4*d^5 - 2*b^2*c^3*d^4*e + 2*b^4*c*d^2*e^3 - b^5*d*e^4)*x)*log(x))/((b^3*c^4*d^6*e - 3*b^4*c^3*d^5*e^2 + 3*b^5*c^2*d^4*e^3 - b^6*c*d^3*e^4)*x^3 + (b^3*c^4*d^7 - 2*b^4*c^3*d^6*e + 2*b^6*c*d^4*e^3 - b^7*d^3*e^4)*x^2 + (b^4*c^3*d^7 - 3*b^5*c^2*d^6*e + 3*b^6*c*d^5*e^2 - b^7*d^4*e^3)*x)","B",0
275,1,694,0,0.468392," ","integrate((e*x+d)^7/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{b^{5} c^{4} e^{7} x^{6} - b^{4} c^{5} d^{7} + 2 \, {\left(7 \, b^{5} c^{4} d e^{6} - 2 \, b^{6} c^{3} e^{7}\right)} x^{5} + {\left(28 \, b^{6} c^{3} d e^{6} - 11 \, b^{7} c^{2} e^{7}\right)} x^{4} + 2 \, {\left(6 \, b c^{8} d^{7} - 21 \, b^{2} c^{7} d^{6} e + 21 \, b^{3} c^{6} d^{5} e^{2} - 35 \, b^{5} c^{4} d^{3} e^{4} + 42 \, b^{6} c^{3} d^{2} e^{5} - 14 \, b^{7} c^{2} d e^{6} + b^{8} c e^{7}\right)} x^{3} + {\left(18 \, b^{2} c^{7} d^{7} - 63 \, b^{3} c^{6} d^{6} e + 63 \, b^{4} c^{5} d^{5} e^{2} - 35 \, b^{5} c^{4} d^{4} e^{3} - 35 \, b^{6} c^{3} d^{3} e^{4} + 63 \, b^{7} c^{2} d^{2} e^{5} - 35 \, b^{8} c d e^{6} + 7 \, b^{9} e^{7}\right)} x^{2} + 2 \, {\left(2 \, b^{3} c^{6} d^{7} - 7 \, b^{4} c^{5} d^{6} e\right)} x - 6 \, {\left({\left(2 \, c^{9} d^{7} - 7 \, b c^{8} d^{6} e + 7 \, b^{2} c^{7} d^{5} e^{2} - 7 \, b^{5} c^{4} d^{2} e^{5} + 7 \, b^{6} c^{3} d e^{6} - 2 \, b^{7} c^{2} e^{7}\right)} x^{4} + 2 \, {\left(2 \, b c^{8} d^{7} - 7 \, b^{2} c^{7} d^{6} e + 7 \, b^{3} c^{6} d^{5} e^{2} - 7 \, b^{6} c^{3} d^{2} e^{5} + 7 \, b^{7} c^{2} d e^{6} - 2 \, b^{8} c e^{7}\right)} x^{3} + {\left(2 \, b^{2} c^{7} d^{7} - 7 \, b^{3} c^{6} d^{6} e + 7 \, b^{4} c^{5} d^{5} e^{2} - 7 \, b^{7} c^{2} d^{2} e^{5} + 7 \, b^{8} c d e^{6} - 2 \, b^{9} e^{7}\right)} x^{2}\right)} \log\left(c x + b\right) + 6 \, {\left({\left(2 \, c^{9} d^{7} - 7 \, b c^{8} d^{6} e + 7 \, b^{2} c^{7} d^{5} e^{2}\right)} x^{4} + 2 \, {\left(2 \, b c^{8} d^{7} - 7 \, b^{2} c^{7} d^{6} e + 7 \, b^{3} c^{6} d^{5} e^{2}\right)} x^{3} + {\left(2 \, b^{2} c^{7} d^{7} - 7 \, b^{3} c^{6} d^{6} e + 7 \, b^{4} c^{5} d^{5} e^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{7} x^{4} + 2 \, b^{6} c^{6} x^{3} + b^{7} c^{5} x^{2}\right)}}"," ",0,"1/2*(b^5*c^4*e^7*x^6 - b^4*c^5*d^7 + 2*(7*b^5*c^4*d*e^6 - 2*b^6*c^3*e^7)*x^5 + (28*b^6*c^3*d*e^6 - 11*b^7*c^2*e^7)*x^4 + 2*(6*b*c^8*d^7 - 21*b^2*c^7*d^6*e + 21*b^3*c^6*d^5*e^2 - 35*b^5*c^4*d^3*e^4 + 42*b^6*c^3*d^2*e^5 - 14*b^7*c^2*d*e^6 + b^8*c*e^7)*x^3 + (18*b^2*c^7*d^7 - 63*b^3*c^6*d^6*e + 63*b^4*c^5*d^5*e^2 - 35*b^5*c^4*d^4*e^3 - 35*b^6*c^3*d^3*e^4 + 63*b^7*c^2*d^2*e^5 - 35*b^8*c*d*e^6 + 7*b^9*e^7)*x^2 + 2*(2*b^3*c^6*d^7 - 7*b^4*c^5*d^6*e)*x - 6*((2*c^9*d^7 - 7*b*c^8*d^6*e + 7*b^2*c^7*d^5*e^2 - 7*b^5*c^4*d^2*e^5 + 7*b^6*c^3*d*e^6 - 2*b^7*c^2*e^7)*x^4 + 2*(2*b*c^8*d^7 - 7*b^2*c^7*d^6*e + 7*b^3*c^6*d^5*e^2 - 7*b^6*c^3*d^2*e^5 + 7*b^7*c^2*d*e^6 - 2*b^8*c*e^7)*x^3 + (2*b^2*c^7*d^7 - 7*b^3*c^6*d^6*e + 7*b^4*c^5*d^5*e^2 - 7*b^7*c^2*d^2*e^5 + 7*b^8*c*d*e^6 - 2*b^9*e^7)*x^2)*log(c*x + b) + 6*((2*c^9*d^7 - 7*b*c^8*d^6*e + 7*b^2*c^7*d^5*e^2)*x^4 + 2*(2*b*c^8*d^7 - 7*b^2*c^7*d^6*e + 7*b^3*c^6*d^5*e^2)*x^3 + (2*b^2*c^7*d^7 - 7*b^3*c^6*d^6*e + 7*b^4*c^5*d^5*e^2)*x^2)*log(x))/(b^5*c^7*x^4 + 2*b^6*c^6*x^3 + b^7*c^5*x^2)","B",0
276,1,579,0,0.435043," ","integrate((e*x+d)^6/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2 \, b^{5} c^{3} e^{6} x^{5} + 4 \, b^{6} c^{2} e^{6} x^{4} - b^{4} c^{4} d^{6} + 2 \, {\left(6 \, b c^{7} d^{6} - 18 \, b^{2} c^{6} d^{5} e + 15 \, b^{3} c^{5} d^{4} e^{2} - 15 \, b^{5} c^{3} d^{2} e^{4} + 12 \, b^{6} c^{2} d e^{5} - 2 \, b^{7} c e^{6}\right)} x^{3} + {\left(18 \, b^{2} c^{6} d^{6} - 54 \, b^{3} c^{5} d^{5} e + 45 \, b^{4} c^{4} d^{4} e^{2} - 20 \, b^{5} c^{3} d^{3} e^{3} - 15 \, b^{6} c^{2} d^{2} e^{4} + 18 \, b^{7} c d e^{5} - 5 \, b^{8} e^{6}\right)} x^{2} + 4 \, {\left(b^{3} c^{5} d^{6} - 3 \, b^{4} c^{4} d^{5} e\right)} x - 6 \, {\left({\left(2 \, c^{8} d^{6} - 6 \, b c^{7} d^{5} e + 5 \, b^{2} c^{6} d^{4} e^{2} - 2 \, b^{5} c^{3} d e^{5} + b^{6} c^{2} e^{6}\right)} x^{4} + 2 \, {\left(2 \, b c^{7} d^{6} - 6 \, b^{2} c^{6} d^{5} e + 5 \, b^{3} c^{5} d^{4} e^{2} - 2 \, b^{6} c^{2} d e^{5} + b^{7} c e^{6}\right)} x^{3} + {\left(2 \, b^{2} c^{6} d^{6} - 6 \, b^{3} c^{5} d^{5} e + 5 \, b^{4} c^{4} d^{4} e^{2} - 2 \, b^{7} c d e^{5} + b^{8} e^{6}\right)} x^{2}\right)} \log\left(c x + b\right) + 6 \, {\left({\left(2 \, c^{8} d^{6} - 6 \, b c^{7} d^{5} e + 5 \, b^{2} c^{6} d^{4} e^{2}\right)} x^{4} + 2 \, {\left(2 \, b c^{7} d^{6} - 6 \, b^{2} c^{6} d^{5} e + 5 \, b^{3} c^{5} d^{4} e^{2}\right)} x^{3} + {\left(2 \, b^{2} c^{6} d^{6} - 6 \, b^{3} c^{5} d^{5} e + 5 \, b^{4} c^{4} d^{4} e^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{6} x^{4} + 2 \, b^{6} c^{5} x^{3} + b^{7} c^{4} x^{2}\right)}}"," ",0,"1/2*(2*b^5*c^3*e^6*x^5 + 4*b^6*c^2*e^6*x^4 - b^4*c^4*d^6 + 2*(6*b*c^7*d^6 - 18*b^2*c^6*d^5*e + 15*b^3*c^5*d^4*e^2 - 15*b^5*c^3*d^2*e^4 + 12*b^6*c^2*d*e^5 - 2*b^7*c*e^6)*x^3 + (18*b^2*c^6*d^6 - 54*b^3*c^5*d^5*e + 45*b^4*c^4*d^4*e^2 - 20*b^5*c^3*d^3*e^3 - 15*b^6*c^2*d^2*e^4 + 18*b^7*c*d*e^5 - 5*b^8*e^6)*x^2 + 4*(b^3*c^5*d^6 - 3*b^4*c^4*d^5*e)*x - 6*((2*c^8*d^6 - 6*b*c^7*d^5*e + 5*b^2*c^6*d^4*e^2 - 2*b^5*c^3*d*e^5 + b^6*c^2*e^6)*x^4 + 2*(2*b*c^7*d^6 - 6*b^2*c^6*d^5*e + 5*b^3*c^5*d^4*e^2 - 2*b^6*c^2*d*e^5 + b^7*c*e^6)*x^3 + (2*b^2*c^6*d^6 - 6*b^3*c^5*d^5*e + 5*b^4*c^4*d^4*e^2 - 2*b^7*c*d*e^5 + b^8*e^6)*x^2)*log(c*x + b) + 6*((2*c^8*d^6 - 6*b*c^7*d^5*e + 5*b^2*c^6*d^4*e^2)*x^4 + 2*(2*b*c^7*d^6 - 6*b^2*c^6*d^5*e + 5*b^3*c^5*d^4*e^2)*x^3 + (2*b^2*c^6*d^6 - 6*b^3*c^5*d^5*e + 5*b^4*c^4*d^4*e^2)*x^2)*log(x))/(b^5*c^6*x^4 + 2*b^6*c^5*x^3 + b^7*c^4*x^2)","B",0
277,1,493,0,0.426737," ","integrate((e*x+d)^5/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{b^{4} c^{3} d^{5} - 2 \, {\left(6 \, b c^{6} d^{5} - 15 \, b^{2} c^{5} d^{4} e + 10 \, b^{3} c^{4} d^{3} e^{2} - 5 \, b^{5} c^{2} d e^{4} + 2 \, b^{6} c e^{5}\right)} x^{3} - {\left(18 \, b^{2} c^{5} d^{5} - 45 \, b^{3} c^{4} d^{4} e + 30 \, b^{4} c^{3} d^{3} e^{2} - 10 \, b^{5} c^{2} d^{2} e^{3} - 5 \, b^{6} c d e^{4} + 3 \, b^{7} e^{5}\right)} x^{2} - 2 \, {\left(2 \, b^{3} c^{4} d^{5} - 5 \, b^{4} c^{3} d^{4} e\right)} x + 2 \, {\left({\left(6 \, c^{7} d^{5} - 15 \, b c^{6} d^{4} e + 10 \, b^{2} c^{5} d^{3} e^{2} - b^{5} c^{2} e^{5}\right)} x^{4} + 2 \, {\left(6 \, b c^{6} d^{5} - 15 \, b^{2} c^{5} d^{4} e + 10 \, b^{3} c^{4} d^{3} e^{2} - b^{6} c e^{5}\right)} x^{3} + {\left(6 \, b^{2} c^{5} d^{5} - 15 \, b^{3} c^{4} d^{4} e + 10 \, b^{4} c^{3} d^{3} e^{2} - b^{7} e^{5}\right)} x^{2}\right)} \log\left(c x + b\right) - 2 \, {\left({\left(6 \, c^{7} d^{5} - 15 \, b c^{6} d^{4} e + 10 \, b^{2} c^{5} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(6 \, b c^{6} d^{5} - 15 \, b^{2} c^{5} d^{4} e + 10 \, b^{3} c^{4} d^{3} e^{2}\right)} x^{3} + {\left(6 \, b^{2} c^{5} d^{5} - 15 \, b^{3} c^{4} d^{4} e + 10 \, b^{4} c^{3} d^{3} e^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{5} x^{4} + 2 \, b^{6} c^{4} x^{3} + b^{7} c^{3} x^{2}\right)}}"," ",0,"-1/2*(b^4*c^3*d^5 - 2*(6*b*c^6*d^5 - 15*b^2*c^5*d^4*e + 10*b^3*c^4*d^3*e^2 - 5*b^5*c^2*d*e^4 + 2*b^6*c*e^5)*x^3 - (18*b^2*c^5*d^5 - 45*b^3*c^4*d^4*e + 30*b^4*c^3*d^3*e^2 - 10*b^5*c^2*d^2*e^3 - 5*b^6*c*d*e^4 + 3*b^7*e^5)*x^2 - 2*(2*b^3*c^4*d^5 - 5*b^4*c^3*d^4*e)*x + 2*((6*c^7*d^5 - 15*b*c^6*d^4*e + 10*b^2*c^5*d^3*e^2 - b^5*c^2*e^5)*x^4 + 2*(6*b*c^6*d^5 - 15*b^2*c^5*d^4*e + 10*b^3*c^4*d^3*e^2 - b^6*c*e^5)*x^3 + (6*b^2*c^5*d^5 - 15*b^3*c^4*d^4*e + 10*b^4*c^3*d^3*e^2 - b^7*e^5)*x^2)*log(c*x + b) - 2*((6*c^7*d^5 - 15*b*c^6*d^4*e + 10*b^2*c^5*d^3*e^2)*x^4 + 2*(6*b*c^6*d^5 - 15*b^2*c^5*d^4*e + 10*b^3*c^4*d^3*e^2)*x^3 + (6*b^2*c^5*d^5 - 15*b^3*c^4*d^4*e + 10*b^4*c^3*d^3*e^2)*x^2)*log(x))/(b^5*c^5*x^4 + 2*b^6*c^4*x^3 + b^7*c^3*x^2)","B",0
278,1,426,0,0.432479," ","integrate((e*x+d)^4/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{b^{4} c^{2} d^{4} - 2 \, {\left(6 \, b c^{5} d^{4} - 12 \, b^{2} c^{4} d^{3} e + 6 \, b^{3} c^{3} d^{2} e^{2} - b^{5} c e^{4}\right)} x^{3} - {\left(18 \, b^{2} c^{4} d^{4} - 36 \, b^{3} c^{3} d^{3} e + 18 \, b^{4} c^{2} d^{2} e^{2} - 4 \, b^{5} c d e^{3} - b^{6} e^{4}\right)} x^{2} - 4 \, {\left(b^{3} c^{3} d^{4} - 2 \, b^{4} c^{2} d^{3} e\right)} x + 12 \, {\left({\left(c^{6} d^{4} - 2 \, b c^{5} d^{3} e + b^{2} c^{4} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(b c^{5} d^{4} - 2 \, b^{2} c^{4} d^{3} e + b^{3} c^{3} d^{2} e^{2}\right)} x^{3} + {\left(b^{2} c^{4} d^{4} - 2 \, b^{3} c^{3} d^{3} e + b^{4} c^{2} d^{2} e^{2}\right)} x^{2}\right)} \log\left(c x + b\right) - 12 \, {\left({\left(c^{6} d^{4} - 2 \, b c^{5} d^{3} e + b^{2} c^{4} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(b c^{5} d^{4} - 2 \, b^{2} c^{4} d^{3} e + b^{3} c^{3} d^{2} e^{2}\right)} x^{3} + {\left(b^{2} c^{4} d^{4} - 2 \, b^{3} c^{3} d^{3} e + b^{4} c^{2} d^{2} e^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{4} x^{4} + 2 \, b^{6} c^{3} x^{3} + b^{7} c^{2} x^{2}\right)}}"," ",0,"-1/2*(b^4*c^2*d^4 - 2*(6*b*c^5*d^4 - 12*b^2*c^4*d^3*e + 6*b^3*c^3*d^2*e^2 - b^5*c*e^4)*x^3 - (18*b^2*c^4*d^4 - 36*b^3*c^3*d^3*e + 18*b^4*c^2*d^2*e^2 - 4*b^5*c*d*e^3 - b^6*e^4)*x^2 - 4*(b^3*c^3*d^4 - 2*b^4*c^2*d^3*e)*x + 12*((c^6*d^4 - 2*b*c^5*d^3*e + b^2*c^4*d^2*e^2)*x^4 + 2*(b*c^5*d^4 - 2*b^2*c^4*d^3*e + b^3*c^3*d^2*e^2)*x^3 + (b^2*c^4*d^4 - 2*b^3*c^3*d^3*e + b^4*c^2*d^2*e^2)*x^2)*log(c*x + b) - 12*((c^6*d^4 - 2*b*c^5*d^3*e + b^2*c^4*d^2*e^2)*x^4 + 2*(b*c^5*d^4 - 2*b^2*c^4*d^3*e + b^3*c^3*d^2*e^2)*x^3 + (b^2*c^4*d^4 - 2*b^3*c^3*d^3*e + b^4*c^2*d^2*e^2)*x^2)*log(x))/(b^5*c^4*x^4 + 2*b^6*c^3*x^3 + b^7*c^2*x^2)","B",0
279,1,385,0,0.417864," ","integrate((e*x+d)^3/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{b^{4} c d^{3} - 6 \, {\left(2 \, b c^{4} d^{3} - 3 \, b^{2} c^{3} d^{2} e + b^{3} c^{2} d e^{2}\right)} x^{3} - {\left(18 \, b^{2} c^{3} d^{3} - 27 \, b^{3} c^{2} d^{2} e + 9 \, b^{4} c d e^{2} - b^{5} e^{3}\right)} x^{2} - 2 \, {\left(2 \, b^{3} c^{2} d^{3} - 3 \, b^{4} c d^{2} e\right)} x + 6 \, {\left({\left(2 \, c^{5} d^{3} - 3 \, b c^{4} d^{2} e + b^{2} c^{3} d e^{2}\right)} x^{4} + 2 \, {\left(2 \, b c^{4} d^{3} - 3 \, b^{2} c^{3} d^{2} e + b^{3} c^{2} d e^{2}\right)} x^{3} + {\left(2 \, b^{2} c^{3} d^{3} - 3 \, b^{3} c^{2} d^{2} e + b^{4} c d e^{2}\right)} x^{2}\right)} \log\left(c x + b\right) - 6 \, {\left({\left(2 \, c^{5} d^{3} - 3 \, b c^{4} d^{2} e + b^{2} c^{3} d e^{2}\right)} x^{4} + 2 \, {\left(2 \, b c^{4} d^{3} - 3 \, b^{2} c^{3} d^{2} e + b^{3} c^{2} d e^{2}\right)} x^{3} + {\left(2 \, b^{2} c^{3} d^{3} - 3 \, b^{3} c^{2} d^{2} e + b^{4} c d e^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{3} x^{4} + 2 \, b^{6} c^{2} x^{3} + b^{7} c x^{2}\right)}}"," ",0,"-1/2*(b^4*c*d^3 - 6*(2*b*c^4*d^3 - 3*b^2*c^3*d^2*e + b^3*c^2*d*e^2)*x^3 - (18*b^2*c^3*d^3 - 27*b^3*c^2*d^2*e + 9*b^4*c*d*e^2 - b^5*e^3)*x^2 - 2*(2*b^3*c^2*d^3 - 3*b^4*c*d^2*e)*x + 6*((2*c^5*d^3 - 3*b*c^4*d^2*e + b^2*c^3*d*e^2)*x^4 + 2*(2*b*c^4*d^3 - 3*b^2*c^3*d^2*e + b^3*c^2*d*e^2)*x^3 + (2*b^2*c^3*d^3 - 3*b^3*c^2*d^2*e + b^4*c*d*e^2)*x^2)*log(c*x + b) - 6*((2*c^5*d^3 - 3*b*c^4*d^2*e + b^2*c^3*d*e^2)*x^4 + 2*(2*b*c^4*d^3 - 3*b^2*c^3*d^2*e + b^3*c^2*d*e^2)*x^3 + (2*b^2*c^3*d^3 - 3*b^3*c^2*d^2*e + b^4*c*d*e^2)*x^2)*log(x))/(b^5*c^3*x^4 + 2*b^6*c^2*x^3 + b^7*c*x^2)","B",0
280,1,327,0,0.419966," ","integrate((e*x+d)^2/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{b^{4} d^{2} - 2 \, {\left(6 \, b c^{3} d^{2} - 6 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} - 3 \, {\left(6 \, b^{2} c^{2} d^{2} - 6 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2} - 4 \, {\left(b^{3} c d^{2} - b^{4} d e\right)} x + 2 \, {\left({\left(6 \, c^{4} d^{2} - 6 \, b c^{3} d e + b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(6 \, b c^{3} d^{2} - 6 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} + {\left(6 \, b^{2} c^{2} d^{2} - 6 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2}\right)} \log\left(c x + b\right) - 2 \, {\left({\left(6 \, c^{4} d^{2} - 6 \, b c^{3} d e + b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(6 \, b c^{3} d^{2} - 6 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} + {\left(6 \, b^{2} c^{2} d^{2} - 6 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{2} x^{4} + 2 \, b^{6} c x^{3} + b^{7} x^{2}\right)}}"," ",0,"-1/2*(b^4*d^2 - 2*(6*b*c^3*d^2 - 6*b^2*c^2*d*e + b^3*c*e^2)*x^3 - 3*(6*b^2*c^2*d^2 - 6*b^3*c*d*e + b^4*e^2)*x^2 - 4*(b^3*c*d^2 - b^4*d*e)*x + 2*((6*c^4*d^2 - 6*b*c^3*d*e + b^2*c^2*e^2)*x^4 + 2*(6*b*c^3*d^2 - 6*b^2*c^2*d*e + b^3*c*e^2)*x^3 + (6*b^2*c^2*d^2 - 6*b^3*c*d*e + b^4*e^2)*x^2)*log(c*x + b) - 2*((6*c^4*d^2 - 6*b*c^3*d*e + b^2*c^2*e^2)*x^4 + 2*(6*b*c^3*d^2 - 6*b^2*c^2*d*e + b^3*c*e^2)*x^3 + (6*b^2*c^2*d^2 - 6*b^3*c*d*e + b^4*e^2)*x^2)*log(x))/(b^5*c^2*x^4 + 2*b^6*c*x^3 + b^7*x^2)","B",0
281,1,234,0,0.417861," ","integrate((e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{b^{4} d - 6 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} x^{3} - 9 \, {\left(2 \, b^{2} c^{2} d - b^{3} c e\right)} x^{2} - 2 \, {\left(2 \, b^{3} c d - b^{4} e\right)} x + 6 \, {\left({\left(2 \, c^{4} d - b c^{3} e\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} x^{3} + {\left(2 \, b^{2} c^{2} d - b^{3} c e\right)} x^{2}\right)} \log\left(c x + b\right) - 6 \, {\left({\left(2 \, c^{4} d - b c^{3} e\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} x^{3} + {\left(2 \, b^{2} c^{2} d - b^{3} c e\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{2} x^{4} + 2 \, b^{6} c x^{3} + b^{7} x^{2}\right)}}"," ",0,"-1/2*(b^4*d - 6*(2*b*c^3*d - b^2*c^2*e)*x^3 - 9*(2*b^2*c^2*d - b^3*c*e)*x^2 - 2*(2*b^3*c*d - b^4*e)*x + 6*((2*c^4*d - b*c^3*e)*x^4 + 2*(2*b*c^3*d - b^2*c^2*e)*x^3 + (2*b^2*c^2*d - b^3*c*e)*x^2)*log(c*x + b) - 6*((2*c^4*d - b*c^3*e)*x^4 + 2*(2*b*c^3*d - b^2*c^2*e)*x^3 + (2*b^2*c^2*d - b^3*c*e)*x^2)*log(x))/(b^5*c^2*x^4 + 2*b^6*c*x^3 + b^7*x^2)","B",0
282,1,130,0,0.409086," ","integrate(1/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{12 \, b c^{3} x^{3} + 18 \, b^{2} c^{2} x^{2} + 4 \, b^{3} c x - b^{4} - 12 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{3} + b^{2} c^{2} x^{2}\right)} \log\left(c x + b\right) + 12 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{3} + b^{2} c^{2} x^{2}\right)} \log\left(x\right)}{2 \, {\left(b^{5} c^{2} x^{4} + 2 \, b^{6} c x^{3} + b^{7} x^{2}\right)}}"," ",0,"1/2*(12*b*c^3*x^3 + 18*b^2*c^2*x^2 + 4*b^3*c*x - b^4 - 12*(c^4*x^4 + 2*b*c^3*x^3 + b^2*c^2*x^2)*log(c*x + b) + 12*(c^4*x^4 + 2*b*c^3*x^3 + b^2*c^2*x^2)*log(x))/(b^5*c^2*x^4 + 2*b^6*c*x^3 + b^7*x^2)","A",0
283,1,716,0,33.190567," ","integrate(1/(e*x+d)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{b^{4} c^{3} d^{5} - 3 \, b^{5} c^{2} d^{4} e + 3 \, b^{6} c d^{3} e^{2} - b^{7} d^{2} e^{3} - 2 \, {\left(6 \, b c^{6} d^{5} - 15 \, b^{2} c^{5} d^{4} e + 10 \, b^{3} c^{4} d^{3} e^{2} - b^{5} c^{2} d e^{4}\right)} x^{3} - {\left(18 \, b^{2} c^{5} d^{5} - 45 \, b^{3} c^{4} d^{4} e + 30 \, b^{4} c^{3} d^{3} e^{2} + b^{5} c^{2} d^{2} e^{3} - 4 \, b^{6} c d e^{4}\right)} x^{2} - 2 \, {\left(2 \, b^{3} c^{4} d^{5} - 5 \, b^{4} c^{3} d^{4} e + 3 \, b^{5} c^{2} d^{3} e^{2} + b^{6} c d^{2} e^{3} - b^{7} d e^{4}\right)} x + 2 \, {\left({\left(6 \, c^{7} d^{5} - 15 \, b c^{6} d^{4} e + 10 \, b^{2} c^{5} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(6 \, b c^{6} d^{5} - 15 \, b^{2} c^{5} d^{4} e + 10 \, b^{3} c^{4} d^{3} e^{2}\right)} x^{3} + {\left(6 \, b^{2} c^{5} d^{5} - 15 \, b^{3} c^{4} d^{4} e + 10 \, b^{4} c^{3} d^{3} e^{2}\right)} x^{2}\right)} \log\left(c x + b\right) - 2 \, {\left(b^{5} c^{2} e^{5} x^{4} + 2 \, b^{6} c e^{5} x^{3} + b^{7} e^{5} x^{2}\right)} \log\left(e x + d\right) - 2 \, {\left({\left(6 \, c^{7} d^{5} - 15 \, b c^{6} d^{4} e + 10 \, b^{2} c^{5} d^{3} e^{2} - b^{5} c^{2} e^{5}\right)} x^{4} + 2 \, {\left(6 \, b c^{6} d^{5} - 15 \, b^{2} c^{5} d^{4} e + 10 \, b^{3} c^{4} d^{3} e^{2} - b^{6} c e^{5}\right)} x^{3} + {\left(6 \, b^{2} c^{5} d^{5} - 15 \, b^{3} c^{4} d^{4} e + 10 \, b^{4} c^{3} d^{3} e^{2} - b^{7} e^{5}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(b^{5} c^{5} d^{6} - 3 \, b^{6} c^{4} d^{5} e + 3 \, b^{7} c^{3} d^{4} e^{2} - b^{8} c^{2} d^{3} e^{3}\right)} x^{4} + 2 \, {\left(b^{6} c^{4} d^{6} - 3 \, b^{7} c^{3} d^{5} e + 3 \, b^{8} c^{2} d^{4} e^{2} - b^{9} c d^{3} e^{3}\right)} x^{3} + {\left(b^{7} c^{3} d^{6} - 3 \, b^{8} c^{2} d^{5} e + 3 \, b^{9} c d^{4} e^{2} - b^{10} d^{3} e^{3}\right)} x^{2}\right)}}"," ",0,"-1/2*(b^4*c^3*d^5 - 3*b^5*c^2*d^4*e + 3*b^6*c*d^3*e^2 - b^7*d^2*e^3 - 2*(6*b*c^6*d^5 - 15*b^2*c^5*d^4*e + 10*b^3*c^4*d^3*e^2 - b^5*c^2*d*e^4)*x^3 - (18*b^2*c^5*d^5 - 45*b^3*c^4*d^4*e + 30*b^4*c^3*d^3*e^2 + b^5*c^2*d^2*e^3 - 4*b^6*c*d*e^4)*x^2 - 2*(2*b^3*c^4*d^5 - 5*b^4*c^3*d^4*e + 3*b^5*c^2*d^3*e^2 + b^6*c*d^2*e^3 - b^7*d*e^4)*x + 2*((6*c^7*d^5 - 15*b*c^6*d^4*e + 10*b^2*c^5*d^3*e^2)*x^4 + 2*(6*b*c^6*d^5 - 15*b^2*c^5*d^4*e + 10*b^3*c^4*d^3*e^2)*x^3 + (6*b^2*c^5*d^5 - 15*b^3*c^4*d^4*e + 10*b^4*c^3*d^3*e^2)*x^2)*log(c*x + b) - 2*(b^5*c^2*e^5*x^4 + 2*b^6*c*e^5*x^3 + b^7*e^5*x^2)*log(e*x + d) - 2*((6*c^7*d^5 - 15*b*c^6*d^4*e + 10*b^2*c^5*d^3*e^2 - b^5*c^2*e^5)*x^4 + 2*(6*b*c^6*d^5 - 15*b^2*c^5*d^4*e + 10*b^3*c^4*d^3*e^2 - b^6*c*e^5)*x^3 + (6*b^2*c^5*d^5 - 15*b^3*c^4*d^4*e + 10*b^4*c^3*d^3*e^2 - b^7*e^5)*x^2)*log(x))/((b^5*c^5*d^6 - 3*b^6*c^4*d^5*e + 3*b^7*c^3*d^4*e^2 - b^8*c^2*d^3*e^3)*x^4 + 2*(b^6*c^4*d^6 - 3*b^7*c^3*d^5*e + 3*b^8*c^2*d^4*e^2 - b^9*c*d^3*e^3)*x^3 + (b^7*c^3*d^6 - 3*b^8*c^2*d^5*e + 3*b^9*c*d^4*e^2 - b^10*d^3*e^3)*x^2)","B",0
284,1,1305,0,56.144926," ","integrate(1/(e*x+d)^2/(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{b^{4} c^{4} d^{7} - 4 \, b^{5} c^{3} d^{6} e + 6 \, b^{6} c^{2} d^{5} e^{2} - 4 \, b^{7} c d^{4} e^{3} + b^{8} d^{3} e^{4} - 6 \, {\left(2 \, b c^{7} d^{6} e - 6 \, b^{2} c^{6} d^{5} e^{2} + 5 \, b^{3} c^{5} d^{4} e^{3} - 2 \, b^{5} c^{3} d^{2} e^{5} + b^{6} c^{2} d e^{6}\right)} x^{4} - 3 \, {\left(4 \, b c^{7} d^{7} - 6 \, b^{2} c^{6} d^{6} e - 8 \, b^{3} c^{5} d^{5} e^{2} + 15 \, b^{4} c^{4} d^{4} e^{3} - 2 \, b^{5} c^{3} d^{3} e^{4} - 7 \, b^{6} c^{2} d^{2} e^{5} + 4 \, b^{7} c d e^{6}\right)} x^{3} - {\left(18 \, b^{2} c^{6} d^{7} - 50 \, b^{3} c^{5} d^{6} e + 33 \, b^{4} c^{4} d^{5} e^{2} + 12 \, b^{5} c^{3} d^{4} e^{3} - 13 \, b^{6} c^{2} d^{3} e^{4} - 6 \, b^{7} c d^{2} e^{5} + 6 \, b^{8} d e^{6}\right)} x^{2} - {\left(4 \, b^{3} c^{5} d^{7} - 13 \, b^{4} c^{4} d^{6} e + 12 \, b^{5} c^{3} d^{5} e^{2} + 2 \, b^{6} c^{2} d^{4} e^{3} - 8 \, b^{7} c d^{3} e^{4} + 3 \, b^{8} d^{2} e^{5}\right)} x + 6 \, {\left({\left(2 \, c^{8} d^{6} e - 6 \, b c^{7} d^{5} e^{2} + 5 \, b^{2} c^{6} d^{4} e^{3}\right)} x^{5} + {\left(2 \, c^{8} d^{7} - 2 \, b c^{7} d^{6} e - 7 \, b^{2} c^{6} d^{5} e^{2} + 10 \, b^{3} c^{5} d^{4} e^{3}\right)} x^{4} + {\left(4 \, b c^{7} d^{7} - 10 \, b^{2} c^{6} d^{6} e + 4 \, b^{3} c^{5} d^{5} e^{2} + 5 \, b^{4} c^{4} d^{4} e^{3}\right)} x^{3} + {\left(2 \, b^{2} c^{6} d^{7} - 6 \, b^{3} c^{5} d^{6} e + 5 \, b^{4} c^{4} d^{5} e^{2}\right)} x^{2}\right)} \log\left(c x + b\right) - 6 \, {\left({\left(2 \, b^{5} c^{3} d e^{6} - b^{6} c^{2} e^{7}\right)} x^{5} + {\left(2 \, b^{5} c^{3} d^{2} e^{5} + 3 \, b^{6} c^{2} d e^{6} - 2 \, b^{7} c e^{7}\right)} x^{4} + {\left(4 \, b^{6} c^{2} d^{2} e^{5} - b^{8} e^{7}\right)} x^{3} + {\left(2 \, b^{7} c d^{2} e^{5} - b^{8} d e^{6}\right)} x^{2}\right)} \log\left(e x + d\right) - 6 \, {\left({\left(2 \, c^{8} d^{6} e - 6 \, b c^{7} d^{5} e^{2} + 5 \, b^{2} c^{6} d^{4} e^{3} - 2 \, b^{5} c^{3} d e^{6} + b^{6} c^{2} e^{7}\right)} x^{5} + {\left(2 \, c^{8} d^{7} - 2 \, b c^{7} d^{6} e - 7 \, b^{2} c^{6} d^{5} e^{2} + 10 \, b^{3} c^{5} d^{4} e^{3} - 2 \, b^{5} c^{3} d^{2} e^{5} - 3 \, b^{6} c^{2} d e^{6} + 2 \, b^{7} c e^{7}\right)} x^{4} + {\left(4 \, b c^{7} d^{7} - 10 \, b^{2} c^{6} d^{6} e + 4 \, b^{3} c^{5} d^{5} e^{2} + 5 \, b^{4} c^{4} d^{4} e^{3} - 4 \, b^{6} c^{2} d^{2} e^{5} + b^{8} e^{7}\right)} x^{3} + {\left(2 \, b^{2} c^{6} d^{7} - 6 \, b^{3} c^{5} d^{6} e + 5 \, b^{4} c^{4} d^{5} e^{2} - 2 \, b^{7} c d^{2} e^{5} + b^{8} d e^{6}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(b^{5} c^{6} d^{8} e - 4 \, b^{6} c^{5} d^{7} e^{2} + 6 \, b^{7} c^{4} d^{6} e^{3} - 4 \, b^{8} c^{3} d^{5} e^{4} + b^{9} c^{2} d^{4} e^{5}\right)} x^{5} + {\left(b^{5} c^{6} d^{9} - 2 \, b^{6} c^{5} d^{8} e - 2 \, b^{7} c^{4} d^{7} e^{2} + 8 \, b^{8} c^{3} d^{6} e^{3} - 7 \, b^{9} c^{2} d^{5} e^{4} + 2 \, b^{10} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{6} c^{5} d^{9} - 7 \, b^{7} c^{4} d^{8} e + 8 \, b^{8} c^{3} d^{7} e^{2} - 2 \, b^{9} c^{2} d^{6} e^{3} - 2 \, b^{10} c d^{5} e^{4} + b^{11} d^{4} e^{5}\right)} x^{3} + {\left(b^{7} c^{4} d^{9} - 4 \, b^{8} c^{3} d^{8} e + 6 \, b^{9} c^{2} d^{7} e^{2} - 4 \, b^{10} c d^{6} e^{3} + b^{11} d^{5} e^{4}\right)} x^{2}\right)}}"," ",0,"-1/2*(b^4*c^4*d^7 - 4*b^5*c^3*d^6*e + 6*b^6*c^2*d^5*e^2 - 4*b^7*c*d^4*e^3 + b^8*d^3*e^4 - 6*(2*b*c^7*d^6*e - 6*b^2*c^6*d^5*e^2 + 5*b^3*c^5*d^4*e^3 - 2*b^5*c^3*d^2*e^5 + b^6*c^2*d*e^6)*x^4 - 3*(4*b*c^7*d^7 - 6*b^2*c^6*d^6*e - 8*b^3*c^5*d^5*e^2 + 15*b^4*c^4*d^4*e^3 - 2*b^5*c^3*d^3*e^4 - 7*b^6*c^2*d^2*e^5 + 4*b^7*c*d*e^6)*x^3 - (18*b^2*c^6*d^7 - 50*b^3*c^5*d^6*e + 33*b^4*c^4*d^5*e^2 + 12*b^5*c^3*d^4*e^3 - 13*b^6*c^2*d^3*e^4 - 6*b^7*c*d^2*e^5 + 6*b^8*d*e^6)*x^2 - (4*b^3*c^5*d^7 - 13*b^4*c^4*d^6*e + 12*b^5*c^3*d^5*e^2 + 2*b^6*c^2*d^4*e^3 - 8*b^7*c*d^3*e^4 + 3*b^8*d^2*e^5)*x + 6*((2*c^8*d^6*e - 6*b*c^7*d^5*e^2 + 5*b^2*c^6*d^4*e^3)*x^5 + (2*c^8*d^7 - 2*b*c^7*d^6*e - 7*b^2*c^6*d^5*e^2 + 10*b^3*c^5*d^4*e^3)*x^4 + (4*b*c^7*d^7 - 10*b^2*c^6*d^6*e + 4*b^3*c^5*d^5*e^2 + 5*b^4*c^4*d^4*e^3)*x^3 + (2*b^2*c^6*d^7 - 6*b^3*c^5*d^6*e + 5*b^4*c^4*d^5*e^2)*x^2)*log(c*x + b) - 6*((2*b^5*c^3*d*e^6 - b^6*c^2*e^7)*x^5 + (2*b^5*c^3*d^2*e^5 + 3*b^6*c^2*d*e^6 - 2*b^7*c*e^7)*x^4 + (4*b^6*c^2*d^2*e^5 - b^8*e^7)*x^3 + (2*b^7*c*d^2*e^5 - b^8*d*e^6)*x^2)*log(e*x + d) - 6*((2*c^8*d^6*e - 6*b*c^7*d^5*e^2 + 5*b^2*c^6*d^4*e^3 - 2*b^5*c^3*d*e^6 + b^6*c^2*e^7)*x^5 + (2*c^8*d^7 - 2*b*c^7*d^6*e - 7*b^2*c^6*d^5*e^2 + 10*b^3*c^5*d^4*e^3 - 2*b^5*c^3*d^2*e^5 - 3*b^6*c^2*d*e^6 + 2*b^7*c*e^7)*x^4 + (4*b*c^7*d^7 - 10*b^2*c^6*d^6*e + 4*b^3*c^5*d^5*e^2 + 5*b^4*c^4*d^4*e^3 - 4*b^6*c^2*d^2*e^5 + b^8*e^7)*x^3 + (2*b^2*c^6*d^7 - 6*b^3*c^5*d^6*e + 5*b^4*c^4*d^5*e^2 - 2*b^7*c*d^2*e^5 + b^8*d*e^6)*x^2)*log(x))/((b^5*c^6*d^8*e - 4*b^6*c^5*d^7*e^2 + 6*b^7*c^4*d^6*e^3 - 4*b^8*c^3*d^5*e^4 + b^9*c^2*d^4*e^5)*x^5 + (b^5*c^6*d^9 - 2*b^6*c^5*d^8*e - 2*b^7*c^4*d^7*e^2 + 8*b^8*c^3*d^6*e^3 - 7*b^9*c^2*d^5*e^4 + 2*b^10*c*d^4*e^5)*x^4 + (2*b^6*c^5*d^9 - 7*b^7*c^4*d^8*e + 8*b^8*c^3*d^7*e^2 - 2*b^9*c^2*d^6*e^3 - 2*b^10*c*d^5*e^4 + b^11*d^4*e^5)*x^3 + (b^7*c^4*d^9 - 4*b^8*c^3*d^8*e + 6*b^9*c^2*d^7*e^2 - 4*b^10*c*d^6*e^3 + b^11*d^5*e^4)*x^2)","B",0
285,1,497,0,0.432702," ","integrate((e*x+d)^3*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\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)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(384 \, c^{5} e^{3} x^{4} + 480 \, b c^{4} d^{3} - 720 \, b^{2} c^{3} d^{2} e + 450 \, b^{3} c^{2} d e^{2} - 105 \, b^{4} c e^{3} + 48 \, {\left(30 \, c^{5} d e^{2} + b c^{4} e^{3}\right)} x^{3} + 8 \, {\left(240 \, c^{5} d^{2} e + 30 \, b c^{4} d e^{2} - 7 \, b^{2} c^{3} e^{3}\right)} x^{2} + 10 \, {\left(96 \, c^{5} d^{3} + 48 \, b c^{4} d^{2} e - 30 \, b^{2} c^{3} d e^{2} + 7 \, b^{3} c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, c^{5}}, \frac{15 \, {\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)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(384 \, c^{5} e^{3} x^{4} + 480 \, b c^{4} d^{3} - 720 \, b^{2} c^{3} d^{2} e + 450 \, b^{3} c^{2} d e^{2} - 105 \, b^{4} c e^{3} + 48 \, {\left(30 \, c^{5} d e^{2} + b c^{4} e^{3}\right)} x^{3} + 8 \, {\left(240 \, c^{5} d^{2} e + 30 \, b c^{4} d e^{2} - 7 \, b^{2} c^{3} e^{3}\right)} x^{2} + 10 \, {\left(96 \, c^{5} d^{3} + 48 \, b c^{4} d^{2} e - 30 \, b^{2} c^{3} d e^{2} + 7 \, b^{3} c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, c^{5}}\right]"," ",0,"[-1/3840*(15*(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)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(384*c^5*e^3*x^4 + 480*b*c^4*d^3 - 720*b^2*c^3*d^2*e + 450*b^3*c^2*d*e^2 - 105*b^4*c*e^3 + 48*(30*c^5*d*e^2 + b*c^4*e^3)*x^3 + 8*(240*c^5*d^2*e + 30*b*c^4*d*e^2 - 7*b^2*c^3*e^3)*x^2 + 10*(96*c^5*d^3 + 48*b*c^4*d^2*e - 30*b^2*c^3*d*e^2 + 7*b^3*c^2*e^3)*x)*sqrt(c*x^2 + b*x))/c^5, 1/1920*(15*(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)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (384*c^5*e^3*x^4 + 480*b*c^4*d^3 - 720*b^2*c^3*d^2*e + 450*b^3*c^2*d*e^2 - 105*b^4*c*e^3 + 48*(30*c^5*d*e^2 + b*c^4*e^3)*x^3 + 8*(240*c^5*d^2*e + 30*b*c^4*d*e^2 - 7*b^2*c^3*e^3)*x^2 + 10*(96*c^5*d^3 + 48*b*c^4*d^2*e - 30*b^2*c^3*d*e^2 + 7*b^3*c^2*e^3)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
286,1,337,0,0.424411," ","integrate((e*x+d)^2*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, b^{2} c^{2} d^{2} - 16 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(48 \, c^{4} e^{2} x^{3} + 48 \, b c^{3} d^{2} - 48 \, b^{2} c^{2} d e + 15 \, b^{3} c e^{2} + 8 \, {\left(16 \, c^{4} d e + b c^{3} e^{2}\right)} x^{2} + 2 \, {\left(48 \, c^{4} d^{2} + 16 \, b c^{3} d e - 5 \, b^{2} c^{2} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, c^{4}}, \frac{3 \, {\left(16 \, b^{2} c^{2} d^{2} - 16 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(48 \, c^{4} e^{2} x^{3} + 48 \, b c^{3} d^{2} - 48 \, b^{2} c^{2} d e + 15 \, b^{3} c e^{2} + 8 \, {\left(16 \, c^{4} d e + b c^{3} e^{2}\right)} x^{2} + 2 \, {\left(48 \, c^{4} d^{2} + 16 \, b c^{3} d e - 5 \, b^{2} c^{2} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, c^{4}}\right]"," ",0,"[1/384*(3*(16*b^2*c^2*d^2 - 16*b^3*c*d*e + 5*b^4*e^2)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(48*c^4*e^2*x^3 + 48*b*c^3*d^2 - 48*b^2*c^2*d*e + 15*b^3*c*e^2 + 8*(16*c^4*d*e + b*c^3*e^2)*x^2 + 2*(48*c^4*d^2 + 16*b*c^3*d*e - 5*b^2*c^2*e^2)*x)*sqrt(c*x^2 + b*x))/c^4, 1/192*(3*(16*b^2*c^2*d^2 - 16*b^3*c*d*e + 5*b^4*e^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (48*c^4*e^2*x^3 + 48*b*c^3*d^2 - 48*b^2*c^2*d*e + 15*b^3*c*e^2 + 8*(16*c^4*d*e + b*c^3*e^2)*x^2 + 2*(48*c^4*d^2 + 16*b*c^3*d*e - 5*b^2*c^2*e^2)*x)*sqrt(c*x^2 + b*x))/c^4]","A",0
287,1,205,0,0.419125," ","integrate((e*x+d)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, b^{2} c d - b^{3} e\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(8 \, c^{3} e x^{2} + 6 \, b c^{2} d - 3 \, b^{2} c e + 2 \, {\left(6 \, c^{3} d + b c^{2} e\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, c^{3}}, \frac{3 \, {\left(2 \, b^{2} c d - b^{3} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, c^{3} e x^{2} + 6 \, b c^{2} d - 3 \, b^{2} c e + 2 \, {\left(6 \, c^{3} d + b c^{2} e\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, c^{3}}\right]"," ",0,"[-1/48*(3*(2*b^2*c*d - b^3*e)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(8*c^3*e*x^2 + 6*b*c^2*d - 3*b^2*c*e + 2*(6*c^3*d + b*c^2*e)*x)*sqrt(c*x^2 + b*x))/c^3, 1/24*(3*(2*b^2*c*d - b^3*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*c^3*e*x^2 + 6*b*c^2*d - 3*b^2*c*e + 2*(6*c^3*d + b*c^2*e)*x)*sqrt(c*x^2 + b*x))/c^3]","A",0
288,1,121,0,0.422122," ","integrate((c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{b^{2} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(2 \, c^{2} x + b c\right)} \sqrt{c x^{2} + b x}}{8 \, c^{2}}, \frac{b^{2} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(2 \, c^{2} x + b c\right)} \sqrt{c x^{2} + b x}}{4 \, c^{2}}\right]"," ",0,"[1/8*(b^2*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(2*c^2*x + b*c)*sqrt(c*x^2 + b*x))/c^2, 1/4*(b^2*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (2*c^2*x + b*c)*sqrt(c*x^2 + b*x))/c^2]","A",0
289,1,488,0,0.455671," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c x^{2} + b x} c e - {\left(2 \, c d - b e\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, \sqrt{c d^{2} - b d e} c \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right)}{2 \, c e^{2}}, \frac{2 \, \sqrt{c x^{2} + b x} c e + 4 \, \sqrt{-c d^{2} + b d e} c \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(2 \, c d - b e\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right)}{2 \, c e^{2}}, \frac{\sqrt{c x^{2} + b x} c e + {\left(2 \, c d - b e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + \sqrt{c d^{2} - b d e} c \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right)}{c e^{2}}, \frac{\sqrt{c x^{2} + b x} c e + 2 \, \sqrt{-c d^{2} + b d e} c \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + {\left(2 \, c d - b e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right)}{c e^{2}}\right]"," ",0,"[1/2*(2*sqrt(c*x^2 + b*x)*c*e - (2*c*d - b*e)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*sqrt(c*d^2 - b*d*e)*c*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)))/(c*e^2), 1/2*(2*sqrt(c*x^2 + b*x)*c*e + 4*sqrt(-c*d^2 + b*d*e)*c*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (2*c*d - b*e)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)))/(c*e^2), (sqrt(c*x^2 + b*x)*c*e + (2*c*d - b*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + sqrt(c*d^2 - b*d*e)*c*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)))/(c*e^2), (sqrt(c*x^2 + b*x)*c*e + 2*sqrt(-c*d^2 + b*d*e)*c*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + (2*c*d - b*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)))/(c*e^2)]","A",0
290,1,846,0,0.461444," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(c d^{3} - b d^{2} e + {\left(c d^{2} e - b d e^{2}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - {\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(c d^{2} e - b d e^{2}\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(c d^{3} e^{2} - b d^{2} e^{3} + {\left(c d^{2} e^{3} - b d e^{4}\right)} x\right)}}, -\frac{{\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(c d^{3} - b d^{2} e + {\left(c d^{2} e - b d e^{2}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + {\left(c d^{2} e - b d e^{2}\right)} \sqrt{c x^{2} + b x}}{c d^{3} e^{2} - b d^{2} e^{3} + {\left(c d^{2} e^{3} - b d e^{4}\right)} x}, -\frac{4 \, {\left(c d^{3} - b d^{2} e + {\left(c d^{2} e - b d e^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(c d^{2} e - b d e^{2}\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(c d^{3} e^{2} - b d^{2} e^{3} + {\left(c d^{2} e^{3} - b d e^{4}\right)} x\right)}}, -\frac{{\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 2 \, {\left(c d^{3} - b d^{2} e + {\left(c d^{2} e - b d e^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(c d^{2} e - b d e^{2}\right)} \sqrt{c x^{2} + b x}}{c d^{3} e^{2} - b d^{2} e^{3} + {\left(c d^{2} e^{3} - b d e^{4}\right)} x}\right]"," ",0,"[1/2*(2*(c*d^3 - b*d^2*e + (c*d^2*e - b*d*e^2)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - (2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(c*d^2*e - b*d*e^2)*sqrt(c*x^2 + b*x))/(c*d^3*e^2 - b*d^2*e^3 + (c*d^2*e^3 - b*d*e^4)*x), -((2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (c*d^3 - b*d^2*e + (c*d^2*e - b*d*e^2)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + (c*d^2*e - b*d*e^2)*sqrt(c*x^2 + b*x))/(c*d^3*e^2 - b*d^2*e^3 + (c*d^2*e^3 - b*d*e^4)*x), -1/2*(4*(c*d^3 - b*d^2*e + (c*d^2*e - b*d*e^2)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(c*d^2*e - b*d*e^2)*sqrt(c*x^2 + b*x))/(c*d^3*e^2 - b*d^2*e^3 + (c*d^2*e^3 - b*d*e^4)*x), -((2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 2*(c*d^3 - b*d^2*e + (c*d^2*e - b*d*e^2)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (c*d^2*e - b*d*e^2)*sqrt(c*x^2 + b*x))/(c*d^3*e^2 - b*d^2*e^3 + (c*d^2*e^3 - b*d*e^4)*x)]","A",0
291,1,479,0,0.423054," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} e^{2} x^{2} + 2 \, b^{2} d e x + b^{2} d^{2}\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(b c d^{3} - b^{2} d^{2} e + {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c^{2} d^{6} - 2 \, b c d^{5} e + b^{2} d^{4} e^{2} + {\left(c^{2} d^{4} e^{2} - 2 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e - 2 \, b c d^{4} e^{2} + b^{2} d^{3} e^{3}\right)} x\right)}}, -\frac{{\left(b^{2} e^{2} x^{2} + 2 \, b^{2} d e x + b^{2} d^{2}\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(b c d^{3} - b^{2} d^{2} e + {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e + b^{2} d e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c^{2} d^{6} - 2 \, b c d^{5} e + b^{2} d^{4} e^{2} + {\left(c^{2} d^{4} e^{2} - 2 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e - 2 \, b c d^{4} e^{2} + b^{2} d^{3} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/8*((b^2*e^2*x^2 + 2*b^2*d*e*x + b^2*d^2)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(b*c*d^3 - b^2*d^2*e + (2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2)*x)*sqrt(c*x^2 + b*x))/(c^2*d^6 - 2*b*c*d^5*e + b^2*d^4*e^2 + (c^2*d^4*e^2 - 2*b*c*d^3*e^3 + b^2*d^2*e^4)*x^2 + 2*(c^2*d^5*e - 2*b*c*d^4*e^2 + b^2*d^3*e^3)*x), -1/4*((b^2*e^2*x^2 + 2*b^2*d*e*x + b^2*d^2)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (b*c*d^3 - b^2*d^2*e + (2*c^2*d^3 - 3*b*c*d^2*e + b^2*d*e^2)*x)*sqrt(c*x^2 + b*x))/(c^2*d^6 - 2*b*c*d^5*e + b^2*d^4*e^2 + (c^2*d^4*e^2 - 2*b*c*d^3*e^3 + b^2*d^2*e^4)*x^2 + 2*(c^2*d^5*e - 2*b*c*d^4*e^2 + b^2*d^3*e^3)*x)]","B",0
292,1,969,0,0.433814," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, b^{2} c d^{4} - b^{3} d^{3} e + {\left(2 \, b^{2} c d e^{3} - b^{3} e^{4}\right)} x^{3} + 3 \, {\left(2 \, b^{2} c d^{2} e^{2} - b^{3} d e^{3}\right)} x^{2} + 3 \, {\left(2 \, b^{2} c d^{3} e - b^{3} d^{2} e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(6 \, b c^{2} d^{5} - 9 \, b^{2} c d^{4} e + 3 \, b^{3} d^{3} e^{2} + {\left(4 \, c^{3} d^{4} e - 8 \, b c^{2} d^{3} e^{2} + 7 \, b^{2} c d^{2} e^{3} - 3 \, b^{3} d e^{4}\right)} x^{2} + 2 \, {\left(6 \, c^{3} d^{5} - 13 \, b c^{2} d^{4} e + 11 \, b^{2} c d^{3} e^{2} - 4 \, b^{3} d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c^{3} d^{9} - 3 \, b c^{2} d^{8} e + 3 \, b^{2} c d^{7} e^{2} - b^{3} d^{6} e^{3} + {\left(c^{3} d^{6} e^{3} - 3 \, b c^{2} d^{5} e^{4} + 3 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{3} d^{7} e^{2} - 3 \, b c^{2} d^{6} e^{3} + 3 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5}\right)} x^{2} + 3 \, {\left(c^{3} d^{8} e - 3 \, b c^{2} d^{7} e^{2} + 3 \, b^{2} c d^{6} e^{3} - b^{3} d^{5} e^{4}\right)} x\right)}}, -\frac{3 \, {\left(2 \, b^{2} c d^{4} - b^{3} d^{3} e + {\left(2 \, b^{2} c d e^{3} - b^{3} e^{4}\right)} x^{3} + 3 \, {\left(2 \, b^{2} c d^{2} e^{2} - b^{3} d e^{3}\right)} x^{2} + 3 \, {\left(2 \, b^{2} c d^{3} e - b^{3} d^{2} e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(6 \, b c^{2} d^{5} - 9 \, b^{2} c d^{4} e + 3 \, b^{3} d^{3} e^{2} + {\left(4 \, c^{3} d^{4} e - 8 \, b c^{2} d^{3} e^{2} + 7 \, b^{2} c d^{2} e^{3} - 3 \, b^{3} d e^{4}\right)} x^{2} + 2 \, {\left(6 \, c^{3} d^{5} - 13 \, b c^{2} d^{4} e + 11 \, b^{2} c d^{3} e^{2} - 4 \, b^{3} d^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c^{3} d^{9} - 3 \, b c^{2} d^{8} e + 3 \, b^{2} c d^{7} e^{2} - b^{3} d^{6} e^{3} + {\left(c^{3} d^{6} e^{3} - 3 \, b c^{2} d^{5} e^{4} + 3 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{3} d^{7} e^{2} - 3 \, b c^{2} d^{6} e^{3} + 3 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5}\right)} x^{2} + 3 \, {\left(c^{3} d^{8} e - 3 \, b c^{2} d^{7} e^{2} + 3 \, b^{2} c d^{6} e^{3} - b^{3} d^{5} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(2*b^2*c*d^4 - b^3*d^3*e + (2*b^2*c*d*e^3 - b^3*e^4)*x^3 + 3*(2*b^2*c*d^2*e^2 - b^3*d*e^3)*x^2 + 3*(2*b^2*c*d^3*e - b^3*d^2*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(6*b*c^2*d^5 - 9*b^2*c*d^4*e + 3*b^3*d^3*e^2 + (4*c^3*d^4*e - 8*b*c^2*d^3*e^2 + 7*b^2*c*d^2*e^3 - 3*b^3*d*e^4)*x^2 + 2*(6*c^3*d^5 - 13*b*c^2*d^4*e + 11*b^2*c*d^3*e^2 - 4*b^3*d^2*e^3)*x)*sqrt(c*x^2 + b*x))/(c^3*d^9 - 3*b*c^2*d^8*e + 3*b^2*c*d^7*e^2 - b^3*d^6*e^3 + (c^3*d^6*e^3 - 3*b*c^2*d^5*e^4 + 3*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x^3 + 3*(c^3*d^7*e^2 - 3*b*c^2*d^6*e^3 + 3*b^2*c*d^5*e^4 - b^3*d^4*e^5)*x^2 + 3*(c^3*d^8*e - 3*b*c^2*d^7*e^2 + 3*b^2*c*d^6*e^3 - b^3*d^5*e^4)*x), -1/24*(3*(2*b^2*c*d^4 - b^3*d^3*e + (2*b^2*c*d*e^3 - b^3*e^4)*x^3 + 3*(2*b^2*c*d^2*e^2 - b^3*d*e^3)*x^2 + 3*(2*b^2*c*d^3*e - b^3*d^2*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (6*b*c^2*d^5 - 9*b^2*c*d^4*e + 3*b^3*d^3*e^2 + (4*c^3*d^4*e - 8*b*c^2*d^3*e^2 + 7*b^2*c*d^2*e^3 - 3*b^3*d*e^4)*x^2 + 2*(6*c^3*d^5 - 13*b*c^2*d^4*e + 11*b^2*c*d^3*e^2 - 4*b^3*d^2*e^3)*x)*sqrt(c*x^2 + b*x))/(c^3*d^9 - 3*b*c^2*d^8*e + 3*b^2*c*d^7*e^2 - b^3*d^6*e^3 + (c^3*d^6*e^3 - 3*b*c^2*d^5*e^4 + 3*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x^3 + 3*(c^3*d^7*e^2 - 3*b*c^2*d^6*e^3 + 3*b^2*c*d^5*e^4 - b^3*d^4*e^5)*x^2 + 3*(c^3*d^8*e - 3*b*c^2*d^7*e^2 + 3*b^2*c*d^6*e^3 - b^3*d^5*e^4)*x)]","B",0
293,1,1611,0,0.452492," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(16 \, b^{2} c^{2} d^{6} - 16 \, b^{3} c d^{5} e + 5 \, b^{4} d^{4} e^{2} + {\left(16 \, b^{2} c^{2} d^{2} e^{4} - 16 \, b^{3} c d e^{5} + 5 \, b^{4} e^{6}\right)} x^{4} + 4 \, {\left(16 \, b^{2} c^{2} d^{3} e^{3} - 16 \, b^{3} c d^{2} e^{4} + 5 \, b^{4} d e^{5}\right)} x^{3} + 6 \, {\left(16 \, b^{2} c^{2} d^{4} e^{2} - 16 \, b^{3} c d^{3} e^{3} + 5 \, b^{4} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(16 \, b^{2} c^{2} d^{5} e - 16 \, b^{3} c d^{4} e^{2} + 5 \, b^{4} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(48 \, b c^{3} d^{7} - 96 \, b^{2} c^{2} d^{6} e + 63 \, b^{3} c d^{5} e^{2} - 15 \, b^{4} d^{4} e^{3} + {\left(16 \, c^{4} d^{5} e^{2} - 40 \, b c^{3} d^{4} e^{3} + 62 \, b^{2} c^{2} d^{3} e^{4} - 53 \, b^{3} c d^{2} e^{5} + 15 \, b^{4} d e^{6}\right)} x^{3} + {\left(64 \, c^{4} d^{6} e - 168 \, b c^{3} d^{5} e^{2} + 244 \, b^{2} c^{2} d^{4} e^{3} - 195 \, b^{3} c d^{3} e^{4} + 55 \, b^{4} d^{2} e^{5}\right)} x^{2} + {\left(96 \, c^{4} d^{7} - 272 \, b c^{3} d^{6} e + 374 \, b^{2} c^{2} d^{5} e^{2} - 271 \, b^{3} c d^{4} e^{3} + 73 \, b^{4} d^{3} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, {\left(c^{4} d^{12} - 4 \, b c^{3} d^{11} e + 6 \, b^{2} c^{2} d^{10} e^{2} - 4 \, b^{3} c d^{9} e^{3} + b^{4} d^{8} e^{4} + {\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 \, b^{3} c d^{5} e^{7} + b^{4} d^{4} e^{8}\right)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, b c^{3} d^{8} e^{4} + 6 \, b^{2} c^{2} d^{7} e^{5} - 4 \, b^{3} c d^{6} e^{6} + b^{4} d^{5} e^{7}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, b c^{3} d^{9} e^{3} + 6 \, b^{2} c^{2} d^{8} e^{4} - 4 \, b^{3} c d^{7} e^{5} + b^{4} d^{6} e^{6}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, b c^{3} d^{10} e^{2} + 6 \, b^{2} c^{2} d^{9} e^{3} - 4 \, b^{3} c d^{8} e^{4} + b^{4} d^{7} e^{5}\right)} x\right)}}, -\frac{3 \, {\left(16 \, b^{2} c^{2} d^{6} - 16 \, b^{3} c d^{5} e + 5 \, b^{4} d^{4} e^{2} + {\left(16 \, b^{2} c^{2} d^{2} e^{4} - 16 \, b^{3} c d e^{5} + 5 \, b^{4} e^{6}\right)} x^{4} + 4 \, {\left(16 \, b^{2} c^{2} d^{3} e^{3} - 16 \, b^{3} c d^{2} e^{4} + 5 \, b^{4} d e^{5}\right)} x^{3} + 6 \, {\left(16 \, b^{2} c^{2} d^{4} e^{2} - 16 \, b^{3} c d^{3} e^{3} + 5 \, b^{4} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(16 \, b^{2} c^{2} d^{5} e - 16 \, b^{3} c d^{4} e^{2} + 5 \, b^{4} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(48 \, b c^{3} d^{7} - 96 \, b^{2} c^{2} d^{6} e + 63 \, b^{3} c d^{5} e^{2} - 15 \, b^{4} d^{4} e^{3} + {\left(16 \, c^{4} d^{5} e^{2} - 40 \, b c^{3} d^{4} e^{3} + 62 \, b^{2} c^{2} d^{3} e^{4} - 53 \, b^{3} c d^{2} e^{5} + 15 \, b^{4} d e^{6}\right)} x^{3} + {\left(64 \, c^{4} d^{6} e - 168 \, b c^{3} d^{5} e^{2} + 244 \, b^{2} c^{2} d^{4} e^{3} - 195 \, b^{3} c d^{3} e^{4} + 55 \, b^{4} d^{2} e^{5}\right)} x^{2} + {\left(96 \, c^{4} d^{7} - 272 \, b c^{3} d^{6} e + 374 \, b^{2} c^{2} d^{5} e^{2} - 271 \, b^{3} c d^{4} e^{3} + 73 \, b^{4} d^{3} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, {\left(c^{4} d^{12} - 4 \, b c^{3} d^{11} e + 6 \, b^{2} c^{2} d^{10} e^{2} - 4 \, b^{3} c d^{9} e^{3} + b^{4} d^{8} e^{4} + {\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 \, b^{3} c d^{5} e^{7} + b^{4} d^{4} e^{8}\right)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, b c^{3} d^{8} e^{4} + 6 \, b^{2} c^{2} d^{7} e^{5} - 4 \, b^{3} c d^{6} e^{6} + b^{4} d^{5} e^{7}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, b c^{3} d^{9} e^{3} + 6 \, b^{2} c^{2} d^{8} e^{4} - 4 \, b^{3} c d^{7} e^{5} + b^{4} d^{6} e^{6}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, b c^{3} d^{10} e^{2} + 6 \, b^{2} c^{2} d^{9} e^{3} - 4 \, b^{3} c d^{8} e^{4} + b^{4} d^{7} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/384*(3*(16*b^2*c^2*d^6 - 16*b^3*c*d^5*e + 5*b^4*d^4*e^2 + (16*b^2*c^2*d^2*e^4 - 16*b^3*c*d*e^5 + 5*b^4*e^6)*x^4 + 4*(16*b^2*c^2*d^3*e^3 - 16*b^3*c*d^2*e^4 + 5*b^4*d*e^5)*x^3 + 6*(16*b^2*c^2*d^4*e^2 - 16*b^3*c*d^3*e^3 + 5*b^4*d^2*e^4)*x^2 + 4*(16*b^2*c^2*d^5*e - 16*b^3*c*d^4*e^2 + 5*b^4*d^3*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(48*b*c^3*d^7 - 96*b^2*c^2*d^6*e + 63*b^3*c*d^5*e^2 - 15*b^4*d^4*e^3 + (16*c^4*d^5*e^2 - 40*b*c^3*d^4*e^3 + 62*b^2*c^2*d^3*e^4 - 53*b^3*c*d^2*e^5 + 15*b^4*d*e^6)*x^3 + (64*c^4*d^6*e - 168*b*c^3*d^5*e^2 + 244*b^2*c^2*d^4*e^3 - 195*b^3*c*d^3*e^4 + 55*b^4*d^2*e^5)*x^2 + (96*c^4*d^7 - 272*b*c^3*d^6*e + 374*b^2*c^2*d^5*e^2 - 271*b^3*c*d^4*e^3 + 73*b^4*d^3*e^4)*x)*sqrt(c*x^2 + b*x))/(c^4*d^12 - 4*b*c^3*d^11*e + 6*b^2*c^2*d^10*e^2 - 4*b^3*c*d^9*e^3 + b^4*d^8*e^4 + (c^4*d^8*e^4 - 4*b*c^3*d^7*e^5 + 6*b^2*c^2*d^6*e^6 - 4*b^3*c*d^5*e^7 + b^4*d^4*e^8)*x^4 + 4*(c^4*d^9*e^3 - 4*b*c^3*d^8*e^4 + 6*b^2*c^2*d^7*e^5 - 4*b^3*c*d^6*e^6 + b^4*d^5*e^7)*x^3 + 6*(c^4*d^10*e^2 - 4*b*c^3*d^9*e^3 + 6*b^2*c^2*d^8*e^4 - 4*b^3*c*d^7*e^5 + b^4*d^6*e^6)*x^2 + 4*(c^4*d^11*e - 4*b*c^3*d^10*e^2 + 6*b^2*c^2*d^9*e^3 - 4*b^3*c*d^8*e^4 + b^4*d^7*e^5)*x), -1/192*(3*(16*b^2*c^2*d^6 - 16*b^3*c*d^5*e + 5*b^4*d^4*e^2 + (16*b^2*c^2*d^2*e^4 - 16*b^3*c*d*e^5 + 5*b^4*e^6)*x^4 + 4*(16*b^2*c^2*d^3*e^3 - 16*b^3*c*d^2*e^4 + 5*b^4*d*e^5)*x^3 + 6*(16*b^2*c^2*d^4*e^2 - 16*b^3*c*d^3*e^3 + 5*b^4*d^2*e^4)*x^2 + 4*(16*b^2*c^2*d^5*e - 16*b^3*c*d^4*e^2 + 5*b^4*d^3*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (48*b*c^3*d^7 - 96*b^2*c^2*d^6*e + 63*b^3*c*d^5*e^2 - 15*b^4*d^4*e^3 + (16*c^4*d^5*e^2 - 40*b*c^3*d^4*e^3 + 62*b^2*c^2*d^3*e^4 - 53*b^3*c*d^2*e^5 + 15*b^4*d*e^6)*x^3 + (64*c^4*d^6*e - 168*b*c^3*d^5*e^2 + 244*b^2*c^2*d^4*e^3 - 195*b^3*c*d^3*e^4 + 55*b^4*d^2*e^5)*x^2 + (96*c^4*d^7 - 272*b*c^3*d^6*e + 374*b^2*c^2*d^5*e^2 - 271*b^3*c*d^4*e^3 + 73*b^4*d^3*e^4)*x)*sqrt(c*x^2 + b*x))/(c^4*d^12 - 4*b*c^3*d^11*e + 6*b^2*c^2*d^10*e^2 - 4*b^3*c*d^9*e^3 + b^4*d^8*e^4 + (c^4*d^8*e^4 - 4*b*c^3*d^7*e^5 + 6*b^2*c^2*d^6*e^6 - 4*b^3*c*d^5*e^7 + b^4*d^4*e^8)*x^4 + 4*(c^4*d^9*e^3 - 4*b*c^3*d^8*e^4 + 6*b^2*c^2*d^7*e^5 - 4*b^3*c*d^6*e^6 + b^4*d^5*e^7)*x^3 + 6*(c^4*d^10*e^2 - 4*b*c^3*d^9*e^3 + 6*b^2*c^2*d^8*e^4 - 4*b^3*c*d^7*e^5 + b^4*d^6*e^6)*x^2 + 4*(c^4*d^11*e - 4*b*c^3*d^10*e^2 + 6*b^2*c^2*d^9*e^3 - 4*b^3*c*d^8*e^4 + b^4*d^7*e^5)*x)]","B",0
294,1,2449,0,0.466202," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(32 \, b^{2} c^{3} d^{8} - 48 \, b^{3} c^{2} d^{7} e + 30 \, b^{4} c d^{6} e^{2} - 7 \, b^{5} d^{5} e^{3} + {\left(32 \, b^{2} c^{3} d^{3} e^{5} - 48 \, b^{3} c^{2} d^{2} e^{6} + 30 \, b^{4} c d e^{7} - 7 \, b^{5} e^{8}\right)} x^{5} + 5 \, {\left(32 \, b^{2} c^{3} d^{4} e^{4} - 48 \, b^{3} c^{2} d^{3} e^{5} + 30 \, b^{4} c d^{2} e^{6} - 7 \, b^{5} d e^{7}\right)} x^{4} + 10 \, {\left(32 \, b^{2} c^{3} d^{5} e^{3} - 48 \, b^{3} c^{2} d^{4} e^{4} + 30 \, b^{4} c d^{3} e^{5} - 7 \, b^{5} d^{2} e^{6}\right)} x^{3} + 10 \, {\left(32 \, b^{2} c^{3} d^{6} e^{2} - 48 \, b^{3} c^{2} d^{5} e^{3} + 30 \, b^{4} c d^{4} e^{4} - 7 \, b^{5} d^{3} e^{5}\right)} x^{2} + 5 \, {\left(32 \, b^{2} c^{3} d^{7} e - 48 \, b^{3} c^{2} d^{6} e^{2} + 30 \, b^{4} c d^{5} e^{3} - 7 \, b^{5} d^{4} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(480 \, b c^{4} d^{9} - 1200 \, b^{2} c^{3} d^{8} e + 1170 \, b^{3} c^{2} d^{7} e^{2} - 555 \, b^{4} c d^{6} e^{3} + 105 \, b^{5} d^{5} e^{4} + {\left(96 \, c^{5} d^{6} e^{3} - 288 \, b c^{4} d^{5} e^{4} + 668 \, b^{2} c^{3} d^{4} e^{5} - 856 \, b^{3} c^{2} d^{3} e^{6} + 485 \, b^{4} c d^{2} e^{7} - 105 \, b^{5} d e^{8}\right)} x^{4} + 2 \, {\left(240 \, c^{5} d^{7} e^{2} - 744 \, b c^{4} d^{6} e^{3} + 1622 \, b^{2} c^{3} d^{5} e^{4} - 2007 \, b^{3} c^{2} d^{4} e^{5} + 1134 \, b^{4} c d^{3} e^{6} - 245 \, b^{5} d^{2} e^{7}\right)} x^{3} + 2 \, {\left(480 \, c^{5} d^{8} e - 1560 \, b c^{4} d^{7} e^{2} + 3178 \, b^{2} c^{3} d^{6} e^{3} - 3729 \, b^{3} c^{2} d^{5} e^{4} + 2079 \, b^{4} c d^{4} e^{5} - 448 \, b^{5} d^{3} e^{6}\right)} x^{2} + 10 \, {\left(96 \, c^{5} d^{9} - 336 \, b c^{4} d^{8} e + 642 \, b^{2} c^{3} d^{7} e^{2} - 697 \, b^{3} c^{2} d^{6} e^{3} + 374 \, b^{4} c d^{5} e^{4} - 79 \, b^{5} d^{4} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, {\left(c^{5} d^{15} - 5 \, b c^{4} d^{14} e + 10 \, b^{2} c^{3} d^{13} e^{2} - 10 \, b^{3} c^{2} d^{12} e^{3} + 5 \, b^{4} c d^{11} e^{4} - b^{5} d^{10} e^{5} + {\left(c^{5} d^{10} e^{5} - 5 \, b c^{4} d^{9} e^{6} + 10 \, b^{2} c^{3} d^{8} e^{7} - 10 \, b^{3} c^{2} d^{7} e^{8} + 5 \, b^{4} c d^{6} e^{9} - b^{5} d^{5} e^{10}\right)} x^{5} + 5 \, {\left(c^{5} d^{11} e^{4} - 5 \, b c^{4} d^{10} e^{5} + 10 \, b^{2} c^{3} d^{9} e^{6} - 10 \, b^{3} c^{2} d^{8} e^{7} + 5 \, b^{4} c d^{7} e^{8} - b^{5} d^{6} e^{9}\right)} x^{4} + 10 \, {\left(c^{5} d^{12} e^{3} - 5 \, b c^{4} d^{11} e^{4} + 10 \, b^{2} c^{3} d^{10} e^{5} - 10 \, b^{3} c^{2} d^{9} e^{6} + 5 \, b^{4} c d^{8} e^{7} - b^{5} d^{7} e^{8}\right)} x^{3} + 10 \, {\left(c^{5} d^{13} e^{2} - 5 \, b c^{4} d^{12} e^{3} + 10 \, b^{2} c^{3} d^{11} e^{4} - 10 \, b^{3} c^{2} d^{10} e^{5} + 5 \, b^{4} c d^{9} e^{6} - b^{5} d^{8} e^{7}\right)} x^{2} + 5 \, {\left(c^{5} d^{14} e - 5 \, b c^{4} d^{13} e^{2} + 10 \, b^{2} c^{3} d^{12} e^{3} - 10 \, b^{3} c^{2} d^{11} e^{4} + 5 \, b^{4} c d^{10} e^{5} - b^{5} d^{9} e^{6}\right)} x\right)}}, -\frac{15 \, {\left(32 \, b^{2} c^{3} d^{8} - 48 \, b^{3} c^{2} d^{7} e + 30 \, b^{4} c d^{6} e^{2} - 7 \, b^{5} d^{5} e^{3} + {\left(32 \, b^{2} c^{3} d^{3} e^{5} - 48 \, b^{3} c^{2} d^{2} e^{6} + 30 \, b^{4} c d e^{7} - 7 \, b^{5} e^{8}\right)} x^{5} + 5 \, {\left(32 \, b^{2} c^{3} d^{4} e^{4} - 48 \, b^{3} c^{2} d^{3} e^{5} + 30 \, b^{4} c d^{2} e^{6} - 7 \, b^{5} d e^{7}\right)} x^{4} + 10 \, {\left(32 \, b^{2} c^{3} d^{5} e^{3} - 48 \, b^{3} c^{2} d^{4} e^{4} + 30 \, b^{4} c d^{3} e^{5} - 7 \, b^{5} d^{2} e^{6}\right)} x^{3} + 10 \, {\left(32 \, b^{2} c^{3} d^{6} e^{2} - 48 \, b^{3} c^{2} d^{5} e^{3} + 30 \, b^{4} c d^{4} e^{4} - 7 \, b^{5} d^{3} e^{5}\right)} x^{2} + 5 \, {\left(32 \, b^{2} c^{3} d^{7} e - 48 \, b^{3} c^{2} d^{6} e^{2} + 30 \, b^{4} c d^{5} e^{3} - 7 \, b^{5} d^{4} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(480 \, b c^{4} d^{9} - 1200 \, b^{2} c^{3} d^{8} e + 1170 \, b^{3} c^{2} d^{7} e^{2} - 555 \, b^{4} c d^{6} e^{3} + 105 \, b^{5} d^{5} e^{4} + {\left(96 \, c^{5} d^{6} e^{3} - 288 \, b c^{4} d^{5} e^{4} + 668 \, b^{2} c^{3} d^{4} e^{5} - 856 \, b^{3} c^{2} d^{3} e^{6} + 485 \, b^{4} c d^{2} e^{7} - 105 \, b^{5} d e^{8}\right)} x^{4} + 2 \, {\left(240 \, c^{5} d^{7} e^{2} - 744 \, b c^{4} d^{6} e^{3} + 1622 \, b^{2} c^{3} d^{5} e^{4} - 2007 \, b^{3} c^{2} d^{4} e^{5} + 1134 \, b^{4} c d^{3} e^{6} - 245 \, b^{5} d^{2} e^{7}\right)} x^{3} + 2 \, {\left(480 \, c^{5} d^{8} e - 1560 \, b c^{4} d^{7} e^{2} + 3178 \, b^{2} c^{3} d^{6} e^{3} - 3729 \, b^{3} c^{2} d^{5} e^{4} + 2079 \, b^{4} c d^{4} e^{5} - 448 \, b^{5} d^{3} e^{6}\right)} x^{2} + 10 \, {\left(96 \, c^{5} d^{9} - 336 \, b c^{4} d^{8} e + 642 \, b^{2} c^{3} d^{7} e^{2} - 697 \, b^{3} c^{2} d^{6} e^{3} + 374 \, b^{4} c d^{5} e^{4} - 79 \, b^{5} d^{4} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, {\left(c^{5} d^{15} - 5 \, b c^{4} d^{14} e + 10 \, b^{2} c^{3} d^{13} e^{2} - 10 \, b^{3} c^{2} d^{12} e^{3} + 5 \, b^{4} c d^{11} e^{4} - b^{5} d^{10} e^{5} + {\left(c^{5} d^{10} e^{5} - 5 \, b c^{4} d^{9} e^{6} + 10 \, b^{2} c^{3} d^{8} e^{7} - 10 \, b^{3} c^{2} d^{7} e^{8} + 5 \, b^{4} c d^{6} e^{9} - b^{5} d^{5} e^{10}\right)} x^{5} + 5 \, {\left(c^{5} d^{11} e^{4} - 5 \, b c^{4} d^{10} e^{5} + 10 \, b^{2} c^{3} d^{9} e^{6} - 10 \, b^{3} c^{2} d^{8} e^{7} + 5 \, b^{4} c d^{7} e^{8} - b^{5} d^{6} e^{9}\right)} x^{4} + 10 \, {\left(c^{5} d^{12} e^{3} - 5 \, b c^{4} d^{11} e^{4} + 10 \, b^{2} c^{3} d^{10} e^{5} - 10 \, b^{3} c^{2} d^{9} e^{6} + 5 \, b^{4} c d^{8} e^{7} - b^{5} d^{7} e^{8}\right)} x^{3} + 10 \, {\left(c^{5} d^{13} e^{2} - 5 \, b c^{4} d^{12} e^{3} + 10 \, b^{2} c^{3} d^{11} e^{4} - 10 \, b^{3} c^{2} d^{10} e^{5} + 5 \, b^{4} c d^{9} e^{6} - b^{5} d^{8} e^{7}\right)} x^{2} + 5 \, {\left(c^{5} d^{14} e - 5 \, b c^{4} d^{13} e^{2} + 10 \, b^{2} c^{3} d^{12} e^{3} - 10 \, b^{3} c^{2} d^{11} e^{4} + 5 \, b^{4} c d^{10} e^{5} - b^{5} d^{9} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/3840*(15*(32*b^2*c^3*d^8 - 48*b^3*c^2*d^7*e + 30*b^4*c*d^6*e^2 - 7*b^5*d^5*e^3 + (32*b^2*c^3*d^3*e^5 - 48*b^3*c^2*d^2*e^6 + 30*b^4*c*d*e^7 - 7*b^5*e^8)*x^5 + 5*(32*b^2*c^3*d^4*e^4 - 48*b^3*c^2*d^3*e^5 + 30*b^4*c*d^2*e^6 - 7*b^5*d*e^7)*x^4 + 10*(32*b^2*c^3*d^5*e^3 - 48*b^3*c^2*d^4*e^4 + 30*b^4*c*d^3*e^5 - 7*b^5*d^2*e^6)*x^3 + 10*(32*b^2*c^3*d^6*e^2 - 48*b^3*c^2*d^5*e^3 + 30*b^4*c*d^4*e^4 - 7*b^5*d^3*e^5)*x^2 + 5*(32*b^2*c^3*d^7*e - 48*b^3*c^2*d^6*e^2 + 30*b^4*c*d^5*e^3 - 7*b^5*d^4*e^4)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(480*b*c^4*d^9 - 1200*b^2*c^3*d^8*e + 1170*b^3*c^2*d^7*e^2 - 555*b^4*c*d^6*e^3 + 105*b^5*d^5*e^4 + (96*c^5*d^6*e^3 - 288*b*c^4*d^5*e^4 + 668*b^2*c^3*d^4*e^5 - 856*b^3*c^2*d^3*e^6 + 485*b^4*c*d^2*e^7 - 105*b^5*d*e^8)*x^4 + 2*(240*c^5*d^7*e^2 - 744*b*c^4*d^6*e^3 + 1622*b^2*c^3*d^5*e^4 - 2007*b^3*c^2*d^4*e^5 + 1134*b^4*c*d^3*e^6 - 245*b^5*d^2*e^7)*x^3 + 2*(480*c^5*d^8*e - 1560*b*c^4*d^7*e^2 + 3178*b^2*c^3*d^6*e^3 - 3729*b^3*c^2*d^5*e^4 + 2079*b^4*c*d^4*e^5 - 448*b^5*d^3*e^6)*x^2 + 10*(96*c^5*d^9 - 336*b*c^4*d^8*e + 642*b^2*c^3*d^7*e^2 - 697*b^3*c^2*d^6*e^3 + 374*b^4*c*d^5*e^4 - 79*b^5*d^4*e^5)*x)*sqrt(c*x^2 + b*x))/(c^5*d^15 - 5*b*c^4*d^14*e + 10*b^2*c^3*d^13*e^2 - 10*b^3*c^2*d^12*e^3 + 5*b^4*c*d^11*e^4 - b^5*d^10*e^5 + (c^5*d^10*e^5 - 5*b*c^4*d^9*e^6 + 10*b^2*c^3*d^8*e^7 - 10*b^3*c^2*d^7*e^8 + 5*b^4*c*d^6*e^9 - b^5*d^5*e^10)*x^5 + 5*(c^5*d^11*e^4 - 5*b*c^4*d^10*e^5 + 10*b^2*c^3*d^9*e^6 - 10*b^3*c^2*d^8*e^7 + 5*b^4*c*d^7*e^8 - b^5*d^6*e^9)*x^4 + 10*(c^5*d^12*e^3 - 5*b*c^4*d^11*e^4 + 10*b^2*c^3*d^10*e^5 - 10*b^3*c^2*d^9*e^6 + 5*b^4*c*d^8*e^7 - b^5*d^7*e^8)*x^3 + 10*(c^5*d^13*e^2 - 5*b*c^4*d^12*e^3 + 10*b^2*c^3*d^11*e^4 - 10*b^3*c^2*d^10*e^5 + 5*b^4*c*d^9*e^6 - b^5*d^8*e^7)*x^2 + 5*(c^5*d^14*e - 5*b*c^4*d^13*e^2 + 10*b^2*c^3*d^12*e^3 - 10*b^3*c^2*d^11*e^4 + 5*b^4*c*d^10*e^5 - b^5*d^9*e^6)*x), -1/1920*(15*(32*b^2*c^3*d^8 - 48*b^3*c^2*d^7*e + 30*b^4*c*d^6*e^2 - 7*b^5*d^5*e^3 + (32*b^2*c^3*d^3*e^5 - 48*b^3*c^2*d^2*e^6 + 30*b^4*c*d*e^7 - 7*b^5*e^8)*x^5 + 5*(32*b^2*c^3*d^4*e^4 - 48*b^3*c^2*d^3*e^5 + 30*b^4*c*d^2*e^6 - 7*b^5*d*e^7)*x^4 + 10*(32*b^2*c^3*d^5*e^3 - 48*b^3*c^2*d^4*e^4 + 30*b^4*c*d^3*e^5 - 7*b^5*d^2*e^6)*x^3 + 10*(32*b^2*c^3*d^6*e^2 - 48*b^3*c^2*d^5*e^3 + 30*b^4*c*d^4*e^4 - 7*b^5*d^3*e^5)*x^2 + 5*(32*b^2*c^3*d^7*e - 48*b^3*c^2*d^6*e^2 + 30*b^4*c*d^5*e^3 - 7*b^5*d^4*e^4)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (480*b*c^4*d^9 - 1200*b^2*c^3*d^8*e + 1170*b^3*c^2*d^7*e^2 - 555*b^4*c*d^6*e^3 + 105*b^5*d^5*e^4 + (96*c^5*d^6*e^3 - 288*b*c^4*d^5*e^4 + 668*b^2*c^3*d^4*e^5 - 856*b^3*c^2*d^3*e^6 + 485*b^4*c*d^2*e^7 - 105*b^5*d*e^8)*x^4 + 2*(240*c^5*d^7*e^2 - 744*b*c^4*d^6*e^3 + 1622*b^2*c^3*d^5*e^4 - 2007*b^3*c^2*d^4*e^5 + 1134*b^4*c*d^3*e^6 - 245*b^5*d^2*e^7)*x^3 + 2*(480*c^5*d^8*e - 1560*b*c^4*d^7*e^2 + 3178*b^2*c^3*d^6*e^3 - 3729*b^3*c^2*d^5*e^4 + 2079*b^4*c*d^4*e^5 - 448*b^5*d^3*e^6)*x^2 + 10*(96*c^5*d^9 - 336*b*c^4*d^8*e + 642*b^2*c^3*d^7*e^2 - 697*b^3*c^2*d^6*e^3 + 374*b^4*c*d^5*e^4 - 79*b^5*d^4*e^5)*x)*sqrt(c*x^2 + b*x))/(c^5*d^15 - 5*b*c^4*d^14*e + 10*b^2*c^3*d^13*e^2 - 10*b^3*c^2*d^12*e^3 + 5*b^4*c*d^11*e^4 - b^5*d^10*e^5 + (c^5*d^10*e^5 - 5*b*c^4*d^9*e^6 + 10*b^2*c^3*d^8*e^7 - 10*b^3*c^2*d^7*e^8 + 5*b^4*c*d^6*e^9 - b^5*d^5*e^10)*x^5 + 5*(c^5*d^11*e^4 - 5*b*c^4*d^10*e^5 + 10*b^2*c^3*d^9*e^6 - 10*b^3*c^2*d^8*e^7 + 5*b^4*c*d^7*e^8 - b^5*d^6*e^9)*x^4 + 10*(c^5*d^12*e^3 - 5*b*c^4*d^11*e^4 + 10*b^2*c^3*d^10*e^5 - 10*b^3*c^2*d^9*e^6 + 5*b^4*c*d^8*e^7 - b^5*d^7*e^8)*x^3 + 10*(c^5*d^13*e^2 - 5*b*c^4*d^12*e^3 + 10*b^2*c^3*d^11*e^4 - 10*b^3*c^2*d^10*e^5 + 5*b^4*c*d^9*e^6 - b^5*d^8*e^7)*x^2 + 5*(c^5*d^14*e - 5*b*c^4*d^13*e^2 + 10*b^2*c^3*d^12*e^3 - 10*b^3*c^2*d^11*e^4 + 5*b^4*c*d^10*e^5 - b^5*d^9*e^6)*x)]","B",0
295,1,706,0,0.447059," ","integrate((e*x+d)^3*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\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)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(5120 \, c^{7} e^{3} x^{6} - 1680 \, b^{3} c^{4} d^{3} + 2520 \, b^{4} c^{3} d^{2} e - 1470 \, b^{5} c^{2} d e^{2} + 315 \, b^{6} c e^{3} + 1280 \, {\left(14 \, c^{7} d e^{2} + 5 \, b c^{6} e^{3}\right)} x^{5} + 128 \, {\left(168 \, c^{7} d^{2} e + 182 \, b c^{6} d e^{2} + b^{2} c^{5} e^{3}\right)} x^{4} + 16 \, {\left(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}\right)} x^{3} + 56 \, {\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)} x^{2} + 70 \, {\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)} x\right)} \sqrt{c x^{2} + b x}}{71680 \, c^{6}}, -\frac{105 \, {\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)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(5120 \, c^{7} e^{3} x^{6} - 1680 \, b^{3} c^{4} d^{3} + 2520 \, b^{4} c^{3} d^{2} e - 1470 \, b^{5} c^{2} d e^{2} + 315 \, b^{6} c e^{3} + 1280 \, {\left(14 \, c^{7} d e^{2} + 5 \, b c^{6} e^{3}\right)} x^{5} + 128 \, {\left(168 \, c^{7} d^{2} e + 182 \, b c^{6} d e^{2} + b^{2} c^{5} e^{3}\right)} x^{4} + 16 \, {\left(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}\right)} x^{3} + 56 \, {\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)} x^{2} + 70 \, {\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)} x\right)} \sqrt{c x^{2} + b x}}{35840 \, c^{6}}\right]"," ",0,"[-1/71680*(105*(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)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(5120*c^7*e^3*x^6 - 1680*b^3*c^4*d^3 + 2520*b^4*c^3*d^2*e - 1470*b^5*c^2*d*e^2 + 315*b^6*c*e^3 + 1280*(14*c^7*d*e^2 + 5*b*c^6*e^3)*x^5 + 128*(168*c^7*d^2*e + 182*b*c^6*d*e^2 + b^2*c^5*e^3)*x^4 + 16*(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)*x^3 + 56*(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)*x^2 + 70*(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)*x)*sqrt(c*x^2 + b*x))/c^6, -1/35840*(105*(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)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (5120*c^7*e^3*x^6 - 1680*b^3*c^4*d^3 + 2520*b^4*c^3*d^2*e - 1470*b^5*c^2*d*e^2 + 315*b^6*c*e^3 + 1280*(14*c^7*d*e^2 + 5*b*c^6*e^3)*x^5 + 128*(168*c^7*d^2*e + 182*b*c^6*d*e^2 + b^2*c^5*e^3)*x^4 + 16*(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)*x^3 + 56*(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)*x^2 + 70*(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)*x)*sqrt(c*x^2 + b*x))/c^6]","A",0
296,1,490,0,0.428960," ","integrate((e*x+d)^2*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(24 \, b^{4} c^{2} d^{2} - 24 \, b^{5} c d e + 7 \, b^{6} e^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(1280 \, c^{6} e^{2} x^{5} - 360 \, b^{3} c^{3} d^{2} + 360 \, b^{4} c^{2} d e - 105 \, b^{5} c e^{2} + 128 \, {\left(24 \, c^{6} d e + 13 \, b c^{5} e^{2}\right)} x^{4} + 48 \, {\left(40 \, c^{6} d^{2} + 88 \, b c^{5} d e + b^{2} c^{4} e^{2}\right)} x^{3} + 8 \, {\left(360 \, b c^{5} d^{2} + 24 \, b^{2} c^{4} d e - 7 \, b^{3} c^{3} e^{2}\right)} x^{2} + 10 \, {\left(24 \, b^{2} c^{4} d^{2} - 24 \, b^{3} c^{3} d e + 7 \, b^{4} c^{2} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{15360 \, c^{5}}, -\frac{15 \, {\left(24 \, b^{4} c^{2} d^{2} - 24 \, b^{5} c d e + 7 \, b^{6} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(1280 \, c^{6} e^{2} x^{5} - 360 \, b^{3} c^{3} d^{2} + 360 \, b^{4} c^{2} d e - 105 \, b^{5} c e^{2} + 128 \, {\left(24 \, c^{6} d e + 13 \, b c^{5} e^{2}\right)} x^{4} + 48 \, {\left(40 \, c^{6} d^{2} + 88 \, b c^{5} d e + b^{2} c^{4} e^{2}\right)} x^{3} + 8 \, {\left(360 \, b c^{5} d^{2} + 24 \, b^{2} c^{4} d e - 7 \, b^{3} c^{3} e^{2}\right)} x^{2} + 10 \, {\left(24 \, b^{2} c^{4} d^{2} - 24 \, b^{3} c^{3} d e + 7 \, b^{4} c^{2} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{7680 \, c^{5}}\right]"," ",0,"[1/15360*(15*(24*b^4*c^2*d^2 - 24*b^5*c*d*e + 7*b^6*e^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(1280*c^6*e^2*x^5 - 360*b^3*c^3*d^2 + 360*b^4*c^2*d*e - 105*b^5*c*e^2 + 128*(24*c^6*d*e + 13*b*c^5*e^2)*x^4 + 48*(40*c^6*d^2 + 88*b*c^5*d*e + b^2*c^4*e^2)*x^3 + 8*(360*b*c^5*d^2 + 24*b^2*c^4*d*e - 7*b^3*c^3*e^2)*x^2 + 10*(24*b^2*c^4*d^2 - 24*b^3*c^3*d*e + 7*b^4*c^2*e^2)*x)*sqrt(c*x^2 + b*x))/c^5, -1/7680*(15*(24*b^4*c^2*d^2 - 24*b^5*c*d*e + 7*b^6*e^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (1280*c^6*e^2*x^5 - 360*b^3*c^3*d^2 + 360*b^4*c^2*d*e - 105*b^5*c*e^2 + 128*(24*c^6*d*e + 13*b*c^5*e^2)*x^4 + 48*(40*c^6*d^2 + 88*b*c^5*d*e + b^2*c^4*e^2)*x^3 + 8*(360*b*c^5*d^2 + 24*b^2*c^4*d*e - 7*b^3*c^3*e^2)*x^2 + 10*(24*b^2*c^4*d^2 - 24*b^3*c^3*d*e + 7*b^4*c^2*e^2)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
297,1,302,0,0.429080," ","integrate((e*x+d)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, b^{4} c d - b^{5} e\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(128 \, c^{5} e x^{4} - 30 \, b^{3} c^{2} d + 15 \, b^{4} c e + 16 \, {\left(10 \, c^{5} d + 11 \, b c^{4} e\right)} x^{3} + 8 \, {\left(30 \, b c^{4} d + b^{2} c^{3} e\right)} x^{2} + 10 \, {\left(2 \, b^{2} c^{3} d - b^{3} c^{2} e\right)} x\right)} \sqrt{c x^{2} + b x}}{1280 \, c^{4}}, -\frac{15 \, {\left(2 \, b^{4} c d - b^{5} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(128 \, c^{5} e x^{4} - 30 \, b^{3} c^{2} d + 15 \, b^{4} c e + 16 \, {\left(10 \, c^{5} d + 11 \, b c^{4} e\right)} x^{3} + 8 \, {\left(30 \, b c^{4} d + b^{2} c^{3} e\right)} x^{2} + 10 \, {\left(2 \, b^{2} c^{3} d - b^{3} c^{2} e\right)} x\right)} \sqrt{c x^{2} + b x}}{640 \, c^{4}}\right]"," ",0,"[-1/1280*(15*(2*b^4*c*d - b^5*e)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(128*c^5*e*x^4 - 30*b^3*c^2*d + 15*b^4*c*e + 16*(10*c^5*d + 11*b*c^4*e)*x^3 + 8*(30*b*c^4*d + b^2*c^3*e)*x^2 + 10*(2*b^2*c^3*d - b^3*c^2*e)*x)*sqrt(c*x^2 + b*x))/c^4, -1/640*(15*(2*b^4*c*d - b^5*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (128*c^5*e*x^4 - 30*b^3*c^2*d + 15*b^4*c*e + 16*(10*c^5*d + 11*b*c^4*e)*x^3 + 8*(30*b*c^4*d + b^2*c^3*e)*x^2 + 10*(2*b^2*c^3*d - b^3*c^2*e)*x)*sqrt(c*x^2 + b*x))/c^4]","A",0
298,1,170,0,0.418672," ","integrate((c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, b^{4} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(16 \, c^{4} x^{3} + 24 \, b c^{3} x^{2} + 2 \, b^{2} c^{2} x - 3 \, b^{3} c\right)} \sqrt{c x^{2} + b x}}{128 \, c^{3}}, -\frac{3 \, b^{4} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(16 \, c^{4} x^{3} + 24 \, b c^{3} x^{2} + 2 \, b^{2} c^{2} x - 3 \, b^{3} c\right)} \sqrt{c x^{2} + b x}}{64 \, c^{3}}\right]"," ",0,"[1/128*(3*b^4*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(16*c^4*x^3 + 24*b*c^3*x^2 + 2*b^2*c^2*x - 3*b^3*c)*sqrt(c*x^2 + b*x))/c^3, -1/64*(3*b^4*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (16*c^4*x^3 + 24*b*c^3*x^2 + 2*b^2*c^2*x - 3*b^3*c)*sqrt(c*x^2 + b*x))/c^3]","A",0
299,1,901,0,0.792080," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{3 \, {\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)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 48 \, {\left(c^{3} d^{2} - b c^{2} d e\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(8 \, c^{3} e^{3} x^{2} + 24 \, c^{3} d^{2} e - 30 \, b c^{2} d e^{2} + 3 \, b^{2} c e^{3} - 2 \, {\left(6 \, c^{3} d e^{2} - 7 \, b c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, c^{2} e^{4}}, \frac{96 \, {\left(c^{3} d^{2} - b c^{2} d e\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 3 \, {\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)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(8 \, c^{3} e^{3} x^{2} + 24 \, c^{3} d^{2} e - 30 \, b c^{2} d e^{2} + 3 \, b^{2} c e^{3} - 2 \, {\left(6 \, c^{3} d e^{2} - 7 \, b c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, c^{2} e^{4}}, \frac{3 \, {\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)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - 24 \, {\left(c^{3} d^{2} - b c^{2} d e\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + {\left(8 \, c^{3} e^{3} x^{2} + 24 \, c^{3} d^{2} e - 30 \, b c^{2} d e^{2} + 3 \, b^{2} c e^{3} - 2 \, {\left(6 \, c^{3} d e^{2} - 7 \, b c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, c^{2} e^{4}}, \frac{48 \, {\left(c^{3} d^{2} - b c^{2} d e\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 3 \, {\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)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, c^{3} e^{3} x^{2} + 24 \, c^{3} d^{2} e - 30 \, b c^{2} d e^{2} + 3 \, b^{2} c e^{3} - 2 \, {\left(6 \, c^{3} d e^{2} - 7 \, b c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, c^{2} e^{4}}\right]"," ",0,"[1/48*(3*(16*c^3*d^3 - 24*b*c^2*d^2*e + 6*b^2*c*d*e^2 + b^3*e^3)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 48*(c^3*d^2 - b*c^2*d*e)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(8*c^3*e^3*x^2 + 24*c^3*d^2*e - 30*b*c^2*d*e^2 + 3*b^2*c*e^3 - 2*(6*c^3*d*e^2 - 7*b*c^2*e^3)*x)*sqrt(c*x^2 + b*x))/(c^2*e^4), 1/48*(96*(c^3*d^2 - b*c^2*d*e)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 3*(16*c^3*d^3 - 24*b*c^2*d^2*e + 6*b^2*c*d*e^2 + b^3*e^3)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(8*c^3*e^3*x^2 + 24*c^3*d^2*e - 30*b*c^2*d*e^2 + 3*b^2*c*e^3 - 2*(6*c^3*d*e^2 - 7*b*c^2*e^3)*x)*sqrt(c*x^2 + b*x))/(c^2*e^4), 1/24*(3*(16*c^3*d^3 - 24*b*c^2*d^2*e + 6*b^2*c*d*e^2 + b^3*e^3)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - 24*(c^3*d^2 - b*c^2*d*e)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + (8*c^3*e^3*x^2 + 24*c^3*d^2*e - 30*b*c^2*d*e^2 + 3*b^2*c*e^3 - 2*(6*c^3*d*e^2 - 7*b*c^2*e^3)*x)*sqrt(c*x^2 + b*x))/(c^2*e^4), 1/24*(48*(c^3*d^2 - b*c^2*d*e)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 3*(16*c^3*d^3 - 24*b*c^2*d^2*e + 6*b^2*c*d*e^2 + b^3*e^3)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*c^3*e^3*x^2 + 24*c^3*d^2*e - 30*b*c^2*d*e^2 + 3*b^2*c*e^3 - 2*(6*c^3*d*e^2 - 7*b*c^2*e^3)*x)*sqrt(c*x^2 + b*x))/(c^2*e^4)]","A",0
300,1,1015,0,0.506249," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + b^{2} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + b^{2} e^{3}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 12 \, {\left(2 \, c^{2} d^{2} - b c d e + {\left(2 \, c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(2 \, c^{2} e^{3} x^{2} - 12 \, c^{2} d^{2} e + 9 \, b c d e^{2} - {\left(6 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c e^{5} x + c d e^{4}\right)}}, -\frac{24 \, {\left(2 \, c^{2} d^{2} - b c d e + {\left(2 \, c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 3 \, {\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + b^{2} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + b^{2} e^{3}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(2 \, c^{2} e^{3} x^{2} - 12 \, c^{2} d^{2} e + 9 \, b c d e^{2} - {\left(6 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c e^{5} x + c d e^{4}\right)}}, -\frac{3 \, {\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + b^{2} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + b^{2} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + 6 \, {\left(2 \, c^{2} d^{2} - b c d e + {\left(2 \, c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - {\left(2 \, c^{2} e^{3} x^{2} - 12 \, c^{2} d^{2} e + 9 \, b c d e^{2} - {\left(6 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c e^{5} x + c d e^{4}\right)}}, -\frac{12 \, {\left(2 \, c^{2} d^{2} - b c d e + {\left(2 \, c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 3 \, {\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + b^{2} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + b^{2} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(2 \, c^{2} e^{3} x^{2} - 12 \, c^{2} d^{2} e + 9 \, b c d e^{2} - {\left(6 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c e^{5} x + c d e^{4}\right)}}\right]"," ",0,"[1/8*(3*(8*c^2*d^3 - 8*b*c*d^2*e + b^2*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + b^2*e^3)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 12*(2*c^2*d^2 - b*c*d*e + (2*c^2*d*e - b*c*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(2*c^2*e^3*x^2 - 12*c^2*d^2*e + 9*b*c*d*e^2 - (6*c^2*d*e^2 - 5*b*c*e^3)*x)*sqrt(c*x^2 + b*x))/(c*e^5*x + c*d*e^4), -1/8*(24*(2*c^2*d^2 - b*c*d*e + (2*c^2*d*e - b*c*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 3*(8*c^2*d^3 - 8*b*c*d^2*e + b^2*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + b^2*e^3)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(2*c^2*e^3*x^2 - 12*c^2*d^2*e + 9*b*c*d*e^2 - (6*c^2*d*e^2 - 5*b*c*e^3)*x)*sqrt(c*x^2 + b*x))/(c*e^5*x + c*d*e^4), -1/4*(3*(8*c^2*d^3 - 8*b*c*d^2*e + b^2*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + b^2*e^3)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + 6*(2*c^2*d^2 - b*c*d*e + (2*c^2*d*e - b*c*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - (2*c^2*e^3*x^2 - 12*c^2*d^2*e + 9*b*c*d*e^2 - (6*c^2*d*e^2 - 5*b*c*e^3)*x)*sqrt(c*x^2 + b*x))/(c*e^5*x + c*d*e^4), -1/4*(12*(2*c^2*d^2 - b*c*d*e + (2*c^2*d*e - b*c*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 3*(8*c^2*d^3 - 8*b*c*d^2*e + b^2*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + b^2*e^3)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (2*c^2*e^3*x^2 - 12*c^2*d^2*e + 9*b*c*d*e^2 - (6*c^2*d*e^2 - 5*b*c*e^3)*x)*sqrt(c*x^2 + b*x))/(c*e^5*x + c*d*e^4)]","A",0
301,1,1749,0,0.524377," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(2 \, c^{2} d^{5} - 3 \, b c d^{4} e + b^{2} d^{3} e^{2} + {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} + b^{2} d e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{4} e - 3 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 3 \, {\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(12 \, c^{2} d^{4} e - 15 \, b c d^{3} e^{2} + 3 \, b^{2} d^{2} e^{3} + 4 \, {\left(c^{2} d^{2} e^{3} - b c d e^{4}\right)} x^{2} + {\left(18 \, c^{2} d^{3} e^{2} - 23 \, b c d^{2} e^{3} + 5 \, b^{2} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c d^{4} e^{4} - b d^{3} e^{5} + {\left(c d^{2} e^{6} - b d e^{7}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} - b d^{2} e^{6}\right)} x\right)}}, \frac{3 \, {\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 6 \, {\left(2 \, c^{2} d^{5} - 3 \, b c d^{4} e + b^{2} d^{3} e^{2} + {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} + b^{2} d e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{4} e - 3 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + {\left(12 \, c^{2} d^{4} e - 15 \, b c d^{3} e^{2} + 3 \, b^{2} d^{2} e^{3} + 4 \, {\left(c^{2} d^{2} e^{3} - b c d e^{4}\right)} x^{2} + {\left(18 \, c^{2} d^{3} e^{2} - 23 \, b c d^{2} e^{3} + 5 \, b^{2} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c d^{4} e^{4} - b d^{3} e^{5} + {\left(c d^{2} e^{6} - b d e^{7}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} - b d^{2} e^{6}\right)} x\right)}}, \frac{24 \, {\left(2 \, c^{2} d^{5} - 3 \, b c d^{4} e + b^{2} d^{3} e^{2} + {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} + b^{2} d e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{4} e - 3 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + 3 \, {\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(12 \, c^{2} d^{4} e - 15 \, b c d^{3} e^{2} + 3 \, b^{2} d^{2} e^{3} + 4 \, {\left(c^{2} d^{2} e^{3} - b c d e^{4}\right)} x^{2} + {\left(18 \, c^{2} d^{3} e^{2} - 23 \, b c d^{2} e^{3} + 5 \, b^{2} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c d^{4} e^{4} - b d^{3} e^{5} + {\left(c d^{2} e^{6} - b d e^{7}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} - b d^{2} e^{6}\right)} x\right)}}, \frac{3 \, {\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 12 \, {\left(2 \, c^{2} d^{5} - 3 \, b c d^{4} e + b^{2} d^{3} e^{2} + {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} + b^{2} d e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{4} e - 3 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(12 \, c^{2} d^{4} e - 15 \, b c d^{3} e^{2} + 3 \, b^{2} d^{2} e^{3} + 4 \, {\left(c^{2} d^{2} e^{3} - b c d e^{4}\right)} x^{2} + {\left(18 \, c^{2} d^{3} e^{2} - 23 \, b c d^{2} e^{3} + 5 \, b^{2} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c d^{4} e^{4} - b d^{3} e^{5} + {\left(c d^{2} e^{6} - b d e^{7}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} - b d^{2} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/8*(12*(2*c^2*d^5 - 3*b*c*d^4*e + b^2*d^3*e^2 + (2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 + b^2*d*e^4)*x^2 + 2*(2*c^2*d^4*e - 3*b*c*d^3*e^2 + b^2*d^2*e^3)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 3*(8*c^2*d^4 - 8*b*c*d^3*e + b^2*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + b^2*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(12*c^2*d^4*e - 15*b*c*d^3*e^2 + 3*b^2*d^2*e^3 + 4*(c^2*d^2*e^3 - b*c*d*e^4)*x^2 + (18*c^2*d^3*e^2 - 23*b*c*d^2*e^3 + 5*b^2*d*e^4)*x)*sqrt(c*x^2 + b*x))/(c*d^4*e^4 - b*d^3*e^5 + (c*d^2*e^6 - b*d*e^7)*x^2 + 2*(c*d^3*e^5 - b*d^2*e^6)*x), 1/4*(3*(8*c^2*d^4 - 8*b*c*d^3*e + b^2*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + b^2*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 6*(2*c^2*d^5 - 3*b*c*d^4*e + b^2*d^3*e^2 + (2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 + b^2*d*e^4)*x^2 + 2*(2*c^2*d^4*e - 3*b*c*d^3*e^2 + b^2*d^2*e^3)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + (12*c^2*d^4*e - 15*b*c*d^3*e^2 + 3*b^2*d^2*e^3 + 4*(c^2*d^2*e^3 - b*c*d*e^4)*x^2 + (18*c^2*d^3*e^2 - 23*b*c*d^2*e^3 + 5*b^2*d*e^4)*x)*sqrt(c*x^2 + b*x))/(c*d^4*e^4 - b*d^3*e^5 + (c*d^2*e^6 - b*d*e^7)*x^2 + 2*(c*d^3*e^5 - b*d^2*e^6)*x), 1/8*(24*(2*c^2*d^5 - 3*b*c*d^4*e + b^2*d^3*e^2 + (2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 + b^2*d*e^4)*x^2 + 2*(2*c^2*d^4*e - 3*b*c*d^3*e^2 + b^2*d^2*e^3)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + 3*(8*c^2*d^4 - 8*b*c*d^3*e + b^2*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + b^2*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(12*c^2*d^4*e - 15*b*c*d^3*e^2 + 3*b^2*d^2*e^3 + 4*(c^2*d^2*e^3 - b*c*d*e^4)*x^2 + (18*c^2*d^3*e^2 - 23*b*c*d^2*e^3 + 5*b^2*d*e^4)*x)*sqrt(c*x^2 + b*x))/(c*d^4*e^4 - b*d^3*e^5 + (c*d^2*e^6 - b*d*e^7)*x^2 + 2*(c*d^3*e^5 - b*d^2*e^6)*x), 1/4*(3*(8*c^2*d^4 - 8*b*c*d^3*e + b^2*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + b^2*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 12*(2*c^2*d^5 - 3*b*c*d^4*e + b^2*d^3*e^2 + (2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 + b^2*d*e^4)*x^2 + 2*(2*c^2*d^4*e - 3*b*c*d^3*e^2 + b^2*d^2*e^3)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (12*c^2*d^4*e - 15*b*c*d^3*e^2 + 3*b^2*d^2*e^3 + 4*(c^2*d^2*e^3 - b*c*d*e^4)*x^2 + (18*c^2*d^3*e^2 - 23*b*c*d^2*e^3 + 5*b^2*d*e^4)*x)*sqrt(c*x^2 + b*x))/(c*d^4*e^4 - b*d^3*e^5 + (c*d^2*e^6 - b*d*e^7)*x^2 + 2*(c*d^3*e^5 - b*d^2*e^6)*x)]","B",0
302,1,915,0,0.452219," ","integrate((e*x+d)^3*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\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)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(229376 \, c^{9} e^{3} x^{8} + 20160 \, b^{5} c^{4} d^{3} - 30240 \, b^{6} c^{3} d^{2} e + 17010 \, b^{7} c^{2} d e^{2} - 3465 \, b^{8} c e^{3} + 14336 \, {\left(54 \, c^{9} d e^{2} + 37 \, b c^{8} e^{3}\right)} x^{7} + 3072 \, {\left(288 \, c^{9} d^{2} e + 594 \, b c^{8} d e^{2} + 103 \, b^{2} c^{7} e^{3}\right)} x^{6} + 256 \, {\left(1344 \, c^{9} d^{3} + 8352 \, b c^{8} d^{2} e + 4374 \, b^{2} c^{7} d e^{2} + 5 \, b^{3} c^{6} e^{3}\right)} x^{5} + 128 \, {\left(6720 \, b c^{8} d^{3} + 10656 \, b^{2} c^{7} d^{2} e + 54 \, b^{3} c^{6} d e^{2} - 11 \, b^{4} c^{5} e^{3}\right)} x^{4} + 144 \, {\left(4032 \, b^{2} c^{7} d^{3} + 96 \, b^{3} c^{6} d^{2} e - 54 \, b^{4} c^{5} d e^{2} + 11 \, b^{5} c^{4} e^{3}\right)} x^{3} + 168 \, {\left(64 \, b^{3} c^{6} d^{3} - 96 \, b^{4} c^{5} d^{2} e + 54 \, b^{5} c^{4} d e^{2} - 11 \, b^{6} c^{3} e^{3}\right)} x^{2} - 210 \, {\left(64 \, b^{4} c^{5} d^{3} - 96 \, b^{5} c^{4} d^{2} e + 54 \, b^{6} c^{3} d e^{2} - 11 \, b^{7} c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{4128768 \, c^{7}}, \frac{315 \, {\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)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(229376 \, c^{9} e^{3} x^{8} + 20160 \, b^{5} c^{4} d^{3} - 30240 \, b^{6} c^{3} d^{2} e + 17010 \, b^{7} c^{2} d e^{2} - 3465 \, b^{8} c e^{3} + 14336 \, {\left(54 \, c^{9} d e^{2} + 37 \, b c^{8} e^{3}\right)} x^{7} + 3072 \, {\left(288 \, c^{9} d^{2} e + 594 \, b c^{8} d e^{2} + 103 \, b^{2} c^{7} e^{3}\right)} x^{6} + 256 \, {\left(1344 \, c^{9} d^{3} + 8352 \, b c^{8} d^{2} e + 4374 \, b^{2} c^{7} d e^{2} + 5 \, b^{3} c^{6} e^{3}\right)} x^{5} + 128 \, {\left(6720 \, b c^{8} d^{3} + 10656 \, b^{2} c^{7} d^{2} e + 54 \, b^{3} c^{6} d e^{2} - 11 \, b^{4} c^{5} e^{3}\right)} x^{4} + 144 \, {\left(4032 \, b^{2} c^{7} d^{3} + 96 \, b^{3} c^{6} d^{2} e - 54 \, b^{4} c^{5} d e^{2} + 11 \, b^{5} c^{4} e^{3}\right)} x^{3} + 168 \, {\left(64 \, b^{3} c^{6} d^{3} - 96 \, b^{4} c^{5} d^{2} e + 54 \, b^{5} c^{4} d e^{2} - 11 \, b^{6} c^{3} e^{3}\right)} x^{2} - 210 \, {\left(64 \, b^{4} c^{5} d^{3} - 96 \, b^{5} c^{4} d^{2} e + 54 \, b^{6} c^{3} d e^{2} - 11 \, b^{7} c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{2064384 \, c^{7}}\right]"," ",0,"[-1/4128768*(315*(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)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(229376*c^9*e^3*x^8 + 20160*b^5*c^4*d^3 - 30240*b^6*c^3*d^2*e + 17010*b^7*c^2*d*e^2 - 3465*b^8*c*e^3 + 14336*(54*c^9*d*e^2 + 37*b*c^8*e^3)*x^7 + 3072*(288*c^9*d^2*e + 594*b*c^8*d*e^2 + 103*b^2*c^7*e^3)*x^6 + 256*(1344*c^9*d^3 + 8352*b*c^8*d^2*e + 4374*b^2*c^7*d*e^2 + 5*b^3*c^6*e^3)*x^5 + 128*(6720*b*c^8*d^3 + 10656*b^2*c^7*d^2*e + 54*b^3*c^6*d*e^2 - 11*b^4*c^5*e^3)*x^4 + 144*(4032*b^2*c^7*d^3 + 96*b^3*c^6*d^2*e - 54*b^4*c^5*d*e^2 + 11*b^5*c^4*e^3)*x^3 + 168*(64*b^3*c^6*d^3 - 96*b^4*c^5*d^2*e + 54*b^5*c^4*d*e^2 - 11*b^6*c^3*e^3)*x^2 - 210*(64*b^4*c^5*d^3 - 96*b^5*c^4*d^2*e + 54*b^6*c^3*d*e^2 - 11*b^7*c^2*e^3)*x)*sqrt(c*x^2 + b*x))/c^7, 1/2064384*(315*(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)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (229376*c^9*e^3*x^8 + 20160*b^5*c^4*d^3 - 30240*b^6*c^3*d^2*e + 17010*b^7*c^2*d*e^2 - 3465*b^8*c*e^3 + 14336*(54*c^9*d*e^2 + 37*b*c^8*e^3)*x^7 + 3072*(288*c^9*d^2*e + 594*b*c^8*d*e^2 + 103*b^2*c^7*e^3)*x^6 + 256*(1344*c^9*d^3 + 8352*b*c^8*d^2*e + 4374*b^2*c^7*d*e^2 + 5*b^3*c^6*e^3)*x^5 + 128*(6720*b*c^8*d^3 + 10656*b^2*c^7*d^2*e + 54*b^3*c^6*d*e^2 - 11*b^4*c^5*e^3)*x^4 + 144*(4032*b^2*c^7*d^3 + 96*b^3*c^6*d^2*e - 54*b^4*c^5*d*e^2 + 11*b^5*c^4*e^3)*x^3 + 168*(64*b^3*c^6*d^3 - 96*b^4*c^5*d^2*e + 54*b^5*c^4*d*e^2 - 11*b^6*c^3*e^3)*x^2 - 210*(64*b^4*c^5*d^3 - 96*b^5*c^4*d^2*e + 54*b^6*c^3*d*e^2 - 11*b^7*c^2*e^3)*x)*sqrt(c*x^2 + b*x))/c^7]","A",0
303,1,643,0,0.433156," ","integrate((e*x+d)^2*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(32 \, b^{6} c^{2} d^{2} - 32 \, b^{7} c d e + 9 \, b^{8} e^{2}\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(43008 \, c^{8} e^{2} x^{7} + 3360 \, b^{5} c^{3} d^{2} - 3360 \, b^{6} c^{2} d e + 945 \, b^{7} c e^{2} + 3072 \, {\left(32 \, c^{8} d e + 33 \, b c^{7} e^{2}\right)} x^{6} + 256 \, {\left(224 \, c^{8} d^{2} + 928 \, b c^{7} d e + 243 \, b^{2} c^{6} e^{2}\right)} x^{5} + 128 \, {\left(1120 \, b c^{7} d^{2} + 1184 \, b^{2} c^{6} d e + 3 \, b^{3} c^{5} e^{2}\right)} x^{4} + 48 \, {\left(2016 \, b^{2} c^{6} d^{2} + 32 \, b^{3} c^{5} d e - 9 \, b^{4} c^{4} e^{2}\right)} x^{3} + 56 \, {\left(32 \, b^{3} c^{5} d^{2} - 32 \, b^{4} c^{4} d e + 9 \, b^{5} c^{3} e^{2}\right)} x^{2} - 70 \, {\left(32 \, b^{4} c^{4} d^{2} - 32 \, b^{5} c^{3} d e + 9 \, b^{6} c^{2} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{688128 \, c^{6}}, \frac{105 \, {\left(32 \, b^{6} c^{2} d^{2} - 32 \, b^{7} c d e + 9 \, b^{8} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(43008 \, c^{8} e^{2} x^{7} + 3360 \, b^{5} c^{3} d^{2} - 3360 \, b^{6} c^{2} d e + 945 \, b^{7} c e^{2} + 3072 \, {\left(32 \, c^{8} d e + 33 \, b c^{7} e^{2}\right)} x^{6} + 256 \, {\left(224 \, c^{8} d^{2} + 928 \, b c^{7} d e + 243 \, b^{2} c^{6} e^{2}\right)} x^{5} + 128 \, {\left(1120 \, b c^{7} d^{2} + 1184 \, b^{2} c^{6} d e + 3 \, b^{3} c^{5} e^{2}\right)} x^{4} + 48 \, {\left(2016 \, b^{2} c^{6} d^{2} + 32 \, b^{3} c^{5} d e - 9 \, b^{4} c^{4} e^{2}\right)} x^{3} + 56 \, {\left(32 \, b^{3} c^{5} d^{2} - 32 \, b^{4} c^{4} d e + 9 \, b^{5} c^{3} e^{2}\right)} x^{2} - 70 \, {\left(32 \, b^{4} c^{4} d^{2} - 32 \, b^{5} c^{3} d e + 9 \, b^{6} c^{2} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{344064 \, c^{6}}\right]"," ",0,"[1/688128*(105*(32*b^6*c^2*d^2 - 32*b^7*c*d*e + 9*b^8*e^2)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(43008*c^8*e^2*x^7 + 3360*b^5*c^3*d^2 - 3360*b^6*c^2*d*e + 945*b^7*c*e^2 + 3072*(32*c^8*d*e + 33*b*c^7*e^2)*x^6 + 256*(224*c^8*d^2 + 928*b*c^7*d*e + 243*b^2*c^6*e^2)*x^5 + 128*(1120*b*c^7*d^2 + 1184*b^2*c^6*d*e + 3*b^3*c^5*e^2)*x^4 + 48*(2016*b^2*c^6*d^2 + 32*b^3*c^5*d*e - 9*b^4*c^4*e^2)*x^3 + 56*(32*b^3*c^5*d^2 - 32*b^4*c^4*d*e + 9*b^5*c^3*e^2)*x^2 - 70*(32*b^4*c^4*d^2 - 32*b^5*c^3*d*e + 9*b^6*c^2*e^2)*x)*sqrt(c*x^2 + b*x))/c^6, 1/344064*(105*(32*b^6*c^2*d^2 - 32*b^7*c*d*e + 9*b^8*e^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (43008*c^8*e^2*x^7 + 3360*b^5*c^3*d^2 - 3360*b^6*c^2*d*e + 945*b^7*c*e^2 + 3072*(32*c^8*d*e + 33*b*c^7*e^2)*x^6 + 256*(224*c^8*d^2 + 928*b*c^7*d*e + 243*b^2*c^6*e^2)*x^5 + 128*(1120*b*c^7*d^2 + 1184*b^2*c^6*d*e + 3*b^3*c^5*e^2)*x^4 + 48*(2016*b^2*c^6*d^2 + 32*b^3*c^5*d*e - 9*b^4*c^4*e^2)*x^3 + 56*(32*b^3*c^5*d^2 - 32*b^4*c^4*d*e + 9*b^5*c^3*e^2)*x^2 - 70*(32*b^4*c^4*d^2 - 32*b^5*c^3*d*e + 9*b^6*c^2*e^2)*x)*sqrt(c*x^2 + b*x))/c^6]","A",0
304,1,397,0,0.423620," ","integrate((e*x+d)*(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(2 \, b^{6} c d - b^{7} e\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(3072 \, c^{7} e x^{6} + 210 \, b^{5} c^{2} d - 105 \, b^{6} c e + 256 \, {\left(14 \, c^{7} d + 29 \, b c^{6} e\right)} x^{5} + 128 \, {\left(70 \, b c^{6} d + 37 \, b^{2} c^{5} e\right)} x^{4} + 48 \, {\left(126 \, b^{2} c^{5} d + b^{3} c^{4} e\right)} x^{3} + 56 \, {\left(2 \, b^{3} c^{4} d - b^{4} c^{3} e\right)} x^{2} - 70 \, {\left(2 \, b^{4} c^{3} d - b^{5} c^{2} e\right)} x\right)} \sqrt{c x^{2} + b x}}{43008 \, c^{5}}, \frac{105 \, {\left(2 \, b^{6} c d - b^{7} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(3072 \, c^{7} e x^{6} + 210 \, b^{5} c^{2} d - 105 \, b^{6} c e + 256 \, {\left(14 \, c^{7} d + 29 \, b c^{6} e\right)} x^{5} + 128 \, {\left(70 \, b c^{6} d + 37 \, b^{2} c^{5} e\right)} x^{4} + 48 \, {\left(126 \, b^{2} c^{5} d + b^{3} c^{4} e\right)} x^{3} + 56 \, {\left(2 \, b^{3} c^{4} d - b^{4} c^{3} e\right)} x^{2} - 70 \, {\left(2 \, b^{4} c^{3} d - b^{5} c^{2} e\right)} x\right)} \sqrt{c x^{2} + b x}}{21504 \, c^{5}}\right]"," ",0,"[-1/43008*(105*(2*b^6*c*d - b^7*e)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(3072*c^7*e*x^6 + 210*b^5*c^2*d - 105*b^6*c*e + 256*(14*c^7*d + 29*b*c^6*e)*x^5 + 128*(70*b*c^6*d + 37*b^2*c^5*e)*x^4 + 48*(126*b^2*c^5*d + b^3*c^4*e)*x^3 + 56*(2*b^3*c^4*d - b^4*c^3*e)*x^2 - 70*(2*b^4*c^3*d - b^5*c^2*e)*x)*sqrt(c*x^2 + b*x))/c^5, 1/21504*(105*(2*b^6*c*d - b^7*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (3072*c^7*e*x^6 + 210*b^5*c^2*d - 105*b^6*c*e + 256*(14*c^7*d + 29*b*c^6*e)*x^5 + 128*(70*b*c^6*d + 37*b^2*c^5*e)*x^4 + 48*(126*b^2*c^5*d + b^3*c^4*e)*x^3 + 56*(2*b^3*c^4*d - b^4*c^3*e)*x^2 - 70*(2*b^4*c^3*d - b^5*c^2*e)*x)*sqrt(c*x^2 + b*x))/c^5]","A",0
305,1,213,0,0.419492," ","integrate((c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, b^{6} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(256 \, c^{6} x^{5} + 640 \, b c^{5} x^{4} + 432 \, b^{2} c^{4} x^{3} + 8 \, b^{3} c^{3} x^{2} - 10 \, b^{4} c^{2} x + 15 \, b^{5} c\right)} \sqrt{c x^{2} + b x}}{3072 \, c^{4}}, \frac{15 \, b^{6} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(256 \, c^{6} x^{5} + 640 \, b c^{5} x^{4} + 432 \, b^{2} c^{4} x^{3} + 8 \, b^{3} c^{3} x^{2} - 10 \, b^{4} c^{2} x + 15 \, b^{5} c\right)} \sqrt{c x^{2} + b x}}{1536 \, c^{4}}\right]"," ",0,"[1/3072*(15*b^6*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(256*c^6*x^5 + 640*b*c^5*x^4 + 432*b^2*c^4*x^3 + 8*b^3*c^3*x^2 - 10*b^4*c^2*x + 15*b^5*c)*sqrt(c*x^2 + b*x))/c^4, 1/1536*(15*b^6*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (256*c^6*x^5 + 640*b*c^5*x^4 + 432*b^2*c^4*x^3 + 8*b^3*c^3*x^2 - 10*b^4*c^2*x + 15*b^5*c)*sqrt(c*x^2 + b*x))/c^4]","A",0
306,1,1549,0,4.816543," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(256 \, c^{5} d^{5} - 640 \, b c^{4} d^{4} e + 480 \, b^{2} c^{3} d^{3} e^{2} - 80 \, b^{3} c^{2} d^{2} e^{3} - 10 \, b^{4} c d e^{4} - 3 \, b^{5} e^{5}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 3840 \, {\left(c^{5} d^{4} - 2 \, b c^{4} d^{3} e + b^{2} c^{3} d^{2} e^{2}\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(384 \, c^{5} e^{5} x^{4} + 1920 \, c^{5} d^{4} e - 4320 \, b c^{4} d^{3} e^{2} + 2640 \, b^{2} c^{3} d^{2} e^{3} - 150 \, b^{3} c^{2} d e^{4} - 45 \, b^{4} c e^{5} - 48 \, {\left(10 \, c^{5} d e^{4} - 21 \, b c^{4} e^{5}\right)} x^{3} + 8 \, {\left(80 \, c^{5} d^{2} e^{3} - 170 \, b c^{4} d e^{4} + 93 \, b^{2} c^{3} e^{5}\right)} x^{2} - 10 \, {\left(96 \, c^{5} d^{3} e^{2} - 208 \, b c^{4} d^{2} e^{3} + 118 \, b^{2} c^{3} d e^{4} - 3 \, b^{3} c^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, c^{3} e^{6}}, \frac{7680 \, {\left(c^{5} d^{4} - 2 \, b c^{4} d^{3} e + b^{2} c^{3} d^{2} e^{2}\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 15 \, {\left(256 \, c^{5} d^{5} - 640 \, b c^{4} d^{4} e + 480 \, b^{2} c^{3} d^{3} e^{2} - 80 \, b^{3} c^{2} d^{2} e^{3} - 10 \, b^{4} c d e^{4} - 3 \, b^{5} e^{5}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(384 \, c^{5} e^{5} x^{4} + 1920 \, c^{5} d^{4} e - 4320 \, b c^{4} d^{3} e^{2} + 2640 \, b^{2} c^{3} d^{2} e^{3} - 150 \, b^{3} c^{2} d e^{4} - 45 \, b^{4} c e^{5} - 48 \, {\left(10 \, c^{5} d e^{4} - 21 \, b c^{4} e^{5}\right)} x^{3} + 8 \, {\left(80 \, c^{5} d^{2} e^{3} - 170 \, b c^{4} d e^{4} + 93 \, b^{2} c^{3} e^{5}\right)} x^{2} - 10 \, {\left(96 \, c^{5} d^{3} e^{2} - 208 \, b c^{4} d^{2} e^{3} + 118 \, b^{2} c^{3} d e^{4} - 3 \, b^{3} c^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{3840 \, c^{3} e^{6}}, \frac{15 \, {\left(256 \, c^{5} d^{5} - 640 \, b c^{4} d^{4} e + 480 \, b^{2} c^{3} d^{3} e^{2} - 80 \, b^{3} c^{2} d^{2} e^{3} - 10 \, b^{4} c d e^{4} - 3 \, b^{5} e^{5}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + 1920 \, {\left(c^{5} d^{4} - 2 \, b c^{4} d^{3} e + b^{2} c^{3} d^{2} e^{2}\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + {\left(384 \, c^{5} e^{5} x^{4} + 1920 \, c^{5} d^{4} e - 4320 \, b c^{4} d^{3} e^{2} + 2640 \, b^{2} c^{3} d^{2} e^{3} - 150 \, b^{3} c^{2} d e^{4} - 45 \, b^{4} c e^{5} - 48 \, {\left(10 \, c^{5} d e^{4} - 21 \, b c^{4} e^{5}\right)} x^{3} + 8 \, {\left(80 \, c^{5} d^{2} e^{3} - 170 \, b c^{4} d e^{4} + 93 \, b^{2} c^{3} e^{5}\right)} x^{2} - 10 \, {\left(96 \, c^{5} d^{3} e^{2} - 208 \, b c^{4} d^{2} e^{3} + 118 \, b^{2} c^{3} d e^{4} - 3 \, b^{3} c^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, c^{3} e^{6}}, \frac{3840 \, {\left(c^{5} d^{4} - 2 \, b c^{4} d^{3} e + b^{2} c^{3} d^{2} e^{2}\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 15 \, {\left(256 \, c^{5} d^{5} - 640 \, b c^{4} d^{4} e + 480 \, b^{2} c^{3} d^{3} e^{2} - 80 \, b^{3} c^{2} d^{2} e^{3} - 10 \, b^{4} c d e^{4} - 3 \, b^{5} e^{5}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(384 \, c^{5} e^{5} x^{4} + 1920 \, c^{5} d^{4} e - 4320 \, b c^{4} d^{3} e^{2} + 2640 \, b^{2} c^{3} d^{2} e^{3} - 150 \, b^{3} c^{2} d e^{4} - 45 \, b^{4} c e^{5} - 48 \, {\left(10 \, c^{5} d e^{4} - 21 \, b c^{4} e^{5}\right)} x^{3} + 8 \, {\left(80 \, c^{5} d^{2} e^{3} - 170 \, b c^{4} d e^{4} + 93 \, b^{2} c^{3} e^{5}\right)} x^{2} - 10 \, {\left(96 \, c^{5} d^{3} e^{2} - 208 \, b c^{4} d^{2} e^{3} + 118 \, b^{2} c^{3} d e^{4} - 3 \, b^{3} c^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{1920 \, c^{3} e^{6}}\right]"," ",0,"[-1/3840*(15*(256*c^5*d^5 - 640*b*c^4*d^4*e + 480*b^2*c^3*d^3*e^2 - 80*b^3*c^2*d^2*e^3 - 10*b^4*c*d*e^4 - 3*b^5*e^5)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 3840*(c^5*d^4 - 2*b*c^4*d^3*e + b^2*c^3*d^2*e^2)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(384*c^5*e^5*x^4 + 1920*c^5*d^4*e - 4320*b*c^4*d^3*e^2 + 2640*b^2*c^3*d^2*e^3 - 150*b^3*c^2*d*e^4 - 45*b^4*c*e^5 - 48*(10*c^5*d*e^4 - 21*b*c^4*e^5)*x^3 + 8*(80*c^5*d^2*e^3 - 170*b*c^4*d*e^4 + 93*b^2*c^3*e^5)*x^2 - 10*(96*c^5*d^3*e^2 - 208*b*c^4*d^2*e^3 + 118*b^2*c^3*d*e^4 - 3*b^3*c^2*e^5)*x)*sqrt(c*x^2 + b*x))/(c^3*e^6), 1/3840*(7680*(c^5*d^4 - 2*b*c^4*d^3*e + b^2*c^3*d^2*e^2)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 15*(256*c^5*d^5 - 640*b*c^4*d^4*e + 480*b^2*c^3*d^3*e^2 - 80*b^3*c^2*d^2*e^3 - 10*b^4*c*d*e^4 - 3*b^5*e^5)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(384*c^5*e^5*x^4 + 1920*c^5*d^4*e - 4320*b*c^4*d^3*e^2 + 2640*b^2*c^3*d^2*e^3 - 150*b^3*c^2*d*e^4 - 45*b^4*c*e^5 - 48*(10*c^5*d*e^4 - 21*b*c^4*e^5)*x^3 + 8*(80*c^5*d^2*e^3 - 170*b*c^4*d*e^4 + 93*b^2*c^3*e^5)*x^2 - 10*(96*c^5*d^3*e^2 - 208*b*c^4*d^2*e^3 + 118*b^2*c^3*d*e^4 - 3*b^3*c^2*e^5)*x)*sqrt(c*x^2 + b*x))/(c^3*e^6), 1/1920*(15*(256*c^5*d^5 - 640*b*c^4*d^4*e + 480*b^2*c^3*d^3*e^2 - 80*b^3*c^2*d^2*e^3 - 10*b^4*c*d*e^4 - 3*b^5*e^5)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + 1920*(c^5*d^4 - 2*b*c^4*d^3*e + b^2*c^3*d^2*e^2)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + (384*c^5*e^5*x^4 + 1920*c^5*d^4*e - 4320*b*c^4*d^3*e^2 + 2640*b^2*c^3*d^2*e^3 - 150*b^3*c^2*d*e^4 - 45*b^4*c*e^5 - 48*(10*c^5*d*e^4 - 21*b*c^4*e^5)*x^3 + 8*(80*c^5*d^2*e^3 - 170*b*c^4*d*e^4 + 93*b^2*c^3*e^5)*x^2 - 10*(96*c^5*d^3*e^2 - 208*b*c^4*d^2*e^3 + 118*b^2*c^3*d*e^4 - 3*b^3*c^2*e^5)*x)*sqrt(c*x^2 + b*x))/(c^3*e^6), 1/1920*(3840*(c^5*d^4 - 2*b*c^4*d^3*e + b^2*c^3*d^2*e^2)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 15*(256*c^5*d^5 - 640*b*c^4*d^4*e + 480*b^2*c^3*d^3*e^2 - 80*b^3*c^2*d^2*e^3 - 10*b^4*c*d*e^4 - 3*b^5*e^5)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (384*c^5*e^5*x^4 + 1920*c^5*d^4*e - 4320*b*c^4*d^3*e^2 + 2640*b^2*c^3*d^2*e^3 - 150*b^3*c^2*d*e^4 - 45*b^4*c*e^5 - 48*(10*c^5*d*e^4 - 21*b*c^4*e^5)*x^3 + 8*(80*c^5*d^2*e^3 - 170*b*c^4*d*e^4 + 93*b^2*c^3*e^5)*x^2 - 10*(96*c^5*d^3*e^2 - 208*b*c^4*d^2*e^3 + 118*b^2*c^3*d*e^4 - 3*b^3*c^2*e^5)*x)*sqrt(c*x^2 + b*x))/(c^3*e^6)]","A",0
307,1,1875,0,1.660354," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(128 \, c^{4} d^{5} - 256 \, b c^{3} d^{4} e + 144 \, b^{2} c^{2} d^{3} e^{2} - 16 \, b^{3} c d^{2} e^{3} - b^{4} d e^{4} + {\left(128 \, c^{4} d^{4} e - 256 \, b c^{3} d^{3} e^{2} + 144 \, b^{2} c^{2} d^{2} e^{3} - 16 \, b^{3} c d e^{4} - b^{4} e^{5}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 960 \, {\left(2 \, c^{4} d^{4} - 3 \, b c^{3} d^{3} e + b^{2} c^{2} d^{2} e^{2} + {\left(2 \, c^{4} d^{3} e - 3 \, b c^{3} d^{2} e^{2} + b^{2} c^{2} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(48 \, c^{4} e^{5} x^{4} - 960 \, c^{4} d^{4} e + 1680 \, b c^{3} d^{3} e^{2} - 720 \, b^{2} c^{2} d^{2} e^{3} + 15 \, b^{3} c d e^{4} - 8 \, {\left(10 \, c^{4} d e^{4} - 17 \, b c^{3} e^{5}\right)} x^{3} + 2 \, {\left(80 \, c^{4} d^{2} e^{3} - 140 \, b c^{3} d e^{4} + 59 \, b^{2} c^{2} e^{5}\right)} x^{2} - 5 \, {\left(96 \, c^{4} d^{3} e^{2} - 176 \, b c^{3} d^{2} e^{3} + 82 \, b^{2} c^{2} d e^{4} - 3 \, b^{3} c e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, {\left(c^{2} e^{7} x + c^{2} d e^{6}\right)}}, -\frac{1920 \, {\left(2 \, c^{4} d^{4} - 3 \, b c^{3} d^{3} e + b^{2} c^{2} d^{2} e^{2} + {\left(2 \, c^{4} d^{3} e - 3 \, b c^{3} d^{2} e^{2} + b^{2} c^{2} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 15 \, {\left(128 \, c^{4} d^{5} - 256 \, b c^{3} d^{4} e + 144 \, b^{2} c^{2} d^{3} e^{2} - 16 \, b^{3} c d^{2} e^{3} - b^{4} d e^{4} + {\left(128 \, c^{4} d^{4} e - 256 \, b c^{3} d^{3} e^{2} + 144 \, b^{2} c^{2} d^{2} e^{3} - 16 \, b^{3} c d e^{4} - b^{4} e^{5}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(48 \, c^{4} e^{5} x^{4} - 960 \, c^{4} d^{4} e + 1680 \, b c^{3} d^{3} e^{2} - 720 \, b^{2} c^{2} d^{2} e^{3} + 15 \, b^{3} c d e^{4} - 8 \, {\left(10 \, c^{4} d e^{4} - 17 \, b c^{3} e^{5}\right)} x^{3} + 2 \, {\left(80 \, c^{4} d^{2} e^{3} - 140 \, b c^{3} d e^{4} + 59 \, b^{2} c^{2} e^{5}\right)} x^{2} - 5 \, {\left(96 \, c^{4} d^{3} e^{2} - 176 \, b c^{3} d^{2} e^{3} + 82 \, b^{2} c^{2} d e^{4} - 3 \, b^{3} c e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{384 \, {\left(c^{2} e^{7} x + c^{2} d e^{6}\right)}}, -\frac{15 \, {\left(128 \, c^{4} d^{5} - 256 \, b c^{3} d^{4} e + 144 \, b^{2} c^{2} d^{3} e^{2} - 16 \, b^{3} c d^{2} e^{3} - b^{4} d e^{4} + {\left(128 \, c^{4} d^{4} e - 256 \, b c^{3} d^{3} e^{2} + 144 \, b^{2} c^{2} d^{2} e^{3} - 16 \, b^{3} c d e^{4} - b^{4} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - 480 \, {\left(2 \, c^{4} d^{4} - 3 \, b c^{3} d^{3} e + b^{2} c^{2} d^{2} e^{2} + {\left(2 \, c^{4} d^{3} e - 3 \, b c^{3} d^{2} e^{2} + b^{2} c^{2} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - {\left(48 \, c^{4} e^{5} x^{4} - 960 \, c^{4} d^{4} e + 1680 \, b c^{3} d^{3} e^{2} - 720 \, b^{2} c^{2} d^{2} e^{3} + 15 \, b^{3} c d e^{4} - 8 \, {\left(10 \, c^{4} d e^{4} - 17 \, b c^{3} e^{5}\right)} x^{3} + 2 \, {\left(80 \, c^{4} d^{2} e^{3} - 140 \, b c^{3} d e^{4} + 59 \, b^{2} c^{2} e^{5}\right)} x^{2} - 5 \, {\left(96 \, c^{4} d^{3} e^{2} - 176 \, b c^{3} d^{2} e^{3} + 82 \, b^{2} c^{2} d e^{4} - 3 \, b^{3} c e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, {\left(c^{2} e^{7} x + c^{2} d e^{6}\right)}}, -\frac{960 \, {\left(2 \, c^{4} d^{4} - 3 \, b c^{3} d^{3} e + b^{2} c^{2} d^{2} e^{2} + {\left(2 \, c^{4} d^{3} e - 3 \, b c^{3} d^{2} e^{2} + b^{2} c^{2} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 15 \, {\left(128 \, c^{4} d^{5} - 256 \, b c^{3} d^{4} e + 144 \, b^{2} c^{2} d^{3} e^{2} - 16 \, b^{3} c d^{2} e^{3} - b^{4} d e^{4} + {\left(128 \, c^{4} d^{4} e - 256 \, b c^{3} d^{3} e^{2} + 144 \, b^{2} c^{2} d^{2} e^{3} - 16 \, b^{3} c d e^{4} - b^{4} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(48 \, c^{4} e^{5} x^{4} - 960 \, c^{4} d^{4} e + 1680 \, b c^{3} d^{3} e^{2} - 720 \, b^{2} c^{2} d^{2} e^{3} + 15 \, b^{3} c d e^{4} - 8 \, {\left(10 \, c^{4} d e^{4} - 17 \, b c^{3} e^{5}\right)} x^{3} + 2 \, {\left(80 \, c^{4} d^{2} e^{3} - 140 \, b c^{3} d e^{4} + 59 \, b^{2} c^{2} e^{5}\right)} x^{2} - 5 \, {\left(96 \, c^{4} d^{3} e^{2} - 176 \, b c^{3} d^{2} e^{3} + 82 \, b^{2} c^{2} d e^{4} - 3 \, b^{3} c e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{192 \, {\left(c^{2} e^{7} x + c^{2} d e^{6}\right)}}\right]"," ",0,"[-1/384*(15*(128*c^4*d^5 - 256*b*c^3*d^4*e + 144*b^2*c^2*d^3*e^2 - 16*b^3*c*d^2*e^3 - b^4*d*e^4 + (128*c^4*d^4*e - 256*b*c^3*d^3*e^2 + 144*b^2*c^2*d^2*e^3 - 16*b^3*c*d*e^4 - b^4*e^5)*x)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 960*(2*c^4*d^4 - 3*b*c^3*d^3*e + b^2*c^2*d^2*e^2 + (2*c^4*d^3*e - 3*b*c^3*d^2*e^2 + b^2*c^2*d*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(48*c^4*e^5*x^4 - 960*c^4*d^4*e + 1680*b*c^3*d^3*e^2 - 720*b^2*c^2*d^2*e^3 + 15*b^3*c*d*e^4 - 8*(10*c^4*d*e^4 - 17*b*c^3*e^5)*x^3 + 2*(80*c^4*d^2*e^3 - 140*b*c^3*d*e^4 + 59*b^2*c^2*e^5)*x^2 - 5*(96*c^4*d^3*e^2 - 176*b*c^3*d^2*e^3 + 82*b^2*c^2*d*e^4 - 3*b^3*c*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*e^7*x + c^2*d*e^6), -1/384*(1920*(2*c^4*d^4 - 3*b*c^3*d^3*e + b^2*c^2*d^2*e^2 + (2*c^4*d^3*e - 3*b*c^3*d^2*e^2 + b^2*c^2*d*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 15*(128*c^4*d^5 - 256*b*c^3*d^4*e + 144*b^2*c^2*d^3*e^2 - 16*b^3*c*d^2*e^3 - b^4*d*e^4 + (128*c^4*d^4*e - 256*b*c^3*d^3*e^2 + 144*b^2*c^2*d^2*e^3 - 16*b^3*c*d*e^4 - b^4*e^5)*x)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(48*c^4*e^5*x^4 - 960*c^4*d^4*e + 1680*b*c^3*d^3*e^2 - 720*b^2*c^2*d^2*e^3 + 15*b^3*c*d*e^4 - 8*(10*c^4*d*e^4 - 17*b*c^3*e^5)*x^3 + 2*(80*c^4*d^2*e^3 - 140*b*c^3*d*e^4 + 59*b^2*c^2*e^5)*x^2 - 5*(96*c^4*d^3*e^2 - 176*b*c^3*d^2*e^3 + 82*b^2*c^2*d*e^4 - 3*b^3*c*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*e^7*x + c^2*d*e^6), -1/192*(15*(128*c^4*d^5 - 256*b*c^3*d^4*e + 144*b^2*c^2*d^3*e^2 - 16*b^3*c*d^2*e^3 - b^4*d*e^4 + (128*c^4*d^4*e - 256*b*c^3*d^3*e^2 + 144*b^2*c^2*d^2*e^3 - 16*b^3*c*d*e^4 - b^4*e^5)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - 480*(2*c^4*d^4 - 3*b*c^3*d^3*e + b^2*c^2*d^2*e^2 + (2*c^4*d^3*e - 3*b*c^3*d^2*e^2 + b^2*c^2*d*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - (48*c^4*e^5*x^4 - 960*c^4*d^4*e + 1680*b*c^3*d^3*e^2 - 720*b^2*c^2*d^2*e^3 + 15*b^3*c*d*e^4 - 8*(10*c^4*d*e^4 - 17*b*c^3*e^5)*x^3 + 2*(80*c^4*d^2*e^3 - 140*b*c^3*d*e^4 + 59*b^2*c^2*e^5)*x^2 - 5*(96*c^4*d^3*e^2 - 176*b*c^3*d^2*e^3 + 82*b^2*c^2*d*e^4 - 3*b^3*c*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*e^7*x + c^2*d*e^6), -1/192*(960*(2*c^4*d^4 - 3*b*c^3*d^3*e + b^2*c^2*d^2*e^2 + (2*c^4*d^3*e - 3*b*c^3*d^2*e^2 + b^2*c^2*d*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 15*(128*c^4*d^5 - 256*b*c^3*d^4*e + 144*b^2*c^2*d^3*e^2 - 16*b^3*c*d^2*e^3 - b^4*d*e^4 + (128*c^4*d^4*e - 256*b*c^3*d^3*e^2 + 144*b^2*c^2*d^2*e^3 - 16*b^3*c*d*e^4 - b^4*e^5)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (48*c^4*e^5*x^4 - 960*c^4*d^4*e + 1680*b*c^3*d^3*e^2 - 720*b^2*c^2*d^2*e^3 + 15*b^3*c*d*e^4 - 8*(10*c^4*d*e^4 - 17*b*c^3*e^5)*x^3 + 2*(80*c^4*d^2*e^3 - 140*b*c^3*d*e^4 + 59*b^2*c^2*e^5)*x^2 - 5*(96*c^4*d^3*e^2 - 176*b*c^3*d^2*e^3 + 82*b^2*c^2*d*e^4 - 3*b^3*c*e^5)*x)*sqrt(c*x^2 + b*x))/(c^2*e^7*x + c^2*d*e^6)]","A",0
308,1,2033,0,0.709831," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(32 \, c^{3} d^{5} - 48 \, b c^{2} d^{4} e + 18 \, b^{2} c d^{3} e^{2} - b^{3} d^{2} e^{3} + {\left(32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 18 \, b^{2} c d e^{4} - b^{3} e^{5}\right)} x^{2} + 2 \, {\left(32 \, c^{3} d^{4} e - 48 \, b c^{2} d^{3} e^{2} + 18 \, b^{2} c d^{2} e^{3} - b^{3} d e^{4}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 30 \, {\left(16 \, c^{3} d^{4} - 16 \, b c^{2} d^{3} e + 3 \, b^{2} c d^{2} e^{2} + {\left(16 \, c^{3} d^{2} e^{2} - 16 \, b c^{2} d e^{3} + 3 \, b^{2} c e^{4}\right)} x^{2} + 2 \, {\left(16 \, c^{3} d^{3} e - 16 \, b c^{2} d^{2} e^{2} + 3 \, b^{2} c d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(8 \, c^{3} e^{5} x^{4} + 240 \, c^{3} d^{4} e - 300 \, b c^{2} d^{3} e^{2} + 75 \, b^{2} c d^{2} e^{3} - 2 \, {\left(10 \, c^{3} d e^{4} - 13 \, b c^{2} e^{5}\right)} x^{3} + {\left(80 \, c^{3} d^{2} e^{3} - 110 \, b c^{2} d e^{4} + 33 \, b^{2} c e^{5}\right)} x^{2} + 20 \, {\left(18 \, c^{3} d^{3} e^{2} - 23 \, b c^{2} d^{2} e^{3} + 6 \, b^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c e^{8} x^{2} + 2 \, c d e^{7} x + c d^{2} e^{6}\right)}}, \frac{60 \, {\left(16 \, c^{3} d^{4} - 16 \, b c^{2} d^{3} e + 3 \, b^{2} c d^{2} e^{2} + {\left(16 \, c^{3} d^{2} e^{2} - 16 \, b c^{2} d e^{3} + 3 \, b^{2} c e^{4}\right)} x^{2} + 2 \, {\left(16 \, c^{3} d^{3} e - 16 \, b c^{2} d^{2} e^{2} + 3 \, b^{2} c d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - 15 \, {\left(32 \, c^{3} d^{5} - 48 \, b c^{2} d^{4} e + 18 \, b^{2} c d^{3} e^{2} - b^{3} d^{2} e^{3} + {\left(32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 18 \, b^{2} c d e^{4} - b^{3} e^{5}\right)} x^{2} + 2 \, {\left(32 \, c^{3} d^{4} e - 48 \, b c^{2} d^{3} e^{2} + 18 \, b^{2} c d^{2} e^{3} - b^{3} d e^{4}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(8 \, c^{3} e^{5} x^{4} + 240 \, c^{3} d^{4} e - 300 \, b c^{2} d^{3} e^{2} + 75 \, b^{2} c d^{2} e^{3} - 2 \, {\left(10 \, c^{3} d e^{4} - 13 \, b c^{2} e^{5}\right)} x^{3} + {\left(80 \, c^{3} d^{2} e^{3} - 110 \, b c^{2} d e^{4} + 33 \, b^{2} c e^{5}\right)} x^{2} + 20 \, {\left(18 \, c^{3} d^{3} e^{2} - 23 \, b c^{2} d^{2} e^{3} + 6 \, b^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, {\left(c e^{8} x^{2} + 2 \, c d e^{7} x + c d^{2} e^{6}\right)}}, \frac{15 \, {\left(32 \, c^{3} d^{5} - 48 \, b c^{2} d^{4} e + 18 \, b^{2} c d^{3} e^{2} - b^{3} d^{2} e^{3} + {\left(32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 18 \, b^{2} c d e^{4} - b^{3} e^{5}\right)} x^{2} + 2 \, {\left(32 \, c^{3} d^{4} e - 48 \, b c^{2} d^{3} e^{2} + 18 \, b^{2} c d^{2} e^{3} - b^{3} d e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + 15 \, {\left(16 \, c^{3} d^{4} - 16 \, b c^{2} d^{3} e + 3 \, b^{2} c d^{2} e^{2} + {\left(16 \, c^{3} d^{2} e^{2} - 16 \, b c^{2} d e^{3} + 3 \, b^{2} c e^{4}\right)} x^{2} + 2 \, {\left(16 \, c^{3} d^{3} e - 16 \, b c^{2} d^{2} e^{2} + 3 \, b^{2} c d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + {\left(8 \, c^{3} e^{5} x^{4} + 240 \, c^{3} d^{4} e - 300 \, b c^{2} d^{3} e^{2} + 75 \, b^{2} c d^{2} e^{3} - 2 \, {\left(10 \, c^{3} d e^{4} - 13 \, b c^{2} e^{5}\right)} x^{3} + {\left(80 \, c^{3} d^{2} e^{3} - 110 \, b c^{2} d e^{4} + 33 \, b^{2} c e^{5}\right)} x^{2} + 20 \, {\left(18 \, c^{3} d^{3} e^{2} - 23 \, b c^{2} d^{2} e^{3} + 6 \, b^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c e^{8} x^{2} + 2 \, c d e^{7} x + c d^{2} e^{6}\right)}}, \frac{30 \, {\left(16 \, c^{3} d^{4} - 16 \, b c^{2} d^{3} e + 3 \, b^{2} c d^{2} e^{2} + {\left(16 \, c^{3} d^{2} e^{2} - 16 \, b c^{2} d e^{3} + 3 \, b^{2} c e^{4}\right)} x^{2} + 2 \, {\left(16 \, c^{3} d^{3} e - 16 \, b c^{2} d^{2} e^{2} + 3 \, b^{2} c d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) + 15 \, {\left(32 \, c^{3} d^{5} - 48 \, b c^{2} d^{4} e + 18 \, b^{2} c d^{3} e^{2} - b^{3} d^{2} e^{3} + {\left(32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 18 \, b^{2} c d e^{4} - b^{3} e^{5}\right)} x^{2} + 2 \, {\left(32 \, c^{3} d^{4} e - 48 \, b c^{2} d^{3} e^{2} + 18 \, b^{2} c d^{2} e^{3} - b^{3} d e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(8 \, c^{3} e^{5} x^{4} + 240 \, c^{3} d^{4} e - 300 \, b c^{2} d^{3} e^{2} + 75 \, b^{2} c d^{2} e^{3} - 2 \, {\left(10 \, c^{3} d e^{4} - 13 \, b c^{2} e^{5}\right)} x^{3} + {\left(80 \, c^{3} d^{2} e^{3} - 110 \, b c^{2} d e^{4} + 33 \, b^{2} c e^{5}\right)} x^{2} + 20 \, {\left(18 \, c^{3} d^{3} e^{2} - 23 \, b c^{2} d^{2} e^{3} + 6 \, b^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, {\left(c e^{8} x^{2} + 2 \, c d e^{7} x + c d^{2} e^{6}\right)}}\right]"," ",0,"[-1/48*(15*(32*c^3*d^5 - 48*b*c^2*d^4*e + 18*b^2*c*d^3*e^2 - b^3*d^2*e^3 + (32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 18*b^2*c*d*e^4 - b^3*e^5)*x^2 + 2*(32*c^3*d^4*e - 48*b*c^2*d^3*e^2 + 18*b^2*c*d^2*e^3 - b^3*d*e^4)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 30*(16*c^3*d^4 - 16*b*c^2*d^3*e + 3*b^2*c*d^2*e^2 + (16*c^3*d^2*e^2 - 16*b*c^2*d*e^3 + 3*b^2*c*e^4)*x^2 + 2*(16*c^3*d^3*e - 16*b*c^2*d^2*e^2 + 3*b^2*c*d*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(8*c^3*e^5*x^4 + 240*c^3*d^4*e - 300*b*c^2*d^3*e^2 + 75*b^2*c*d^2*e^3 - 2*(10*c^3*d*e^4 - 13*b*c^2*e^5)*x^3 + (80*c^3*d^2*e^3 - 110*b*c^2*d*e^4 + 33*b^2*c*e^5)*x^2 + 20*(18*c^3*d^3*e^2 - 23*b*c^2*d^2*e^3 + 6*b^2*c*d*e^4)*x)*sqrt(c*x^2 + b*x))/(c*e^8*x^2 + 2*c*d*e^7*x + c*d^2*e^6), 1/48*(60*(16*c^3*d^4 - 16*b*c^2*d^3*e + 3*b^2*c*d^2*e^2 + (16*c^3*d^2*e^2 - 16*b*c^2*d*e^3 + 3*b^2*c*e^4)*x^2 + 2*(16*c^3*d^3*e - 16*b*c^2*d^2*e^2 + 3*b^2*c*d*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - 15*(32*c^3*d^5 - 48*b*c^2*d^4*e + 18*b^2*c*d^3*e^2 - b^3*d^2*e^3 + (32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 18*b^2*c*d*e^4 - b^3*e^5)*x^2 + 2*(32*c^3*d^4*e - 48*b*c^2*d^3*e^2 + 18*b^2*c*d^2*e^3 - b^3*d*e^4)*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(8*c^3*e^5*x^4 + 240*c^3*d^4*e - 300*b*c^2*d^3*e^2 + 75*b^2*c*d^2*e^3 - 2*(10*c^3*d*e^4 - 13*b*c^2*e^5)*x^3 + (80*c^3*d^2*e^3 - 110*b*c^2*d*e^4 + 33*b^2*c*e^5)*x^2 + 20*(18*c^3*d^3*e^2 - 23*b*c^2*d^2*e^3 + 6*b^2*c*d*e^4)*x)*sqrt(c*x^2 + b*x))/(c*e^8*x^2 + 2*c*d*e^7*x + c*d^2*e^6), 1/24*(15*(32*c^3*d^5 - 48*b*c^2*d^4*e + 18*b^2*c*d^3*e^2 - b^3*d^2*e^3 + (32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 18*b^2*c*d*e^4 - b^3*e^5)*x^2 + 2*(32*c^3*d^4*e - 48*b*c^2*d^3*e^2 + 18*b^2*c*d^2*e^3 - b^3*d*e^4)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + 15*(16*c^3*d^4 - 16*b*c^2*d^3*e + 3*b^2*c*d^2*e^2 + (16*c^3*d^2*e^2 - 16*b*c^2*d*e^3 + 3*b^2*c*e^4)*x^2 + 2*(16*c^3*d^3*e - 16*b*c^2*d^2*e^2 + 3*b^2*c*d*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + (8*c^3*e^5*x^4 + 240*c^3*d^4*e - 300*b*c^2*d^3*e^2 + 75*b^2*c*d^2*e^3 - 2*(10*c^3*d*e^4 - 13*b*c^2*e^5)*x^3 + (80*c^3*d^2*e^3 - 110*b*c^2*d*e^4 + 33*b^2*c*e^5)*x^2 + 20*(18*c^3*d^3*e^2 - 23*b*c^2*d^2*e^3 + 6*b^2*c*d*e^4)*x)*sqrt(c*x^2 + b*x))/(c*e^8*x^2 + 2*c*d*e^7*x + c*d^2*e^6), 1/24*(30*(16*c^3*d^4 - 16*b*c^2*d^3*e + 3*b^2*c*d^2*e^2 + (16*c^3*d^2*e^2 - 16*b*c^2*d*e^3 + 3*b^2*c*e^4)*x^2 + 2*(16*c^3*d^3*e - 16*b*c^2*d^2*e^2 + 3*b^2*c*d*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) + 15*(32*c^3*d^5 - 48*b*c^2*d^4*e + 18*b^2*c*d^3*e^2 - b^3*d^2*e^3 + (32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 18*b^2*c*d*e^4 - b^3*e^5)*x^2 + 2*(32*c^3*d^4*e - 48*b*c^2*d^3*e^2 + 18*b^2*c*d^2*e^3 - b^3*d*e^4)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (8*c^3*e^5*x^4 + 240*c^3*d^4*e - 300*b*c^2*d^3*e^2 + 75*b^2*c*d^2*e^3 - 2*(10*c^3*d*e^4 - 13*b*c^2*e^5)*x^3 + (80*c^3*d^2*e^3 - 110*b*c^2*d*e^4 + 33*b^2*c*e^5)*x^2 + 20*(18*c^3*d^3*e^2 - 23*b*c^2*d^2*e^3 + 6*b^2*c*d*e^4)*x)*sqrt(c*x^2 + b*x))/(c*e^8*x^2 + 2*c*d*e^7*x + c*d^2*e^6)]","B",0
309,1,27,0,0.409341," ","integrate((x^2+2*x)^(1/2)/(1+x),x, algorithm=""fricas"")","\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
310,1,65,0,0.409089," ","integrate((-x^2+2*x)^(3/2)/(2-2*x),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(x^{2} - 2 \, x - 3\right)} \sqrt{-x^{2} + 2 \, x} + \frac{1}{2} \, \log\left(\frac{x + \sqrt{-x^{2} + 2 \, x}}{x}\right) - \frac{1}{2} \, \log\left(-\frac{x - \sqrt{-x^{2} + 2 \, x}}{x}\right)"," ",0,"1/6*(x^2 - 2*x - 3)*sqrt(-x^2 + 2*x) + 1/2*log((x + sqrt(-x^2 + 2*x))/x) - 1/2*log(-(x - sqrt(-x^2 + 2*x))/x)","A",0
311,1,57,0,0.413676," ","integrate((-x^2+2*x)^(1/2)/(2-2*x),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-x^{2} + 2 \, x} + \frac{1}{2} \, \log\left(\frac{x + \sqrt{-x^{2} + 2 \, x}}{x}\right) - \frac{1}{2} \, \log\left(-\frac{x - \sqrt{-x^{2} + 2 \, x}}{x}\right)"," ",0,"-1/2*sqrt(-x^2 + 2*x) + 1/2*log((x + sqrt(-x^2 + 2*x))/x) - 1/2*log(-(x - sqrt(-x^2 + 2*x))/x)","B",0
312,1,44,0,0.413170," ","integrate(1/(2-2*x)/(-x^2+2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\frac{x + \sqrt{-x^{2} + 2 \, x}}{x}\right) - \frac{1}{2} \, \log\left(-\frac{x - \sqrt{-x^{2} + 2 \, x}}{x}\right)"," ",0,"1/2*log((x + sqrt(-x^2 + 2*x))/x) - 1/2*log(-(x - sqrt(-x^2 + 2*x))/x)","B",0
313,1,79,0,0.411484," ","integrate(1/(2-2*x)/(-x^2+2*x)^(3/2),x, algorithm=""fricas"")","\frac{{\left(x^{2} - 2 \, x\right)} \log\left(\frac{x + \sqrt{-x^{2} + 2 \, x}}{x}\right) - {\left(x^{2} - 2 \, x\right)} \log\left(-\frac{x - \sqrt{-x^{2} + 2 \, x}}{x}\right) + \sqrt{-x^{2} + 2 \, x}}{2 \, {\left(x^{2} - 2 \, x\right)}}"," ",0,"1/2*((x^2 - 2*x)*log((x + sqrt(-x^2 + 2*x))/x) - (x^2 - 2*x)*log(-(x - sqrt(-x^2 + 2*x))/x) + sqrt(-x^2 + 2*x))/(x^2 - 2*x)","B",0
314,1,112,0,0.394870," ","integrate(1/(2-2*x)/(-x^2+2*x)^(5/2),x, algorithm=""fricas"")","\frac{3 \, {\left(x^{4} - 4 \, x^{3} + 4 \, x^{2}\right)} \log\left(\frac{x + \sqrt{-x^{2} + 2 \, x}}{x}\right) - 3 \, {\left(x^{4} - 4 \, x^{3} + 4 \, x^{2}\right)} \log\left(-\frac{x - \sqrt{-x^{2} + 2 \, x}}{x}\right) + {\left(3 \, x^{2} - 6 \, x - 1\right)} \sqrt{-x^{2} + 2 \, x}}{6 \, {\left(x^{4} - 4 \, x^{3} + 4 \, x^{2}\right)}}"," ",0,"1/6*(3*(x^4 - 4*x^3 + 4*x^2)*log((x + sqrt(-x^2 + 2*x))/x) - 3*(x^4 - 4*x^3 + 4*x^2)*log(-(x - sqrt(-x^2 + 2*x))/x) + (3*x^2 - 6*x - 1)*sqrt(-x^2 + 2*x))/(x^4 - 4*x^3 + 4*x^2)","B",0
315,1,296,0,0.436981," ","integrate((e*x+d)^3/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\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)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(8 \, c^{3} e^{3} x^{2} + 72 \, c^{3} d^{2} e - 54 \, b c^{2} d e^{2} + 15 \, b^{2} c e^{3} + 2 \, {\left(18 \, c^{3} d e^{2} - 5 \, b c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{48 \, c^{4}}, -\frac{3 \, {\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)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(8 \, c^{3} e^{3} x^{2} + 72 \, c^{3} d^{2} e - 54 \, b c^{2} d e^{2} + 15 \, b^{2} c e^{3} + 2 \, {\left(18 \, c^{3} d e^{2} - 5 \, b c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{24 \, c^{4}}\right]"," ",0,"[-1/48*(3*(16*c^3*d^3 - 24*b*c^2*d^2*e + 18*b^2*c*d*e^2 - 5*b^3*e^3)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(8*c^3*e^3*x^2 + 72*c^3*d^2*e - 54*b*c^2*d*e^2 + 15*b^2*c*e^3 + 2*(18*c^3*d*e^2 - 5*b*c^2*e^3)*x)*sqrt(c*x^2 + b*x))/c^4, -1/24*(3*(16*c^3*d^3 - 24*b*c^2*d^2*e + 18*b^2*c*d*e^2 - 5*b^3*e^3)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (8*c^3*e^3*x^2 + 72*c^3*d^2*e - 54*b*c^2*d*e^2 + 15*b^2*c*e^3 + 2*(18*c^3*d*e^2 - 5*b*c^2*e^3)*x)*sqrt(c*x^2 + b*x))/c^4]","A",0
316,1,190,0,0.434217," ","integrate((e*x+d)^2/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + 3 \, b^{2} e^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) + 2 \, {\left(2 \, c^{2} e^{2} x + 8 \, c^{2} d e - 3 \, b c e^{2}\right)} \sqrt{c x^{2} + b x}}{8 \, c^{3}}, -\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + 3 \, b^{2} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(2 \, c^{2} e^{2} x + 8 \, c^{2} d e - 3 \, b c e^{2}\right)} \sqrt{c x^{2} + b x}}{4 \, c^{3}}\right]"," ",0,"[1/8*((8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) + 2*(2*c^2*e^2*x + 8*c^2*d*e - 3*b*c*e^2)*sqrt(c*x^2 + b*x))/c^3, -1/4*((8*c^2*d^2 - 8*b*c*d*e + 3*b^2*e^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (2*c^2*e^2*x + 8*c^2*d*e - 3*b*c*e^2)*sqrt(c*x^2 + b*x))/c^3]","A",0
317,1,118,0,0.418471," ","integrate((e*x+d)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{c x^{2} + b x} c e - {\left(2 \, c d - b e\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right)}{2 \, c^{2}}, \frac{\sqrt{c x^{2} + b x} c e - {\left(2 \, c d - b e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right)}{c^{2}}\right]"," ",0,"[1/2*(2*sqrt(c*x^2 + b*x)*c*e - (2*c*d - b*e)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)))/c^2, (sqrt(c*x^2 + b*x)*c*e - (2*c*d - b*e)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)))/c^2]","A",0
318,1,62,0,0.422727," ","integrate(1/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right)}{\sqrt{c}}, -\frac{2 \, \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right)}{c}\right]"," ",0,"[log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c))/sqrt(c), -2*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x))/c]","A",0
319,1,133,0,0.427532," ","integrate(1/(e*x+d)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right)}{\sqrt{c d^{2} - b d e}}, \frac{2 \, \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right)}{c d^{2} - b d e}\right]"," ",0,"[log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d))/sqrt(c*d^2 - b*d*e), 2*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x))/(c*d^2 - b*d*e)]","A",0
320,1,348,0,0.443951," ","integrate(1/(e*x+d)^2/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(c d^{2} e - b d e^{2}\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e + b^{2} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} x\right)}}, \frac{{\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(c d^{2} e - b d e^{2}\right)} \sqrt{c x^{2} + b x}}{c^{2} d^{5} - 2 \, b c d^{4} e + b^{2} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3}\right)} x}\right]"," ",0,"[1/2*((2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(c*d^2*e - b*d*e^2)*sqrt(c*x^2 + b*x))/(c^2*d^5 - 2*b*c*d^4*e + b^2*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3)*x), ((2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (c*d^2*e - b*d*e^2)*sqrt(c*x^2 + b*x))/(c^2*d^5 - 2*b*c*d^4*e + b^2*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3)*x)]","A",0
321,1,743,0,0.449358," ","integrate(1/(e*x+d)^3/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + 3 \, b^{2} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + 3 \, b^{2} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(8 \, c^{2} d^{4} e - 13 \, b c d^{3} e^{2} + 5 \, b^{2} d^{2} e^{3} + 3 \, {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} + b^{2} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e + 3 \, b^{2} c d^{6} e^{2} - b^{3} d^{5} e^{3} + {\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)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} + 3 \, b^{2} c d^{5} e^{3} - b^{3} d^{4} e^{4}\right)} x\right)}}, \frac{{\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + 3 \, b^{2} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + 3 \, b^{2} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(8 \, c^{2} d^{4} e - 13 \, b c d^{3} e^{2} + 5 \, b^{2} d^{2} e^{3} + 3 \, {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} + b^{2} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e + 3 \, b^{2} c d^{6} e^{2} - b^{3} d^{5} e^{3} + {\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)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} + 3 \, b^{2} c d^{5} e^{3} - b^{3} d^{4} e^{4}\right)} x\right)}}\right]"," ",0,"[1/8*((8*c^2*d^4 - 8*b*c*d^3*e + 3*b^2*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + 3*b^2*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + 3*b^2*d*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(8*c^2*d^4*e - 13*b*c*d^3*e^2 + 5*b^2*d^2*e^3 + 3*(2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 + b^2*d*e^4)*x)*sqrt(c*x^2 + b*x))/(c^3*d^8 - 3*b*c^2*d^7*e + 3*b^2*c*d^6*e^2 - b^3*d^5*e^3 + (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)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 + 3*b^2*c*d^5*e^3 - b^3*d^4*e^4)*x), 1/4*((8*c^2*d^4 - 8*b*c*d^3*e + 3*b^2*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + 3*b^2*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + 3*b^2*d*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (8*c^2*d^4*e - 13*b*c*d^3*e^2 + 5*b^2*d^2*e^3 + 3*(2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 + b^2*d*e^4)*x)*sqrt(c*x^2 + b*x))/(c^3*d^8 - 3*b*c^2*d^7*e + 3*b^2*c*d^6*e^2 - b^3*d^5*e^3 + (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)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 + 3*b^2*c*d^5*e^3 - b^3*d^4*e^4)*x)]","B",0
322,1,362,0,0.429049," ","integrate((e*x+d)^3/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, b^{2} c^{2} d e^{2} - b^{3} c e^{3}\right)} x^{2} + {\left(2 \, b^{3} c d e^{2} - b^{4} e^{3}\right)} x\right)} \sqrt{c} \log\left(2 \, c x + b - 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(b^{2} c^{2} e^{3} x^{2} - 2 \, b c^{3} d^{3} - {\left(4 \, c^{4} d^{3} - 6 \, b c^{3} d^{2} e + 6 \, b^{2} c^{2} d e^{2} - 3 \, b^{3} c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{2 \, {\left(b^{2} c^{4} x^{2} + b^{3} c^{3} x\right)}}, -\frac{3 \, {\left({\left(2 \, b^{2} c^{2} d e^{2} - b^{3} c e^{3}\right)} x^{2} + {\left(2 \, b^{3} c d e^{2} - b^{4} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) - {\left(b^{2} c^{2} e^{3} x^{2} - 2 \, b c^{3} d^{3} - {\left(4 \, c^{4} d^{3} - 6 \, b c^{3} d^{2} e + 6 \, b^{2} c^{2} d e^{2} - 3 \, b^{3} c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x}}{b^{2} c^{4} x^{2} + b^{3} c^{3} x}\right]"," ",0,"[-1/2*(3*((2*b^2*c^2*d*e^2 - b^3*c*e^3)*x^2 + (2*b^3*c*d*e^2 - b^4*e^3)*x)*sqrt(c)*log(2*c*x + b - 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(b^2*c^2*e^3*x^2 - 2*b*c^3*d^3 - (4*c^4*d^3 - 6*b*c^3*d^2*e + 6*b^2*c^2*d*e^2 - 3*b^3*c*e^3)*x)*sqrt(c*x^2 + b*x))/(b^2*c^4*x^2 + b^3*c^3*x), -(3*((2*b^2*c^2*d*e^2 - b^3*c*e^3)*x^2 + (2*b^3*c*d*e^2 - b^4*e^3)*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) - (b^2*c^2*e^3*x^2 - 2*b*c^3*d^3 - (4*c^4*d^3 - 6*b*c^3*d^2*e + 6*b^2*c^2*d*e^2 - 3*b^3*c*e^3)*x)*sqrt(c*x^2 + b*x))/(b^2*c^4*x^2 + b^3*c^3*x)]","A",0
323,1,242,0,0.419688," ","integrate((e*x+d)^2/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c e^{2} x^{2} + b^{3} e^{2} x\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(b c^{2} d^{2} + {\left(2 \, c^{3} d^{2} - 2 \, b c^{2} d e + b^{2} c e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}}{b^{2} c^{3} x^{2} + b^{3} c^{2} x}, -\frac{2 \, {\left({\left(b^{2} c e^{2} x^{2} + b^{3} e^{2} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(b c^{2} d^{2} + {\left(2 \, c^{3} d^{2} - 2 \, b c^{2} d e + b^{2} c e^{2}\right)} x\right)} \sqrt{c x^{2} + b x}\right)}}{b^{2} c^{3} x^{2} + b^{3} c^{2} x}\right]"," ",0,"[((b^2*c*e^2*x^2 + b^3*e^2*x)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(b*c^2*d^2 + (2*c^3*d^2 - 2*b*c^2*d*e + b^2*c*e^2)*x)*sqrt(c*x^2 + b*x))/(b^2*c^3*x^2 + b^3*c^2*x), -2*((b^2*c*e^2*x^2 + b^3*e^2*x)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (b*c^2*d^2 + (2*c^3*d^2 - 2*b*c^2*d*e + b^2*c*e^2)*x)*sqrt(c*x^2 + b*x))/(b^2*c^3*x^2 + b^3*c^2*x)]","A",0
324,1,44,0,0.417787," ","integrate((e*x+d)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x} {\left(b d + {\left(2 \, c d - b e\right)} x\right)}}{b^{2} c x^{2} + b^{3} x}"," ",0,"-2*sqrt(c*x^2 + b*x)*(b*d + (2*c*d - b*e)*x)/(b^2*c*x^2 + b^3*x)","A",0
325,1,35,0,0.418082," ","integrate(1/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x} {\left(2 \, c x + b\right)}}{b^{2} c x^{2} + b^{3} x}"," ",0,"-2*sqrt(c*x^2 + b*x)*(2*c*x + b)/(b^2*c*x^2 + b^3*x)","A",0
326,1,453,0,0.432374," ","integrate(1/(e*x+d)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} c e^{2} x^{2} + b^{3} e^{2} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(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\right)} \sqrt{c x^{2} + b x}}{{\left(b^{2} c^{3} d^{4} - 2 \, b^{3} c^{2} d^{3} e + b^{4} c d^{2} e^{2}\right)} x^{2} + {\left(b^{3} c^{2} d^{4} - 2 \, b^{4} c d^{3} e + b^{5} d^{2} e^{2}\right)} x}, \frac{2 \, {\left({\left(b^{2} c e^{2} x^{2} + b^{3} e^{2} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(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\right)} \sqrt{c x^{2} + b x}\right)}}{{\left(b^{2} c^{3} d^{4} - 2 \, b^{3} c^{2} d^{3} e + b^{4} c d^{2} e^{2}\right)} x^{2} + {\left(b^{3} c^{2} d^{4} - 2 \, b^{4} c d^{3} e + b^{5} d^{2} e^{2}\right)} x}\right]"," ",0,"[-((b^2*c*e^2*x^2 + b^3*e^2*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + 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)*sqrt(c*x^2 + b*x))/((b^2*c^3*d^4 - 2*b^3*c^2*d^3*e + b^4*c*d^2*e^2)*x^2 + (b^3*c^2*d^4 - 2*b^4*c*d^3*e + b^5*d^2*e^2)*x), 2*((b^2*c*e^2*x^2 + b^3*e^2*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (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)*sqrt(c*x^2 + b*x))/((b^2*c^3*d^4 - 2*b^3*c^2*d^3*e + b^4*c*d^2*e^2)*x^2 + (b^3*c^2*d^4 - 2*b^4*c*d^3*e + b^5*d^2*e^2)*x)]","A",0
327,1,914,0,0.442314," ","integrate(1/(e*x+d)^2/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} x^{3} + {\left(2 \, b^{2} c^{2} d^{2} e^{2} + b^{3} c d e^{3} - b^{4} e^{4}\right)} x^{2} + {\left(2 \, b^{3} c d^{2} e^{2} - b^{4} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(2 \, b c^{3} d^{5} - 6 \, b^{2} c^{2} d^{4} e + 6 \, b^{3} c d^{3} e^{2} - 2 \, b^{4} d^{2} e^{3} + {\left(4 \, c^{4} d^{4} e - 8 \, b c^{3} d^{3} e^{2} + 7 \, b^{2} c^{2} d^{2} e^{3} - 3 \, b^{3} c d e^{4}\right)} x^{2} + {\left(4 \, c^{4} d^{5} - 6 \, b c^{3} d^{4} e + 5 \, b^{3} c d^{2} e^{3} - 3 \, b^{4} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{2 \, {\left({\left(b^{2} c^{4} d^{6} e - 3 \, b^{3} c^{3} d^{5} e^{2} + 3 \, b^{4} c^{2} d^{4} e^{3} - b^{5} c d^{3} e^{4}\right)} x^{3} + {\left(b^{2} c^{4} d^{7} - 2 \, b^{3} c^{3} d^{6} e + 2 \, b^{5} c d^{4} e^{3} - b^{6} d^{3} e^{4}\right)} x^{2} + {\left(b^{3} c^{3} d^{7} - 3 \, b^{4} c^{2} d^{6} e + 3 \, b^{5} c d^{5} e^{2} - b^{6} d^{4} e^{3}\right)} x\right)}}, \frac{3 \, {\left({\left(2 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} x^{3} + {\left(2 \, b^{2} c^{2} d^{2} e^{2} + b^{3} c d e^{3} - b^{4} e^{4}\right)} x^{2} + {\left(2 \, b^{3} c d^{2} e^{2} - b^{4} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(2 \, b c^{3} d^{5} - 6 \, b^{2} c^{2} d^{4} e + 6 \, b^{3} c d^{3} e^{2} - 2 \, b^{4} d^{2} e^{3} + {\left(4 \, c^{4} d^{4} e - 8 \, b c^{3} d^{3} e^{2} + 7 \, b^{2} c^{2} d^{2} e^{3} - 3 \, b^{3} c d e^{4}\right)} x^{2} + {\left(4 \, c^{4} d^{5} - 6 \, b c^{3} d^{4} e + 5 \, b^{3} c d^{2} e^{3} - 3 \, b^{4} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x}}{{\left(b^{2} c^{4} d^{6} e - 3 \, b^{3} c^{3} d^{5} e^{2} + 3 \, b^{4} c^{2} d^{4} e^{3} - b^{5} c d^{3} e^{4}\right)} x^{3} + {\left(b^{2} c^{4} d^{7} - 2 \, b^{3} c^{3} d^{6} e + 2 \, b^{5} c d^{4} e^{3} - b^{6} d^{3} e^{4}\right)} x^{2} + {\left(b^{3} c^{3} d^{7} - 3 \, b^{4} c^{2} d^{6} e + 3 \, b^{5} c d^{5} e^{2} - b^{6} d^{4} e^{3}\right)} x}\right]"," ",0,"[-1/2*(3*((2*b^2*c^2*d*e^3 - b^3*c*e^4)*x^3 + (2*b^2*c^2*d^2*e^2 + b^3*c*d*e^3 - b^4*e^4)*x^2 + (2*b^3*c*d^2*e^2 - b^4*d*e^3)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(2*b*c^3*d^5 - 6*b^2*c^2*d^4*e + 6*b^3*c*d^3*e^2 - 2*b^4*d^2*e^3 + (4*c^4*d^4*e - 8*b*c^3*d^3*e^2 + 7*b^2*c^2*d^2*e^3 - 3*b^3*c*d*e^4)*x^2 + (4*c^4*d^5 - 6*b*c^3*d^4*e + 5*b^3*c*d^2*e^3 - 3*b^4*d*e^4)*x)*sqrt(c*x^2 + b*x))/((b^2*c^4*d^6*e - 3*b^3*c^3*d^5*e^2 + 3*b^4*c^2*d^4*e^3 - b^5*c*d^3*e^4)*x^3 + (b^2*c^4*d^7 - 2*b^3*c^3*d^6*e + 2*b^5*c*d^4*e^3 - b^6*d^3*e^4)*x^2 + (b^3*c^3*d^7 - 3*b^4*c^2*d^6*e + 3*b^5*c*d^5*e^2 - b^6*d^4*e^3)*x), (3*((2*b^2*c^2*d*e^3 - b^3*c*e^4)*x^3 + (2*b^2*c^2*d^2*e^2 + b^3*c*d*e^3 - b^4*e^4)*x^2 + (2*b^3*c*d^2*e^2 - b^4*d*e^3)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (2*b*c^3*d^5 - 6*b^2*c^2*d^4*e + 6*b^3*c*d^3*e^2 - 2*b^4*d^2*e^3 + (4*c^4*d^4*e - 8*b*c^3*d^3*e^2 + 7*b^2*c^2*d^2*e^3 - 3*b^3*c*d*e^4)*x^2 + (4*c^4*d^5 - 6*b*c^3*d^4*e + 5*b^3*c*d^2*e^3 - 3*b^4*d*e^4)*x)*sqrt(c*x^2 + b*x))/((b^2*c^4*d^6*e - 3*b^3*c^3*d^5*e^2 + 3*b^4*c^2*d^4*e^3 - b^5*c*d^3*e^4)*x^3 + (b^2*c^4*d^7 - 2*b^3*c^3*d^6*e + 2*b^5*c*d^4*e^3 - b^6*d^3*e^4)*x^2 + (b^3*c^3*d^7 - 3*b^4*c^2*d^6*e + 3*b^5*c*d^5*e^2 - b^6*d^4*e^3)*x)]","B",0
328,1,1657,0,0.493879," ","integrate(1/(e*x+d)^3/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(16 \, b^{2} c^{3} d^{2} e^{4} - 16 \, b^{3} c^{2} d e^{5} + 5 \, b^{4} c e^{6}\right)} x^{4} + {\left(32 \, b^{2} c^{3} d^{3} e^{3} - 16 \, b^{3} c^{2} d^{2} e^{4} - 6 \, b^{4} c d e^{5} + 5 \, b^{5} e^{6}\right)} x^{3} + {\left(16 \, b^{2} c^{3} d^{4} e^{2} + 16 \, b^{3} c^{2} d^{3} e^{3} - 27 \, b^{4} c d^{2} e^{4} + 10 \, b^{5} d e^{5}\right)} x^{2} + {\left(16 \, b^{3} c^{2} d^{4} e^{2} - 16 \, b^{4} c d^{3} e^{3} + 5 \, b^{5} d^{2} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x - 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) + 2 \, {\left(8 \, b c^{4} d^{7} - 32 \, b^{2} c^{3} d^{6} e + 48 \, b^{3} c^{2} d^{5} e^{2} - 32 \, b^{4} c d^{4} e^{3} + 8 \, b^{5} d^{3} e^{4} + {\left(16 \, c^{5} d^{5} e^{2} - 40 \, b c^{4} d^{4} e^{3} + 62 \, b^{2} c^{3} d^{3} e^{4} - 53 \, b^{3} c^{2} d^{2} e^{5} + 15 \, b^{4} c d e^{6}\right)} x^{3} + {\left(32 \, c^{5} d^{6} e - 72 \, b c^{4} d^{5} e^{2} + 80 \, b^{2} c^{3} d^{4} e^{3} - 27 \, b^{3} c^{2} d^{3} e^{4} - 28 \, b^{4} c d^{2} e^{5} + 15 \, b^{5} d e^{6}\right)} x^{2} + {\left(16 \, c^{5} d^{7} - 24 \, b c^{4} d^{6} e - 16 \, b^{2} c^{3} d^{5} e^{2} + 80 \, b^{3} c^{2} d^{4} e^{3} - 81 \, b^{4} c d^{3} e^{4} + 25 \, b^{5} d^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{8 \, {\left({\left(b^{2} c^{5} d^{8} e^{2} - 4 \, b^{3} c^{4} d^{7} e^{3} + 6 \, b^{4} c^{3} d^{6} e^{4} - 4 \, b^{5} c^{2} d^{5} e^{5} + b^{6} c d^{4} e^{6}\right)} x^{4} + {\left(2 \, b^{2} c^{5} d^{9} e - 7 \, b^{3} c^{4} d^{8} e^{2} + 8 \, b^{4} c^{3} d^{7} e^{3} - 2 \, b^{5} c^{2} d^{6} e^{4} - 2 \, b^{6} c d^{5} e^{5} + b^{7} d^{4} e^{6}\right)} x^{3} + {\left(b^{2} c^{5} d^{10} - 2 \, b^{3} c^{4} d^{9} e - 2 \, b^{4} c^{3} d^{8} e^{2} + 8 \, b^{5} c^{2} d^{7} e^{3} - 7 \, b^{6} c d^{6} e^{4} + 2 \, b^{7} d^{5} e^{5}\right)} x^{2} + {\left(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}\right)} x\right)}}, \frac{3 \, {\left({\left(16 \, b^{2} c^{3} d^{2} e^{4} - 16 \, b^{3} c^{2} d e^{5} + 5 \, b^{4} c e^{6}\right)} x^{4} + {\left(32 \, b^{2} c^{3} d^{3} e^{3} - 16 \, b^{3} c^{2} d^{2} e^{4} - 6 \, b^{4} c d e^{5} + 5 \, b^{5} e^{6}\right)} x^{3} + {\left(16 \, b^{2} c^{3} d^{4} e^{2} + 16 \, b^{3} c^{2} d^{3} e^{3} - 27 \, b^{4} c d^{2} e^{4} + 10 \, b^{5} d e^{5}\right)} x^{2} + {\left(16 \, b^{3} c^{2} d^{4} e^{2} - 16 \, b^{4} c d^{3} e^{3} + 5 \, b^{5} d^{2} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(8 \, b c^{4} d^{7} - 32 \, b^{2} c^{3} d^{6} e + 48 \, b^{3} c^{2} d^{5} e^{2} - 32 \, b^{4} c d^{4} e^{3} + 8 \, b^{5} d^{3} e^{4} + {\left(16 \, c^{5} d^{5} e^{2} - 40 \, b c^{4} d^{4} e^{3} + 62 \, b^{2} c^{3} d^{3} e^{4} - 53 \, b^{3} c^{2} d^{2} e^{5} + 15 \, b^{4} c d e^{6}\right)} x^{3} + {\left(32 \, c^{5} d^{6} e - 72 \, b c^{4} d^{5} e^{2} + 80 \, b^{2} c^{3} d^{4} e^{3} - 27 \, b^{3} c^{2} d^{3} e^{4} - 28 \, b^{4} c d^{2} e^{5} + 15 \, b^{5} d e^{6}\right)} x^{2} + {\left(16 \, c^{5} d^{7} - 24 \, b c^{4} d^{6} e - 16 \, b^{2} c^{3} d^{5} e^{2} + 80 \, b^{3} c^{2} d^{4} e^{3} - 81 \, b^{4} c d^{3} e^{4} + 25 \, b^{5} d^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{4 \, {\left({\left(b^{2} c^{5} d^{8} e^{2} - 4 \, b^{3} c^{4} d^{7} e^{3} + 6 \, b^{4} c^{3} d^{6} e^{4} - 4 \, b^{5} c^{2} d^{5} e^{5} + b^{6} c d^{4} e^{6}\right)} x^{4} + {\left(2 \, b^{2} c^{5} d^{9} e - 7 \, b^{3} c^{4} d^{8} e^{2} + 8 \, b^{4} c^{3} d^{7} e^{3} - 2 \, b^{5} c^{2} d^{6} e^{4} - 2 \, b^{6} c d^{5} e^{5} + b^{7} d^{4} e^{6}\right)} x^{3} + {\left(b^{2} c^{5} d^{10} - 2 \, b^{3} c^{4} d^{9} e - 2 \, b^{4} c^{3} d^{8} e^{2} + 8 \, b^{5} c^{2} d^{7} e^{3} - 7 \, b^{6} c d^{6} e^{4} + 2 \, b^{7} d^{5} e^{5}\right)} x^{2} + {\left(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}\right)} x\right)}}\right]"," ",0,"[-1/8*(3*((16*b^2*c^3*d^2*e^4 - 16*b^3*c^2*d*e^5 + 5*b^4*c*e^6)*x^4 + (32*b^2*c^3*d^3*e^3 - 16*b^3*c^2*d^2*e^4 - 6*b^4*c*d*e^5 + 5*b^5*e^6)*x^3 + (16*b^2*c^3*d^4*e^2 + 16*b^3*c^2*d^3*e^3 - 27*b^4*c*d^2*e^4 + 10*b^5*d*e^5)*x^2 + (16*b^3*c^2*d^4*e^2 - 16*b^4*c*d^3*e^3 + 5*b^5*d^2*e^4)*x)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x - 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) + 2*(8*b*c^4*d^7 - 32*b^2*c^3*d^6*e + 48*b^3*c^2*d^5*e^2 - 32*b^4*c*d^4*e^3 + 8*b^5*d^3*e^4 + (16*c^5*d^5*e^2 - 40*b*c^4*d^4*e^3 + 62*b^2*c^3*d^3*e^4 - 53*b^3*c^2*d^2*e^5 + 15*b^4*c*d*e^6)*x^3 + (32*c^5*d^6*e - 72*b*c^4*d^5*e^2 + 80*b^2*c^3*d^4*e^3 - 27*b^3*c^2*d^3*e^4 - 28*b^4*c*d^2*e^5 + 15*b^5*d*e^6)*x^2 + (16*c^5*d^7 - 24*b*c^4*d^6*e - 16*b^2*c^3*d^5*e^2 + 80*b^3*c^2*d^4*e^3 - 81*b^4*c*d^3*e^4 + 25*b^5*d^2*e^5)*x)*sqrt(c*x^2 + b*x))/((b^2*c^5*d^8*e^2 - 4*b^3*c^4*d^7*e^3 + 6*b^4*c^3*d^6*e^4 - 4*b^5*c^2*d^5*e^5 + b^6*c*d^4*e^6)*x^4 + (2*b^2*c^5*d^9*e - 7*b^3*c^4*d^8*e^2 + 8*b^4*c^3*d^7*e^3 - 2*b^5*c^2*d^6*e^4 - 2*b^6*c*d^5*e^5 + b^7*d^4*e^6)*x^3 + (b^2*c^5*d^10 - 2*b^3*c^4*d^9*e - 2*b^4*c^3*d^8*e^2 + 8*b^5*c^2*d^7*e^3 - 7*b^6*c*d^6*e^4 + 2*b^7*d^5*e^5)*x^2 + (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)*x), 1/4*(3*((16*b^2*c^3*d^2*e^4 - 16*b^3*c^2*d*e^5 + 5*b^4*c*e^6)*x^4 + (32*b^2*c^3*d^3*e^3 - 16*b^3*c^2*d^2*e^4 - 6*b^4*c*d*e^5 + 5*b^5*e^6)*x^3 + (16*b^2*c^3*d^4*e^2 + 16*b^3*c^2*d^3*e^3 - 27*b^4*c*d^2*e^4 + 10*b^5*d*e^5)*x^2 + (16*b^3*c^2*d^4*e^2 - 16*b^4*c*d^3*e^3 + 5*b^5*d^2*e^4)*x)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (8*b*c^4*d^7 - 32*b^2*c^3*d^6*e + 48*b^3*c^2*d^5*e^2 - 32*b^4*c*d^4*e^3 + 8*b^5*d^3*e^4 + (16*c^5*d^5*e^2 - 40*b*c^4*d^4*e^3 + 62*b^2*c^3*d^3*e^4 - 53*b^3*c^2*d^2*e^5 + 15*b^4*c*d*e^6)*x^3 + (32*c^5*d^6*e - 72*b*c^4*d^5*e^2 + 80*b^2*c^3*d^4*e^3 - 27*b^3*c^2*d^3*e^4 - 28*b^4*c*d^2*e^5 + 15*b^5*d*e^6)*x^2 + (16*c^5*d^7 - 24*b*c^4*d^6*e - 16*b^2*c^3*d^5*e^2 + 80*b^3*c^2*d^4*e^3 - 81*b^4*c*d^3*e^4 + 25*b^5*d^2*e^5)*x)*sqrt(c*x^2 + b*x))/((b^2*c^5*d^8*e^2 - 4*b^3*c^4*d^7*e^3 + 6*b^4*c^3*d^6*e^4 - 4*b^5*c^2*d^5*e^5 + b^6*c*d^4*e^6)*x^4 + (2*b^2*c^5*d^9*e - 7*b^3*c^4*d^8*e^2 + 8*b^4*c^3*d^7*e^3 - 2*b^5*c^2*d^6*e^4 - 2*b^6*c*d^5*e^5 + b^7*d^4*e^6)*x^3 + (b^2*c^5*d^10 - 2*b^3*c^4*d^9*e - 2*b^4*c^3*d^8*e^2 + 8*b^5*c^2*d^7*e^3 - 7*b^6*c*d^6*e^4 + 2*b^7*d^5*e^5)*x^2 + (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)*x)]","B",0
329,1,525,0,0.437848," ","integrate((e*x+d)^4/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} c^{2} e^{4} x^{4} + 2 \, b^{5} c e^{4} x^{3} + b^{6} e^{4} x^{2}\right)} \sqrt{c} \log\left(2 \, c x + b + 2 \, \sqrt{c x^{2} + b x} \sqrt{c}\right) - 2 \, {\left(b^{3} c^{3} d^{4} - 4 \, {\left(4 \, c^{6} d^{4} - 8 \, b c^{5} d^{3} e + 3 \, b^{2} c^{4} d^{2} e^{2} + b^{3} c^{3} d e^{3} - b^{4} c^{2} e^{4}\right)} x^{3} - 3 \, {\left(8 \, b c^{5} d^{4} - 16 \, b^{2} c^{4} d^{3} e + 6 \, b^{3} c^{3} d^{2} e^{2} - b^{5} c e^{4}\right)} x^{2} - 6 \, {\left(b^{2} c^{4} d^{4} - 2 \, b^{3} c^{3} d^{3} e\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{5} x^{4} + 2 \, b^{5} c^{4} x^{3} + b^{6} c^{3} x^{2}\right)}}, -\frac{2 \, {\left(3 \, {\left(b^{4} c^{2} e^{4} x^{4} + 2 \, b^{5} c e^{4} x^{3} + b^{6} e^{4} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x} \sqrt{-c}}{c x}\right) + {\left(b^{3} c^{3} d^{4} - 4 \, {\left(4 \, c^{6} d^{4} - 8 \, b c^{5} d^{3} e + 3 \, b^{2} c^{4} d^{2} e^{2} + b^{3} c^{3} d e^{3} - b^{4} c^{2} e^{4}\right)} x^{3} - 3 \, {\left(8 \, b c^{5} d^{4} - 16 \, b^{2} c^{4} d^{3} e + 6 \, b^{3} c^{3} d^{2} e^{2} - b^{5} c e^{4}\right)} x^{2} - 6 \, {\left(b^{2} c^{4} d^{4} - 2 \, b^{3} c^{3} d^{3} e\right)} x\right)} \sqrt{c x^{2} + b x}\right)}}{3 \, {\left(b^{4} c^{5} x^{4} + 2 \, b^{5} c^{4} x^{3} + b^{6} c^{3} x^{2}\right)}}\right]"," ",0,"[1/3*(3*(b^4*c^2*e^4*x^4 + 2*b^5*c*e^4*x^3 + b^6*e^4*x^2)*sqrt(c)*log(2*c*x + b + 2*sqrt(c*x^2 + b*x)*sqrt(c)) - 2*(b^3*c^3*d^4 - 4*(4*c^6*d^4 - 8*b*c^5*d^3*e + 3*b^2*c^4*d^2*e^2 + b^3*c^3*d*e^3 - b^4*c^2*e^4)*x^3 - 3*(8*b*c^5*d^4 - 16*b^2*c^4*d^3*e + 6*b^3*c^3*d^2*e^2 - b^5*c*e^4)*x^2 - 6*(b^2*c^4*d^4 - 2*b^3*c^3*d^3*e)*x)*sqrt(c*x^2 + b*x))/(b^4*c^5*x^4 + 2*b^5*c^4*x^3 + b^6*c^3*x^2), -2/3*(3*(b^4*c^2*e^4*x^4 + 2*b^5*c*e^4*x^3 + b^6*e^4*x^2)*sqrt(-c)*arctan(sqrt(c*x^2 + b*x)*sqrt(-c)/(c*x)) + (b^3*c^3*d^4 - 4*(4*c^6*d^4 - 8*b*c^5*d^3*e + 3*b^2*c^4*d^2*e^2 + b^3*c^3*d*e^3 - b^4*c^2*e^4)*x^3 - 3*(8*b*c^5*d^4 - 16*b^2*c^4*d^3*e + 6*b^3*c^3*d^2*e^2 - b^5*c*e^4)*x^2 - 6*(b^2*c^4*d^4 - 2*b^3*c^3*d^3*e)*x)*sqrt(c*x^2 + b*x))/(b^4*c^5*x^4 + 2*b^5*c^4*x^3 + b^6*c^3*x^2)]","A",0
330,1,147,0,0.420012," ","integrate((e*x+d)^3/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{3} d^{3} - {\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^{3} - 3 \, {\left(8 \, b c^{2} d^{3} - 12 \, b^{2} c d^{2} e + 3 \, b^{3} d e^{2}\right)} x^{2} - 3 \, {\left(2 \, b^{2} c d^{3} - 3 \, b^{3} d^{2} e\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}"," ",0,"-2/3*(b^3*d^3 - (16*c^3*d^3 - 24*b*c^2*d^2*e + 6*b^2*c*d*e^2 + b^3*e^3)*x^3 - 3*(8*b*c^2*d^3 - 12*b^2*c*d^2*e + 3*b^3*d*e^2)*x^2 - 3*(2*b^2*c*d^3 - 3*b^3*d^2*e)*x)*sqrt(c*x^2 + b*x)/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2)","A",0
331,1,129,0,0.403215," ","integrate((e*x+d)^2/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{3} d^{2} - 2 \, {\left(8 \, c^{3} d^{2} - 8 \, b c^{2} d e + b^{2} c e^{2}\right)} x^{3} - 3 \, {\left(8 \, b c^{2} d^{2} - 8 \, b^{2} c d e + b^{3} e^{2}\right)} x^{2} - 6 \, {\left(b^{2} c d^{2} - b^{3} d e\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}"," ",0,"-2/3*(b^3*d^2 - 2*(8*c^3*d^2 - 8*b*c^2*d*e + b^2*c*e^2)*x^3 - 3*(8*b*c^2*d^2 - 8*b^2*c*d*e + b^3*e^2)*x^2 - 6*(b^2*c*d^2 - b^3*d*e)*x)*sqrt(c*x^2 + b*x)/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2)","A",0
332,1,104,0,0.413816," ","integrate((e*x+d)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{3} d - 8 \, {\left(2 \, c^{3} d - b c^{2} e\right)} x^{3} - 12 \, {\left(2 \, b c^{2} d - b^{2} c e\right)} x^{2} - 3 \, {\left(2 \, b^{2} c d - b^{3} e\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}"," ",0,"-2/3*(b^3*d - 8*(2*c^3*d - b*c^2*e)*x^3 - 12*(2*b*c^2*d - b^2*c*e)*x^2 - 3*(2*b^2*c*d - b^3*e)*x)*sqrt(c*x^2 + b*x)/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2)","A",0
333,1,72,0,0.411635," ","integrate(1/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{3} x^{3} + 24 \, b c^{2} x^{2} + 6 \, b^{2} c x - b^{3}\right)} \sqrt{c x^{2} + b x}}{3 \, {\left(b^{4} c^{2} x^{4} + 2 \, b^{5} c x^{3} + b^{6} x^{2}\right)}}"," ",0,"2/3*(16*c^3*x^3 + 24*b*c^2*x^2 + 6*b^2*c*x - b^3)*sqrt(c*x^2 + b*x)/(b^4*c^2*x^4 + 2*b^5*c*x^3 + b^6*x^2)","A",0
334,1,1017,0,0.447612," ","integrate(1/(e*x+d)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} c^{2} e^{4} x^{4} + 2 \, b^{5} c e^{4} x^{3} + b^{6} e^{4} x^{2}\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(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} - {\left(16 \, c^{6} d^{5} - 40 \, b c^{5} d^{4} e + 26 \, b^{2} c^{4} d^{3} e^{2} + b^{3} c^{3} d^{2} e^{3} - 3 \, b^{4} c^{2} d e^{4}\right)} x^{3} - 3 \, {\left(8 \, b c^{5} d^{5} - 20 \, b^{2} c^{4} d^{4} e + 13 \, b^{3} c^{3} d^{3} e^{2} + b^{4} c^{2} d^{2} e^{3} - 2 \, b^{5} c d e^{4}\right)} x^{2} - 3 \, {\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\right)} \sqrt{c x^{2} + b x}}{3 \, {\left({\left(b^{4} c^{5} d^{6} - 3 \, b^{5} c^{4} d^{5} e + 3 \, b^{6} c^{3} d^{4} e^{2} - b^{7} c^{2} d^{3} e^{3}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} d^{6} - 3 \, b^{6} c^{3} d^{5} e + 3 \, b^{7} c^{2} d^{4} e^{2} - b^{8} c d^{3} e^{3}\right)} x^{3} + {\left(b^{6} c^{3} d^{6} - 3 \, b^{7} c^{2} d^{5} e + 3 \, b^{8} c d^{4} e^{2} - b^{9} d^{3} e^{3}\right)} x^{2}\right)}}, \frac{2 \, {\left(3 \, {\left(b^{4} c^{2} e^{4} x^{4} + 2 \, b^{5} c e^{4} x^{3} + b^{6} e^{4} x^{2}\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(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} - {\left(16 \, c^{6} d^{5} - 40 \, b c^{5} d^{4} e + 26 \, b^{2} c^{4} d^{3} e^{2} + b^{3} c^{3} d^{2} e^{3} - 3 \, b^{4} c^{2} d e^{4}\right)} x^{3} - 3 \, {\left(8 \, b c^{5} d^{5} - 20 \, b^{2} c^{4} d^{4} e + 13 \, b^{3} c^{3} d^{3} e^{2} + b^{4} c^{2} d^{2} e^{3} - 2 \, b^{5} c d e^{4}\right)} x^{2} - 3 \, {\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\right)} \sqrt{c x^{2} + b x}\right)}}{3 \, {\left({\left(b^{4} c^{5} d^{6} - 3 \, b^{5} c^{4} d^{5} e + 3 \, b^{6} c^{3} d^{4} e^{2} - b^{7} c^{2} d^{3} e^{3}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} d^{6} - 3 \, b^{6} c^{3} d^{5} e + 3 \, b^{7} c^{2} d^{4} e^{2} - b^{8} c d^{3} e^{3}\right)} x^{3} + {\left(b^{6} c^{3} d^{6} - 3 \, b^{7} c^{2} d^{5} e + 3 \, b^{8} c d^{4} e^{2} - b^{9} d^{3} e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/3*(3*(b^4*c^2*e^4*x^4 + 2*b^5*c*e^4*x^3 + b^6*e^4*x^2)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 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 - (16*c^6*d^5 - 40*b*c^5*d^4*e + 26*b^2*c^4*d^3*e^2 + b^3*c^3*d^2*e^3 - 3*b^4*c^2*d*e^4)*x^3 - 3*(8*b*c^5*d^5 - 20*b^2*c^4*d^4*e + 13*b^3*c^3*d^3*e^2 + b^4*c^2*d^2*e^3 - 2*b^5*c*d*e^4)*x^2 - 3*(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)*sqrt(c*x^2 + b*x))/((b^4*c^5*d^6 - 3*b^5*c^4*d^5*e + 3*b^6*c^3*d^4*e^2 - b^7*c^2*d^3*e^3)*x^4 + 2*(b^5*c^4*d^6 - 3*b^6*c^3*d^5*e + 3*b^7*c^2*d^4*e^2 - b^8*c*d^3*e^3)*x^3 + (b^6*c^3*d^6 - 3*b^7*c^2*d^5*e + 3*b^8*c*d^4*e^2 - b^9*d^3*e^3)*x^2), 2/3*(3*(b^4*c^2*e^4*x^4 + 2*b^5*c*e^4*x^3 + b^6*e^4*x^2)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (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 - (16*c^6*d^5 - 40*b*c^5*d^4*e + 26*b^2*c^4*d^3*e^2 + b^3*c^3*d^2*e^3 - 3*b^4*c^2*d*e^4)*x^3 - 3*(8*b*c^5*d^5 - 20*b^2*c^4*d^4*e + 13*b^3*c^3*d^3*e^2 + b^4*c^2*d^2*e^3 - 2*b^5*c*d*e^4)*x^2 - 3*(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)*sqrt(c*x^2 + b*x))/((b^4*c^5*d^6 - 3*b^5*c^4*d^5*e + 3*b^6*c^3*d^4*e^2 - b^7*c^2*d^3*e^3)*x^4 + 2*(b^5*c^4*d^6 - 3*b^6*c^3*d^5*e + 3*b^7*c^2*d^4*e^2 - b^8*c*d^3*e^3)*x^3 + (b^6*c^3*d^6 - 3*b^7*c^2*d^5*e + 3*b^8*c*d^4*e^2 - b^9*d^3*e^3)*x^2)]","B",0
335,1,1789,0,0.538400," ","integrate(1/(e*x+d)^2/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(2 \, b^{4} c^{3} d e^{5} - b^{5} c^{2} e^{6}\right)} x^{5} + {\left(2 \, b^{4} c^{3} d^{2} e^{4} + 3 \, b^{5} c^{2} d e^{5} - 2 \, b^{6} c e^{6}\right)} x^{4} + {\left(4 \, b^{5} c^{2} d^{2} e^{4} - b^{7} e^{6}\right)} x^{3} + {\left(2 \, b^{6} c d^{2} e^{4} - b^{7} d e^{5}\right)} x^{2}\right)} \sqrt{c d^{2} - b d e} \log\left(\frac{b d + {\left(2 \, c d - b e\right)} x + 2 \, \sqrt{c d^{2} - b d e} \sqrt{c x^{2} + b x}}{e x + d}\right) - 2 \, {\left(2 \, b^{3} c^{4} d^{7} - 8 \, b^{4} c^{3} d^{6} e + 12 \, b^{5} c^{2} d^{5} e^{2} - 8 \, b^{6} c d^{4} e^{3} + 2 \, b^{7} d^{3} e^{4} - {\left(32 \, c^{7} d^{6} e - 96 \, b c^{6} d^{5} e^{2} + 76 \, b^{2} c^{5} d^{4} e^{3} + 8 \, b^{3} c^{4} d^{3} e^{4} - 35 \, b^{4} c^{3} d^{2} e^{5} + 15 \, b^{5} c^{2} d e^{6}\right)} x^{4} - 2 \, {\left(16 \, c^{7} d^{7} - 24 \, b c^{6} d^{6} e - 34 \, b^{2} c^{5} d^{5} e^{2} + 61 \, b^{3} c^{4} d^{4} e^{3} - 4 \, b^{4} c^{3} d^{3} e^{4} - 30 \, b^{5} c^{2} d^{2} e^{5} + 15 \, b^{6} c d e^{6}\right)} x^{3} - 3 \, {\left(16 \, b c^{6} d^{7} - 44 \, b^{2} c^{5} d^{6} e + 26 \, b^{3} c^{4} d^{5} e^{2} + 16 \, b^{4} c^{3} d^{4} e^{3} - 14 \, b^{5} c^{2} d^{3} e^{4} - 5 \, b^{6} c d^{2} e^{5} + 5 \, b^{7} d e^{6}\right)} x^{2} - 2 \, {\left(6 \, b^{2} c^{5} d^{7} - 19 \, b^{3} c^{4} d^{6} e + 16 \, b^{4} c^{3} d^{5} e^{2} + 6 \, b^{5} c^{2} d^{4} e^{3} - 14 \, b^{6} c d^{3} e^{4} + 5 \, b^{7} d^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{6 \, {\left({\left(b^{4} c^{6} d^{8} e - 4 \, b^{5} c^{5} d^{7} e^{2} + 6 \, b^{6} c^{4} d^{6} e^{3} - 4 \, b^{7} c^{3} d^{5} e^{4} + b^{8} c^{2} d^{4} e^{5}\right)} x^{5} + {\left(b^{4} c^{6} d^{9} - 2 \, b^{5} c^{5} d^{8} e - 2 \, b^{6} c^{4} d^{7} e^{2} + 8 \, b^{7} c^{3} d^{6} e^{3} - 7 \, b^{8} c^{2} d^{5} e^{4} + 2 \, b^{9} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{5} c^{5} d^{9} - 7 \, b^{6} c^{4} d^{8} e + 8 \, b^{7} c^{3} d^{7} e^{2} - 2 \, b^{8} c^{2} d^{6} e^{3} - 2 \, b^{9} c d^{5} e^{4} + b^{10} d^{4} e^{5}\right)} x^{3} + {\left(b^{6} c^{4} d^{9} - 4 \, b^{7} c^{3} d^{8} e + 6 \, b^{8} c^{2} d^{7} e^{2} - 4 \, b^{9} c d^{6} e^{3} + b^{10} d^{5} e^{4}\right)} x^{2}\right)}}, \frac{15 \, {\left({\left(2 \, b^{4} c^{3} d e^{5} - b^{5} c^{2} e^{6}\right)} x^{5} + {\left(2 \, b^{4} c^{3} d^{2} e^{4} + 3 \, b^{5} c^{2} d e^{5} - 2 \, b^{6} c e^{6}\right)} x^{4} + {\left(4 \, b^{5} c^{2} d^{2} e^{4} - b^{7} e^{6}\right)} x^{3} + {\left(2 \, b^{6} c d^{2} e^{4} - b^{7} d e^{5}\right)} x^{2}\right)} \sqrt{-c d^{2} + b d e} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e} \sqrt{c x^{2} + b x}}{{\left(c d - b e\right)} x}\right) - {\left(2 \, b^{3} c^{4} d^{7} - 8 \, b^{4} c^{3} d^{6} e + 12 \, b^{5} c^{2} d^{5} e^{2} - 8 \, b^{6} c d^{4} e^{3} + 2 \, b^{7} d^{3} e^{4} - {\left(32 \, c^{7} d^{6} e - 96 \, b c^{6} d^{5} e^{2} + 76 \, b^{2} c^{5} d^{4} e^{3} + 8 \, b^{3} c^{4} d^{3} e^{4} - 35 \, b^{4} c^{3} d^{2} e^{5} + 15 \, b^{5} c^{2} d e^{6}\right)} x^{4} - 2 \, {\left(16 \, c^{7} d^{7} - 24 \, b c^{6} d^{6} e - 34 \, b^{2} c^{5} d^{5} e^{2} + 61 \, b^{3} c^{4} d^{4} e^{3} - 4 \, b^{4} c^{3} d^{3} e^{4} - 30 \, b^{5} c^{2} d^{2} e^{5} + 15 \, b^{6} c d e^{6}\right)} x^{3} - 3 \, {\left(16 \, b c^{6} d^{7} - 44 \, b^{2} c^{5} d^{6} e + 26 \, b^{3} c^{4} d^{5} e^{2} + 16 \, b^{4} c^{3} d^{4} e^{3} - 14 \, b^{5} c^{2} d^{3} e^{4} - 5 \, b^{6} c d^{2} e^{5} + 5 \, b^{7} d e^{6}\right)} x^{2} - 2 \, {\left(6 \, b^{2} c^{5} d^{7} - 19 \, b^{3} c^{4} d^{6} e + 16 \, b^{4} c^{3} d^{5} e^{2} + 6 \, b^{5} c^{2} d^{4} e^{3} - 14 \, b^{6} c d^{3} e^{4} + 5 \, b^{7} d^{2} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x}}{3 \, {\left({\left(b^{4} c^{6} d^{8} e - 4 \, b^{5} c^{5} d^{7} e^{2} + 6 \, b^{6} c^{4} d^{6} e^{3} - 4 \, b^{7} c^{3} d^{5} e^{4} + b^{8} c^{2} d^{4} e^{5}\right)} x^{5} + {\left(b^{4} c^{6} d^{9} - 2 \, b^{5} c^{5} d^{8} e - 2 \, b^{6} c^{4} d^{7} e^{2} + 8 \, b^{7} c^{3} d^{6} e^{3} - 7 \, b^{8} c^{2} d^{5} e^{4} + 2 \, b^{9} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{5} c^{5} d^{9} - 7 \, b^{6} c^{4} d^{8} e + 8 \, b^{7} c^{3} d^{7} e^{2} - 2 \, b^{8} c^{2} d^{6} e^{3} - 2 \, b^{9} c d^{5} e^{4} + b^{10} d^{4} e^{5}\right)} x^{3} + {\left(b^{6} c^{4} d^{9} - 4 \, b^{7} c^{3} d^{8} e + 6 \, b^{8} c^{2} d^{7} e^{2} - 4 \, b^{9} c d^{6} e^{3} + b^{10} d^{5} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/6*(15*((2*b^4*c^3*d*e^5 - b^5*c^2*e^6)*x^5 + (2*b^4*c^3*d^2*e^4 + 3*b^5*c^2*d*e^5 - 2*b^6*c*e^6)*x^4 + (4*b^5*c^2*d^2*e^4 - b^7*e^6)*x^3 + (2*b^6*c*d^2*e^4 - b^7*d*e^5)*x^2)*sqrt(c*d^2 - b*d*e)*log((b*d + (2*c*d - b*e)*x + 2*sqrt(c*d^2 - b*d*e)*sqrt(c*x^2 + b*x))/(e*x + d)) - 2*(2*b^3*c^4*d^7 - 8*b^4*c^3*d^6*e + 12*b^5*c^2*d^5*e^2 - 8*b^6*c*d^4*e^3 + 2*b^7*d^3*e^4 - (32*c^7*d^6*e - 96*b*c^6*d^5*e^2 + 76*b^2*c^5*d^4*e^3 + 8*b^3*c^4*d^3*e^4 - 35*b^4*c^3*d^2*e^5 + 15*b^5*c^2*d*e^6)*x^4 - 2*(16*c^7*d^7 - 24*b*c^6*d^6*e - 34*b^2*c^5*d^5*e^2 + 61*b^3*c^4*d^4*e^3 - 4*b^4*c^3*d^3*e^4 - 30*b^5*c^2*d^2*e^5 + 15*b^6*c*d*e^6)*x^3 - 3*(16*b*c^6*d^7 - 44*b^2*c^5*d^6*e + 26*b^3*c^4*d^5*e^2 + 16*b^4*c^3*d^4*e^3 - 14*b^5*c^2*d^3*e^4 - 5*b^6*c*d^2*e^5 + 5*b^7*d*e^6)*x^2 - 2*(6*b^2*c^5*d^7 - 19*b^3*c^4*d^6*e + 16*b^4*c^3*d^5*e^2 + 6*b^5*c^2*d^4*e^3 - 14*b^6*c*d^3*e^4 + 5*b^7*d^2*e^5)*x)*sqrt(c*x^2 + b*x))/((b^4*c^6*d^8*e - 4*b^5*c^5*d^7*e^2 + 6*b^6*c^4*d^6*e^3 - 4*b^7*c^3*d^5*e^4 + b^8*c^2*d^4*e^5)*x^5 + (b^4*c^6*d^9 - 2*b^5*c^5*d^8*e - 2*b^6*c^4*d^7*e^2 + 8*b^7*c^3*d^6*e^3 - 7*b^8*c^2*d^5*e^4 + 2*b^9*c*d^4*e^5)*x^4 + (2*b^5*c^5*d^9 - 7*b^6*c^4*d^8*e + 8*b^7*c^3*d^7*e^2 - 2*b^8*c^2*d^6*e^3 - 2*b^9*c*d^5*e^4 + b^10*d^4*e^5)*x^3 + (b^6*c^4*d^9 - 4*b^7*c^3*d^8*e + 6*b^8*c^2*d^7*e^2 - 4*b^9*c*d^6*e^3 + b^10*d^5*e^4)*x^2), 1/3*(15*((2*b^4*c^3*d*e^5 - b^5*c^2*e^6)*x^5 + (2*b^4*c^3*d^2*e^4 + 3*b^5*c^2*d*e^5 - 2*b^6*c*e^6)*x^4 + (4*b^5*c^2*d^2*e^4 - b^7*e^6)*x^3 + (2*b^6*c*d^2*e^4 - b^7*d*e^5)*x^2)*sqrt(-c*d^2 + b*d*e)*arctan(-sqrt(-c*d^2 + b*d*e)*sqrt(c*x^2 + b*x)/((c*d - b*e)*x)) - (2*b^3*c^4*d^7 - 8*b^4*c^3*d^6*e + 12*b^5*c^2*d^5*e^2 - 8*b^6*c*d^4*e^3 + 2*b^7*d^3*e^4 - (32*c^7*d^6*e - 96*b*c^6*d^5*e^2 + 76*b^2*c^5*d^4*e^3 + 8*b^3*c^4*d^3*e^4 - 35*b^4*c^3*d^2*e^5 + 15*b^5*c^2*d*e^6)*x^4 - 2*(16*c^7*d^7 - 24*b*c^6*d^6*e - 34*b^2*c^5*d^5*e^2 + 61*b^3*c^4*d^4*e^3 - 4*b^4*c^3*d^3*e^4 - 30*b^5*c^2*d^2*e^5 + 15*b^6*c*d*e^6)*x^3 - 3*(16*b*c^6*d^7 - 44*b^2*c^5*d^6*e + 26*b^3*c^4*d^5*e^2 + 16*b^4*c^3*d^4*e^3 - 14*b^5*c^2*d^3*e^4 - 5*b^6*c*d^2*e^5 + 5*b^7*d*e^6)*x^2 - 2*(6*b^2*c^5*d^7 - 19*b^3*c^4*d^6*e + 16*b^4*c^3*d^5*e^2 + 6*b^5*c^2*d^4*e^3 - 14*b^6*c*d^3*e^4 + 5*b^7*d^2*e^5)*x)*sqrt(c*x^2 + b*x))/((b^4*c^6*d^8*e - 4*b^5*c^5*d^7*e^2 + 6*b^6*c^4*d^6*e^3 - 4*b^7*c^3*d^5*e^4 + b^8*c^2*d^4*e^5)*x^5 + (b^4*c^6*d^9 - 2*b^5*c^5*d^8*e - 2*b^6*c^4*d^7*e^2 + 8*b^7*c^3*d^6*e^3 - 7*b^8*c^2*d^5*e^4 + 2*b^9*c*d^4*e^5)*x^4 + (2*b^5*c^5*d^9 - 7*b^6*c^4*d^8*e + 8*b^7*c^3*d^7*e^2 - 2*b^8*c^2*d^6*e^3 - 2*b^9*c*d^5*e^4 + b^10*d^4*e^5)*x^3 + (b^6*c^4*d^9 - 4*b^7*c^3*d^8*e + 6*b^8*c^2*d^7*e^2 - 4*b^9*c*d^6*e^3 + b^10*d^5*e^4)*x^2)]","B",0
336,1,18,0,0.406382," ","integrate(1/(2+x)/(x^2+2*x)^(1/2),x, algorithm=""fricas"")","\frac{x + \sqrt{x^{2} + 2 \, x} + 2}{x + 2}"," ",0,"(x + sqrt(x^2 + 2*x) + 2)/(x + 2)","A",0
337,1,143,0,0.407391," ","integrate((e*x+d)^(7/2)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, {\left(99 \, c e^{6} x^{6} + 8 \, c d^{6} - 26 \, b d^{5} e + 9 \, {\left(40 \, c d e^{5} + 13 \, b e^{6}\right)} x^{5} + 2 \, {\left(229 \, c d^{2} e^{4} + 221 \, b d e^{5}\right)} x^{4} + 2 \, {\left(106 \, c d^{3} e^{3} + 299 \, b d^{2} e^{4}\right)} x^{3} + 3 \, {\left(c d^{4} e^{2} + 104 \, b d^{3} e^{3}\right)} x^{2} - {\left(4 \, c d^{5} e - 13 \, b d^{4} e^{2}\right)} x\right)} \sqrt{e x + d}}{1287 \, e^{3}}"," ",0,"2/1287*(99*c*e^6*x^6 + 8*c*d^6 - 26*b*d^5*e + 9*(40*c*d*e^5 + 13*b*e^6)*x^5 + 2*(229*c*d^2*e^4 + 221*b*d*e^5)*x^4 + 2*(106*c*d^3*e^3 + 299*b*d^2*e^4)*x^3 + 3*(c*d^4*e^2 + 104*b*d^3*e^3)*x^2 - (4*c*d^5*e - 13*b*d^4*e^2)*x)*sqrt(e*x + d)/e^3","B",0
338,1,118,0,0.412679," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, c e^{5} x^{5} + 8 \, c d^{5} - 22 \, b d^{4} e + 7 \, {\left(23 \, c d e^{4} + 11 \, b e^{5}\right)} x^{4} + {\left(113 \, c d^{2} e^{3} + 209 \, b d e^{4}\right)} x^{3} + 3 \, {\left(c d^{3} e^{2} + 55 \, b d^{2} e^{3}\right)} x^{2} - {\left(4 \, c d^{4} e - 11 \, b d^{3} e^{2}\right)} x\right)} \sqrt{e x + d}}{693 \, e^{3}}"," ",0,"2/693*(63*c*e^5*x^5 + 8*c*d^5 - 22*b*d^4*e + 7*(23*c*d*e^4 + 11*b*e^5)*x^4 + (113*c*d^2*e^3 + 209*b*d*e^4)*x^3 + 3*(c*d^3*e^2 + 55*b*d^2*e^3)*x^2 - (4*c*d^4*e - 11*b*d^3*e^2)*x)*sqrt(e*x + d)/e^3","B",0
339,1,95,0,0.407043," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c e^{4} x^{4} + 8 \, c d^{4} - 18 \, b d^{3} e + 5 \, {\left(10 \, c d e^{3} + 9 \, b e^{4}\right)} x^{3} + 3 \, {\left(c d^{2} e^{2} + 24 \, b d e^{3}\right)} x^{2} - {\left(4 \, c d^{3} e - 9 \, b d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{3}}"," ",0,"2/315*(35*c*e^4*x^4 + 8*c*d^4 - 18*b*d^3*e + 5*(10*c*d*e^3 + 9*b*e^4)*x^3 + 3*(c*d^2*e^2 + 24*b*d*e^3)*x^2 - (4*c*d^3*e - 9*b*d^2*e^2)*x)*sqrt(e*x + d)/e^3","A",0
340,1,71,0,0.408781," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c e^{3} x^{3} + 8 \, c d^{3} - 14 \, b d^{2} e + 3 \, {\left(c d e^{2} + 7 \, b e^{3}\right)} x^{2} - {\left(4 \, c d^{2} e - 7 \, b d e^{2}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{3}}"," ",0,"2/105*(15*c*e^3*x^3 + 8*c*d^3 - 14*b*d^2*e + 3*(c*d*e^2 + 7*b*e^3)*x^2 - (4*c*d^2*e - 7*b*d*e^2)*x)*sqrt(e*x + d)/e^3","A",0
341,1,48,0,0.411452," ","integrate((c*x^2+b*x)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c e^{2} x^{2} + 8 \, c d^{2} - 10 \, b d e - {\left(4 \, c d e - 5 \, b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, e^{3}}"," ",0,"2/15*(3*c*e^2*x^2 + 8*c*d^2 - 10*b*d*e - (4*c*d*e - 5*b*e^2)*x)*sqrt(e*x + d)/e^3","A",0
342,1,57,0,0.411187," ","integrate((c*x^2+b*x)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c e^{2} x^{2} - 8 \, c d^{2} + 6 \, b d e - {\left(4 \, c d e - 3 \, b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{4} x + d e^{3}\right)}}"," ",0,"2/3*(c*e^2*x^2 - 8*c*d^2 + 6*b*d*e - (4*c*d*e - 3*b*e^2)*x)*sqrt(e*x + d)/(e^4*x + d*e^3)","A",0
343,1,69,0,0.410607," ","integrate((c*x^2+b*x)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c e^{2} x^{2} + 8 \, c d^{2} - 2 \, b d e + 3 \, {\left(4 \, c d e - b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"2/3*(3*c*e^2*x^2 + 8*c*d^2 - 2*b*d*e + 3*(4*c*d*e - b*e^2)*x)*sqrt(e*x + d)/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
344,1,79,0,0.412599," ","integrate((c*x^2+b*x)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, c e^{2} x^{2} + 8 \, c d^{2} + 2 \, b d e + 5 \, {\left(4 \, c d e + b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-2/15*(15*c*e^2*x^2 + 8*c*d^2 + 2*b*d*e + 5*(4*c*d*e + b*e^2)*x)*sqrt(e*x + d)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
345,1,290,0,0.423463," ","integrate((e*x+d)^(7/2)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(6435 \, c^{2} e^{8} x^{8} + 128 \, c^{2} d^{8} - 544 \, b c d^{7} e + 680 \, b^{2} d^{6} e^{2} + 858 \, {\left(26 \, c^{2} d e^{7} + 17 \, b c e^{8}\right)} x^{7} + 33 \, {\left(802 \, c^{2} d^{2} e^{6} + 1564 \, b c d e^{7} + 255 \, b^{2} e^{8}\right)} x^{6} + 36 \, {\left(303 \, c^{2} d^{3} e^{5} + 1751 \, b c d^{2} e^{6} + 850 \, b^{2} d e^{7}\right)} x^{5} + 5 \, {\left(7 \, c^{2} d^{4} e^{4} + 5440 \, b c d^{3} e^{5} + 7786 \, b^{2} d^{2} e^{6}\right)} x^{4} - 10 \, {\left(4 \, c^{2} d^{5} e^{3} - 17 \, b c d^{4} e^{4} - 1802 \, b^{2} d^{3} e^{5}\right)} x^{3} + 3 \, {\left(16 \, c^{2} d^{6} e^{2} - 68 \, b c d^{5} e^{3} + 85 \, b^{2} d^{4} e^{4}\right)} x^{2} - 4 \, {\left(16 \, c^{2} d^{7} e - 68 \, b c d^{6} e^{2} + 85 \, b^{2} d^{5} e^{3}\right)} x\right)} \sqrt{e x + d}}{109395 \, e^{5}}"," ",0,"2/109395*(6435*c^2*e^8*x^8 + 128*c^2*d^8 - 544*b*c*d^7*e + 680*b^2*d^6*e^2 + 858*(26*c^2*d*e^7 + 17*b*c*e^8)*x^7 + 33*(802*c^2*d^2*e^6 + 1564*b*c*d*e^7 + 255*b^2*e^8)*x^6 + 36*(303*c^2*d^3*e^5 + 1751*b*c*d^2*e^6 + 850*b^2*d*e^7)*x^5 + 5*(7*c^2*d^4*e^4 + 5440*b*c*d^3*e^5 + 7786*b^2*d^2*e^6)*x^4 - 10*(4*c^2*d^5*e^3 - 17*b*c*d^4*e^4 - 1802*b^2*d^3*e^5)*x^3 + 3*(16*c^2*d^6*e^2 - 68*b*c*d^5*e^3 + 85*b^2*d^4*e^4)*x^2 - 4*(16*c^2*d^7*e - 68*b*c*d^6*e^2 + 85*b^2*d^5*e^3)*x)*sqrt(e*x + d)/e^5","B",0
346,1,251,0,0.415449," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, c^{2} e^{7} x^{7} + 128 \, c^{2} d^{7} - 480 \, b c d^{6} e + 520 \, b^{2} d^{5} e^{2} + 231 \, {\left(31 \, c^{2} d e^{6} + 30 \, b c e^{7}\right)} x^{6} + 63 \, {\left(71 \, c^{2} d^{2} e^{5} + 270 \, b c d e^{6} + 65 \, b^{2} e^{7}\right)} x^{5} + 35 \, {\left(c^{2} d^{3} e^{4} + 318 \, b c d^{2} e^{5} + 299 \, b^{2} d e^{6}\right)} x^{4} - 5 \, {\left(8 \, c^{2} d^{4} e^{3} - 30 \, b c d^{3} e^{4} - 1469 \, b^{2} d^{2} e^{5}\right)} x^{3} + 3 \, {\left(16 \, c^{2} d^{5} e^{2} - 60 \, b c d^{4} e^{3} + 65 \, b^{2} d^{3} e^{4}\right)} x^{2} - 4 \, {\left(16 \, c^{2} d^{6} e - 60 \, b c d^{5} e^{2} + 65 \, b^{2} d^{4} e^{3}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{5}}"," ",0,"2/45045*(3003*c^2*e^7*x^7 + 128*c^2*d^7 - 480*b*c*d^6*e + 520*b^2*d^5*e^2 + 231*(31*c^2*d*e^6 + 30*b*c*e^7)*x^6 + 63*(71*c^2*d^2*e^5 + 270*b*c*d*e^6 + 65*b^2*e^7)*x^5 + 35*(c^2*d^3*e^4 + 318*b*c*d^2*e^5 + 299*b^2*d*e^6)*x^4 - 5*(8*c^2*d^4*e^3 - 30*b*c*d^3*e^4 - 1469*b^2*d^2*e^5)*x^3 + 3*(16*c^2*d^5*e^2 - 60*b*c*d^4*e^3 + 65*b^2*d^3*e^4)*x^2 - 4*(16*c^2*d^6*e - 60*b*c*d^5*e^2 + 65*b^2*d^4*e^3)*x)*sqrt(e*x + d)/e^5","A",0
347,1,214,0,0.413913," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, c^{2} e^{6} x^{6} + 384 \, c^{2} d^{6} - 1248 \, b c d^{5} e + 1144 \, b^{2} d^{4} e^{2} + 630 \, {\left(7 \, c^{2} d e^{5} + 13 \, b c e^{6}\right)} x^{5} + 35 \, {\left(3 \, c^{2} d^{2} e^{4} + 312 \, b c d e^{5} + 143 \, b^{2} e^{6}\right)} x^{4} - 10 \, {\left(12 \, c^{2} d^{3} e^{3} - 39 \, b c d^{2} e^{4} - 715 \, b^{2} d e^{5}\right)} x^{3} + 3 \, {\left(48 \, c^{2} d^{4} e^{2} - 156 \, b c d^{3} e^{3} + 143 \, b^{2} d^{2} e^{4}\right)} x^{2} - 4 \, {\left(48 \, c^{2} d^{5} e - 156 \, b c d^{4} e^{2} + 143 \, b^{2} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{5}}"," ",0,"2/45045*(3465*c^2*e^6*x^6 + 384*c^2*d^6 - 1248*b*c*d^5*e + 1144*b^2*d^4*e^2 + 630*(7*c^2*d*e^5 + 13*b*c*e^6)*x^5 + 35*(3*c^2*d^2*e^4 + 312*b*c*d*e^5 + 143*b^2*e^6)*x^4 - 10*(12*c^2*d^3*e^3 - 39*b*c*d^2*e^4 - 715*b^2*d*e^5)*x^3 + 3*(48*c^2*d^4*e^2 - 156*b*c*d^3*e^3 + 143*b^2*d^2*e^4)*x^2 - 4*(48*c^2*d^5*e - 156*b*c*d^4*e^2 + 143*b^2*d^3*e^3)*x)*sqrt(e*x + d)/e^5","A",0
348,1,175,0,0.404024," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, c^{2} e^{5} x^{5} + 128 \, c^{2} d^{5} - 352 \, b c d^{4} e + 264 \, b^{2} d^{3} e^{2} + 35 \, {\left(c^{2} d e^{4} + 22 \, b c e^{5}\right)} x^{4} - 5 \, {\left(8 \, c^{2} d^{2} e^{3} - 22 \, b c d e^{4} - 99 \, b^{2} e^{5}\right)} x^{3} + 3 \, {\left(16 \, c^{2} d^{3} e^{2} - 44 \, b c d^{2} e^{3} + 33 \, b^{2} d e^{4}\right)} x^{2} - 4 \, {\left(16 \, c^{2} d^{4} e - 44 \, b c d^{3} e^{2} + 33 \, b^{2} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{5}}"," ",0,"2/3465*(315*c^2*e^5*x^5 + 128*c^2*d^5 - 352*b*c*d^4*e + 264*b^2*d^3*e^2 + 35*(c^2*d*e^4 + 22*b*c*e^5)*x^4 - 5*(8*c^2*d^2*e^3 - 22*b*c*d*e^4 - 99*b^2*e^5)*x^3 + 3*(16*c^2*d^3*e^2 - 44*b*c*d^2*e^3 + 33*b^2*d*e^4)*x^2 - 4*(16*c^2*d^4*e - 44*b*c*d^3*e^2 + 33*b^2*d^2*e^3)*x)*sqrt(e*x + d)/e^5","A",0
349,1,138,0,0.409719," ","integrate((c*x^2+b*x)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{2} e^{4} x^{4} + 128 \, c^{2} d^{4} - 288 \, b c d^{3} e + 168 \, b^{2} d^{2} e^{2} - 10 \, {\left(4 \, c^{2} d e^{3} - 9 \, b c e^{4}\right)} x^{3} + 3 \, {\left(16 \, c^{2} d^{2} e^{2} - 36 \, b c d e^{3} + 21 \, b^{2} e^{4}\right)} x^{2} - 4 \, {\left(16 \, c^{2} d^{3} e - 36 \, b c d^{2} e^{2} + 21 \, b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{5}}"," ",0,"2/315*(35*c^2*e^4*x^4 + 128*c^2*d^4 - 288*b*c*d^3*e + 168*b^2*d^2*e^2 - 10*(4*c^2*d*e^3 - 9*b*c*e^4)*x^3 + 3*(16*c^2*d^2*e^2 - 36*b*c*d*e^3 + 21*b^2*e^4)*x^2 - 4*(16*c^2*d^3*e - 36*b*c*d^2*e^2 + 21*b^2*d*e^3)*x)*sqrt(e*x + d)/e^5","A",0
350,1,147,0,0.410893," ","integrate((c*x^2+b*x)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c^{2} e^{4} x^{4} - 384 \, c^{2} d^{4} + 672 \, b c d^{3} e - 280 \, b^{2} d^{2} e^{2} - 6 \, {\left(4 \, c^{2} d e^{3} - 7 \, b c e^{4}\right)} x^{3} + {\left(48 \, c^{2} d^{2} e^{2} - 84 \, b c d e^{3} + 35 \, b^{2} e^{4}\right)} x^{2} - 4 \, {\left(48 \, c^{2} d^{3} e - 84 \, b c d^{2} e^{2} + 35 \, b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"2/105*(15*c^2*e^4*x^4 - 384*c^2*d^4 + 672*b*c*d^3*e - 280*b^2*d^2*e^2 - 6*(4*c^2*d*e^3 - 7*b*c*e^4)*x^3 + (48*c^2*d^2*e^2 - 84*b*c*d*e^3 + 35*b^2*e^4)*x^2 - 4*(48*c^2*d^3*e - 84*b*c*d^2*e^2 + 35*b^2*d*e^3)*x)*sqrt(e*x + d)/(e^6*x + d*e^5)","A",0
351,1,159,0,0.400721," ","integrate((c*x^2+b*x)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} e^{4} x^{4} + 128 \, c^{2} d^{4} - 160 \, b c d^{3} e + 40 \, b^{2} d^{2} e^{2} - 2 \, {\left(4 \, c^{2} d e^{3} - 5 \, b c e^{4}\right)} x^{3} + 3 \, {\left(16 \, c^{2} d^{2} e^{2} - 20 \, b c d e^{3} + 5 \, b^{2} e^{4}\right)} x^{2} + 12 \, {\left(16 \, c^{2} d^{3} e - 20 \, b c d^{2} e^{2} + 5 \, b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"2/15*(3*c^2*e^4*x^4 + 128*c^2*d^4 - 160*b*c*d^3*e + 40*b^2*d^2*e^2 - 2*(4*c^2*d*e^3 - 5*b*c*e^4)*x^3 + 3*(16*c^2*d^2*e^2 - 20*b*c*d*e^3 + 5*b^2*e^4)*x^2 + 12*(16*c^2*d^3*e - 20*b*c*d^2*e^2 + 5*b^2*d*e^3)*x)*sqrt(e*x + d)/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
352,1,168,0,0.399845," ","integrate((c*x^2+b*x)^2/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{2} e^{4} x^{4} - 128 \, c^{2} d^{4} + 96 \, b c d^{3} e - 8 \, b^{2} d^{2} e^{2} - 10 \, {\left(4 \, c^{2} d e^{3} - 3 \, b c e^{4}\right)} x^{3} - 15 \, {\left(16 \, c^{2} d^{2} e^{2} - 12 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} - 20 \, {\left(16 \, c^{2} d^{3} e - 12 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"2/15*(5*c^2*e^4*x^4 - 128*c^2*d^4 + 96*b*c*d^3*e - 8*b^2*d^2*e^2 - 10*(4*c^2*d*e^3 - 3*b*c*e^4)*x^3 - 15*(16*c^2*d^2*e^2 - 12*b*c*d*e^3 + b^2*e^4)*x^2 - 20*(16*c^2*d^3*e - 12*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(e*x + d)/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
353,1,478,0,0.399214," ","integrate((e*x+d)^(7/2)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(692835 \, c^{3} e^{10} x^{10} + 5120 \, c^{3} d^{10} - 26880 \, b c^{2} d^{9} e + 51072 \, b^{2} c d^{8} e^{2} - 36176 \, b^{3} d^{7} e^{3} + 36465 \, {\left(64 \, c^{3} d e^{9} + 63 \, b c^{2} e^{10}\right)} x^{9} + 19305 \, {\left(138 \, c^{3} d^{2} e^{8} + 406 \, b c^{2} d e^{9} + 133 \, b^{2} c e^{10}\right)} x^{8} + 429 \, {\left(2420 \, c^{3} d^{3} e^{7} + 21210 \, b c^{2} d^{2} e^{8} + 20748 \, b^{2} c d e^{9} + 2261 \, b^{3} e^{10}\right)} x^{7} + 231 \, {\left(5 \, c^{3} d^{4} e^{6} + 15720 \, b c^{2} d^{3} e^{7} + 45714 \, b^{2} c d^{2} e^{8} + 14858 \, b^{3} d e^{9}\right)} x^{6} - 63 \, {\left(20 \, c^{3} d^{5} e^{5} - 105 \, b c^{2} d^{4} e^{6} - 69084 \, b^{2} c d^{3} e^{7} - 66538 \, b^{3} d^{2} e^{8}\right)} x^{5} + 35 \, {\left(40 \, c^{3} d^{6} e^{4} - 210 \, b c^{2} d^{5} e^{5} + 399 \, b^{2} c d^{4} e^{6} + 51680 \, b^{3} d^{3} e^{7}\right)} x^{4} - 5 \, {\left(320 \, c^{3} d^{7} e^{3} - 1680 \, b c^{2} d^{6} e^{4} + 3192 \, b^{2} c d^{5} e^{5} - 2261 \, b^{3} d^{4} e^{6}\right)} x^{3} + 6 \, {\left(320 \, c^{3} d^{8} e^{2} - 1680 \, b c^{2} d^{7} e^{3} + 3192 \, b^{2} c d^{6} e^{4} - 2261 \, b^{3} d^{5} e^{5}\right)} x^{2} - 8 \, {\left(320 \, c^{3} d^{9} e - 1680 \, b c^{2} d^{8} e^{2} + 3192 \, b^{2} c d^{7} e^{3} - 2261 \, b^{3} d^{6} e^{4}\right)} x\right)} \sqrt{e x + d}}{14549535 \, e^{7}}"," ",0,"2/14549535*(692835*c^3*e^10*x^10 + 5120*c^3*d^10 - 26880*b*c^2*d^9*e + 51072*b^2*c*d^8*e^2 - 36176*b^3*d^7*e^3 + 36465*(64*c^3*d*e^9 + 63*b*c^2*e^10)*x^9 + 19305*(138*c^3*d^2*e^8 + 406*b*c^2*d*e^9 + 133*b^2*c*e^10)*x^8 + 429*(2420*c^3*d^3*e^7 + 21210*b*c^2*d^2*e^8 + 20748*b^2*c*d*e^9 + 2261*b^3*e^10)*x^7 + 231*(5*c^3*d^4*e^6 + 15720*b*c^2*d^3*e^7 + 45714*b^2*c*d^2*e^8 + 14858*b^3*d*e^9)*x^6 - 63*(20*c^3*d^5*e^5 - 105*b*c^2*d^4*e^6 - 69084*b^2*c*d^3*e^7 - 66538*b^3*d^2*e^8)*x^5 + 35*(40*c^3*d^6*e^4 - 210*b*c^2*d^5*e^5 + 399*b^2*c*d^4*e^6 + 51680*b^3*d^3*e^7)*x^4 - 5*(320*c^3*d^7*e^3 - 1680*b*c^2*d^6*e^4 + 3192*b^2*c*d^5*e^5 - 2261*b^3*d^4*e^6)*x^3 + 6*(320*c^3*d^8*e^2 - 1680*b*c^2*d^7*e^3 + 3192*b^2*c*d^6*e^4 - 2261*b^3*d^5*e^5)*x^2 - 8*(320*c^3*d^9*e - 1680*b*c^2*d^8*e^2 + 3192*b^2*c*d^7*e^3 - 2261*b^3*d^6*e^4)*x)*sqrt(e*x + d)/e^7","B",0
354,1,426,0,0.410753," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(255255 \, c^{3} e^{9} x^{9} + 5120 \, c^{3} d^{9} - 24320 \, b c^{2} d^{8} e + 41344 \, b^{2} c d^{7} e^{2} - 25840 \, b^{3} d^{6} e^{3} + 45045 \, {\left(13 \, c^{3} d e^{8} + 19 \, b c^{2} e^{9}\right)} x^{8} + 3003 \, {\left(115 \, c^{3} d^{2} e^{7} + 665 \, b c^{2} d e^{8} + 323 \, b^{2} c e^{9}\right)} x^{7} + 231 \, {\left(5 \, c^{3} d^{3} e^{6} + 5225 \, b c^{2} d^{2} e^{7} + 10013 \, b^{2} c d e^{8} + 1615 \, b^{3} e^{9}\right)} x^{6} - 63 \, {\left(20 \, c^{3} d^{4} e^{5} - 95 \, b c^{2} d^{3} e^{6} - 22933 \, b^{2} c d^{2} e^{7} - 14535 \, b^{3} d e^{8}\right)} x^{5} + 35 \, {\left(40 \, c^{3} d^{5} e^{4} - 190 \, b c^{2} d^{4} e^{5} + 323 \, b^{2} c d^{3} e^{6} + 17119 \, b^{3} d^{2} e^{7}\right)} x^{4} - 5 \, {\left(320 \, c^{3} d^{6} e^{3} - 1520 \, b c^{2} d^{5} e^{4} + 2584 \, b^{2} c d^{4} e^{5} - 1615 \, b^{3} d^{3} e^{6}\right)} x^{3} + 6 \, {\left(320 \, c^{3} d^{7} e^{2} - 1520 \, b c^{2} d^{6} e^{3} + 2584 \, b^{2} c d^{5} e^{4} - 1615 \, b^{3} d^{4} e^{5}\right)} x^{2} - 8 \, {\left(320 \, c^{3} d^{8} e - 1520 \, b c^{2} d^{7} e^{2} + 2584 \, b^{2} c d^{6} e^{3} - 1615 \, b^{3} d^{5} e^{4}\right)} x\right)} \sqrt{e x + d}}{4849845 \, e^{7}}"," ",0,"2/4849845*(255255*c^3*e^9*x^9 + 5120*c^3*d^9 - 24320*b*c^2*d^8*e + 41344*b^2*c*d^7*e^2 - 25840*b^3*d^6*e^3 + 45045*(13*c^3*d*e^8 + 19*b*c^2*e^9)*x^8 + 3003*(115*c^3*d^2*e^7 + 665*b*c^2*d*e^8 + 323*b^2*c*e^9)*x^7 + 231*(5*c^3*d^3*e^6 + 5225*b*c^2*d^2*e^7 + 10013*b^2*c*d*e^8 + 1615*b^3*e^9)*x^6 - 63*(20*c^3*d^4*e^5 - 95*b*c^2*d^3*e^6 - 22933*b^2*c*d^2*e^7 - 14535*b^3*d*e^8)*x^5 + 35*(40*c^3*d^5*e^4 - 190*b*c^2*d^4*e^5 + 323*b^2*c*d^3*e^6 + 17119*b^3*d^2*e^7)*x^4 - 5*(320*c^3*d^6*e^3 - 1520*b*c^2*d^5*e^4 + 2584*b^2*c*d^4*e^5 - 1615*b^3*d^3*e^6)*x^3 + 6*(320*c^3*d^7*e^2 - 1520*b*c^2*d^6*e^3 + 2584*b^2*c*d^5*e^4 - 1615*b^3*d^4*e^5)*x^2 - 8*(320*c^3*d^8*e - 1520*b*c^2*d^7*e^2 + 2584*b^2*c*d^6*e^3 - 1615*b^3*d^5*e^4)*x)*sqrt(e*x + d)/e^7","A",0
355,1,373,0,0.393315," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(15015 \, c^{3} e^{8} x^{8} + 1024 \, c^{3} d^{8} - 4352 \, b c^{2} d^{7} e + 6528 \, b^{2} c d^{6} e^{2} - 3536 \, b^{3} d^{5} e^{3} + 3003 \, {\left(6 \, c^{3} d e^{7} + 17 \, b c^{2} e^{8}\right)} x^{7} + 231 \, {\left(c^{3} d^{2} e^{6} + 272 \, b c^{2} d e^{7} + 255 \, b^{2} c e^{8}\right)} x^{6} - 21 \, {\left(12 \, c^{3} d^{3} e^{5} - 51 \, b c^{2} d^{2} e^{6} - 3570 \, b^{2} c d e^{7} - 1105 \, b^{3} e^{8}\right)} x^{5} + 35 \, {\left(8 \, c^{3} d^{4} e^{4} - 34 \, b c^{2} d^{3} e^{5} + 51 \, b^{2} c d^{2} e^{6} + 884 \, b^{3} d e^{7}\right)} x^{4} - 5 \, {\left(64 \, c^{3} d^{5} e^{3} - 272 \, b c^{2} d^{4} e^{4} + 408 \, b^{2} c d^{3} e^{5} - 221 \, b^{3} d^{2} e^{6}\right)} x^{3} + 6 \, {\left(64 \, c^{3} d^{6} e^{2} - 272 \, b c^{2} d^{5} e^{3} + 408 \, b^{2} c d^{4} e^{4} - 221 \, b^{3} d^{3} e^{5}\right)} x^{2} - 8 \, {\left(64 \, c^{3} d^{7} e - 272 \, b c^{2} d^{6} e^{2} + 408 \, b^{2} c d^{5} e^{3} - 221 \, b^{3} d^{4} e^{4}\right)} x\right)} \sqrt{e x + d}}{255255 \, e^{7}}"," ",0,"2/255255*(15015*c^3*e^8*x^8 + 1024*c^3*d^8 - 4352*b*c^2*d^7*e + 6528*b^2*c*d^6*e^2 - 3536*b^3*d^5*e^3 + 3003*(6*c^3*d*e^7 + 17*b*c^2*e^8)*x^7 + 231*(c^3*d^2*e^6 + 272*b*c^2*d*e^7 + 255*b^2*c*e^8)*x^6 - 21*(12*c^3*d^3*e^5 - 51*b*c^2*d^2*e^6 - 3570*b^2*c*d*e^7 - 1105*b^3*e^8)*x^5 + 35*(8*c^3*d^4*e^4 - 34*b*c^2*d^3*e^5 + 51*b^2*c*d^2*e^6 + 884*b^3*d*e^7)*x^4 - 5*(64*c^3*d^5*e^3 - 272*b*c^2*d^4*e^4 + 408*b^2*c*d^3*e^5 - 221*b^3*d^2*e^6)*x^3 + 6*(64*c^3*d^6*e^2 - 272*b*c^2*d^5*e^3 + 408*b^2*c*d^4*e^4 - 221*b^3*d^3*e^5)*x^2 - 8*(64*c^3*d^7*e - 272*b*c^2*d^6*e^2 + 408*b^2*c*d^5*e^3 - 221*b^3*d^4*e^4)*x)*sqrt(e*x + d)/e^7","A",0
356,1,321,0,0.405212," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, c^{3} e^{7} x^{7} + 1024 \, c^{3} d^{7} - 3840 \, b c^{2} d^{6} e + 4992 \, b^{2} c d^{5} e^{2} - 2288 \, b^{3} d^{4} e^{3} + 231 \, {\left(c^{3} d e^{6} + 45 \, b c^{2} e^{7}\right)} x^{6} - 63 \, {\left(4 \, c^{3} d^{2} e^{5} - 15 \, b c^{2} d e^{6} - 195 \, b^{2} c e^{7}\right)} x^{5} + 35 \, {\left(8 \, c^{3} d^{3} e^{4} - 30 \, b c^{2} d^{2} e^{5} + 39 \, b^{2} c d e^{6} + 143 \, b^{3} e^{7}\right)} x^{4} - 5 \, {\left(64 \, c^{3} d^{4} e^{3} - 240 \, b c^{2} d^{3} e^{4} + 312 \, b^{2} c d^{2} e^{5} - 143 \, b^{3} d e^{6}\right)} x^{3} + 6 \, {\left(64 \, c^{3} d^{5} e^{2} - 240 \, b c^{2} d^{4} e^{3} + 312 \, b^{2} c d^{3} e^{4} - 143 \, b^{3} d^{2} e^{5}\right)} x^{2} - 8 \, {\left(64 \, c^{3} d^{6} e - 240 \, b c^{2} d^{5} e^{2} + 312 \, b^{2} c d^{4} e^{3} - 143 \, b^{3} d^{3} e^{4}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{7}}"," ",0,"2/45045*(3003*c^3*e^7*x^7 + 1024*c^3*d^7 - 3840*b*c^2*d^6*e + 4992*b^2*c*d^5*e^2 - 2288*b^3*d^4*e^3 + 231*(c^3*d*e^6 + 45*b*c^2*e^7)*x^6 - 63*(4*c^3*d^2*e^5 - 15*b*c^2*d*e^6 - 195*b^2*c*e^7)*x^5 + 35*(8*c^3*d^3*e^4 - 30*b*c^2*d^2*e^5 + 39*b^2*c*d*e^6 + 143*b^3*e^7)*x^4 - 5*(64*c^3*d^4*e^3 - 240*b*c^2*d^3*e^4 + 312*b^2*c*d^2*e^5 - 143*b^3*d*e^6)*x^3 + 6*(64*c^3*d^5*e^2 - 240*b*c^2*d^4*e^3 + 312*b^2*c*d^3*e^4 - 143*b^3*d^2*e^5)*x^2 - 8*(64*c^3*d^6*e - 240*b*c^2*d^5*e^2 + 312*b^2*c*d^4*e^3 - 143*b^3*d^3*e^4)*x)*sqrt(e*x + d)/e^7","A",0
357,1,270,0,0.394199," ","integrate((c*x^2+b*x)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, c^{3} e^{6} x^{6} + 5120 \, c^{3} d^{6} - 16640 \, b c^{2} d^{5} e + 18304 \, b^{2} c d^{4} e^{2} - 6864 \, b^{3} d^{3} e^{3} - 315 \, {\left(4 \, c^{3} d e^{5} - 13 \, b c^{2} e^{6}\right)} x^{5} + 35 \, {\left(40 \, c^{3} d^{2} e^{4} - 130 \, b c^{2} d e^{5} + 143 \, b^{2} c e^{6}\right)} x^{4} - 5 \, {\left(320 \, c^{3} d^{3} e^{3} - 1040 \, b c^{2} d^{2} e^{4} + 1144 \, b^{2} c d e^{5} - 429 \, b^{3} e^{6}\right)} x^{3} + 6 \, {\left(320 \, c^{3} d^{4} e^{2} - 1040 \, b c^{2} d^{3} e^{3} + 1144 \, b^{2} c d^{2} e^{4} - 429 \, b^{3} d e^{5}\right)} x^{2} - 8 \, {\left(320 \, c^{3} d^{5} e - 1040 \, b c^{2} d^{4} e^{2} + 1144 \, b^{2} c d^{3} e^{3} - 429 \, b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{15015 \, e^{7}}"," ",0,"2/15015*(1155*c^3*e^6*x^6 + 5120*c^3*d^6 - 16640*b*c^2*d^5*e + 18304*b^2*c*d^4*e^2 - 6864*b^3*d^3*e^3 - 315*(4*c^3*d*e^5 - 13*b*c^2*e^6)*x^5 + 35*(40*c^3*d^2*e^4 - 130*b*c^2*d*e^5 + 143*b^2*c*e^6)*x^4 - 5*(320*c^3*d^3*e^3 - 1040*b*c^2*d^2*e^4 + 1144*b^2*c*d*e^5 - 429*b^3*e^6)*x^3 + 6*(320*c^3*d^4*e^2 - 1040*b*c^2*d^3*e^3 + 1144*b^2*c*d^2*e^4 - 429*b^3*d*e^5)*x^2 - 8*(320*c^3*d^5*e - 1040*b*c^2*d^4*e^2 + 1144*b^2*c*d^3*e^3 - 429*b^3*d^2*e^4)*x)*sqrt(e*x + d)/e^7","A",0
358,1,280,0,0.390565," ","integrate((c*x^2+b*x)^3/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, c^{3} e^{6} x^{6} - 5120 \, c^{3} d^{6} + 14080 \, b c^{2} d^{5} e - 12672 \, b^{2} c d^{4} e^{2} + 3696 \, b^{3} d^{3} e^{3} - 35 \, {\left(4 \, c^{3} d e^{5} - 11 \, b c^{2} e^{6}\right)} x^{5} + 5 \, {\left(40 \, c^{3} d^{2} e^{4} - 110 \, b c^{2} d e^{5} + 99 \, b^{2} c e^{6}\right)} x^{4} - {\left(320 \, c^{3} d^{3} e^{3} - 880 \, b c^{2} d^{2} e^{4} + 792 \, b^{2} c d e^{5} - 231 \, b^{3} e^{6}\right)} x^{3} + 2 \, {\left(320 \, c^{3} d^{4} e^{2} - 880 \, b c^{2} d^{3} e^{3} + 792 \, b^{2} c d^{2} e^{4} - 231 \, b^{3} d e^{5}\right)} x^{2} - 8 \, {\left(320 \, c^{3} d^{5} e - 880 \, b c^{2} d^{4} e^{2} + 792 \, b^{2} c d^{3} e^{3} - 231 \, b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{1155 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"2/1155*(105*c^3*e^6*x^6 - 5120*c^3*d^6 + 14080*b*c^2*d^5*e - 12672*b^2*c*d^4*e^2 + 3696*b^3*d^3*e^3 - 35*(4*c^3*d*e^5 - 11*b*c^2*e^6)*x^5 + 5*(40*c^3*d^2*e^4 - 110*b*c^2*d*e^5 + 99*b^2*c*e^6)*x^4 - (320*c^3*d^3*e^3 - 880*b*c^2*d^2*e^4 + 792*b^2*c*d*e^5 - 231*b^3*e^6)*x^3 + 2*(320*c^3*d^4*e^2 - 880*b*c^2*d^3*e^3 + 792*b^2*c*d^2*e^4 - 231*b^3*d*e^5)*x^2 - 8*(320*c^3*d^5*e - 880*b*c^2*d^4*e^2 + 792*b^2*c*d^3*e^3 - 231*b^3*d^2*e^4)*x)*sqrt(e*x + d)/(e^8*x + d*e^7)","A",0
359,1,291,0,0.399657," ","integrate((c*x^2+b*x)^3/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{3} e^{6} x^{6} + 5120 \, c^{3} d^{6} - 11520 \, b c^{2} d^{5} e + 8064 \, b^{2} c d^{4} e^{2} - 1680 \, b^{3} d^{3} e^{3} - 15 \, {\left(4 \, c^{3} d e^{5} - 9 \, b c^{2} e^{6}\right)} x^{5} + 3 \, {\left(40 \, c^{3} d^{2} e^{4} - 90 \, b c^{2} d e^{5} + 63 \, b^{2} c e^{6}\right)} x^{4} - {\left(320 \, c^{3} d^{3} e^{3} - 720 \, b c^{2} d^{2} e^{4} + 504 \, b^{2} c d e^{5} - 105 \, b^{3} e^{6}\right)} x^{3} + 6 \, {\left(320 \, c^{3} d^{4} e^{2} - 720 \, b c^{2} d^{3} e^{3} + 504 \, b^{2} c d^{2} e^{4} - 105 \, b^{3} d e^{5}\right)} x^{2} + 24 \, {\left(320 \, c^{3} d^{5} e - 720 \, b c^{2} d^{4} e^{2} + 504 \, b^{2} c d^{3} e^{3} - 105 \, b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"2/315*(35*c^3*e^6*x^6 + 5120*c^3*d^6 - 11520*b*c^2*d^5*e + 8064*b^2*c*d^4*e^2 - 1680*b^3*d^3*e^3 - 15*(4*c^3*d*e^5 - 9*b*c^2*e^6)*x^5 + 3*(40*c^3*d^2*e^4 - 90*b*c^2*d*e^5 + 63*b^2*c*e^6)*x^4 - (320*c^3*d^3*e^3 - 720*b*c^2*d^2*e^4 + 504*b^2*c*d*e^5 - 105*b^3*e^6)*x^3 + 6*(320*c^3*d^4*e^2 - 720*b*c^2*d^3*e^3 + 504*b^2*c*d^2*e^4 - 105*b^3*d*e^5)*x^2 + 24*(320*c^3*d^5*e - 720*b*c^2*d^4*e^2 + 504*b^2*c*d^3*e^3 - 105*b^3*d^2*e^4)*x)*sqrt(e*x + d)/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","A",0
360,1,302,0,0.397493," ","integrate((c*x^2+b*x)^3/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{3} e^{6} x^{6} - 1024 \, c^{3} d^{6} + 1792 \, b c^{2} d^{5} e - 896 \, b^{2} c d^{4} e^{2} + 112 \, b^{3} d^{3} e^{3} - 3 \, {\left(4 \, c^{3} d e^{5} - 7 \, b c^{2} e^{6}\right)} x^{5} + 5 \, {\left(8 \, c^{3} d^{2} e^{4} - 14 \, b c^{2} d e^{5} + 7 \, b^{2} c e^{6}\right)} x^{4} - 5 \, {\left(64 \, c^{3} d^{3} e^{3} - 112 \, b c^{2} d^{2} e^{4} + 56 \, b^{2} c d e^{5} - 7 \, b^{3} e^{6}\right)} x^{3} - 30 \, {\left(64 \, c^{3} d^{4} e^{2} - 112 \, b c^{2} d^{3} e^{3} + 56 \, b^{2} c d^{2} e^{4} - 7 \, b^{3} d e^{5}\right)} x^{2} - 40 \, {\left(64 \, c^{3} d^{5} e - 112 \, b c^{2} d^{4} e^{2} + 56 \, b^{2} c d^{3} e^{3} - 7 \, b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"2/35*(5*c^3*e^6*x^6 - 1024*c^3*d^6 + 1792*b*c^2*d^5*e - 896*b^2*c*d^4*e^2 + 112*b^3*d^3*e^3 - 3*(4*c^3*d*e^5 - 7*b*c^2*e^6)*x^5 + 5*(8*c^3*d^2*e^4 - 14*b*c^2*d*e^5 + 7*b^2*c*e^6)*x^4 - 5*(64*c^3*d^3*e^3 - 112*b*c^2*d^2*e^4 + 56*b^2*c*d*e^5 - 7*b^3*e^6)*x^3 - 30*(64*c^3*d^4*e^2 - 112*b*c^2*d^3*e^3 + 56*b^2*c*d^2*e^4 - 7*b^3*d*e^5)*x^2 - 40*(64*c^3*d^5*e - 112*b*c^2*d^4*e^2 + 56*b^2*c*d^3*e^3 - 7*b^3*d^2*e^4)*x)*sqrt(e*x + d)/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","A",0
361,1,822,0,1.252966," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{15 \, c^{3} d^{\frac{7}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 15 \, {\left(c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(3 \, b c^{2} e^{3} x^{2} + 58 \, b c^{2} d^{2} e - 50 \, b^{2} c d e^{2} + 15 \, b^{3} e^{3} + {\left(16 \, b c^{2} d e^{2} - 5 \, b^{2} c e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, b c^{3}}, \frac{15 \, c^{3} d^{\frac{7}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 30 \, {\left(c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 2 \, {\left(3 \, b c^{2} e^{3} x^{2} + 58 \, b c^{2} d^{2} e - 50 \, b^{2} c d e^{2} + 15 \, b^{3} e^{3} + {\left(16 \, b c^{2} d e^{2} - 5 \, b^{2} c e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, b c^{3}}, \frac{30 \, c^{3} \sqrt{-d} d^{3} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 15 \, {\left(c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(3 \, b c^{2} e^{3} x^{2} + 58 \, b c^{2} d^{2} e - 50 \, b^{2} c d e^{2} + 15 \, b^{3} e^{3} + {\left(16 \, b c^{2} d e^{2} - 5 \, b^{2} c e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, b c^{3}}, \frac{2 \, {\left(15 \, c^{3} \sqrt{-d} d^{3} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 15 \, {\left(c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left(3 \, b c^{2} e^{3} x^{2} + 58 \, b c^{2} d^{2} e - 50 \, b^{2} c d e^{2} + 15 \, b^{3} e^{3} + {\left(16 \, b c^{2} d e^{2} - 5 \, b^{2} c e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, b c^{3}}\right]"," ",0,"[1/15*(15*c^3*d^(7/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 15*(c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - b^3*e^3)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(3*b*c^2*e^3*x^2 + 58*b*c^2*d^2*e - 50*b^2*c*d*e^2 + 15*b^3*e^3 + (16*b*c^2*d*e^2 - 5*b^2*c*e^3)*x)*sqrt(e*x + d))/(b*c^3), 1/15*(15*c^3*d^(7/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 30*(c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - b^3*e^3)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 2*(3*b*c^2*e^3*x^2 + 58*b*c^2*d^2*e - 50*b^2*c*d*e^2 + 15*b^3*e^3 + (16*b*c^2*d*e^2 - 5*b^2*c*e^3)*x)*sqrt(e*x + d))/(b*c^3), 1/15*(30*c^3*sqrt(-d)*d^3*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 15*(c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - b^3*e^3)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(3*b*c^2*e^3*x^2 + 58*b*c^2*d^2*e - 50*b^2*c*d*e^2 + 15*b^3*e^3 + (16*b*c^2*d*e^2 - 5*b^2*c*e^3)*x)*sqrt(e*x + d))/(b*c^3), 2/15*(15*c^3*sqrt(-d)*d^3*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 15*(c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - b^3*e^3)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + (3*b*c^2*e^3*x^2 + 58*b*c^2*d^2*e - 50*b^2*c*d*e^2 + 15*b^3*e^3 + (16*b*c^2*d*e^2 - 5*b^2*c*e^3)*x)*sqrt(e*x + d))/(b*c^3)]","A",0
362,1,598,0,0.597604," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{3 \, c^{2} d^{\frac{5}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 3 \, {\left(c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(b c e^{2} x + 7 \, b c d e - 3 \, b^{2} e^{2}\right)} \sqrt{e x + d}}{3 \, b c^{2}}, \frac{3 \, c^{2} d^{\frac{5}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 6 \, {\left(c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 2 \, {\left(b c e^{2} x + 7 \, b c d e - 3 \, b^{2} e^{2}\right)} \sqrt{e x + d}}{3 \, b c^{2}}, \frac{6 \, c^{2} \sqrt{-d} d^{2} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left(c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(b c e^{2} x + 7 \, b c d e - 3 \, b^{2} e^{2}\right)} \sqrt{e x + d}}{3 \, b c^{2}}, \frac{2 \, {\left(3 \, c^{2} \sqrt{-d} d^{2} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left(c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left(b c e^{2} x + 7 \, b c d e - 3 \, b^{2} e^{2}\right)} \sqrt{e x + d}\right)}}{3 \, b c^{2}}\right]"," ",0,"[1/3*(3*c^2*d^(5/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 3*(c^2*d^2 - 2*b*c*d*e + b^2*e^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(b*c*e^2*x + 7*b*c*d*e - 3*b^2*e^2)*sqrt(e*x + d))/(b*c^2), 1/3*(3*c^2*d^(5/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 6*(c^2*d^2 - 2*b*c*d*e + b^2*e^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 2*(b*c*e^2*x + 7*b*c*d*e - 3*b^2*e^2)*sqrt(e*x + d))/(b*c^2), 1/3*(6*c^2*sqrt(-d)*d^2*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*(c^2*d^2 - 2*b*c*d*e + b^2*e^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(b*c*e^2*x + 7*b*c*d*e - 3*b^2*e^2)*sqrt(e*x + d))/(b*c^2), 2/3*(3*c^2*sqrt(-d)*d^2*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*(c^2*d^2 - 2*b*c*d*e + b^2*e^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + (b*c*e^2*x + 7*b*c*d*e - 3*b^2*e^2)*sqrt(e*x + d))/(b*c^2)]","A",0
363,1,447,0,0.478448," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{c d^{\frac{3}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, \sqrt{e x + d} b e - {\left(c d - b e\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right)}{b c}, \frac{c d^{\frac{3}{2}} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, \sqrt{e x + d} b e + 2 \, {\left(c d - b e\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right)}{b c}, \frac{2 \, c \sqrt{-d} d \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 2 \, \sqrt{e x + d} b e - {\left(c d - b e\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right)}{b c}, \frac{2 \, {\left(c \sqrt{-d} d \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + \sqrt{e x + d} b e + {\left(c d - b e\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right)\right)}}{b c}\right]"," ",0,"[(c*d^(3/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*sqrt(e*x + d)*b*e - (c*d - b*e)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)))/(b*c), (c*d^(3/2)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*sqrt(e*x + d)*b*e + 2*(c*d - b*e)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)))/(b*c), (2*c*sqrt(-d)*d*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 2*sqrt(e*x + d)*b*e - (c*d - b*e)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)))/(b*c), 2*(c*sqrt(-d)*d*arctan(sqrt(e*x + d)*sqrt(-d)/d) + sqrt(e*x + d)*b*e + (c*d - b*e)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)))/(b*c)]","A",0
364,1,352,0,0.442024," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right)}{b}, \frac{2 \, \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right)}{b}, \frac{2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right)}{b}, \frac{2 \, {\left(\sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right)\right)}}{b}\right]"," ",0,"[(sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x))/b, (2*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x))/b, (2*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)))/b, 2*(sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d))/b]","A",0
365,1,396,0,0.437804," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{d \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right)}{b d}, \frac{2 \, d \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right)}{b d}, \frac{d \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right)}{b d}, \frac{2 \, {\left(d \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right)\right)}}{b d}\right]"," ",0,"[(d*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x))/(b*d), (2*d*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x))/(b*d), (d*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d))/(b*d), 2*(d*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d))/(b*d)]","A",0
366,1,726,0,0.466770," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{e x + d} b d e + {\left(c d^{2} e x + c d^{3}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - {\left(c d^{2} - b d e + {\left(c d e - b e^{2}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right)}{b c d^{4} - b^{2} d^{3} e + {\left(b c d^{3} e - b^{2} d^{2} e^{2}\right)} x}, -\frac{2 \, \sqrt{e x + d} b d e - 2 \, {\left(c d^{2} e x + c d^{3}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left(c d^{2} - b d e + {\left(c d e - b e^{2}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right)}{b c d^{4} - b^{2} d^{3} e + {\left(b c d^{3} e - b^{2} d^{2} e^{2}\right)} x}, -\frac{2 \, \sqrt{e x + d} b d e - 2 \, {\left(c d^{2} - b d e + {\left(c d e - b e^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(c d^{2} e x + c d^{3}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right)}{b c d^{4} - b^{2} d^{3} e + {\left(b c d^{3} e - b^{2} d^{2} e^{2}\right)} x}, -\frac{2 \, {\left(\sqrt{e x + d} b d e - {\left(c d^{2} e x + c d^{3}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left(c d^{2} - b d e + {\left(c d e - b e^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right)\right)}}{b c d^{4} - b^{2} d^{3} e + {\left(b c d^{3} e - b^{2} d^{2} e^{2}\right)} x}\right]"," ",0,"[-(2*sqrt(e*x + d)*b*d*e + (c*d^2*e*x + c*d^3)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - (c*d^2 - b*d*e + (c*d*e - b*e^2)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x))/(b*c*d^4 - b^2*d^3*e + (b*c*d^3*e - b^2*d^2*e^2)*x), -(2*sqrt(e*x + d)*b*d*e - 2*(c*d^2*e*x + c*d^3)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - (c*d^2 - b*d*e + (c*d*e - b*e^2)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x))/(b*c*d^4 - b^2*d^3*e + (b*c*d^3*e - b^2*d^2*e^2)*x), -(2*sqrt(e*x + d)*b*d*e - 2*(c*d^2 - b*d*e + (c*d*e - b*e^2)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (c*d^2*e*x + c*d^3)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)))/(b*c*d^4 - b^2*d^3*e + (b*c*d^3*e - b^2*d^2*e^2)*x), -2*(sqrt(e*x + d)*b*d*e - (c*d^2*e*x + c*d^3)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - (c*d^2 - b*d*e + (c*d*e - b*e^2)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d))/(b*c*d^4 - b^2*d^3*e + (b*c*d^3*e - b^2*d^2*e^2)*x)]","B",0
367,1,1469,0,0.586397," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{3} e^{2} x^{2} + 2 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 3 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} - 2 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(7 \, b c d^{3} e - 4 \, b^{2} d^{2} e^{2} + 3 \, {\left(2 \, b c d^{2} e^{2} - b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b c^{2} d^{7} - 2 \, b^{2} c d^{6} e + b^{3} d^{5} e^{2} + {\left(b c^{2} d^{5} e^{2} - 2 \, b^{2} c d^{4} e^{3} + b^{3} d^{3} e^{4}\right)} x^{2} + 2 \, {\left(b c^{2} d^{6} e - 2 \, b^{2} c d^{5} e^{2} + b^{3} d^{4} e^{3}\right)} x\right)}}, \frac{6 \, {\left(c^{2} d^{3} e^{2} x^{2} + 2 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} - 2 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(7 \, b c d^{3} e - 4 \, b^{2} d^{2} e^{2} + 3 \, {\left(2 \, b c d^{2} e^{2} - b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b c^{2} d^{7} - 2 \, b^{2} c d^{6} e + b^{3} d^{5} e^{2} + {\left(b c^{2} d^{5} e^{2} - 2 \, b^{2} c d^{4} e^{3} + b^{3} d^{3} e^{4}\right)} x^{2} + 2 \, {\left(b c^{2} d^{6} e - 2 \, b^{2} c d^{5} e^{2} + b^{3} d^{4} e^{3}\right)} x\right)}}, \frac{6 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} - 2 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left(c^{2} d^{3} e^{2} x^{2} + 2 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(7 \, b c d^{3} e - 4 \, b^{2} d^{2} e^{2} + 3 \, {\left(2 \, b c d^{2} e^{2} - b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b c^{2} d^{7} - 2 \, b^{2} c d^{6} e + b^{3} d^{5} e^{2} + {\left(b c^{2} d^{5} e^{2} - 2 \, b^{2} c d^{4} e^{3} + b^{3} d^{3} e^{4}\right)} x^{2} + 2 \, {\left(b c^{2} d^{6} e - 2 \, b^{2} c d^{5} e^{2} + b^{3} d^{4} e^{3}\right)} x\right)}}, \frac{2 \, {\left(3 \, {\left(c^{2} d^{3} e^{2} x^{2} + 2 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} - 2 \, b c d e^{3} + b^{2} e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(7 \, b c d^{3} e - 4 \, b^{2} d^{2} e^{2} + 3 \, {\left(2 \, b c d^{2} e^{2} - b^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{3 \, {\left(b c^{2} d^{7} - 2 \, b^{2} c d^{6} e + b^{3} d^{5} e^{2} + {\left(b c^{2} d^{5} e^{2} - 2 \, b^{2} c d^{4} e^{3} + b^{3} d^{3} e^{4}\right)} x^{2} + 2 \, {\left(b c^{2} d^{6} e - 2 \, b^{2} c d^{5} e^{2} + b^{3} d^{4} e^{3}\right)} x\right)}}\right]"," ",0,"[1/3*(3*(c^2*d^3*e^2*x^2 + 2*c^2*d^4*e*x + c^2*d^5)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 3*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (c^2*d^2*e^2 - 2*b*c*d*e^3 + b^2*e^4)*x^2 + 2*(c^2*d^3*e - 2*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(7*b*c*d^3*e - 4*b^2*d^2*e^2 + 3*(2*b*c*d^2*e^2 - b^2*d*e^3)*x)*sqrt(e*x + d))/(b*c^2*d^7 - 2*b^2*c*d^6*e + b^3*d^5*e^2 + (b*c^2*d^5*e^2 - 2*b^2*c*d^4*e^3 + b^3*d^3*e^4)*x^2 + 2*(b*c^2*d^6*e - 2*b^2*c*d^5*e^2 + b^3*d^4*e^3)*x), 1/3*(6*(c^2*d^3*e^2*x^2 + 2*c^2*d^4*e*x + c^2*d^5)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (c^2*d^2*e^2 - 2*b*c*d*e^3 + b^2*e^4)*x^2 + 2*(c^2*d^3*e - 2*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(7*b*c*d^3*e - 4*b^2*d^2*e^2 + 3*(2*b*c*d^2*e^2 - b^2*d*e^3)*x)*sqrt(e*x + d))/(b*c^2*d^7 - 2*b^2*c*d^6*e + b^3*d^5*e^2 + (b*c^2*d^5*e^2 - 2*b^2*c*d^4*e^3 + b^3*d^3*e^4)*x^2 + 2*(b*c^2*d^6*e - 2*b^2*c*d^5*e^2 + b^3*d^4*e^3)*x), 1/3*(6*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (c^2*d^2*e^2 - 2*b*c*d*e^3 + b^2*e^4)*x^2 + 2*(c^2*d^3*e - 2*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*(c^2*d^3*e^2*x^2 + 2*c^2*d^4*e*x + c^2*d^5)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(7*b*c*d^3*e - 4*b^2*d^2*e^2 + 3*(2*b*c*d^2*e^2 - b^2*d*e^3)*x)*sqrt(e*x + d))/(b*c^2*d^7 - 2*b^2*c*d^6*e + b^3*d^5*e^2 + (b*c^2*d^5*e^2 - 2*b^2*c*d^4*e^3 + b^3*d^3*e^4)*x^2 + 2*(b*c^2*d^6*e - 2*b^2*c*d^5*e^2 + b^3*d^4*e^3)*x), 2/3*(3*(c^2*d^3*e^2*x^2 + 2*c^2*d^4*e*x + c^2*d^5)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*(c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (c^2*d^2*e^2 - 2*b*c*d*e^3 + b^2*e^4)*x^2 + 2*(c^2*d^3*e - 2*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (7*b*c*d^3*e - 4*b^2*d^2*e^2 + 3*(2*b*c*d^2*e^2 - b^2*d*e^3)*x)*sqrt(e*x + d))/(b*c^2*d^7 - 2*b^2*c*d^6*e + b^3*d^5*e^2 + (b*c^2*d^5*e^2 - 2*b^2*c*d^4*e^3 + b^3*d^3*e^4)*x^2 + 2*(b*c^2*d^6*e - 2*b^2*c*d^5*e^2 + b^3*d^4*e^3)*x)]","B",0
368,1,2577,0,1.170803," ","integrate(1/(e*x+d)^(7/2)/(c*x^2+b*x),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(c^{3} d^{4} e^{3} x^{3} + 3 \, c^{3} d^{5} e^{2} x^{2} + 3 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\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} + {\left(c^{3} d^{3} e^{3} - 3 \, b c^{2} d^{2} e^{4} + 3 \, b^{2} c d e^{5} - b^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} + 3 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(c^{3} d^{5} e - 3 \, b c^{2} d^{4} e^{2} + 3 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(58 \, b c^{2} d^{5} e - 66 \, b^{2} c d^{4} e^{2} + 23 \, b^{3} d^{3} e^{3} + 15 \, {\left(3 \, b c^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{4} + b^{3} d e^{5}\right)} x^{2} + 5 \, {\left(20 \, b c^{2} d^{4} e^{2} - 21 \, b^{2} c d^{3} e^{3} + 7 \, b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b c^{3} d^{10} - 3 \, b^{2} c^{2} d^{9} e + 3 \, b^{3} c d^{8} e^{2} - b^{4} d^{7} e^{3} + {\left(b c^{3} d^{7} e^{3} - 3 \, b^{2} c^{2} d^{6} e^{4} + 3 \, b^{3} c d^{5} e^{5} - b^{4} d^{4} e^{6}\right)} x^{3} + 3 \, {\left(b c^{3} d^{8} e^{2} - 3 \, b^{2} c^{2} d^{7} e^{3} + 3 \, b^{3} c d^{6} e^{4} - b^{4} d^{5} e^{5}\right)} x^{2} + 3 \, {\left(b c^{3} d^{9} e - 3 \, b^{2} c^{2} d^{8} e^{2} + 3 \, b^{3} c d^{7} e^{3} - b^{4} d^{6} e^{4}\right)} x\right)}}, \frac{30 \, {\left(c^{3} d^{4} e^{3} x^{3} + 3 \, c^{3} d^{5} e^{2} x^{2} + 3 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\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} + {\left(c^{3} d^{3} e^{3} - 3 \, b c^{2} d^{2} e^{4} + 3 \, b^{2} c d e^{5} - b^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} + 3 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(c^{3} d^{5} e - 3 \, b c^{2} d^{4} e^{2} + 3 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(58 \, b c^{2} d^{5} e - 66 \, b^{2} c d^{4} e^{2} + 23 \, b^{3} d^{3} e^{3} + 15 \, {\left(3 \, b c^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{4} + b^{3} d e^{5}\right)} x^{2} + 5 \, {\left(20 \, b c^{2} d^{4} e^{2} - 21 \, b^{2} c d^{3} e^{3} + 7 \, b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b c^{3} d^{10} - 3 \, b^{2} c^{2} d^{9} e + 3 \, b^{3} c d^{8} e^{2} - b^{4} d^{7} e^{3} + {\left(b c^{3} d^{7} e^{3} - 3 \, b^{2} c^{2} d^{6} e^{4} + 3 \, b^{3} c d^{5} e^{5} - b^{4} d^{4} e^{6}\right)} x^{3} + 3 \, {\left(b c^{3} d^{8} e^{2} - 3 \, b^{2} c^{2} d^{7} e^{3} + 3 \, b^{3} c d^{6} e^{4} - b^{4} d^{5} e^{5}\right)} x^{2} + 3 \, {\left(b c^{3} d^{9} e - 3 \, b^{2} c^{2} d^{8} e^{2} + 3 \, b^{3} c d^{7} e^{3} - b^{4} d^{6} e^{4}\right)} x\right)}}, \frac{30 \, {\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} + {\left(c^{3} d^{3} e^{3} - 3 \, b c^{2} d^{2} e^{4} + 3 \, b^{2} c d e^{5} - b^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} + 3 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(c^{3} d^{5} e - 3 \, b c^{2} d^{4} e^{2} + 3 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 15 \, {\left(c^{3} d^{4} e^{3} x^{3} + 3 \, c^{3} d^{5} e^{2} x^{2} + 3 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(58 \, b c^{2} d^{5} e - 66 \, b^{2} c d^{4} e^{2} + 23 \, b^{3} d^{3} e^{3} + 15 \, {\left(3 \, b c^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{4} + b^{3} d e^{5}\right)} x^{2} + 5 \, {\left(20 \, b c^{2} d^{4} e^{2} - 21 \, b^{2} c d^{3} e^{3} + 7 \, b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b c^{3} d^{10} - 3 \, b^{2} c^{2} d^{9} e + 3 \, b^{3} c d^{8} e^{2} - b^{4} d^{7} e^{3} + {\left(b c^{3} d^{7} e^{3} - 3 \, b^{2} c^{2} d^{6} e^{4} + 3 \, b^{3} c d^{5} e^{5} - b^{4} d^{4} e^{6}\right)} x^{3} + 3 \, {\left(b c^{3} d^{8} e^{2} - 3 \, b^{2} c^{2} d^{7} e^{3} + 3 \, b^{3} c d^{6} e^{4} - b^{4} d^{5} e^{5}\right)} x^{2} + 3 \, {\left(b c^{3} d^{9} e - 3 \, b^{2} c^{2} d^{8} e^{2} + 3 \, b^{3} c d^{7} e^{3} - b^{4} d^{6} e^{4}\right)} x\right)}}, \frac{2 \, {\left(15 \, {\left(c^{3} d^{4} e^{3} x^{3} + 3 \, c^{3} d^{5} e^{2} x^{2} + 3 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\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} + {\left(c^{3} d^{3} e^{3} - 3 \, b c^{2} d^{2} e^{4} + 3 \, b^{2} c d e^{5} - b^{3} e^{6}\right)} x^{3} + 3 \, {\left(c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} + 3 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(c^{3} d^{5} e - 3 \, b c^{2} d^{4} e^{2} + 3 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(58 \, b c^{2} d^{5} e - 66 \, b^{2} c d^{4} e^{2} + 23 \, b^{3} d^{3} e^{3} + 15 \, {\left(3 \, b c^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{4} + b^{3} d e^{5}\right)} x^{2} + 5 \, {\left(20 \, b c^{2} d^{4} e^{2} - 21 \, b^{2} c d^{3} e^{3} + 7 \, b^{3} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, {\left(b c^{3} d^{10} - 3 \, b^{2} c^{2} d^{9} e + 3 \, b^{3} c d^{8} e^{2} - b^{4} d^{7} e^{3} + {\left(b c^{3} d^{7} e^{3} - 3 \, b^{2} c^{2} d^{6} e^{4} + 3 \, b^{3} c d^{5} e^{5} - b^{4} d^{4} e^{6}\right)} x^{3} + 3 \, {\left(b c^{3} d^{8} e^{2} - 3 \, b^{2} c^{2} d^{7} e^{3} + 3 \, b^{3} c d^{6} e^{4} - b^{4} d^{5} e^{5}\right)} x^{2} + 3 \, {\left(b c^{3} d^{9} e - 3 \, b^{2} c^{2} d^{8} e^{2} + 3 \, b^{3} c d^{7} e^{3} - b^{4} d^{6} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/15*(15*(c^3*d^4*e^3*x^3 + 3*c^3*d^5*e^2*x^2 + 3*c^3*d^6*e*x + c^3*d^7)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 15*(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 + (c^3*d^3*e^3 - 3*b*c^2*d^2*e^4 + 3*b^2*c*d*e^5 - b^3*e^6)*x^3 + 3*(c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 + 3*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2 + 3*(c^3*d^5*e - 3*b*c^2*d^4*e^2 + 3*b^2*c*d^3*e^3 - b^3*d^2*e^4)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(58*b*c^2*d^5*e - 66*b^2*c*d^4*e^2 + 23*b^3*d^3*e^3 + 15*(3*b*c^2*d^3*e^3 - 3*b^2*c*d^2*e^4 + b^3*d*e^5)*x^2 + 5*(20*b*c^2*d^4*e^2 - 21*b^2*c*d^3*e^3 + 7*b^3*d^2*e^4)*x)*sqrt(e*x + d))/(b*c^3*d^10 - 3*b^2*c^2*d^9*e + 3*b^3*c*d^8*e^2 - b^4*d^7*e^3 + (b*c^3*d^7*e^3 - 3*b^2*c^2*d^6*e^4 + 3*b^3*c*d^5*e^5 - b^4*d^4*e^6)*x^3 + 3*(b*c^3*d^8*e^2 - 3*b^2*c^2*d^7*e^3 + 3*b^3*c*d^6*e^4 - b^4*d^5*e^5)*x^2 + 3*(b*c^3*d^9*e - 3*b^2*c^2*d^8*e^2 + 3*b^3*c*d^7*e^3 - b^4*d^6*e^4)*x), 1/15*(30*(c^3*d^4*e^3*x^3 + 3*c^3*d^5*e^2*x^2 + 3*c^3*d^6*e*x + c^3*d^7)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 15*(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 + (c^3*d^3*e^3 - 3*b*c^2*d^2*e^4 + 3*b^2*c*d*e^5 - b^3*e^6)*x^3 + 3*(c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 + 3*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2 + 3*(c^3*d^5*e - 3*b*c^2*d^4*e^2 + 3*b^2*c*d^3*e^3 - b^3*d^2*e^4)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(58*b*c^2*d^5*e - 66*b^2*c*d^4*e^2 + 23*b^3*d^3*e^3 + 15*(3*b*c^2*d^3*e^3 - 3*b^2*c*d^2*e^4 + b^3*d*e^5)*x^2 + 5*(20*b*c^2*d^4*e^2 - 21*b^2*c*d^3*e^3 + 7*b^3*d^2*e^4)*x)*sqrt(e*x + d))/(b*c^3*d^10 - 3*b^2*c^2*d^9*e + 3*b^3*c*d^8*e^2 - b^4*d^7*e^3 + (b*c^3*d^7*e^3 - 3*b^2*c^2*d^6*e^4 + 3*b^3*c*d^5*e^5 - b^4*d^4*e^6)*x^3 + 3*(b*c^3*d^8*e^2 - 3*b^2*c^2*d^7*e^3 + 3*b^3*c*d^6*e^4 - b^4*d^5*e^5)*x^2 + 3*(b*c^3*d^9*e - 3*b^2*c^2*d^8*e^2 + 3*b^3*c*d^7*e^3 - b^4*d^6*e^4)*x), 1/15*(30*(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 + (c^3*d^3*e^3 - 3*b*c^2*d^2*e^4 + 3*b^2*c*d*e^5 - b^3*e^6)*x^3 + 3*(c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 + 3*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2 + 3*(c^3*d^5*e - 3*b*c^2*d^4*e^2 + 3*b^2*c*d^3*e^3 - b^3*d^2*e^4)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 15*(c^3*d^4*e^3*x^3 + 3*c^3*d^5*e^2*x^2 + 3*c^3*d^6*e*x + c^3*d^7)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(58*b*c^2*d^5*e - 66*b^2*c*d^4*e^2 + 23*b^3*d^3*e^3 + 15*(3*b*c^2*d^3*e^3 - 3*b^2*c*d^2*e^4 + b^3*d*e^5)*x^2 + 5*(20*b*c^2*d^4*e^2 - 21*b^2*c*d^3*e^3 + 7*b^3*d^2*e^4)*x)*sqrt(e*x + d))/(b*c^3*d^10 - 3*b^2*c^2*d^9*e + 3*b^3*c*d^8*e^2 - b^4*d^7*e^3 + (b*c^3*d^7*e^3 - 3*b^2*c^2*d^6*e^4 + 3*b^3*c*d^5*e^5 - b^4*d^4*e^6)*x^3 + 3*(b*c^3*d^8*e^2 - 3*b^2*c^2*d^7*e^3 + 3*b^3*c*d^6*e^4 - b^4*d^5*e^5)*x^2 + 3*(b*c^3*d^9*e - 3*b^2*c^2*d^8*e^2 + 3*b^3*c*d^7*e^3 - b^4*d^6*e^4)*x), 2/15*(15*(c^3*d^4*e^3*x^3 + 3*c^3*d^5*e^2*x^2 + 3*c^3*d^6*e*x + c^3*d^7)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 15*(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 + (c^3*d^3*e^3 - 3*b*c^2*d^2*e^4 + 3*b^2*c*d*e^5 - b^3*e^6)*x^3 + 3*(c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 + 3*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2 + 3*(c^3*d^5*e - 3*b*c^2*d^4*e^2 + 3*b^2*c*d^3*e^3 - b^3*d^2*e^4)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (58*b*c^2*d^5*e - 66*b^2*c*d^4*e^2 + 23*b^3*d^3*e^3 + 15*(3*b*c^2*d^3*e^3 - 3*b^2*c*d^2*e^4 + b^3*d*e^5)*x^2 + 5*(20*b*c^2*d^4*e^2 - 21*b^2*c*d^3*e^3 + 7*b^3*d^2*e^4)*x)*sqrt(e*x + d))/(b*c^3*d^10 - 3*b^2*c^2*d^9*e + 3*b^3*c*d^8*e^2 - b^4*d^7*e^3 + (b*c^3*d^7*e^3 - 3*b^2*c^2*d^6*e^4 + 3*b^3*c*d^5*e^5 - b^4*d^4*e^6)*x^3 + 3*(b*c^3*d^8*e^2 - 3*b^2*c^2*d^7*e^3 + 3*b^3*c*d^6*e^4 - b^4*d^5*e^5)*x^2 + 3*(b*c^3*d^9*e - 3*b^2*c^2*d^8*e^2 + 3*b^3*c*d^7*e^3 - b^4*d^6*e^4)*x)]","B",0
369,1,1561,0,3.328096," ","integrate((e*x+d)^(9/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(4 \, c^{5} d^{4} - 7 \, b c^{4} d^{3} e - 3 \, b^{2} c^{3} d^{2} e^{2} + 11 \, b^{3} c^{2} d e^{3} - 5 \, b^{4} c e^{4}\right)} x^{2} + {\left(4 \, b c^{4} d^{4} - 7 \, b^{2} c^{3} d^{3} e - 3 \, b^{3} c^{2} d^{2} e^{2} + 11 \, b^{4} c d e^{3} - 5 \, b^{5} e^{4}\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 3 \, {\left({\left(4 \, c^{5} d^{4} - 9 \, b c^{4} d^{3} e\right)} x^{2} + {\left(4 \, b c^{4} d^{4} - 9 \, b^{2} c^{3} d^{3} e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{3} c^{2} e^{4} x^{3} - 3 \, b^{2} c^{3} d^{4} + 2 \, {\left(13 \, b^{3} c^{2} d e^{3} - 5 \, b^{4} c e^{4}\right)} x^{2} - {\left(6 \, b c^{4} d^{4} - 12 \, b^{2} c^{3} d^{3} e + 18 \, b^{3} c^{2} d^{2} e^{2} - 38 \, b^{4} c d e^{3} + 15 \, b^{5} e^{4}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(b^{3} c^{4} x^{2} + b^{4} c^{3} x\right)}}, -\frac{6 \, {\left({\left(4 \, c^{5} d^{4} - 7 \, b c^{4} d^{3} e - 3 \, b^{2} c^{3} d^{2} e^{2} + 11 \, b^{3} c^{2} d e^{3} - 5 \, b^{4} c e^{4}\right)} x^{2} + {\left(4 \, b c^{4} d^{4} - 7 \, b^{2} c^{3} d^{3} e - 3 \, b^{3} c^{2} d^{2} e^{2} + 11 \, b^{4} c d e^{3} - 5 \, b^{5} e^{4}\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 3 \, {\left({\left(4 \, c^{5} d^{4} - 9 \, b c^{4} d^{3} e\right)} x^{2} + {\left(4 \, b c^{4} d^{4} - 9 \, b^{2} c^{3} d^{3} e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{3} c^{2} e^{4} x^{3} - 3 \, b^{2} c^{3} d^{4} + 2 \, {\left(13 \, b^{3} c^{2} d e^{3} - 5 \, b^{4} c e^{4}\right)} x^{2} - {\left(6 \, b c^{4} d^{4} - 12 \, b^{2} c^{3} d^{3} e + 18 \, b^{3} c^{2} d^{2} e^{2} - 38 \, b^{4} c d e^{3} + 15 \, b^{5} e^{4}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(b^{3} c^{4} x^{2} + b^{4} c^{3} x\right)}}, -\frac{6 \, {\left({\left(4 \, c^{5} d^{4} - 9 \, b c^{4} d^{3} e\right)} x^{2} + {\left(4 \, b c^{4} d^{4} - 9 \, b^{2} c^{3} d^{3} e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left({\left(4 \, c^{5} d^{4} - 7 \, b c^{4} d^{3} e - 3 \, b^{2} c^{3} d^{2} e^{2} + 11 \, b^{3} c^{2} d e^{3} - 5 \, b^{4} c e^{4}\right)} x^{2} + {\left(4 \, b c^{4} d^{4} - 7 \, b^{2} c^{3} d^{3} e - 3 \, b^{3} c^{2} d^{2} e^{2} + 11 \, b^{4} c d e^{3} - 5 \, b^{5} e^{4}\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - 2 \, {\left(2 \, b^{3} c^{2} e^{4} x^{3} - 3 \, b^{2} c^{3} d^{4} + 2 \, {\left(13 \, b^{3} c^{2} d e^{3} - 5 \, b^{4} c e^{4}\right)} x^{2} - {\left(6 \, b c^{4} d^{4} - 12 \, b^{2} c^{3} d^{3} e + 18 \, b^{3} c^{2} d^{2} e^{2} - 38 \, b^{4} c d e^{3} + 15 \, b^{5} e^{4}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(b^{3} c^{4} x^{2} + b^{4} c^{3} x\right)}}, -\frac{3 \, {\left({\left(4 \, c^{5} d^{4} - 7 \, b c^{4} d^{3} e - 3 \, b^{2} c^{3} d^{2} e^{2} + 11 \, b^{3} c^{2} d e^{3} - 5 \, b^{4} c e^{4}\right)} x^{2} + {\left(4 \, b c^{4} d^{4} - 7 \, b^{2} c^{3} d^{3} e - 3 \, b^{3} c^{2} d^{2} e^{2} + 11 \, b^{4} c d e^{3} - 5 \, b^{5} e^{4}\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 3 \, {\left({\left(4 \, c^{5} d^{4} - 9 \, b c^{4} d^{3} e\right)} x^{2} + {\left(4 \, b c^{4} d^{4} - 9 \, b^{2} c^{3} d^{3} e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, b^{3} c^{2} e^{4} x^{3} - 3 \, b^{2} c^{3} d^{4} + 2 \, {\left(13 \, b^{3} c^{2} d e^{3} - 5 \, b^{4} c e^{4}\right)} x^{2} - {\left(6 \, b c^{4} d^{4} - 12 \, b^{2} c^{3} d^{3} e + 18 \, b^{3} c^{2} d^{2} e^{2} - 38 \, b^{4} c d e^{3} + 15 \, b^{5} e^{4}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b^{3} c^{4} x^{2} + b^{4} c^{3} x\right)}}\right]"," ",0,"[-1/6*(3*((4*c^5*d^4 - 7*b*c^4*d^3*e - 3*b^2*c^3*d^2*e^2 + 11*b^3*c^2*d*e^3 - 5*b^4*c*e^4)*x^2 + (4*b*c^4*d^4 - 7*b^2*c^3*d^3*e - 3*b^3*c^2*d^2*e^2 + 11*b^4*c*d*e^3 - 5*b^5*e^4)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 3*((4*c^5*d^4 - 9*b*c^4*d^3*e)*x^2 + (4*b*c^4*d^4 - 9*b^2*c^3*d^3*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^3*c^2*e^4*x^3 - 3*b^2*c^3*d^4 + 2*(13*b^3*c^2*d*e^3 - 5*b^4*c*e^4)*x^2 - (6*b*c^4*d^4 - 12*b^2*c^3*d^3*e + 18*b^3*c^2*d^2*e^2 - 38*b^4*c*d*e^3 + 15*b^5*e^4)*x)*sqrt(e*x + d))/(b^3*c^4*x^2 + b^4*c^3*x), -1/6*(6*((4*c^5*d^4 - 7*b*c^4*d^3*e - 3*b^2*c^3*d^2*e^2 + 11*b^3*c^2*d*e^3 - 5*b^4*c*e^4)*x^2 + (4*b*c^4*d^4 - 7*b^2*c^3*d^3*e - 3*b^3*c^2*d^2*e^2 + 11*b^4*c*d*e^3 - 5*b^5*e^4)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 3*((4*c^5*d^4 - 9*b*c^4*d^3*e)*x^2 + (4*b*c^4*d^4 - 9*b^2*c^3*d^3*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^3*c^2*e^4*x^3 - 3*b^2*c^3*d^4 + 2*(13*b^3*c^2*d*e^3 - 5*b^4*c*e^4)*x^2 - (6*b*c^4*d^4 - 12*b^2*c^3*d^3*e + 18*b^3*c^2*d^2*e^2 - 38*b^4*c*d*e^3 + 15*b^5*e^4)*x)*sqrt(e*x + d))/(b^3*c^4*x^2 + b^4*c^3*x), -1/6*(6*((4*c^5*d^4 - 9*b*c^4*d^3*e)*x^2 + (4*b*c^4*d^4 - 9*b^2*c^3*d^3*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*((4*c^5*d^4 - 7*b*c^4*d^3*e - 3*b^2*c^3*d^2*e^2 + 11*b^3*c^2*d*e^3 - 5*b^4*c*e^4)*x^2 + (4*b*c^4*d^4 - 7*b^2*c^3*d^3*e - 3*b^3*c^2*d^2*e^2 + 11*b^4*c*d*e^3 - 5*b^5*e^4)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - 2*(2*b^3*c^2*e^4*x^3 - 3*b^2*c^3*d^4 + 2*(13*b^3*c^2*d*e^3 - 5*b^4*c*e^4)*x^2 - (6*b*c^4*d^4 - 12*b^2*c^3*d^3*e + 18*b^3*c^2*d^2*e^2 - 38*b^4*c*d*e^3 + 15*b^5*e^4)*x)*sqrt(e*x + d))/(b^3*c^4*x^2 + b^4*c^3*x), -1/3*(3*((4*c^5*d^4 - 7*b*c^4*d^3*e - 3*b^2*c^3*d^2*e^2 + 11*b^3*c^2*d*e^3 - 5*b^4*c*e^4)*x^2 + (4*b*c^4*d^4 - 7*b^2*c^3*d^3*e - 3*b^3*c^2*d^2*e^2 + 11*b^4*c*d*e^3 - 5*b^5*e^4)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 3*((4*c^5*d^4 - 9*b*c^4*d^3*e)*x^2 + (4*b*c^4*d^4 - 9*b^2*c^3*d^3*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*b^3*c^2*e^4*x^3 - 3*b^2*c^3*d^4 + 2*(13*b^3*c^2*d*e^3 - 5*b^4*c*e^4)*x^2 - (6*b*c^4*d^4 - 12*b^2*c^3*d^3*e + 18*b^3*c^2*d^2*e^2 - 38*b^4*c*d*e^3 + 15*b^5*e^4)*x)*sqrt(e*x + d))/(b^3*c^4*x^2 + b^4*c^3*x)]","A",0
370,1,1273,0,1.045544," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, c^{4} d^{3} - 5 \, b c^{3} d^{2} e - 2 \, b^{2} c^{2} d e^{2} + 3 \, b^{3} c e^{3}\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 5 \, b^{2} c^{2} d^{2} e - 2 \, b^{3} c d e^{2} + 3 \, b^{4} e^{3}\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - {\left({\left(4 \, c^{4} d^{3} - 7 \, b c^{3} d^{2} e\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 7 \, b^{2} c^{2} d^{2} e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, b^{3} c e^{3} x^{2} - b^{2} c^{2} d^{3} - {\left(2 \, b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e + 3 \, b^{3} c d e^{2} - 3 \, b^{4} e^{3}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{3} x^{2} + b^{4} c^{2} x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{4} d^{3} - 5 \, b c^{3} d^{2} e - 2 \, b^{2} c^{2} d e^{2} + 3 \, b^{3} c e^{3}\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 5 \, b^{2} c^{2} d^{2} e - 2 \, b^{3} c d e^{2} + 3 \, b^{4} e^{3}\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(4 \, c^{4} d^{3} - 7 \, b c^{3} d^{2} e\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 7 \, b^{2} c^{2} d^{2} e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{3} c e^{3} x^{2} - b^{2} c^{2} d^{3} - {\left(2 \, b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e + 3 \, b^{3} c d e^{2} - 3 \, b^{4} e^{3}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{3} x^{2} + b^{4} c^{2} x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{4} d^{3} - 7 \, b c^{3} d^{2} e\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 7 \, b^{2} c^{2} d^{2} e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left({\left(4 \, c^{4} d^{3} - 5 \, b c^{3} d^{2} e - 2 \, b^{2} c^{2} d e^{2} + 3 \, b^{3} c e^{3}\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 5 \, b^{2} c^{2} d^{2} e - 2 \, b^{3} c d e^{2} + 3 \, b^{4} e^{3}\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - 2 \, {\left(2 \, b^{3} c e^{3} x^{2} - b^{2} c^{2} d^{3} - {\left(2 \, b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e + 3 \, b^{3} c d e^{2} - 3 \, b^{4} e^{3}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{3} x^{2} + b^{4} c^{2} x\right)}}, -\frac{{\left({\left(4 \, c^{4} d^{3} - 5 \, b c^{3} d^{2} e - 2 \, b^{2} c^{2} d e^{2} + 3 \, b^{3} c e^{3}\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 5 \, b^{2} c^{2} d^{2} e - 2 \, b^{3} c d e^{2} + 3 \, b^{4} e^{3}\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(4 \, c^{4} d^{3} - 7 \, b c^{3} d^{2} e\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 7 \, b^{2} c^{2} d^{2} e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, b^{3} c e^{3} x^{2} - b^{2} c^{2} d^{3} - {\left(2 \, b c^{3} d^{3} - 3 \, b^{2} c^{2} d^{2} e + 3 \, b^{3} c d e^{2} - 3 \, b^{4} e^{3}\right)} x\right)} \sqrt{e x + d}}{b^{3} c^{3} x^{2} + b^{4} c^{2} x}\right]"," ",0,"[1/2*(((4*c^4*d^3 - 5*b*c^3*d^2*e - 2*b^2*c^2*d*e^2 + 3*b^3*c*e^3)*x^2 + (4*b*c^3*d^3 - 5*b^2*c^2*d^2*e - 2*b^3*c*d*e^2 + 3*b^4*e^3)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - ((4*c^4*d^3 - 7*b*c^3*d^2*e)*x^2 + (4*b*c^3*d^3 - 7*b^2*c^2*d^2*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*b^3*c*e^3*x^2 - b^2*c^2*d^3 - (2*b*c^3*d^3 - 3*b^2*c^2*d^2*e + 3*b^3*c*d*e^2 - 3*b^4*e^3)*x)*sqrt(e*x + d))/(b^3*c^3*x^2 + b^4*c^2*x), -1/2*(2*((4*c^4*d^3 - 5*b*c^3*d^2*e - 2*b^2*c^2*d*e^2 + 3*b^3*c*e^3)*x^2 + (4*b*c^3*d^3 - 5*b^2*c^2*d^2*e - 2*b^3*c*d*e^2 + 3*b^4*e^3)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((4*c^4*d^3 - 7*b*c^3*d^2*e)*x^2 + (4*b*c^3*d^3 - 7*b^2*c^2*d^2*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^3*c*e^3*x^2 - b^2*c^2*d^3 - (2*b*c^3*d^3 - 3*b^2*c^2*d^2*e + 3*b^3*c*d*e^2 - 3*b^4*e^3)*x)*sqrt(e*x + d))/(b^3*c^3*x^2 + b^4*c^2*x), -1/2*(2*((4*c^4*d^3 - 7*b*c^3*d^2*e)*x^2 + (4*b*c^3*d^3 - 7*b^2*c^2*d^2*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - ((4*c^4*d^3 - 5*b*c^3*d^2*e - 2*b^2*c^2*d*e^2 + 3*b^3*c*e^3)*x^2 + (4*b*c^3*d^3 - 5*b^2*c^2*d^2*e - 2*b^3*c*d*e^2 + 3*b^4*e^3)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e - 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - 2*(2*b^3*c*e^3*x^2 - b^2*c^2*d^3 - (2*b*c^3*d^3 - 3*b^2*c^2*d^2*e + 3*b^3*c*d*e^2 - 3*b^4*e^3)*x)*sqrt(e*x + d))/(b^3*c^3*x^2 + b^4*c^2*x), -(((4*c^4*d^3 - 5*b*c^3*d^2*e - 2*b^2*c^2*d*e^2 + 3*b^3*c*e^3)*x^2 + (4*b*c^3*d^3 - 5*b^2*c^2*d^2*e - 2*b^3*c*d*e^2 + 3*b^4*e^3)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((4*c^4*d^3 - 7*b*c^3*d^2*e)*x^2 + (4*b*c^3*d^3 - 7*b^2*c^2*d^2*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*b^3*c*e^3*x^2 - b^2*c^2*d^3 - (2*b*c^3*d^3 - 3*b^2*c^2*d^2*e + 3*b^3*c*d*e^2 - 3*b^4*e^3)*x)*sqrt(e*x + d))/(b^3*c^3*x^2 + b^4*c^2*x)]","A",0
371,1,1002,0,0.523571," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, c^{3} d^{2} - 3 \, b c^{2} d e - b^{2} c e^{2}\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 3 \, b^{2} c d e - b^{3} e^{2}\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + {\left({\left(4 \, c^{3} d^{2} - 5 \, b c^{2} d e\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 5 \, b^{2} c d e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(b^{2} c d^{2} + {\left(2 \, b c^{2} d^{2} - 2 \, b^{2} c d e + b^{3} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{2} x^{2} + b^{4} c x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{3} d^{2} - 3 \, b c^{2} d e - b^{2} c e^{2}\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 3 \, b^{2} c d e - b^{3} e^{2}\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(4 \, c^{3} d^{2} - 5 \, b c^{2} d e\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 5 \, b^{2} c d e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(b^{2} c d^{2} + {\left(2 \, b c^{2} d^{2} - 2 \, b^{2} c d e + b^{3} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{2} x^{2} + b^{4} c x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{3} d^{2} - 5 \, b c^{2} d e\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 5 \, b^{2} c d e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left({\left(4 \, c^{3} d^{2} - 3 \, b c^{2} d e - b^{2} c e^{2}\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 3 \, b^{2} c d e - b^{3} e^{2}\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(b^{2} c d^{2} + {\left(2 \, b c^{2} d^{2} - 2 \, b^{2} c d e + b^{3} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c^{2} x^{2} + b^{4} c x\right)}}, -\frac{{\left({\left(4 \, c^{3} d^{2} - 3 \, b c^{2} d e - b^{2} c e^{2}\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 3 \, b^{2} c d e - b^{3} e^{2}\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(4 \, c^{3} d^{2} - 5 \, b c^{2} d e\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 5 \, b^{2} c d e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(b^{2} c d^{2} + {\left(2 \, b c^{2} d^{2} - 2 \, b^{2} c d e + b^{3} e^{2}\right)} x\right)} \sqrt{e x + d}}{b^{3} c^{2} x^{2} + b^{4} c x}\right]"," ",0,"[-1/2*(((4*c^3*d^2 - 3*b*c^2*d*e - b^2*c*e^2)*x^2 + (4*b*c^2*d^2 - 3*b^2*c*d*e - b^3*e^2)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + ((4*c^3*d^2 - 5*b*c^2*d*e)*x^2 + (4*b*c^2*d^2 - 5*b^2*c*d*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(b^2*c*d^2 + (2*b*c^2*d^2 - 2*b^2*c*d*e + b^3*e^2)*x)*sqrt(e*x + d))/(b^3*c^2*x^2 + b^4*c*x), -1/2*(2*((4*c^3*d^2 - 3*b*c^2*d*e - b^2*c*e^2)*x^2 + (4*b*c^2*d^2 - 3*b^2*c*d*e - b^3*e^2)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((4*c^3*d^2 - 5*b*c^2*d*e)*x^2 + (4*b*c^2*d^2 - 5*b^2*c*d*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(b^2*c*d^2 + (2*b*c^2*d^2 - 2*b^2*c*d*e + b^3*e^2)*x)*sqrt(e*x + d))/(b^3*c^2*x^2 + b^4*c*x), -1/2*(2*((4*c^3*d^2 - 5*b*c^2*d*e)*x^2 + (4*b*c^2*d^2 - 5*b^2*c*d*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + ((4*c^3*d^2 - 3*b*c^2*d*e - b^2*c*e^2)*x^2 + (4*b*c^2*d^2 - 3*b^2*c*d*e - b^3*e^2)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(b^2*c*d^2 + (2*b*c^2*d^2 - 2*b^2*c*d*e + b^3*e^2)*x)*sqrt(e*x + d))/(b^3*c^2*x^2 + b^4*c*x), -(((4*c^3*d^2 - 3*b*c^2*d*e - b^2*c*e^2)*x^2 + (4*b*c^2*d^2 - 3*b^2*c*d*e - b^3*e^2)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((4*c^3*d^2 - 5*b*c^2*d*e)*x^2 + (4*b*c^2*d^2 - 5*b^2*c*d*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (b^2*c*d^2 + (2*b*c^2*d^2 - 2*b^2*c*d*e + b^3*e^2)*x)*sqrt(e*x + d))/(b^3*c^2*x^2 + b^4*c*x)]","A",0
372,1,770,0,0.461967," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, c^{2} d - b c e\right)} x^{2} + {\left(4 \, b c d - b^{2} e\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + {\left({\left(4 \, c^{2} d - 3 \, b c e\right)} x^{2} + {\left(4 \, b c d - 3 \, b^{2} e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(b^{2} d + {\left(2 \, b c d - b^{2} e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c x^{2} + b^{4} x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{2} d - b c e\right)} x^{2} + {\left(4 \, b c d - b^{2} e\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(4 \, c^{2} d - 3 \, b c e\right)} x^{2} + {\left(4 \, b c d - 3 \, b^{2} e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(b^{2} d + {\left(2 \, b c d - b^{2} e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c x^{2} + b^{4} x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{2} d - 3 \, b c e\right)} x^{2} + {\left(4 \, b c d - 3 \, b^{2} e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left({\left(4 \, c^{2} d - b c e\right)} x^{2} + {\left(4 \, b c d - b^{2} e\right)} x\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 2 \, {\left(b^{2} d + {\left(2 \, b c d - b^{2} e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c x^{2} + b^{4} x\right)}}, -\frac{{\left({\left(4 \, c^{2} d - b c e\right)} x^{2} + {\left(4 \, b c d - b^{2} e\right)} x\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(4 \, c^{2} d - 3 \, b c e\right)} x^{2} + {\left(4 \, b c d - 3 \, b^{2} e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(b^{2} d + {\left(2 \, b c d - b^{2} e\right)} x\right)} \sqrt{e x + d}}{b^{3} c x^{2} + b^{4} x}\right]"," ",0,"[-1/2*(((4*c^2*d - b*c*e)*x^2 + (4*b*c*d - b^2*e)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + ((4*c^2*d - 3*b*c*e)*x^2 + (4*b*c*d - 3*b^2*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(b^2*d + (2*b*c*d - b^2*e)*x)*sqrt(e*x + d))/(b^3*c*x^2 + b^4*x), -1/2*(2*((4*c^2*d - b*c*e)*x^2 + (4*b*c*d - b^2*e)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((4*c^2*d - 3*b*c*e)*x^2 + (4*b*c*d - 3*b^2*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(b^2*d + (2*b*c*d - b^2*e)*x)*sqrt(e*x + d))/(b^3*c*x^2 + b^4*x), -1/2*(2*((4*c^2*d - 3*b*c*e)*x^2 + (4*b*c*d - 3*b^2*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + ((4*c^2*d - b*c*e)*x^2 + (4*b*c*d - b^2*e)*x)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 2*(b^2*d + (2*b*c*d - b^2*e)*x)*sqrt(e*x + d))/(b^3*c*x^2 + b^4*x), -(((4*c^2*d - b*c*e)*x^2 + (4*b*c*d - b^2*e)*x)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((4*c^2*d - 3*b*c*e)*x^2 + (4*b*c*d - 3*b^2*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (b^2*d + (2*b*c*d - b^2*e)*x)*sqrt(e*x + d))/(b^3*c*x^2 + b^4*x)]","A",0
373,1,798,0,0.467643," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, c^{2} d^{2} - 3 \, b c d e\right)} x^{2} + {\left(4 \, b c d^{2} - 3 \, b^{2} d e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + {\left({\left(4 \, c^{2} d - b c e\right)} x^{2} + {\left(4 \, b c d - b^{2} e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, b c d x + b^{2} d\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c d x^{2} + b^{4} d x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{2} d^{2} - 3 \, b c d e\right)} x^{2} + {\left(4 \, b c d^{2} - 3 \, b^{2} d e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + {\left({\left(4 \, c^{2} d - b c e\right)} x^{2} + {\left(4 \, b c d - b^{2} e\right)} x\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, b c d x + b^{2} d\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c d x^{2} + b^{4} d x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{2} d - b c e\right)} x^{2} + {\left(4 \, b c d - b^{2} e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left({\left(4 \, c^{2} d^{2} - 3 \, b c d e\right)} x^{2} + {\left(4 \, b c d^{2} - 3 \, b^{2} d e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(2 \, b c d x + b^{2} d\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} c d x^{2} + b^{4} d x\right)}}, -\frac{{\left({\left(4 \, c^{2} d^{2} - 3 \, b c d e\right)} x^{2} + {\left(4 \, b c d^{2} - 3 \, b^{2} d e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + {\left({\left(4 \, c^{2} d - b c e\right)} x^{2} + {\left(4 \, b c d - b^{2} e\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(2 \, b c d x + b^{2} d\right)} \sqrt{e x + d}}{b^{3} c d x^{2} + b^{4} d x}\right]"," ",0,"[-1/2*(((4*c^2*d^2 - 3*b*c*d*e)*x^2 + (4*b*c*d^2 - 3*b^2*d*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + ((4*c^2*d - b*c*e)*x^2 + (4*b*c*d - b^2*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*b*c*d*x + b^2*d)*sqrt(e*x + d))/(b^3*c*d*x^2 + b^4*d*x), -1/2*(2*((4*c^2*d^2 - 3*b*c*d*e)*x^2 + (4*b*c*d^2 - 3*b^2*d*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + ((4*c^2*d - b*c*e)*x^2 + (4*b*c*d - b^2*e)*x)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*b*c*d*x + b^2*d)*sqrt(e*x + d))/(b^3*c*d*x^2 + b^4*d*x), -1/2*(2*((4*c^2*d - b*c*e)*x^2 + (4*b*c*d - b^2*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + ((4*c^2*d^2 - 3*b*c*d*e)*x^2 + (4*b*c*d^2 - 3*b^2*d*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(2*b*c*d*x + b^2*d)*sqrt(e*x + d))/(b^3*c*d*x^2 + b^4*d*x), -(((4*c^2*d^2 - 3*b*c*d*e)*x^2 + (4*b*c*d^2 - 3*b^2*d*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + ((4*c^2*d - b*c*e)*x^2 + (4*b*c*d - b^2*e)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (2*b*c*d*x + b^2*d)*sqrt(e*x + d))/(b^3*c*d*x^2 + b^4*d*x)]","A",0
374,1,1164,0,0.571556," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[\frac{{\left({\left(4 \, c^{3} d^{3} - 5 \, b c^{2} d^{2} e\right)} x^{2} + {\left(4 \, b c^{2} d^{3} - 5 \, b^{2} c d^{2} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + {\left({\left(4 \, c^{3} d^{2} - 3 \, b c^{2} d e - b^{2} c e^{2}\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 3 \, b^{2} c d e - b^{3} e^{2}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(b^{2} c d^{2} - b^{3} d e + {\left(2 \, b c^{2} d^{2} - b^{2} c d e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{2} d^{3} - b^{4} c d^{2} e\right)} x^{2} + {\left(b^{4} c d^{3} - b^{5} d^{2} e\right)} x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{3} d^{3} - 5 \, b c^{2} d^{2} e\right)} x^{2} + {\left(4 \, b c^{2} d^{3} - 5 \, b^{2} c d^{2} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left({\left(4 \, c^{3} d^{2} - 3 \, b c^{2} d e - b^{2} c e^{2}\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 3 \, b^{2} c d e - b^{3} e^{2}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(b^{2} c d^{2} - b^{3} d e + {\left(2 \, b c^{2} d^{2} - b^{2} c d e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{2} d^{3} - b^{4} c d^{2} e\right)} x^{2} + {\left(b^{4} c d^{3} - b^{5} d^{2} e\right)} x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{3} d^{2} - 3 \, b c^{2} d e - b^{2} c e^{2}\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 3 \, b^{2} c d e - b^{3} e^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left({\left(4 \, c^{3} d^{3} - 5 \, b c^{2} d^{2} e\right)} x^{2} + {\left(4 \, b c^{2} d^{3} - 5 \, b^{2} c d^{2} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(b^{2} c d^{2} - b^{3} d e + {\left(2 \, b c^{2} d^{2} - b^{2} c d e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{2} d^{3} - b^{4} c d^{2} e\right)} x^{2} + {\left(b^{4} c d^{3} - b^{5} d^{2} e\right)} x\right)}}, -\frac{{\left({\left(4 \, c^{3} d^{3} - 5 \, b c^{2} d^{2} e\right)} x^{2} + {\left(4 \, b c^{2} d^{3} - 5 \, b^{2} c d^{2} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + {\left({\left(4 \, c^{3} d^{2} - 3 \, b c^{2} d e - b^{2} c e^{2}\right)} x^{2} + {\left(4 \, b c^{2} d^{2} - 3 \, b^{2} c d e - b^{3} e^{2}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(b^{2} c d^{2} - b^{3} d e + {\left(2 \, b c^{2} d^{2} - b^{2} c d e\right)} x\right)} \sqrt{e x + d}}{{\left(b^{3} c^{2} d^{3} - b^{4} c d^{2} e\right)} x^{2} + {\left(b^{4} c d^{3} - b^{5} d^{2} e\right)} x}\right]"," ",0,"[1/2*(((4*c^3*d^3 - 5*b*c^2*d^2*e)*x^2 + (4*b*c^2*d^3 - 5*b^2*c*d^2*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + ((4*c^3*d^2 - 3*b*c^2*d*e - b^2*c*e^2)*x^2 + (4*b*c^2*d^2 - 3*b^2*c*d*e - b^3*e^2)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(b^2*c*d^2 - b^3*d*e + (2*b*c^2*d^2 - b^2*c*d*e)*x)*sqrt(e*x + d))/((b^3*c^2*d^3 - b^4*c*d^2*e)*x^2 + (b^4*c*d^3 - b^5*d^2*e)*x), -1/2*(2*((4*c^3*d^3 - 5*b*c^2*d^2*e)*x^2 + (4*b*c^2*d^3 - 5*b^2*c*d^2*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - ((4*c^3*d^2 - 3*b*c^2*d*e - b^2*c*e^2)*x^2 + (4*b*c^2*d^2 - 3*b^2*c*d*e - b^3*e^2)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(b^2*c*d^2 - b^3*d*e + (2*b*c^2*d^2 - b^2*c*d*e)*x)*sqrt(e*x + d))/((b^3*c^2*d^3 - b^4*c*d^2*e)*x^2 + (b^4*c*d^3 - b^5*d^2*e)*x), -1/2*(2*((4*c^3*d^2 - 3*b*c^2*d*e - b^2*c*e^2)*x^2 + (4*b*c^2*d^2 - 3*b^2*c*d*e - b^3*e^2)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - ((4*c^3*d^3 - 5*b*c^2*d^2*e)*x^2 + (4*b*c^2*d^3 - 5*b^2*c*d^2*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(b^2*c*d^2 - b^3*d*e + (2*b*c^2*d^2 - b^2*c*d*e)*x)*sqrt(e*x + d))/((b^3*c^2*d^3 - b^4*c*d^2*e)*x^2 + (b^4*c*d^3 - b^5*d^2*e)*x), -(((4*c^3*d^3 - 5*b*c^2*d^2*e)*x^2 + (4*b*c^2*d^3 - 5*b^2*c*d^2*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + ((4*c^3*d^2 - 3*b*c^2*d*e - b^2*c*e^2)*x^2 + (4*b*c^2*d^2 - 3*b^2*c*d*e - b^3*e^2)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (b^2*c*d^2 - b^3*d*e + (2*b*c^2*d^2 - b^2*c*d*e)*x)*sqrt(e*x + d))/((b^3*c^2*d^3 - b^4*c*d^2*e)*x^2 + (b^4*c*d^3 - b^5*d^2*e)*x)]","B",0
375,1,2312,0,1.015774," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(4 \, c^{4} d^{4} e - 7 \, b c^{3} d^{3} e^{2}\right)} x^{3} + {\left(4 \, c^{4} d^{5} - 3 \, b c^{3} d^{4} e - 7 \, b^{2} c^{2} d^{3} e^{2}\right)} x^{2} + {\left(4 \, b c^{3} d^{5} - 7 \, b^{2} c^{2} d^{4} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - {\left({\left(4 \, c^{4} d^{3} e - 5 \, b c^{3} d^{2} e^{2} - 2 \, b^{2} c^{2} d e^{3} + 3 \, b^{3} c e^{4}\right)} x^{3} + {\left(4 \, c^{4} d^{4} - b c^{3} d^{3} e - 7 \, b^{2} c^{2} d^{2} e^{2} + b^{3} c d e^{3} + 3 \, b^{4} e^{4}\right)} x^{2} + {\left(4 \, b c^{3} d^{4} - 5 \, b^{2} c^{2} d^{3} e - 2 \, b^{3} c d^{2} e^{2} + 3 \, b^{4} d e^{3}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(b^{2} c^{2} d^{4} - 2 \, b^{3} c d^{3} e + b^{4} d^{2} e^{2} + {\left(2 \, b c^{3} d^{3} e - 2 \, b^{2} c^{2} d^{2} e^{2} + 3 \, b^{3} c d e^{3}\right)} x^{2} + {\left(2 \, b c^{3} d^{4} - b^{2} c^{2} d^{3} e - b^{3} c d^{2} e^{2} + 3 \, b^{4} d e^{3}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{3} d^{5} e - 2 \, b^{4} c^{2} d^{4} e^{2} + b^{5} c d^{3} e^{3}\right)} x^{3} + {\left(b^{3} c^{3} d^{6} - b^{4} c^{2} d^{5} e - b^{5} c d^{4} e^{2} + b^{6} d^{3} e^{3}\right)} x^{2} + {\left(b^{4} c^{2} d^{6} - 2 \, b^{5} c d^{5} e + b^{6} d^{4} e^{2}\right)} x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{4} d^{4} e - 7 \, b c^{3} d^{3} e^{2}\right)} x^{3} + {\left(4 \, c^{4} d^{5} - 3 \, b c^{3} d^{4} e - 7 \, b^{2} c^{2} d^{3} e^{2}\right)} x^{2} + {\left(4 \, b c^{3} d^{5} - 7 \, b^{2} c^{2} d^{4} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left({\left(4 \, c^{4} d^{3} e - 5 \, b c^{3} d^{2} e^{2} - 2 \, b^{2} c^{2} d e^{3} + 3 \, b^{3} c e^{4}\right)} x^{3} + {\left(4 \, c^{4} d^{4} - b c^{3} d^{3} e - 7 \, b^{2} c^{2} d^{2} e^{2} + b^{3} c d e^{3} + 3 \, b^{4} e^{4}\right)} x^{2} + {\left(4 \, b c^{3} d^{4} - 5 \, b^{2} c^{2} d^{3} e - 2 \, b^{3} c d^{2} e^{2} + 3 \, b^{4} d e^{3}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(b^{2} c^{2} d^{4} - 2 \, b^{3} c d^{3} e + b^{4} d^{2} e^{2} + {\left(2 \, b c^{3} d^{3} e - 2 \, b^{2} c^{2} d^{2} e^{2} + 3 \, b^{3} c d e^{3}\right)} x^{2} + {\left(2 \, b c^{3} d^{4} - b^{2} c^{2} d^{3} e - b^{3} c d^{2} e^{2} + 3 \, b^{4} d e^{3}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{3} d^{5} e - 2 \, b^{4} c^{2} d^{4} e^{2} + b^{5} c d^{3} e^{3}\right)} x^{3} + {\left(b^{3} c^{3} d^{6} - b^{4} c^{2} d^{5} e - b^{5} c d^{4} e^{2} + b^{6} d^{3} e^{3}\right)} x^{2} + {\left(b^{4} c^{2} d^{6} - 2 \, b^{5} c d^{5} e + b^{6} d^{4} e^{2}\right)} x\right)}}, -\frac{2 \, {\left({\left(4 \, c^{4} d^{3} e - 5 \, b c^{3} d^{2} e^{2} - 2 \, b^{2} c^{2} d e^{3} + 3 \, b^{3} c e^{4}\right)} x^{3} + {\left(4 \, c^{4} d^{4} - b c^{3} d^{3} e - 7 \, b^{2} c^{2} d^{2} e^{2} + b^{3} c d e^{3} + 3 \, b^{4} e^{4}\right)} x^{2} + {\left(4 \, b c^{3} d^{4} - 5 \, b^{2} c^{2} d^{3} e - 2 \, b^{3} c d^{2} e^{2} + 3 \, b^{4} d e^{3}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left({\left(4 \, c^{4} d^{4} e - 7 \, b c^{3} d^{3} e^{2}\right)} x^{3} + {\left(4 \, c^{4} d^{5} - 3 \, b c^{3} d^{4} e - 7 \, b^{2} c^{2} d^{3} e^{2}\right)} x^{2} + {\left(4 \, b c^{3} d^{5} - 7 \, b^{2} c^{2} d^{4} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(b^{2} c^{2} d^{4} - 2 \, b^{3} c d^{3} e + b^{4} d^{2} e^{2} + {\left(2 \, b c^{3} d^{3} e - 2 \, b^{2} c^{2} d^{2} e^{2} + 3 \, b^{3} c d e^{3}\right)} x^{2} + {\left(2 \, b c^{3} d^{4} - b^{2} c^{2} d^{3} e - b^{3} c d^{2} e^{2} + 3 \, b^{4} d e^{3}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left({\left(b^{3} c^{3} d^{5} e - 2 \, b^{4} c^{2} d^{4} e^{2} + b^{5} c d^{3} e^{3}\right)} x^{3} + {\left(b^{3} c^{3} d^{6} - b^{4} c^{2} d^{5} e - b^{5} c d^{4} e^{2} + b^{6} d^{3} e^{3}\right)} x^{2} + {\left(b^{4} c^{2} d^{6} - 2 \, b^{5} c d^{5} e + b^{6} d^{4} e^{2}\right)} x\right)}}, -\frac{{\left({\left(4 \, c^{4} d^{4} e - 7 \, b c^{3} d^{3} e^{2}\right)} x^{3} + {\left(4 \, c^{4} d^{5} - 3 \, b c^{3} d^{4} e - 7 \, b^{2} c^{2} d^{3} e^{2}\right)} x^{2} + {\left(4 \, b c^{3} d^{5} - 7 \, b^{2} c^{2} d^{4} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + {\left({\left(4 \, c^{4} d^{3} e - 5 \, b c^{3} d^{2} e^{2} - 2 \, b^{2} c^{2} d e^{3} + 3 \, b^{3} c e^{4}\right)} x^{3} + {\left(4 \, c^{4} d^{4} - b c^{3} d^{3} e - 7 \, b^{2} c^{2} d^{2} e^{2} + b^{3} c d e^{3} + 3 \, b^{4} e^{4}\right)} x^{2} + {\left(4 \, b c^{3} d^{4} - 5 \, b^{2} c^{2} d^{3} e - 2 \, b^{3} c d^{2} e^{2} + 3 \, b^{4} d e^{3}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(b^{2} c^{2} d^{4} - 2 \, b^{3} c d^{3} e + b^{4} d^{2} e^{2} + {\left(2 \, b c^{3} d^{3} e - 2 \, b^{2} c^{2} d^{2} e^{2} + 3 \, b^{3} c d e^{3}\right)} x^{2} + {\left(2 \, b c^{3} d^{4} - b^{2} c^{2} d^{3} e - b^{3} c d^{2} e^{2} + 3 \, b^{4} d e^{3}\right)} x\right)} \sqrt{e x + d}}{{\left(b^{3} c^{3} d^{5} e - 2 \, b^{4} c^{2} d^{4} e^{2} + b^{5} c d^{3} e^{3}\right)} x^{3} + {\left(b^{3} c^{3} d^{6} - b^{4} c^{2} d^{5} e - b^{5} c d^{4} e^{2} + b^{6} d^{3} e^{3}\right)} x^{2} + {\left(b^{4} c^{2} d^{6} - 2 \, b^{5} c d^{5} e + b^{6} d^{4} e^{2}\right)} x}\right]"," ",0,"[-1/2*(((4*c^4*d^4*e - 7*b*c^3*d^3*e^2)*x^3 + (4*c^4*d^5 - 3*b*c^3*d^4*e - 7*b^2*c^2*d^3*e^2)*x^2 + (4*b*c^3*d^5 - 7*b^2*c^2*d^4*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - ((4*c^4*d^3*e - 5*b*c^3*d^2*e^2 - 2*b^2*c^2*d*e^3 + 3*b^3*c*e^4)*x^3 + (4*c^4*d^4 - b*c^3*d^3*e - 7*b^2*c^2*d^2*e^2 + b^3*c*d*e^3 + 3*b^4*e^4)*x^2 + (4*b*c^3*d^4 - 5*b^2*c^2*d^3*e - 2*b^3*c*d^2*e^2 + 3*b^4*d*e^3)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(b^2*c^2*d^4 - 2*b^3*c*d^3*e + b^4*d^2*e^2 + (2*b*c^3*d^3*e - 2*b^2*c^2*d^2*e^2 + 3*b^3*c*d*e^3)*x^2 + (2*b*c^3*d^4 - b^2*c^2*d^3*e - b^3*c*d^2*e^2 + 3*b^4*d*e^3)*x)*sqrt(e*x + d))/((b^3*c^3*d^5*e - 2*b^4*c^2*d^4*e^2 + b^5*c*d^3*e^3)*x^3 + (b^3*c^3*d^6 - b^4*c^2*d^5*e - b^5*c*d^4*e^2 + b^6*d^3*e^3)*x^2 + (b^4*c^2*d^6 - 2*b^5*c*d^5*e + b^6*d^4*e^2)*x), -1/2*(2*((4*c^4*d^4*e - 7*b*c^3*d^3*e^2)*x^3 + (4*c^4*d^5 - 3*b*c^3*d^4*e - 7*b^2*c^2*d^3*e^2)*x^2 + (4*b*c^3*d^5 - 7*b^2*c^2*d^4*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - ((4*c^4*d^3*e - 5*b*c^3*d^2*e^2 - 2*b^2*c^2*d*e^3 + 3*b^3*c*e^4)*x^3 + (4*c^4*d^4 - b*c^3*d^3*e - 7*b^2*c^2*d^2*e^2 + b^3*c*d*e^3 + 3*b^4*e^4)*x^2 + (4*b*c^3*d^4 - 5*b^2*c^2*d^3*e - 2*b^3*c*d^2*e^2 + 3*b^4*d*e^3)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(b^2*c^2*d^4 - 2*b^3*c*d^3*e + b^4*d^2*e^2 + (2*b*c^3*d^3*e - 2*b^2*c^2*d^2*e^2 + 3*b^3*c*d*e^3)*x^2 + (2*b*c^3*d^4 - b^2*c^2*d^3*e - b^3*c*d^2*e^2 + 3*b^4*d*e^3)*x)*sqrt(e*x + d))/((b^3*c^3*d^5*e - 2*b^4*c^2*d^4*e^2 + b^5*c*d^3*e^3)*x^3 + (b^3*c^3*d^6 - b^4*c^2*d^5*e - b^5*c*d^4*e^2 + b^6*d^3*e^3)*x^2 + (b^4*c^2*d^6 - 2*b^5*c*d^5*e + b^6*d^4*e^2)*x), -1/2*(2*((4*c^4*d^3*e - 5*b*c^3*d^2*e^2 - 2*b^2*c^2*d*e^3 + 3*b^3*c*e^4)*x^3 + (4*c^4*d^4 - b*c^3*d^3*e - 7*b^2*c^2*d^2*e^2 + b^3*c*d*e^3 + 3*b^4*e^4)*x^2 + (4*b*c^3*d^4 - 5*b^2*c^2*d^3*e - 2*b^3*c*d^2*e^2 + 3*b^4*d*e^3)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + ((4*c^4*d^4*e - 7*b*c^3*d^3*e^2)*x^3 + (4*c^4*d^5 - 3*b*c^3*d^4*e - 7*b^2*c^2*d^3*e^2)*x^2 + (4*b*c^3*d^5 - 7*b^2*c^2*d^4*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(b^2*c^2*d^4 - 2*b^3*c*d^3*e + b^4*d^2*e^2 + (2*b*c^3*d^3*e - 2*b^2*c^2*d^2*e^2 + 3*b^3*c*d*e^3)*x^2 + (2*b*c^3*d^4 - b^2*c^2*d^3*e - b^3*c*d^2*e^2 + 3*b^4*d*e^3)*x)*sqrt(e*x + d))/((b^3*c^3*d^5*e - 2*b^4*c^2*d^4*e^2 + b^5*c*d^3*e^3)*x^3 + (b^3*c^3*d^6 - b^4*c^2*d^5*e - b^5*c*d^4*e^2 + b^6*d^3*e^3)*x^2 + (b^4*c^2*d^6 - 2*b^5*c*d^5*e + b^6*d^4*e^2)*x), -(((4*c^4*d^4*e - 7*b*c^3*d^3*e^2)*x^3 + (4*c^4*d^5 - 3*b*c^3*d^4*e - 7*b^2*c^2*d^3*e^2)*x^2 + (4*b*c^3*d^5 - 7*b^2*c^2*d^4*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + ((4*c^4*d^3*e - 5*b*c^3*d^2*e^2 - 2*b^2*c^2*d*e^3 + 3*b^3*c*e^4)*x^3 + (4*c^4*d^4 - b*c^3*d^3*e - 7*b^2*c^2*d^2*e^2 + b^3*c*d*e^3 + 3*b^4*e^4)*x^2 + (4*b*c^3*d^4 - 5*b^2*c^2*d^3*e - 2*b^3*c*d^2*e^2 + 3*b^4*d*e^3)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (b^2*c^2*d^4 - 2*b^3*c*d^3*e + b^4*d^2*e^2 + (2*b*c^3*d^3*e - 2*b^2*c^2*d^2*e^2 + 3*b^3*c*d*e^3)*x^2 + (2*b*c^3*d^4 - b^2*c^2*d^3*e - b^3*c*d^2*e^2 + 3*b^4*d*e^3)*x)*sqrt(e*x + d))/((b^3*c^3*d^5*e - 2*b^4*c^2*d^4*e^2 + b^5*c*d^3*e^3)*x^3 + (b^3*c^3*d^6 - b^4*c^2*d^5*e - b^5*c*d^4*e^2 + b^6*d^3*e^3)*x^2 + (b^4*c^2*d^6 - 2*b^5*c*d^5*e + b^6*d^4*e^2)*x)]","B",0
376,1,3872,0,2.664343," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(4 \, c^{5} d^{5} e^{2} - 9 \, b c^{4} d^{4} e^{3}\right)} x^{4} + {\left(8 \, c^{5} d^{6} e - 14 \, b c^{4} d^{5} e^{2} - 9 \, b^{2} c^{3} d^{4} e^{3}\right)} x^{3} + {\left(4 \, c^{5} d^{7} - b c^{4} d^{6} e - 18 \, b^{2} c^{3} d^{5} e^{2}\right)} x^{2} + {\left(4 \, b c^{4} d^{7} - 9 \, b^{2} c^{3} d^{6} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 3 \, {\left({\left(4 \, c^{5} d^{4} e^{2} - 7 \, b c^{4} d^{3} e^{3} - 3 \, b^{2} c^{3} d^{2} e^{4} + 11 \, b^{3} c^{2} d e^{5} - 5 \, b^{4} c e^{6}\right)} x^{4} + {\left(8 \, c^{5} d^{5} e - 10 \, b c^{4} d^{4} e^{2} - 13 \, b^{2} c^{3} d^{3} e^{3} + 19 \, b^{3} c^{2} d^{2} e^{4} + b^{4} c d e^{5} - 5 \, b^{5} e^{6}\right)} x^{3} + {\left(4 \, c^{5} d^{6} + b c^{4} d^{5} e - 17 \, b^{2} c^{3} d^{4} e^{2} + 5 \, b^{3} c^{2} d^{3} e^{3} + 17 \, b^{4} c d^{2} e^{4} - 10 \, b^{5} d e^{5}\right)} x^{2} + {\left(4 \, b c^{4} d^{6} - 7 \, b^{2} c^{3} d^{5} e - 3 \, b^{3} c^{2} d^{4} e^{2} + 11 \, b^{4} c d^{3} e^{3} - 5 \, b^{5} d^{2} e^{4}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(3 \, b^{2} c^{3} d^{6} - 9 \, b^{3} c^{2} d^{5} e + 9 \, b^{4} c d^{4} e^{2} - 3 \, b^{5} d^{3} e^{3} + 3 \, {\left(2 \, b c^{4} d^{4} e^{2} - 3 \, b^{2} c^{3} d^{3} e^{3} + 11 \, b^{3} c^{2} d^{2} e^{4} - 5 \, b^{4} c d e^{5}\right)} x^{3} + {\left(12 \, b c^{4} d^{5} e - 15 \, b^{2} c^{3} d^{4} e^{2} + 35 \, b^{3} c^{2} d^{3} e^{3} + 13 \, b^{4} c d^{2} e^{4} - 15 \, b^{5} d e^{5}\right)} x^{2} + {\left(6 \, b c^{4} d^{6} - 3 \, b^{2} c^{3} d^{5} e - 9 \, b^{3} c^{2} d^{4} e^{2} + 41 \, b^{4} c d^{3} e^{3} - 20 \, b^{5} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left({\left(b^{3} c^{4} d^{7} e^{2} - 3 \, b^{4} c^{3} d^{6} e^{3} + 3 \, b^{5} c^{2} d^{5} e^{4} - b^{6} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{3} c^{4} d^{8} e - 5 \, b^{4} c^{3} d^{7} e^{2} + 3 \, b^{5} c^{2} d^{6} e^{3} + b^{6} c d^{5} e^{4} - b^{7} d^{4} e^{5}\right)} x^{3} + {\left(b^{3} c^{4} d^{9} - b^{4} c^{3} d^{8} e - 3 \, b^{5} c^{2} d^{7} e^{2} + 5 \, b^{6} c d^{6} e^{3} - 2 \, b^{7} d^{5} e^{4}\right)} x^{2} + {\left(b^{4} c^{3} d^{9} - 3 \, b^{5} c^{2} d^{8} e + 3 \, b^{6} c d^{7} e^{2} - b^{7} d^{6} e^{3}\right)} x\right)}}, -\frac{6 \, {\left({\left(4 \, c^{5} d^{5} e^{2} - 9 \, b c^{4} d^{4} e^{3}\right)} x^{4} + {\left(8 \, c^{5} d^{6} e - 14 \, b c^{4} d^{5} e^{2} - 9 \, b^{2} c^{3} d^{4} e^{3}\right)} x^{3} + {\left(4 \, c^{5} d^{7} - b c^{4} d^{6} e - 18 \, b^{2} c^{3} d^{5} e^{2}\right)} x^{2} + {\left(4 \, b c^{4} d^{7} - 9 \, b^{2} c^{3} d^{6} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 3 \, {\left({\left(4 \, c^{5} d^{4} e^{2} - 7 \, b c^{4} d^{3} e^{3} - 3 \, b^{2} c^{3} d^{2} e^{4} + 11 \, b^{3} c^{2} d e^{5} - 5 \, b^{4} c e^{6}\right)} x^{4} + {\left(8 \, c^{5} d^{5} e - 10 \, b c^{4} d^{4} e^{2} - 13 \, b^{2} c^{3} d^{3} e^{3} + 19 \, b^{3} c^{2} d^{2} e^{4} + b^{4} c d e^{5} - 5 \, b^{5} e^{6}\right)} x^{3} + {\left(4 \, c^{5} d^{6} + b c^{4} d^{5} e - 17 \, b^{2} c^{3} d^{4} e^{2} + 5 \, b^{3} c^{2} d^{3} e^{3} + 17 \, b^{4} c d^{2} e^{4} - 10 \, b^{5} d e^{5}\right)} x^{2} + {\left(4 \, b c^{4} d^{6} - 7 \, b^{2} c^{3} d^{5} e - 3 \, b^{3} c^{2} d^{4} e^{2} + 11 \, b^{4} c d^{3} e^{3} - 5 \, b^{5} d^{2} e^{4}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(3 \, b^{2} c^{3} d^{6} - 9 \, b^{3} c^{2} d^{5} e + 9 \, b^{4} c d^{4} e^{2} - 3 \, b^{5} d^{3} e^{3} + 3 \, {\left(2 \, b c^{4} d^{4} e^{2} - 3 \, b^{2} c^{3} d^{3} e^{3} + 11 \, b^{3} c^{2} d^{2} e^{4} - 5 \, b^{4} c d e^{5}\right)} x^{3} + {\left(12 \, b c^{4} d^{5} e - 15 \, b^{2} c^{3} d^{4} e^{2} + 35 \, b^{3} c^{2} d^{3} e^{3} + 13 \, b^{4} c d^{2} e^{4} - 15 \, b^{5} d e^{5}\right)} x^{2} + {\left(6 \, b c^{4} d^{6} - 3 \, b^{2} c^{3} d^{5} e - 9 \, b^{3} c^{2} d^{4} e^{2} + 41 \, b^{4} c d^{3} e^{3} - 20 \, b^{5} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left({\left(b^{3} c^{4} d^{7} e^{2} - 3 \, b^{4} c^{3} d^{6} e^{3} + 3 \, b^{5} c^{2} d^{5} e^{4} - b^{6} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{3} c^{4} d^{8} e - 5 \, b^{4} c^{3} d^{7} e^{2} + 3 \, b^{5} c^{2} d^{6} e^{3} + b^{6} c d^{5} e^{4} - b^{7} d^{4} e^{5}\right)} x^{3} + {\left(b^{3} c^{4} d^{9} - b^{4} c^{3} d^{8} e - 3 \, b^{5} c^{2} d^{7} e^{2} + 5 \, b^{6} c d^{6} e^{3} - 2 \, b^{7} d^{5} e^{4}\right)} x^{2} + {\left(b^{4} c^{3} d^{9} - 3 \, b^{5} c^{2} d^{8} e + 3 \, b^{6} c d^{7} e^{2} - b^{7} d^{6} e^{3}\right)} x\right)}}, -\frac{6 \, {\left({\left(4 \, c^{5} d^{4} e^{2} - 7 \, b c^{4} d^{3} e^{3} - 3 \, b^{2} c^{3} d^{2} e^{4} + 11 \, b^{3} c^{2} d e^{5} - 5 \, b^{4} c e^{6}\right)} x^{4} + {\left(8 \, c^{5} d^{5} e - 10 \, b c^{4} d^{4} e^{2} - 13 \, b^{2} c^{3} d^{3} e^{3} + 19 \, b^{3} c^{2} d^{2} e^{4} + b^{4} c d e^{5} - 5 \, b^{5} e^{6}\right)} x^{3} + {\left(4 \, c^{5} d^{6} + b c^{4} d^{5} e - 17 \, b^{2} c^{3} d^{4} e^{2} + 5 \, b^{3} c^{2} d^{3} e^{3} + 17 \, b^{4} c d^{2} e^{4} - 10 \, b^{5} d e^{5}\right)} x^{2} + {\left(4 \, b c^{4} d^{6} - 7 \, b^{2} c^{3} d^{5} e - 3 \, b^{3} c^{2} d^{4} e^{2} + 11 \, b^{4} c d^{3} e^{3} - 5 \, b^{5} d^{2} e^{4}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 3 \, {\left({\left(4 \, c^{5} d^{5} e^{2} - 9 \, b c^{4} d^{4} e^{3}\right)} x^{4} + {\left(8 \, c^{5} d^{6} e - 14 \, b c^{4} d^{5} e^{2} - 9 \, b^{2} c^{3} d^{4} e^{3}\right)} x^{3} + {\left(4 \, c^{5} d^{7} - b c^{4} d^{6} e - 18 \, b^{2} c^{3} d^{5} e^{2}\right)} x^{2} + {\left(4 \, b c^{4} d^{7} - 9 \, b^{2} c^{3} d^{6} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(3 \, b^{2} c^{3} d^{6} - 9 \, b^{3} c^{2} d^{5} e + 9 \, b^{4} c d^{4} e^{2} - 3 \, b^{5} d^{3} e^{3} + 3 \, {\left(2 \, b c^{4} d^{4} e^{2} - 3 \, b^{2} c^{3} d^{3} e^{3} + 11 \, b^{3} c^{2} d^{2} e^{4} - 5 \, b^{4} c d e^{5}\right)} x^{3} + {\left(12 \, b c^{4} d^{5} e - 15 \, b^{2} c^{3} d^{4} e^{2} + 35 \, b^{3} c^{2} d^{3} e^{3} + 13 \, b^{4} c d^{2} e^{4} - 15 \, b^{5} d e^{5}\right)} x^{2} + {\left(6 \, b c^{4} d^{6} - 3 \, b^{2} c^{3} d^{5} e - 9 \, b^{3} c^{2} d^{4} e^{2} + 41 \, b^{4} c d^{3} e^{3} - 20 \, b^{5} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left({\left(b^{3} c^{4} d^{7} e^{2} - 3 \, b^{4} c^{3} d^{6} e^{3} + 3 \, b^{5} c^{2} d^{5} e^{4} - b^{6} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{3} c^{4} d^{8} e - 5 \, b^{4} c^{3} d^{7} e^{2} + 3 \, b^{5} c^{2} d^{6} e^{3} + b^{6} c d^{5} e^{4} - b^{7} d^{4} e^{5}\right)} x^{3} + {\left(b^{3} c^{4} d^{9} - b^{4} c^{3} d^{8} e - 3 \, b^{5} c^{2} d^{7} e^{2} + 5 \, b^{6} c d^{6} e^{3} - 2 \, b^{7} d^{5} e^{4}\right)} x^{2} + {\left(b^{4} c^{3} d^{9} - 3 \, b^{5} c^{2} d^{8} e + 3 \, b^{6} c d^{7} e^{2} - b^{7} d^{6} e^{3}\right)} x\right)}}, -\frac{3 \, {\left({\left(4 \, c^{5} d^{5} e^{2} - 9 \, b c^{4} d^{4} e^{3}\right)} x^{4} + {\left(8 \, c^{5} d^{6} e - 14 \, b c^{4} d^{5} e^{2} - 9 \, b^{2} c^{3} d^{4} e^{3}\right)} x^{3} + {\left(4 \, c^{5} d^{7} - b c^{4} d^{6} e - 18 \, b^{2} c^{3} d^{5} e^{2}\right)} x^{2} + {\left(4 \, b c^{4} d^{7} - 9 \, b^{2} c^{3} d^{6} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(4 \, c^{5} d^{4} e^{2} - 7 \, b c^{4} d^{3} e^{3} - 3 \, b^{2} c^{3} d^{2} e^{4} + 11 \, b^{3} c^{2} d e^{5} - 5 \, b^{4} c e^{6}\right)} x^{4} + {\left(8 \, c^{5} d^{5} e - 10 \, b c^{4} d^{4} e^{2} - 13 \, b^{2} c^{3} d^{3} e^{3} + 19 \, b^{3} c^{2} d^{2} e^{4} + b^{4} c d e^{5} - 5 \, b^{5} e^{6}\right)} x^{3} + {\left(4 \, c^{5} d^{6} + b c^{4} d^{5} e - 17 \, b^{2} c^{3} d^{4} e^{2} + 5 \, b^{3} c^{2} d^{3} e^{3} + 17 \, b^{4} c d^{2} e^{4} - 10 \, b^{5} d e^{5}\right)} x^{2} + {\left(4 \, b c^{4} d^{6} - 7 \, b^{2} c^{3} d^{5} e - 3 \, b^{3} c^{2} d^{4} e^{2} + 11 \, b^{4} c d^{3} e^{3} - 5 \, b^{5} d^{2} e^{4}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(3 \, b^{2} c^{3} d^{6} - 9 \, b^{3} c^{2} d^{5} e + 9 \, b^{4} c d^{4} e^{2} - 3 \, b^{5} d^{3} e^{3} + 3 \, {\left(2 \, b c^{4} d^{4} e^{2} - 3 \, b^{2} c^{3} d^{3} e^{3} + 11 \, b^{3} c^{2} d^{2} e^{4} - 5 \, b^{4} c d e^{5}\right)} x^{3} + {\left(12 \, b c^{4} d^{5} e - 15 \, b^{2} c^{3} d^{4} e^{2} + 35 \, b^{3} c^{2} d^{3} e^{3} + 13 \, b^{4} c d^{2} e^{4} - 15 \, b^{5} d e^{5}\right)} x^{2} + {\left(6 \, b c^{4} d^{6} - 3 \, b^{2} c^{3} d^{5} e - 9 \, b^{3} c^{2} d^{4} e^{2} + 41 \, b^{4} c d^{3} e^{3} - 20 \, b^{5} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left({\left(b^{3} c^{4} d^{7} e^{2} - 3 \, b^{4} c^{3} d^{6} e^{3} + 3 \, b^{5} c^{2} d^{5} e^{4} - b^{6} c d^{4} e^{5}\right)} x^{4} + {\left(2 \, b^{3} c^{4} d^{8} e - 5 \, b^{4} c^{3} d^{7} e^{2} + 3 \, b^{5} c^{2} d^{6} e^{3} + b^{6} c d^{5} e^{4} - b^{7} d^{4} e^{5}\right)} x^{3} + {\left(b^{3} c^{4} d^{9} - b^{4} c^{3} d^{8} e - 3 \, b^{5} c^{2} d^{7} e^{2} + 5 \, b^{6} c d^{6} e^{3} - 2 \, b^{7} d^{5} e^{4}\right)} x^{2} + {\left(b^{4} c^{3} d^{9} - 3 \, b^{5} c^{2} d^{8} e + 3 \, b^{6} c d^{7} e^{2} - b^{7} d^{6} e^{3}\right)} x\right)}}\right]"," ",0,"[1/6*(3*((4*c^5*d^5*e^2 - 9*b*c^4*d^4*e^3)*x^4 + (8*c^5*d^6*e - 14*b*c^4*d^5*e^2 - 9*b^2*c^3*d^4*e^3)*x^3 + (4*c^5*d^7 - b*c^4*d^6*e - 18*b^2*c^3*d^5*e^2)*x^2 + (4*b*c^4*d^7 - 9*b^2*c^3*d^6*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 3*((4*c^5*d^4*e^2 - 7*b*c^4*d^3*e^3 - 3*b^2*c^3*d^2*e^4 + 11*b^3*c^2*d*e^5 - 5*b^4*c*e^6)*x^4 + (8*c^5*d^5*e - 10*b*c^4*d^4*e^2 - 13*b^2*c^3*d^3*e^3 + 19*b^3*c^2*d^2*e^4 + b^4*c*d*e^5 - 5*b^5*e^6)*x^3 + (4*c^5*d^6 + b*c^4*d^5*e - 17*b^2*c^3*d^4*e^2 + 5*b^3*c^2*d^3*e^3 + 17*b^4*c*d^2*e^4 - 10*b^5*d*e^5)*x^2 + (4*b*c^4*d^6 - 7*b^2*c^3*d^5*e - 3*b^3*c^2*d^4*e^2 + 11*b^4*c*d^3*e^3 - 5*b^5*d^2*e^4)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(3*b^2*c^3*d^6 - 9*b^3*c^2*d^5*e + 9*b^4*c*d^4*e^2 - 3*b^5*d^3*e^3 + 3*(2*b*c^4*d^4*e^2 - 3*b^2*c^3*d^3*e^3 + 11*b^3*c^2*d^2*e^4 - 5*b^4*c*d*e^5)*x^3 + (12*b*c^4*d^5*e - 15*b^2*c^3*d^4*e^2 + 35*b^3*c^2*d^3*e^3 + 13*b^4*c*d^2*e^4 - 15*b^5*d*e^5)*x^2 + (6*b*c^4*d^6 - 3*b^2*c^3*d^5*e - 9*b^3*c^2*d^4*e^2 + 41*b^4*c*d^3*e^3 - 20*b^5*d^2*e^4)*x)*sqrt(e*x + d))/((b^3*c^4*d^7*e^2 - 3*b^4*c^3*d^6*e^3 + 3*b^5*c^2*d^5*e^4 - b^6*c*d^4*e^5)*x^4 + (2*b^3*c^4*d^8*e - 5*b^4*c^3*d^7*e^2 + 3*b^5*c^2*d^6*e^3 + b^6*c*d^5*e^4 - b^7*d^4*e^5)*x^3 + (b^3*c^4*d^9 - b^4*c^3*d^8*e - 3*b^5*c^2*d^7*e^2 + 5*b^6*c*d^6*e^3 - 2*b^7*d^5*e^4)*x^2 + (b^4*c^3*d^9 - 3*b^5*c^2*d^8*e + 3*b^6*c*d^7*e^2 - b^7*d^6*e^3)*x), -1/6*(6*((4*c^5*d^5*e^2 - 9*b*c^4*d^4*e^3)*x^4 + (8*c^5*d^6*e - 14*b*c^4*d^5*e^2 - 9*b^2*c^3*d^4*e^3)*x^3 + (4*c^5*d^7 - b*c^4*d^6*e - 18*b^2*c^3*d^5*e^2)*x^2 + (4*b*c^4*d^7 - 9*b^2*c^3*d^6*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 3*((4*c^5*d^4*e^2 - 7*b*c^4*d^3*e^3 - 3*b^2*c^3*d^2*e^4 + 11*b^3*c^2*d*e^5 - 5*b^4*c*e^6)*x^4 + (8*c^5*d^5*e - 10*b*c^4*d^4*e^2 - 13*b^2*c^3*d^3*e^3 + 19*b^3*c^2*d^2*e^4 + b^4*c*d*e^5 - 5*b^5*e^6)*x^3 + (4*c^5*d^6 + b*c^4*d^5*e - 17*b^2*c^3*d^4*e^2 + 5*b^3*c^2*d^3*e^3 + 17*b^4*c*d^2*e^4 - 10*b^5*d*e^5)*x^2 + (4*b*c^4*d^6 - 7*b^2*c^3*d^5*e - 3*b^3*c^2*d^4*e^2 + 11*b^4*c*d^3*e^3 - 5*b^5*d^2*e^4)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(3*b^2*c^3*d^6 - 9*b^3*c^2*d^5*e + 9*b^4*c*d^4*e^2 - 3*b^5*d^3*e^3 + 3*(2*b*c^4*d^4*e^2 - 3*b^2*c^3*d^3*e^3 + 11*b^3*c^2*d^2*e^4 - 5*b^4*c*d*e^5)*x^3 + (12*b*c^4*d^5*e - 15*b^2*c^3*d^4*e^2 + 35*b^3*c^2*d^3*e^3 + 13*b^4*c*d^2*e^4 - 15*b^5*d*e^5)*x^2 + (6*b*c^4*d^6 - 3*b^2*c^3*d^5*e - 9*b^3*c^2*d^4*e^2 + 41*b^4*c*d^3*e^3 - 20*b^5*d^2*e^4)*x)*sqrt(e*x + d))/((b^3*c^4*d^7*e^2 - 3*b^4*c^3*d^6*e^3 + 3*b^5*c^2*d^5*e^4 - b^6*c*d^4*e^5)*x^4 + (2*b^3*c^4*d^8*e - 5*b^4*c^3*d^7*e^2 + 3*b^5*c^2*d^6*e^3 + b^6*c*d^5*e^4 - b^7*d^4*e^5)*x^3 + (b^3*c^4*d^9 - b^4*c^3*d^8*e - 3*b^5*c^2*d^7*e^2 + 5*b^6*c*d^6*e^3 - 2*b^7*d^5*e^4)*x^2 + (b^4*c^3*d^9 - 3*b^5*c^2*d^8*e + 3*b^6*c*d^7*e^2 - b^7*d^6*e^3)*x), -1/6*(6*((4*c^5*d^4*e^2 - 7*b*c^4*d^3*e^3 - 3*b^2*c^3*d^2*e^4 + 11*b^3*c^2*d*e^5 - 5*b^4*c*e^6)*x^4 + (8*c^5*d^5*e - 10*b*c^4*d^4*e^2 - 13*b^2*c^3*d^3*e^3 + 19*b^3*c^2*d^2*e^4 + b^4*c*d*e^5 - 5*b^5*e^6)*x^3 + (4*c^5*d^6 + b*c^4*d^5*e - 17*b^2*c^3*d^4*e^2 + 5*b^3*c^2*d^3*e^3 + 17*b^4*c*d^2*e^4 - 10*b^5*d*e^5)*x^2 + (4*b*c^4*d^6 - 7*b^2*c^3*d^5*e - 3*b^3*c^2*d^4*e^2 + 11*b^4*c*d^3*e^3 - 5*b^5*d^2*e^4)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 3*((4*c^5*d^5*e^2 - 9*b*c^4*d^4*e^3)*x^4 + (8*c^5*d^6*e - 14*b*c^4*d^5*e^2 - 9*b^2*c^3*d^4*e^3)*x^3 + (4*c^5*d^7 - b*c^4*d^6*e - 18*b^2*c^3*d^5*e^2)*x^2 + (4*b*c^4*d^7 - 9*b^2*c^3*d^6*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(3*b^2*c^3*d^6 - 9*b^3*c^2*d^5*e + 9*b^4*c*d^4*e^2 - 3*b^5*d^3*e^3 + 3*(2*b*c^4*d^4*e^2 - 3*b^2*c^3*d^3*e^3 + 11*b^3*c^2*d^2*e^4 - 5*b^4*c*d*e^5)*x^3 + (12*b*c^4*d^5*e - 15*b^2*c^3*d^4*e^2 + 35*b^3*c^2*d^3*e^3 + 13*b^4*c*d^2*e^4 - 15*b^5*d*e^5)*x^2 + (6*b*c^4*d^6 - 3*b^2*c^3*d^5*e - 9*b^3*c^2*d^4*e^2 + 41*b^4*c*d^3*e^3 - 20*b^5*d^2*e^4)*x)*sqrt(e*x + d))/((b^3*c^4*d^7*e^2 - 3*b^4*c^3*d^6*e^3 + 3*b^5*c^2*d^5*e^4 - b^6*c*d^4*e^5)*x^4 + (2*b^3*c^4*d^8*e - 5*b^4*c^3*d^7*e^2 + 3*b^5*c^2*d^6*e^3 + b^6*c*d^5*e^4 - b^7*d^4*e^5)*x^3 + (b^3*c^4*d^9 - b^4*c^3*d^8*e - 3*b^5*c^2*d^7*e^2 + 5*b^6*c*d^6*e^3 - 2*b^7*d^5*e^4)*x^2 + (b^4*c^3*d^9 - 3*b^5*c^2*d^8*e + 3*b^6*c*d^7*e^2 - b^7*d^6*e^3)*x), -1/3*(3*((4*c^5*d^5*e^2 - 9*b*c^4*d^4*e^3)*x^4 + (8*c^5*d^6*e - 14*b*c^4*d^5*e^2 - 9*b^2*c^3*d^4*e^3)*x^3 + (4*c^5*d^7 - b*c^4*d^6*e - 18*b^2*c^3*d^5*e^2)*x^2 + (4*b*c^4*d^7 - 9*b^2*c^3*d^6*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((4*c^5*d^4*e^2 - 7*b*c^4*d^3*e^3 - 3*b^2*c^3*d^2*e^4 + 11*b^3*c^2*d*e^5 - 5*b^4*c*e^6)*x^4 + (8*c^5*d^5*e - 10*b*c^4*d^4*e^2 - 13*b^2*c^3*d^3*e^3 + 19*b^3*c^2*d^2*e^4 + b^4*c*d*e^5 - 5*b^5*e^6)*x^3 + (4*c^5*d^6 + b*c^4*d^5*e - 17*b^2*c^3*d^4*e^2 + 5*b^3*c^2*d^3*e^3 + 17*b^4*c*d^2*e^4 - 10*b^5*d*e^5)*x^2 + (4*b*c^4*d^6 - 7*b^2*c^3*d^5*e - 3*b^3*c^2*d^4*e^2 + 11*b^4*c*d^3*e^3 - 5*b^5*d^2*e^4)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (3*b^2*c^3*d^6 - 9*b^3*c^2*d^5*e + 9*b^4*c*d^4*e^2 - 3*b^5*d^3*e^3 + 3*(2*b*c^4*d^4*e^2 - 3*b^2*c^3*d^3*e^3 + 11*b^3*c^2*d^2*e^4 - 5*b^4*c*d*e^5)*x^3 + (12*b*c^4*d^5*e - 15*b^2*c^3*d^4*e^2 + 35*b^3*c^2*d^3*e^3 + 13*b^4*c*d^2*e^4 - 15*b^5*d*e^5)*x^2 + (6*b*c^4*d^6 - 3*b^2*c^3*d^5*e - 9*b^3*c^2*d^4*e^2 + 41*b^4*c*d^3*e^3 - 20*b^5*d^2*e^4)*x)*sqrt(e*x + d))/((b^3*c^4*d^7*e^2 - 3*b^4*c^3*d^6*e^3 + 3*b^5*c^2*d^5*e^4 - b^6*c*d^4*e^5)*x^4 + (2*b^3*c^4*d^8*e - 5*b^4*c^3*d^7*e^2 + 3*b^5*c^2*d^6*e^3 + b^6*c*d^5*e^4 - b^7*d^4*e^5)*x^3 + (b^3*c^4*d^9 - b^4*c^3*d^8*e - 3*b^5*c^2*d^7*e^2 + 5*b^6*c*d^6*e^3 - 2*b^7*d^5*e^4)*x^2 + (b^4*c^3*d^9 - 3*b^5*c^2*d^8*e + 3*b^6*c*d^7*e^2 - b^7*d^6*e^3)*x)]","B",0
377,1,5752,0,6.901973," ","integrate(1/(e*x+d)^(7/2)/(c*x^2+b*x)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left({\left(4 \, c^{6} d^{6} e^{3} - 11 \, b c^{5} d^{5} e^{4}\right)} x^{5} + {\left(12 \, c^{6} d^{7} e^{2} - 29 \, b c^{5} d^{6} e^{3} - 11 \, b^{2} c^{4} d^{5} e^{4}\right)} x^{4} + 3 \, {\left(4 \, c^{6} d^{8} e - 7 \, b c^{5} d^{7} e^{2} - 11 \, b^{2} c^{4} d^{6} e^{3}\right)} x^{3} + {\left(4 \, c^{6} d^{9} + b c^{5} d^{8} e - 33 \, b^{2} c^{4} d^{7} e^{2}\right)} x^{2} + {\left(4 \, b c^{5} d^{9} - 11 \, b^{2} c^{4} d^{8} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 15 \, {\left({\left(4 \, c^{6} d^{5} e^{3} - 9 \, b c^{5} d^{4} e^{4} - 4 \, b^{2} c^{4} d^{3} e^{5} + 26 \, b^{3} c^{3} d^{2} e^{6} - 24 \, b^{4} c^{2} d e^{7} + 7 \, b^{5} c e^{8}\right)} x^{5} + {\left(12 \, c^{6} d^{6} e^{2} - 23 \, b c^{5} d^{5} e^{3} - 21 \, b^{2} c^{4} d^{4} e^{4} + 74 \, b^{3} c^{3} d^{3} e^{5} - 46 \, b^{4} c^{2} d^{2} e^{6} - 3 \, b^{5} c d e^{7} + 7 \, b^{6} e^{8}\right)} x^{4} + 3 \, {\left(4 \, c^{6} d^{7} e - 5 \, b c^{5} d^{6} e^{2} - 13 \, b^{2} c^{4} d^{5} e^{3} + 22 \, b^{3} c^{3} d^{4} e^{4} + 2 \, b^{4} c^{2} d^{3} e^{5} - 17 \, b^{5} c d^{2} e^{6} + 7 \, b^{6} d e^{7}\right)} x^{3} + {\left(4 \, c^{6} d^{8} + 3 \, b c^{5} d^{7} e - 31 \, b^{2} c^{4} d^{6} e^{2} + 14 \, b^{3} c^{3} d^{5} e^{3} + 54 \, b^{4} c^{2} d^{4} e^{4} - 65 \, b^{5} c d^{3} e^{5} + 21 \, b^{6} d^{2} e^{6}\right)} x^{2} + {\left(4 \, b c^{5} d^{8} - 9 \, b^{2} c^{4} d^{7} e - 4 \, b^{3} c^{3} d^{6} e^{2} + 26 \, b^{4} c^{2} d^{5} e^{3} - 24 \, b^{5} c d^{4} e^{4} + 7 \, b^{6} d^{3} e^{5}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(15 \, b^{2} c^{4} d^{8} - 60 \, b^{3} c^{3} d^{7} e + 90 \, b^{4} c^{2} d^{6} e^{2} - 60 \, b^{5} c d^{5} e^{3} + 15 \, b^{6} d^{4} e^{4} + 15 \, {\left(2 \, b c^{5} d^{5} e^{3} - 4 \, b^{2} c^{4} d^{4} e^{4} + 26 \, b^{3} c^{3} d^{3} e^{5} - 24 \, b^{4} c^{2} d^{2} e^{6} + 7 \, b^{5} c d e^{7}\right)} x^{4} + 5 \, {\left(18 \, b c^{5} d^{6} e^{2} - 33 \, b^{2} c^{4} d^{5} e^{3} + 170 \, b^{3} c^{3} d^{4} e^{4} - 90 \, b^{4} c^{2} d^{3} e^{5} - 23 \, b^{5} c d^{2} e^{6} + 21 \, b^{6} d e^{7}\right)} x^{3} + {\left(90 \, b c^{5} d^{7} e - 135 \, b^{2} c^{4} d^{6} e^{2} + 436 \, b^{3} c^{3} d^{5} e^{3} + 358 \, b^{4} c^{2} d^{4} e^{4} - 679 \, b^{5} c d^{3} e^{5} + 245 \, b^{6} d^{2} e^{6}\right)} x^{2} + {\left(30 \, b c^{5} d^{8} - 15 \, b^{2} c^{4} d^{7} e - 90 \, b^{3} c^{3} d^{6} e^{2} + 556 \, b^{4} c^{2} d^{5} e^{3} - 537 \, b^{5} c d^{4} e^{4} + 161 \, b^{6} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left({\left(b^{3} c^{5} d^{9} e^{3} - 4 \, b^{4} c^{4} d^{8} e^{4} + 6 \, b^{5} c^{3} d^{7} e^{5} - 4 \, b^{6} c^{2} d^{6} e^{6} + b^{7} c d^{5} e^{7}\right)} x^{5} + {\left(3 \, b^{3} c^{5} d^{10} e^{2} - 11 \, b^{4} c^{4} d^{9} e^{3} + 14 \, b^{5} c^{3} d^{8} e^{4} - 6 \, b^{6} c^{2} d^{7} e^{5} - b^{7} c d^{6} e^{6} + b^{8} d^{5} e^{7}\right)} x^{4} + 3 \, {\left(b^{3} c^{5} d^{11} e - 3 \, b^{4} c^{4} d^{10} e^{2} + 2 \, b^{5} c^{3} d^{9} e^{3} + 2 \, b^{6} c^{2} d^{8} e^{4} - 3 \, b^{7} c d^{7} e^{5} + b^{8} d^{6} e^{6}\right)} x^{3} + {\left(b^{3} c^{5} d^{12} - b^{4} c^{4} d^{11} e - 6 \, b^{5} c^{3} d^{10} e^{2} + 14 \, b^{6} c^{2} d^{9} e^{3} - 11 \, b^{7} c d^{8} e^{4} + 3 \, b^{8} d^{7} e^{5}\right)} x^{2} + {\left(b^{4} c^{4} d^{12} - 4 \, b^{5} c^{3} d^{11} e + 6 \, b^{6} c^{2} d^{10} e^{2} - 4 \, b^{7} c d^{9} e^{3} + b^{8} d^{8} e^{4}\right)} x\right)}}, -\frac{30 \, {\left({\left(4 \, c^{6} d^{6} e^{3} - 11 \, b c^{5} d^{5} e^{4}\right)} x^{5} + {\left(12 \, c^{6} d^{7} e^{2} - 29 \, b c^{5} d^{6} e^{3} - 11 \, b^{2} c^{4} d^{5} e^{4}\right)} x^{4} + 3 \, {\left(4 \, c^{6} d^{8} e - 7 \, b c^{5} d^{7} e^{2} - 11 \, b^{2} c^{4} d^{6} e^{3}\right)} x^{3} + {\left(4 \, c^{6} d^{9} + b c^{5} d^{8} e - 33 \, b^{2} c^{4} d^{7} e^{2}\right)} x^{2} + {\left(4 \, b c^{5} d^{9} - 11 \, b^{2} c^{4} d^{8} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - 15 \, {\left({\left(4 \, c^{6} d^{5} e^{3} - 9 \, b c^{5} d^{4} e^{4} - 4 \, b^{2} c^{4} d^{3} e^{5} + 26 \, b^{3} c^{3} d^{2} e^{6} - 24 \, b^{4} c^{2} d e^{7} + 7 \, b^{5} c e^{8}\right)} x^{5} + {\left(12 \, c^{6} d^{6} e^{2} - 23 \, b c^{5} d^{5} e^{3} - 21 \, b^{2} c^{4} d^{4} e^{4} + 74 \, b^{3} c^{3} d^{3} e^{5} - 46 \, b^{4} c^{2} d^{2} e^{6} - 3 \, b^{5} c d e^{7} + 7 \, b^{6} e^{8}\right)} x^{4} + 3 \, {\left(4 \, c^{6} d^{7} e - 5 \, b c^{5} d^{6} e^{2} - 13 \, b^{2} c^{4} d^{5} e^{3} + 22 \, b^{3} c^{3} d^{4} e^{4} + 2 \, b^{4} c^{2} d^{3} e^{5} - 17 \, b^{5} c d^{2} e^{6} + 7 \, b^{6} d e^{7}\right)} x^{3} + {\left(4 \, c^{6} d^{8} + 3 \, b c^{5} d^{7} e - 31 \, b^{2} c^{4} d^{6} e^{2} + 14 \, b^{3} c^{3} d^{5} e^{3} + 54 \, b^{4} c^{2} d^{4} e^{4} - 65 \, b^{5} c d^{3} e^{5} + 21 \, b^{6} d^{2} e^{6}\right)} x^{2} + {\left(4 \, b c^{5} d^{8} - 9 \, b^{2} c^{4} d^{7} e - 4 \, b^{3} c^{3} d^{6} e^{2} + 26 \, b^{4} c^{2} d^{5} e^{3} - 24 \, b^{5} c d^{4} e^{4} + 7 \, b^{6} d^{3} e^{5}\right)} x\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(15 \, b^{2} c^{4} d^{8} - 60 \, b^{3} c^{3} d^{7} e + 90 \, b^{4} c^{2} d^{6} e^{2} - 60 \, b^{5} c d^{5} e^{3} + 15 \, b^{6} d^{4} e^{4} + 15 \, {\left(2 \, b c^{5} d^{5} e^{3} - 4 \, b^{2} c^{4} d^{4} e^{4} + 26 \, b^{3} c^{3} d^{3} e^{5} - 24 \, b^{4} c^{2} d^{2} e^{6} + 7 \, b^{5} c d e^{7}\right)} x^{4} + 5 \, {\left(18 \, b c^{5} d^{6} e^{2} - 33 \, b^{2} c^{4} d^{5} e^{3} + 170 \, b^{3} c^{3} d^{4} e^{4} - 90 \, b^{4} c^{2} d^{3} e^{5} - 23 \, b^{5} c d^{2} e^{6} + 21 \, b^{6} d e^{7}\right)} x^{3} + {\left(90 \, b c^{5} d^{7} e - 135 \, b^{2} c^{4} d^{6} e^{2} + 436 \, b^{3} c^{3} d^{5} e^{3} + 358 \, b^{4} c^{2} d^{4} e^{4} - 679 \, b^{5} c d^{3} e^{5} + 245 \, b^{6} d^{2} e^{6}\right)} x^{2} + {\left(30 \, b c^{5} d^{8} - 15 \, b^{2} c^{4} d^{7} e - 90 \, b^{3} c^{3} d^{6} e^{2} + 556 \, b^{4} c^{2} d^{5} e^{3} - 537 \, b^{5} c d^{4} e^{4} + 161 \, b^{6} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left({\left(b^{3} c^{5} d^{9} e^{3} - 4 \, b^{4} c^{4} d^{8} e^{4} + 6 \, b^{5} c^{3} d^{7} e^{5} - 4 \, b^{6} c^{2} d^{6} e^{6} + b^{7} c d^{5} e^{7}\right)} x^{5} + {\left(3 \, b^{3} c^{5} d^{10} e^{2} - 11 \, b^{4} c^{4} d^{9} e^{3} + 14 \, b^{5} c^{3} d^{8} e^{4} - 6 \, b^{6} c^{2} d^{7} e^{5} - b^{7} c d^{6} e^{6} + b^{8} d^{5} e^{7}\right)} x^{4} + 3 \, {\left(b^{3} c^{5} d^{11} e - 3 \, b^{4} c^{4} d^{10} e^{2} + 2 \, b^{5} c^{3} d^{9} e^{3} + 2 \, b^{6} c^{2} d^{8} e^{4} - 3 \, b^{7} c d^{7} e^{5} + b^{8} d^{6} e^{6}\right)} x^{3} + {\left(b^{3} c^{5} d^{12} - b^{4} c^{4} d^{11} e - 6 \, b^{5} c^{3} d^{10} e^{2} + 14 \, b^{6} c^{2} d^{9} e^{3} - 11 \, b^{7} c d^{8} e^{4} + 3 \, b^{8} d^{7} e^{5}\right)} x^{2} + {\left(b^{4} c^{4} d^{12} - 4 \, b^{5} c^{3} d^{11} e + 6 \, b^{6} c^{2} d^{10} e^{2} - 4 \, b^{7} c d^{9} e^{3} + b^{8} d^{8} e^{4}\right)} x\right)}}, -\frac{30 \, {\left({\left(4 \, c^{6} d^{5} e^{3} - 9 \, b c^{5} d^{4} e^{4} - 4 \, b^{2} c^{4} d^{3} e^{5} + 26 \, b^{3} c^{3} d^{2} e^{6} - 24 \, b^{4} c^{2} d e^{7} + 7 \, b^{5} c e^{8}\right)} x^{5} + {\left(12 \, c^{6} d^{6} e^{2} - 23 \, b c^{5} d^{5} e^{3} - 21 \, b^{2} c^{4} d^{4} e^{4} + 74 \, b^{3} c^{3} d^{3} e^{5} - 46 \, b^{4} c^{2} d^{2} e^{6} - 3 \, b^{5} c d e^{7} + 7 \, b^{6} e^{8}\right)} x^{4} + 3 \, {\left(4 \, c^{6} d^{7} e - 5 \, b c^{5} d^{6} e^{2} - 13 \, b^{2} c^{4} d^{5} e^{3} + 22 \, b^{3} c^{3} d^{4} e^{4} + 2 \, b^{4} c^{2} d^{3} e^{5} - 17 \, b^{5} c d^{2} e^{6} + 7 \, b^{6} d e^{7}\right)} x^{3} + {\left(4 \, c^{6} d^{8} + 3 \, b c^{5} d^{7} e - 31 \, b^{2} c^{4} d^{6} e^{2} + 14 \, b^{3} c^{3} d^{5} e^{3} + 54 \, b^{4} c^{2} d^{4} e^{4} - 65 \, b^{5} c d^{3} e^{5} + 21 \, b^{6} d^{2} e^{6}\right)} x^{2} + {\left(4 \, b c^{5} d^{8} - 9 \, b^{2} c^{4} d^{7} e - 4 \, b^{3} c^{3} d^{6} e^{2} + 26 \, b^{4} c^{2} d^{5} e^{3} - 24 \, b^{5} c d^{4} e^{4} + 7 \, b^{6} d^{3} e^{5}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 15 \, {\left({\left(4 \, c^{6} d^{6} e^{3} - 11 \, b c^{5} d^{5} e^{4}\right)} x^{5} + {\left(12 \, c^{6} d^{7} e^{2} - 29 \, b c^{5} d^{6} e^{3} - 11 \, b^{2} c^{4} d^{5} e^{4}\right)} x^{4} + 3 \, {\left(4 \, c^{6} d^{8} e - 7 \, b c^{5} d^{7} e^{2} - 11 \, b^{2} c^{4} d^{6} e^{3}\right)} x^{3} + {\left(4 \, c^{6} d^{9} + b c^{5} d^{8} e - 33 \, b^{2} c^{4} d^{7} e^{2}\right)} x^{2} + {\left(4 \, b c^{5} d^{9} - 11 \, b^{2} c^{4} d^{8} e\right)} x\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 2 \, {\left(15 \, b^{2} c^{4} d^{8} - 60 \, b^{3} c^{3} d^{7} e + 90 \, b^{4} c^{2} d^{6} e^{2} - 60 \, b^{5} c d^{5} e^{3} + 15 \, b^{6} d^{4} e^{4} + 15 \, {\left(2 \, b c^{5} d^{5} e^{3} - 4 \, b^{2} c^{4} d^{4} e^{4} + 26 \, b^{3} c^{3} d^{3} e^{5} - 24 \, b^{4} c^{2} d^{2} e^{6} + 7 \, b^{5} c d e^{7}\right)} x^{4} + 5 \, {\left(18 \, b c^{5} d^{6} e^{2} - 33 \, b^{2} c^{4} d^{5} e^{3} + 170 \, b^{3} c^{3} d^{4} e^{4} - 90 \, b^{4} c^{2} d^{3} e^{5} - 23 \, b^{5} c d^{2} e^{6} + 21 \, b^{6} d e^{7}\right)} x^{3} + {\left(90 \, b c^{5} d^{7} e - 135 \, b^{2} c^{4} d^{6} e^{2} + 436 \, b^{3} c^{3} d^{5} e^{3} + 358 \, b^{4} c^{2} d^{4} e^{4} - 679 \, b^{5} c d^{3} e^{5} + 245 \, b^{6} d^{2} e^{6}\right)} x^{2} + {\left(30 \, b c^{5} d^{8} - 15 \, b^{2} c^{4} d^{7} e - 90 \, b^{3} c^{3} d^{6} e^{2} + 556 \, b^{4} c^{2} d^{5} e^{3} - 537 \, b^{5} c d^{4} e^{4} + 161 \, b^{6} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left({\left(b^{3} c^{5} d^{9} e^{3} - 4 \, b^{4} c^{4} d^{8} e^{4} + 6 \, b^{5} c^{3} d^{7} e^{5} - 4 \, b^{6} c^{2} d^{6} e^{6} + b^{7} c d^{5} e^{7}\right)} x^{5} + {\left(3 \, b^{3} c^{5} d^{10} e^{2} - 11 \, b^{4} c^{4} d^{9} e^{3} + 14 \, b^{5} c^{3} d^{8} e^{4} - 6 \, b^{6} c^{2} d^{7} e^{5} - b^{7} c d^{6} e^{6} + b^{8} d^{5} e^{7}\right)} x^{4} + 3 \, {\left(b^{3} c^{5} d^{11} e - 3 \, b^{4} c^{4} d^{10} e^{2} + 2 \, b^{5} c^{3} d^{9} e^{3} + 2 \, b^{6} c^{2} d^{8} e^{4} - 3 \, b^{7} c d^{7} e^{5} + b^{8} d^{6} e^{6}\right)} x^{3} + {\left(b^{3} c^{5} d^{12} - b^{4} c^{4} d^{11} e - 6 \, b^{5} c^{3} d^{10} e^{2} + 14 \, b^{6} c^{2} d^{9} e^{3} - 11 \, b^{7} c d^{8} e^{4} + 3 \, b^{8} d^{7} e^{5}\right)} x^{2} + {\left(b^{4} c^{4} d^{12} - 4 \, b^{5} c^{3} d^{11} e + 6 \, b^{6} c^{2} d^{10} e^{2} - 4 \, b^{7} c d^{9} e^{3} + b^{8} d^{8} e^{4}\right)} x\right)}}, -\frac{15 \, {\left({\left(4 \, c^{6} d^{6} e^{3} - 11 \, b c^{5} d^{5} e^{4}\right)} x^{5} + {\left(12 \, c^{6} d^{7} e^{2} - 29 \, b c^{5} d^{6} e^{3} - 11 \, b^{2} c^{4} d^{5} e^{4}\right)} x^{4} + 3 \, {\left(4 \, c^{6} d^{8} e - 7 \, b c^{5} d^{7} e^{2} - 11 \, b^{2} c^{4} d^{6} e^{3}\right)} x^{3} + {\left(4 \, c^{6} d^{9} + b c^{5} d^{8} e - 33 \, b^{2} c^{4} d^{7} e^{2}\right)} x^{2} + {\left(4 \, b c^{5} d^{9} - 11 \, b^{2} c^{4} d^{8} e\right)} x\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 15 \, {\left({\left(4 \, c^{6} d^{5} e^{3} - 9 \, b c^{5} d^{4} e^{4} - 4 \, b^{2} c^{4} d^{3} e^{5} + 26 \, b^{3} c^{3} d^{2} e^{6} - 24 \, b^{4} c^{2} d e^{7} + 7 \, b^{5} c e^{8}\right)} x^{5} + {\left(12 \, c^{6} d^{6} e^{2} - 23 \, b c^{5} d^{5} e^{3} - 21 \, b^{2} c^{4} d^{4} e^{4} + 74 \, b^{3} c^{3} d^{3} e^{5} - 46 \, b^{4} c^{2} d^{2} e^{6} - 3 \, b^{5} c d e^{7} + 7 \, b^{6} e^{8}\right)} x^{4} + 3 \, {\left(4 \, c^{6} d^{7} e - 5 \, b c^{5} d^{6} e^{2} - 13 \, b^{2} c^{4} d^{5} e^{3} + 22 \, b^{3} c^{3} d^{4} e^{4} + 2 \, b^{4} c^{2} d^{3} e^{5} - 17 \, b^{5} c d^{2} e^{6} + 7 \, b^{6} d e^{7}\right)} x^{3} + {\left(4 \, c^{6} d^{8} + 3 \, b c^{5} d^{7} e - 31 \, b^{2} c^{4} d^{6} e^{2} + 14 \, b^{3} c^{3} d^{5} e^{3} + 54 \, b^{4} c^{2} d^{4} e^{4} - 65 \, b^{5} c d^{3} e^{5} + 21 \, b^{6} d^{2} e^{6}\right)} x^{2} + {\left(4 \, b c^{5} d^{8} - 9 \, b^{2} c^{4} d^{7} e - 4 \, b^{3} c^{3} d^{6} e^{2} + 26 \, b^{4} c^{2} d^{5} e^{3} - 24 \, b^{5} c d^{4} e^{4} + 7 \, b^{6} d^{3} e^{5}\right)} x\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left(15 \, b^{2} c^{4} d^{8} - 60 \, b^{3} c^{3} d^{7} e + 90 \, b^{4} c^{2} d^{6} e^{2} - 60 \, b^{5} c d^{5} e^{3} + 15 \, b^{6} d^{4} e^{4} + 15 \, {\left(2 \, b c^{5} d^{5} e^{3} - 4 \, b^{2} c^{4} d^{4} e^{4} + 26 \, b^{3} c^{3} d^{3} e^{5} - 24 \, b^{4} c^{2} d^{2} e^{6} + 7 \, b^{5} c d e^{7}\right)} x^{4} + 5 \, {\left(18 \, b c^{5} d^{6} e^{2} - 33 \, b^{2} c^{4} d^{5} e^{3} + 170 \, b^{3} c^{3} d^{4} e^{4} - 90 \, b^{4} c^{2} d^{3} e^{5} - 23 \, b^{5} c d^{2} e^{6} + 21 \, b^{6} d e^{7}\right)} x^{3} + {\left(90 \, b c^{5} d^{7} e - 135 \, b^{2} c^{4} d^{6} e^{2} + 436 \, b^{3} c^{3} d^{5} e^{3} + 358 \, b^{4} c^{2} d^{4} e^{4} - 679 \, b^{5} c d^{3} e^{5} + 245 \, b^{6} d^{2} e^{6}\right)} x^{2} + {\left(30 \, b c^{5} d^{8} - 15 \, b^{2} c^{4} d^{7} e - 90 \, b^{3} c^{3} d^{6} e^{2} + 556 \, b^{4} c^{2} d^{5} e^{3} - 537 \, b^{5} c d^{4} e^{4} + 161 \, b^{6} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left({\left(b^{3} c^{5} d^{9} e^{3} - 4 \, b^{4} c^{4} d^{8} e^{4} + 6 \, b^{5} c^{3} d^{7} e^{5} - 4 \, b^{6} c^{2} d^{6} e^{6} + b^{7} c d^{5} e^{7}\right)} x^{5} + {\left(3 \, b^{3} c^{5} d^{10} e^{2} - 11 \, b^{4} c^{4} d^{9} e^{3} + 14 \, b^{5} c^{3} d^{8} e^{4} - 6 \, b^{6} c^{2} d^{7} e^{5} - b^{7} c d^{6} e^{6} + b^{8} d^{5} e^{7}\right)} x^{4} + 3 \, {\left(b^{3} c^{5} d^{11} e - 3 \, b^{4} c^{4} d^{10} e^{2} + 2 \, b^{5} c^{3} d^{9} e^{3} + 2 \, b^{6} c^{2} d^{8} e^{4} - 3 \, b^{7} c d^{7} e^{5} + b^{8} d^{6} e^{6}\right)} x^{3} + {\left(b^{3} c^{5} d^{12} - b^{4} c^{4} d^{11} e - 6 \, b^{5} c^{3} d^{10} e^{2} + 14 \, b^{6} c^{2} d^{9} e^{3} - 11 \, b^{7} c d^{8} e^{4} + 3 \, b^{8} d^{7} e^{5}\right)} x^{2} + {\left(b^{4} c^{4} d^{12} - 4 \, b^{5} c^{3} d^{11} e + 6 \, b^{6} c^{2} d^{10} e^{2} - 4 \, b^{7} c d^{9} e^{3} + b^{8} d^{8} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/30*(15*((4*c^6*d^6*e^3 - 11*b*c^5*d^5*e^4)*x^5 + (12*c^6*d^7*e^2 - 29*b*c^5*d^6*e^3 - 11*b^2*c^4*d^5*e^4)*x^4 + 3*(4*c^6*d^8*e - 7*b*c^5*d^7*e^2 - 11*b^2*c^4*d^6*e^3)*x^3 + (4*c^6*d^9 + b*c^5*d^8*e - 33*b^2*c^4*d^7*e^2)*x^2 + (4*b*c^5*d^9 - 11*b^2*c^4*d^8*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 15*((4*c^6*d^5*e^3 - 9*b*c^5*d^4*e^4 - 4*b^2*c^4*d^3*e^5 + 26*b^3*c^3*d^2*e^6 - 24*b^4*c^2*d*e^7 + 7*b^5*c*e^8)*x^5 + (12*c^6*d^6*e^2 - 23*b*c^5*d^5*e^3 - 21*b^2*c^4*d^4*e^4 + 74*b^3*c^3*d^3*e^5 - 46*b^4*c^2*d^2*e^6 - 3*b^5*c*d*e^7 + 7*b^6*e^8)*x^4 + 3*(4*c^6*d^7*e - 5*b*c^5*d^6*e^2 - 13*b^2*c^4*d^5*e^3 + 22*b^3*c^3*d^4*e^4 + 2*b^4*c^2*d^3*e^5 - 17*b^5*c*d^2*e^6 + 7*b^6*d*e^7)*x^3 + (4*c^6*d^8 + 3*b*c^5*d^7*e - 31*b^2*c^4*d^6*e^2 + 14*b^3*c^3*d^5*e^3 + 54*b^4*c^2*d^4*e^4 - 65*b^5*c*d^3*e^5 + 21*b^6*d^2*e^6)*x^2 + (4*b*c^5*d^8 - 9*b^2*c^4*d^7*e - 4*b^3*c^3*d^6*e^2 + 26*b^4*c^2*d^5*e^3 - 24*b^5*c*d^4*e^4 + 7*b^6*d^3*e^5)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(15*b^2*c^4*d^8 - 60*b^3*c^3*d^7*e + 90*b^4*c^2*d^6*e^2 - 60*b^5*c*d^5*e^3 + 15*b^6*d^4*e^4 + 15*(2*b*c^5*d^5*e^3 - 4*b^2*c^4*d^4*e^4 + 26*b^3*c^3*d^3*e^5 - 24*b^4*c^2*d^2*e^6 + 7*b^5*c*d*e^7)*x^4 + 5*(18*b*c^5*d^6*e^2 - 33*b^2*c^4*d^5*e^3 + 170*b^3*c^3*d^4*e^4 - 90*b^4*c^2*d^3*e^5 - 23*b^5*c*d^2*e^6 + 21*b^6*d*e^7)*x^3 + (90*b*c^5*d^7*e - 135*b^2*c^4*d^6*e^2 + 436*b^3*c^3*d^5*e^3 + 358*b^4*c^2*d^4*e^4 - 679*b^5*c*d^3*e^5 + 245*b^6*d^2*e^6)*x^2 + (30*b*c^5*d^8 - 15*b^2*c^4*d^7*e - 90*b^3*c^3*d^6*e^2 + 556*b^4*c^2*d^5*e^3 - 537*b^5*c*d^4*e^4 + 161*b^6*d^3*e^5)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x), -1/30*(30*((4*c^6*d^6*e^3 - 11*b*c^5*d^5*e^4)*x^5 + (12*c^6*d^7*e^2 - 29*b*c^5*d^6*e^3 - 11*b^2*c^4*d^5*e^4)*x^4 + 3*(4*c^6*d^8*e - 7*b*c^5*d^7*e^2 - 11*b^2*c^4*d^6*e^3)*x^3 + (4*c^6*d^9 + b*c^5*d^8*e - 33*b^2*c^4*d^7*e^2)*x^2 + (4*b*c^5*d^9 - 11*b^2*c^4*d^8*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - 15*((4*c^6*d^5*e^3 - 9*b*c^5*d^4*e^4 - 4*b^2*c^4*d^3*e^5 + 26*b^3*c^3*d^2*e^6 - 24*b^4*c^2*d*e^7 + 7*b^5*c*e^8)*x^5 + (12*c^6*d^6*e^2 - 23*b*c^5*d^5*e^3 - 21*b^2*c^4*d^4*e^4 + 74*b^3*c^3*d^3*e^5 - 46*b^4*c^2*d^2*e^6 - 3*b^5*c*d*e^7 + 7*b^6*e^8)*x^4 + 3*(4*c^6*d^7*e - 5*b*c^5*d^6*e^2 - 13*b^2*c^4*d^5*e^3 + 22*b^3*c^3*d^4*e^4 + 2*b^4*c^2*d^3*e^5 - 17*b^5*c*d^2*e^6 + 7*b^6*d*e^7)*x^3 + (4*c^6*d^8 + 3*b*c^5*d^7*e - 31*b^2*c^4*d^6*e^2 + 14*b^3*c^3*d^5*e^3 + 54*b^4*c^2*d^4*e^4 - 65*b^5*c*d^3*e^5 + 21*b^6*d^2*e^6)*x^2 + (4*b*c^5*d^8 - 9*b^2*c^4*d^7*e - 4*b^3*c^3*d^6*e^2 + 26*b^4*c^2*d^5*e^3 - 24*b^5*c*d^4*e^4 + 7*b^6*d^3*e^5)*x)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(15*b^2*c^4*d^8 - 60*b^3*c^3*d^7*e + 90*b^4*c^2*d^6*e^2 - 60*b^5*c*d^5*e^3 + 15*b^6*d^4*e^4 + 15*(2*b*c^5*d^5*e^3 - 4*b^2*c^4*d^4*e^4 + 26*b^3*c^3*d^3*e^5 - 24*b^4*c^2*d^2*e^6 + 7*b^5*c*d*e^7)*x^4 + 5*(18*b*c^5*d^6*e^2 - 33*b^2*c^4*d^5*e^3 + 170*b^3*c^3*d^4*e^4 - 90*b^4*c^2*d^3*e^5 - 23*b^5*c*d^2*e^6 + 21*b^6*d*e^7)*x^3 + (90*b*c^5*d^7*e - 135*b^2*c^4*d^6*e^2 + 436*b^3*c^3*d^5*e^3 + 358*b^4*c^2*d^4*e^4 - 679*b^5*c*d^3*e^5 + 245*b^6*d^2*e^6)*x^2 + (30*b*c^5*d^8 - 15*b^2*c^4*d^7*e - 90*b^3*c^3*d^6*e^2 + 556*b^4*c^2*d^5*e^3 - 537*b^5*c*d^4*e^4 + 161*b^6*d^3*e^5)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x), -1/30*(30*((4*c^6*d^5*e^3 - 9*b*c^5*d^4*e^4 - 4*b^2*c^4*d^3*e^5 + 26*b^3*c^3*d^2*e^6 - 24*b^4*c^2*d*e^7 + 7*b^5*c*e^8)*x^5 + (12*c^6*d^6*e^2 - 23*b*c^5*d^5*e^3 - 21*b^2*c^4*d^4*e^4 + 74*b^3*c^3*d^3*e^5 - 46*b^4*c^2*d^2*e^6 - 3*b^5*c*d*e^7 + 7*b^6*e^8)*x^4 + 3*(4*c^6*d^7*e - 5*b*c^5*d^6*e^2 - 13*b^2*c^4*d^5*e^3 + 22*b^3*c^3*d^4*e^4 + 2*b^4*c^2*d^3*e^5 - 17*b^5*c*d^2*e^6 + 7*b^6*d*e^7)*x^3 + (4*c^6*d^8 + 3*b*c^5*d^7*e - 31*b^2*c^4*d^6*e^2 + 14*b^3*c^3*d^5*e^3 + 54*b^4*c^2*d^4*e^4 - 65*b^5*c*d^3*e^5 + 21*b^6*d^2*e^6)*x^2 + (4*b*c^5*d^8 - 9*b^2*c^4*d^7*e - 4*b^3*c^3*d^6*e^2 + 26*b^4*c^2*d^5*e^3 - 24*b^5*c*d^4*e^4 + 7*b^6*d^3*e^5)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 15*((4*c^6*d^6*e^3 - 11*b*c^5*d^5*e^4)*x^5 + (12*c^6*d^7*e^2 - 29*b*c^5*d^6*e^3 - 11*b^2*c^4*d^5*e^4)*x^4 + 3*(4*c^6*d^8*e - 7*b*c^5*d^7*e^2 - 11*b^2*c^4*d^6*e^3)*x^3 + (4*c^6*d^9 + b*c^5*d^8*e - 33*b^2*c^4*d^7*e^2)*x^2 + (4*b*c^5*d^9 - 11*b^2*c^4*d^8*e)*x)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 2*(15*b^2*c^4*d^8 - 60*b^3*c^3*d^7*e + 90*b^4*c^2*d^6*e^2 - 60*b^5*c*d^5*e^3 + 15*b^6*d^4*e^4 + 15*(2*b*c^5*d^5*e^3 - 4*b^2*c^4*d^4*e^4 + 26*b^3*c^3*d^3*e^5 - 24*b^4*c^2*d^2*e^6 + 7*b^5*c*d*e^7)*x^4 + 5*(18*b*c^5*d^6*e^2 - 33*b^2*c^4*d^5*e^3 + 170*b^3*c^3*d^4*e^4 - 90*b^4*c^2*d^3*e^5 - 23*b^5*c*d^2*e^6 + 21*b^6*d*e^7)*x^3 + (90*b*c^5*d^7*e - 135*b^2*c^4*d^6*e^2 + 436*b^3*c^3*d^5*e^3 + 358*b^4*c^2*d^4*e^4 - 679*b^5*c*d^3*e^5 + 245*b^6*d^2*e^6)*x^2 + (30*b*c^5*d^8 - 15*b^2*c^4*d^7*e - 90*b^3*c^3*d^6*e^2 + 556*b^4*c^2*d^5*e^3 - 537*b^5*c*d^4*e^4 + 161*b^6*d^3*e^5)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x), -1/15*(15*((4*c^6*d^6*e^3 - 11*b*c^5*d^5*e^4)*x^5 + (12*c^6*d^7*e^2 - 29*b*c^5*d^6*e^3 - 11*b^2*c^4*d^5*e^4)*x^4 + 3*(4*c^6*d^8*e - 7*b*c^5*d^7*e^2 - 11*b^2*c^4*d^6*e^3)*x^3 + (4*c^6*d^9 + b*c^5*d^8*e - 33*b^2*c^4*d^7*e^2)*x^2 + (4*b*c^5*d^9 - 11*b^2*c^4*d^8*e)*x)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 15*((4*c^6*d^5*e^3 - 9*b*c^5*d^4*e^4 - 4*b^2*c^4*d^3*e^5 + 26*b^3*c^3*d^2*e^6 - 24*b^4*c^2*d*e^7 + 7*b^5*c*e^8)*x^5 + (12*c^6*d^6*e^2 - 23*b*c^5*d^5*e^3 - 21*b^2*c^4*d^4*e^4 + 74*b^3*c^3*d^3*e^5 - 46*b^4*c^2*d^2*e^6 - 3*b^5*c*d*e^7 + 7*b^6*e^8)*x^4 + 3*(4*c^6*d^7*e - 5*b*c^5*d^6*e^2 - 13*b^2*c^4*d^5*e^3 + 22*b^3*c^3*d^4*e^4 + 2*b^4*c^2*d^3*e^5 - 17*b^5*c*d^2*e^6 + 7*b^6*d*e^7)*x^3 + (4*c^6*d^8 + 3*b*c^5*d^7*e - 31*b^2*c^4*d^6*e^2 + 14*b^3*c^3*d^5*e^3 + 54*b^4*c^2*d^4*e^4 - 65*b^5*c*d^3*e^5 + 21*b^6*d^2*e^6)*x^2 + (4*b*c^5*d^8 - 9*b^2*c^4*d^7*e - 4*b^3*c^3*d^6*e^2 + 26*b^4*c^2*d^5*e^3 - 24*b^5*c*d^4*e^4 + 7*b^6*d^3*e^5)*x)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + (15*b^2*c^4*d^8 - 60*b^3*c^3*d^7*e + 90*b^4*c^2*d^6*e^2 - 60*b^5*c*d^5*e^3 + 15*b^6*d^4*e^4 + 15*(2*b*c^5*d^5*e^3 - 4*b^2*c^4*d^4*e^4 + 26*b^3*c^3*d^3*e^5 - 24*b^4*c^2*d^2*e^6 + 7*b^5*c*d*e^7)*x^4 + 5*(18*b*c^5*d^6*e^2 - 33*b^2*c^4*d^5*e^3 + 170*b^3*c^3*d^4*e^4 - 90*b^4*c^2*d^3*e^5 - 23*b^5*c*d^2*e^6 + 21*b^6*d*e^7)*x^3 + (90*b*c^5*d^7*e - 135*b^2*c^4*d^6*e^2 + 436*b^3*c^3*d^5*e^3 + 358*b^4*c^2*d^4*e^4 - 679*b^5*c*d^3*e^5 + 245*b^6*d^2*e^6)*x^2 + (30*b*c^5*d^8 - 15*b^2*c^4*d^7*e - 90*b^3*c^3*d^6*e^2 + 556*b^4*c^2*d^5*e^3 - 537*b^5*c*d^4*e^4 + 161*b^6*d^3*e^5)*x)*sqrt(e*x + d))/((b^3*c^5*d^9*e^3 - 4*b^4*c^4*d^8*e^4 + 6*b^5*c^3*d^7*e^5 - 4*b^6*c^2*d^6*e^6 + b^7*c*d^5*e^7)*x^5 + (3*b^3*c^5*d^10*e^2 - 11*b^4*c^4*d^9*e^3 + 14*b^5*c^3*d^8*e^4 - 6*b^6*c^2*d^7*e^5 - b^7*c*d^6*e^6 + b^8*d^5*e^7)*x^4 + 3*(b^3*c^5*d^11*e - 3*b^4*c^4*d^10*e^2 + 2*b^5*c^3*d^9*e^3 + 2*b^6*c^2*d^8*e^4 - 3*b^7*c*d^7*e^5 + b^8*d^6*e^6)*x^3 + (b^3*c^5*d^12 - b^4*c^4*d^11*e - 6*b^5*c^3*d^10*e^2 + 14*b^6*c^2*d^9*e^3 - 11*b^7*c*d^8*e^4 + 3*b^8*d^7*e^5)*x^2 + (b^4*c^4*d^12 - 4*b^5*c^3*d^11*e + 6*b^6*c^2*d^10*e^2 - 4*b^7*c*d^9*e^3 + b^8*d^8*e^4)*x)]","B",0
378,1,2373,0,1.931752," ","integrate((e*x+d)^(9/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(16 \, c^{6} d^{4} - 28 \, b c^{5} d^{3} e + 9 \, b^{2} c^{4} d^{2} e^{2} + 2 \, b^{3} c^{3} d e^{3} + b^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 28 \, b^{2} c^{4} d^{3} e + 9 \, b^{3} c^{3} d^{2} e^{2} + 2 \, b^{4} c^{2} d e^{3} + b^{5} c e^{4}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 28 \, b^{3} c^{3} d^{3} e + 9 \, b^{4} c^{2} d^{2} e^{2} + 2 \, b^{5} c d e^{3} + b^{6} e^{4}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 3 \, {\left({\left(16 \, c^{6} d^{4} - 36 \, b c^{5} d^{3} e + 21 \, b^{2} c^{4} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 36 \, b^{2} c^{4} d^{3} e + 21 \, b^{3} c^{3} d^{2} e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 36 \, b^{3} c^{3} d^{3} e + 21 \, b^{4} c^{2} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} c^{2} d^{4} - {\left(24 \, b c^{5} d^{4} - 48 \, b^{2} c^{4} d^{3} e + 21 \, b^{3} c^{3} d^{2} e^{2} + 3 \, b^{4} c^{2} d e^{3} - 5 \, b^{5} c e^{4}\right)} x^{3} - {\left(36 \, b^{2} c^{4} d^{4} - 73 \, b^{3} c^{3} d^{3} e + 33 \, b^{4} c^{2} d^{2} e^{2} - 5 \, b^{5} c d e^{3} - 3 \, b^{6} e^{4}\right)} x^{2} - {\left(8 \, b^{3} c^{3} d^{4} - 17 \, b^{4} c^{2} d^{3} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{4} x^{4} + 2 \, b^{6} c^{3} x^{3} + b^{7} c^{2} x^{2}\right)}}, \frac{6 \, {\left({\left(16 \, c^{6} d^{4} - 28 \, b c^{5} d^{3} e + 9 \, b^{2} c^{4} d^{2} e^{2} + 2 \, b^{3} c^{3} d e^{3} + b^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 28 \, b^{2} c^{4} d^{3} e + 9 \, b^{3} c^{3} d^{2} e^{2} + 2 \, b^{4} c^{2} d e^{3} + b^{5} c e^{4}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 28 \, b^{3} c^{3} d^{3} e + 9 \, b^{4} c^{2} d^{2} e^{2} + 2 \, b^{5} c d e^{3} + b^{6} e^{4}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 3 \, {\left({\left(16 \, c^{6} d^{4} - 36 \, b c^{5} d^{3} e + 21 \, b^{2} c^{4} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 36 \, b^{2} c^{4} d^{3} e + 21 \, b^{3} c^{3} d^{2} e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 36 \, b^{3} c^{3} d^{3} e + 21 \, b^{4} c^{2} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} c^{2} d^{4} - {\left(24 \, b c^{5} d^{4} - 48 \, b^{2} c^{4} d^{3} e + 21 \, b^{3} c^{3} d^{2} e^{2} + 3 \, b^{4} c^{2} d e^{3} - 5 \, b^{5} c e^{4}\right)} x^{3} - {\left(36 \, b^{2} c^{4} d^{4} - 73 \, b^{3} c^{3} d^{3} e + 33 \, b^{4} c^{2} d^{2} e^{2} - 5 \, b^{5} c d e^{3} - 3 \, b^{6} e^{4}\right)} x^{2} - {\left(8 \, b^{3} c^{3} d^{4} - 17 \, b^{4} c^{2} d^{3} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{4} x^{4} + 2 \, b^{6} c^{3} x^{3} + b^{7} c^{2} x^{2}\right)}}, \frac{6 \, {\left({\left(16 \, c^{6} d^{4} - 36 \, b c^{5} d^{3} e + 21 \, b^{2} c^{4} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 36 \, b^{2} c^{4} d^{3} e + 21 \, b^{3} c^{3} d^{2} e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 36 \, b^{3} c^{3} d^{3} e + 21 \, b^{4} c^{2} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left({\left(16 \, c^{6} d^{4} - 28 \, b c^{5} d^{3} e + 9 \, b^{2} c^{4} d^{2} e^{2} + 2 \, b^{3} c^{3} d e^{3} + b^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 28 \, b^{2} c^{4} d^{3} e + 9 \, b^{3} c^{3} d^{2} e^{2} + 2 \, b^{4} c^{2} d e^{3} + b^{5} c e^{4}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 28 \, b^{3} c^{3} d^{3} e + 9 \, b^{4} c^{2} d^{2} e^{2} + 2 \, b^{5} c d e^{3} + b^{6} e^{4}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - 2 \, {\left(2 \, b^{4} c^{2} d^{4} - {\left(24 \, b c^{5} d^{4} - 48 \, b^{2} c^{4} d^{3} e + 21 \, b^{3} c^{3} d^{2} e^{2} + 3 \, b^{4} c^{2} d e^{3} - 5 \, b^{5} c e^{4}\right)} x^{3} - {\left(36 \, b^{2} c^{4} d^{4} - 73 \, b^{3} c^{3} d^{3} e + 33 \, b^{4} c^{2} d^{2} e^{2} - 5 \, b^{5} c d e^{3} - 3 \, b^{6} e^{4}\right)} x^{2} - {\left(8 \, b^{3} c^{3} d^{4} - 17 \, b^{4} c^{2} d^{3} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{4} x^{4} + 2 \, b^{6} c^{3} x^{3} + b^{7} c^{2} x^{2}\right)}}, \frac{3 \, {\left({\left(16 \, c^{6} d^{4} - 28 \, b c^{5} d^{3} e + 9 \, b^{2} c^{4} d^{2} e^{2} + 2 \, b^{3} c^{3} d e^{3} + b^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 28 \, b^{2} c^{4} d^{3} e + 9 \, b^{3} c^{3} d^{2} e^{2} + 2 \, b^{4} c^{2} d e^{3} + b^{5} c e^{4}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 28 \, b^{3} c^{3} d^{3} e + 9 \, b^{4} c^{2} d^{2} e^{2} + 2 \, b^{5} c d e^{3} + b^{6} e^{4}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 3 \, {\left({\left(16 \, c^{6} d^{4} - 36 \, b c^{5} d^{3} e + 21 \, b^{2} c^{4} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 36 \, b^{2} c^{4} d^{3} e + 21 \, b^{3} c^{3} d^{2} e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 36 \, b^{3} c^{3} d^{3} e + 21 \, b^{4} c^{2} d^{2} e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, b^{4} c^{2} d^{4} - {\left(24 \, b c^{5} d^{4} - 48 \, b^{2} c^{4} d^{3} e + 21 \, b^{3} c^{3} d^{2} e^{2} + 3 \, b^{4} c^{2} d e^{3} - 5 \, b^{5} c e^{4}\right)} x^{3} - {\left(36 \, b^{2} c^{4} d^{4} - 73 \, b^{3} c^{3} d^{3} e + 33 \, b^{4} c^{2} d^{2} e^{2} - 5 \, b^{5} c d e^{3} - 3 \, b^{6} e^{4}\right)} x^{2} - {\left(8 \, b^{3} c^{3} d^{4} - 17 \, b^{4} c^{2} d^{3} e\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(b^{5} c^{4} x^{4} + 2 \, b^{6} c^{3} x^{3} + b^{7} c^{2} x^{2}\right)}}\right]"," ",0,"[1/8*(3*((16*c^6*d^4 - 28*b*c^5*d^3*e + 9*b^2*c^4*d^2*e^2 + 2*b^3*c^3*d*e^3 + b^4*c^2*e^4)*x^4 + 2*(16*b*c^5*d^4 - 28*b^2*c^4*d^3*e + 9*b^3*c^3*d^2*e^2 + 2*b^4*c^2*d*e^3 + b^5*c*e^4)*x^3 + (16*b^2*c^4*d^4 - 28*b^3*c^3*d^3*e + 9*b^4*c^2*d^2*e^2 + 2*b^5*c*d*e^3 + b^6*e^4)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 3*((16*c^6*d^4 - 36*b*c^5*d^3*e + 21*b^2*c^4*d^2*e^2)*x^4 + 2*(16*b*c^5*d^4 - 36*b^2*c^4*d^3*e + 21*b^3*c^3*d^2*e^2)*x^3 + (16*b^2*c^4*d^4 - 36*b^3*c^3*d^3*e + 21*b^4*c^2*d^2*e^2)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*c^2*d^4 - (24*b*c^5*d^4 - 48*b^2*c^4*d^3*e + 21*b^3*c^3*d^2*e^2 + 3*b^4*c^2*d*e^3 - 5*b^5*c*e^4)*x^3 - (36*b^2*c^4*d^4 - 73*b^3*c^3*d^3*e + 33*b^4*c^2*d^2*e^2 - 5*b^5*c*d*e^3 - 3*b^6*e^4)*x^2 - (8*b^3*c^3*d^4 - 17*b^4*c^2*d^3*e)*x)*sqrt(e*x + d))/(b^5*c^4*x^4 + 2*b^6*c^3*x^3 + b^7*c^2*x^2), 1/8*(6*((16*c^6*d^4 - 28*b*c^5*d^3*e + 9*b^2*c^4*d^2*e^2 + 2*b^3*c^3*d*e^3 + b^4*c^2*e^4)*x^4 + 2*(16*b*c^5*d^4 - 28*b^2*c^4*d^3*e + 9*b^3*c^3*d^2*e^2 + 2*b^4*c^2*d*e^3 + b^5*c*e^4)*x^3 + (16*b^2*c^4*d^4 - 28*b^3*c^3*d^3*e + 9*b^4*c^2*d^2*e^2 + 2*b^5*c*d*e^3 + b^6*e^4)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 3*((16*c^6*d^4 - 36*b*c^5*d^3*e + 21*b^2*c^4*d^2*e^2)*x^4 + 2*(16*b*c^5*d^4 - 36*b^2*c^4*d^3*e + 21*b^3*c^3*d^2*e^2)*x^3 + (16*b^2*c^4*d^4 - 36*b^3*c^3*d^3*e + 21*b^4*c^2*d^2*e^2)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*c^2*d^4 - (24*b*c^5*d^4 - 48*b^2*c^4*d^3*e + 21*b^3*c^3*d^2*e^2 + 3*b^4*c^2*d*e^3 - 5*b^5*c*e^4)*x^3 - (36*b^2*c^4*d^4 - 73*b^3*c^3*d^3*e + 33*b^4*c^2*d^2*e^2 - 5*b^5*c*d*e^3 - 3*b^6*e^4)*x^2 - (8*b^3*c^3*d^4 - 17*b^4*c^2*d^3*e)*x)*sqrt(e*x + d))/(b^5*c^4*x^4 + 2*b^6*c^3*x^3 + b^7*c^2*x^2), 1/8*(6*((16*c^6*d^4 - 36*b*c^5*d^3*e + 21*b^2*c^4*d^2*e^2)*x^4 + 2*(16*b*c^5*d^4 - 36*b^2*c^4*d^3*e + 21*b^3*c^3*d^2*e^2)*x^3 + (16*b^2*c^4*d^4 - 36*b^3*c^3*d^3*e + 21*b^4*c^2*d^2*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*((16*c^6*d^4 - 28*b*c^5*d^3*e + 9*b^2*c^4*d^2*e^2 + 2*b^3*c^3*d*e^3 + b^4*c^2*e^4)*x^4 + 2*(16*b*c^5*d^4 - 28*b^2*c^4*d^3*e + 9*b^3*c^3*d^2*e^2 + 2*b^4*c^2*d*e^3 + b^5*c*e^4)*x^3 + (16*b^2*c^4*d^4 - 28*b^3*c^3*d^3*e + 9*b^4*c^2*d^2*e^2 + 2*b^5*c*d*e^3 + b^6*e^4)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - 2*(2*b^4*c^2*d^4 - (24*b*c^5*d^4 - 48*b^2*c^4*d^3*e + 21*b^3*c^3*d^2*e^2 + 3*b^4*c^2*d*e^3 - 5*b^5*c*e^4)*x^3 - (36*b^2*c^4*d^4 - 73*b^3*c^3*d^3*e + 33*b^4*c^2*d^2*e^2 - 5*b^5*c*d*e^3 - 3*b^6*e^4)*x^2 - (8*b^3*c^3*d^4 - 17*b^4*c^2*d^3*e)*x)*sqrt(e*x + d))/(b^5*c^4*x^4 + 2*b^6*c^3*x^3 + b^7*c^2*x^2), 1/4*(3*((16*c^6*d^4 - 28*b*c^5*d^3*e + 9*b^2*c^4*d^2*e^2 + 2*b^3*c^3*d*e^3 + b^4*c^2*e^4)*x^4 + 2*(16*b*c^5*d^4 - 28*b^2*c^4*d^3*e + 9*b^3*c^3*d^2*e^2 + 2*b^4*c^2*d*e^3 + b^5*c*e^4)*x^3 + (16*b^2*c^4*d^4 - 28*b^3*c^3*d^3*e + 9*b^4*c^2*d^2*e^2 + 2*b^5*c*d*e^3 + b^6*e^4)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 3*((16*c^6*d^4 - 36*b*c^5*d^3*e + 21*b^2*c^4*d^2*e^2)*x^4 + 2*(16*b*c^5*d^4 - 36*b^2*c^4*d^3*e + 21*b^3*c^3*d^2*e^2)*x^3 + (16*b^2*c^4*d^4 - 36*b^3*c^3*d^3*e + 21*b^4*c^2*d^2*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*b^4*c^2*d^4 - (24*b*c^5*d^4 - 48*b^2*c^4*d^3*e + 21*b^3*c^3*d^2*e^2 + 3*b^4*c^2*d*e^3 - 5*b^5*c*e^4)*x^3 - (36*b^2*c^4*d^4 - 73*b^3*c^3*d^3*e + 33*b^4*c^2*d^2*e^2 - 5*b^5*c*d*e^3 - 3*b^6*e^4)*x^2 - (8*b^3*c^3*d^4 - 17*b^4*c^2*d^3*e)*x)*sqrt(e*x + d))/(b^5*c^4*x^4 + 2*b^6*c^3*x^3 + b^7*c^2*x^2)]","B",0
379,1,2027,0,0.866233," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{{\left({\left(48 \, c^{5} d^{3} - 60 \, b c^{4} d^{2} e + 11 \, b^{2} c^{3} d e^{2} + b^{3} c^{2} e^{3}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 60 \, b^{2} c^{3} d^{2} e + 11 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 60 \, b^{3} c^{2} d^{2} e + 11 \, b^{4} c d e^{2} + b^{5} e^{3}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + {\left({\left(48 \, c^{5} d^{3} - 84 \, b c^{4} d^{2} e + 35 \, b^{2} c^{3} d e^{2}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 84 \, b^{2} c^{3} d^{2} e + 35 \, b^{3} c^{2} d e^{2}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 84 \, b^{3} c^{2} d^{2} e + 35 \, b^{4} c d e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} c d^{3} - {\left(24 \, b c^{4} d^{3} - 36 \, b^{2} c^{3} d^{2} e + 10 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} - {\left(36 \, b^{2} c^{3} d^{3} - 55 \, b^{3} c^{2} d^{2} e + 16 \, b^{4} c d e^{2} - b^{5} e^{3}\right)} x^{2} - {\left(8 \, b^{3} c^{2} d^{3} - 13 \, b^{4} c d^{2} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{3} x^{4} + 2 \, b^{6} c^{2} x^{3} + b^{7} c x^{2}\right)}}, \frac{2 \, {\left({\left(48 \, c^{5} d^{3} - 60 \, b c^{4} d^{2} e + 11 \, b^{2} c^{3} d e^{2} + b^{3} c^{2} e^{3}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 60 \, b^{2} c^{3} d^{2} e + 11 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 60 \, b^{3} c^{2} d^{2} e + 11 \, b^{4} c d e^{2} + b^{5} e^{3}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(48 \, c^{5} d^{3} - 84 \, b c^{4} d^{2} e + 35 \, b^{2} c^{3} d e^{2}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 84 \, b^{2} c^{3} d^{2} e + 35 \, b^{3} c^{2} d e^{2}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 84 \, b^{3} c^{2} d^{2} e + 35 \, b^{4} c d e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} c d^{3} - {\left(24 \, b c^{4} d^{3} - 36 \, b^{2} c^{3} d^{2} e + 10 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} - {\left(36 \, b^{2} c^{3} d^{3} - 55 \, b^{3} c^{2} d^{2} e + 16 \, b^{4} c d e^{2} - b^{5} e^{3}\right)} x^{2} - {\left(8 \, b^{3} c^{2} d^{3} - 13 \, b^{4} c d^{2} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{3} x^{4} + 2 \, b^{6} c^{2} x^{3} + b^{7} c x^{2}\right)}}, \frac{2 \, {\left({\left(48 \, c^{5} d^{3} - 84 \, b c^{4} d^{2} e + 35 \, b^{2} c^{3} d e^{2}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 84 \, b^{2} c^{3} d^{2} e + 35 \, b^{3} c^{2} d e^{2}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 84 \, b^{3} c^{2} d^{2} e + 35 \, b^{4} c d e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + {\left({\left(48 \, c^{5} d^{3} - 60 \, b c^{4} d^{2} e + 11 \, b^{2} c^{3} d e^{2} + b^{3} c^{2} e^{3}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 60 \, b^{2} c^{3} d^{2} e + 11 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 60 \, b^{3} c^{2} d^{2} e + 11 \, b^{4} c d e^{2} + b^{5} e^{3}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - 2 \, {\left(2 \, b^{4} c d^{3} - {\left(24 \, b c^{4} d^{3} - 36 \, b^{2} c^{3} d^{2} e + 10 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} - {\left(36 \, b^{2} c^{3} d^{3} - 55 \, b^{3} c^{2} d^{2} e + 16 \, b^{4} c d e^{2} - b^{5} e^{3}\right)} x^{2} - {\left(8 \, b^{3} c^{2} d^{3} - 13 \, b^{4} c d^{2} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{3} x^{4} + 2 \, b^{6} c^{2} x^{3} + b^{7} c x^{2}\right)}}, \frac{{\left({\left(48 \, c^{5} d^{3} - 60 \, b c^{4} d^{2} e + 11 \, b^{2} c^{3} d e^{2} + b^{3} c^{2} e^{3}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 60 \, b^{2} c^{3} d^{2} e + 11 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 60 \, b^{3} c^{2} d^{2} e + 11 \, b^{4} c d e^{2} + b^{5} e^{3}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + {\left({\left(48 \, c^{5} d^{3} - 84 \, b c^{4} d^{2} e + 35 \, b^{2} c^{3} d e^{2}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 84 \, b^{2} c^{3} d^{2} e + 35 \, b^{3} c^{2} d e^{2}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 84 \, b^{3} c^{2} d^{2} e + 35 \, b^{4} c d e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, b^{4} c d^{3} - {\left(24 \, b c^{4} d^{3} - 36 \, b^{2} c^{3} d^{2} e + 10 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} - {\left(36 \, b^{2} c^{3} d^{3} - 55 \, b^{3} c^{2} d^{2} e + 16 \, b^{4} c d e^{2} - b^{5} e^{3}\right)} x^{2} - {\left(8 \, b^{3} c^{2} d^{3} - 13 \, b^{4} c d^{2} e\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(b^{5} c^{3} x^{4} + 2 \, b^{6} c^{2} x^{3} + b^{7} c x^{2}\right)}}\right]"," ",0,"[1/8*(((48*c^5*d^3 - 60*b*c^4*d^2*e + 11*b^2*c^3*d*e^2 + b^3*c^2*e^3)*x^4 + 2*(48*b*c^4*d^3 - 60*b^2*c^3*d^2*e + 11*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 + (48*b^2*c^3*d^3 - 60*b^3*c^2*d^2*e + 11*b^4*c*d*e^2 + b^5*e^3)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + ((48*c^5*d^3 - 84*b*c^4*d^2*e + 35*b^2*c^3*d*e^2)*x^4 + 2*(48*b*c^4*d^3 - 84*b^2*c^3*d^2*e + 35*b^3*c^2*d*e^2)*x^3 + (48*b^2*c^3*d^3 - 84*b^3*c^2*d^2*e + 35*b^4*c*d*e^2)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*c*d^3 - (24*b*c^4*d^3 - 36*b^2*c^3*d^2*e + 10*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 - (36*b^2*c^3*d^3 - 55*b^3*c^2*d^2*e + 16*b^4*c*d*e^2 - b^5*e^3)*x^2 - (8*b^3*c^2*d^3 - 13*b^4*c*d^2*e)*x)*sqrt(e*x + d))/(b^5*c^3*x^4 + 2*b^6*c^2*x^3 + b^7*c*x^2), 1/8*(2*((48*c^5*d^3 - 60*b*c^4*d^2*e + 11*b^2*c^3*d*e^2 + b^3*c^2*e^3)*x^4 + 2*(48*b*c^4*d^3 - 60*b^2*c^3*d^2*e + 11*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 + (48*b^2*c^3*d^3 - 60*b^3*c^2*d^2*e + 11*b^4*c*d*e^2 + b^5*e^3)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((48*c^5*d^3 - 84*b*c^4*d^2*e + 35*b^2*c^3*d*e^2)*x^4 + 2*(48*b*c^4*d^3 - 84*b^2*c^3*d^2*e + 35*b^3*c^2*d*e^2)*x^3 + (48*b^2*c^3*d^3 - 84*b^3*c^2*d^2*e + 35*b^4*c*d*e^2)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*c*d^3 - (24*b*c^4*d^3 - 36*b^2*c^3*d^2*e + 10*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 - (36*b^2*c^3*d^3 - 55*b^3*c^2*d^2*e + 16*b^4*c*d*e^2 - b^5*e^3)*x^2 - (8*b^3*c^2*d^3 - 13*b^4*c*d^2*e)*x)*sqrt(e*x + d))/(b^5*c^3*x^4 + 2*b^6*c^2*x^3 + b^7*c*x^2), 1/8*(2*((48*c^5*d^3 - 84*b*c^4*d^2*e + 35*b^2*c^3*d*e^2)*x^4 + 2*(48*b*c^4*d^3 - 84*b^2*c^3*d^2*e + 35*b^3*c^2*d*e^2)*x^3 + (48*b^2*c^3*d^3 - 84*b^3*c^2*d^2*e + 35*b^4*c*d*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + ((48*c^5*d^3 - 60*b*c^4*d^2*e + 11*b^2*c^3*d*e^2 + b^3*c^2*e^3)*x^4 + 2*(48*b*c^4*d^3 - 60*b^2*c^3*d^2*e + 11*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 + (48*b^2*c^3*d^3 - 60*b^3*c^2*d^2*e + 11*b^4*c*d*e^2 + b^5*e^3)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - 2*(2*b^4*c*d^3 - (24*b*c^4*d^3 - 36*b^2*c^3*d^2*e + 10*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 - (36*b^2*c^3*d^3 - 55*b^3*c^2*d^2*e + 16*b^4*c*d*e^2 - b^5*e^3)*x^2 - (8*b^3*c^2*d^3 - 13*b^4*c*d^2*e)*x)*sqrt(e*x + d))/(b^5*c^3*x^4 + 2*b^6*c^2*x^3 + b^7*c*x^2), 1/4*(((48*c^5*d^3 - 60*b*c^4*d^2*e + 11*b^2*c^3*d*e^2 + b^3*c^2*e^3)*x^4 + 2*(48*b*c^4*d^3 - 60*b^2*c^3*d^2*e + 11*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 + (48*b^2*c^3*d^3 - 60*b^3*c^2*d^2*e + 11*b^4*c*d*e^2 + b^5*e^3)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + ((48*c^5*d^3 - 84*b*c^4*d^2*e + 35*b^2*c^3*d*e^2)*x^4 + 2*(48*b*c^4*d^3 - 84*b^2*c^3*d^2*e + 35*b^3*c^2*d*e^2)*x^3 + (48*b^2*c^3*d^3 - 84*b^3*c^2*d^2*e + 35*b^4*c*d*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*b^4*c*d^3 - (24*b*c^4*d^3 - 36*b^2*c^3*d^2*e + 10*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 - (36*b^2*c^3*d^3 - 55*b^3*c^2*d^2*e + 16*b^4*c*d*e^2 - b^5*e^3)*x^2 - (8*b^3*c^2*d^3 - 13*b^4*c*d^2*e)*x)*sqrt(e*x + d))/(b^5*c^3*x^4 + 2*b^6*c^2*x^3 + b^7*c*x^2)]","B",0
380,1,1661,0,0.528736," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(16 \, c^{4} d^{2} - 12 \, b c^{3} d e + b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 12 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 12 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) + 3 \, {\left({\left(16 \, c^{4} d^{2} - 20 \, b c^{3} d e + 5 \, b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 20 \, b^{2} c^{2} d e + 5 \, b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 20 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} d^{2} - 3 \, {\left(8 \, b c^{3} d^{2} - 8 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} - {\left(36 \, b^{2} c^{2} d^{2} - 37 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} x^{2} - {\left(8 \, b^{3} c d^{2} - 9 \, b^{4} d e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{2} x^{4} + 2 \, b^{6} c x^{3} + b^{7} x^{2}\right)}}, \frac{6 \, {\left({\left(16 \, c^{4} d^{2} - 12 \, b c^{3} d e + b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 12 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 12 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 3 \, {\left({\left(16 \, c^{4} d^{2} - 20 \, b c^{3} d e + 5 \, b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 20 \, b^{2} c^{2} d e + 5 \, b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 20 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} d^{2} - 3 \, {\left(8 \, b c^{3} d^{2} - 8 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} - {\left(36 \, b^{2} c^{2} d^{2} - 37 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} x^{2} - {\left(8 \, b^{3} c d^{2} - 9 \, b^{4} d e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{2} x^{4} + 2 \, b^{6} c x^{3} + b^{7} x^{2}\right)}}, \frac{6 \, {\left({\left(16 \, c^{4} d^{2} - 20 \, b c^{3} d e + 5 \, b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 20 \, b^{2} c^{2} d e + 5 \, b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 20 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left({\left(16 \, c^{4} d^{2} - 12 \, b c^{3} d e + b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 12 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 12 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c d - b e}{c}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, \sqrt{e x + d} c \sqrt{\frac{c d - b e}{c}}}{c x + b}\right) - 2 \, {\left(2 \, b^{4} d^{2} - 3 \, {\left(8 \, b c^{3} d^{2} - 8 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} - {\left(36 \, b^{2} c^{2} d^{2} - 37 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} x^{2} - {\left(8 \, b^{3} c d^{2} - 9 \, b^{4} d e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{2} x^{4} + 2 \, b^{6} c x^{3} + b^{7} x^{2}\right)}}, \frac{3 \, {\left({\left(16 \, c^{4} d^{2} - 12 \, b c^{3} d e + b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 12 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 12 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c d - b e}{c}} \arctan\left(-\frac{\sqrt{e x + d} c \sqrt{-\frac{c d - b e}{c}}}{c d - b e}\right) + 3 \, {\left({\left(16 \, c^{4} d^{2} - 20 \, b c^{3} d e + 5 \, b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 20 \, b^{2} c^{2} d e + 5 \, b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 20 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, b^{4} d^{2} - 3 \, {\left(8 \, b c^{3} d^{2} - 8 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} - {\left(36 \, b^{2} c^{2} d^{2} - 37 \, b^{3} c d e + 5 \, b^{4} e^{2}\right)} x^{2} - {\left(8 \, b^{3} c d^{2} - 9 \, b^{4} d e\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(b^{5} c^{2} x^{4} + 2 \, b^{6} c x^{3} + b^{7} x^{2}\right)}}\right]"," ",0,"[1/8*(3*((16*c^4*d^2 - 12*b*c^3*d*e + b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 12*b^2*c^2*d*e + b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 12*b^3*c*d*e + b^4*e^2)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) + 3*((16*c^4*d^2 - 20*b*c^3*d*e + 5*b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 20*b^2*c^2*d*e + 5*b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 20*b^3*c*d*e + 5*b^4*e^2)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*d^2 - 3*(8*b*c^3*d^2 - 8*b^2*c^2*d*e + b^3*c*e^2)*x^3 - (36*b^2*c^2*d^2 - 37*b^3*c*d*e + 5*b^4*e^2)*x^2 - (8*b^3*c*d^2 - 9*b^4*d*e)*x)*sqrt(e*x + d))/(b^5*c^2*x^4 + 2*b^6*c*x^3 + b^7*x^2), 1/8*(6*((16*c^4*d^2 - 12*b*c^3*d*e + b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 12*b^2*c^2*d*e + b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 12*b^3*c*d*e + b^4*e^2)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 3*((16*c^4*d^2 - 20*b*c^3*d*e + 5*b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 20*b^2*c^2*d*e + 5*b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 20*b^3*c*d*e + 5*b^4*e^2)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*d^2 - 3*(8*b*c^3*d^2 - 8*b^2*c^2*d*e + b^3*c*e^2)*x^3 - (36*b^2*c^2*d^2 - 37*b^3*c*d*e + 5*b^4*e^2)*x^2 - (8*b^3*c*d^2 - 9*b^4*d*e)*x)*sqrt(e*x + d))/(b^5*c^2*x^4 + 2*b^6*c*x^3 + b^7*x^2), 1/8*(6*((16*c^4*d^2 - 20*b*c^3*d*e + 5*b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 20*b^2*c^2*d*e + 5*b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 20*b^3*c*d*e + 5*b^4*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*((16*c^4*d^2 - 12*b*c^3*d*e + b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 12*b^2*c^2*d*e + b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 12*b^3*c*d*e + b^4*e^2)*x^2)*sqrt((c*d - b*e)/c)*log((c*e*x + 2*c*d - b*e + 2*sqrt(e*x + d)*c*sqrt((c*d - b*e)/c))/(c*x + b)) - 2*(2*b^4*d^2 - 3*(8*b*c^3*d^2 - 8*b^2*c^2*d*e + b^3*c*e^2)*x^3 - (36*b^2*c^2*d^2 - 37*b^3*c*d*e + 5*b^4*e^2)*x^2 - (8*b^3*c*d^2 - 9*b^4*d*e)*x)*sqrt(e*x + d))/(b^5*c^2*x^4 + 2*b^6*c*x^3 + b^7*x^2), 1/4*(3*((16*c^4*d^2 - 12*b*c^3*d*e + b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 12*b^2*c^2*d*e + b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 12*b^3*c*d*e + b^4*e^2)*x^2)*sqrt(-(c*d - b*e)/c)*arctan(-sqrt(e*x + d)*c*sqrt(-(c*d - b*e)/c)/(c*d - b*e)) + 3*((16*c^4*d^2 - 20*b*c^3*d*e + 5*b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 20*b^2*c^2*d*e + 5*b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 20*b^3*c*d*e + 5*b^4*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*b^4*d^2 - 3*(8*b*c^3*d^2 - 8*b^2*c^2*d*e + b^3*c*e^2)*x^3 - (36*b^2*c^2*d^2 - 37*b^3*c*d*e + 5*b^4*e^2)*x^2 - (8*b^3*c*d^2 - 9*b^4*d*e)*x)*sqrt(e*x + d))/(b^5*c^2*x^4 + 2*b^6*c*x^3 + b^7*x^2)]","A",0
381,1,1673,0,0.535800," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(16 \, c^{4} d^{3} - 20 \, b c^{3} d^{2} e + 5 \, b^{2} c^{2} d e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{3} - 20 \, b^{2} c^{2} d^{2} e + 5 \, b^{3} c d e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{3} - 20 \, b^{3} c d^{2} e + 5 \, b^{4} d e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 3 \, {\left({\left(16 \, c^{4} d^{2} - 12 \, b c^{3} d e + b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 12 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 12 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} d^{2} - 12 \, {\left(2 \, b c^{3} d^{2} - b^{2} c^{2} d e\right)} x^{3} - {\left(36 \, b^{2} c^{2} d^{2} - 19 \, b^{3} c d e\right)} x^{2} - {\left(8 \, b^{3} c d^{2} - 5 \, b^{4} d e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{2} d x^{4} + 2 \, b^{6} c d x^{3} + b^{7} d x^{2}\right)}}, \frac{6 \, {\left({\left(16 \, c^{4} d^{3} - 20 \, b c^{3} d^{2} e + 5 \, b^{2} c^{2} d e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{3} - 20 \, b^{2} c^{2} d^{2} e + 5 \, b^{3} c d e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{3} - 20 \, b^{3} c d^{2} e + 5 \, b^{4} d e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(16 \, c^{4} d^{2} - 12 \, b c^{3} d e + b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 12 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 12 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} d^{2} - 12 \, {\left(2 \, b c^{3} d^{2} - b^{2} c^{2} d e\right)} x^{3} - {\left(36 \, b^{2} c^{2} d^{2} - 19 \, b^{3} c d e\right)} x^{2} - {\left(8 \, b^{3} c d^{2} - 5 \, b^{4} d e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{2} d x^{4} + 2 \, b^{6} c d x^{3} + b^{7} d x^{2}\right)}}, \frac{6 \, {\left({\left(16 \, c^{4} d^{2} - 12 \, b c^{3} d e + b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 12 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 12 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left({\left(16 \, c^{4} d^{3} - 20 \, b c^{3} d^{2} e + 5 \, b^{2} c^{2} d e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{3} - 20 \, b^{2} c^{2} d^{2} e + 5 \, b^{3} c d e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{3} - 20 \, b^{3} c d^{2} e + 5 \, b^{4} d e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(2 \, b^{4} d^{2} - 12 \, {\left(2 \, b c^{3} d^{2} - b^{2} c^{2} d e\right)} x^{3} - {\left(36 \, b^{2} c^{2} d^{2} - 19 \, b^{3} c d e\right)} x^{2} - {\left(8 \, b^{3} c d^{2} - 5 \, b^{4} d e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} c^{2} d x^{4} + 2 \, b^{6} c d x^{3} + b^{7} d x^{2}\right)}}, \frac{3 \, {\left({\left(16 \, c^{4} d^{3} - 20 \, b c^{3} d^{2} e + 5 \, b^{2} c^{2} d e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{3} - 20 \, b^{2} c^{2} d^{2} e + 5 \, b^{3} c d e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{3} - 20 \, b^{3} c d^{2} e + 5 \, b^{4} d e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(16 \, c^{4} d^{2} - 12 \, b c^{3} d e + b^{2} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{3} d^{2} - 12 \, b^{2} c^{2} d e + b^{3} c e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{2} d^{2} - 12 \, b^{3} c d e + b^{4} e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, b^{4} d^{2} - 12 \, {\left(2 \, b c^{3} d^{2} - b^{2} c^{2} d e\right)} x^{3} - {\left(36 \, b^{2} c^{2} d^{2} - 19 \, b^{3} c d e\right)} x^{2} - {\left(8 \, b^{3} c d^{2} - 5 \, b^{4} d e\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(b^{5} c^{2} d x^{4} + 2 \, b^{6} c d x^{3} + b^{7} d x^{2}\right)}}\right]"," ",0,"[1/8*(3*((16*c^4*d^3 - 20*b*c^3*d^2*e + 5*b^2*c^2*d*e^2)*x^4 + 2*(16*b*c^3*d^3 - 20*b^2*c^2*d^2*e + 5*b^3*c*d*e^2)*x^3 + (16*b^2*c^2*d^3 - 20*b^3*c*d^2*e + 5*b^4*d*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 3*((16*c^4*d^2 - 12*b*c^3*d*e + b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 12*b^2*c^2*d*e + b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 12*b^3*c*d*e + b^4*e^2)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*d^2 - 12*(2*b*c^3*d^2 - b^2*c^2*d*e)*x^3 - (36*b^2*c^2*d^2 - 19*b^3*c*d*e)*x^2 - (8*b^3*c*d^2 - 5*b^4*d*e)*x)*sqrt(e*x + d))/(b^5*c^2*d*x^4 + 2*b^6*c*d*x^3 + b^7*d*x^2), 1/8*(6*((16*c^4*d^3 - 20*b*c^3*d^2*e + 5*b^2*c^2*d*e^2)*x^4 + 2*(16*b*c^3*d^3 - 20*b^2*c^2*d^2*e + 5*b^3*c*d*e^2)*x^3 + (16*b^2*c^2*d^3 - 20*b^3*c*d^2*e + 5*b^4*d*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((16*c^4*d^2 - 12*b*c^3*d*e + b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 12*b^2*c^2*d*e + b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 12*b^3*c*d*e + b^4*e^2)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*d^2 - 12*(2*b*c^3*d^2 - b^2*c^2*d*e)*x^3 - (36*b^2*c^2*d^2 - 19*b^3*c*d*e)*x^2 - (8*b^3*c*d^2 - 5*b^4*d*e)*x)*sqrt(e*x + d))/(b^5*c^2*d*x^4 + 2*b^6*c*d*x^3 + b^7*d*x^2), 1/8*(6*((16*c^4*d^2 - 12*b*c^3*d*e + b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 12*b^2*c^2*d*e + b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 12*b^3*c*d*e + b^4*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*((16*c^4*d^3 - 20*b*c^3*d^2*e + 5*b^2*c^2*d*e^2)*x^4 + 2*(16*b*c^3*d^3 - 20*b^2*c^2*d^2*e + 5*b^3*c*d*e^2)*x^3 + (16*b^2*c^2*d^3 - 20*b^3*c*d^2*e + 5*b^4*d*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(2*b^4*d^2 - 12*(2*b*c^3*d^2 - b^2*c^2*d*e)*x^3 - (36*b^2*c^2*d^2 - 19*b^3*c*d*e)*x^2 - (8*b^3*c*d^2 - 5*b^4*d*e)*x)*sqrt(e*x + d))/(b^5*c^2*d*x^4 + 2*b^6*c*d*x^3 + b^7*d*x^2), 1/4*(3*((16*c^4*d^3 - 20*b*c^3*d^2*e + 5*b^2*c^2*d*e^2)*x^4 + 2*(16*b*c^3*d^3 - 20*b^2*c^2*d^2*e + 5*b^3*c*d*e^2)*x^3 + (16*b^2*c^2*d^3 - 20*b^3*c*d^2*e + 5*b^4*d*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((16*c^4*d^2 - 12*b*c^3*d*e + b^2*c^2*e^2)*x^4 + 2*(16*b*c^3*d^2 - 12*b^2*c^2*d*e + b^3*c*e^2)*x^3 + (16*b^2*c^2*d^2 - 12*b^3*c*d*e + b^4*e^2)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*b^4*d^2 - 12*(2*b*c^3*d^2 - b^2*c^2*d*e)*x^3 - (36*b^2*c^2*d^2 - 19*b^3*c*d*e)*x^2 - (8*b^3*c*d^2 - 5*b^4*d*e)*x)*sqrt(e*x + d))/(b^5*c^2*d*x^4 + 2*b^6*c*d*x^3 + b^7*d*x^2)]","A",0
382,1,2265,0,0.754051," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(48 \, c^{5} d^{4} - 84 \, b c^{4} d^{3} e + 35 \, b^{2} c^{3} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{4} - 84 \, b^{2} c^{3} d^{3} e + 35 \, b^{3} c^{2} d^{2} e^{2}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{4} - 84 \, b^{3} c^{2} d^{3} e + 35 \, b^{4} c d^{2} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + {\left({\left(48 \, c^{5} d^{3} - 60 \, b c^{4} d^{2} e + 11 \, b^{2} c^{3} d e^{2} + b^{3} c^{2} e^{3}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 60 \, b^{2} c^{3} d^{2} e + 11 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 60 \, b^{3} c^{2} d^{2} e + 11 \, b^{4} c d e^{2} + b^{5} e^{3}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, b^{4} c d^{3} - 2 \, b^{5} d^{2} e - {\left(24 \, b c^{4} d^{3} - 24 \, b^{2} c^{3} d^{2} e + b^{3} c^{2} d e^{2}\right)} x^{3} - {\left(36 \, b^{2} c^{3} d^{3} - 37 \, b^{3} c^{2} d^{2} e + 2 \, b^{4} c d e^{2}\right)} x^{2} - {\left(8 \, b^{3} c^{2} d^{3} - 9 \, b^{4} c d^{2} e + b^{5} d e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{3} d^{3} - b^{6} c^{2} d^{2} e\right)} x^{4} + 2 \, {\left(b^{6} c^{2} d^{3} - b^{7} c d^{2} e\right)} x^{3} + {\left(b^{7} c d^{3} - b^{8} d^{2} e\right)} x^{2}\right)}}, \frac{2 \, {\left({\left(48 \, c^{5} d^{4} - 84 \, b c^{4} d^{3} e + 35 \, b^{2} c^{3} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{4} - 84 \, b^{2} c^{3} d^{3} e + 35 \, b^{3} c^{2} d^{2} e^{2}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{4} - 84 \, b^{3} c^{2} d^{3} e + 35 \, b^{4} c d^{2} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) - {\left({\left(48 \, c^{5} d^{3} - 60 \, b c^{4} d^{2} e + 11 \, b^{2} c^{3} d e^{2} + b^{3} c^{2} e^{3}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 60 \, b^{2} c^{3} d^{2} e + 11 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 60 \, b^{3} c^{2} d^{2} e + 11 \, b^{4} c d e^{2} + b^{5} e^{3}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x + 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} c d^{3} - 2 \, b^{5} d^{2} e - {\left(24 \, b c^{4} d^{3} - 24 \, b^{2} c^{3} d^{2} e + b^{3} c^{2} d e^{2}\right)} x^{3} - {\left(36 \, b^{2} c^{3} d^{3} - 37 \, b^{3} c^{2} d^{2} e + 2 \, b^{4} c d e^{2}\right)} x^{2} - {\left(8 \, b^{3} c^{2} d^{3} - 9 \, b^{4} c d^{2} e + b^{5} d e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{3} d^{3} - b^{6} c^{2} d^{2} e\right)} x^{4} + 2 \, {\left(b^{6} c^{2} d^{3} - b^{7} c d^{2} e\right)} x^{3} + {\left(b^{7} c d^{3} - b^{8} d^{2} e\right)} x^{2}\right)}}, \frac{2 \, {\left({\left(48 \, c^{5} d^{3} - 60 \, b c^{4} d^{2} e + 11 \, b^{2} c^{3} d e^{2} + b^{3} c^{2} e^{3}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 60 \, b^{2} c^{3} d^{2} e + 11 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 60 \, b^{3} c^{2} d^{2} e + 11 \, b^{4} c d e^{2} + b^{5} e^{3}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left({\left(48 \, c^{5} d^{4} - 84 \, b c^{4} d^{3} e + 35 \, b^{2} c^{3} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{4} - 84 \, b^{2} c^{3} d^{3} e + 35 \, b^{3} c^{2} d^{2} e^{2}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{4} - 84 \, b^{3} c^{2} d^{3} e + 35 \, b^{4} c d^{2} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(2 \, b^{4} c d^{3} - 2 \, b^{5} d^{2} e - {\left(24 \, b c^{4} d^{3} - 24 \, b^{2} c^{3} d^{2} e + b^{3} c^{2} d e^{2}\right)} x^{3} - {\left(36 \, b^{2} c^{3} d^{3} - 37 \, b^{3} c^{2} d^{2} e + 2 \, b^{4} c d e^{2}\right)} x^{2} - {\left(8 \, b^{3} c^{2} d^{3} - 9 \, b^{4} c d^{2} e + b^{5} d e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{3} d^{3} - b^{6} c^{2} d^{2} e\right)} x^{4} + 2 \, {\left(b^{6} c^{2} d^{3} - b^{7} c d^{2} e\right)} x^{3} + {\left(b^{7} c d^{3} - b^{8} d^{2} e\right)} x^{2}\right)}}, \frac{{\left({\left(48 \, c^{5} d^{4} - 84 \, b c^{4} d^{3} e + 35 \, b^{2} c^{3} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{4} - 84 \, b^{2} c^{3} d^{3} e + 35 \, b^{3} c^{2} d^{2} e^{2}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{4} - 84 \, b^{3} c^{2} d^{3} e + 35 \, b^{4} c d^{2} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + {\left({\left(48 \, c^{5} d^{3} - 60 \, b c^{4} d^{2} e + 11 \, b^{2} c^{3} d e^{2} + b^{3} c^{2} e^{3}\right)} x^{4} + 2 \, {\left(48 \, b c^{4} d^{3} - 60 \, b^{2} c^{3} d^{2} e + 11 \, b^{3} c^{2} d e^{2} + b^{4} c e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{3} d^{3} - 60 \, b^{3} c^{2} d^{2} e + 11 \, b^{4} c d e^{2} + b^{5} e^{3}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, b^{4} c d^{3} - 2 \, b^{5} d^{2} e - {\left(24 \, b c^{4} d^{3} - 24 \, b^{2} c^{3} d^{2} e + b^{3} c^{2} d e^{2}\right)} x^{3} - {\left(36 \, b^{2} c^{3} d^{3} - 37 \, b^{3} c^{2} d^{2} e + 2 \, b^{4} c d e^{2}\right)} x^{2} - {\left(8 \, b^{3} c^{2} d^{3} - 9 \, b^{4} c d^{2} e + b^{5} d e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left({\left(b^{5} c^{3} d^{3} - b^{6} c^{2} d^{2} e\right)} x^{4} + 2 \, {\left(b^{6} c^{2} d^{3} - b^{7} c d^{2} e\right)} x^{3} + {\left(b^{7} c d^{3} - b^{8} d^{2} e\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*(((48*c^5*d^4 - 84*b*c^4*d^3*e + 35*b^2*c^3*d^2*e^2)*x^4 + 2*(48*b*c^4*d^4 - 84*b^2*c^3*d^3*e + 35*b^3*c^2*d^2*e^2)*x^3 + (48*b^2*c^3*d^4 - 84*b^3*c^2*d^3*e + 35*b^4*c*d^2*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + ((48*c^5*d^3 - 60*b*c^4*d^2*e + 11*b^2*c^3*d*e^2 + b^3*c^2*e^3)*x^4 + 2*(48*b*c^4*d^3 - 60*b^2*c^3*d^2*e + 11*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 + (48*b^2*c^3*d^3 - 60*b^3*c^2*d^2*e + 11*b^4*c*d*e^2 + b^5*e^3)*x^2)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*b^4*c*d^3 - 2*b^5*d^2*e - (24*b*c^4*d^3 - 24*b^2*c^3*d^2*e + b^3*c^2*d*e^2)*x^3 - (36*b^2*c^3*d^3 - 37*b^3*c^2*d^2*e + 2*b^4*c*d*e^2)*x^2 - (8*b^3*c^2*d^3 - 9*b^4*c*d^2*e + b^5*d*e^2)*x)*sqrt(e*x + d))/((b^5*c^3*d^3 - b^6*c^2*d^2*e)*x^4 + 2*(b^6*c^2*d^3 - b^7*c*d^2*e)*x^3 + (b^7*c*d^3 - b^8*d^2*e)*x^2), 1/8*(2*((48*c^5*d^4 - 84*b*c^4*d^3*e + 35*b^2*c^3*d^2*e^2)*x^4 + 2*(48*b*c^4*d^4 - 84*b^2*c^3*d^3*e + 35*b^3*c^2*d^2*e^2)*x^3 + (48*b^2*c^3*d^4 - 84*b^3*c^2*d^3*e + 35*b^4*c*d^2*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) - ((48*c^5*d^3 - 60*b*c^4*d^2*e + 11*b^2*c^3*d*e^2 + b^3*c^2*e^3)*x^4 + 2*(48*b*c^4*d^3 - 60*b^2*c^3*d^2*e + 11*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 + (48*b^2*c^3*d^3 - 60*b^3*c^2*d^2*e + 11*b^4*c*d*e^2 + b^5*e^3)*x^2)*sqrt(d)*log((e*x + 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*c*d^3 - 2*b^5*d^2*e - (24*b*c^4*d^3 - 24*b^2*c^3*d^2*e + b^3*c^2*d*e^2)*x^3 - (36*b^2*c^3*d^3 - 37*b^3*c^2*d^2*e + 2*b^4*c*d*e^2)*x^2 - (8*b^3*c^2*d^3 - 9*b^4*c*d^2*e + b^5*d*e^2)*x)*sqrt(e*x + d))/((b^5*c^3*d^3 - b^6*c^2*d^2*e)*x^4 + 2*(b^6*c^2*d^3 - b^7*c*d^2*e)*x^3 + (b^7*c*d^3 - b^8*d^2*e)*x^2), 1/8*(2*((48*c^5*d^3 - 60*b*c^4*d^2*e + 11*b^2*c^3*d*e^2 + b^3*c^2*e^3)*x^4 + 2*(48*b*c^4*d^3 - 60*b^2*c^3*d^2*e + 11*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 + (48*b^2*c^3*d^3 - 60*b^3*c^2*d^2*e + 11*b^4*c*d*e^2 + b^5*e^3)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - ((48*c^5*d^4 - 84*b*c^4*d^3*e + 35*b^2*c^3*d^2*e^2)*x^4 + 2*(48*b*c^4*d^4 - 84*b^2*c^3*d^3*e + 35*b^3*c^2*d^2*e^2)*x^3 + (48*b^2*c^3*d^4 - 84*b^3*c^2*d^3*e + 35*b^4*c*d^2*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(2*b^4*c*d^3 - 2*b^5*d^2*e - (24*b*c^4*d^3 - 24*b^2*c^3*d^2*e + b^3*c^2*d*e^2)*x^3 - (36*b^2*c^3*d^3 - 37*b^3*c^2*d^2*e + 2*b^4*c*d*e^2)*x^2 - (8*b^3*c^2*d^3 - 9*b^4*c*d^2*e + b^5*d*e^2)*x)*sqrt(e*x + d))/((b^5*c^3*d^3 - b^6*c^2*d^2*e)*x^4 + 2*(b^6*c^2*d^3 - b^7*c*d^2*e)*x^3 + (b^7*c*d^3 - b^8*d^2*e)*x^2), 1/4*(((48*c^5*d^4 - 84*b*c^4*d^3*e + 35*b^2*c^3*d^2*e^2)*x^4 + 2*(48*b*c^4*d^4 - 84*b^2*c^3*d^3*e + 35*b^3*c^2*d^2*e^2)*x^3 + (48*b^2*c^3*d^4 - 84*b^3*c^2*d^3*e + 35*b^4*c*d^2*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + ((48*c^5*d^3 - 60*b*c^4*d^2*e + 11*b^2*c^3*d*e^2 + b^3*c^2*e^3)*x^4 + 2*(48*b*c^4*d^3 - 60*b^2*c^3*d^2*e + 11*b^3*c^2*d*e^2 + b^4*c*e^3)*x^3 + (48*b^2*c^3*d^3 - 60*b^3*c^2*d^2*e + 11*b^4*c*d*e^2 + b^5*e^3)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*b^4*c*d^3 - 2*b^5*d^2*e - (24*b*c^4*d^3 - 24*b^2*c^3*d^2*e + b^3*c^2*d*e^2)*x^3 - (36*b^2*c^3*d^3 - 37*b^3*c^2*d^2*e + 2*b^4*c*d*e^2)*x^2 - (8*b^3*c^2*d^3 - 9*b^4*c*d^2*e + b^5*d*e^2)*x)*sqrt(e*x + d))/((b^5*c^3*d^3 - b^6*c^2*d^2*e)*x^4 + 2*(b^6*c^2*d^3 - b^7*c*d^2*e)*x^3 + (b^7*c*d^3 - b^8*d^2*e)*x^2)]","B",0
383,1,2829,0,1.704225," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(16 \, c^{6} d^{5} - 36 \, b c^{5} d^{4} e + 21 \, b^{2} c^{4} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{5} - 36 \, b^{2} c^{4} d^{4} e + 21 \, b^{3} c^{3} d^{3} e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{5} - 36 \, b^{3} c^{3} d^{4} e + 21 \, b^{4} c^{2} d^{3} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 3 \, {\left({\left(16 \, c^{6} d^{4} - 28 \, b c^{5} d^{3} e + 9 \, b^{2} c^{4} d^{2} e^{2} + 2 \, b^{3} c^{3} d e^{3} + b^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 28 \, b^{2} c^{4} d^{3} e + 9 \, b^{3} c^{3} d^{2} e^{2} + 2 \, b^{4} c^{2} d e^{3} + b^{5} c e^{4}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 28 \, b^{3} c^{3} d^{3} e + 9 \, b^{4} c^{2} d^{2} e^{2} + 2 \, b^{5} c d e^{3} + b^{6} e^{4}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} c^{2} d^{4} - 4 \, b^{5} c d^{3} e + 2 \, b^{6} d^{2} e^{2} - 3 \, {\left(8 \, b c^{5} d^{4} - 12 \, b^{2} c^{4} d^{3} e + 2 \, b^{3} c^{3} d^{2} e^{2} + b^{4} c^{2} d e^{3}\right)} x^{3} - {\left(36 \, b^{2} c^{4} d^{4} - 55 \, b^{3} c^{3} d^{3} e + 10 \, b^{4} c^{2} d^{2} e^{2} + 6 \, b^{5} c d e^{3}\right)} x^{2} - {\left(8 \, b^{3} c^{3} d^{4} - 13 \, b^{4} c^{2} d^{3} e + 2 \, b^{5} c d^{2} e^{2} + 3 \, b^{6} d e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{4} d^{5} - 2 \, b^{6} c^{3} d^{4} e + b^{7} c^{2} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{5} - 2 \, b^{7} c^{2} d^{4} e + b^{8} c d^{3} e^{2}\right)} x^{3} + {\left(b^{7} c^{2} d^{5} - 2 \, b^{8} c d^{4} e + b^{9} d^{3} e^{2}\right)} x^{2}\right)}}, \frac{6 \, {\left({\left(16 \, c^{6} d^{5} - 36 \, b c^{5} d^{4} e + 21 \, b^{2} c^{4} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{5} - 36 \, b^{2} c^{4} d^{4} e + 21 \, b^{3} c^{3} d^{3} e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{5} - 36 \, b^{3} c^{3} d^{4} e + 21 \, b^{4} c^{2} d^{3} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(16 \, c^{6} d^{4} - 28 \, b c^{5} d^{3} e + 9 \, b^{2} c^{4} d^{2} e^{2} + 2 \, b^{3} c^{3} d e^{3} + b^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 28 \, b^{2} c^{4} d^{3} e + 9 \, b^{3} c^{3} d^{2} e^{2} + 2 \, b^{4} c^{2} d e^{3} + b^{5} c e^{4}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 28 \, b^{3} c^{3} d^{3} e + 9 \, b^{4} c^{2} d^{2} e^{2} + 2 \, b^{5} c d e^{3} + b^{6} e^{4}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} c^{2} d^{4} - 4 \, b^{5} c d^{3} e + 2 \, b^{6} d^{2} e^{2} - 3 \, {\left(8 \, b c^{5} d^{4} - 12 \, b^{2} c^{4} d^{3} e + 2 \, b^{3} c^{3} d^{2} e^{2} + b^{4} c^{2} d e^{3}\right)} x^{3} - {\left(36 \, b^{2} c^{4} d^{4} - 55 \, b^{3} c^{3} d^{3} e + 10 \, b^{4} c^{2} d^{2} e^{2} + 6 \, b^{5} c d e^{3}\right)} x^{2} - {\left(8 \, b^{3} c^{3} d^{4} - 13 \, b^{4} c^{2} d^{3} e + 2 \, b^{5} c d^{2} e^{2} + 3 \, b^{6} d e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{4} d^{5} - 2 \, b^{6} c^{3} d^{4} e + b^{7} c^{2} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{5} - 2 \, b^{7} c^{2} d^{4} e + b^{8} c d^{3} e^{2}\right)} x^{3} + {\left(b^{7} c^{2} d^{5} - 2 \, b^{8} c d^{4} e + b^{9} d^{3} e^{2}\right)} x^{2}\right)}}, \frac{6 \, {\left({\left(16 \, c^{6} d^{4} - 28 \, b c^{5} d^{3} e + 9 \, b^{2} c^{4} d^{2} e^{2} + 2 \, b^{3} c^{3} d e^{3} + b^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 28 \, b^{2} c^{4} d^{3} e + 9 \, b^{3} c^{3} d^{2} e^{2} + 2 \, b^{4} c^{2} d e^{3} + b^{5} c e^{4}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 28 \, b^{3} c^{3} d^{3} e + 9 \, b^{4} c^{2} d^{2} e^{2} + 2 \, b^{5} c d e^{3} + b^{6} e^{4}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left({\left(16 \, c^{6} d^{5} - 36 \, b c^{5} d^{4} e + 21 \, b^{2} c^{4} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{5} - 36 \, b^{2} c^{4} d^{4} e + 21 \, b^{3} c^{3} d^{3} e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{5} - 36 \, b^{3} c^{3} d^{4} e + 21 \, b^{4} c^{2} d^{3} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(2 \, b^{4} c^{2} d^{4} - 4 \, b^{5} c d^{3} e + 2 \, b^{6} d^{2} e^{2} - 3 \, {\left(8 \, b c^{5} d^{4} - 12 \, b^{2} c^{4} d^{3} e + 2 \, b^{3} c^{3} d^{2} e^{2} + b^{4} c^{2} d e^{3}\right)} x^{3} - {\left(36 \, b^{2} c^{4} d^{4} - 55 \, b^{3} c^{3} d^{3} e + 10 \, b^{4} c^{2} d^{2} e^{2} + 6 \, b^{5} c d e^{3}\right)} x^{2} - {\left(8 \, b^{3} c^{3} d^{4} - 13 \, b^{4} c^{2} d^{3} e + 2 \, b^{5} c d^{2} e^{2} + 3 \, b^{6} d e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{4} d^{5} - 2 \, b^{6} c^{3} d^{4} e + b^{7} c^{2} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{5} - 2 \, b^{7} c^{2} d^{4} e + b^{8} c d^{3} e^{2}\right)} x^{3} + {\left(b^{7} c^{2} d^{5} - 2 \, b^{8} c d^{4} e + b^{9} d^{3} e^{2}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(16 \, c^{6} d^{5} - 36 \, b c^{5} d^{4} e + 21 \, b^{2} c^{4} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{5} - 36 \, b^{2} c^{4} d^{4} e + 21 \, b^{3} c^{3} d^{3} e^{2}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{5} - 36 \, b^{3} c^{3} d^{4} e + 21 \, b^{4} c^{2} d^{3} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(16 \, c^{6} d^{4} - 28 \, b c^{5} d^{3} e + 9 \, b^{2} c^{4} d^{2} e^{2} + 2 \, b^{3} c^{3} d e^{3} + b^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(16 \, b c^{5} d^{4} - 28 \, b^{2} c^{4} d^{3} e + 9 \, b^{3} c^{3} d^{2} e^{2} + 2 \, b^{4} c^{2} d e^{3} + b^{5} c e^{4}\right)} x^{3} + {\left(16 \, b^{2} c^{4} d^{4} - 28 \, b^{3} c^{3} d^{3} e + 9 \, b^{4} c^{2} d^{2} e^{2} + 2 \, b^{5} c d e^{3} + b^{6} e^{4}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, b^{4} c^{2} d^{4} - 4 \, b^{5} c d^{3} e + 2 \, b^{6} d^{2} e^{2} - 3 \, {\left(8 \, b c^{5} d^{4} - 12 \, b^{2} c^{4} d^{3} e + 2 \, b^{3} c^{3} d^{2} e^{2} + b^{4} c^{2} d e^{3}\right)} x^{3} - {\left(36 \, b^{2} c^{4} d^{4} - 55 \, b^{3} c^{3} d^{3} e + 10 \, b^{4} c^{2} d^{2} e^{2} + 6 \, b^{5} c d e^{3}\right)} x^{2} - {\left(8 \, b^{3} c^{3} d^{4} - 13 \, b^{4} c^{2} d^{3} e + 2 \, b^{5} c d^{2} e^{2} + 3 \, b^{6} d e^{3}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left({\left(b^{5} c^{4} d^{5} - 2 \, b^{6} c^{3} d^{4} e + b^{7} c^{2} d^{3} e^{2}\right)} x^{4} + 2 \, {\left(b^{6} c^{3} d^{5} - 2 \, b^{7} c^{2} d^{4} e + b^{8} c d^{3} e^{2}\right)} x^{3} + {\left(b^{7} c^{2} d^{5} - 2 \, b^{8} c d^{4} e + b^{9} d^{3} e^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/8*(3*((16*c^6*d^5 - 36*b*c^5*d^4*e + 21*b^2*c^4*d^3*e^2)*x^4 + 2*(16*b*c^5*d^5 - 36*b^2*c^4*d^4*e + 21*b^3*c^3*d^3*e^2)*x^3 + (16*b^2*c^4*d^5 - 36*b^3*c^3*d^4*e + 21*b^4*c^2*d^3*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 3*((16*c^6*d^4 - 28*b*c^5*d^3*e + 9*b^2*c^4*d^2*e^2 + 2*b^3*c^3*d*e^3 + b^4*c^2*e^4)*x^4 + 2*(16*b*c^5*d^4 - 28*b^2*c^4*d^3*e + 9*b^3*c^3*d^2*e^2 + 2*b^4*c^2*d*e^3 + b^5*c*e^4)*x^3 + (16*b^2*c^4*d^4 - 28*b^3*c^3*d^3*e + 9*b^4*c^2*d^2*e^2 + 2*b^5*c*d*e^3 + b^6*e^4)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*c^2*d^4 - 4*b^5*c*d^3*e + 2*b^6*d^2*e^2 - 3*(8*b*c^5*d^4 - 12*b^2*c^4*d^3*e + 2*b^3*c^3*d^2*e^2 + b^4*c^2*d*e^3)*x^3 - (36*b^2*c^4*d^4 - 55*b^3*c^3*d^3*e + 10*b^4*c^2*d^2*e^2 + 6*b^5*c*d*e^3)*x^2 - (8*b^3*c^3*d^4 - 13*b^4*c^2*d^3*e + 2*b^5*c*d^2*e^2 + 3*b^6*d*e^3)*x)*sqrt(e*x + d))/((b^5*c^4*d^5 - 2*b^6*c^3*d^4*e + b^7*c^2*d^3*e^2)*x^4 + 2*(b^6*c^3*d^5 - 2*b^7*c^2*d^4*e + b^8*c*d^3*e^2)*x^3 + (b^7*c^2*d^5 - 2*b^8*c*d^4*e + b^9*d^3*e^2)*x^2), 1/8*(6*((16*c^6*d^5 - 36*b*c^5*d^4*e + 21*b^2*c^4*d^3*e^2)*x^4 + 2*(16*b*c^5*d^5 - 36*b^2*c^4*d^4*e + 21*b^3*c^3*d^3*e^2)*x^3 + (16*b^2*c^4*d^5 - 36*b^3*c^3*d^4*e + 21*b^4*c^2*d^3*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((16*c^6*d^4 - 28*b*c^5*d^3*e + 9*b^2*c^4*d^2*e^2 + 2*b^3*c^3*d*e^3 + b^4*c^2*e^4)*x^4 + 2*(16*b*c^5*d^4 - 28*b^2*c^4*d^3*e + 9*b^3*c^3*d^2*e^2 + 2*b^4*c^2*d*e^3 + b^5*c*e^4)*x^3 + (16*b^2*c^4*d^4 - 28*b^3*c^3*d^3*e + 9*b^4*c^2*d^2*e^2 + 2*b^5*c*d*e^3 + b^6*e^4)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*c^2*d^4 - 4*b^5*c*d^3*e + 2*b^6*d^2*e^2 - 3*(8*b*c^5*d^4 - 12*b^2*c^4*d^3*e + 2*b^3*c^3*d^2*e^2 + b^4*c^2*d*e^3)*x^3 - (36*b^2*c^4*d^4 - 55*b^3*c^3*d^3*e + 10*b^4*c^2*d^2*e^2 + 6*b^5*c*d*e^3)*x^2 - (8*b^3*c^3*d^4 - 13*b^4*c^2*d^3*e + 2*b^5*c*d^2*e^2 + 3*b^6*d*e^3)*x)*sqrt(e*x + d))/((b^5*c^4*d^5 - 2*b^6*c^3*d^4*e + b^7*c^2*d^3*e^2)*x^4 + 2*(b^6*c^3*d^5 - 2*b^7*c^2*d^4*e + b^8*c*d^3*e^2)*x^3 + (b^7*c^2*d^5 - 2*b^8*c*d^4*e + b^9*d^3*e^2)*x^2), 1/8*(6*((16*c^6*d^4 - 28*b*c^5*d^3*e + 9*b^2*c^4*d^2*e^2 + 2*b^3*c^3*d*e^3 + b^4*c^2*e^4)*x^4 + 2*(16*b*c^5*d^4 - 28*b^2*c^4*d^3*e + 9*b^3*c^3*d^2*e^2 + 2*b^4*c^2*d*e^3 + b^5*c*e^4)*x^3 + (16*b^2*c^4*d^4 - 28*b^3*c^3*d^3*e + 9*b^4*c^2*d^2*e^2 + 2*b^5*c*d*e^3 + b^6*e^4)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*((16*c^6*d^5 - 36*b*c^5*d^4*e + 21*b^2*c^4*d^3*e^2)*x^4 + 2*(16*b*c^5*d^5 - 36*b^2*c^4*d^4*e + 21*b^3*c^3*d^3*e^2)*x^3 + (16*b^2*c^4*d^5 - 36*b^3*c^3*d^4*e + 21*b^4*c^2*d^3*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(2*b^4*c^2*d^4 - 4*b^5*c*d^3*e + 2*b^6*d^2*e^2 - 3*(8*b*c^5*d^4 - 12*b^2*c^4*d^3*e + 2*b^3*c^3*d^2*e^2 + b^4*c^2*d*e^3)*x^3 - (36*b^2*c^4*d^4 - 55*b^3*c^3*d^3*e + 10*b^4*c^2*d^2*e^2 + 6*b^5*c*d*e^3)*x^2 - (8*b^3*c^3*d^4 - 13*b^4*c^2*d^3*e + 2*b^5*c*d^2*e^2 + 3*b^6*d*e^3)*x)*sqrt(e*x + d))/((b^5*c^4*d^5 - 2*b^6*c^3*d^4*e + b^7*c^2*d^3*e^2)*x^4 + 2*(b^6*c^3*d^5 - 2*b^7*c^2*d^4*e + b^8*c*d^3*e^2)*x^3 + (b^7*c^2*d^5 - 2*b^8*c*d^4*e + b^9*d^3*e^2)*x^2), 1/4*(3*((16*c^6*d^5 - 36*b*c^5*d^4*e + 21*b^2*c^4*d^3*e^2)*x^4 + 2*(16*b*c^5*d^5 - 36*b^2*c^4*d^4*e + 21*b^3*c^3*d^3*e^2)*x^3 + (16*b^2*c^4*d^5 - 36*b^3*c^3*d^4*e + 21*b^4*c^2*d^3*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((16*c^6*d^4 - 28*b*c^5*d^3*e + 9*b^2*c^4*d^2*e^2 + 2*b^3*c^3*d*e^3 + b^4*c^2*e^4)*x^4 + 2*(16*b*c^5*d^4 - 28*b^2*c^4*d^3*e + 9*b^3*c^3*d^2*e^2 + 2*b^4*c^2*d*e^3 + b^5*c*e^4)*x^3 + (16*b^2*c^4*d^4 - 28*b^3*c^3*d^3*e + 9*b^4*c^2*d^2*e^2 + 2*b^5*c*d*e^3 + b^6*e^4)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*b^4*c^2*d^4 - 4*b^5*c*d^3*e + 2*b^6*d^2*e^2 - 3*(8*b*c^5*d^4 - 12*b^2*c^4*d^3*e + 2*b^3*c^3*d^2*e^2 + b^4*c^2*d*e^3)*x^3 - (36*b^2*c^4*d^4 - 55*b^3*c^3*d^3*e + 10*b^4*c^2*d^2*e^2 + 6*b^5*c*d*e^3)*x^2 - (8*b^3*c^3*d^4 - 13*b^4*c^2*d^3*e + 2*b^5*c*d^2*e^2 + 3*b^6*d*e^3)*x)*sqrt(e*x + d))/((b^5*c^4*d^5 - 2*b^6*c^3*d^4*e + b^7*c^2*d^3*e^2)*x^4 + 2*(b^6*c^3*d^5 - 2*b^7*c^2*d^4*e + b^8*c*d^3*e^2)*x^3 + (b^7*c^2*d^5 - 2*b^8*c*d^4*e + b^9*d^3*e^2)*x^2)]","B",0
384,1,4789,0,5.049473," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(16 \, c^{7} d^{6} e - 44 \, b c^{6} d^{5} e^{2} + 33 \, b^{2} c^{5} d^{4} e^{3}\right)} x^{5} + {\left(16 \, c^{7} d^{7} - 12 \, b c^{6} d^{6} e - 55 \, b^{2} c^{5} d^{5} e^{2} + 66 \, b^{3} c^{4} d^{4} e^{3}\right)} x^{4} + {\left(32 \, b c^{6} d^{7} - 72 \, b^{2} c^{5} d^{6} e + 22 \, b^{3} c^{4} d^{5} e^{2} + 33 \, b^{4} c^{3} d^{4} e^{3}\right)} x^{3} + {\left(16 \, b^{2} c^{5} d^{7} - 44 \, b^{3} c^{4} d^{6} e + 33 \, b^{4} c^{3} d^{5} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 3 \, {\left({\left(16 \, c^{7} d^{5} e - 36 \, b c^{6} d^{4} e^{2} + 17 \, b^{2} c^{5} d^{3} e^{3} + 5 \, b^{3} c^{4} d^{2} e^{4} + 3 \, b^{4} c^{3} d e^{5} - 5 \, b^{5} c^{2} e^{6}\right)} x^{5} + {\left(16 \, c^{7} d^{6} - 4 \, b c^{6} d^{5} e - 55 \, b^{2} c^{5} d^{4} e^{2} + 39 \, b^{3} c^{4} d^{3} e^{3} + 13 \, b^{4} c^{3} d^{2} e^{4} + b^{5} c^{2} d e^{5} - 10 \, b^{6} c e^{6}\right)} x^{4} + {\left(32 \, b c^{6} d^{6} - 56 \, b^{2} c^{5} d^{5} e - 2 \, b^{3} c^{4} d^{4} e^{2} + 27 \, b^{4} c^{3} d^{3} e^{3} + 11 \, b^{5} c^{2} d^{2} e^{4} - 7 \, b^{6} c d e^{5} - 5 \, b^{7} e^{6}\right)} x^{3} + {\left(16 \, b^{2} c^{5} d^{6} - 36 \, b^{3} c^{4} d^{5} e + 17 \, b^{4} c^{3} d^{4} e^{2} + 5 \, b^{5} c^{2} d^{3} e^{3} + 3 \, b^{6} c d^{2} e^{4} - 5 \, b^{7} d e^{5}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) + 2 \, {\left(2 \, b^{4} c^{3} d^{6} - 6 \, b^{5} c^{2} d^{5} e + 6 \, b^{6} c d^{4} e^{2} - 2 \, b^{7} d^{3} e^{3} - 3 \, {\left(8 \, b c^{6} d^{5} e - 16 \, b^{2} c^{5} d^{4} e^{2} + 5 \, b^{3} c^{4} d^{3} e^{3} + 3 \, b^{4} c^{3} d^{2} e^{4} - 5 \, b^{5} c^{2} d e^{5}\right)} x^{4} - {\left(24 \, b c^{6} d^{6} - 12 \, b^{2} c^{5} d^{5} e - 58 \, b^{3} c^{4} d^{4} e^{2} + 33 \, b^{4} c^{3} d^{3} e^{3} + 13 \, b^{5} c^{2} d^{2} e^{4} - 30 \, b^{6} c d e^{5}\right)} x^{3} - {\left(36 \, b^{2} c^{5} d^{6} - 65 \, b^{3} c^{4} d^{5} e + 7 \, b^{4} c^{3} d^{4} e^{2} + 23 \, b^{5} c^{2} d^{3} e^{3} - b^{6} c d^{2} e^{4} - 15 \, b^{7} d e^{5}\right)} x^{2} - {\left(8 \, b^{3} c^{4} d^{6} - 19 \, b^{4} c^{3} d^{5} e + 9 \, b^{5} c^{2} d^{4} e^{2} + 7 \, b^{6} c d^{3} e^{3} - 5 \, b^{7} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{5} d^{7} e - 3 \, b^{6} c^{4} d^{6} e^{2} + 3 \, b^{7} c^{3} d^{5} e^{3} - b^{8} c^{2} d^{4} e^{4}\right)} x^{5} + {\left(b^{5} c^{5} d^{8} - b^{6} c^{4} d^{7} e - 3 \, b^{7} c^{3} d^{6} e^{2} + 5 \, b^{8} c^{2} d^{5} e^{3} - 2 \, b^{9} c d^{4} e^{4}\right)} x^{4} + {\left(2 \, b^{6} c^{4} d^{8} - 5 \, b^{7} c^{3} d^{7} e + 3 \, b^{8} c^{2} d^{6} e^{2} + b^{9} c d^{5} e^{3} - b^{10} d^{4} e^{4}\right)} x^{3} + {\left(b^{7} c^{3} d^{8} - 3 \, b^{8} c^{2} d^{7} e + 3 \, b^{9} c d^{6} e^{2} - b^{10} d^{5} e^{3}\right)} x^{2}\right)}}, \frac{6 \, {\left({\left(16 \, c^{7} d^{6} e - 44 \, b c^{6} d^{5} e^{2} + 33 \, b^{2} c^{5} d^{4} e^{3}\right)} x^{5} + {\left(16 \, c^{7} d^{7} - 12 \, b c^{6} d^{6} e - 55 \, b^{2} c^{5} d^{5} e^{2} + 66 \, b^{3} c^{4} d^{4} e^{3}\right)} x^{4} + {\left(32 \, b c^{6} d^{7} - 72 \, b^{2} c^{5} d^{6} e + 22 \, b^{3} c^{4} d^{5} e^{2} + 33 \, b^{4} c^{3} d^{4} e^{3}\right)} x^{3} + {\left(16 \, b^{2} c^{5} d^{7} - 44 \, b^{3} c^{4} d^{6} e + 33 \, b^{4} c^{3} d^{5} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(16 \, c^{7} d^{5} e - 36 \, b c^{6} d^{4} e^{2} + 17 \, b^{2} c^{5} d^{3} e^{3} + 5 \, b^{3} c^{4} d^{2} e^{4} + 3 \, b^{4} c^{3} d e^{5} - 5 \, b^{5} c^{2} e^{6}\right)} x^{5} + {\left(16 \, c^{7} d^{6} - 4 \, b c^{6} d^{5} e - 55 \, b^{2} c^{5} d^{4} e^{2} + 39 \, b^{3} c^{4} d^{3} e^{3} + 13 \, b^{4} c^{3} d^{2} e^{4} + b^{5} c^{2} d e^{5} - 10 \, b^{6} c e^{6}\right)} x^{4} + {\left(32 \, b c^{6} d^{6} - 56 \, b^{2} c^{5} d^{5} e - 2 \, b^{3} c^{4} d^{4} e^{2} + 27 \, b^{4} c^{3} d^{3} e^{3} + 11 \, b^{5} c^{2} d^{2} e^{4} - 7 \, b^{6} c d e^{5} - 5 \, b^{7} e^{6}\right)} x^{3} + {\left(16 \, b^{2} c^{5} d^{6} - 36 \, b^{3} c^{4} d^{5} e + 17 \, b^{4} c^{3} d^{4} e^{2} + 5 \, b^{5} c^{2} d^{3} e^{3} + 3 \, b^{6} c d^{2} e^{4} - 5 \, b^{7} d e^{5}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(2 \, b^{4} c^{3} d^{6} - 6 \, b^{5} c^{2} d^{5} e + 6 \, b^{6} c d^{4} e^{2} - 2 \, b^{7} d^{3} e^{3} - 3 \, {\left(8 \, b c^{6} d^{5} e - 16 \, b^{2} c^{5} d^{4} e^{2} + 5 \, b^{3} c^{4} d^{3} e^{3} + 3 \, b^{4} c^{3} d^{2} e^{4} - 5 \, b^{5} c^{2} d e^{5}\right)} x^{4} - {\left(24 \, b c^{6} d^{6} - 12 \, b^{2} c^{5} d^{5} e - 58 \, b^{3} c^{4} d^{4} e^{2} + 33 \, b^{4} c^{3} d^{3} e^{3} + 13 \, b^{5} c^{2} d^{2} e^{4} - 30 \, b^{6} c d e^{5}\right)} x^{3} - {\left(36 \, b^{2} c^{5} d^{6} - 65 \, b^{3} c^{4} d^{5} e + 7 \, b^{4} c^{3} d^{4} e^{2} + 23 \, b^{5} c^{2} d^{3} e^{3} - b^{6} c d^{2} e^{4} - 15 \, b^{7} d e^{5}\right)} x^{2} - {\left(8 \, b^{3} c^{4} d^{6} - 19 \, b^{4} c^{3} d^{5} e + 9 \, b^{5} c^{2} d^{4} e^{2} + 7 \, b^{6} c d^{3} e^{3} - 5 \, b^{7} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{5} d^{7} e - 3 \, b^{6} c^{4} d^{6} e^{2} + 3 \, b^{7} c^{3} d^{5} e^{3} - b^{8} c^{2} d^{4} e^{4}\right)} x^{5} + {\left(b^{5} c^{5} d^{8} - b^{6} c^{4} d^{7} e - 3 \, b^{7} c^{3} d^{6} e^{2} + 5 \, b^{8} c^{2} d^{5} e^{3} - 2 \, b^{9} c d^{4} e^{4}\right)} x^{4} + {\left(2 \, b^{6} c^{4} d^{8} - 5 \, b^{7} c^{3} d^{7} e + 3 \, b^{8} c^{2} d^{6} e^{2} + b^{9} c d^{5} e^{3} - b^{10} d^{4} e^{4}\right)} x^{3} + {\left(b^{7} c^{3} d^{8} - 3 \, b^{8} c^{2} d^{7} e + 3 \, b^{9} c d^{6} e^{2} - b^{10} d^{5} e^{3}\right)} x^{2}\right)}}, \frac{6 \, {\left({\left(16 \, c^{7} d^{5} e - 36 \, b c^{6} d^{4} e^{2} + 17 \, b^{2} c^{5} d^{3} e^{3} + 5 \, b^{3} c^{4} d^{2} e^{4} + 3 \, b^{4} c^{3} d e^{5} - 5 \, b^{5} c^{2} e^{6}\right)} x^{5} + {\left(16 \, c^{7} d^{6} - 4 \, b c^{6} d^{5} e - 55 \, b^{2} c^{5} d^{4} e^{2} + 39 \, b^{3} c^{4} d^{3} e^{3} + 13 \, b^{4} c^{3} d^{2} e^{4} + b^{5} c^{2} d e^{5} - 10 \, b^{6} c e^{6}\right)} x^{4} + {\left(32 \, b c^{6} d^{6} - 56 \, b^{2} c^{5} d^{5} e - 2 \, b^{3} c^{4} d^{4} e^{2} + 27 \, b^{4} c^{3} d^{3} e^{3} + 11 \, b^{5} c^{2} d^{2} e^{4} - 7 \, b^{6} c d e^{5} - 5 \, b^{7} e^{6}\right)} x^{3} + {\left(16 \, b^{2} c^{5} d^{6} - 36 \, b^{3} c^{4} d^{5} e + 17 \, b^{4} c^{3} d^{4} e^{2} + 5 \, b^{5} c^{2} d^{3} e^{3} + 3 \, b^{6} c d^{2} e^{4} - 5 \, b^{7} d e^{5}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - 3 \, {\left({\left(16 \, c^{7} d^{6} e - 44 \, b c^{6} d^{5} e^{2} + 33 \, b^{2} c^{5} d^{4} e^{3}\right)} x^{5} + {\left(16 \, c^{7} d^{7} - 12 \, b c^{6} d^{6} e - 55 \, b^{2} c^{5} d^{5} e^{2} + 66 \, b^{3} c^{4} d^{4} e^{3}\right)} x^{4} + {\left(32 \, b c^{6} d^{7} - 72 \, b^{2} c^{5} d^{6} e + 22 \, b^{3} c^{4} d^{5} e^{2} + 33 \, b^{4} c^{3} d^{4} e^{3}\right)} x^{3} + {\left(16 \, b^{2} c^{5} d^{7} - 44 \, b^{3} c^{4} d^{6} e + 33 \, b^{4} c^{3} d^{5} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e - 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(2 \, b^{4} c^{3} d^{6} - 6 \, b^{5} c^{2} d^{5} e + 6 \, b^{6} c d^{4} e^{2} - 2 \, b^{7} d^{3} e^{3} - 3 \, {\left(8 \, b c^{6} d^{5} e - 16 \, b^{2} c^{5} d^{4} e^{2} + 5 \, b^{3} c^{4} d^{3} e^{3} + 3 \, b^{4} c^{3} d^{2} e^{4} - 5 \, b^{5} c^{2} d e^{5}\right)} x^{4} - {\left(24 \, b c^{6} d^{6} - 12 \, b^{2} c^{5} d^{5} e - 58 \, b^{3} c^{4} d^{4} e^{2} + 33 \, b^{4} c^{3} d^{3} e^{3} + 13 \, b^{5} c^{2} d^{2} e^{4} - 30 \, b^{6} c d e^{5}\right)} x^{3} - {\left(36 \, b^{2} c^{5} d^{6} - 65 \, b^{3} c^{4} d^{5} e + 7 \, b^{4} c^{3} d^{4} e^{2} + 23 \, b^{5} c^{2} d^{3} e^{3} - b^{6} c d^{2} e^{4} - 15 \, b^{7} d e^{5}\right)} x^{2} - {\left(8 \, b^{3} c^{4} d^{6} - 19 \, b^{4} c^{3} d^{5} e + 9 \, b^{5} c^{2} d^{4} e^{2} + 7 \, b^{6} c d^{3} e^{3} - 5 \, b^{7} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left({\left(b^{5} c^{5} d^{7} e - 3 \, b^{6} c^{4} d^{6} e^{2} + 3 \, b^{7} c^{3} d^{5} e^{3} - b^{8} c^{2} d^{4} e^{4}\right)} x^{5} + {\left(b^{5} c^{5} d^{8} - b^{6} c^{4} d^{7} e - 3 \, b^{7} c^{3} d^{6} e^{2} + 5 \, b^{8} c^{2} d^{5} e^{3} - 2 \, b^{9} c d^{4} e^{4}\right)} x^{4} + {\left(2 \, b^{6} c^{4} d^{8} - 5 \, b^{7} c^{3} d^{7} e + 3 \, b^{8} c^{2} d^{6} e^{2} + b^{9} c d^{5} e^{3} - b^{10} d^{4} e^{4}\right)} x^{3} + {\left(b^{7} c^{3} d^{8} - 3 \, b^{8} c^{2} d^{7} e + 3 \, b^{9} c d^{6} e^{2} - b^{10} d^{5} e^{3}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(16 \, c^{7} d^{6} e - 44 \, b c^{6} d^{5} e^{2} + 33 \, b^{2} c^{5} d^{4} e^{3}\right)} x^{5} + {\left(16 \, c^{7} d^{7} - 12 \, b c^{6} d^{6} e - 55 \, b^{2} c^{5} d^{5} e^{2} + 66 \, b^{3} c^{4} d^{4} e^{3}\right)} x^{4} + {\left(32 \, b c^{6} d^{7} - 72 \, b^{2} c^{5} d^{6} e + 22 \, b^{3} c^{4} d^{5} e^{2} + 33 \, b^{4} c^{3} d^{4} e^{3}\right)} x^{3} + {\left(16 \, b^{2} c^{5} d^{7} - 44 \, b^{3} c^{4} d^{6} e + 33 \, b^{4} c^{3} d^{5} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(16 \, c^{7} d^{5} e - 36 \, b c^{6} d^{4} e^{2} + 17 \, b^{2} c^{5} d^{3} e^{3} + 5 \, b^{3} c^{4} d^{2} e^{4} + 3 \, b^{4} c^{3} d e^{5} - 5 \, b^{5} c^{2} e^{6}\right)} x^{5} + {\left(16 \, c^{7} d^{6} - 4 \, b c^{6} d^{5} e - 55 \, b^{2} c^{5} d^{4} e^{2} + 39 \, b^{3} c^{4} d^{3} e^{3} + 13 \, b^{4} c^{3} d^{2} e^{4} + b^{5} c^{2} d e^{5} - 10 \, b^{6} c e^{6}\right)} x^{4} + {\left(32 \, b c^{6} d^{6} - 56 \, b^{2} c^{5} d^{5} e - 2 \, b^{3} c^{4} d^{4} e^{2} + 27 \, b^{4} c^{3} d^{3} e^{3} + 11 \, b^{5} c^{2} d^{2} e^{4} - 7 \, b^{6} c d e^{5} - 5 \, b^{7} e^{6}\right)} x^{3} + {\left(16 \, b^{2} c^{5} d^{6} - 36 \, b^{3} c^{4} d^{5} e + 17 \, b^{4} c^{3} d^{4} e^{2} + 5 \, b^{5} c^{2} d^{3} e^{3} + 3 \, b^{6} c d^{2} e^{4} - 5 \, b^{7} d e^{5}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(2 \, b^{4} c^{3} d^{6} - 6 \, b^{5} c^{2} d^{5} e + 6 \, b^{6} c d^{4} e^{2} - 2 \, b^{7} d^{3} e^{3} - 3 \, {\left(8 \, b c^{6} d^{5} e - 16 \, b^{2} c^{5} d^{4} e^{2} + 5 \, b^{3} c^{4} d^{3} e^{3} + 3 \, b^{4} c^{3} d^{2} e^{4} - 5 \, b^{5} c^{2} d e^{5}\right)} x^{4} - {\left(24 \, b c^{6} d^{6} - 12 \, b^{2} c^{5} d^{5} e - 58 \, b^{3} c^{4} d^{4} e^{2} + 33 \, b^{4} c^{3} d^{3} e^{3} + 13 \, b^{5} c^{2} d^{2} e^{4} - 30 \, b^{6} c d e^{5}\right)} x^{3} - {\left(36 \, b^{2} c^{5} d^{6} - 65 \, b^{3} c^{4} d^{5} e + 7 \, b^{4} c^{3} d^{4} e^{2} + 23 \, b^{5} c^{2} d^{3} e^{3} - b^{6} c d^{2} e^{4} - 15 \, b^{7} d e^{5}\right)} x^{2} - {\left(8 \, b^{3} c^{4} d^{6} - 19 \, b^{4} c^{3} d^{5} e + 9 \, b^{5} c^{2} d^{4} e^{2} + 7 \, b^{6} c d^{3} e^{3} - 5 \, b^{7} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left({\left(b^{5} c^{5} d^{7} e - 3 \, b^{6} c^{4} d^{6} e^{2} + 3 \, b^{7} c^{3} d^{5} e^{3} - b^{8} c^{2} d^{4} e^{4}\right)} x^{5} + {\left(b^{5} c^{5} d^{8} - b^{6} c^{4} d^{7} e - 3 \, b^{7} c^{3} d^{6} e^{2} + 5 \, b^{8} c^{2} d^{5} e^{3} - 2 \, b^{9} c d^{4} e^{4}\right)} x^{4} + {\left(2 \, b^{6} c^{4} d^{8} - 5 \, b^{7} c^{3} d^{7} e + 3 \, b^{8} c^{2} d^{6} e^{2} + b^{9} c d^{5} e^{3} - b^{10} d^{4} e^{4}\right)} x^{3} + {\left(b^{7} c^{3} d^{8} - 3 \, b^{8} c^{2} d^{7} e + 3 \, b^{9} c d^{6} e^{2} - b^{10} d^{5} e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*(3*((16*c^7*d^6*e - 44*b*c^6*d^5*e^2 + 33*b^2*c^5*d^4*e^3)*x^5 + (16*c^7*d^7 - 12*b*c^6*d^6*e - 55*b^2*c^5*d^5*e^2 + 66*b^3*c^4*d^4*e^3)*x^4 + (32*b*c^6*d^7 - 72*b^2*c^5*d^6*e + 22*b^3*c^4*d^5*e^2 + 33*b^4*c^3*d^4*e^3)*x^3 + (16*b^2*c^5*d^7 - 44*b^3*c^4*d^6*e + 33*b^4*c^3*d^5*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 3*((16*c^7*d^5*e - 36*b*c^6*d^4*e^2 + 17*b^2*c^5*d^3*e^3 + 5*b^3*c^4*d^2*e^4 + 3*b^4*c^3*d*e^5 - 5*b^5*c^2*e^6)*x^5 + (16*c^7*d^6 - 4*b*c^6*d^5*e - 55*b^2*c^5*d^4*e^2 + 39*b^3*c^4*d^3*e^3 + 13*b^4*c^3*d^2*e^4 + b^5*c^2*d*e^5 - 10*b^6*c*e^6)*x^4 + (32*b*c^6*d^6 - 56*b^2*c^5*d^5*e - 2*b^3*c^4*d^4*e^2 + 27*b^4*c^3*d^3*e^3 + 11*b^5*c^2*d^2*e^4 - 7*b^6*c*d*e^5 - 5*b^7*e^6)*x^3 + (16*b^2*c^5*d^6 - 36*b^3*c^4*d^5*e + 17*b^4*c^3*d^4*e^2 + 5*b^5*c^2*d^3*e^3 + 3*b^6*c*d^2*e^4 - 5*b^7*d*e^5)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) + 2*(2*b^4*c^3*d^6 - 6*b^5*c^2*d^5*e + 6*b^6*c*d^4*e^2 - 2*b^7*d^3*e^3 - 3*(8*b*c^6*d^5*e - 16*b^2*c^5*d^4*e^2 + 5*b^3*c^4*d^3*e^3 + 3*b^4*c^3*d^2*e^4 - 5*b^5*c^2*d*e^5)*x^4 - (24*b*c^6*d^6 - 12*b^2*c^5*d^5*e - 58*b^3*c^4*d^4*e^2 + 33*b^4*c^3*d^3*e^3 + 13*b^5*c^2*d^2*e^4 - 30*b^6*c*d*e^5)*x^3 - (36*b^2*c^5*d^6 - 65*b^3*c^4*d^5*e + 7*b^4*c^3*d^4*e^2 + 23*b^5*c^2*d^3*e^3 - b^6*c*d^2*e^4 - 15*b^7*d*e^5)*x^2 - (8*b^3*c^4*d^6 - 19*b^4*c^3*d^5*e + 9*b^5*c^2*d^4*e^2 + 7*b^6*c*d^3*e^3 - 5*b^7*d^2*e^4)*x)*sqrt(e*x + d))/((b^5*c^5*d^7*e - 3*b^6*c^4*d^6*e^2 + 3*b^7*c^3*d^5*e^3 - b^8*c^2*d^4*e^4)*x^5 + (b^5*c^5*d^8 - b^6*c^4*d^7*e - 3*b^7*c^3*d^6*e^2 + 5*b^8*c^2*d^5*e^3 - 2*b^9*c*d^4*e^4)*x^4 + (2*b^6*c^4*d^8 - 5*b^7*c^3*d^7*e + 3*b^8*c^2*d^6*e^2 + b^9*c*d^5*e^3 - b^10*d^4*e^4)*x^3 + (b^7*c^3*d^8 - 3*b^8*c^2*d^7*e + 3*b^9*c*d^6*e^2 - b^10*d^5*e^3)*x^2), 1/8*(6*((16*c^7*d^6*e - 44*b*c^6*d^5*e^2 + 33*b^2*c^5*d^4*e^3)*x^5 + (16*c^7*d^7 - 12*b*c^6*d^6*e - 55*b^2*c^5*d^5*e^2 + 66*b^3*c^4*d^4*e^3)*x^4 + (32*b*c^6*d^7 - 72*b^2*c^5*d^6*e + 22*b^3*c^4*d^5*e^2 + 33*b^4*c^3*d^4*e^3)*x^3 + (16*b^2*c^5*d^7 - 44*b^3*c^4*d^6*e + 33*b^4*c^3*d^5*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((16*c^7*d^5*e - 36*b*c^6*d^4*e^2 + 17*b^2*c^5*d^3*e^3 + 5*b^3*c^4*d^2*e^4 + 3*b^4*c^3*d*e^5 - 5*b^5*c^2*e^6)*x^5 + (16*c^7*d^6 - 4*b*c^6*d^5*e - 55*b^2*c^5*d^4*e^2 + 39*b^3*c^4*d^3*e^3 + 13*b^4*c^3*d^2*e^4 + b^5*c^2*d*e^5 - 10*b^6*c*e^6)*x^4 + (32*b*c^6*d^6 - 56*b^2*c^5*d^5*e - 2*b^3*c^4*d^4*e^2 + 27*b^4*c^3*d^3*e^3 + 11*b^5*c^2*d^2*e^4 - 7*b^6*c*d*e^5 - 5*b^7*e^6)*x^3 + (16*b^2*c^5*d^6 - 36*b^3*c^4*d^5*e + 17*b^4*c^3*d^4*e^2 + 5*b^5*c^2*d^3*e^3 + 3*b^6*c*d^2*e^4 - 5*b^7*d*e^5)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(2*b^4*c^3*d^6 - 6*b^5*c^2*d^5*e + 6*b^6*c*d^4*e^2 - 2*b^7*d^3*e^3 - 3*(8*b*c^6*d^5*e - 16*b^2*c^5*d^4*e^2 + 5*b^3*c^4*d^3*e^3 + 3*b^4*c^3*d^2*e^4 - 5*b^5*c^2*d*e^5)*x^4 - (24*b*c^6*d^6 - 12*b^2*c^5*d^5*e - 58*b^3*c^4*d^4*e^2 + 33*b^4*c^3*d^3*e^3 + 13*b^5*c^2*d^2*e^4 - 30*b^6*c*d*e^5)*x^3 - (36*b^2*c^5*d^6 - 65*b^3*c^4*d^5*e + 7*b^4*c^3*d^4*e^2 + 23*b^5*c^2*d^3*e^3 - b^6*c*d^2*e^4 - 15*b^7*d*e^5)*x^2 - (8*b^3*c^4*d^6 - 19*b^4*c^3*d^5*e + 9*b^5*c^2*d^4*e^2 + 7*b^6*c*d^3*e^3 - 5*b^7*d^2*e^4)*x)*sqrt(e*x + d))/((b^5*c^5*d^7*e - 3*b^6*c^4*d^6*e^2 + 3*b^7*c^3*d^5*e^3 - b^8*c^2*d^4*e^4)*x^5 + (b^5*c^5*d^8 - b^6*c^4*d^7*e - 3*b^7*c^3*d^6*e^2 + 5*b^8*c^2*d^5*e^3 - 2*b^9*c*d^4*e^4)*x^4 + (2*b^6*c^4*d^8 - 5*b^7*c^3*d^7*e + 3*b^8*c^2*d^6*e^2 + b^9*c*d^5*e^3 - b^10*d^4*e^4)*x^3 + (b^7*c^3*d^8 - 3*b^8*c^2*d^7*e + 3*b^9*c*d^6*e^2 - b^10*d^5*e^3)*x^2), 1/8*(6*((16*c^7*d^5*e - 36*b*c^6*d^4*e^2 + 17*b^2*c^5*d^3*e^3 + 5*b^3*c^4*d^2*e^4 + 3*b^4*c^3*d*e^5 - 5*b^5*c^2*e^6)*x^5 + (16*c^7*d^6 - 4*b*c^6*d^5*e - 55*b^2*c^5*d^4*e^2 + 39*b^3*c^4*d^3*e^3 + 13*b^4*c^3*d^2*e^4 + b^5*c^2*d*e^5 - 10*b^6*c*e^6)*x^4 + (32*b*c^6*d^6 - 56*b^2*c^5*d^5*e - 2*b^3*c^4*d^4*e^2 + 27*b^4*c^3*d^3*e^3 + 11*b^5*c^2*d^2*e^4 - 7*b^6*c*d*e^5 - 5*b^7*e^6)*x^3 + (16*b^2*c^5*d^6 - 36*b^3*c^4*d^5*e + 17*b^4*c^3*d^4*e^2 + 5*b^5*c^2*d^3*e^3 + 3*b^6*c*d^2*e^4 - 5*b^7*d*e^5)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - 3*((16*c^7*d^6*e - 44*b*c^6*d^5*e^2 + 33*b^2*c^5*d^4*e^3)*x^5 + (16*c^7*d^7 - 12*b*c^6*d^6*e - 55*b^2*c^5*d^5*e^2 + 66*b^3*c^4*d^4*e^3)*x^4 + (32*b*c^6*d^7 - 72*b^2*c^5*d^6*e + 22*b^3*c^4*d^5*e^2 + 33*b^4*c^3*d^4*e^3)*x^3 + (16*b^2*c^5*d^7 - 44*b^3*c^4*d^6*e + 33*b^4*c^3*d^5*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e - 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(2*b^4*c^3*d^6 - 6*b^5*c^2*d^5*e + 6*b^6*c*d^4*e^2 - 2*b^7*d^3*e^3 - 3*(8*b*c^6*d^5*e - 16*b^2*c^5*d^4*e^2 + 5*b^3*c^4*d^3*e^3 + 3*b^4*c^3*d^2*e^4 - 5*b^5*c^2*d*e^5)*x^4 - (24*b*c^6*d^6 - 12*b^2*c^5*d^5*e - 58*b^3*c^4*d^4*e^2 + 33*b^4*c^3*d^3*e^3 + 13*b^5*c^2*d^2*e^4 - 30*b^6*c*d*e^5)*x^3 - (36*b^2*c^5*d^6 - 65*b^3*c^4*d^5*e + 7*b^4*c^3*d^4*e^2 + 23*b^5*c^2*d^3*e^3 - b^6*c*d^2*e^4 - 15*b^7*d*e^5)*x^2 - (8*b^3*c^4*d^6 - 19*b^4*c^3*d^5*e + 9*b^5*c^2*d^4*e^2 + 7*b^6*c*d^3*e^3 - 5*b^7*d^2*e^4)*x)*sqrt(e*x + d))/((b^5*c^5*d^7*e - 3*b^6*c^4*d^6*e^2 + 3*b^7*c^3*d^5*e^3 - b^8*c^2*d^4*e^4)*x^5 + (b^5*c^5*d^8 - b^6*c^4*d^7*e - 3*b^7*c^3*d^6*e^2 + 5*b^8*c^2*d^5*e^3 - 2*b^9*c*d^4*e^4)*x^4 + (2*b^6*c^4*d^8 - 5*b^7*c^3*d^7*e + 3*b^8*c^2*d^6*e^2 + b^9*c*d^5*e^3 - b^10*d^4*e^4)*x^3 + (b^7*c^3*d^8 - 3*b^8*c^2*d^7*e + 3*b^9*c*d^6*e^2 - b^10*d^5*e^3)*x^2), 1/4*(3*((16*c^7*d^6*e - 44*b*c^6*d^5*e^2 + 33*b^2*c^5*d^4*e^3)*x^5 + (16*c^7*d^7 - 12*b*c^6*d^6*e - 55*b^2*c^5*d^5*e^2 + 66*b^3*c^4*d^4*e^3)*x^4 + (32*b*c^6*d^7 - 72*b^2*c^5*d^6*e + 22*b^3*c^4*d^5*e^2 + 33*b^4*c^3*d^4*e^3)*x^3 + (16*b^2*c^5*d^7 - 44*b^3*c^4*d^6*e + 33*b^4*c^3*d^5*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((16*c^7*d^5*e - 36*b*c^6*d^4*e^2 + 17*b^2*c^5*d^3*e^3 + 5*b^3*c^4*d^2*e^4 + 3*b^4*c^3*d*e^5 - 5*b^5*c^2*e^6)*x^5 + (16*c^7*d^6 - 4*b*c^6*d^5*e - 55*b^2*c^5*d^4*e^2 + 39*b^3*c^4*d^3*e^3 + 13*b^4*c^3*d^2*e^4 + b^5*c^2*d*e^5 - 10*b^6*c*e^6)*x^4 + (32*b*c^6*d^6 - 56*b^2*c^5*d^5*e - 2*b^3*c^4*d^4*e^2 + 27*b^4*c^3*d^3*e^3 + 11*b^5*c^2*d^2*e^4 - 7*b^6*c*d*e^5 - 5*b^7*e^6)*x^3 + (16*b^2*c^5*d^6 - 36*b^3*c^4*d^5*e + 17*b^4*c^3*d^4*e^2 + 5*b^5*c^2*d^3*e^3 + 3*b^6*c*d^2*e^4 - 5*b^7*d*e^5)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (2*b^4*c^3*d^6 - 6*b^5*c^2*d^5*e + 6*b^6*c*d^4*e^2 - 2*b^7*d^3*e^3 - 3*(8*b*c^6*d^5*e - 16*b^2*c^5*d^4*e^2 + 5*b^3*c^4*d^3*e^3 + 3*b^4*c^3*d^2*e^4 - 5*b^5*c^2*d*e^5)*x^4 - (24*b*c^6*d^6 - 12*b^2*c^5*d^5*e - 58*b^3*c^4*d^4*e^2 + 33*b^4*c^3*d^3*e^3 + 13*b^5*c^2*d^2*e^4 - 30*b^6*c*d*e^5)*x^3 - (36*b^2*c^5*d^6 - 65*b^3*c^4*d^5*e + 7*b^4*c^3*d^4*e^2 + 23*b^5*c^2*d^3*e^3 - b^6*c*d^2*e^4 - 15*b^7*d*e^5)*x^2 - (8*b^3*c^4*d^6 - 19*b^4*c^3*d^5*e + 9*b^5*c^2*d^4*e^2 + 7*b^6*c*d^3*e^3 - 5*b^7*d^2*e^4)*x)*sqrt(e*x + d))/((b^5*c^5*d^7*e - 3*b^6*c^4*d^6*e^2 + 3*b^7*c^3*d^5*e^3 - b^8*c^2*d^4*e^4)*x^5 + (b^5*c^5*d^8 - b^6*c^4*d^7*e - 3*b^7*c^3*d^6*e^2 + 5*b^8*c^2*d^5*e^3 - 2*b^9*c*d^4*e^4)*x^4 + (2*b^6*c^4*d^8 - 5*b^7*c^3*d^7*e + 3*b^8*c^2*d^6*e^2 + b^9*c*d^5*e^3 - b^10*d^4*e^4)*x^3 + (b^7*c^3*d^8 - 3*b^8*c^2*d^7*e + 3*b^9*c*d^6*e^2 - b^10*d^5*e^3)*x^2)]","B",0
385,1,6969,0,13.813936," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(48 \, c^{8} d^{7} e^{2} - 156 \, b c^{7} d^{6} e^{3} + 143 \, b^{2} c^{6} d^{5} e^{4}\right)} x^{6} + 2 \, {\left(48 \, c^{8} d^{8} e - 108 \, b c^{7} d^{7} e^{2} - 13 \, b^{2} c^{6} d^{6} e^{3} + 143 \, b^{3} c^{5} d^{5} e^{4}\right)} x^{5} + {\left(48 \, c^{8} d^{9} + 36 \, b c^{7} d^{8} e - 433 \, b^{2} c^{6} d^{7} e^{2} + 416 \, b^{3} c^{5} d^{6} e^{3} + 143 \, b^{4} c^{4} d^{5} e^{4}\right)} x^{4} + 2 \, {\left(48 \, b c^{7} d^{9} - 108 \, b^{2} c^{6} d^{8} e - 13 \, b^{3} c^{5} d^{7} e^{2} + 143 \, b^{4} c^{4} d^{6} e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{6} d^{9} - 156 \, b^{3} c^{5} d^{8} e + 143 \, b^{4} c^{4} d^{7} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) + 3 \, {\left({\left(48 \, c^{8} d^{6} e^{2} - 132 \, b c^{7} d^{5} e^{3} + 83 \, b^{2} c^{6} d^{4} e^{4} + 28 \, b^{3} c^{5} d^{3} e^{5} + 18 \, b^{4} c^{4} d^{2} e^{6} - 80 \, b^{5} c^{3} d e^{7} + 35 \, b^{6} c^{2} e^{8}\right)} x^{6} + 2 \, {\left(48 \, c^{8} d^{7} e - 84 \, b c^{7} d^{6} e^{2} - 49 \, b^{2} c^{6} d^{5} e^{3} + 111 \, b^{3} c^{5} d^{4} e^{4} + 46 \, b^{4} c^{4} d^{3} e^{5} - 62 \, b^{5} c^{3} d^{2} e^{6} - 45 \, b^{6} c^{2} d e^{7} + 35 \, b^{7} c e^{8}\right)} x^{5} + {\left(48 \, c^{8} d^{8} + 60 \, b c^{7} d^{7} e - 397 \, b^{2} c^{6} d^{6} e^{2} + 228 \, b^{3} c^{5} d^{5} e^{3} + 213 \, b^{4} c^{4} d^{4} e^{4} + 20 \, b^{5} c^{3} d^{3} e^{5} - 267 \, b^{6} c^{2} d^{2} e^{6} + 60 \, b^{7} c d e^{7} + 35 \, b^{8} e^{8}\right)} x^{4} + 2 \, {\left(48 \, b c^{7} d^{8} - 84 \, b^{2} c^{6} d^{7} e - 49 \, b^{3} c^{5} d^{6} e^{2} + 111 \, b^{4} c^{4} d^{5} e^{3} + 46 \, b^{5} c^{3} d^{4} e^{4} - 62 \, b^{6} c^{2} d^{3} e^{5} - 45 \, b^{7} c d^{2} e^{6} + 35 \, b^{8} d e^{7}\right)} x^{3} + {\left(48 \, b^{2} c^{6} d^{8} - 132 \, b^{3} c^{5} d^{7} e + 83 \, b^{4} c^{4} d^{6} e^{2} + 28 \, b^{5} c^{3} d^{5} e^{3} + 18 \, b^{6} c^{2} d^{4} e^{4} - 80 \, b^{7} c d^{3} e^{5} + 35 \, b^{8} d^{2} e^{6}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(6 \, b^{4} c^{4} d^{8} - 24 \, b^{5} c^{3} d^{7} e + 36 \, b^{6} c^{2} d^{6} e^{2} - 24 \, b^{7} c d^{5} e^{3} + 6 \, b^{8} d^{4} e^{4} - 3 \, {\left(24 \, b c^{7} d^{6} e^{2} - 60 \, b^{2} c^{6} d^{5} e^{3} + 28 \, b^{3} c^{5} d^{4} e^{4} + 18 \, b^{4} c^{4} d^{3} e^{5} - 80 \, b^{5} c^{3} d^{2} e^{6} + 35 \, b^{6} c^{2} d e^{7}\right)} x^{5} - {\left(144 \, b c^{7} d^{7} e - 252 \, b^{2} c^{6} d^{6} e^{2} - 105 \, b^{3} c^{5} d^{5} e^{3} + 240 \, b^{4} c^{4} d^{4} e^{4} - 212 \, b^{5} c^{3} d^{3} e^{5} - 340 \, b^{6} c^{2} d^{2} e^{6} + 210 \, b^{7} c d e^{7}\right)} x^{4} - {\left(72 \, b c^{7} d^{8} + 36 \, b^{2} c^{6} d^{7} e - 438 \, b^{3} c^{5} d^{6} e^{2} + 255 \, b^{4} c^{4} d^{5} e^{3} + 180 \, b^{5} c^{3} d^{4} e^{4} - 565 \, b^{6} c^{2} d^{3} e^{5} + 40 \, b^{7} c d^{2} e^{6} + 105 \, b^{8} d e^{7}\right)} x^{3} - {\left(108 \, b^{2} c^{6} d^{8} - 225 \, b^{3} c^{5} d^{7} e + 180 \, b^{5} c^{3} d^{5} e^{3} - 30 \, b^{6} c^{2} d^{4} e^{4} - 278 \, b^{7} c d^{3} e^{5} + 140 \, b^{8} d^{2} e^{6}\right)} x^{2} - 3 \, {\left(8 \, b^{3} c^{5} d^{8} - 25 \, b^{4} c^{4} d^{7} e + 20 \, b^{5} c^{3} d^{6} e^{2} + 10 \, b^{6} c^{2} d^{5} e^{3} - 20 \, b^{7} c d^{4} e^{4} + 7 \, b^{8} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left({\left(b^{5} c^{6} d^{9} e^{2} - 4 \, b^{6} c^{5} d^{8} e^{3} + 6 \, b^{7} c^{4} d^{7} e^{4} - 4 \, b^{8} c^{3} d^{6} e^{5} + b^{9} c^{2} d^{5} e^{6}\right)} x^{6} + 2 \, {\left(b^{5} c^{6} d^{10} e - 3 \, b^{6} c^{5} d^{9} e^{2} + 2 \, b^{7} c^{4} d^{8} e^{3} + 2 \, b^{8} c^{3} d^{7} e^{4} - 3 \, b^{9} c^{2} d^{6} e^{5} + b^{10} c d^{5} e^{6}\right)} x^{5} + {\left(b^{5} c^{6} d^{11} - 9 \, b^{7} c^{4} d^{9} e^{2} + 16 \, b^{8} c^{3} d^{8} e^{3} - 9 \, b^{9} c^{2} d^{7} e^{4} + b^{11} d^{5} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d^{11} - 3 \, b^{7} c^{4} d^{10} e + 2 \, b^{8} c^{3} d^{9} e^{2} + 2 \, b^{9} c^{2} d^{8} e^{3} - 3 \, b^{10} c d^{7} e^{4} + b^{11} d^{6} e^{5}\right)} x^{3} + {\left(b^{7} c^{4} d^{11} - 4 \, b^{8} c^{3} d^{10} e + 6 \, b^{9} c^{2} d^{9} e^{2} - 4 \, b^{10} c d^{8} e^{3} + b^{11} d^{7} e^{4}\right)} x^{2}\right)}}, \frac{6 \, {\left({\left(48 \, c^{8} d^{7} e^{2} - 156 \, b c^{7} d^{6} e^{3} + 143 \, b^{2} c^{6} d^{5} e^{4}\right)} x^{6} + 2 \, {\left(48 \, c^{8} d^{8} e - 108 \, b c^{7} d^{7} e^{2} - 13 \, b^{2} c^{6} d^{6} e^{3} + 143 \, b^{3} c^{5} d^{5} e^{4}\right)} x^{5} + {\left(48 \, c^{8} d^{9} + 36 \, b c^{7} d^{8} e - 433 \, b^{2} c^{6} d^{7} e^{2} + 416 \, b^{3} c^{5} d^{6} e^{3} + 143 \, b^{4} c^{4} d^{5} e^{4}\right)} x^{4} + 2 \, {\left(48 \, b c^{7} d^{9} - 108 \, b^{2} c^{6} d^{8} e - 13 \, b^{3} c^{5} d^{7} e^{2} + 143 \, b^{4} c^{4} d^{6} e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{6} d^{9} - 156 \, b^{3} c^{5} d^{8} e + 143 \, b^{4} c^{4} d^{7} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(48 \, c^{8} d^{6} e^{2} - 132 \, b c^{7} d^{5} e^{3} + 83 \, b^{2} c^{6} d^{4} e^{4} + 28 \, b^{3} c^{5} d^{3} e^{5} + 18 \, b^{4} c^{4} d^{2} e^{6} - 80 \, b^{5} c^{3} d e^{7} + 35 \, b^{6} c^{2} e^{8}\right)} x^{6} + 2 \, {\left(48 \, c^{8} d^{7} e - 84 \, b c^{7} d^{6} e^{2} - 49 \, b^{2} c^{6} d^{5} e^{3} + 111 \, b^{3} c^{5} d^{4} e^{4} + 46 \, b^{4} c^{4} d^{3} e^{5} - 62 \, b^{5} c^{3} d^{2} e^{6} - 45 \, b^{6} c^{2} d e^{7} + 35 \, b^{7} c e^{8}\right)} x^{5} + {\left(48 \, c^{8} d^{8} + 60 \, b c^{7} d^{7} e - 397 \, b^{2} c^{6} d^{6} e^{2} + 228 \, b^{3} c^{5} d^{5} e^{3} + 213 \, b^{4} c^{4} d^{4} e^{4} + 20 \, b^{5} c^{3} d^{3} e^{5} - 267 \, b^{6} c^{2} d^{2} e^{6} + 60 \, b^{7} c d e^{7} + 35 \, b^{8} e^{8}\right)} x^{4} + 2 \, {\left(48 \, b c^{7} d^{8} - 84 \, b^{2} c^{6} d^{7} e - 49 \, b^{3} c^{5} d^{6} e^{2} + 111 \, b^{4} c^{4} d^{5} e^{3} + 46 \, b^{5} c^{3} d^{4} e^{4} - 62 \, b^{6} c^{2} d^{3} e^{5} - 45 \, b^{7} c d^{2} e^{6} + 35 \, b^{8} d e^{7}\right)} x^{3} + {\left(48 \, b^{2} c^{6} d^{8} - 132 \, b^{3} c^{5} d^{7} e + 83 \, b^{4} c^{4} d^{6} e^{2} + 28 \, b^{5} c^{3} d^{5} e^{3} + 18 \, b^{6} c^{2} d^{4} e^{4} - 80 \, b^{7} c d^{3} e^{5} + 35 \, b^{8} d^{2} e^{6}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{e x - 2 \, \sqrt{e x + d} \sqrt{d} + 2 \, d}{x}\right) - 2 \, {\left(6 \, b^{4} c^{4} d^{8} - 24 \, b^{5} c^{3} d^{7} e + 36 \, b^{6} c^{2} d^{6} e^{2} - 24 \, b^{7} c d^{5} e^{3} + 6 \, b^{8} d^{4} e^{4} - 3 \, {\left(24 \, b c^{7} d^{6} e^{2} - 60 \, b^{2} c^{6} d^{5} e^{3} + 28 \, b^{3} c^{5} d^{4} e^{4} + 18 \, b^{4} c^{4} d^{3} e^{5} - 80 \, b^{5} c^{3} d^{2} e^{6} + 35 \, b^{6} c^{2} d e^{7}\right)} x^{5} - {\left(144 \, b c^{7} d^{7} e - 252 \, b^{2} c^{6} d^{6} e^{2} - 105 \, b^{3} c^{5} d^{5} e^{3} + 240 \, b^{4} c^{4} d^{4} e^{4} - 212 \, b^{5} c^{3} d^{3} e^{5} - 340 \, b^{6} c^{2} d^{2} e^{6} + 210 \, b^{7} c d e^{7}\right)} x^{4} - {\left(72 \, b c^{7} d^{8} + 36 \, b^{2} c^{6} d^{7} e - 438 \, b^{3} c^{5} d^{6} e^{2} + 255 \, b^{4} c^{4} d^{5} e^{3} + 180 \, b^{5} c^{3} d^{4} e^{4} - 565 \, b^{6} c^{2} d^{3} e^{5} + 40 \, b^{7} c d^{2} e^{6} + 105 \, b^{8} d e^{7}\right)} x^{3} - {\left(108 \, b^{2} c^{6} d^{8} - 225 \, b^{3} c^{5} d^{7} e + 180 \, b^{5} c^{3} d^{5} e^{3} - 30 \, b^{6} c^{2} d^{4} e^{4} - 278 \, b^{7} c d^{3} e^{5} + 140 \, b^{8} d^{2} e^{6}\right)} x^{2} - 3 \, {\left(8 \, b^{3} c^{5} d^{8} - 25 \, b^{4} c^{4} d^{7} e + 20 \, b^{5} c^{3} d^{6} e^{2} + 10 \, b^{6} c^{2} d^{5} e^{3} - 20 \, b^{7} c d^{4} e^{4} + 7 \, b^{8} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left({\left(b^{5} c^{6} d^{9} e^{2} - 4 \, b^{6} c^{5} d^{8} e^{3} + 6 \, b^{7} c^{4} d^{7} e^{4} - 4 \, b^{8} c^{3} d^{6} e^{5} + b^{9} c^{2} d^{5} e^{6}\right)} x^{6} + 2 \, {\left(b^{5} c^{6} d^{10} e - 3 \, b^{6} c^{5} d^{9} e^{2} + 2 \, b^{7} c^{4} d^{8} e^{3} + 2 \, b^{8} c^{3} d^{7} e^{4} - 3 \, b^{9} c^{2} d^{6} e^{5} + b^{10} c d^{5} e^{6}\right)} x^{5} + {\left(b^{5} c^{6} d^{11} - 9 \, b^{7} c^{4} d^{9} e^{2} + 16 \, b^{8} c^{3} d^{8} e^{3} - 9 \, b^{9} c^{2} d^{7} e^{4} + b^{11} d^{5} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d^{11} - 3 \, b^{7} c^{4} d^{10} e + 2 \, b^{8} c^{3} d^{9} e^{2} + 2 \, b^{9} c^{2} d^{8} e^{3} - 3 \, b^{10} c d^{7} e^{4} + b^{11} d^{6} e^{5}\right)} x^{3} + {\left(b^{7} c^{4} d^{11} - 4 \, b^{8} c^{3} d^{10} e + 6 \, b^{9} c^{2} d^{9} e^{2} - 4 \, b^{10} c d^{8} e^{3} + b^{11} d^{7} e^{4}\right)} x^{2}\right)}}, \frac{6 \, {\left({\left(48 \, c^{8} d^{6} e^{2} - 132 \, b c^{7} d^{5} e^{3} + 83 \, b^{2} c^{6} d^{4} e^{4} + 28 \, b^{3} c^{5} d^{3} e^{5} + 18 \, b^{4} c^{4} d^{2} e^{6} - 80 \, b^{5} c^{3} d e^{7} + 35 \, b^{6} c^{2} e^{8}\right)} x^{6} + 2 \, {\left(48 \, c^{8} d^{7} e - 84 \, b c^{7} d^{6} e^{2} - 49 \, b^{2} c^{6} d^{5} e^{3} + 111 \, b^{3} c^{5} d^{4} e^{4} + 46 \, b^{4} c^{4} d^{3} e^{5} - 62 \, b^{5} c^{3} d^{2} e^{6} - 45 \, b^{6} c^{2} d e^{7} + 35 \, b^{7} c e^{8}\right)} x^{5} + {\left(48 \, c^{8} d^{8} + 60 \, b c^{7} d^{7} e - 397 \, b^{2} c^{6} d^{6} e^{2} + 228 \, b^{3} c^{5} d^{5} e^{3} + 213 \, b^{4} c^{4} d^{4} e^{4} + 20 \, b^{5} c^{3} d^{3} e^{5} - 267 \, b^{6} c^{2} d^{2} e^{6} + 60 \, b^{7} c d e^{7} + 35 \, b^{8} e^{8}\right)} x^{4} + 2 \, {\left(48 \, b c^{7} d^{8} - 84 \, b^{2} c^{6} d^{7} e - 49 \, b^{3} c^{5} d^{6} e^{2} + 111 \, b^{4} c^{4} d^{5} e^{3} + 46 \, b^{5} c^{3} d^{4} e^{4} - 62 \, b^{6} c^{2} d^{3} e^{5} - 45 \, b^{7} c d^{2} e^{6} + 35 \, b^{8} d e^{7}\right)} x^{3} + {\left(48 \, b^{2} c^{6} d^{8} - 132 \, b^{3} c^{5} d^{7} e + 83 \, b^{4} c^{4} d^{6} e^{2} + 28 \, b^{5} c^{3} d^{5} e^{3} + 18 \, b^{6} c^{2} d^{4} e^{4} - 80 \, b^{7} c d^{3} e^{5} + 35 \, b^{8} d^{2} e^{6}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) + 3 \, {\left({\left(48 \, c^{8} d^{7} e^{2} - 156 \, b c^{7} d^{6} e^{3} + 143 \, b^{2} c^{6} d^{5} e^{4}\right)} x^{6} + 2 \, {\left(48 \, c^{8} d^{8} e - 108 \, b c^{7} d^{7} e^{2} - 13 \, b^{2} c^{6} d^{6} e^{3} + 143 \, b^{3} c^{5} d^{5} e^{4}\right)} x^{5} + {\left(48 \, c^{8} d^{9} + 36 \, b c^{7} d^{8} e - 433 \, b^{2} c^{6} d^{7} e^{2} + 416 \, b^{3} c^{5} d^{6} e^{3} + 143 \, b^{4} c^{4} d^{5} e^{4}\right)} x^{4} + 2 \, {\left(48 \, b c^{7} d^{9} - 108 \, b^{2} c^{6} d^{8} e - 13 \, b^{3} c^{5} d^{7} e^{2} + 143 \, b^{4} c^{4} d^{6} e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{6} d^{9} - 156 \, b^{3} c^{5} d^{8} e + 143 \, b^{4} c^{4} d^{7} e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{c d - b e}} \log\left(\frac{c e x + 2 \, c d - b e + 2 \, {\left(c d - b e\right)} \sqrt{e x + d} \sqrt{\frac{c}{c d - b e}}}{c x + b}\right) - 2 \, {\left(6 \, b^{4} c^{4} d^{8} - 24 \, b^{5} c^{3} d^{7} e + 36 \, b^{6} c^{2} d^{6} e^{2} - 24 \, b^{7} c d^{5} e^{3} + 6 \, b^{8} d^{4} e^{4} - 3 \, {\left(24 \, b c^{7} d^{6} e^{2} - 60 \, b^{2} c^{6} d^{5} e^{3} + 28 \, b^{3} c^{5} d^{4} e^{4} + 18 \, b^{4} c^{4} d^{3} e^{5} - 80 \, b^{5} c^{3} d^{2} e^{6} + 35 \, b^{6} c^{2} d e^{7}\right)} x^{5} - {\left(144 \, b c^{7} d^{7} e - 252 \, b^{2} c^{6} d^{6} e^{2} - 105 \, b^{3} c^{5} d^{5} e^{3} + 240 \, b^{4} c^{4} d^{4} e^{4} - 212 \, b^{5} c^{3} d^{3} e^{5} - 340 \, b^{6} c^{2} d^{2} e^{6} + 210 \, b^{7} c d e^{7}\right)} x^{4} - {\left(72 \, b c^{7} d^{8} + 36 \, b^{2} c^{6} d^{7} e - 438 \, b^{3} c^{5} d^{6} e^{2} + 255 \, b^{4} c^{4} d^{5} e^{3} + 180 \, b^{5} c^{3} d^{4} e^{4} - 565 \, b^{6} c^{2} d^{3} e^{5} + 40 \, b^{7} c d^{2} e^{6} + 105 \, b^{8} d e^{7}\right)} x^{3} - {\left(108 \, b^{2} c^{6} d^{8} - 225 \, b^{3} c^{5} d^{7} e + 180 \, b^{5} c^{3} d^{5} e^{3} - 30 \, b^{6} c^{2} d^{4} e^{4} - 278 \, b^{7} c d^{3} e^{5} + 140 \, b^{8} d^{2} e^{6}\right)} x^{2} - 3 \, {\left(8 \, b^{3} c^{5} d^{8} - 25 \, b^{4} c^{4} d^{7} e + 20 \, b^{5} c^{3} d^{6} e^{2} + 10 \, b^{6} c^{2} d^{5} e^{3} - 20 \, b^{7} c d^{4} e^{4} + 7 \, b^{8} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left({\left(b^{5} c^{6} d^{9} e^{2} - 4 \, b^{6} c^{5} d^{8} e^{3} + 6 \, b^{7} c^{4} d^{7} e^{4} - 4 \, b^{8} c^{3} d^{6} e^{5} + b^{9} c^{2} d^{5} e^{6}\right)} x^{6} + 2 \, {\left(b^{5} c^{6} d^{10} e - 3 \, b^{6} c^{5} d^{9} e^{2} + 2 \, b^{7} c^{4} d^{8} e^{3} + 2 \, b^{8} c^{3} d^{7} e^{4} - 3 \, b^{9} c^{2} d^{6} e^{5} + b^{10} c d^{5} e^{6}\right)} x^{5} + {\left(b^{5} c^{6} d^{11} - 9 \, b^{7} c^{4} d^{9} e^{2} + 16 \, b^{8} c^{3} d^{8} e^{3} - 9 \, b^{9} c^{2} d^{7} e^{4} + b^{11} d^{5} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d^{11} - 3 \, b^{7} c^{4} d^{10} e + 2 \, b^{8} c^{3} d^{9} e^{2} + 2 \, b^{9} c^{2} d^{8} e^{3} - 3 \, b^{10} c d^{7} e^{4} + b^{11} d^{6} e^{5}\right)} x^{3} + {\left(b^{7} c^{4} d^{11} - 4 \, b^{8} c^{3} d^{10} e + 6 \, b^{9} c^{2} d^{9} e^{2} - 4 \, b^{10} c d^{8} e^{3} + b^{11} d^{7} e^{4}\right)} x^{2}\right)}}, \frac{3 \, {\left({\left(48 \, c^{8} d^{7} e^{2} - 156 \, b c^{7} d^{6} e^{3} + 143 \, b^{2} c^{6} d^{5} e^{4}\right)} x^{6} + 2 \, {\left(48 \, c^{8} d^{8} e - 108 \, b c^{7} d^{7} e^{2} - 13 \, b^{2} c^{6} d^{6} e^{3} + 143 \, b^{3} c^{5} d^{5} e^{4}\right)} x^{5} + {\left(48 \, c^{8} d^{9} + 36 \, b c^{7} d^{8} e - 433 \, b^{2} c^{6} d^{7} e^{2} + 416 \, b^{3} c^{5} d^{6} e^{3} + 143 \, b^{4} c^{4} d^{5} e^{4}\right)} x^{4} + 2 \, {\left(48 \, b c^{7} d^{9} - 108 \, b^{2} c^{6} d^{8} e - 13 \, b^{3} c^{5} d^{7} e^{2} + 143 \, b^{4} c^{4} d^{6} e^{3}\right)} x^{3} + {\left(48 \, b^{2} c^{6} d^{9} - 156 \, b^{3} c^{5} d^{8} e + 143 \, b^{4} c^{4} d^{7} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{c d - b e}} \arctan\left(-\frac{{\left(c d - b e\right)} \sqrt{e x + d} \sqrt{-\frac{c}{c d - b e}}}{c e x + c d}\right) + 3 \, {\left({\left(48 \, c^{8} d^{6} e^{2} - 132 \, b c^{7} d^{5} e^{3} + 83 \, b^{2} c^{6} d^{4} e^{4} + 28 \, b^{3} c^{5} d^{3} e^{5} + 18 \, b^{4} c^{4} d^{2} e^{6} - 80 \, b^{5} c^{3} d e^{7} + 35 \, b^{6} c^{2} e^{8}\right)} x^{6} + 2 \, {\left(48 \, c^{8} d^{7} e - 84 \, b c^{7} d^{6} e^{2} - 49 \, b^{2} c^{6} d^{5} e^{3} + 111 \, b^{3} c^{5} d^{4} e^{4} + 46 \, b^{4} c^{4} d^{3} e^{5} - 62 \, b^{5} c^{3} d^{2} e^{6} - 45 \, b^{6} c^{2} d e^{7} + 35 \, b^{7} c e^{8}\right)} x^{5} + {\left(48 \, c^{8} d^{8} + 60 \, b c^{7} d^{7} e - 397 \, b^{2} c^{6} d^{6} e^{2} + 228 \, b^{3} c^{5} d^{5} e^{3} + 213 \, b^{4} c^{4} d^{4} e^{4} + 20 \, b^{5} c^{3} d^{3} e^{5} - 267 \, b^{6} c^{2} d^{2} e^{6} + 60 \, b^{7} c d e^{7} + 35 \, b^{8} e^{8}\right)} x^{4} + 2 \, {\left(48 \, b c^{7} d^{8} - 84 \, b^{2} c^{6} d^{7} e - 49 \, b^{3} c^{5} d^{6} e^{2} + 111 \, b^{4} c^{4} d^{5} e^{3} + 46 \, b^{5} c^{3} d^{4} e^{4} - 62 \, b^{6} c^{2} d^{3} e^{5} - 45 \, b^{7} c d^{2} e^{6} + 35 \, b^{8} d e^{7}\right)} x^{3} + {\left(48 \, b^{2} c^{6} d^{8} - 132 \, b^{3} c^{5} d^{7} e + 83 \, b^{4} c^{4} d^{6} e^{2} + 28 \, b^{5} c^{3} d^{5} e^{3} + 18 \, b^{6} c^{2} d^{4} e^{4} - 80 \, b^{7} c d^{3} e^{5} + 35 \, b^{8} d^{2} e^{6}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{e x + d} \sqrt{-d}}{d}\right) - {\left(6 \, b^{4} c^{4} d^{8} - 24 \, b^{5} c^{3} d^{7} e + 36 \, b^{6} c^{2} d^{6} e^{2} - 24 \, b^{7} c d^{5} e^{3} + 6 \, b^{8} d^{4} e^{4} - 3 \, {\left(24 \, b c^{7} d^{6} e^{2} - 60 \, b^{2} c^{6} d^{5} e^{3} + 28 \, b^{3} c^{5} d^{4} e^{4} + 18 \, b^{4} c^{4} d^{3} e^{5} - 80 \, b^{5} c^{3} d^{2} e^{6} + 35 \, b^{6} c^{2} d e^{7}\right)} x^{5} - {\left(144 \, b c^{7} d^{7} e - 252 \, b^{2} c^{6} d^{6} e^{2} - 105 \, b^{3} c^{5} d^{5} e^{3} + 240 \, b^{4} c^{4} d^{4} e^{4} - 212 \, b^{5} c^{3} d^{3} e^{5} - 340 \, b^{6} c^{2} d^{2} e^{6} + 210 \, b^{7} c d e^{7}\right)} x^{4} - {\left(72 \, b c^{7} d^{8} + 36 \, b^{2} c^{6} d^{7} e - 438 \, b^{3} c^{5} d^{6} e^{2} + 255 \, b^{4} c^{4} d^{5} e^{3} + 180 \, b^{5} c^{3} d^{4} e^{4} - 565 \, b^{6} c^{2} d^{3} e^{5} + 40 \, b^{7} c d^{2} e^{6} + 105 \, b^{8} d e^{7}\right)} x^{3} - {\left(108 \, b^{2} c^{6} d^{8} - 225 \, b^{3} c^{5} d^{7} e + 180 \, b^{5} c^{3} d^{5} e^{3} - 30 \, b^{6} c^{2} d^{4} e^{4} - 278 \, b^{7} c d^{3} e^{5} + 140 \, b^{8} d^{2} e^{6}\right)} x^{2} - 3 \, {\left(8 \, b^{3} c^{5} d^{8} - 25 \, b^{4} c^{4} d^{7} e + 20 \, b^{5} c^{3} d^{6} e^{2} + 10 \, b^{6} c^{2} d^{5} e^{3} - 20 \, b^{7} c d^{4} e^{4} + 7 \, b^{8} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left({\left(b^{5} c^{6} d^{9} e^{2} - 4 \, b^{6} c^{5} d^{8} e^{3} + 6 \, b^{7} c^{4} d^{7} e^{4} - 4 \, b^{8} c^{3} d^{6} e^{5} + b^{9} c^{2} d^{5} e^{6}\right)} x^{6} + 2 \, {\left(b^{5} c^{6} d^{10} e - 3 \, b^{6} c^{5} d^{9} e^{2} + 2 \, b^{7} c^{4} d^{8} e^{3} + 2 \, b^{8} c^{3} d^{7} e^{4} - 3 \, b^{9} c^{2} d^{6} e^{5} + b^{10} c d^{5} e^{6}\right)} x^{5} + {\left(b^{5} c^{6} d^{11} - 9 \, b^{7} c^{4} d^{9} e^{2} + 16 \, b^{8} c^{3} d^{8} e^{3} - 9 \, b^{9} c^{2} d^{7} e^{4} + b^{11} d^{5} e^{6}\right)} x^{4} + 2 \, {\left(b^{6} c^{5} d^{11} - 3 \, b^{7} c^{4} d^{10} e + 2 \, b^{8} c^{3} d^{9} e^{2} + 2 \, b^{9} c^{2} d^{8} e^{3} - 3 \, b^{10} c d^{7} e^{4} + b^{11} d^{6} e^{5}\right)} x^{3} + {\left(b^{7} c^{4} d^{11} - 4 \, b^{8} c^{3} d^{10} e + 6 \, b^{9} c^{2} d^{9} e^{2} - 4 \, b^{10} c d^{8} e^{3} + b^{11} d^{7} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/24*(3*((48*c^8*d^7*e^2 - 156*b*c^7*d^6*e^3 + 143*b^2*c^6*d^5*e^4)*x^6 + 2*(48*c^8*d^8*e - 108*b*c^7*d^7*e^2 - 13*b^2*c^6*d^6*e^3 + 143*b^3*c^5*d^5*e^4)*x^5 + (48*c^8*d^9 + 36*b*c^7*d^8*e - 433*b^2*c^6*d^7*e^2 + 416*b^3*c^5*d^6*e^3 + 143*b^4*c^4*d^5*e^4)*x^4 + 2*(48*b*c^7*d^9 - 108*b^2*c^6*d^8*e - 13*b^3*c^5*d^7*e^2 + 143*b^4*c^4*d^6*e^3)*x^3 + (48*b^2*c^6*d^9 - 156*b^3*c^5*d^8*e + 143*b^4*c^4*d^7*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) + 3*((48*c^8*d^6*e^2 - 132*b*c^7*d^5*e^3 + 83*b^2*c^6*d^4*e^4 + 28*b^3*c^5*d^3*e^5 + 18*b^4*c^4*d^2*e^6 - 80*b^5*c^3*d*e^7 + 35*b^6*c^2*e^8)*x^6 + 2*(48*c^8*d^7*e - 84*b*c^7*d^6*e^2 - 49*b^2*c^6*d^5*e^3 + 111*b^3*c^5*d^4*e^4 + 46*b^4*c^4*d^3*e^5 - 62*b^5*c^3*d^2*e^6 - 45*b^6*c^2*d*e^7 + 35*b^7*c*e^8)*x^5 + (48*c^8*d^8 + 60*b*c^7*d^7*e - 397*b^2*c^6*d^6*e^2 + 228*b^3*c^5*d^5*e^3 + 213*b^4*c^4*d^4*e^4 + 20*b^5*c^3*d^3*e^5 - 267*b^6*c^2*d^2*e^6 + 60*b^7*c*d*e^7 + 35*b^8*e^8)*x^4 + 2*(48*b*c^7*d^8 - 84*b^2*c^6*d^7*e - 49*b^3*c^5*d^6*e^2 + 111*b^4*c^4*d^5*e^3 + 46*b^5*c^3*d^4*e^4 - 62*b^6*c^2*d^3*e^5 - 45*b^7*c*d^2*e^6 + 35*b^8*d*e^7)*x^3 + (48*b^2*c^6*d^8 - 132*b^3*c^5*d^7*e + 83*b^4*c^4*d^6*e^2 + 28*b^5*c^3*d^5*e^3 + 18*b^6*c^2*d^4*e^4 - 80*b^7*c*d^3*e^5 + 35*b^8*d^2*e^6)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(6*b^4*c^4*d^8 - 24*b^5*c^3*d^7*e + 36*b^6*c^2*d^6*e^2 - 24*b^7*c*d^5*e^3 + 6*b^8*d^4*e^4 - 3*(24*b*c^7*d^6*e^2 - 60*b^2*c^6*d^5*e^3 + 28*b^3*c^5*d^4*e^4 + 18*b^4*c^4*d^3*e^5 - 80*b^5*c^3*d^2*e^6 + 35*b^6*c^2*d*e^7)*x^5 - (144*b*c^7*d^7*e - 252*b^2*c^6*d^6*e^2 - 105*b^3*c^5*d^5*e^3 + 240*b^4*c^4*d^4*e^4 - 212*b^5*c^3*d^3*e^5 - 340*b^6*c^2*d^2*e^6 + 210*b^7*c*d*e^7)*x^4 - (72*b*c^7*d^8 + 36*b^2*c^6*d^7*e - 438*b^3*c^5*d^6*e^2 + 255*b^4*c^4*d^5*e^3 + 180*b^5*c^3*d^4*e^4 - 565*b^6*c^2*d^3*e^5 + 40*b^7*c*d^2*e^6 + 105*b^8*d*e^7)*x^3 - (108*b^2*c^6*d^8 - 225*b^3*c^5*d^7*e + 180*b^5*c^3*d^5*e^3 - 30*b^6*c^2*d^4*e^4 - 278*b^7*c*d^3*e^5 + 140*b^8*d^2*e^6)*x^2 - 3*(8*b^3*c^5*d^8 - 25*b^4*c^4*d^7*e + 20*b^5*c^3*d^6*e^2 + 10*b^6*c^2*d^5*e^3 - 20*b^7*c*d^4*e^4 + 7*b^8*d^3*e^5)*x)*sqrt(e*x + d))/((b^5*c^6*d^9*e^2 - 4*b^6*c^5*d^8*e^3 + 6*b^7*c^4*d^7*e^4 - 4*b^8*c^3*d^6*e^5 + b^9*c^2*d^5*e^6)*x^6 + 2*(b^5*c^6*d^10*e - 3*b^6*c^5*d^9*e^2 + 2*b^7*c^4*d^8*e^3 + 2*b^8*c^3*d^7*e^4 - 3*b^9*c^2*d^6*e^5 + b^10*c*d^5*e^6)*x^5 + (b^5*c^6*d^11 - 9*b^7*c^4*d^9*e^2 + 16*b^8*c^3*d^8*e^3 - 9*b^9*c^2*d^7*e^4 + b^11*d^5*e^6)*x^4 + 2*(b^6*c^5*d^11 - 3*b^7*c^4*d^10*e + 2*b^8*c^3*d^9*e^2 + 2*b^9*c^2*d^8*e^3 - 3*b^10*c*d^7*e^4 + b^11*d^6*e^5)*x^3 + (b^7*c^4*d^11 - 4*b^8*c^3*d^10*e + 6*b^9*c^2*d^9*e^2 - 4*b^10*c*d^8*e^3 + b^11*d^7*e^4)*x^2), 1/24*(6*((48*c^8*d^7*e^2 - 156*b*c^7*d^6*e^3 + 143*b^2*c^6*d^5*e^4)*x^6 + 2*(48*c^8*d^8*e - 108*b*c^7*d^7*e^2 - 13*b^2*c^6*d^6*e^3 + 143*b^3*c^5*d^5*e^4)*x^5 + (48*c^8*d^9 + 36*b*c^7*d^8*e - 433*b^2*c^6*d^7*e^2 + 416*b^3*c^5*d^6*e^3 + 143*b^4*c^4*d^5*e^4)*x^4 + 2*(48*b*c^7*d^9 - 108*b^2*c^6*d^8*e - 13*b^3*c^5*d^7*e^2 + 143*b^4*c^4*d^6*e^3)*x^3 + (48*b^2*c^6*d^9 - 156*b^3*c^5*d^8*e + 143*b^4*c^4*d^7*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((48*c^8*d^6*e^2 - 132*b*c^7*d^5*e^3 + 83*b^2*c^6*d^4*e^4 + 28*b^3*c^5*d^3*e^5 + 18*b^4*c^4*d^2*e^6 - 80*b^5*c^3*d*e^7 + 35*b^6*c^2*e^8)*x^6 + 2*(48*c^8*d^7*e - 84*b*c^7*d^6*e^2 - 49*b^2*c^6*d^5*e^3 + 111*b^3*c^5*d^4*e^4 + 46*b^4*c^4*d^3*e^5 - 62*b^5*c^3*d^2*e^6 - 45*b^6*c^2*d*e^7 + 35*b^7*c*e^8)*x^5 + (48*c^8*d^8 + 60*b*c^7*d^7*e - 397*b^2*c^6*d^6*e^2 + 228*b^3*c^5*d^5*e^3 + 213*b^4*c^4*d^4*e^4 + 20*b^5*c^3*d^3*e^5 - 267*b^6*c^2*d^2*e^6 + 60*b^7*c*d*e^7 + 35*b^8*e^8)*x^4 + 2*(48*b*c^7*d^8 - 84*b^2*c^6*d^7*e - 49*b^3*c^5*d^6*e^2 + 111*b^4*c^4*d^5*e^3 + 46*b^5*c^3*d^4*e^4 - 62*b^6*c^2*d^3*e^5 - 45*b^7*c*d^2*e^6 + 35*b^8*d*e^7)*x^3 + (48*b^2*c^6*d^8 - 132*b^3*c^5*d^7*e + 83*b^4*c^4*d^6*e^2 + 28*b^5*c^3*d^5*e^3 + 18*b^6*c^2*d^4*e^4 - 80*b^7*c*d^3*e^5 + 35*b^8*d^2*e^6)*x^2)*sqrt(d)*log((e*x - 2*sqrt(e*x + d)*sqrt(d) + 2*d)/x) - 2*(6*b^4*c^4*d^8 - 24*b^5*c^3*d^7*e + 36*b^6*c^2*d^6*e^2 - 24*b^7*c*d^5*e^3 + 6*b^8*d^4*e^4 - 3*(24*b*c^7*d^6*e^2 - 60*b^2*c^6*d^5*e^3 + 28*b^3*c^5*d^4*e^4 + 18*b^4*c^4*d^3*e^5 - 80*b^5*c^3*d^2*e^6 + 35*b^6*c^2*d*e^7)*x^5 - (144*b*c^7*d^7*e - 252*b^2*c^6*d^6*e^2 - 105*b^3*c^5*d^5*e^3 + 240*b^4*c^4*d^4*e^4 - 212*b^5*c^3*d^3*e^5 - 340*b^6*c^2*d^2*e^6 + 210*b^7*c*d*e^7)*x^4 - (72*b*c^7*d^8 + 36*b^2*c^6*d^7*e - 438*b^3*c^5*d^6*e^2 + 255*b^4*c^4*d^5*e^3 + 180*b^5*c^3*d^4*e^4 - 565*b^6*c^2*d^3*e^5 + 40*b^7*c*d^2*e^6 + 105*b^8*d*e^7)*x^3 - (108*b^2*c^6*d^8 - 225*b^3*c^5*d^7*e + 180*b^5*c^3*d^5*e^3 - 30*b^6*c^2*d^4*e^4 - 278*b^7*c*d^3*e^5 + 140*b^8*d^2*e^6)*x^2 - 3*(8*b^3*c^5*d^8 - 25*b^4*c^4*d^7*e + 20*b^5*c^3*d^6*e^2 + 10*b^6*c^2*d^5*e^3 - 20*b^7*c*d^4*e^4 + 7*b^8*d^3*e^5)*x)*sqrt(e*x + d))/((b^5*c^6*d^9*e^2 - 4*b^6*c^5*d^8*e^3 + 6*b^7*c^4*d^7*e^4 - 4*b^8*c^3*d^6*e^5 + b^9*c^2*d^5*e^6)*x^6 + 2*(b^5*c^6*d^10*e - 3*b^6*c^5*d^9*e^2 + 2*b^7*c^4*d^8*e^3 + 2*b^8*c^3*d^7*e^4 - 3*b^9*c^2*d^6*e^5 + b^10*c*d^5*e^6)*x^5 + (b^5*c^6*d^11 - 9*b^7*c^4*d^9*e^2 + 16*b^8*c^3*d^8*e^3 - 9*b^9*c^2*d^7*e^4 + b^11*d^5*e^6)*x^4 + 2*(b^6*c^5*d^11 - 3*b^7*c^4*d^10*e + 2*b^8*c^3*d^9*e^2 + 2*b^9*c^2*d^8*e^3 - 3*b^10*c*d^7*e^4 + b^11*d^6*e^5)*x^3 + (b^7*c^4*d^11 - 4*b^8*c^3*d^10*e + 6*b^9*c^2*d^9*e^2 - 4*b^10*c*d^8*e^3 + b^11*d^7*e^4)*x^2), 1/24*(6*((48*c^8*d^6*e^2 - 132*b*c^7*d^5*e^3 + 83*b^2*c^6*d^4*e^4 + 28*b^3*c^5*d^3*e^5 + 18*b^4*c^4*d^2*e^6 - 80*b^5*c^3*d*e^7 + 35*b^6*c^2*e^8)*x^6 + 2*(48*c^8*d^7*e - 84*b*c^7*d^6*e^2 - 49*b^2*c^6*d^5*e^3 + 111*b^3*c^5*d^4*e^4 + 46*b^4*c^4*d^3*e^5 - 62*b^5*c^3*d^2*e^6 - 45*b^6*c^2*d*e^7 + 35*b^7*c*e^8)*x^5 + (48*c^8*d^8 + 60*b*c^7*d^7*e - 397*b^2*c^6*d^6*e^2 + 228*b^3*c^5*d^5*e^3 + 213*b^4*c^4*d^4*e^4 + 20*b^5*c^3*d^3*e^5 - 267*b^6*c^2*d^2*e^6 + 60*b^7*c*d*e^7 + 35*b^8*e^8)*x^4 + 2*(48*b*c^7*d^8 - 84*b^2*c^6*d^7*e - 49*b^3*c^5*d^6*e^2 + 111*b^4*c^4*d^5*e^3 + 46*b^5*c^3*d^4*e^4 - 62*b^6*c^2*d^3*e^5 - 45*b^7*c*d^2*e^6 + 35*b^8*d*e^7)*x^3 + (48*b^2*c^6*d^8 - 132*b^3*c^5*d^7*e + 83*b^4*c^4*d^6*e^2 + 28*b^5*c^3*d^5*e^3 + 18*b^6*c^2*d^4*e^4 - 80*b^7*c*d^3*e^5 + 35*b^8*d^2*e^6)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) + 3*((48*c^8*d^7*e^2 - 156*b*c^7*d^6*e^3 + 143*b^2*c^6*d^5*e^4)*x^6 + 2*(48*c^8*d^8*e - 108*b*c^7*d^7*e^2 - 13*b^2*c^6*d^6*e^3 + 143*b^3*c^5*d^5*e^4)*x^5 + (48*c^8*d^9 + 36*b*c^7*d^8*e - 433*b^2*c^6*d^7*e^2 + 416*b^3*c^5*d^6*e^3 + 143*b^4*c^4*d^5*e^4)*x^4 + 2*(48*b*c^7*d^9 - 108*b^2*c^6*d^8*e - 13*b^3*c^5*d^7*e^2 + 143*b^4*c^4*d^6*e^3)*x^3 + (48*b^2*c^6*d^9 - 156*b^3*c^5*d^8*e + 143*b^4*c^4*d^7*e^2)*x^2)*sqrt(c/(c*d - b*e))*log((c*e*x + 2*c*d - b*e + 2*(c*d - b*e)*sqrt(e*x + d)*sqrt(c/(c*d - b*e)))/(c*x + b)) - 2*(6*b^4*c^4*d^8 - 24*b^5*c^3*d^7*e + 36*b^6*c^2*d^6*e^2 - 24*b^7*c*d^5*e^3 + 6*b^8*d^4*e^4 - 3*(24*b*c^7*d^6*e^2 - 60*b^2*c^6*d^5*e^3 + 28*b^3*c^5*d^4*e^4 + 18*b^4*c^4*d^3*e^5 - 80*b^5*c^3*d^2*e^6 + 35*b^6*c^2*d*e^7)*x^5 - (144*b*c^7*d^7*e - 252*b^2*c^6*d^6*e^2 - 105*b^3*c^5*d^5*e^3 + 240*b^4*c^4*d^4*e^4 - 212*b^5*c^3*d^3*e^5 - 340*b^6*c^2*d^2*e^6 + 210*b^7*c*d*e^7)*x^4 - (72*b*c^7*d^8 + 36*b^2*c^6*d^7*e - 438*b^3*c^5*d^6*e^2 + 255*b^4*c^4*d^5*e^3 + 180*b^5*c^3*d^4*e^4 - 565*b^6*c^2*d^3*e^5 + 40*b^7*c*d^2*e^6 + 105*b^8*d*e^7)*x^3 - (108*b^2*c^6*d^8 - 225*b^3*c^5*d^7*e + 180*b^5*c^3*d^5*e^3 - 30*b^6*c^2*d^4*e^4 - 278*b^7*c*d^3*e^5 + 140*b^8*d^2*e^6)*x^2 - 3*(8*b^3*c^5*d^8 - 25*b^4*c^4*d^7*e + 20*b^5*c^3*d^6*e^2 + 10*b^6*c^2*d^5*e^3 - 20*b^7*c*d^4*e^4 + 7*b^8*d^3*e^5)*x)*sqrt(e*x + d))/((b^5*c^6*d^9*e^2 - 4*b^6*c^5*d^8*e^3 + 6*b^7*c^4*d^7*e^4 - 4*b^8*c^3*d^6*e^5 + b^9*c^2*d^5*e^6)*x^6 + 2*(b^5*c^6*d^10*e - 3*b^6*c^5*d^9*e^2 + 2*b^7*c^4*d^8*e^3 + 2*b^8*c^3*d^7*e^4 - 3*b^9*c^2*d^6*e^5 + b^10*c*d^5*e^6)*x^5 + (b^5*c^6*d^11 - 9*b^7*c^4*d^9*e^2 + 16*b^8*c^3*d^8*e^3 - 9*b^9*c^2*d^7*e^4 + b^11*d^5*e^6)*x^4 + 2*(b^6*c^5*d^11 - 3*b^7*c^4*d^10*e + 2*b^8*c^3*d^9*e^2 + 2*b^9*c^2*d^8*e^3 - 3*b^10*c*d^7*e^4 + b^11*d^6*e^5)*x^3 + (b^7*c^4*d^11 - 4*b^8*c^3*d^10*e + 6*b^9*c^2*d^9*e^2 - 4*b^10*c*d^8*e^3 + b^11*d^7*e^4)*x^2), 1/12*(3*((48*c^8*d^7*e^2 - 156*b*c^7*d^6*e^3 + 143*b^2*c^6*d^5*e^4)*x^6 + 2*(48*c^8*d^8*e - 108*b*c^7*d^7*e^2 - 13*b^2*c^6*d^6*e^3 + 143*b^3*c^5*d^5*e^4)*x^5 + (48*c^8*d^9 + 36*b*c^7*d^8*e - 433*b^2*c^6*d^7*e^2 + 416*b^3*c^5*d^6*e^3 + 143*b^4*c^4*d^5*e^4)*x^4 + 2*(48*b*c^7*d^9 - 108*b^2*c^6*d^8*e - 13*b^3*c^5*d^7*e^2 + 143*b^4*c^4*d^6*e^3)*x^3 + (48*b^2*c^6*d^9 - 156*b^3*c^5*d^8*e + 143*b^4*c^4*d^7*e^2)*x^2)*sqrt(-c/(c*d - b*e))*arctan(-(c*d - b*e)*sqrt(e*x + d)*sqrt(-c/(c*d - b*e))/(c*e*x + c*d)) + 3*((48*c^8*d^6*e^2 - 132*b*c^7*d^5*e^3 + 83*b^2*c^6*d^4*e^4 + 28*b^3*c^5*d^3*e^5 + 18*b^4*c^4*d^2*e^6 - 80*b^5*c^3*d*e^7 + 35*b^6*c^2*e^8)*x^6 + 2*(48*c^8*d^7*e - 84*b*c^7*d^6*e^2 - 49*b^2*c^6*d^5*e^3 + 111*b^3*c^5*d^4*e^4 + 46*b^4*c^4*d^3*e^5 - 62*b^5*c^3*d^2*e^6 - 45*b^6*c^2*d*e^7 + 35*b^7*c*e^8)*x^5 + (48*c^8*d^8 + 60*b*c^7*d^7*e - 397*b^2*c^6*d^6*e^2 + 228*b^3*c^5*d^5*e^3 + 213*b^4*c^4*d^4*e^4 + 20*b^5*c^3*d^3*e^5 - 267*b^6*c^2*d^2*e^6 + 60*b^7*c*d*e^7 + 35*b^8*e^8)*x^4 + 2*(48*b*c^7*d^8 - 84*b^2*c^6*d^7*e - 49*b^3*c^5*d^6*e^2 + 111*b^4*c^4*d^5*e^3 + 46*b^5*c^3*d^4*e^4 - 62*b^6*c^2*d^3*e^5 - 45*b^7*c*d^2*e^6 + 35*b^8*d*e^7)*x^3 + (48*b^2*c^6*d^8 - 132*b^3*c^5*d^7*e + 83*b^4*c^4*d^6*e^2 + 28*b^5*c^3*d^5*e^3 + 18*b^6*c^2*d^4*e^4 - 80*b^7*c*d^3*e^5 + 35*b^8*d^2*e^6)*x^2)*sqrt(-d)*arctan(sqrt(e*x + d)*sqrt(-d)/d) - (6*b^4*c^4*d^8 - 24*b^5*c^3*d^7*e + 36*b^6*c^2*d^6*e^2 - 24*b^7*c*d^5*e^3 + 6*b^8*d^4*e^4 - 3*(24*b*c^7*d^6*e^2 - 60*b^2*c^6*d^5*e^3 + 28*b^3*c^5*d^4*e^4 + 18*b^4*c^4*d^3*e^5 - 80*b^5*c^3*d^2*e^6 + 35*b^6*c^2*d*e^7)*x^5 - (144*b*c^7*d^7*e - 252*b^2*c^6*d^6*e^2 - 105*b^3*c^5*d^5*e^3 + 240*b^4*c^4*d^4*e^4 - 212*b^5*c^3*d^3*e^5 - 340*b^6*c^2*d^2*e^6 + 210*b^7*c*d*e^7)*x^4 - (72*b*c^7*d^8 + 36*b^2*c^6*d^7*e - 438*b^3*c^5*d^6*e^2 + 255*b^4*c^4*d^5*e^3 + 180*b^5*c^3*d^4*e^4 - 565*b^6*c^2*d^3*e^5 + 40*b^7*c*d^2*e^6 + 105*b^8*d*e^7)*x^3 - (108*b^2*c^6*d^8 - 225*b^3*c^5*d^7*e + 180*b^5*c^3*d^5*e^3 - 30*b^6*c^2*d^4*e^4 - 278*b^7*c*d^3*e^5 + 140*b^8*d^2*e^6)*x^2 - 3*(8*b^3*c^5*d^8 - 25*b^4*c^4*d^7*e + 20*b^5*c^3*d^6*e^2 + 10*b^6*c^2*d^5*e^3 - 20*b^7*c*d^4*e^4 + 7*b^8*d^3*e^5)*x)*sqrt(e*x + d))/((b^5*c^6*d^9*e^2 - 4*b^6*c^5*d^8*e^3 + 6*b^7*c^4*d^7*e^4 - 4*b^8*c^3*d^6*e^5 + b^9*c^2*d^5*e^6)*x^6 + 2*(b^5*c^6*d^10*e - 3*b^6*c^5*d^9*e^2 + 2*b^7*c^4*d^8*e^3 + 2*b^8*c^3*d^7*e^4 - 3*b^9*c^2*d^6*e^5 + b^10*c*d^5*e^6)*x^5 + (b^5*c^6*d^11 - 9*b^7*c^4*d^9*e^2 + 16*b^8*c^3*d^8*e^3 - 9*b^9*c^2*d^7*e^4 + b^11*d^5*e^6)*x^4 + 2*(b^6*c^5*d^11 - 3*b^7*c^4*d^10*e + 2*b^8*c^3*d^9*e^2 + 2*b^9*c^2*d^8*e^3 - 3*b^10*c*d^7*e^4 + b^11*d^6*e^5)*x^3 + (b^7*c^4*d^11 - 4*b^8*c^3*d^10*e + 6*b^9*c^2*d^9*e^2 - 4*b^10*c*d^8*e^3 + b^11*d^7*e^4)*x^2)]","B",0
386,0,0,0,0.487958," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(e*x + d)^(3/2), x)","F",0
387,0,0,0,0.475250," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x} \sqrt{e x + d}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d), x)","F",0
388,0,0,0,0.474116," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x}}{\sqrt{e x + d}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)/sqrt(e*x + d), x)","F",0
389,0,0,0,0.472995," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
390,0,0,0,0.411834," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
391,0,0,0,0.410976," ","integrate((c*x^2+b*x)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
392,0,0,0,0.504223," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e x^{3} + b d x + {\left(c d + b e\right)} x^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}, x\right)"," ",0,"integral((c*e*x^3 + b*d*x + (c*d + b*e)*x^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d), x)","F",0
393,0,0,0,0.484809," ","integrate((c*x^2+b*x)^(3/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x\right)}^{\frac{3}{2}} \sqrt{e x + d}, x\right)"," ",0,"integral((c*x^2 + b*x)^(3/2)*sqrt(e*x + d), x)","F",0
394,0,0,0,0.470862," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((c*x^2 + b*x)^(3/2)/sqrt(e*x + d), x)","F",0
395,0,0,0,0.484772," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x)^(3/2)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
396,0,0,0,0.483741," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c*x^2 + b*x)^(3/2)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
397,0,0,0,0.518050," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((c*x^2 + b*x)^(3/2)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
398,0,0,0,0.434916," ","integrate((c*x^2+b*x)^(3/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{5} x^{5} + 5 \, d e^{4} x^{4} + 10 \, d^{2} e^{3} x^{3} + 10 \, d^{3} e^{2} x^{2} + 5 \, d^{4} e x + d^{5}}, x\right)"," ",0,"integral((c*x^2 + b*x)^(3/2)*sqrt(e*x + d)/(e^5*x^5 + 5*d*e^4*x^4 + 10*d^2*e^3*x^3 + 10*d^3*e^2*x^2 + 5*d^4*e*x + d^5), x)","F",0
399,0,0,0,0.521138," ","integrate((c*x^2+b*x)^(5/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + b^2*x^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d), x)","F",0
400,0,0,0,0.500144," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}\right)} \sqrt{c x^{2} + b x}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + b^2*x^2)*sqrt(c*x^2 + b*x)/sqrt(e*x + d), x)","F",0
401,0,0,0,0.522497," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + b^2*x^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
402,0,0,0,0.522137," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + b^2*x^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
403,0,0,0,0.545979," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + b^2*x^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
404,0,0,0,0.591822," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{5} x^{5} + 5 \, d e^{4} x^{4} + 10 \, d^{2} e^{3} x^{3} + 10 \, d^{3} e^{2} x^{2} + 5 \, d^{4} e x + d^{5}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + b^2*x^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^5*x^5 + 5*d*e^4*x^4 + 10*d^2*e^3*x^3 + 10*d^3*e^2*x^2 + 5*d^4*e*x + d^5), x)","F",0
405,0,0,0,0.694171," ","integrate((c*x^2+b*x)^(5/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{e^{6} x^{6} + 6 \, d e^{5} x^{5} + 15 \, d^{2} e^{4} x^{4} + 20 \, d^{3} e^{3} x^{3} + 15 \, d^{4} e^{2} x^{2} + 6 \, d^{5} e x + d^{6}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + b^2*x^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(e^6*x^6 + 6*d*e^5*x^5 + 15*d^2*e^4*x^4 + 20*d^3*e^3*x^3 + 15*d^4*e^2*x^2 + 6*d^5*e*x + d^6), x)","F",0
406,0,0,0,0.489454," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(e*x + d)/sqrt(c*x^2 + b*x), x)","F",0
407,0,0,0,0.487960," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(e*x + d)/sqrt(c*x^2 + b*x), x)","F",0
408,0,0,0,0.485990," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x}}, x\right)"," ",0,"integral((e*x + d)^(3/2)/sqrt(c*x^2 + b*x), x)","F",0
409,0,0,0,0.491694," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x + d}}{\sqrt{c x^{2} + b x}}, x\right)"," ",0,"integral(sqrt(e*x + d)/sqrt(c*x^2 + b*x), x)","F",0
410,0,0,0,0.425421," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c e x^{3} + b d x + {\left(c d + b e\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c*e*x^3 + b*d*x + (c*d + b*e)*x^2), x)","F",0
411,0,0,0,0.420901," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c e^{2} x^{4} + b d^{2} x + {\left(2 \, c d e + b e^{2}\right)} x^{3} + {\left(c d^{2} + 2 \, b d e\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c*e^2*x^4 + b*d^2*x + (2*c*d*e + b*e^2)*x^3 + (c*d^2 + 2*b*d*e)*x^2), x)","F",0
412,0,0,0,0.431671," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c e^{3} x^{5} + b d^{3} x + {\left(3 \, c d e^{2} + b e^{3}\right)} x^{4} + 3 \, {\left(c d^{2} e + b d e^{2}\right)} x^{3} + {\left(c d^{3} + 3 \, b d^{2} e\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c*e^3*x^5 + b*d^3*x + (3*c*d*e^2 + b*e^3)*x^4 + 3*(c*d^2*e + b*d*e^2)*x^3 + (c*d^3 + 3*b*d^2*e)*x^2), x)","F",0
413,0,0,0,0.416931," ","integrate(1/(e*x+d)^(7/2)/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c e^{4} x^{6} + b d^{4} x + {\left(4 \, c d e^{3} + b e^{4}\right)} x^{5} + 2 \, {\left(3 \, c d^{2} e^{2} + 2 \, b d e^{3}\right)} x^{4} + 2 \, {\left(2 \, c d^{3} e + 3 \, b d^{2} e^{2}\right)} x^{3} + {\left(c d^{4} + 4 \, b d^{3} e\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c*e^4*x^6 + b*d^4*x + (4*c*d*e^3 + b*e^4)*x^5 + 2*(3*c*d^2*e^2 + 2*b*d*e^3)*x^4 + 2*(2*c*d^3*e + 3*b*d^2*e^2)*x^3 + (c*d^4 + 4*b*d^3*e)*x^2), x)","F",0
414,0,0,0,0.522912," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
415,0,0,0,0.502449," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
416,0,0,0,0.430023," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{\frac{3}{2}}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(e*x + d)^(3/2)/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
417,0,0,0,0.419570," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
418,0,0,0,0.427498," ","integrate(1/(c*x^2+b*x)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{2} e x^{5} + b^{2} d x^{2} + {\left(c^{2} d + 2 \, b c e\right)} x^{4} + {\left(2 \, b c d + b^{2} e\right)} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^2*e*x^5 + b^2*d*x^2 + (c^2*d + 2*b*c*e)*x^4 + (2*b*c*d + b^2*e)*x^3), x)","F",0
419,0,0,0,0.419829," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{2} e^{2} x^{6} + b^{2} d^{2} x^{2} + 2 \, {\left(c^{2} d e + b c e^{2}\right)} x^{5} + {\left(c^{2} d^{2} + 4 \, b c d e + b^{2} e^{2}\right)} x^{4} + 2 \, {\left(b c d^{2} + b^{2} d e\right)} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^2*e^2*x^6 + b^2*d^2*x^2 + 2*(c^2*d*e + b*c*e^2)*x^5 + (c^2*d^2 + 4*b*c*d*e + b^2*e^2)*x^4 + 2*(b*c*d^2 + b^2*d*e)*x^3), x)","F",0
420,0,0,0,0.443793," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{2} e^{3} x^{7} + b^{2} d^{3} x^{2} + {\left(3 \, c^{2} d e^{2} + 2 \, b c e^{3}\right)} x^{6} + {\left(3 \, c^{2} d^{2} e + 6 \, b c d e^{2} + b^{2} e^{3}\right)} x^{5} + {\left(c^{2} d^{3} + 6 \, b c d^{2} e + 3 \, b^{2} d e^{2}\right)} x^{4} + {\left(2 \, b c d^{3} + 3 \, b^{2} d^{2} e\right)} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^2*e^3*x^7 + b^2*d^3*x^2 + (3*c^2*d*e^2 + 2*b*c*e^3)*x^6 + (3*c^2*d^2*e + 6*b*c*d*e^2 + b^2*e^3)*x^5 + (c^2*d^3 + 6*b*c*d^2*e + 3*b^2*d*e^2)*x^4 + (2*b*c*d^3 + 3*b^2*d^2*e)*x^3), x)","F",0
421,0,0,0,0.535881," ","integrate((e*x+d)^(9/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral((e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
422,0,0,0,0.426668," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
423,0,0,0,0.424144," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
424,0,0,0,0.412972," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{\frac{3}{2}}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(e*x + d)^(3/2)/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
425,0,0,0,0.434067," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
426,0,0,0,0.440710," ","integrate(1/(c*x^2+b*x)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{3} e x^{7} + b^{3} d x^{3} + {\left(c^{3} d + 3 \, b c^{2} e\right)} x^{6} + 3 \, {\left(b c^{2} d + b^{2} c e\right)} x^{5} + {\left(3 \, b^{2} c d + b^{3} e\right)} x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^3*e*x^7 + b^3*d*x^3 + (c^3*d + 3*b*c^2*e)*x^6 + 3*(b*c^2*d + b^2*c*e)*x^5 + (3*b^2*c*d + b^3*e)*x^4), x)","F",0
427,0,0,0,0.457829," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} \sqrt{e x + d}}{c^{3} e^{2} x^{8} + b^{3} d^{2} x^{3} + {\left(2 \, c^{3} d e + 3 \, b c^{2} e^{2}\right)} x^{7} + {\left(c^{3} d^{2} + 6 \, b c^{2} d e + 3 \, b^{2} c e^{2}\right)} x^{6} + {\left(3 \, b c^{2} d^{2} + 6 \, b^{2} c d e + b^{3} e^{2}\right)} x^{5} + {\left(3 \, b^{2} c d^{2} + 2 \, b^{3} d e\right)} x^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*sqrt(e*x + d)/(c^3*e^2*x^8 + b^3*d^2*x^3 + (2*c^3*d*e + 3*b*c^2*e^2)*x^7 + (c^3*d^2 + 6*b*c^2*d*e + 3*b^2*c*e^2)*x^6 + (3*b*c^2*d^2 + 6*b^2*c*d*e + b^3*e^2)*x^5 + (3*b^2*c*d^2 + 2*b^3*d*e)*x^4), x)","F",0
428,0,0,0,0.422337," ","integrate((e*x+d)^(1/2)/(-3*x^2+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x + d} \sqrt{-3 \, x^{2} + 2 \, x}}{3 \, x^{2} - 2 \, x}, x\right)"," ",0,"integral(-sqrt(e*x + d)*sqrt(-3*x^2 + 2*x)/(3*x^2 - 2*x), x)","F",0
429,0,0,0,0.406428," ","integrate(1/(e*x+d)^(1/2)/(-3*x^2+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x + d} \sqrt{-3 \, x^{2} + 2 \, x}}{3 \, e x^{3} + {\left(3 \, d - 2 \, e\right)} x^{2} - 2 \, d x}, x\right)"," ",0,"integral(-sqrt(e*x + d)*sqrt(-3*x^2 + 2*x)/(3*e*x^3 + (3*d - 2*e)*x^2 - 2*d*x), x)","F",0
430,0,0,0,0.414992," ","integrate((e*x+d)^(1/2)/(-3*x^2-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x + d} \sqrt{-3 \, x^{2} - 2 \, x}}{3 \, x^{2} + 2 \, x}, x\right)"," ",0,"integral(-sqrt(e*x + d)*sqrt(-3*x^2 - 2*x)/(3*x^2 + 2*x), x)","F",0
431,0,0,0,0.418902," ","integrate(1/(e*x+d)^(1/2)/(-3*x^2-2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{e x + d} \sqrt{-3 \, x^{2} - 2 \, x}}{3 \, e x^{3} + {\left(3 \, d + 2 \, e\right)} x^{2} + 2 \, d x}, x\right)"," ",0,"integral(-sqrt(e*x + d)*sqrt(-3*x^2 - 2*x)/(3*e*x^3 + (3*d + 2*e)*x^2 + 2*d*x), x)","F",0
432,0,0,0,0.420971," ","integrate((1-x)^(1/2)/(-x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x} \sqrt{x + 1} \sqrt{-x + 1}}{x^{2} + x}, x\right)"," ",0,"integral(-sqrt(-x)*sqrt(x + 1)*sqrt(-x + 1)/(x^2 + x), x)","F",0
433,0,0,0,0.419368," ","integrate((1-x)^(1/2)/(-x^2-x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{2} - x} \sqrt{-x + 1}}{x^{2} + x}, x\right)"," ",0,"integral(-sqrt(-x^2 - x)*sqrt(-x + 1)/(x^2 + x), x)","F",0
434,1,343,0,0.434862," ","integrate((e*x+d)^m*(c*e*x^2+c*d*x)^3,x, algorithm=""fricas"")","\frac{{\left(6 \, c^{3} d^{6} e m x - 6 \, c^{3} d^{7} + {\left(c^{3} e^{7} m^{3} + 15 \, c^{3} e^{7} m^{2} + 74 \, c^{3} e^{7} m + 120 \, c^{3} e^{7}\right)} x^{7} + {\left(4 \, c^{3} d e^{6} m^{3} + 57 \, c^{3} d e^{6} m^{2} + 269 \, c^{3} d e^{6} m + 420 \, c^{3} d e^{6}\right)} x^{6} + 6 \, {\left(c^{3} d^{2} e^{5} m^{3} + 13 \, c^{3} d^{2} e^{5} m^{2} + 57 \, c^{3} d^{2} e^{5} m + 84 \, c^{3} d^{2} e^{5}\right)} x^{5} + 2 \, {\left(2 \, c^{3} d^{3} e^{4} m^{3} + 21 \, c^{3} d^{3} e^{4} m^{2} + 79 \, c^{3} d^{3} e^{4} m + 105 \, c^{3} d^{3} e^{4}\right)} x^{4} + {\left(c^{3} d^{4} e^{3} m^{3} + 3 \, c^{3} d^{4} e^{3} m^{2} + 2 \, c^{3} d^{4} e^{3} m\right)} x^{3} - 3 \, {\left(c^{3} d^{5} e^{2} m^{2} + c^{3} d^{5} e^{2} m\right)} x^{2}\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 22 \, e^{4} m^{3} + 179 \, e^{4} m^{2} + 638 \, e^{4} m + 840 \, e^{4}}"," ",0,"(6*c^3*d^6*e*m*x - 6*c^3*d^7 + (c^3*e^7*m^3 + 15*c^3*e^7*m^2 + 74*c^3*e^7*m + 120*c^3*e^7)*x^7 + (4*c^3*d*e^6*m^3 + 57*c^3*d*e^6*m^2 + 269*c^3*d*e^6*m + 420*c^3*d*e^6)*x^6 + 6*(c^3*d^2*e^5*m^3 + 13*c^3*d^2*e^5*m^2 + 57*c^3*d^2*e^5*m + 84*c^3*d^2*e^5)*x^5 + 2*(2*c^3*d^3*e^4*m^3 + 21*c^3*d^3*e^4*m^2 + 79*c^3*d^3*e^4*m + 105*c^3*d^3*e^4)*x^4 + (c^3*d^4*e^3*m^3 + 3*c^3*d^4*e^3*m^2 + 2*c^3*d^4*e^3*m)*x^3 - 3*(c^3*d^5*e^2*m^2 + c^3*d^5*e^2*m)*x^2)*(e*x + d)^m/(e^4*m^4 + 22*e^4*m^3 + 179*e^4*m^2 + 638*e^4*m + 840*e^4)","B",0
435,1,201,0,0.414077," ","integrate((e*x+d)^m*(c*e*x^2+c*d*x)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, c^{2} d^{4} e m x - 2 \, c^{2} d^{5} - {\left(c^{2} e^{5} m^{2} + 7 \, c^{2} e^{5} m + 12 \, c^{2} e^{5}\right)} x^{5} - {\left(3 \, c^{2} d e^{4} m^{2} + 19 \, c^{2} d e^{4} m + 30 \, c^{2} d e^{4}\right)} x^{4} - {\left(3 \, c^{2} d^{2} e^{3} m^{2} + 15 \, c^{2} d^{2} e^{3} m + 20 \, c^{2} d^{2} e^{3}\right)} x^{3} - {\left(c^{2} d^{3} e^{2} m^{2} + c^{2} d^{3} e^{2} m\right)} x^{2}\right)} {\left(e x + d\right)}^{m}}{e^{3} m^{3} + 12 \, e^{3} m^{2} + 47 \, e^{3} m + 60 \, e^{3}}"," ",0,"-(2*c^2*d^4*e*m*x - 2*c^2*d^5 - (c^2*e^5*m^2 + 7*c^2*e^5*m + 12*c^2*e^5)*x^5 - (3*c^2*d*e^4*m^2 + 19*c^2*d*e^4*m + 30*c^2*d*e^4)*x^4 - (3*c^2*d^2*e^3*m^2 + 15*c^2*d^2*e^3*m + 20*c^2*d^2*e^3)*x^3 - (c^2*d^3*e^2*m^2 + c^2*d^3*e^2*m)*x^2)*(e*x + d)^m/(e^3*m^3 + 12*e^3*m^2 + 47*e^3*m + 60*e^3)","B",0
436,1,81,0,0.411756," ","integrate((e*x+d)^m*(c*e*x^2+c*d*x),x, algorithm=""fricas"")","\frac{{\left(c d^{2} e m x - c d^{3} + {\left(c e^{3} m + 2 \, c e^{3}\right)} x^{3} + {\left(2 \, c d e^{2} m + 3 \, c d e^{2}\right)} x^{2}\right)} {\left(e x + d\right)}^{m}}{e^{2} m^{2} + 5 \, e^{2} m + 6 \, e^{2}}"," ",0,"(c*d^2*e*m*x - c*d^3 + (c*e^3*m + 2*c*e^3)*x^3 + (2*c*d*e^2*m + 3*c*d*e^2)*x^2)*(e*x + d)^m/(e^2*m^2 + 5*e^2*m + 6*e^2)","A",0
437,1,20,0,0.419792," ","integrate((e*x+d)^m,x, algorithm=""fricas"")","\frac{{\left(e x + d\right)} {\left(e x + d\right)}^{m}}{e m + e}"," ",0,"(e*x + d)*(e*x + d)^m/(e*m + e)","A",0
438,0,0,0,0.437558," ","integrate((e*x+d)^m/(c*e*x^2+c*d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c e x^{2} + c d x}, x\right)"," ",0,"integral((e*x + d)^m/(c*e*x^2 + c*d*x), x)","F",0
439,0,0,0,0.426450," ","integrate((e*x+d)^m/(c*e*x^2+c*d*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c^{2} e^{2} x^{4} + 2 \, c^{2} d e x^{3} + c^{2} d^{2} x^{2}}, x\right)"," ",0,"integral((e*x + d)^m/(c^2*e^2*x^4 + 2*c^2*d*e*x^3 + c^2*d^2*x^2), x)","F",0
440,1,1449,0,0.456414," ","integrate((e*x+d)^m*(c*x^2+b*x)^3,x, algorithm=""fricas"")","-\frac{{\left(6 \, b^{3} d^{4} e^{3} m^{3} - 720 \, c^{3} d^{7} + 2520 \, b c^{2} d^{6} e - 3024 \, b^{2} c d^{5} e^{2} + 1260 \, b^{3} d^{4} e^{3} - {\left(c^{3} e^{7} m^{6} + 21 \, c^{3} e^{7} m^{5} + 175 \, c^{3} e^{7} m^{4} + 735 \, c^{3} e^{7} m^{3} + 1624 \, c^{3} e^{7} m^{2} + 1764 \, c^{3} e^{7} m + 720 \, c^{3} e^{7}\right)} x^{7} - {\left(2520 \, b c^{2} e^{7} + {\left(c^{3} d e^{6} + 3 \, b c^{2} e^{7}\right)} m^{6} + 3 \, {\left(5 \, c^{3} d e^{6} + 22 \, b c^{2} e^{7}\right)} m^{5} + 5 \, {\left(17 \, c^{3} d e^{6} + 114 \, b c^{2} e^{7}\right)} m^{4} + 15 \, {\left(15 \, c^{3} d e^{6} + 164 \, b c^{2} e^{7}\right)} m^{3} + {\left(274 \, c^{3} d e^{6} + 5547 \, b c^{2} e^{7}\right)} m^{2} + 6 \, {\left(20 \, c^{3} d e^{6} + 1019 \, b c^{2} e^{7}\right)} m\right)} x^{6} - 3 \, {\left(1008 \, b^{2} c e^{7} + {\left(b c^{2} d e^{6} + b^{2} c e^{7}\right)} m^{6} - {\left(2 \, c^{3} d^{2} e^{5} - 17 \, b c^{2} d e^{6} - 23 \, b^{2} c e^{7}\right)} m^{5} - {\left(20 \, c^{3} d^{2} e^{5} - 105 \, b c^{2} d e^{6} - 207 \, b^{2} c e^{7}\right)} m^{4} - 5 \, {\left(14 \, c^{3} d^{2} e^{5} - 59 \, b c^{2} d e^{6} - 185 \, b^{2} c e^{7}\right)} m^{3} - 2 \, {\left(50 \, c^{3} d^{2} e^{5} - 187 \, b c^{2} d e^{6} - 1072 \, b^{2} c e^{7}\right)} m^{2} - 12 \, {\left(4 \, c^{3} d^{2} e^{5} - 14 \, b c^{2} d e^{6} - 201 \, b^{2} c e^{7}\right)} m\right)} x^{5} - {\left(1260 \, b^{3} e^{7} + {\left(3 \, b^{2} c d e^{6} + b^{3} e^{7}\right)} m^{6} - 3 \, {\left(5 \, b c^{2} d^{2} e^{5} - 19 \, b^{2} c d e^{6} - 8 \, b^{3} e^{7}\right)} m^{5} + {\left(30 \, c^{3} d^{3} e^{4} - 195 \, b c^{2} d^{2} e^{5} + 393 \, b^{2} c d e^{6} + 226 \, b^{3} e^{7}\right)} m^{4} + 3 \, {\left(60 \, c^{3} d^{3} e^{4} - 265 \, b c^{2} d^{2} e^{5} + 401 \, b^{2} c d e^{6} + 352 \, b^{3} e^{7}\right)} m^{3} + 5 \, {\left(66 \, c^{3} d^{3} e^{4} - 249 \, b c^{2} d^{2} e^{5} + 324 \, b^{2} c d e^{6} + 509 \, b^{3} e^{7}\right)} m^{2} + 18 \, {\left(10 \, c^{3} d^{3} e^{4} - 35 \, b c^{2} d^{2} e^{5} + 42 \, b^{2} c d e^{6} + 164 \, b^{3} e^{7}\right)} m\right)} x^{4} - {\left(b^{3} d e^{6} m^{6} - 3 \, {\left(4 \, b^{2} c d^{2} e^{5} - 7 \, b^{3} d e^{6}\right)} m^{5} + {\left(60 \, b c^{2} d^{3} e^{4} - 192 \, b^{2} c d^{2} e^{5} + 163 \, b^{3} d e^{6}\right)} m^{4} - 3 \, {\left(40 \, c^{3} d^{4} e^{3} - 200 \, b c^{2} d^{3} e^{4} + 332 \, b^{2} c d^{2} e^{5} - 189 \, b^{3} d e^{6}\right)} m^{3} - 4 \, {\left(90 \, c^{3} d^{4} e^{3} - 345 \, b c^{2} d^{3} e^{4} + 456 \, b^{2} c d^{2} e^{5} - 211 \, b^{3} d e^{6}\right)} m^{2} - 12 \, {\left(20 \, c^{3} d^{4} e^{3} - 70 \, b c^{2} d^{3} e^{4} + 84 \, b^{2} c d^{2} e^{5} - 35 \, b^{3} d e^{6}\right)} m\right)} x^{3} - 36 \, {\left(2 \, b^{2} c d^{5} e^{2} - 3 \, b^{3} d^{4} e^{3}\right)} m^{2} + 3 \, {\left(b^{3} d^{2} e^{5} m^{5} - {\left(12 \, b^{2} c d^{3} e^{4} - 19 \, b^{3} d^{2} e^{5}\right)} m^{4} + {\left(60 \, b c^{2} d^{4} e^{3} - 168 \, b^{2} c d^{3} e^{4} + 125 \, b^{3} d^{2} e^{5}\right)} m^{3} - {\left(120 \, c^{3} d^{5} e^{2} - 480 \, b c^{2} d^{4} e^{3} + 660 \, b^{2} c d^{3} e^{4} - 317 \, b^{3} d^{2} e^{5}\right)} m^{2} - 6 \, {\left(20 \, c^{3} d^{5} e^{2} - 70 \, b c^{2} d^{4} e^{3} + 84 \, b^{2} c d^{3} e^{4} - 35 \, b^{3} d^{2} e^{5}\right)} m\right)} x^{2} + 6 \, {\left(60 \, b c^{2} d^{6} e - 156 \, b^{2} c d^{5} e^{2} + 107 \, b^{3} d^{4} e^{3}\right)} m - 6 \, {\left(b^{3} d^{3} e^{4} m^{4} - 6 \, {\left(2 \, b^{2} c d^{4} e^{3} - 3 \, b^{3} d^{3} e^{4}\right)} m^{3} + {\left(60 \, b c^{2} d^{5} e^{2} - 156 \, b^{2} c d^{4} e^{3} + 107 \, b^{3} d^{3} e^{4}\right)} m^{2} - 6 \, {\left(20 \, c^{3} d^{6} e - 70 \, b c^{2} d^{5} e^{2} + 84 \, b^{2} c d^{4} e^{3} - 35 \, b^{3} d^{3} e^{4}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{7} m^{7} + 28 \, e^{7} m^{6} + 322 \, e^{7} m^{5} + 1960 \, e^{7} m^{4} + 6769 \, e^{7} m^{3} + 13132 \, e^{7} m^{2} + 13068 \, e^{7} m + 5040 \, e^{7}}"," ",0,"-(6*b^3*d^4*e^3*m^3 - 720*c^3*d^7 + 2520*b*c^2*d^6*e - 3024*b^2*c*d^5*e^2 + 1260*b^3*d^4*e^3 - (c^3*e^7*m^6 + 21*c^3*e^7*m^5 + 175*c^3*e^7*m^4 + 735*c^3*e^7*m^3 + 1624*c^3*e^7*m^2 + 1764*c^3*e^7*m + 720*c^3*e^7)*x^7 - (2520*b*c^2*e^7 + (c^3*d*e^6 + 3*b*c^2*e^7)*m^6 + 3*(5*c^3*d*e^6 + 22*b*c^2*e^7)*m^5 + 5*(17*c^3*d*e^6 + 114*b*c^2*e^7)*m^4 + 15*(15*c^3*d*e^6 + 164*b*c^2*e^7)*m^3 + (274*c^3*d*e^6 + 5547*b*c^2*e^7)*m^2 + 6*(20*c^3*d*e^6 + 1019*b*c^2*e^7)*m)*x^6 - 3*(1008*b^2*c*e^7 + (b*c^2*d*e^6 + b^2*c*e^7)*m^6 - (2*c^3*d^2*e^5 - 17*b*c^2*d*e^6 - 23*b^2*c*e^7)*m^5 - (20*c^3*d^2*e^5 - 105*b*c^2*d*e^6 - 207*b^2*c*e^7)*m^4 - 5*(14*c^3*d^2*e^5 - 59*b*c^2*d*e^6 - 185*b^2*c*e^7)*m^3 - 2*(50*c^3*d^2*e^5 - 187*b*c^2*d*e^6 - 1072*b^2*c*e^7)*m^2 - 12*(4*c^3*d^2*e^5 - 14*b*c^2*d*e^6 - 201*b^2*c*e^7)*m)*x^5 - (1260*b^3*e^7 + (3*b^2*c*d*e^6 + b^3*e^7)*m^6 - 3*(5*b*c^2*d^2*e^5 - 19*b^2*c*d*e^6 - 8*b^3*e^7)*m^5 + (30*c^3*d^3*e^4 - 195*b*c^2*d^2*e^5 + 393*b^2*c*d*e^6 + 226*b^3*e^7)*m^4 + 3*(60*c^3*d^3*e^4 - 265*b*c^2*d^2*e^5 + 401*b^2*c*d*e^6 + 352*b^3*e^7)*m^3 + 5*(66*c^3*d^3*e^4 - 249*b*c^2*d^2*e^5 + 324*b^2*c*d*e^6 + 509*b^3*e^7)*m^2 + 18*(10*c^3*d^3*e^4 - 35*b*c^2*d^2*e^5 + 42*b^2*c*d*e^6 + 164*b^3*e^7)*m)*x^4 - (b^3*d*e^6*m^6 - 3*(4*b^2*c*d^2*e^5 - 7*b^3*d*e^6)*m^5 + (60*b*c^2*d^3*e^4 - 192*b^2*c*d^2*e^5 + 163*b^3*d*e^6)*m^4 - 3*(40*c^3*d^4*e^3 - 200*b*c^2*d^3*e^4 + 332*b^2*c*d^2*e^5 - 189*b^3*d*e^6)*m^3 - 4*(90*c^3*d^4*e^3 - 345*b*c^2*d^3*e^4 + 456*b^2*c*d^2*e^5 - 211*b^3*d*e^6)*m^2 - 12*(20*c^3*d^4*e^3 - 70*b*c^2*d^3*e^4 + 84*b^2*c*d^2*e^5 - 35*b^3*d*e^6)*m)*x^3 - 36*(2*b^2*c*d^5*e^2 - 3*b^3*d^4*e^3)*m^2 + 3*(b^3*d^2*e^5*m^5 - (12*b^2*c*d^3*e^4 - 19*b^3*d^2*e^5)*m^4 + (60*b*c^2*d^4*e^3 - 168*b^2*c*d^3*e^4 + 125*b^3*d^2*e^5)*m^3 - (120*c^3*d^5*e^2 - 480*b*c^2*d^4*e^3 + 660*b^2*c*d^3*e^4 - 317*b^3*d^2*e^5)*m^2 - 6*(20*c^3*d^5*e^2 - 70*b*c^2*d^4*e^3 + 84*b^2*c*d^3*e^4 - 35*b^3*d^2*e^5)*m)*x^2 + 6*(60*b*c^2*d^6*e - 156*b^2*c*d^5*e^2 + 107*b^3*d^4*e^3)*m - 6*(b^3*d^3*e^4*m^4 - 6*(2*b^2*c*d^4*e^3 - 3*b^3*d^3*e^4)*m^3 + (60*b*c^2*d^5*e^2 - 156*b^2*c*d^4*e^3 + 107*b^3*d^3*e^4)*m^2 - 6*(20*c^3*d^6*e - 70*b*c^2*d^5*e^2 + 84*b^2*c*d^4*e^3 - 35*b^3*d^3*e^4)*m)*x)*(e*x + d)^m/(e^7*m^7 + 28*e^7*m^6 + 322*e^7*m^5 + 1960*e^7*m^4 + 6769*e^7*m^3 + 13132*e^7*m^2 + 13068*e^7*m + 5040*e^7)","B",0
441,1,584,0,0.433946," ","integrate((e*x+d)^m*(c*x^2+b*x)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, b^{2} d^{3} e^{2} m^{2} + 24 \, c^{2} d^{5} - 60 \, b c d^{4} e + 40 \, b^{2} d^{3} e^{2} + {\left(c^{2} e^{5} m^{4} + 10 \, c^{2} e^{5} m^{3} + 35 \, c^{2} e^{5} m^{2} + 50 \, c^{2} e^{5} m + 24 \, c^{2} e^{5}\right)} x^{5} + {\left(60 \, b c e^{5} + {\left(c^{2} d e^{4} + 2 \, b c e^{5}\right)} m^{4} + 2 \, {\left(3 \, c^{2} d e^{4} + 11 \, b c e^{5}\right)} m^{3} + {\left(11 \, c^{2} d e^{4} + 82 \, b c e^{5}\right)} m^{2} + 2 \, {\left(3 \, c^{2} d e^{4} + 61 \, b c e^{5}\right)} m\right)} x^{4} + {\left(40 \, b^{2} e^{5} + {\left(2 \, b c d e^{4} + b^{2} e^{5}\right)} m^{4} - 4 \, {\left(c^{2} d^{2} e^{3} - 4 \, b c d e^{4} - 3 \, b^{2} e^{5}\right)} m^{3} - {\left(12 \, c^{2} d^{2} e^{3} - 34 \, b c d e^{4} - 49 \, b^{2} e^{5}\right)} m^{2} - 2 \, {\left(4 \, c^{2} d^{2} e^{3} - 10 \, b c d e^{4} - 39 \, b^{2} e^{5}\right)} m\right)} x^{3} + {\left(b^{2} d e^{4} m^{4} - 2 \, {\left(3 \, b c d^{2} e^{3} - 5 \, b^{2} d e^{4}\right)} m^{3} + {\left(12 \, c^{2} d^{3} e^{2} - 36 \, b c d^{2} e^{3} + 29 \, b^{2} d e^{4}\right)} m^{2} + 2 \, {\left(6 \, c^{2} d^{3} e^{2} - 15 \, b c d^{2} e^{3} + 10 \, b^{2} d e^{4}\right)} m\right)} x^{2} - 6 \, {\left(2 \, b c d^{4} e - 3 \, b^{2} d^{3} e^{2}\right)} m - 2 \, {\left(b^{2} d^{2} e^{3} m^{3} - 3 \, {\left(2 \, b c d^{3} e^{2} - 3 \, b^{2} d^{2} e^{3}\right)} m^{2} + 2 \, {\left(6 \, c^{2} d^{4} e - 15 \, b c d^{3} e^{2} + 10 \, b^{2} d^{2} e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{5} m^{5} + 15 \, e^{5} m^{4} + 85 \, e^{5} m^{3} + 225 \, e^{5} m^{2} + 274 \, e^{5} m + 120 \, e^{5}}"," ",0,"(2*b^2*d^3*e^2*m^2 + 24*c^2*d^5 - 60*b*c*d^4*e + 40*b^2*d^3*e^2 + (c^2*e^5*m^4 + 10*c^2*e^5*m^3 + 35*c^2*e^5*m^2 + 50*c^2*e^5*m + 24*c^2*e^5)*x^5 + (60*b*c*e^5 + (c^2*d*e^4 + 2*b*c*e^5)*m^4 + 2*(3*c^2*d*e^4 + 11*b*c*e^5)*m^3 + (11*c^2*d*e^4 + 82*b*c*e^5)*m^2 + 2*(3*c^2*d*e^4 + 61*b*c*e^5)*m)*x^4 + (40*b^2*e^5 + (2*b*c*d*e^4 + b^2*e^5)*m^4 - 4*(c^2*d^2*e^3 - 4*b*c*d*e^4 - 3*b^2*e^5)*m^3 - (12*c^2*d^2*e^3 - 34*b*c*d*e^4 - 49*b^2*e^5)*m^2 - 2*(4*c^2*d^2*e^3 - 10*b*c*d*e^4 - 39*b^2*e^5)*m)*x^3 + (b^2*d*e^4*m^4 - 2*(3*b*c*d^2*e^3 - 5*b^2*d*e^4)*m^3 + (12*c^2*d^3*e^2 - 36*b*c*d^2*e^3 + 29*b^2*d*e^4)*m^2 + 2*(6*c^2*d^3*e^2 - 15*b*c*d^2*e^3 + 10*b^2*d*e^4)*m)*x^2 - 6*(2*b*c*d^4*e - 3*b^2*d^3*e^2)*m - 2*(b^2*d^2*e^3*m^3 - 3*(2*b*c*d^3*e^2 - 3*b^2*d^2*e^3)*m^2 + 2*(6*c^2*d^4*e - 15*b*c*d^3*e^2 + 10*b^2*d^2*e^3)*m)*x)*(e*x + d)^m/(e^5*m^5 + 15*e^5*m^4 + 85*e^5*m^3 + 225*e^5*m^2 + 274*e^5*m + 120*e^5)","B",0
442,1,160,0,0.430052," ","integrate((e*x+d)^m*(c*x^2+b*x),x, algorithm=""fricas"")","-\frac{{\left(b d^{2} e m - 2 \, c d^{3} + 3 \, b d^{2} e - {\left(c e^{3} m^{2} + 3 \, c e^{3} m + 2 \, c e^{3}\right)} x^{3} - {\left(3 \, b e^{3} + {\left(c d e^{2} + b e^{3}\right)} m^{2} + {\left(c d e^{2} + 4 \, b e^{3}\right)} m\right)} x^{2} - {\left(b d e^{2} m^{2} - {\left(2 \, c d^{2} e - 3 \, b d e^{2}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{3} m^{3} + 6 \, e^{3} m^{2} + 11 \, e^{3} m + 6 \, e^{3}}"," ",0,"-(b*d^2*e*m - 2*c*d^3 + 3*b*d^2*e - (c*e^3*m^2 + 3*c*e^3*m + 2*c*e^3)*x^3 - (3*b*e^3 + (c*d*e^2 + b*e^3)*m^2 + (c*d*e^2 + 4*b*e^3)*m)*x^2 - (b*d*e^2*m^2 - (2*c*d^2*e - 3*b*d*e^2)*m)*x)*(e*x + d)^m/(e^3*m^3 + 6*e^3*m^2 + 11*e^3*m + 6*e^3)","B",0
443,0,0,0,0.439279," ","integrate((e*x+d)^m/(c*x^2+b*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c x^{2} + b x}, x\right)"," ",0,"integral((e*x + d)^m/(c*x^2 + b*x), x)","F",0
444,0,0,0,0.445343," ","integrate((e*x+d)^m/(c*x^2+b*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral((e*x + d)^m/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
445,0,0,0,0.452984," ","integrate((e*x+d)^m/(c*x^2+b*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, b^{2} c x^{4} + b^{3} x^{3}}, x\right)"," ",0,"integral((e*x + d)^m/(c^3*x^6 + 3*b*c^2*x^5 + 3*b^2*c*x^4 + b^3*x^3), x)","F",0
446,0,0,0,0.451662," ","integrate((e*x+d)^m*(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + b*x)^(3/2)*(e*x + d)^m, x)","F",0
447,0,0,0,0.441335," ","integrate((e*x+d)^m*(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(e*x + d)^m, x)","F",0
448,0,0,0,0.443682," ","integrate((e*x+d)^m/(c*x^2+b*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{\sqrt{c x^{2} + b x}}, x\right)"," ",0,"integral((e*x + d)^m/sqrt(c*x^2 + b*x), x)","F",0
449,0,0,0,0.447193," ","integrate((e*x+d)^m/(c*x^2+b*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x} {\left(e x + d\right)}^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + b^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x)*(e*x + d)^m/(c^2*x^4 + 2*b*c*x^3 + b^2*x^2), x)","F",0
450,0,0,0,0.450135," ","integrate((e*x+d)^m*(c*x^2+b*x)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x\right)}^{p} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + b*x)^p*(e*x + d)^m, x)","F",0
451,1,96,0,0.370243," ","integrate((e*x+d)^4*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{4} c + \frac{2}{3} x^{6} e^{3} d c + \frac{6}{5} x^{5} e^{2} d^{2} c + \frac{1}{5} x^{5} e^{4} a + x^{4} e d^{3} c + x^{4} e^{3} d a + \frac{1}{3} x^{3} d^{4} c + 2 x^{3} e^{2} d^{2} a + 2 x^{2} e d^{3} a + x d^{4} a"," ",0,"1/7*x^7*e^4*c + 2/3*x^6*e^3*d*c + 6/5*x^5*e^2*d^2*c + 1/5*x^5*e^4*a + x^4*e*d^3*c + x^4*e^3*d*a + 1/3*x^3*d^4*c + 2*x^3*e^2*d^2*a + 2*x^2*e*d^3*a + x*d^4*a","A",0
452,1,73,0,0.363141," ","integrate((e*x+d)^3*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{3} c + \frac{3}{5} x^{5} e^{2} d c + \frac{3}{4} x^{4} e d^{2} c + \frac{1}{4} x^{4} e^{3} a + \frac{1}{3} x^{3} d^{3} c + x^{3} e^{2} d a + \frac{3}{2} x^{2} e d^{2} a + x d^{3} a"," ",0,"1/6*x^6*e^3*c + 3/5*x^5*e^2*d*c + 3/4*x^4*e*d^2*c + 1/4*x^4*e^3*a + 1/3*x^3*d^3*c + x^3*e^2*d*a + 3/2*x^2*e*d^2*a + x*d^3*a","A",0
453,1,49,0,0.364815," ","integrate((e*x+d)^2*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e^{2} c + \frac{1}{2} x^{4} e d c + \frac{1}{3} x^{3} d^{2} c + \frac{1}{3} x^{3} e^{2} a + x^{2} e d a + x d^{2} a"," ",0,"1/5*x^5*e^2*c + 1/2*x^4*e*d*c + 1/3*x^3*d^2*c + 1/3*x^3*e^2*a + x^2*e*d*a + x*d^2*a","A",0
454,1,26,0,0.373986," ","integrate((e*x+d)*(c*x^2+a),x, algorithm=""fricas"")","\frac{1}{4} x^{4} e c + \frac{1}{3} x^{3} d c + \frac{1}{2} x^{2} e a + x d a"," ",0,"1/4*x^4*e*c + 1/3*x^3*d*c + 1/2*x^2*e*a + x*d*a","A",0
455,1,39,0,0.395716," ","integrate((c*x^2+a)/(e*x+d),x, algorithm=""fricas"")","\frac{c e^{2} x^{2} - 2 \, c d e x + 2 \, {\left(c d^{2} + a e^{2}\right)} \log\left(e x + d\right)}{2 \, e^{3}}"," ",0,"1/2*(c*e^2*x^2 - 2*c*d*e*x + 2*(c*d^2 + a*e^2)*log(e*x + d))/e^3","A",0
456,1,59,0,0.393371," ","integrate((c*x^2+a)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{c e^{2} x^{2} + c d e x - c d^{2} - a e^{2} - 2 \, {\left(c d e x + c d^{2}\right)} \log\left(e x + d\right)}{e^{4} x + d e^{3}}"," ",0,"(c*e^2*x^2 + c*d*e*x - c*d^2 - a*e^2 - 2*(c*d*e*x + c*d^2)*log(e*x + d))/(e^4*x + d*e^3)","A",0
457,1,73,0,0.397144," ","integrate((c*x^2+a)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{4 \, c d e x + 3 \, c d^{2} - a e^{2} + 2 \, {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"1/2*(4*c*d*e*x + 3*c*d^2 - a*e^2 + 2*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*log(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
458,1,63,0,0.390423," ","integrate((c*x^2+a)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{3 \, c e^{2} x^{2} + 3 \, c d e x + c d^{2} + a e^{2}}{3 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/3*(3*c*e^2*x^2 + 3*c*d*e*x + c*d^2 + a*e^2)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
459,1,75,0,0.388802," ","integrate((c*x^2+a)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{6 \, c e^{2} x^{2} + 4 \, c d e x + c d^{2} + 3 \, a e^{2}}{12 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/12*(6*c*e^2*x^2 + 4*c*d*e*x + c*d^2 + 3*a*e^2)/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)","A",0
460,1,172,0,0.347551," ","integrate((e*x+d)^4*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{4} c^{2} + \frac{1}{2} x^{8} e^{3} d c^{2} + \frac{6}{7} x^{7} e^{2} d^{2} c^{2} + \frac{2}{7} x^{7} e^{4} c a + \frac{2}{3} x^{6} e d^{3} c^{2} + \frac{4}{3} x^{6} e^{3} d c a + \frac{1}{5} x^{5} d^{4} c^{2} + \frac{12}{5} x^{5} e^{2} d^{2} c a + \frac{1}{5} x^{5} e^{4} a^{2} + 2 x^{4} e d^{3} c a + x^{4} e^{3} d a^{2} + \frac{2}{3} x^{3} d^{4} c a + 2 x^{3} e^{2} d^{2} a^{2} + 2 x^{2} e d^{3} a^{2} + x d^{4} a^{2}"," ",0,"1/9*x^9*e^4*c^2 + 1/2*x^8*e^3*d*c^2 + 6/7*x^7*e^2*d^2*c^2 + 2/7*x^7*e^4*c*a + 2/3*x^6*e*d^3*c^2 + 4/3*x^6*e^3*d*c*a + 1/5*x^5*d^4*c^2 + 12/5*x^5*e^2*d^2*c*a + 1/5*x^5*e^4*a^2 + 2*x^4*e*d^3*c*a + x^4*e^3*d*a^2 + 2/3*x^3*d^4*c*a + 2*x^3*e^2*d^2*a^2 + 2*x^2*e*d^3*a^2 + x*d^4*a^2","A",0
461,1,131,0,0.359174," ","integrate((e*x+d)^3*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{3} c^{2} + \frac{3}{7} x^{7} e^{2} d c^{2} + \frac{1}{2} x^{6} e d^{2} c^{2} + \frac{1}{3} x^{6} e^{3} c a + \frac{1}{5} x^{5} d^{3} c^{2} + \frac{6}{5} x^{5} e^{2} d c a + \frac{3}{2} x^{4} e d^{2} c a + \frac{1}{4} x^{4} e^{3} a^{2} + \frac{2}{3} x^{3} d^{3} c a + x^{3} e^{2} d a^{2} + \frac{3}{2} x^{2} e d^{2} a^{2} + x d^{3} a^{2}"," ",0,"1/8*x^8*e^3*c^2 + 3/7*x^7*e^2*d*c^2 + 1/2*x^6*e*d^2*c^2 + 1/3*x^6*e^3*c*a + 1/5*x^5*d^3*c^2 + 6/5*x^5*e^2*d*c*a + 3/2*x^4*e*d^2*c*a + 1/4*x^4*e^3*a^2 + 2/3*x^3*d^3*c*a + x^3*e^2*d*a^2 + 3/2*x^2*e*d^2*a^2 + x*d^3*a^2","A",0
462,1,89,0,0.359246," ","integrate((e*x+d)^2*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{2} c^{2} + \frac{1}{3} x^{6} e d c^{2} + \frac{1}{5} x^{5} d^{2} c^{2} + \frac{2}{5} x^{5} e^{2} c a + x^{4} e d c a + \frac{2}{3} x^{3} d^{2} c a + \frac{1}{3} x^{3} e^{2} a^{2} + x^{2} e d a^{2} + x d^{2} a^{2}"," ",0,"1/7*x^7*e^2*c^2 + 1/3*x^6*e*d*c^2 + 1/5*x^5*d^2*c^2 + 2/5*x^5*e^2*c*a + x^4*e*d*c*a + 2/3*x^3*d^2*c*a + 1/3*x^3*e^2*a^2 + x^2*e*d*a^2 + x*d^2*a^2","A",0
463,1,50,0,0.346079," ","integrate((e*x+d)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} e c^{2} + \frac{1}{5} x^{5} d c^{2} + \frac{1}{2} x^{4} e c a + \frac{2}{3} x^{3} d c a + \frac{1}{2} x^{2} e a^{2} + x d a^{2}"," ",0,"1/6*x^6*e*c^2 + 1/5*x^5*d*c^2 + 1/2*x^4*e*c*a + 2/3*x^3*d*c*a + 1/2*x^2*e*a^2 + x*d*a^2","A",0
464,1,105,0,0.391120," ","integrate((c*x^2+a)^2/(e*x+d),x, algorithm=""fricas"")","\frac{3 \, c^{2} e^{4} x^{4} - 4 \, c^{2} d e^{3} x^{3} + 6 \, {\left(c^{2} d^{2} e^{2} + 2 \, a c e^{4}\right)} x^{2} - 12 \, {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x + 12 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \log\left(e x + d\right)}{12 \, e^{5}}"," ",0,"1/12*(3*c^2*e^4*x^4 - 4*c^2*d*e^3*x^3 + 6*(c^2*d^2*e^2 + 2*a*c*e^4)*x^2 - 12*(c^2*d^3*e + 2*a*c*d*e^3)*x + 12*(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*log(e*x + d))/e^5","A",0
465,1,150,0,0.391283," ","integrate((c*x^2+a)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{c^{2} e^{4} x^{4} - 2 \, c^{2} d e^{3} x^{3} - 3 \, c^{2} d^{4} - 6 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4} + 6 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 3 \, {\left(3 \, c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x - 12 \, {\left(c^{2} d^{4} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"1/3*(c^2*e^4*x^4 - 2*c^2*d*e^3*x^3 - 3*c^2*d^4 - 6*a*c*d^2*e^2 - 3*a^2*e^4 + 6*(c^2*d^2*e^2 + a*c*e^4)*x^2 + 3*(3*c^2*d^3*e + 2*a*c*d*e^3)*x - 12*(c^2*d^4 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)*log(e*x + d))/(e^6*x + d*e^5)","A",0
466,1,177,0,0.397097," ","integrate((c*x^2+a)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{c^{2} e^{4} x^{4} - 4 \, c^{2} d e^{3} x^{3} - 11 \, c^{2} d^{2} e^{2} x^{2} + 7 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} - a^{2} e^{4} + 2 \, {\left(c^{2} d^{3} e + 4 \, a c d e^{3}\right)} x + 4 \, {\left(3 \, c^{2} d^{4} + a c d^{2} e^{2} + {\left(3 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 2 \, {\left(3 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"1/2*(c^2*e^4*x^4 - 4*c^2*d*e^3*x^3 - 11*c^2*d^2*e^2*x^2 + 7*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4 + 2*(c^2*d^3*e + 4*a*c*d*e^3)*x + 4*(3*c^2*d^4 + a*c*d^2*e^2 + (3*c^2*d^2*e^2 + a*c*e^4)*x^2 + 2*(3*c^2*d^3*e + a*c*d*e^3)*x)*log(e*x + d))/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
467,1,183,0,0.400397," ","integrate((c*x^2+a)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, c^{2} e^{4} x^{4} + 9 \, c^{2} d e^{3} x^{3} - 13 \, c^{2} d^{4} - 2 \, a c d^{2} e^{2} - a^{2} e^{4} - 3 \, {\left(3 \, c^{2} d^{2} e^{2} + 2 \, a c e^{4}\right)} x^{2} - 3 \, {\left(9 \, c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x - 12 \, {\left(c^{2} d e^{3} x^{3} + 3 \, c^{2} d^{2} e^{2} x^{2} + 3 \, c^{2} d^{3} e x + c^{2} d^{4}\right)} \log\left(e x + d\right)}{3 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"1/3*(3*c^2*e^4*x^4 + 9*c^2*d*e^3*x^3 - 13*c^2*d^4 - 2*a*c*d^2*e^2 - a^2*e^4 - 3*(3*c^2*d^2*e^2 + 2*a*c*e^4)*x^2 - 3*(9*c^2*d^3*e + 2*a*c*d*e^3)*x - 12*(c^2*d*e^3*x^3 + 3*c^2*d^2*e^2*x^2 + 3*c^2*d^3*e*x + c^2*d^4)*log(e*x + d))/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
468,1,194,0,0.387371," ","integrate((c*x^2+a)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{48 \, c^{2} d e^{3} x^{3} + 25 \, c^{2} d^{4} - 2 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4} + 12 \, {\left(9 \, c^{2} d^{2} e^{2} - a c e^{4}\right)} x^{2} + 8 \, {\left(11 \, c^{2} d^{3} e - a c d e^{3}\right)} x + 12 \, {\left(c^{2} e^{4} x^{4} + 4 \, c^{2} d e^{3} x^{3} + 6 \, c^{2} d^{2} e^{2} x^{2} + 4 \, c^{2} d^{3} e x + c^{2} d^{4}\right)} \log\left(e x + d\right)}{12 \, {\left(e^{9} x^{4} + 4 \, d e^{8} x^{3} + 6 \, d^{2} e^{7} x^{2} + 4 \, d^{3} e^{6} x + d^{4} e^{5}\right)}}"," ",0,"1/12*(48*c^2*d*e^3*x^3 + 25*c^2*d^4 - 2*a*c*d^2*e^2 - 3*a^2*e^4 + 12*(9*c^2*d^2*e^2 - a*c*e^4)*x^2 + 8*(11*c^2*d^3*e - a*c*d*e^3)*x + 12*(c^2*e^4*x^4 + 4*c^2*d*e^3*x^3 + 6*c^2*d^2*e^2*x^2 + 4*c^2*d^3*e*x + c^2*d^4)*log(e*x + d))/(e^9*x^4 + 4*d*e^8*x^3 + 6*d^2*e^7*x^2 + 4*d^3*e^6*x + d^4*e^5)","A",0
469,1,151,0,0.389122," ","integrate((c*x^2+a)^2/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{15 \, c^{2} e^{4} x^{4} + 30 \, c^{2} d e^{3} x^{3} + 3 \, c^{2} d^{4} + a c d^{2} e^{2} + 3 \, a^{2} e^{4} + 10 \, {\left(3 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 5 \, {\left(3 \, c^{2} d^{3} e + a c d e^{3}\right)} x}{15 \, {\left(e^{10} x^{5} + 5 \, d e^{9} x^{4} + 10 \, d^{2} e^{8} x^{3} + 10 \, d^{3} e^{7} x^{2} + 5 \, d^{4} e^{6} x + d^{5} e^{5}\right)}}"," ",0,"-1/15*(15*c^2*e^4*x^4 + 30*c^2*d*e^3*x^3 + 3*c^2*d^4 + a*c*d^2*e^2 + 3*a^2*e^4 + 10*(3*c^2*d^2*e^2 + a*c*e^4)*x^2 + 5*(3*c^2*d^3*e + a*c*d*e^3)*x)/(e^10*x^5 + 5*d*e^9*x^4 + 10*d^2*e^8*x^3 + 10*d^3*e^7*x^2 + 5*d^4*e^6*x + d^5*e^5)","A",0
470,1,159,0,0.376305," ","integrate((c*x^2+a)^2/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{15 \, c^{2} e^{4} x^{4} + 20 \, c^{2} d e^{3} x^{3} + c^{2} d^{4} + a c d^{2} e^{2} + 5 \, a^{2} e^{4} + 15 \, {\left(c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 6 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x}{30 \, {\left(e^{11} x^{6} + 6 \, d e^{10} x^{5} + 15 \, d^{2} e^{9} x^{4} + 20 \, d^{3} e^{8} x^{3} + 15 \, d^{4} e^{7} x^{2} + 6 \, d^{5} e^{6} x + d^{6} e^{5}\right)}}"," ",0,"-1/30*(15*c^2*e^4*x^4 + 20*c^2*d*e^3*x^3 + c^2*d^4 + a*c*d^2*e^2 + 5*a^2*e^4 + 15*(c^2*d^2*e^2 + a*c*e^4)*x^2 + 6*(c^2*d^3*e + a*c*d*e^3)*x)/(e^11*x^6 + 6*d*e^10*x^5 + 15*d^2*e^9*x^4 + 20*d^3*e^8*x^3 + 15*d^4*e^7*x^2 + 6*d^5*e^6*x + d^6*e^5)","A",0
471,1,173,0,0.400693," ","integrate((c*x^2+a)^2/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{35 \, c^{2} e^{4} x^{4} + 35 \, c^{2} d e^{3} x^{3} + c^{2} d^{4} + 2 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} + 21 \, {\left(c^{2} d^{2} e^{2} + 2 \, a c e^{4}\right)} x^{2} + 7 \, {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x}{105 \, {\left(e^{12} x^{7} + 7 \, d e^{11} x^{6} + 21 \, d^{2} e^{10} x^{5} + 35 \, d^{3} e^{9} x^{4} + 35 \, d^{4} e^{8} x^{3} + 21 \, d^{5} e^{7} x^{2} + 7 \, d^{6} e^{6} x + d^{7} e^{5}\right)}}"," ",0,"-1/105*(35*c^2*e^4*x^4 + 35*c^2*d*e^3*x^3 + c^2*d^4 + 2*a*c*d^2*e^2 + 15*a^2*e^4 + 21*(c^2*d^2*e^2 + 2*a*c*e^4)*x^2 + 7*(c^2*d^3*e + 2*a*c*d*e^3)*x)/(e^12*x^7 + 7*d*e^11*x^6 + 21*d^2*e^10*x^5 + 35*d^3*e^9*x^4 + 35*d^4*e^8*x^3 + 21*d^5*e^7*x^2 + 7*d^6*e^6*x + d^7*e^5)","A",0
472,1,362,0,0.359398," ","integrate((e*x+d)^6*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{6} c^{3} + \frac{1}{2} x^{12} e^{5} d c^{3} + \frac{15}{11} x^{11} e^{4} d^{2} c^{3} + \frac{3}{11} x^{11} e^{6} c^{2} a + 2 x^{10} e^{3} d^{3} c^{3} + \frac{9}{5} x^{10} e^{5} d c^{2} a + \frac{5}{3} x^{9} e^{2} d^{4} c^{3} + 5 x^{9} e^{4} d^{2} c^{2} a + \frac{1}{3} x^{9} e^{6} c a^{2} + \frac{3}{4} x^{8} e d^{5} c^{3} + \frac{15}{2} x^{8} e^{3} d^{3} c^{2} a + \frac{9}{4} x^{8} e^{5} d c a^{2} + \frac{1}{7} x^{7} d^{6} c^{3} + \frac{45}{7} x^{7} e^{2} d^{4} c^{2} a + \frac{45}{7} x^{7} e^{4} d^{2} c a^{2} + \frac{1}{7} x^{7} e^{6} a^{3} + 3 x^{6} e d^{5} c^{2} a + 10 x^{6} e^{3} d^{3} c a^{2} + x^{6} e^{5} d a^{3} + \frac{3}{5} x^{5} d^{6} c^{2} a + 9 x^{5} e^{2} d^{4} c a^{2} + 3 x^{5} e^{4} d^{2} a^{3} + \frac{9}{2} x^{4} e d^{5} c a^{2} + 5 x^{4} e^{3} d^{3} a^{3} + x^{3} d^{6} c a^{2} + 5 x^{3} e^{2} d^{4} a^{3} + 3 x^{2} e d^{5} a^{3} + x d^{6} a^{3}"," ",0,"1/13*x^13*e^6*c^3 + 1/2*x^12*e^5*d*c^3 + 15/11*x^11*e^4*d^2*c^3 + 3/11*x^11*e^6*c^2*a + 2*x^10*e^3*d^3*c^3 + 9/5*x^10*e^5*d*c^2*a + 5/3*x^9*e^2*d^4*c^3 + 5*x^9*e^4*d^2*c^2*a + 1/3*x^9*e^6*c*a^2 + 3/4*x^8*e*d^5*c^3 + 15/2*x^8*e^3*d^3*c^2*a + 9/4*x^8*e^5*d*c*a^2 + 1/7*x^7*d^6*c^3 + 45/7*x^7*e^2*d^4*c^2*a + 45/7*x^7*e^4*d^2*c*a^2 + 1/7*x^7*e^6*a^3 + 3*x^6*e*d^5*c^2*a + 10*x^6*e^3*d^3*c*a^2 + x^6*e^5*d*a^3 + 3/5*x^5*d^6*c^2*a + 9*x^5*e^2*d^4*c*a^2 + 3*x^5*e^4*d^2*a^3 + 9/2*x^4*e*d^5*c*a^2 + 5*x^4*e^3*d^3*a^3 + x^3*d^6*c*a^2 + 5*x^3*e^2*d^4*a^3 + 3*x^2*e*d^5*a^3 + x*d^6*a^3","B",0
473,1,303,0,0.366055," ","integrate((e*x+d)^5*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{5} c^{3} + \frac{5}{11} x^{11} e^{4} d c^{3} + x^{10} e^{3} d^{2} c^{3} + \frac{3}{10} x^{10} e^{5} c^{2} a + \frac{10}{9} x^{9} e^{2} d^{3} c^{3} + \frac{5}{3} x^{9} e^{4} d c^{2} a + \frac{5}{8} x^{8} e d^{4} c^{3} + \frac{15}{4} x^{8} e^{3} d^{2} c^{2} a + \frac{3}{8} x^{8} e^{5} c a^{2} + \frac{1}{7} x^{7} d^{5} c^{3} + \frac{30}{7} x^{7} e^{2} d^{3} c^{2} a + \frac{15}{7} x^{7} e^{4} d c a^{2} + \frac{5}{2} x^{6} e d^{4} c^{2} a + 5 x^{6} e^{3} d^{2} c a^{2} + \frac{1}{6} x^{6} e^{5} a^{3} + \frac{3}{5} x^{5} d^{5} c^{2} a + 6 x^{5} e^{2} d^{3} c a^{2} + x^{5} e^{4} d a^{3} + \frac{15}{4} x^{4} e d^{4} c a^{2} + \frac{5}{2} x^{4} e^{3} d^{2} a^{3} + x^{3} d^{5} c a^{2} + \frac{10}{3} x^{3} e^{2} d^{3} a^{3} + \frac{5}{2} x^{2} e d^{4} a^{3} + x d^{5} a^{3}"," ",0,"1/12*x^12*e^5*c^3 + 5/11*x^11*e^4*d*c^3 + x^10*e^3*d^2*c^3 + 3/10*x^10*e^5*c^2*a + 10/9*x^9*e^2*d^3*c^3 + 5/3*x^9*e^4*d*c^2*a + 5/8*x^8*e*d^4*c^3 + 15/4*x^8*e^3*d^2*c^2*a + 3/8*x^8*e^5*c*a^2 + 1/7*x^7*d^5*c^3 + 30/7*x^7*e^2*d^3*c^2*a + 15/7*x^7*e^4*d*c*a^2 + 5/2*x^6*e*d^4*c^2*a + 5*x^6*e^3*d^2*c*a^2 + 1/6*x^6*e^5*a^3 + 3/5*x^5*d^5*c^2*a + 6*x^5*e^2*d^3*c*a^2 + x^5*e^4*d*a^3 + 15/4*x^4*e*d^4*c*a^2 + 5/2*x^4*e^3*d^2*a^3 + x^3*d^5*c*a^2 + 10/3*x^3*e^2*d^3*a^3 + 5/2*x^2*e*d^4*a^3 + x*d^5*a^3","A",0
474,1,246,0,0.366019," ","integrate((e*x+d)^4*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{4} c^{3} + \frac{2}{5} x^{10} e^{3} d c^{3} + \frac{2}{3} x^{9} e^{2} d^{2} c^{3} + \frac{1}{3} x^{9} e^{4} c^{2} a + \frac{1}{2} x^{8} e d^{3} c^{3} + \frac{3}{2} x^{8} e^{3} d c^{2} a + \frac{1}{7} x^{7} d^{4} c^{3} + \frac{18}{7} x^{7} e^{2} d^{2} c^{2} a + \frac{3}{7} x^{7} e^{4} c a^{2} + 2 x^{6} e d^{3} c^{2} a + 2 x^{6} e^{3} d c a^{2} + \frac{3}{5} x^{5} d^{4} c^{2} a + \frac{18}{5} x^{5} e^{2} d^{2} c a^{2} + \frac{1}{5} x^{5} e^{4} a^{3} + 3 x^{4} e d^{3} c a^{2} + x^{4} e^{3} d a^{3} + x^{3} d^{4} c a^{2} + 2 x^{3} e^{2} d^{2} a^{3} + 2 x^{2} e d^{3} a^{3} + x d^{4} a^{3}"," ",0,"1/11*x^11*e^4*c^3 + 2/5*x^10*e^3*d*c^3 + 2/3*x^9*e^2*d^2*c^3 + 1/3*x^9*e^4*c^2*a + 1/2*x^8*e*d^3*c^3 + 3/2*x^8*e^3*d*c^2*a + 1/7*x^7*d^4*c^3 + 18/7*x^7*e^2*d^2*c^2*a + 3/7*x^7*e^4*c*a^2 + 2*x^6*e*d^3*c^2*a + 2*x^6*e^3*d*c*a^2 + 3/5*x^5*d^4*c^2*a + 18/5*x^5*e^2*d^2*c*a^2 + 1/5*x^5*e^4*a^3 + 3*x^4*e*d^3*c*a^2 + x^4*e^3*d*a^3 + x^3*d^4*c*a^2 + 2*x^3*e^2*d^2*a^3 + 2*x^2*e*d^3*a^3 + x*d^4*a^3","A",0
475,1,188,0,0.364047," ","integrate((e*x+d)^3*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{3} c^{3} + \frac{1}{3} x^{9} e^{2} d c^{3} + \frac{3}{8} x^{8} e d^{2} c^{3} + \frac{3}{8} x^{8} e^{3} c^{2} a + \frac{1}{7} x^{7} d^{3} c^{3} + \frac{9}{7} x^{7} e^{2} d c^{2} a + \frac{3}{2} x^{6} e d^{2} c^{2} a + \frac{1}{2} x^{6} e^{3} c a^{2} + \frac{3}{5} x^{5} d^{3} c^{2} a + \frac{9}{5} x^{5} e^{2} d c a^{2} + \frac{9}{4} x^{4} e d^{2} c a^{2} + \frac{1}{4} x^{4} e^{3} a^{3} + x^{3} d^{3} c a^{2} + x^{3} e^{2} d a^{3} + \frac{3}{2} x^{2} e d^{2} a^{3} + x d^{3} a^{3}"," ",0,"1/10*x^10*e^3*c^3 + 1/3*x^9*e^2*d*c^3 + 3/8*x^8*e*d^2*c^3 + 3/8*x^8*e^3*c^2*a + 1/7*x^7*d^3*c^3 + 9/7*x^7*e^2*d*c^2*a + 3/2*x^6*e*d^2*c^2*a + 1/2*x^6*e^3*c*a^2 + 3/5*x^5*d^3*c^2*a + 9/5*x^5*e^2*d*c*a^2 + 9/4*x^4*e*d^2*c*a^2 + 1/4*x^4*e^3*a^3 + x^3*d^3*c*a^2 + x^3*e^2*d*a^3 + 3/2*x^2*e*d^2*a^3 + x*d^3*a^3","A",0
476,1,129,0,0.367125," ","integrate((e*x+d)^2*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{2} c^{3} + \frac{1}{4} x^{8} e d c^{3} + \frac{1}{7} x^{7} d^{2} c^{3} + \frac{3}{7} x^{7} e^{2} c^{2} a + x^{6} e d c^{2} a + \frac{3}{5} x^{5} d^{2} c^{2} a + \frac{3}{5} x^{5} e^{2} c a^{2} + \frac{3}{2} x^{4} e d c a^{2} + x^{3} d^{2} c a^{2} + \frac{1}{3} x^{3} e^{2} a^{3} + x^{2} e d a^{3} + x d^{2} a^{3}"," ",0,"1/9*x^9*e^2*c^3 + 1/4*x^8*e*d*c^3 + 1/7*x^7*d^2*c^3 + 3/7*x^7*e^2*c^2*a + x^6*e*d*c^2*a + 3/5*x^5*d^2*c^2*a + 3/5*x^5*e^2*c*a^2 + 3/2*x^4*e*d*c*a^2 + x^3*d^2*c*a^2 + 1/3*x^3*e^2*a^3 + x^2*e*d*a^3 + x*d^2*a^3","A",0
477,1,73,0,0.367527," ","integrate((e*x+d)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e c^{3} + \frac{1}{7} x^{7} d c^{3} + \frac{1}{2} x^{6} e c^{2} a + \frac{3}{5} x^{5} d c^{2} a + \frac{3}{4} x^{4} e c a^{2} + x^{3} d c a^{2} + \frac{1}{2} x^{2} e a^{3} + x d a^{3}"," ",0,"1/8*x^8*e*c^3 + 1/7*x^7*d*c^3 + 1/2*x^6*e*c^2*a + 3/5*x^5*d*c^2*a + 3/4*x^4*e*c*a^2 + x^3*d*c*a^2 + 1/2*x^2*e*a^3 + x*d*a^3","A",0
478,1,198,0,0.394660," ","integrate((c*x^2+a)^3/(e*x+d),x, algorithm=""fricas"")","\frac{10 \, c^{3} e^{6} x^{6} - 12 \, c^{3} d e^{5} x^{5} + 15 \, {\left(c^{3} d^{2} e^{4} + 3 \, a c^{2} e^{6}\right)} x^{4} - 20 \, {\left(c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 30 \, {\left(c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4} + 3 \, a^{2} c e^{6}\right)} x^{2} - 60 \, {\left(c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x + 60 \, {\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(e x + d\right)}{60 \, e^{7}}"," ",0,"1/60*(10*c^3*e^6*x^6 - 12*c^3*d*e^5*x^5 + 15*(c^3*d^2*e^4 + 3*a*c^2*e^6)*x^4 - 20*(c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 30*(c^3*d^4*e^2 + 3*a*c^2*d^2*e^4 + 3*a^2*c*e^6)*x^2 - 60*(c^3*d^5*e + 3*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x + 60*(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(e*x + d))/e^7","A",0
479,1,272,0,0.394735," ","integrate((c*x^2+a)^3/(e*x+d)^2,x, algorithm=""fricas"")","\frac{2 \, c^{3} e^{6} x^{6} - 3 \, c^{3} d e^{5} x^{5} - 10 \, c^{3} d^{6} - 30 \, a c^{2} d^{4} e^{2} - 30 \, a^{2} c d^{2} e^{4} - 10 \, a^{3} e^{6} + 5 \, {\left(c^{3} d^{2} e^{4} + 2 \, a c^{2} e^{6}\right)} x^{4} - 10 \, {\left(c^{3} d^{3} e^{3} + 2 \, a c^{2} d e^{5}\right)} x^{3} + 30 \, {\left(c^{3} d^{4} e^{2} + 2 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} x^{2} + 10 \, {\left(5 \, c^{3} d^{5} e + 9 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x - 60 \, {\left(c^{3} d^{6} + 2 \, a c^{2} d^{4} e^{2} + a^{2} c d^{2} e^{4} + {\left(c^{3} d^{5} e + 2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} \log\left(e x + d\right)}{10 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"1/10*(2*c^3*e^6*x^6 - 3*c^3*d*e^5*x^5 - 10*c^3*d^6 - 30*a*c^2*d^4*e^2 - 30*a^2*c*d^2*e^4 - 10*a^3*e^6 + 5*(c^3*d^2*e^4 + 2*a*c^2*e^6)*x^4 - 10*(c^3*d^3*e^3 + 2*a*c^2*d*e^5)*x^3 + 30*(c^3*d^4*e^2 + 2*a*c^2*d^2*e^4 + a^2*c*e^6)*x^2 + 10*(5*c^3*d^5*e + 9*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x - 60*(c^3*d^6 + 2*a*c^2*d^4*e^2 + a^2*c*d^2*e^4 + (c^3*d^5*e + 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*log(e*x + d))/(e^8*x + d*e^7)","A",0
480,1,315,0,0.409572," ","integrate((c*x^2+a)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{c^{3} e^{6} x^{6} - 2 \, c^{3} d e^{5} x^{5} + 22 \, c^{3} d^{6} + 42 \, a c^{2} d^{4} e^{2} + 18 \, a^{2} c d^{2} e^{4} - 2 \, a^{3} e^{6} + {\left(5 \, c^{3} d^{2} e^{4} + 6 \, a c^{2} e^{6}\right)} x^{4} - 4 \, {\left(5 \, c^{3} d^{3} e^{3} + 6 \, a c^{2} d e^{5}\right)} x^{3} - 2 \, {\left(34 \, c^{3} d^{4} e^{2} + 33 \, a c^{2} d^{2} e^{4}\right)} x^{2} - 4 \, {\left(4 \, c^{3} d^{5} e - 3 \, a c^{2} d^{3} e^{3} - 6 \, a^{2} c d e^{5}\right)} x + 12 \, {\left(5 \, c^{3} d^{6} + 6 \, a c^{2} d^{4} e^{2} + a^{2} c d^{2} e^{4} + {\left(5 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} x^{2} + 2 \, {\left(5 \, c^{3} d^{5} e + 6 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"1/4*(c^3*e^6*x^6 - 2*c^3*d*e^5*x^5 + 22*c^3*d^6 + 42*a*c^2*d^4*e^2 + 18*a^2*c*d^2*e^4 - 2*a^3*e^6 + (5*c^3*d^2*e^4 + 6*a*c^2*e^6)*x^4 - 4*(5*c^3*d^3*e^3 + 6*a*c^2*d*e^5)*x^3 - 2*(34*c^3*d^4*e^2 + 33*a*c^2*d^2*e^4)*x^2 - 4*(4*c^3*d^5*e - 3*a*c^2*d^3*e^3 - 6*a^2*c*d*e^5)*x + 12*(5*c^3*d^6 + 6*a*c^2*d^4*e^2 + a^2*c*d^2*e^4 + (5*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)*x^2 + 2*(5*c^3*d^5*e + 6*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*log(e*x + d))/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","B",0
481,1,334,0,0.404053," ","integrate((c*x^2+a)^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{c^{3} e^{6} x^{6} - 3 \, c^{3} d e^{5} x^{5} - 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} + 3 \, {\left(5 \, c^{3} d^{2} e^{4} + 3 \, a c^{2} e^{6}\right)} x^{4} + {\left(73 \, c^{3} d^{3} e^{3} + 27 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(13 \, c^{3} d^{4} e^{2} - 9 \, a c^{2} d^{2} e^{4} - 3 \, a^{2} c e^{6}\right)} x^{2} - 3 \, {\left(17 \, c^{3} d^{5} e + 27 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x - 12 \, {\left(5 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + {\left(5 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(5 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(5 \, c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"1/3*(c^3*e^6*x^6 - 3*c^3*d*e^5*x^5 - 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 + 3*(5*c^3*d^2*e^4 + 3*a*c^2*e^6)*x^4 + (73*c^3*d^3*e^3 + 27*a*c^2*d*e^5)*x^3 + 3*(13*c^3*d^4*e^2 - 9*a*c^2*d^2*e^4 - 3*a^2*c*e^6)*x^2 - 3*(17*c^3*d^5*e + 27*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x - 12*(5*c^3*d^6 + 3*a*c^2*d^4*e^2 + (5*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 3*(5*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4)*x^2 + 3*(5*c^3*d^5*e + 3*a*c^2*d^3*e^3)*x)*log(e*x + d))/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","B",0
482,1,356,0,0.393146," ","integrate((c*x^2+a)^3/(e*x+d)^5,x, algorithm=""fricas"")","\frac{2 \, c^{3} e^{6} x^{6} - 12 \, c^{3} d e^{5} x^{5} - 68 \, c^{3} d^{2} e^{4} x^{4} + 57 \, c^{3} d^{6} + 25 \, a c^{2} d^{4} e^{2} - a^{2} c d^{2} e^{4} - a^{3} e^{6} - 16 \, {\left(2 \, c^{3} d^{3} e^{3} - 3 \, a c^{2} d e^{5}\right)} x^{3} + 6 \, {\left(22 \, c^{3} d^{4} e^{2} + 18 \, a c^{2} d^{2} e^{4} - a^{2} c e^{6}\right)} x^{2} + 4 \, {\left(42 \, c^{3} d^{5} e + 22 \, a c^{2} d^{3} e^{3} - a^{2} c d e^{5}\right)} x + 12 \, {\left(5 \, c^{3} d^{6} + a c^{2} d^{4} e^{2} + {\left(5 \, c^{3} d^{2} e^{4} + a c^{2} e^{6}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{3} + a c^{2} d e^{5}\right)} x^{3} + 6 \, {\left(5 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(5 \, c^{3} d^{5} e + a c^{2} d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(e^{11} x^{4} + 4 \, d e^{10} x^{3} + 6 \, d^{2} e^{9} x^{2} + 4 \, d^{3} e^{8} x + d^{4} e^{7}\right)}}"," ",0,"1/4*(2*c^3*e^6*x^6 - 12*c^3*d*e^5*x^5 - 68*c^3*d^2*e^4*x^4 + 57*c^3*d^6 + 25*a*c^2*d^4*e^2 - a^2*c*d^2*e^4 - a^3*e^6 - 16*(2*c^3*d^3*e^3 - 3*a*c^2*d*e^5)*x^3 + 6*(22*c^3*d^4*e^2 + 18*a*c^2*d^2*e^4 - a^2*c*e^6)*x^2 + 4*(42*c^3*d^5*e + 22*a*c^2*d^3*e^3 - a^2*c*d*e^5)*x + 12*(5*c^3*d^6 + a*c^2*d^4*e^2 + (5*c^3*d^2*e^4 + a*c^2*e^6)*x^4 + 4*(5*c^3*d^3*e^3 + a*c^2*d*e^5)*x^3 + 6*(5*c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^2 + 4*(5*c^3*d^5*e + a*c^2*d^3*e^3)*x)*log(e*x + d))/(e^11*x^4 + 4*d*e^10*x^3 + 6*d^2*e^9*x^2 + 4*d^3*e^8*x + d^4*e^7)","B",0
483,1,326,0,0.412438," ","integrate((c*x^2+a)^3/(e*x+d)^6,x, algorithm=""fricas"")","\frac{10 \, c^{3} e^{6} x^{6} + 50 \, c^{3} d e^{5} x^{5} - 87 \, c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} - a^{2} c d^{2} e^{4} - 2 \, a^{3} e^{6} - 10 \, {\left(5 \, c^{3} d^{2} e^{4} + 3 \, a c^{2} e^{6}\right)} x^{4} - 20 \, {\left(20 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} - 10 \, {\left(60 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} x^{2} - 5 \, {\left(75 \, c^{3} d^{5} e + 6 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x - 60 \, {\left(c^{3} d e^{5} x^{5} + 5 \, c^{3} d^{2} e^{4} x^{4} + 10 \, c^{3} d^{3} e^{3} x^{3} + 10 \, c^{3} d^{4} e^{2} x^{2} + 5 \, c^{3} d^{5} e x + c^{3} d^{6}\right)} \log\left(e x + d\right)}{10 \, {\left(e^{12} x^{5} + 5 \, d e^{11} x^{4} + 10 \, d^{2} e^{10} x^{3} + 10 \, d^{3} e^{9} x^{2} + 5 \, d^{4} e^{8} x + d^{5} e^{7}\right)}}"," ",0,"1/10*(10*c^3*e^6*x^6 + 50*c^3*d*e^5*x^5 - 87*c^3*d^6 - 6*a*c^2*d^4*e^2 - a^2*c*d^2*e^4 - 2*a^3*e^6 - 10*(5*c^3*d^2*e^4 + 3*a*c^2*e^6)*x^4 - 20*(20*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 - 10*(60*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)*x^2 - 5*(75*c^3*d^5*e + 6*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x - 60*(c^3*d*e^5*x^5 + 5*c^3*d^2*e^4*x^4 + 10*c^3*d^3*e^3*x^3 + 10*c^3*d^4*e^2*x^2 + 5*c^3*d^5*e*x + c^3*d^6)*log(e*x + d))/(e^12*x^5 + 5*d*e^11*x^4 + 10*d^2*e^10*x^3 + 10*d^3*e^9*x^2 + 5*d^4*e^8*x + d^5*e^7)","A",0
484,1,339,0,0.389115," ","integrate((c*x^2+a)^3/(e*x+d)^7,x, algorithm=""fricas"")","\frac{360 \, c^{3} d e^{5} x^{5} + 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} + 90 \, {\left(15 \, c^{3} d^{2} e^{4} - a c^{2} e^{6}\right)} x^{4} + 40 \, {\left(55 \, c^{3} d^{3} e^{3} - 3 \, a c^{2} d e^{5}\right)} x^{3} + 15 \, {\left(125 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} - 3 \, a^{2} c e^{6}\right)} x^{2} + 6 \, {\left(137 \, c^{3} d^{5} e - 6 \, a c^{2} d^{3} e^{3} - 3 \, a^{2} c d e^{5}\right)} x + 60 \, {\left(c^{3} e^{6} x^{6} + 6 \, c^{3} d e^{5} x^{5} + 15 \, c^{3} d^{2} e^{4} x^{4} + 20 \, c^{3} d^{3} e^{3} x^{3} + 15 \, c^{3} d^{4} e^{2} x^{2} + 6 \, c^{3} d^{5} e x + c^{3} d^{6}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{13} x^{6} + 6 \, d e^{12} x^{5} + 15 \, d^{2} e^{11} x^{4} + 20 \, d^{3} e^{10} x^{3} + 15 \, d^{4} e^{9} x^{2} + 6 \, d^{5} e^{8} x + d^{6} e^{7}\right)}}"," ",0,"1/60*(360*c^3*d*e^5*x^5 + 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 + 90*(15*c^3*d^2*e^4 - a*c^2*e^6)*x^4 + 40*(55*c^3*d^3*e^3 - 3*a*c^2*d*e^5)*x^3 + 15*(125*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 - 3*a^2*c*e^6)*x^2 + 6*(137*c^3*d^5*e - 6*a*c^2*d^3*e^3 - 3*a^2*c*d*e^5)*x + 60*(c^3*e^6*x^6 + 6*c^3*d*e^5*x^5 + 15*c^3*d^2*e^4*x^4 + 20*c^3*d^3*e^3*x^3 + 15*c^3*d^4*e^2*x^2 + 6*c^3*d^5*e*x + c^3*d^6)*log(e*x + d))/(e^13*x^6 + 6*d*e^12*x^5 + 15*d^2*e^11*x^4 + 20*d^3*e^10*x^3 + 15*d^4*e^9*x^2 + 6*d^5*e^8*x + d^6*e^7)","A",0
485,1,263,0,0.391634," ","integrate((c*x^2+a)^3/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{35 \, c^{3} e^{6} x^{6} + 105 \, c^{3} d e^{5} x^{5} + 5 \, c^{3} d^{6} + a c^{2} d^{4} e^{2} + a^{2} c d^{2} e^{4} + 5 \, a^{3} e^{6} + 35 \, {\left(5 \, c^{3} d^{2} e^{4} + a c^{2} e^{6}\right)} x^{4} + 35 \, {\left(5 \, c^{3} d^{3} e^{3} + a c^{2} d e^{5}\right)} x^{3} + 21 \, {\left(5 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4} + a^{2} c e^{6}\right)} x^{2} + 7 \, {\left(5 \, c^{3} d^{5} e + a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x}{35 \, {\left(e^{14} x^{7} + 7 \, d e^{13} x^{6} + 21 \, d^{2} e^{12} x^{5} + 35 \, d^{3} e^{11} x^{4} + 35 \, d^{4} e^{10} x^{3} + 21 \, d^{5} e^{9} x^{2} + 7 \, d^{6} e^{8} x + d^{7} e^{7}\right)}}"," ",0,"-1/35*(35*c^3*e^6*x^6 + 105*c^3*d*e^5*x^5 + 5*c^3*d^6 + a*c^2*d^4*e^2 + a^2*c*d^2*e^4 + 5*a^3*e^6 + 35*(5*c^3*d^2*e^4 + a*c^2*e^6)*x^4 + 35*(5*c^3*d^3*e^3 + a*c^2*d*e^5)*x^3 + 21*(5*c^3*d^4*e^2 + a*c^2*d^2*e^4 + a^2*c*e^6)*x^2 + 7*(5*c^3*d^5*e + a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)/(e^14*x^7 + 7*d*e^13*x^6 + 21*d^2*e^12*x^5 + 35*d^3*e^11*x^4 + 35*d^4*e^10*x^3 + 21*d^5*e^9*x^2 + 7*d^6*e^8*x + d^7*e^7)","A",0
486,1,282,0,0.401773," ","integrate((c*x^2+a)^3/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{140 \, c^{3} e^{6} x^{6} + 280 \, c^{3} d e^{5} x^{5} + 5 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 5 \, a^{2} c d^{2} e^{4} + 35 \, a^{3} e^{6} + 70 \, {\left(5 \, c^{3} d^{2} e^{4} + 3 \, a c^{2} e^{6}\right)} x^{4} + 56 \, {\left(5 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 28 \, {\left(5 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4} + 5 \, a^{2} c e^{6}\right)} x^{2} + 8 \, {\left(5 \, c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3} + 5 \, a^{2} c d e^{5}\right)} x}{280 \, {\left(e^{15} x^{8} + 8 \, d e^{14} x^{7} + 28 \, d^{2} e^{13} x^{6} + 56 \, d^{3} e^{12} x^{5} + 70 \, d^{4} e^{11} x^{4} + 56 \, d^{5} e^{10} x^{3} + 28 \, d^{6} e^{9} x^{2} + 8 \, d^{7} e^{8} x + d^{8} e^{7}\right)}}"," ",0,"-1/280*(140*c^3*e^6*x^6 + 280*c^3*d*e^5*x^5 + 5*c^3*d^6 + 3*a*c^2*d^4*e^2 + 5*a^2*c*d^2*e^4 + 35*a^3*e^6 + 70*(5*c^3*d^2*e^4 + 3*a*c^2*e^6)*x^4 + 56*(5*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 28*(5*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4 + 5*a^2*c*e^6)*x^2 + 8*(5*c^3*d^5*e + 3*a*c^2*d^3*e^3 + 5*a^2*c*d*e^5)*x)/(e^15*x^8 + 8*d*e^14*x^7 + 28*d^2*e^13*x^6 + 56*d^3*e^12*x^5 + 70*d^4*e^11*x^4 + 56*d^5*e^10*x^3 + 28*d^6*e^9*x^2 + 8*d^7*e^8*x + d^8*e^7)","A",0
487,1,293,0,0.383612," ","integrate((c*x^2+a)^3/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{420 \, c^{3} e^{6} x^{6} + 630 \, c^{3} d e^{5} x^{5} + 5 \, c^{3} d^{6} + 6 \, a c^{2} d^{4} e^{2} + 15 \, a^{2} c d^{2} e^{4} + 140 \, a^{3} e^{6} + 126 \, {\left(5 \, c^{3} d^{2} e^{4} + 6 \, a c^{2} e^{6}\right)} x^{4} + 84 \, {\left(5 \, c^{3} d^{3} e^{3} + 6 \, a c^{2} d e^{5}\right)} x^{3} + 36 \, {\left(5 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + 15 \, a^{2} c e^{6}\right)} x^{2} + 9 \, {\left(5 \, c^{3} d^{5} e + 6 \, a c^{2} d^{3} e^{3} + 15 \, a^{2} c d e^{5}\right)} x}{1260 \, {\left(e^{16} x^{9} + 9 \, d e^{15} x^{8} + 36 \, d^{2} e^{14} x^{7} + 84 \, d^{3} e^{13} x^{6} + 126 \, d^{4} e^{12} x^{5} + 126 \, d^{5} e^{11} x^{4} + 84 \, d^{6} e^{10} x^{3} + 36 \, d^{7} e^{9} x^{2} + 9 \, d^{8} e^{8} x + d^{9} e^{7}\right)}}"," ",0,"-1/1260*(420*c^3*e^6*x^6 + 630*c^3*d*e^5*x^5 + 5*c^3*d^6 + 6*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 + 140*a^3*e^6 + 126*(5*c^3*d^2*e^4 + 6*a*c^2*e^6)*x^4 + 84*(5*c^3*d^3*e^3 + 6*a*c^2*d*e^5)*x^3 + 36*(5*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + 15*a^2*c*e^6)*x^2 + 9*(5*c^3*d^5*e + 6*a*c^2*d^3*e^3 + 15*a^2*c*d*e^5)*x)/(e^16*x^9 + 9*d*e^15*x^8 + 36*d^2*e^14*x^7 + 84*d^3*e^13*x^6 + 126*d^4*e^12*x^5 + 126*d^5*e^11*x^4 + 84*d^6*e^10*x^3 + 36*d^7*e^9*x^2 + 9*d^8*e^8*x + d^9*e^7)","A",0
488,1,547,0,0.355342," ","integrate((e*x+d)^7*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{16} x^{16} e^{7} c^{4} + \frac{7}{15} x^{15} e^{6} d c^{4} + \frac{3}{2} x^{14} e^{5} d^{2} c^{4} + \frac{2}{7} x^{14} e^{7} c^{3} a + \frac{35}{13} x^{13} e^{4} d^{3} c^{4} + \frac{28}{13} x^{13} e^{6} d c^{3} a + \frac{35}{12} x^{12} e^{3} d^{4} c^{4} + 7 x^{12} e^{5} d^{2} c^{3} a + \frac{1}{2} x^{12} e^{7} c^{2} a^{2} + \frac{21}{11} x^{11} e^{2} d^{5} c^{4} + \frac{140}{11} x^{11} e^{4} d^{3} c^{3} a + \frac{42}{11} x^{11} e^{6} d c^{2} a^{2} + \frac{7}{10} x^{10} e d^{6} c^{4} + 14 x^{10} e^{3} d^{4} c^{3} a + \frac{63}{5} x^{10} e^{5} d^{2} c^{2} a^{2} + \frac{2}{5} x^{10} e^{7} c a^{3} + \frac{1}{9} x^{9} d^{7} c^{4} + \frac{28}{3} x^{9} e^{2} d^{5} c^{3} a + \frac{70}{3} x^{9} e^{4} d^{3} c^{2} a^{2} + \frac{28}{9} x^{9} e^{6} d c a^{3} + \frac{7}{2} x^{8} e d^{6} c^{3} a + \frac{105}{4} x^{8} e^{3} d^{4} c^{2} a^{2} + \frac{21}{2} x^{8} e^{5} d^{2} c a^{3} + \frac{1}{8} x^{8} e^{7} a^{4} + \frac{4}{7} x^{7} d^{7} c^{3} a + 18 x^{7} e^{2} d^{5} c^{2} a^{2} + 20 x^{7} e^{4} d^{3} c a^{3} + x^{7} e^{6} d a^{4} + 7 x^{6} e d^{6} c^{2} a^{2} + \frac{70}{3} x^{6} e^{3} d^{4} c a^{3} + \frac{7}{2} x^{6} e^{5} d^{2} a^{4} + \frac{6}{5} x^{5} d^{7} c^{2} a^{2} + \frac{84}{5} x^{5} e^{2} d^{5} c a^{3} + 7 x^{5} e^{4} d^{3} a^{4} + 7 x^{4} e d^{6} c a^{3} + \frac{35}{4} x^{4} e^{3} d^{4} a^{4} + \frac{4}{3} x^{3} d^{7} c a^{3} + 7 x^{3} e^{2} d^{5} a^{4} + \frac{7}{2} x^{2} e d^{6} a^{4} + x d^{7} a^{4}"," ",0,"1/16*x^16*e^7*c^4 + 7/15*x^15*e^6*d*c^4 + 3/2*x^14*e^5*d^2*c^4 + 2/7*x^14*e^7*c^3*a + 35/13*x^13*e^4*d^3*c^4 + 28/13*x^13*e^6*d*c^3*a + 35/12*x^12*e^3*d^4*c^4 + 7*x^12*e^5*d^2*c^3*a + 1/2*x^12*e^7*c^2*a^2 + 21/11*x^11*e^2*d^5*c^4 + 140/11*x^11*e^4*d^3*c^3*a + 42/11*x^11*e^6*d*c^2*a^2 + 7/10*x^10*e*d^6*c^4 + 14*x^10*e^3*d^4*c^3*a + 63/5*x^10*e^5*d^2*c^2*a^2 + 2/5*x^10*e^7*c*a^3 + 1/9*x^9*d^7*c^4 + 28/3*x^9*e^2*d^5*c^3*a + 70/3*x^9*e^4*d^3*c^2*a^2 + 28/9*x^9*e^6*d*c*a^3 + 7/2*x^8*e*d^6*c^3*a + 105/4*x^8*e^3*d^4*c^2*a^2 + 21/2*x^8*e^5*d^2*c*a^3 + 1/8*x^8*e^7*a^4 + 4/7*x^7*d^7*c^3*a + 18*x^7*e^2*d^5*c^2*a^2 + 20*x^7*e^4*d^3*c*a^3 + x^7*e^6*d*a^4 + 7*x^6*e*d^6*c^2*a^2 + 70/3*x^6*e^3*d^4*c*a^3 + 7/2*x^6*e^5*d^2*a^4 + 6/5*x^5*d^7*c^2*a^2 + 84/5*x^5*e^2*d^5*c*a^3 + 7*x^5*e^4*d^3*a^4 + 7*x^4*e*d^6*c*a^3 + 35/4*x^4*e^3*d^4*a^4 + 4/3*x^3*d^7*c*a^3 + 7*x^3*e^2*d^5*a^4 + 7/2*x^2*e*d^6*a^4 + x*d^7*a^4","B",0
489,1,472,0,0.349233," ","integrate((e*x+d)^6*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{15} x^{15} e^{6} c^{4} + \frac{3}{7} x^{14} e^{5} d c^{4} + \frac{15}{13} x^{13} e^{4} d^{2} c^{4} + \frac{4}{13} x^{13} e^{6} c^{3} a + \frac{5}{3} x^{12} e^{3} d^{3} c^{4} + 2 x^{12} e^{5} d c^{3} a + \frac{15}{11} x^{11} e^{2} d^{4} c^{4} + \frac{60}{11} x^{11} e^{4} d^{2} c^{3} a + \frac{6}{11} x^{11} e^{6} c^{2} a^{2} + \frac{3}{5} x^{10} e d^{5} c^{4} + 8 x^{10} e^{3} d^{3} c^{3} a + \frac{18}{5} x^{10} e^{5} d c^{2} a^{2} + \frac{1}{9} x^{9} d^{6} c^{4} + \frac{20}{3} x^{9} e^{2} d^{4} c^{3} a + 10 x^{9} e^{4} d^{2} c^{2} a^{2} + \frac{4}{9} x^{9} e^{6} c a^{3} + 3 x^{8} e d^{5} c^{3} a + 15 x^{8} e^{3} d^{3} c^{2} a^{2} + 3 x^{8} e^{5} d c a^{3} + \frac{4}{7} x^{7} d^{6} c^{3} a + \frac{90}{7} x^{7} e^{2} d^{4} c^{2} a^{2} + \frac{60}{7} x^{7} e^{4} d^{2} c a^{3} + \frac{1}{7} x^{7} e^{6} a^{4} + 6 x^{6} e d^{5} c^{2} a^{2} + \frac{40}{3} x^{6} e^{3} d^{3} c a^{3} + x^{6} e^{5} d a^{4} + \frac{6}{5} x^{5} d^{6} c^{2} a^{2} + 12 x^{5} e^{2} d^{4} c a^{3} + 3 x^{5} e^{4} d^{2} a^{4} + 6 x^{4} e d^{5} c a^{3} + 5 x^{4} e^{3} d^{3} a^{4} + \frac{4}{3} x^{3} d^{6} c a^{3} + 5 x^{3} e^{2} d^{4} a^{4} + 3 x^{2} e d^{5} a^{4} + x d^{6} a^{4}"," ",0,"1/15*x^15*e^6*c^4 + 3/7*x^14*e^5*d*c^4 + 15/13*x^13*e^4*d^2*c^4 + 4/13*x^13*e^6*c^3*a + 5/3*x^12*e^3*d^3*c^4 + 2*x^12*e^5*d*c^3*a + 15/11*x^11*e^2*d^4*c^4 + 60/11*x^11*e^4*d^2*c^3*a + 6/11*x^11*e^6*c^2*a^2 + 3/5*x^10*e*d^5*c^4 + 8*x^10*e^3*d^3*c^3*a + 18/5*x^10*e^5*d*c^2*a^2 + 1/9*x^9*d^6*c^4 + 20/3*x^9*e^2*d^4*c^3*a + 10*x^9*e^4*d^2*c^2*a^2 + 4/9*x^9*e^6*c*a^3 + 3*x^8*e*d^5*c^3*a + 15*x^8*e^3*d^3*c^2*a^2 + 3*x^8*e^5*d*c*a^3 + 4/7*x^7*d^6*c^3*a + 90/7*x^7*e^2*d^4*c^2*a^2 + 60/7*x^7*e^4*d^2*c*a^3 + 1/7*x^7*e^6*a^4 + 6*x^6*e*d^5*c^2*a^2 + 40/3*x^6*e^3*d^3*c*a^3 + x^6*e^5*d*a^4 + 6/5*x^5*d^6*c^2*a^2 + 12*x^5*e^2*d^4*c*a^3 + 3*x^5*e^4*d^2*a^4 + 6*x^4*e*d^5*c*a^3 + 5*x^4*e^3*d^3*a^4 + 4/3*x^3*d^6*c*a^3 + 5*x^3*e^2*d^4*a^4 + 3*x^2*e*d^5*a^4 + x*d^6*a^4","A",0
490,1,397,0,0.350165," ","integrate((e*x+d)^5*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{14} x^{14} e^{5} c^{4} + \frac{5}{13} x^{13} e^{4} d c^{4} + \frac{5}{6} x^{12} e^{3} d^{2} c^{4} + \frac{1}{3} x^{12} e^{5} c^{3} a + \frac{10}{11} x^{11} e^{2} d^{3} c^{4} + \frac{20}{11} x^{11} e^{4} d c^{3} a + \frac{1}{2} x^{10} e d^{4} c^{4} + 4 x^{10} e^{3} d^{2} c^{3} a + \frac{3}{5} x^{10} e^{5} c^{2} a^{2} + \frac{1}{9} x^{9} d^{5} c^{4} + \frac{40}{9} x^{9} e^{2} d^{3} c^{3} a + \frac{10}{3} x^{9} e^{4} d c^{2} a^{2} + \frac{5}{2} x^{8} e d^{4} c^{3} a + \frac{15}{2} x^{8} e^{3} d^{2} c^{2} a^{2} + \frac{1}{2} x^{8} e^{5} c a^{3} + \frac{4}{7} x^{7} d^{5} c^{3} a + \frac{60}{7} x^{7} e^{2} d^{3} c^{2} a^{2} + \frac{20}{7} x^{7} e^{4} d c a^{3} + 5 x^{6} e d^{4} c^{2} a^{2} + \frac{20}{3} x^{6} e^{3} d^{2} c a^{3} + \frac{1}{6} x^{6} e^{5} a^{4} + \frac{6}{5} x^{5} d^{5} c^{2} a^{2} + 8 x^{5} e^{2} d^{3} c a^{3} + x^{5} e^{4} d a^{4} + 5 x^{4} e d^{4} c a^{3} + \frac{5}{2} x^{4} e^{3} d^{2} a^{4} + \frac{4}{3} x^{3} d^{5} c a^{3} + \frac{10}{3} x^{3} e^{2} d^{3} a^{4} + \frac{5}{2} x^{2} e d^{4} a^{4} + x d^{5} a^{4}"," ",0,"1/14*x^14*e^5*c^4 + 5/13*x^13*e^4*d*c^4 + 5/6*x^12*e^3*d^2*c^4 + 1/3*x^12*e^5*c^3*a + 10/11*x^11*e^2*d^3*c^4 + 20/11*x^11*e^4*d*c^3*a + 1/2*x^10*e*d^4*c^4 + 4*x^10*e^3*d^2*c^3*a + 3/5*x^10*e^5*c^2*a^2 + 1/9*x^9*d^5*c^4 + 40/9*x^9*e^2*d^3*c^3*a + 10/3*x^9*e^4*d*c^2*a^2 + 5/2*x^8*e*d^4*c^3*a + 15/2*x^8*e^3*d^2*c^2*a^2 + 1/2*x^8*e^5*c*a^3 + 4/7*x^7*d^5*c^3*a + 60/7*x^7*e^2*d^3*c^2*a^2 + 20/7*x^7*e^4*d*c*a^3 + 5*x^6*e*d^4*c^2*a^2 + 20/3*x^6*e^3*d^2*c*a^3 + 1/6*x^6*e^5*a^4 + 6/5*x^5*d^5*c^2*a^2 + 8*x^5*e^2*d^3*c*a^3 + x^5*e^4*d*a^4 + 5*x^4*e*d^4*c*a^3 + 5/2*x^4*e^3*d^2*a^4 + 4/3*x^3*d^5*c*a^3 + 10/3*x^3*e^2*d^3*a^4 + 5/2*x^2*e*d^4*a^4 + x*d^5*a^4","A",0
491,1,322,0,0.351687," ","integrate((e*x+d)^4*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{4} c^{4} + \frac{1}{3} x^{12} e^{3} d c^{4} + \frac{6}{11} x^{11} e^{2} d^{2} c^{4} + \frac{4}{11} x^{11} e^{4} c^{3} a + \frac{2}{5} x^{10} e d^{3} c^{4} + \frac{8}{5} x^{10} e^{3} d c^{3} a + \frac{1}{9} x^{9} d^{4} c^{4} + \frac{8}{3} x^{9} e^{2} d^{2} c^{3} a + \frac{2}{3} x^{9} e^{4} c^{2} a^{2} + 2 x^{8} e d^{3} c^{3} a + 3 x^{8} e^{3} d c^{2} a^{2} + \frac{4}{7} x^{7} d^{4} c^{3} a + \frac{36}{7} x^{7} e^{2} d^{2} c^{2} a^{2} + \frac{4}{7} x^{7} e^{4} c a^{3} + 4 x^{6} e d^{3} c^{2} a^{2} + \frac{8}{3} x^{6} e^{3} d c a^{3} + \frac{6}{5} x^{5} d^{4} c^{2} a^{2} + \frac{24}{5} x^{5} e^{2} d^{2} c a^{3} + \frac{1}{5} x^{5} e^{4} a^{4} + 4 x^{4} e d^{3} c a^{3} + x^{4} e^{3} d a^{4} + \frac{4}{3} x^{3} d^{4} c a^{3} + 2 x^{3} e^{2} d^{2} a^{4} + 2 x^{2} e d^{3} a^{4} + x d^{4} a^{4}"," ",0,"1/13*x^13*e^4*c^4 + 1/3*x^12*e^3*d*c^4 + 6/11*x^11*e^2*d^2*c^4 + 4/11*x^11*e^4*c^3*a + 2/5*x^10*e*d^3*c^4 + 8/5*x^10*e^3*d*c^3*a + 1/9*x^9*d^4*c^4 + 8/3*x^9*e^2*d^2*c^3*a + 2/3*x^9*e^4*c^2*a^2 + 2*x^8*e*d^3*c^3*a + 3*x^8*e^3*d*c^2*a^2 + 4/7*x^7*d^4*c^3*a + 36/7*x^7*e^2*d^2*c^2*a^2 + 4/7*x^7*e^4*c*a^3 + 4*x^6*e*d^3*c^2*a^2 + 8/3*x^6*e^3*d*c*a^3 + 6/5*x^5*d^4*c^2*a^2 + 24/5*x^5*e^2*d^2*c*a^3 + 1/5*x^5*e^4*a^4 + 4*x^4*e*d^3*c*a^3 + x^4*e^3*d*a^4 + 4/3*x^3*d^4*c*a^3 + 2*x^3*e^2*d^2*a^4 + 2*x^2*e*d^3*a^4 + x*d^4*a^4","A",0
492,1,247,0,0.338334," ","integrate((e*x+d)^3*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{3} c^{4} + \frac{3}{11} x^{11} e^{2} d c^{4} + \frac{3}{10} x^{10} e d^{2} c^{4} + \frac{2}{5} x^{10} e^{3} c^{3} a + \frac{1}{9} x^{9} d^{3} c^{4} + \frac{4}{3} x^{9} e^{2} d c^{3} a + \frac{3}{2} x^{8} e d^{2} c^{3} a + \frac{3}{4} x^{8} e^{3} c^{2} a^{2} + \frac{4}{7} x^{7} d^{3} c^{3} a + \frac{18}{7} x^{7} e^{2} d c^{2} a^{2} + 3 x^{6} e d^{2} c^{2} a^{2} + \frac{2}{3} x^{6} e^{3} c a^{3} + \frac{6}{5} x^{5} d^{3} c^{2} a^{2} + \frac{12}{5} x^{5} e^{2} d c a^{3} + 3 x^{4} e d^{2} c a^{3} + \frac{1}{4} x^{4} e^{3} a^{4} + \frac{4}{3} x^{3} d^{3} c a^{3} + x^{3} e^{2} d a^{4} + \frac{3}{2} x^{2} e d^{2} a^{4} + x d^{3} a^{4}"," ",0,"1/12*x^12*e^3*c^4 + 3/11*x^11*e^2*d*c^4 + 3/10*x^10*e*d^2*c^4 + 2/5*x^10*e^3*c^3*a + 1/9*x^9*d^3*c^4 + 4/3*x^9*e^2*d*c^3*a + 3/2*x^8*e*d^2*c^3*a + 3/4*x^8*e^3*c^2*a^2 + 4/7*x^7*d^3*c^3*a + 18/7*x^7*e^2*d*c^2*a^2 + 3*x^6*e*d^2*c^2*a^2 + 2/3*x^6*e^3*c*a^3 + 6/5*x^5*d^3*c^2*a^2 + 12/5*x^5*e^2*d*c*a^3 + 3*x^4*e*d^2*c*a^3 + 1/4*x^4*e^3*a^4 + 4/3*x^3*d^3*c*a^3 + x^3*e^2*d*a^4 + 3/2*x^2*e*d^2*a^4 + x*d^3*a^4","A",0
493,1,171,0,0.338624," ","integrate((e*x+d)^2*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{2} c^{4} + \frac{1}{5} x^{10} e d c^{4} + \frac{1}{9} x^{9} d^{2} c^{4} + \frac{4}{9} x^{9} e^{2} c^{3} a + x^{8} e d c^{3} a + \frac{4}{7} x^{7} d^{2} c^{3} a + \frac{6}{7} x^{7} e^{2} c^{2} a^{2} + 2 x^{6} e d c^{2} a^{2} + \frac{6}{5} x^{5} d^{2} c^{2} a^{2} + \frac{4}{5} x^{5} e^{2} c a^{3} + 2 x^{4} e d c a^{3} + \frac{4}{3} x^{3} d^{2} c a^{3} + \frac{1}{3} x^{3} e^{2} a^{4} + x^{2} e d a^{4} + x d^{2} a^{4}"," ",0,"1/11*x^11*e^2*c^4 + 1/5*x^10*e*d*c^4 + 1/9*x^9*d^2*c^4 + 4/9*x^9*e^2*c^3*a + x^8*e*d*c^3*a + 4/7*x^7*d^2*c^3*a + 6/7*x^7*e^2*c^2*a^2 + 2*x^6*e*d*c^2*a^2 + 6/5*x^5*d^2*c^2*a^2 + 4/5*x^5*e^2*c*a^3 + 2*x^4*e*d*c*a^3 + 4/3*x^3*d^2*c*a^3 + 1/3*x^3*e^2*a^4 + x^2*e*d*a^4 + x*d^2*a^4","A",0
494,1,96,0,0.346672," ","integrate((e*x+d)*(c*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e c^{4} + \frac{1}{9} x^{9} d c^{4} + \frac{1}{2} x^{8} e c^{3} a + \frac{4}{7} x^{7} d c^{3} a + x^{6} e c^{2} a^{2} + \frac{6}{5} x^{5} d c^{2} a^{2} + x^{4} e c a^{3} + \frac{4}{3} x^{3} d c a^{3} + \frac{1}{2} x^{2} e a^{4} + x d a^{4}"," ",0,"1/10*x^10*e*c^4 + 1/9*x^9*d*c^4 + 1/2*x^8*e*c^3*a + 4/7*x^7*d*c^3*a + x^6*e*c^2*a^2 + 6/5*x^5*d*c^2*a^2 + x^4*e*c*a^3 + 4/3*x^3*d*c*a^3 + 1/2*x^2*e*a^4 + x*d*a^4","A",0
495,1,319,0,0.381722," ","integrate((c*x^2+a)^4/(e*x+d),x, algorithm=""fricas"")","\frac{105 \, c^{4} e^{8} x^{8} - 120 \, c^{4} d e^{7} x^{7} + 140 \, {\left(c^{4} d^{2} e^{6} + 4 \, a c^{3} e^{8}\right)} x^{6} - 168 \, {\left(c^{4} d^{3} e^{5} + 4 \, a c^{3} d e^{7}\right)} x^{5} + 210 \, {\left(c^{4} d^{4} e^{4} + 4 \, a c^{3} d^{2} e^{6} + 6 \, a^{2} c^{2} e^{8}\right)} x^{4} - 280 \, {\left(c^{4} d^{5} e^{3} + 4 \, a c^{3} d^{3} e^{5} + 6 \, a^{2} c^{2} d e^{7}\right)} x^{3} + 420 \, {\left(c^{4} d^{6} e^{2} + 4 \, a c^{3} d^{4} e^{4} + 6 \, a^{2} c^{2} d^{2} e^{6} + 4 \, a^{3} c e^{8}\right)} x^{2} - 840 \, {\left(c^{4} d^{7} e + 4 \, a c^{3} d^{5} e^{3} + 6 \, a^{2} c^{2} d^{3} e^{5} + 4 \, a^{3} c d e^{7}\right)} x + 840 \, {\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(e x + d\right)}{840 \, e^{9}}"," ",0,"1/840*(105*c^4*e^8*x^8 - 120*c^4*d*e^7*x^7 + 140*(c^4*d^2*e^6 + 4*a*c^3*e^8)*x^6 - 168*(c^4*d^3*e^5 + 4*a*c^3*d*e^7)*x^5 + 210*(c^4*d^4*e^4 + 4*a*c^3*d^2*e^6 + 6*a^2*c^2*e^8)*x^4 - 280*(c^4*d^5*e^3 + 4*a*c^3*d^3*e^5 + 6*a^2*c^2*d*e^7)*x^3 + 420*(c^4*d^6*e^2 + 4*a*c^3*d^4*e^4 + 6*a^2*c^2*d^2*e^6 + 4*a^3*c*e^8)*x^2 - 840*(c^4*d^7*e + 4*a*c^3*d^5*e^3 + 6*a^2*c^2*d^3*e^5 + 4*a^3*c*d*e^7)*x + 840*(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(e*x + d))/e^9","A",0
496,1,421,0,0.377427," ","integrate((c*x^2+a)^4/(e*x+d)^2,x, algorithm=""fricas"")","\frac{15 \, c^{4} e^{8} x^{8} - 20 \, c^{4} d e^{7} x^{7} - 105 \, c^{4} d^{8} - 420 \, a c^{3} d^{6} e^{2} - 630 \, a^{2} c^{2} d^{4} e^{4} - 420 \, a^{3} c d^{2} e^{6} - 105 \, a^{4} e^{8} + 28 \, {\left(c^{4} d^{2} e^{6} + 3 \, a c^{3} e^{8}\right)} x^{6} - 42 \, {\left(c^{4} d^{3} e^{5} + 3 \, a c^{3} d e^{7}\right)} x^{5} + 70 \, {\left(c^{4} d^{4} e^{4} + 3 \, a c^{3} d^{2} e^{6} + 3 \, a^{2} c^{2} e^{8}\right)} x^{4} - 140 \, {\left(c^{4} d^{5} e^{3} + 3 \, a c^{3} d^{3} e^{5} + 3 \, a^{2} c^{2} d e^{7}\right)} x^{3} + 420 \, {\left(c^{4} d^{6} e^{2} + 3 \, a c^{3} d^{4} e^{4} + 3 \, a^{2} c^{2} d^{2} e^{6} + a^{3} c e^{8}\right)} x^{2} + 105 \, {\left(7 \, c^{4} d^{7} e + 20 \, a c^{3} d^{5} e^{3} + 18 \, a^{2} c^{2} d^{3} e^{5} + 4 \, a^{3} c d e^{7}\right)} x - 840 \, {\left(c^{4} d^{8} + 3 \, a c^{3} d^{6} e^{2} + 3 \, a^{2} c^{2} d^{4} e^{4} + a^{3} c d^{2} e^{6} + {\left(c^{4} d^{7} e + 3 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5} + a^{3} c d e^{7}\right)} x\right)} \log\left(e x + d\right)}{105 \, {\left(e^{10} x + d e^{9}\right)}}"," ",0,"1/105*(15*c^4*e^8*x^8 - 20*c^4*d*e^7*x^7 - 105*c^4*d^8 - 420*a*c^3*d^6*e^2 - 630*a^2*c^2*d^4*e^4 - 420*a^3*c*d^2*e^6 - 105*a^4*e^8 + 28*(c^4*d^2*e^6 + 3*a*c^3*e^8)*x^6 - 42*(c^4*d^3*e^5 + 3*a*c^3*d*e^7)*x^5 + 70*(c^4*d^4*e^4 + 3*a*c^3*d^2*e^6 + 3*a^2*c^2*e^8)*x^4 - 140*(c^4*d^5*e^3 + 3*a*c^3*d^3*e^5 + 3*a^2*c^2*d*e^7)*x^3 + 420*(c^4*d^6*e^2 + 3*a*c^3*d^4*e^4 + 3*a^2*c^2*d^2*e^6 + a^3*c*e^8)*x^2 + 105*(7*c^4*d^7*e + 20*a*c^3*d^5*e^3 + 18*a^2*c^2*d^3*e^5 + 4*a^3*c*d*e^7)*x - 840*(c^4*d^8 + 3*a*c^3*d^6*e^2 + 3*a^2*c^2*d^4*e^4 + a^3*c*d^2*e^6 + (c^4*d^7*e + 3*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5 + a^3*c*d*e^7)*x)*log(e*x + d))/(e^10*x + d*e^9)","A",0
497,1,96,0,0.349469," ","integrate((d*x+c)*(b*x^2+a)^4,x, algorithm=""fricas"")","\frac{1}{10} x^{10} d b^{4} + \frac{1}{9} x^{9} c b^{4} + \frac{1}{2} x^{8} d b^{3} a + \frac{4}{7} x^{7} c b^{3} a + x^{6} d b^{2} a^{2} + \frac{6}{5} x^{5} c b^{2} a^{2} + x^{4} d b a^{3} + \frac{4}{3} x^{3} c b a^{3} + \frac{1}{2} x^{2} d a^{4} + x c a^{4}"," ",0,"1/10*x^10*d*b^4 + 1/9*x^9*c*b^4 + 1/2*x^8*d*b^3*a + 4/7*x^7*c*b^3*a + x^6*d*b^2*a^2 + 6/5*x^5*c*b^2*a^2 + x^4*d*b*a^3 + 4/3*x^3*c*b*a^3 + 1/2*x^2*d*a^4 + x*c*a^4","A",0
498,1,283,0,0.407611," ","integrate((e*x+d)^4/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, a c^{2} e^{4} x^{3} + 12 \, a c^{2} d e^{3} x^{2} - 3 \, {\left(c^{2} d^{4} - 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 6 \, {\left(6 \, a c^{2} d^{2} e^{2} - a^{2} c e^{4}\right)} x + 12 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} \log\left(c x^{2} + a\right)}{6 \, a c^{3}}, \frac{a c^{2} e^{4} x^{3} + 6 \, a c^{2} d e^{3} x^{2} + 3 \, {\left(c^{2} d^{4} - 6 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + 3 \, {\left(6 \, a c^{2} d^{2} e^{2} - a^{2} c e^{4}\right)} x + 6 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} \log\left(c x^{2} + a\right)}{3 \, a c^{3}}\right]"," ",0,"[1/6*(2*a*c^2*e^4*x^3 + 12*a*c^2*d*e^3*x^2 - 3*(c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 6*(6*a*c^2*d^2*e^2 - a^2*c*e^4)*x + 12*(a*c^2*d^3*e - a^2*c*d*e^3)*log(c*x^2 + a))/(a*c^3), 1/3*(a*c^2*e^4*x^3 + 6*a*c^2*d*e^3*x^2 + 3*(c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + 3*(6*a*c^2*d^2*e^2 - a^2*c*e^4)*x + 6*(a*c^2*d^3*e - a^2*c*d*e^3)*log(c*x^2 + a))/(a*c^3)]","A",0
499,1,187,0,0.394232," ","integrate((e*x+d)^3/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{a c e^{3} x^{2} + 6 \, a c d e^{2} x + {\left(c d^{3} - 3 \, a d e^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, a c^{2}}, \frac{a c e^{3} x^{2} + 6 \, a c d e^{2} x + 2 \, {\left(c d^{3} - 3 \, a d e^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(3 \, a c d^{2} e - a^{2} e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, a c^{2}}\right]"," ",0,"[1/2*(a*c*e^3*x^2 + 6*a*c*d*e^2*x + (c*d^3 - 3*a*d*e^2)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + (3*a*c*d^2*e - a^2*e^3)*log(c*x^2 + a))/(a*c^2), 1/2*(a*c*e^3*x^2 + 6*a*c*d*e^2*x + 2*(c*d^3 - 3*a*d*e^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (3*a*c*d^2*e - a^2*e^3)*log(c*x^2 + a))/(a*c^2)]","A",0
500,1,137,0,0.403777," ","integrate((e*x+d)^2/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{2 \, a c e^{2} x + 2 \, a c d e \log\left(c x^{2} + a\right) + {\left(c d^{2} - a e^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{2 \, a c^{2}}, \frac{a c e^{2} x + a c d e \log\left(c x^{2} + a\right) + {\left(c d^{2} - a e^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{a c^{2}}\right]"," ",0,"[1/2*(2*a*c*e^2*x + 2*a*c*d*e*log(c*x^2 + a) + (c*d^2 - a*e^2)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a*c^2), (a*c*e^2*x + a*c*d*e*log(c*x^2 + a) + (c*d^2 - a*e^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a))/(a*c^2)]","A",0
501,1,98,0,0.394384," ","integrate((e*x+d)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{a e \log\left(c x^{2} + a\right) - \sqrt{-a c} d \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{2 \, a c}, \frac{a e \log\left(c x^{2} + a\right) + 2 \, \sqrt{a c} d \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{2 \, a c}\right]"," ",0,"[1/2*(a*e*log(c*x^2 + a) - sqrt(-a*c)*d*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a*c), 1/2*(a*e*log(c*x^2 + a) + 2*sqrt(a*c)*d*arctan(sqrt(a*c)*x/a))/(a*c)]","A",0
502,1,135,0,0.424773," ","integrate(1/(e*x+d)/(c*x^2+a),x, algorithm=""fricas"")","\left[\frac{d \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} + 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) - e \log\left(c x^{2} + a\right) + 2 \, e \log\left(e x + d\right)}{2 \, {\left(c d^{2} + a e^{2}\right)}}, \frac{2 \, d \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) - e \log\left(c x^{2} + a\right) + 2 \, e \log\left(e x + d\right)}{2 \, {\left(c d^{2} + a e^{2}\right)}}\right]"," ",0,"[1/2*(d*sqrt(-c/a)*log((c*x^2 + 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) - e*log(c*x^2 + a) + 2*e*log(e*x + d))/(c*d^2 + a*e^2), 1/2*(2*d*sqrt(c/a)*arctan(x*sqrt(c/a)) - e*log(c*x^2 + a) + 2*e*log(e*x + d))/(c*d^2 + a*e^2)]","A",0
503,1,350,0,0.536600," ","integrate(1/(e*x+d)^2/(c*x^2+a),x, algorithm=""fricas"")","\left[-\frac{2 \, c d^{2} e + 2 \, a e^{3} + {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 2 \, {\left(c d e^{2} x + c d^{2} e\right)} \log\left(c x^{2} + a\right) - 4 \, {\left(c d e^{2} x + c d^{2} e\right)} \log\left(e x + d\right)}{2 \, {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)}}, -\frac{c d^{2} e + a e^{3} - {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + {\left(c d e^{2} x + c d^{2} e\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(c d e^{2} x + c d^{2} e\right)} \log\left(e x + d\right)}{c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x}\right]"," ",0,"[-1/2*(2*c*d^2*e + 2*a*e^3 + (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 2*(c*d*e^2*x + c*d^2*e)*log(c*x^2 + a) - 4*(c*d*e^2*x + c*d^2*e)*log(e*x + d))/(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x), -(c*d^2*e + a*e^3 - (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(c/a)*arctan(x*sqrt(c/a)) + (c*d*e^2*x + c*d^2*e)*log(c*x^2 + a) - 2*(c*d*e^2*x + c*d^2*e)*log(e*x + d))/(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)]","A",0
504,1,853,0,1.363441," ","integrate(1/(e*x+d)^3/(c*x^2+a),x, algorithm=""fricas"")","\left[-\frac{5 \, c^{2} d^{4} e + 6 \, a c d^{2} e^{3} + a^{2} e^{5} + {\left(c^{2} d^{5} - 3 \, a c d^{3} e^{2} + {\left(c^{2} d^{3} e^{2} - 3 \, a c d e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{4} e - 3 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 4 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x + {\left(3 \, c^{2} d^{4} e - a c d^{2} e^{3} + {\left(3 \, c^{2} d^{2} e^{3} - a c e^{5}\right)} x^{2} + 2 \, {\left(3 \, c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(3 \, c^{2} d^{4} e - a c d^{2} e^{3} + {\left(3 \, c^{2} d^{2} e^{3} - a c e^{5}\right)} x^{2} + 2 \, {\left(3 \, c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(c^{3} d^{8} + 3 \, a c^{2} d^{6} e^{2} + 3 \, a^{2} c d^{4} e^{4} + a^{3} d^{2} e^{6} + {\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)} x^{2} + 2 \, {\left(c^{3} d^{7} e + 3 \, a c^{2} d^{5} e^{3} + 3 \, a^{2} c d^{3} e^{5} + a^{3} d e^{7}\right)} x\right)}}, -\frac{5 \, c^{2} d^{4} e + 6 \, a c d^{2} e^{3} + a^{2} e^{5} - 2 \, {\left(c^{2} d^{5} - 3 \, a c d^{3} e^{2} + {\left(c^{2} d^{3} e^{2} - 3 \, a c d e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{4} e - 3 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + 4 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x + {\left(3 \, c^{2} d^{4} e - a c d^{2} e^{3} + {\left(3 \, c^{2} d^{2} e^{3} - a c e^{5}\right)} x^{2} + 2 \, {\left(3 \, c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \log\left(c x^{2} + a\right) - 2 \, {\left(3 \, c^{2} d^{4} e - a c d^{2} e^{3} + {\left(3 \, c^{2} d^{2} e^{3} - a c e^{5}\right)} x^{2} + 2 \, {\left(3 \, c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(c^{3} d^{8} + 3 \, a c^{2} d^{6} e^{2} + 3 \, a^{2} c d^{4} e^{4} + a^{3} d^{2} e^{6} + {\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)} x^{2} + 2 \, {\left(c^{3} d^{7} e + 3 \, a c^{2} d^{5} e^{3} + 3 \, a^{2} c d^{3} e^{5} + a^{3} d e^{7}\right)} x\right)}}\right]"," ",0,"[-1/2*(5*c^2*d^4*e + 6*a*c*d^2*e^3 + a^2*e^5 + (c^2*d^5 - 3*a*c*d^3*e^2 + (c^2*d^3*e^2 - 3*a*c*d*e^4)*x^2 + 2*(c^2*d^4*e - 3*a*c*d^2*e^3)*x)*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 4*(c^2*d^3*e^2 + a*c*d*e^4)*x + (3*c^2*d^4*e - a*c*d^2*e^3 + (3*c^2*d^2*e^3 - a*c*e^5)*x^2 + 2*(3*c^2*d^3*e^2 - a*c*d*e^4)*x)*log(c*x^2 + a) - 2*(3*c^2*d^4*e - a*c*d^2*e^3 + (3*c^2*d^2*e^3 - a*c*e^5)*x^2 + 2*(3*c^2*d^3*e^2 - a*c*d*e^4)*x)*log(e*x + d))/(c^3*d^8 + 3*a*c^2*d^6*e^2 + 3*a^2*c*d^4*e^4 + a^3*d^2*e^6 + (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)*x^2 + 2*(c^3*d^7*e + 3*a*c^2*d^5*e^3 + 3*a^2*c*d^3*e^5 + a^3*d*e^7)*x), -1/2*(5*c^2*d^4*e + 6*a*c*d^2*e^3 + a^2*e^5 - 2*(c^2*d^5 - 3*a*c*d^3*e^2 + (c^2*d^3*e^2 - 3*a*c*d*e^4)*x^2 + 2*(c^2*d^4*e - 3*a*c*d^2*e^3)*x)*sqrt(c/a)*arctan(x*sqrt(c/a)) + 4*(c^2*d^3*e^2 + a*c*d*e^4)*x + (3*c^2*d^4*e - a*c*d^2*e^3 + (3*c^2*d^2*e^3 - a*c*e^5)*x^2 + 2*(3*c^2*d^3*e^2 - a*c*d*e^4)*x)*log(c*x^2 + a) - 2*(3*c^2*d^4*e - a*c*d^2*e^3 + (3*c^2*d^2*e^3 - a*c*e^5)*x^2 + 2*(3*c^2*d^3*e^2 - a*c*d*e^4)*x)*log(e*x + d))/(c^3*d^8 + 3*a*c^2*d^6*e^2 + 3*a^2*c*d^4*e^4 + a^3*d^2*e^6 + (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)*x^2 + 2*(c^3*d^7*e + 3*a*c^2*d^5*e^3 + 3*a^2*c*d^3*e^5 + a^3*d*e^7)*x)]","B",0
505,1,561,0,0.422563," ","integrate((e*x+d)^5/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} c^{2} e^{5} x^{4} + 20 \, a^{2} c^{2} d e^{4} x^{3} + 2 \, a^{3} c e^{5} x^{2} - 10 \, a^{2} c^{2} d^{4} e + 20 \, a^{3} c d^{2} e^{3} - 2 \, a^{4} e^{5} + {\left(a c^{2} d^{5} + 10 \, a^{2} c d^{3} e^{2} - 15 \, a^{3} d e^{4} + {\left(c^{3} d^{5} + 10 \, a c^{2} d^{3} e^{2} - 15 \, a^{2} c d e^{4}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 2 \, {\left(a c^{3} d^{5} - 10 \, a^{2} c^{2} d^{3} e^{2} + 15 \, a^{3} c d e^{4}\right)} x + 4 \, {\left(5 \, a^{3} c d^{2} e^{3} - a^{4} e^{5} + {\left(5 \, a^{2} c^{2} d^{2} e^{3} - a^{3} c e^{5}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}, \frac{a^{2} c^{2} e^{5} x^{4} + 10 \, a^{2} c^{2} d e^{4} x^{3} + a^{3} c e^{5} x^{2} - 5 \, a^{2} c^{2} d^{4} e + 10 \, a^{3} c d^{2} e^{3} - a^{4} e^{5} + {\left(a c^{2} d^{5} + 10 \, a^{2} c d^{3} e^{2} - 15 \, a^{3} d e^{4} + {\left(c^{3} d^{5} + 10 \, a c^{2} d^{3} e^{2} - 15 \, a^{2} c d e^{4}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(a c^{3} d^{5} - 10 \, a^{2} c^{2} d^{3} e^{2} + 15 \, a^{3} c d e^{4}\right)} x + 2 \, {\left(5 \, a^{3} c d^{2} e^{3} - a^{4} e^{5} + {\left(5 \, a^{2} c^{2} d^{2} e^{3} - a^{3} c e^{5}\right)} x^{2}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}\right]"," ",0,"[1/4*(2*a^2*c^2*e^5*x^4 + 20*a^2*c^2*d*e^4*x^3 + 2*a^3*c*e^5*x^2 - 10*a^2*c^2*d^4*e + 20*a^3*c*d^2*e^3 - 2*a^4*e^5 + (a*c^2*d^5 + 10*a^2*c*d^3*e^2 - 15*a^3*d*e^4 + (c^3*d^5 + 10*a*c^2*d^3*e^2 - 15*a^2*c*d*e^4)*x^2)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 2*(a*c^3*d^5 - 10*a^2*c^2*d^3*e^2 + 15*a^3*c*d*e^4)*x + 4*(5*a^3*c*d^2*e^3 - a^4*e^5 + (5*a^2*c^2*d^2*e^3 - a^3*c*e^5)*x^2)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3), 1/2*(a^2*c^2*e^5*x^4 + 10*a^2*c^2*d*e^4*x^3 + a^3*c*e^5*x^2 - 5*a^2*c^2*d^4*e + 10*a^3*c*d^2*e^3 - a^4*e^5 + (a*c^2*d^5 + 10*a^2*c*d^3*e^2 - 15*a^3*d*e^4 + (c^3*d^5 + 10*a*c^2*d^3*e^2 - 15*a^2*c*d*e^4)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (a*c^3*d^5 - 10*a^2*c^2*d^3*e^2 + 15*a^3*c*d*e^4)*x + 2*(5*a^3*c*d^2*e^3 - a^4*e^5 + (5*a^2*c^2*d^2*e^3 - a^3*c*e^5)*x^2)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3)]","A",0
506,1,433,0,0.417355," ","integrate((e*x+d)^4/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} c^{2} e^{4} x^{3} - 8 \, a^{2} c^{2} d^{3} e + 8 \, a^{3} c d e^{3} + {\left(a c^{2} d^{4} + 6 \, a^{2} c d^{2} e^{2} - 3 \, a^{3} e^{4} + {\left(c^{3} d^{4} + 6 \, a c^{2} d^{2} e^{2} - 3 \, a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) + 2 \, {\left(a c^{3} d^{4} - 6 \, a^{2} c^{2} d^{2} e^{2} + 3 \, a^{3} c e^{4}\right)} x + 8 \, {\left(a^{2} c^{2} d e^{3} x^{2} + a^{3} c d e^{3}\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}, \frac{2 \, a^{2} c^{2} e^{4} x^{3} - 4 \, a^{2} c^{2} d^{3} e + 4 \, a^{3} c d e^{3} + {\left(a c^{2} d^{4} + 6 \, a^{2} c d^{2} e^{2} - 3 \, a^{3} e^{4} + {\left(c^{3} d^{4} + 6 \, a c^{2} d^{2} e^{2} - 3 \, a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) + {\left(a c^{3} d^{4} - 6 \, a^{2} c^{2} d^{2} e^{2} + 3 \, a^{3} c e^{4}\right)} x + 4 \, {\left(a^{2} c^{2} d e^{3} x^{2} + a^{3} c d e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(a^{2} c^{4} x^{2} + a^{3} c^{3}\right)}}\right]"," ",0,"[1/4*(4*a^2*c^2*e^4*x^3 - 8*a^2*c^2*d^3*e + 8*a^3*c*d*e^3 + (a*c^2*d^4 + 6*a^2*c*d^2*e^2 - 3*a^3*e^4 + (c^3*d^4 + 6*a*c^2*d^2*e^2 - 3*a^2*c*e^4)*x^2)*sqrt(-a*c)*log((c*x^2 + 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) + 2*(a*c^3*d^4 - 6*a^2*c^2*d^2*e^2 + 3*a^3*c*e^4)*x + 8*(a^2*c^2*d*e^3*x^2 + a^3*c*d*e^3)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3), 1/2*(2*a^2*c^2*e^4*x^3 - 4*a^2*c^2*d^3*e + 4*a^3*c*d*e^3 + (a*c^2*d^4 + 6*a^2*c*d^2*e^2 - 3*a^3*e^4 + (c^3*d^4 + 6*a*c^2*d^2*e^2 - 3*a^2*c*e^4)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) + (a*c^3*d^4 - 6*a^2*c^2*d^2*e^2 + 3*a^3*c*e^4)*x + 4*(a^2*c^2*d*e^3*x^2 + a^3*c*d*e^3)*log(c*x^2 + a))/(a^2*c^4*x^2 + a^3*c^3)]","A",0
507,1,311,0,0.412025," ","integrate((e*x+d)^3/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{6 \, a^{2} c d^{2} e - 2 \, a^{3} e^{3} + {\left(a c d^{3} + 3 \, a^{2} d e^{2} + {\left(c^{2} d^{3} + 3 \, a c d e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(a c^{2} d^{3} - 3 \, a^{2} c d e^{2}\right)} x - 2 \, {\left(a^{2} c e^{3} x^{2} + a^{3} e^{3}\right)} \log\left(c x^{2} + a\right)}{4 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}, -\frac{3 \, a^{2} c d^{2} e - a^{3} e^{3} - {\left(a c d^{3} + 3 \, a^{2} d e^{2} + {\left(c^{2} d^{3} + 3 \, a c d e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(a c^{2} d^{3} - 3 \, a^{2} c d e^{2}\right)} x - {\left(a^{2} c e^{3} x^{2} + a^{3} e^{3}\right)} \log\left(c x^{2} + a\right)}{2 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}\right]"," ",0,"[-1/4*(6*a^2*c*d^2*e - 2*a^3*e^3 + (a*c*d^3 + 3*a^2*d*e^2 + (c^2*d^3 + 3*a*c*d*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(a*c^2*d^3 - 3*a^2*c*d*e^2)*x - 2*(a^2*c*e^3*x^2 + a^3*e^3)*log(c*x^2 + a))/(a^2*c^3*x^2 + a^3*c^2), -1/2*(3*a^2*c*d^2*e - a^3*e^3 - (a*c*d^3 + 3*a^2*d*e^2 + (c^2*d^3 + 3*a*c*d*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (a*c^2*d^3 - 3*a^2*c*d*e^2)*x - (a^2*c*e^3*x^2 + a^3*e^3)*log(c*x^2 + a))/(a^2*c^3*x^2 + a^3*c^2)]","A",0
508,1,223,0,0.401824," ","integrate((e*x+d)^2/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} c d e + {\left(a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x}{4 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}, -\frac{2 \, a^{2} c d e - {\left(a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x}{2 \, {\left(a^{2} c^{3} x^{2} + a^{3} c^{2}\right)}}\right]"," ",0,"[-1/4*(4*a^2*c*d*e + (a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(a*c^2*d^2 - a^2*c*e^2)*x)/(a^2*c^3*x^2 + a^3*c^2), -1/2*(2*a^2*c*d*e - (a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (a*c^2*d^2 - a^2*c*e^2)*x)/(a^2*c^3*x^2 + a^3*c^2)]","A",0
509,1,140,0,0.399364," ","integrate((e*x+d)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a c d x - 2 \, a^{2} e - {\left(c d x^{2} + a d\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{4 \, {\left(a^{2} c^{2} x^{2} + a^{3} c\right)}}, \frac{a c d x - a^{2} e + {\left(c d x^{2} + a d\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{2 \, {\left(a^{2} c^{2} x^{2} + a^{3} c\right)}}\right]"," ",0,"[1/4*(2*a*c*d*x - 2*a^2*e - (c*d*x^2 + a*d)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a^2*c^2*x^2 + a^3*c), 1/2*(a*c*d*x - a^2*e + (c*d*x^2 + a*d)*sqrt(a*c)*arctan(sqrt(a*c)*x/a))/(a^2*c^2*x^2 + a^3*c)]","A",0
510,1,441,0,0.972235," ","integrate(1/(e*x+d)/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a c d^{2} e + 2 \, a^{2} e^{3} + {\left(a c d^{3} + 3 \, a^{2} d e^{2} + {\left(c^{2} d^{3} + 3 \, a c d e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} + 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 2 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} x - 2 \, {\left(a c e^{3} x^{2} + a^{2} e^{3}\right)} \log\left(c x^{2} + a\right) + 4 \, {\left(a c e^{3} x^{2} + a^{2} e^{3}\right)} \log\left(e x + d\right)}{4 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{2}\right)}}, \frac{a c d^{2} e + a^{2} e^{3} + {\left(a c d^{3} + 3 \, a^{2} d e^{2} + {\left(c^{2} d^{3} + 3 \, a c d e^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + {\left(c^{2} d^{3} + a c d e^{2}\right)} x - {\left(a c e^{3} x^{2} + a^{2} e^{3}\right)} \log\left(c x^{2} + a\right) + 2 \, {\left(a c e^{3} x^{2} + a^{2} e^{3}\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*a*c*d^2*e + 2*a^2*e^3 + (a*c*d^3 + 3*a^2*d*e^2 + (c^2*d^3 + 3*a*c*d*e^2)*x^2)*sqrt(-c/a)*log((c*x^2 + 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 2*(c^2*d^3 + a*c*d*e^2)*x - 2*(a*c*e^3*x^2 + a^2*e^3)*log(c*x^2 + a) + 4*(a*c*e^3*x^2 + a^2*e^3)*log(e*x + d))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^2), 1/2*(a*c*d^2*e + a^2*e^3 + (a*c*d^3 + 3*a^2*d*e^2 + (c^2*d^3 + 3*a*c*d*e^2)*x^2)*sqrt(c/a)*arctan(x*sqrt(c/a)) + (c^2*d^3 + a*c*d*e^2)*x - (a*c*e^3*x^2 + a^2*e^3)*log(c*x^2 + a) + 2*(a*c*e^3*x^2 + a^2*e^3)*log(e*x + d))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^2)]","A",0
511,1,1111,0,2.377077," ","integrate(1/(e*x+d)^2/(c*x^2+a)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a c^{2} d^{4} e - 4 \, a^{3} e^{5} + 2 \, {\left(c^{3} d^{4} e - 2 \, a c^{2} d^{2} e^{3} - 3 \, a^{2} c e^{5}\right)} x^{2} - {\left(a c^{2} d^{5} + 6 \, a^{2} c d^{3} e^{2} - 3 \, a^{3} d e^{4} + {\left(c^{3} d^{4} e + 6 \, a c^{2} d^{2} e^{3} - 3 \, a^{2} c e^{5}\right)} x^{3} + {\left(c^{3} d^{5} + 6 \, a c^{2} d^{3} e^{2} - 3 \, a^{2} c d e^{4}\right)} x^{2} + {\left(a c^{2} d^{4} e + 6 \, a^{2} c d^{2} e^{3} - 3 \, a^{3} e^{5}\right)} x\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 2 \, {\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x - 8 \, {\left(a c^{2} d e^{4} x^{3} + a c^{2} d^{2} e^{3} x^{2} + a^{2} c d e^{4} x + a^{2} c d^{2} e^{3}\right)} \log\left(c x^{2} + a\right) + 16 \, {\left(a c^{2} d e^{4} x^{3} + a c^{2} d^{2} e^{3} x^{2} + a^{2} c d e^{4} x + a^{2} c d^{2} e^{3}\right)} \log\left(e x + d\right)}{4 \, {\left(a^{2} c^{3} d^{7} + 3 \, a^{3} c^{2} d^{5} e^{2} + 3 \, a^{4} c d^{3} e^{4} + a^{5} d e^{6} + {\left(a c^{4} d^{6} e + 3 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} + a^{4} c e^{7}\right)} x^{3} + {\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)} x^{2} + {\left(a^{2} c^{3} d^{6} e + 3 \, a^{3} c^{2} d^{4} e^{3} + 3 \, a^{4} c d^{2} e^{5} + a^{5} e^{7}\right)} x\right)}}, \frac{2 \, a c^{2} d^{4} e - 2 \, a^{3} e^{5} + {\left(c^{3} d^{4} e - 2 \, a c^{2} d^{2} e^{3} - 3 \, a^{2} c e^{5}\right)} x^{2} + {\left(a c^{2} d^{5} + 6 \, a^{2} c d^{3} e^{2} - 3 \, a^{3} d e^{4} + {\left(c^{3} d^{4} e + 6 \, a c^{2} d^{2} e^{3} - 3 \, a^{2} c e^{5}\right)} x^{3} + {\left(c^{3} d^{5} + 6 \, a c^{2} d^{3} e^{2} - 3 \, a^{2} c d e^{4}\right)} x^{2} + {\left(a c^{2} d^{4} e + 6 \, a^{2} c d^{2} e^{3} - 3 \, a^{3} e^{5}\right)} x\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + {\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x - 4 \, {\left(a c^{2} d e^{4} x^{3} + a c^{2} d^{2} e^{3} x^{2} + a^{2} c d e^{4} x + a^{2} c d^{2} e^{3}\right)} \log\left(c x^{2} + a\right) + 8 \, {\left(a c^{2} d e^{4} x^{3} + a c^{2} d^{2} e^{3} x^{2} + a^{2} c d e^{4} x + a^{2} c d^{2} e^{3}\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} c^{3} d^{7} + 3 \, a^{3} c^{2} d^{5} e^{2} + 3 \, a^{4} c d^{3} e^{4} + a^{5} d e^{6} + {\left(a c^{4} d^{6} e + 3 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} + a^{4} c e^{7}\right)} x^{3} + {\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)} x^{2} + {\left(a^{2} c^{3} d^{6} e + 3 \, a^{3} c^{2} d^{4} e^{3} + 3 \, a^{4} c d^{2} e^{5} + a^{5} e^{7}\right)} x\right)}}\right]"," ",0,"[1/4*(4*a*c^2*d^4*e - 4*a^3*e^5 + 2*(c^3*d^4*e - 2*a*c^2*d^2*e^3 - 3*a^2*c*e^5)*x^2 - (a*c^2*d^5 + 6*a^2*c*d^3*e^2 - 3*a^3*d*e^4 + (c^3*d^4*e + 6*a*c^2*d^2*e^3 - 3*a^2*c*e^5)*x^3 + (c^3*d^5 + 6*a*c^2*d^3*e^2 - 3*a^2*c*d*e^4)*x^2 + (a*c^2*d^4*e + 6*a^2*c*d^2*e^3 - 3*a^3*e^5)*x)*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 2*(c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x - 8*(a*c^2*d*e^4*x^3 + a*c^2*d^2*e^3*x^2 + a^2*c*d*e^4*x + a^2*c*d^2*e^3)*log(c*x^2 + a) + 16*(a*c^2*d*e^4*x^3 + a*c^2*d^2*e^3*x^2 + a^2*c*d*e^4*x + a^2*c*d^2*e^3)*log(e*x + d))/(a^2*c^3*d^7 + 3*a^3*c^2*d^5*e^2 + 3*a^4*c*d^3*e^4 + a^5*d*e^6 + (a*c^4*d^6*e + 3*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 + a^4*c*e^7)*x^3 + (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)*x^2 + (a^2*c^3*d^6*e + 3*a^3*c^2*d^4*e^3 + 3*a^4*c*d^2*e^5 + a^5*e^7)*x), 1/2*(2*a*c^2*d^4*e - 2*a^3*e^5 + (c^3*d^4*e - 2*a*c^2*d^2*e^3 - 3*a^2*c*e^5)*x^2 + (a*c^2*d^5 + 6*a^2*c*d^3*e^2 - 3*a^3*d*e^4 + (c^3*d^4*e + 6*a*c^2*d^2*e^3 - 3*a^2*c*e^5)*x^3 + (c^3*d^5 + 6*a*c^2*d^3*e^2 - 3*a^2*c*d*e^4)*x^2 + (a*c^2*d^4*e + 6*a^2*c*d^2*e^3 - 3*a^3*e^5)*x)*sqrt(c/a)*arctan(x*sqrt(c/a)) + (c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x - 4*(a*c^2*d*e^4*x^3 + a*c^2*d^2*e^3*x^2 + a^2*c*d*e^4*x + a^2*c*d^2*e^3)*log(c*x^2 + a) + 8*(a*c^2*d*e^4*x^3 + a*c^2*d^2*e^3*x^2 + a^2*c*d*e^4*x + a^2*c*d^2*e^3)*log(e*x + d))/(a^2*c^3*d^7 + 3*a^3*c^2*d^5*e^2 + 3*a^4*c*d^3*e^4 + a^5*d*e^6 + (a*c^4*d^6*e + 3*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 + a^4*c*e^7)*x^3 + (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)*x^2 + (a^2*c^3*d^6*e + 3*a^3*c^2*d^4*e^3 + 3*a^4*c*d^2*e^5 + a^5*e^7)*x)]","B",0
512,1,707,0,0.414248," ","integrate((e*x+d)^5/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{20 \, a^{3} c^{2} d^{4} e + 40 \, a^{4} c d^{2} e^{3} - 12 \, a^{5} e^{5} - 2 \, {\left(3 \, a c^{4} d^{5} + 10 \, a^{2} c^{3} d^{3} e^{2} - 25 \, a^{3} c^{2} d e^{4}\right)} x^{3} + 16 \, {\left(5 \, a^{3} c^{2} d^{2} e^{3} - a^{4} c e^{5}\right)} x^{2} + {\left(3 \, a^{2} c^{2} d^{5} + 10 \, a^{3} c d^{3} e^{2} + 15 \, a^{4} d e^{4} + {\left(3 \, c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 15 \, a^{2} c^{2} d e^{4}\right)} x^{4} + 2 \, {\left(3 \, a c^{3} d^{5} + 10 \, a^{2} c^{2} d^{3} e^{2} + 15 \, a^{3} c d e^{4}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 10 \, {\left(a^{2} c^{3} d^{5} - 2 \, a^{3} c^{2} d^{3} e^{2} - 3 \, a^{4} c d e^{4}\right)} x - 8 \, {\left(a^{3} c^{2} e^{5} x^{4} + 2 \, a^{4} c e^{5} x^{2} + a^{5} e^{5}\right)} \log\left(c x^{2} + a\right)}{16 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}, -\frac{10 \, a^{3} c^{2} d^{4} e + 20 \, a^{4} c d^{2} e^{3} - 6 \, a^{5} e^{5} - {\left(3 \, a c^{4} d^{5} + 10 \, a^{2} c^{3} d^{3} e^{2} - 25 \, a^{3} c^{2} d e^{4}\right)} x^{3} + 8 \, {\left(5 \, a^{3} c^{2} d^{2} e^{3} - a^{4} c e^{5}\right)} x^{2} - {\left(3 \, a^{2} c^{2} d^{5} + 10 \, a^{3} c d^{3} e^{2} + 15 \, a^{4} d e^{4} + {\left(3 \, c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 15 \, a^{2} c^{2} d e^{4}\right)} x^{4} + 2 \, {\left(3 \, a c^{3} d^{5} + 10 \, a^{2} c^{2} d^{3} e^{2} + 15 \, a^{3} c d e^{4}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - 5 \, {\left(a^{2} c^{3} d^{5} - 2 \, a^{3} c^{2} d^{3} e^{2} - 3 \, a^{4} c d e^{4}\right)} x - 4 \, {\left(a^{3} c^{2} e^{5} x^{4} + 2 \, a^{4} c e^{5} x^{2} + a^{5} e^{5}\right)} \log\left(c x^{2} + a\right)}{8 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}\right]"," ",0,"[-1/16*(20*a^3*c^2*d^4*e + 40*a^4*c*d^2*e^3 - 12*a^5*e^5 - 2*(3*a*c^4*d^5 + 10*a^2*c^3*d^3*e^2 - 25*a^3*c^2*d*e^4)*x^3 + 16*(5*a^3*c^2*d^2*e^3 - a^4*c*e^5)*x^2 + (3*a^2*c^2*d^5 + 10*a^3*c*d^3*e^2 + 15*a^4*d*e^4 + (3*c^4*d^5 + 10*a*c^3*d^3*e^2 + 15*a^2*c^2*d*e^4)*x^4 + 2*(3*a*c^3*d^5 + 10*a^2*c^2*d^3*e^2 + 15*a^3*c*d*e^4)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 10*(a^2*c^3*d^5 - 2*a^3*c^2*d^3*e^2 - 3*a^4*c*d*e^4)*x - 8*(a^3*c^2*e^5*x^4 + 2*a^4*c*e^5*x^2 + a^5*e^5)*log(c*x^2 + a))/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3), -1/8*(10*a^3*c^2*d^4*e + 20*a^4*c*d^2*e^3 - 6*a^5*e^5 - (3*a*c^4*d^5 + 10*a^2*c^3*d^3*e^2 - 25*a^3*c^2*d*e^4)*x^3 + 8*(5*a^3*c^2*d^2*e^3 - a^4*c*e^5)*x^2 - (3*a^2*c^2*d^5 + 10*a^3*c*d^3*e^2 + 15*a^4*d*e^4 + (3*c^4*d^5 + 10*a*c^3*d^3*e^2 + 15*a^2*c^2*d*e^4)*x^4 + 2*(3*a*c^3*d^5 + 10*a^2*c^2*d^3*e^2 + 15*a^3*c*d*e^4)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - 5*(a^2*c^3*d^5 - 2*a^3*c^2*d^3*e^2 - 3*a^4*c*d*e^4)*x - 4*(a^3*c^2*e^5*x^4 + 2*a^4*c*e^5*x^2 + a^5*e^5)*log(c*x^2 + a))/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3)]","A",0
513,1,554,0,0.411479," ","integrate((e*x+d)^4/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{32 \, a^{3} c^{2} d e^{3} x^{2} + 16 \, a^{3} c^{2} d^{3} e + 16 \, a^{4} c d e^{3} - 2 \, {\left(3 \, a c^{4} d^{4} + 6 \, a^{2} c^{3} d^{2} e^{2} - 5 \, a^{3} c^{2} e^{4}\right)} x^{3} + 3 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(5 \, a^{2} c^{3} d^{4} - 6 \, a^{3} c^{2} d^{2} e^{2} - 3 \, a^{4} c e^{4}\right)} x}{16 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}, -\frac{16 \, a^{3} c^{2} d e^{3} x^{2} + 8 \, a^{3} c^{2} d^{3} e + 8 \, a^{4} c d e^{3} - {\left(3 \, a c^{4} d^{4} + 6 \, a^{2} c^{3} d^{2} e^{2} - 5 \, a^{3} c^{2} e^{4}\right)} x^{3} - 3 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(c^{4} d^{4} + 2 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(5 \, a^{2} c^{3} d^{4} - 6 \, a^{3} c^{2} d^{2} e^{2} - 3 \, a^{4} c e^{4}\right)} x}{8 \, {\left(a^{3} c^{5} x^{4} + 2 \, a^{4} c^{4} x^{2} + a^{5} c^{3}\right)}}\right]"," ",0,"[-1/16*(32*a^3*c^2*d*e^3*x^2 + 16*a^3*c^2*d^3*e + 16*a^4*c*d*e^3 - 2*(3*a*c^4*d^4 + 6*a^2*c^3*d^2*e^2 - 5*a^3*c^2*e^4)*x^3 + 3*(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4 + 2*(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(5*a^2*c^3*d^4 - 6*a^3*c^2*d^2*e^2 - 3*a^4*c*e^4)*x)/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3), -1/8*(16*a^3*c^2*d*e^3*x^2 + 8*a^3*c^2*d^3*e + 8*a^4*c*d*e^3 - (3*a*c^4*d^4 + 6*a^2*c^3*d^2*e^2 - 5*a^3*c^2*e^4)*x^3 - 3*(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (c^4*d^4 + 2*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^4 + 2*(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (5*a^2*c^3*d^4 - 6*a^3*c^2*d^2*e^2 - 3*a^4*c*e^4)*x)/(a^3*c^5*x^4 + 2*a^4*c^4*x^2 + a^5*c^3)]","B",0
514,1,406,0,0.412702," ","integrate((e*x+d)^3/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{8 \, a^{3} c e^{3} x^{2} + 12 \, a^{3} c d^{2} e + 4 \, a^{4} e^{3} - 6 \, {\left(a c^{3} d^{3} + a^{2} c^{2} d e^{2}\right)} x^{3} + 3 \, {\left(a^{2} c d^{3} + a^{3} d e^{2} + {\left(c^{3} d^{3} + a c^{2} d e^{2}\right)} x^{4} + 2 \, {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(5 \, a^{2} c^{2} d^{3} - 3 \, a^{3} c d e^{2}\right)} x}{16 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}, -\frac{4 \, a^{3} c e^{3} x^{2} + 6 \, a^{3} c d^{2} e + 2 \, a^{4} e^{3} - 3 \, {\left(a c^{3} d^{3} + a^{2} c^{2} d e^{2}\right)} x^{3} - 3 \, {\left(a^{2} c d^{3} + a^{3} d e^{2} + {\left(c^{3} d^{3} + a c^{2} d e^{2}\right)} x^{4} + 2 \, {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(5 \, a^{2} c^{2} d^{3} - 3 \, a^{3} c d e^{2}\right)} x}{8 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}\right]"," ",0,"[-1/16*(8*a^3*c*e^3*x^2 + 12*a^3*c*d^2*e + 4*a^4*e^3 - 6*(a*c^3*d^3 + a^2*c^2*d*e^2)*x^3 + 3*(a^2*c*d^3 + a^3*d*e^2 + (c^3*d^3 + a*c^2*d*e^2)*x^4 + 2*(a*c^2*d^3 + a^2*c*d*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(5*a^2*c^2*d^3 - 3*a^3*c*d*e^2)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2), -1/8*(4*a^3*c*e^3*x^2 + 6*a^3*c*d^2*e + 2*a^4*e^3 - 3*(a*c^3*d^3 + a^2*c^2*d*e^2)*x^3 - 3*(a^2*c*d^3 + a^3*d*e^2 + (c^3*d^3 + a*c^2*d*e^2)*x^4 + 2*(a*c^2*d^3 + a^2*c*d*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (5*a^2*c^2*d^3 - 3*a^3*c*d*e^2)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2)]","B",0
515,1,359,0,0.413040," ","integrate((e*x+d)^2/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[-\frac{8 \, a^{3} c d e - 2 \, {\left(3 \, a c^{3} d^{2} + a^{2} c^{2} e^{2}\right)} x^{3} + {\left(3 \, a^{2} c d^{2} + a^{3} e^{2} + {\left(3 \, c^{3} d^{2} + a c^{2} e^{2}\right)} x^{4} + 2 \, {\left(3 \, a c^{2} d^{2} + a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 2 \, {\left(5 \, a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)} x}{16 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}, -\frac{4 \, a^{3} c d e - {\left(3 \, a c^{3} d^{2} + a^{2} c^{2} e^{2}\right)} x^{3} - {\left(3 \, a^{2} c d^{2} + a^{3} e^{2} + {\left(3 \, c^{3} d^{2} + a c^{2} e^{2}\right)} x^{4} + 2 \, {\left(3 \, a c^{2} d^{2} + a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - {\left(5 \, a^{2} c^{2} d^{2} - a^{3} c e^{2}\right)} x}{8 \, {\left(a^{3} c^{4} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{5} c^{2}\right)}}\right]"," ",0,"[-1/16*(8*a^3*c*d*e - 2*(3*a*c^3*d^2 + a^2*c^2*e^2)*x^3 + (3*a^2*c*d^2 + a^3*e^2 + (3*c^3*d^2 + a*c^2*e^2)*x^4 + 2*(3*a*c^2*d^2 + a^2*c*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 2*(5*a^2*c^2*d^2 - a^3*c*e^2)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2), -1/8*(4*a^3*c*d*e - (3*a*c^3*d^2 + a^2*c^2*e^2)*x^3 - (3*a^2*c*d^2 + a^3*e^2 + (3*c^3*d^2 + a*c^2*e^2)*x^4 + 2*(3*a*c^2*d^2 + a^2*c*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - (5*a^2*c^2*d^2 - a^3*c*e^2)*x)/(a^3*c^4*x^4 + 2*a^4*c^3*x^2 + a^5*c^2)]","A",0
516,1,212,0,0.406384," ","integrate((e*x+d)/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{6 \, a c^{2} d x^{3} + 10 \, a^{2} c d x - 4 \, a^{3} e - 3 \, {\left(c^{2} d x^{4} + 2 \, a c d x^{2} + a^{2} d\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{16 \, {\left(a^{3} c^{3} x^{4} + 2 \, a^{4} c^{2} x^{2} + a^{5} c\right)}}, \frac{3 \, a c^{2} d x^{3} + 5 \, a^{2} c d x - 2 \, a^{3} e + 3 \, {\left(c^{2} d x^{4} + 2 \, a c d x^{2} + a^{2} d\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{8 \, {\left(a^{3} c^{3} x^{4} + 2 \, a^{4} c^{2} x^{2} + a^{5} c\right)}}\right]"," ",0,"[1/16*(6*a*c^2*d*x^3 + 10*a^2*c*d*x - 4*a^3*e - 3*(c^2*d*x^4 + 2*a*c*d*x^2 + a^2*d)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a^3*c^3*x^4 + 2*a^4*c^2*x^2 + a^5*c), 1/8*(3*a*c^2*d*x^3 + 5*a^2*c*d*x - 2*a^3*e + 3*(c^2*d*x^4 + 2*a*c*d*x^2 + a^2*d)*sqrt(a*c)*arctan(sqrt(a*c)*x/a))/(a^3*c^3*x^4 + 2*a^4*c^2*x^2 + a^5*c)]","A",0
517,1,1020,0,3.593017," ","integrate(1/(e*x+d)/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} c^{2} d^{4} e + 16 \, a^{3} c d^{2} e^{3} + 12 \, a^{4} e^{5} + 2 \, {\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} + 8 \, {\left(a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{2} + {\left(3 \, a^{2} c^{2} d^{5} + 10 \, a^{3} c d^{3} e^{2} + 15 \, a^{4} d e^{4} + {\left(3 \, c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 15 \, a^{2} c^{2} d e^{4}\right)} x^{4} + 2 \, {\left(3 \, a c^{3} d^{5} + 10 \, a^{2} c^{2} d^{3} e^{2} + 15 \, a^{3} c d e^{4}\right)} x^{2}\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} + 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 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(a^{2} c^{2} e^{5} x^{4} + 2 \, a^{3} c e^{5} x^{2} + a^{4} e^{5}\right)} \log\left(c x^{2} + a\right) + 16 \, {\left(a^{2} c^{2} e^{5} x^{4} + 2 \, a^{3} c e^{5} x^{2} + a^{4} e^{5}\right)} \log\left(e x + d\right)}{16 \, {\left(a^{4} c^{3} d^{6} + 3 \, a^{5} c^{2} d^{4} e^{2} + 3 \, a^{6} c d^{2} e^{4} + a^{7} e^{6} + {\left(a^{2} c^{5} d^{6} + 3 \, a^{3} c^{4} d^{4} e^{2} + 3 \, a^{4} c^{3} d^{2} e^{4} + a^{5} c^{2} e^{6}\right)} x^{4} + 2 \, {\left(a^{3} c^{4} d^{6} + 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} + a^{6} c e^{6}\right)} x^{2}\right)}}, \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(3 \, a^{2} c^{2} d^{5} + 10 \, a^{3} c d^{3} e^{2} + 15 \, a^{4} d e^{4} + {\left(3 \, c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 15 \, a^{2} c^{2} d e^{4}\right)} x^{4} + 2 \, {\left(3 \, a c^{3} d^{5} + 10 \, a^{2} c^{2} d^{3} e^{2} + 15 \, a^{3} c d e^{4}\right)} x^{2}\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + {\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 - 4 \, {\left(a^{2} c^{2} e^{5} x^{4} + 2 \, a^{3} c e^{5} x^{2} + a^{4} e^{5}\right)} \log\left(c x^{2} + a\right) + 8 \, {\left(a^{2} c^{2} e^{5} x^{4} + 2 \, a^{3} c e^{5} x^{2} + a^{4} e^{5}\right)} \log\left(e x + d\right)}{8 \, {\left(a^{4} c^{3} d^{6} + 3 \, a^{5} c^{2} d^{4} e^{2} + 3 \, a^{6} c d^{2} e^{4} + a^{7} e^{6} + {\left(a^{2} c^{5} d^{6} + 3 \, a^{3} c^{4} d^{4} e^{2} + 3 \, a^{4} c^{3} d^{2} e^{4} + a^{5} c^{2} e^{6}\right)} x^{4} + 2 \, {\left(a^{3} c^{4} d^{6} + 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} + a^{6} c e^{6}\right)} x^{2}\right)}}\right]"," ",0,"[1/16*(4*a^2*c^2*d^4*e + 16*a^3*c*d^2*e^3 + 12*a^4*e^5 + 2*(3*c^4*d^5 + 10*a*c^3*d^3*e^2 + 7*a^2*c^2*d*e^4)*x^3 + 8*(a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^2 + (3*a^2*c^2*d^5 + 10*a^3*c*d^3*e^2 + 15*a^4*d*e^4 + (3*c^4*d^5 + 10*a*c^3*d^3*e^2 + 15*a^2*c^2*d*e^4)*x^4 + 2*(3*a*c^3*d^5 + 10*a^2*c^2*d^3*e^2 + 15*a^3*c*d*e^4)*x^2)*sqrt(-c/a)*log((c*x^2 + 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 2*(5*a*c^3*d^5 + 14*a^2*c^2*d^3*e^2 + 9*a^3*c*d*e^4)*x - 8*(a^2*c^2*e^5*x^4 + 2*a^3*c*e^5*x^2 + a^4*e^5)*log(c*x^2 + a) + 16*(a^2*c^2*e^5*x^4 + 2*a^3*c*e^5*x^2 + a^4*e^5)*log(e*x + d))/(a^4*c^3*d^6 + 3*a^5*c^2*d^4*e^2 + 3*a^6*c*d^2*e^4 + a^7*e^6 + (a^2*c^5*d^6 + 3*a^3*c^4*d^4*e^2 + 3*a^4*c^3*d^2*e^4 + a^5*c^2*e^6)*x^4 + 2*(a^3*c^4*d^6 + 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 + a^6*c*e^6)*x^2), 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 + (3*a^2*c^2*d^5 + 10*a^3*c*d^3*e^2 + 15*a^4*d*e^4 + (3*c^4*d^5 + 10*a*c^3*d^3*e^2 + 15*a^2*c^2*d*e^4)*x^4 + 2*(3*a*c^3*d^5 + 10*a^2*c^2*d^3*e^2 + 15*a^3*c*d*e^4)*x^2)*sqrt(c/a)*arctan(x*sqrt(c/a)) + (5*a*c^3*d^5 + 14*a^2*c^2*d^3*e^2 + 9*a^3*c*d*e^4)*x - 4*(a^2*c^2*e^5*x^4 + 2*a^3*c*e^5*x^2 + a^4*e^5)*log(c*x^2 + a) + 8*(a^2*c^2*e^5*x^4 + 2*a^3*c*e^5*x^2 + a^4*e^5)*log(e*x + d))/(a^4*c^3*d^6 + 3*a^5*c^2*d^4*e^2 + 3*a^6*c*d^2*e^4 + a^7*e^6 + (a^2*c^5*d^6 + 3*a^3*c^4*d^4*e^2 + 3*a^4*c^3*d^2*e^4 + a^5*c^2*e^6)*x^4 + 2*(a^3*c^4*d^6 + 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 + a^6*c*e^6)*x^2)]","B",0
518,1,2322,0,9.386539," ","integrate(1/(e*x+d)^2/(c*x^2+a)^3,x, algorithm=""fricas"")","\left[\frac{8 \, a^{2} c^{3} d^{6} e + 48 \, a^{3} c^{2} d^{4} e^{3} + 24 \, a^{4} c d^{2} e^{5} - 16 \, a^{5} e^{7} + 6 \, {\left(c^{5} d^{6} e + 5 \, a c^{4} d^{4} e^{3} - a^{2} c^{3} d^{2} e^{5} - 5 \, a^{3} c^{2} e^{7}\right)} x^{4} + 6 \, {\left(c^{5} d^{7} + 5 \, a c^{4} d^{5} e^{2} + 7 \, a^{2} c^{3} d^{3} e^{4} + 3 \, a^{3} c^{2} d e^{6}\right)} x^{3} + 2 \, {\left(5 \, a c^{4} d^{6} e + 33 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} - 25 \, a^{4} c e^{7}\right)} x^{2} + 3 \, {\left(a^{2} c^{3} d^{7} + 5 \, a^{3} c^{2} d^{5} e^{2} + 15 \, a^{4} c d^{3} e^{4} - 5 \, a^{5} d e^{6} + {\left(c^{5} d^{6} e + 5 \, a c^{4} d^{4} e^{3} + 15 \, a^{2} c^{3} d^{2} e^{5} - 5 \, a^{3} c^{2} e^{7}\right)} x^{5} + {\left(c^{5} d^{7} + 5 \, a c^{4} d^{5} e^{2} + 15 \, a^{2} c^{3} d^{3} e^{4} - 5 \, a^{3} c^{2} d e^{6}\right)} x^{4} + 2 \, {\left(a c^{4} d^{6} e + 5 \, a^{2} c^{3} d^{4} e^{3} + 15 \, a^{3} c^{2} d^{2} e^{5} - 5 \, a^{4} c e^{7}\right)} x^{3} + 2 \, {\left(a c^{4} d^{7} + 5 \, a^{2} c^{3} d^{5} e^{2} + 15 \, a^{3} c^{2} d^{3} e^{4} - 5 \, a^{4} c d e^{6}\right)} x^{2} + {\left(a^{2} c^{3} d^{6} e + 5 \, a^{3} c^{2} d^{4} e^{3} + 15 \, a^{4} c d^{2} e^{5} - 5 \, a^{5} e^{7}\right)} x\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} + 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 2 \, {\left(5 \, a c^{4} d^{7} + 21 \, a^{2} c^{3} d^{5} e^{2} + 27 \, a^{3} c^{2} d^{3} e^{4} + 11 \, a^{4} c d e^{6}\right)} x - 48 \, {\left(a^{2} c^{3} d e^{6} x^{5} + a^{2} c^{3} d^{2} e^{5} x^{4} + 2 \, a^{3} c^{2} d e^{6} x^{3} + 2 \, a^{3} c^{2} d^{2} e^{5} x^{2} + a^{4} c d e^{6} x + a^{4} c d^{2} e^{5}\right)} \log\left(c x^{2} + a\right) + 96 \, {\left(a^{2} c^{3} d e^{6} x^{5} + a^{2} c^{3} d^{2} e^{5} x^{4} + 2 \, a^{3} c^{2} d e^{6} x^{3} + 2 \, a^{3} c^{2} d^{2} e^{5} x^{2} + a^{4} c d e^{6} x + a^{4} c d^{2} e^{5}\right)} \log\left(e x + d\right)}{16 \, {\left(a^{4} c^{4} d^{9} + 4 \, a^{5} c^{3} d^{7} e^{2} + 6 \, a^{6} c^{2} d^{5} e^{4} + 4 \, a^{7} c d^{3} e^{6} + a^{8} d e^{8} + {\left(a^{2} c^{6} d^{8} e + 4 \, a^{3} c^{5} d^{6} e^{3} + 6 \, a^{4} c^{4} d^{4} e^{5} + 4 \, a^{5} c^{3} d^{2} e^{7} + a^{6} c^{2} e^{9}\right)} x^{5} + {\left(a^{2} c^{6} d^{9} + 4 \, a^{3} c^{5} d^{7} e^{2} + 6 \, a^{4} c^{4} d^{5} e^{4} + 4 \, a^{5} c^{3} d^{3} e^{6} + a^{6} c^{2} d e^{8}\right)} x^{4} + 2 \, {\left(a^{3} c^{5} d^{8} e + 4 \, a^{4} c^{4} d^{6} e^{3} + 6 \, a^{5} c^{3} d^{4} e^{5} + 4 \, a^{6} c^{2} d^{2} e^{7} + a^{7} c e^{9}\right)} x^{3} + 2 \, {\left(a^{3} c^{5} d^{9} + 4 \, a^{4} c^{4} d^{7} e^{2} + 6 \, a^{5} c^{3} d^{5} e^{4} + 4 \, a^{6} c^{2} d^{3} e^{6} + a^{7} c d e^{8}\right)} x^{2} + {\left(a^{4} c^{4} d^{8} e + 4 \, a^{5} c^{3} d^{6} e^{3} + 6 \, a^{6} c^{2} d^{4} e^{5} + 4 \, a^{7} c d^{2} e^{7} + a^{8} e^{9}\right)} x\right)}}, \frac{4 \, a^{2} c^{3} d^{6} e + 24 \, a^{3} c^{2} d^{4} e^{3} + 12 \, a^{4} c d^{2} e^{5} - 8 \, a^{5} e^{7} + 3 \, {\left(c^{5} d^{6} e + 5 \, a c^{4} d^{4} e^{3} - a^{2} c^{3} d^{2} e^{5} - 5 \, a^{3} c^{2} e^{7}\right)} x^{4} + 3 \, {\left(c^{5} d^{7} + 5 \, a c^{4} d^{5} e^{2} + 7 \, a^{2} c^{3} d^{3} e^{4} + 3 \, a^{3} c^{2} d e^{6}\right)} x^{3} + {\left(5 \, a c^{4} d^{6} e + 33 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} - 25 \, a^{4} c e^{7}\right)} x^{2} + 3 \, {\left(a^{2} c^{3} d^{7} + 5 \, a^{3} c^{2} d^{5} e^{2} + 15 \, a^{4} c d^{3} e^{4} - 5 \, a^{5} d e^{6} + {\left(c^{5} d^{6} e + 5 \, a c^{4} d^{4} e^{3} + 15 \, a^{2} c^{3} d^{2} e^{5} - 5 \, a^{3} c^{2} e^{7}\right)} x^{5} + {\left(c^{5} d^{7} + 5 \, a c^{4} d^{5} e^{2} + 15 \, a^{2} c^{3} d^{3} e^{4} - 5 \, a^{3} c^{2} d e^{6}\right)} x^{4} + 2 \, {\left(a c^{4} d^{6} e + 5 \, a^{2} c^{3} d^{4} e^{3} + 15 \, a^{3} c^{2} d^{2} e^{5} - 5 \, a^{4} c e^{7}\right)} x^{3} + 2 \, {\left(a c^{4} d^{7} + 5 \, a^{2} c^{3} d^{5} e^{2} + 15 \, a^{3} c^{2} d^{3} e^{4} - 5 \, a^{4} c d e^{6}\right)} x^{2} + {\left(a^{2} c^{3} d^{6} e + 5 \, a^{3} c^{2} d^{4} e^{3} + 15 \, a^{4} c d^{2} e^{5} - 5 \, a^{5} e^{7}\right)} x\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + {\left(5 \, a c^{4} d^{7} + 21 \, a^{2} c^{3} d^{5} e^{2} + 27 \, a^{3} c^{2} d^{3} e^{4} + 11 \, a^{4} c d e^{6}\right)} x - 24 \, {\left(a^{2} c^{3} d e^{6} x^{5} + a^{2} c^{3} d^{2} e^{5} x^{4} + 2 \, a^{3} c^{2} d e^{6} x^{3} + 2 \, a^{3} c^{2} d^{2} e^{5} x^{2} + a^{4} c d e^{6} x + a^{4} c d^{2} e^{5}\right)} \log\left(c x^{2} + a\right) + 48 \, {\left(a^{2} c^{3} d e^{6} x^{5} + a^{2} c^{3} d^{2} e^{5} x^{4} + 2 \, a^{3} c^{2} d e^{6} x^{3} + 2 \, a^{3} c^{2} d^{2} e^{5} x^{2} + a^{4} c d e^{6} x + a^{4} c d^{2} e^{5}\right)} \log\left(e x + d\right)}{8 \, {\left(a^{4} c^{4} d^{9} + 4 \, a^{5} c^{3} d^{7} e^{2} + 6 \, a^{6} c^{2} d^{5} e^{4} + 4 \, a^{7} c d^{3} e^{6} + a^{8} d e^{8} + {\left(a^{2} c^{6} d^{8} e + 4 \, a^{3} c^{5} d^{6} e^{3} + 6 \, a^{4} c^{4} d^{4} e^{5} + 4 \, a^{5} c^{3} d^{2} e^{7} + a^{6} c^{2} e^{9}\right)} x^{5} + {\left(a^{2} c^{6} d^{9} + 4 \, a^{3} c^{5} d^{7} e^{2} + 6 \, a^{4} c^{4} d^{5} e^{4} + 4 \, a^{5} c^{3} d^{3} e^{6} + a^{6} c^{2} d e^{8}\right)} x^{4} + 2 \, {\left(a^{3} c^{5} d^{8} e + 4 \, a^{4} c^{4} d^{6} e^{3} + 6 \, a^{5} c^{3} d^{4} e^{5} + 4 \, a^{6} c^{2} d^{2} e^{7} + a^{7} c e^{9}\right)} x^{3} + 2 \, {\left(a^{3} c^{5} d^{9} + 4 \, a^{4} c^{4} d^{7} e^{2} + 6 \, a^{5} c^{3} d^{5} e^{4} + 4 \, a^{6} c^{2} d^{3} e^{6} + a^{7} c d e^{8}\right)} x^{2} + {\left(a^{4} c^{4} d^{8} e + 4 \, a^{5} c^{3} d^{6} e^{3} + 6 \, a^{6} c^{2} d^{4} e^{5} + 4 \, a^{7} c d^{2} e^{7} + a^{8} e^{9}\right)} x\right)}}\right]"," ",0,"[1/16*(8*a^2*c^3*d^6*e + 48*a^3*c^2*d^4*e^3 + 24*a^4*c*d^2*e^5 - 16*a^5*e^7 + 6*(c^5*d^6*e + 5*a*c^4*d^4*e^3 - a^2*c^3*d^2*e^5 - 5*a^3*c^2*e^7)*x^4 + 6*(c^5*d^7 + 5*a*c^4*d^5*e^2 + 7*a^2*c^3*d^3*e^4 + 3*a^3*c^2*d*e^6)*x^3 + 2*(5*a*c^4*d^6*e + 33*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 - 25*a^4*c*e^7)*x^2 + 3*(a^2*c^3*d^7 + 5*a^3*c^2*d^5*e^2 + 15*a^4*c*d^3*e^4 - 5*a^5*d*e^6 + (c^5*d^6*e + 5*a*c^4*d^4*e^3 + 15*a^2*c^3*d^2*e^5 - 5*a^3*c^2*e^7)*x^5 + (c^5*d^7 + 5*a*c^4*d^5*e^2 + 15*a^2*c^3*d^3*e^4 - 5*a^3*c^2*d*e^6)*x^4 + 2*(a*c^4*d^6*e + 5*a^2*c^3*d^4*e^3 + 15*a^3*c^2*d^2*e^5 - 5*a^4*c*e^7)*x^3 + 2*(a*c^4*d^7 + 5*a^2*c^3*d^5*e^2 + 15*a^3*c^2*d^3*e^4 - 5*a^4*c*d*e^6)*x^2 + (a^2*c^3*d^6*e + 5*a^3*c^2*d^4*e^3 + 15*a^4*c*d^2*e^5 - 5*a^5*e^7)*x)*sqrt(-c/a)*log((c*x^2 + 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 2*(5*a*c^4*d^7 + 21*a^2*c^3*d^5*e^2 + 27*a^3*c^2*d^3*e^4 + 11*a^4*c*d*e^6)*x - 48*(a^2*c^3*d*e^6*x^5 + a^2*c^3*d^2*e^5*x^4 + 2*a^3*c^2*d*e^6*x^3 + 2*a^3*c^2*d^2*e^5*x^2 + a^4*c*d*e^6*x + a^4*c*d^2*e^5)*log(c*x^2 + a) + 96*(a^2*c^3*d*e^6*x^5 + a^2*c^3*d^2*e^5*x^4 + 2*a^3*c^2*d*e^6*x^3 + 2*a^3*c^2*d^2*e^5*x^2 + a^4*c*d*e^6*x + a^4*c*d^2*e^5)*log(e*x + d))/(a^4*c^4*d^9 + 4*a^5*c^3*d^7*e^2 + 6*a^6*c^2*d^5*e^4 + 4*a^7*c*d^3*e^6 + a^8*d*e^8 + (a^2*c^6*d^8*e + 4*a^3*c^5*d^6*e^3 + 6*a^4*c^4*d^4*e^5 + 4*a^5*c^3*d^2*e^7 + a^6*c^2*e^9)*x^5 + (a^2*c^6*d^9 + 4*a^3*c^5*d^7*e^2 + 6*a^4*c^4*d^5*e^4 + 4*a^5*c^3*d^3*e^6 + a^6*c^2*d*e^8)*x^4 + 2*(a^3*c^5*d^8*e + 4*a^4*c^4*d^6*e^3 + 6*a^5*c^3*d^4*e^5 + 4*a^6*c^2*d^2*e^7 + a^7*c*e^9)*x^3 + 2*(a^3*c^5*d^9 + 4*a^4*c^4*d^7*e^2 + 6*a^5*c^3*d^5*e^4 + 4*a^6*c^2*d^3*e^6 + a^7*c*d*e^8)*x^2 + (a^4*c^4*d^8*e + 4*a^5*c^3*d^6*e^3 + 6*a^6*c^2*d^4*e^5 + 4*a^7*c*d^2*e^7 + a^8*e^9)*x), 1/8*(4*a^2*c^3*d^6*e + 24*a^3*c^2*d^4*e^3 + 12*a^4*c*d^2*e^5 - 8*a^5*e^7 + 3*(c^5*d^6*e + 5*a*c^4*d^4*e^3 - a^2*c^3*d^2*e^5 - 5*a^3*c^2*e^7)*x^4 + 3*(c^5*d^7 + 5*a*c^4*d^5*e^2 + 7*a^2*c^3*d^3*e^4 + 3*a^3*c^2*d*e^6)*x^3 + (5*a*c^4*d^6*e + 33*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 - 25*a^4*c*e^7)*x^2 + 3*(a^2*c^3*d^7 + 5*a^3*c^2*d^5*e^2 + 15*a^4*c*d^3*e^4 - 5*a^5*d*e^6 + (c^5*d^6*e + 5*a*c^4*d^4*e^3 + 15*a^2*c^3*d^2*e^5 - 5*a^3*c^2*e^7)*x^5 + (c^5*d^7 + 5*a*c^4*d^5*e^2 + 15*a^2*c^3*d^3*e^4 - 5*a^3*c^2*d*e^6)*x^4 + 2*(a*c^4*d^6*e + 5*a^2*c^3*d^4*e^3 + 15*a^3*c^2*d^2*e^5 - 5*a^4*c*e^7)*x^3 + 2*(a*c^4*d^7 + 5*a^2*c^3*d^5*e^2 + 15*a^3*c^2*d^3*e^4 - 5*a^4*c*d*e^6)*x^2 + (a^2*c^3*d^6*e + 5*a^3*c^2*d^4*e^3 + 15*a^4*c*d^2*e^5 - 5*a^5*e^7)*x)*sqrt(c/a)*arctan(x*sqrt(c/a)) + (5*a*c^4*d^7 + 21*a^2*c^3*d^5*e^2 + 27*a^3*c^2*d^3*e^4 + 11*a^4*c*d*e^6)*x - 24*(a^2*c^3*d*e^6*x^5 + a^2*c^3*d^2*e^5*x^4 + 2*a^3*c^2*d*e^6*x^3 + 2*a^3*c^2*d^2*e^5*x^2 + a^4*c*d*e^6*x + a^4*c*d^2*e^5)*log(c*x^2 + a) + 48*(a^2*c^3*d*e^6*x^5 + a^2*c^3*d^2*e^5*x^4 + 2*a^3*c^2*d*e^6*x^3 + 2*a^3*c^2*d^2*e^5*x^2 + a^4*c*d*e^6*x + a^4*c*d^2*e^5)*log(e*x + d))/(a^4*c^4*d^9 + 4*a^5*c^3*d^7*e^2 + 6*a^6*c^2*d^5*e^4 + 4*a^7*c*d^3*e^6 + a^8*d*e^8 + (a^2*c^6*d^8*e + 4*a^3*c^5*d^6*e^3 + 6*a^4*c^4*d^4*e^5 + 4*a^5*c^3*d^2*e^7 + a^6*c^2*e^9)*x^5 + (a^2*c^6*d^9 + 4*a^3*c^5*d^7*e^2 + 6*a^4*c^4*d^5*e^4 + 4*a^5*c^3*d^3*e^6 + a^6*c^2*d*e^8)*x^4 + 2*(a^3*c^5*d^8*e + 4*a^4*c^4*d^6*e^3 + 6*a^5*c^3*d^4*e^5 + 4*a^6*c^2*d^2*e^7 + a^7*c*e^9)*x^3 + 2*(a^3*c^5*d^9 + 4*a^4*c^4*d^7*e^2 + 6*a^5*c^3*d^5*e^4 + 4*a^6*c^2*d^3*e^6 + a^7*c*d*e^8)*x^2 + (a^4*c^4*d^8*e + 4*a^5*c^3*d^6*e^3 + 6*a^6*c^2*d^4*e^5 + 4*a^7*c*d^2*e^7 + a^8*e^9)*x)]","B",0
519,1,746,0,0.416339," ","integrate((e*x+d)^4/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[-\frac{96 \, a^{4} c^{2} d e^{3} x^{2} + 64 \, a^{4} c^{2} d^{3} e + 32 \, a^{5} c d e^{3} - 6 \, {\left(5 \, a c^{5} d^{4} + 6 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}\right)} x^{5} - 16 \, {\left(5 \, a^{2} c^{4} d^{4} + 6 \, a^{3} c^{3} d^{2} e^{2} - a^{4} c^{2} e^{4}\right)} x^{3} + 3 \, {\left(5 \, a^{3} c^{2} d^{4} + 6 \, a^{4} c d^{2} e^{2} + a^{5} e^{4} + {\left(5 \, c^{5} d^{4} + 6 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} x^{6} + 3 \, {\left(5 \, a c^{4} d^{4} + 6 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} x^{4} + 3 \, {\left(5 \, a^{2} c^{3} d^{4} + 6 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 6 \, {\left(11 \, a^{3} c^{3} d^{4} - 6 \, a^{4} c^{2} d^{2} e^{2} - a^{5} c e^{4}\right)} x}{96 \, {\left(a^{4} c^{6} x^{6} + 3 \, a^{5} c^{5} x^{4} + 3 \, a^{6} c^{4} x^{2} + a^{7} c^{3}\right)}}, -\frac{48 \, a^{4} c^{2} d e^{3} x^{2} + 32 \, a^{4} c^{2} d^{3} e + 16 \, a^{5} c d e^{3} - 3 \, {\left(5 \, a c^{5} d^{4} + 6 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4}\right)} x^{5} - 8 \, {\left(5 \, a^{2} c^{4} d^{4} + 6 \, a^{3} c^{3} d^{2} e^{2} - a^{4} c^{2} e^{4}\right)} x^{3} - 3 \, {\left(5 \, a^{3} c^{2} d^{4} + 6 \, a^{4} c d^{2} e^{2} + a^{5} e^{4} + {\left(5 \, c^{5} d^{4} + 6 \, a c^{4} d^{2} e^{2} + a^{2} c^{3} e^{4}\right)} x^{6} + 3 \, {\left(5 \, a c^{4} d^{4} + 6 \, a^{2} c^{3} d^{2} e^{2} + a^{3} c^{2} e^{4}\right)} x^{4} + 3 \, {\left(5 \, a^{2} c^{3} d^{4} + 6 \, a^{3} c^{2} d^{2} e^{2} + a^{4} c e^{4}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - 3 \, {\left(11 \, a^{3} c^{3} d^{4} - 6 \, a^{4} c^{2} d^{2} e^{2} - a^{5} c e^{4}\right)} x}{48 \, {\left(a^{4} c^{6} x^{6} + 3 \, a^{5} c^{5} x^{4} + 3 \, a^{6} c^{4} x^{2} + a^{7} c^{3}\right)}}\right]"," ",0,"[-1/96*(96*a^4*c^2*d*e^3*x^2 + 64*a^4*c^2*d^3*e + 32*a^5*c*d*e^3 - 6*(5*a*c^5*d^4 + 6*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)*x^5 - 16*(5*a^2*c^4*d^4 + 6*a^3*c^3*d^2*e^2 - a^4*c^2*e^4)*x^3 + 3*(5*a^3*c^2*d^4 + 6*a^4*c*d^2*e^2 + a^5*e^4 + (5*c^5*d^4 + 6*a*c^4*d^2*e^2 + a^2*c^3*e^4)*x^6 + 3*(5*a*c^4*d^4 + 6*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*x^4 + 3*(5*a^2*c^3*d^4 + 6*a^3*c^2*d^2*e^2 + a^4*c*e^4)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 6*(11*a^3*c^3*d^4 - 6*a^4*c^2*d^2*e^2 - a^5*c*e^4)*x)/(a^4*c^6*x^6 + 3*a^5*c^5*x^4 + 3*a^6*c^4*x^2 + a^7*c^3), -1/48*(48*a^4*c^2*d*e^3*x^2 + 32*a^4*c^2*d^3*e + 16*a^5*c*d*e^3 - 3*(5*a*c^5*d^4 + 6*a^2*c^4*d^2*e^2 + a^3*c^3*e^4)*x^5 - 8*(5*a^2*c^4*d^4 + 6*a^3*c^3*d^2*e^2 - a^4*c^2*e^4)*x^3 - 3*(5*a^3*c^2*d^4 + 6*a^4*c*d^2*e^2 + a^5*e^4 + (5*c^5*d^4 + 6*a*c^4*d^2*e^2 + a^2*c^3*e^4)*x^6 + 3*(5*a*c^4*d^4 + 6*a^2*c^3*d^2*e^2 + a^3*c^2*e^4)*x^4 + 3*(5*a^2*c^3*d^4 + 6*a^3*c^2*d^2*e^2 + a^4*c*e^4)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - 3*(11*a^3*c^3*d^4 - 6*a^4*c^2*d^2*e^2 - a^5*c*e^4)*x)/(a^4*c^6*x^6 + 3*a^5*c^5*x^4 + 3*a^6*c^4*x^2 + a^7*c^3)]","B",0
520,1,560,0,0.408764," ","integrate((e*x+d)^3/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[-\frac{24 \, a^{4} c e^{3} x^{2} + 48 \, a^{4} c d^{2} e + 8 \, a^{5} e^{3} - 6 \, {\left(5 \, a c^{4} d^{3} + 3 \, a^{2} c^{3} d e^{2}\right)} x^{5} - 16 \, {\left(5 \, a^{2} c^{3} d^{3} + 3 \, a^{3} c^{2} d e^{2}\right)} x^{3} + 3 \, {\left(5 \, a^{3} c d^{3} + 3 \, a^{4} d e^{2} + {\left(5 \, c^{4} d^{3} + 3 \, a c^{3} d e^{2}\right)} x^{6} + 3 \, {\left(5 \, a c^{3} d^{3} + 3 \, a^{2} c^{2} d e^{2}\right)} x^{4} + 3 \, {\left(5 \, a^{2} c^{2} d^{3} + 3 \, a^{3} c d e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 6 \, {\left(11 \, a^{3} c^{2} d^{3} - 3 \, a^{4} c d e^{2}\right)} x}{96 \, {\left(a^{4} c^{5} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{6} c^{3} x^{2} + a^{7} c^{2}\right)}}, -\frac{12 \, a^{4} c e^{3} x^{2} + 24 \, a^{4} c d^{2} e + 4 \, a^{5} e^{3} - 3 \, {\left(5 \, a c^{4} d^{3} + 3 \, a^{2} c^{3} d e^{2}\right)} x^{5} - 8 \, {\left(5 \, a^{2} c^{3} d^{3} + 3 \, a^{3} c^{2} d e^{2}\right)} x^{3} - 3 \, {\left(5 \, a^{3} c d^{3} + 3 \, a^{4} d e^{2} + {\left(5 \, c^{4} d^{3} + 3 \, a c^{3} d e^{2}\right)} x^{6} + 3 \, {\left(5 \, a c^{3} d^{3} + 3 \, a^{2} c^{2} d e^{2}\right)} x^{4} + 3 \, {\left(5 \, a^{2} c^{2} d^{3} + 3 \, a^{3} c d e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - 3 \, {\left(11 \, a^{3} c^{2} d^{3} - 3 \, a^{4} c d e^{2}\right)} x}{48 \, {\left(a^{4} c^{5} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{6} c^{3} x^{2} + a^{7} c^{2}\right)}}\right]"," ",0,"[-1/96*(24*a^4*c*e^3*x^2 + 48*a^4*c*d^2*e + 8*a^5*e^3 - 6*(5*a*c^4*d^3 + 3*a^2*c^3*d*e^2)*x^5 - 16*(5*a^2*c^3*d^3 + 3*a^3*c^2*d*e^2)*x^3 + 3*(5*a^3*c*d^3 + 3*a^4*d*e^2 + (5*c^4*d^3 + 3*a*c^3*d*e^2)*x^6 + 3*(5*a*c^3*d^3 + 3*a^2*c^2*d*e^2)*x^4 + 3*(5*a^2*c^2*d^3 + 3*a^3*c*d*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 6*(11*a^3*c^2*d^3 - 3*a^4*c*d*e^2)*x)/(a^4*c^5*x^6 + 3*a^5*c^4*x^4 + 3*a^6*c^3*x^2 + a^7*c^2), -1/48*(12*a^4*c*e^3*x^2 + 24*a^4*c*d^2*e + 4*a^5*e^3 - 3*(5*a*c^4*d^3 + 3*a^2*c^3*d*e^2)*x^5 - 8*(5*a^2*c^3*d^3 + 3*a^3*c^2*d*e^2)*x^3 - 3*(5*a^3*c*d^3 + 3*a^4*d*e^2 + (5*c^4*d^3 + 3*a*c^3*d*e^2)*x^6 + 3*(5*a*c^3*d^3 + 3*a^2*c^2*d*e^2)*x^4 + 3*(5*a^2*c^2*d^3 + 3*a^3*c*d*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - 3*(11*a^3*c^2*d^3 - 3*a^4*c*d*e^2)*x)/(a^4*c^5*x^6 + 3*a^5*c^4*x^4 + 3*a^6*c^3*x^2 + a^7*c^2)]","A",0
521,1,490,0,0.403753," ","integrate((e*x+d)^2/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[-\frac{32 \, a^{4} c d e - 6 \, {\left(5 \, a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} x^{5} - 16 \, {\left(5 \, a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} x^{3} + 3 \, {\left({\left(5 \, c^{4} d^{2} + a c^{3} e^{2}\right)} x^{6} + 5 \, a^{3} c d^{2} + a^{4} e^{2} + 3 \, {\left(5 \, a c^{3} d^{2} + a^{2} c^{2} e^{2}\right)} x^{4} + 3 \, {\left(5 \, a^{2} c^{2} d^{2} + a^{3} c e^{2}\right)} x^{2}\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right) - 6 \, {\left(11 \, a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} x}{96 \, {\left(a^{4} c^{5} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{6} c^{3} x^{2} + a^{7} c^{2}\right)}}, -\frac{16 \, a^{4} c d e - 3 \, {\left(5 \, a c^{4} d^{2} + a^{2} c^{3} e^{2}\right)} x^{5} - 8 \, {\left(5 \, a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} x^{3} - 3 \, {\left({\left(5 \, c^{4} d^{2} + a c^{3} e^{2}\right)} x^{6} + 5 \, a^{3} c d^{2} + a^{4} e^{2} + 3 \, {\left(5 \, a c^{3} d^{2} + a^{2} c^{2} e^{2}\right)} x^{4} + 3 \, {\left(5 \, a^{2} c^{2} d^{2} + a^{3} c e^{2}\right)} x^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right) - 3 \, {\left(11 \, a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} x}{48 \, {\left(a^{4} c^{5} x^{6} + 3 \, a^{5} c^{4} x^{4} + 3 \, a^{6} c^{3} x^{2} + a^{7} c^{2}\right)}}\right]"," ",0,"[-1/96*(32*a^4*c*d*e - 6*(5*a*c^4*d^2 + a^2*c^3*e^2)*x^5 - 16*(5*a^2*c^3*d^2 + a^3*c^2*e^2)*x^3 + 3*((5*c^4*d^2 + a*c^3*e^2)*x^6 + 5*a^3*c*d^2 + a^4*e^2 + 3*(5*a*c^3*d^2 + a^2*c^2*e^2)*x^4 + 3*(5*a^2*c^2*d^2 + a^3*c*e^2)*x^2)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)) - 6*(11*a^3*c^2*d^2 - a^4*c*e^2)*x)/(a^4*c^5*x^6 + 3*a^5*c^4*x^4 + 3*a^6*c^3*x^2 + a^7*c^2), -1/48*(16*a^4*c*d*e - 3*(5*a*c^4*d^2 + a^2*c^3*e^2)*x^5 - 8*(5*a^2*c^3*d^2 + a^3*c^2*e^2)*x^3 - 3*((5*c^4*d^2 + a*c^3*e^2)*x^6 + 5*a^3*c*d^2 + a^4*e^2 + 3*(5*a*c^3*d^2 + a^2*c^2*e^2)*x^4 + 3*(5*a^2*c^2*d^2 + a^3*c*e^2)*x^2)*sqrt(a*c)*arctan(sqrt(a*c)*x/a) - 3*(11*a^3*c^2*d^2 - a^4*c*e^2)*x)/(a^4*c^5*x^6 + 3*a^5*c^4*x^4 + 3*a^6*c^3*x^2 + a^7*c^2)]","A",0
522,1,282,0,0.404334," ","integrate((e*x+d)/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[\frac{30 \, a c^{3} d x^{5} + 80 \, a^{2} c^{2} d x^{3} + 66 \, a^{3} c d x - 16 \, a^{4} e - 15 \, {\left(c^{3} d x^{6} + 3 \, a c^{2} d x^{4} + 3 \, a^{2} c d x^{2} + a^{3} d\right)} \sqrt{-a c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-a c} x - a}{c x^{2} + a}\right)}{96 \, {\left(a^{4} c^{4} x^{6} + 3 \, a^{5} c^{3} x^{4} + 3 \, a^{6} c^{2} x^{2} + a^{7} c\right)}}, \frac{15 \, a c^{3} d x^{5} + 40 \, a^{2} c^{2} d x^{3} + 33 \, a^{3} c d x - 8 \, a^{4} e + 15 \, {\left(c^{3} d x^{6} + 3 \, a c^{2} d x^{4} + 3 \, a^{2} c d x^{2} + a^{3} d\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} x}{a}\right)}{48 \, {\left(a^{4} c^{4} x^{6} + 3 \, a^{5} c^{3} x^{4} + 3 \, a^{6} c^{2} x^{2} + a^{7} c\right)}}\right]"," ",0,"[1/96*(30*a*c^3*d*x^5 + 80*a^2*c^2*d*x^3 + 66*a^3*c*d*x - 16*a^4*e - 15*(c^3*d*x^6 + 3*a*c^2*d*x^4 + 3*a^2*c*d*x^2 + a^3*d)*sqrt(-a*c)*log((c*x^2 - 2*sqrt(-a*c)*x - a)/(c*x^2 + a)))/(a^4*c^4*x^6 + 3*a^5*c^3*x^4 + 3*a^6*c^2*x^2 + a^7*c), 1/48*(15*a*c^3*d*x^5 + 40*a^2*c^2*d*x^3 + 33*a^3*c*d*x - 8*a^4*e + 15*(c^3*d*x^6 + 3*a*c^2*d*x^4 + 3*a^2*c*d*x^2 + a^3*d)*sqrt(a*c)*arctan(sqrt(a*c)*x/a))/(a^4*c^4*x^6 + 3*a^5*c^3*x^4 + 3*a^6*c^2*x^2 + a^7*c)]","A",0
523,1,1784,0,16.754349," ","integrate(1/(e*x+d)/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[\frac{16 \, a^{3} c^{3} d^{6} e + 72 \, a^{4} c^{2} d^{4} e^{3} + 144 \, a^{5} c d^{2} e^{5} + 88 \, a^{6} e^{7} + 6 \, {\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} + 48 \, {\left(a^{3} c^{3} d^{2} e^{5} + a^{4} c^{2} e^{7}\right)} x^{4} + 16 \, {\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} + 24 \, {\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(5 \, a^{3} c^{3} d^{7} + 21 \, a^{4} c^{2} d^{5} e^{2} + 35 \, a^{5} c d^{3} e^{4} + 35 \, a^{6} d e^{6} + {\left(5 \, c^{6} d^{7} + 21 \, a c^{5} d^{5} e^{2} + 35 \, a^{2} c^{4} d^{3} e^{4} + 35 \, a^{3} c^{3} d e^{6}\right)} x^{6} + 3 \, {\left(5 \, a c^{5} d^{7} + 21 \, a^{2} c^{4} d^{5} e^{2} + 35 \, a^{3} c^{3} d^{3} e^{4} + 35 \, a^{4} c^{2} d e^{6}\right)} x^{4} + 3 \, {\left(5 \, a^{2} c^{4} d^{7} + 21 \, a^{3} c^{3} d^{5} e^{2} + 35 \, a^{4} c^{2} d^{3} e^{4} + 35 \, a^{5} c d e^{6}\right)} x^{2}\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} + 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 6 \, {\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(a^{3} c^{3} e^{7} x^{6} + 3 \, a^{4} c^{2} e^{7} x^{4} + 3 \, a^{5} c e^{7} x^{2} + a^{6} e^{7}\right)} \log\left(c x^{2} + a\right) + 96 \, {\left(a^{3} c^{3} e^{7} x^{6} + 3 \, a^{4} c^{2} e^{7} x^{4} + 3 \, a^{5} c e^{7} x^{2} + a^{6} e^{7}\right)} \log\left(e x + d\right)}{96 \, {\left(a^{6} c^{4} d^{8} + 4 \, a^{7} c^{3} d^{6} e^{2} + 6 \, a^{8} c^{2} d^{4} e^{4} + 4 \, a^{9} c d^{2} e^{6} + a^{10} e^{8} + {\left(a^{3} c^{7} d^{8} + 4 \, a^{4} c^{6} d^{6} e^{2} + 6 \, a^{5} c^{5} d^{4} e^{4} + 4 \, a^{6} c^{4} d^{2} e^{6} + a^{7} c^{3} e^{8}\right)} x^{6} + 3 \, {\left(a^{4} c^{6} d^{8} + 4 \, a^{5} c^{5} d^{6} e^{2} + 6 \, a^{6} c^{4} d^{4} e^{4} + 4 \, a^{7} c^{3} d^{2} e^{6} + a^{8} c^{2} e^{8}\right)} x^{4} + 3 \, {\left(a^{5} c^{5} d^{8} + 4 \, a^{6} c^{4} d^{6} e^{2} + 6 \, a^{7} c^{3} d^{4} e^{4} + 4 \, a^{8} c^{2} d^{2} e^{6} + a^{9} c e^{8}\right)} x^{2}\right)}}, \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(5 \, a^{3} c^{3} d^{7} + 21 \, a^{4} c^{2} d^{5} e^{2} + 35 \, a^{5} c d^{3} e^{4} + 35 \, a^{6} d e^{6} + {\left(5 \, c^{6} d^{7} + 21 \, a c^{5} d^{5} e^{2} + 35 \, a^{2} c^{4} d^{3} e^{4} + 35 \, a^{3} c^{3} d e^{6}\right)} x^{6} + 3 \, {\left(5 \, a c^{5} d^{7} + 21 \, a^{2} c^{4} d^{5} e^{2} + 35 \, a^{3} c^{3} d^{3} e^{4} + 35 \, a^{4} c^{2} d e^{6}\right)} x^{4} + 3 \, {\left(5 \, a^{2} c^{4} d^{7} + 21 \, a^{3} c^{3} d^{5} e^{2} + 35 \, a^{4} c^{2} d^{3} e^{4} + 35 \, a^{5} c d e^{6}\right)} x^{2}\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + 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 - 24 \, {\left(a^{3} c^{3} e^{7} x^{6} + 3 \, a^{4} c^{2} e^{7} x^{4} + 3 \, a^{5} c e^{7} x^{2} + a^{6} e^{7}\right)} \log\left(c x^{2} + a\right) + 48 \, {\left(a^{3} c^{3} e^{7} x^{6} + 3 \, a^{4} c^{2} e^{7} x^{4} + 3 \, a^{5} c e^{7} x^{2} + a^{6} e^{7}\right)} \log\left(e x + d\right)}{48 \, {\left(a^{6} c^{4} d^{8} + 4 \, a^{7} c^{3} d^{6} e^{2} + 6 \, a^{8} c^{2} d^{4} e^{4} + 4 \, a^{9} c d^{2} e^{6} + a^{10} e^{8} + {\left(a^{3} c^{7} d^{8} + 4 \, a^{4} c^{6} d^{6} e^{2} + 6 \, a^{5} c^{5} d^{4} e^{4} + 4 \, a^{6} c^{4} d^{2} e^{6} + a^{7} c^{3} e^{8}\right)} x^{6} + 3 \, {\left(a^{4} c^{6} d^{8} + 4 \, a^{5} c^{5} d^{6} e^{2} + 6 \, a^{6} c^{4} d^{4} e^{4} + 4 \, a^{7} c^{3} d^{2} e^{6} + a^{8} c^{2} e^{8}\right)} x^{4} + 3 \, {\left(a^{5} c^{5} d^{8} + 4 \, a^{6} c^{4} d^{6} e^{2} + 6 \, a^{7} c^{3} d^{4} e^{4} + 4 \, a^{8} c^{2} d^{2} e^{6} + a^{9} c e^{8}\right)} x^{2}\right)}}\right]"," ",0,"[1/96*(16*a^3*c^3*d^6*e + 72*a^4*c^2*d^4*e^3 + 144*a^5*c*d^2*e^5 + 88*a^6*e^7 + 6*(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 + 48*(a^3*c^3*d^2*e^5 + a^4*c^2*e^7)*x^4 + 16*(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 + 24*(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*(5*a^3*c^3*d^7 + 21*a^4*c^2*d^5*e^2 + 35*a^5*c*d^3*e^4 + 35*a^6*d*e^6 + (5*c^6*d^7 + 21*a*c^5*d^5*e^2 + 35*a^2*c^4*d^3*e^4 + 35*a^3*c^3*d*e^6)*x^6 + 3*(5*a*c^5*d^7 + 21*a^2*c^4*d^5*e^2 + 35*a^3*c^3*d^3*e^4 + 35*a^4*c^2*d*e^6)*x^4 + 3*(5*a^2*c^4*d^7 + 21*a^3*c^3*d^5*e^2 + 35*a^4*c^2*d^3*e^4 + 35*a^5*c*d*e^6)*x^2)*sqrt(-c/a)*log((c*x^2 + 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 6*(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 - 48*(a^3*c^3*e^7*x^6 + 3*a^4*c^2*e^7*x^4 + 3*a^5*c*e^7*x^2 + a^6*e^7)*log(c*x^2 + a) + 96*(a^3*c^3*e^7*x^6 + 3*a^4*c^2*e^7*x^4 + 3*a^5*c*e^7*x^2 + a^6*e^7)*log(e*x + d))/(a^6*c^4*d^8 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4 + 4*a^9*c*d^2*e^6 + a^10*e^8 + (a^3*c^7*d^8 + 4*a^4*c^6*d^6*e^2 + 6*a^5*c^5*d^4*e^4 + 4*a^6*c^4*d^2*e^6 + a^7*c^3*e^8)*x^6 + 3*(a^4*c^6*d^8 + 4*a^5*c^5*d^6*e^2 + 6*a^6*c^4*d^4*e^4 + 4*a^7*c^3*d^2*e^6 + a^8*c^2*e^8)*x^4 + 3*(a^5*c^5*d^8 + 4*a^6*c^4*d^6*e^2 + 6*a^7*c^3*d^4*e^4 + 4*a^8*c^2*d^2*e^6 + a^9*c*e^8)*x^2), 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*(5*a^3*c^3*d^7 + 21*a^4*c^2*d^5*e^2 + 35*a^5*c*d^3*e^4 + 35*a^6*d*e^6 + (5*c^6*d^7 + 21*a*c^5*d^5*e^2 + 35*a^2*c^4*d^3*e^4 + 35*a^3*c^3*d*e^6)*x^6 + 3*(5*a*c^5*d^7 + 21*a^2*c^4*d^5*e^2 + 35*a^3*c^3*d^3*e^4 + 35*a^4*c^2*d*e^6)*x^4 + 3*(5*a^2*c^4*d^7 + 21*a^3*c^3*d^5*e^2 + 35*a^4*c^2*d^3*e^4 + 35*a^5*c*d*e^6)*x^2)*sqrt(c/a)*arctan(x*sqrt(c/a)) + 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 - 24*(a^3*c^3*e^7*x^6 + 3*a^4*c^2*e^7*x^4 + 3*a^5*c*e^7*x^2 + a^6*e^7)*log(c*x^2 + a) + 48*(a^3*c^3*e^7*x^6 + 3*a^4*c^2*e^7*x^4 + 3*a^5*c*e^7*x^2 + a^6*e^7)*log(e*x + d))/(a^6*c^4*d^8 + 4*a^7*c^3*d^6*e^2 + 6*a^8*c^2*d^4*e^4 + 4*a^9*c*d^2*e^6 + a^10*e^8 + (a^3*c^7*d^8 + 4*a^4*c^6*d^6*e^2 + 6*a^5*c^5*d^4*e^4 + 4*a^6*c^4*d^2*e^6 + a^7*c^3*e^8)*x^6 + 3*(a^4*c^6*d^8 + 4*a^5*c^5*d^6*e^2 + 6*a^6*c^4*d^4*e^4 + 4*a^7*c^3*d^2*e^6 + a^8*c^2*e^8)*x^4 + 3*(a^5*c^5*d^8 + 4*a^6*c^4*d^6*e^2 + 6*a^7*c^3*d^4*e^4 + 4*a^8*c^2*d^2*e^6 + a^9*c*e^8)*x^2)]","B",0
524,1,3843,0,35.858370," ","integrate(1/(e*x+d)^2/(c*x^2+a)^4,x, algorithm=""fricas"")","\left[\frac{32 \, a^{3} c^{4} d^{8} e + 192 \, a^{4} c^{3} d^{6} e^{3} + 576 \, a^{5} c^{2} d^{4} e^{5} + 320 \, a^{6} c d^{2} e^{7} - 96 \, a^{7} e^{9} + 6 \, {\left(5 \, c^{7} d^{8} e + 28 \, a c^{6} d^{6} e^{3} + 70 \, a^{2} c^{5} d^{4} e^{5} + 12 \, a^{3} c^{4} d^{2} e^{7} - 35 \, a^{4} c^{3} e^{9}\right)} x^{6} + 6 \, {\left(5 \, c^{7} d^{9} + 28 \, a c^{6} d^{7} e^{2} + 70 \, a^{2} c^{5} d^{5} e^{4} + 76 \, a^{3} c^{4} d^{3} e^{6} + 29 \, a^{4} c^{3} d e^{8}\right)} x^{5} + 16 \, {\left(5 \, a c^{6} d^{8} e + 28 \, a^{2} c^{5} d^{6} e^{3} + 78 \, a^{3} c^{4} d^{4} e^{5} + 20 \, a^{4} c^{3} d^{2} e^{7} - 35 \, a^{5} c^{2} e^{9}\right)} x^{4} + 16 \, {\left(5 \, a c^{6} d^{9} + 28 \, a^{2} c^{5} d^{7} e^{2} + 66 \, a^{3} c^{4} d^{5} e^{4} + 68 \, a^{4} c^{3} d^{3} e^{6} + 25 \, a^{5} c^{2} d e^{8}\right)} x^{3} + 6 \, {\left(11 \, a^{2} c^{5} d^{8} e + 68 \, a^{3} c^{4} d^{6} e^{3} + 218 \, a^{4} c^{3} d^{4} e^{5} + 84 \, a^{5} c^{2} d^{2} e^{7} - 77 \, a^{6} c e^{9}\right)} x^{2} - 3 \, {\left(5 \, a^{3} c^{4} d^{9} + 28 \, a^{4} c^{3} d^{7} e^{2} + 70 \, a^{5} c^{2} d^{5} e^{4} + 140 \, a^{6} c d^{3} e^{6} - 35 \, a^{7} d e^{8} + {\left(5 \, c^{7} d^{8} e + 28 \, a c^{6} d^{6} e^{3} + 70 \, a^{2} c^{5} d^{4} e^{5} + 140 \, a^{3} c^{4} d^{2} e^{7} - 35 \, a^{4} c^{3} e^{9}\right)} x^{7} + {\left(5 \, c^{7} d^{9} + 28 \, a c^{6} d^{7} e^{2} + 70 \, a^{2} c^{5} d^{5} e^{4} + 140 \, a^{3} c^{4} d^{3} e^{6} - 35 \, a^{4} c^{3} d e^{8}\right)} x^{6} + 3 \, {\left(5 \, a c^{6} d^{8} e + 28 \, a^{2} c^{5} d^{6} e^{3} + 70 \, a^{3} c^{4} d^{4} e^{5} + 140 \, a^{4} c^{3} d^{2} e^{7} - 35 \, a^{5} c^{2} e^{9}\right)} x^{5} + 3 \, {\left(5 \, a c^{6} d^{9} + 28 \, a^{2} c^{5} d^{7} e^{2} + 70 \, a^{3} c^{4} d^{5} e^{4} + 140 \, a^{4} c^{3} d^{3} e^{6} - 35 \, a^{5} c^{2} d e^{8}\right)} x^{4} + 3 \, {\left(5 \, a^{2} c^{5} d^{8} e + 28 \, a^{3} c^{4} d^{6} e^{3} + 70 \, a^{4} c^{3} d^{4} e^{5} + 140 \, a^{5} c^{2} d^{2} e^{7} - 35 \, a^{6} c e^{9}\right)} x^{3} + 3 \, {\left(5 \, a^{2} c^{5} d^{9} + 28 \, a^{3} c^{4} d^{7} e^{2} + 70 \, a^{4} c^{3} d^{5} e^{4} + 140 \, a^{5} c^{2} d^{3} e^{6} - 35 \, a^{6} c d e^{8}\right)} x^{2} + {\left(5 \, a^{3} c^{4} d^{8} e + 28 \, a^{4} c^{3} d^{6} e^{3} + 70 \, a^{5} c^{2} d^{4} e^{5} + 140 \, a^{6} c d^{2} e^{7} - 35 \, a^{7} e^{9}\right)} x\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c x^{2} - 2 \, a x \sqrt{-\frac{c}{a}} - a}{c x^{2} + a}\right) + 2 \, {\left(33 \, a^{2} c^{5} d^{9} + 172 \, a^{3} c^{4} d^{7} e^{2} + 366 \, a^{4} c^{3} d^{5} e^{4} + 348 \, a^{5} c^{2} d^{3} e^{6} + 121 \, a^{6} c d e^{8}\right)} x - 384 \, {\left(a^{3} c^{4} d e^{8} x^{7} + a^{3} c^{4} d^{2} e^{7} x^{6} + 3 \, a^{4} c^{3} d e^{8} x^{5} + 3 \, a^{4} c^{3} d^{2} e^{7} x^{4} + 3 \, a^{5} c^{2} d e^{8} x^{3} + 3 \, a^{5} c^{2} d^{2} e^{7} x^{2} + a^{6} c d e^{8} x + a^{6} c d^{2} e^{7}\right)} \log\left(c x^{2} + a\right) + 768 \, {\left(a^{3} c^{4} d e^{8} x^{7} + a^{3} c^{4} d^{2} e^{7} x^{6} + 3 \, a^{4} c^{3} d e^{8} x^{5} + 3 \, a^{4} c^{3} d^{2} e^{7} x^{4} + 3 \, a^{5} c^{2} d e^{8} x^{3} + 3 \, a^{5} c^{2} d^{2} e^{7} x^{2} + a^{6} c d e^{8} x + a^{6} c d^{2} e^{7}\right)} \log\left(e x + d\right)}{96 \, {\left(a^{6} c^{5} d^{11} + 5 \, a^{7} c^{4} d^{9} e^{2} + 10 \, a^{8} c^{3} d^{7} e^{4} + 10 \, a^{9} c^{2} d^{5} e^{6} + 5 \, a^{10} c d^{3} e^{8} + a^{11} d e^{10} + {\left(a^{3} c^{8} d^{10} e + 5 \, a^{4} c^{7} d^{8} e^{3} + 10 \, a^{5} c^{6} d^{6} e^{5} + 10 \, a^{6} c^{5} d^{4} e^{7} + 5 \, a^{7} c^{4} d^{2} e^{9} + a^{8} c^{3} e^{11}\right)} x^{7} + {\left(a^{3} c^{8} d^{11} + 5 \, a^{4} c^{7} d^{9} e^{2} + 10 \, a^{5} c^{6} d^{7} e^{4} + 10 \, a^{6} c^{5} d^{5} e^{6} + 5 \, a^{7} c^{4} d^{3} e^{8} + a^{8} c^{3} d e^{10}\right)} x^{6} + 3 \, {\left(a^{4} c^{7} d^{10} e + 5 \, a^{5} c^{6} d^{8} e^{3} + 10 \, a^{6} c^{5} d^{6} e^{5} + 10 \, a^{7} c^{4} d^{4} e^{7} + 5 \, a^{8} c^{3} d^{2} e^{9} + a^{9} c^{2} e^{11}\right)} x^{5} + 3 \, {\left(a^{4} c^{7} d^{11} + 5 \, a^{5} c^{6} d^{9} e^{2} + 10 \, a^{6} c^{5} d^{7} e^{4} + 10 \, a^{7} c^{4} d^{5} e^{6} + 5 \, a^{8} c^{3} d^{3} e^{8} + a^{9} c^{2} d e^{10}\right)} x^{4} + 3 \, {\left(a^{5} c^{6} d^{10} e + 5 \, a^{6} c^{5} d^{8} e^{3} + 10 \, a^{7} c^{4} d^{6} e^{5} + 10 \, a^{8} c^{3} d^{4} e^{7} + 5 \, a^{9} c^{2} d^{2} e^{9} + a^{10} c e^{11}\right)} x^{3} + 3 \, {\left(a^{5} c^{6} d^{11} + 5 \, a^{6} c^{5} d^{9} e^{2} + 10 \, a^{7} c^{4} d^{7} e^{4} + 10 \, a^{8} c^{3} d^{5} e^{6} + 5 \, a^{9} c^{2} d^{3} e^{8} + a^{10} c d e^{10}\right)} x^{2} + {\left(a^{6} c^{5} d^{10} e + 5 \, a^{7} c^{4} d^{8} e^{3} + 10 \, a^{8} c^{3} d^{6} e^{5} + 10 \, a^{9} c^{2} d^{4} e^{7} + 5 \, a^{10} c d^{2} e^{9} + a^{11} e^{11}\right)} x\right)}}, \frac{16 \, a^{3} c^{4} d^{8} e + 96 \, a^{4} c^{3} d^{6} e^{3} + 288 \, a^{5} c^{2} d^{4} e^{5} + 160 \, a^{6} c d^{2} e^{7} - 48 \, a^{7} e^{9} + 3 \, {\left(5 \, c^{7} d^{8} e + 28 \, a c^{6} d^{6} e^{3} + 70 \, a^{2} c^{5} d^{4} e^{5} + 12 \, a^{3} c^{4} d^{2} e^{7} - 35 \, a^{4} c^{3} e^{9}\right)} x^{6} + 3 \, {\left(5 \, c^{7} d^{9} + 28 \, a c^{6} d^{7} e^{2} + 70 \, a^{2} c^{5} d^{5} e^{4} + 76 \, a^{3} c^{4} d^{3} e^{6} + 29 \, a^{4} c^{3} d e^{8}\right)} x^{5} + 8 \, {\left(5 \, a c^{6} d^{8} e + 28 \, a^{2} c^{5} d^{6} e^{3} + 78 \, a^{3} c^{4} d^{4} e^{5} + 20 \, a^{4} c^{3} d^{2} e^{7} - 35 \, a^{5} c^{2} e^{9}\right)} x^{4} + 8 \, {\left(5 \, a c^{6} d^{9} + 28 \, a^{2} c^{5} d^{7} e^{2} + 66 \, a^{3} c^{4} d^{5} e^{4} + 68 \, a^{4} c^{3} d^{3} e^{6} + 25 \, a^{5} c^{2} d e^{8}\right)} x^{3} + 3 \, {\left(11 \, a^{2} c^{5} d^{8} e + 68 \, a^{3} c^{4} d^{6} e^{3} + 218 \, a^{4} c^{3} d^{4} e^{5} + 84 \, a^{5} c^{2} d^{2} e^{7} - 77 \, a^{6} c e^{9}\right)} x^{2} + 3 \, {\left(5 \, a^{3} c^{4} d^{9} + 28 \, a^{4} c^{3} d^{7} e^{2} + 70 \, a^{5} c^{2} d^{5} e^{4} + 140 \, a^{6} c d^{3} e^{6} - 35 \, a^{7} d e^{8} + {\left(5 \, c^{7} d^{8} e + 28 \, a c^{6} d^{6} e^{3} + 70 \, a^{2} c^{5} d^{4} e^{5} + 140 \, a^{3} c^{4} d^{2} e^{7} - 35 \, a^{4} c^{3} e^{9}\right)} x^{7} + {\left(5 \, c^{7} d^{9} + 28 \, a c^{6} d^{7} e^{2} + 70 \, a^{2} c^{5} d^{5} e^{4} + 140 \, a^{3} c^{4} d^{3} e^{6} - 35 \, a^{4} c^{3} d e^{8}\right)} x^{6} + 3 \, {\left(5 \, a c^{6} d^{8} e + 28 \, a^{2} c^{5} d^{6} e^{3} + 70 \, a^{3} c^{4} d^{4} e^{5} + 140 \, a^{4} c^{3} d^{2} e^{7} - 35 \, a^{5} c^{2} e^{9}\right)} x^{5} + 3 \, {\left(5 \, a c^{6} d^{9} + 28 \, a^{2} c^{5} d^{7} e^{2} + 70 \, a^{3} c^{4} d^{5} e^{4} + 140 \, a^{4} c^{3} d^{3} e^{6} - 35 \, a^{5} c^{2} d e^{8}\right)} x^{4} + 3 \, {\left(5 \, a^{2} c^{5} d^{8} e + 28 \, a^{3} c^{4} d^{6} e^{3} + 70 \, a^{4} c^{3} d^{4} e^{5} + 140 \, a^{5} c^{2} d^{2} e^{7} - 35 \, a^{6} c e^{9}\right)} x^{3} + 3 \, {\left(5 \, a^{2} c^{5} d^{9} + 28 \, a^{3} c^{4} d^{7} e^{2} + 70 \, a^{4} c^{3} d^{5} e^{4} + 140 \, a^{5} c^{2} d^{3} e^{6} - 35 \, a^{6} c d e^{8}\right)} x^{2} + {\left(5 \, a^{3} c^{4} d^{8} e + 28 \, a^{4} c^{3} d^{6} e^{3} + 70 \, a^{5} c^{2} d^{4} e^{5} + 140 \, a^{6} c d^{2} e^{7} - 35 \, a^{7} e^{9}\right)} x\right)} \sqrt{\frac{c}{a}} \arctan\left(x \sqrt{\frac{c}{a}}\right) + {\left(33 \, a^{2} c^{5} d^{9} + 172 \, a^{3} c^{4} d^{7} e^{2} + 366 \, a^{4} c^{3} d^{5} e^{4} + 348 \, a^{5} c^{2} d^{3} e^{6} + 121 \, a^{6} c d e^{8}\right)} x - 192 \, {\left(a^{3} c^{4} d e^{8} x^{7} + a^{3} c^{4} d^{2} e^{7} x^{6} + 3 \, a^{4} c^{3} d e^{8} x^{5} + 3 \, a^{4} c^{3} d^{2} e^{7} x^{4} + 3 \, a^{5} c^{2} d e^{8} x^{3} + 3 \, a^{5} c^{2} d^{2} e^{7} x^{2} + a^{6} c d e^{8} x + a^{6} c d^{2} e^{7}\right)} \log\left(c x^{2} + a\right) + 384 \, {\left(a^{3} c^{4} d e^{8} x^{7} + a^{3} c^{4} d^{2} e^{7} x^{6} + 3 \, a^{4} c^{3} d e^{8} x^{5} + 3 \, a^{4} c^{3} d^{2} e^{7} x^{4} + 3 \, a^{5} c^{2} d e^{8} x^{3} + 3 \, a^{5} c^{2} d^{2} e^{7} x^{2} + a^{6} c d e^{8} x + a^{6} c d^{2} e^{7}\right)} \log\left(e x + d\right)}{48 \, {\left(a^{6} c^{5} d^{11} + 5 \, a^{7} c^{4} d^{9} e^{2} + 10 \, a^{8} c^{3} d^{7} e^{4} + 10 \, a^{9} c^{2} d^{5} e^{6} + 5 \, a^{10} c d^{3} e^{8} + a^{11} d e^{10} + {\left(a^{3} c^{8} d^{10} e + 5 \, a^{4} c^{7} d^{8} e^{3} + 10 \, a^{5} c^{6} d^{6} e^{5} + 10 \, a^{6} c^{5} d^{4} e^{7} + 5 \, a^{7} c^{4} d^{2} e^{9} + a^{8} c^{3} e^{11}\right)} x^{7} + {\left(a^{3} c^{8} d^{11} + 5 \, a^{4} c^{7} d^{9} e^{2} + 10 \, a^{5} c^{6} d^{7} e^{4} + 10 \, a^{6} c^{5} d^{5} e^{6} + 5 \, a^{7} c^{4} d^{3} e^{8} + a^{8} c^{3} d e^{10}\right)} x^{6} + 3 \, {\left(a^{4} c^{7} d^{10} e + 5 \, a^{5} c^{6} d^{8} e^{3} + 10 \, a^{6} c^{5} d^{6} e^{5} + 10 \, a^{7} c^{4} d^{4} e^{7} + 5 \, a^{8} c^{3} d^{2} e^{9} + a^{9} c^{2} e^{11}\right)} x^{5} + 3 \, {\left(a^{4} c^{7} d^{11} + 5 \, a^{5} c^{6} d^{9} e^{2} + 10 \, a^{6} c^{5} d^{7} e^{4} + 10 \, a^{7} c^{4} d^{5} e^{6} + 5 \, a^{8} c^{3} d^{3} e^{8} + a^{9} c^{2} d e^{10}\right)} x^{4} + 3 \, {\left(a^{5} c^{6} d^{10} e + 5 \, a^{6} c^{5} d^{8} e^{3} + 10 \, a^{7} c^{4} d^{6} e^{5} + 10 \, a^{8} c^{3} d^{4} e^{7} + 5 \, a^{9} c^{2} d^{2} e^{9} + a^{10} c e^{11}\right)} x^{3} + 3 \, {\left(a^{5} c^{6} d^{11} + 5 \, a^{6} c^{5} d^{9} e^{2} + 10 \, a^{7} c^{4} d^{7} e^{4} + 10 \, a^{8} c^{3} d^{5} e^{6} + 5 \, a^{9} c^{2} d^{3} e^{8} + a^{10} c d e^{10}\right)} x^{2} + {\left(a^{6} c^{5} d^{10} e + 5 \, a^{7} c^{4} d^{8} e^{3} + 10 \, a^{8} c^{3} d^{6} e^{5} + 10 \, a^{9} c^{2} d^{4} e^{7} + 5 \, a^{10} c d^{2} e^{9} + a^{11} e^{11}\right)} x\right)}}\right]"," ",0,"[1/96*(32*a^3*c^4*d^8*e + 192*a^4*c^3*d^6*e^3 + 576*a^5*c^2*d^4*e^5 + 320*a^6*c*d^2*e^7 - 96*a^7*e^9 + 6*(5*c^7*d^8*e + 28*a*c^6*d^6*e^3 + 70*a^2*c^5*d^4*e^5 + 12*a^3*c^4*d^2*e^7 - 35*a^4*c^3*e^9)*x^6 + 6*(5*c^7*d^9 + 28*a*c^6*d^7*e^2 + 70*a^2*c^5*d^5*e^4 + 76*a^3*c^4*d^3*e^6 + 29*a^4*c^3*d*e^8)*x^5 + 16*(5*a*c^6*d^8*e + 28*a^2*c^5*d^6*e^3 + 78*a^3*c^4*d^4*e^5 + 20*a^4*c^3*d^2*e^7 - 35*a^5*c^2*e^9)*x^4 + 16*(5*a*c^6*d^9 + 28*a^2*c^5*d^7*e^2 + 66*a^3*c^4*d^5*e^4 + 68*a^4*c^3*d^3*e^6 + 25*a^5*c^2*d*e^8)*x^3 + 6*(11*a^2*c^5*d^8*e + 68*a^3*c^4*d^6*e^3 + 218*a^4*c^3*d^4*e^5 + 84*a^5*c^2*d^2*e^7 - 77*a^6*c*e^9)*x^2 - 3*(5*a^3*c^4*d^9 + 28*a^4*c^3*d^7*e^2 + 70*a^5*c^2*d^5*e^4 + 140*a^6*c*d^3*e^6 - 35*a^7*d*e^8 + (5*c^7*d^8*e + 28*a*c^6*d^6*e^3 + 70*a^2*c^5*d^4*e^5 + 140*a^3*c^4*d^2*e^7 - 35*a^4*c^3*e^9)*x^7 + (5*c^7*d^9 + 28*a*c^6*d^7*e^2 + 70*a^2*c^5*d^5*e^4 + 140*a^3*c^4*d^3*e^6 - 35*a^4*c^3*d*e^8)*x^6 + 3*(5*a*c^6*d^8*e + 28*a^2*c^5*d^6*e^3 + 70*a^3*c^4*d^4*e^5 + 140*a^4*c^3*d^2*e^7 - 35*a^5*c^2*e^9)*x^5 + 3*(5*a*c^6*d^9 + 28*a^2*c^5*d^7*e^2 + 70*a^3*c^4*d^5*e^4 + 140*a^4*c^3*d^3*e^6 - 35*a^5*c^2*d*e^8)*x^4 + 3*(5*a^2*c^5*d^8*e + 28*a^3*c^4*d^6*e^3 + 70*a^4*c^3*d^4*e^5 + 140*a^5*c^2*d^2*e^7 - 35*a^6*c*e^9)*x^3 + 3*(5*a^2*c^5*d^9 + 28*a^3*c^4*d^7*e^2 + 70*a^4*c^3*d^5*e^4 + 140*a^5*c^2*d^3*e^6 - 35*a^6*c*d*e^8)*x^2 + (5*a^3*c^4*d^8*e + 28*a^4*c^3*d^6*e^3 + 70*a^5*c^2*d^4*e^5 + 140*a^6*c*d^2*e^7 - 35*a^7*e^9)*x)*sqrt(-c/a)*log((c*x^2 - 2*a*x*sqrt(-c/a) - a)/(c*x^2 + a)) + 2*(33*a^2*c^5*d^9 + 172*a^3*c^4*d^7*e^2 + 366*a^4*c^3*d^5*e^4 + 348*a^5*c^2*d^3*e^6 + 121*a^6*c*d*e^8)*x - 384*(a^3*c^4*d*e^8*x^7 + a^3*c^4*d^2*e^7*x^6 + 3*a^4*c^3*d*e^8*x^5 + 3*a^4*c^3*d^2*e^7*x^4 + 3*a^5*c^2*d*e^8*x^3 + 3*a^5*c^2*d^2*e^7*x^2 + a^6*c*d*e^8*x + a^6*c*d^2*e^7)*log(c*x^2 + a) + 768*(a^3*c^4*d*e^8*x^7 + a^3*c^4*d^2*e^7*x^6 + 3*a^4*c^3*d*e^8*x^5 + 3*a^4*c^3*d^2*e^7*x^4 + 3*a^5*c^2*d*e^8*x^3 + 3*a^5*c^2*d^2*e^7*x^2 + a^6*c*d*e^8*x + a^6*c*d^2*e^7)*log(e*x + d))/(a^6*c^5*d^11 + 5*a^7*c^4*d^9*e^2 + 10*a^8*c^3*d^7*e^4 + 10*a^9*c^2*d^5*e^6 + 5*a^10*c*d^3*e^8 + a^11*d*e^10 + (a^3*c^8*d^10*e + 5*a^4*c^7*d^8*e^3 + 10*a^5*c^6*d^6*e^5 + 10*a^6*c^5*d^4*e^7 + 5*a^7*c^4*d^2*e^9 + a^8*c^3*e^11)*x^7 + (a^3*c^8*d^11 + 5*a^4*c^7*d^9*e^2 + 10*a^5*c^6*d^7*e^4 + 10*a^6*c^5*d^5*e^6 + 5*a^7*c^4*d^3*e^8 + a^8*c^3*d*e^10)*x^6 + 3*(a^4*c^7*d^10*e + 5*a^5*c^6*d^8*e^3 + 10*a^6*c^5*d^6*e^5 + 10*a^7*c^4*d^4*e^7 + 5*a^8*c^3*d^2*e^9 + a^9*c^2*e^11)*x^5 + 3*(a^4*c^7*d^11 + 5*a^5*c^6*d^9*e^2 + 10*a^6*c^5*d^7*e^4 + 10*a^7*c^4*d^5*e^6 + 5*a^8*c^3*d^3*e^8 + a^9*c^2*d*e^10)*x^4 + 3*(a^5*c^6*d^10*e + 5*a^6*c^5*d^8*e^3 + 10*a^7*c^4*d^6*e^5 + 10*a^8*c^3*d^4*e^7 + 5*a^9*c^2*d^2*e^9 + a^10*c*e^11)*x^3 + 3*(a^5*c^6*d^11 + 5*a^6*c^5*d^9*e^2 + 10*a^7*c^4*d^7*e^4 + 10*a^8*c^3*d^5*e^6 + 5*a^9*c^2*d^3*e^8 + a^10*c*d*e^10)*x^2 + (a^6*c^5*d^10*e + 5*a^7*c^4*d^8*e^3 + 10*a^8*c^3*d^6*e^5 + 10*a^9*c^2*d^4*e^7 + 5*a^10*c*d^2*e^9 + a^11*e^11)*x), 1/48*(16*a^3*c^4*d^8*e + 96*a^4*c^3*d^6*e^3 + 288*a^5*c^2*d^4*e^5 + 160*a^6*c*d^2*e^7 - 48*a^7*e^9 + 3*(5*c^7*d^8*e + 28*a*c^6*d^6*e^3 + 70*a^2*c^5*d^4*e^5 + 12*a^3*c^4*d^2*e^7 - 35*a^4*c^3*e^9)*x^6 + 3*(5*c^7*d^9 + 28*a*c^6*d^7*e^2 + 70*a^2*c^5*d^5*e^4 + 76*a^3*c^4*d^3*e^6 + 29*a^4*c^3*d*e^8)*x^5 + 8*(5*a*c^6*d^8*e + 28*a^2*c^5*d^6*e^3 + 78*a^3*c^4*d^4*e^5 + 20*a^4*c^3*d^2*e^7 - 35*a^5*c^2*e^9)*x^4 + 8*(5*a*c^6*d^9 + 28*a^2*c^5*d^7*e^2 + 66*a^3*c^4*d^5*e^4 + 68*a^4*c^3*d^3*e^6 + 25*a^5*c^2*d*e^8)*x^3 + 3*(11*a^2*c^5*d^8*e + 68*a^3*c^4*d^6*e^3 + 218*a^4*c^3*d^4*e^5 + 84*a^5*c^2*d^2*e^7 - 77*a^6*c*e^9)*x^2 + 3*(5*a^3*c^4*d^9 + 28*a^4*c^3*d^7*e^2 + 70*a^5*c^2*d^5*e^4 + 140*a^6*c*d^3*e^6 - 35*a^7*d*e^8 + (5*c^7*d^8*e + 28*a*c^6*d^6*e^3 + 70*a^2*c^5*d^4*e^5 + 140*a^3*c^4*d^2*e^7 - 35*a^4*c^3*e^9)*x^7 + (5*c^7*d^9 + 28*a*c^6*d^7*e^2 + 70*a^2*c^5*d^5*e^4 + 140*a^3*c^4*d^3*e^6 - 35*a^4*c^3*d*e^8)*x^6 + 3*(5*a*c^6*d^8*e + 28*a^2*c^5*d^6*e^3 + 70*a^3*c^4*d^4*e^5 + 140*a^4*c^3*d^2*e^7 - 35*a^5*c^2*e^9)*x^5 + 3*(5*a*c^6*d^9 + 28*a^2*c^5*d^7*e^2 + 70*a^3*c^4*d^5*e^4 + 140*a^4*c^3*d^3*e^6 - 35*a^5*c^2*d*e^8)*x^4 + 3*(5*a^2*c^5*d^8*e + 28*a^3*c^4*d^6*e^3 + 70*a^4*c^3*d^4*e^5 + 140*a^5*c^2*d^2*e^7 - 35*a^6*c*e^9)*x^3 + 3*(5*a^2*c^5*d^9 + 28*a^3*c^4*d^7*e^2 + 70*a^4*c^3*d^5*e^4 + 140*a^5*c^2*d^3*e^6 - 35*a^6*c*d*e^8)*x^2 + (5*a^3*c^4*d^8*e + 28*a^4*c^3*d^6*e^3 + 70*a^5*c^2*d^4*e^5 + 140*a^6*c*d^2*e^7 - 35*a^7*e^9)*x)*sqrt(c/a)*arctan(x*sqrt(c/a)) + (33*a^2*c^5*d^9 + 172*a^3*c^4*d^7*e^2 + 366*a^4*c^3*d^5*e^4 + 348*a^5*c^2*d^3*e^6 + 121*a^6*c*d*e^8)*x - 192*(a^3*c^4*d*e^8*x^7 + a^3*c^4*d^2*e^7*x^6 + 3*a^4*c^3*d*e^8*x^5 + 3*a^4*c^3*d^2*e^7*x^4 + 3*a^5*c^2*d*e^8*x^3 + 3*a^5*c^2*d^2*e^7*x^2 + a^6*c*d*e^8*x + a^6*c*d^2*e^7)*log(c*x^2 + a) + 384*(a^3*c^4*d*e^8*x^7 + a^3*c^4*d^2*e^7*x^6 + 3*a^4*c^3*d*e^8*x^5 + 3*a^4*c^3*d^2*e^7*x^4 + 3*a^5*c^2*d*e^8*x^3 + 3*a^5*c^2*d^2*e^7*x^2 + a^6*c*d*e^8*x + a^6*c*d^2*e^7)*log(e*x + d))/(a^6*c^5*d^11 + 5*a^7*c^4*d^9*e^2 + 10*a^8*c^3*d^7*e^4 + 10*a^9*c^2*d^5*e^6 + 5*a^10*c*d^3*e^8 + a^11*d*e^10 + (a^3*c^8*d^10*e + 5*a^4*c^7*d^8*e^3 + 10*a^5*c^6*d^6*e^5 + 10*a^6*c^5*d^4*e^7 + 5*a^7*c^4*d^2*e^9 + a^8*c^3*e^11)*x^7 + (a^3*c^8*d^11 + 5*a^4*c^7*d^9*e^2 + 10*a^5*c^6*d^7*e^4 + 10*a^6*c^5*d^5*e^6 + 5*a^7*c^4*d^3*e^8 + a^8*c^3*d*e^10)*x^6 + 3*(a^4*c^7*d^10*e + 5*a^5*c^6*d^8*e^3 + 10*a^6*c^5*d^6*e^5 + 10*a^7*c^4*d^4*e^7 + 5*a^8*c^3*d^2*e^9 + a^9*c^2*e^11)*x^5 + 3*(a^4*c^7*d^11 + 5*a^5*c^6*d^9*e^2 + 10*a^6*c^5*d^7*e^4 + 10*a^7*c^4*d^5*e^6 + 5*a^8*c^3*d^3*e^8 + a^9*c^2*d*e^10)*x^4 + 3*(a^5*c^6*d^10*e + 5*a^6*c^5*d^8*e^3 + 10*a^7*c^4*d^6*e^5 + 10*a^8*c^3*d^4*e^7 + 5*a^9*c^2*d^2*e^9 + a^10*c*e^11)*x^3 + 3*(a^5*c^6*d^11 + 5*a^6*c^5*d^9*e^2 + 10*a^7*c^4*d^7*e^4 + 10*a^8*c^3*d^5*e^6 + 5*a^9*c^2*d^3*e^8 + a^10*c*d*e^10)*x^2 + (a^6*c^5*d^10*e + 5*a^7*c^4*d^8*e^3 + 10*a^8*c^3*d^6*e^5 + 10*a^9*c^2*d^4*e^7 + 5*a^10*c*d^2*e^9 + a^11*e^11)*x)]","B",0
525,1,400,0,0.443806," ","integrate((e*x+d)^4*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(8 \, a c^{2} d^{4} - 12 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(40 \, c^{3} e^{4} x^{5} + 192 \, c^{3} d e^{3} x^{4} + 320 \, a c^{2} d^{3} e - 128 \, a^{2} c d e^{3} + 10 \, {\left(36 \, c^{3} d^{2} e^{2} + a c^{2} e^{4}\right)} x^{3} + 64 \, {\left(5 \, c^{3} d^{3} e + a c^{2} d e^{3}\right)} x^{2} + 15 \, {\left(8 \, c^{3} d^{4} + 12 \, a c^{2} d^{2} e^{2} - a^{2} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{480 \, c^{3}}, -\frac{15 \, {\left(8 \, a c^{2} d^{4} - 12 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(40 \, c^{3} e^{4} x^{5} + 192 \, c^{3} d e^{3} x^{4} + 320 \, a c^{2} d^{3} e - 128 \, a^{2} c d e^{3} + 10 \, {\left(36 \, c^{3} d^{2} e^{2} + a c^{2} e^{4}\right)} x^{3} + 64 \, {\left(5 \, c^{3} d^{3} e + a c^{2} d e^{3}\right)} x^{2} + 15 \, {\left(8 \, c^{3} d^{4} + 12 \, a c^{2} d^{2} e^{2} - a^{2} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, c^{3}}\right]"," ",0,"[1/480*(15*(8*a*c^2*d^4 - 12*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(40*c^3*e^4*x^5 + 192*c^3*d*e^3*x^4 + 320*a*c^2*d^3*e - 128*a^2*c*d*e^3 + 10*(36*c^3*d^2*e^2 + a*c^2*e^4)*x^3 + 64*(5*c^3*d^3*e + a*c^2*d*e^3)*x^2 + 15*(8*c^3*d^4 + 12*a*c^2*d^2*e^2 - a^2*c*e^4)*x)*sqrt(c*x^2 + a))/c^3, -1/240*(15*(8*a*c^2*d^4 - 12*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (40*c^3*e^4*x^5 + 192*c^3*d*e^3*x^4 + 320*a*c^2*d^3*e - 128*a^2*c*d*e^3 + 10*(36*c^3*d^2*e^2 + a*c^2*e^4)*x^3 + 64*(5*c^3*d^3*e + a*c^2*d*e^3)*x^2 + 15*(8*c^3*d^4 + 12*a*c^2*d^2*e^2 - a^2*c*e^4)*x)*sqrt(c*x^2 + a))/c^3]","A",0
526,1,286,0,0.423519," ","integrate((e*x+d)^3*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(4 \, a c d^{3} - 3 \, a^{2} d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(24 \, c^{2} e^{3} x^{4} + 90 \, c^{2} d e^{2} x^{3} + 120 \, a c d^{2} e - 16 \, a^{2} e^{3} + 8 \, {\left(15 \, c^{2} d^{2} e + a c e^{3}\right)} x^{2} + 15 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, c^{2}}, -\frac{15 \, {\left(4 \, a c d^{3} - 3 \, a^{2} d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(24 \, c^{2} e^{3} x^{4} + 90 \, c^{2} d e^{2} x^{3} + 120 \, a c d^{2} e - 16 \, a^{2} e^{3} + 8 \, {\left(15 \, c^{2} d^{2} e + a c e^{3}\right)} x^{2} + 15 \, {\left(4 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{120 \, c^{2}}\right]"," ",0,"[-1/240*(15*(4*a*c*d^3 - 3*a^2*d*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(24*c^2*e^3*x^4 + 90*c^2*d*e^2*x^3 + 120*a*c*d^2*e - 16*a^2*e^3 + 8*(15*c^2*d^2*e + a*c*e^3)*x^2 + 15*(4*c^2*d^3 + 3*a*c*d*e^2)*x)*sqrt(c*x^2 + a))/c^2, -1/120*(15*(4*a*c*d^3 - 3*a^2*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (24*c^2*e^3*x^4 + 90*c^2*d*e^2*x^3 + 120*a*c*d^2*e - 16*a^2*e^3 + 8*(15*c^2*d^2*e + a*c*e^3)*x^2 + 15*(4*c^2*d^3 + 3*a*c*d*e^2)*x)*sqrt(c*x^2 + a))/c^2]","A",0
527,1,214,0,0.437727," ","integrate((e*x+d)^2*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(4 \, a c d^{2} - a^{2} e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(6 \, c^{2} e^{2} x^{3} + 16 \, c^{2} d e x^{2} + 16 \, a c d e + 3 \, {\left(4 \, c^{2} d^{2} + a c e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, c^{2}}, -\frac{3 \, {\left(4 \, a c d^{2} - a^{2} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, c^{2} e^{2} x^{3} + 16 \, c^{2} d e x^{2} + 16 \, a c d e + 3 \, {\left(4 \, c^{2} d^{2} + a c e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, c^{2}}\right]"," ",0,"[-1/48*(3*(4*a*c*d^2 - a^2*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(6*c^2*e^2*x^3 + 16*c^2*d*e*x^2 + 16*a*c*d*e + 3*(4*c^2*d^2 + a*c*e^2)*x)*sqrt(c*x^2 + a))/c^2, -1/24*(3*(4*a*c*d^2 - a^2*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (6*c^2*e^2*x^3 + 16*c^2*d*e*x^2 + 16*a*c*d*e + 3*(4*c^2*d^2 + a*c*e^2)*x)*sqrt(c*x^2 + a))/c^2]","A",0
528,1,128,0,0.427223," ","integrate((e*x+d)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{c} d \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(2 \, c e x^{2} + 3 \, c d x + 2 \, a e\right)} \sqrt{c x^{2} + a}}{12 \, c}, -\frac{3 \, a \sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, c e x^{2} + 3 \, c d x + 2 \, a e\right)} \sqrt{c x^{2} + a}}{6 \, c}\right]"," ",0,"[1/12*(3*a*sqrt(c)*d*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(2*c*e*x^2 + 3*c*d*x + 2*a*e)*sqrt(c*x^2 + a))/c, -1/6*(3*a*sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (2*c*e*x^2 + 3*c*d*x + 2*a*e)*sqrt(c*x^2 + a))/c]","A",0
529,1,574,0,0.519558," ","integrate((c*x^2+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{\sqrt{c} d \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, \sqrt{c x^{2} + a} e + \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, e^{2}}, \frac{2 \, \sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + 2 \, \sqrt{c x^{2} + a} e + \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, e^{2}}, \frac{\sqrt{c} d \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, \sqrt{c x^{2} + a} e - 2 \, \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{2 \, e^{2}}, \frac{\sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + \sqrt{c x^{2} + a} e - \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{e^{2}}\right]"," ",0,"[1/2*(sqrt(c)*d*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*sqrt(c*x^2 + a)*e + sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)))/e^2, 1/2*(2*sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + 2*sqrt(c*x^2 + a)*e + sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)))/e^2, 1/2*(sqrt(c)*d*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*sqrt(c*x^2 + a)*e - 2*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)))/e^2, (sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + sqrt(c*x^2 + a)*e - sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)))/e^2]","A",0
530,1,884,0,0.542511," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{{\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + {\left(c d e x + c d^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c d^{3} e^{2} + a d e^{4} + {\left(c d^{2} e^{3} + a e^{5}\right)} x\right)}}, \frac{2 \, {\left(c d e x + c d^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c d^{3} e^{2} + a d e^{4} + {\left(c d^{2} e^{3} + a e^{5}\right)} x\right)}}, -\frac{2 \, {\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(c d e x + c d^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c d^{3} e^{2} + a d e^{4} + {\left(c d^{2} e^{3} + a e^{5}\right)} x\right)}}, \frac{{\left(c d e x + c d^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{c d^{3} e^{2} + a d e^{4} + {\left(c d^{2} e^{3} + a e^{5}\right)} x}\right]"," ",0,"[1/2*((c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + (c*d*e*x + c*d^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c*d^3*e^2 + a*d*e^4 + (c*d^2*e^3 + a*e^5)*x), 1/2*(2*(c*d*e*x + c*d^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c*d^3*e^2 + a*d*e^4 + (c*d^2*e^3 + a*e^5)*x), -1/2*(2*(c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (c*d*e*x + c*d^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c*d^3*e^2 + a*d*e^4 + (c*d^2*e^3 + a*e^5)*x), ((c*d*e*x + c*d^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c*d^3*e^2 + a*d*e^4 + (c*d^2*e^3 + a*e^5)*x)]","B",0
531,1,519,0,0.567924," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{{\left(a c e^{2} x^{2} + 2 \, a c d e x + a c d^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(a c d^{2} e + a^{2} e^{3} - {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\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)}}, -\frac{{\left(a c e^{2} x^{2} + 2 \, a c d e x + a c d^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(a c d^{2} e + a^{2} e^{3} - {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\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)}}\right]"," ",0,"[1/4*((a*c*e^2*x^2 + 2*a*c*d*e*x + a*c*d^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(a*c*d^2*e + a^2*e^3 - (c^2*d^3 + a*c*d*e^2)*x)*sqrt(c*x^2 + a))/(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), -1/2*((a*c*e^2*x^2 + 2*a*c*d*e*x + a*c*d^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (a*c*d^2*e + a^2*e^3 - (c^2*d^3 + a*c*d*e^2)*x)*sqrt(c*x^2 + a))/(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)]","B",0
532,1,861,0,0.828273," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a c^{2} d e^{3} x^{3} + 3 \, a c^{2} d^{2} e^{2} x^{2} + 3 \, a c^{2} d^{3} e x + a c^{2} d^{4}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(5 \, a c^{2} d^{4} e + 7 \, a^{2} c d^{2} e^{3} + 2 \, a^{3} e^{5} - {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3} - 2 \, a^{2} c e^{5}\right)} x^{2} - 3 \, {\left(c^{3} d^{5} - a^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(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} + {\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^{3} + 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)} x^{2} + 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)} x\right)}}, -\frac{3 \, {\left(a c^{2} d e^{3} x^{3} + 3 \, a c^{2} d^{2} e^{2} x^{2} + 3 \, a c^{2} d^{3} e x + a c^{2} d^{4}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(5 \, a c^{2} d^{4} e + 7 \, a^{2} c d^{2} e^{3} + 2 \, a^{3} e^{5} - {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3} - 2 \, a^{2} c e^{5}\right)} x^{2} - 3 \, {\left(c^{3} d^{5} - a^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(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} + {\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^{3} + 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)} x^{2} + 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)} x\right)}}\right]"," ",0,"[1/12*(3*(a*c^2*d*e^3*x^3 + 3*a*c^2*d^2*e^2*x^2 + 3*a*c^2*d^3*e*x + a*c^2*d^4)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(5*a*c^2*d^4*e + 7*a^2*c*d^2*e^3 + 2*a^3*e^5 - (c^3*d^4*e - a*c^2*d^2*e^3 - 2*a^2*c*e^5)*x^2 - 3*(c^3*d^5 - a^2*c*d*e^4)*x)*sqrt(c*x^2 + a))/(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^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^3 + 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)*x^2 + 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)*x), -1/6*(3*(a*c^2*d*e^3*x^3 + 3*a*c^2*d^2*e^2*x^2 + 3*a*c^2*d^3*e*x + a*c^2*d^4)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (5*a*c^2*d^4*e + 7*a^2*c*d^2*e^3 + 2*a^3*e^5 - (c^3*d^4*e - a*c^2*d^2*e^3 - 2*a^2*c*e^5)*x^2 - 3*(c^3*d^5 - a^2*c*d*e^4)*x)*sqrt(c*x^2 + a))/(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^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^3 + 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)*x^2 + 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)*x)]","B",0
533,1,1485,0,2.417836," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(4 \, a c^{3} d^{6} - a^{2} c^{2} d^{4} e^{2} + {\left(4 \, a c^{3} d^{2} e^{4} - a^{2} c^{2} e^{6}\right)} x^{4} + 4 \, {\left(4 \, a c^{3} d^{3} e^{3} - a^{2} c^{2} d e^{5}\right)} x^{3} + 6 \, {\left(4 \, a c^{3} d^{4} e^{2} - a^{2} c^{2} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(4 \, a c^{3} d^{5} e - a^{2} c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(28 \, a c^{3} d^{6} e + 47 \, a^{2} c^{2} d^{4} e^{3} + 25 \, a^{3} c d^{2} e^{5} + 6 \, a^{4} e^{7} - {\left(2 \, c^{4} d^{5} e^{2} - 11 \, a c^{3} d^{3} e^{4} - 13 \, a^{2} c^{2} d e^{6}\right)} x^{3} - {\left(8 \, c^{4} d^{6} e - 32 \, a c^{3} d^{4} e^{3} - 43 \, a^{2} c^{2} d^{2} e^{5} - 3 \, a^{3} c e^{7}\right)} x^{2} - {\left(12 \, c^{4} d^{7} - 25 \, a c^{3} d^{5} e^{2} - 41 \, a^{2} c^{2} d^{3} e^{4} - 4 \, a^{3} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, {\left(c^{4} d^{12} + 4 \, a c^{3} d^{10} e^{2} + 6 \, a^{2} c^{2} d^{8} e^{4} + 4 \, a^{3} c d^{6} e^{6} + a^{4} d^{4} e^{8} + {\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)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} + 4 \, a c^{3} d^{7} e^{5} + 6 \, a^{2} c^{2} d^{5} e^{7} + 4 \, a^{3} c d^{3} e^{9} + a^{4} d e^{11}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} + 4 \, a c^{3} d^{8} e^{4} + 6 \, a^{2} c^{2} d^{6} e^{6} + 4 \, a^{3} c d^{4} e^{8} + a^{4} d^{2} e^{10}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e + 4 \, a c^{3} d^{9} e^{3} + 6 \, a^{2} c^{2} d^{7} e^{5} + 4 \, a^{3} c d^{5} e^{7} + a^{4} d^{3} e^{9}\right)} x\right)}}, -\frac{3 \, {\left(4 \, a c^{3} d^{6} - a^{2} c^{2} d^{4} e^{2} + {\left(4 \, a c^{3} d^{2} e^{4} - a^{2} c^{2} e^{6}\right)} x^{4} + 4 \, {\left(4 \, a c^{3} d^{3} e^{3} - a^{2} c^{2} d e^{5}\right)} x^{3} + 6 \, {\left(4 \, a c^{3} d^{4} e^{2} - a^{2} c^{2} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(4 \, a c^{3} d^{5} e - a^{2} c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(28 \, a c^{3} d^{6} e + 47 \, a^{2} c^{2} d^{4} e^{3} + 25 \, a^{3} c d^{2} e^{5} + 6 \, a^{4} e^{7} - {\left(2 \, c^{4} d^{5} e^{2} - 11 \, a c^{3} d^{3} e^{4} - 13 \, a^{2} c^{2} d e^{6}\right)} x^{3} - {\left(8 \, c^{4} d^{6} e - 32 \, a c^{3} d^{4} e^{3} - 43 \, a^{2} c^{2} d^{2} e^{5} - 3 \, a^{3} c e^{7}\right)} x^{2} - {\left(12 \, c^{4} d^{7} - 25 \, a c^{3} d^{5} e^{2} - 41 \, a^{2} c^{2} d^{3} e^{4} - 4 \, a^{3} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, {\left(c^{4} d^{12} + 4 \, a c^{3} d^{10} e^{2} + 6 \, a^{2} c^{2} d^{8} e^{4} + 4 \, a^{3} c d^{6} e^{6} + a^{4} d^{4} e^{8} + {\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)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} + 4 \, a c^{3} d^{7} e^{5} + 6 \, a^{2} c^{2} d^{5} e^{7} + 4 \, a^{3} c d^{3} e^{9} + a^{4} d e^{11}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} + 4 \, a c^{3} d^{8} e^{4} + 6 \, a^{2} c^{2} d^{6} e^{6} + 4 \, a^{3} c d^{4} e^{8} + a^{4} d^{2} e^{10}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e + 4 \, a c^{3} d^{9} e^{3} + 6 \, a^{2} c^{2} d^{7} e^{5} + 4 \, a^{3} c d^{5} e^{7} + a^{4} d^{3} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(4*a*c^3*d^6 - a^2*c^2*d^4*e^2 + (4*a*c^3*d^2*e^4 - a^2*c^2*e^6)*x^4 + 4*(4*a*c^3*d^3*e^3 - a^2*c^2*d*e^5)*x^3 + 6*(4*a*c^3*d^4*e^2 - a^2*c^2*d^2*e^4)*x^2 + 4*(4*a*c^3*d^5*e - a^2*c^2*d^3*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(28*a*c^3*d^6*e + 47*a^2*c^2*d^4*e^3 + 25*a^3*c*d^2*e^5 + 6*a^4*e^7 - (2*c^4*d^5*e^2 - 11*a*c^3*d^3*e^4 - 13*a^2*c^2*d*e^6)*x^3 - (8*c^4*d^6*e - 32*a*c^3*d^4*e^3 - 43*a^2*c^2*d^2*e^5 - 3*a^3*c*e^7)*x^2 - (12*c^4*d^7 - 25*a*c^3*d^5*e^2 - 41*a^2*c^2*d^3*e^4 - 4*a^3*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^12 + 4*a*c^3*d^10*e^2 + 6*a^2*c^2*d^8*e^4 + 4*a^3*c*d^6*e^6 + a^4*d^4*e^8 + (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)*x^4 + 4*(c^4*d^9*e^3 + 4*a*c^3*d^7*e^5 + 6*a^2*c^2*d^5*e^7 + 4*a^3*c*d^3*e^9 + a^4*d*e^11)*x^3 + 6*(c^4*d^10*e^2 + 4*a*c^3*d^8*e^4 + 6*a^2*c^2*d^6*e^6 + 4*a^3*c*d^4*e^8 + a^4*d^2*e^10)*x^2 + 4*(c^4*d^11*e + 4*a*c^3*d^9*e^3 + 6*a^2*c^2*d^7*e^5 + 4*a^3*c*d^5*e^7 + a^4*d^3*e^9)*x), -1/24*(3*(4*a*c^3*d^6 - a^2*c^2*d^4*e^2 + (4*a*c^3*d^2*e^4 - a^2*c^2*e^6)*x^4 + 4*(4*a*c^3*d^3*e^3 - a^2*c^2*d*e^5)*x^3 + 6*(4*a*c^3*d^4*e^2 - a^2*c^2*d^2*e^4)*x^2 + 4*(4*a*c^3*d^5*e - a^2*c^2*d^3*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (28*a*c^3*d^6*e + 47*a^2*c^2*d^4*e^3 + 25*a^3*c*d^2*e^5 + 6*a^4*e^7 - (2*c^4*d^5*e^2 - 11*a*c^3*d^3*e^4 - 13*a^2*c^2*d*e^6)*x^3 - (8*c^4*d^6*e - 32*a*c^3*d^4*e^3 - 43*a^2*c^2*d^2*e^5 - 3*a^3*c*e^7)*x^2 - (12*c^4*d^7 - 25*a*c^3*d^5*e^2 - 41*a^2*c^2*d^3*e^4 - 4*a^3*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^12 + 4*a*c^3*d^10*e^2 + 6*a^2*c^2*d^8*e^4 + 4*a^3*c*d^6*e^6 + a^4*d^4*e^8 + (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)*x^4 + 4*(c^4*d^9*e^3 + 4*a*c^3*d^7*e^5 + 6*a^2*c^2*d^5*e^7 + 4*a^3*c*d^3*e^9 + a^4*d*e^11)*x^3 + 6*(c^4*d^10*e^2 + 4*a*c^3*d^8*e^4 + 6*a^2*c^2*d^6*e^6 + 4*a^3*c*d^4*e^8 + a^4*d^2*e^10)*x^2 + 4*(c^4*d^11*e + 4*a*c^3*d^9*e^3 + 6*a^2*c^2*d^7*e^5 + 4*a^3*c*d^5*e^7 + a^4*d^3*e^9)*x)]","B",0
534,1,544,0,0.476982," ","integrate((e*x+d)^4*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(16 \, a^{2} c^{2} d^{4} - 16 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(560 \, c^{4} e^{4} x^{7} + 2560 \, c^{4} d e^{3} x^{6} + 3584 \, a^{2} c^{2} d^{3} e - 1024 \, a^{3} c d e^{3} + 280 \, {\left(16 \, c^{4} d^{2} e^{2} + 3 \, a c^{3} e^{4}\right)} x^{5} + 512 \, {\left(7 \, c^{4} d^{3} e + 8 \, a c^{3} d e^{3}\right)} x^{4} + 70 \, {\left(16 \, c^{4} d^{4} + 112 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{3} + 512 \, {\left(14 \, a c^{3} d^{3} e + a^{2} c^{2} d e^{3}\right)} x^{2} + 35 \, {\left(80 \, a c^{3} d^{4} + 48 \, a^{2} c^{2} d^{2} e^{2} - 3 \, a^{3} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{8960 \, c^{3}}, -\frac{105 \, {\left(16 \, a^{2} c^{2} d^{4} - 16 \, a^{3} c d^{2} e^{2} + a^{4} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(560 \, c^{4} e^{4} x^{7} + 2560 \, c^{4} d e^{3} x^{6} + 3584 \, a^{2} c^{2} d^{3} e - 1024 \, a^{3} c d e^{3} + 280 \, {\left(16 \, c^{4} d^{2} e^{2} + 3 \, a c^{3} e^{4}\right)} x^{5} + 512 \, {\left(7 \, c^{4} d^{3} e + 8 \, a c^{3} d e^{3}\right)} x^{4} + 70 \, {\left(16 \, c^{4} d^{4} + 112 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x^{3} + 512 \, {\left(14 \, a c^{3} d^{3} e + a^{2} c^{2} d e^{3}\right)} x^{2} + 35 \, {\left(80 \, a c^{3} d^{4} + 48 \, a^{2} c^{2} d^{2} e^{2} - 3 \, a^{3} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{4480 \, c^{3}}\right]"," ",0,"[1/8960*(105*(16*a^2*c^2*d^4 - 16*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(560*c^4*e^4*x^7 + 2560*c^4*d*e^3*x^6 + 3584*a^2*c^2*d^3*e - 1024*a^3*c*d*e^3 + 280*(16*c^4*d^2*e^2 + 3*a*c^3*e^4)*x^5 + 512*(7*c^4*d^3*e + 8*a*c^3*d*e^3)*x^4 + 70*(16*c^4*d^4 + 112*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^3 + 512*(14*a*c^3*d^3*e + a^2*c^2*d*e^3)*x^2 + 35*(80*a*c^3*d^4 + 48*a^2*c^2*d^2*e^2 - 3*a^3*c*e^4)*x)*sqrt(c*x^2 + a))/c^3, -1/4480*(105*(16*a^2*c^2*d^4 - 16*a^3*c*d^2*e^2 + a^4*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (560*c^4*e^4*x^7 + 2560*c^4*d*e^3*x^6 + 3584*a^2*c^2*d^3*e - 1024*a^3*c*d*e^3 + 280*(16*c^4*d^2*e^2 + 3*a*c^3*e^4)*x^5 + 512*(7*c^4*d^3*e + 8*a*c^3*d*e^3)*x^4 + 70*(16*c^4*d^4 + 112*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x^3 + 512*(14*a*c^3*d^3*e + a^2*c^2*d*e^3)*x^2 + 35*(80*a*c^3*d^4 + 48*a^2*c^2*d^2*e^2 - 3*a^3*c*e^4)*x)*sqrt(c*x^2 + a))/c^3]","A",0
535,1,402,0,0.459322," ","integrate((e*x+d)^3*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(2 \, a^{2} c d^{3} - a^{3} d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(80 \, c^{3} e^{3} x^{6} + 280 \, c^{3} d e^{2} x^{5} + 336 \, a^{2} c d^{2} e - 32 \, a^{3} e^{3} + 16 \, {\left(21 \, c^{3} d^{2} e + 8 \, a c^{2} e^{3}\right)} x^{4} + 70 \, {\left(2 \, c^{3} d^{3} + 7 \, a c^{2} d e^{2}\right)} x^{3} + 16 \, {\left(42 \, a c^{2} d^{2} e + a^{2} c e^{3}\right)} x^{2} + 35 \, {\left(10 \, a c^{2} d^{3} + 3 \, a^{2} c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{1120 \, c^{2}}, -\frac{105 \, {\left(2 \, a^{2} c d^{3} - a^{3} d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(80 \, c^{3} e^{3} x^{6} + 280 \, c^{3} d e^{2} x^{5} + 336 \, a^{2} c d^{2} e - 32 \, a^{3} e^{3} + 16 \, {\left(21 \, c^{3} d^{2} e + 8 \, a c^{2} e^{3}\right)} x^{4} + 70 \, {\left(2 \, c^{3} d^{3} + 7 \, a c^{2} d e^{2}\right)} x^{3} + 16 \, {\left(42 \, a c^{2} d^{2} e + a^{2} c e^{3}\right)} x^{2} + 35 \, {\left(10 \, a c^{2} d^{3} + 3 \, a^{2} c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{560 \, c^{2}}\right]"," ",0,"[1/1120*(105*(2*a^2*c*d^3 - a^3*d*e^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(80*c^3*e^3*x^6 + 280*c^3*d*e^2*x^5 + 336*a^2*c*d^2*e - 32*a^3*e^3 + 16*(21*c^3*d^2*e + 8*a*c^2*e^3)*x^4 + 70*(2*c^3*d^3 + 7*a*c^2*d*e^2)*x^3 + 16*(42*a*c^2*d^2*e + a^2*c*e^3)*x^2 + 35*(10*a*c^2*d^3 + 3*a^2*c*d*e^2)*x)*sqrt(c*x^2 + a))/c^2, -1/560*(105*(2*a^2*c*d^3 - a^3*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (80*c^3*e^3*x^6 + 280*c^3*d*e^2*x^5 + 336*a^2*c*d^2*e - 32*a^3*e^3 + 16*(21*c^3*d^2*e + 8*a*c^2*e^3)*x^4 + 70*(2*c^3*d^3 + 7*a*c^2*d*e^2)*x^3 + 16*(42*a*c^2*d^2*e + a^2*c*e^3)*x^2 + 35*(10*a*c^2*d^3 + 3*a^2*c*d*e^2)*x)*sqrt(c*x^2 + a))/c^2]","A",0
536,1,296,0,0.453667," ","integrate((e*x+d)^2*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(6 \, a^{2} c d^{2} - a^{3} e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(40 \, c^{3} e^{2} x^{5} + 96 \, c^{3} d e x^{4} + 192 \, a c^{2} d e x^{2} + 96 \, a^{2} c d e + 10 \, {\left(6 \, c^{3} d^{2} + 7 \, a c^{2} e^{2}\right)} x^{3} + 15 \, {\left(10 \, a c^{2} d^{2} + a^{2} c e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{480 \, c^{2}}, -\frac{15 \, {\left(6 \, a^{2} c d^{2} - a^{3} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(40 \, c^{3} e^{2} x^{5} + 96 \, c^{3} d e x^{4} + 192 \, a c^{2} d e x^{2} + 96 \, a^{2} c d e + 10 \, {\left(6 \, c^{3} d^{2} + 7 \, a c^{2} e^{2}\right)} x^{3} + 15 \, {\left(10 \, a c^{2} d^{2} + a^{2} c e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, c^{2}}\right]"," ",0,"[-1/480*(15*(6*a^2*c*d^2 - a^3*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(40*c^3*e^2*x^5 + 96*c^3*d*e*x^4 + 192*a*c^2*d*e*x^2 + 96*a^2*c*d*e + 10*(6*c^3*d^2 + 7*a*c^2*e^2)*x^3 + 15*(10*a*c^2*d^2 + a^2*c*e^2)*x)*sqrt(c*x^2 + a))/c^2, -1/240*(15*(6*a^2*c*d^2 - a^3*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (40*c^3*e^2*x^5 + 96*c^3*d*e*x^4 + 192*a*c^2*d*e*x^2 + 96*a^2*c*d*e + 10*(6*c^3*d^2 + 7*a*c^2*e^2)*x^3 + 15*(10*a*c^2*d^2 + a^2*c*e^2)*x)*sqrt(c*x^2 + a))/c^2]","A",0
537,1,176,0,0.438133," ","integrate((e*x+d)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} \sqrt{c} d \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(8 \, c^{2} e x^{4} + 10 \, c^{2} d x^{3} + 16 \, a c e x^{2} + 25 \, a c d x + 8 \, a^{2} e\right)} \sqrt{c x^{2} + a}}{80 \, c}, -\frac{15 \, a^{2} \sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(8 \, c^{2} e x^{4} + 10 \, c^{2} d x^{3} + 16 \, a c e x^{2} + 25 \, a c d x + 8 \, a^{2} e\right)} \sqrt{c x^{2} + a}}{40 \, c}\right]"," ",0,"[1/80*(15*a^2*sqrt(c)*d*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(8*c^2*e*x^4 + 10*c^2*d*x^3 + 16*a*c*e*x^2 + 25*a*c*d*x + 8*a^2*e)*sqrt(c*x^2 + a))/c, -1/40*(15*a^2*sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (8*c^2*e*x^4 + 10*c^2*d*x^3 + 16*a*c*e*x^2 + 25*a*c*d*x + 8*a^2*e)*sqrt(c*x^2 + a))/c]","A",0
538,1,774,0,2.537186," ","integrate((c*x^2+a)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, c d^{3} + 3 \, a d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 6 \, {\left(c d^{2} + a e^{2}\right)}^{\frac{3}{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(2 \, c e^{3} x^{2} - 3 \, c d e^{2} x + 6 \, c d^{2} e + 8 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{12 \, e^{4}}, \frac{3 \, {\left(2 \, c d^{3} + 3 \, a d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + 3 \, {\left(c d^{2} + a e^{2}\right)}^{\frac{3}{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(2 \, c e^{3} x^{2} - 3 \, c d e^{2} x + 6 \, c d^{2} e + 8 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{6 \, e^{4}}, -\frac{12 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(2 \, c d^{3} + 3 \, a d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(2 \, c e^{3} x^{2} - 3 \, c d e^{2} x + 6 \, c d^{2} e + 8 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{12 \, e^{4}}, -\frac{6 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(2 \, c d^{3} + 3 \, a d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, c e^{3} x^{2} - 3 \, c d e^{2} x + 6 \, c d^{2} e + 8 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{6 \, e^{4}}\right]"," ",0,"[1/12*(3*(2*c*d^3 + 3*a*d*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 6*(c*d^2 + a*e^2)^(3/2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(2*c*e^3*x^2 - 3*c*d*e^2*x + 6*c*d^2*e + 8*a*e^3)*sqrt(c*x^2 + a))/e^4, 1/6*(3*(2*c*d^3 + 3*a*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + 3*(c*d^2 + a*e^2)^(3/2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (2*c*e^3*x^2 - 3*c*d*e^2*x + 6*c*d^2*e + 8*a*e^3)*sqrt(c*x^2 + a))/e^4, -1/12*(12*(c*d^2 + a*e^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(2*c*d^3 + 3*a*d*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(2*c*e^3*x^2 - 3*c*d*e^2*x + 6*c*d^2*e + 8*a*e^3)*sqrt(c*x^2 + a))/e^4, -1/6*(6*(c*d^2 + a*e^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(2*c*d^3 + 3*a*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (2*c*e^3*x^2 - 3*c*d*e^2*x + 6*c*d^2*e + 8*a*e^3)*sqrt(c*x^2 + a))/e^4]","A",0
539,1,888,0,0.718298," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, c d^{3} + a d e^{2} + {\left(2 \, c d^{2} e + a e^{3}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 6 \, {\left(c d e x + c d^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(c e^{3} x^{2} - 3 \, c d e^{2} x - 6 \, c d^{2} e - 2 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{4 \, {\left(e^{5} x + d e^{4}\right)}}, \frac{12 \, {\left(c d e x + c d^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + 3 \, {\left(2 \, c d^{3} + a d e^{2} + {\left(2 \, c d^{2} e + a e^{3}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(c e^{3} x^{2} - 3 \, c d e^{2} x - 6 \, c d^{2} e - 2 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{4 \, {\left(e^{5} x + d e^{4}\right)}}, -\frac{3 \, {\left(2 \, c d^{3} + a d e^{2} + {\left(2 \, c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 3 \, {\left(c d e x + c d^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - {\left(c e^{3} x^{2} - 3 \, c d e^{2} x - 6 \, c d^{2} e - 2 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(e^{5} x + d e^{4}\right)}}, \frac{6 \, {\left(c d e x + c d^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(2 \, c d^{3} + a d e^{2} + {\left(2 \, c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(c e^{3} x^{2} - 3 \, c d e^{2} x - 6 \, c d^{2} e - 2 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(e^{5} x + d e^{4}\right)}}\right]"," ",0,"[1/4*(3*(2*c*d^3 + a*d*e^2 + (2*c*d^2*e + a*e^3)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 6*(c*d*e*x + c*d^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(c*e^3*x^2 - 3*c*d*e^2*x - 6*c*d^2*e - 2*a*e^3)*sqrt(c*x^2 + a))/(e^5*x + d*e^4), 1/4*(12*(c*d*e*x + c*d^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + 3*(2*c*d^3 + a*d*e^2 + (2*c*d^2*e + a*e^3)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(c*e^3*x^2 - 3*c*d*e^2*x - 6*c*d^2*e - 2*a*e^3)*sqrt(c*x^2 + a))/(e^5*x + d*e^4), -1/2*(3*(2*c*d^3 + a*d*e^2 + (2*c*d^2*e + a*e^3)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 3*(c*d*e*x + c*d^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - (c*e^3*x^2 - 3*c*d*e^2*x - 6*c*d^2*e - 2*a*e^3)*sqrt(c*x^2 + a))/(e^5*x + d*e^4), 1/2*(6*(c*d*e*x + c*d^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(2*c*d^3 + a*d*e^2 + (2*c*d^2*e + a*e^3)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (c*e^3*x^2 - 3*c*d*e^2*x - 6*c*d^2*e - 2*a*e^3)*sqrt(c*x^2 + a))/(e^5*x + d*e^4)]","A",0
540,1,1545,0,0.953307," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(c^{2} d^{5} + a c d^{3} e^{2} + {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{4} e + a c d^{2} e^{3}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 3 \, {\left(2 \, c^{2} d^{4} + a c d^{2} e^{2} + {\left(2 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(6 \, c^{2} d^{4} e + 5 \, a c d^{2} e^{3} - a^{2} e^{5} + 2 \, {\left(c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} + 9 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(c d^{4} e^{4} + a d^{2} e^{6} + {\left(c d^{2} e^{6} + a e^{8}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} + a d e^{7}\right)} x\right)}}, \frac{12 \, {\left(c^{2} d^{5} + a c d^{3} e^{2} + {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{4} e + a c d^{2} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + 3 \, {\left(2 \, c^{2} d^{4} + a c d^{2} e^{2} + {\left(2 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(6 \, c^{2} d^{4} e + 5 \, a c d^{2} e^{3} - a^{2} e^{5} + 2 \, {\left(c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} + 9 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(c d^{4} e^{4} + a d^{2} e^{6} + {\left(c d^{2} e^{6} + a e^{8}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} + a d e^{7}\right)} x\right)}}, -\frac{3 \, {\left(2 \, c^{2} d^{4} + a c d^{2} e^{2} + {\left(2 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 3 \, {\left(c^{2} d^{5} + a c d^{3} e^{2} + {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{4} e + a c d^{2} e^{3}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - {\left(6 \, c^{2} d^{4} e + 5 \, a c d^{2} e^{3} - a^{2} e^{5} + 2 \, {\left(c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} + 9 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c d^{4} e^{4} + a d^{2} e^{6} + {\left(c d^{2} e^{6} + a e^{8}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} + a d e^{7}\right)} x\right)}}, -\frac{3 \, {\left(2 \, c^{2} d^{4} + a c d^{2} e^{2} + {\left(2 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 6 \, {\left(c^{2} d^{5} + a c d^{3} e^{2} + {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{4} e + a c d^{2} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, c^{2} d^{4} e + 5 \, a c d^{2} e^{3} - a^{2} e^{5} + 2 \, {\left(c^{2} d^{2} e^{3} + a c e^{5}\right)} x^{2} + 9 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c d^{4} e^{4} + a d^{2} e^{6} + {\left(c d^{2} e^{6} + a e^{8}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} + a d e^{7}\right)} x\right)}}\right]"," ",0,"[1/4*(6*(c^2*d^5 + a*c*d^3*e^2 + (c^2*d^3*e^2 + a*c*d*e^4)*x^2 + 2*(c^2*d^4*e + a*c*d^2*e^3)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 3*(2*c^2*d^4 + a*c*d^2*e^2 + (2*c^2*d^2*e^2 + a*c*e^4)*x^2 + 2*(2*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(6*c^2*d^4*e + 5*a*c*d^2*e^3 - a^2*e^5 + 2*(c^2*d^2*e^3 + a*c*e^5)*x^2 + 9*(c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c*d^4*e^4 + a*d^2*e^6 + (c*d^2*e^6 + a*e^8)*x^2 + 2*(c*d^3*e^5 + a*d*e^7)*x), 1/4*(12*(c^2*d^5 + a*c*d^3*e^2 + (c^2*d^3*e^2 + a*c*d*e^4)*x^2 + 2*(c^2*d^4*e + a*c*d^2*e^3)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + 3*(2*c^2*d^4 + a*c*d^2*e^2 + (2*c^2*d^2*e^2 + a*c*e^4)*x^2 + 2*(2*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(6*c^2*d^4*e + 5*a*c*d^2*e^3 - a^2*e^5 + 2*(c^2*d^2*e^3 + a*c*e^5)*x^2 + 9*(c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c*d^4*e^4 + a*d^2*e^6 + (c*d^2*e^6 + a*e^8)*x^2 + 2*(c*d^3*e^5 + a*d*e^7)*x), -1/2*(3*(2*c^2*d^4 + a*c*d^2*e^2 + (2*c^2*d^2*e^2 + a*c*e^4)*x^2 + 2*(2*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 3*(c^2*d^5 + a*c*d^3*e^2 + (c^2*d^3*e^2 + a*c*d*e^4)*x^2 + 2*(c^2*d^4*e + a*c*d^2*e^3)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - (6*c^2*d^4*e + 5*a*c*d^2*e^3 - a^2*e^5 + 2*(c^2*d^2*e^3 + a*c*e^5)*x^2 + 9*(c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c*d^4*e^4 + a*d^2*e^6 + (c*d^2*e^6 + a*e^8)*x^2 + 2*(c*d^3*e^5 + a*d*e^7)*x), -1/2*(3*(2*c^2*d^4 + a*c*d^2*e^2 + (2*c^2*d^2*e^2 + a*c*e^4)*x^2 + 2*(2*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 6*(c^2*d^5 + a*c*d^3*e^2 + (c^2*d^3*e^2 + a*c*d*e^4)*x^2 + 2*(c^2*d^4*e + a*c*d^2*e^3)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (6*c^2*d^4*e + 5*a*c*d^2*e^3 - a^2*e^5 + 2*(c^2*d^2*e^3 + a*c*e^5)*x^2 + 9*(c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c*d^4*e^4 + a*d^2*e^6 + (c*d^2*e^6 + a*e^8)*x^2 + 2*(c*d^3*e^5 + a*d*e^7)*x)]","B",0
541,1,2513,0,6.889822," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(c^{3} d^{7} + 2 \, a c^{2} d^{5} e^{2} + a^{2} c d^{3} e^{4} + {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{3} + 3 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{2} + 3 \, {\left(c^{3} d^{6} e + 2 \, a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 3 \, {\left(2 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + {\left(2 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(2 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(2 \, c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(6 \, c^{3} d^{6} e + 11 \, a c^{2} d^{4} e^{3} + 7 \, a^{2} c d^{2} e^{5} + 2 \, a^{3} e^{7} + {\left(11 \, c^{3} d^{4} e^{3} + 19 \, a c^{2} d^{2} e^{5} + 8 \, a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(5 \, c^{3} d^{5} e^{2} + 8 \, a c^{2} d^{3} e^{4} + 3 \, a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(c^{2} d^{7} e^{4} + 2 \, a c d^{5} e^{6} + a^{2} d^{3} e^{8} + {\left(c^{2} d^{4} e^{7} + 2 \, a c d^{2} e^{9} + a^{2} e^{11}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{6} + 2 \, a c d^{3} e^{8} + a^{2} d e^{10}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e^{5} + 2 \, a c d^{4} e^{7} + a^{2} d^{2} e^{9}\right)} x\right)}}, \frac{3 \, {\left(2 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + {\left(2 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(2 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(2 \, c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + 3 \, {\left(c^{3} d^{7} + 2 \, a c^{2} d^{5} e^{2} + a^{2} c d^{3} e^{4} + {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{3} + 3 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{2} + 3 \, {\left(c^{3} d^{6} e + 2 \, a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - {\left(6 \, c^{3} d^{6} e + 11 \, a c^{2} d^{4} e^{3} + 7 \, a^{2} c d^{2} e^{5} + 2 \, a^{3} e^{7} + {\left(11 \, c^{3} d^{4} e^{3} + 19 \, a c^{2} d^{2} e^{5} + 8 \, a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(5 \, c^{3} d^{5} e^{2} + 8 \, a c^{2} d^{3} e^{4} + 3 \, a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{2} d^{7} e^{4} + 2 \, a c d^{5} e^{6} + a^{2} d^{3} e^{8} + {\left(c^{2} d^{4} e^{7} + 2 \, a c d^{2} e^{9} + a^{2} e^{11}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{6} + 2 \, a c d^{3} e^{8} + a^{2} d e^{10}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e^{5} + 2 \, a c d^{4} e^{7} + a^{2} d^{2} e^{9}\right)} x\right)}}, -\frac{12 \, {\left(c^{3} d^{7} + 2 \, a c^{2} d^{5} e^{2} + a^{2} c d^{3} e^{4} + {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{3} + 3 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{2} + 3 \, {\left(c^{3} d^{6} e + 2 \, a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 3 \, {\left(2 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + {\left(2 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(2 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(2 \, c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(6 \, c^{3} d^{6} e + 11 \, a c^{2} d^{4} e^{3} + 7 \, a^{2} c d^{2} e^{5} + 2 \, a^{3} e^{7} + {\left(11 \, c^{3} d^{4} e^{3} + 19 \, a c^{2} d^{2} e^{5} + 8 \, a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(5 \, c^{3} d^{5} e^{2} + 8 \, a c^{2} d^{3} e^{4} + 3 \, a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(c^{2} d^{7} e^{4} + 2 \, a c d^{5} e^{6} + a^{2} d^{3} e^{8} + {\left(c^{2} d^{4} e^{7} + 2 \, a c d^{2} e^{9} + a^{2} e^{11}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{6} + 2 \, a c d^{3} e^{8} + a^{2} d e^{10}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e^{5} + 2 \, a c d^{4} e^{7} + a^{2} d^{2} e^{9}\right)} x\right)}}, \frac{3 \, {\left(2 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + {\left(2 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(2 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(2 \, c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 6 \, {\left(c^{3} d^{7} + 2 \, a c^{2} d^{5} e^{2} + a^{2} c d^{3} e^{4} + {\left(c^{3} d^{4} e^{3} + 2 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{3} + 3 \, {\left(c^{3} d^{5} e^{2} + 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{2} + 3 \, {\left(c^{3} d^{6} e + 2 \, a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, c^{3} d^{6} e + 11 \, a c^{2} d^{4} e^{3} + 7 \, a^{2} c d^{2} e^{5} + 2 \, a^{3} e^{7} + {\left(11 \, c^{3} d^{4} e^{3} + 19 \, a c^{2} d^{2} e^{5} + 8 \, a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(5 \, c^{3} d^{5} e^{2} + 8 \, a c^{2} d^{3} e^{4} + 3 \, a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{2} d^{7} e^{4} + 2 \, a c d^{5} e^{6} + a^{2} d^{3} e^{8} + {\left(c^{2} d^{4} e^{7} + 2 \, a c d^{2} e^{9} + a^{2} e^{11}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{6} + 2 \, a c d^{3} e^{8} + a^{2} d e^{10}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e^{5} + 2 \, a c d^{4} e^{7} + a^{2} d^{2} e^{9}\right)} x\right)}}\right]"," ",0,"[1/12*(6*(c^3*d^7 + 2*a*c^2*d^5*e^2 + a^2*c*d^3*e^4 + (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x^3 + 3*(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^2 + 3*(c^3*d^6*e + 2*a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 3*(2*c^3*d^6 + 3*a*c^2*d^4*e^2 + (2*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 3*(2*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4)*x^2 + 3*(2*c^3*d^5*e + 3*a*c^2*d^3*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(6*c^3*d^6*e + 11*a*c^2*d^4*e^3 + 7*a^2*c*d^2*e^5 + 2*a^3*e^7 + (11*c^3*d^4*e^3 + 19*a*c^2*d^2*e^5 + 8*a^2*c*e^7)*x^2 + 3*(5*c^3*d^5*e^2 + 8*a*c^2*d^3*e^4 + 3*a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^2*d^7*e^4 + 2*a*c*d^5*e^6 + a^2*d^3*e^8 + (c^2*d^4*e^7 + 2*a*c*d^2*e^9 + a^2*e^11)*x^3 + 3*(c^2*d^5*e^6 + 2*a*c*d^3*e^8 + a^2*d*e^10)*x^2 + 3*(c^2*d^6*e^5 + 2*a*c*d^4*e^7 + a^2*d^2*e^9)*x), 1/6*(3*(2*c^3*d^6 + 3*a*c^2*d^4*e^2 + (2*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 3*(2*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4)*x^2 + 3*(2*c^3*d^5*e + 3*a*c^2*d^3*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + 3*(c^3*d^7 + 2*a*c^2*d^5*e^2 + a^2*c*d^3*e^4 + (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x^3 + 3*(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^2 + 3*(c^3*d^6*e + 2*a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - (6*c^3*d^6*e + 11*a*c^2*d^4*e^3 + 7*a^2*c*d^2*e^5 + 2*a^3*e^7 + (11*c^3*d^4*e^3 + 19*a*c^2*d^2*e^5 + 8*a^2*c*e^7)*x^2 + 3*(5*c^3*d^5*e^2 + 8*a*c^2*d^3*e^4 + 3*a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^2*d^7*e^4 + 2*a*c*d^5*e^6 + a^2*d^3*e^8 + (c^2*d^4*e^7 + 2*a*c*d^2*e^9 + a^2*e^11)*x^3 + 3*(c^2*d^5*e^6 + 2*a*c*d^3*e^8 + a^2*d*e^10)*x^2 + 3*(c^2*d^6*e^5 + 2*a*c*d^4*e^7 + a^2*d^2*e^9)*x), -1/12*(12*(c^3*d^7 + 2*a*c^2*d^5*e^2 + a^2*c*d^3*e^4 + (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x^3 + 3*(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^2 + 3*(c^3*d^6*e + 2*a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 3*(2*c^3*d^6 + 3*a*c^2*d^4*e^2 + (2*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 3*(2*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4)*x^2 + 3*(2*c^3*d^5*e + 3*a*c^2*d^3*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(6*c^3*d^6*e + 11*a*c^2*d^4*e^3 + 7*a^2*c*d^2*e^5 + 2*a^3*e^7 + (11*c^3*d^4*e^3 + 19*a*c^2*d^2*e^5 + 8*a^2*c*e^7)*x^2 + 3*(5*c^3*d^5*e^2 + 8*a*c^2*d^3*e^4 + 3*a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^2*d^7*e^4 + 2*a*c*d^5*e^6 + a^2*d^3*e^8 + (c^2*d^4*e^7 + 2*a*c*d^2*e^9 + a^2*e^11)*x^3 + 3*(c^2*d^5*e^6 + 2*a*c*d^3*e^8 + a^2*d*e^10)*x^2 + 3*(c^2*d^6*e^5 + 2*a*c*d^4*e^7 + a^2*d^2*e^9)*x), 1/6*(3*(2*c^3*d^6 + 3*a*c^2*d^4*e^2 + (2*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 3*(2*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4)*x^2 + 3*(2*c^3*d^5*e + 3*a*c^2*d^3*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 6*(c^3*d^7 + 2*a*c^2*d^5*e^2 + a^2*c*d^3*e^4 + (c^3*d^4*e^3 + 2*a*c^2*d^2*e^5 + a^2*c*e^7)*x^3 + 3*(c^3*d^5*e^2 + 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^2 + 3*(c^3*d^6*e + 2*a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (6*c^3*d^6*e + 11*a*c^2*d^4*e^3 + 7*a^2*c*d^2*e^5 + 2*a^3*e^7 + (11*c^3*d^4*e^3 + 19*a*c^2*d^2*e^5 + 8*a^2*c*e^7)*x^2 + 3*(5*c^3*d^5*e^2 + 8*a*c^2*d^3*e^4 + 3*a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^2*d^7*e^4 + 2*a*c*d^5*e^6 + a^2*d^3*e^8 + (c^2*d^4*e^7 + 2*a*c*d^2*e^9 + a^2*e^11)*x^3 + 3*(c^2*d^5*e^6 + 2*a*c*d^3*e^8 + a^2*d*e^10)*x^2 + 3*(c^2*d^6*e^5 + 2*a*c*d^4*e^7 + a^2*d^2*e^9)*x)]","B",0
542,1,1123,0,2.226365," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} c^{2} e^{4} x^{4} + 4 \, a^{2} c^{2} d e^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} e^{2} x^{2} + 4 \, a^{2} c^{2} d^{3} e x + a^{2} c^{2} d^{4}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(5 \, a^{2} c^{2} d^{4} e + 7 \, a^{3} c d^{2} e^{3} + 2 \, a^{4} e^{5} - {\left(2 \, c^{4} d^{5} + 7 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4}\right)} x^{3} - {\left(4 \, a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3} - 5 \, a^{3} c e^{5}\right)} x^{2} - {\left(5 \, a c^{3} d^{5} + a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{16 \, {\left(c^{3} d^{10} + 3 \, a c^{2} d^{8} e^{2} + 3 \, a^{2} c d^{6} e^{4} + a^{3} d^{4} e^{6} + {\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)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{3} + 3 \, a c^{2} d^{5} e^{5} + 3 \, a^{2} c d^{3} e^{7} + a^{3} d e^{9}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{2} + 3 \, a c^{2} d^{6} e^{4} + 3 \, a^{2} c d^{4} e^{6} + a^{3} d^{2} e^{8}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e + 3 \, a c^{2} d^{7} e^{3} + 3 \, a^{2} c d^{5} e^{5} + a^{3} d^{3} e^{7}\right)} x\right)}}, -\frac{3 \, {\left(a^{2} c^{2} e^{4} x^{4} + 4 \, a^{2} c^{2} d e^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} e^{2} x^{2} + 4 \, a^{2} c^{2} d^{3} e x + a^{2} c^{2} d^{4}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(5 \, a^{2} c^{2} d^{4} e + 7 \, a^{3} c d^{2} e^{3} + 2 \, a^{4} e^{5} - {\left(2 \, c^{4} d^{5} + 7 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4}\right)} x^{3} - {\left(4 \, a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3} - 5 \, a^{3} c e^{5}\right)} x^{2} - {\left(5 \, a c^{3} d^{5} + a^{2} c^{2} d^{3} e^{2} - 4 \, a^{3} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{8 \, {\left(c^{3} d^{10} + 3 \, a c^{2} d^{8} e^{2} + 3 \, a^{2} c d^{6} e^{4} + a^{3} d^{4} e^{6} + {\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)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{3} + 3 \, a c^{2} d^{5} e^{5} + 3 \, a^{2} c d^{3} e^{7} + a^{3} d e^{9}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{2} + 3 \, a c^{2} d^{6} e^{4} + 3 \, a^{2} c d^{4} e^{6} + a^{3} d^{2} e^{8}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e + 3 \, a c^{2} d^{7} e^{3} + 3 \, a^{2} c d^{5} e^{5} + a^{3} d^{3} e^{7}\right)} x\right)}}\right]"," ",0,"[1/16*(3*(a^2*c^2*e^4*x^4 + 4*a^2*c^2*d*e^3*x^3 + 6*a^2*c^2*d^2*e^2*x^2 + 4*a^2*c^2*d^3*e*x + a^2*c^2*d^4)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(5*a^2*c^2*d^4*e + 7*a^3*c*d^2*e^3 + 2*a^4*e^5 - (2*c^4*d^5 + 7*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4)*x^3 - (4*a*c^3*d^4*e - a^2*c^2*d^2*e^3 - 5*a^3*c*e^5)*x^2 - (5*a*c^3*d^5 + a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^10 + 3*a*c^2*d^8*e^2 + 3*a^2*c*d^6*e^4 + a^3*d^4*e^6 + (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)*x^4 + 4*(c^3*d^7*e^3 + 3*a*c^2*d^5*e^5 + 3*a^2*c*d^3*e^7 + a^3*d*e^9)*x^3 + 6*(c^3*d^8*e^2 + 3*a*c^2*d^6*e^4 + 3*a^2*c*d^4*e^6 + a^3*d^2*e^8)*x^2 + 4*(c^3*d^9*e + 3*a*c^2*d^7*e^3 + 3*a^2*c*d^5*e^5 + a^3*d^3*e^7)*x), -1/8*(3*(a^2*c^2*e^4*x^4 + 4*a^2*c^2*d*e^3*x^3 + 6*a^2*c^2*d^2*e^2*x^2 + 4*a^2*c^2*d^3*e*x + a^2*c^2*d^4)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (5*a^2*c^2*d^4*e + 7*a^3*c*d^2*e^3 + 2*a^4*e^5 - (2*c^4*d^5 + 7*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4)*x^3 - (4*a*c^3*d^4*e - a^2*c^2*d^2*e^3 - 5*a^3*c*e^5)*x^2 - (5*a*c^3*d^5 + a^2*c^2*d^3*e^2 - 4*a^3*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^10 + 3*a*c^2*d^8*e^2 + 3*a^2*c*d^6*e^4 + a^3*d^4*e^6 + (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)*x^4 + 4*(c^3*d^7*e^3 + 3*a*c^2*d^5*e^5 + 3*a^2*c*d^3*e^7 + a^3*d*e^9)*x^3 + 6*(c^3*d^8*e^2 + 3*a*c^2*d^6*e^4 + 3*a^2*c*d^4*e^6 + a^3*d^2*e^8)*x^2 + 4*(c^3*d^9*e + 3*a*c^2*d^7*e^3 + 3*a^2*c*d^5*e^5 + a^3*d^3*e^7)*x)]","B",0
543,1,1647,0,5.953509," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} c^{3} d e^{5} x^{5} + 5 \, a^{2} c^{3} d^{2} e^{4} x^{4} + 10 \, a^{2} c^{3} d^{3} e^{3} x^{3} + 10 \, a^{2} c^{3} d^{4} e^{2} x^{2} + 5 \, a^{2} c^{3} d^{5} e x + a^{2} c^{3} d^{6}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(33 \, a^{2} c^{3} d^{6} e + 59 \, a^{3} c^{2} d^{4} e^{3} + 34 \, a^{4} c d^{2} e^{5} + 8 \, a^{5} e^{7} - {\left(2 \, c^{5} d^{6} e + 11 \, a c^{4} d^{4} e^{3} + a^{2} c^{3} d^{2} e^{5} - 8 \, a^{3} c^{2} e^{7}\right)} x^{4} - 5 \, {\left(2 \, c^{5} d^{7} + 11 \, a c^{4} d^{5} e^{2} + 4 \, a^{2} c^{3} d^{3} e^{4} - 5 \, a^{3} c^{2} d e^{6}\right)} x^{3} - {\left(29 \, a c^{4} d^{6} e - 48 \, a^{2} c^{3} d^{4} e^{3} - 93 \, a^{3} c^{2} d^{2} e^{5} - 16 \, a^{4} c e^{7}\right)} x^{2} - 5 \, {\left(5 \, a c^{4} d^{7} - 4 \, a^{2} c^{3} d^{5} e^{2} - 11 \, a^{3} c^{2} d^{3} e^{4} - 2 \, a^{4} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{80 \, {\left(c^{4} d^{13} + 4 \, a c^{3} d^{11} e^{2} + 6 \, a^{2} c^{2} d^{9} e^{4} + 4 \, a^{3} c d^{7} e^{6} + a^{4} d^{5} e^{8} + {\left(c^{4} d^{8} e^{5} + 4 \, a c^{3} d^{6} e^{7} + 6 \, a^{2} c^{2} d^{4} e^{9} + 4 \, a^{3} c d^{2} e^{11} + a^{4} e^{13}\right)} x^{5} + 5 \, {\left(c^{4} d^{9} e^{4} + 4 \, a c^{3} d^{7} e^{6} + 6 \, a^{2} c^{2} d^{5} e^{8} + 4 \, a^{3} c d^{3} e^{10} + a^{4} d e^{12}\right)} x^{4} + 10 \, {\left(c^{4} d^{10} e^{3} + 4 \, a c^{3} d^{8} e^{5} + 6 \, a^{2} c^{2} d^{6} e^{7} + 4 \, a^{3} c d^{4} e^{9} + a^{4} d^{2} e^{11}\right)} x^{3} + 10 \, {\left(c^{4} d^{11} e^{2} + 4 \, a c^{3} d^{9} e^{4} + 6 \, a^{2} c^{2} d^{7} e^{6} + 4 \, a^{3} c d^{5} e^{8} + a^{4} d^{3} e^{10}\right)} x^{2} + 5 \, {\left(c^{4} d^{12} e + 4 \, a c^{3} d^{10} e^{3} + 6 \, a^{2} c^{2} d^{8} e^{5} + 4 \, a^{3} c d^{6} e^{7} + a^{4} d^{4} e^{9}\right)} x\right)}}, -\frac{15 \, {\left(a^{2} c^{3} d e^{5} x^{5} + 5 \, a^{2} c^{3} d^{2} e^{4} x^{4} + 10 \, a^{2} c^{3} d^{3} e^{3} x^{3} + 10 \, a^{2} c^{3} d^{4} e^{2} x^{2} + 5 \, a^{2} c^{3} d^{5} e x + a^{2} c^{3} d^{6}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(33 \, a^{2} c^{3} d^{6} e + 59 \, a^{3} c^{2} d^{4} e^{3} + 34 \, a^{4} c d^{2} e^{5} + 8 \, a^{5} e^{7} - {\left(2 \, c^{5} d^{6} e + 11 \, a c^{4} d^{4} e^{3} + a^{2} c^{3} d^{2} e^{5} - 8 \, a^{3} c^{2} e^{7}\right)} x^{4} - 5 \, {\left(2 \, c^{5} d^{7} + 11 \, a c^{4} d^{5} e^{2} + 4 \, a^{2} c^{3} d^{3} e^{4} - 5 \, a^{3} c^{2} d e^{6}\right)} x^{3} - {\left(29 \, a c^{4} d^{6} e - 48 \, a^{2} c^{3} d^{4} e^{3} - 93 \, a^{3} c^{2} d^{2} e^{5} - 16 \, a^{4} c e^{7}\right)} x^{2} - 5 \, {\left(5 \, a c^{4} d^{7} - 4 \, a^{2} c^{3} d^{5} e^{2} - 11 \, a^{3} c^{2} d^{3} e^{4} - 2 \, a^{4} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{40 \, {\left(c^{4} d^{13} + 4 \, a c^{3} d^{11} e^{2} + 6 \, a^{2} c^{2} d^{9} e^{4} + 4 \, a^{3} c d^{7} e^{6} + a^{4} d^{5} e^{8} + {\left(c^{4} d^{8} e^{5} + 4 \, a c^{3} d^{6} e^{7} + 6 \, a^{2} c^{2} d^{4} e^{9} + 4 \, a^{3} c d^{2} e^{11} + a^{4} e^{13}\right)} x^{5} + 5 \, {\left(c^{4} d^{9} e^{4} + 4 \, a c^{3} d^{7} e^{6} + 6 \, a^{2} c^{2} d^{5} e^{8} + 4 \, a^{3} c d^{3} e^{10} + a^{4} d e^{12}\right)} x^{4} + 10 \, {\left(c^{4} d^{10} e^{3} + 4 \, a c^{3} d^{8} e^{5} + 6 \, a^{2} c^{2} d^{6} e^{7} + 4 \, a^{3} c d^{4} e^{9} + a^{4} d^{2} e^{11}\right)} x^{3} + 10 \, {\left(c^{4} d^{11} e^{2} + 4 \, a c^{3} d^{9} e^{4} + 6 \, a^{2} c^{2} d^{7} e^{6} + 4 \, a^{3} c d^{5} e^{8} + a^{4} d^{3} e^{10}\right)} x^{2} + 5 \, {\left(c^{4} d^{12} e + 4 \, a c^{3} d^{10} e^{3} + 6 \, a^{2} c^{2} d^{8} e^{5} + 4 \, a^{3} c d^{6} e^{7} + a^{4} d^{4} e^{9}\right)} x\right)}}\right]"," ",0,"[1/80*(15*(a^2*c^3*d*e^5*x^5 + 5*a^2*c^3*d^2*e^4*x^4 + 10*a^2*c^3*d^3*e^3*x^3 + 10*a^2*c^3*d^4*e^2*x^2 + 5*a^2*c^3*d^5*e*x + a^2*c^3*d^6)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(33*a^2*c^3*d^6*e + 59*a^3*c^2*d^4*e^3 + 34*a^4*c*d^2*e^5 + 8*a^5*e^7 - (2*c^5*d^6*e + 11*a*c^4*d^4*e^3 + a^2*c^3*d^2*e^5 - 8*a^3*c^2*e^7)*x^4 - 5*(2*c^5*d^7 + 11*a*c^4*d^5*e^2 + 4*a^2*c^3*d^3*e^4 - 5*a^3*c^2*d*e^6)*x^3 - (29*a*c^4*d^6*e - 48*a^2*c^3*d^4*e^3 - 93*a^3*c^2*d^2*e^5 - 16*a^4*c*e^7)*x^2 - 5*(5*a*c^4*d^7 - 4*a^2*c^3*d^5*e^2 - 11*a^3*c^2*d^3*e^4 - 2*a^4*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^13 + 4*a*c^3*d^11*e^2 + 6*a^2*c^2*d^9*e^4 + 4*a^3*c*d^7*e^6 + a^4*d^5*e^8 + (c^4*d^8*e^5 + 4*a*c^3*d^6*e^7 + 6*a^2*c^2*d^4*e^9 + 4*a^3*c*d^2*e^11 + a^4*e^13)*x^5 + 5*(c^4*d^9*e^4 + 4*a*c^3*d^7*e^6 + 6*a^2*c^2*d^5*e^8 + 4*a^3*c*d^3*e^10 + a^4*d*e^12)*x^4 + 10*(c^4*d^10*e^3 + 4*a*c^3*d^8*e^5 + 6*a^2*c^2*d^6*e^7 + 4*a^3*c*d^4*e^9 + a^4*d^2*e^11)*x^3 + 10*(c^4*d^11*e^2 + 4*a*c^3*d^9*e^4 + 6*a^2*c^2*d^7*e^6 + 4*a^3*c*d^5*e^8 + a^4*d^3*e^10)*x^2 + 5*(c^4*d^12*e + 4*a*c^3*d^10*e^3 + 6*a^2*c^2*d^8*e^5 + 4*a^3*c*d^6*e^7 + a^4*d^4*e^9)*x), -1/40*(15*(a^2*c^3*d*e^5*x^5 + 5*a^2*c^3*d^2*e^4*x^4 + 10*a^2*c^3*d^3*e^3*x^3 + 10*a^2*c^3*d^4*e^2*x^2 + 5*a^2*c^3*d^5*e*x + a^2*c^3*d^6)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (33*a^2*c^3*d^6*e + 59*a^3*c^2*d^4*e^3 + 34*a^4*c*d^2*e^5 + 8*a^5*e^7 - (2*c^5*d^6*e + 11*a*c^4*d^4*e^3 + a^2*c^3*d^2*e^5 - 8*a^3*c^2*e^7)*x^4 - 5*(2*c^5*d^7 + 11*a*c^4*d^5*e^2 + 4*a^2*c^3*d^3*e^4 - 5*a^3*c^2*d*e^6)*x^3 - (29*a*c^4*d^6*e - 48*a^2*c^3*d^4*e^3 - 93*a^3*c^2*d^2*e^5 - 16*a^4*c*e^7)*x^2 - 5*(5*a*c^4*d^7 - 4*a^2*c^3*d^5*e^2 - 11*a^3*c^2*d^3*e^4 - 2*a^4*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^13 + 4*a*c^3*d^11*e^2 + 6*a^2*c^2*d^9*e^4 + 4*a^3*c*d^7*e^6 + a^4*d^5*e^8 + (c^4*d^8*e^5 + 4*a*c^3*d^6*e^7 + 6*a^2*c^2*d^4*e^9 + 4*a^3*c*d^2*e^11 + a^4*e^13)*x^5 + 5*(c^4*d^9*e^4 + 4*a*c^3*d^7*e^6 + 6*a^2*c^2*d^5*e^8 + 4*a^3*c*d^3*e^10 + a^4*d*e^12)*x^4 + 10*(c^4*d^10*e^3 + 4*a*c^3*d^8*e^5 + 6*a^2*c^2*d^6*e^7 + 4*a^3*c*d^4*e^9 + a^4*d^2*e^11)*x^3 + 10*(c^4*d^11*e^2 + 4*a*c^3*d^9*e^4 + 6*a^2*c^2*d^7*e^6 + 4*a^3*c*d^5*e^8 + a^4*d^3*e^10)*x^2 + 5*(c^4*d^12*e + 4*a*c^3*d^10*e^3 + 6*a^2*c^2*d^8*e^5 + 4*a^3*c*d^6*e^7 + a^4*d^4*e^9)*x)]","B",0
544,1,2485,0,14.020984," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^7,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(6 \, a^{2} c^{4} d^{8} - a^{3} c^{3} d^{6} e^{2} + {\left(6 \, a^{2} c^{4} d^{2} e^{6} - a^{3} c^{3} e^{8}\right)} x^{6} + 6 \, {\left(6 \, a^{2} c^{4} d^{3} e^{5} - a^{3} c^{3} d e^{7}\right)} x^{5} + 15 \, {\left(6 \, a^{2} c^{4} d^{4} e^{4} - a^{3} c^{3} d^{2} e^{6}\right)} x^{4} + 20 \, {\left(6 \, a^{2} c^{4} d^{5} e^{3} - a^{3} c^{3} d^{3} e^{5}\right)} x^{3} + 15 \, {\left(6 \, a^{2} c^{4} d^{6} e^{2} - a^{3} c^{3} d^{4} e^{4}\right)} x^{2} + 6 \, {\left(6 \, a^{2} c^{4} d^{7} e - a^{3} c^{3} d^{5} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(246 \, a^{2} c^{4} d^{8} e + 513 \, a^{3} c^{3} d^{6} e^{3} + 433 \, a^{4} c^{2} d^{4} e^{5} + 206 \, a^{5} c d^{2} e^{7} + 40 \, a^{6} e^{9} - {\left(4 \, c^{6} d^{7} e^{2} + 32 \, a c^{5} d^{5} e^{4} - 53 \, a^{2} c^{4} d^{3} e^{6} - 81 \, a^{3} c^{3} d e^{8}\right)} x^{5} - 3 \, {\left(8 \, c^{6} d^{8} e + 64 \, a c^{5} d^{6} e^{3} - 76 \, a^{2} c^{4} d^{4} e^{5} - 137 \, a^{3} c^{3} d^{2} e^{7} - 5 \, a^{4} c^{2} e^{9}\right)} x^{4} - 2 \, {\left(30 \, c^{6} d^{9} + 239 \, a c^{5} d^{7} e^{2} - 158 \, a^{2} c^{4} d^{5} e^{4} - 388 \, a^{3} c^{3} d^{3} e^{6} - 21 \, a^{4} c^{2} d e^{8}\right)} x^{3} - 2 \, {\left(114 \, a c^{5} d^{8} e - 423 \, a^{2} c^{4} d^{6} e^{3} - 698 \, a^{3} c^{3} d^{4} e^{5} - 196 \, a^{4} c^{2} d^{2} e^{7} - 35 \, a^{5} c e^{9}\right)} x^{2} - 3 \, {\left(50 \, a c^{5} d^{9} - 117 \, a^{2} c^{4} d^{7} e^{2} - 221 \, a^{3} c^{3} d^{5} e^{4} - 66 \, a^{4} c^{2} d^{3} e^{6} - 12 \, a^{5} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{480 \, {\left(c^{5} d^{16} + 5 \, a c^{4} d^{14} e^{2} + 10 \, a^{2} c^{3} d^{12} e^{4} + 10 \, a^{3} c^{2} d^{10} e^{6} + 5 \, a^{4} c d^{8} e^{8} + a^{5} d^{6} e^{10} + {\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)} x^{6} + 6 \, {\left(c^{5} d^{11} e^{5} + 5 \, a c^{4} d^{9} e^{7} + 10 \, a^{2} c^{3} d^{7} e^{9} + 10 \, a^{3} c^{2} d^{5} e^{11} + 5 \, a^{4} c d^{3} e^{13} + a^{5} d e^{15}\right)} x^{5} + 15 \, {\left(c^{5} d^{12} e^{4} + 5 \, a c^{4} d^{10} e^{6} + 10 \, a^{2} c^{3} d^{8} e^{8} + 10 \, a^{3} c^{2} d^{6} e^{10} + 5 \, a^{4} c d^{4} e^{12} + a^{5} d^{2} e^{14}\right)} x^{4} + 20 \, {\left(c^{5} d^{13} e^{3} + 5 \, a c^{4} d^{11} e^{5} + 10 \, a^{2} c^{3} d^{9} e^{7} + 10 \, a^{3} c^{2} d^{7} e^{9} + 5 \, a^{4} c d^{5} e^{11} + a^{5} d^{3} e^{13}\right)} x^{3} + 15 \, {\left(c^{5} d^{14} e^{2} + 5 \, a c^{4} d^{12} e^{4} + 10 \, a^{2} c^{3} d^{10} e^{6} + 10 \, a^{3} c^{2} d^{8} e^{8} + 5 \, a^{4} c d^{6} e^{10} + a^{5} d^{4} e^{12}\right)} x^{2} + 6 \, {\left(c^{5} d^{15} e + 5 \, a c^{4} d^{13} e^{3} + 10 \, a^{2} c^{3} d^{11} e^{5} + 10 \, a^{3} c^{2} d^{9} e^{7} + 5 \, a^{4} c d^{7} e^{9} + a^{5} d^{5} e^{11}\right)} x\right)}}, -\frac{15 \, {\left(6 \, a^{2} c^{4} d^{8} - a^{3} c^{3} d^{6} e^{2} + {\left(6 \, a^{2} c^{4} d^{2} e^{6} - a^{3} c^{3} e^{8}\right)} x^{6} + 6 \, {\left(6 \, a^{2} c^{4} d^{3} e^{5} - a^{3} c^{3} d e^{7}\right)} x^{5} + 15 \, {\left(6 \, a^{2} c^{4} d^{4} e^{4} - a^{3} c^{3} d^{2} e^{6}\right)} x^{4} + 20 \, {\left(6 \, a^{2} c^{4} d^{5} e^{3} - a^{3} c^{3} d^{3} e^{5}\right)} x^{3} + 15 \, {\left(6 \, a^{2} c^{4} d^{6} e^{2} - a^{3} c^{3} d^{4} e^{4}\right)} x^{2} + 6 \, {\left(6 \, a^{2} c^{4} d^{7} e - a^{3} c^{3} d^{5} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(246 \, a^{2} c^{4} d^{8} e + 513 \, a^{3} c^{3} d^{6} e^{3} + 433 \, a^{4} c^{2} d^{4} e^{5} + 206 \, a^{5} c d^{2} e^{7} + 40 \, a^{6} e^{9} - {\left(4 \, c^{6} d^{7} e^{2} + 32 \, a c^{5} d^{5} e^{4} - 53 \, a^{2} c^{4} d^{3} e^{6} - 81 \, a^{3} c^{3} d e^{8}\right)} x^{5} - 3 \, {\left(8 \, c^{6} d^{8} e + 64 \, a c^{5} d^{6} e^{3} - 76 \, a^{2} c^{4} d^{4} e^{5} - 137 \, a^{3} c^{3} d^{2} e^{7} - 5 \, a^{4} c^{2} e^{9}\right)} x^{4} - 2 \, {\left(30 \, c^{6} d^{9} + 239 \, a c^{5} d^{7} e^{2} - 158 \, a^{2} c^{4} d^{5} e^{4} - 388 \, a^{3} c^{3} d^{3} e^{6} - 21 \, a^{4} c^{2} d e^{8}\right)} x^{3} - 2 \, {\left(114 \, a c^{5} d^{8} e - 423 \, a^{2} c^{4} d^{6} e^{3} - 698 \, a^{3} c^{3} d^{4} e^{5} - 196 \, a^{4} c^{2} d^{2} e^{7} - 35 \, a^{5} c e^{9}\right)} x^{2} - 3 \, {\left(50 \, a c^{5} d^{9} - 117 \, a^{2} c^{4} d^{7} e^{2} - 221 \, a^{3} c^{3} d^{5} e^{4} - 66 \, a^{4} c^{2} d^{3} e^{6} - 12 \, a^{5} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, {\left(c^{5} d^{16} + 5 \, a c^{4} d^{14} e^{2} + 10 \, a^{2} c^{3} d^{12} e^{4} + 10 \, a^{3} c^{2} d^{10} e^{6} + 5 \, a^{4} c d^{8} e^{8} + a^{5} d^{6} e^{10} + {\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)} x^{6} + 6 \, {\left(c^{5} d^{11} e^{5} + 5 \, a c^{4} d^{9} e^{7} + 10 \, a^{2} c^{3} d^{7} e^{9} + 10 \, a^{3} c^{2} d^{5} e^{11} + 5 \, a^{4} c d^{3} e^{13} + a^{5} d e^{15}\right)} x^{5} + 15 \, {\left(c^{5} d^{12} e^{4} + 5 \, a c^{4} d^{10} e^{6} + 10 \, a^{2} c^{3} d^{8} e^{8} + 10 \, a^{3} c^{2} d^{6} e^{10} + 5 \, a^{4} c d^{4} e^{12} + a^{5} d^{2} e^{14}\right)} x^{4} + 20 \, {\left(c^{5} d^{13} e^{3} + 5 \, a c^{4} d^{11} e^{5} + 10 \, a^{2} c^{3} d^{9} e^{7} + 10 \, a^{3} c^{2} d^{7} e^{9} + 5 \, a^{4} c d^{5} e^{11} + a^{5} d^{3} e^{13}\right)} x^{3} + 15 \, {\left(c^{5} d^{14} e^{2} + 5 \, a c^{4} d^{12} e^{4} + 10 \, a^{2} c^{3} d^{10} e^{6} + 10 \, a^{3} c^{2} d^{8} e^{8} + 5 \, a^{4} c d^{6} e^{10} + a^{5} d^{4} e^{12}\right)} x^{2} + 6 \, {\left(c^{5} d^{15} e + 5 \, a c^{4} d^{13} e^{3} + 10 \, a^{2} c^{3} d^{11} e^{5} + 10 \, a^{3} c^{2} d^{9} e^{7} + 5 \, a^{4} c d^{7} e^{9} + a^{5} d^{5} e^{11}\right)} x\right)}}\right]"," ",0,"[-1/480*(15*(6*a^2*c^4*d^8 - a^3*c^3*d^6*e^2 + (6*a^2*c^4*d^2*e^6 - a^3*c^3*e^8)*x^6 + 6*(6*a^2*c^4*d^3*e^5 - a^3*c^3*d*e^7)*x^5 + 15*(6*a^2*c^4*d^4*e^4 - a^3*c^3*d^2*e^6)*x^4 + 20*(6*a^2*c^4*d^5*e^3 - a^3*c^3*d^3*e^5)*x^3 + 15*(6*a^2*c^4*d^6*e^2 - a^3*c^3*d^4*e^4)*x^2 + 6*(6*a^2*c^4*d^7*e - a^3*c^3*d^5*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(246*a^2*c^4*d^8*e + 513*a^3*c^3*d^6*e^3 + 433*a^4*c^2*d^4*e^5 + 206*a^5*c*d^2*e^7 + 40*a^6*e^9 - (4*c^6*d^7*e^2 + 32*a*c^5*d^5*e^4 - 53*a^2*c^4*d^3*e^6 - 81*a^3*c^3*d*e^8)*x^5 - 3*(8*c^6*d^8*e + 64*a*c^5*d^6*e^3 - 76*a^2*c^4*d^4*e^5 - 137*a^3*c^3*d^2*e^7 - 5*a^4*c^2*e^9)*x^4 - 2*(30*c^6*d^9 + 239*a*c^5*d^7*e^2 - 158*a^2*c^4*d^5*e^4 - 388*a^3*c^3*d^3*e^6 - 21*a^4*c^2*d*e^8)*x^3 - 2*(114*a*c^5*d^8*e - 423*a^2*c^4*d^6*e^3 - 698*a^3*c^3*d^4*e^5 - 196*a^4*c^2*d^2*e^7 - 35*a^5*c*e^9)*x^2 - 3*(50*a*c^5*d^9 - 117*a^2*c^4*d^7*e^2 - 221*a^3*c^3*d^5*e^4 - 66*a^4*c^2*d^3*e^6 - 12*a^5*c*d*e^8)*x)*sqrt(c*x^2 + a))/(c^5*d^16 + 5*a*c^4*d^14*e^2 + 10*a^2*c^3*d^12*e^4 + 10*a^3*c^2*d^10*e^6 + 5*a^4*c*d^8*e^8 + a^5*d^6*e^10 + (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)*x^6 + 6*(c^5*d^11*e^5 + 5*a*c^4*d^9*e^7 + 10*a^2*c^3*d^7*e^9 + 10*a^3*c^2*d^5*e^11 + 5*a^4*c*d^3*e^13 + a^5*d*e^15)*x^5 + 15*(c^5*d^12*e^4 + 5*a*c^4*d^10*e^6 + 10*a^2*c^3*d^8*e^8 + 10*a^3*c^2*d^6*e^10 + 5*a^4*c*d^4*e^12 + a^5*d^2*e^14)*x^4 + 20*(c^5*d^13*e^3 + 5*a*c^4*d^11*e^5 + 10*a^2*c^3*d^9*e^7 + 10*a^3*c^2*d^7*e^9 + 5*a^4*c*d^5*e^11 + a^5*d^3*e^13)*x^3 + 15*(c^5*d^14*e^2 + 5*a*c^4*d^12*e^4 + 10*a^2*c^3*d^10*e^6 + 10*a^3*c^2*d^8*e^8 + 5*a^4*c*d^6*e^10 + a^5*d^4*e^12)*x^2 + 6*(c^5*d^15*e + 5*a*c^4*d^13*e^3 + 10*a^2*c^3*d^11*e^5 + 10*a^3*c^2*d^9*e^7 + 5*a^4*c*d^7*e^9 + a^5*d^5*e^11)*x), -1/240*(15*(6*a^2*c^4*d^8 - a^3*c^3*d^6*e^2 + (6*a^2*c^4*d^2*e^6 - a^3*c^3*e^8)*x^6 + 6*(6*a^2*c^4*d^3*e^5 - a^3*c^3*d*e^7)*x^5 + 15*(6*a^2*c^4*d^4*e^4 - a^3*c^3*d^2*e^6)*x^4 + 20*(6*a^2*c^4*d^5*e^3 - a^3*c^3*d^3*e^5)*x^3 + 15*(6*a^2*c^4*d^6*e^2 - a^3*c^3*d^4*e^4)*x^2 + 6*(6*a^2*c^4*d^7*e - a^3*c^3*d^5*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (246*a^2*c^4*d^8*e + 513*a^3*c^3*d^6*e^3 + 433*a^4*c^2*d^4*e^5 + 206*a^5*c*d^2*e^7 + 40*a^6*e^9 - (4*c^6*d^7*e^2 + 32*a*c^5*d^5*e^4 - 53*a^2*c^4*d^3*e^6 - 81*a^3*c^3*d*e^8)*x^5 - 3*(8*c^6*d^8*e + 64*a*c^5*d^6*e^3 - 76*a^2*c^4*d^4*e^5 - 137*a^3*c^3*d^2*e^7 - 5*a^4*c^2*e^9)*x^4 - 2*(30*c^6*d^9 + 239*a*c^5*d^7*e^2 - 158*a^2*c^4*d^5*e^4 - 388*a^3*c^3*d^3*e^6 - 21*a^4*c^2*d*e^8)*x^3 - 2*(114*a*c^5*d^8*e - 423*a^2*c^4*d^6*e^3 - 698*a^3*c^3*d^4*e^5 - 196*a^4*c^2*d^2*e^7 - 35*a^5*c*e^9)*x^2 - 3*(50*a*c^5*d^9 - 117*a^2*c^4*d^7*e^2 - 221*a^3*c^3*d^5*e^4 - 66*a^4*c^2*d^3*e^6 - 12*a^5*c*d*e^8)*x)*sqrt(c*x^2 + a))/(c^5*d^16 + 5*a*c^4*d^14*e^2 + 10*a^2*c^3*d^12*e^4 + 10*a^3*c^2*d^10*e^6 + 5*a^4*c*d^8*e^8 + a^5*d^6*e^10 + (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)*x^6 + 6*(c^5*d^11*e^5 + 5*a*c^4*d^9*e^7 + 10*a^2*c^3*d^7*e^9 + 10*a^3*c^2*d^5*e^11 + 5*a^4*c*d^3*e^13 + a^5*d*e^15)*x^5 + 15*(c^5*d^12*e^4 + 5*a*c^4*d^10*e^6 + 10*a^2*c^3*d^8*e^8 + 10*a^3*c^2*d^6*e^10 + 5*a^4*c*d^4*e^12 + a^5*d^2*e^14)*x^4 + 20*(c^5*d^13*e^3 + 5*a*c^4*d^11*e^5 + 10*a^2*c^3*d^9*e^7 + 10*a^3*c^2*d^7*e^9 + 5*a^4*c*d^5*e^11 + a^5*d^3*e^13)*x^3 + 15*(c^5*d^14*e^2 + 5*a*c^4*d^12*e^4 + 10*a^2*c^3*d^10*e^6 + 10*a^3*c^2*d^8*e^8 + 5*a^4*c*d^6*e^10 + a^5*d^4*e^12)*x^2 + 6*(c^5*d^15*e + 5*a*c^4*d^13*e^3 + 10*a^2*c^3*d^11*e^5 + 10*a^3*c^2*d^9*e^7 + 5*a^4*c*d^7*e^9 + a^5*d^5*e^11)*x)]","B",0
545,1,692,0,0.485064," ","integrate((e*x+d)^4*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(80 \, a^{3} c^{2} d^{4} - 60 \, a^{4} c d^{2} e^{2} + 3 \, a^{5} e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(8064 \, c^{5} e^{4} x^{9} + 35840 \, c^{5} d e^{3} x^{8} + 46080 \, a^{3} c^{2} d^{3} e - 10240 \, a^{4} c d e^{3} + 3024 \, {\left(20 \, c^{5} d^{2} e^{2} + 7 \, a c^{4} e^{4}\right)} x^{7} + 5120 \, {\left(9 \, c^{5} d^{3} e + 19 \, a c^{4} d e^{3}\right)} x^{6} + 168 \, {\left(80 \, c^{5} d^{4} + 1020 \, a c^{4} d^{2} e^{2} + 93 \, a^{2} c^{3} e^{4}\right)} x^{5} + 15360 \, {\left(9 \, a c^{4} d^{3} e + 5 \, a^{2} c^{3} d e^{3}\right)} x^{4} + 210 \, {\left(208 \, a c^{4} d^{4} + 708 \, a^{2} c^{3} d^{2} e^{2} + 3 \, a^{3} c^{2} e^{4}\right)} x^{3} + 5120 \, {\left(27 \, a^{2} c^{3} d^{3} e + a^{3} c^{2} d e^{3}\right)} x^{2} + 315 \, {\left(176 \, a^{2} c^{3} d^{4} + 60 \, a^{3} c^{2} d^{2} e^{2} - 3 \, a^{4} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{161280 \, c^{3}}, -\frac{315 \, {\left(80 \, a^{3} c^{2} d^{4} - 60 \, a^{4} c d^{2} e^{2} + 3 \, a^{5} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(8064 \, c^{5} e^{4} x^{9} + 35840 \, c^{5} d e^{3} x^{8} + 46080 \, a^{3} c^{2} d^{3} e - 10240 \, a^{4} c d e^{3} + 3024 \, {\left(20 \, c^{5} d^{2} e^{2} + 7 \, a c^{4} e^{4}\right)} x^{7} + 5120 \, {\left(9 \, c^{5} d^{3} e + 19 \, a c^{4} d e^{3}\right)} x^{6} + 168 \, {\left(80 \, c^{5} d^{4} + 1020 \, a c^{4} d^{2} e^{2} + 93 \, a^{2} c^{3} e^{4}\right)} x^{5} + 15360 \, {\left(9 \, a c^{4} d^{3} e + 5 \, a^{2} c^{3} d e^{3}\right)} x^{4} + 210 \, {\left(208 \, a c^{4} d^{4} + 708 \, a^{2} c^{3} d^{2} e^{2} + 3 \, a^{3} c^{2} e^{4}\right)} x^{3} + 5120 \, {\left(27 \, a^{2} c^{3} d^{3} e + a^{3} c^{2} d e^{3}\right)} x^{2} + 315 \, {\left(176 \, a^{2} c^{3} d^{4} + 60 \, a^{3} c^{2} d^{2} e^{2} - 3 \, a^{4} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{80640 \, c^{3}}\right]"," ",0,"[1/161280*(315*(80*a^3*c^2*d^4 - 60*a^4*c*d^2*e^2 + 3*a^5*e^4)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(8064*c^5*e^4*x^9 + 35840*c^5*d*e^3*x^8 + 46080*a^3*c^2*d^3*e - 10240*a^4*c*d*e^3 + 3024*(20*c^5*d^2*e^2 + 7*a*c^4*e^4)*x^7 + 5120*(9*c^5*d^3*e + 19*a*c^4*d*e^3)*x^6 + 168*(80*c^5*d^4 + 1020*a*c^4*d^2*e^2 + 93*a^2*c^3*e^4)*x^5 + 15360*(9*a*c^4*d^3*e + 5*a^2*c^3*d*e^3)*x^4 + 210*(208*a*c^4*d^4 + 708*a^2*c^3*d^2*e^2 + 3*a^3*c^2*e^4)*x^3 + 5120*(27*a^2*c^3*d^3*e + a^3*c^2*d*e^3)*x^2 + 315*(176*a^2*c^3*d^4 + 60*a^3*c^2*d^2*e^2 - 3*a^4*c*e^4)*x)*sqrt(c*x^2 + a))/c^3, -1/80640*(315*(80*a^3*c^2*d^4 - 60*a^4*c*d^2*e^2 + 3*a^5*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (8064*c^5*e^4*x^9 + 35840*c^5*d*e^3*x^8 + 46080*a^3*c^2*d^3*e - 10240*a^4*c*d*e^3 + 3024*(20*c^5*d^2*e^2 + 7*a*c^4*e^4)*x^7 + 5120*(9*c^5*d^3*e + 19*a*c^4*d*e^3)*x^6 + 168*(80*c^5*d^4 + 1020*a*c^4*d^2*e^2 + 93*a^2*c^3*e^4)*x^5 + 15360*(9*a*c^4*d^3*e + 5*a^2*c^3*d*e^3)*x^4 + 210*(208*a*c^4*d^4 + 708*a^2*c^3*d^2*e^2 + 3*a^3*c^2*e^4)*x^3 + 5120*(27*a^2*c^3*d^3*e + a^3*c^2*d*e^3)*x^2 + 315*(176*a^2*c^3*d^4 + 60*a^3*c^2*d^2*e^2 - 3*a^4*c*e^4)*x)*sqrt(c*x^2 + a))/c^3]","A",0
546,1,518,0,0.461913," ","integrate((e*x+d)^3*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(8 \, a^{3} c d^{3} - 3 \, a^{4} d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(896 \, c^{4} e^{3} x^{8} + 3024 \, c^{4} d e^{2} x^{7} + 3456 \, a^{3} c d^{2} e - 256 \, a^{4} e^{3} + 128 \, {\left(27 \, c^{4} d^{2} e + 19 \, a c^{3} e^{3}\right)} x^{6} + 168 \, {\left(8 \, c^{4} d^{3} + 51 \, a c^{3} d e^{2}\right)} x^{5} + 384 \, {\left(27 \, a c^{3} d^{2} e + 5 \, a^{2} c^{2} e^{3}\right)} x^{4} + 42 \, {\left(104 \, a c^{3} d^{3} + 177 \, a^{2} c^{2} d e^{2}\right)} x^{3} + 128 \, {\left(81 \, a^{2} c^{2} d^{2} e + a^{3} c e^{3}\right)} x^{2} + 63 \, {\left(88 \, a^{2} c^{2} d^{3} + 15 \, a^{3} c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{16128 \, c^{2}}, -\frac{315 \, {\left(8 \, a^{3} c d^{3} - 3 \, a^{4} d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(896 \, c^{4} e^{3} x^{8} + 3024 \, c^{4} d e^{2} x^{7} + 3456 \, a^{3} c d^{2} e - 256 \, a^{4} e^{3} + 128 \, {\left(27 \, c^{4} d^{2} e + 19 \, a c^{3} e^{3}\right)} x^{6} + 168 \, {\left(8 \, c^{4} d^{3} + 51 \, a c^{3} d e^{2}\right)} x^{5} + 384 \, {\left(27 \, a c^{3} d^{2} e + 5 \, a^{2} c^{2} e^{3}\right)} x^{4} + 42 \, {\left(104 \, a c^{3} d^{3} + 177 \, a^{2} c^{2} d e^{2}\right)} x^{3} + 128 \, {\left(81 \, a^{2} c^{2} d^{2} e + a^{3} c e^{3}\right)} x^{2} + 63 \, {\left(88 \, a^{2} c^{2} d^{3} + 15 \, a^{3} c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{8064 \, c^{2}}\right]"," ",0,"[1/16128*(315*(8*a^3*c*d^3 - 3*a^4*d*e^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(896*c^4*e^3*x^8 + 3024*c^4*d*e^2*x^7 + 3456*a^3*c*d^2*e - 256*a^4*e^3 + 128*(27*c^4*d^2*e + 19*a*c^3*e^3)*x^6 + 168*(8*c^4*d^3 + 51*a*c^3*d*e^2)*x^5 + 384*(27*a*c^3*d^2*e + 5*a^2*c^2*e^3)*x^4 + 42*(104*a*c^3*d^3 + 177*a^2*c^2*d*e^2)*x^3 + 128*(81*a^2*c^2*d^2*e + a^3*c*e^3)*x^2 + 63*(88*a^2*c^2*d^3 + 15*a^3*c*d*e^2)*x)*sqrt(c*x^2 + a))/c^2, -1/8064*(315*(8*a^3*c*d^3 - 3*a^4*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (896*c^4*e^3*x^8 + 3024*c^4*d*e^2*x^7 + 3456*a^3*c*d^2*e - 256*a^4*e^3 + 128*(27*c^4*d^2*e + 19*a*c^3*e^3)*x^6 + 168*(8*c^4*d^3 + 51*a*c^3*d*e^2)*x^5 + 384*(27*a*c^3*d^2*e + 5*a^2*c^2*e^3)*x^4 + 42*(104*a*c^3*d^3 + 177*a^2*c^2*d*e^2)*x^3 + 128*(81*a^2*c^2*d^2*e + a^3*c*e^3)*x^2 + 63*(88*a^2*c^2*d^3 + 15*a^3*c*d*e^2)*x)*sqrt(c*x^2 + a))/c^2]","A",0
547,1,380,0,0.447746," ","integrate((e*x+d)^2*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(8 \, a^{3} c d^{2} - a^{4} e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(336 \, c^{4} e^{2} x^{7} + 768 \, c^{4} d e x^{6} + 2304 \, a c^{3} d e x^{4} + 2304 \, a^{2} c^{2} d e x^{2} + 768 \, a^{3} c d e + 56 \, {\left(8 \, c^{4} d^{2} + 17 \, a c^{3} e^{2}\right)} x^{5} + 14 \, {\left(104 \, a c^{3} d^{2} + 59 \, a^{2} c^{2} e^{2}\right)} x^{3} + 21 \, {\left(88 \, a^{2} c^{2} d^{2} + 5 \, a^{3} c e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{5376 \, c^{2}}, -\frac{105 \, {\left(8 \, a^{3} c d^{2} - a^{4} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(336 \, c^{4} e^{2} x^{7} + 768 \, c^{4} d e x^{6} + 2304 \, a c^{3} d e x^{4} + 2304 \, a^{2} c^{2} d e x^{2} + 768 \, a^{3} c d e + 56 \, {\left(8 \, c^{4} d^{2} + 17 \, a c^{3} e^{2}\right)} x^{5} + 14 \, {\left(104 \, a c^{3} d^{2} + 59 \, a^{2} c^{2} e^{2}\right)} x^{3} + 21 \, {\left(88 \, a^{2} c^{2} d^{2} + 5 \, a^{3} c e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{2688 \, c^{2}}\right]"," ",0,"[1/5376*(105*(8*a^3*c*d^2 - a^4*e^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(336*c^4*e^2*x^7 + 768*c^4*d*e*x^6 + 2304*a*c^3*d*e*x^4 + 2304*a^2*c^2*d*e*x^2 + 768*a^3*c*d*e + 56*(8*c^4*d^2 + 17*a*c^3*e^2)*x^5 + 14*(104*a*c^3*d^2 + 59*a^2*c^2*e^2)*x^3 + 21*(88*a^2*c^2*d^2 + 5*a^3*c*e^2)*x)*sqrt(c*x^2 + a))/c^2, -1/2688*(105*(8*a^3*c*d^2 - a^4*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (336*c^4*e^2*x^7 + 768*c^4*d*e*x^6 + 2304*a*c^3*d*e*x^4 + 2304*a^2*c^2*d*e*x^2 + 768*a^3*c*d*e + 56*(8*c^4*d^2 + 17*a*c^3*e^2)*x^5 + 14*(104*a*c^3*d^2 + 59*a^2*c^2*e^2)*x^3 + 21*(88*a^2*c^2*d^2 + 5*a^3*c*e^2)*x)*sqrt(c*x^2 + a))/c^2]","A",0
548,1,224,0,0.430542," ","integrate((e*x+d)*(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, a^{3} \sqrt{c} d \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(48 \, c^{3} e x^{6} + 56 \, c^{3} d x^{5} + 144 \, a c^{2} e x^{4} + 182 \, a c^{2} d x^{3} + 144 \, a^{2} c e x^{2} + 231 \, a^{2} c d x + 48 \, a^{3} e\right)} \sqrt{c x^{2} + a}}{672 \, c}, -\frac{105 \, a^{3} \sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(48 \, c^{3} e x^{6} + 56 \, c^{3} d x^{5} + 144 \, a c^{2} e x^{4} + 182 \, a c^{2} d x^{3} + 144 \, a^{2} c e x^{2} + 231 \, a^{2} c d x + 48 \, a^{3} e\right)} \sqrt{c x^{2} + a}}{336 \, c}\right]"," ",0,"[1/672*(105*a^3*sqrt(c)*d*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(48*c^3*e*x^6 + 56*c^3*d*x^5 + 144*a*c^2*e*x^4 + 182*a*c^2*d*x^3 + 144*a^2*c*e*x^2 + 231*a^2*c*d*x + 48*a^3*e)*sqrt(c*x^2 + a))/c, -1/336*(105*a^3*sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (48*c^3*e*x^6 + 56*c^3*d*x^5 + 144*a*c^2*e*x^4 + 182*a*c^2*d*x^3 + 144*a^2*c*e*x^2 + 231*a^2*c*d*x + 48*a^3*e)*sqrt(c*x^2 + a))/c]","A",0
549,1,1176,0,51.026098," ","integrate((c*x^2+a)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(8 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 120 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(24 \, c^{2} e^{5} x^{4} - 30 \, c^{2} d e^{4} x^{3} + 120 \, c^{2} d^{4} e + 280 \, a c d^{2} e^{3} + 184 \, a^{2} e^{5} + 8 \, {\left(5 \, c^{2} d^{2} e^{3} + 11 \, a c e^{5}\right)} x^{2} - 15 \, {\left(4 \, c^{2} d^{3} e^{2} + 9 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, e^{6}}, \frac{15 \, {\left(8 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + 60 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + {\left(24 \, c^{2} e^{5} x^{4} - 30 \, c^{2} d e^{4} x^{3} + 120 \, c^{2} d^{4} e + 280 \, a c d^{2} e^{3} + 184 \, a^{2} e^{5} + 8 \, {\left(5 \, c^{2} d^{2} e^{3} + 11 \, a c e^{5}\right)} x^{2} - 15 \, {\left(4 \, c^{2} d^{3} e^{2} + 9 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{120 \, e^{6}}, -\frac{240 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 15 \, {\left(8 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(24 \, c^{2} e^{5} x^{4} - 30 \, c^{2} d e^{4} x^{3} + 120 \, c^{2} d^{4} e + 280 \, a c d^{2} e^{3} + 184 \, a^{2} e^{5} + 8 \, {\left(5 \, c^{2} d^{2} e^{3} + 11 \, a c e^{5}\right)} x^{2} - 15 \, {\left(4 \, c^{2} d^{3} e^{2} + 9 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, e^{6}}, -\frac{120 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 15 \, {\left(8 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(24 \, c^{2} e^{5} x^{4} - 30 \, c^{2} d e^{4} x^{3} + 120 \, c^{2} d^{4} e + 280 \, a c d^{2} e^{3} + 184 \, a^{2} e^{5} + 8 \, {\left(5 \, c^{2} d^{2} e^{3} + 11 \, a c e^{5}\right)} x^{2} - 15 \, {\left(4 \, c^{2} d^{3} e^{2} + 9 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{120 \, e^{6}}\right]"," ",0,"[1/240*(15*(8*c^2*d^5 + 20*a*c*d^3*e^2 + 15*a^2*d*e^4)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 120*(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(24*c^2*e^5*x^4 - 30*c^2*d*e^4*x^3 + 120*c^2*d^4*e + 280*a*c*d^2*e^3 + 184*a^2*e^5 + 8*(5*c^2*d^2*e^3 + 11*a*c*e^5)*x^2 - 15*(4*c^2*d^3*e^2 + 9*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/e^6, 1/120*(15*(8*c^2*d^5 + 20*a*c*d^3*e^2 + 15*a^2*d*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + 60*(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + (24*c^2*e^5*x^4 - 30*c^2*d*e^4*x^3 + 120*c^2*d^4*e + 280*a*c*d^2*e^3 + 184*a^2*e^5 + 8*(5*c^2*d^2*e^3 + 11*a*c*e^5)*x^2 - 15*(4*c^2*d^3*e^2 + 9*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/e^6, -1/240*(240*(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 15*(8*c^2*d^5 + 20*a*c*d^3*e^2 + 15*a^2*d*e^4)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(24*c^2*e^5*x^4 - 30*c^2*d*e^4*x^3 + 120*c^2*d^4*e + 280*a*c*d^2*e^3 + 184*a^2*e^5 + 8*(5*c^2*d^2*e^3 + 11*a*c*e^5)*x^2 - 15*(4*c^2*d^3*e^2 + 9*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/e^6, -1/120*(120*(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 15*(8*c^2*d^5 + 20*a*c*d^3*e^2 + 15*a^2*d*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (24*c^2*e^5*x^4 - 30*c^2*d*e^4*x^3 + 120*c^2*d^4*e + 280*a*c*d^2*e^3 + 184*a^2*e^5 + 8*(5*c^2*d^2*e^3 + 11*a*c*e^5)*x^2 - 15*(4*c^2*d^3*e^2 + 9*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/e^6]","A",0
550,1,1372,0,12.492417," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(8 \, c^{2} d^{5} + 12 \, a c d^{3} e^{2} + 3 \, a^{2} d e^{4} + {\left(8 \, c^{2} d^{4} e + 12 \, a c d^{2} e^{3} + 3 \, a^{2} e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 120 \, {\left(c^{2} d^{4} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(6 \, c^{2} e^{5} x^{4} - 10 \, c^{2} d e^{4} x^{3} - 120 \, c^{2} d^{4} e - 160 \, a c d^{2} e^{3} - 24 \, a^{2} e^{5} + {\left(20 \, c^{2} d^{2} e^{3} + 27 \, a c e^{5}\right)} x^{2} - 5 \, {\left(12 \, c^{2} d^{3} e^{2} + 17 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, {\left(e^{7} x + d e^{6}\right)}}, \frac{240 \, {\left(c^{2} d^{4} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + 15 \, {\left(8 \, c^{2} d^{5} + 12 \, a c d^{3} e^{2} + 3 \, a^{2} d e^{4} + {\left(8 \, c^{2} d^{4} e + 12 \, a c d^{2} e^{3} + 3 \, a^{2} e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(6 \, c^{2} e^{5} x^{4} - 10 \, c^{2} d e^{4} x^{3} - 120 \, c^{2} d^{4} e - 160 \, a c d^{2} e^{3} - 24 \, a^{2} e^{5} + {\left(20 \, c^{2} d^{2} e^{3} + 27 \, a c e^{5}\right)} x^{2} - 5 \, {\left(12 \, c^{2} d^{3} e^{2} + 17 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, {\left(e^{7} x + d e^{6}\right)}}, -\frac{15 \, {\left(8 \, c^{2} d^{5} + 12 \, a c d^{3} e^{2} + 3 \, a^{2} d e^{4} + {\left(8 \, c^{2} d^{4} e + 12 \, a c d^{2} e^{3} + 3 \, a^{2} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 60 \, {\left(c^{2} d^{4} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - {\left(6 \, c^{2} e^{5} x^{4} - 10 \, c^{2} d e^{4} x^{3} - 120 \, c^{2} d^{4} e - 160 \, a c d^{2} e^{3} - 24 \, a^{2} e^{5} + {\left(20 \, c^{2} d^{2} e^{3} + 27 \, a c e^{5}\right)} x^{2} - 5 \, {\left(12 \, c^{2} d^{3} e^{2} + 17 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, {\left(e^{7} x + d e^{6}\right)}}, \frac{120 \, {\left(c^{2} d^{4} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 15 \, {\left(8 \, c^{2} d^{5} + 12 \, a c d^{3} e^{2} + 3 \, a^{2} d e^{4} + {\left(8 \, c^{2} d^{4} e + 12 \, a c d^{2} e^{3} + 3 \, a^{2} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(6 \, c^{2} e^{5} x^{4} - 10 \, c^{2} d e^{4} x^{3} - 120 \, c^{2} d^{4} e - 160 \, a c d^{2} e^{3} - 24 \, a^{2} e^{5} + {\left(20 \, c^{2} d^{2} e^{3} + 27 \, a c e^{5}\right)} x^{2} - 5 \, {\left(12 \, c^{2} d^{3} e^{2} + 17 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, {\left(e^{7} x + d e^{6}\right)}}\right]"," ",0,"[1/48*(15*(8*c^2*d^5 + 12*a*c*d^3*e^2 + 3*a^2*d*e^4 + (8*c^2*d^4*e + 12*a*c*d^2*e^3 + 3*a^2*e^5)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 120*(c^2*d^4 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(6*c^2*e^5*x^4 - 10*c^2*d*e^4*x^3 - 120*c^2*d^4*e - 160*a*c*d^2*e^3 - 24*a^2*e^5 + (20*c^2*d^2*e^3 + 27*a*c*e^5)*x^2 - 5*(12*c^2*d^3*e^2 + 17*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(e^7*x + d*e^6), 1/48*(240*(c^2*d^4 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + 15*(8*c^2*d^5 + 12*a*c*d^3*e^2 + 3*a^2*d*e^4 + (8*c^2*d^4*e + 12*a*c*d^2*e^3 + 3*a^2*e^5)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(6*c^2*e^5*x^4 - 10*c^2*d*e^4*x^3 - 120*c^2*d^4*e - 160*a*c*d^2*e^3 - 24*a^2*e^5 + (20*c^2*d^2*e^3 + 27*a*c*e^5)*x^2 - 5*(12*c^2*d^3*e^2 + 17*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(e^7*x + d*e^6), -1/24*(15*(8*c^2*d^5 + 12*a*c*d^3*e^2 + 3*a^2*d*e^4 + (8*c^2*d^4*e + 12*a*c*d^2*e^3 + 3*a^2*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 60*(c^2*d^4 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - (6*c^2*e^5*x^4 - 10*c^2*d*e^4*x^3 - 120*c^2*d^4*e - 160*a*c*d^2*e^3 - 24*a^2*e^5 + (20*c^2*d^2*e^3 + 27*a*c*e^5)*x^2 - 5*(12*c^2*d^3*e^2 + 17*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(e^7*x + d*e^6), 1/24*(120*(c^2*d^4 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 15*(8*c^2*d^5 + 12*a*c*d^3*e^2 + 3*a^2*d*e^4 + (8*c^2*d^4*e + 12*a*c*d^2*e^3 + 3*a^2*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (6*c^2*e^5*x^4 - 10*c^2*d*e^4*x^3 - 120*c^2*d^4*e - 160*a*c*d^2*e^3 - 24*a^2*e^5 + (20*c^2*d^2*e^3 + 27*a*c*e^5)*x^2 - 5*(12*c^2*d^3*e^2 + 17*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(e^7*x + d*e^6)]","A",0
551,1,1553,0,1.653920," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(4 \, c^{2} d^{5} + 3 \, a c d^{3} e^{2} + {\left(4 \, c^{2} d^{3} e^{2} + 3 \, a c d e^{4}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{4} e + 3 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 15 \, {\left(4 \, c^{2} d^{4} + a c d^{2} e^{2} + {\left(4 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(2 \, c^{2} e^{5} x^{4} - 5 \, c^{2} d e^{4} x^{3} + 60 \, c^{2} d^{4} e + 35 \, a c d^{2} e^{3} - 3 \, a^{2} e^{5} + 2 \, {\left(10 \, c^{2} d^{2} e^{3} + 7 \, a c e^{5}\right)} x^{2} + 5 \, {\left(18 \, c^{2} d^{3} e^{2} + 11 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}, \frac{30 \, {\left(4 \, c^{2} d^{5} + 3 \, a c d^{3} e^{2} + {\left(4 \, c^{2} d^{3} e^{2} + 3 \, a c d e^{4}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{4} e + 3 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + 15 \, {\left(4 \, c^{2} d^{4} + a c d^{2} e^{2} + {\left(4 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(2 \, c^{2} e^{5} x^{4} - 5 \, c^{2} d e^{4} x^{3} + 60 \, c^{2} d^{4} e + 35 \, a c d^{2} e^{3} - 3 \, a^{2} e^{5} + 2 \, {\left(10 \, c^{2} d^{2} e^{3} + 7 \, a c e^{5}\right)} x^{2} + 5 \, {\left(18 \, c^{2} d^{3} e^{2} + 11 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}, -\frac{30 \, {\left(4 \, c^{2} d^{4} + a c d^{2} e^{2} + {\left(4 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 15 \, {\left(4 \, c^{2} d^{5} + 3 \, a c d^{3} e^{2} + {\left(4 \, c^{2} d^{3} e^{2} + 3 \, a c d e^{4}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{4} e + 3 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(2 \, c^{2} e^{5} x^{4} - 5 \, c^{2} d e^{4} x^{3} + 60 \, c^{2} d^{4} e + 35 \, a c d^{2} e^{3} - 3 \, a^{2} e^{5} + 2 \, {\left(10 \, c^{2} d^{2} e^{3} + 7 \, a c e^{5}\right)} x^{2} + 5 \, {\left(18 \, c^{2} d^{3} e^{2} + 11 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}, -\frac{15 \, {\left(4 \, c^{2} d^{4} + a c d^{2} e^{2} + {\left(4 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 15 \, {\left(4 \, c^{2} d^{5} + 3 \, a c d^{3} e^{2} + {\left(4 \, c^{2} d^{3} e^{2} + 3 \, a c d e^{4}\right)} x^{2} + 2 \, {\left(4 \, c^{2} d^{4} e + 3 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, c^{2} e^{5} x^{4} - 5 \, c^{2} d e^{4} x^{3} + 60 \, c^{2} d^{4} e + 35 \, a c d^{2} e^{3} - 3 \, a^{2} e^{5} + 2 \, {\left(10 \, c^{2} d^{2} e^{3} + 7 \, a c e^{5}\right)} x^{2} + 5 \, {\left(18 \, c^{2} d^{3} e^{2} + 11 \, a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}\right]"," ",0,"[1/12*(15*(4*c^2*d^5 + 3*a*c*d^3*e^2 + (4*c^2*d^3*e^2 + 3*a*c*d*e^4)*x^2 + 2*(4*c^2*d^4*e + 3*a*c*d^2*e^3)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 15*(4*c^2*d^4 + a*c*d^2*e^2 + (4*c^2*d^2*e^2 + a*c*e^4)*x^2 + 2*(4*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(2*c^2*e^5*x^4 - 5*c^2*d*e^4*x^3 + 60*c^2*d^4*e + 35*a*c*d^2*e^3 - 3*a^2*e^5 + 2*(10*c^2*d^2*e^3 + 7*a*c*e^5)*x^2 + 5*(18*c^2*d^3*e^2 + 11*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6), 1/12*(30*(4*c^2*d^5 + 3*a*c*d^3*e^2 + (4*c^2*d^3*e^2 + 3*a*c*d*e^4)*x^2 + 2*(4*c^2*d^4*e + 3*a*c*d^2*e^3)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + 15*(4*c^2*d^4 + a*c*d^2*e^2 + (4*c^2*d^2*e^2 + a*c*e^4)*x^2 + 2*(4*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(2*c^2*e^5*x^4 - 5*c^2*d*e^4*x^3 + 60*c^2*d^4*e + 35*a*c*d^2*e^3 - 3*a^2*e^5 + 2*(10*c^2*d^2*e^3 + 7*a*c*e^5)*x^2 + 5*(18*c^2*d^3*e^2 + 11*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6), -1/12*(30*(4*c^2*d^4 + a*c*d^2*e^2 + (4*c^2*d^2*e^2 + a*c*e^4)*x^2 + 2*(4*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 15*(4*c^2*d^5 + 3*a*c*d^3*e^2 + (4*c^2*d^3*e^2 + 3*a*c*d*e^4)*x^2 + 2*(4*c^2*d^4*e + 3*a*c*d^2*e^3)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(2*c^2*e^5*x^4 - 5*c^2*d*e^4*x^3 + 60*c^2*d^4*e + 35*a*c*d^2*e^3 - 3*a^2*e^5 + 2*(10*c^2*d^2*e^3 + 7*a*c*e^5)*x^2 + 5*(18*c^2*d^3*e^2 + 11*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6), -1/6*(15*(4*c^2*d^4 + a*c*d^2*e^2 + (4*c^2*d^2*e^2 + a*c*e^4)*x^2 + 2*(4*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 15*(4*c^2*d^5 + 3*a*c*d^3*e^2 + (4*c^2*d^3*e^2 + 3*a*c*d*e^4)*x^2 + 2*(4*c^2*d^4*e + 3*a*c*d^2*e^3)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (2*c^2*e^5*x^4 - 5*c^2*d*e^4*x^3 + 60*c^2*d^4*e + 35*a*c*d^2*e^3 - 3*a^2*e^5 + 2*(10*c^2*d^2*e^3 + 7*a*c*e^5)*x^2 + 5*(18*c^2*d^3*e^2 + 11*a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)]","A",0
552,1,2501,0,3.586710," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(4 \, c^{3} d^{7} + 5 \, a c^{2} d^{5} e^{2} + a^{2} c d^{3} e^{4} + {\left(4 \, c^{3} d^{4} e^{3} + 5 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{3} + 3 \, {\left(4 \, c^{3} d^{5} e^{2} + 5 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{2} + 3 \, {\left(4 \, c^{3} d^{6} e + 5 \, a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 15 \, {\left(4 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + {\left(4 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(4 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(4 \, c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(60 \, c^{3} d^{6} e + 65 \, a c^{2} d^{4} e^{3} + 7 \, a^{2} c d^{2} e^{5} + 2 \, a^{3} e^{7} - 3 \, {\left(c^{3} d^{2} e^{5} + a c^{2} e^{7}\right)} x^{4} + 15 \, {\left(c^{3} d^{3} e^{4} + a c^{2} d e^{6}\right)} x^{3} + 2 \, {\left(55 \, c^{3} d^{4} e^{3} + 62 \, a c^{2} d^{2} e^{5} + 7 \, a^{2} c e^{7}\right)} x^{2} + 15 \, {\left(10 \, c^{3} d^{5} e^{2} + 11 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(c d^{5} e^{6} + a d^{3} e^{8} + {\left(c d^{2} e^{9} + a e^{11}\right)} x^{3} + 3 \, {\left(c d^{3} e^{8} + a d e^{10}\right)} x^{2} + 3 \, {\left(c d^{4} e^{7} + a d^{2} e^{9}\right)} x\right)}}, \frac{30 \, {\left(4 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + {\left(4 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(4 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(4 \, c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + 15 \, {\left(4 \, c^{3} d^{7} + 5 \, a c^{2} d^{5} e^{2} + a^{2} c d^{3} e^{4} + {\left(4 \, c^{3} d^{4} e^{3} + 5 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{3} + 3 \, {\left(4 \, c^{3} d^{5} e^{2} + 5 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{2} + 3 \, {\left(4 \, c^{3} d^{6} e + 5 \, a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(60 \, c^{3} d^{6} e + 65 \, a c^{2} d^{4} e^{3} + 7 \, a^{2} c d^{2} e^{5} + 2 \, a^{3} e^{7} - 3 \, {\left(c^{3} d^{2} e^{5} + a c^{2} e^{7}\right)} x^{4} + 15 \, {\left(c^{3} d^{3} e^{4} + a c^{2} d e^{6}\right)} x^{3} + 2 \, {\left(55 \, c^{3} d^{4} e^{3} + 62 \, a c^{2} d^{2} e^{5} + 7 \, a^{2} c e^{7}\right)} x^{2} + 15 \, {\left(10 \, c^{3} d^{5} e^{2} + 11 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(c d^{5} e^{6} + a d^{3} e^{8} + {\left(c d^{2} e^{9} + a e^{11}\right)} x^{3} + 3 \, {\left(c d^{3} e^{8} + a d e^{10}\right)} x^{2} + 3 \, {\left(c d^{4} e^{7} + a d^{2} e^{9}\right)} x\right)}}, -\frac{30 \, {\left(4 \, c^{3} d^{7} + 5 \, a c^{2} d^{5} e^{2} + a^{2} c d^{3} e^{4} + {\left(4 \, c^{3} d^{4} e^{3} + 5 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{3} + 3 \, {\left(4 \, c^{3} d^{5} e^{2} + 5 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{2} + 3 \, {\left(4 \, c^{3} d^{6} e + 5 \, a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 15 \, {\left(4 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + {\left(4 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(4 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(4 \, c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(60 \, c^{3} d^{6} e + 65 \, a c^{2} d^{4} e^{3} + 7 \, a^{2} c d^{2} e^{5} + 2 \, a^{3} e^{7} - 3 \, {\left(c^{3} d^{2} e^{5} + a c^{2} e^{7}\right)} x^{4} + 15 \, {\left(c^{3} d^{3} e^{4} + a c^{2} d e^{6}\right)} x^{3} + 2 \, {\left(55 \, c^{3} d^{4} e^{3} + 62 \, a c^{2} d^{2} e^{5} + 7 \, a^{2} c e^{7}\right)} x^{2} + 15 \, {\left(10 \, c^{3} d^{5} e^{2} + 11 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(c d^{5} e^{6} + a d^{3} e^{8} + {\left(c d^{2} e^{9} + a e^{11}\right)} x^{3} + 3 \, {\left(c d^{3} e^{8} + a d e^{10}\right)} x^{2} + 3 \, {\left(c d^{4} e^{7} + a d^{2} e^{9}\right)} x\right)}}, \frac{15 \, {\left(4 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + {\left(4 \, c^{3} d^{3} e^{3} + 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(4 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(4 \, c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 15 \, {\left(4 \, c^{3} d^{7} + 5 \, a c^{2} d^{5} e^{2} + a^{2} c d^{3} e^{4} + {\left(4 \, c^{3} d^{4} e^{3} + 5 \, a c^{2} d^{2} e^{5} + a^{2} c e^{7}\right)} x^{3} + 3 \, {\left(4 \, c^{3} d^{5} e^{2} + 5 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{2} + 3 \, {\left(4 \, c^{3} d^{6} e + 5 \, a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(60 \, c^{3} d^{6} e + 65 \, a c^{2} d^{4} e^{3} + 7 \, a^{2} c d^{2} e^{5} + 2 \, a^{3} e^{7} - 3 \, {\left(c^{3} d^{2} e^{5} + a c^{2} e^{7}\right)} x^{4} + 15 \, {\left(c^{3} d^{3} e^{4} + a c^{2} d e^{6}\right)} x^{3} + 2 \, {\left(55 \, c^{3} d^{4} e^{3} + 62 \, a c^{2} d^{2} e^{5} + 7 \, a^{2} c e^{7}\right)} x^{2} + 15 \, {\left(10 \, c^{3} d^{5} e^{2} + 11 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c d^{5} e^{6} + a d^{3} e^{8} + {\left(c d^{2} e^{9} + a e^{11}\right)} x^{3} + 3 \, {\left(c d^{3} e^{8} + a d e^{10}\right)} x^{2} + 3 \, {\left(c d^{4} e^{7} + a d^{2} e^{9}\right)} x\right)}}\right]"," ",0,"[1/12*(15*(4*c^3*d^7 + 5*a*c^2*d^5*e^2 + a^2*c*d^3*e^4 + (4*c^3*d^4*e^3 + 5*a*c^2*d^2*e^5 + a^2*c*e^7)*x^3 + 3*(4*c^3*d^5*e^2 + 5*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^2 + 3*(4*c^3*d^6*e + 5*a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 15*(4*c^3*d^6 + 3*a*c^2*d^4*e^2 + (4*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 3*(4*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4)*x^2 + 3*(4*c^3*d^5*e + 3*a*c^2*d^3*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(60*c^3*d^6*e + 65*a*c^2*d^4*e^3 + 7*a^2*c*d^2*e^5 + 2*a^3*e^7 - 3*(c^3*d^2*e^5 + a*c^2*e^7)*x^4 + 15*(c^3*d^3*e^4 + a*c^2*d*e^6)*x^3 + 2*(55*c^3*d^4*e^3 + 62*a*c^2*d^2*e^5 + 7*a^2*c*e^7)*x^2 + 15*(10*c^3*d^5*e^2 + 11*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c*d^5*e^6 + a*d^3*e^8 + (c*d^2*e^9 + a*e^11)*x^3 + 3*(c*d^3*e^8 + a*d*e^10)*x^2 + 3*(c*d^4*e^7 + a*d^2*e^9)*x), 1/12*(30*(4*c^3*d^6 + 3*a*c^2*d^4*e^2 + (4*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 3*(4*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4)*x^2 + 3*(4*c^3*d^5*e + 3*a*c^2*d^3*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + 15*(4*c^3*d^7 + 5*a*c^2*d^5*e^2 + a^2*c*d^3*e^4 + (4*c^3*d^4*e^3 + 5*a*c^2*d^2*e^5 + a^2*c*e^7)*x^3 + 3*(4*c^3*d^5*e^2 + 5*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^2 + 3*(4*c^3*d^6*e + 5*a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(60*c^3*d^6*e + 65*a*c^2*d^4*e^3 + 7*a^2*c*d^2*e^5 + 2*a^3*e^7 - 3*(c^3*d^2*e^5 + a*c^2*e^7)*x^4 + 15*(c^3*d^3*e^4 + a*c^2*d*e^6)*x^3 + 2*(55*c^3*d^4*e^3 + 62*a*c^2*d^2*e^5 + 7*a^2*c*e^7)*x^2 + 15*(10*c^3*d^5*e^2 + 11*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c*d^5*e^6 + a*d^3*e^8 + (c*d^2*e^9 + a*e^11)*x^3 + 3*(c*d^3*e^8 + a*d*e^10)*x^2 + 3*(c*d^4*e^7 + a*d^2*e^9)*x), -1/12*(30*(4*c^3*d^7 + 5*a*c^2*d^5*e^2 + a^2*c*d^3*e^4 + (4*c^3*d^4*e^3 + 5*a*c^2*d^2*e^5 + a^2*c*e^7)*x^3 + 3*(4*c^3*d^5*e^2 + 5*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^2 + 3*(4*c^3*d^6*e + 5*a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 15*(4*c^3*d^6 + 3*a*c^2*d^4*e^2 + (4*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 3*(4*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4)*x^2 + 3*(4*c^3*d^5*e + 3*a*c^2*d^3*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(60*c^3*d^6*e + 65*a*c^2*d^4*e^3 + 7*a^2*c*d^2*e^5 + 2*a^3*e^7 - 3*(c^3*d^2*e^5 + a*c^2*e^7)*x^4 + 15*(c^3*d^3*e^4 + a*c^2*d*e^6)*x^3 + 2*(55*c^3*d^4*e^3 + 62*a*c^2*d^2*e^5 + 7*a^2*c*e^7)*x^2 + 15*(10*c^3*d^5*e^2 + 11*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c*d^5*e^6 + a*d^3*e^8 + (c*d^2*e^9 + a*e^11)*x^3 + 3*(c*d^3*e^8 + a*d*e^10)*x^2 + 3*(c*d^4*e^7 + a*d^2*e^9)*x), 1/6*(15*(4*c^3*d^6 + 3*a*c^2*d^4*e^2 + (4*c^3*d^3*e^3 + 3*a*c^2*d*e^5)*x^3 + 3*(4*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4)*x^2 + 3*(4*c^3*d^5*e + 3*a*c^2*d^3*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 15*(4*c^3*d^7 + 5*a*c^2*d^5*e^2 + a^2*c*d^3*e^4 + (4*c^3*d^4*e^3 + 5*a*c^2*d^2*e^5 + a^2*c*e^7)*x^3 + 3*(4*c^3*d^5*e^2 + 5*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^2 + 3*(4*c^3*d^6*e + 5*a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (60*c^3*d^6*e + 65*a*c^2*d^4*e^3 + 7*a^2*c*d^2*e^5 + 2*a^3*e^7 - 3*(c^3*d^2*e^5 + a*c^2*e^7)*x^4 + 15*(c^3*d^3*e^4 + a*c^2*d*e^6)*x^3 + 2*(55*c^3*d^4*e^3 + 62*a*c^2*d^2*e^5 + 7*a^2*c*e^7)*x^2 + 15*(10*c^3*d^5*e^2 + 11*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c*d^5*e^6 + a*d^3*e^8 + (c*d^2*e^9 + a*e^11)*x^3 + 3*(c*d^3*e^8 + a*d*e^10)*x^2 + 3*(c*d^4*e^7 + a*d^2*e^9)*x)]","B",0
553,1,3733,0,12.833685," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[\frac{120 \, {\left(c^{4} d^{9} + 2 \, a c^{3} d^{7} e^{2} + a^{2} c^{2} d^{5} e^{4} + {\left(c^{4} d^{5} e^{4} + 2 \, a c^{3} d^{3} e^{6} + a^{2} c^{2} d e^{8}\right)} x^{4} + 4 \, {\left(c^{4} d^{6} e^{3} + 2 \, a c^{3} d^{4} e^{5} + a^{2} c^{2} d^{2} e^{7}\right)} x^{3} + 6 \, {\left(c^{4} d^{7} e^{2} + 2 \, a c^{3} d^{5} e^{4} + a^{2} c^{2} d^{3} e^{6}\right)} x^{2} + 4 \, {\left(c^{4} d^{8} e + 2 \, a c^{3} d^{6} e^{3} + a^{2} c^{2} d^{4} e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 15 \, {\left(8 \, c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 3 \, a^{2} c^{2} d^{4} e^{4} + {\left(8 \, c^{4} d^{4} e^{4} + 12 \, a c^{3} d^{2} e^{6} + 3 \, a^{2} c^{2} e^{8}\right)} x^{4} + 4 \, {\left(8 \, c^{4} d^{5} e^{3} + 12 \, a c^{3} d^{3} e^{5} + 3 \, a^{2} c^{2} d e^{7}\right)} x^{3} + 6 \, {\left(8 \, c^{4} d^{6} e^{2} + 12 \, a c^{3} d^{4} e^{4} + 3 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(8 \, c^{4} d^{7} e + 12 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(120 \, c^{4} d^{8} e + 220 \, a c^{3} d^{6} e^{3} + 89 \, a^{2} c^{2} d^{4} e^{5} - 17 \, a^{3} c d^{2} e^{7} - 6 \, a^{4} e^{9} + 24 \, {\left(c^{4} d^{4} e^{5} + 2 \, a c^{3} d^{2} e^{7} + a^{2} c^{2} e^{9}\right)} x^{4} + 5 \, {\left(50 \, c^{4} d^{5} e^{4} + 97 \, a c^{3} d^{3} e^{6} + 47 \, a^{2} c^{2} d e^{8}\right)} x^{3} + {\left(520 \, c^{4} d^{6} e^{3} + 968 \, a c^{3} d^{4} e^{5} + 421 \, a^{2} c^{2} d^{2} e^{7} - 27 \, a^{3} c e^{9}\right)} x^{2} + 5 \, {\left(84 \, c^{4} d^{7} e^{2} + 155 \, a c^{3} d^{5} e^{4} + 67 \, a^{2} c^{2} d^{3} e^{6} - 4 \, a^{3} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, {\left(c^{2} d^{8} e^{6} + 2 \, a c d^{6} e^{8} + a^{2} d^{4} e^{10} + {\left(c^{2} d^{4} e^{10} + 2 \, a c d^{2} e^{12} + a^{2} e^{14}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{9} + 2 \, a c d^{3} e^{11} + a^{2} d e^{13}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{8} + 2 \, a c d^{4} e^{10} + a^{2} d^{2} e^{12}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e^{7} + 2 \, a c d^{5} e^{9} + a^{2} d^{3} e^{11}\right)} x\right)}}, \frac{240 \, {\left(c^{4} d^{9} + 2 \, a c^{3} d^{7} e^{2} + a^{2} c^{2} d^{5} e^{4} + {\left(c^{4} d^{5} e^{4} + 2 \, a c^{3} d^{3} e^{6} + a^{2} c^{2} d e^{8}\right)} x^{4} + 4 \, {\left(c^{4} d^{6} e^{3} + 2 \, a c^{3} d^{4} e^{5} + a^{2} c^{2} d^{2} e^{7}\right)} x^{3} + 6 \, {\left(c^{4} d^{7} e^{2} + 2 \, a c^{3} d^{5} e^{4} + a^{2} c^{2} d^{3} e^{6}\right)} x^{2} + 4 \, {\left(c^{4} d^{8} e + 2 \, a c^{3} d^{6} e^{3} + a^{2} c^{2} d^{4} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + 15 \, {\left(8 \, c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 3 \, a^{2} c^{2} d^{4} e^{4} + {\left(8 \, c^{4} d^{4} e^{4} + 12 \, a c^{3} d^{2} e^{6} + 3 \, a^{2} c^{2} e^{8}\right)} x^{4} + 4 \, {\left(8 \, c^{4} d^{5} e^{3} + 12 \, a c^{3} d^{3} e^{5} + 3 \, a^{2} c^{2} d e^{7}\right)} x^{3} + 6 \, {\left(8 \, c^{4} d^{6} e^{2} + 12 \, a c^{3} d^{4} e^{4} + 3 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(8 \, c^{4} d^{7} e + 12 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(120 \, c^{4} d^{8} e + 220 \, a c^{3} d^{6} e^{3} + 89 \, a^{2} c^{2} d^{4} e^{5} - 17 \, a^{3} c d^{2} e^{7} - 6 \, a^{4} e^{9} + 24 \, {\left(c^{4} d^{4} e^{5} + 2 \, a c^{3} d^{2} e^{7} + a^{2} c^{2} e^{9}\right)} x^{4} + 5 \, {\left(50 \, c^{4} d^{5} e^{4} + 97 \, a c^{3} d^{3} e^{6} + 47 \, a^{2} c^{2} d e^{8}\right)} x^{3} + {\left(520 \, c^{4} d^{6} e^{3} + 968 \, a c^{3} d^{4} e^{5} + 421 \, a^{2} c^{2} d^{2} e^{7} - 27 \, a^{3} c e^{9}\right)} x^{2} + 5 \, {\left(84 \, c^{4} d^{7} e^{2} + 155 \, a c^{3} d^{5} e^{4} + 67 \, a^{2} c^{2} d^{3} e^{6} - 4 \, a^{3} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, {\left(c^{2} d^{8} e^{6} + 2 \, a c d^{6} e^{8} + a^{2} d^{4} e^{10} + {\left(c^{2} d^{4} e^{10} + 2 \, a c d^{2} e^{12} + a^{2} e^{14}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{9} + 2 \, a c d^{3} e^{11} + a^{2} d e^{13}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{8} + 2 \, a c d^{4} e^{10} + a^{2} d^{2} e^{12}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e^{7} + 2 \, a c d^{5} e^{9} + a^{2} d^{3} e^{11}\right)} x\right)}}, -\frac{15 \, {\left(8 \, c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 3 \, a^{2} c^{2} d^{4} e^{4} + {\left(8 \, c^{4} d^{4} e^{4} + 12 \, a c^{3} d^{2} e^{6} + 3 \, a^{2} c^{2} e^{8}\right)} x^{4} + 4 \, {\left(8 \, c^{4} d^{5} e^{3} + 12 \, a c^{3} d^{3} e^{5} + 3 \, a^{2} c^{2} d e^{7}\right)} x^{3} + 6 \, {\left(8 \, c^{4} d^{6} e^{2} + 12 \, a c^{3} d^{4} e^{4} + 3 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(8 \, c^{4} d^{7} e + 12 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 60 \, {\left(c^{4} d^{9} + 2 \, a c^{3} d^{7} e^{2} + a^{2} c^{2} d^{5} e^{4} + {\left(c^{4} d^{5} e^{4} + 2 \, a c^{3} d^{3} e^{6} + a^{2} c^{2} d e^{8}\right)} x^{4} + 4 \, {\left(c^{4} d^{6} e^{3} + 2 \, a c^{3} d^{4} e^{5} + a^{2} c^{2} d^{2} e^{7}\right)} x^{3} + 6 \, {\left(c^{4} d^{7} e^{2} + 2 \, a c^{3} d^{5} e^{4} + a^{2} c^{2} d^{3} e^{6}\right)} x^{2} + 4 \, {\left(c^{4} d^{8} e + 2 \, a c^{3} d^{6} e^{3} + a^{2} c^{2} d^{4} e^{5}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - {\left(120 \, c^{4} d^{8} e + 220 \, a c^{3} d^{6} e^{3} + 89 \, a^{2} c^{2} d^{4} e^{5} - 17 \, a^{3} c d^{2} e^{7} - 6 \, a^{4} e^{9} + 24 \, {\left(c^{4} d^{4} e^{5} + 2 \, a c^{3} d^{2} e^{7} + a^{2} c^{2} e^{9}\right)} x^{4} + 5 \, {\left(50 \, c^{4} d^{5} e^{4} + 97 \, a c^{3} d^{3} e^{6} + 47 \, a^{2} c^{2} d e^{8}\right)} x^{3} + {\left(520 \, c^{4} d^{6} e^{3} + 968 \, a c^{3} d^{4} e^{5} + 421 \, a^{2} c^{2} d^{2} e^{7} - 27 \, a^{3} c e^{9}\right)} x^{2} + 5 \, {\left(84 \, c^{4} d^{7} e^{2} + 155 \, a c^{3} d^{5} e^{4} + 67 \, a^{2} c^{2} d^{3} e^{6} - 4 \, a^{3} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, {\left(c^{2} d^{8} e^{6} + 2 \, a c d^{6} e^{8} + a^{2} d^{4} e^{10} + {\left(c^{2} d^{4} e^{10} + 2 \, a c d^{2} e^{12} + a^{2} e^{14}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{9} + 2 \, a c d^{3} e^{11} + a^{2} d e^{13}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{8} + 2 \, a c d^{4} e^{10} + a^{2} d^{2} e^{12}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e^{7} + 2 \, a c d^{5} e^{9} + a^{2} d^{3} e^{11}\right)} x\right)}}, -\frac{15 \, {\left(8 \, c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 3 \, a^{2} c^{2} d^{4} e^{4} + {\left(8 \, c^{4} d^{4} e^{4} + 12 \, a c^{3} d^{2} e^{6} + 3 \, a^{2} c^{2} e^{8}\right)} x^{4} + 4 \, {\left(8 \, c^{4} d^{5} e^{3} + 12 \, a c^{3} d^{3} e^{5} + 3 \, a^{2} c^{2} d e^{7}\right)} x^{3} + 6 \, {\left(8 \, c^{4} d^{6} e^{2} + 12 \, a c^{3} d^{4} e^{4} + 3 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(8 \, c^{4} d^{7} e + 12 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 120 \, {\left(c^{4} d^{9} + 2 \, a c^{3} d^{7} e^{2} + a^{2} c^{2} d^{5} e^{4} + {\left(c^{4} d^{5} e^{4} + 2 \, a c^{3} d^{3} e^{6} + a^{2} c^{2} d e^{8}\right)} x^{4} + 4 \, {\left(c^{4} d^{6} e^{3} + 2 \, a c^{3} d^{4} e^{5} + a^{2} c^{2} d^{2} e^{7}\right)} x^{3} + 6 \, {\left(c^{4} d^{7} e^{2} + 2 \, a c^{3} d^{5} e^{4} + a^{2} c^{2} d^{3} e^{6}\right)} x^{2} + 4 \, {\left(c^{4} d^{8} e + 2 \, a c^{3} d^{6} e^{3} + a^{2} c^{2} d^{4} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(120 \, c^{4} d^{8} e + 220 \, a c^{3} d^{6} e^{3} + 89 \, a^{2} c^{2} d^{4} e^{5} - 17 \, a^{3} c d^{2} e^{7} - 6 \, a^{4} e^{9} + 24 \, {\left(c^{4} d^{4} e^{5} + 2 \, a c^{3} d^{2} e^{7} + a^{2} c^{2} e^{9}\right)} x^{4} + 5 \, {\left(50 \, c^{4} d^{5} e^{4} + 97 \, a c^{3} d^{3} e^{6} + 47 \, a^{2} c^{2} d e^{8}\right)} x^{3} + {\left(520 \, c^{4} d^{6} e^{3} + 968 \, a c^{3} d^{4} e^{5} + 421 \, a^{2} c^{2} d^{2} e^{7} - 27 \, a^{3} c e^{9}\right)} x^{2} + 5 \, {\left(84 \, c^{4} d^{7} e^{2} + 155 \, a c^{3} d^{5} e^{4} + 67 \, a^{2} c^{2} d^{3} e^{6} - 4 \, a^{3} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, {\left(c^{2} d^{8} e^{6} + 2 \, a c d^{6} e^{8} + a^{2} d^{4} e^{10} + {\left(c^{2} d^{4} e^{10} + 2 \, a c d^{2} e^{12} + a^{2} e^{14}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{9} + 2 \, a c d^{3} e^{11} + a^{2} d e^{13}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{8} + 2 \, a c d^{4} e^{10} + a^{2} d^{2} e^{12}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e^{7} + 2 \, a c d^{5} e^{9} + a^{2} d^{3} e^{11}\right)} x\right)}}\right]"," ",0,"[1/48*(120*(c^4*d^9 + 2*a*c^3*d^7*e^2 + a^2*c^2*d^5*e^4 + (c^4*d^5*e^4 + 2*a*c^3*d^3*e^6 + a^2*c^2*d*e^8)*x^4 + 4*(c^4*d^6*e^3 + 2*a*c^3*d^4*e^5 + a^2*c^2*d^2*e^7)*x^3 + 6*(c^4*d^7*e^2 + 2*a*c^3*d^5*e^4 + a^2*c^2*d^3*e^6)*x^2 + 4*(c^4*d^8*e + 2*a*c^3*d^6*e^3 + a^2*c^2*d^4*e^5)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 15*(8*c^4*d^8 + 12*a*c^3*d^6*e^2 + 3*a^2*c^2*d^4*e^4 + (8*c^4*d^4*e^4 + 12*a*c^3*d^2*e^6 + 3*a^2*c^2*e^8)*x^4 + 4*(8*c^4*d^5*e^3 + 12*a*c^3*d^3*e^5 + 3*a^2*c^2*d*e^7)*x^3 + 6*(8*c^4*d^6*e^2 + 12*a*c^3*d^4*e^4 + 3*a^2*c^2*d^2*e^6)*x^2 + 4*(8*c^4*d^7*e + 12*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(120*c^4*d^8*e + 220*a*c^3*d^6*e^3 + 89*a^2*c^2*d^4*e^5 - 17*a^3*c*d^2*e^7 - 6*a^4*e^9 + 24*(c^4*d^4*e^5 + 2*a*c^3*d^2*e^7 + a^2*c^2*e^9)*x^4 + 5*(50*c^4*d^5*e^4 + 97*a*c^3*d^3*e^6 + 47*a^2*c^2*d*e^8)*x^3 + (520*c^4*d^6*e^3 + 968*a*c^3*d^4*e^5 + 421*a^2*c^2*d^2*e^7 - 27*a^3*c*e^9)*x^2 + 5*(84*c^4*d^7*e^2 + 155*a*c^3*d^5*e^4 + 67*a^2*c^2*d^3*e^6 - 4*a^3*c*d*e^8)*x)*sqrt(c*x^2 + a))/(c^2*d^8*e^6 + 2*a*c*d^6*e^8 + a^2*d^4*e^10 + (c^2*d^4*e^10 + 2*a*c*d^2*e^12 + a^2*e^14)*x^4 + 4*(c^2*d^5*e^9 + 2*a*c*d^3*e^11 + a^2*d*e^13)*x^3 + 6*(c^2*d^6*e^8 + 2*a*c*d^4*e^10 + a^2*d^2*e^12)*x^2 + 4*(c^2*d^7*e^7 + 2*a*c*d^5*e^9 + a^2*d^3*e^11)*x), 1/48*(240*(c^4*d^9 + 2*a*c^3*d^7*e^2 + a^2*c^2*d^5*e^4 + (c^4*d^5*e^4 + 2*a*c^3*d^3*e^6 + a^2*c^2*d*e^8)*x^4 + 4*(c^4*d^6*e^3 + 2*a*c^3*d^4*e^5 + a^2*c^2*d^2*e^7)*x^3 + 6*(c^4*d^7*e^2 + 2*a*c^3*d^5*e^4 + a^2*c^2*d^3*e^6)*x^2 + 4*(c^4*d^8*e + 2*a*c^3*d^6*e^3 + a^2*c^2*d^4*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + 15*(8*c^4*d^8 + 12*a*c^3*d^6*e^2 + 3*a^2*c^2*d^4*e^4 + (8*c^4*d^4*e^4 + 12*a*c^3*d^2*e^6 + 3*a^2*c^2*e^8)*x^4 + 4*(8*c^4*d^5*e^3 + 12*a*c^3*d^3*e^5 + 3*a^2*c^2*d*e^7)*x^3 + 6*(8*c^4*d^6*e^2 + 12*a*c^3*d^4*e^4 + 3*a^2*c^2*d^2*e^6)*x^2 + 4*(8*c^4*d^7*e + 12*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(120*c^4*d^8*e + 220*a*c^3*d^6*e^3 + 89*a^2*c^2*d^4*e^5 - 17*a^3*c*d^2*e^7 - 6*a^4*e^9 + 24*(c^4*d^4*e^5 + 2*a*c^3*d^2*e^7 + a^2*c^2*e^9)*x^4 + 5*(50*c^4*d^5*e^4 + 97*a*c^3*d^3*e^6 + 47*a^2*c^2*d*e^8)*x^3 + (520*c^4*d^6*e^3 + 968*a*c^3*d^4*e^5 + 421*a^2*c^2*d^2*e^7 - 27*a^3*c*e^9)*x^2 + 5*(84*c^4*d^7*e^2 + 155*a*c^3*d^5*e^4 + 67*a^2*c^2*d^3*e^6 - 4*a^3*c*d*e^8)*x)*sqrt(c*x^2 + a))/(c^2*d^8*e^6 + 2*a*c*d^6*e^8 + a^2*d^4*e^10 + (c^2*d^4*e^10 + 2*a*c*d^2*e^12 + a^2*e^14)*x^4 + 4*(c^2*d^5*e^9 + 2*a*c*d^3*e^11 + a^2*d*e^13)*x^3 + 6*(c^2*d^6*e^8 + 2*a*c*d^4*e^10 + a^2*d^2*e^12)*x^2 + 4*(c^2*d^7*e^7 + 2*a*c*d^5*e^9 + a^2*d^3*e^11)*x), -1/24*(15*(8*c^4*d^8 + 12*a*c^3*d^6*e^2 + 3*a^2*c^2*d^4*e^4 + (8*c^4*d^4*e^4 + 12*a*c^3*d^2*e^6 + 3*a^2*c^2*e^8)*x^4 + 4*(8*c^4*d^5*e^3 + 12*a*c^3*d^3*e^5 + 3*a^2*c^2*d*e^7)*x^3 + 6*(8*c^4*d^6*e^2 + 12*a*c^3*d^4*e^4 + 3*a^2*c^2*d^2*e^6)*x^2 + 4*(8*c^4*d^7*e + 12*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 60*(c^4*d^9 + 2*a*c^3*d^7*e^2 + a^2*c^2*d^5*e^4 + (c^4*d^5*e^4 + 2*a*c^3*d^3*e^6 + a^2*c^2*d*e^8)*x^4 + 4*(c^4*d^6*e^3 + 2*a*c^3*d^4*e^5 + a^2*c^2*d^2*e^7)*x^3 + 6*(c^4*d^7*e^2 + 2*a*c^3*d^5*e^4 + a^2*c^2*d^3*e^6)*x^2 + 4*(c^4*d^8*e + 2*a*c^3*d^6*e^3 + a^2*c^2*d^4*e^5)*x)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - (120*c^4*d^8*e + 220*a*c^3*d^6*e^3 + 89*a^2*c^2*d^4*e^5 - 17*a^3*c*d^2*e^7 - 6*a^4*e^9 + 24*(c^4*d^4*e^5 + 2*a*c^3*d^2*e^7 + a^2*c^2*e^9)*x^4 + 5*(50*c^4*d^5*e^4 + 97*a*c^3*d^3*e^6 + 47*a^2*c^2*d*e^8)*x^3 + (520*c^4*d^6*e^3 + 968*a*c^3*d^4*e^5 + 421*a^2*c^2*d^2*e^7 - 27*a^3*c*e^9)*x^2 + 5*(84*c^4*d^7*e^2 + 155*a*c^3*d^5*e^4 + 67*a^2*c^2*d^3*e^6 - 4*a^3*c*d*e^8)*x)*sqrt(c*x^2 + a))/(c^2*d^8*e^6 + 2*a*c*d^6*e^8 + a^2*d^4*e^10 + (c^2*d^4*e^10 + 2*a*c*d^2*e^12 + a^2*e^14)*x^4 + 4*(c^2*d^5*e^9 + 2*a*c*d^3*e^11 + a^2*d*e^13)*x^3 + 6*(c^2*d^6*e^8 + 2*a*c*d^4*e^10 + a^2*d^2*e^12)*x^2 + 4*(c^2*d^7*e^7 + 2*a*c*d^5*e^9 + a^2*d^3*e^11)*x), -1/24*(15*(8*c^4*d^8 + 12*a*c^3*d^6*e^2 + 3*a^2*c^2*d^4*e^4 + (8*c^4*d^4*e^4 + 12*a*c^3*d^2*e^6 + 3*a^2*c^2*e^8)*x^4 + 4*(8*c^4*d^5*e^3 + 12*a*c^3*d^3*e^5 + 3*a^2*c^2*d*e^7)*x^3 + 6*(8*c^4*d^6*e^2 + 12*a*c^3*d^4*e^4 + 3*a^2*c^2*d^2*e^6)*x^2 + 4*(8*c^4*d^7*e + 12*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 120*(c^4*d^9 + 2*a*c^3*d^7*e^2 + a^2*c^2*d^5*e^4 + (c^4*d^5*e^4 + 2*a*c^3*d^3*e^6 + a^2*c^2*d*e^8)*x^4 + 4*(c^4*d^6*e^3 + 2*a*c^3*d^4*e^5 + a^2*c^2*d^2*e^7)*x^3 + 6*(c^4*d^7*e^2 + 2*a*c^3*d^5*e^4 + a^2*c^2*d^3*e^6)*x^2 + 4*(c^4*d^8*e + 2*a*c^3*d^6*e^3 + a^2*c^2*d^4*e^5)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (120*c^4*d^8*e + 220*a*c^3*d^6*e^3 + 89*a^2*c^2*d^4*e^5 - 17*a^3*c*d^2*e^7 - 6*a^4*e^9 + 24*(c^4*d^4*e^5 + 2*a*c^3*d^2*e^7 + a^2*c^2*e^9)*x^4 + 5*(50*c^4*d^5*e^4 + 97*a*c^3*d^3*e^6 + 47*a^2*c^2*d*e^8)*x^3 + (520*c^4*d^6*e^3 + 968*a*c^3*d^4*e^5 + 421*a^2*c^2*d^2*e^7 - 27*a^3*c*e^9)*x^2 + 5*(84*c^4*d^7*e^2 + 155*a*c^3*d^5*e^4 + 67*a^2*c^2*d^3*e^6 - 4*a^3*c*d*e^8)*x)*sqrt(c*x^2 + a))/(c^2*d^8*e^6 + 2*a*c*d^6*e^8 + a^2*d^4*e^10 + (c^2*d^4*e^10 + 2*a*c*d^2*e^12 + a^2*e^14)*x^4 + 4*(c^2*d^5*e^9 + 2*a*c*d^3*e^11 + a^2*d*e^13)*x^3 + 6*(c^2*d^6*e^8 + 2*a*c*d^4*e^10 + a^2*d^2*e^12)*x^2 + 4*(c^2*d^7*e^7 + 2*a*c*d^5*e^9 + a^2*d^3*e^11)*x)]","B",0
554,1,5169,0,80.428995," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^6,x, algorithm=""fricas"")","\left[\frac{120 \, {\left(c^{5} d^{11} + 3 \, a c^{4} d^{9} e^{2} + 3 \, a^{2} c^{3} d^{7} e^{4} + a^{3} c^{2} d^{5} e^{6} + {\left(c^{5} d^{6} e^{5} + 3 \, a c^{4} d^{4} e^{7} + 3 \, a^{2} c^{3} d^{2} e^{9} + a^{3} c^{2} e^{11}\right)} x^{5} + 5 \, {\left(c^{5} d^{7} e^{4} + 3 \, a c^{4} d^{5} e^{6} + 3 \, a^{2} c^{3} d^{3} e^{8} + a^{3} c^{2} d e^{10}\right)} x^{4} + 10 \, {\left(c^{5} d^{8} e^{3} + 3 \, a c^{4} d^{6} e^{5} + 3 \, a^{2} c^{3} d^{4} e^{7} + a^{3} c^{2} d^{2} e^{9}\right)} x^{3} + 10 \, {\left(c^{5} d^{9} e^{2} + 3 \, a c^{4} d^{7} e^{4} + 3 \, a^{2} c^{3} d^{5} e^{6} + a^{3} c^{2} d^{3} e^{8}\right)} x^{2} + 5 \, {\left(c^{5} d^{10} e + 3 \, a c^{4} d^{8} e^{3} + 3 \, a^{2} c^{3} d^{6} e^{5} + a^{3} c^{2} d^{4} e^{7}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 15 \, {\left(8 \, c^{5} d^{10} + 20 \, a c^{4} d^{8} e^{2} + 15 \, a^{2} c^{3} d^{6} e^{4} + {\left(8 \, c^{5} d^{5} e^{5} + 20 \, a c^{4} d^{3} e^{7} + 15 \, a^{2} c^{3} d e^{9}\right)} x^{5} + 5 \, {\left(8 \, c^{5} d^{6} e^{4} + 20 \, a c^{4} d^{4} e^{6} + 15 \, a^{2} c^{3} d^{2} e^{8}\right)} x^{4} + 10 \, {\left(8 \, c^{5} d^{7} e^{3} + 20 \, a c^{4} d^{5} e^{5} + 15 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 10 \, {\left(8 \, c^{5} d^{8} e^{2} + 20 \, a c^{4} d^{6} e^{4} + 15 \, a^{2} c^{3} d^{4} e^{6}\right)} x^{2} + 5 \, {\left(8 \, c^{5} d^{9} e + 20 \, a c^{4} d^{7} e^{3} + 15 \, a^{2} c^{3} d^{5} e^{5}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(120 \, c^{5} d^{10} e + 340 \, a c^{4} d^{8} e^{3} + 309 \, a^{2} c^{3} d^{6} e^{5} + 147 \, a^{3} c^{2} d^{4} e^{7} + 82 \, a^{4} c d^{2} e^{9} + 24 \, a^{5} e^{11} + {\left(274 \, c^{5} d^{6} e^{5} + 777 \, a c^{4} d^{4} e^{7} + 687 \, a^{2} c^{3} d^{2} e^{9} + 184 \, a^{3} c^{2} e^{11}\right)} x^{4} + 5 \, {\left(154 \, c^{5} d^{7} e^{4} + 429 \, a c^{4} d^{5} e^{6} + 360 \, a^{2} c^{3} d^{3} e^{8} + 85 \, a^{3} c^{2} d e^{10}\right)} x^{3} + {\left(940 \, c^{5} d^{8} e^{3} + 2683 \, a c^{4} d^{6} e^{5} + 2364 \, a^{2} c^{3} d^{4} e^{7} + 709 \, a^{3} c^{2} d^{2} e^{9} + 88 \, a^{4} c e^{11}\right)} x^{2} + 5 \, {\left(108 \, c^{5} d^{9} e^{2} + 307 \, a c^{4} d^{7} e^{4} + 264 \, a^{2} c^{3} d^{5} e^{6} + 75 \, a^{3} c^{2} d^{3} e^{8} + 10 \, a^{4} c d e^{10}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, {\left(c^{3} d^{11} e^{6} + 3 \, a c^{2} d^{9} e^{8} + 3 \, a^{2} c d^{7} e^{10} + a^{3} d^{5} e^{12} + {\left(c^{3} d^{6} e^{11} + 3 \, a c^{2} d^{4} e^{13} + 3 \, a^{2} c d^{2} e^{15} + a^{3} e^{17}\right)} x^{5} + 5 \, {\left(c^{3} d^{7} e^{10} + 3 \, a c^{2} d^{5} e^{12} + 3 \, a^{2} c d^{3} e^{14} + a^{3} d e^{16}\right)} x^{4} + 10 \, {\left(c^{3} d^{8} e^{9} + 3 \, a c^{2} d^{6} e^{11} + 3 \, a^{2} c d^{4} e^{13} + a^{3} d^{2} e^{15}\right)} x^{3} + 10 \, {\left(c^{3} d^{9} e^{8} + 3 \, a c^{2} d^{7} e^{10} + 3 \, a^{2} c d^{5} e^{12} + a^{3} d^{3} e^{14}\right)} x^{2} + 5 \, {\left(c^{3} d^{10} e^{7} + 3 \, a c^{2} d^{8} e^{9} + 3 \, a^{2} c d^{6} e^{11} + a^{3} d^{4} e^{13}\right)} x\right)}}, \frac{15 \, {\left(8 \, c^{5} d^{10} + 20 \, a c^{4} d^{8} e^{2} + 15 \, a^{2} c^{3} d^{6} e^{4} + {\left(8 \, c^{5} d^{5} e^{5} + 20 \, a c^{4} d^{3} e^{7} + 15 \, a^{2} c^{3} d e^{9}\right)} x^{5} + 5 \, {\left(8 \, c^{5} d^{6} e^{4} + 20 \, a c^{4} d^{4} e^{6} + 15 \, a^{2} c^{3} d^{2} e^{8}\right)} x^{4} + 10 \, {\left(8 \, c^{5} d^{7} e^{3} + 20 \, a c^{4} d^{5} e^{5} + 15 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 10 \, {\left(8 \, c^{5} d^{8} e^{2} + 20 \, a c^{4} d^{6} e^{4} + 15 \, a^{2} c^{3} d^{4} e^{6}\right)} x^{2} + 5 \, {\left(8 \, c^{5} d^{9} e + 20 \, a c^{4} d^{7} e^{3} + 15 \, a^{2} c^{3} d^{5} e^{5}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + 60 \, {\left(c^{5} d^{11} + 3 \, a c^{4} d^{9} e^{2} + 3 \, a^{2} c^{3} d^{7} e^{4} + a^{3} c^{2} d^{5} e^{6} + {\left(c^{5} d^{6} e^{5} + 3 \, a c^{4} d^{4} e^{7} + 3 \, a^{2} c^{3} d^{2} e^{9} + a^{3} c^{2} e^{11}\right)} x^{5} + 5 \, {\left(c^{5} d^{7} e^{4} + 3 \, a c^{4} d^{5} e^{6} + 3 \, a^{2} c^{3} d^{3} e^{8} + a^{3} c^{2} d e^{10}\right)} x^{4} + 10 \, {\left(c^{5} d^{8} e^{3} + 3 \, a c^{4} d^{6} e^{5} + 3 \, a^{2} c^{3} d^{4} e^{7} + a^{3} c^{2} d^{2} e^{9}\right)} x^{3} + 10 \, {\left(c^{5} d^{9} e^{2} + 3 \, a c^{4} d^{7} e^{4} + 3 \, a^{2} c^{3} d^{5} e^{6} + a^{3} c^{2} d^{3} e^{8}\right)} x^{2} + 5 \, {\left(c^{5} d^{10} e + 3 \, a c^{4} d^{8} e^{3} + 3 \, a^{2} c^{3} d^{6} e^{5} + a^{3} c^{2} d^{4} e^{7}\right)} x\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - {\left(120 \, c^{5} d^{10} e + 340 \, a c^{4} d^{8} e^{3} + 309 \, a^{2} c^{3} d^{6} e^{5} + 147 \, a^{3} c^{2} d^{4} e^{7} + 82 \, a^{4} c d^{2} e^{9} + 24 \, a^{5} e^{11} + {\left(274 \, c^{5} d^{6} e^{5} + 777 \, a c^{4} d^{4} e^{7} + 687 \, a^{2} c^{3} d^{2} e^{9} + 184 \, a^{3} c^{2} e^{11}\right)} x^{4} + 5 \, {\left(154 \, c^{5} d^{7} e^{4} + 429 \, a c^{4} d^{5} e^{6} + 360 \, a^{2} c^{3} d^{3} e^{8} + 85 \, a^{3} c^{2} d e^{10}\right)} x^{3} + {\left(940 \, c^{5} d^{8} e^{3} + 2683 \, a c^{4} d^{6} e^{5} + 2364 \, a^{2} c^{3} d^{4} e^{7} + 709 \, a^{3} c^{2} d^{2} e^{9} + 88 \, a^{4} c e^{11}\right)} x^{2} + 5 \, {\left(108 \, c^{5} d^{9} e^{2} + 307 \, a c^{4} d^{7} e^{4} + 264 \, a^{2} c^{3} d^{5} e^{6} + 75 \, a^{3} c^{2} d^{3} e^{8} + 10 \, a^{4} c d e^{10}\right)} x\right)} \sqrt{c x^{2} + a}}{120 \, {\left(c^{3} d^{11} e^{6} + 3 \, a c^{2} d^{9} e^{8} + 3 \, a^{2} c d^{7} e^{10} + a^{3} d^{5} e^{12} + {\left(c^{3} d^{6} e^{11} + 3 \, a c^{2} d^{4} e^{13} + 3 \, a^{2} c d^{2} e^{15} + a^{3} e^{17}\right)} x^{5} + 5 \, {\left(c^{3} d^{7} e^{10} + 3 \, a c^{2} d^{5} e^{12} + 3 \, a^{2} c d^{3} e^{14} + a^{3} d e^{16}\right)} x^{4} + 10 \, {\left(c^{3} d^{8} e^{9} + 3 \, a c^{2} d^{6} e^{11} + 3 \, a^{2} c d^{4} e^{13} + a^{3} d^{2} e^{15}\right)} x^{3} + 10 \, {\left(c^{3} d^{9} e^{8} + 3 \, a c^{2} d^{7} e^{10} + 3 \, a^{2} c d^{5} e^{12} + a^{3} d^{3} e^{14}\right)} x^{2} + 5 \, {\left(c^{3} d^{10} e^{7} + 3 \, a c^{2} d^{8} e^{9} + 3 \, a^{2} c d^{6} e^{11} + a^{3} d^{4} e^{13}\right)} x\right)}}, -\frac{240 \, {\left(c^{5} d^{11} + 3 \, a c^{4} d^{9} e^{2} + 3 \, a^{2} c^{3} d^{7} e^{4} + a^{3} c^{2} d^{5} e^{6} + {\left(c^{5} d^{6} e^{5} + 3 \, a c^{4} d^{4} e^{7} + 3 \, a^{2} c^{3} d^{2} e^{9} + a^{3} c^{2} e^{11}\right)} x^{5} + 5 \, {\left(c^{5} d^{7} e^{4} + 3 \, a c^{4} d^{5} e^{6} + 3 \, a^{2} c^{3} d^{3} e^{8} + a^{3} c^{2} d e^{10}\right)} x^{4} + 10 \, {\left(c^{5} d^{8} e^{3} + 3 \, a c^{4} d^{6} e^{5} + 3 \, a^{2} c^{3} d^{4} e^{7} + a^{3} c^{2} d^{2} e^{9}\right)} x^{3} + 10 \, {\left(c^{5} d^{9} e^{2} + 3 \, a c^{4} d^{7} e^{4} + 3 \, a^{2} c^{3} d^{5} e^{6} + a^{3} c^{2} d^{3} e^{8}\right)} x^{2} + 5 \, {\left(c^{5} d^{10} e + 3 \, a c^{4} d^{8} e^{3} + 3 \, a^{2} c^{3} d^{6} e^{5} + a^{3} c^{2} d^{4} e^{7}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - 15 \, {\left(8 \, c^{5} d^{10} + 20 \, a c^{4} d^{8} e^{2} + 15 \, a^{2} c^{3} d^{6} e^{4} + {\left(8 \, c^{5} d^{5} e^{5} + 20 \, a c^{4} d^{3} e^{7} + 15 \, a^{2} c^{3} d e^{9}\right)} x^{5} + 5 \, {\left(8 \, c^{5} d^{6} e^{4} + 20 \, a c^{4} d^{4} e^{6} + 15 \, a^{2} c^{3} d^{2} e^{8}\right)} x^{4} + 10 \, {\left(8 \, c^{5} d^{7} e^{3} + 20 \, a c^{4} d^{5} e^{5} + 15 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 10 \, {\left(8 \, c^{5} d^{8} e^{2} + 20 \, a c^{4} d^{6} e^{4} + 15 \, a^{2} c^{3} d^{4} e^{6}\right)} x^{2} + 5 \, {\left(8 \, c^{5} d^{9} e + 20 \, a c^{4} d^{7} e^{3} + 15 \, a^{2} c^{3} d^{5} e^{5}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(120 \, c^{5} d^{10} e + 340 \, a c^{4} d^{8} e^{3} + 309 \, a^{2} c^{3} d^{6} e^{5} + 147 \, a^{3} c^{2} d^{4} e^{7} + 82 \, a^{4} c d^{2} e^{9} + 24 \, a^{5} e^{11} + {\left(274 \, c^{5} d^{6} e^{5} + 777 \, a c^{4} d^{4} e^{7} + 687 \, a^{2} c^{3} d^{2} e^{9} + 184 \, a^{3} c^{2} e^{11}\right)} x^{4} + 5 \, {\left(154 \, c^{5} d^{7} e^{4} + 429 \, a c^{4} d^{5} e^{6} + 360 \, a^{2} c^{3} d^{3} e^{8} + 85 \, a^{3} c^{2} d e^{10}\right)} x^{3} + {\left(940 \, c^{5} d^{8} e^{3} + 2683 \, a c^{4} d^{6} e^{5} + 2364 \, a^{2} c^{3} d^{4} e^{7} + 709 \, a^{3} c^{2} d^{2} e^{9} + 88 \, a^{4} c e^{11}\right)} x^{2} + 5 \, {\left(108 \, c^{5} d^{9} e^{2} + 307 \, a c^{4} d^{7} e^{4} + 264 \, a^{2} c^{3} d^{5} e^{6} + 75 \, a^{3} c^{2} d^{3} e^{8} + 10 \, a^{4} c d e^{10}\right)} x\right)} \sqrt{c x^{2} + a}}{240 \, {\left(c^{3} d^{11} e^{6} + 3 \, a c^{2} d^{9} e^{8} + 3 \, a^{2} c d^{7} e^{10} + a^{3} d^{5} e^{12} + {\left(c^{3} d^{6} e^{11} + 3 \, a c^{2} d^{4} e^{13} + 3 \, a^{2} c d^{2} e^{15} + a^{3} e^{17}\right)} x^{5} + 5 \, {\left(c^{3} d^{7} e^{10} + 3 \, a c^{2} d^{5} e^{12} + 3 \, a^{2} c d^{3} e^{14} + a^{3} d e^{16}\right)} x^{4} + 10 \, {\left(c^{3} d^{8} e^{9} + 3 \, a c^{2} d^{6} e^{11} + 3 \, a^{2} c d^{4} e^{13} + a^{3} d^{2} e^{15}\right)} x^{3} + 10 \, {\left(c^{3} d^{9} e^{8} + 3 \, a c^{2} d^{7} e^{10} + 3 \, a^{2} c d^{5} e^{12} + a^{3} d^{3} e^{14}\right)} x^{2} + 5 \, {\left(c^{3} d^{10} e^{7} + 3 \, a c^{2} d^{8} e^{9} + 3 \, a^{2} c d^{6} e^{11} + a^{3} d^{4} e^{13}\right)} x\right)}}, \frac{15 \, {\left(8 \, c^{5} d^{10} + 20 \, a c^{4} d^{8} e^{2} + 15 \, a^{2} c^{3} d^{6} e^{4} + {\left(8 \, c^{5} d^{5} e^{5} + 20 \, a c^{4} d^{3} e^{7} + 15 \, a^{2} c^{3} d e^{9}\right)} x^{5} + 5 \, {\left(8 \, c^{5} d^{6} e^{4} + 20 \, a c^{4} d^{4} e^{6} + 15 \, a^{2} c^{3} d^{2} e^{8}\right)} x^{4} + 10 \, {\left(8 \, c^{5} d^{7} e^{3} + 20 \, a c^{4} d^{5} e^{5} + 15 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 10 \, {\left(8 \, c^{5} d^{8} e^{2} + 20 \, a c^{4} d^{6} e^{4} + 15 \, a^{2} c^{3} d^{4} e^{6}\right)} x^{2} + 5 \, {\left(8 \, c^{5} d^{9} e + 20 \, a c^{4} d^{7} e^{3} + 15 \, a^{2} c^{3} d^{5} e^{5}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - 120 \, {\left(c^{5} d^{11} + 3 \, a c^{4} d^{9} e^{2} + 3 \, a^{2} c^{3} d^{7} e^{4} + a^{3} c^{2} d^{5} e^{6} + {\left(c^{5} d^{6} e^{5} + 3 \, a c^{4} d^{4} e^{7} + 3 \, a^{2} c^{3} d^{2} e^{9} + a^{3} c^{2} e^{11}\right)} x^{5} + 5 \, {\left(c^{5} d^{7} e^{4} + 3 \, a c^{4} d^{5} e^{6} + 3 \, a^{2} c^{3} d^{3} e^{8} + a^{3} c^{2} d e^{10}\right)} x^{4} + 10 \, {\left(c^{5} d^{8} e^{3} + 3 \, a c^{4} d^{6} e^{5} + 3 \, a^{2} c^{3} d^{4} e^{7} + a^{3} c^{2} d^{2} e^{9}\right)} x^{3} + 10 \, {\left(c^{5} d^{9} e^{2} + 3 \, a c^{4} d^{7} e^{4} + 3 \, a^{2} c^{3} d^{5} e^{6} + a^{3} c^{2} d^{3} e^{8}\right)} x^{2} + 5 \, {\left(c^{5} d^{10} e + 3 \, a c^{4} d^{8} e^{3} + 3 \, a^{2} c^{3} d^{6} e^{5} + a^{3} c^{2} d^{4} e^{7}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(120 \, c^{5} d^{10} e + 340 \, a c^{4} d^{8} e^{3} + 309 \, a^{2} c^{3} d^{6} e^{5} + 147 \, a^{3} c^{2} d^{4} e^{7} + 82 \, a^{4} c d^{2} e^{9} + 24 \, a^{5} e^{11} + {\left(274 \, c^{5} d^{6} e^{5} + 777 \, a c^{4} d^{4} e^{7} + 687 \, a^{2} c^{3} d^{2} e^{9} + 184 \, a^{3} c^{2} e^{11}\right)} x^{4} + 5 \, {\left(154 \, c^{5} d^{7} e^{4} + 429 \, a c^{4} d^{5} e^{6} + 360 \, a^{2} c^{3} d^{3} e^{8} + 85 \, a^{3} c^{2} d e^{10}\right)} x^{3} + {\left(940 \, c^{5} d^{8} e^{3} + 2683 \, a c^{4} d^{6} e^{5} + 2364 \, a^{2} c^{3} d^{4} e^{7} + 709 \, a^{3} c^{2} d^{2} e^{9} + 88 \, a^{4} c e^{11}\right)} x^{2} + 5 \, {\left(108 \, c^{5} d^{9} e^{2} + 307 \, a c^{4} d^{7} e^{4} + 264 \, a^{2} c^{3} d^{5} e^{6} + 75 \, a^{3} c^{2} d^{3} e^{8} + 10 \, a^{4} c d e^{10}\right)} x\right)} \sqrt{c x^{2} + a}}{120 \, {\left(c^{3} d^{11} e^{6} + 3 \, a c^{2} d^{9} e^{8} + 3 \, a^{2} c d^{7} e^{10} + a^{3} d^{5} e^{12} + {\left(c^{3} d^{6} e^{11} + 3 \, a c^{2} d^{4} e^{13} + 3 \, a^{2} c d^{2} e^{15} + a^{3} e^{17}\right)} x^{5} + 5 \, {\left(c^{3} d^{7} e^{10} + 3 \, a c^{2} d^{5} e^{12} + 3 \, a^{2} c d^{3} e^{14} + a^{3} d e^{16}\right)} x^{4} + 10 \, {\left(c^{3} d^{8} e^{9} + 3 \, a c^{2} d^{6} e^{11} + 3 \, a^{2} c d^{4} e^{13} + a^{3} d^{2} e^{15}\right)} x^{3} + 10 \, {\left(c^{3} d^{9} e^{8} + 3 \, a c^{2} d^{7} e^{10} + 3 \, a^{2} c d^{5} e^{12} + a^{3} d^{3} e^{14}\right)} x^{2} + 5 \, {\left(c^{3} d^{10} e^{7} + 3 \, a c^{2} d^{8} e^{9} + 3 \, a^{2} c d^{6} e^{11} + a^{3} d^{4} e^{13}\right)} x\right)}}\right]"," ",0,"[1/240*(120*(c^5*d^11 + 3*a*c^4*d^9*e^2 + 3*a^2*c^3*d^7*e^4 + a^3*c^2*d^5*e^6 + (c^5*d^6*e^5 + 3*a*c^4*d^4*e^7 + 3*a^2*c^3*d^2*e^9 + a^3*c^2*e^11)*x^5 + 5*(c^5*d^7*e^4 + 3*a*c^4*d^5*e^6 + 3*a^2*c^3*d^3*e^8 + a^3*c^2*d*e^10)*x^4 + 10*(c^5*d^8*e^3 + 3*a*c^4*d^6*e^5 + 3*a^2*c^3*d^4*e^7 + a^3*c^2*d^2*e^9)*x^3 + 10*(c^5*d^9*e^2 + 3*a*c^4*d^7*e^4 + 3*a^2*c^3*d^5*e^6 + a^3*c^2*d^3*e^8)*x^2 + 5*(c^5*d^10*e + 3*a*c^4*d^8*e^3 + 3*a^2*c^3*d^6*e^5 + a^3*c^2*d^4*e^7)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 15*(8*c^5*d^10 + 20*a*c^4*d^8*e^2 + 15*a^2*c^3*d^6*e^4 + (8*c^5*d^5*e^5 + 20*a*c^4*d^3*e^7 + 15*a^2*c^3*d*e^9)*x^5 + 5*(8*c^5*d^6*e^4 + 20*a*c^4*d^4*e^6 + 15*a^2*c^3*d^2*e^8)*x^4 + 10*(8*c^5*d^7*e^3 + 20*a*c^4*d^5*e^5 + 15*a^2*c^3*d^3*e^7)*x^3 + 10*(8*c^5*d^8*e^2 + 20*a*c^4*d^6*e^4 + 15*a^2*c^3*d^4*e^6)*x^2 + 5*(8*c^5*d^9*e + 20*a*c^4*d^7*e^3 + 15*a^2*c^3*d^5*e^5)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(120*c^5*d^10*e + 340*a*c^4*d^8*e^3 + 309*a^2*c^3*d^6*e^5 + 147*a^3*c^2*d^4*e^7 + 82*a^4*c*d^2*e^9 + 24*a^5*e^11 + (274*c^5*d^6*e^5 + 777*a*c^4*d^4*e^7 + 687*a^2*c^3*d^2*e^9 + 184*a^3*c^2*e^11)*x^4 + 5*(154*c^5*d^7*e^4 + 429*a*c^4*d^5*e^6 + 360*a^2*c^3*d^3*e^8 + 85*a^3*c^2*d*e^10)*x^3 + (940*c^5*d^8*e^3 + 2683*a*c^4*d^6*e^5 + 2364*a^2*c^3*d^4*e^7 + 709*a^3*c^2*d^2*e^9 + 88*a^4*c*e^11)*x^2 + 5*(108*c^5*d^9*e^2 + 307*a*c^4*d^7*e^4 + 264*a^2*c^3*d^5*e^6 + 75*a^3*c^2*d^3*e^8 + 10*a^4*c*d*e^10)*x)*sqrt(c*x^2 + a))/(c^3*d^11*e^6 + 3*a*c^2*d^9*e^8 + 3*a^2*c*d^7*e^10 + a^3*d^5*e^12 + (c^3*d^6*e^11 + 3*a*c^2*d^4*e^13 + 3*a^2*c*d^2*e^15 + a^3*e^17)*x^5 + 5*(c^3*d^7*e^10 + 3*a*c^2*d^5*e^12 + 3*a^2*c*d^3*e^14 + a^3*d*e^16)*x^4 + 10*(c^3*d^8*e^9 + 3*a*c^2*d^6*e^11 + 3*a^2*c*d^4*e^13 + a^3*d^2*e^15)*x^3 + 10*(c^3*d^9*e^8 + 3*a*c^2*d^7*e^10 + 3*a^2*c*d^5*e^12 + a^3*d^3*e^14)*x^2 + 5*(c^3*d^10*e^7 + 3*a*c^2*d^8*e^9 + 3*a^2*c*d^6*e^11 + a^3*d^4*e^13)*x), 1/120*(15*(8*c^5*d^10 + 20*a*c^4*d^8*e^2 + 15*a^2*c^3*d^6*e^4 + (8*c^5*d^5*e^5 + 20*a*c^4*d^3*e^7 + 15*a^2*c^3*d*e^9)*x^5 + 5*(8*c^5*d^6*e^4 + 20*a*c^4*d^4*e^6 + 15*a^2*c^3*d^2*e^8)*x^4 + 10*(8*c^5*d^7*e^3 + 20*a*c^4*d^5*e^5 + 15*a^2*c^3*d^3*e^7)*x^3 + 10*(8*c^5*d^8*e^2 + 20*a*c^4*d^6*e^4 + 15*a^2*c^3*d^4*e^6)*x^2 + 5*(8*c^5*d^9*e + 20*a*c^4*d^7*e^3 + 15*a^2*c^3*d^5*e^5)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + 60*(c^5*d^11 + 3*a*c^4*d^9*e^2 + 3*a^2*c^3*d^7*e^4 + a^3*c^2*d^5*e^6 + (c^5*d^6*e^5 + 3*a*c^4*d^4*e^7 + 3*a^2*c^3*d^2*e^9 + a^3*c^2*e^11)*x^5 + 5*(c^5*d^7*e^4 + 3*a*c^4*d^5*e^6 + 3*a^2*c^3*d^3*e^8 + a^3*c^2*d*e^10)*x^4 + 10*(c^5*d^8*e^3 + 3*a*c^4*d^6*e^5 + 3*a^2*c^3*d^4*e^7 + a^3*c^2*d^2*e^9)*x^3 + 10*(c^5*d^9*e^2 + 3*a*c^4*d^7*e^4 + 3*a^2*c^3*d^5*e^6 + a^3*c^2*d^3*e^8)*x^2 + 5*(c^5*d^10*e + 3*a*c^4*d^8*e^3 + 3*a^2*c^3*d^6*e^5 + a^3*c^2*d^4*e^7)*x)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - (120*c^5*d^10*e + 340*a*c^4*d^8*e^3 + 309*a^2*c^3*d^6*e^5 + 147*a^3*c^2*d^4*e^7 + 82*a^4*c*d^2*e^9 + 24*a^5*e^11 + (274*c^5*d^6*e^5 + 777*a*c^4*d^4*e^7 + 687*a^2*c^3*d^2*e^9 + 184*a^3*c^2*e^11)*x^4 + 5*(154*c^5*d^7*e^4 + 429*a*c^4*d^5*e^6 + 360*a^2*c^3*d^3*e^8 + 85*a^3*c^2*d*e^10)*x^3 + (940*c^5*d^8*e^3 + 2683*a*c^4*d^6*e^5 + 2364*a^2*c^3*d^4*e^7 + 709*a^3*c^2*d^2*e^9 + 88*a^4*c*e^11)*x^2 + 5*(108*c^5*d^9*e^2 + 307*a*c^4*d^7*e^4 + 264*a^2*c^3*d^5*e^6 + 75*a^3*c^2*d^3*e^8 + 10*a^4*c*d*e^10)*x)*sqrt(c*x^2 + a))/(c^3*d^11*e^6 + 3*a*c^2*d^9*e^8 + 3*a^2*c*d^7*e^10 + a^3*d^5*e^12 + (c^3*d^6*e^11 + 3*a*c^2*d^4*e^13 + 3*a^2*c*d^2*e^15 + a^3*e^17)*x^5 + 5*(c^3*d^7*e^10 + 3*a*c^2*d^5*e^12 + 3*a^2*c*d^3*e^14 + a^3*d*e^16)*x^4 + 10*(c^3*d^8*e^9 + 3*a*c^2*d^6*e^11 + 3*a^2*c*d^4*e^13 + a^3*d^2*e^15)*x^3 + 10*(c^3*d^9*e^8 + 3*a*c^2*d^7*e^10 + 3*a^2*c*d^5*e^12 + a^3*d^3*e^14)*x^2 + 5*(c^3*d^10*e^7 + 3*a*c^2*d^8*e^9 + 3*a^2*c*d^6*e^11 + a^3*d^4*e^13)*x), -1/240*(240*(c^5*d^11 + 3*a*c^4*d^9*e^2 + 3*a^2*c^3*d^7*e^4 + a^3*c^2*d^5*e^6 + (c^5*d^6*e^5 + 3*a*c^4*d^4*e^7 + 3*a^2*c^3*d^2*e^9 + a^3*c^2*e^11)*x^5 + 5*(c^5*d^7*e^4 + 3*a*c^4*d^5*e^6 + 3*a^2*c^3*d^3*e^8 + a^3*c^2*d*e^10)*x^4 + 10*(c^5*d^8*e^3 + 3*a*c^4*d^6*e^5 + 3*a^2*c^3*d^4*e^7 + a^3*c^2*d^2*e^9)*x^3 + 10*(c^5*d^9*e^2 + 3*a*c^4*d^7*e^4 + 3*a^2*c^3*d^5*e^6 + a^3*c^2*d^3*e^8)*x^2 + 5*(c^5*d^10*e + 3*a*c^4*d^8*e^3 + 3*a^2*c^3*d^6*e^5 + a^3*c^2*d^4*e^7)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - 15*(8*c^5*d^10 + 20*a*c^4*d^8*e^2 + 15*a^2*c^3*d^6*e^4 + (8*c^5*d^5*e^5 + 20*a*c^4*d^3*e^7 + 15*a^2*c^3*d*e^9)*x^5 + 5*(8*c^5*d^6*e^4 + 20*a*c^4*d^4*e^6 + 15*a^2*c^3*d^2*e^8)*x^4 + 10*(8*c^5*d^7*e^3 + 20*a*c^4*d^5*e^5 + 15*a^2*c^3*d^3*e^7)*x^3 + 10*(8*c^5*d^8*e^2 + 20*a*c^4*d^6*e^4 + 15*a^2*c^3*d^4*e^6)*x^2 + 5*(8*c^5*d^9*e + 20*a*c^4*d^7*e^3 + 15*a^2*c^3*d^5*e^5)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(120*c^5*d^10*e + 340*a*c^4*d^8*e^3 + 309*a^2*c^3*d^6*e^5 + 147*a^3*c^2*d^4*e^7 + 82*a^4*c*d^2*e^9 + 24*a^5*e^11 + (274*c^5*d^6*e^5 + 777*a*c^4*d^4*e^7 + 687*a^2*c^3*d^2*e^9 + 184*a^3*c^2*e^11)*x^4 + 5*(154*c^5*d^7*e^4 + 429*a*c^4*d^5*e^6 + 360*a^2*c^3*d^3*e^8 + 85*a^3*c^2*d*e^10)*x^3 + (940*c^5*d^8*e^3 + 2683*a*c^4*d^6*e^5 + 2364*a^2*c^3*d^4*e^7 + 709*a^3*c^2*d^2*e^9 + 88*a^4*c*e^11)*x^2 + 5*(108*c^5*d^9*e^2 + 307*a*c^4*d^7*e^4 + 264*a^2*c^3*d^5*e^6 + 75*a^3*c^2*d^3*e^8 + 10*a^4*c*d*e^10)*x)*sqrt(c*x^2 + a))/(c^3*d^11*e^6 + 3*a*c^2*d^9*e^8 + 3*a^2*c*d^7*e^10 + a^3*d^5*e^12 + (c^3*d^6*e^11 + 3*a*c^2*d^4*e^13 + 3*a^2*c*d^2*e^15 + a^3*e^17)*x^5 + 5*(c^3*d^7*e^10 + 3*a*c^2*d^5*e^12 + 3*a^2*c*d^3*e^14 + a^3*d*e^16)*x^4 + 10*(c^3*d^8*e^9 + 3*a*c^2*d^6*e^11 + 3*a^2*c*d^4*e^13 + a^3*d^2*e^15)*x^3 + 10*(c^3*d^9*e^8 + 3*a*c^2*d^7*e^10 + 3*a^2*c*d^5*e^12 + a^3*d^3*e^14)*x^2 + 5*(c^3*d^10*e^7 + 3*a*c^2*d^8*e^9 + 3*a^2*c*d^6*e^11 + a^3*d^4*e^13)*x), 1/120*(15*(8*c^5*d^10 + 20*a*c^4*d^8*e^2 + 15*a^2*c^3*d^6*e^4 + (8*c^5*d^5*e^5 + 20*a*c^4*d^3*e^7 + 15*a^2*c^3*d*e^9)*x^5 + 5*(8*c^5*d^6*e^4 + 20*a*c^4*d^4*e^6 + 15*a^2*c^3*d^2*e^8)*x^4 + 10*(8*c^5*d^7*e^3 + 20*a*c^4*d^5*e^5 + 15*a^2*c^3*d^3*e^7)*x^3 + 10*(8*c^5*d^8*e^2 + 20*a*c^4*d^6*e^4 + 15*a^2*c^3*d^4*e^6)*x^2 + 5*(8*c^5*d^9*e + 20*a*c^4*d^7*e^3 + 15*a^2*c^3*d^5*e^5)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - 120*(c^5*d^11 + 3*a*c^4*d^9*e^2 + 3*a^2*c^3*d^7*e^4 + a^3*c^2*d^5*e^6 + (c^5*d^6*e^5 + 3*a*c^4*d^4*e^7 + 3*a^2*c^3*d^2*e^9 + a^3*c^2*e^11)*x^5 + 5*(c^5*d^7*e^4 + 3*a*c^4*d^5*e^6 + 3*a^2*c^3*d^3*e^8 + a^3*c^2*d*e^10)*x^4 + 10*(c^5*d^8*e^3 + 3*a*c^4*d^6*e^5 + 3*a^2*c^3*d^4*e^7 + a^3*c^2*d^2*e^9)*x^3 + 10*(c^5*d^9*e^2 + 3*a*c^4*d^7*e^4 + 3*a^2*c^3*d^5*e^6 + a^3*c^2*d^3*e^8)*x^2 + 5*(c^5*d^10*e + 3*a*c^4*d^8*e^3 + 3*a^2*c^3*d^6*e^5 + a^3*c^2*d^4*e^7)*x)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (120*c^5*d^10*e + 340*a*c^4*d^8*e^3 + 309*a^2*c^3*d^6*e^5 + 147*a^3*c^2*d^4*e^7 + 82*a^4*c*d^2*e^9 + 24*a^5*e^11 + (274*c^5*d^6*e^5 + 777*a*c^4*d^4*e^7 + 687*a^2*c^3*d^2*e^9 + 184*a^3*c^2*e^11)*x^4 + 5*(154*c^5*d^7*e^4 + 429*a*c^4*d^5*e^6 + 360*a^2*c^3*d^3*e^8 + 85*a^3*c^2*d*e^10)*x^3 + (940*c^5*d^8*e^3 + 2683*a*c^4*d^6*e^5 + 2364*a^2*c^3*d^4*e^7 + 709*a^3*c^2*d^2*e^9 + 88*a^4*c*e^11)*x^2 + 5*(108*c^5*d^9*e^2 + 307*a*c^4*d^7*e^4 + 264*a^2*c^3*d^5*e^6 + 75*a^3*c^2*d^3*e^8 + 10*a^4*c*d*e^10)*x)*sqrt(c*x^2 + a))/(c^3*d^11*e^6 + 3*a*c^2*d^9*e^8 + 3*a^2*c*d^7*e^10 + a^3*d^5*e^12 + (c^3*d^6*e^11 + 3*a*c^2*d^4*e^13 + 3*a^2*c*d^2*e^15 + a^3*e^17)*x^5 + 5*(c^3*d^7*e^10 + 3*a*c^2*d^5*e^12 + 3*a^2*c*d^3*e^14 + a^3*d*e^16)*x^4 + 10*(c^3*d^8*e^9 + 3*a*c^2*d^6*e^11 + 3*a^2*c*d^4*e^13 + a^3*d^2*e^15)*x^3 + 10*(c^3*d^9*e^8 + 3*a*c^2*d^7*e^10 + 3*a^2*c*d^5*e^12 + a^3*d^3*e^14)*x^2 + 5*(c^3*d^10*e^7 + 3*a*c^2*d^8*e^9 + 3*a^2*c*d^6*e^11 + a^3*d^4*e^13)*x)]","B",0
555,1,1929,0,13.690911," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^7,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{3} c^{3} e^{6} x^{6} + 6 \, a^{3} c^{3} d e^{5} x^{5} + 15 \, a^{3} c^{3} d^{2} e^{4} x^{4} + 20 \, a^{3} c^{3} d^{3} e^{3} x^{3} + 15 \, a^{3} c^{3} d^{4} e^{2} x^{2} + 6 \, a^{3} c^{3} d^{5} e x + a^{3} c^{3} d^{6}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(33 \, a^{3} c^{3} d^{6} e + 59 \, a^{4} c^{2} d^{4} e^{3} + 34 \, a^{5} c d^{2} e^{5} + 8 \, a^{6} e^{7} - {\left(8 \, c^{6} d^{7} + 34 \, a c^{5} d^{5} e^{2} + 59 \, a^{2} c^{4} d^{3} e^{4} + 33 \, a^{3} c^{3} d e^{6}\right)} x^{5} - 3 \, {\left(4 \, a c^{5} d^{6} e + 22 \, a^{2} c^{4} d^{4} e^{3} + 7 \, a^{3} c^{3} d^{2} e^{5} - 11 \, a^{4} c^{2} e^{7}\right)} x^{4} - 2 \, {\left(13 \, a c^{5} d^{7} + 74 \, a^{2} c^{4} d^{5} e^{2} + 34 \, a^{3} c^{3} d^{3} e^{4} - 27 \, a^{4} c^{2} d e^{6}\right)} x^{3} - 2 \, {\left(27 \, a^{2} c^{4} d^{6} e - 34 \, a^{3} c^{3} d^{4} e^{3} - 74 \, a^{4} c^{2} d^{2} e^{5} - 13 \, a^{5} c e^{7}\right)} x^{2} - 3 \, {\left(11 \, a^{2} c^{4} d^{7} - 7 \, a^{3} c^{3} d^{5} e^{2} - 22 \, a^{4} c^{2} d^{3} e^{4} - 4 \, a^{5} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{96 \, {\left(c^{4} d^{14} + 4 \, a c^{3} d^{12} e^{2} + 6 \, a^{2} c^{2} d^{10} e^{4} + 4 \, a^{3} c d^{8} e^{6} + a^{4} d^{6} e^{8} + {\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)} x^{6} + 6 \, {\left(c^{4} d^{9} e^{5} + 4 \, a c^{3} d^{7} e^{7} + 6 \, a^{2} c^{2} d^{5} e^{9} + 4 \, a^{3} c d^{3} e^{11} + a^{4} d e^{13}\right)} x^{5} + 15 \, {\left(c^{4} d^{10} e^{4} + 4 \, a c^{3} d^{8} e^{6} + 6 \, a^{2} c^{2} d^{6} e^{8} + 4 \, a^{3} c d^{4} e^{10} + a^{4} d^{2} e^{12}\right)} x^{4} + 20 \, {\left(c^{4} d^{11} e^{3} + 4 \, a c^{3} d^{9} e^{5} + 6 \, a^{2} c^{2} d^{7} e^{7} + 4 \, a^{3} c d^{5} e^{9} + a^{4} d^{3} e^{11}\right)} x^{3} + 15 \, {\left(c^{4} d^{12} e^{2} + 4 \, a c^{3} d^{10} e^{4} + 6 \, a^{2} c^{2} d^{8} e^{6} + 4 \, a^{3} c d^{6} e^{8} + a^{4} d^{4} e^{10}\right)} x^{2} + 6 \, {\left(c^{4} d^{13} e + 4 \, a c^{3} d^{11} e^{3} + 6 \, a^{2} c^{2} d^{9} e^{5} + 4 \, a^{3} c d^{7} e^{7} + a^{4} d^{5} e^{9}\right)} x\right)}}, -\frac{15 \, {\left(a^{3} c^{3} e^{6} x^{6} + 6 \, a^{3} c^{3} d e^{5} x^{5} + 15 \, a^{3} c^{3} d^{2} e^{4} x^{4} + 20 \, a^{3} c^{3} d^{3} e^{3} x^{3} + 15 \, a^{3} c^{3} d^{4} e^{2} x^{2} + 6 \, a^{3} c^{3} d^{5} e x + a^{3} c^{3} d^{6}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(33 \, a^{3} c^{3} d^{6} e + 59 \, a^{4} c^{2} d^{4} e^{3} + 34 \, a^{5} c d^{2} e^{5} + 8 \, a^{6} e^{7} - {\left(8 \, c^{6} d^{7} + 34 \, a c^{5} d^{5} e^{2} + 59 \, a^{2} c^{4} d^{3} e^{4} + 33 \, a^{3} c^{3} d e^{6}\right)} x^{5} - 3 \, {\left(4 \, a c^{5} d^{6} e + 22 \, a^{2} c^{4} d^{4} e^{3} + 7 \, a^{3} c^{3} d^{2} e^{5} - 11 \, a^{4} c^{2} e^{7}\right)} x^{4} - 2 \, {\left(13 \, a c^{5} d^{7} + 74 \, a^{2} c^{4} d^{5} e^{2} + 34 \, a^{3} c^{3} d^{3} e^{4} - 27 \, a^{4} c^{2} d e^{6}\right)} x^{3} - 2 \, {\left(27 \, a^{2} c^{4} d^{6} e - 34 \, a^{3} c^{3} d^{4} e^{3} - 74 \, a^{4} c^{2} d^{2} e^{5} - 13 \, a^{5} c e^{7}\right)} x^{2} - 3 \, {\left(11 \, a^{2} c^{4} d^{7} - 7 \, a^{3} c^{3} d^{5} e^{2} - 22 \, a^{4} c^{2} d^{3} e^{4} - 4 \, a^{5} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, {\left(c^{4} d^{14} + 4 \, a c^{3} d^{12} e^{2} + 6 \, a^{2} c^{2} d^{10} e^{4} + 4 \, a^{3} c d^{8} e^{6} + a^{4} d^{6} e^{8} + {\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)} x^{6} + 6 \, {\left(c^{4} d^{9} e^{5} + 4 \, a c^{3} d^{7} e^{7} + 6 \, a^{2} c^{2} d^{5} e^{9} + 4 \, a^{3} c d^{3} e^{11} + a^{4} d e^{13}\right)} x^{5} + 15 \, {\left(c^{4} d^{10} e^{4} + 4 \, a c^{3} d^{8} e^{6} + 6 \, a^{2} c^{2} d^{6} e^{8} + 4 \, a^{3} c d^{4} e^{10} + a^{4} d^{2} e^{12}\right)} x^{4} + 20 \, {\left(c^{4} d^{11} e^{3} + 4 \, a c^{3} d^{9} e^{5} + 6 \, a^{2} c^{2} d^{7} e^{7} + 4 \, a^{3} c d^{5} e^{9} + a^{4} d^{3} e^{11}\right)} x^{3} + 15 \, {\left(c^{4} d^{12} e^{2} + 4 \, a c^{3} d^{10} e^{4} + 6 \, a^{2} c^{2} d^{8} e^{6} + 4 \, a^{3} c d^{6} e^{8} + a^{4} d^{4} e^{10}\right)} x^{2} + 6 \, {\left(c^{4} d^{13} e + 4 \, a c^{3} d^{11} e^{3} + 6 \, a^{2} c^{2} d^{9} e^{5} + 4 \, a^{3} c d^{7} e^{7} + a^{4} d^{5} e^{9}\right)} x\right)}}\right]"," ",0,"[1/96*(15*(a^3*c^3*e^6*x^6 + 6*a^3*c^3*d*e^5*x^5 + 15*a^3*c^3*d^2*e^4*x^4 + 20*a^3*c^3*d^3*e^3*x^3 + 15*a^3*c^3*d^4*e^2*x^2 + 6*a^3*c^3*d^5*e*x + a^3*c^3*d^6)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(33*a^3*c^3*d^6*e + 59*a^4*c^2*d^4*e^3 + 34*a^5*c*d^2*e^5 + 8*a^6*e^7 - (8*c^6*d^7 + 34*a*c^5*d^5*e^2 + 59*a^2*c^4*d^3*e^4 + 33*a^3*c^3*d*e^6)*x^5 - 3*(4*a*c^5*d^6*e + 22*a^2*c^4*d^4*e^3 + 7*a^3*c^3*d^2*e^5 - 11*a^4*c^2*e^7)*x^4 - 2*(13*a*c^5*d^7 + 74*a^2*c^4*d^5*e^2 + 34*a^3*c^3*d^3*e^4 - 27*a^4*c^2*d*e^6)*x^3 - 2*(27*a^2*c^4*d^6*e - 34*a^3*c^3*d^4*e^3 - 74*a^4*c^2*d^2*e^5 - 13*a^5*c*e^7)*x^2 - 3*(11*a^2*c^4*d^7 - 7*a^3*c^3*d^5*e^2 - 22*a^4*c^2*d^3*e^4 - 4*a^5*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^14 + 4*a*c^3*d^12*e^2 + 6*a^2*c^2*d^10*e^4 + 4*a^3*c*d^8*e^6 + a^4*d^6*e^8 + (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)*x^6 + 6*(c^4*d^9*e^5 + 4*a*c^3*d^7*e^7 + 6*a^2*c^2*d^5*e^9 + 4*a^3*c*d^3*e^11 + a^4*d*e^13)*x^5 + 15*(c^4*d^10*e^4 + 4*a*c^3*d^8*e^6 + 6*a^2*c^2*d^6*e^8 + 4*a^3*c*d^4*e^10 + a^4*d^2*e^12)*x^4 + 20*(c^4*d^11*e^3 + 4*a*c^3*d^9*e^5 + 6*a^2*c^2*d^7*e^7 + 4*a^3*c*d^5*e^9 + a^4*d^3*e^11)*x^3 + 15*(c^4*d^12*e^2 + 4*a*c^3*d^10*e^4 + 6*a^2*c^2*d^8*e^6 + 4*a^3*c*d^6*e^8 + a^4*d^4*e^10)*x^2 + 6*(c^4*d^13*e + 4*a*c^3*d^11*e^3 + 6*a^2*c^2*d^9*e^5 + 4*a^3*c*d^7*e^7 + a^4*d^5*e^9)*x), -1/48*(15*(a^3*c^3*e^6*x^6 + 6*a^3*c^3*d*e^5*x^5 + 15*a^3*c^3*d^2*e^4*x^4 + 20*a^3*c^3*d^3*e^3*x^3 + 15*a^3*c^3*d^4*e^2*x^2 + 6*a^3*c^3*d^5*e*x + a^3*c^3*d^6)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (33*a^3*c^3*d^6*e + 59*a^4*c^2*d^4*e^3 + 34*a^5*c*d^2*e^5 + 8*a^6*e^7 - (8*c^6*d^7 + 34*a*c^5*d^5*e^2 + 59*a^2*c^4*d^3*e^4 + 33*a^3*c^3*d*e^6)*x^5 - 3*(4*a*c^5*d^6*e + 22*a^2*c^4*d^4*e^3 + 7*a^3*c^3*d^2*e^5 - 11*a^4*c^2*e^7)*x^4 - 2*(13*a*c^5*d^7 + 74*a^2*c^4*d^5*e^2 + 34*a^3*c^3*d^3*e^4 - 27*a^4*c^2*d*e^6)*x^3 - 2*(27*a^2*c^4*d^6*e - 34*a^3*c^3*d^4*e^3 - 74*a^4*c^2*d^2*e^5 - 13*a^5*c*e^7)*x^2 - 3*(11*a^2*c^4*d^7 - 7*a^3*c^3*d^5*e^2 - 22*a^4*c^2*d^3*e^4 - 4*a^5*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^14 + 4*a*c^3*d^12*e^2 + 6*a^2*c^2*d^10*e^4 + 4*a^3*c*d^8*e^6 + a^4*d^6*e^8 + (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)*x^6 + 6*(c^4*d^9*e^5 + 4*a*c^3*d^7*e^7 + 6*a^2*c^2*d^5*e^9 + 4*a^3*c*d^3*e^11 + a^4*d*e^13)*x^5 + 15*(c^4*d^10*e^4 + 4*a*c^3*d^8*e^6 + 6*a^2*c^2*d^6*e^8 + 4*a^3*c*d^4*e^10 + a^4*d^2*e^12)*x^4 + 20*(c^4*d^11*e^3 + 4*a*c^3*d^9*e^5 + 6*a^2*c^2*d^7*e^7 + 4*a^3*c*d^5*e^9 + a^4*d^3*e^11)*x^3 + 15*(c^4*d^12*e^2 + 4*a*c^3*d^10*e^4 + 6*a^2*c^2*d^8*e^6 + 4*a^3*c*d^6*e^8 + a^4*d^4*e^10)*x^2 + 6*(c^4*d^13*e + 4*a*c^3*d^11*e^3 + 6*a^2*c^2*d^9*e^5 + 4*a^3*c*d^7*e^7 + a^4*d^5*e^9)*x)]","B",0
556,1,2593,0,29.204923," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^8,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{3} c^{4} d e^{7} x^{7} + 7 \, a^{3} c^{4} d^{2} e^{6} x^{6} + 21 \, a^{3} c^{4} d^{3} e^{5} x^{5} + 35 \, a^{3} c^{4} d^{4} e^{4} x^{4} + 35 \, a^{3} c^{4} d^{5} e^{3} x^{3} + 21 \, a^{3} c^{4} d^{6} e^{2} x^{2} + 7 \, a^{3} c^{4} d^{7} e x + a^{3} c^{4} d^{8}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(279 \, a^{3} c^{4} d^{8} e + 605 \, a^{4} c^{3} d^{6} e^{3} + 526 \, a^{5} c^{2} d^{4} e^{5} + 248 \, a^{6} c d^{2} e^{7} + 48 \, a^{7} e^{9} - {\left(8 \, c^{7} d^{8} e + 46 \, a c^{6} d^{6} e^{3} + 125 \, a^{2} c^{5} d^{4} e^{5} + 39 \, a^{3} c^{4} d^{2} e^{7} - 48 \, a^{4} c^{3} e^{9}\right)} x^{6} - 7 \, {\left(8 \, c^{7} d^{9} + 46 \, a c^{6} d^{7} e^{2} + 125 \, a^{2} c^{5} d^{5} e^{4} + 54 \, a^{3} c^{4} d^{3} e^{6} - 33 \, a^{4} c^{3} d e^{8}\right)} x^{5} - {\left(122 \, a c^{6} d^{8} e + 922 \, a^{2} c^{5} d^{6} e^{3} - 241 \, a^{3} c^{4} d^{4} e^{5} - 1185 \, a^{4} c^{3} d^{2} e^{7} - 144 \, a^{5} c^{2} e^{9}\right)} x^{4} - 14 \, {\left(13 \, a c^{6} d^{9} + 101 \, a^{2} c^{5} d^{7} e^{2} - 101 \, a^{4} c^{3} d^{3} e^{6} - 13 \, a^{5} c^{2} d e^{8}\right)} x^{3} - {\left(465 \, a^{2} c^{5} d^{8} e - 1199 \, a^{3} c^{4} d^{6} e^{3} - 2362 \, a^{4} c^{3} d^{4} e^{5} - 842 \, a^{5} c^{2} d^{2} e^{7} - 144 \, a^{6} c e^{9}\right)} x^{2} - 7 \, {\left(33 \, a^{2} c^{5} d^{9} - 54 \, a^{3} c^{4} d^{7} e^{2} - 125 \, a^{4} c^{3} d^{5} e^{4} - 46 \, a^{5} c^{2} d^{3} e^{6} - 8 \, a^{6} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{672 \, {\left(c^{5} d^{17} + 5 \, a c^{4} d^{15} e^{2} + 10 \, a^{2} c^{3} d^{13} e^{4} + 10 \, a^{3} c^{2} d^{11} e^{6} + 5 \, a^{4} c d^{9} e^{8} + a^{5} d^{7} e^{10} + {\left(c^{5} d^{10} e^{7} + 5 \, a c^{4} d^{8} e^{9} + 10 \, a^{2} c^{3} d^{6} e^{11} + 10 \, a^{3} c^{2} d^{4} e^{13} + 5 \, a^{4} c d^{2} e^{15} + a^{5} e^{17}\right)} x^{7} + 7 \, {\left(c^{5} d^{11} e^{6} + 5 \, a c^{4} d^{9} e^{8} + 10 \, a^{2} c^{3} d^{7} e^{10} + 10 \, a^{3} c^{2} d^{5} e^{12} + 5 \, a^{4} c d^{3} e^{14} + a^{5} d e^{16}\right)} x^{6} + 21 \, {\left(c^{5} d^{12} e^{5} + 5 \, a c^{4} d^{10} e^{7} + 10 \, a^{2} c^{3} d^{8} e^{9} + 10 \, a^{3} c^{2} d^{6} e^{11} + 5 \, a^{4} c d^{4} e^{13} + a^{5} d^{2} e^{15}\right)} x^{5} + 35 \, {\left(c^{5} d^{13} e^{4} + 5 \, a c^{4} d^{11} e^{6} + 10 \, a^{2} c^{3} d^{9} e^{8} + 10 \, a^{3} c^{2} d^{7} e^{10} + 5 \, a^{4} c d^{5} e^{12} + a^{5} d^{3} e^{14}\right)} x^{4} + 35 \, {\left(c^{5} d^{14} e^{3} + 5 \, a c^{4} d^{12} e^{5} + 10 \, a^{2} c^{3} d^{10} e^{7} + 10 \, a^{3} c^{2} d^{8} e^{9} + 5 \, a^{4} c d^{6} e^{11} + a^{5} d^{4} e^{13}\right)} x^{3} + 21 \, {\left(c^{5} d^{15} e^{2} + 5 \, a c^{4} d^{13} e^{4} + 10 \, a^{2} c^{3} d^{11} e^{6} + 10 \, a^{3} c^{2} d^{9} e^{8} + 5 \, a^{4} c d^{7} e^{10} + a^{5} d^{5} e^{12}\right)} x^{2} + 7 \, {\left(c^{5} d^{16} e + 5 \, a c^{4} d^{14} e^{3} + 10 \, a^{2} c^{3} d^{12} e^{5} + 10 \, a^{3} c^{2} d^{10} e^{7} + 5 \, a^{4} c d^{8} e^{9} + a^{5} d^{6} e^{11}\right)} x\right)}}, -\frac{105 \, {\left(a^{3} c^{4} d e^{7} x^{7} + 7 \, a^{3} c^{4} d^{2} e^{6} x^{6} + 21 \, a^{3} c^{4} d^{3} e^{5} x^{5} + 35 \, a^{3} c^{4} d^{4} e^{4} x^{4} + 35 \, a^{3} c^{4} d^{5} e^{3} x^{3} + 21 \, a^{3} c^{4} d^{6} e^{2} x^{2} + 7 \, a^{3} c^{4} d^{7} e x + a^{3} c^{4} d^{8}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(279 \, a^{3} c^{4} d^{8} e + 605 \, a^{4} c^{3} d^{6} e^{3} + 526 \, a^{5} c^{2} d^{4} e^{5} + 248 \, a^{6} c d^{2} e^{7} + 48 \, a^{7} e^{9} - {\left(8 \, c^{7} d^{8} e + 46 \, a c^{6} d^{6} e^{3} + 125 \, a^{2} c^{5} d^{4} e^{5} + 39 \, a^{3} c^{4} d^{2} e^{7} - 48 \, a^{4} c^{3} e^{9}\right)} x^{6} - 7 \, {\left(8 \, c^{7} d^{9} + 46 \, a c^{6} d^{7} e^{2} + 125 \, a^{2} c^{5} d^{5} e^{4} + 54 \, a^{3} c^{4} d^{3} e^{6} - 33 \, a^{4} c^{3} d e^{8}\right)} x^{5} - {\left(122 \, a c^{6} d^{8} e + 922 \, a^{2} c^{5} d^{6} e^{3} - 241 \, a^{3} c^{4} d^{4} e^{5} - 1185 \, a^{4} c^{3} d^{2} e^{7} - 144 \, a^{5} c^{2} e^{9}\right)} x^{4} - 14 \, {\left(13 \, a c^{6} d^{9} + 101 \, a^{2} c^{5} d^{7} e^{2} - 101 \, a^{4} c^{3} d^{3} e^{6} - 13 \, a^{5} c^{2} d e^{8}\right)} x^{3} - {\left(465 \, a^{2} c^{5} d^{8} e - 1199 \, a^{3} c^{4} d^{6} e^{3} - 2362 \, a^{4} c^{3} d^{4} e^{5} - 842 \, a^{5} c^{2} d^{2} e^{7} - 144 \, a^{6} c e^{9}\right)} x^{2} - 7 \, {\left(33 \, a^{2} c^{5} d^{9} - 54 \, a^{3} c^{4} d^{7} e^{2} - 125 \, a^{4} c^{3} d^{5} e^{4} - 46 \, a^{5} c^{2} d^{3} e^{6} - 8 \, a^{6} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{336 \, {\left(c^{5} d^{17} + 5 \, a c^{4} d^{15} e^{2} + 10 \, a^{2} c^{3} d^{13} e^{4} + 10 \, a^{3} c^{2} d^{11} e^{6} + 5 \, a^{4} c d^{9} e^{8} + a^{5} d^{7} e^{10} + {\left(c^{5} d^{10} e^{7} + 5 \, a c^{4} d^{8} e^{9} + 10 \, a^{2} c^{3} d^{6} e^{11} + 10 \, a^{3} c^{2} d^{4} e^{13} + 5 \, a^{4} c d^{2} e^{15} + a^{5} e^{17}\right)} x^{7} + 7 \, {\left(c^{5} d^{11} e^{6} + 5 \, a c^{4} d^{9} e^{8} + 10 \, a^{2} c^{3} d^{7} e^{10} + 10 \, a^{3} c^{2} d^{5} e^{12} + 5 \, a^{4} c d^{3} e^{14} + a^{5} d e^{16}\right)} x^{6} + 21 \, {\left(c^{5} d^{12} e^{5} + 5 \, a c^{4} d^{10} e^{7} + 10 \, a^{2} c^{3} d^{8} e^{9} + 10 \, a^{3} c^{2} d^{6} e^{11} + 5 \, a^{4} c d^{4} e^{13} + a^{5} d^{2} e^{15}\right)} x^{5} + 35 \, {\left(c^{5} d^{13} e^{4} + 5 \, a c^{4} d^{11} e^{6} + 10 \, a^{2} c^{3} d^{9} e^{8} + 10 \, a^{3} c^{2} d^{7} e^{10} + 5 \, a^{4} c d^{5} e^{12} + a^{5} d^{3} e^{14}\right)} x^{4} + 35 \, {\left(c^{5} d^{14} e^{3} + 5 \, a c^{4} d^{12} e^{5} + 10 \, a^{2} c^{3} d^{10} e^{7} + 10 \, a^{3} c^{2} d^{8} e^{9} + 5 \, a^{4} c d^{6} e^{11} + a^{5} d^{4} e^{13}\right)} x^{3} + 21 \, {\left(c^{5} d^{15} e^{2} + 5 \, a c^{4} d^{13} e^{4} + 10 \, a^{2} c^{3} d^{11} e^{6} + 10 \, a^{3} c^{2} d^{9} e^{8} + 5 \, a^{4} c d^{7} e^{10} + a^{5} d^{5} e^{12}\right)} x^{2} + 7 \, {\left(c^{5} d^{16} e + 5 \, a c^{4} d^{14} e^{3} + 10 \, a^{2} c^{3} d^{12} e^{5} + 10 \, a^{3} c^{2} d^{10} e^{7} + 5 \, a^{4} c d^{8} e^{9} + a^{5} d^{6} e^{11}\right)} x\right)}}\right]"," ",0,"[1/672*(105*(a^3*c^4*d*e^7*x^7 + 7*a^3*c^4*d^2*e^6*x^6 + 21*a^3*c^4*d^3*e^5*x^5 + 35*a^3*c^4*d^4*e^4*x^4 + 35*a^3*c^4*d^5*e^3*x^3 + 21*a^3*c^4*d^6*e^2*x^2 + 7*a^3*c^4*d^7*e*x + a^3*c^4*d^8)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(279*a^3*c^4*d^8*e + 605*a^4*c^3*d^6*e^3 + 526*a^5*c^2*d^4*e^5 + 248*a^6*c*d^2*e^7 + 48*a^7*e^9 - (8*c^7*d^8*e + 46*a*c^6*d^6*e^3 + 125*a^2*c^5*d^4*e^5 + 39*a^3*c^4*d^2*e^7 - 48*a^4*c^3*e^9)*x^6 - 7*(8*c^7*d^9 + 46*a*c^6*d^7*e^2 + 125*a^2*c^5*d^5*e^4 + 54*a^3*c^4*d^3*e^6 - 33*a^4*c^3*d*e^8)*x^5 - (122*a*c^6*d^8*e + 922*a^2*c^5*d^6*e^3 - 241*a^3*c^4*d^4*e^5 - 1185*a^4*c^3*d^2*e^7 - 144*a^5*c^2*e^9)*x^4 - 14*(13*a*c^6*d^9 + 101*a^2*c^5*d^7*e^2 - 101*a^4*c^3*d^3*e^6 - 13*a^5*c^2*d*e^8)*x^3 - (465*a^2*c^5*d^8*e - 1199*a^3*c^4*d^6*e^3 - 2362*a^4*c^3*d^4*e^5 - 842*a^5*c^2*d^2*e^7 - 144*a^6*c*e^9)*x^2 - 7*(33*a^2*c^5*d^9 - 54*a^3*c^4*d^7*e^2 - 125*a^4*c^3*d^5*e^4 - 46*a^5*c^2*d^3*e^6 - 8*a^6*c*d*e^8)*x)*sqrt(c*x^2 + a))/(c^5*d^17 + 5*a*c^4*d^15*e^2 + 10*a^2*c^3*d^13*e^4 + 10*a^3*c^2*d^11*e^6 + 5*a^4*c*d^9*e^8 + a^5*d^7*e^10 + (c^5*d^10*e^7 + 5*a*c^4*d^8*e^9 + 10*a^2*c^3*d^6*e^11 + 10*a^3*c^2*d^4*e^13 + 5*a^4*c*d^2*e^15 + a^5*e^17)*x^7 + 7*(c^5*d^11*e^6 + 5*a*c^4*d^9*e^8 + 10*a^2*c^3*d^7*e^10 + 10*a^3*c^2*d^5*e^12 + 5*a^4*c*d^3*e^14 + a^5*d*e^16)*x^6 + 21*(c^5*d^12*e^5 + 5*a*c^4*d^10*e^7 + 10*a^2*c^3*d^8*e^9 + 10*a^3*c^2*d^6*e^11 + 5*a^4*c*d^4*e^13 + a^5*d^2*e^15)*x^5 + 35*(c^5*d^13*e^4 + 5*a*c^4*d^11*e^6 + 10*a^2*c^3*d^9*e^8 + 10*a^3*c^2*d^7*e^10 + 5*a^4*c*d^5*e^12 + a^5*d^3*e^14)*x^4 + 35*(c^5*d^14*e^3 + 5*a*c^4*d^12*e^5 + 10*a^2*c^3*d^10*e^7 + 10*a^3*c^2*d^8*e^9 + 5*a^4*c*d^6*e^11 + a^5*d^4*e^13)*x^3 + 21*(c^5*d^15*e^2 + 5*a*c^4*d^13*e^4 + 10*a^2*c^3*d^11*e^6 + 10*a^3*c^2*d^9*e^8 + 5*a^4*c*d^7*e^10 + a^5*d^5*e^12)*x^2 + 7*(c^5*d^16*e + 5*a*c^4*d^14*e^3 + 10*a^2*c^3*d^12*e^5 + 10*a^3*c^2*d^10*e^7 + 5*a^4*c*d^8*e^9 + a^5*d^6*e^11)*x), -1/336*(105*(a^3*c^4*d*e^7*x^7 + 7*a^3*c^4*d^2*e^6*x^6 + 21*a^3*c^4*d^3*e^5*x^5 + 35*a^3*c^4*d^4*e^4*x^4 + 35*a^3*c^4*d^5*e^3*x^3 + 21*a^3*c^4*d^6*e^2*x^2 + 7*a^3*c^4*d^7*e*x + a^3*c^4*d^8)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (279*a^3*c^4*d^8*e + 605*a^4*c^3*d^6*e^3 + 526*a^5*c^2*d^4*e^5 + 248*a^6*c*d^2*e^7 + 48*a^7*e^9 - (8*c^7*d^8*e + 46*a*c^6*d^6*e^3 + 125*a^2*c^5*d^4*e^5 + 39*a^3*c^4*d^2*e^7 - 48*a^4*c^3*e^9)*x^6 - 7*(8*c^7*d^9 + 46*a*c^6*d^7*e^2 + 125*a^2*c^5*d^5*e^4 + 54*a^3*c^4*d^3*e^6 - 33*a^4*c^3*d*e^8)*x^5 - (122*a*c^6*d^8*e + 922*a^2*c^5*d^6*e^3 - 241*a^3*c^4*d^4*e^5 - 1185*a^4*c^3*d^2*e^7 - 144*a^5*c^2*e^9)*x^4 - 14*(13*a*c^6*d^9 + 101*a^2*c^5*d^7*e^2 - 101*a^4*c^3*d^3*e^6 - 13*a^5*c^2*d*e^8)*x^3 - (465*a^2*c^5*d^8*e - 1199*a^3*c^4*d^6*e^3 - 2362*a^4*c^3*d^4*e^5 - 842*a^5*c^2*d^2*e^7 - 144*a^6*c*e^9)*x^2 - 7*(33*a^2*c^5*d^9 - 54*a^3*c^4*d^7*e^2 - 125*a^4*c^3*d^5*e^4 - 46*a^5*c^2*d^3*e^6 - 8*a^6*c*d*e^8)*x)*sqrt(c*x^2 + a))/(c^5*d^17 + 5*a*c^4*d^15*e^2 + 10*a^2*c^3*d^13*e^4 + 10*a^3*c^2*d^11*e^6 + 5*a^4*c*d^9*e^8 + a^5*d^7*e^10 + (c^5*d^10*e^7 + 5*a*c^4*d^8*e^9 + 10*a^2*c^3*d^6*e^11 + 10*a^3*c^2*d^4*e^13 + 5*a^4*c*d^2*e^15 + a^5*e^17)*x^7 + 7*(c^5*d^11*e^6 + 5*a*c^4*d^9*e^8 + 10*a^2*c^3*d^7*e^10 + 10*a^3*c^2*d^5*e^12 + 5*a^4*c*d^3*e^14 + a^5*d*e^16)*x^6 + 21*(c^5*d^12*e^5 + 5*a*c^4*d^10*e^7 + 10*a^2*c^3*d^8*e^9 + 10*a^3*c^2*d^6*e^11 + 5*a^4*c*d^4*e^13 + a^5*d^2*e^15)*x^5 + 35*(c^5*d^13*e^4 + 5*a*c^4*d^11*e^6 + 10*a^2*c^3*d^9*e^8 + 10*a^3*c^2*d^7*e^10 + 5*a^4*c*d^5*e^12 + a^5*d^3*e^14)*x^4 + 35*(c^5*d^14*e^3 + 5*a*c^4*d^12*e^5 + 10*a^2*c^3*d^10*e^7 + 10*a^3*c^2*d^8*e^9 + 5*a^4*c*d^6*e^11 + a^5*d^4*e^13)*x^3 + 21*(c^5*d^15*e^2 + 5*a*c^4*d^13*e^4 + 10*a^2*c^3*d^11*e^6 + 10*a^3*c^2*d^9*e^8 + 5*a^4*c*d^7*e^10 + a^5*d^5*e^12)*x^2 + 7*(c^5*d^16*e + 5*a*c^4*d^14*e^3 + 10*a^2*c^3*d^12*e^5 + 10*a^3*c^2*d^10*e^7 + 5*a^4*c*d^8*e^9 + a^5*d^6*e^11)*x)]","B",0
557,1,3693,0,59.580958," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^9,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(8 \, a^{3} c^{5} d^{10} - a^{4} c^{4} d^{8} e^{2} + {\left(8 \, a^{3} c^{5} d^{2} e^{8} - a^{4} c^{4} e^{10}\right)} x^{8} + 8 \, {\left(8 \, a^{3} c^{5} d^{3} e^{7} - a^{4} c^{4} d e^{9}\right)} x^{7} + 28 \, {\left(8 \, a^{3} c^{5} d^{4} e^{6} - a^{4} c^{4} d^{2} e^{8}\right)} x^{6} + 56 \, {\left(8 \, a^{3} c^{5} d^{5} e^{5} - a^{4} c^{4} d^{3} e^{7}\right)} x^{5} + 70 \, {\left(8 \, a^{3} c^{5} d^{6} e^{4} - a^{4} c^{4} d^{4} e^{6}\right)} x^{4} + 56 \, {\left(8 \, a^{3} c^{5} d^{7} e^{3} - a^{4} c^{4} d^{5} e^{5}\right)} x^{3} + 28 \, {\left(8 \, a^{3} c^{5} d^{8} e^{2} - a^{4} c^{4} d^{6} e^{4}\right)} x^{2} + 8 \, {\left(8 \, a^{3} c^{5} d^{9} e - a^{4} c^{4} d^{7} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(2616 \, a^{3} c^{5} d^{10} e + 6481 \, a^{4} c^{4} d^{8} e^{3} + 7443 \, a^{5} c^{3} d^{6} e^{5} + 5298 \, a^{6} c^{2} d^{4} e^{7} + 2056 \, a^{7} c d^{2} e^{9} + 336 \, a^{8} e^{11} - {\left(16 \, c^{8} d^{9} e^{2} + 120 \, a c^{7} d^{7} e^{4} + 474 \, a^{2} c^{6} d^{5} e^{6} - 293 \, a^{3} c^{5} d^{3} e^{8} - 663 \, a^{4} c^{4} d e^{10}\right)} x^{7} - {\left(128 \, c^{8} d^{10} e + 960 \, a c^{7} d^{8} e^{3} + 3792 \, a^{2} c^{6} d^{6} e^{5} - 1504 \, a^{3} c^{5} d^{4} e^{7} - 4569 \, a^{4} c^{4} d^{2} e^{9} - 105 \, a^{5} c^{3} e^{11}\right)} x^{6} - {\left(448 \, c^{8} d^{11} + 3352 \, a c^{7} d^{9} e^{2} + 13212 \, a^{2} c^{6} d^{7} e^{4} - 2141 \, a^{3} c^{5} d^{5} e^{6} - 12905 \, a^{4} c^{4} d^{3} e^{8} - 456 \, a^{5} c^{3} d e^{10}\right)} x^{5} - {\left(1280 \, a c^{7} d^{10} e + 12624 \, a^{2} c^{6} d^{8} e^{3} - 15784 \, a^{3} c^{5} d^{6} e^{5} - 32071 \, a^{4} c^{4} d^{4} e^{7} - 5769 \, a^{5} c^{3} d^{2} e^{9} - 826 \, a^{6} c^{2} e^{11}\right)} x^{4} - {\left(1456 \, a c^{7} d^{11} + 14706 \, a^{2} c^{6} d^{9} e^{2} - 12191 \, a^{3} c^{5} d^{7} e^{4} - 30449 \, a^{4} c^{4} d^{5} e^{6} - 5856 \, a^{5} c^{3} d^{3} e^{8} - 848 \, a^{6} c^{2} d e^{10}\right)} x^{3} - {\left(4416 \, a^{2} c^{6} d^{10} e - 19072 \, a^{3} c^{5} d^{8} e^{3} - 35839 \, a^{4} c^{4} d^{6} e^{5} - 17595 \, a^{5} c^{3} d^{4} e^{7} - 6196 \, a^{6} c^{2} d^{2} e^{9} - 952 \, a^{7} c e^{11}\right)} x^{2} - {\left(1848 \, a^{2} c^{6} d^{11} - 5535 \, a^{3} c^{5} d^{9} e^{2} - 11423 \, a^{4} c^{4} d^{7} e^{4} - 5784 \, a^{5} c^{3} d^{5} e^{6} - 2064 \, a^{6} c^{2} d^{3} e^{8} - 320 \, a^{7} c d e^{10}\right)} x\right)} \sqrt{c x^{2} + a}}{5376 \, {\left(c^{6} d^{20} + 6 \, a c^{5} d^{18} e^{2} + 15 \, a^{2} c^{4} d^{16} e^{4} + 20 \, a^{3} c^{3} d^{14} e^{6} + 15 \, a^{4} c^{2} d^{12} e^{8} + 6 \, a^{5} c d^{10} e^{10} + a^{6} d^{8} e^{12} + {\left(c^{6} d^{12} e^{8} + 6 \, a c^{5} d^{10} e^{10} + 15 \, a^{2} c^{4} d^{8} e^{12} + 20 \, a^{3} c^{3} d^{6} e^{14} + 15 \, a^{4} c^{2} d^{4} e^{16} + 6 \, a^{5} c d^{2} e^{18} + a^{6} e^{20}\right)} x^{8} + 8 \, {\left(c^{6} d^{13} e^{7} + 6 \, a c^{5} d^{11} e^{9} + 15 \, a^{2} c^{4} d^{9} e^{11} + 20 \, a^{3} c^{3} d^{7} e^{13} + 15 \, a^{4} c^{2} d^{5} e^{15} + 6 \, a^{5} c d^{3} e^{17} + a^{6} d e^{19}\right)} x^{7} + 28 \, {\left(c^{6} d^{14} e^{6} + 6 \, a c^{5} d^{12} e^{8} + 15 \, a^{2} c^{4} d^{10} e^{10} + 20 \, a^{3} c^{3} d^{8} e^{12} + 15 \, a^{4} c^{2} d^{6} e^{14} + 6 \, a^{5} c d^{4} e^{16} + a^{6} d^{2} e^{18}\right)} x^{6} + 56 \, {\left(c^{6} d^{15} e^{5} + 6 \, a c^{5} d^{13} e^{7} + 15 \, a^{2} c^{4} d^{11} e^{9} + 20 \, a^{3} c^{3} d^{9} e^{11} + 15 \, a^{4} c^{2} d^{7} e^{13} + 6 \, a^{5} c d^{5} e^{15} + a^{6} d^{3} e^{17}\right)} x^{5} + 70 \, {\left(c^{6} d^{16} e^{4} + 6 \, a c^{5} d^{14} e^{6} + 15 \, a^{2} c^{4} d^{12} e^{8} + 20 \, a^{3} c^{3} d^{10} e^{10} + 15 \, a^{4} c^{2} d^{8} e^{12} + 6 \, a^{5} c d^{6} e^{14} + a^{6} d^{4} e^{16}\right)} x^{4} + 56 \, {\left(c^{6} d^{17} e^{3} + 6 \, a c^{5} d^{15} e^{5} + 15 \, a^{2} c^{4} d^{13} e^{7} + 20 \, a^{3} c^{3} d^{11} e^{9} + 15 \, a^{4} c^{2} d^{9} e^{11} + 6 \, a^{5} c d^{7} e^{13} + a^{6} d^{5} e^{15}\right)} x^{3} + 28 \, {\left(c^{6} d^{18} e^{2} + 6 \, a c^{5} d^{16} e^{4} + 15 \, a^{2} c^{4} d^{14} e^{6} + 20 \, a^{3} c^{3} d^{12} e^{8} + 15 \, a^{4} c^{2} d^{10} e^{10} + 6 \, a^{5} c d^{8} e^{12} + a^{6} d^{6} e^{14}\right)} x^{2} + 8 \, {\left(c^{6} d^{19} e + 6 \, a c^{5} d^{17} e^{3} + 15 \, a^{2} c^{4} d^{15} e^{5} + 20 \, a^{3} c^{3} d^{13} e^{7} + 15 \, a^{4} c^{2} d^{11} e^{9} + 6 \, a^{5} c d^{9} e^{11} + a^{6} d^{7} e^{13}\right)} x\right)}}, -\frac{105 \, {\left(8 \, a^{3} c^{5} d^{10} - a^{4} c^{4} d^{8} e^{2} + {\left(8 \, a^{3} c^{5} d^{2} e^{8} - a^{4} c^{4} e^{10}\right)} x^{8} + 8 \, {\left(8 \, a^{3} c^{5} d^{3} e^{7} - a^{4} c^{4} d e^{9}\right)} x^{7} + 28 \, {\left(8 \, a^{3} c^{5} d^{4} e^{6} - a^{4} c^{4} d^{2} e^{8}\right)} x^{6} + 56 \, {\left(8 \, a^{3} c^{5} d^{5} e^{5} - a^{4} c^{4} d^{3} e^{7}\right)} x^{5} + 70 \, {\left(8 \, a^{3} c^{5} d^{6} e^{4} - a^{4} c^{4} d^{4} e^{6}\right)} x^{4} + 56 \, {\left(8 \, a^{3} c^{5} d^{7} e^{3} - a^{4} c^{4} d^{5} e^{5}\right)} x^{3} + 28 \, {\left(8 \, a^{3} c^{5} d^{8} e^{2} - a^{4} c^{4} d^{6} e^{4}\right)} x^{2} + 8 \, {\left(8 \, a^{3} c^{5} d^{9} e - a^{4} c^{4} d^{7} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(2616 \, a^{3} c^{5} d^{10} e + 6481 \, a^{4} c^{4} d^{8} e^{3} + 7443 \, a^{5} c^{3} d^{6} e^{5} + 5298 \, a^{6} c^{2} d^{4} e^{7} + 2056 \, a^{7} c d^{2} e^{9} + 336 \, a^{8} e^{11} - {\left(16 \, c^{8} d^{9} e^{2} + 120 \, a c^{7} d^{7} e^{4} + 474 \, a^{2} c^{6} d^{5} e^{6} - 293 \, a^{3} c^{5} d^{3} e^{8} - 663 \, a^{4} c^{4} d e^{10}\right)} x^{7} - {\left(128 \, c^{8} d^{10} e + 960 \, a c^{7} d^{8} e^{3} + 3792 \, a^{2} c^{6} d^{6} e^{5} - 1504 \, a^{3} c^{5} d^{4} e^{7} - 4569 \, a^{4} c^{4} d^{2} e^{9} - 105 \, a^{5} c^{3} e^{11}\right)} x^{6} - {\left(448 \, c^{8} d^{11} + 3352 \, a c^{7} d^{9} e^{2} + 13212 \, a^{2} c^{6} d^{7} e^{4} - 2141 \, a^{3} c^{5} d^{5} e^{6} - 12905 \, a^{4} c^{4} d^{3} e^{8} - 456 \, a^{5} c^{3} d e^{10}\right)} x^{5} - {\left(1280 \, a c^{7} d^{10} e + 12624 \, a^{2} c^{6} d^{8} e^{3} - 15784 \, a^{3} c^{5} d^{6} e^{5} - 32071 \, a^{4} c^{4} d^{4} e^{7} - 5769 \, a^{5} c^{3} d^{2} e^{9} - 826 \, a^{6} c^{2} e^{11}\right)} x^{4} - {\left(1456 \, a c^{7} d^{11} + 14706 \, a^{2} c^{6} d^{9} e^{2} - 12191 \, a^{3} c^{5} d^{7} e^{4} - 30449 \, a^{4} c^{4} d^{5} e^{6} - 5856 \, a^{5} c^{3} d^{3} e^{8} - 848 \, a^{6} c^{2} d e^{10}\right)} x^{3} - {\left(4416 \, a^{2} c^{6} d^{10} e - 19072 \, a^{3} c^{5} d^{8} e^{3} - 35839 \, a^{4} c^{4} d^{6} e^{5} - 17595 \, a^{5} c^{3} d^{4} e^{7} - 6196 \, a^{6} c^{2} d^{2} e^{9} - 952 \, a^{7} c e^{11}\right)} x^{2} - {\left(1848 \, a^{2} c^{6} d^{11} - 5535 \, a^{3} c^{5} d^{9} e^{2} - 11423 \, a^{4} c^{4} d^{7} e^{4} - 5784 \, a^{5} c^{3} d^{5} e^{6} - 2064 \, a^{6} c^{2} d^{3} e^{8} - 320 \, a^{7} c d e^{10}\right)} x\right)} \sqrt{c x^{2} + a}}{2688 \, {\left(c^{6} d^{20} + 6 \, a c^{5} d^{18} e^{2} + 15 \, a^{2} c^{4} d^{16} e^{4} + 20 \, a^{3} c^{3} d^{14} e^{6} + 15 \, a^{4} c^{2} d^{12} e^{8} + 6 \, a^{5} c d^{10} e^{10} + a^{6} d^{8} e^{12} + {\left(c^{6} d^{12} e^{8} + 6 \, a c^{5} d^{10} e^{10} + 15 \, a^{2} c^{4} d^{8} e^{12} + 20 \, a^{3} c^{3} d^{6} e^{14} + 15 \, a^{4} c^{2} d^{4} e^{16} + 6 \, a^{5} c d^{2} e^{18} + a^{6} e^{20}\right)} x^{8} + 8 \, {\left(c^{6} d^{13} e^{7} + 6 \, a c^{5} d^{11} e^{9} + 15 \, a^{2} c^{4} d^{9} e^{11} + 20 \, a^{3} c^{3} d^{7} e^{13} + 15 \, a^{4} c^{2} d^{5} e^{15} + 6 \, a^{5} c d^{3} e^{17} + a^{6} d e^{19}\right)} x^{7} + 28 \, {\left(c^{6} d^{14} e^{6} + 6 \, a c^{5} d^{12} e^{8} + 15 \, a^{2} c^{4} d^{10} e^{10} + 20 \, a^{3} c^{3} d^{8} e^{12} + 15 \, a^{4} c^{2} d^{6} e^{14} + 6 \, a^{5} c d^{4} e^{16} + a^{6} d^{2} e^{18}\right)} x^{6} + 56 \, {\left(c^{6} d^{15} e^{5} + 6 \, a c^{5} d^{13} e^{7} + 15 \, a^{2} c^{4} d^{11} e^{9} + 20 \, a^{3} c^{3} d^{9} e^{11} + 15 \, a^{4} c^{2} d^{7} e^{13} + 6 \, a^{5} c d^{5} e^{15} + a^{6} d^{3} e^{17}\right)} x^{5} + 70 \, {\left(c^{6} d^{16} e^{4} + 6 \, a c^{5} d^{14} e^{6} + 15 \, a^{2} c^{4} d^{12} e^{8} + 20 \, a^{3} c^{3} d^{10} e^{10} + 15 \, a^{4} c^{2} d^{8} e^{12} + 6 \, a^{5} c d^{6} e^{14} + a^{6} d^{4} e^{16}\right)} x^{4} + 56 \, {\left(c^{6} d^{17} e^{3} + 6 \, a c^{5} d^{15} e^{5} + 15 \, a^{2} c^{4} d^{13} e^{7} + 20 \, a^{3} c^{3} d^{11} e^{9} + 15 \, a^{4} c^{2} d^{9} e^{11} + 6 \, a^{5} c d^{7} e^{13} + a^{6} d^{5} e^{15}\right)} x^{3} + 28 \, {\left(c^{6} d^{18} e^{2} + 6 \, a c^{5} d^{16} e^{4} + 15 \, a^{2} c^{4} d^{14} e^{6} + 20 \, a^{3} c^{3} d^{12} e^{8} + 15 \, a^{4} c^{2} d^{10} e^{10} + 6 \, a^{5} c d^{8} e^{12} + a^{6} d^{6} e^{14}\right)} x^{2} + 8 \, {\left(c^{6} d^{19} e + 6 \, a c^{5} d^{17} e^{3} + 15 \, a^{2} c^{4} d^{15} e^{5} + 20 \, a^{3} c^{3} d^{13} e^{7} + 15 \, a^{4} c^{2} d^{11} e^{9} + 6 \, a^{5} c d^{9} e^{11} + a^{6} d^{7} e^{13}\right)} x\right)}}\right]"," ",0,"[1/5376*(105*(8*a^3*c^5*d^10 - a^4*c^4*d^8*e^2 + (8*a^3*c^5*d^2*e^8 - a^4*c^4*e^10)*x^8 + 8*(8*a^3*c^5*d^3*e^7 - a^4*c^4*d*e^9)*x^7 + 28*(8*a^3*c^5*d^4*e^6 - a^4*c^4*d^2*e^8)*x^6 + 56*(8*a^3*c^5*d^5*e^5 - a^4*c^4*d^3*e^7)*x^5 + 70*(8*a^3*c^5*d^6*e^4 - a^4*c^4*d^4*e^6)*x^4 + 56*(8*a^3*c^5*d^7*e^3 - a^4*c^4*d^5*e^5)*x^3 + 28*(8*a^3*c^5*d^8*e^2 - a^4*c^4*d^6*e^4)*x^2 + 8*(8*a^3*c^5*d^9*e - a^4*c^4*d^7*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(2616*a^3*c^5*d^10*e + 6481*a^4*c^4*d^8*e^3 + 7443*a^5*c^3*d^6*e^5 + 5298*a^6*c^2*d^4*e^7 + 2056*a^7*c*d^2*e^9 + 336*a^8*e^11 - (16*c^8*d^9*e^2 + 120*a*c^7*d^7*e^4 + 474*a^2*c^6*d^5*e^6 - 293*a^3*c^5*d^3*e^8 - 663*a^4*c^4*d*e^10)*x^7 - (128*c^8*d^10*e + 960*a*c^7*d^8*e^3 + 3792*a^2*c^6*d^6*e^5 - 1504*a^3*c^5*d^4*e^7 - 4569*a^4*c^4*d^2*e^9 - 105*a^5*c^3*e^11)*x^6 - (448*c^8*d^11 + 3352*a*c^7*d^9*e^2 + 13212*a^2*c^6*d^7*e^4 - 2141*a^3*c^5*d^5*e^6 - 12905*a^4*c^4*d^3*e^8 - 456*a^5*c^3*d*e^10)*x^5 - (1280*a*c^7*d^10*e + 12624*a^2*c^6*d^8*e^3 - 15784*a^3*c^5*d^6*e^5 - 32071*a^4*c^4*d^4*e^7 - 5769*a^5*c^3*d^2*e^9 - 826*a^6*c^2*e^11)*x^4 - (1456*a*c^7*d^11 + 14706*a^2*c^6*d^9*e^2 - 12191*a^3*c^5*d^7*e^4 - 30449*a^4*c^4*d^5*e^6 - 5856*a^5*c^3*d^3*e^8 - 848*a^6*c^2*d*e^10)*x^3 - (4416*a^2*c^6*d^10*e - 19072*a^3*c^5*d^8*e^3 - 35839*a^4*c^4*d^6*e^5 - 17595*a^5*c^3*d^4*e^7 - 6196*a^6*c^2*d^2*e^9 - 952*a^7*c*e^11)*x^2 - (1848*a^2*c^6*d^11 - 5535*a^3*c^5*d^9*e^2 - 11423*a^4*c^4*d^7*e^4 - 5784*a^5*c^3*d^5*e^6 - 2064*a^6*c^2*d^3*e^8 - 320*a^7*c*d*e^10)*x)*sqrt(c*x^2 + a))/(c^6*d^20 + 6*a*c^5*d^18*e^2 + 15*a^2*c^4*d^16*e^4 + 20*a^3*c^3*d^14*e^6 + 15*a^4*c^2*d^12*e^8 + 6*a^5*c*d^10*e^10 + a^6*d^8*e^12 + (c^6*d^12*e^8 + 6*a*c^5*d^10*e^10 + 15*a^2*c^4*d^8*e^12 + 20*a^3*c^3*d^6*e^14 + 15*a^4*c^2*d^4*e^16 + 6*a^5*c*d^2*e^18 + a^6*e^20)*x^8 + 8*(c^6*d^13*e^7 + 6*a*c^5*d^11*e^9 + 15*a^2*c^4*d^9*e^11 + 20*a^3*c^3*d^7*e^13 + 15*a^4*c^2*d^5*e^15 + 6*a^5*c*d^3*e^17 + a^6*d*e^19)*x^7 + 28*(c^6*d^14*e^6 + 6*a*c^5*d^12*e^8 + 15*a^2*c^4*d^10*e^10 + 20*a^3*c^3*d^8*e^12 + 15*a^4*c^2*d^6*e^14 + 6*a^5*c*d^4*e^16 + a^6*d^2*e^18)*x^6 + 56*(c^6*d^15*e^5 + 6*a*c^5*d^13*e^7 + 15*a^2*c^4*d^11*e^9 + 20*a^3*c^3*d^9*e^11 + 15*a^4*c^2*d^7*e^13 + 6*a^5*c*d^5*e^15 + a^6*d^3*e^17)*x^5 + 70*(c^6*d^16*e^4 + 6*a*c^5*d^14*e^6 + 15*a^2*c^4*d^12*e^8 + 20*a^3*c^3*d^10*e^10 + 15*a^4*c^2*d^8*e^12 + 6*a^5*c*d^6*e^14 + a^6*d^4*e^16)*x^4 + 56*(c^6*d^17*e^3 + 6*a*c^5*d^15*e^5 + 15*a^2*c^4*d^13*e^7 + 20*a^3*c^3*d^11*e^9 + 15*a^4*c^2*d^9*e^11 + 6*a^5*c*d^7*e^13 + a^6*d^5*e^15)*x^3 + 28*(c^6*d^18*e^2 + 6*a*c^5*d^16*e^4 + 15*a^2*c^4*d^14*e^6 + 20*a^3*c^3*d^12*e^8 + 15*a^4*c^2*d^10*e^10 + 6*a^5*c*d^8*e^12 + a^6*d^6*e^14)*x^2 + 8*(c^6*d^19*e + 6*a*c^5*d^17*e^3 + 15*a^2*c^4*d^15*e^5 + 20*a^3*c^3*d^13*e^7 + 15*a^4*c^2*d^11*e^9 + 6*a^5*c*d^9*e^11 + a^6*d^7*e^13)*x), -1/2688*(105*(8*a^3*c^5*d^10 - a^4*c^4*d^8*e^2 + (8*a^3*c^5*d^2*e^8 - a^4*c^4*e^10)*x^8 + 8*(8*a^3*c^5*d^3*e^7 - a^4*c^4*d*e^9)*x^7 + 28*(8*a^3*c^5*d^4*e^6 - a^4*c^4*d^2*e^8)*x^6 + 56*(8*a^3*c^5*d^5*e^5 - a^4*c^4*d^3*e^7)*x^5 + 70*(8*a^3*c^5*d^6*e^4 - a^4*c^4*d^4*e^6)*x^4 + 56*(8*a^3*c^5*d^7*e^3 - a^4*c^4*d^5*e^5)*x^3 + 28*(8*a^3*c^5*d^8*e^2 - a^4*c^4*d^6*e^4)*x^2 + 8*(8*a^3*c^5*d^9*e - a^4*c^4*d^7*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (2616*a^3*c^5*d^10*e + 6481*a^4*c^4*d^8*e^3 + 7443*a^5*c^3*d^6*e^5 + 5298*a^6*c^2*d^4*e^7 + 2056*a^7*c*d^2*e^9 + 336*a^8*e^11 - (16*c^8*d^9*e^2 + 120*a*c^7*d^7*e^4 + 474*a^2*c^6*d^5*e^6 - 293*a^3*c^5*d^3*e^8 - 663*a^4*c^4*d*e^10)*x^7 - (128*c^8*d^10*e + 960*a*c^7*d^8*e^3 + 3792*a^2*c^6*d^6*e^5 - 1504*a^3*c^5*d^4*e^7 - 4569*a^4*c^4*d^2*e^9 - 105*a^5*c^3*e^11)*x^6 - (448*c^8*d^11 + 3352*a*c^7*d^9*e^2 + 13212*a^2*c^6*d^7*e^4 - 2141*a^3*c^5*d^5*e^6 - 12905*a^4*c^4*d^3*e^8 - 456*a^5*c^3*d*e^10)*x^5 - (1280*a*c^7*d^10*e + 12624*a^2*c^6*d^8*e^3 - 15784*a^3*c^5*d^6*e^5 - 32071*a^4*c^4*d^4*e^7 - 5769*a^5*c^3*d^2*e^9 - 826*a^6*c^2*e^11)*x^4 - (1456*a*c^7*d^11 + 14706*a^2*c^6*d^9*e^2 - 12191*a^3*c^5*d^7*e^4 - 30449*a^4*c^4*d^5*e^6 - 5856*a^5*c^3*d^3*e^8 - 848*a^6*c^2*d*e^10)*x^3 - (4416*a^2*c^6*d^10*e - 19072*a^3*c^5*d^8*e^3 - 35839*a^4*c^4*d^6*e^5 - 17595*a^5*c^3*d^4*e^7 - 6196*a^6*c^2*d^2*e^9 - 952*a^7*c*e^11)*x^2 - (1848*a^2*c^6*d^11 - 5535*a^3*c^5*d^9*e^2 - 11423*a^4*c^4*d^7*e^4 - 5784*a^5*c^3*d^5*e^6 - 2064*a^6*c^2*d^3*e^8 - 320*a^7*c*d*e^10)*x)*sqrt(c*x^2 + a))/(c^6*d^20 + 6*a*c^5*d^18*e^2 + 15*a^2*c^4*d^16*e^4 + 20*a^3*c^3*d^14*e^6 + 15*a^4*c^2*d^12*e^8 + 6*a^5*c*d^10*e^10 + a^6*d^8*e^12 + (c^6*d^12*e^8 + 6*a*c^5*d^10*e^10 + 15*a^2*c^4*d^8*e^12 + 20*a^3*c^3*d^6*e^14 + 15*a^4*c^2*d^4*e^16 + 6*a^5*c*d^2*e^18 + a^6*e^20)*x^8 + 8*(c^6*d^13*e^7 + 6*a*c^5*d^11*e^9 + 15*a^2*c^4*d^9*e^11 + 20*a^3*c^3*d^7*e^13 + 15*a^4*c^2*d^5*e^15 + 6*a^5*c*d^3*e^17 + a^6*d*e^19)*x^7 + 28*(c^6*d^14*e^6 + 6*a*c^5*d^12*e^8 + 15*a^2*c^4*d^10*e^10 + 20*a^3*c^3*d^8*e^12 + 15*a^4*c^2*d^6*e^14 + 6*a^5*c*d^4*e^16 + a^6*d^2*e^18)*x^6 + 56*(c^6*d^15*e^5 + 6*a*c^5*d^13*e^7 + 15*a^2*c^4*d^11*e^9 + 20*a^3*c^3*d^9*e^11 + 15*a^4*c^2*d^7*e^13 + 6*a^5*c*d^5*e^15 + a^6*d^3*e^17)*x^5 + 70*(c^6*d^16*e^4 + 6*a*c^5*d^14*e^6 + 15*a^2*c^4*d^12*e^8 + 20*a^3*c^3*d^10*e^10 + 15*a^4*c^2*d^8*e^12 + 6*a^5*c*d^6*e^14 + a^6*d^4*e^16)*x^4 + 56*(c^6*d^17*e^3 + 6*a*c^5*d^15*e^5 + 15*a^2*c^4*d^13*e^7 + 20*a^3*c^3*d^11*e^9 + 15*a^4*c^2*d^9*e^11 + 6*a^5*c*d^7*e^13 + a^6*d^5*e^15)*x^3 + 28*(c^6*d^18*e^2 + 6*a*c^5*d^16*e^4 + 15*a^2*c^4*d^14*e^6 + 20*a^3*c^3*d^12*e^8 + 15*a^4*c^2*d^10*e^10 + 6*a^5*c*d^8*e^12 + a^6*d^6*e^14)*x^2 + 8*(c^6*d^19*e + 6*a*c^5*d^17*e^3 + 15*a^2*c^4*d^15*e^5 + 20*a^3*c^3*d^13*e^7 + 15*a^4*c^2*d^11*e^9 + 6*a^5*c*d^9*e^11 + a^6*d^7*e^13)*x)]","B",0
558,1,62,0,0.415867," ","integrate((x^2+2)^(1/2)/(1+4*x),x, algorithm=""fricas"")","\frac{1}{16} \, \sqrt{33} \log\left(-\frac{\sqrt{33} {\left(x - 8\right)} + \sqrt{x^{2} + 2} {\left(\sqrt{33} + 33\right)} + x - 8}{4 \, x + 1}\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(-(sqrt(33)*(x - 8) + sqrt(x^2 + 2)*(sqrt(33) + 33) + x - 8)/(4*x + 1)) + 1/4*sqrt(x^2 + 2) + 1/16*log(-x + sqrt(x^2 + 2))","A",0
559,1,75,0,0.410082," ","integrate((4*x^2+2)^(1/2)/(5+4*x),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{33} \log\left(-\frac{2 \, \sqrt{33} {\left(5 \, x - 2\right)} + \sqrt{4 \, x^{2} + 2} {\left(5 \, \sqrt{33} + 33\right)} + 50 \, x - 20}{4 \, x + 5}\right) + \frac{1}{4} \, \sqrt{4 \, x^{2} + 2} + \frac{5}{8} \, \log\left(-2 \, x + \sqrt{4 \, x^{2} + 2}\right)"," ",0,"1/8*sqrt(33)*log(-(2*sqrt(33)*(5*x - 2) + sqrt(4*x^2 + 2)*(5*sqrt(33) + 33) + 50*x - 20)/(4*x + 5)) + 1/4*sqrt(4*x^2 + 2) + 5/8*log(-2*x + sqrt(4*x^2 + 2))","A",0
560,1,50,0,0.403664," ","integrate((2+3*x)*(7*x^2-5)^(1/2),x, algorithm=""fricas"")","\frac{1}{7} \, {\left(7 \, x^{2} + 7 \, x - 5\right)} \sqrt{7 \, x^{2} - 5} + \frac{5}{14} \, \sqrt{7} \log\left(-2 \, \sqrt{7} \sqrt{7 \, x^{2} - 5} x + 14 \, x^{2} - 5\right)"," ",0,"1/7*(7*x^2 + 7*x - 5)*sqrt(7*x^2 - 5) + 5/14*sqrt(7)*log(-2*sqrt(7)*sqrt(7*x^2 - 5)*x + 14*x^2 - 5)","A",0
561,1,270,0,0.431698," ","integrate((e*x+d)^4/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, c^{2} d^{4} - 24 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(6 \, c^{2} e^{4} x^{3} + 32 \, c^{2} d e^{3} x^{2} + 96 \, c^{2} d^{3} e - 64 \, a c d e^{3} + 9 \, {\left(8 \, c^{2} d^{2} e^{2} - a c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{48 \, c^{3}}, -\frac{3 \, {\left(8 \, c^{2} d^{4} - 24 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(6 \, c^{2} e^{4} x^{3} + 32 \, c^{2} d e^{3} x^{2} + 96 \, c^{2} d^{3} e - 64 \, a c d e^{3} + 9 \, {\left(8 \, c^{2} d^{2} e^{2} - a c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{24 \, c^{3}}\right]"," ",0,"[1/48*(3*(8*c^2*d^4 - 24*a*c*d^2*e^2 + 3*a^2*e^4)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(6*c^2*e^4*x^3 + 32*c^2*d*e^3*x^2 + 96*c^2*d^3*e - 64*a*c*d*e^3 + 9*(8*c^2*d^2*e^2 - a*c*e^4)*x)*sqrt(c*x^2 + a))/c^3, -1/24*(3*(8*c^2*d^4 - 24*a*c*d^2*e^2 + 3*a^2*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (6*c^2*e^4*x^3 + 32*c^2*d*e^3*x^2 + 96*c^2*d^3*e - 64*a*c*d*e^3 + 9*(8*c^2*d^2*e^2 - a*c*e^4)*x)*sqrt(c*x^2 + a))/c^3]","A",0
562,1,180,0,0.429036," ","integrate((e*x+d)^3/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, c d^{3} - 3 \, a d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(2 \, c e^{3} x^{2} + 9 \, c d e^{2} x + 18 \, c d^{2} e - 4 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{12 \, c^{2}}, -\frac{3 \, {\left(2 \, c d^{3} - 3 \, a d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(2 \, c e^{3} x^{2} + 9 \, c d e^{2} x + 18 \, c d^{2} e - 4 \, a e^{3}\right)} \sqrt{c x^{2} + a}}{6 \, c^{2}}\right]"," ",0,"[-1/12*(3*(2*c*d^3 - 3*a*d*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(2*c*e^3*x^2 + 9*c*d*e^2*x + 18*c*d^2*e - 4*a*e^3)*sqrt(c*x^2 + a))/c^2, -1/6*(3*(2*c*d^3 - 3*a*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (2*c*e^3*x^2 + 9*c*d*e^2*x + 18*c*d^2*e - 4*a*e^3)*sqrt(c*x^2 + a))/c^2]","A",0
563,1,138,0,0.436711," ","integrate((e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, c d^{2} - a e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} + 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(c e^{2} x + 4 \, c d e\right)} \sqrt{c x^{2} + a}}{4 \, c^{2}}, -\frac{{\left(2 \, c d^{2} - a e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(c e^{2} x + 4 \, c d e\right)} \sqrt{c x^{2} + a}}{2 \, c^{2}}\right]"," ",0,"[-1/4*((2*c*d^2 - a*e^2)*sqrt(c)*log(-2*c*x^2 + 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(c*e^2*x + 4*c*d*e)*sqrt(c*x^2 + a))/c^2, -1/2*((2*c*d^2 - a*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (c*e^2*x + 4*c*d*e)*sqrt(c*x^2 + a))/c^2]","A",0
564,1,92,0,0.423044," ","integrate((e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c} d \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, \sqrt{c x^{2} + a} e}{2 \, c}, -\frac{\sqrt{-c} d \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - \sqrt{c x^{2} + a} e}{c}\right]"," ",0,"[1/2*(sqrt(c)*d*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*sqrt(c*x^2 + a)*e)/c, -(sqrt(-c)*d*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - sqrt(c*x^2 + a)*e)/c]","A",0
565,1,211,0,0.450783," ","integrate(1/(e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, \sqrt{c d^{2} + a e^{2}}}, -\frac{\sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right)}{c d^{2} + a e^{2}}\right]"," ",0,"[1/2*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2))/sqrt(c*d^2 + a*e^2), -sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2))/(c*d^2 + a*e^2)]","B",0
566,1,381,0,0.472967," ","integrate(1/(e*x+d)^2/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c d e x + c d^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)}}, -\frac{{\left(c d e x + c d^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(c d^{2} e + a e^{3}\right)} \sqrt{c x^{2} + a}}{c^{2} d^{5} + 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x}\right]"," ",0,"[1/2*((c*d*e*x + c*d^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x), -((c*d*e*x + c*d^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (c*d^2*e + a*e^3)*sqrt(c*x^2 + a))/(c^2*d^5 + 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e + 2*a*c*d^2*e^3 + a^2*e^5)*x)]","B",0
567,1,713,0,0.669381," ","integrate(1/(e*x+d)^3/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, c^{2} d^{4} - a c d^{2} e^{2} + {\left(2 \, c^{2} d^{2} e^{2} - a c e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{3} e - a c d e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(4 \, c^{2} d^{4} e + 5 \, a c d^{2} e^{3} + a^{2} e^{5} + 3 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(c^{3} d^{8} + 3 \, a c^{2} d^{6} e^{2} + 3 \, a^{2} c d^{4} e^{4} + a^{3} d^{2} e^{6} + {\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)} x^{2} + 2 \, {\left(c^{3} d^{7} e + 3 \, a c^{2} d^{5} e^{3} + 3 \, a^{2} c d^{3} e^{5} + a^{3} d e^{7}\right)} x\right)}}, -\frac{{\left(2 \, c^{2} d^{4} - a c d^{2} e^{2} + {\left(2 \, c^{2} d^{2} e^{2} - a c e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{3} e - a c d e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(4 \, c^{2} d^{4} e + 5 \, a c d^{2} e^{3} + a^{2} e^{5} + 3 \, {\left(c^{2} d^{3} e^{2} + a c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(c^{3} d^{8} + 3 \, a c^{2} d^{6} e^{2} + 3 \, a^{2} c d^{4} e^{4} + a^{3} d^{2} e^{6} + {\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)} x^{2} + 2 \, {\left(c^{3} d^{7} e + 3 \, a c^{2} d^{5} e^{3} + 3 \, a^{2} c d^{3} e^{5} + a^{3} d e^{7}\right)} x\right)}}\right]"," ",0,"[-1/4*((2*c^2*d^4 - a*c*d^2*e^2 + (2*c^2*d^2*e^2 - a*c*e^4)*x^2 + 2*(2*c^2*d^3*e - a*c*d*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(4*c^2*d^4*e + 5*a*c*d^2*e^3 + a^2*e^5 + 3*(c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^8 + 3*a*c^2*d^6*e^2 + 3*a^2*c*d^4*e^4 + a^3*d^2*e^6 + (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)*x^2 + 2*(c^3*d^7*e + 3*a*c^2*d^5*e^3 + 3*a^2*c*d^3*e^5 + a^3*d*e^7)*x), -1/2*((2*c^2*d^4 - a*c*d^2*e^2 + (2*c^2*d^2*e^2 - a*c*e^4)*x^2 + 2*(2*c^2*d^3*e - a*c*d*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (4*c^2*d^4*e + 5*a*c*d^2*e^3 + a^2*e^5 + 3*(c^2*d^3*e^2 + a*c*d*e^4)*x)*sqrt(c*x^2 + a))/(c^3*d^8 + 3*a*c^2*d^6*e^2 + 3*a^2*c*d^4*e^4 + a^3*d^2*e^6 + (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)*x^2 + 2*(c^3*d^7*e + 3*a*c^2*d^5*e^3 + 3*a^2*c*d^3*e^5 + a^3*d*e^7)*x)]","B",0
568,1,1139,0,1.019617," ","integrate(1/(e*x+d)^4/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + {\left(2 \, c^{3} d^{3} e^{3} - 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(2 \, c^{3} d^{4} e^{2} - 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(2 \, c^{3} d^{5} e - 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} + 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(18 \, c^{3} d^{6} e + 23 \, a c^{2} d^{4} e^{3} + 7 \, a^{2} c d^{2} e^{5} + 2 \, a^{3} e^{7} + {\left(11 \, c^{3} d^{4} e^{3} + 7 \, a c^{2} d^{2} e^{5} - 4 \, a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(9 \, c^{3} d^{5} e^{2} + 8 \, a c^{2} d^{3} e^{4} - a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(c^{4} d^{11} + 4 \, a c^{3} d^{9} e^{2} + 6 \, a^{2} c^{2} d^{7} e^{4} + 4 \, a^{3} c d^{5} e^{6} + a^{4} d^{3} e^{8} + {\left(c^{4} d^{8} e^{3} + 4 \, a c^{3} d^{6} e^{5} + 6 \, a^{2} c^{2} d^{4} e^{7} + 4 \, a^{3} c d^{2} e^{9} + a^{4} e^{11}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} + 4 \, a c^{3} d^{7} e^{4} + 6 \, a^{2} c^{2} d^{5} e^{6} + 4 \, a^{3} c d^{3} e^{8} + a^{4} d e^{10}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e + 4 \, a c^{3} d^{8} e^{3} + 6 \, a^{2} c^{2} d^{6} e^{5} + 4 \, a^{3} c d^{4} e^{7} + a^{4} d^{2} e^{9}\right)} x\right)}}, -\frac{3 \, {\left(2 \, c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + {\left(2 \, c^{3} d^{3} e^{3} - 3 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(2 \, c^{3} d^{4} e^{2} - 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(2 \, c^{3} d^{5} e - 3 \, a c^{2} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) + {\left(18 \, c^{3} d^{6} e + 23 \, a c^{2} d^{4} e^{3} + 7 \, a^{2} c d^{2} e^{5} + 2 \, a^{3} e^{7} + {\left(11 \, c^{3} d^{4} e^{3} + 7 \, a c^{2} d^{2} e^{5} - 4 \, a^{2} c e^{7}\right)} x^{2} + 3 \, {\left(9 \, c^{3} d^{5} e^{2} + 8 \, a c^{2} d^{3} e^{4} - a^{2} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(c^{4} d^{11} + 4 \, a c^{3} d^{9} e^{2} + 6 \, a^{2} c^{2} d^{7} e^{4} + 4 \, a^{3} c d^{5} e^{6} + a^{4} d^{3} e^{8} + {\left(c^{4} d^{8} e^{3} + 4 \, a c^{3} d^{6} e^{5} + 6 \, a^{2} c^{2} d^{4} e^{7} + 4 \, a^{3} c d^{2} e^{9} + a^{4} e^{11}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} + 4 \, a c^{3} d^{7} e^{4} + 6 \, a^{2} c^{2} d^{5} e^{6} + 4 \, a^{3} c d^{3} e^{8} + a^{4} d e^{10}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e + 4 \, a c^{3} d^{8} e^{3} + 6 \, a^{2} c^{2} d^{6} e^{5} + 4 \, a^{3} c d^{4} e^{7} + a^{4} d^{2} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/12*(3*(2*c^3*d^6 - 3*a*c^2*d^4*e^2 + (2*c^3*d^3*e^3 - 3*a*c^2*d*e^5)*x^3 + 3*(2*c^3*d^4*e^2 - 3*a*c^2*d^2*e^4)*x^2 + 3*(2*c^3*d^5*e - 3*a*c^2*d^3*e^3)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 + 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(18*c^3*d^6*e + 23*a*c^2*d^4*e^3 + 7*a^2*c*d^2*e^5 + 2*a^3*e^7 + (11*c^3*d^4*e^3 + 7*a*c^2*d^2*e^5 - 4*a^2*c*e^7)*x^2 + 3*(9*c^3*d^5*e^2 + 8*a*c^2*d^3*e^4 - a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^11 + 4*a*c^3*d^9*e^2 + 6*a^2*c^2*d^7*e^4 + 4*a^3*c*d^5*e^6 + a^4*d^3*e^8 + (c^4*d^8*e^3 + 4*a*c^3*d^6*e^5 + 6*a^2*c^2*d^4*e^7 + 4*a^3*c*d^2*e^9 + a^4*e^11)*x^3 + 3*(c^4*d^9*e^2 + 4*a*c^3*d^7*e^4 + 6*a^2*c^2*d^5*e^6 + 4*a^3*c*d^3*e^8 + a^4*d*e^10)*x^2 + 3*(c^4*d^10*e + 4*a*c^3*d^8*e^3 + 6*a^2*c^2*d^6*e^5 + 4*a^3*c*d^4*e^7 + a^4*d^2*e^9)*x), -1/6*(3*(2*c^3*d^6 - 3*a*c^2*d^4*e^2 + (2*c^3*d^3*e^3 - 3*a*c^2*d*e^5)*x^3 + 3*(2*c^3*d^4*e^2 - 3*a*c^2*d^2*e^4)*x^2 + 3*(2*c^3*d^5*e - 3*a*c^2*d^3*e^3)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) + (18*c^3*d^6*e + 23*a*c^2*d^4*e^3 + 7*a^2*c*d^2*e^5 + 2*a^3*e^7 + (11*c^3*d^4*e^3 + 7*a*c^2*d^2*e^5 - 4*a^2*c*e^7)*x^2 + 3*(9*c^3*d^5*e^2 + 8*a*c^2*d^3*e^4 - a^2*c*d*e^6)*x)*sqrt(c*x^2 + a))/(c^4*d^11 + 4*a*c^3*d^9*e^2 + 6*a^2*c^2*d^7*e^4 + 4*a^3*c*d^5*e^6 + a^4*d^3*e^8 + (c^4*d^8*e^3 + 4*a*c^3*d^6*e^5 + 6*a^2*c^2*d^4*e^7 + 4*a^3*c*d^2*e^9 + a^4*e^11)*x^3 + 3*(c^4*d^9*e^2 + 4*a*c^3*d^7*e^4 + 6*a^2*c^2*d^5*e^6 + 4*a^3*c*d^3*e^8 + a^4*d*e^10)*x^2 + 3*(c^4*d^10*e + 4*a*c^3*d^8*e^3 + 6*a^2*c^2*d^6*e^5 + 4*a^3*c*d^4*e^7 + a^4*d^2*e^9)*x)]","B",0
569,1,368,0,0.440349," ","integrate((e*x+d)^4/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, a^{2} c d^{2} e^{2} - a^{3} e^{4} + {\left(4 \, a c^{2} d^{2} e^{2} - a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(a c^{2} e^{4} x^{3} + 8 \, a c^{2} d e^{3} x^{2} - 8 \, a c^{2} d^{3} e + 16 \, a^{2} c d e^{3} + {\left(2 \, c^{3} d^{4} - 12 \, a c^{2} d^{2} e^{2} + 3 \, a^{2} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(a c^{4} x^{2} + a^{2} c^{3}\right)}}, -\frac{3 \, {\left(4 \, a^{2} c d^{2} e^{2} - a^{3} e^{4} + {\left(4 \, a c^{2} d^{2} e^{2} - a^{2} c e^{4}\right)} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(a c^{2} e^{4} x^{3} + 8 \, a c^{2} d e^{3} x^{2} - 8 \, a c^{2} d^{3} e + 16 \, a^{2} c d e^{3} + {\left(2 \, c^{3} d^{4} - 12 \, a c^{2} d^{2} e^{2} + 3 \, a^{2} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{4} x^{2} + a^{2} c^{3}\right)}}\right]"," ",0,"[1/4*(3*(4*a^2*c*d^2*e^2 - a^3*e^4 + (4*a*c^2*d^2*e^2 - a^2*c*e^4)*x^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(a*c^2*e^4*x^3 + 8*a*c^2*d*e^3*x^2 - 8*a*c^2*d^3*e + 16*a^2*c*d*e^3 + (2*c^3*d^4 - 12*a*c^2*d^2*e^2 + 3*a^2*c*e^4)*x)*sqrt(c*x^2 + a))/(a*c^4*x^2 + a^2*c^3), -1/2*(3*(4*a^2*c*d^2*e^2 - a^3*e^4 + (4*a*c^2*d^2*e^2 - a^2*c*e^4)*x^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (a*c^2*e^4*x^3 + 8*a*c^2*d*e^3*x^2 - 8*a*c^2*d^3*e + 16*a^2*c*d*e^3 + (2*c^3*d^4 - 12*a*c^2*d^2*e^2 + 3*a^2*c*e^4)*x)*sqrt(c*x^2 + a))/(a*c^4*x^2 + a^2*c^3)]","A",0
570,1,246,0,0.433030," ","integrate((e*x+d)^3/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a c d e^{2} x^{2} + a^{2} d e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(a c e^{3} x^{2} - 3 \, a c d^{2} e + 2 \, a^{2} e^{3} + {\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}}, -\frac{3 \, {\left(a c d e^{2} x^{2} + a^{2} d e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(a c e^{3} x^{2} - 3 \, a c d^{2} e + 2 \, a^{2} e^{3} + {\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{a c^{3} x^{2} + a^{2} c^{2}}\right]"," ",0,"[1/2*(3*(a*c*d*e^2*x^2 + a^2*d*e^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(a*c*e^3*x^2 - 3*a*c*d^2*e + 2*a^2*e^3 + (c^2*d^3 - 3*a*c*d*e^2)*x)*sqrt(c*x^2 + a))/(a*c^3*x^2 + a^2*c^2), -(3*(a*c*d*e^2*x^2 + a^2*d*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (a*c*e^3*x^2 - 3*a*c*d^2*e + 2*a^2*e^3 + (c^2*d^3 - 3*a*c*d*e^2)*x)*sqrt(c*x^2 + a))/(a*c^3*x^2 + a^2*c^2)]","A",0
571,1,201,0,0.439475," ","integrate((e*x+d)^2/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a c e^{2} x^{2} + a^{2} e^{2}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(2 \, a c d e - {\left(c^{2} d^{2} - a c e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}}, -\frac{{\left(a c e^{2} x^{2} + a^{2} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(2 \, a c d e - {\left(c^{2} d^{2} - a c e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{a c^{3} x^{2} + a^{2} c^{2}}\right]"," ",0,"[1/2*((a*c*e^2*x^2 + a^2*e^2)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(2*a*c*d*e - (c^2*d^2 - a*c*e^2)*x)*sqrt(c*x^2 + a))/(a*c^3*x^2 + a^2*c^2), -((a*c*e^2*x^2 + a^2*e^2)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (2*a*c*d*e - (c^2*d^2 - a*c*e^2)*x)*sqrt(c*x^2 + a))/(a*c^3*x^2 + a^2*c^2)]","A",0
572,1,35,0,0.406202," ","integrate((e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{{\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c^{2} x^{2} + a^{2} c}"," ",0,"(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c^2*x^2 + a^2*c)","A",0
573,1,456,0,0.484393," ","integrate(1/(e*x+d)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a c e^{2} x^{2} + a^{2} e^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(a c d^{2} e + a^{2} e^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{2}\right)}}, -\frac{{\left(a c e^{2} x^{2} + a^{2} e^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(a c d^{2} e + a^{2} e^{3} + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)} \sqrt{c x^{2} + a}}{a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{2}}\right]"," ",0,"[1/2*((a*c*e^2*x^2 + a^2*e^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(a*c*d^2*e + a^2*e^3 + (c^2*d^3 + a*c*d*e^2)*x)*sqrt(c*x^2 + a))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^2), -((a*c*e^2*x^2 + a^2*e^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (a*c*d^2*e + a^2*e^3 + (c^2*d^3 + a*c*d*e^2)*x)*sqrt(c*x^2 + a))/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^2)]","B",0
574,1,900,0,0.539862," ","integrate(1/(e*x+d)^2/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a c^{2} d e^{3} x^{3} + a c^{2} d^{2} e^{2} x^{2} + a^{2} c d e^{3} x + a^{2} c d^{2} e^{2}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(2 \, a c^{2} d^{4} e + a^{2} c d^{2} e^{3} - a^{3} e^{5} + {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3} - 2 \, a^{2} c e^{5}\right)} x^{2} + {\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c^{3} d^{7} + 3 \, a^{3} c^{2} d^{5} e^{2} + 3 \, a^{4} c d^{3} e^{4} + a^{5} d e^{6} + {\left(a c^{4} d^{6} e + 3 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} + a^{4} c e^{7}\right)} x^{3} + {\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)} x^{2} + {\left(a^{2} c^{3} d^{6} e + 3 \, a^{3} c^{2} d^{4} e^{3} + 3 \, a^{4} c d^{2} e^{5} + a^{5} e^{7}\right)} x\right)}}, -\frac{3 \, {\left(a c^{2} d e^{3} x^{3} + a c^{2} d^{2} e^{2} x^{2} + a^{2} c d e^{3} x + a^{2} c d^{2} e^{2}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(2 \, a c^{2} d^{4} e + a^{2} c d^{2} e^{3} - a^{3} e^{5} + {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3} - 2 \, a^{2} c e^{5}\right)} x^{2} + {\left(c^{3} d^{5} + 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{a^{2} c^{3} d^{7} + 3 \, a^{3} c^{2} d^{5} e^{2} + 3 \, a^{4} c d^{3} e^{4} + a^{5} d e^{6} + {\left(a c^{4} d^{6} e + 3 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} + a^{4} c e^{7}\right)} x^{3} + {\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)} x^{2} + {\left(a^{2} c^{3} d^{6} e + 3 \, a^{3} c^{2} d^{4} e^{3} + 3 \, a^{4} c d^{2} e^{5} + a^{5} e^{7}\right)} x}\right]"," ",0,"[1/2*(3*(a*c^2*d*e^3*x^3 + a*c^2*d^2*e^2*x^2 + a^2*c*d*e^3*x + a^2*c*d^2*e^2)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(2*a*c^2*d^4*e + a^2*c*d^2*e^3 - a^3*e^5 + (c^3*d^4*e - a*c^2*d^2*e^3 - 2*a^2*c*e^5)*x^2 + (c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x)*sqrt(c*x^2 + a))/(a^2*c^3*d^7 + 3*a^3*c^2*d^5*e^2 + 3*a^4*c*d^3*e^4 + a^5*d*e^6 + (a*c^4*d^6*e + 3*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 + a^4*c*e^7)*x^3 + (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)*x^2 + (a^2*c^3*d^6*e + 3*a^3*c^2*d^4*e^3 + 3*a^4*c*d^2*e^5 + a^5*e^7)*x), -(3*(a*c^2*d*e^3*x^3 + a*c^2*d^2*e^2*x^2 + a^2*c*d*e^3*x + a^2*c*d^2*e^2)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (2*a*c^2*d^4*e + a^2*c*d^2*e^3 - a^3*e^5 + (c^3*d^4*e - a*c^2*d^2*e^3 - 2*a^2*c*e^5)*x^2 + (c^3*d^5 + 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x)*sqrt(c*x^2 + a))/(a^2*c^3*d^7 + 3*a^3*c^2*d^5*e^2 + 3*a^4*c*d^3*e^4 + a^5*d*e^6 + (a*c^4*d^6*e + 3*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 + a^4*c*e^7)*x^3 + (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)*x^2 + (a^2*c^3*d^6*e + 3*a^3*c^2*d^4*e^3 + 3*a^4*c*d^2*e^5 + a^5*e^7)*x)]","B",0
575,1,1558,0,0.915273," ","integrate(1/(e*x+d)^3/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, a^{2} c^{2} d^{4} e^{2} - a^{3} c d^{2} e^{4} + {\left(4 \, a c^{3} d^{2} e^{4} - a^{2} c^{2} e^{6}\right)} x^{4} + 2 \, {\left(4 \, a c^{3} d^{3} e^{3} - a^{2} c^{2} d e^{5}\right)} x^{3} + {\left(4 \, a c^{3} d^{4} e^{2} + 3 \, a^{2} c^{2} d^{2} e^{4} - a^{3} c e^{6}\right)} x^{2} + 2 \, {\left(4 \, a^{2} c^{2} d^{3} e^{3} - a^{3} c d e^{5}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(6 \, a c^{3} d^{6} e - 4 \, a^{2} c^{2} d^{4} e^{3} - 11 \, a^{3} c d^{2} e^{5} - a^{4} e^{7} + {\left(2 \, c^{4} d^{5} e^{2} - 11 \, a c^{3} d^{3} e^{4} - 13 \, a^{2} c^{2} d e^{6}\right)} x^{3} + {\left(4 \, c^{4} d^{6} e - 10 \, a c^{3} d^{4} e^{3} - 17 \, a^{2} c^{2} d^{2} e^{5} - 3 \, a^{3} c e^{7}\right)} x^{2} + {\left(2 \, c^{4} d^{7} + 8 \, a c^{3} d^{5} e^{2} - 5 \, a^{2} c^{2} d^{3} e^{4} - 11 \, a^{3} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{4 \, {\left(a^{2} c^{4} d^{10} + 4 \, a^{3} c^{3} d^{8} e^{2} + 6 \, a^{4} c^{2} d^{6} e^{4} + 4 \, a^{5} c d^{4} e^{6} + a^{6} d^{2} e^{8} + {\left(a c^{5} d^{8} e^{2} + 4 \, a^{2} c^{4} d^{6} e^{4} + 6 \, a^{3} c^{3} d^{4} e^{6} + 4 \, a^{4} c^{2} d^{2} e^{8} + a^{5} c e^{10}\right)} x^{4} + 2 \, {\left(a c^{5} d^{9} e + 4 \, a^{2} c^{4} d^{7} e^{3} + 6 \, a^{3} c^{3} d^{5} e^{5} + 4 \, a^{4} c^{2} d^{3} e^{7} + a^{5} c d e^{9}\right)} x^{3} + {\left(a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}\right)} x^{2} + 2 \, {\left(a^{2} c^{4} d^{9} e + 4 \, a^{3} c^{3} d^{7} e^{3} + 6 \, a^{4} c^{2} d^{5} e^{5} + 4 \, a^{5} c d^{3} e^{7} + a^{6} d e^{9}\right)} x\right)}}, -\frac{3 \, {\left(4 \, a^{2} c^{2} d^{4} e^{2} - a^{3} c d^{2} e^{4} + {\left(4 \, a c^{3} d^{2} e^{4} - a^{2} c^{2} e^{6}\right)} x^{4} + 2 \, {\left(4 \, a c^{3} d^{3} e^{3} - a^{2} c^{2} d e^{5}\right)} x^{3} + {\left(4 \, a c^{3} d^{4} e^{2} + 3 \, a^{2} c^{2} d^{2} e^{4} - a^{3} c e^{6}\right)} x^{2} + 2 \, {\left(4 \, a^{2} c^{2} d^{3} e^{3} - a^{3} c d e^{5}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(6 \, a c^{3} d^{6} e - 4 \, a^{2} c^{2} d^{4} e^{3} - 11 \, a^{3} c d^{2} e^{5} - a^{4} e^{7} + {\left(2 \, c^{4} d^{5} e^{2} - 11 \, a c^{3} d^{3} e^{4} - 13 \, a^{2} c^{2} d e^{6}\right)} x^{3} + {\left(4 \, c^{4} d^{6} e - 10 \, a c^{3} d^{4} e^{3} - 17 \, a^{2} c^{2} d^{2} e^{5} - 3 \, a^{3} c e^{7}\right)} x^{2} + {\left(2 \, c^{4} d^{7} + 8 \, a c^{3} d^{5} e^{2} - 5 \, a^{2} c^{2} d^{3} e^{4} - 11 \, a^{3} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{2 \, {\left(a^{2} c^{4} d^{10} + 4 \, a^{3} c^{3} d^{8} e^{2} + 6 \, a^{4} c^{2} d^{6} e^{4} + 4 \, a^{5} c d^{4} e^{6} + a^{6} d^{2} e^{8} + {\left(a c^{5} d^{8} e^{2} + 4 \, a^{2} c^{4} d^{6} e^{4} + 6 \, a^{3} c^{3} d^{4} e^{6} + 4 \, a^{4} c^{2} d^{2} e^{8} + a^{5} c e^{10}\right)} x^{4} + 2 \, {\left(a c^{5} d^{9} e + 4 \, a^{2} c^{4} d^{7} e^{3} + 6 \, a^{3} c^{3} d^{5} e^{5} + 4 \, a^{4} c^{2} d^{3} e^{7} + a^{5} c d e^{9}\right)} x^{3} + {\left(a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}\right)} x^{2} + 2 \, {\left(a^{2} c^{4} d^{9} e + 4 \, a^{3} c^{3} d^{7} e^{3} + 6 \, a^{4} c^{2} d^{5} e^{5} + 4 \, a^{5} c d^{3} e^{7} + a^{6} d e^{9}\right)} x\right)}}\right]"," ",0,"[1/4*(3*(4*a^2*c^2*d^4*e^2 - a^3*c*d^2*e^4 + (4*a*c^3*d^2*e^4 - a^2*c^2*e^6)*x^4 + 2*(4*a*c^3*d^3*e^3 - a^2*c^2*d*e^5)*x^3 + (4*a*c^3*d^4*e^2 + 3*a^2*c^2*d^2*e^4 - a^3*c*e^6)*x^2 + 2*(4*a^2*c^2*d^3*e^3 - a^3*c*d*e^5)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(6*a*c^3*d^6*e - 4*a^2*c^2*d^4*e^3 - 11*a^3*c*d^2*e^5 - a^4*e^7 + (2*c^4*d^5*e^2 - 11*a*c^3*d^3*e^4 - 13*a^2*c^2*d*e^6)*x^3 + (4*c^4*d^6*e - 10*a*c^3*d^4*e^3 - 17*a^2*c^2*d^2*e^5 - 3*a^3*c*e^7)*x^2 + (2*c^4*d^7 + 8*a*c^3*d^5*e^2 - 5*a^2*c^2*d^3*e^4 - 11*a^3*c*d*e^6)*x)*sqrt(c*x^2 + a))/(a^2*c^4*d^10 + 4*a^3*c^3*d^8*e^2 + 6*a^4*c^2*d^6*e^4 + 4*a^5*c*d^4*e^6 + a^6*d^2*e^8 + (a*c^5*d^8*e^2 + 4*a^2*c^4*d^6*e^4 + 6*a^3*c^3*d^4*e^6 + 4*a^4*c^2*d^2*e^8 + a^5*c*e^10)*x^4 + 2*(a*c^5*d^9*e + 4*a^2*c^4*d^7*e^3 + 6*a^3*c^3*d^5*e^5 + 4*a^4*c^2*d^3*e^7 + a^5*c*d*e^9)*x^3 + (a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10)*x^2 + 2*(a^2*c^4*d^9*e + 4*a^3*c^3*d^7*e^3 + 6*a^4*c^2*d^5*e^5 + 4*a^5*c*d^3*e^7 + a^6*d*e^9)*x), -1/2*(3*(4*a^2*c^2*d^4*e^2 - a^3*c*d^2*e^4 + (4*a*c^3*d^2*e^4 - a^2*c^2*e^6)*x^4 + 2*(4*a*c^3*d^3*e^3 - a^2*c^2*d*e^5)*x^3 + (4*a*c^3*d^4*e^2 + 3*a^2*c^2*d^2*e^4 - a^3*c*e^6)*x^2 + 2*(4*a^2*c^2*d^3*e^3 - a^3*c*d*e^5)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (6*a*c^3*d^6*e - 4*a^2*c^2*d^4*e^3 - 11*a^3*c*d^2*e^5 - a^4*e^7 + (2*c^4*d^5*e^2 - 11*a*c^3*d^3*e^4 - 13*a^2*c^2*d*e^6)*x^3 + (4*c^4*d^6*e - 10*a*c^3*d^4*e^3 - 17*a^2*c^2*d^2*e^5 - 3*a^3*c*e^7)*x^2 + (2*c^4*d^7 + 8*a*c^3*d^5*e^2 - 5*a^2*c^2*d^3*e^4 - 11*a^3*c*d*e^6)*x)*sqrt(c*x^2 + a))/(a^2*c^4*d^10 + 4*a^3*c^3*d^8*e^2 + 6*a^4*c^2*d^6*e^4 + 4*a^5*c*d^4*e^6 + a^6*d^2*e^8 + (a*c^5*d^8*e^2 + 4*a^2*c^4*d^6*e^4 + 6*a^3*c^3*d^4*e^6 + 4*a^4*c^2*d^2*e^8 + a^5*c*e^10)*x^4 + 2*(a*c^5*d^9*e + 4*a^2*c^4*d^7*e^3 + 6*a^3*c^3*d^5*e^5 + 4*a^4*c^2*d^3*e^7 + a^5*c*d*e^9)*x^3 + (a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10)*x^2 + 2*(a^2*c^4*d^9*e + 4*a^3*c^3*d^7*e^3 + 6*a^4*c^2*d^5*e^5 + 4*a^5*c*d^3*e^7 + a^6*d*e^9)*x)]","B",0
576,1,2226,0,1.715153," ","integrate(1/(e*x+d)^4/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(4 \, a^{2} c^{3} d^{6} e^{2} - 3 \, a^{3} c^{2} d^{4} e^{4} + {\left(4 \, a c^{4} d^{3} e^{5} - 3 \, a^{2} c^{3} d e^{7}\right)} x^{5} + 3 \, {\left(4 \, a c^{4} d^{4} e^{4} - 3 \, a^{2} c^{3} d^{2} e^{6}\right)} x^{4} + {\left(12 \, a c^{4} d^{5} e^{3} - 5 \, a^{2} c^{3} d^{3} e^{5} - 3 \, a^{3} c^{2} d e^{7}\right)} x^{3} + {\left(4 \, a c^{4} d^{6} e^{2} + 9 \, a^{2} c^{3} d^{4} e^{4} - 9 \, a^{3} c^{2} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(4 \, a^{2} c^{3} d^{5} e^{3} - 3 \, a^{3} c^{2} d^{3} e^{5}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(24 \, a c^{4} d^{8} e - 60 \, a^{2} c^{3} d^{6} e^{3} - 89 \, a^{3} c^{2} d^{4} e^{5} - 7 \, a^{4} c d^{2} e^{7} - 2 \, a^{5} e^{9} + {\left(6 \, c^{5} d^{6} e^{3} - 77 \, a c^{4} d^{4} e^{5} - 67 \, a^{2} c^{3} d^{2} e^{7} + 16 \, a^{3} c^{2} e^{9}\right)} x^{4} + 3 \, {\left(6 \, c^{5} d^{7} e^{2} - 57 \, a c^{4} d^{5} e^{4} - 62 \, a^{2} c^{3} d^{3} e^{6} + a^{3} c^{2} d e^{8}\right)} x^{3} + 2 \, {\left(9 \, c^{5} d^{8} e - 39 \, a c^{4} d^{6} e^{3} - 101 \, a^{2} c^{3} d^{4} e^{5} - 49 \, a^{3} c^{2} d^{2} e^{7} + 4 \, a^{4} c e^{9}\right)} x^{2} + 3 \, {\left(2 \, c^{5} d^{9} + 14 \, a c^{4} d^{7} e^{2} - 45 \, a^{2} c^{3} d^{5} e^{4} - 54 \, a^{3} c^{2} d^{3} e^{6} + 3 \, a^{4} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(a^{2} c^{5} d^{13} + 5 \, a^{3} c^{4} d^{11} e^{2} + 10 \, a^{4} c^{3} d^{9} e^{4} + 10 \, a^{5} c^{2} d^{7} e^{6} + 5 \, a^{6} c d^{5} e^{8} + a^{7} d^{3} e^{10} + {\left(a c^{6} d^{10} e^{3} + 5 \, a^{2} c^{5} d^{8} e^{5} + 10 \, a^{3} c^{4} d^{6} e^{7} + 10 \, a^{4} c^{3} d^{4} e^{9} + 5 \, a^{5} c^{2} d^{2} e^{11} + a^{6} c e^{13}\right)} x^{5} + 3 \, {\left(a c^{6} d^{11} e^{2} + 5 \, a^{2} c^{5} d^{9} e^{4} + 10 \, a^{3} c^{4} d^{7} e^{6} + 10 \, a^{4} c^{3} d^{5} e^{8} + 5 \, a^{5} c^{2} d^{3} e^{10} + a^{6} c d e^{12}\right)} x^{4} + {\left(3 \, a c^{6} d^{12} e + 16 \, a^{2} c^{5} d^{10} e^{3} + 35 \, a^{3} c^{4} d^{8} e^{5} + 40 \, a^{4} c^{3} d^{6} e^{7} + 25 \, a^{5} c^{2} d^{4} e^{9} + 8 \, a^{6} c d^{2} e^{11} + a^{7} e^{13}\right)} x^{3} + {\left(a c^{6} d^{13} + 8 \, a^{2} c^{5} d^{11} e^{2} + 25 \, a^{3} c^{4} d^{9} e^{4} + 40 \, a^{4} c^{3} d^{7} e^{6} + 35 \, a^{5} c^{2} d^{5} e^{8} + 16 \, a^{6} c d^{3} e^{10} + 3 \, a^{7} d e^{12}\right)} x^{2} + 3 \, {\left(a^{2} c^{5} d^{12} e + 5 \, a^{3} c^{4} d^{10} e^{3} + 10 \, a^{4} c^{3} d^{8} e^{5} + 10 \, a^{5} c^{2} d^{6} e^{7} + 5 \, a^{6} c d^{4} e^{9} + a^{7} d^{2} e^{11}\right)} x\right)}}, -\frac{15 \, {\left(4 \, a^{2} c^{3} d^{6} e^{2} - 3 \, a^{3} c^{2} d^{4} e^{4} + {\left(4 \, a c^{4} d^{3} e^{5} - 3 \, a^{2} c^{3} d e^{7}\right)} x^{5} + 3 \, {\left(4 \, a c^{4} d^{4} e^{4} - 3 \, a^{2} c^{3} d^{2} e^{6}\right)} x^{4} + {\left(12 \, a c^{4} d^{5} e^{3} - 5 \, a^{2} c^{3} d^{3} e^{5} - 3 \, a^{3} c^{2} d e^{7}\right)} x^{3} + {\left(4 \, a c^{4} d^{6} e^{2} + 9 \, a^{2} c^{3} d^{4} e^{4} - 9 \, a^{3} c^{2} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(4 \, a^{2} c^{3} d^{5} e^{3} - 3 \, a^{3} c^{2} d^{3} e^{5}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(24 \, a c^{4} d^{8} e - 60 \, a^{2} c^{3} d^{6} e^{3} - 89 \, a^{3} c^{2} d^{4} e^{5} - 7 \, a^{4} c d^{2} e^{7} - 2 \, a^{5} e^{9} + {\left(6 \, c^{5} d^{6} e^{3} - 77 \, a c^{4} d^{4} e^{5} - 67 \, a^{2} c^{3} d^{2} e^{7} + 16 \, a^{3} c^{2} e^{9}\right)} x^{4} + 3 \, {\left(6 \, c^{5} d^{7} e^{2} - 57 \, a c^{4} d^{5} e^{4} - 62 \, a^{2} c^{3} d^{3} e^{6} + a^{3} c^{2} d e^{8}\right)} x^{3} + 2 \, {\left(9 \, c^{5} d^{8} e - 39 \, a c^{4} d^{6} e^{3} - 101 \, a^{2} c^{3} d^{4} e^{5} - 49 \, a^{3} c^{2} d^{2} e^{7} + 4 \, a^{4} c e^{9}\right)} x^{2} + 3 \, {\left(2 \, c^{5} d^{9} + 14 \, a c^{4} d^{7} e^{2} - 45 \, a^{2} c^{3} d^{5} e^{4} - 54 \, a^{3} c^{2} d^{3} e^{6} + 3 \, a^{4} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a^{2} c^{5} d^{13} + 5 \, a^{3} c^{4} d^{11} e^{2} + 10 \, a^{4} c^{3} d^{9} e^{4} + 10 \, a^{5} c^{2} d^{7} e^{6} + 5 \, a^{6} c d^{5} e^{8} + a^{7} d^{3} e^{10} + {\left(a c^{6} d^{10} e^{3} + 5 \, a^{2} c^{5} d^{8} e^{5} + 10 \, a^{3} c^{4} d^{6} e^{7} + 10 \, a^{4} c^{3} d^{4} e^{9} + 5 \, a^{5} c^{2} d^{2} e^{11} + a^{6} c e^{13}\right)} x^{5} + 3 \, {\left(a c^{6} d^{11} e^{2} + 5 \, a^{2} c^{5} d^{9} e^{4} + 10 \, a^{3} c^{4} d^{7} e^{6} + 10 \, a^{4} c^{3} d^{5} e^{8} + 5 \, a^{5} c^{2} d^{3} e^{10} + a^{6} c d e^{12}\right)} x^{4} + {\left(3 \, a c^{6} d^{12} e + 16 \, a^{2} c^{5} d^{10} e^{3} + 35 \, a^{3} c^{4} d^{8} e^{5} + 40 \, a^{4} c^{3} d^{6} e^{7} + 25 \, a^{5} c^{2} d^{4} e^{9} + 8 \, a^{6} c d^{2} e^{11} + a^{7} e^{13}\right)} x^{3} + {\left(a c^{6} d^{13} + 8 \, a^{2} c^{5} d^{11} e^{2} + 25 \, a^{3} c^{4} d^{9} e^{4} + 40 \, a^{4} c^{3} d^{7} e^{6} + 35 \, a^{5} c^{2} d^{5} e^{8} + 16 \, a^{6} c d^{3} e^{10} + 3 \, a^{7} d e^{12}\right)} x^{2} + 3 \, {\left(a^{2} c^{5} d^{12} e + 5 \, a^{3} c^{4} d^{10} e^{3} + 10 \, a^{4} c^{3} d^{8} e^{5} + 10 \, a^{5} c^{2} d^{6} e^{7} + 5 \, a^{6} c d^{4} e^{9} + a^{7} d^{2} e^{11}\right)} x\right)}}\right]"," ",0,"[1/12*(15*(4*a^2*c^3*d^6*e^2 - 3*a^3*c^2*d^4*e^4 + (4*a*c^4*d^3*e^5 - 3*a^2*c^3*d*e^7)*x^5 + 3*(4*a*c^4*d^4*e^4 - 3*a^2*c^3*d^2*e^6)*x^4 + (12*a*c^4*d^5*e^3 - 5*a^2*c^3*d^3*e^5 - 3*a^3*c^2*d*e^7)*x^3 + (4*a*c^4*d^6*e^2 + 9*a^2*c^3*d^4*e^4 - 9*a^3*c^2*d^2*e^6)*x^2 + 3*(4*a^2*c^3*d^5*e^3 - 3*a^3*c^2*d^3*e^5)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(24*a*c^4*d^8*e - 60*a^2*c^3*d^6*e^3 - 89*a^3*c^2*d^4*e^5 - 7*a^4*c*d^2*e^7 - 2*a^5*e^9 + (6*c^5*d^6*e^3 - 77*a*c^4*d^4*e^5 - 67*a^2*c^3*d^2*e^7 + 16*a^3*c^2*e^9)*x^4 + 3*(6*c^5*d^7*e^2 - 57*a*c^4*d^5*e^4 - 62*a^2*c^3*d^3*e^6 + a^3*c^2*d*e^8)*x^3 + 2*(9*c^5*d^8*e - 39*a*c^4*d^6*e^3 - 101*a^2*c^3*d^4*e^5 - 49*a^3*c^2*d^2*e^7 + 4*a^4*c*e^9)*x^2 + 3*(2*c^5*d^9 + 14*a*c^4*d^7*e^2 - 45*a^2*c^3*d^5*e^4 - 54*a^3*c^2*d^3*e^6 + 3*a^4*c*d*e^8)*x)*sqrt(c*x^2 + a))/(a^2*c^5*d^13 + 5*a^3*c^4*d^11*e^2 + 10*a^4*c^3*d^9*e^4 + 10*a^5*c^2*d^7*e^6 + 5*a^6*c*d^5*e^8 + a^7*d^3*e^10 + (a*c^6*d^10*e^3 + 5*a^2*c^5*d^8*e^5 + 10*a^3*c^4*d^6*e^7 + 10*a^4*c^3*d^4*e^9 + 5*a^5*c^2*d^2*e^11 + a^6*c*e^13)*x^5 + 3*(a*c^6*d^11*e^2 + 5*a^2*c^5*d^9*e^4 + 10*a^3*c^4*d^7*e^6 + 10*a^4*c^3*d^5*e^8 + 5*a^5*c^2*d^3*e^10 + a^6*c*d*e^12)*x^4 + (3*a*c^6*d^12*e + 16*a^2*c^5*d^10*e^3 + 35*a^3*c^4*d^8*e^5 + 40*a^4*c^3*d^6*e^7 + 25*a^5*c^2*d^4*e^9 + 8*a^6*c*d^2*e^11 + a^7*e^13)*x^3 + (a*c^6*d^13 + 8*a^2*c^5*d^11*e^2 + 25*a^3*c^4*d^9*e^4 + 40*a^4*c^3*d^7*e^6 + 35*a^5*c^2*d^5*e^8 + 16*a^6*c*d^3*e^10 + 3*a^7*d*e^12)*x^2 + 3*(a^2*c^5*d^12*e + 5*a^3*c^4*d^10*e^3 + 10*a^4*c^3*d^8*e^5 + 10*a^5*c^2*d^6*e^7 + 5*a^6*c*d^4*e^9 + a^7*d^2*e^11)*x), -1/6*(15*(4*a^2*c^3*d^6*e^2 - 3*a^3*c^2*d^4*e^4 + (4*a*c^4*d^3*e^5 - 3*a^2*c^3*d*e^7)*x^5 + 3*(4*a*c^4*d^4*e^4 - 3*a^2*c^3*d^2*e^6)*x^4 + (12*a*c^4*d^5*e^3 - 5*a^2*c^3*d^3*e^5 - 3*a^3*c^2*d*e^7)*x^3 + (4*a*c^4*d^6*e^2 + 9*a^2*c^3*d^4*e^4 - 9*a^3*c^2*d^2*e^6)*x^2 + 3*(4*a^2*c^3*d^5*e^3 - 3*a^3*c^2*d^3*e^5)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (24*a*c^4*d^8*e - 60*a^2*c^3*d^6*e^3 - 89*a^3*c^2*d^4*e^5 - 7*a^4*c*d^2*e^7 - 2*a^5*e^9 + (6*c^5*d^6*e^3 - 77*a*c^4*d^4*e^5 - 67*a^2*c^3*d^2*e^7 + 16*a^3*c^2*e^9)*x^4 + 3*(6*c^5*d^7*e^2 - 57*a*c^4*d^5*e^4 - 62*a^2*c^3*d^3*e^6 + a^3*c^2*d*e^8)*x^3 + 2*(9*c^5*d^8*e - 39*a*c^4*d^6*e^3 - 101*a^2*c^3*d^4*e^5 - 49*a^3*c^2*d^2*e^7 + 4*a^4*c*e^9)*x^2 + 3*(2*c^5*d^9 + 14*a*c^4*d^7*e^2 - 45*a^2*c^3*d^5*e^4 - 54*a^3*c^2*d^3*e^6 + 3*a^4*c*d*e^8)*x)*sqrt(c*x^2 + a))/(a^2*c^5*d^13 + 5*a^3*c^4*d^11*e^2 + 10*a^4*c^3*d^9*e^4 + 10*a^5*c^2*d^7*e^6 + 5*a^6*c*d^5*e^8 + a^7*d^3*e^10 + (a*c^6*d^10*e^3 + 5*a^2*c^5*d^8*e^5 + 10*a^3*c^4*d^6*e^7 + 10*a^4*c^3*d^4*e^9 + 5*a^5*c^2*d^2*e^11 + a^6*c*e^13)*x^5 + 3*(a*c^6*d^11*e^2 + 5*a^2*c^5*d^9*e^4 + 10*a^3*c^4*d^7*e^6 + 10*a^4*c^3*d^5*e^8 + 5*a^5*c^2*d^3*e^10 + a^6*c*d*e^12)*x^4 + (3*a*c^6*d^12*e + 16*a^2*c^5*d^10*e^3 + 35*a^3*c^4*d^8*e^5 + 40*a^4*c^3*d^6*e^7 + 25*a^5*c^2*d^4*e^9 + 8*a^6*c*d^2*e^11 + a^7*e^13)*x^3 + (a*c^6*d^13 + 8*a^2*c^5*d^11*e^2 + 25*a^3*c^4*d^9*e^4 + 40*a^4*c^3*d^7*e^6 + 35*a^5*c^2*d^5*e^8 + 16*a^6*c*d^3*e^10 + 3*a^7*d*e^12)*x^2 + 3*(a^2*c^5*d^12*e + 5*a^3*c^4*d^10*e^3 + 10*a^4*c^3*d^8*e^5 + 10*a^5*c^2*d^6*e^7 + 5*a^6*c*d^4*e^9 + a^7*d^2*e^11)*x)]","B",0
577,1,488,0,0.469470," ","integrate((e*x+d)^5/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} c^{2} d e^{4} x^{4} + 2 \, a^{3} c d e^{4} x^{2} + a^{4} d e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) + 2 \, {\left(3 \, a^{2} c^{2} e^{5} x^{4} - 5 \, a^{2} c^{2} d^{4} e - 20 \, a^{3} c d^{2} e^{3} + 8 \, a^{4} e^{5} + 2 \, {\left(c^{4} d^{5} + 5 \, a c^{3} d^{3} e^{2} - 10 \, a^{2} c^{2} d e^{4}\right)} x^{3} - 6 \, {\left(5 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a^{3} c e^{5}\right)} x^{2} + 3 \, {\left(a c^{3} d^{5} - 5 \, a^{3} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a^{2} c^{5} x^{4} + 2 \, a^{3} c^{4} x^{2} + a^{4} c^{3}\right)}}, -\frac{15 \, {\left(a^{2} c^{2} d e^{4} x^{4} + 2 \, a^{3} c d e^{4} x^{2} + a^{4} d e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) - {\left(3 \, a^{2} c^{2} e^{5} x^{4} - 5 \, a^{2} c^{2} d^{4} e - 20 \, a^{3} c d^{2} e^{3} + 8 \, a^{4} e^{5} + 2 \, {\left(c^{4} d^{5} + 5 \, a c^{3} d^{3} e^{2} - 10 \, a^{2} c^{2} d e^{4}\right)} x^{3} - 6 \, {\left(5 \, a^{2} c^{2} d^{2} e^{3} - 2 \, a^{3} c e^{5}\right)} x^{2} + 3 \, {\left(a c^{3} d^{5} - 5 \, a^{3} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{2} c^{5} x^{4} + 2 \, a^{3} c^{4} x^{2} + a^{4} c^{3}\right)}}\right]"," ",0,"[1/6*(15*(a^2*c^2*d*e^4*x^4 + 2*a^3*c*d*e^4*x^2 + a^4*d*e^4)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) + 2*(3*a^2*c^2*e^5*x^4 - 5*a^2*c^2*d^4*e - 20*a^3*c*d^2*e^3 + 8*a^4*e^5 + 2*(c^4*d^5 + 5*a*c^3*d^3*e^2 - 10*a^2*c^2*d*e^4)*x^3 - 6*(5*a^2*c^2*d^2*e^3 - 2*a^3*c*e^5)*x^2 + 3*(a*c^3*d^5 - 5*a^3*c*d*e^4)*x)*sqrt(c*x^2 + a))/(a^2*c^5*x^4 + 2*a^3*c^4*x^2 + a^4*c^3), -1/3*(15*(a^2*c^2*d*e^4*x^4 + 2*a^3*c*d*e^4*x^2 + a^4*d*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) - (3*a^2*c^2*e^5*x^4 - 5*a^2*c^2*d^4*e - 20*a^3*c*d^2*e^3 + 8*a^4*e^5 + 2*(c^4*d^5 + 5*a*c^3*d^3*e^2 - 10*a^2*c^2*d*e^4)*x^3 - 6*(5*a^2*c^2*d^2*e^3 - 2*a^3*c*e^5)*x^2 + 3*(a*c^3*d^5 - 5*a^3*c*d*e^4)*x)*sqrt(c*x^2 + a))/(a^2*c^5*x^4 + 2*a^3*c^4*x^2 + a^4*c^3)]","A",0
578,1,401,0,0.433628," ","integrate((e*x+d)^4/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} c^{2} e^{4} x^{4} + 2 \, a^{3} c e^{4} x^{2} + a^{4} e^{4}\right)} \sqrt{c} \log\left(-2 \, c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{c} x - a\right) - 2 \, {\left(12 \, a^{2} c^{2} d e^{3} x^{2} + 4 \, a^{2} c^{2} d^{3} e + 8 \, a^{3} c d e^{3} - 2 \, {\left(c^{4} d^{4} + 3 \, a c^{3} d^{2} e^{2} - 2 \, a^{2} c^{2} e^{4}\right)} x^{3} - 3 \, {\left(a c^{3} d^{4} - a^{3} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a^{2} c^{5} x^{4} + 2 \, a^{3} c^{4} x^{2} + a^{4} c^{3}\right)}}, -\frac{3 \, {\left(a^{2} c^{2} e^{4} x^{4} + 2 \, a^{3} c e^{4} x^{2} + a^{4} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{\sqrt{c x^{2} + a}}\right) + {\left(12 \, a^{2} c^{2} d e^{3} x^{2} + 4 \, a^{2} c^{2} d^{3} e + 8 \, a^{3} c d e^{3} - 2 \, {\left(c^{4} d^{4} + 3 \, a c^{3} d^{2} e^{2} - 2 \, a^{2} c^{2} e^{4}\right)} x^{3} - 3 \, {\left(a c^{3} d^{4} - a^{3} c e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{2} c^{5} x^{4} + 2 \, a^{3} c^{4} x^{2} + a^{4} c^{3}\right)}}\right]"," ",0,"[1/6*(3*(a^2*c^2*e^4*x^4 + 2*a^3*c*e^4*x^2 + a^4*e^4)*sqrt(c)*log(-2*c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(c)*x - a) - 2*(12*a^2*c^2*d*e^3*x^2 + 4*a^2*c^2*d^3*e + 8*a^3*c*d*e^3 - 2*(c^4*d^4 + 3*a*c^3*d^2*e^2 - 2*a^2*c^2*e^4)*x^3 - 3*(a*c^3*d^4 - a^3*c*e^4)*x)*sqrt(c*x^2 + a))/(a^2*c^5*x^4 + 2*a^3*c^4*x^2 + a^4*c^3), -1/3*(3*(a^2*c^2*e^4*x^4 + 2*a^3*c*e^4*x^2 + a^4*e^4)*sqrt(-c)*arctan(sqrt(-c)*x/sqrt(c*x^2 + a)) + (12*a^2*c^2*d*e^3*x^2 + 4*a^2*c^2*d^3*e + 8*a^3*c*d*e^3 - 2*(c^4*d^4 + 3*a*c^3*d^2*e^2 - 2*a^2*c^2*e^4)*x^3 - 3*(a*c^3*d^4 - a^3*c*e^4)*x)*sqrt(c*x^2 + a))/(a^2*c^5*x^4 + 2*a^3*c^4*x^2 + a^4*c^3)]","A",0
579,1,107,0,0.419075," ","integrate((e*x+d)^3/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{2} c e^{3} x^{2} - 3 \, a c^{2} d^{3} x + 3 \, a^{2} c d^{2} e + 2 \, a^{3} e^{3} - {\left(2 \, c^{3} d^{3} + 3 \, a c^{2} d e^{2}\right)} x^{3}\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{2} c^{4} x^{4} + 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)}}"," ",0,"-1/3*(3*a^2*c*e^3*x^2 - 3*a*c^2*d^3*x + 3*a^2*c*d^2*e + 2*a^3*e^3 - (2*c^3*d^3 + 3*a*c^2*d*e^2)*x^3)*sqrt(c*x^2 + a)/(a^2*c^4*x^4 + 2*a^3*c^3*x^2 + a^4*c^2)","A",0
580,1,75,0,0.421219," ","integrate((e*x+d)^2/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a c d^{2} x - 2 \, a^{2} d e + {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{3}\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}}"," ",0,"1/3*(3*a*c*d^2*x - 2*a^2*d*e + (2*c^2*d^2 + a*c*e^2)*x^3)*sqrt(c*x^2 + a)/(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)","A",0
581,1,62,0,0.398072," ","integrate((e*x+d)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, c^{2} d x^{3} + 3 \, a c d x - a^{2} e\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}}"," ",0,"1/3*(2*c^2*d*x^3 + 3*a*c*d*x - a^2*e)*sqrt(c*x^2 + a)/(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)","A",0
582,1,858,0,0.555205," ","integrate(1/(e*x+d)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} c^{2} e^{4} x^{4} + 2 \, a^{3} c e^{4} x^{2} + a^{4} e^{4}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(a^{2} c^{2} d^{4} e + 5 \, a^{3} c d^{2} e^{3} + 4 \, a^{4} e^{5} + {\left(2 \, c^{4} d^{5} + 7 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4}\right)} x^{3} + 3 \, {\left(a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{2} + 3 \, {\left(a c^{3} d^{5} + 3 \, a^{2} c^{2} d^{3} e^{2} + 2 \, a^{3} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a^{4} c^{3} d^{6} + 3 \, a^{5} c^{2} d^{4} e^{2} + 3 \, a^{6} c d^{2} e^{4} + a^{7} e^{6} + {\left(a^{2} c^{5} d^{6} + 3 \, a^{3} c^{4} d^{4} e^{2} + 3 \, a^{4} c^{3} d^{2} e^{4} + a^{5} c^{2} e^{6}\right)} x^{4} + 2 \, {\left(a^{3} c^{4} d^{6} + 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} + a^{6} c e^{6}\right)} x^{2}\right)}}, -\frac{3 \, {\left(a^{2} c^{2} e^{4} x^{4} + 2 \, a^{3} c e^{4} x^{2} + a^{4} e^{4}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(a^{2} c^{2} d^{4} e + 5 \, a^{3} c d^{2} e^{3} + 4 \, a^{4} e^{5} + {\left(2 \, c^{4} d^{5} + 7 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4}\right)} x^{3} + 3 \, {\left(a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{2} + 3 \, {\left(a c^{3} d^{5} + 3 \, a^{2} c^{2} d^{3} e^{2} + 2 \, a^{3} c d e^{4}\right)} x\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{4} c^{3} d^{6} + 3 \, a^{5} c^{2} d^{4} e^{2} + 3 \, a^{6} c d^{2} e^{4} + a^{7} e^{6} + {\left(a^{2} c^{5} d^{6} + 3 \, a^{3} c^{4} d^{4} e^{2} + 3 \, a^{4} c^{3} d^{2} e^{4} + a^{5} c^{2} e^{6}\right)} x^{4} + 2 \, {\left(a^{3} c^{4} d^{6} + 3 \, a^{4} c^{3} d^{4} e^{2} + 3 \, a^{5} c^{2} d^{2} e^{4} + a^{6} c e^{6}\right)} x^{2}\right)}}\right]"," ",0,"[1/6*(3*(a^2*c^2*e^4*x^4 + 2*a^3*c*e^4*x^2 + a^4*e^4)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(a^2*c^2*d^4*e + 5*a^3*c*d^2*e^3 + 4*a^4*e^5 + (2*c^4*d^5 + 7*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4)*x^3 + 3*(a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^2 + 3*(a*c^3*d^5 + 3*a^2*c^2*d^3*e^2 + 2*a^3*c*d*e^4)*x)*sqrt(c*x^2 + a))/(a^4*c^3*d^6 + 3*a^5*c^2*d^4*e^2 + 3*a^6*c*d^2*e^4 + a^7*e^6 + (a^2*c^5*d^6 + 3*a^3*c^4*d^4*e^2 + 3*a^4*c^3*d^2*e^4 + a^5*c^2*e^6)*x^4 + 2*(a^3*c^4*d^6 + 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 + a^6*c*e^6)*x^2), -1/3*(3*(a^2*c^2*e^4*x^4 + 2*a^3*c*e^4*x^2 + a^4*e^4)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (a^2*c^2*d^4*e + 5*a^3*c*d^2*e^3 + 4*a^4*e^5 + (2*c^4*d^5 + 7*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4)*x^3 + 3*(a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^2 + 3*(a*c^3*d^5 + 3*a^2*c^2*d^3*e^2 + 2*a^3*c*d*e^4)*x)*sqrt(c*x^2 + a))/(a^4*c^3*d^6 + 3*a^5*c^2*d^4*e^2 + 3*a^6*c*d^2*e^4 + a^7*e^6 + (a^2*c^5*d^6 + 3*a^3*c^4*d^4*e^2 + 3*a^4*c^3*d^2*e^4 + a^5*c^2*e^6)*x^4 + 2*(a^3*c^4*d^6 + 3*a^4*c^3*d^4*e^2 + 3*a^5*c^2*d^2*e^4 + a^6*c*e^6)*x^2)]","B",0
583,1,1678,0,0.751137," ","integrate(1/(e*x+d)^2/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} c^{3} d e^{5} x^{5} + a^{2} c^{3} d^{2} e^{4} x^{4} + 2 \, a^{3} c^{2} d e^{5} x^{3} + 2 \, a^{3} c^{2} d^{2} e^{4} x^{2} + a^{4} c d e^{5} x + a^{4} c d^{2} e^{4}\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(2 \, a^{2} c^{3} d^{6} e + 16 \, a^{3} c^{2} d^{4} e^{3} + 11 \, a^{4} c d^{2} e^{5} - 3 \, a^{5} e^{7} + {\left(2 \, c^{5} d^{6} e + 11 \, a c^{4} d^{4} e^{3} + a^{2} c^{3} d^{2} e^{5} - 8 \, a^{3} c^{2} e^{7}\right)} x^{4} + {\left(2 \, c^{5} d^{7} + 11 \, a c^{4} d^{5} e^{2} + 16 \, a^{2} c^{3} d^{3} e^{4} + 7 \, a^{3} c^{2} d e^{6}\right)} x^{3} + 3 \, {\left(a c^{4} d^{6} e + 8 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} - 4 \, a^{4} c e^{7}\right)} x^{2} + {\left(3 \, a c^{4} d^{7} + 14 \, a^{2} c^{3} d^{5} e^{2} + 19 \, a^{3} c^{2} d^{3} e^{4} + 8 \, a^{4} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a^{4} c^{4} d^{9} + 4 \, a^{5} c^{3} d^{7} e^{2} + 6 \, a^{6} c^{2} d^{5} e^{4} + 4 \, a^{7} c d^{3} e^{6} + a^{8} d e^{8} + {\left(a^{2} c^{6} d^{8} e + 4 \, a^{3} c^{5} d^{6} e^{3} + 6 \, a^{4} c^{4} d^{4} e^{5} + 4 \, a^{5} c^{3} d^{2} e^{7} + a^{6} c^{2} e^{9}\right)} x^{5} + {\left(a^{2} c^{6} d^{9} + 4 \, a^{3} c^{5} d^{7} e^{2} + 6 \, a^{4} c^{4} d^{5} e^{4} + 4 \, a^{5} c^{3} d^{3} e^{6} + a^{6} c^{2} d e^{8}\right)} x^{4} + 2 \, {\left(a^{3} c^{5} d^{8} e + 4 \, a^{4} c^{4} d^{6} e^{3} + 6 \, a^{5} c^{3} d^{4} e^{5} + 4 \, a^{6} c^{2} d^{2} e^{7} + a^{7} c e^{9}\right)} x^{3} + 2 \, {\left(a^{3} c^{5} d^{9} + 4 \, a^{4} c^{4} d^{7} e^{2} + 6 \, a^{5} c^{3} d^{5} e^{4} + 4 \, a^{6} c^{2} d^{3} e^{6} + a^{7} c d e^{8}\right)} x^{2} + {\left(a^{4} c^{4} d^{8} e + 4 \, a^{5} c^{3} d^{6} e^{3} + 6 \, a^{6} c^{2} d^{4} e^{5} + 4 \, a^{7} c d^{2} e^{7} + a^{8} e^{9}\right)} x\right)}}, -\frac{15 \, {\left(a^{2} c^{3} d e^{5} x^{5} + a^{2} c^{3} d^{2} e^{4} x^{4} + 2 \, a^{3} c^{2} d e^{5} x^{3} + 2 \, a^{3} c^{2} d^{2} e^{4} x^{2} + a^{4} c d e^{5} x + a^{4} c d^{2} e^{4}\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(2 \, a^{2} c^{3} d^{6} e + 16 \, a^{3} c^{2} d^{4} e^{3} + 11 \, a^{4} c d^{2} e^{5} - 3 \, a^{5} e^{7} + {\left(2 \, c^{5} d^{6} e + 11 \, a c^{4} d^{4} e^{3} + a^{2} c^{3} d^{2} e^{5} - 8 \, a^{3} c^{2} e^{7}\right)} x^{4} + {\left(2 \, c^{5} d^{7} + 11 \, a c^{4} d^{5} e^{2} + 16 \, a^{2} c^{3} d^{3} e^{4} + 7 \, a^{3} c^{2} d e^{6}\right)} x^{3} + 3 \, {\left(a c^{4} d^{6} e + 8 \, a^{2} c^{3} d^{4} e^{3} + 3 \, a^{3} c^{2} d^{2} e^{5} - 4 \, a^{4} c e^{7}\right)} x^{2} + {\left(3 \, a c^{4} d^{7} + 14 \, a^{2} c^{3} d^{5} e^{2} + 19 \, a^{3} c^{2} d^{3} e^{4} + 8 \, a^{4} c d e^{6}\right)} x\right)} \sqrt{c x^{2} + a}}{3 \, {\left(a^{4} c^{4} d^{9} + 4 \, a^{5} c^{3} d^{7} e^{2} + 6 \, a^{6} c^{2} d^{5} e^{4} + 4 \, a^{7} c d^{3} e^{6} + a^{8} d e^{8} + {\left(a^{2} c^{6} d^{8} e + 4 \, a^{3} c^{5} d^{6} e^{3} + 6 \, a^{4} c^{4} d^{4} e^{5} + 4 \, a^{5} c^{3} d^{2} e^{7} + a^{6} c^{2} e^{9}\right)} x^{5} + {\left(a^{2} c^{6} d^{9} + 4 \, a^{3} c^{5} d^{7} e^{2} + 6 \, a^{4} c^{4} d^{5} e^{4} + 4 \, a^{5} c^{3} d^{3} e^{6} + a^{6} c^{2} d e^{8}\right)} x^{4} + 2 \, {\left(a^{3} c^{5} d^{8} e + 4 \, a^{4} c^{4} d^{6} e^{3} + 6 \, a^{5} c^{3} d^{4} e^{5} + 4 \, a^{6} c^{2} d^{2} e^{7} + a^{7} c e^{9}\right)} x^{3} + 2 \, {\left(a^{3} c^{5} d^{9} + 4 \, a^{4} c^{4} d^{7} e^{2} + 6 \, a^{5} c^{3} d^{5} e^{4} + 4 \, a^{6} c^{2} d^{3} e^{6} + a^{7} c d e^{8}\right)} x^{2} + {\left(a^{4} c^{4} d^{8} e + 4 \, a^{5} c^{3} d^{6} e^{3} + 6 \, a^{6} c^{2} d^{4} e^{5} + 4 \, a^{7} c d^{2} e^{7} + a^{8} e^{9}\right)} x\right)}}\right]"," ",0,"[1/6*(15*(a^2*c^3*d*e^5*x^5 + a^2*c^3*d^2*e^4*x^4 + 2*a^3*c^2*d*e^5*x^3 + 2*a^3*c^2*d^2*e^4*x^2 + a^4*c*d*e^5*x + a^4*c*d^2*e^4)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(2*a^2*c^3*d^6*e + 16*a^3*c^2*d^4*e^3 + 11*a^4*c*d^2*e^5 - 3*a^5*e^7 + (2*c^5*d^6*e + 11*a*c^4*d^4*e^3 + a^2*c^3*d^2*e^5 - 8*a^3*c^2*e^7)*x^4 + (2*c^5*d^7 + 11*a*c^4*d^5*e^2 + 16*a^2*c^3*d^3*e^4 + 7*a^3*c^2*d*e^6)*x^3 + 3*(a*c^4*d^6*e + 8*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 - 4*a^4*c*e^7)*x^2 + (3*a*c^4*d^7 + 14*a^2*c^3*d^5*e^2 + 19*a^3*c^2*d^3*e^4 + 8*a^4*c*d*e^6)*x)*sqrt(c*x^2 + a))/(a^4*c^4*d^9 + 4*a^5*c^3*d^7*e^2 + 6*a^6*c^2*d^5*e^4 + 4*a^7*c*d^3*e^6 + a^8*d*e^8 + (a^2*c^6*d^8*e + 4*a^3*c^5*d^6*e^3 + 6*a^4*c^4*d^4*e^5 + 4*a^5*c^3*d^2*e^7 + a^6*c^2*e^9)*x^5 + (a^2*c^6*d^9 + 4*a^3*c^5*d^7*e^2 + 6*a^4*c^4*d^5*e^4 + 4*a^5*c^3*d^3*e^6 + a^6*c^2*d*e^8)*x^4 + 2*(a^3*c^5*d^8*e + 4*a^4*c^4*d^6*e^3 + 6*a^5*c^3*d^4*e^5 + 4*a^6*c^2*d^2*e^7 + a^7*c*e^9)*x^3 + 2*(a^3*c^5*d^9 + 4*a^4*c^4*d^7*e^2 + 6*a^5*c^3*d^5*e^4 + 4*a^6*c^2*d^3*e^6 + a^7*c*d*e^8)*x^2 + (a^4*c^4*d^8*e + 4*a^5*c^3*d^6*e^3 + 6*a^6*c^2*d^4*e^5 + 4*a^7*c*d^2*e^7 + a^8*e^9)*x), -1/3*(15*(a^2*c^3*d*e^5*x^5 + a^2*c^3*d^2*e^4*x^4 + 2*a^3*c^2*d*e^5*x^3 + 2*a^3*c^2*d^2*e^4*x^2 + a^4*c*d*e^5*x + a^4*c*d^2*e^4)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (2*a^2*c^3*d^6*e + 16*a^3*c^2*d^4*e^3 + 11*a^4*c*d^2*e^5 - 3*a^5*e^7 + (2*c^5*d^6*e + 11*a*c^4*d^4*e^3 + a^2*c^3*d^2*e^5 - 8*a^3*c^2*e^7)*x^4 + (2*c^5*d^7 + 11*a*c^4*d^5*e^2 + 16*a^2*c^3*d^3*e^4 + 7*a^3*c^2*d*e^6)*x^3 + 3*(a*c^4*d^6*e + 8*a^2*c^3*d^4*e^3 + 3*a^3*c^2*d^2*e^5 - 4*a^4*c*e^7)*x^2 + (3*a*c^4*d^7 + 14*a^2*c^3*d^5*e^2 + 19*a^3*c^2*d^3*e^4 + 8*a^4*c*d*e^6)*x)*sqrt(c*x^2 + a))/(a^4*c^4*d^9 + 4*a^5*c^3*d^7*e^2 + 6*a^6*c^2*d^5*e^4 + 4*a^7*c*d^3*e^6 + a^8*d*e^8 + (a^2*c^6*d^8*e + 4*a^3*c^5*d^6*e^3 + 6*a^4*c^4*d^4*e^5 + 4*a^5*c^3*d^2*e^7 + a^6*c^2*e^9)*x^5 + (a^2*c^6*d^9 + 4*a^3*c^5*d^7*e^2 + 6*a^4*c^4*d^5*e^4 + 4*a^5*c^3*d^3*e^6 + a^6*c^2*d*e^8)*x^4 + 2*(a^3*c^5*d^8*e + 4*a^4*c^4*d^6*e^3 + 6*a^5*c^3*d^4*e^5 + 4*a^6*c^2*d^2*e^7 + a^7*c*e^9)*x^3 + 2*(a^3*c^5*d^9 + 4*a^4*c^4*d^7*e^2 + 6*a^5*c^3*d^5*e^4 + 4*a^6*c^2*d^3*e^6 + a^7*c*d*e^8)*x^2 + (a^4*c^4*d^8*e + 4*a^5*c^3*d^6*e^3 + 6*a^6*c^2*d^4*e^5 + 4*a^7*c*d^2*e^7 + a^8*e^9)*x)]","B",0
584,1,2628,0,1.662431," ","integrate(1/(e*x+d)^3/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(6 \, a^{4} c^{2} d^{4} e^{4} - a^{5} c d^{2} e^{6} + {\left(6 \, a^{2} c^{4} d^{2} e^{6} - a^{3} c^{3} e^{8}\right)} x^{6} + 2 \, {\left(6 \, a^{2} c^{4} d^{3} e^{5} - a^{3} c^{3} d e^{7}\right)} x^{5} + {\left(6 \, a^{2} c^{4} d^{4} e^{4} + 11 \, a^{3} c^{3} d^{2} e^{6} - 2 \, a^{4} c^{2} e^{8}\right)} x^{4} + 4 \, {\left(6 \, a^{3} c^{3} d^{3} e^{5} - a^{4} c^{2} d e^{7}\right)} x^{3} + {\left(12 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} - a^{5} c e^{8}\right)} x^{2} + 2 \, {\left(6 \, a^{4} c^{2} d^{3} e^{5} - a^{5} c d e^{7}\right)} x\right)} \sqrt{c d^{2} + a e^{2}} \log\left(\frac{2 \, a c d e x - a c d^{2} - 2 \, a^{2} e^{2} - {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{2} - 2 \, \sqrt{c d^{2} + a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(6 \, a^{2} c^{4} d^{8} e + 70 \, a^{3} c^{3} d^{6} e^{3} + 14 \, a^{4} c^{2} d^{4} e^{5} - 53 \, a^{5} c d^{2} e^{7} - 3 \, a^{6} e^{9} + {\left(4 \, c^{6} d^{7} e^{2} + 32 \, a c^{5} d^{5} e^{4} - 53 \, a^{2} c^{4} d^{3} e^{6} - 81 \, a^{3} c^{3} d e^{8}\right)} x^{5} + {\left(8 \, c^{6} d^{8} e + 64 \, a c^{5} d^{6} e^{3} - 16 \, a^{2} c^{4} d^{4} e^{5} - 87 \, a^{3} c^{3} d^{2} e^{7} - 15 \, a^{4} c^{2} e^{9}\right)} x^{4} + 2 \, {\left(2 \, c^{6} d^{9} + 19 \, a c^{5} d^{7} e^{2} + 65 \, a^{2} c^{4} d^{5} e^{4} - 24 \, a^{3} c^{3} d^{3} e^{6} - 72 \, a^{4} c^{2} d e^{8}\right)} x^{3} + 2 \, {\left(6 \, a c^{5} d^{8} e + 63 \, a^{2} c^{4} d^{6} e^{3} - 7 \, a^{3} c^{3} d^{4} e^{5} - 74 \, a^{4} c^{2} d^{2} e^{7} - 10 \, a^{5} c e^{9}\right)} x^{2} + {\left(6 \, a c^{5} d^{9} + 42 \, a^{2} c^{4} d^{7} e^{2} + 110 \, a^{3} c^{3} d^{5} e^{4} + 13 \, a^{4} c^{2} d^{3} e^{6} - 61 \, a^{5} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{12 \, {\left(a^{4} c^{5} d^{12} + 5 \, a^{5} c^{4} d^{10} e^{2} + 10 \, a^{6} c^{3} d^{8} e^{4} + 10 \, a^{7} c^{2} d^{6} e^{6} + 5 \, a^{8} c d^{4} e^{8} + a^{9} d^{2} e^{10} + {\left(a^{2} c^{7} d^{10} e^{2} + 5 \, a^{3} c^{6} d^{8} e^{4} + 10 \, a^{4} c^{5} d^{6} e^{6} + 10 \, a^{5} c^{4} d^{4} e^{8} + 5 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} x^{6} + 2 \, {\left(a^{2} c^{7} d^{11} e + 5 \, a^{3} c^{6} d^{9} e^{3} + 10 \, a^{4} c^{5} d^{7} e^{5} + 10 \, a^{5} c^{4} d^{5} e^{7} + 5 \, a^{6} c^{3} d^{3} e^{9} + a^{7} c^{2} d e^{11}\right)} x^{5} + {\left(a^{2} c^{7} d^{12} + 7 \, a^{3} c^{6} d^{10} e^{2} + 20 \, a^{4} c^{5} d^{8} e^{4} + 30 \, a^{5} c^{4} d^{6} e^{6} + 25 \, a^{6} c^{3} d^{4} e^{8} + 11 \, a^{7} c^{2} d^{2} e^{10} + 2 \, a^{8} c e^{12}\right)} x^{4} + 4 \, {\left(a^{3} c^{6} d^{11} e + 5 \, a^{4} c^{5} d^{9} e^{3} + 10 \, a^{5} c^{4} d^{7} e^{5} + 10 \, a^{6} c^{3} d^{5} e^{7} + 5 \, a^{7} c^{2} d^{3} e^{9} + a^{8} c d e^{11}\right)} x^{3} + {\left(2 \, a^{3} c^{6} d^{12} + 11 \, a^{4} c^{5} d^{10} e^{2} + 25 \, a^{5} c^{4} d^{8} e^{4} + 30 \, a^{6} c^{3} d^{6} e^{6} + 20 \, a^{7} c^{2} d^{4} e^{8} + 7 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} x^{2} + 2 \, {\left(a^{4} c^{5} d^{11} e + 5 \, a^{5} c^{4} d^{9} e^{3} + 10 \, a^{6} c^{3} d^{7} e^{5} + 10 \, a^{7} c^{2} d^{5} e^{7} + 5 \, a^{8} c d^{3} e^{9} + a^{9} d e^{11}\right)} x\right)}}, -\frac{15 \, {\left(6 \, a^{4} c^{2} d^{4} e^{4} - a^{5} c d^{2} e^{6} + {\left(6 \, a^{2} c^{4} d^{2} e^{6} - a^{3} c^{3} e^{8}\right)} x^{6} + 2 \, {\left(6 \, a^{2} c^{4} d^{3} e^{5} - a^{3} c^{3} d e^{7}\right)} x^{5} + {\left(6 \, a^{2} c^{4} d^{4} e^{4} + 11 \, a^{3} c^{3} d^{2} e^{6} - 2 \, a^{4} c^{2} e^{8}\right)} x^{4} + 4 \, {\left(6 \, a^{3} c^{3} d^{3} e^{5} - a^{4} c^{2} d e^{7}\right)} x^{3} + {\left(12 \, a^{3} c^{3} d^{4} e^{4} + 4 \, a^{4} c^{2} d^{2} e^{6} - a^{5} c e^{8}\right)} x^{2} + 2 \, {\left(6 \, a^{4} c^{2} d^{3} e^{5} - a^{5} c d e^{7}\right)} x\right)} \sqrt{-c d^{2} - a e^{2}} \arctan\left(\frac{\sqrt{-c d^{2} - a e^{2}} {\left(c d x - a e\right)} \sqrt{c x^{2} + a}}{a c d^{2} + a^{2} e^{2} + {\left(c^{2} d^{2} + a c e^{2}\right)} x^{2}}\right) - {\left(6 \, a^{2} c^{4} d^{8} e + 70 \, a^{3} c^{3} d^{6} e^{3} + 14 \, a^{4} c^{2} d^{4} e^{5} - 53 \, a^{5} c d^{2} e^{7} - 3 \, a^{6} e^{9} + {\left(4 \, c^{6} d^{7} e^{2} + 32 \, a c^{5} d^{5} e^{4} - 53 \, a^{2} c^{4} d^{3} e^{6} - 81 \, a^{3} c^{3} d e^{8}\right)} x^{5} + {\left(8 \, c^{6} d^{8} e + 64 \, a c^{5} d^{6} e^{3} - 16 \, a^{2} c^{4} d^{4} e^{5} - 87 \, a^{3} c^{3} d^{2} e^{7} - 15 \, a^{4} c^{2} e^{9}\right)} x^{4} + 2 \, {\left(2 \, c^{6} d^{9} + 19 \, a c^{5} d^{7} e^{2} + 65 \, a^{2} c^{4} d^{5} e^{4} - 24 \, a^{3} c^{3} d^{3} e^{6} - 72 \, a^{4} c^{2} d e^{8}\right)} x^{3} + 2 \, {\left(6 \, a c^{5} d^{8} e + 63 \, a^{2} c^{4} d^{6} e^{3} - 7 \, a^{3} c^{3} d^{4} e^{5} - 74 \, a^{4} c^{2} d^{2} e^{7} - 10 \, a^{5} c e^{9}\right)} x^{2} + {\left(6 \, a c^{5} d^{9} + 42 \, a^{2} c^{4} d^{7} e^{2} + 110 \, a^{3} c^{3} d^{5} e^{4} + 13 \, a^{4} c^{2} d^{3} e^{6} - 61 \, a^{5} c d e^{8}\right)} x\right)} \sqrt{c x^{2} + a}}{6 \, {\left(a^{4} c^{5} d^{12} + 5 \, a^{5} c^{4} d^{10} e^{2} + 10 \, a^{6} c^{3} d^{8} e^{4} + 10 \, a^{7} c^{2} d^{6} e^{6} + 5 \, a^{8} c d^{4} e^{8} + a^{9} d^{2} e^{10} + {\left(a^{2} c^{7} d^{10} e^{2} + 5 \, a^{3} c^{6} d^{8} e^{4} + 10 \, a^{4} c^{5} d^{6} e^{6} + 10 \, a^{5} c^{4} d^{4} e^{8} + 5 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12}\right)} x^{6} + 2 \, {\left(a^{2} c^{7} d^{11} e + 5 \, a^{3} c^{6} d^{9} e^{3} + 10 \, a^{4} c^{5} d^{7} e^{5} + 10 \, a^{5} c^{4} d^{5} e^{7} + 5 \, a^{6} c^{3} d^{3} e^{9} + a^{7} c^{2} d e^{11}\right)} x^{5} + {\left(a^{2} c^{7} d^{12} + 7 \, a^{3} c^{6} d^{10} e^{2} + 20 \, a^{4} c^{5} d^{8} e^{4} + 30 \, a^{5} c^{4} d^{6} e^{6} + 25 \, a^{6} c^{3} d^{4} e^{8} + 11 \, a^{7} c^{2} d^{2} e^{10} + 2 \, a^{8} c e^{12}\right)} x^{4} + 4 \, {\left(a^{3} c^{6} d^{11} e + 5 \, a^{4} c^{5} d^{9} e^{3} + 10 \, a^{5} c^{4} d^{7} e^{5} + 10 \, a^{6} c^{3} d^{5} e^{7} + 5 \, a^{7} c^{2} d^{3} e^{9} + a^{8} c d e^{11}\right)} x^{3} + {\left(2 \, a^{3} c^{6} d^{12} + 11 \, a^{4} c^{5} d^{10} e^{2} + 25 \, a^{5} c^{4} d^{8} e^{4} + 30 \, a^{6} c^{3} d^{6} e^{6} + 20 \, a^{7} c^{2} d^{4} e^{8} + 7 \, a^{8} c d^{2} e^{10} + a^{9} e^{12}\right)} x^{2} + 2 \, {\left(a^{4} c^{5} d^{11} e + 5 \, a^{5} c^{4} d^{9} e^{3} + 10 \, a^{6} c^{3} d^{7} e^{5} + 10 \, a^{7} c^{2} d^{5} e^{7} + 5 \, a^{8} c d^{3} e^{9} + a^{9} d e^{11}\right)} x\right)}}\right]"," ",0,"[1/12*(15*(6*a^4*c^2*d^4*e^4 - a^5*c*d^2*e^6 + (6*a^2*c^4*d^2*e^6 - a^3*c^3*e^8)*x^6 + 2*(6*a^2*c^4*d^3*e^5 - a^3*c^3*d*e^7)*x^5 + (6*a^2*c^4*d^4*e^4 + 11*a^3*c^3*d^2*e^6 - 2*a^4*c^2*e^8)*x^4 + 4*(6*a^3*c^3*d^3*e^5 - a^4*c^2*d*e^7)*x^3 + (12*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 - a^5*c*e^8)*x^2 + 2*(6*a^4*c^2*d^3*e^5 - a^5*c*d*e^7)*x)*sqrt(c*d^2 + a*e^2)*log((2*a*c*d*e*x - a*c*d^2 - 2*a^2*e^2 - (2*c^2*d^2 + a*c*e^2)*x^2 - 2*sqrt(c*d^2 + a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(6*a^2*c^4*d^8*e + 70*a^3*c^3*d^6*e^3 + 14*a^4*c^2*d^4*e^5 - 53*a^5*c*d^2*e^7 - 3*a^6*e^9 + (4*c^6*d^7*e^2 + 32*a*c^5*d^5*e^4 - 53*a^2*c^4*d^3*e^6 - 81*a^3*c^3*d*e^8)*x^5 + (8*c^6*d^8*e + 64*a*c^5*d^6*e^3 - 16*a^2*c^4*d^4*e^5 - 87*a^3*c^3*d^2*e^7 - 15*a^4*c^2*e^9)*x^4 + 2*(2*c^6*d^9 + 19*a*c^5*d^7*e^2 + 65*a^2*c^4*d^5*e^4 - 24*a^3*c^3*d^3*e^6 - 72*a^4*c^2*d*e^8)*x^3 + 2*(6*a*c^5*d^8*e + 63*a^2*c^4*d^6*e^3 - 7*a^3*c^3*d^4*e^5 - 74*a^4*c^2*d^2*e^7 - 10*a^5*c*e^9)*x^2 + (6*a*c^5*d^9 + 42*a^2*c^4*d^7*e^2 + 110*a^3*c^3*d^5*e^4 + 13*a^4*c^2*d^3*e^6 - 61*a^5*c*d*e^8)*x)*sqrt(c*x^2 + a))/(a^4*c^5*d^12 + 5*a^5*c^4*d^10*e^2 + 10*a^6*c^3*d^8*e^4 + 10*a^7*c^2*d^6*e^6 + 5*a^8*c*d^4*e^8 + a^9*d^2*e^10 + (a^2*c^7*d^10*e^2 + 5*a^3*c^6*d^8*e^4 + 10*a^4*c^5*d^6*e^6 + 10*a^5*c^4*d^4*e^8 + 5*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*x^6 + 2*(a^2*c^7*d^11*e + 5*a^3*c^6*d^9*e^3 + 10*a^4*c^5*d^7*e^5 + 10*a^5*c^4*d^5*e^7 + 5*a^6*c^3*d^3*e^9 + a^7*c^2*d*e^11)*x^5 + (a^2*c^7*d^12 + 7*a^3*c^6*d^10*e^2 + 20*a^4*c^5*d^8*e^4 + 30*a^5*c^4*d^6*e^6 + 25*a^6*c^3*d^4*e^8 + 11*a^7*c^2*d^2*e^10 + 2*a^8*c*e^12)*x^4 + 4*(a^3*c^6*d^11*e + 5*a^4*c^5*d^9*e^3 + 10*a^5*c^4*d^7*e^5 + 10*a^6*c^3*d^5*e^7 + 5*a^7*c^2*d^3*e^9 + a^8*c*d*e^11)*x^3 + (2*a^3*c^6*d^12 + 11*a^4*c^5*d^10*e^2 + 25*a^5*c^4*d^8*e^4 + 30*a^6*c^3*d^6*e^6 + 20*a^7*c^2*d^4*e^8 + 7*a^8*c*d^2*e^10 + a^9*e^12)*x^2 + 2*(a^4*c^5*d^11*e + 5*a^5*c^4*d^9*e^3 + 10*a^6*c^3*d^7*e^5 + 10*a^7*c^2*d^5*e^7 + 5*a^8*c*d^3*e^9 + a^9*d*e^11)*x), -1/6*(15*(6*a^4*c^2*d^4*e^4 - a^5*c*d^2*e^6 + (6*a^2*c^4*d^2*e^6 - a^3*c^3*e^8)*x^6 + 2*(6*a^2*c^4*d^3*e^5 - a^3*c^3*d*e^7)*x^5 + (6*a^2*c^4*d^4*e^4 + 11*a^3*c^3*d^2*e^6 - 2*a^4*c^2*e^8)*x^4 + 4*(6*a^3*c^3*d^3*e^5 - a^4*c^2*d*e^7)*x^3 + (12*a^3*c^3*d^4*e^4 + 4*a^4*c^2*d^2*e^6 - a^5*c*e^8)*x^2 + 2*(6*a^4*c^2*d^3*e^5 - a^5*c*d*e^7)*x)*sqrt(-c*d^2 - a*e^2)*arctan(sqrt(-c*d^2 - a*e^2)*(c*d*x - a*e)*sqrt(c*x^2 + a)/(a*c*d^2 + a^2*e^2 + (c^2*d^2 + a*c*e^2)*x^2)) - (6*a^2*c^4*d^8*e + 70*a^3*c^3*d^6*e^3 + 14*a^4*c^2*d^4*e^5 - 53*a^5*c*d^2*e^7 - 3*a^6*e^9 + (4*c^6*d^7*e^2 + 32*a*c^5*d^5*e^4 - 53*a^2*c^4*d^3*e^6 - 81*a^3*c^3*d*e^8)*x^5 + (8*c^6*d^8*e + 64*a*c^5*d^6*e^3 - 16*a^2*c^4*d^4*e^5 - 87*a^3*c^3*d^2*e^7 - 15*a^4*c^2*e^9)*x^4 + 2*(2*c^6*d^9 + 19*a*c^5*d^7*e^2 + 65*a^2*c^4*d^5*e^4 - 24*a^3*c^3*d^3*e^6 - 72*a^4*c^2*d*e^8)*x^3 + 2*(6*a*c^5*d^8*e + 63*a^2*c^4*d^6*e^3 - 7*a^3*c^3*d^4*e^5 - 74*a^4*c^2*d^2*e^7 - 10*a^5*c*e^9)*x^2 + (6*a*c^5*d^9 + 42*a^2*c^4*d^7*e^2 + 110*a^3*c^3*d^5*e^4 + 13*a^4*c^2*d^3*e^6 - 61*a^5*c*d*e^8)*x)*sqrt(c*x^2 + a))/(a^4*c^5*d^12 + 5*a^5*c^4*d^10*e^2 + 10*a^6*c^3*d^8*e^4 + 10*a^7*c^2*d^6*e^6 + 5*a^8*c*d^4*e^8 + a^9*d^2*e^10 + (a^2*c^7*d^10*e^2 + 5*a^3*c^6*d^8*e^4 + 10*a^4*c^5*d^6*e^6 + 10*a^5*c^4*d^4*e^8 + 5*a^6*c^3*d^2*e^10 + a^7*c^2*e^12)*x^6 + 2*(a^2*c^7*d^11*e + 5*a^3*c^6*d^9*e^3 + 10*a^4*c^5*d^7*e^5 + 10*a^5*c^4*d^5*e^7 + 5*a^6*c^3*d^3*e^9 + a^7*c^2*d*e^11)*x^5 + (a^2*c^7*d^12 + 7*a^3*c^6*d^10*e^2 + 20*a^4*c^5*d^8*e^4 + 30*a^5*c^4*d^6*e^6 + 25*a^6*c^3*d^4*e^8 + 11*a^7*c^2*d^2*e^10 + 2*a^8*c*e^12)*x^4 + 4*(a^3*c^6*d^11*e + 5*a^4*c^5*d^9*e^3 + 10*a^5*c^4*d^7*e^5 + 10*a^6*c^3*d^5*e^7 + 5*a^7*c^2*d^3*e^9 + a^8*c*d*e^11)*x^3 + (2*a^3*c^6*d^12 + 11*a^4*c^5*d^10*e^2 + 25*a^5*c^4*d^8*e^4 + 30*a^6*c^3*d^6*e^6 + 20*a^7*c^2*d^4*e^8 + 7*a^8*c*d^2*e^10 + a^9*e^12)*x^2 + 2*(a^4*c^5*d^11*e + 5*a^5*c^4*d^9*e^3 + 10*a^6*c^3*d^7*e^5 + 10*a^7*c^2*d^5*e^7 + 5*a^8*c*d^3*e^9 + a^9*d*e^11)*x)]","B",0
585,1,30,0,0.395769," ","integrate((3+x)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\sqrt{-x^{2} + 1} - 6 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-sqrt(-x^2 + 1) - 6*arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
586,1,30,0,0.396283," ","integrate((1+x)/(-x^2+4)^(1/2),x, algorithm=""fricas"")","-\sqrt{-x^{2} + 4} - 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 4} - 2}{x}\right)"," ",0,"-sqrt(-x^2 + 4) - 2*arctan((sqrt(-x^2 + 4) - 2)/x)","A",0
587,1,22,0,0.397356," ","integrate((2+x)/(x^2+9)^(1/2),x, algorithm=""fricas"")","\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
588,1,49,0,0.410443," ","integrate((b*x+a)^2/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-{\left(2 \, a^{2} + b^{2}\right)} \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) - \frac{1}{2} \, {\left(b^{2} x + 4 \, a b\right)} \sqrt{-x^{2} + 1}"," ",0,"-(2*a^2 + b^2)*arctan((sqrt(-x^2 + 1) - 1)/x) - 1/2*(b^2*x + 4*a*b)*sqrt(-x^2 + 1)","A",0
589,1,45,0,0.396710," ","integrate((b*x+a)^2/(x^2+1)^(1/2),x, algorithm=""fricas"")","-\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
590,1,25,0,0.379949," ","integrate((2+3*x)/(x^2+4)^(3/2),x, algorithm=""fricas"")","\frac{x^{2} + \sqrt{x^{2} + 4} {\left(x - 6\right)} + 4}{2 \, {\left(x^{2} + 4\right)}}"," ",0,"1/2*(x^2 + sqrt(x^2 + 4)*(x - 6) + 4)/(x^2 + 4)","B",0
591,1,108,0,0.394436," ","integrate((e*x+d)^(5/2)*(c*x^2+a),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, c e^{5} x^{5} + 161 \, c d e^{4} x^{4} + 8 \, c d^{5} + 99 \, a d^{3} e^{2} + {\left(113 \, c d^{2} e^{3} + 99 \, a e^{5}\right)} x^{3} + 3 \, {\left(c d^{3} e^{2} + 99 \, a d e^{4}\right)} x^{2} - {\left(4 \, c d^{4} e - 297 \, a d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{693 \, e^{3}}"," ",0,"2/693*(63*c*e^5*x^5 + 161*c*d*e^4*x^4 + 8*c*d^5 + 99*a*d^3*e^2 + (113*c*d^2*e^3 + 99*a*e^5)*x^3 + 3*(c*d^3*e^2 + 99*a*d*e^4)*x^2 - (4*c*d^4*e - 297*a*d^2*e^3)*x)*sqrt(e*x + d)/e^3","B",0
592,1,85,0,0.395205," ","integrate((e*x+d)^(3/2)*(c*x^2+a),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c e^{4} x^{4} + 50 \, c d e^{3} x^{3} + 8 \, c d^{4} + 63 \, a d^{2} e^{2} + 3 \, {\left(c d^{2} e^{2} + 21 \, a e^{4}\right)} x^{2} - 2 \, {\left(2 \, c d^{3} e - 63 \, a d e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{3}}"," ",0,"2/315*(35*c*e^4*x^4 + 50*c*d*e^3*x^3 + 8*c*d^4 + 63*a*d^2*e^2 + 3*(c*d^2*e^2 + 21*a*e^4)*x^2 - 2*(2*c*d^3*e - 63*a*d*e^3)*x)*sqrt(e*x + d)/e^3","A",0
593,1,62,0,0.399361," ","integrate((c*x^2+a)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c e^{3} x^{3} + 3 \, c d e^{2} x^{2} + 8 \, c d^{3} + 35 \, a d e^{2} - {\left(4 \, c d^{2} e - 35 \, a e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{3}}"," ",0,"2/105*(15*c*e^3*x^3 + 3*c*d*e^2*x^2 + 8*c*d^3 + 35*a*d*e^2 - (4*c*d^2*e - 35*a*e^3)*x)*sqrt(e*x + d)/e^3","A",0
594,1,40,0,0.391078," ","integrate((c*x^2+a)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c e^{2} x^{2} - 4 \, c d e x + 8 \, c d^{2} + 15 \, a e^{2}\right)} \sqrt{e x + d}}{15 \, e^{3}}"," ",0,"2/15*(3*c*e^2*x^2 - 4*c*d*e*x + 8*c*d^2 + 15*a*e^2)*sqrt(e*x + d)/e^3","A",0
595,1,49,0,0.379375," ","integrate((c*x^2+a)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c e^{2} x^{2} - 4 \, c d e x - 8 \, c d^{2} - 3 \, a e^{2}\right)} \sqrt{e x + d}}{3 \, {\left(e^{4} x + d e^{3}\right)}}"," ",0,"2/3*(c*e^2*x^2 - 4*c*d*e*x - 8*c*d^2 - 3*a*e^2)*sqrt(e*x + d)/(e^4*x + d*e^3)","A",0
596,1,61,0,0.407282," ","integrate((c*x^2+a)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c e^{2} x^{2} + 12 \, c d e x + 8 \, c d^{2} - a e^{2}\right)} \sqrt{e x + d}}{3 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"2/3*(3*c*e^2*x^2 + 12*c*d*e*x + 8*c*d^2 - a*e^2)*sqrt(e*x + d)/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
597,1,72,0,0.402029," ","integrate((c*x^2+a)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, c e^{2} x^{2} + 20 \, c d e x + 8 \, c d^{2} + 3 \, a e^{2}\right)} \sqrt{e x + d}}{15 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-2/15*(15*c*e^2*x^2 + 20*c*d*e*x + 8*c*d^2 + 3*a*e^2)*sqrt(e*x + d)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
598,1,218,0,0.379715," ","integrate((e*x+d)^(5/2)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, c^{2} e^{7} x^{7} + 7161 \, c^{2} d e^{6} x^{6} + 128 \, c^{2} d^{7} + 1040 \, a c d^{5} e^{2} + 6435 \, a^{2} d^{3} e^{4} + 63 \, {\left(71 \, c^{2} d^{2} e^{5} + 130 \, a c e^{7}\right)} x^{5} + 35 \, {\left(c^{2} d^{3} e^{4} + 598 \, a c d e^{6}\right)} x^{4} - 5 \, {\left(8 \, c^{2} d^{4} e^{3} - 2938 \, a c d^{2} e^{5} - 1287 \, a^{2} e^{7}\right)} x^{3} + 3 \, {\left(16 \, c^{2} d^{5} e^{2} + 130 \, a c d^{3} e^{4} + 6435 \, a^{2} d e^{6}\right)} x^{2} - {\left(64 \, c^{2} d^{6} e + 520 \, a c d^{4} e^{3} - 19305 \, a^{2} d^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{5}}"," ",0,"2/45045*(3003*c^2*e^7*x^7 + 7161*c^2*d*e^6*x^6 + 128*c^2*d^7 + 1040*a*c*d^5*e^2 + 6435*a^2*d^3*e^4 + 63*(71*c^2*d^2*e^5 + 130*a*c*e^7)*x^5 + 35*(c^2*d^3*e^4 + 598*a*c*d*e^6)*x^4 - 5*(8*c^2*d^4*e^3 - 2938*a*c*d^2*e^5 - 1287*a^2*e^7)*x^3 + 3*(16*c^2*d^5*e^2 + 130*a*c*d^3*e^4 + 6435*a^2*d*e^6)*x^2 - (64*c^2*d^6*e + 520*a*c*d^4*e^3 - 19305*a^2*d^2*e^5)*x)*sqrt(e*x + d)/e^5","B",0
599,1,181,0,0.399570," ","integrate((e*x+d)^(3/2)*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, c^{2} e^{6} x^{6} + 4410 \, c^{2} d e^{5} x^{5} + 384 \, c^{2} d^{6} + 2288 \, a c d^{4} e^{2} + 9009 \, a^{2} d^{2} e^{4} + 35 \, {\left(3 \, c^{2} d^{2} e^{4} + 286 \, a c e^{6}\right)} x^{4} - 20 \, {\left(6 \, c^{2} d^{3} e^{3} - 715 \, a c d e^{5}\right)} x^{3} + 3 \, {\left(48 \, c^{2} d^{4} e^{2} + 286 \, a c d^{2} e^{4} + 3003 \, a^{2} e^{6}\right)} x^{2} - 2 \, {\left(96 \, c^{2} d^{5} e + 572 \, a c d^{3} e^{3} - 9009 \, a^{2} d e^{5}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{5}}"," ",0,"2/45045*(3465*c^2*e^6*x^6 + 4410*c^2*d*e^5*x^5 + 384*c^2*d^6 + 2288*a*c*d^4*e^2 + 9009*a^2*d^2*e^4 + 35*(3*c^2*d^2*e^4 + 286*a*c*e^6)*x^4 - 20*(6*c^2*d^3*e^3 - 715*a*c*d*e^5)*x^3 + 3*(48*c^2*d^4*e^2 + 286*a*c*d^2*e^4 + 3003*a^2*e^6)*x^2 - 2*(96*c^2*d^5*e + 572*a*c*d^3*e^3 - 9009*a^2*d*e^5)*x)*sqrt(e*x + d)/e^5","A",0
600,1,143,0,0.387169," ","integrate((c*x^2+a)^2*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, c^{2} e^{5} x^{5} + 35 \, c^{2} d e^{4} x^{4} + 128 \, c^{2} d^{5} + 528 \, a c d^{3} e^{2} + 1155 \, a^{2} d e^{4} - 10 \, {\left(4 \, c^{2} d^{2} e^{3} - 99 \, a c e^{5}\right)} x^{3} + 6 \, {\left(8 \, c^{2} d^{3} e^{2} + 33 \, a c d e^{4}\right)} x^{2} - {\left(64 \, c^{2} d^{4} e + 264 \, a c d^{2} e^{3} - 1155 \, a^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{5}}"," ",0,"2/3465*(315*c^2*e^5*x^5 + 35*c^2*d*e^4*x^4 + 128*c^2*d^5 + 528*a*c*d^3*e^2 + 1155*a^2*d*e^4 - 10*(4*c^2*d^2*e^3 - 99*a*c*e^5)*x^3 + 6*(8*c^2*d^3*e^2 + 33*a*c*d*e^4)*x^2 - (64*c^2*d^4*e + 264*a*c*d^2*e^3 - 1155*a^2*e^5)*x)*sqrt(e*x + d)/e^5","A",0
601,1,107,0,0.381862," ","integrate((c*x^2+a)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{2} e^{4} x^{4} - 40 \, c^{2} d e^{3} x^{3} + 128 \, c^{2} d^{4} + 336 \, a c d^{2} e^{2} + 315 \, a^{2} e^{4} + 6 \, {\left(8 \, c^{2} d^{2} e^{2} + 21 \, a c e^{4}\right)} x^{2} - 8 \, {\left(8 \, c^{2} d^{3} e + 21 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{5}}"," ",0,"2/315*(35*c^2*e^4*x^4 - 40*c^2*d*e^3*x^3 + 128*c^2*d^4 + 336*a*c*d^2*e^2 + 315*a^2*e^4 + 6*(8*c^2*d^2*e^2 + 21*a*c*e^4)*x^2 - 8*(8*c^2*d^3*e + 21*a*c*d*e^3)*x)*sqrt(e*x + d)/e^5","A",0
602,1,117,0,0.392332," ","integrate((c*x^2+a)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c^{2} e^{4} x^{4} - 24 \, c^{2} d e^{3} x^{3} - 384 \, c^{2} d^{4} - 560 \, a c d^{2} e^{2} - 105 \, a^{2} e^{4} + 2 \, {\left(24 \, c^{2} d^{2} e^{2} + 35 \, a c e^{4}\right)} x^{2} - 8 \, {\left(24 \, c^{2} d^{3} e + 35 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"2/105*(15*c^2*e^4*x^4 - 24*c^2*d*e^3*x^3 - 384*c^2*d^4 - 560*a*c*d^2*e^2 - 105*a^2*e^4 + 2*(24*c^2*d^2*e^2 + 35*a*c*e^4)*x^2 - 8*(24*c^2*d^3*e + 35*a*c*d*e^3)*x)*sqrt(e*x + d)/(e^6*x + d*e^5)","A",0
603,1,128,0,0.388793," ","integrate((c*x^2+a)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} e^{4} x^{4} - 8 \, c^{2} d e^{3} x^{3} + 128 \, c^{2} d^{4} + 80 \, a c d^{2} e^{2} - 5 \, a^{2} e^{4} + 6 \, {\left(8 \, c^{2} d^{2} e^{2} + 5 \, a c e^{4}\right)} x^{2} + 24 \, {\left(8 \, c^{2} d^{3} e + 5 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"2/15*(3*c^2*e^4*x^4 - 8*c^2*d*e^3*x^3 + 128*c^2*d^4 + 80*a*c*d^2*e^2 - 5*a^2*e^4 + 6*(8*c^2*d^2*e^2 + 5*a*c*e^4)*x^2 + 24*(8*c^2*d^3*e + 5*a*c*d*e^3)*x)*sqrt(e*x + d)/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
604,1,137,0,0.394862," ","integrate((c*x^2+a)^2/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{2} e^{4} x^{4} - 40 \, c^{2} d e^{3} x^{3} - 128 \, c^{2} d^{4} - 16 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4} - 30 \, {\left(8 \, c^{2} d^{2} e^{2} + a c e^{4}\right)} x^{2} - 40 \, {\left(8 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"2/15*(5*c^2*e^4*x^4 - 40*c^2*d*e^3*x^3 - 128*c^2*d^4 - 16*a*c*d^2*e^2 - 3*a^2*e^4 - 30*(8*c^2*d^2*e^2 + a*c*e^4)*x^2 - 40*(8*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(e*x + d)/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
605,1,356,0,0.402287," ","integrate((e*x+d)^(5/2)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(255255 \, c^{3} e^{9} x^{9} + 585585 \, c^{3} d e^{8} x^{8} + 5120 \, c^{3} d^{9} + 41344 \, a c^{2} d^{7} e^{2} + 167960 \, a^{2} c d^{5} e^{4} + 692835 \, a^{3} d^{3} e^{6} + 3003 \, {\left(115 \, c^{3} d^{2} e^{7} + 323 \, a c^{2} e^{9}\right)} x^{7} + 231 \, {\left(5 \, c^{3} d^{3} e^{6} + 10013 \, a c^{2} d e^{8}\right)} x^{6} - 63 \, {\left(20 \, c^{3} d^{4} e^{5} - 22933 \, a c^{2} d^{2} e^{7} - 20995 \, a^{2} c e^{9}\right)} x^{5} + 35 \, {\left(40 \, c^{3} d^{5} e^{4} + 323 \, a c^{2} d^{3} e^{6} + 96577 \, a^{2} c d e^{8}\right)} x^{4} - 5 \, {\left(320 \, c^{3} d^{6} e^{3} + 2584 \, a c^{2} d^{4} e^{5} - 474487 \, a^{2} c d^{2} e^{7} - 138567 \, a^{3} e^{9}\right)} x^{3} + 3 \, {\left(640 \, c^{3} d^{7} e^{2} + 5168 \, a c^{2} d^{5} e^{4} + 20995 \, a^{2} c d^{3} e^{6} + 692835 \, a^{3} d e^{8}\right)} x^{2} - {\left(2560 \, c^{3} d^{8} e + 20672 \, a c^{2} d^{6} e^{3} + 83980 \, a^{2} c d^{4} e^{5} - 2078505 \, a^{3} d^{2} e^{7}\right)} x\right)} \sqrt{e x + d}}{4849845 \, e^{7}}"," ",0,"2/4849845*(255255*c^3*e^9*x^9 + 585585*c^3*d*e^8*x^8 + 5120*c^3*d^9 + 41344*a*c^2*d^7*e^2 + 167960*a^2*c*d^5*e^4 + 692835*a^3*d^3*e^6 + 3003*(115*c^3*d^2*e^7 + 323*a*c^2*e^9)*x^7 + 231*(5*c^3*d^3*e^6 + 10013*a*c^2*d*e^8)*x^6 - 63*(20*c^3*d^4*e^5 - 22933*a*c^2*d^2*e^7 - 20995*a^2*c*e^9)*x^5 + 35*(40*c^3*d^5*e^4 + 323*a*c^2*d^3*e^6 + 96577*a^2*c*d*e^8)*x^4 - 5*(320*c^3*d^6*e^3 + 2584*a*c^2*d^4*e^5 - 474487*a^2*c*d^2*e^7 - 138567*a^3*e^9)*x^3 + 3*(640*c^3*d^7*e^2 + 5168*a*c^2*d^5*e^4 + 20995*a^2*c*d^3*e^6 + 692835*a^3*d*e^8)*x^2 - (2560*c^3*d^8*e + 20672*a*c^2*d^6*e^3 + 83980*a^2*c*d^4*e^5 - 2078505*a^3*d^2*e^7)*x)*sqrt(e*x + d)/e^7","B",0
606,1,303,0,0.395135," ","integrate((e*x+d)^(3/2)*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(15015 \, c^{3} e^{8} x^{8} + 18018 \, c^{3} d e^{7} x^{7} + 1024 \, c^{3} d^{8} + 6528 \, a c^{2} d^{6} e^{2} + 19448 \, a^{2} c d^{4} e^{4} + 51051 \, a^{3} d^{2} e^{6} + 231 \, {\left(c^{3} d^{2} e^{6} + 255 \, a c^{2} e^{8}\right)} x^{6} - 126 \, {\left(2 \, c^{3} d^{3} e^{5} - 595 \, a c^{2} d e^{7}\right)} x^{5} + 35 \, {\left(8 \, c^{3} d^{4} e^{4} + 51 \, a c^{2} d^{2} e^{6} + 2431 \, a^{2} c e^{8}\right)} x^{4} - 10 \, {\left(32 \, c^{3} d^{5} e^{3} + 204 \, a c^{2} d^{3} e^{5} - 12155 \, a^{2} c d e^{7}\right)} x^{3} + 3 \, {\left(128 \, c^{3} d^{6} e^{2} + 816 \, a c^{2} d^{4} e^{4} + 2431 \, a^{2} c d^{2} e^{6} + 17017 \, a^{3} e^{8}\right)} x^{2} - 2 \, {\left(256 \, c^{3} d^{7} e + 1632 \, a c^{2} d^{5} e^{3} + 4862 \, a^{2} c d^{3} e^{5} - 51051 \, a^{3} d e^{7}\right)} x\right)} \sqrt{e x + d}}{255255 \, e^{7}}"," ",0,"2/255255*(15015*c^3*e^8*x^8 + 18018*c^3*d*e^7*x^7 + 1024*c^3*d^8 + 6528*a*c^2*d^6*e^2 + 19448*a^2*c*d^4*e^4 + 51051*a^3*d^2*e^6 + 231*(c^3*d^2*e^6 + 255*a*c^2*e^8)*x^6 - 126*(2*c^3*d^3*e^5 - 595*a*c^2*d*e^7)*x^5 + 35*(8*c^3*d^4*e^4 + 51*a*c^2*d^2*e^6 + 2431*a^2*c*e^8)*x^4 - 10*(32*c^3*d^5*e^3 + 204*a*c^2*d^3*e^5 - 12155*a^2*c*d*e^7)*x^3 + 3*(128*c^3*d^6*e^2 + 816*a*c^2*d^4*e^4 + 2431*a^2*c*d^2*e^6 + 17017*a^3*e^8)*x^2 - 2*(256*c^3*d^7*e + 1632*a*c^2*d^5*e^3 + 4862*a^2*c*d^3*e^5 - 51051*a^3*d*e^7)*x)*sqrt(e*x + d)/e^7","A",0
607,1,252,0,0.392779," ","integrate((c*x^2+a)^3*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, c^{3} e^{7} x^{7} + 231 \, c^{3} d e^{6} x^{6} + 1024 \, c^{3} d^{7} + 4992 \, a c^{2} d^{5} e^{2} + 10296 \, a^{2} c d^{3} e^{4} + 15015 \, a^{3} d e^{6} - 63 \, {\left(4 \, c^{3} d^{2} e^{5} - 195 \, a c^{2} e^{7}\right)} x^{5} + 35 \, {\left(8 \, c^{3} d^{3} e^{4} + 39 \, a c^{2} d e^{6}\right)} x^{4} - 5 \, {\left(64 \, c^{3} d^{4} e^{3} + 312 \, a c^{2} d^{2} e^{5} - 3861 \, a^{2} c e^{7}\right)} x^{3} + 3 \, {\left(128 \, c^{3} d^{5} e^{2} + 624 \, a c^{2} d^{3} e^{4} + 1287 \, a^{2} c d e^{6}\right)} x^{2} - {\left(512 \, c^{3} d^{6} e + 2496 \, a c^{2} d^{4} e^{3} + 5148 \, a^{2} c d^{2} e^{5} - 15015 \, a^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{7}}"," ",0,"2/45045*(3003*c^3*e^7*x^7 + 231*c^3*d*e^6*x^6 + 1024*c^3*d^7 + 4992*a*c^2*d^5*e^2 + 10296*a^2*c*d^3*e^4 + 15015*a^3*d*e^6 - 63*(4*c^3*d^2*e^5 - 195*a*c^2*e^7)*x^5 + 35*(8*c^3*d^3*e^4 + 39*a*c^2*d*e^6)*x^4 - 5*(64*c^3*d^4*e^3 + 312*a*c^2*d^2*e^5 - 3861*a^2*c*e^7)*x^3 + 3*(128*c^3*d^5*e^2 + 624*a*c^2*d^3*e^4 + 1287*a^2*c*d*e^6)*x^2 - (512*c^3*d^6*e + 2496*a*c^2*d^4*e^3 + 5148*a^2*c*d^2*e^5 - 15015*a^3*e^7)*x)*sqrt(e*x + d)/e^7","A",0
608,1,202,0,0.387227," ","integrate((c*x^2+a)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, c^{3} e^{6} x^{6} - 1260 \, c^{3} d e^{5} x^{5} + 5120 \, c^{3} d^{6} + 18304 \, a c^{2} d^{4} e^{2} + 24024 \, a^{2} c d^{2} e^{4} + 15015 \, a^{3} e^{6} + 35 \, {\left(40 \, c^{3} d^{2} e^{4} + 143 \, a c^{2} e^{6}\right)} x^{4} - 40 \, {\left(40 \, c^{3} d^{3} e^{3} + 143 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(640 \, c^{3} d^{4} e^{2} + 2288 \, a c^{2} d^{2} e^{4} + 3003 \, a^{2} c e^{6}\right)} x^{2} - 4 \, {\left(640 \, c^{3} d^{5} e + 2288 \, a c^{2} d^{3} e^{3} + 3003 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{15015 \, e^{7}}"," ",0,"2/15015*(1155*c^3*e^6*x^6 - 1260*c^3*d*e^5*x^5 + 5120*c^3*d^6 + 18304*a*c^2*d^4*e^2 + 24024*a^2*c*d^2*e^4 + 15015*a^3*e^6 + 35*(40*c^3*d^2*e^4 + 143*a*c^2*e^6)*x^4 - 40*(40*c^3*d^3*e^3 + 143*a*c^2*d*e^5)*x^3 + 3*(640*c^3*d^4*e^2 + 2288*a*c^2*d^2*e^4 + 3003*a^2*c*e^6)*x^2 - 4*(640*c^3*d^5*e + 2288*a*c^2*d^3*e^3 + 3003*a^2*c*d*e^5)*x)*sqrt(e*x + d)/e^7","A",0
609,1,211,0,0.393646," ","integrate((c*x^2+a)^3/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, c^{3} e^{6} x^{6} - 140 \, c^{3} d e^{5} x^{5} - 5120 \, c^{3} d^{6} - 12672 \, a c^{2} d^{4} e^{2} - 9240 \, a^{2} c d^{2} e^{4} - 1155 \, a^{3} e^{6} + 5 \, {\left(40 \, c^{3} d^{2} e^{4} + 99 \, a c^{2} e^{6}\right)} x^{4} - 8 \, {\left(40 \, c^{3} d^{3} e^{3} + 99 \, a c^{2} d e^{5}\right)} x^{3} + {\left(640 \, c^{3} d^{4} e^{2} + 1584 \, a c^{2} d^{2} e^{4} + 1155 \, a^{2} c e^{6}\right)} x^{2} - 4 \, {\left(640 \, c^{3} d^{5} e + 1584 \, a c^{2} d^{3} e^{3} + 1155 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{1155 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"2/1155*(105*c^3*e^6*x^6 - 140*c^3*d*e^5*x^5 - 5120*c^3*d^6 - 12672*a*c^2*d^4*e^2 - 9240*a^2*c*d^2*e^4 - 1155*a^3*e^6 + 5*(40*c^3*d^2*e^4 + 99*a*c^2*e^6)*x^4 - 8*(40*c^3*d^3*e^3 + 99*a*c^2*d*e^5)*x^3 + (640*c^3*d^4*e^2 + 1584*a*c^2*d^2*e^4 + 1155*a^2*c*e^6)*x^2 - 4*(640*c^3*d^5*e + 1584*a*c^2*d^3*e^3 + 1155*a^2*c*d*e^5)*x)*sqrt(e*x + d)/(e^8*x + d*e^7)","A",0
610,1,223,0,0.400937," ","integrate((c*x^2+a)^3/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{3} e^{6} x^{6} - 60 \, c^{3} d e^{5} x^{5} + 5120 \, c^{3} d^{6} + 8064 \, a c^{2} d^{4} e^{2} + 2520 \, a^{2} c d^{2} e^{4} - 105 \, a^{3} e^{6} + 3 \, {\left(40 \, c^{3} d^{2} e^{4} + 63 \, a c^{2} e^{6}\right)} x^{4} - 8 \, {\left(40 \, c^{3} d^{3} e^{3} + 63 \, a c^{2} d e^{5}\right)} x^{3} + 3 \, {\left(640 \, c^{3} d^{4} e^{2} + 1008 \, a c^{2} d^{2} e^{4} + 315 \, a^{2} c e^{6}\right)} x^{2} + 12 \, {\left(640 \, c^{3} d^{5} e + 1008 \, a c^{2} d^{3} e^{3} + 315 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"2/315*(35*c^3*e^6*x^6 - 60*c^3*d*e^5*x^5 + 5120*c^3*d^6 + 8064*a*c^2*d^4*e^2 + 2520*a^2*c*d^2*e^4 - 105*a^3*e^6 + 3*(40*c^3*d^2*e^4 + 63*a*c^2*e^6)*x^4 - 8*(40*c^3*d^3*e^3 + 63*a*c^2*d*e^5)*x^3 + 3*(640*c^3*d^4*e^2 + 1008*a*c^2*d^2*e^4 + 315*a^2*c*e^6)*x^2 + 12*(640*c^3*d^5*e + 1008*a*c^2*d^3*e^3 + 315*a^2*c*d*e^5)*x)*sqrt(e*x + d)/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","A",0
611,1,234,0,0.401509," ","integrate((c*x^2+a)^3/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{3} e^{6} x^{6} - 12 \, c^{3} d e^{5} x^{5} - 1024 \, c^{3} d^{6} - 896 \, a c^{2} d^{4} e^{2} - 56 \, a^{2} c d^{2} e^{4} - 7 \, a^{3} e^{6} + 5 \, {\left(8 \, c^{3} d^{2} e^{4} + 7 \, a c^{2} e^{6}\right)} x^{4} - 40 \, {\left(8 \, c^{3} d^{3} e^{3} + 7 \, a c^{2} d e^{5}\right)} x^{3} - 15 \, {\left(128 \, c^{3} d^{4} e^{2} + 112 \, a c^{2} d^{2} e^{4} + 7 \, a^{2} c e^{6}\right)} x^{2} - 20 \, {\left(128 \, c^{3} d^{5} e + 112 \, a c^{2} d^{3} e^{3} + 7 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"2/35*(5*c^3*e^6*x^6 - 12*c^3*d*e^5*x^5 - 1024*c^3*d^6 - 896*a*c^2*d^4*e^2 - 56*a^2*c*d^2*e^4 - 7*a^3*e^6 + 5*(8*c^3*d^2*e^4 + 7*a*c^2*e^6)*x^4 - 40*(8*c^3*d^3*e^3 + 7*a*c^2*d*e^5)*x^3 - 15*(128*c^3*d^4*e^2 + 112*a*c^2*d^2*e^4 + 7*a^2*c*e^6)*x^2 - 20*(128*c^3*d^5*e + 112*a*c^2*d^3*e^3 + 7*a^2*c*d*e^5)*x)*sqrt(e*x + d)/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","A",0
612,1,1617,0,0.515009," ","integrate((e*x+d)^(5/2)/(-c*x^2+a),x, algorithm=""fricas"")","-\frac{3 \, c \sqrt{\frac{c^{2} d^{5} + 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + a c^{3} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}} \log\left({\left(5 \, c^{4} d^{8} e - 14 \, a^{2} c^{2} d^{4} e^{5} + 8 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} \sqrt{e x + d} + {\left(10 \, a c^{4} d^{5} e^{2} + 20 \, a^{2} c^{3} d^{3} e^{4} + 2 \, a^{3} c^{2} d e^{6} - {\left(a c^{6} d^{2} + a^{2} c^{5} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}\right)} \sqrt{\frac{c^{2} d^{5} + 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + a c^{3} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}}\right) - 3 \, c \sqrt{\frac{c^{2} d^{5} + 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + a c^{3} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}} \log\left({\left(5 \, c^{4} d^{8} e - 14 \, a^{2} c^{2} d^{4} e^{5} + 8 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} \sqrt{e x + d} - {\left(10 \, a c^{4} d^{5} e^{2} + 20 \, a^{2} c^{3} d^{3} e^{4} + 2 \, a^{3} c^{2} d e^{6} - {\left(a c^{6} d^{2} + a^{2} c^{5} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}\right)} \sqrt{\frac{c^{2} d^{5} + 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + a c^{3} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}}\right) + 3 \, c \sqrt{\frac{c^{2} d^{5} + 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - a c^{3} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}} \log\left({\left(5 \, c^{4} d^{8} e - 14 \, a^{2} c^{2} d^{4} e^{5} + 8 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} \sqrt{e x + d} + {\left(10 \, a c^{4} d^{5} e^{2} + 20 \, a^{2} c^{3} d^{3} e^{4} + 2 \, a^{3} c^{2} d e^{6} + {\left(a c^{6} d^{2} + a^{2} c^{5} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}\right)} \sqrt{\frac{c^{2} d^{5} + 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - a c^{3} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}}\right) - 3 \, c \sqrt{\frac{c^{2} d^{5} + 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - a c^{3} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}} \log\left({\left(5 \, c^{4} d^{8} e - 14 \, a^{2} c^{2} d^{4} e^{5} + 8 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} \sqrt{e x + d} - {\left(10 \, a c^{4} d^{5} e^{2} + 20 \, a^{2} c^{3} d^{3} e^{4} + 2 \, a^{3} c^{2} d e^{6} + {\left(a c^{6} d^{2} + a^{2} c^{5} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}\right)} \sqrt{\frac{c^{2} d^{5} + 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - a c^{3} \sqrt{\frac{25 \, c^{4} d^{8} e^{2} + 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} + 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}}\right) + 4 \, {\left(e^{2} x + 7 \, d e\right)} \sqrt{e x + d}}{6 \, c}"," ",0,"-1/6*(3*c*sqrt((c^2*d^5 + 10*a*c*d^3*e^2 + 5*a^2*d*e^4 + a*c^3*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))*log((5*c^4*d^8*e - 14*a^2*c^2*d^4*e^5 + 8*a^3*c*d^2*e^7 + a^4*e^9)*sqrt(e*x + d) + (10*a*c^4*d^5*e^2 + 20*a^2*c^3*d^3*e^4 + 2*a^3*c^2*d*e^6 - (a*c^6*d^2 + a^2*c^5*e^2)*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))*sqrt((c^2*d^5 + 10*a*c*d^3*e^2 + 5*a^2*d*e^4 + a*c^3*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))) - 3*c*sqrt((c^2*d^5 + 10*a*c*d^3*e^2 + 5*a^2*d*e^4 + a*c^3*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))*log((5*c^4*d^8*e - 14*a^2*c^2*d^4*e^5 + 8*a^3*c*d^2*e^7 + a^4*e^9)*sqrt(e*x + d) - (10*a*c^4*d^5*e^2 + 20*a^2*c^3*d^3*e^4 + 2*a^3*c^2*d*e^6 - (a*c^6*d^2 + a^2*c^5*e^2)*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))*sqrt((c^2*d^5 + 10*a*c*d^3*e^2 + 5*a^2*d*e^4 + a*c^3*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))) + 3*c*sqrt((c^2*d^5 + 10*a*c*d^3*e^2 + 5*a^2*d*e^4 - a*c^3*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))*log((5*c^4*d^8*e - 14*a^2*c^2*d^4*e^5 + 8*a^3*c*d^2*e^7 + a^4*e^9)*sqrt(e*x + d) + (10*a*c^4*d^5*e^2 + 20*a^2*c^3*d^3*e^4 + 2*a^3*c^2*d*e^6 + (a*c^6*d^2 + a^2*c^5*e^2)*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))*sqrt((c^2*d^5 + 10*a*c*d^3*e^2 + 5*a^2*d*e^4 - a*c^3*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))) - 3*c*sqrt((c^2*d^5 + 10*a*c*d^3*e^2 + 5*a^2*d*e^4 - a*c^3*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))*log((5*c^4*d^8*e - 14*a^2*c^2*d^4*e^5 + 8*a^3*c*d^2*e^7 + a^4*e^9)*sqrt(e*x + d) - (10*a*c^4*d^5*e^2 + 20*a^2*c^3*d^3*e^4 + 2*a^3*c^2*d*e^6 + (a*c^6*d^2 + a^2*c^5*e^2)*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))*sqrt((c^2*d^5 + 10*a*c*d^3*e^2 + 5*a^2*d*e^4 - a*c^3*sqrt((25*c^4*d^8*e^2 + 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 + 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))) + 4*(e^2*x + 7*d*e)*sqrt(e*x + d))/c","B",0
613,1,974,0,0.423382," ","integrate((e*x+d)^(3/2)/(-c*x^2+a),x, algorithm=""fricas"")","\frac{c \sqrt{\frac{c d^{3} + 3 \, a d e^{2} + a c^{2} \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}} \log\left(-{\left(3 \, c^{2} d^{4} e - 2 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} \sqrt{e x + d} + {\left(3 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4} - a c^{4} d \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}\right)} \sqrt{\frac{c d^{3} + 3 \, a d e^{2} + a c^{2} \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}}\right) - c \sqrt{\frac{c d^{3} + 3 \, a d e^{2} + a c^{2} \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}} \log\left(-{\left(3 \, c^{2} d^{4} e - 2 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} \sqrt{e x + d} - {\left(3 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4} - a c^{4} d \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}\right)} \sqrt{\frac{c d^{3} + 3 \, a d e^{2} + a c^{2} \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}}\right) + c \sqrt{\frac{c d^{3} + 3 \, a d e^{2} - a c^{2} \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}} \log\left(-{\left(3 \, c^{2} d^{4} e - 2 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} \sqrt{e x + d} + {\left(3 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4} + a c^{4} d \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}\right)} \sqrt{\frac{c d^{3} + 3 \, a d e^{2} - a c^{2} \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}}\right) - c \sqrt{\frac{c d^{3} + 3 \, a d e^{2} - a c^{2} \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}} \log\left(-{\left(3 \, c^{2} d^{4} e - 2 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} \sqrt{e x + d} - {\left(3 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4} + a c^{4} d \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}\right)} \sqrt{\frac{c d^{3} + 3 \, a d e^{2} - a c^{2} \sqrt{\frac{9 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}}\right) - 4 \, \sqrt{e x + d} e}{2 \, c}"," ",0,"1/2*(c*sqrt((c*d^3 + 3*a*d*e^2 + a*c^2*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))*log(-(3*c^2*d^4*e - 2*a*c*d^2*e^3 - a^2*e^5)*sqrt(e*x + d) + (3*a*c^2*d^2*e^2 + a^2*c*e^4 - a*c^4*d*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))*sqrt((c*d^3 + 3*a*d*e^2 + a*c^2*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))) - c*sqrt((c*d^3 + 3*a*d*e^2 + a*c^2*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))*log(-(3*c^2*d^4*e - 2*a*c*d^2*e^3 - a^2*e^5)*sqrt(e*x + d) - (3*a*c^2*d^2*e^2 + a^2*c*e^4 - a*c^4*d*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))*sqrt((c*d^3 + 3*a*d*e^2 + a*c^2*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))) + c*sqrt((c*d^3 + 3*a*d*e^2 - a*c^2*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))*log(-(3*c^2*d^4*e - 2*a*c*d^2*e^3 - a^2*e^5)*sqrt(e*x + d) + (3*a*c^2*d^2*e^2 + a^2*c*e^4 + a*c^4*d*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))*sqrt((c*d^3 + 3*a*d*e^2 - a*c^2*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))) - c*sqrt((c*d^3 + 3*a*d*e^2 - a*c^2*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))*log(-(3*c^2*d^4*e - 2*a*c*d^2*e^3 - a^2*e^5)*sqrt(e*x + d) - (3*a*c^2*d^2*e^2 + a^2*c*e^4 + a*c^4*d*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))*sqrt((c*d^3 + 3*a*d*e^2 - a*c^2*sqrt((9*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))) - 4*sqrt(e*x + d)*e)/c","B",0
614,1,343,0,0.415221," ","integrate((e*x+d)^(1/2)/(-c*x^2+a),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{a c \sqrt{\frac{e^{2}}{a c^{3}}} + d}{a c}} \log\left(a c^{2} \sqrt{\frac{a c \sqrt{\frac{e^{2}}{a c^{3}}} + d}{a c}} \sqrt{\frac{e^{2}}{a c^{3}}} + \sqrt{e x + d} e\right) - \frac{1}{2} \, \sqrt{\frac{a c \sqrt{\frac{e^{2}}{a c^{3}}} + d}{a c}} \log\left(-a c^{2} \sqrt{\frac{a c \sqrt{\frac{e^{2}}{a c^{3}}} + d}{a c}} \sqrt{\frac{e^{2}}{a c^{3}}} + \sqrt{e x + d} e\right) - \frac{1}{2} \, \sqrt{-\frac{a c \sqrt{\frac{e^{2}}{a c^{3}}} - d}{a c}} \log\left(a c^{2} \sqrt{-\frac{a c \sqrt{\frac{e^{2}}{a c^{3}}} - d}{a c}} \sqrt{\frac{e^{2}}{a c^{3}}} + \sqrt{e x + d} e\right) + \frac{1}{2} \, \sqrt{-\frac{a c \sqrt{\frac{e^{2}}{a c^{3}}} - d}{a c}} \log\left(-a c^{2} \sqrt{-\frac{a c \sqrt{\frac{e^{2}}{a c^{3}}} - d}{a c}} \sqrt{\frac{e^{2}}{a c^{3}}} + \sqrt{e x + d} e\right)"," ",0,"1/2*sqrt((a*c*sqrt(e^2/(a*c^3)) + d)/(a*c))*log(a*c^2*sqrt((a*c*sqrt(e^2/(a*c^3)) + d)/(a*c))*sqrt(e^2/(a*c^3)) + sqrt(e*x + d)*e) - 1/2*sqrt((a*c*sqrt(e^2/(a*c^3)) + d)/(a*c))*log(-a*c^2*sqrt((a*c*sqrt(e^2/(a*c^3)) + d)/(a*c))*sqrt(e^2/(a*c^3)) + sqrt(e*x + d)*e) - 1/2*sqrt(-(a*c*sqrt(e^2/(a*c^3)) - d)/(a*c))*log(a*c^2*sqrt(-(a*c*sqrt(e^2/(a*c^3)) - d)/(a*c))*sqrt(e^2/(a*c^3)) + sqrt(e*x + d)*e) + 1/2*sqrt(-(a*c*sqrt(e^2/(a*c^3)) - d)/(a*c))*log(-a*c^2*sqrt(-(a*c*sqrt(e^2/(a*c^3)) - d)/(a*c))*sqrt(e^2/(a*c^3)) + sqrt(e*x + d)*e)","B",0
615,1,949,0,0.426013," ","integrate(1/(-c*x^2+a)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{{\left(a c d^{2} - a^{2} e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} + d}{a c d^{2} - a^{2} e^{2}}} \log\left(\sqrt{e x + d} e + {\left(a e^{2} - {\left(a c^{2} d^{3} - a^{2} c d e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{\frac{{\left(a c d^{2} - a^{2} e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} + d}{a c d^{2} - a^{2} e^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{{\left(a c d^{2} - a^{2} e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} + d}{a c d^{2} - a^{2} e^{2}}} \log\left(\sqrt{e x + d} e - {\left(a e^{2} - {\left(a c^{2} d^{3} - a^{2} c d e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{\frac{{\left(a c d^{2} - a^{2} e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} + d}{a c d^{2} - a^{2} e^{2}}}\right) + \frac{1}{2} \, \sqrt{-\frac{{\left(a c d^{2} - a^{2} e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} - d}{a c d^{2} - a^{2} e^{2}}} \log\left(\sqrt{e x + d} e + {\left(a e^{2} + {\left(a c^{2} d^{3} - a^{2} c d e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{-\frac{{\left(a c d^{2} - a^{2} e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} - d}{a c d^{2} - a^{2} e^{2}}}\right) - \frac{1}{2} \, \sqrt{-\frac{{\left(a c d^{2} - a^{2} e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} - d}{a c d^{2} - a^{2} e^{2}}} \log\left(\sqrt{e x + d} e - {\left(a e^{2} + {\left(a c^{2} d^{3} - a^{2} c d e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{-\frac{{\left(a c d^{2} - a^{2} e^{2}\right)} \sqrt{\frac{e^{2}}{a c^{3} d^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} - d}{a c d^{2} - a^{2} e^{2}}}\right)"," ",0,"1/2*sqrt(((a*c*d^2 - a^2*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) + d)/(a*c*d^2 - a^2*e^2))*log(sqrt(e*x + d)*e + (a*e^2 - (a*c^2*d^3 - a^2*c*d*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(((a*c*d^2 - a^2*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) + d)/(a*c*d^2 - a^2*e^2))) - 1/2*sqrt(((a*c*d^2 - a^2*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) + d)/(a*c*d^2 - a^2*e^2))*log(sqrt(e*x + d)*e - (a*e^2 - (a*c^2*d^3 - a^2*c*d*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(((a*c*d^2 - a^2*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) + d)/(a*c*d^2 - a^2*e^2))) + 1/2*sqrt(-((a*c*d^2 - a^2*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) - d)/(a*c*d^2 - a^2*e^2))*log(sqrt(e*x + d)*e + (a*e^2 + (a*c^2*d^3 - a^2*c*d*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(-((a*c*d^2 - a^2*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) - d)/(a*c*d^2 - a^2*e^2))) - 1/2*sqrt(-((a*c*d^2 - a^2*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) - d)/(a*c*d^2 - a^2*e^2))*log(sqrt(e*x + d)*e - (a*e^2 + (a*c^2*d^3 - a^2*c*d*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(-((a*c*d^2 - a^2*e^2)*sqrt(e^2/(a*c^3*d^4 - 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) - d)/(a*c*d^2 - a^2*e^2)))","B",0
616,1,2861,0,0.470809," ","integrate(1/(e*x+d)^(3/2)/(-c*x^2+a),x, algorithm=""fricas"")","\frac{{\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{\frac{c^{2} d^{3} + 3 \, a c d e^{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{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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}}} \log\left({\left(3 \, c^{2} d^{2} e + a c e^{3}\right)} \sqrt{e x + d} + {\left(6 \, a c^{2} d^{3} e^{2} + 2 \, a^{2} c d e^{4} - {\left(a c^{4} d^{8} - 2 \, a^{2} c^{3} d^{6} e^{2} + 2 \, a^{4} c d^{2} e^{6} - a^{5} e^{8}\right)} \sqrt{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}\right)} \sqrt{\frac{c^{2} d^{3} + 3 \, a c d e^{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{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{\frac{c^{2} d^{3} + 3 \, a c d e^{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{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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}}} \log\left({\left(3 \, c^{2} d^{2} e + a c e^{3}\right)} \sqrt{e x + d} - {\left(6 \, a c^{2} d^{3} e^{2} + 2 \, a^{2} c d e^{4} - {\left(a c^{4} d^{8} - 2 \, a^{2} c^{3} d^{6} e^{2} + 2 \, a^{4} c d^{2} e^{6} - a^{5} e^{8}\right)} \sqrt{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}\right)} \sqrt{\frac{c^{2} d^{3} + 3 \, a c d e^{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{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{\frac{c^{2} d^{3} + 3 \, a c d e^{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{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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}}} \log\left({\left(3 \, c^{2} d^{2} e + a c e^{3}\right)} \sqrt{e x + d} + {\left(6 \, a c^{2} d^{3} e^{2} + 2 \, a^{2} c d e^{4} + {\left(a c^{4} d^{8} - 2 \, a^{2} c^{3} d^{6} e^{2} + 2 \, a^{4} c d^{2} e^{6} - a^{5} e^{8}\right)} \sqrt{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}\right)} \sqrt{\frac{c^{2} d^{3} + 3 \, a c d e^{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{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{\frac{c^{2} d^{3} + 3 \, a c d e^{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{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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}}} \log\left({\left(3 \, c^{2} d^{2} e + a c e^{3}\right)} \sqrt{e x + d} - {\left(6 \, a c^{2} d^{3} e^{2} + 2 \, a^{2} c d e^{4} + {\left(a c^{4} d^{8} - 2 \, a^{2} c^{3} d^{6} e^{2} + 2 \, a^{4} c d^{2} e^{6} - a^{5} e^{8}\right)} \sqrt{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}\right)} \sqrt{\frac{c^{2} d^{3} + 3 \, a c d e^{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{\frac{9 \, c^{3} d^{4} e^{2} + 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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) + 4 \, \sqrt{e x + d} e}{2 \, {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)}}"," ",0,"1/2*((c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt((c^2*d^3 + 3*a*c*d*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((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))*log((3*c^2*d^2*e + a*c*e^3)*sqrt(e*x + d) + (6*a*c^2*d^3*e^2 + 2*a^2*c*d*e^4 - (a*c^4*d^8 - 2*a^2*c^3*d^6*e^2 + 2*a^4*c*d^2*e^6 - a^5*e^8)*sqrt((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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^2*d^3 + 3*a*c*d*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((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))) - (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt((c^2*d^3 + 3*a*c*d*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((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))*log((3*c^2*d^2*e + a*c*e^3)*sqrt(e*x + d) - (6*a*c^2*d^3*e^2 + 2*a^2*c*d*e^4 - (a*c^4*d^8 - 2*a^2*c^3*d^6*e^2 + 2*a^4*c*d^2*e^6 - a^5*e^8)*sqrt((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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^2*d^3 + 3*a*c*d*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((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))) + (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt((c^2*d^3 + 3*a*c*d*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((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))*log((3*c^2*d^2*e + a*c*e^3)*sqrt(e*x + d) + (6*a*c^2*d^3*e^2 + 2*a^2*c*d*e^4 + (a*c^4*d^8 - 2*a^2*c^3*d^6*e^2 + 2*a^4*c*d^2*e^6 - a^5*e^8)*sqrt((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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^2*d^3 + 3*a*c*d*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((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))) - (c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt((c^2*d^3 + 3*a*c*d*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((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))*log((3*c^2*d^2*e + a*c*e^3)*sqrt(e*x + d) - (6*a*c^2*d^3*e^2 + 2*a^2*c*d*e^4 + (a*c^4*d^8 - 2*a^2*c^3*d^6*e^2 + 2*a^4*c*d^2*e^6 - a^5*e^8)*sqrt((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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^2*d^3 + 3*a*c*d*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((9*c^3*d^4*e^2 + 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))) + 4*sqrt(e*x + d)*e)/(c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)","B",0
617,1,5142,0,0.572794," ","integrate(1/(e*x+d)^(5/2)/(-c*x^2+a),x, algorithm=""fricas"")","\frac{3 \, {\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)} \sqrt{\frac{c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} + {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}} \log\left({\left(5 \, c^{4} d^{4} e + 10 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{e x + d} + {\left(15 \, a c^{4} d^{6} e^{2} + 35 \, a^{2} c^{3} d^{4} e^{4} + 13 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8} - {\left(a c^{6} d^{13} - 2 \, a^{2} c^{5} d^{11} e^{2} - 5 \, a^{3} c^{4} d^{9} e^{4} + 20 \, a^{4} c^{3} d^{7} e^{6} - 25 \, a^{5} c^{2} d^{5} e^{8} + 14 \, a^{6} c d^{3} e^{10} - 3 \, a^{7} d e^{12}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{\frac{c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} + {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}}\right) - 3 \, {\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)} \sqrt{\frac{c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} + {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}} \log\left({\left(5 \, c^{4} d^{4} e + 10 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{e x + d} - {\left(15 \, a c^{4} d^{6} e^{2} + 35 \, a^{2} c^{3} d^{4} e^{4} + 13 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8} - {\left(a c^{6} d^{13} - 2 \, a^{2} c^{5} d^{11} e^{2} - 5 \, a^{3} c^{4} d^{9} e^{4} + 20 \, a^{4} c^{3} d^{7} e^{6} - 25 \, a^{5} c^{2} d^{5} e^{8} + 14 \, a^{6} c d^{3} e^{10} - 3 \, a^{7} d e^{12}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{\frac{c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} + {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}}\right) + 3 \, {\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)} \sqrt{\frac{c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} - {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}} \log\left({\left(5 \, c^{4} d^{4} e + 10 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{e x + d} + {\left(15 \, a c^{4} d^{6} e^{2} + 35 \, a^{2} c^{3} d^{4} e^{4} + 13 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8} + {\left(a c^{6} d^{13} - 2 \, a^{2} c^{5} d^{11} e^{2} - 5 \, a^{3} c^{4} d^{9} e^{4} + 20 \, a^{4} c^{3} d^{7} e^{6} - 25 \, a^{5} c^{2} d^{5} e^{8} + 14 \, a^{6} c d^{3} e^{10} - 3 \, a^{7} d e^{12}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{\frac{c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} - {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}}\right) - 3 \, {\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)} \sqrt{\frac{c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} - {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}} \log\left({\left(5 \, c^{4} d^{4} e + 10 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{e x + d} - {\left(15 \, a c^{4} d^{6} e^{2} + 35 \, a^{2} c^{3} d^{4} e^{4} + 13 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8} + {\left(a c^{6} d^{13} - 2 \, a^{2} c^{5} d^{11} e^{2} - 5 \, a^{3} c^{4} d^{9} e^{4} + 20 \, a^{4} c^{3} d^{7} e^{6} - 25 \, a^{5} c^{2} d^{5} e^{8} + 14 \, a^{6} c d^{3} e^{10} - 3 \, a^{7} d e^{12}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{\frac{c^{4} d^{5} + 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} - {\left(a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}\right)} \sqrt{\frac{25 \, c^{7} d^{8} e^{2} + 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} + 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} - 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} - 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} - 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} - 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} - 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} - 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} - 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} - a^{6} e^{10}}}\right) + 4 \, {\left(6 \, c d e^{2} x + 7 \, c d^{2} e - a e^{3}\right)} \sqrt{e x + d}}{6 \, {\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)}}"," ",0,"1/6*(3*(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)*sqrt((c^4*d^5 + 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 + (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))*log((5*c^4*d^4*e + 10*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(e*x + d) + (15*a*c^4*d^6*e^2 + 35*a^2*c^3*d^4*e^4 + 13*a^3*c^2*d^2*e^6 + a^4*c*e^8 - (a*c^6*d^13 - 2*a^2*c^5*d^11*e^2 - 5*a^3*c^4*d^9*e^4 + 20*a^4*c^3*d^7*e^6 - 25*a^5*c^2*d^5*e^8 + 14*a^6*c*d^3*e^10 - 3*a^7*d*e^12)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt((c^4*d^5 + 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 + (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))) - 3*(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)*sqrt((c^4*d^5 + 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 + (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))*log((5*c^4*d^4*e + 10*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(e*x + d) - (15*a*c^4*d^6*e^2 + 35*a^2*c^3*d^4*e^4 + 13*a^3*c^2*d^2*e^6 + a^4*c*e^8 - (a*c^6*d^13 - 2*a^2*c^5*d^11*e^2 - 5*a^3*c^4*d^9*e^4 + 20*a^4*c^3*d^7*e^6 - 25*a^5*c^2*d^5*e^8 + 14*a^6*c*d^3*e^10 - 3*a^7*d*e^12)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt((c^4*d^5 + 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 + (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))) + 3*(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)*sqrt((c^4*d^5 + 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 - (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))*log((5*c^4*d^4*e + 10*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(e*x + d) + (15*a*c^4*d^6*e^2 + 35*a^2*c^3*d^4*e^4 + 13*a^3*c^2*d^2*e^6 + a^4*c*e^8 + (a*c^6*d^13 - 2*a^2*c^5*d^11*e^2 - 5*a^3*c^4*d^9*e^4 + 20*a^4*c^3*d^7*e^6 - 25*a^5*c^2*d^5*e^8 + 14*a^6*c*d^3*e^10 - 3*a^7*d*e^12)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt((c^4*d^5 + 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 - (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))) - 3*(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)*sqrt((c^4*d^5 + 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 - (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))*log((5*c^4*d^4*e + 10*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(e*x + d) - (15*a*c^4*d^6*e^2 + 35*a^2*c^3*d^4*e^4 + 13*a^3*c^2*d^2*e^6 + a^4*c*e^8 + (a*c^6*d^13 - 2*a^2*c^5*d^11*e^2 - 5*a^3*c^4*d^9*e^4 + 20*a^4*c^3*d^7*e^6 - 25*a^5*c^2*d^5*e^8 + 14*a^6*c*d^3*e^10 - 3*a^7*d*e^12)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt((c^4*d^5 + 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 - (a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10)*sqrt((25*c^7*d^8*e^2 + 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 + 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 - 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 - 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 - 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 - 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 - 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 - 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 - 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 - a^6*e^10))) + 4*(6*c*d*e^2*x + 7*c*d^2*e - a*e^3)*sqrt(e*x + 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)","B",0
618,1,1641,0,0.514292," ","integrate((e*x+d)^(5/2)/(c*x^2+a),x, algorithm=""fricas"")","-\frac{3 \, c \sqrt{-\frac{c^{2} d^{5} - 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + a c^{3} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}} \log\left({\left(5 \, c^{4} d^{8} e - 14 \, a^{2} c^{2} d^{4} e^{5} - 8 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} \sqrt{e x + d} + {\left(10 \, a c^{4} d^{5} e^{2} - 20 \, a^{2} c^{3} d^{3} e^{4} + 2 \, a^{3} c^{2} d e^{6} + {\left(a c^{6} d^{2} - a^{2} c^{5} e^{2}\right)} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}\right)} \sqrt{-\frac{c^{2} d^{5} - 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + a c^{3} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}}\right) - 3 \, c \sqrt{-\frac{c^{2} d^{5} - 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + a c^{3} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}} \log\left({\left(5 \, c^{4} d^{8} e - 14 \, a^{2} c^{2} d^{4} e^{5} - 8 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} \sqrt{e x + d} - {\left(10 \, a c^{4} d^{5} e^{2} - 20 \, a^{2} c^{3} d^{3} e^{4} + 2 \, a^{3} c^{2} d e^{6} + {\left(a c^{6} d^{2} - a^{2} c^{5} e^{2}\right)} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}\right)} \sqrt{-\frac{c^{2} d^{5} - 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + a c^{3} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}}\right) + 3 \, c \sqrt{-\frac{c^{2} d^{5} - 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - a c^{3} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}} \log\left({\left(5 \, c^{4} d^{8} e - 14 \, a^{2} c^{2} d^{4} e^{5} - 8 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} \sqrt{e x + d} + {\left(10 \, a c^{4} d^{5} e^{2} - 20 \, a^{2} c^{3} d^{3} e^{4} + 2 \, a^{3} c^{2} d e^{6} - {\left(a c^{6} d^{2} - a^{2} c^{5} e^{2}\right)} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}\right)} \sqrt{-\frac{c^{2} d^{5} - 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - a c^{3} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}}\right) - 3 \, c \sqrt{-\frac{c^{2} d^{5} - 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - a c^{3} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}} \log\left({\left(5 \, c^{4} d^{8} e - 14 \, a^{2} c^{2} d^{4} e^{5} - 8 \, a^{3} c d^{2} e^{7} + a^{4} e^{9}\right)} \sqrt{e x + d} - {\left(10 \, a c^{4} d^{5} e^{2} - 20 \, a^{2} c^{3} d^{3} e^{4} + 2 \, a^{3} c^{2} d e^{6} - {\left(a c^{6} d^{2} - a^{2} c^{5} e^{2}\right)} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}\right)} \sqrt{-\frac{c^{2} d^{5} - 10 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - a c^{3} \sqrt{-\frac{25 \, c^{4} d^{8} e^{2} - 100 \, a c^{3} d^{6} e^{4} + 110 \, a^{2} c^{2} d^{4} e^{6} - 20 \, a^{3} c d^{2} e^{8} + a^{4} e^{10}}{a c^{7}}}}{a c^{3}}}\right) - 4 \, {\left(e^{2} x + 7 \, d e\right)} \sqrt{e x + d}}{6 \, c}"," ",0,"-1/6*(3*c*sqrt(-(c^2*d^5 - 10*a*c*d^3*e^2 + 5*a^2*d*e^4 + a*c^3*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))*log((5*c^4*d^8*e - 14*a^2*c^2*d^4*e^5 - 8*a^3*c*d^2*e^7 + a^4*e^9)*sqrt(e*x + d) + (10*a*c^4*d^5*e^2 - 20*a^2*c^3*d^3*e^4 + 2*a^3*c^2*d*e^6 + (a*c^6*d^2 - a^2*c^5*e^2)*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))*sqrt(-(c^2*d^5 - 10*a*c*d^3*e^2 + 5*a^2*d*e^4 + a*c^3*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))) - 3*c*sqrt(-(c^2*d^5 - 10*a*c*d^3*e^2 + 5*a^2*d*e^4 + a*c^3*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))*log((5*c^4*d^8*e - 14*a^2*c^2*d^4*e^5 - 8*a^3*c*d^2*e^7 + a^4*e^9)*sqrt(e*x + d) - (10*a*c^4*d^5*e^2 - 20*a^2*c^3*d^3*e^4 + 2*a^3*c^2*d*e^6 + (a*c^6*d^2 - a^2*c^5*e^2)*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))*sqrt(-(c^2*d^5 - 10*a*c*d^3*e^2 + 5*a^2*d*e^4 + a*c^3*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))) + 3*c*sqrt(-(c^2*d^5 - 10*a*c*d^3*e^2 + 5*a^2*d*e^4 - a*c^3*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))*log((5*c^4*d^8*e - 14*a^2*c^2*d^4*e^5 - 8*a^3*c*d^2*e^7 + a^4*e^9)*sqrt(e*x + d) + (10*a*c^4*d^5*e^2 - 20*a^2*c^3*d^3*e^4 + 2*a^3*c^2*d*e^6 - (a*c^6*d^2 - a^2*c^5*e^2)*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))*sqrt(-(c^2*d^5 - 10*a*c*d^3*e^2 + 5*a^2*d*e^4 - a*c^3*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))) - 3*c*sqrt(-(c^2*d^5 - 10*a*c*d^3*e^2 + 5*a^2*d*e^4 - a*c^3*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))*log((5*c^4*d^8*e - 14*a^2*c^2*d^4*e^5 - 8*a^3*c*d^2*e^7 + a^4*e^9)*sqrt(e*x + d) - (10*a*c^4*d^5*e^2 - 20*a^2*c^3*d^3*e^4 + 2*a^3*c^2*d*e^6 - (a*c^6*d^2 - a^2*c^5*e^2)*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))*sqrt(-(c^2*d^5 - 10*a*c*d^3*e^2 + 5*a^2*d*e^4 - a*c^3*sqrt(-(25*c^4*d^8*e^2 - 100*a*c^3*d^6*e^4 + 110*a^2*c^2*d^4*e^6 - 20*a^3*c*d^2*e^8 + a^4*e^10)/(a*c^7)))/(a*c^3))) - 4*(e^2*x + 7*d*e)*sqrt(e*x + d))/c","B",0
619,1,998,0,0.436311," ","integrate((e*x+d)^(3/2)/(c*x^2+a),x, algorithm=""fricas"")","\frac{c \sqrt{-\frac{c d^{3} - 3 \, a d e^{2} + a c^{2} \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}} \log\left(-{\left(3 \, c^{2} d^{4} e + 2 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} \sqrt{e x + d} + {\left(3 \, a c^{2} d^{2} e^{2} - a^{2} c e^{4} + a c^{4} d \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}\right)} \sqrt{-\frac{c d^{3} - 3 \, a d e^{2} + a c^{2} \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}}\right) - c \sqrt{-\frac{c d^{3} - 3 \, a d e^{2} + a c^{2} \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}} \log\left(-{\left(3 \, c^{2} d^{4} e + 2 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} \sqrt{e x + d} - {\left(3 \, a c^{2} d^{2} e^{2} - a^{2} c e^{4} + a c^{4} d \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}\right)} \sqrt{-\frac{c d^{3} - 3 \, a d e^{2} + a c^{2} \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}}\right) + c \sqrt{-\frac{c d^{3} - 3 \, a d e^{2} - a c^{2} \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}} \log\left(-{\left(3 \, c^{2} d^{4} e + 2 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} \sqrt{e x + d} + {\left(3 \, a c^{2} d^{2} e^{2} - a^{2} c e^{4} - a c^{4} d \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}\right)} \sqrt{-\frac{c d^{3} - 3 \, a d e^{2} - a c^{2} \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}}\right) - c \sqrt{-\frac{c d^{3} - 3 \, a d e^{2} - a c^{2} \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}} \log\left(-{\left(3 \, c^{2} d^{4} e + 2 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} \sqrt{e x + d} - {\left(3 \, a c^{2} d^{2} e^{2} - a^{2} c e^{4} - a c^{4} d \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}\right)} \sqrt{-\frac{c d^{3} - 3 \, a d e^{2} - a c^{2} \sqrt{-\frac{9 \, c^{2} d^{4} e^{2} - 6 \, a c d^{2} e^{4} + a^{2} e^{6}}{a c^{5}}}}{a c^{2}}}\right) + 4 \, \sqrt{e x + d} e}{2 \, c}"," ",0,"1/2*(c*sqrt(-(c*d^3 - 3*a*d*e^2 + a*c^2*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))*log(-(3*c^2*d^4*e + 2*a*c*d^2*e^3 - a^2*e^5)*sqrt(e*x + d) + (3*a*c^2*d^2*e^2 - a^2*c*e^4 + a*c^4*d*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))*sqrt(-(c*d^3 - 3*a*d*e^2 + a*c^2*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))) - c*sqrt(-(c*d^3 - 3*a*d*e^2 + a*c^2*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))*log(-(3*c^2*d^4*e + 2*a*c*d^2*e^3 - a^2*e^5)*sqrt(e*x + d) - (3*a*c^2*d^2*e^2 - a^2*c*e^4 + a*c^4*d*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))*sqrt(-(c*d^3 - 3*a*d*e^2 + a*c^2*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))) + c*sqrt(-(c*d^3 - 3*a*d*e^2 - a*c^2*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))*log(-(3*c^2*d^4*e + 2*a*c*d^2*e^3 - a^2*e^5)*sqrt(e*x + d) + (3*a*c^2*d^2*e^2 - a^2*c*e^4 - a*c^4*d*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))*sqrt(-(c*d^3 - 3*a*d*e^2 - a*c^2*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))) - c*sqrt(-(c*d^3 - 3*a*d*e^2 - a*c^2*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))*log(-(3*c^2*d^4*e + 2*a*c*d^2*e^3 - a^2*e^5)*sqrt(e*x + d) - (3*a*c^2*d^2*e^2 - a^2*c*e^4 - a*c^4*d*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))*sqrt(-(c*d^3 - 3*a*d*e^2 - a*c^2*sqrt(-(9*c^2*d^4*e^2 - 6*a*c*d^2*e^4 + a^2*e^6)/(a*c^5)))/(a*c^2))) + 4*sqrt(e*x + d)*e)/c","A",0
620,1,355,0,0.416094," ","integrate((e*x+d)^(1/2)/(c*x^2+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-\frac{a c \sqrt{-\frac{e^{2}}{a c^{3}}} + d}{a c}} \log\left(a c^{2} \sqrt{-\frac{a c \sqrt{-\frac{e^{2}}{a c^{3}}} + d}{a c}} \sqrt{-\frac{e^{2}}{a c^{3}}} + \sqrt{e x + d} e\right) + \frac{1}{2} \, \sqrt{-\frac{a c \sqrt{-\frac{e^{2}}{a c^{3}}} + d}{a c}} \log\left(-a c^{2} \sqrt{-\frac{a c \sqrt{-\frac{e^{2}}{a c^{3}}} + d}{a c}} \sqrt{-\frac{e^{2}}{a c^{3}}} + \sqrt{e x + d} e\right) + \frac{1}{2} \, \sqrt{\frac{a c \sqrt{-\frac{e^{2}}{a c^{3}}} - d}{a c}} \log\left(a c^{2} \sqrt{\frac{a c \sqrt{-\frac{e^{2}}{a c^{3}}} - d}{a c}} \sqrt{-\frac{e^{2}}{a c^{3}}} + \sqrt{e x + d} e\right) - \frac{1}{2} \, \sqrt{\frac{a c \sqrt{-\frac{e^{2}}{a c^{3}}} - d}{a c}} \log\left(-a c^{2} \sqrt{\frac{a c \sqrt{-\frac{e^{2}}{a c^{3}}} - d}{a c}} \sqrt{-\frac{e^{2}}{a c^{3}}} + \sqrt{e x + d} e\right)"," ",0,"-1/2*sqrt(-(a*c*sqrt(-e^2/(a*c^3)) + d)/(a*c))*log(a*c^2*sqrt(-(a*c*sqrt(-e^2/(a*c^3)) + d)/(a*c))*sqrt(-e^2/(a*c^3)) + sqrt(e*x + d)*e) + 1/2*sqrt(-(a*c*sqrt(-e^2/(a*c^3)) + d)/(a*c))*log(-a*c^2*sqrt(-(a*c*sqrt(-e^2/(a*c^3)) + d)/(a*c))*sqrt(-e^2/(a*c^3)) + sqrt(e*x + d)*e) + 1/2*sqrt((a*c*sqrt(-e^2/(a*c^3)) - d)/(a*c))*log(a*c^2*sqrt((a*c*sqrt(-e^2/(a*c^3)) - d)/(a*c))*sqrt(-e^2/(a*c^3)) + sqrt(e*x + d)*e) - 1/2*sqrt((a*c*sqrt(-e^2/(a*c^3)) - d)/(a*c))*log(-a*c^2*sqrt((a*c*sqrt(-e^2/(a*c^3)) - d)/(a*c))*sqrt(-e^2/(a*c^3)) + sqrt(e*x + d)*e)","A",0
621,1,941,0,0.430779," ","integrate(1/(c*x^2+a)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-\frac{{\left(a c d^{2} + a^{2} e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} + d}{a c d^{2} + a^{2} e^{2}}} \log\left(\sqrt{e x + d} e + {\left(a e^{2} + {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{-\frac{{\left(a c d^{2} + a^{2} e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} + d}{a c d^{2} + a^{2} e^{2}}}\right) - \frac{1}{2} \, \sqrt{-\frac{{\left(a c d^{2} + a^{2} e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} + d}{a c d^{2} + a^{2} e^{2}}} \log\left(\sqrt{e x + d} e - {\left(a e^{2} + {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{-\frac{{\left(a c d^{2} + a^{2} e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} + d}{a c d^{2} + a^{2} e^{2}}}\right) + \frac{1}{2} \, \sqrt{\frac{{\left(a c d^{2} + a^{2} e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} - d}{a c d^{2} + a^{2} e^{2}}} \log\left(\sqrt{e x + d} e + {\left(a e^{2} - {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{\frac{{\left(a c d^{2} + a^{2} e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} - d}{a c d^{2} + a^{2} e^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{{\left(a c d^{2} + a^{2} e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} - d}{a c d^{2} + a^{2} e^{2}}} \log\left(\sqrt{e x + d} e - {\left(a e^{2} - {\left(a c^{2} d^{3} + a^{2} c d e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}}\right)} \sqrt{\frac{{\left(a c d^{2} + a^{2} e^{2}\right)} \sqrt{-\frac{e^{2}}{a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}}} - d}{a c d^{2} + a^{2} e^{2}}}\right)"," ",0,"1/2*sqrt(-((a*c*d^2 + a^2*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) + d)/(a*c*d^2 + a^2*e^2))*log(sqrt(e*x + d)*e + (a*e^2 + (a*c^2*d^3 + a^2*c*d*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(-((a*c*d^2 + a^2*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) + d)/(a*c*d^2 + a^2*e^2))) - 1/2*sqrt(-((a*c*d^2 + a^2*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) + d)/(a*c*d^2 + a^2*e^2))*log(sqrt(e*x + d)*e - (a*e^2 + (a*c^2*d^3 + a^2*c*d*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(-((a*c*d^2 + a^2*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) + d)/(a*c*d^2 + a^2*e^2))) + 1/2*sqrt(((a*c*d^2 + a^2*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) - d)/(a*c*d^2 + a^2*e^2))*log(sqrt(e*x + d)*e + (a*e^2 - (a*c^2*d^3 + a^2*c*d*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(((a*c*d^2 + a^2*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) - d)/(a*c*d^2 + a^2*e^2))) - 1/2*sqrt(((a*c*d^2 + a^2*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) - d)/(a*c*d^2 + a^2*e^2))*log(sqrt(e*x + d)*e - (a*e^2 - (a*c^2*d^3 + a^2*c*d*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)))*sqrt(((a*c*d^2 + a^2*e^2)*sqrt(-e^2/(a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)) - d)/(a*c*d^2 + a^2*e^2)))","B",0
622,1,2863,0,0.462133," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a),x, algorithm=""fricas"")","-\frac{{\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} d^{3} - 3 \, a c d e^{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{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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}}} \log\left(-{\left(3 \, c^{2} d^{2} e - a c e^{3}\right)} \sqrt{e x + d} + {\left(6 \, a c^{2} d^{3} e^{2} - 2 \, a^{2} c d e^{4} + {\left(a c^{4} d^{8} + 2 \, a^{2} c^{3} d^{6} e^{2} - 2 \, a^{4} c d^{2} e^{6} - a^{5} e^{8}\right)} \sqrt{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}\right)} \sqrt{-\frac{c^{2} d^{3} - 3 \, a c d e^{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{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} d^{3} - 3 \, a c d e^{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{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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}}} \log\left(-{\left(3 \, c^{2} d^{2} e - a c e^{3}\right)} \sqrt{e x + d} - {\left(6 \, a c^{2} d^{3} e^{2} - 2 \, a^{2} c d e^{4} + {\left(a c^{4} d^{8} + 2 \, a^{2} c^{3} d^{6} e^{2} - 2 \, a^{4} c d^{2} e^{6} - a^{5} e^{8}\right)} \sqrt{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}\right)} \sqrt{-\frac{c^{2} d^{3} - 3 \, a c d e^{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{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} d^{3} - 3 \, a c d e^{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{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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}}} \log\left(-{\left(3 \, c^{2} d^{2} e - a c e^{3}\right)} \sqrt{e x + d} + {\left(6 \, a c^{2} d^{3} e^{2} - 2 \, a^{2} c d e^{4} - {\left(a c^{4} d^{8} + 2 \, a^{2} c^{3} d^{6} e^{2} - 2 \, a^{4} c d^{2} e^{6} - a^{5} e^{8}\right)} \sqrt{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}\right)} \sqrt{-\frac{c^{2} d^{3} - 3 \, a c d e^{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{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} d^{3} - 3 \, a c d e^{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{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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}}} \log\left(-{\left(3 \, c^{2} d^{2} e - a c e^{3}\right)} \sqrt{e x + d} - {\left(6 \, a c^{2} d^{3} e^{2} - 2 \, a^{2} c d e^{4} - {\left(a c^{4} d^{8} + 2 \, a^{2} c^{3} d^{6} e^{2} - 2 \, a^{4} c d^{2} e^{6} - a^{5} e^{8}\right)} \sqrt{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}\right)} \sqrt{-\frac{c^{2} d^{3} - 3 \, a c d e^{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{-\frac{9 \, c^{3} d^{4} e^{2} - 6 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6}}{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}}}}{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) + 4 \, \sqrt{e x + d} e}{2 \, {\left(c d^{3} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)}}"," ",0,"-1/2*((c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-(c^2*d^3 - 3*a*c*d*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(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))*log(-(3*c^2*d^2*e - a*c*e^3)*sqrt(e*x + d) + (6*a*c^2*d^3*e^2 - 2*a^2*c*d*e^4 + (a*c^4*d^8 + 2*a^2*c^3*d^6*e^2 - 2*a^4*c*d^2*e^6 - a^5*e^8)*sqrt(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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^2*d^3 - 3*a*c*d*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(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))) - (c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-(c^2*d^3 - 3*a*c*d*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(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))*log(-(3*c^2*d^2*e - a*c*e^3)*sqrt(e*x + d) - (6*a*c^2*d^3*e^2 - 2*a^2*c*d*e^4 + (a*c^4*d^8 + 2*a^2*c^3*d^6*e^2 - 2*a^4*c*d^2*e^6 - a^5*e^8)*sqrt(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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^2*d^3 - 3*a*c*d*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(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))) + (c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-(c^2*d^3 - 3*a*c*d*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(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))*log(-(3*c^2*d^2*e - a*c*e^3)*sqrt(e*x + d) + (6*a*c^2*d^3*e^2 - 2*a^2*c*d*e^4 - (a*c^4*d^8 + 2*a^2*c^3*d^6*e^2 - 2*a^4*c*d^2*e^6 - a^5*e^8)*sqrt(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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^2*d^3 - 3*a*c*d*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(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))) - (c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-(c^2*d^3 - 3*a*c*d*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(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))*log(-(3*c^2*d^2*e - a*c*e^3)*sqrt(e*x + d) - (6*a*c^2*d^3*e^2 - 2*a^2*c*d*e^4 - (a*c^4*d^8 + 2*a^2*c^3*d^6*e^2 - 2*a^4*c*d^2*e^6 - a^5*e^8)*sqrt(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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^2*d^3 - 3*a*c*d*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(-(9*c^3*d^4*e^2 - 6*a*c^2*d^2*e^4 + a^2*c*e^6)/(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)))/(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))) + 4*sqrt(e*x + d)*e)/(c*d^3 + a*d*e^2 + (c*d^2*e + a*e^3)*x)","B",0
623,1,5149,0,0.554214," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+a),x, algorithm=""fricas"")","\frac{3 \, {\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)} \sqrt{-\frac{c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} + {\left(a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}}} \log\left({\left(5 \, c^{4} d^{4} e - 10 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{e x + d} + {\left(15 \, a c^{4} d^{6} e^{2} - 35 \, a^{2} c^{3} d^{4} e^{4} + 13 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8} + {\left(a c^{6} d^{13} + 2 \, a^{2} c^{5} d^{11} e^{2} - 5 \, a^{3} c^{4} d^{9} e^{4} - 20 \, a^{4} c^{3} d^{7} e^{6} - 25 \, a^{5} c^{2} d^{5} e^{8} - 14 \, a^{6} c d^{3} e^{10} - 3 \, a^{7} d e^{12}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{-\frac{c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} + {\left(a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}}}\right) - 3 \, {\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)} \sqrt{-\frac{c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} + {\left(a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}}} \log\left({\left(5 \, c^{4} d^{4} e - 10 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{e x + d} - {\left(15 \, a c^{4} d^{6} e^{2} - 35 \, a^{2} c^{3} d^{4} e^{4} + 13 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8} + {\left(a c^{6} d^{13} + 2 \, a^{2} c^{5} d^{11} e^{2} - 5 \, a^{3} c^{4} d^{9} e^{4} - 20 \, a^{4} c^{3} d^{7} e^{6} - 25 \, a^{5} c^{2} d^{5} e^{8} - 14 \, a^{6} c d^{3} e^{10} - 3 \, a^{7} d e^{12}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{-\frac{c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} + {\left(a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}}}\right) + 3 \, {\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)} \sqrt{-\frac{c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} - {\left(a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}}} \log\left({\left(5 \, c^{4} d^{4} e - 10 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{e x + d} + {\left(15 \, a c^{4} d^{6} e^{2} - 35 \, a^{2} c^{3} d^{4} e^{4} + 13 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8} - {\left(a c^{6} d^{13} + 2 \, a^{2} c^{5} d^{11} e^{2} - 5 \, a^{3} c^{4} d^{9} e^{4} - 20 \, a^{4} c^{3} d^{7} e^{6} - 25 \, a^{5} c^{2} d^{5} e^{8} - 14 \, a^{6} c d^{3} e^{10} - 3 \, a^{7} d e^{12}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{-\frac{c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} - {\left(a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}}}\right) - 3 \, {\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)} \sqrt{-\frac{c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} - {\left(a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}}} \log\left({\left(5 \, c^{4} d^{4} e - 10 \, a c^{3} d^{2} e^{3} + a^{2} c^{2} e^{5}\right)} \sqrt{e x + d} - {\left(15 \, a c^{4} d^{6} e^{2} - 35 \, a^{2} c^{3} d^{4} e^{4} + 13 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8} - {\left(a c^{6} d^{13} + 2 \, a^{2} c^{5} d^{11} e^{2} - 5 \, a^{3} c^{4} d^{9} e^{4} - 20 \, a^{4} c^{3} d^{7} e^{6} - 25 \, a^{5} c^{2} d^{5} e^{8} - 14 \, a^{6} c d^{3} e^{10} - 3 \, a^{7} d e^{12}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}\right)} \sqrt{-\frac{c^{4} d^{5} - 10 \, a c^{3} d^{3} e^{2} + 5 \, a^{2} c^{2} d e^{4} - {\left(a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}\right)} \sqrt{-\frac{25 \, c^{7} d^{8} e^{2} - 100 \, a c^{6} d^{6} e^{4} + 110 \, a^{2} c^{5} d^{4} e^{6} - 20 \, a^{3} c^{4} d^{2} e^{8} + a^{4} c^{3} e^{10}}{a c^{10} d^{20} + 10 \, a^{2} c^{9} d^{18} e^{2} + 45 \, a^{3} c^{8} d^{16} e^{4} + 120 \, a^{4} c^{7} d^{14} e^{6} + 210 \, a^{5} c^{6} d^{12} e^{8} + 252 \, a^{6} c^{5} d^{10} e^{10} + 210 \, a^{7} c^{4} d^{8} e^{12} + 120 \, a^{8} c^{3} d^{6} e^{14} + 45 \, a^{9} c^{2} d^{4} e^{16} + 10 \, a^{10} c d^{2} e^{18} + a^{11} e^{20}}}}{a c^{5} d^{10} + 5 \, a^{2} c^{4} d^{8} e^{2} + 10 \, a^{3} c^{3} d^{6} e^{4} + 10 \, a^{4} c^{2} d^{4} e^{6} + 5 \, a^{5} c d^{2} e^{8} + a^{6} e^{10}}}\right) - 4 \, {\left(6 \, c d e^{2} x + 7 \, c d^{2} e + a e^{3}\right)} \sqrt{e x + d}}{6 \, {\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)}}"," ",0,"1/6*(3*(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)*sqrt(-(c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 + (a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10))*log((5*c^4*d^4*e - 10*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(e*x + d) + (15*a*c^4*d^6*e^2 - 35*a^2*c^3*d^4*e^4 + 13*a^3*c^2*d^2*e^6 - a^4*c*e^8 + (a*c^6*d^13 + 2*a^2*c^5*d^11*e^2 - 5*a^3*c^4*d^9*e^4 - 20*a^4*c^3*d^7*e^6 - 25*a^5*c^2*d^5*e^8 - 14*a^6*c*d^3*e^10 - 3*a^7*d*e^12)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt(-(c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 + (a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10))) - 3*(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)*sqrt(-(c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 + (a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10))*log((5*c^4*d^4*e - 10*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(e*x + d) - (15*a*c^4*d^6*e^2 - 35*a^2*c^3*d^4*e^4 + 13*a^3*c^2*d^2*e^6 - a^4*c*e^8 + (a*c^6*d^13 + 2*a^2*c^5*d^11*e^2 - 5*a^3*c^4*d^9*e^4 - 20*a^4*c^3*d^7*e^6 - 25*a^5*c^2*d^5*e^8 - 14*a^6*c*d^3*e^10 - 3*a^7*d*e^12)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt(-(c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 + (a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10))) + 3*(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)*sqrt(-(c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 - (a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10))*log((5*c^4*d^4*e - 10*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(e*x + d) + (15*a*c^4*d^6*e^2 - 35*a^2*c^3*d^4*e^4 + 13*a^3*c^2*d^2*e^6 - a^4*c*e^8 - (a*c^6*d^13 + 2*a^2*c^5*d^11*e^2 - 5*a^3*c^4*d^9*e^4 - 20*a^4*c^3*d^7*e^6 - 25*a^5*c^2*d^5*e^8 - 14*a^6*c*d^3*e^10 - 3*a^7*d*e^12)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt(-(c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 - (a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10))) - 3*(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)*sqrt(-(c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 - (a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10))*log((5*c^4*d^4*e - 10*a*c^3*d^2*e^3 + a^2*c^2*e^5)*sqrt(e*x + d) - (15*a*c^4*d^6*e^2 - 35*a^2*c^3*d^4*e^4 + 13*a^3*c^2*d^2*e^6 - a^4*c*e^8 - (a*c^6*d^13 + 2*a^2*c^5*d^11*e^2 - 5*a^3*c^4*d^9*e^4 - 20*a^4*c^3*d^7*e^6 - 25*a^5*c^2*d^5*e^8 - 14*a^6*c*d^3*e^10 - 3*a^7*d*e^12)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))*sqrt(-(c^4*d^5 - 10*a*c^3*d^3*e^2 + 5*a^2*c^2*d*e^4 - (a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10)*sqrt(-(25*c^7*d^8*e^2 - 100*a*c^6*d^6*e^4 + 110*a^2*c^5*d^4*e^6 - 20*a^3*c^4*d^2*e^8 + a^4*c^3*e^10)/(a*c^10*d^20 + 10*a^2*c^9*d^18*e^2 + 45*a^3*c^8*d^16*e^4 + 120*a^4*c^7*d^14*e^6 + 210*a^5*c^6*d^12*e^8 + 252*a^6*c^5*d^10*e^10 + 210*a^7*c^4*d^8*e^12 + 120*a^8*c^3*d^6*e^14 + 45*a^9*c^2*d^4*e^16 + 10*a^10*c*d^2*e^18 + a^11*e^20)))/(a*c^5*d^10 + 5*a^2*c^4*d^8*e^2 + 10*a^3*c^3*d^6*e^4 + 10*a^4*c^2*d^4*e^6 + 5*a^5*c*d^2*e^8 + a^6*e^10))) - 4*(6*c*d*e^2*x + 7*c*d^2*e + a*e^3)*sqrt(e*x + 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)","B",0
624,1,2073,0,0.632992," ","integrate((e*x+d)^(7/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(a c^{3} x^{2} - a^{2} c^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{7} - 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + a^{3} c^{4} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}} \log\left({\left(140 \, c^{5} d^{10} e^{3} - 1771 \, a c^{4} d^{8} e^{5} + 6872 \, a^{2} c^{3} d^{6} e^{7} - 8366 \, a^{3} c^{2} d^{4} e^{9} + 2500 \, a^{4} c d^{2} e^{11} + 625 \, a^{5} e^{13}\right)} \sqrt{e x + d} + {\left(35 \, a^{2} c^{5} d^{6} e^{4} + 21 \, a^{3} c^{4} d^{4} e^{6} - 795 \, a^{4} c^{3} d^{2} e^{8} - 125 \, a^{5} c^{2} e^{10} - 2 \, {\left(a^{3} c^{8} d^{3} - 4 \, a^{4} c^{7} d e^{2}\right)} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}\right)} \sqrt{\frac{4 \, c^{3} d^{7} - 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + a^{3} c^{4} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}}\right) - {\left(a c^{3} x^{2} - a^{2} c^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{7} - 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + a^{3} c^{4} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}} \log\left({\left(140 \, c^{5} d^{10} e^{3} - 1771 \, a c^{4} d^{8} e^{5} + 6872 \, a^{2} c^{3} d^{6} e^{7} - 8366 \, a^{3} c^{2} d^{4} e^{9} + 2500 \, a^{4} c d^{2} e^{11} + 625 \, a^{5} e^{13}\right)} \sqrt{e x + d} - {\left(35 \, a^{2} c^{5} d^{6} e^{4} + 21 \, a^{3} c^{4} d^{4} e^{6} - 795 \, a^{4} c^{3} d^{2} e^{8} - 125 \, a^{5} c^{2} e^{10} - 2 \, {\left(a^{3} c^{8} d^{3} - 4 \, a^{4} c^{7} d e^{2}\right)} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}\right)} \sqrt{\frac{4 \, c^{3} d^{7} - 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + a^{3} c^{4} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}}\right) + {\left(a c^{3} x^{2} - a^{2} c^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{7} - 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - a^{3} c^{4} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}} \log\left({\left(140 \, c^{5} d^{10} e^{3} - 1771 \, a c^{4} d^{8} e^{5} + 6872 \, a^{2} c^{3} d^{6} e^{7} - 8366 \, a^{3} c^{2} d^{4} e^{9} + 2500 \, a^{4} c d^{2} e^{11} + 625 \, a^{5} e^{13}\right)} \sqrt{e x + d} + {\left(35 \, a^{2} c^{5} d^{6} e^{4} + 21 \, a^{3} c^{4} d^{4} e^{6} - 795 \, a^{4} c^{3} d^{2} e^{8} - 125 \, a^{5} c^{2} e^{10} + 2 \, {\left(a^{3} c^{8} d^{3} - 4 \, a^{4} c^{7} d e^{2}\right)} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}\right)} \sqrt{\frac{4 \, c^{3} d^{7} - 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - a^{3} c^{4} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}}\right) - {\left(a c^{3} x^{2} - a^{2} c^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{7} - 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - a^{3} c^{4} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}} \log\left({\left(140 \, c^{5} d^{10} e^{3} - 1771 \, a c^{4} d^{8} e^{5} + 6872 \, a^{2} c^{3} d^{6} e^{7} - 8366 \, a^{3} c^{2} d^{4} e^{9} + 2500 \, a^{4} c d^{2} e^{11} + 625 \, a^{5} e^{13}\right)} \sqrt{e x + d} - {\left(35 \, a^{2} c^{5} d^{6} e^{4} + 21 \, a^{3} c^{4} d^{4} e^{6} - 795 \, a^{4} c^{3} d^{2} e^{8} - 125 \, a^{5} c^{2} e^{10} + 2 \, {\left(a^{3} c^{8} d^{3} - 4 \, a^{4} c^{7} d e^{2}\right)} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}\right)} \sqrt{\frac{4 \, c^{3} d^{7} - 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - a^{3} c^{4} \sqrt{\frac{1225 \, c^{4} d^{8} e^{6} - 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} + 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}}\right) + 4 \, {\left(4 \, a c e^{3} x^{2} - 3 \, a c d^{2} e - 5 \, a^{2} e^{3} - {\left(c^{2} d^{3} + 3 \, a c d e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a c^{3} x^{2} - a^{2} c^{2}\right)}}"," ",0,"1/8*((a*c^3*x^2 - a^2*c^2)*sqrt((4*c^3*d^7 - 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + a^3*c^4*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))*log((140*c^5*d^10*e^3 - 1771*a*c^4*d^8*e^5 + 6872*a^2*c^3*d^6*e^7 - 8366*a^3*c^2*d^4*e^9 + 2500*a^4*c*d^2*e^11 + 625*a^5*e^13)*sqrt(e*x + d) + (35*a^2*c^5*d^6*e^4 + 21*a^3*c^4*d^4*e^6 - 795*a^4*c^3*d^2*e^8 - 125*a^5*c^2*e^10 - 2*(a^3*c^8*d^3 - 4*a^4*c^7*d*e^2)*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))*sqrt((4*c^3*d^7 - 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + a^3*c^4*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))) - (a*c^3*x^2 - a^2*c^2)*sqrt((4*c^3*d^7 - 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + a^3*c^4*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))*log((140*c^5*d^10*e^3 - 1771*a*c^4*d^8*e^5 + 6872*a^2*c^3*d^6*e^7 - 8366*a^3*c^2*d^4*e^9 + 2500*a^4*c*d^2*e^11 + 625*a^5*e^13)*sqrt(e*x + d) - (35*a^2*c^5*d^6*e^4 + 21*a^3*c^4*d^4*e^6 - 795*a^4*c^3*d^2*e^8 - 125*a^5*c^2*e^10 - 2*(a^3*c^8*d^3 - 4*a^4*c^7*d*e^2)*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))*sqrt((4*c^3*d^7 - 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + a^3*c^4*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))) + (a*c^3*x^2 - a^2*c^2)*sqrt((4*c^3*d^7 - 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - a^3*c^4*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))*log((140*c^5*d^10*e^3 - 1771*a*c^4*d^8*e^5 + 6872*a^2*c^3*d^6*e^7 - 8366*a^3*c^2*d^4*e^9 + 2500*a^4*c*d^2*e^11 + 625*a^5*e^13)*sqrt(e*x + d) + (35*a^2*c^5*d^6*e^4 + 21*a^3*c^4*d^4*e^6 - 795*a^4*c^3*d^2*e^8 - 125*a^5*c^2*e^10 + 2*(a^3*c^8*d^3 - 4*a^4*c^7*d*e^2)*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))*sqrt((4*c^3*d^7 - 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - a^3*c^4*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))) - (a*c^3*x^2 - a^2*c^2)*sqrt((4*c^3*d^7 - 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - a^3*c^4*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))*log((140*c^5*d^10*e^3 - 1771*a*c^4*d^8*e^5 + 6872*a^2*c^3*d^6*e^7 - 8366*a^3*c^2*d^4*e^9 + 2500*a^4*c*d^2*e^11 + 625*a^5*e^13)*sqrt(e*x + d) - (35*a^2*c^5*d^6*e^4 + 21*a^3*c^4*d^4*e^6 - 795*a^4*c^3*d^2*e^8 - 125*a^5*c^2*e^10 + 2*(a^3*c^8*d^3 - 4*a^4*c^7*d*e^2)*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))*sqrt((4*c^3*d^7 - 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - a^3*c^4*sqrt((1225*c^4*d^8*e^6 - 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 + 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))) + 4*(4*a*c*e^3*x^2 - 3*a*c*d^2*e - 5*a^2*e^3 - (c^2*d^3 + 3*a*c*d*e^2)*x)*sqrt(e*x + d))/(a*c^3*x^2 - a^2*c^2)","B",0
625,1,1370,0,0.494645," ","integrate((e*x+d)^(5/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{{\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + a^{3} c^{3} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}} \log\left(-{\left(20 \, c^{3} d^{6} e^{3} - 101 \, a c^{2} d^{4} e^{5} + 162 \, a^{2} c d^{2} e^{7} - 81 \, a^{3} e^{9}\right)} \sqrt{e x + d} + {\left(5 \, a^{2} c^{3} d^{3} e^{4} - 9 \, a^{3} c^{2} d e^{6} - {\left(2 \, a^{3} c^{6} d^{2} - 3 \, a^{4} c^{5} e^{2}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + a^{3} c^{3} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}}\right) - {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + a^{3} c^{3} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}} \log\left(-{\left(20 \, c^{3} d^{6} e^{3} - 101 \, a c^{2} d^{4} e^{5} + 162 \, a^{2} c d^{2} e^{7} - 81 \, a^{3} e^{9}\right)} \sqrt{e x + d} - {\left(5 \, a^{2} c^{3} d^{3} e^{4} - 9 \, a^{3} c^{2} d e^{6} - {\left(2 \, a^{3} c^{6} d^{2} - 3 \, a^{4} c^{5} e^{2}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + a^{3} c^{3} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}}\right) + {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - a^{3} c^{3} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}} \log\left(-{\left(20 \, c^{3} d^{6} e^{3} - 101 \, a c^{2} d^{4} e^{5} + 162 \, a^{2} c d^{2} e^{7} - 81 \, a^{3} e^{9}\right)} \sqrt{e x + d} + {\left(5 \, a^{2} c^{3} d^{3} e^{4} - 9 \, a^{3} c^{2} d e^{6} + {\left(2 \, a^{3} c^{6} d^{2} - 3 \, a^{4} c^{5} e^{2}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - a^{3} c^{3} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}}\right) - {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - a^{3} c^{3} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}} \log\left(-{\left(20 \, c^{3} d^{6} e^{3} - 101 \, a c^{2} d^{4} e^{5} + 162 \, a^{2} c d^{2} e^{7} - 81 \, a^{3} e^{9}\right)} \sqrt{e x + d} - {\left(5 \, a^{2} c^{3} d^{3} e^{4} - 9 \, a^{3} c^{2} d e^{6} + {\left(2 \, a^{3} c^{6} d^{2} - 3 \, a^{4} c^{5} e^{2}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - a^{3} c^{3} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}}\right) + 4 \, {\left(2 \, a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a c^{2} x^{2} - a^{2} c\right)}}"," ",0,"-1/8*((a*c^2*x^2 - a^2*c)*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + a^3*c^3*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))*log(-(20*c^3*d^6*e^3 - 101*a*c^2*d^4*e^5 + 162*a^2*c*d^2*e^7 - 81*a^3*e^9)*sqrt(e*x + d) + (5*a^2*c^3*d^3*e^4 - 9*a^3*c^2*d*e^6 - (2*a^3*c^6*d^2 - 3*a^4*c^5*e^2)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + a^3*c^3*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))) - (a*c^2*x^2 - a^2*c)*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + a^3*c^3*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))*log(-(20*c^3*d^6*e^3 - 101*a*c^2*d^4*e^5 + 162*a^2*c*d^2*e^7 - 81*a^3*e^9)*sqrt(e*x + d) - (5*a^2*c^3*d^3*e^4 - 9*a^3*c^2*d*e^6 - (2*a^3*c^6*d^2 - 3*a^4*c^5*e^2)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + a^3*c^3*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))) + (a*c^2*x^2 - a^2*c)*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - a^3*c^3*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))*log(-(20*c^3*d^6*e^3 - 101*a*c^2*d^4*e^5 + 162*a^2*c*d^2*e^7 - 81*a^3*e^9)*sqrt(e*x + d) + (5*a^2*c^3*d^3*e^4 - 9*a^3*c^2*d*e^6 + (2*a^3*c^6*d^2 - 3*a^4*c^5*e^2)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - a^3*c^3*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))) - (a*c^2*x^2 - a^2*c)*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - a^3*c^3*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))*log(-(20*c^3*d^6*e^3 - 101*a*c^2*d^4*e^5 + 162*a^2*c*d^2*e^7 - 81*a^3*e^9)*sqrt(e*x + d) - (5*a^2*c^3*d^3*e^4 - 9*a^3*c^2*d*e^6 + (2*a^3*c^6*d^2 - 3*a^4*c^5*e^2)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - a^3*c^3*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))) + 4*(2*a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c^2*x^2 - a^2*c)","B",0
626,1,679,0,0.433318," ","integrate((e*x+d)^(3/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{{\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{\frac{e^{6}}{a^{3} c^{5}}} + 4 \, c d^{3} - 3 \, a d e^{2}}{a^{3} c^{2}}} \log\left(-{\left(4 \, c d^{2} e^{3} - a e^{5}\right)} \sqrt{e x + d} + {\left(2 \, a^{3} c^{4} d \sqrt{\frac{e^{6}}{a^{3} c^{5}}} + a^{2} c e^{4}\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{\frac{e^{6}}{a^{3} c^{5}}} + 4 \, c d^{3} - 3 \, a d e^{2}}{a^{3} c^{2}}}\right) - {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{\frac{e^{6}}{a^{3} c^{5}}} + 4 \, c d^{3} - 3 \, a d e^{2}}{a^{3} c^{2}}} \log\left(-{\left(4 \, c d^{2} e^{3} - a e^{5}\right)} \sqrt{e x + d} - {\left(2 \, a^{3} c^{4} d \sqrt{\frac{e^{6}}{a^{3} c^{5}}} + a^{2} c e^{4}\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{\frac{e^{6}}{a^{3} c^{5}}} + 4 \, c d^{3} - 3 \, a d e^{2}}{a^{3} c^{2}}}\right) - {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{\frac{e^{6}}{a^{3} c^{5}}} - 4 \, c d^{3} + 3 \, a d e^{2}}{a^{3} c^{2}}} \log\left(-{\left(4 \, c d^{2} e^{3} - a e^{5}\right)} \sqrt{e x + d} + {\left(2 \, a^{3} c^{4} d \sqrt{\frac{e^{6}}{a^{3} c^{5}}} - a^{2} c e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{\frac{e^{6}}{a^{3} c^{5}}} - 4 \, c d^{3} + 3 \, a d e^{2}}{a^{3} c^{2}}}\right) + {\left(a c^{2} x^{2} - a^{2} c\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{\frac{e^{6}}{a^{3} c^{5}}} - 4 \, c d^{3} + 3 \, a d e^{2}}{a^{3} c^{2}}} \log\left(-{\left(4 \, c d^{2} e^{3} - a e^{5}\right)} \sqrt{e x + d} - {\left(2 \, a^{3} c^{4} d \sqrt{\frac{e^{6}}{a^{3} c^{5}}} - a^{2} c e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{\frac{e^{6}}{a^{3} c^{5}}} - 4 \, c d^{3} + 3 \, a d e^{2}}{a^{3} c^{2}}}\right) + 4 \, {\left(c d x + a e\right)} \sqrt{e x + d}}{8 \, {\left(a c^{2} x^{2} - a^{2} c\right)}}"," ",0,"-1/8*((a*c^2*x^2 - a^2*c)*sqrt((a^3*c^2*sqrt(e^6/(a^3*c^5)) + 4*c*d^3 - 3*a*d*e^2)/(a^3*c^2))*log(-(4*c*d^2*e^3 - a*e^5)*sqrt(e*x + d) + (2*a^3*c^4*d*sqrt(e^6/(a^3*c^5)) + a^2*c*e^4)*sqrt((a^3*c^2*sqrt(e^6/(a^3*c^5)) + 4*c*d^3 - 3*a*d*e^2)/(a^3*c^2))) - (a*c^2*x^2 - a^2*c)*sqrt((a^3*c^2*sqrt(e^6/(a^3*c^5)) + 4*c*d^3 - 3*a*d*e^2)/(a^3*c^2))*log(-(4*c*d^2*e^3 - a*e^5)*sqrt(e*x + d) - (2*a^3*c^4*d*sqrt(e^6/(a^3*c^5)) + a^2*c*e^4)*sqrt((a^3*c^2*sqrt(e^6/(a^3*c^5)) + 4*c*d^3 - 3*a*d*e^2)/(a^3*c^2))) - (a*c^2*x^2 - a^2*c)*sqrt(-(a^3*c^2*sqrt(e^6/(a^3*c^5)) - 4*c*d^3 + 3*a*d*e^2)/(a^3*c^2))*log(-(4*c*d^2*e^3 - a*e^5)*sqrt(e*x + d) + (2*a^3*c^4*d*sqrt(e^6/(a^3*c^5)) - a^2*c*e^4)*sqrt(-(a^3*c^2*sqrt(e^6/(a^3*c^5)) - 4*c*d^3 + 3*a*d*e^2)/(a^3*c^2))) + (a*c^2*x^2 - a^2*c)*sqrt(-(a^3*c^2*sqrt(e^6/(a^3*c^5)) - 4*c*d^3 + 3*a*d*e^2)/(a^3*c^2))*log(-(4*c*d^2*e^3 - a*e^5)*sqrt(e*x + d) - (2*a^3*c^4*d*sqrt(e^6/(a^3*c^5)) - a^2*c*e^4)*sqrt(-(a^3*c^2*sqrt(e^6/(a^3*c^5)) - 4*c*d^3 + 3*a*d*e^2)/(a^3*c^2))) + 4*(c*d*x + a*e)*sqrt(e*x + d))/(a*c^2*x^2 - a^2*c)","B",0
627,1,1385,0,0.438593," ","integrate((e*x+d)^(1/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{{\left(a c x^{2} - a^{2}\right)} \sqrt{\frac{4 \, c d^{3} - 3 \, a d e^{2} + {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} - a^{4} c e^{2}}} \log\left(-{\left(4 \, c d^{2} e^{3} - a e^{5}\right)} \sqrt{e x + d} + {\left(a^{2} c d e^{4} - {\left(2 \, a^{3} c^{4} d^{4} - 3 \, a^{4} c^{3} d^{2} e^{2} + a^{5} c^{2} e^{4}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}\right)} \sqrt{\frac{4 \, c d^{3} - 3 \, a d e^{2} + {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} - a^{4} c e^{2}}}\right) - {\left(a c x^{2} - a^{2}\right)} \sqrt{\frac{4 \, c d^{3} - 3 \, a d e^{2} + {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} - a^{4} c e^{2}}} \log\left(-{\left(4 \, c d^{2} e^{3} - a e^{5}\right)} \sqrt{e x + d} - {\left(a^{2} c d e^{4} - {\left(2 \, a^{3} c^{4} d^{4} - 3 \, a^{4} c^{3} d^{2} e^{2} + a^{5} c^{2} e^{4}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}\right)} \sqrt{\frac{4 \, c d^{3} - 3 \, a d e^{2} + {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} - a^{4} c e^{2}}}\right) + {\left(a c x^{2} - a^{2}\right)} \sqrt{\frac{4 \, c d^{3} - 3 \, a d e^{2} - {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} - a^{4} c e^{2}}} \log\left(-{\left(4 \, c d^{2} e^{3} - a e^{5}\right)} \sqrt{e x + d} + {\left(a^{2} c d e^{4} + {\left(2 \, a^{3} c^{4} d^{4} - 3 \, a^{4} c^{3} d^{2} e^{2} + a^{5} c^{2} e^{4}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}\right)} \sqrt{\frac{4 \, c d^{3} - 3 \, a d e^{2} - {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} - a^{4} c e^{2}}}\right) - {\left(a c x^{2} - a^{2}\right)} \sqrt{\frac{4 \, c d^{3} - 3 \, a d e^{2} - {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} - a^{4} c e^{2}}} \log\left(-{\left(4 \, c d^{2} e^{3} - a e^{5}\right)} \sqrt{e x + d} - {\left(a^{2} c d e^{4} + {\left(2 \, a^{3} c^{4} d^{4} - 3 \, a^{4} c^{3} d^{2} e^{2} + a^{5} c^{2} e^{4}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}\right)} \sqrt{\frac{4 \, c d^{3} - 3 \, a d e^{2} - {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} \sqrt{\frac{e^{6}}{a^{3} c^{5} d^{4} - 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} - a^{4} c e^{2}}}\right) + 4 \, \sqrt{e x + d} x}{8 \, {\left(a c x^{2} - a^{2}\right)}}"," ",0,"-1/8*((a*c*x^2 - a^2)*sqrt((4*c*d^3 - 3*a*d*e^2 + (a^3*c^2*d^2 - a^4*c*e^2)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 - a^4*c*e^2))*log(-(4*c*d^2*e^3 - a*e^5)*sqrt(e*x + d) + (a^2*c*d*e^4 - (2*a^3*c^4*d^4 - 3*a^4*c^3*d^2*e^2 + a^5*c^2*e^4)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))*sqrt((4*c*d^3 - 3*a*d*e^2 + (a^3*c^2*d^2 - a^4*c*e^2)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 - a^4*c*e^2))) - (a*c*x^2 - a^2)*sqrt((4*c*d^3 - 3*a*d*e^2 + (a^3*c^2*d^2 - a^4*c*e^2)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 - a^4*c*e^2))*log(-(4*c*d^2*e^3 - a*e^5)*sqrt(e*x + d) - (a^2*c*d*e^4 - (2*a^3*c^4*d^4 - 3*a^4*c^3*d^2*e^2 + a^5*c^2*e^4)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))*sqrt((4*c*d^3 - 3*a*d*e^2 + (a^3*c^2*d^2 - a^4*c*e^2)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 - a^4*c*e^2))) + (a*c*x^2 - a^2)*sqrt((4*c*d^3 - 3*a*d*e^2 - (a^3*c^2*d^2 - a^4*c*e^2)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 - a^4*c*e^2))*log(-(4*c*d^2*e^3 - a*e^5)*sqrt(e*x + d) + (a^2*c*d*e^4 + (2*a^3*c^4*d^4 - 3*a^4*c^3*d^2*e^2 + a^5*c^2*e^4)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))*sqrt((4*c*d^3 - 3*a*d*e^2 - (a^3*c^2*d^2 - a^4*c*e^2)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 - a^4*c*e^2))) - (a*c*x^2 - a^2)*sqrt((4*c*d^3 - 3*a*d*e^2 - (a^3*c^2*d^2 - a^4*c*e^2)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 - a^4*c*e^2))*log(-(4*c*d^2*e^3 - a*e^5)*sqrt(e*x + d) - (a^2*c*d*e^4 + (2*a^3*c^4*d^4 - 3*a^4*c^3*d^2*e^2 + a^5*c^2*e^4)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))*sqrt((4*c*d^3 - 3*a*d*e^2 - (a^3*c^2*d^2 - a^4*c*e^2)*sqrt(e^6/(a^3*c^5*d^4 - 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 - a^4*c*e^2))) + 4*sqrt(e*x + d)*x)/(a*c*x^2 - a^2)","B",0
628,1,3279,0,0.560598," ","integrate(1/(-c*x^2+a)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} c d^{2} - a^{3} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + {\left(a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}}} \log\left({\left(20 \, c^{2} d^{4} e^{3} - 81 \, a c d^{2} e^{5} + 81 \, a^{2} e^{7}\right)} \sqrt{e x + d} + {\left(5 \, a^{2} c^{2} d^{4} e^{4} - 24 \, a^{3} c d^{2} e^{6} + 27 \, a^{4} e^{8} + 2 \, {\left(a^{3} c^{5} d^{9} - 5 \, a^{4} c^{4} d^{7} e^{2} + 9 \, a^{5} c^{3} d^{5} e^{4} - 7 \, a^{6} c^{2} d^{3} e^{6} + 2 \, a^{7} c d e^{8}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + {\left(a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}}}\right) - {\left(a^{2} c d^{2} - a^{3} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + {\left(a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}}} \log\left({\left(20 \, c^{2} d^{4} e^{3} - 81 \, a c d^{2} e^{5} + 81 \, a^{2} e^{7}\right)} \sqrt{e x + d} - {\left(5 \, a^{2} c^{2} d^{4} e^{4} - 24 \, a^{3} c d^{2} e^{6} + 27 \, a^{4} e^{8} + 2 \, {\left(a^{3} c^{5} d^{9} - 5 \, a^{4} c^{4} d^{7} e^{2} + 9 \, a^{5} c^{3} d^{5} e^{4} - 7 \, a^{6} c^{2} d^{3} e^{6} + 2 \, a^{7} c d e^{8}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + {\left(a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}}}\right) + {\left(a^{2} c d^{2} - a^{3} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - {\left(a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}}} \log\left({\left(20 \, c^{2} d^{4} e^{3} - 81 \, a c d^{2} e^{5} + 81 \, a^{2} e^{7}\right)} \sqrt{e x + d} + {\left(5 \, a^{2} c^{2} d^{4} e^{4} - 24 \, a^{3} c d^{2} e^{6} + 27 \, a^{4} e^{8} - 2 \, {\left(a^{3} c^{5} d^{9} - 5 \, a^{4} c^{4} d^{7} e^{2} + 9 \, a^{5} c^{3} d^{5} e^{4} - 7 \, a^{6} c^{2} d^{3} e^{6} + 2 \, a^{7} c d e^{8}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - {\left(a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}}}\right) - {\left(a^{2} c d^{2} - a^{3} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - {\left(a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}}} \log\left({\left(20 \, c^{2} d^{4} e^{3} - 81 \, a c d^{2} e^{5} + 81 \, a^{2} e^{7}\right)} \sqrt{e x + d} - {\left(5 \, a^{2} c^{2} d^{4} e^{4} - 24 \, a^{3} c d^{2} e^{6} + 27 \, a^{4} e^{8} - 2 \, {\left(a^{3} c^{5} d^{9} - 5 \, a^{4} c^{4} d^{7} e^{2} + 9 \, a^{5} c^{3} d^{5} e^{4} - 7 \, a^{6} c^{2} d^{3} e^{6} + 2 \, a^{7} c d e^{8}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}\right)} \sqrt{\frac{4 \, c^{2} d^{5} - 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - {\left(a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}\right)} \sqrt{\frac{25 \, c^{2} d^{4} e^{6} - 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} - 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} - 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} - 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} - 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} - a^{6} e^{6}}}\right) + 4 \, {\left(c d x - a e\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} c d^{2} - a^{3} e^{2} - {\left(a c^{2} d^{2} - a^{2} c e^{2}\right)} x^{2}\right)}}"," ",0,"1/8*((a^2*c*d^2 - a^3*e^2 - (a*c^2*d^2 - a^2*c*e^2)*x^2)*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + (a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6))*log((20*c^2*d^4*e^3 - 81*a*c*d^2*e^5 + 81*a^2*e^7)*sqrt(e*x + d) + (5*a^2*c^2*d^4*e^4 - 24*a^3*c*d^2*e^6 + 27*a^4*e^8 + 2*(a^3*c^5*d^9 - 5*a^4*c^4*d^7*e^2 + 9*a^5*c^3*d^5*e^4 - 7*a^6*c^2*d^3*e^6 + 2*a^7*c*d*e^8)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + (a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6))) - (a^2*c*d^2 - a^3*e^2 - (a*c^2*d^2 - a^2*c*e^2)*x^2)*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + (a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6))*log((20*c^2*d^4*e^3 - 81*a*c*d^2*e^5 + 81*a^2*e^7)*sqrt(e*x + d) - (5*a^2*c^2*d^4*e^4 - 24*a^3*c*d^2*e^6 + 27*a^4*e^8 + 2*(a^3*c^5*d^9 - 5*a^4*c^4*d^7*e^2 + 9*a^5*c^3*d^5*e^4 - 7*a^6*c^2*d^3*e^6 + 2*a^7*c*d*e^8)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + (a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6))) + (a^2*c*d^2 - a^3*e^2 - (a*c^2*d^2 - a^2*c*e^2)*x^2)*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - (a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6))*log((20*c^2*d^4*e^3 - 81*a*c*d^2*e^5 + 81*a^2*e^7)*sqrt(e*x + d) + (5*a^2*c^2*d^4*e^4 - 24*a^3*c*d^2*e^6 + 27*a^4*e^8 - 2*(a^3*c^5*d^9 - 5*a^4*c^4*d^7*e^2 + 9*a^5*c^3*d^5*e^4 - 7*a^6*c^2*d^3*e^6 + 2*a^7*c*d*e^8)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - (a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6))) - (a^2*c*d^2 - a^3*e^2 - (a*c^2*d^2 - a^2*c*e^2)*x^2)*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - (a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6))*log((20*c^2*d^4*e^3 - 81*a*c*d^2*e^5 + 81*a^2*e^7)*sqrt(e*x + d) - (5*a^2*c^2*d^4*e^4 - 24*a^3*c*d^2*e^6 + 27*a^4*e^8 - 2*(a^3*c^5*d^9 - 5*a^4*c^4*d^7*e^2 + 9*a^5*c^3*d^5*e^4 - 7*a^6*c^2*d^3*e^6 + 2*a^7*c*d*e^8)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))*sqrt((4*c^2*d^5 - 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - (a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6)*sqrt((25*c^2*d^4*e^6 - 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 - 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 - 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 - 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 - 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 - a^6*e^6))) + 4*(c*d*x - a*e)*sqrt(e*x + d))/(a^2*c*d^2 - a^3*e^2 - (a*c^2*d^2 - a^2*c*e^2)*x^2)","B",0
629,1,5703,0,1.027570," ","integrate(1/(e*x+d)^(3/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} c^{2} d^{5} - 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} - {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} - {\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e - 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{\frac{4 \, c^{4} d^{7} - 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} + 105 \, a^{3} c d e^{6} + {\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{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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}}} \log\left({\left(140 \, c^{4} d^{6} e^{3} - 1491 \, a c^{3} d^{4} e^{5} + 3750 \, a^{2} c^{2} d^{2} e^{7} + 625 \, a^{3} c e^{9}\right)} \sqrt{e x + d} + {\left(35 \, a^{2} c^{4} d^{7} e^{4} - 609 \, a^{3} c^{3} d^{5} e^{6} + 1977 \, a^{4} c^{2} d^{3} e^{8} + 325 \, a^{5} c d e^{10} + {\left(2 \, a^{3} c^{7} d^{14} - 19 \, a^{4} c^{6} d^{12} e^{2} + 60 \, a^{5} c^{5} d^{10} e^{4} - 85 \, a^{6} c^{4} d^{8} e^{6} + 50 \, a^{7} c^{3} d^{6} e^{8} + 3 \, a^{8} c^{2} d^{4} e^{10} - 16 \, a^{9} c d^{2} e^{12} + 5 \, a^{10} e^{14}\right)} \sqrt{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}\right)} \sqrt{\frac{4 \, c^{4} d^{7} - 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} + 105 \, a^{3} c d e^{6} + {\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{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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) - {\left(a^{2} c^{2} d^{5} - 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} - {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} - {\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e - 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{\frac{4 \, c^{4} d^{7} - 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} + 105 \, a^{3} c d e^{6} + {\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{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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}}} \log\left({\left(140 \, c^{4} d^{6} e^{3} - 1491 \, a c^{3} d^{4} e^{5} + 3750 \, a^{2} c^{2} d^{2} e^{7} + 625 \, a^{3} c e^{9}\right)} \sqrt{e x + d} - {\left(35 \, a^{2} c^{4} d^{7} e^{4} - 609 \, a^{3} c^{3} d^{5} e^{6} + 1977 \, a^{4} c^{2} d^{3} e^{8} + 325 \, a^{5} c d e^{10} + {\left(2 \, a^{3} c^{7} d^{14} - 19 \, a^{4} c^{6} d^{12} e^{2} + 60 \, a^{5} c^{5} d^{10} e^{4} - 85 \, a^{6} c^{4} d^{8} e^{6} + 50 \, a^{7} c^{3} d^{6} e^{8} + 3 \, a^{8} c^{2} d^{4} e^{10} - 16 \, a^{9} c d^{2} e^{12} + 5 \, a^{10} e^{14}\right)} \sqrt{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}\right)} \sqrt{\frac{4 \, c^{4} d^{7} - 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} + 105 \, a^{3} c d e^{6} + {\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{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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) + {\left(a^{2} c^{2} d^{5} - 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} - {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} - {\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e - 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{\frac{4 \, c^{4} d^{7} - 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} + 105 \, a^{3} c d e^{6} - {\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{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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}}} \log\left({\left(140 \, c^{4} d^{6} e^{3} - 1491 \, a c^{3} d^{4} e^{5} + 3750 \, a^{2} c^{2} d^{2} e^{7} + 625 \, a^{3} c e^{9}\right)} \sqrt{e x + d} + {\left(35 \, a^{2} c^{4} d^{7} e^{4} - 609 \, a^{3} c^{3} d^{5} e^{6} + 1977 \, a^{4} c^{2} d^{3} e^{8} + 325 \, a^{5} c d e^{10} - {\left(2 \, a^{3} c^{7} d^{14} - 19 \, a^{4} c^{6} d^{12} e^{2} + 60 \, a^{5} c^{5} d^{10} e^{4} - 85 \, a^{6} c^{4} d^{8} e^{6} + 50 \, a^{7} c^{3} d^{6} e^{8} + 3 \, a^{8} c^{2} d^{4} e^{10} - 16 \, a^{9} c d^{2} e^{12} + 5 \, a^{10} e^{14}\right)} \sqrt{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}\right)} \sqrt{\frac{4 \, c^{4} d^{7} - 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} + 105 \, a^{3} c d e^{6} - {\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{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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) - {\left(a^{2} c^{2} d^{5} - 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} - {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} - {\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e - 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{\frac{4 \, c^{4} d^{7} - 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} + 105 \, a^{3} c d e^{6} - {\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{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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}}} \log\left({\left(140 \, c^{4} d^{6} e^{3} - 1491 \, a c^{3} d^{4} e^{5} + 3750 \, a^{2} c^{2} d^{2} e^{7} + 625 \, a^{3} c e^{9}\right)} \sqrt{e x + d} - {\left(35 \, a^{2} c^{4} d^{7} e^{4} - 609 \, a^{3} c^{3} d^{5} e^{6} + 1977 \, a^{4} c^{2} d^{3} e^{8} + 325 \, a^{5} c d e^{10} - {\left(2 \, a^{3} c^{7} d^{14} - 19 \, a^{4} c^{6} d^{12} e^{2} + 60 \, a^{5} c^{5} d^{10} e^{4} - 85 \, a^{6} c^{4} d^{8} e^{6} + 50 \, a^{7} c^{3} d^{6} e^{8} + 3 \, a^{8} c^{2} d^{4} e^{10} - 16 \, a^{9} c d^{2} e^{12} + 5 \, a^{10} e^{14}\right)} \sqrt{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}\right)} \sqrt{\frac{4 \, c^{4} d^{7} - 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} + 105 \, a^{3} c d e^{6} - {\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{\frac{1225 \, c^{5} d^{8} e^{6} - 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} + 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} - 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} - 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} - 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} - 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} - 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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) - 4 \, {\left(2 \, a c d^{2} e + 4 \, a^{2} e^{3} - {\left(c^{2} d^{2} e + 5 \, a c e^{3}\right)} x^{2} - {\left(c^{2} d^{3} - a c d e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} c^{2} d^{5} - 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} - {\left(a c^{3} d^{4} e - 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} - {\left(a c^{3} d^{5} - 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e - 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)}}"," ",0,"1/8*((a^2*c^2*d^5 - 2*a^3*c*d^3*e^2 + a^4*d*e^4 - (a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 - (a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e - 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt((4*c^4*d^7 - 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 + 105*a^3*c*d*e^6 + (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((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))*log((140*c^4*d^6*e^3 - 1491*a*c^3*d^4*e^5 + 3750*a^2*c^2*d^2*e^7 + 625*a^3*c*e^9)*sqrt(e*x + d) + (35*a^2*c^4*d^7*e^4 - 609*a^3*c^3*d^5*e^6 + 1977*a^4*c^2*d^3*e^8 + 325*a^5*c*d*e^10 + (2*a^3*c^7*d^14 - 19*a^4*c^6*d^12*e^2 + 60*a^5*c^5*d^10*e^4 - 85*a^6*c^4*d^8*e^6 + 50*a^7*c^3*d^6*e^8 + 3*a^8*c^2*d^4*e^10 - 16*a^9*c*d^2*e^12 + 5*a^10*e^14)*sqrt((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))*sqrt((4*c^4*d^7 - 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 + 105*a^3*c*d*e^6 + (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((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))) - (a^2*c^2*d^5 - 2*a^3*c*d^3*e^2 + a^4*d*e^4 - (a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 - (a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e - 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt((4*c^4*d^7 - 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 + 105*a^3*c*d*e^6 + (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((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))*log((140*c^4*d^6*e^3 - 1491*a*c^3*d^4*e^5 + 3750*a^2*c^2*d^2*e^7 + 625*a^3*c*e^9)*sqrt(e*x + d) - (35*a^2*c^4*d^7*e^4 - 609*a^3*c^3*d^5*e^6 + 1977*a^4*c^2*d^3*e^8 + 325*a^5*c*d*e^10 + (2*a^3*c^7*d^14 - 19*a^4*c^6*d^12*e^2 + 60*a^5*c^5*d^10*e^4 - 85*a^6*c^4*d^8*e^6 + 50*a^7*c^3*d^6*e^8 + 3*a^8*c^2*d^4*e^10 - 16*a^9*c*d^2*e^12 + 5*a^10*e^14)*sqrt((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))*sqrt((4*c^4*d^7 - 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 + 105*a^3*c*d*e^6 + (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((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))) + (a^2*c^2*d^5 - 2*a^3*c*d^3*e^2 + a^4*d*e^4 - (a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 - (a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e - 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt((4*c^4*d^7 - 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 + 105*a^3*c*d*e^6 - (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((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))*log((140*c^4*d^6*e^3 - 1491*a*c^3*d^4*e^5 + 3750*a^2*c^2*d^2*e^7 + 625*a^3*c*e^9)*sqrt(e*x + d) + (35*a^2*c^4*d^7*e^4 - 609*a^3*c^3*d^5*e^6 + 1977*a^4*c^2*d^3*e^8 + 325*a^5*c*d*e^10 - (2*a^3*c^7*d^14 - 19*a^4*c^6*d^12*e^2 + 60*a^5*c^5*d^10*e^4 - 85*a^6*c^4*d^8*e^6 + 50*a^7*c^3*d^6*e^8 + 3*a^8*c^2*d^4*e^10 - 16*a^9*c*d^2*e^12 + 5*a^10*e^14)*sqrt((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))*sqrt((4*c^4*d^7 - 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 + 105*a^3*c*d*e^6 - (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((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))) - (a^2*c^2*d^5 - 2*a^3*c*d^3*e^2 + a^4*d*e^4 - (a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 - (a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e - 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt((4*c^4*d^7 - 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 + 105*a^3*c*d*e^6 - (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((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))*log((140*c^4*d^6*e^3 - 1491*a*c^3*d^4*e^5 + 3750*a^2*c^2*d^2*e^7 + 625*a^3*c*e^9)*sqrt(e*x + d) - (35*a^2*c^4*d^7*e^4 - 609*a^3*c^3*d^5*e^6 + 1977*a^4*c^2*d^3*e^8 + 325*a^5*c*d*e^10 - (2*a^3*c^7*d^14 - 19*a^4*c^6*d^12*e^2 + 60*a^5*c^5*d^10*e^4 - 85*a^6*c^4*d^8*e^6 + 50*a^7*c^3*d^6*e^8 + 3*a^8*c^2*d^4*e^10 - 16*a^9*c*d^2*e^12 + 5*a^10*e^14)*sqrt((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))*sqrt((4*c^4*d^7 - 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 + 105*a^3*c*d*e^6 - (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((1225*c^5*d^8*e^6 - 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 + 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 - 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 - 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 - 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 - 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 - 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))) - 4*(2*a*c*d^2*e + 4*a^2*e^3 - (c^2*d^2*e + 5*a*c*e^3)*x^2 - (c^2*d^3 - a*c*d*e^2)*x)*sqrt(e*x + d))/(a^2*c^2*d^5 - 2*a^3*c*d^3*e^2 + a^4*d*e^4 - (a*c^3*d^4*e - 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 - (a*c^3*d^5 - 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e - 2*a^3*c*d^2*e^3 + a^4*e^5)*x)","B",0
630,1,8308,0,2.435740," ","integrate(1/(e*x+d)^(5/2)/(-c*x^2+a)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} c^{3} d^{8} - 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} - a^{5} d^{2} e^{6} - {\left(a c^{4} d^{6} e^{2} - 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8}\right)} x^{4} - 2 \, {\left(a c^{4} d^{7} e - 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} - a^{4} c d e^{7}\right)} x^{3} - {\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)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e - 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} - a^{5} d e^{7}\right)} x\right)} \sqrt{\frac{4 \, c^{6} d^{9} - 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} + 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} + {\left(a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}}} \log\left({\left(420 \, c^{6} d^{8} e^{3} - 8421 \, a c^{5} d^{6} e^{5} + 36783 \, a^{2} c^{4} d^{4} e^{7} + 40817 \, a^{3} c^{3} d^{2} e^{9} + 2401 \, a^{4} c^{2} e^{11}\right)} \sqrt{e x + d} + {\left(105 \, a^{2} c^{6} d^{10} e^{4} - 4389 \, a^{3} c^{5} d^{8} e^{6} + 26274 \, a^{4} c^{4} d^{6} e^{8} + 34142 \, a^{5} c^{3} d^{4} e^{10} + 7525 \, a^{6} c^{2} d^{2} e^{12} + 343 \, a^{7} c e^{14} + 2 \, {\left(a^{3} c^{9} d^{19} - 15 \, a^{4} c^{8} d^{17} e^{2} + 64 \, a^{5} c^{7} d^{15} e^{4} - 112 \, a^{6} c^{6} d^{13} e^{6} + 42 \, a^{7} c^{5} d^{11} e^{8} + 154 \, a^{8} c^{4} d^{9} e^{10} - 280 \, a^{9} c^{3} d^{7} e^{12} + 216 \, a^{10} c^{2} d^{5} e^{14} - 83 \, a^{11} c d^{3} e^{16} + 13 \, a^{12} d e^{18}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}\right)} \sqrt{\frac{4 \, c^{6} d^{9} - 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} + 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} + {\left(a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}}}\right) - 3 \, {\left(a^{2} c^{3} d^{8} - 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} - a^{5} d^{2} e^{6} - {\left(a c^{4} d^{6} e^{2} - 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8}\right)} x^{4} - 2 \, {\left(a c^{4} d^{7} e - 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} - a^{4} c d e^{7}\right)} x^{3} - {\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)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e - 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} - a^{5} d e^{7}\right)} x\right)} \sqrt{\frac{4 \, c^{6} d^{9} - 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} + 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} + {\left(a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}}} \log\left({\left(420 \, c^{6} d^{8} e^{3} - 8421 \, a c^{5} d^{6} e^{5} + 36783 \, a^{2} c^{4} d^{4} e^{7} + 40817 \, a^{3} c^{3} d^{2} e^{9} + 2401 \, a^{4} c^{2} e^{11}\right)} \sqrt{e x + d} - {\left(105 \, a^{2} c^{6} d^{10} e^{4} - 4389 \, a^{3} c^{5} d^{8} e^{6} + 26274 \, a^{4} c^{4} d^{6} e^{8} + 34142 \, a^{5} c^{3} d^{4} e^{10} + 7525 \, a^{6} c^{2} d^{2} e^{12} + 343 \, a^{7} c e^{14} + 2 \, {\left(a^{3} c^{9} d^{19} - 15 \, a^{4} c^{8} d^{17} e^{2} + 64 \, a^{5} c^{7} d^{15} e^{4} - 112 \, a^{6} c^{6} d^{13} e^{6} + 42 \, a^{7} c^{5} d^{11} e^{8} + 154 \, a^{8} c^{4} d^{9} e^{10} - 280 \, a^{9} c^{3} d^{7} e^{12} + 216 \, a^{10} c^{2} d^{5} e^{14} - 83 \, a^{11} c d^{3} e^{16} + 13 \, a^{12} d e^{18}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}\right)} \sqrt{\frac{4 \, c^{6} d^{9} - 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} + 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} + {\left(a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}}}\right) + 3 \, {\left(a^{2} c^{3} d^{8} - 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} - a^{5} d^{2} e^{6} - {\left(a c^{4} d^{6} e^{2} - 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8}\right)} x^{4} - 2 \, {\left(a c^{4} d^{7} e - 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} - a^{4} c d e^{7}\right)} x^{3} - {\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)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e - 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} - a^{5} d e^{7}\right)} x\right)} \sqrt{\frac{4 \, c^{6} d^{9} - 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} + 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} - {\left(a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}}} \log\left({\left(420 \, c^{6} d^{8} e^{3} - 8421 \, a c^{5} d^{6} e^{5} + 36783 \, a^{2} c^{4} d^{4} e^{7} + 40817 \, a^{3} c^{3} d^{2} e^{9} + 2401 \, a^{4} c^{2} e^{11}\right)} \sqrt{e x + d} + {\left(105 \, a^{2} c^{6} d^{10} e^{4} - 4389 \, a^{3} c^{5} d^{8} e^{6} + 26274 \, a^{4} c^{4} d^{6} e^{8} + 34142 \, a^{5} c^{3} d^{4} e^{10} + 7525 \, a^{6} c^{2} d^{2} e^{12} + 343 \, a^{7} c e^{14} - 2 \, {\left(a^{3} c^{9} d^{19} - 15 \, a^{4} c^{8} d^{17} e^{2} + 64 \, a^{5} c^{7} d^{15} e^{4} - 112 \, a^{6} c^{6} d^{13} e^{6} + 42 \, a^{7} c^{5} d^{11} e^{8} + 154 \, a^{8} c^{4} d^{9} e^{10} - 280 \, a^{9} c^{3} d^{7} e^{12} + 216 \, a^{10} c^{2} d^{5} e^{14} - 83 \, a^{11} c d^{3} e^{16} + 13 \, a^{12} d e^{18}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}\right)} \sqrt{\frac{4 \, c^{6} d^{9} - 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} + 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} - {\left(a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}}}\right) - 3 \, {\left(a^{2} c^{3} d^{8} - 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} - a^{5} d^{2} e^{6} - {\left(a c^{4} d^{6} e^{2} - 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8}\right)} x^{4} - 2 \, {\left(a c^{4} d^{7} e - 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} - a^{4} c d e^{7}\right)} x^{3} - {\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)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e - 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} - a^{5} d e^{7}\right)} x\right)} \sqrt{\frac{4 \, c^{6} d^{9} - 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} + 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} - {\left(a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}}} \log\left({\left(420 \, c^{6} d^{8} e^{3} - 8421 \, a c^{5} d^{6} e^{5} + 36783 \, a^{2} c^{4} d^{4} e^{7} + 40817 \, a^{3} c^{3} d^{2} e^{9} + 2401 \, a^{4} c^{2} e^{11}\right)} \sqrt{e x + d} - {\left(105 \, a^{2} c^{6} d^{10} e^{4} - 4389 \, a^{3} c^{5} d^{8} e^{6} + 26274 \, a^{4} c^{4} d^{6} e^{8} + 34142 \, a^{5} c^{3} d^{4} e^{10} + 7525 \, a^{6} c^{2} d^{2} e^{12} + 343 \, a^{7} c e^{14} - 2 \, {\left(a^{3} c^{9} d^{19} - 15 \, a^{4} c^{8} d^{17} e^{2} + 64 \, a^{5} c^{7} d^{15} e^{4} - 112 \, a^{6} c^{6} d^{13} e^{6} + 42 \, a^{7} c^{5} d^{11} e^{8} + 154 \, a^{8} c^{4} d^{9} e^{10} - 280 \, a^{9} c^{3} d^{7} e^{12} + 216 \, a^{10} c^{2} d^{5} e^{14} - 83 \, a^{11} c d^{3} e^{16} + 13 \, a^{12} d e^{18}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}\right)} \sqrt{\frac{4 \, c^{6} d^{9} - 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} + 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} - {\left(a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}\right)} \sqrt{\frac{11025 \, c^{9} d^{12} e^{6} - 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} + 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} + 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} - 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} - 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} - 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} - 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} - 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} - 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} - 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} - 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} - 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} - 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} - a^{10} e^{14}}}\right) - 4 \, {\left(9 \, a c^{2} d^{4} e + 55 \, a^{2} c d^{2} e^{3} - 4 \, a^{3} e^{5} - 3 \, {\left(c^{3} d^{3} e^{2} + 19 \, a c^{2} d e^{4}\right)} x^{3} - {\left(6 \, c^{3} d^{4} e + 61 \, a c^{2} d^{2} e^{3} - 7 \, a^{2} c e^{5}\right)} x^{2} - 3 \, {\left(c^{3} d^{5} - 3 \, a c^{2} d^{3} e^{2} - 18 \, a^{2} c d e^{4}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{2} c^{3} d^{8} - 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} - a^{5} d^{2} e^{6} - {\left(a c^{4} d^{6} e^{2} - 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8}\right)} x^{4} - 2 \, {\left(a c^{4} d^{7} e - 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} - a^{4} c d e^{7}\right)} x^{3} - {\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)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e - 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} - a^{5} d e^{7}\right)} x\right)}}"," ",0,"1/24*(3*(a^2*c^3*d^8 - 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 - a^5*d^2*e^6 - (a*c^4*d^6*e^2 - 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 - a^4*c*e^8)*x^4 - 2*(a*c^4*d^7*e - 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 - a^4*c*d*e^7)*x^3 - (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)*x^2 + 2*(a^2*c^3*d^7*e - 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 - a^5*d*e^7)*x)*sqrt((4*c^6*d^9 - 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 + 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 + (a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14))*log((420*c^6*d^8*e^3 - 8421*a*c^5*d^6*e^5 + 36783*a^2*c^4*d^4*e^7 + 40817*a^3*c^3*d^2*e^9 + 2401*a^4*c^2*e^11)*sqrt(e*x + d) + (105*a^2*c^6*d^10*e^4 - 4389*a^3*c^5*d^8*e^6 + 26274*a^4*c^4*d^6*e^8 + 34142*a^5*c^3*d^4*e^10 + 7525*a^6*c^2*d^2*e^12 + 343*a^7*c*e^14 + 2*(a^3*c^9*d^19 - 15*a^4*c^8*d^17*e^2 + 64*a^5*c^7*d^15*e^4 - 112*a^6*c^6*d^13*e^6 + 42*a^7*c^5*d^11*e^8 + 154*a^8*c^4*d^9*e^10 - 280*a^9*c^3*d^7*e^12 + 216*a^10*c^2*d^5*e^14 - 83*a^11*c*d^3*e^16 + 13*a^12*d*e^18)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))*sqrt((4*c^6*d^9 - 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 + 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 + (a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14))) - 3*(a^2*c^3*d^8 - 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 - a^5*d^2*e^6 - (a*c^4*d^6*e^2 - 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 - a^4*c*e^8)*x^4 - 2*(a*c^4*d^7*e - 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 - a^4*c*d*e^7)*x^3 - (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)*x^2 + 2*(a^2*c^3*d^7*e - 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 - a^5*d*e^7)*x)*sqrt((4*c^6*d^9 - 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 + 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 + (a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14))*log((420*c^6*d^8*e^3 - 8421*a*c^5*d^6*e^5 + 36783*a^2*c^4*d^4*e^7 + 40817*a^3*c^3*d^2*e^9 + 2401*a^4*c^2*e^11)*sqrt(e*x + d) - (105*a^2*c^6*d^10*e^4 - 4389*a^3*c^5*d^8*e^6 + 26274*a^4*c^4*d^6*e^8 + 34142*a^5*c^3*d^4*e^10 + 7525*a^6*c^2*d^2*e^12 + 343*a^7*c*e^14 + 2*(a^3*c^9*d^19 - 15*a^4*c^8*d^17*e^2 + 64*a^5*c^7*d^15*e^4 - 112*a^6*c^6*d^13*e^6 + 42*a^7*c^5*d^11*e^8 + 154*a^8*c^4*d^9*e^10 - 280*a^9*c^3*d^7*e^12 + 216*a^10*c^2*d^5*e^14 - 83*a^11*c*d^3*e^16 + 13*a^12*d*e^18)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))*sqrt((4*c^6*d^9 - 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 + 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 + (a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14))) + 3*(a^2*c^3*d^8 - 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 - a^5*d^2*e^6 - (a*c^4*d^6*e^2 - 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 - a^4*c*e^8)*x^4 - 2*(a*c^4*d^7*e - 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 - a^4*c*d*e^7)*x^3 - (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)*x^2 + 2*(a^2*c^3*d^7*e - 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 - a^5*d*e^7)*x)*sqrt((4*c^6*d^9 - 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 + 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 - (a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14))*log((420*c^6*d^8*e^3 - 8421*a*c^5*d^6*e^5 + 36783*a^2*c^4*d^4*e^7 + 40817*a^3*c^3*d^2*e^9 + 2401*a^4*c^2*e^11)*sqrt(e*x + d) + (105*a^2*c^6*d^10*e^4 - 4389*a^3*c^5*d^8*e^6 + 26274*a^4*c^4*d^6*e^8 + 34142*a^5*c^3*d^4*e^10 + 7525*a^6*c^2*d^2*e^12 + 343*a^7*c*e^14 - 2*(a^3*c^9*d^19 - 15*a^4*c^8*d^17*e^2 + 64*a^5*c^7*d^15*e^4 - 112*a^6*c^6*d^13*e^6 + 42*a^7*c^5*d^11*e^8 + 154*a^8*c^4*d^9*e^10 - 280*a^9*c^3*d^7*e^12 + 216*a^10*c^2*d^5*e^14 - 83*a^11*c*d^3*e^16 + 13*a^12*d*e^18)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))*sqrt((4*c^6*d^9 - 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 + 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 - (a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14))) - 3*(a^2*c^3*d^8 - 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 - a^5*d^2*e^6 - (a*c^4*d^6*e^2 - 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 - a^4*c*e^8)*x^4 - 2*(a*c^4*d^7*e - 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 - a^4*c*d*e^7)*x^3 - (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)*x^2 + 2*(a^2*c^3*d^7*e - 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 - a^5*d*e^7)*x)*sqrt((4*c^6*d^9 - 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 + 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 - (a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14))*log((420*c^6*d^8*e^3 - 8421*a*c^5*d^6*e^5 + 36783*a^2*c^4*d^4*e^7 + 40817*a^3*c^3*d^2*e^9 + 2401*a^4*c^2*e^11)*sqrt(e*x + d) - (105*a^2*c^6*d^10*e^4 - 4389*a^3*c^5*d^8*e^6 + 26274*a^4*c^4*d^6*e^8 + 34142*a^5*c^3*d^4*e^10 + 7525*a^6*c^2*d^2*e^12 + 343*a^7*c*e^14 - 2*(a^3*c^9*d^19 - 15*a^4*c^8*d^17*e^2 + 64*a^5*c^7*d^15*e^4 - 112*a^6*c^6*d^13*e^6 + 42*a^7*c^5*d^11*e^8 + 154*a^8*c^4*d^9*e^10 - 280*a^9*c^3*d^7*e^12 + 216*a^10*c^2*d^5*e^14 - 83*a^11*c*d^3*e^16 + 13*a^12*d*e^18)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))*sqrt((4*c^6*d^9 - 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 + 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 - (a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14)*sqrt((11025*c^9*d^12*e^6 - 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 + 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 + 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 - 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 - 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 - 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 - 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 - 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 - 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 - 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 - 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 - 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 - 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 - a^10*e^14))) - 4*(9*a*c^2*d^4*e + 55*a^2*c*d^2*e^3 - 4*a^3*e^5 - 3*(c^3*d^3*e^2 + 19*a*c^2*d*e^4)*x^3 - (6*c^3*d^4*e + 61*a*c^2*d^2*e^3 - 7*a^2*c*e^5)*x^2 - 3*(c^3*d^5 - 3*a*c^2*d^3*e^2 - 18*a^2*c*d*e^4)*x)*sqrt(e*x + d))/(a^2*c^3*d^8 - 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 - a^5*d^2*e^6 - (a*c^4*d^6*e^2 - 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 - a^4*c*e^8)*x^4 - 2*(a*c^4*d^7*e - 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 - a^4*c*d*e^7)*x^3 - (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)*x^2 + 2*(a^2*c^3*d^7*e - 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 - a^5*d*e^7)*x)","B",0
631,1,2091,0,0.610915," ","integrate((e*x+d)^(7/2)/(c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{{\left(a c^{3} x^{2} + a^{2} c^{2}\right)} \sqrt{-\frac{4 \, c^{3} d^{7} + 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + a^{3} c^{4} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}} \log\left(-{\left(140 \, c^{5} d^{10} e^{3} + 1771 \, a c^{4} d^{8} e^{5} + 6872 \, a^{2} c^{3} d^{6} e^{7} + 8366 \, a^{3} c^{2} d^{4} e^{9} + 2500 \, a^{4} c d^{2} e^{11} - 625 \, a^{5} e^{13}\right)} \sqrt{e x + d} + {\left(35 \, a^{2} c^{5} d^{6} e^{4} - 21 \, a^{3} c^{4} d^{4} e^{6} - 795 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} - 2 \, {\left(a^{3} c^{8} d^{3} + 4 \, a^{4} c^{7} d e^{2}\right)} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}\right)} \sqrt{-\frac{4 \, c^{3} d^{7} + 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + a^{3} c^{4} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}}\right) - {\left(a c^{3} x^{2} + a^{2} c^{2}\right)} \sqrt{-\frac{4 \, c^{3} d^{7} + 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + a^{3} c^{4} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}} \log\left(-{\left(140 \, c^{5} d^{10} e^{3} + 1771 \, a c^{4} d^{8} e^{5} + 6872 \, a^{2} c^{3} d^{6} e^{7} + 8366 \, a^{3} c^{2} d^{4} e^{9} + 2500 \, a^{4} c d^{2} e^{11} - 625 \, a^{5} e^{13}\right)} \sqrt{e x + d} - {\left(35 \, a^{2} c^{5} d^{6} e^{4} - 21 \, a^{3} c^{4} d^{4} e^{6} - 795 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} - 2 \, {\left(a^{3} c^{8} d^{3} + 4 \, a^{4} c^{7} d e^{2}\right)} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}\right)} \sqrt{-\frac{4 \, c^{3} d^{7} + 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + a^{3} c^{4} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}}\right) + {\left(a c^{3} x^{2} + a^{2} c^{2}\right)} \sqrt{-\frac{4 \, c^{3} d^{7} + 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - a^{3} c^{4} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}} \log\left(-{\left(140 \, c^{5} d^{10} e^{3} + 1771 \, a c^{4} d^{8} e^{5} + 6872 \, a^{2} c^{3} d^{6} e^{7} + 8366 \, a^{3} c^{2} d^{4} e^{9} + 2500 \, a^{4} c d^{2} e^{11} - 625 \, a^{5} e^{13}\right)} \sqrt{e x + d} + {\left(35 \, a^{2} c^{5} d^{6} e^{4} - 21 \, a^{3} c^{4} d^{4} e^{6} - 795 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} + 2 \, {\left(a^{3} c^{8} d^{3} + 4 \, a^{4} c^{7} d e^{2}\right)} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}\right)} \sqrt{-\frac{4 \, c^{3} d^{7} + 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - a^{3} c^{4} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}}\right) - {\left(a c^{3} x^{2} + a^{2} c^{2}\right)} \sqrt{-\frac{4 \, c^{3} d^{7} + 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - a^{3} c^{4} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}} \log\left(-{\left(140 \, c^{5} d^{10} e^{3} + 1771 \, a c^{4} d^{8} e^{5} + 6872 \, a^{2} c^{3} d^{6} e^{7} + 8366 \, a^{3} c^{2} d^{4} e^{9} + 2500 \, a^{4} c d^{2} e^{11} - 625 \, a^{5} e^{13}\right)} \sqrt{e x + d} - {\left(35 \, a^{2} c^{5} d^{6} e^{4} - 21 \, a^{3} c^{4} d^{4} e^{6} - 795 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} + 2 \, {\left(a^{3} c^{8} d^{3} + 4 \, a^{4} c^{7} d e^{2}\right)} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}\right)} \sqrt{-\frac{4 \, c^{3} d^{7} + 35 \, a c^{2} d^{5} e^{2} + 70 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - a^{3} c^{4} \sqrt{-\frac{1225 \, c^{4} d^{8} e^{6} + 10780 \, a c^{3} d^{6} e^{8} + 21966 \, a^{2} c^{2} d^{4} e^{10} - 7700 \, a^{3} c d^{2} e^{12} + 625 \, a^{4} e^{14}}{a^{3} c^{9}}}}{a^{3} c^{4}}}\right) - 4 \, {\left(4 \, a c e^{3} x^{2} - 3 \, a c d^{2} e + 5 \, a^{2} e^{3} + {\left(c^{2} d^{3} - 3 \, a c d e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a c^{3} x^{2} + a^{2} c^{2}\right)}}"," ",0,"-1/8*((a*c^3*x^2 + a^2*c^2)*sqrt(-(4*c^3*d^7 + 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + a^3*c^4*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))*log(-(140*c^5*d^10*e^3 + 1771*a*c^4*d^8*e^5 + 6872*a^2*c^3*d^6*e^7 + 8366*a^3*c^2*d^4*e^9 + 2500*a^4*c*d^2*e^11 - 625*a^5*e^13)*sqrt(e*x + d) + (35*a^2*c^5*d^6*e^4 - 21*a^3*c^4*d^4*e^6 - 795*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 - 2*(a^3*c^8*d^3 + 4*a^4*c^7*d*e^2)*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))*sqrt(-(4*c^3*d^7 + 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + a^3*c^4*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))) - (a*c^3*x^2 + a^2*c^2)*sqrt(-(4*c^3*d^7 + 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + a^3*c^4*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))*log(-(140*c^5*d^10*e^3 + 1771*a*c^4*d^8*e^5 + 6872*a^2*c^3*d^6*e^7 + 8366*a^3*c^2*d^4*e^9 + 2500*a^4*c*d^2*e^11 - 625*a^5*e^13)*sqrt(e*x + d) - (35*a^2*c^5*d^6*e^4 - 21*a^3*c^4*d^4*e^6 - 795*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 - 2*(a^3*c^8*d^3 + 4*a^4*c^7*d*e^2)*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))*sqrt(-(4*c^3*d^7 + 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + a^3*c^4*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))) + (a*c^3*x^2 + a^2*c^2)*sqrt(-(4*c^3*d^7 + 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - a^3*c^4*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))*log(-(140*c^5*d^10*e^3 + 1771*a*c^4*d^8*e^5 + 6872*a^2*c^3*d^6*e^7 + 8366*a^3*c^2*d^4*e^9 + 2500*a^4*c*d^2*e^11 - 625*a^5*e^13)*sqrt(e*x + d) + (35*a^2*c^5*d^6*e^4 - 21*a^3*c^4*d^4*e^6 - 795*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 + 2*(a^3*c^8*d^3 + 4*a^4*c^7*d*e^2)*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))*sqrt(-(4*c^3*d^7 + 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - a^3*c^4*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))) - (a*c^3*x^2 + a^2*c^2)*sqrt(-(4*c^3*d^7 + 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - a^3*c^4*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))*log(-(140*c^5*d^10*e^3 + 1771*a*c^4*d^8*e^5 + 6872*a^2*c^3*d^6*e^7 + 8366*a^3*c^2*d^4*e^9 + 2500*a^4*c*d^2*e^11 - 625*a^5*e^13)*sqrt(e*x + d) - (35*a^2*c^5*d^6*e^4 - 21*a^3*c^4*d^4*e^6 - 795*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 + 2*(a^3*c^8*d^3 + 4*a^4*c^7*d*e^2)*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))*sqrt(-(4*c^3*d^7 + 35*a*c^2*d^5*e^2 + 70*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - a^3*c^4*sqrt(-(1225*c^4*d^8*e^6 + 10780*a*c^3*d^6*e^8 + 21966*a^2*c^2*d^4*e^10 - 7700*a^3*c*d^2*e^12 + 625*a^4*e^14)/(a^3*c^9)))/(a^3*c^4))) - 4*(4*a*c*e^3*x^2 - 3*a*c*d^2*e + 5*a^2*e^3 + (c^2*d^3 - 3*a*c*d*e^2)*x)*sqrt(e*x + d))/(a*c^3*x^2 + a^2*c^2)","B",0
632,1,1383,0,0.472998," ","integrate((e*x+d)^(5/2)/(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + a^{3} c^{3} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}} \log\left({\left(20 \, c^{3} d^{6} e^{3} + 101 \, a c^{2} d^{4} e^{5} + 162 \, a^{2} c d^{2} e^{7} + 81 \, a^{3} e^{9}\right)} \sqrt{e x + d} + {\left(5 \, a^{2} c^{3} d^{3} e^{4} + 9 \, a^{3} c^{2} d e^{6} - {\left(2 \, a^{3} c^{6} d^{2} + 3 \, a^{4} c^{5} e^{2}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + a^{3} c^{3} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}}\right) - {\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + a^{3} c^{3} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}} \log\left({\left(20 \, c^{3} d^{6} e^{3} + 101 \, a c^{2} d^{4} e^{5} + 162 \, a^{2} c d^{2} e^{7} + 81 \, a^{3} e^{9}\right)} \sqrt{e x + d} - {\left(5 \, a^{2} c^{3} d^{3} e^{4} + 9 \, a^{3} c^{2} d e^{6} - {\left(2 \, a^{3} c^{6} d^{2} + 3 \, a^{4} c^{5} e^{2}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + a^{3} c^{3} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}}\right) + {\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - a^{3} c^{3} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}} \log\left({\left(20 \, c^{3} d^{6} e^{3} + 101 \, a c^{2} d^{4} e^{5} + 162 \, a^{2} c d^{2} e^{7} + 81 \, a^{3} e^{9}\right)} \sqrt{e x + d} + {\left(5 \, a^{2} c^{3} d^{3} e^{4} + 9 \, a^{3} c^{2} d e^{6} + {\left(2 \, a^{3} c^{6} d^{2} + 3 \, a^{4} c^{5} e^{2}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - a^{3} c^{3} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}}\right) - {\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - a^{3} c^{3} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}} \log\left({\left(20 \, c^{3} d^{6} e^{3} + 101 \, a c^{2} d^{4} e^{5} + 162 \, a^{2} c d^{2} e^{7} + 81 \, a^{3} e^{9}\right)} \sqrt{e x + d} - {\left(5 \, a^{2} c^{3} d^{3} e^{4} + 9 \, a^{3} c^{2} d e^{6} + {\left(2 \, a^{3} c^{6} d^{2} + 3 \, a^{4} c^{5} e^{2}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - a^{3} c^{3} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7}}}}{a^{3} c^{3}}}\right) - 4 \, {\left(2 \, a d e - {\left(c d^{2} - a e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a c^{2} x^{2} + a^{2} c\right)}}"," ",0,"1/8*((a*c^2*x^2 + a^2*c)*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + a^3*c^3*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))*log((20*c^3*d^6*e^3 + 101*a*c^2*d^4*e^5 + 162*a^2*c*d^2*e^7 + 81*a^3*e^9)*sqrt(e*x + d) + (5*a^2*c^3*d^3*e^4 + 9*a^3*c^2*d*e^6 - (2*a^3*c^6*d^2 + 3*a^4*c^5*e^2)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + a^3*c^3*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))) - (a*c^2*x^2 + a^2*c)*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + a^3*c^3*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))*log((20*c^3*d^6*e^3 + 101*a*c^2*d^4*e^5 + 162*a^2*c*d^2*e^7 + 81*a^3*e^9)*sqrt(e*x + d) - (5*a^2*c^3*d^3*e^4 + 9*a^3*c^2*d*e^6 - (2*a^3*c^6*d^2 + 3*a^4*c^5*e^2)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + a^3*c^3*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))) + (a*c^2*x^2 + a^2*c)*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - a^3*c^3*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))*log((20*c^3*d^6*e^3 + 101*a*c^2*d^4*e^5 + 162*a^2*c*d^2*e^7 + 81*a^3*e^9)*sqrt(e*x + d) + (5*a^2*c^3*d^3*e^4 + 9*a^3*c^2*d*e^6 + (2*a^3*c^6*d^2 + 3*a^4*c^5*e^2)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - a^3*c^3*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))) - (a*c^2*x^2 + a^2*c)*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - a^3*c^3*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))*log((20*c^3*d^6*e^3 + 101*a*c^2*d^4*e^5 + 162*a^2*c*d^2*e^7 + 81*a^3*e^9)*sqrt(e*x + d) - (5*a^2*c^3*d^3*e^4 + 9*a^3*c^2*d*e^6 + (2*a^3*c^6*d^2 + 3*a^4*c^5*e^2)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - a^3*c^3*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7)))/(a^3*c^3))) - 4*(2*a*d*e - (c*d^2 - a*e^2)*x)*sqrt(e*x + d))/(a*c^2*x^2 + a^2*c)","B",0
633,1,679,0,0.441960," ","integrate((e*x+d)^(3/2)/(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} + 4 \, c d^{3} + 3 \, a d e^{2}}{a^{3} c^{2}}} \log\left({\left(4 \, c d^{2} e^{3} + a e^{5}\right)} \sqrt{e x + d} + {\left(2 \, a^{3} c^{4} d \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} + a^{2} c e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} + 4 \, c d^{3} + 3 \, a d e^{2}}{a^{3} c^{2}}}\right) - {\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} + 4 \, c d^{3} + 3 \, a d e^{2}}{a^{3} c^{2}}} \log\left({\left(4 \, c d^{2} e^{3} + a e^{5}\right)} \sqrt{e x + d} - {\left(2 \, a^{3} c^{4} d \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} + a^{2} c e^{4}\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} + 4 \, c d^{3} + 3 \, a d e^{2}}{a^{3} c^{2}}}\right) - {\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} - 4 \, c d^{3} - 3 \, a d e^{2}}{a^{3} c^{2}}} \log\left({\left(4 \, c d^{2} e^{3} + a e^{5}\right)} \sqrt{e x + d} + {\left(2 \, a^{3} c^{4} d \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} - a^{2} c e^{4}\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} - 4 \, c d^{3} - 3 \, a d e^{2}}{a^{3} c^{2}}}\right) + {\left(a c^{2} x^{2} + a^{2} c\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} - 4 \, c d^{3} - 3 \, a d e^{2}}{a^{3} c^{2}}} \log\left({\left(4 \, c d^{2} e^{3} + a e^{5}\right)} \sqrt{e x + d} - {\left(2 \, a^{3} c^{4} d \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} - a^{2} c e^{4}\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{e^{6}}{a^{3} c^{5}}} - 4 \, c d^{3} - 3 \, a d e^{2}}{a^{3} c^{2}}}\right) + 4 \, {\left(c d x - a e\right)} \sqrt{e x + d}}{8 \, {\left(a c^{2} x^{2} + a^{2} c\right)}}"," ",0,"1/8*((a*c^2*x^2 + a^2*c)*sqrt(-(a^3*c^2*sqrt(-e^6/(a^3*c^5)) + 4*c*d^3 + 3*a*d*e^2)/(a^3*c^2))*log((4*c*d^2*e^3 + a*e^5)*sqrt(e*x + d) + (2*a^3*c^4*d*sqrt(-e^6/(a^3*c^5)) + a^2*c*e^4)*sqrt(-(a^3*c^2*sqrt(-e^6/(a^3*c^5)) + 4*c*d^3 + 3*a*d*e^2)/(a^3*c^2))) - (a*c^2*x^2 + a^2*c)*sqrt(-(a^3*c^2*sqrt(-e^6/(a^3*c^5)) + 4*c*d^3 + 3*a*d*e^2)/(a^3*c^2))*log((4*c*d^2*e^3 + a*e^5)*sqrt(e*x + d) - (2*a^3*c^4*d*sqrt(-e^6/(a^3*c^5)) + a^2*c*e^4)*sqrt(-(a^3*c^2*sqrt(-e^6/(a^3*c^5)) + 4*c*d^3 + 3*a*d*e^2)/(a^3*c^2))) - (a*c^2*x^2 + a^2*c)*sqrt((a^3*c^2*sqrt(-e^6/(a^3*c^5)) - 4*c*d^3 - 3*a*d*e^2)/(a^3*c^2))*log((4*c*d^2*e^3 + a*e^5)*sqrt(e*x + d) + (2*a^3*c^4*d*sqrt(-e^6/(a^3*c^5)) - a^2*c*e^4)*sqrt((a^3*c^2*sqrt(-e^6/(a^3*c^5)) - 4*c*d^3 - 3*a*d*e^2)/(a^3*c^2))) + (a*c^2*x^2 + a^2*c)*sqrt((a^3*c^2*sqrt(-e^6/(a^3*c^5)) - 4*c*d^3 - 3*a*d*e^2)/(a^3*c^2))*log((4*c*d^2*e^3 + a*e^5)*sqrt(e*x + d) - (2*a^3*c^4*d*sqrt(-e^6/(a^3*c^5)) - a^2*c*e^4)*sqrt((a^3*c^2*sqrt(-e^6/(a^3*c^5)) - 4*c*d^3 - 3*a*d*e^2)/(a^3*c^2))) + 4*(c*d*x - a*e)*sqrt(e*x + d))/(a*c^2*x^2 + a^2*c)","A",0
634,1,1371,0,0.432404," ","integrate((e*x+d)^(1/2)/(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(a c x^{2} + a^{2}\right)} \sqrt{-\frac{4 \, c d^{3} + 3 \, a d e^{2} + {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} + a^{4} c e^{2}}} \log\left({\left(4 \, c d^{2} e^{3} + a e^{5}\right)} \sqrt{e x + d} + {\left(a^{2} c d e^{4} - {\left(2 \, a^{3} c^{4} d^{4} + 3 \, a^{4} c^{3} d^{2} e^{2} + a^{5} c^{2} e^{4}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}\right)} \sqrt{-\frac{4 \, c d^{3} + 3 \, a d e^{2} + {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} + a^{4} c e^{2}}}\right) - {\left(a c x^{2} + a^{2}\right)} \sqrt{-\frac{4 \, c d^{3} + 3 \, a d e^{2} + {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} + a^{4} c e^{2}}} \log\left({\left(4 \, c d^{2} e^{3} + a e^{5}\right)} \sqrt{e x + d} - {\left(a^{2} c d e^{4} - {\left(2 \, a^{3} c^{4} d^{4} + 3 \, a^{4} c^{3} d^{2} e^{2} + a^{5} c^{2} e^{4}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}\right)} \sqrt{-\frac{4 \, c d^{3} + 3 \, a d e^{2} + {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} + a^{4} c e^{2}}}\right) + {\left(a c x^{2} + a^{2}\right)} \sqrt{-\frac{4 \, c d^{3} + 3 \, a d e^{2} - {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} + a^{4} c e^{2}}} \log\left({\left(4 \, c d^{2} e^{3} + a e^{5}\right)} \sqrt{e x + d} + {\left(a^{2} c d e^{4} + {\left(2 \, a^{3} c^{4} d^{4} + 3 \, a^{4} c^{3} d^{2} e^{2} + a^{5} c^{2} e^{4}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}\right)} \sqrt{-\frac{4 \, c d^{3} + 3 \, a d e^{2} - {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} + a^{4} c e^{2}}}\right) - {\left(a c x^{2} + a^{2}\right)} \sqrt{-\frac{4 \, c d^{3} + 3 \, a d e^{2} - {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} + a^{4} c e^{2}}} \log\left({\left(4 \, c d^{2} e^{3} + a e^{5}\right)} \sqrt{e x + d} - {\left(a^{2} c d e^{4} + {\left(2 \, a^{3} c^{4} d^{4} + 3 \, a^{4} c^{3} d^{2} e^{2} + a^{5} c^{2} e^{4}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}\right)} \sqrt{-\frac{4 \, c d^{3} + 3 \, a d e^{2} - {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} \sqrt{-\frac{e^{6}}{a^{3} c^{5} d^{4} + 2 \, a^{4} c^{4} d^{2} e^{2} + a^{5} c^{3} e^{4}}}}{a^{3} c^{2} d^{2} + a^{4} c e^{2}}}\right) + 4 \, \sqrt{e x + d} x}{8 \, {\left(a c x^{2} + a^{2}\right)}}"," ",0,"1/8*((a*c*x^2 + a^2)*sqrt(-(4*c*d^3 + 3*a*d*e^2 + (a^3*c^2*d^2 + a^4*c*e^2)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 + a^4*c*e^2))*log((4*c*d^2*e^3 + a*e^5)*sqrt(e*x + d) + (a^2*c*d*e^4 - (2*a^3*c^4*d^4 + 3*a^4*c^3*d^2*e^2 + a^5*c^2*e^4)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))*sqrt(-(4*c*d^3 + 3*a*d*e^2 + (a^3*c^2*d^2 + a^4*c*e^2)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 + a^4*c*e^2))) - (a*c*x^2 + a^2)*sqrt(-(4*c*d^3 + 3*a*d*e^2 + (a^3*c^2*d^2 + a^4*c*e^2)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 + a^4*c*e^2))*log((4*c*d^2*e^3 + a*e^5)*sqrt(e*x + d) - (a^2*c*d*e^4 - (2*a^3*c^4*d^4 + 3*a^4*c^3*d^2*e^2 + a^5*c^2*e^4)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))*sqrt(-(4*c*d^3 + 3*a*d*e^2 + (a^3*c^2*d^2 + a^4*c*e^2)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 + a^4*c*e^2))) + (a*c*x^2 + a^2)*sqrt(-(4*c*d^3 + 3*a*d*e^2 - (a^3*c^2*d^2 + a^4*c*e^2)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 + a^4*c*e^2))*log((4*c*d^2*e^3 + a*e^5)*sqrt(e*x + d) + (a^2*c*d*e^4 + (2*a^3*c^4*d^4 + 3*a^4*c^3*d^2*e^2 + a^5*c^2*e^4)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))*sqrt(-(4*c*d^3 + 3*a*d*e^2 - (a^3*c^2*d^2 + a^4*c*e^2)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 + a^4*c*e^2))) - (a*c*x^2 + a^2)*sqrt(-(4*c*d^3 + 3*a*d*e^2 - (a^3*c^2*d^2 + a^4*c*e^2)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 + a^4*c*e^2))*log((4*c*d^2*e^3 + a*e^5)*sqrt(e*x + d) - (a^2*c*d*e^4 + (2*a^3*c^4*d^4 + 3*a^4*c^3*d^2*e^2 + a^5*c^2*e^4)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))*sqrt(-(4*c*d^3 + 3*a*d*e^2 - (a^3*c^2*d^2 + a^4*c*e^2)*sqrt(-e^6/(a^3*c^5*d^4 + 2*a^4*c^4*d^2*e^2 + a^5*c^3*e^4)))/(a^3*c^2*d^2 + a^4*c*e^2))) + 4*sqrt(e*x + d)*x)/(a*c*x^2 + a^2)","B",0
635,1,3267,0,0.557460," ","integrate(1/(c*x^2+a)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} c d^{2} + a^{3} e^{2} + {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + {\left(a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}}} \log\left({\left(20 \, c^{2} d^{4} e^{3} + 81 \, a c d^{2} e^{5} + 81 \, a^{2} e^{7}\right)} \sqrt{e x + d} + {\left(5 \, a^{2} c^{2} d^{4} e^{4} + 24 \, a^{3} c d^{2} e^{6} + 27 \, a^{4} e^{8} + 2 \, {\left(a^{3} c^{5} d^{9} + 5 \, a^{4} c^{4} d^{7} e^{2} + 9 \, a^{5} c^{3} d^{5} e^{4} + 7 \, a^{6} c^{2} d^{3} e^{6} + 2 \, a^{7} c d e^{8}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + {\left(a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}}}\right) - {\left(a^{2} c d^{2} + a^{3} e^{2} + {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + {\left(a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}}} \log\left({\left(20 \, c^{2} d^{4} e^{3} + 81 \, a c d^{2} e^{5} + 81 \, a^{2} e^{7}\right)} \sqrt{e x + d} - {\left(5 \, a^{2} c^{2} d^{4} e^{4} + 24 \, a^{3} c d^{2} e^{6} + 27 \, a^{4} e^{8} + 2 \, {\left(a^{3} c^{5} d^{9} + 5 \, a^{4} c^{4} d^{7} e^{2} + 9 \, a^{5} c^{3} d^{5} e^{4} + 7 \, a^{6} c^{2} d^{3} e^{6} + 2 \, a^{7} c d e^{8}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} + {\left(a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}}}\right) + {\left(a^{2} c d^{2} + a^{3} e^{2} + {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - {\left(a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}}} \log\left({\left(20 \, c^{2} d^{4} e^{3} + 81 \, a c d^{2} e^{5} + 81 \, a^{2} e^{7}\right)} \sqrt{e x + d} + {\left(5 \, a^{2} c^{2} d^{4} e^{4} + 24 \, a^{3} c d^{2} e^{6} + 27 \, a^{4} e^{8} - 2 \, {\left(a^{3} c^{5} d^{9} + 5 \, a^{4} c^{4} d^{7} e^{2} + 9 \, a^{5} c^{3} d^{5} e^{4} + 7 \, a^{6} c^{2} d^{3} e^{6} + 2 \, a^{7} c d e^{8}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - {\left(a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}}}\right) - {\left(a^{2} c d^{2} + a^{3} e^{2} + {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} x^{2}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - {\left(a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}}} \log\left({\left(20 \, c^{2} d^{4} e^{3} + 81 \, a c d^{2} e^{5} + 81 \, a^{2} e^{7}\right)} \sqrt{e x + d} - {\left(5 \, a^{2} c^{2} d^{4} e^{4} + 24 \, a^{3} c d^{2} e^{6} + 27 \, a^{4} e^{8} - 2 \, {\left(a^{3} c^{5} d^{9} + 5 \, a^{4} c^{4} d^{7} e^{2} + 9 \, a^{5} c^{3} d^{5} e^{4} + 7 \, a^{6} c^{2} d^{3} e^{6} + 2 \, a^{7} c d e^{8}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}\right)} \sqrt{-\frac{4 \, c^{2} d^{5} + 15 \, a c d^{3} e^{2} + 15 \, a^{2} d e^{4} - {\left(a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}\right)} \sqrt{-\frac{25 \, c^{2} d^{4} e^{6} + 90 \, a c d^{2} e^{8} + 81 \, a^{2} e^{10}}{a^{3} c^{7} d^{12} + 6 \, a^{4} c^{6} d^{10} e^{2} + 15 \, a^{5} c^{5} d^{8} e^{4} + 20 \, a^{6} c^{4} d^{6} e^{6} + 15 \, a^{7} c^{3} d^{4} e^{8} + 6 \, a^{8} c^{2} d^{2} e^{10} + a^{9} c e^{12}}}}{a^{3} c^{3} d^{6} + 3 \, a^{4} c^{2} d^{4} e^{2} + 3 \, a^{5} c d^{2} e^{4} + a^{6} e^{6}}}\right) + 4 \, {\left(c d x + a e\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} c d^{2} + a^{3} e^{2} + {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} x^{2}\right)}}"," ",0,"1/8*((a^2*c*d^2 + a^3*e^2 + (a*c^2*d^2 + a^2*c*e^2)*x^2)*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + (a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6))*log((20*c^2*d^4*e^3 + 81*a*c*d^2*e^5 + 81*a^2*e^7)*sqrt(e*x + d) + (5*a^2*c^2*d^4*e^4 + 24*a^3*c*d^2*e^6 + 27*a^4*e^8 + 2*(a^3*c^5*d^9 + 5*a^4*c^4*d^7*e^2 + 9*a^5*c^3*d^5*e^4 + 7*a^6*c^2*d^3*e^6 + 2*a^7*c*d*e^8)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + (a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6))) - (a^2*c*d^2 + a^3*e^2 + (a*c^2*d^2 + a^2*c*e^2)*x^2)*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + (a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6))*log((20*c^2*d^4*e^3 + 81*a*c*d^2*e^5 + 81*a^2*e^7)*sqrt(e*x + d) - (5*a^2*c^2*d^4*e^4 + 24*a^3*c*d^2*e^6 + 27*a^4*e^8 + 2*(a^3*c^5*d^9 + 5*a^4*c^4*d^7*e^2 + 9*a^5*c^3*d^5*e^4 + 7*a^6*c^2*d^3*e^6 + 2*a^7*c*d*e^8)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 + (a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6))) + (a^2*c*d^2 + a^3*e^2 + (a*c^2*d^2 + a^2*c*e^2)*x^2)*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - (a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6))*log((20*c^2*d^4*e^3 + 81*a*c*d^2*e^5 + 81*a^2*e^7)*sqrt(e*x + d) + (5*a^2*c^2*d^4*e^4 + 24*a^3*c*d^2*e^6 + 27*a^4*e^8 - 2*(a^3*c^5*d^9 + 5*a^4*c^4*d^7*e^2 + 9*a^5*c^3*d^5*e^4 + 7*a^6*c^2*d^3*e^6 + 2*a^7*c*d*e^8)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - (a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6))) - (a^2*c*d^2 + a^3*e^2 + (a*c^2*d^2 + a^2*c*e^2)*x^2)*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - (a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6))*log((20*c^2*d^4*e^3 + 81*a*c*d^2*e^5 + 81*a^2*e^7)*sqrt(e*x + d) - (5*a^2*c^2*d^4*e^4 + 24*a^3*c*d^2*e^6 + 27*a^4*e^8 - 2*(a^3*c^5*d^9 + 5*a^4*c^4*d^7*e^2 + 9*a^5*c^3*d^5*e^4 + 7*a^6*c^2*d^3*e^6 + 2*a^7*c*d*e^8)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))*sqrt(-(4*c^2*d^5 + 15*a*c*d^3*e^2 + 15*a^2*d*e^4 - (a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6)*sqrt(-(25*c^2*d^4*e^6 + 90*a*c*d^2*e^8 + 81*a^2*e^10)/(a^3*c^7*d^12 + 6*a^4*c^6*d^10*e^2 + 15*a^5*c^5*d^8*e^4 + 20*a^6*c^4*d^6*e^6 + 15*a^7*c^3*d^4*e^8 + 6*a^8*c^2*d^2*e^10 + a^9*c*e^12)))/(a^3*c^3*d^6 + 3*a^4*c^2*d^4*e^2 + 3*a^5*c*d^2*e^4 + a^6*e^6))) + 4*(c*d*x + a*e)*sqrt(e*x + d))/(a^2*c*d^2 + a^3*e^2 + (a*c^2*d^2 + a^2*c*e^2)*x^2)","B",0
636,1,5698,0,1.052331," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} c^{2} d^{5} + 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} + {\left(a c^{3} d^{4} e + 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} + {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e + 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{-\frac{4 \, c^{4} d^{7} + 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} - 105 \, a^{3} c d e^{6} + {\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{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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}}} \log\left(-{\left(140 \, c^{4} d^{6} e^{3} + 1491 \, a c^{3} d^{4} e^{5} + 3750 \, a^{2} c^{2} d^{2} e^{7} - 625 \, a^{3} c e^{9}\right)} \sqrt{e x + d} + {\left(35 \, a^{2} c^{4} d^{7} e^{4} + 609 \, a^{3} c^{3} d^{5} e^{6} + 1977 \, a^{4} c^{2} d^{3} e^{8} - 325 \, a^{5} c d e^{10} + {\left(2 \, a^{3} c^{7} d^{14} + 19 \, a^{4} c^{6} d^{12} e^{2} + 60 \, a^{5} c^{5} d^{10} e^{4} + 85 \, a^{6} c^{4} d^{8} e^{6} + 50 \, a^{7} c^{3} d^{6} e^{8} - 3 \, a^{8} c^{2} d^{4} e^{10} - 16 \, a^{9} c d^{2} e^{12} - 5 \, a^{10} e^{14}\right)} \sqrt{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}\right)} \sqrt{-\frac{4 \, c^{4} d^{7} + 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} - 105 \, a^{3} c d e^{6} + {\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{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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) - {\left(a^{2} c^{2} d^{5} + 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} + {\left(a c^{3} d^{4} e + 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} + {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e + 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{-\frac{4 \, c^{4} d^{7} + 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} - 105 \, a^{3} c d e^{6} + {\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{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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}}} \log\left(-{\left(140 \, c^{4} d^{6} e^{3} + 1491 \, a c^{3} d^{4} e^{5} + 3750 \, a^{2} c^{2} d^{2} e^{7} - 625 \, a^{3} c e^{9}\right)} \sqrt{e x + d} - {\left(35 \, a^{2} c^{4} d^{7} e^{4} + 609 \, a^{3} c^{3} d^{5} e^{6} + 1977 \, a^{4} c^{2} d^{3} e^{8} - 325 \, a^{5} c d e^{10} + {\left(2 \, a^{3} c^{7} d^{14} + 19 \, a^{4} c^{6} d^{12} e^{2} + 60 \, a^{5} c^{5} d^{10} e^{4} + 85 \, a^{6} c^{4} d^{8} e^{6} + 50 \, a^{7} c^{3} d^{6} e^{8} - 3 \, a^{8} c^{2} d^{4} e^{10} - 16 \, a^{9} c d^{2} e^{12} - 5 \, a^{10} e^{14}\right)} \sqrt{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}\right)} \sqrt{-\frac{4 \, c^{4} d^{7} + 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} - 105 \, a^{3} c d e^{6} + {\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{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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) + {\left(a^{2} c^{2} d^{5} + 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} + {\left(a c^{3} d^{4} e + 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} + {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e + 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{-\frac{4 \, c^{4} d^{7} + 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} - 105 \, a^{3} c d e^{6} - {\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{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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}}} \log\left(-{\left(140 \, c^{4} d^{6} e^{3} + 1491 \, a c^{3} d^{4} e^{5} + 3750 \, a^{2} c^{2} d^{2} e^{7} - 625 \, a^{3} c e^{9}\right)} \sqrt{e x + d} + {\left(35 \, a^{2} c^{4} d^{7} e^{4} + 609 \, a^{3} c^{3} d^{5} e^{6} + 1977 \, a^{4} c^{2} d^{3} e^{8} - 325 \, a^{5} c d e^{10} - {\left(2 \, a^{3} c^{7} d^{14} + 19 \, a^{4} c^{6} d^{12} e^{2} + 60 \, a^{5} c^{5} d^{10} e^{4} + 85 \, a^{6} c^{4} d^{8} e^{6} + 50 \, a^{7} c^{3} d^{6} e^{8} - 3 \, a^{8} c^{2} d^{4} e^{10} - 16 \, a^{9} c d^{2} e^{12} - 5 \, a^{10} e^{14}\right)} \sqrt{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}\right)} \sqrt{-\frac{4 \, c^{4} d^{7} + 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} - 105 \, a^{3} c d e^{6} - {\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{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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) - {\left(a^{2} c^{2} d^{5} + 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} + {\left(a c^{3} d^{4} e + 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} + {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e + 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)} \sqrt{-\frac{4 \, c^{4} d^{7} + 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} - 105 \, a^{3} c d e^{6} - {\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{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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}}} \log\left(-{\left(140 \, c^{4} d^{6} e^{3} + 1491 \, a c^{3} d^{4} e^{5} + 3750 \, a^{2} c^{2} d^{2} e^{7} - 625 \, a^{3} c e^{9}\right)} \sqrt{e x + d} - {\left(35 \, a^{2} c^{4} d^{7} e^{4} + 609 \, a^{3} c^{3} d^{5} e^{6} + 1977 \, a^{4} c^{2} d^{3} e^{8} - 325 \, a^{5} c d e^{10} - {\left(2 \, a^{3} c^{7} d^{14} + 19 \, a^{4} c^{6} d^{12} e^{2} + 60 \, a^{5} c^{5} d^{10} e^{4} + 85 \, a^{6} c^{4} d^{8} e^{6} + 50 \, a^{7} c^{3} d^{6} e^{8} - 3 \, a^{8} c^{2} d^{4} e^{10} - 16 \, a^{9} c d^{2} e^{12} - 5 \, a^{10} e^{14}\right)} \sqrt{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}\right)} \sqrt{-\frac{4 \, c^{4} d^{7} + 35 \, a c^{3} d^{5} e^{2} + 70 \, a^{2} c^{2} d^{3} e^{4} - 105 \, a^{3} c d e^{6} - {\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{-\frac{1225 \, c^{5} d^{8} e^{6} + 10780 \, a c^{4} d^{6} e^{8} + 21966 \, a^{2} c^{3} d^{4} e^{10} - 7700 \, a^{3} c^{2} d^{2} e^{12} + 625 \, a^{4} c e^{14}}{a^{3} c^{10} d^{20} + 10 \, a^{4} c^{9} d^{18} e^{2} + 45 \, a^{5} c^{8} d^{16} e^{4} + 120 \, a^{6} c^{7} d^{14} e^{6} + 210 \, a^{7} c^{6} d^{12} e^{8} + 252 \, a^{8} c^{5} d^{10} e^{10} + 210 \, a^{9} c^{4} d^{8} e^{12} + 120 \, a^{10} c^{3} d^{6} e^{14} + 45 \, a^{11} c^{2} d^{4} e^{16} + 10 \, a^{12} c d^{2} e^{18} + a^{13} e^{20}}}}{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) - 4 \, {\left(2 \, a c d^{2} e - 4 \, a^{2} e^{3} + {\left(c^{2} d^{2} e - 5 \, a c e^{3}\right)} x^{2} + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} c^{2} d^{5} + 2 \, a^{3} c d^{3} e^{2} + a^{4} d e^{4} + {\left(a c^{3} d^{4} e + 2 \, a^{2} c^{2} d^{2} e^{3} + a^{3} c e^{5}\right)} x^{3} + {\left(a c^{3} d^{5} + 2 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x^{2} + {\left(a^{2} c^{2} d^{4} e + 2 \, a^{3} c d^{2} e^{3} + a^{4} e^{5}\right)} x\right)}}"," ",0,"-1/8*((a^2*c^2*d^5 + 2*a^3*c*d^3*e^2 + a^4*d*e^4 + (a*c^3*d^4*e + 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 + (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e + 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt(-(4*c^4*d^7 + 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 - 105*a^3*c*d*e^6 + (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(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))*log(-(140*c^4*d^6*e^3 + 1491*a*c^3*d^4*e^5 + 3750*a^2*c^2*d^2*e^7 - 625*a^3*c*e^9)*sqrt(e*x + d) + (35*a^2*c^4*d^7*e^4 + 609*a^3*c^3*d^5*e^6 + 1977*a^4*c^2*d^3*e^8 - 325*a^5*c*d*e^10 + (2*a^3*c^7*d^14 + 19*a^4*c^6*d^12*e^2 + 60*a^5*c^5*d^10*e^4 + 85*a^6*c^4*d^8*e^6 + 50*a^7*c^3*d^6*e^8 - 3*a^8*c^2*d^4*e^10 - 16*a^9*c*d^2*e^12 - 5*a^10*e^14)*sqrt(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))*sqrt(-(4*c^4*d^7 + 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 - 105*a^3*c*d*e^6 + (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(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))) - (a^2*c^2*d^5 + 2*a^3*c*d^3*e^2 + a^4*d*e^4 + (a*c^3*d^4*e + 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 + (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e + 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt(-(4*c^4*d^7 + 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 - 105*a^3*c*d*e^6 + (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(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))*log(-(140*c^4*d^6*e^3 + 1491*a*c^3*d^4*e^5 + 3750*a^2*c^2*d^2*e^7 - 625*a^3*c*e^9)*sqrt(e*x + d) - (35*a^2*c^4*d^7*e^4 + 609*a^3*c^3*d^5*e^6 + 1977*a^4*c^2*d^3*e^8 - 325*a^5*c*d*e^10 + (2*a^3*c^7*d^14 + 19*a^4*c^6*d^12*e^2 + 60*a^5*c^5*d^10*e^4 + 85*a^6*c^4*d^8*e^6 + 50*a^7*c^3*d^6*e^8 - 3*a^8*c^2*d^4*e^10 - 16*a^9*c*d^2*e^12 - 5*a^10*e^14)*sqrt(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))*sqrt(-(4*c^4*d^7 + 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 - 105*a^3*c*d*e^6 + (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(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))) + (a^2*c^2*d^5 + 2*a^3*c*d^3*e^2 + a^4*d*e^4 + (a*c^3*d^4*e + 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 + (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e + 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt(-(4*c^4*d^7 + 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 - 105*a^3*c*d*e^6 - (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(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))*log(-(140*c^4*d^6*e^3 + 1491*a*c^3*d^4*e^5 + 3750*a^2*c^2*d^2*e^7 - 625*a^3*c*e^9)*sqrt(e*x + d) + (35*a^2*c^4*d^7*e^4 + 609*a^3*c^3*d^5*e^6 + 1977*a^4*c^2*d^3*e^8 - 325*a^5*c*d*e^10 - (2*a^3*c^7*d^14 + 19*a^4*c^6*d^12*e^2 + 60*a^5*c^5*d^10*e^4 + 85*a^6*c^4*d^8*e^6 + 50*a^7*c^3*d^6*e^8 - 3*a^8*c^2*d^4*e^10 - 16*a^9*c*d^2*e^12 - 5*a^10*e^14)*sqrt(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))*sqrt(-(4*c^4*d^7 + 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 - 105*a^3*c*d*e^6 - (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(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))) - (a^2*c^2*d^5 + 2*a^3*c*d^3*e^2 + a^4*d*e^4 + (a*c^3*d^4*e + 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 + (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e + 2*a^3*c*d^2*e^3 + a^4*e^5)*x)*sqrt(-(4*c^4*d^7 + 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 - 105*a^3*c*d*e^6 - (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(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))*log(-(140*c^4*d^6*e^3 + 1491*a*c^3*d^4*e^5 + 3750*a^2*c^2*d^2*e^7 - 625*a^3*c*e^9)*sqrt(e*x + d) - (35*a^2*c^4*d^7*e^4 + 609*a^3*c^3*d^5*e^6 + 1977*a^4*c^2*d^3*e^8 - 325*a^5*c*d*e^10 - (2*a^3*c^7*d^14 + 19*a^4*c^6*d^12*e^2 + 60*a^5*c^5*d^10*e^4 + 85*a^6*c^4*d^8*e^6 + 50*a^7*c^3*d^6*e^8 - 3*a^8*c^2*d^4*e^10 - 16*a^9*c*d^2*e^12 - 5*a^10*e^14)*sqrt(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))*sqrt(-(4*c^4*d^7 + 35*a*c^3*d^5*e^2 + 70*a^2*c^2*d^3*e^4 - 105*a^3*c*d*e^6 - (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(-(1225*c^5*d^8*e^6 + 10780*a*c^4*d^6*e^8 + 21966*a^2*c^3*d^4*e^10 - 7700*a^3*c^2*d^2*e^12 + 625*a^4*c*e^14)/(a^3*c^10*d^20 + 10*a^4*c^9*d^18*e^2 + 45*a^5*c^8*d^16*e^4 + 120*a^6*c^7*d^14*e^6 + 210*a^7*c^6*d^12*e^8 + 252*a^8*c^5*d^10*e^10 + 210*a^9*c^4*d^8*e^12 + 120*a^10*c^3*d^6*e^14 + 45*a^11*c^2*d^4*e^16 + 10*a^12*c*d^2*e^18 + a^13*e^20)))/(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))) - 4*(2*a*c*d^2*e - 4*a^2*e^3 + (c^2*d^2*e - 5*a*c*e^3)*x^2 + (c^2*d^3 + a*c*d*e^2)*x)*sqrt(e*x + d))/(a^2*c^2*d^5 + 2*a^3*c*d^3*e^2 + a^4*d*e^4 + (a*c^3*d^4*e + 2*a^2*c^2*d^2*e^3 + a^3*c*e^5)*x^3 + (a*c^3*d^5 + 2*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x^2 + (a^2*c^2*d^4*e + 2*a^3*c*d^2*e^3 + a^4*e^5)*x)","B",0
637,1,8281,0,2.467451," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} c^{3} d^{8} + 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} + a^{5} d^{2} e^{6} + {\left(a c^{4} d^{6} e^{2} + 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8}\right)} x^{4} + 2 \, {\left(a c^{4} d^{7} e + 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} + a^{4} c d e^{7}\right)} x^{3} + {\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)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e + 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} + a^{5} d e^{7}\right)} x\right)} \sqrt{-\frac{4 \, c^{6} d^{9} + 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} - 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} + {\left(a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}}} \log\left({\left(420 \, c^{6} d^{8} e^{3} + 8421 \, a c^{5} d^{6} e^{5} + 36783 \, a^{2} c^{4} d^{4} e^{7} - 40817 \, a^{3} c^{3} d^{2} e^{9} + 2401 \, a^{4} c^{2} e^{11}\right)} \sqrt{e x + d} + {\left(105 \, a^{2} c^{6} d^{10} e^{4} + 4389 \, a^{3} c^{5} d^{8} e^{6} + 26274 \, a^{4} c^{4} d^{6} e^{8} - 34142 \, a^{5} c^{3} d^{4} e^{10} + 7525 \, a^{6} c^{2} d^{2} e^{12} - 343 \, a^{7} c e^{14} + 2 \, {\left(a^{3} c^{9} d^{19} + 15 \, a^{4} c^{8} d^{17} e^{2} + 64 \, a^{5} c^{7} d^{15} e^{4} + 112 \, a^{6} c^{6} d^{13} e^{6} + 42 \, a^{7} c^{5} d^{11} e^{8} - 154 \, a^{8} c^{4} d^{9} e^{10} - 280 \, a^{9} c^{3} d^{7} e^{12} - 216 \, a^{10} c^{2} d^{5} e^{14} - 83 \, a^{11} c d^{3} e^{16} - 13 \, a^{12} d e^{18}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}\right)} \sqrt{-\frac{4 \, c^{6} d^{9} + 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} - 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} + {\left(a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}}}\right) - 3 \, {\left(a^{2} c^{3} d^{8} + 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} + a^{5} d^{2} e^{6} + {\left(a c^{4} d^{6} e^{2} + 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8}\right)} x^{4} + 2 \, {\left(a c^{4} d^{7} e + 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} + a^{4} c d e^{7}\right)} x^{3} + {\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)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e + 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} + a^{5} d e^{7}\right)} x\right)} \sqrt{-\frac{4 \, c^{6} d^{9} + 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} - 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} + {\left(a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}}} \log\left({\left(420 \, c^{6} d^{8} e^{3} + 8421 \, a c^{5} d^{6} e^{5} + 36783 \, a^{2} c^{4} d^{4} e^{7} - 40817 \, a^{3} c^{3} d^{2} e^{9} + 2401 \, a^{4} c^{2} e^{11}\right)} \sqrt{e x + d} - {\left(105 \, a^{2} c^{6} d^{10} e^{4} + 4389 \, a^{3} c^{5} d^{8} e^{6} + 26274 \, a^{4} c^{4} d^{6} e^{8} - 34142 \, a^{5} c^{3} d^{4} e^{10} + 7525 \, a^{6} c^{2} d^{2} e^{12} - 343 \, a^{7} c e^{14} + 2 \, {\left(a^{3} c^{9} d^{19} + 15 \, a^{4} c^{8} d^{17} e^{2} + 64 \, a^{5} c^{7} d^{15} e^{4} + 112 \, a^{6} c^{6} d^{13} e^{6} + 42 \, a^{7} c^{5} d^{11} e^{8} - 154 \, a^{8} c^{4} d^{9} e^{10} - 280 \, a^{9} c^{3} d^{7} e^{12} - 216 \, a^{10} c^{2} d^{5} e^{14} - 83 \, a^{11} c d^{3} e^{16} - 13 \, a^{12} d e^{18}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}\right)} \sqrt{-\frac{4 \, c^{6} d^{9} + 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} - 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} + {\left(a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}}}\right) + 3 \, {\left(a^{2} c^{3} d^{8} + 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} + a^{5} d^{2} e^{6} + {\left(a c^{4} d^{6} e^{2} + 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8}\right)} x^{4} + 2 \, {\left(a c^{4} d^{7} e + 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} + a^{4} c d e^{7}\right)} x^{3} + {\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)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e + 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} + a^{5} d e^{7}\right)} x\right)} \sqrt{-\frac{4 \, c^{6} d^{9} + 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} - 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} - {\left(a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}}} \log\left({\left(420 \, c^{6} d^{8} e^{3} + 8421 \, a c^{5} d^{6} e^{5} + 36783 \, a^{2} c^{4} d^{4} e^{7} - 40817 \, a^{3} c^{3} d^{2} e^{9} + 2401 \, a^{4} c^{2} e^{11}\right)} \sqrt{e x + d} + {\left(105 \, a^{2} c^{6} d^{10} e^{4} + 4389 \, a^{3} c^{5} d^{8} e^{6} + 26274 \, a^{4} c^{4} d^{6} e^{8} - 34142 \, a^{5} c^{3} d^{4} e^{10} + 7525 \, a^{6} c^{2} d^{2} e^{12} - 343 \, a^{7} c e^{14} - 2 \, {\left(a^{3} c^{9} d^{19} + 15 \, a^{4} c^{8} d^{17} e^{2} + 64 \, a^{5} c^{7} d^{15} e^{4} + 112 \, a^{6} c^{6} d^{13} e^{6} + 42 \, a^{7} c^{5} d^{11} e^{8} - 154 \, a^{8} c^{4} d^{9} e^{10} - 280 \, a^{9} c^{3} d^{7} e^{12} - 216 \, a^{10} c^{2} d^{5} e^{14} - 83 \, a^{11} c d^{3} e^{16} - 13 \, a^{12} d e^{18}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}\right)} \sqrt{-\frac{4 \, c^{6} d^{9} + 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} - 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} - {\left(a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}}}\right) - 3 \, {\left(a^{2} c^{3} d^{8} + 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} + a^{5} d^{2} e^{6} + {\left(a c^{4} d^{6} e^{2} + 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8}\right)} x^{4} + 2 \, {\left(a c^{4} d^{7} e + 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} + a^{4} c d e^{7}\right)} x^{3} + {\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)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e + 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} + a^{5} d e^{7}\right)} x\right)} \sqrt{-\frac{4 \, c^{6} d^{9} + 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} - 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} - {\left(a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}}} \log\left({\left(420 \, c^{6} d^{8} e^{3} + 8421 \, a c^{5} d^{6} e^{5} + 36783 \, a^{2} c^{4} d^{4} e^{7} - 40817 \, a^{3} c^{3} d^{2} e^{9} + 2401 \, a^{4} c^{2} e^{11}\right)} \sqrt{e x + d} - {\left(105 \, a^{2} c^{6} d^{10} e^{4} + 4389 \, a^{3} c^{5} d^{8} e^{6} + 26274 \, a^{4} c^{4} d^{6} e^{8} - 34142 \, a^{5} c^{3} d^{4} e^{10} + 7525 \, a^{6} c^{2} d^{2} e^{12} - 343 \, a^{7} c e^{14} - 2 \, {\left(a^{3} c^{9} d^{19} + 15 \, a^{4} c^{8} d^{17} e^{2} + 64 \, a^{5} c^{7} d^{15} e^{4} + 112 \, a^{6} c^{6} d^{13} e^{6} + 42 \, a^{7} c^{5} d^{11} e^{8} - 154 \, a^{8} c^{4} d^{9} e^{10} - 280 \, a^{9} c^{3} d^{7} e^{12} - 216 \, a^{10} c^{2} d^{5} e^{14} - 83 \, a^{11} c d^{3} e^{16} - 13 \, a^{12} d e^{18}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}\right)} \sqrt{-\frac{4 \, c^{6} d^{9} + 63 \, a c^{5} d^{7} e^{2} + 189 \, a^{2} c^{4} d^{5} e^{4} - 1155 \, a^{3} c^{3} d^{3} e^{6} + 315 \, a^{4} c^{2} d e^{8} - {\left(a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}\right)} \sqrt{-\frac{11025 \, c^{9} d^{12} e^{6} + 171990 \, a c^{8} d^{10} e^{8} + 494991 \, a^{2} c^{7} d^{8} e^{10} - 1360716 \, a^{3} c^{6} d^{6} e^{12} + 780831 \, a^{4} c^{5} d^{4} e^{14} - 82026 \, a^{5} c^{4} d^{2} e^{16} + 2401 \, a^{6} c^{3} e^{18}}{a^{3} c^{14} d^{28} + 14 \, a^{4} c^{13} d^{26} e^{2} + 91 \, a^{5} c^{12} d^{24} e^{4} + 364 \, a^{6} c^{11} d^{22} e^{6} + 1001 \, a^{7} c^{10} d^{20} e^{8} + 2002 \, a^{8} c^{9} d^{18} e^{10} + 3003 \, a^{9} c^{8} d^{16} e^{12} + 3432 \, a^{10} c^{7} d^{14} e^{14} + 3003 \, a^{11} c^{6} d^{12} e^{16} + 2002 \, a^{12} c^{5} d^{10} e^{18} + 1001 \, a^{13} c^{4} d^{8} e^{20} + 364 \, a^{14} c^{3} d^{6} e^{22} + 91 \, a^{15} c^{2} d^{4} e^{24} + 14 \, a^{16} c d^{2} e^{26} + a^{17} e^{28}}}}{a^{3} c^{7} d^{14} + 7 \, a^{4} c^{6} d^{12} e^{2} + 21 \, a^{5} c^{5} d^{10} e^{4} + 35 \, a^{6} c^{4} d^{8} e^{6} + 35 \, a^{7} c^{3} d^{6} e^{8} + 21 \, a^{8} c^{2} d^{4} e^{10} + 7 \, a^{9} c d^{2} e^{12} + a^{10} e^{14}}}\right) + 4 \, {\left(9 \, a c^{2} d^{4} e - 55 \, a^{2} c d^{2} e^{3} - 4 \, a^{3} e^{5} + 3 \, {\left(c^{3} d^{3} e^{2} - 19 \, a c^{2} d e^{4}\right)} x^{3} + {\left(6 \, c^{3} d^{4} e - 61 \, a c^{2} d^{2} e^{3} - 7 \, a^{2} c e^{5}\right)} x^{2} + 3 \, {\left(c^{3} d^{5} + 3 \, a c^{2} d^{3} e^{2} - 18 \, a^{2} c d e^{4}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{2} c^{3} d^{8} + 3 \, a^{3} c^{2} d^{6} e^{2} + 3 \, a^{4} c d^{4} e^{4} + a^{5} d^{2} e^{6} + {\left(a c^{4} d^{6} e^{2} + 3 \, a^{2} c^{3} d^{4} e^{4} + 3 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8}\right)} x^{4} + 2 \, {\left(a c^{4} d^{7} e + 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} + a^{4} c d e^{7}\right)} x^{3} + {\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)} x^{2} + 2 \, {\left(a^{2} c^{3} d^{7} e + 3 \, a^{3} c^{2} d^{5} e^{3} + 3 \, a^{4} c d^{3} e^{5} + a^{5} d e^{7}\right)} x\right)}}"," ",0,"1/24*(3*(a^2*c^3*d^8 + 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 + a^5*d^2*e^6 + (a*c^4*d^6*e^2 + 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 + a^4*c*e^8)*x^4 + 2*(a*c^4*d^7*e + 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 + a^4*c*d*e^7)*x^3 + (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)*x^2 + 2*(a^2*c^3*d^7*e + 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 + a^5*d*e^7)*x)*sqrt(-(4*c^6*d^9 + 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 - 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 + (a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14))*log((420*c^6*d^8*e^3 + 8421*a*c^5*d^6*e^5 + 36783*a^2*c^4*d^4*e^7 - 40817*a^3*c^3*d^2*e^9 + 2401*a^4*c^2*e^11)*sqrt(e*x + d) + (105*a^2*c^6*d^10*e^4 + 4389*a^3*c^5*d^8*e^6 + 26274*a^4*c^4*d^6*e^8 - 34142*a^5*c^3*d^4*e^10 + 7525*a^6*c^2*d^2*e^12 - 343*a^7*c*e^14 + 2*(a^3*c^9*d^19 + 15*a^4*c^8*d^17*e^2 + 64*a^5*c^7*d^15*e^4 + 112*a^6*c^6*d^13*e^6 + 42*a^7*c^5*d^11*e^8 - 154*a^8*c^4*d^9*e^10 - 280*a^9*c^3*d^7*e^12 - 216*a^10*c^2*d^5*e^14 - 83*a^11*c*d^3*e^16 - 13*a^12*d*e^18)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))*sqrt(-(4*c^6*d^9 + 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 - 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 + (a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14))) - 3*(a^2*c^3*d^8 + 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 + a^5*d^2*e^6 + (a*c^4*d^6*e^2 + 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 + a^4*c*e^8)*x^4 + 2*(a*c^4*d^7*e + 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 + a^4*c*d*e^7)*x^3 + (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)*x^2 + 2*(a^2*c^3*d^7*e + 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 + a^5*d*e^7)*x)*sqrt(-(4*c^6*d^9 + 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 - 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 + (a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14))*log((420*c^6*d^8*e^3 + 8421*a*c^5*d^6*e^5 + 36783*a^2*c^4*d^4*e^7 - 40817*a^3*c^3*d^2*e^9 + 2401*a^4*c^2*e^11)*sqrt(e*x + d) - (105*a^2*c^6*d^10*e^4 + 4389*a^3*c^5*d^8*e^6 + 26274*a^4*c^4*d^6*e^8 - 34142*a^5*c^3*d^4*e^10 + 7525*a^6*c^2*d^2*e^12 - 343*a^7*c*e^14 + 2*(a^3*c^9*d^19 + 15*a^4*c^8*d^17*e^2 + 64*a^5*c^7*d^15*e^4 + 112*a^6*c^6*d^13*e^6 + 42*a^7*c^5*d^11*e^8 - 154*a^8*c^4*d^9*e^10 - 280*a^9*c^3*d^7*e^12 - 216*a^10*c^2*d^5*e^14 - 83*a^11*c*d^3*e^16 - 13*a^12*d*e^18)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))*sqrt(-(4*c^6*d^9 + 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 - 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 + (a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14))) + 3*(a^2*c^3*d^8 + 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 + a^5*d^2*e^6 + (a*c^4*d^6*e^2 + 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 + a^4*c*e^8)*x^4 + 2*(a*c^4*d^7*e + 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 + a^4*c*d*e^7)*x^3 + (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)*x^2 + 2*(a^2*c^3*d^7*e + 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 + a^5*d*e^7)*x)*sqrt(-(4*c^6*d^9 + 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 - 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 - (a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14))*log((420*c^6*d^8*e^3 + 8421*a*c^5*d^6*e^5 + 36783*a^2*c^4*d^4*e^7 - 40817*a^3*c^3*d^2*e^9 + 2401*a^4*c^2*e^11)*sqrt(e*x + d) + (105*a^2*c^6*d^10*e^4 + 4389*a^3*c^5*d^8*e^6 + 26274*a^4*c^4*d^6*e^8 - 34142*a^5*c^3*d^4*e^10 + 7525*a^6*c^2*d^2*e^12 - 343*a^7*c*e^14 - 2*(a^3*c^9*d^19 + 15*a^4*c^8*d^17*e^2 + 64*a^5*c^7*d^15*e^4 + 112*a^6*c^6*d^13*e^6 + 42*a^7*c^5*d^11*e^8 - 154*a^8*c^4*d^9*e^10 - 280*a^9*c^3*d^7*e^12 - 216*a^10*c^2*d^5*e^14 - 83*a^11*c*d^3*e^16 - 13*a^12*d*e^18)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))*sqrt(-(4*c^6*d^9 + 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 - 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 - (a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14))) - 3*(a^2*c^3*d^8 + 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 + a^5*d^2*e^6 + (a*c^4*d^6*e^2 + 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 + a^4*c*e^8)*x^4 + 2*(a*c^4*d^7*e + 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 + a^4*c*d*e^7)*x^3 + (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)*x^2 + 2*(a^2*c^3*d^7*e + 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 + a^5*d*e^7)*x)*sqrt(-(4*c^6*d^9 + 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 - 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 - (a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14))*log((420*c^6*d^8*e^3 + 8421*a*c^5*d^6*e^5 + 36783*a^2*c^4*d^4*e^7 - 40817*a^3*c^3*d^2*e^9 + 2401*a^4*c^2*e^11)*sqrt(e*x + d) - (105*a^2*c^6*d^10*e^4 + 4389*a^3*c^5*d^8*e^6 + 26274*a^4*c^4*d^6*e^8 - 34142*a^5*c^3*d^4*e^10 + 7525*a^6*c^2*d^2*e^12 - 343*a^7*c*e^14 - 2*(a^3*c^9*d^19 + 15*a^4*c^8*d^17*e^2 + 64*a^5*c^7*d^15*e^4 + 112*a^6*c^6*d^13*e^6 + 42*a^7*c^5*d^11*e^8 - 154*a^8*c^4*d^9*e^10 - 280*a^9*c^3*d^7*e^12 - 216*a^10*c^2*d^5*e^14 - 83*a^11*c*d^3*e^16 - 13*a^12*d*e^18)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))*sqrt(-(4*c^6*d^9 + 63*a*c^5*d^7*e^2 + 189*a^2*c^4*d^5*e^4 - 1155*a^3*c^3*d^3*e^6 + 315*a^4*c^2*d*e^8 - (a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14)*sqrt(-(11025*c^9*d^12*e^6 + 171990*a*c^8*d^10*e^8 + 494991*a^2*c^7*d^8*e^10 - 1360716*a^3*c^6*d^6*e^12 + 780831*a^4*c^5*d^4*e^14 - 82026*a^5*c^4*d^2*e^16 + 2401*a^6*c^3*e^18)/(a^3*c^14*d^28 + 14*a^4*c^13*d^26*e^2 + 91*a^5*c^12*d^24*e^4 + 364*a^6*c^11*d^22*e^6 + 1001*a^7*c^10*d^20*e^8 + 2002*a^8*c^9*d^18*e^10 + 3003*a^9*c^8*d^16*e^12 + 3432*a^10*c^7*d^14*e^14 + 3003*a^11*c^6*d^12*e^16 + 2002*a^12*c^5*d^10*e^18 + 1001*a^13*c^4*d^8*e^20 + 364*a^14*c^3*d^6*e^22 + 91*a^15*c^2*d^4*e^24 + 14*a^16*c*d^2*e^26 + a^17*e^28)))/(a^3*c^7*d^14 + 7*a^4*c^6*d^12*e^2 + 21*a^5*c^5*d^10*e^4 + 35*a^6*c^4*d^8*e^6 + 35*a^7*c^3*d^6*e^8 + 21*a^8*c^2*d^4*e^10 + 7*a^9*c*d^2*e^12 + a^10*e^14))) + 4*(9*a*c^2*d^4*e - 55*a^2*c*d^2*e^3 - 4*a^3*e^5 + 3*(c^3*d^3*e^2 - 19*a*c^2*d*e^4)*x^3 + (6*c^3*d^4*e - 61*a*c^2*d^2*e^3 - 7*a^2*c*e^5)*x^2 + 3*(c^3*d^5 + 3*a*c^2*d^3*e^2 - 18*a^2*c*d*e^4)*x)*sqrt(e*x + d))/(a^2*c^3*d^8 + 3*a^3*c^2*d^6*e^2 + 3*a^4*c*d^4*e^4 + a^5*d^2*e^6 + (a*c^4*d^6*e^2 + 3*a^2*c^3*d^4*e^4 + 3*a^3*c^2*d^2*e^6 + a^4*c*e^8)*x^4 + 2*(a*c^4*d^7*e + 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 + a^4*c*d*e^7)*x^3 + (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)*x^2 + 2*(a^2*c^3*d^7*e + 3*a^3*c^2*d^5*e^3 + 3*a^4*c*d^3*e^5 + a^5*d*e^7)*x)","B",0
638,1,1730,0,0.515121," ","integrate((e*x+d)^(7/2)/(-c*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + a^{5} c^{4} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}} \log\left({\left(3024 \, c^{4} d^{8} e^{5} - 10908 \, a c^{3} d^{6} e^{7} + 13509 \, a^{2} c^{2} d^{4} e^{9} - 6250 \, a^{3} c d^{2} e^{11} + 625 \, a^{4} e^{13}\right)} \sqrt{e x + d} + {\left(126 \, a^{3} c^{4} d^{4} e^{6} - 255 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} - {\left(12 \, a^{5} c^{8} d^{3} - 13 \, a^{6} c^{7} d e^{2}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + a^{5} c^{4} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}}\right) - {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + a^{5} c^{4} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}} \log\left({\left(3024 \, c^{4} d^{8} e^{5} - 10908 \, a c^{3} d^{6} e^{7} + 13509 \, a^{2} c^{2} d^{4} e^{9} - 6250 \, a^{3} c d^{2} e^{11} + 625 \, a^{4} e^{13}\right)} \sqrt{e x + d} - {\left(126 \, a^{3} c^{4} d^{4} e^{6} - 255 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} - {\left(12 \, a^{5} c^{8} d^{3} - 13 \, a^{6} c^{7} d e^{2}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + a^{5} c^{4} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}}\right) + {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - a^{5} c^{4} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}} \log\left({\left(3024 \, c^{4} d^{8} e^{5} - 10908 \, a c^{3} d^{6} e^{7} + 13509 \, a^{2} c^{2} d^{4} e^{9} - 6250 \, a^{3} c d^{2} e^{11} + 625 \, a^{4} e^{13}\right)} \sqrt{e x + d} + {\left(126 \, a^{3} c^{4} d^{4} e^{6} - 255 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} + {\left(12 \, a^{5} c^{8} d^{3} - 13 \, a^{6} c^{7} d e^{2}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - a^{5} c^{4} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}}\right) - {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - a^{5} c^{4} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}} \log\left({\left(3024 \, c^{4} d^{8} e^{5} - 10908 \, a c^{3} d^{6} e^{7} + 13509 \, a^{2} c^{2} d^{4} e^{9} - 6250 \, a^{3} c d^{2} e^{11} + 625 \, a^{4} e^{13}\right)} \sqrt{e x + d} - {\left(126 \, a^{3} c^{4} d^{4} e^{6} - 255 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} + {\left(12 \, a^{5} c^{8} d^{3} - 13 \, a^{6} c^{7} d e^{2}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - a^{5} c^{4} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}}\right) + 4 \, {\left(11 \, a^{2} c d^{2} e - 5 \, a^{3} e^{3} - 2 \, {\left(3 \, c^{3} d^{3} - 4 \, a c^{2} d e^{2}\right)} x^{3} + {\left(a c^{2} d^{2} e + 9 \, a^{2} c e^{3}\right)} x^{2} + 2 \, {\left(5 \, a c^{2} d^{3} + 2 \, a^{2} c d e^{2}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{2} c^{4} x^{4} - 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)}}"," ",0,"1/64*((a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + a^5*c^4*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))*log((3024*c^4*d^8*e^5 - 10908*a*c^3*d^6*e^7 + 13509*a^2*c^2*d^4*e^9 - 6250*a^3*c*d^2*e^11 + 625*a^4*e^13)*sqrt(e*x + d) + (126*a^3*c^4*d^4*e^6 - 255*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 - (12*a^5*c^8*d^3 - 13*a^6*c^7*d*e^2)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + a^5*c^4*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))) - (a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + a^5*c^4*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))*log((3024*c^4*d^8*e^5 - 10908*a*c^3*d^6*e^7 + 13509*a^2*c^2*d^4*e^9 - 6250*a^3*c*d^2*e^11 + 625*a^4*e^13)*sqrt(e*x + d) - (126*a^3*c^4*d^4*e^6 - 255*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 - (12*a^5*c^8*d^3 - 13*a^6*c^7*d*e^2)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + a^5*c^4*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))) + (a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - a^5*c^4*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))*log((3024*c^4*d^8*e^5 - 10908*a*c^3*d^6*e^7 + 13509*a^2*c^2*d^4*e^9 - 6250*a^3*c*d^2*e^11 + 625*a^4*e^13)*sqrt(e*x + d) + (126*a^3*c^4*d^4*e^6 - 255*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 + (12*a^5*c^8*d^3 - 13*a^6*c^7*d*e^2)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - a^5*c^4*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))) - (a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - a^5*c^4*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))*log((3024*c^4*d^8*e^5 - 10908*a*c^3*d^6*e^7 + 13509*a^2*c^2*d^4*e^9 - 6250*a^3*c*d^2*e^11 + 625*a^4*e^13)*sqrt(e*x + d) - (126*a^3*c^4*d^4*e^6 - 255*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 + (12*a^5*c^8*d^3 - 13*a^6*c^7*d*e^2)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - a^5*c^4*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))) + 4*(11*a^2*c*d^2*e - 5*a^3*e^3 - 2*(3*c^3*d^3 - 4*a*c^2*d*e^2)*x^3 + (a*c^2*d^2*e + 9*a^2*c*e^3)*x^2 + 2*(5*a*c^2*d^3 + 2*a^2*c*d*e^2)*x)*sqrt(e*x + d))/(a^2*c^4*x^4 - 2*a^3*c^3*x^2 + a^4*c^2)","B",0
639,1,1029,0,0.450936," ","integrate((e*x+d)^(5/2)/(-c*x^2+a)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{a^{5} c^{3} \sqrt{\frac{e^{10}}{a^{5} c^{7}}} + 16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4}}{a^{5} c^{3}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} - 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} + 27 \, {\left(2 \, a^{3} c^{2} d e^{6} + {\left(4 \, a^{5} c^{6} d^{2} - a^{6} c^{5} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7}}}\right)} \sqrt{\frac{a^{5} c^{3} \sqrt{\frac{e^{10}}{a^{5} c^{7}}} + 16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4}}{a^{5} c^{3}}}\right) - 3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{a^{5} c^{3} \sqrt{\frac{e^{10}}{a^{5} c^{7}}} + 16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4}}{a^{5} c^{3}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} - 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} - 27 \, {\left(2 \, a^{3} c^{2} d e^{6} + {\left(4 \, a^{5} c^{6} d^{2} - a^{6} c^{5} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7}}}\right)} \sqrt{\frac{a^{5} c^{3} \sqrt{\frac{e^{10}}{a^{5} c^{7}}} + 16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4}}{a^{5} c^{3}}}\right) + 3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{-\frac{a^{5} c^{3} \sqrt{\frac{e^{10}}{a^{5} c^{7}}} - 16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} - 5 \, a^{2} d e^{4}}{a^{5} c^{3}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} - 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} + 27 \, {\left(2 \, a^{3} c^{2} d e^{6} - {\left(4 \, a^{5} c^{6} d^{2} - a^{6} c^{5} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7}}}\right)} \sqrt{-\frac{a^{5} c^{3} \sqrt{\frac{e^{10}}{a^{5} c^{7}}} - 16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} - 5 \, a^{2} d e^{4}}{a^{5} c^{3}}}\right) - 3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{-\frac{a^{5} c^{3} \sqrt{\frac{e^{10}}{a^{5} c^{7}}} - 16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} - 5 \, a^{2} d e^{4}}{a^{5} c^{3}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} - 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} - 27 \, {\left(2 \, a^{3} c^{2} d e^{6} - {\left(4 \, a^{5} c^{6} d^{2} - a^{6} c^{5} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7}}}\right)} \sqrt{-\frac{a^{5} c^{3} \sqrt{\frac{e^{10}}{a^{5} c^{7}}} - 16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} - 5 \, a^{2} d e^{4}}{a^{5} c^{3}}}\right) + 4 \, {\left(a c d e x^{2} + 7 \, a^{2} d e - 3 \, {\left(2 \, c^{2} d^{2} - a c e^{2}\right)} x^{3} + {\left(10 \, a c d^{2} + a^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}}"," ",0,"1/64*(3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt((a^5*c^3*sqrt(e^10/(a^5*c^7)) + 16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4)/(a^5*c^3))*log(27*(16*c^2*d^4*e^5 - 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) + 27*(2*a^3*c^2*d*e^6 + (4*a^5*c^6*d^2 - a^6*c^5*e^2)*sqrt(e^10/(a^5*c^7)))*sqrt((a^5*c^3*sqrt(e^10/(a^5*c^7)) + 16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4)/(a^5*c^3))) - 3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt((a^5*c^3*sqrt(e^10/(a^5*c^7)) + 16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4)/(a^5*c^3))*log(27*(16*c^2*d^4*e^5 - 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) - 27*(2*a^3*c^2*d*e^6 + (4*a^5*c^6*d^2 - a^6*c^5*e^2)*sqrt(e^10/(a^5*c^7)))*sqrt((a^5*c^3*sqrt(e^10/(a^5*c^7)) + 16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4)/(a^5*c^3))) + 3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt(-(a^5*c^3*sqrt(e^10/(a^5*c^7)) - 16*c^2*d^5 + 20*a*c*d^3*e^2 - 5*a^2*d*e^4)/(a^5*c^3))*log(27*(16*c^2*d^4*e^5 - 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) + 27*(2*a^3*c^2*d*e^6 - (4*a^5*c^6*d^2 - a^6*c^5*e^2)*sqrt(e^10/(a^5*c^7)))*sqrt(-(a^5*c^3*sqrt(e^10/(a^5*c^7)) - 16*c^2*d^5 + 20*a*c*d^3*e^2 - 5*a^2*d*e^4)/(a^5*c^3))) - 3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt(-(a^5*c^3*sqrt(e^10/(a^5*c^7)) - 16*c^2*d^5 + 20*a*c*d^3*e^2 - 5*a^2*d*e^4)/(a^5*c^3))*log(27*(16*c^2*d^4*e^5 - 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) - 27*(2*a^3*c^2*d*e^6 - (4*a^5*c^6*d^2 - a^6*c^5*e^2)*sqrt(e^10/(a^5*c^7)))*sqrt(-(a^5*c^3*sqrt(e^10/(a^5*c^7)) - 16*c^2*d^5 + 20*a*c*d^3*e^2 - 5*a^2*d*e^4)/(a^5*c^3))) + 4*(a*c*d*e*x^2 + 7*a^2*d*e - 3*(2*c^2*d^2 - a*c*e^2)*x^3 + (10*a*c*d^2 + a^2*e^2)*x)*sqrt(e*x + d))/(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)","B",0
640,1,1753,0,0.467280," ","integrate((e*x+d)^(3/2)/(-c*x^2+a)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + {\left(a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} - 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} + 27 \, {\left(2 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8} - {\left(4 \, a^{5} c^{6} d^{5} - 7 \, a^{6} c^{5} d^{3} e^{2} + 3 \, a^{7} c^{4} d e^{4}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}\right)} \sqrt{\frac{16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + {\left(a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}}}\right) - 3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + {\left(a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} - 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} - 27 \, {\left(2 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8} - {\left(4 \, a^{5} c^{6} d^{5} - 7 \, a^{6} c^{5} d^{3} e^{2} + 3 \, a^{7} c^{4} d e^{4}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}\right)} \sqrt{\frac{16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + {\left(a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}}}\right) + 3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - {\left(a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} - 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} + 27 \, {\left(2 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8} + {\left(4 \, a^{5} c^{6} d^{5} - 7 \, a^{6} c^{5} d^{3} e^{2} + 3 \, a^{7} c^{4} d e^{4}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}\right)} \sqrt{\frac{16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - {\left(a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}}}\right) - 3 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - {\left(a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} - 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} - 27 \, {\left(2 \, a^{3} c^{2} d^{2} e^{6} - a^{4} c e^{8} + {\left(4 \, a^{5} c^{6} d^{5} - 7 \, a^{6} c^{5} d^{3} e^{2} + 3 \, a^{7} c^{4} d e^{4}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}\right)} \sqrt{\frac{16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - {\left(a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}\right)} \sqrt{\frac{e^{10}}{a^{5} c^{7} d^{4} - 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} - a^{6} c^{2} e^{2}}}\right) - 4 \, {\left(6 \, c^{2} d x^{3} - a c e x^{2} - 10 \, a c d x - 3 \, a^{2} e\right)} \sqrt{e x + d}}{64 \, {\left(a^{2} c^{3} x^{4} - 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}}"," ",0,"1/64*(3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt((16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4 + (a^5*c^3*d^2 - a^6*c^2*e^2)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 - a^6*c^2*e^2))*log(27*(16*c^2*d^4*e^5 - 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) + 27*(2*a^3*c^2*d^2*e^6 - a^4*c*e^8 - (4*a^5*c^6*d^5 - 7*a^6*c^5*d^3*e^2 + 3*a^7*c^4*d*e^4)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))*sqrt((16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4 + (a^5*c^3*d^2 - a^6*c^2*e^2)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 - a^6*c^2*e^2))) - 3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt((16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4 + (a^5*c^3*d^2 - a^6*c^2*e^2)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 - a^6*c^2*e^2))*log(27*(16*c^2*d^4*e^5 - 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) - 27*(2*a^3*c^2*d^2*e^6 - a^4*c*e^8 - (4*a^5*c^6*d^5 - 7*a^6*c^5*d^3*e^2 + 3*a^7*c^4*d*e^4)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))*sqrt((16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4 + (a^5*c^3*d^2 - a^6*c^2*e^2)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 - a^6*c^2*e^2))) + 3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt((16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4 - (a^5*c^3*d^2 - a^6*c^2*e^2)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 - a^6*c^2*e^2))*log(27*(16*c^2*d^4*e^5 - 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) + 27*(2*a^3*c^2*d^2*e^6 - a^4*c*e^8 + (4*a^5*c^6*d^5 - 7*a^6*c^5*d^3*e^2 + 3*a^7*c^4*d*e^4)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))*sqrt((16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4 - (a^5*c^3*d^2 - a^6*c^2*e^2)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 - a^6*c^2*e^2))) - 3*(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)*sqrt((16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4 - (a^5*c^3*d^2 - a^6*c^2*e^2)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 - a^6*c^2*e^2))*log(27*(16*c^2*d^4*e^5 - 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) - 27*(2*a^3*c^2*d^2*e^6 - a^4*c*e^8 + (4*a^5*c^6*d^5 - 7*a^6*c^5*d^3*e^2 + 3*a^7*c^4*d*e^4)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))*sqrt((16*c^2*d^5 - 20*a*c*d^3*e^2 + 5*a^2*d*e^4 - (a^5*c^3*d^2 - a^6*c^2*e^2)*sqrt(e^10/(a^5*c^7*d^4 - 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 - a^6*c^2*e^2))) - 4*(6*c^2*d*x^3 - a*c*e*x^2 - 10*a*c*d*x - 3*a^2*e)*sqrt(e*x + d))/(a^2*c^3*x^4 - 2*a^3*c^2*x^2 + a^4*c)","B",0
641,1,3787,0,0.710303," ","integrate((e*x+d)^(1/2)/(-c*x^2+a)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{4} c d^{2} - a^{5} e^{2} + {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)} x^{4} - 2 \, {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + {\left(a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}}} \log\left(-{\left(3024 \, c^{3} d^{6} e^{5} - 7884 \, a c^{2} d^{4} e^{7} + 5625 \, a^{2} c d^{2} e^{9} - 625 \, a^{3} e^{11}\right)} \sqrt{e x + d} + {\left(126 \, a^{3} c^{3} d^{5} e^{6} - 318 \, a^{4} c^{2} d^{3} e^{8} + 200 \, a^{5} c d e^{10} + {\left(12 \, a^{5} c^{7} d^{10} - 55 \, a^{6} c^{6} d^{8} e^{2} + 98 \, a^{7} c^{5} d^{6} e^{4} - 84 \, a^{8} c^{4} d^{4} e^{6} + 34 \, a^{9} c^{3} d^{2} e^{8} - 5 \, a^{10} c^{2} e^{10}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + {\left(a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}}}\right) - {\left(a^{4} c d^{2} - a^{5} e^{2} + {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)} x^{4} - 2 \, {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + {\left(a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}}} \log\left(-{\left(3024 \, c^{3} d^{6} e^{5} - 7884 \, a c^{2} d^{4} e^{7} + 5625 \, a^{2} c d^{2} e^{9} - 625 \, a^{3} e^{11}\right)} \sqrt{e x + d} - {\left(126 \, a^{3} c^{3} d^{5} e^{6} - 318 \, a^{4} c^{2} d^{3} e^{8} + 200 \, a^{5} c d e^{10} + {\left(12 \, a^{5} c^{7} d^{10} - 55 \, a^{6} c^{6} d^{8} e^{2} + 98 \, a^{7} c^{5} d^{6} e^{4} - 84 \, a^{8} c^{4} d^{4} e^{6} + 34 \, a^{9} c^{3} d^{2} e^{8} - 5 \, a^{10} c^{2} e^{10}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} + {\left(a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}}}\right) + {\left(a^{4} c d^{2} - a^{5} e^{2} + {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)} x^{4} - 2 \, {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - {\left(a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}}} \log\left(-{\left(3024 \, c^{3} d^{6} e^{5} - 7884 \, a c^{2} d^{4} e^{7} + 5625 \, a^{2} c d^{2} e^{9} - 625 \, a^{3} e^{11}\right)} \sqrt{e x + d} + {\left(126 \, a^{3} c^{3} d^{5} e^{6} - 318 \, a^{4} c^{2} d^{3} e^{8} + 200 \, a^{5} c d e^{10} - {\left(12 \, a^{5} c^{7} d^{10} - 55 \, a^{6} c^{6} d^{8} e^{2} + 98 \, a^{7} c^{5} d^{6} e^{4} - 84 \, a^{8} c^{4} d^{4} e^{6} + 34 \, a^{9} c^{3} d^{2} e^{8} - 5 \, a^{10} c^{2} e^{10}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - {\left(a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}}}\right) - {\left(a^{4} c d^{2} - a^{5} e^{2} + {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)} x^{4} - 2 \, {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} x^{2}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - {\left(a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}}} \log\left(-{\left(3024 \, c^{3} d^{6} e^{5} - 7884 \, a c^{2} d^{4} e^{7} + 5625 \, a^{2} c d^{2} e^{9} - 625 \, a^{3} e^{11}\right)} \sqrt{e x + d} - {\left(126 \, a^{3} c^{3} d^{5} e^{6} - 318 \, a^{4} c^{2} d^{3} e^{8} + 200 \, a^{5} c d e^{10} - {\left(12 \, a^{5} c^{7} d^{10} - 55 \, a^{6} c^{6} d^{8} e^{2} + 98 \, a^{7} c^{5} d^{6} e^{4} - 84 \, a^{8} c^{4} d^{4} e^{6} + 34 \, a^{9} c^{3} d^{2} e^{8} - 5 \, a^{10} c^{2} e^{10}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}\right)} \sqrt{\frac{144 \, c^{3} d^{7} - 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} - 105 \, a^{3} d e^{6} - {\left(a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}\right)} \sqrt{\frac{441 \, c^{2} d^{4} e^{10} - 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} - 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} - 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} - 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} - 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} - a^{8} c e^{6}}}\right) - 4 \, {\left(a c d e x^{2} - a^{2} d e - {\left(6 \, c^{2} d^{2} - 5 \, a c e^{2}\right)} x^{3} + {\left(10 \, a c d^{2} - 9 \, a^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{4} c d^{2} - a^{5} e^{2} + {\left(a^{2} c^{3} d^{2} - a^{3} c^{2} e^{2}\right)} x^{4} - 2 \, {\left(a^{3} c^{2} d^{2} - a^{4} c e^{2}\right)} x^{2}\right)}}"," ",0,"-1/64*((a^4*c*d^2 - a^5*e^2 + (a^2*c^3*d^2 - a^3*c^2*e^2)*x^4 - 2*(a^3*c^2*d^2 - a^4*c*e^2)*x^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))*log(-(3024*c^3*d^6*e^5 - 7884*a*c^2*d^4*e^7 + 5625*a^2*c*d^2*e^9 - 625*a^3*e^11)*sqrt(e*x + d) + (126*a^3*c^3*d^5*e^6 - 318*a^4*c^2*d^3*e^8 + 200*a^5*c*d*e^10 + (12*a^5*c^7*d^10 - 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*e^4 - 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 - 5*a^10*c^2*e^10)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))) - (a^4*c*d^2 - a^5*e^2 + (a^2*c^3*d^2 - a^3*c^2*e^2)*x^4 - 2*(a^3*c^2*d^2 - a^4*c*e^2)*x^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))*log(-(3024*c^3*d^6*e^5 - 7884*a*c^2*d^4*e^7 + 5625*a^2*c*d^2*e^9 - 625*a^3*e^11)*sqrt(e*x + d) - (126*a^3*c^3*d^5*e^6 - 318*a^4*c^2*d^3*e^8 + 200*a^5*c*d*e^10 + (12*a^5*c^7*d^10 - 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*e^4 - 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 - 5*a^10*c^2*e^10)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 + (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))) + (a^4*c*d^2 - a^5*e^2 + (a^2*c^3*d^2 - a^3*c^2*e^2)*x^4 - 2*(a^3*c^2*d^2 - a^4*c*e^2)*x^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))*log(-(3024*c^3*d^6*e^5 - 7884*a*c^2*d^4*e^7 + 5625*a^2*c*d^2*e^9 - 625*a^3*e^11)*sqrt(e*x + d) + (126*a^3*c^3*d^5*e^6 - 318*a^4*c^2*d^3*e^8 + 200*a^5*c*d*e^10 - (12*a^5*c^7*d^10 - 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*e^4 - 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 - 5*a^10*c^2*e^10)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))) - (a^4*c*d^2 - a^5*e^2 + (a^2*c^3*d^2 - a^3*c^2*e^2)*x^4 - 2*(a^3*c^2*d^2 - a^4*c*e^2)*x^2)*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))*log(-(3024*c^3*d^6*e^5 - 7884*a*c^2*d^4*e^7 + 5625*a^2*c*d^2*e^9 - 625*a^3*e^11)*sqrt(e*x + d) - (126*a^3*c^3*d^5*e^6 - 318*a^4*c^2*d^3*e^8 + 200*a^5*c*d*e^10 - (12*a^5*c^7*d^10 - 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*e^4 - 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 - 5*a^10*c^2*e^10)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))*sqrt((144*c^3*d^7 - 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 - 105*a^3*d*e^6 - (a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6)*sqrt((441*c^2*d^4*e^10 - 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 - 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 - 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 - 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 - 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 - a^8*c*e^6))) - 4*(a*c*d*e*x^2 - a^2*d*e - (6*c^2*d^2 - 5*a*c*e^2)*x^3 + (10*a*c*d^2 - 9*a^2*e^2)*x)*sqrt(e*x + d))/(a^4*c*d^2 - a^5*e^2 + (a^2*c^3*d^2 - a^3*c^2*e^2)*x^4 - 2*(a^3*c^2*d^2 - a^4*c*e^2)*x^2)","B",0
642,1,5776,0,1.790818," ","integrate(1/(-c*x^2+a)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left(a^{4} c^{2} d^{4} - 2 \, a^{5} c d^{2} e^{2} + a^{6} e^{4} + {\left(a^{2} c^{4} d^{4} - 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{4} - 2 \, {\left(a^{3} c^{3} d^{4} - 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4}\right)} x^{2}\right)} \sqrt{\frac{16 \, c^{4} d^{9} - 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} - 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} + {\left(a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}}} \log\left(27 \, {\left(336 \, c^{4} d^{8} e^{5} - 1788 \, a c^{3} d^{6} e^{7} + 4189 \, a^{2} c^{2} d^{4} e^{9} - 4802 \, a^{3} c d^{2} e^{11} + 2401 \, a^{4} e^{13}\right)} \sqrt{e x + d} + 27 \, {\left(42 \, a^{3} c^{4} d^{8} e^{6} - 213 \, a^{4} c^{3} d^{6} e^{8} + 515 \, a^{5} c^{2} d^{4} e^{10} - 623 \, a^{6} c d^{2} e^{12} + 343 \, a^{7} e^{14} - {\left(4 \, a^{5} c^{8} d^{15} - 31 \, a^{6} c^{7} d^{13} e^{2} + 106 \, a^{7} c^{6} d^{11} e^{4} - 205 \, a^{8} c^{5} d^{9} e^{6} + 240 \, a^{9} c^{4} d^{7} e^{8} - 169 \, a^{10} c^{3} d^{5} e^{10} + 66 \, a^{11} c^{2} d^{3} e^{12} - 11 \, a^{12} c d e^{14}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}\right)} \sqrt{\frac{16 \, c^{4} d^{9} - 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} - 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} + {\left(a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}}}\right) - 3 \, {\left(a^{4} c^{2} d^{4} - 2 \, a^{5} c d^{2} e^{2} + a^{6} e^{4} + {\left(a^{2} c^{4} d^{4} - 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{4} - 2 \, {\left(a^{3} c^{3} d^{4} - 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4}\right)} x^{2}\right)} \sqrt{\frac{16 \, c^{4} d^{9} - 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} - 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} + {\left(a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}}} \log\left(27 \, {\left(336 \, c^{4} d^{8} e^{5} - 1788 \, a c^{3} d^{6} e^{7} + 4189 \, a^{2} c^{2} d^{4} e^{9} - 4802 \, a^{3} c d^{2} e^{11} + 2401 \, a^{4} e^{13}\right)} \sqrt{e x + d} - 27 \, {\left(42 \, a^{3} c^{4} d^{8} e^{6} - 213 \, a^{4} c^{3} d^{6} e^{8} + 515 \, a^{5} c^{2} d^{4} e^{10} - 623 \, a^{6} c d^{2} e^{12} + 343 \, a^{7} e^{14} - {\left(4 \, a^{5} c^{8} d^{15} - 31 \, a^{6} c^{7} d^{13} e^{2} + 106 \, a^{7} c^{6} d^{11} e^{4} - 205 \, a^{8} c^{5} d^{9} e^{6} + 240 \, a^{9} c^{4} d^{7} e^{8} - 169 \, a^{10} c^{3} d^{5} e^{10} + 66 \, a^{11} c^{2} d^{3} e^{12} - 11 \, a^{12} c d e^{14}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}\right)} \sqrt{\frac{16 \, c^{4} d^{9} - 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} - 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} + {\left(a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}}}\right) + 3 \, {\left(a^{4} c^{2} d^{4} - 2 \, a^{5} c d^{2} e^{2} + a^{6} e^{4} + {\left(a^{2} c^{4} d^{4} - 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{4} - 2 \, {\left(a^{3} c^{3} d^{4} - 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4}\right)} x^{2}\right)} \sqrt{\frac{16 \, c^{4} d^{9} - 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} - 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} - {\left(a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}}} \log\left(27 \, {\left(336 \, c^{4} d^{8} e^{5} - 1788 \, a c^{3} d^{6} e^{7} + 4189 \, a^{2} c^{2} d^{4} e^{9} - 4802 \, a^{3} c d^{2} e^{11} + 2401 \, a^{4} e^{13}\right)} \sqrt{e x + d} + 27 \, {\left(42 \, a^{3} c^{4} d^{8} e^{6} - 213 \, a^{4} c^{3} d^{6} e^{8} + 515 \, a^{5} c^{2} d^{4} e^{10} - 623 \, a^{6} c d^{2} e^{12} + 343 \, a^{7} e^{14} + {\left(4 \, a^{5} c^{8} d^{15} - 31 \, a^{6} c^{7} d^{13} e^{2} + 106 \, a^{7} c^{6} d^{11} e^{4} - 205 \, a^{8} c^{5} d^{9} e^{6} + 240 \, a^{9} c^{4} d^{7} e^{8} - 169 \, a^{10} c^{3} d^{5} e^{10} + 66 \, a^{11} c^{2} d^{3} e^{12} - 11 \, a^{12} c d e^{14}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}\right)} \sqrt{\frac{16 \, c^{4} d^{9} - 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} - 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} - {\left(a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}}}\right) - 3 \, {\left(a^{4} c^{2} d^{4} - 2 \, a^{5} c d^{2} e^{2} + a^{6} e^{4} + {\left(a^{2} c^{4} d^{4} - 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{4} - 2 \, {\left(a^{3} c^{3} d^{4} - 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4}\right)} x^{2}\right)} \sqrt{\frac{16 \, c^{4} d^{9} - 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} - 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} - {\left(a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}}} \log\left(27 \, {\left(336 \, c^{4} d^{8} e^{5} - 1788 \, a c^{3} d^{6} e^{7} + 4189 \, a^{2} c^{2} d^{4} e^{9} - 4802 \, a^{3} c d^{2} e^{11} + 2401 \, a^{4} e^{13}\right)} \sqrt{e x + d} - 27 \, {\left(42 \, a^{3} c^{4} d^{8} e^{6} - 213 \, a^{4} c^{3} d^{6} e^{8} + 515 \, a^{5} c^{2} d^{4} e^{10} - 623 \, a^{6} c d^{2} e^{12} + 343 \, a^{7} e^{14} + {\left(4 \, a^{5} c^{8} d^{15} - 31 \, a^{6} c^{7} d^{13} e^{2} + 106 \, a^{7} c^{6} d^{11} e^{4} - 205 \, a^{8} c^{5} d^{9} e^{6} + 240 \, a^{9} c^{4} d^{7} e^{8} - 169 \, a^{10} c^{3} d^{5} e^{10} + 66 \, a^{11} c^{2} d^{3} e^{12} - 11 \, a^{12} c d e^{14}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}\right)} \sqrt{\frac{16 \, c^{4} d^{9} - 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} - 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} - {\left(a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}\right)} \sqrt{\frac{441 \, c^{4} d^{8} e^{10} - 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} - 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} - 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} - 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} - 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} - 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} - 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} - 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} - 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} - a^{10} e^{10}}}\right) - 4 \, {\left(5 \, a^{2} c d^{2} e - 11 \, a^{3} e^{3} + 6 \, {\left(c^{3} d^{3} - 2 \, a c^{2} d e^{2}\right)} x^{3} - {\left(a c^{2} d^{2} e - 7 \, a^{2} c e^{3}\right)} x^{2} - 2 \, {\left(5 \, a c^{2} d^{3} - 8 \, a^{2} c d e^{2}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{4} c^{2} d^{4} - 2 \, a^{5} c d^{2} e^{2} + a^{6} e^{4} + {\left(a^{2} c^{4} d^{4} - 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{4} - 2 \, {\left(a^{3} c^{3} d^{4} - 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4}\right)} x^{2}\right)}}"," ",0,"1/64*(3*(a^4*c^2*d^4 - 2*a^5*c*d^2*e^2 + a^6*e^4 + (a^2*c^4*d^4 - 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^4 - 2*(a^3*c^3*d^4 - 2*a^4*c^2*d^2*e^2 + a^5*c*e^4)*x^2)*sqrt((16*c^4*d^9 - 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 - 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 + (a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10))*log(27*(336*c^4*d^8*e^5 - 1788*a*c^3*d^6*e^7 + 4189*a^2*c^2*d^4*e^9 - 4802*a^3*c*d^2*e^11 + 2401*a^4*e^13)*sqrt(e*x + d) + 27*(42*a^3*c^4*d^8*e^6 - 213*a^4*c^3*d^6*e^8 + 515*a^5*c^2*d^4*e^10 - 623*a^6*c*d^2*e^12 + 343*a^7*e^14 - (4*a^5*c^8*d^15 - 31*a^6*c^7*d^13*e^2 + 106*a^7*c^6*d^11*e^4 - 205*a^8*c^5*d^9*e^6 + 240*a^9*c^4*d^7*e^8 - 169*a^10*c^3*d^5*e^10 + 66*a^11*c^2*d^3*e^12 - 11*a^12*c*d*e^14)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))*sqrt((16*c^4*d^9 - 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 - 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 + (a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10))) - 3*(a^4*c^2*d^4 - 2*a^5*c*d^2*e^2 + a^6*e^4 + (a^2*c^4*d^4 - 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^4 - 2*(a^3*c^3*d^4 - 2*a^4*c^2*d^2*e^2 + a^5*c*e^4)*x^2)*sqrt((16*c^4*d^9 - 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 - 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 + (a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10))*log(27*(336*c^4*d^8*e^5 - 1788*a*c^3*d^6*e^7 + 4189*a^2*c^2*d^4*e^9 - 4802*a^3*c*d^2*e^11 + 2401*a^4*e^13)*sqrt(e*x + d) - 27*(42*a^3*c^4*d^8*e^6 - 213*a^4*c^3*d^6*e^8 + 515*a^5*c^2*d^4*e^10 - 623*a^6*c*d^2*e^12 + 343*a^7*e^14 - (4*a^5*c^8*d^15 - 31*a^6*c^7*d^13*e^2 + 106*a^7*c^6*d^11*e^4 - 205*a^8*c^5*d^9*e^6 + 240*a^9*c^4*d^7*e^8 - 169*a^10*c^3*d^5*e^10 + 66*a^11*c^2*d^3*e^12 - 11*a^12*c*d*e^14)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))*sqrt((16*c^4*d^9 - 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 - 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 + (a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10))) + 3*(a^4*c^2*d^4 - 2*a^5*c*d^2*e^2 + a^6*e^4 + (a^2*c^4*d^4 - 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^4 - 2*(a^3*c^3*d^4 - 2*a^4*c^2*d^2*e^2 + a^5*c*e^4)*x^2)*sqrt((16*c^4*d^9 - 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 - 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 - (a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10))*log(27*(336*c^4*d^8*e^5 - 1788*a*c^3*d^6*e^7 + 4189*a^2*c^2*d^4*e^9 - 4802*a^3*c*d^2*e^11 + 2401*a^4*e^13)*sqrt(e*x + d) + 27*(42*a^3*c^4*d^8*e^6 - 213*a^4*c^3*d^6*e^8 + 515*a^5*c^2*d^4*e^10 - 623*a^6*c*d^2*e^12 + 343*a^7*e^14 + (4*a^5*c^8*d^15 - 31*a^6*c^7*d^13*e^2 + 106*a^7*c^6*d^11*e^4 - 205*a^8*c^5*d^9*e^6 + 240*a^9*c^4*d^7*e^8 - 169*a^10*c^3*d^5*e^10 + 66*a^11*c^2*d^3*e^12 - 11*a^12*c*d*e^14)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))*sqrt((16*c^4*d^9 - 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 - 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 - (a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10))) - 3*(a^4*c^2*d^4 - 2*a^5*c*d^2*e^2 + a^6*e^4 + (a^2*c^4*d^4 - 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^4 - 2*(a^3*c^3*d^4 - 2*a^4*c^2*d^2*e^2 + a^5*c*e^4)*x^2)*sqrt((16*c^4*d^9 - 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 - 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 - (a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10))*log(27*(336*c^4*d^8*e^5 - 1788*a*c^3*d^6*e^7 + 4189*a^2*c^2*d^4*e^9 - 4802*a^3*c*d^2*e^11 + 2401*a^4*e^13)*sqrt(e*x + d) - 27*(42*a^3*c^4*d^8*e^6 - 213*a^4*c^3*d^6*e^8 + 515*a^5*c^2*d^4*e^10 - 623*a^6*c*d^2*e^12 + 343*a^7*e^14 + (4*a^5*c^8*d^15 - 31*a^6*c^7*d^13*e^2 + 106*a^7*c^6*d^11*e^4 - 205*a^8*c^5*d^9*e^6 + 240*a^9*c^4*d^7*e^8 - 169*a^10*c^3*d^5*e^10 + 66*a^11*c^2*d^3*e^12 - 11*a^12*c*d*e^14)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))*sqrt((16*c^4*d^9 - 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 - 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 - (a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10)*sqrt((441*c^4*d^8*e^10 - 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 - 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 - 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 - 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 - 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 - 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 - 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 - 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 - 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 - a^10*e^10))) - 4*(5*a^2*c*d^2*e - 11*a^3*e^3 + 6*(c^3*d^3 - 2*a*c^2*d*e^2)*x^3 - (a*c^2*d^2*e - 7*a^2*c*e^3)*x^2 - 2*(5*a*c^2*d^3 - 8*a^2*c*d*e^2)*x)*sqrt(e*x + d))/(a^4*c^2*d^4 - 2*a^5*c*d^2*e^2 + a^6*e^4 + (a^2*c^4*d^4 - 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^4 - 2*(a^3*c^3*d^4 - 2*a^4*c^2*d^2*e^2 + a^5*c*e^4)*x^2)","B",0
643,1,1751,0,0.527116," ","integrate((e*x+d)^(7/2)/(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(a^{2} c^{4} x^{4} + 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + a^{5} c^{4} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}} \log\left({\left(3024 \, c^{4} d^{8} e^{5} + 10908 \, a c^{3} d^{6} e^{7} + 13509 \, a^{2} c^{2} d^{4} e^{9} + 6250 \, a^{3} c d^{2} e^{11} + 625 \, a^{4} e^{13}\right)} \sqrt{e x + d} + {\left(126 \, a^{3} c^{4} d^{4} e^{6} + 255 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} + {\left(12 \, a^{5} c^{8} d^{3} + 13 \, a^{6} c^{7} d e^{2}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + a^{5} c^{4} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}}\right) - {\left(a^{2} c^{4} x^{4} + 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + a^{5} c^{4} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}} \log\left({\left(3024 \, c^{4} d^{8} e^{5} + 10908 \, a c^{3} d^{6} e^{7} + 13509 \, a^{2} c^{2} d^{4} e^{9} + 6250 \, a^{3} c d^{2} e^{11} + 625 \, a^{4} e^{13}\right)} \sqrt{e x + d} - {\left(126 \, a^{3} c^{4} d^{4} e^{6} + 255 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} + {\left(12 \, a^{5} c^{8} d^{3} + 13 \, a^{6} c^{7} d e^{2}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + a^{5} c^{4} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}}\right) + {\left(a^{2} c^{4} x^{4} + 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - a^{5} c^{4} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}} \log\left({\left(3024 \, c^{4} d^{8} e^{5} + 10908 \, a c^{3} d^{6} e^{7} + 13509 \, a^{2} c^{2} d^{4} e^{9} + 6250 \, a^{3} c d^{2} e^{11} + 625 \, a^{4} e^{13}\right)} \sqrt{e x + d} + {\left(126 \, a^{3} c^{4} d^{4} e^{6} + 255 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} - {\left(12 \, a^{5} c^{8} d^{3} + 13 \, a^{6} c^{7} d e^{2}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - a^{5} c^{4} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}}\right) - {\left(a^{2} c^{4} x^{4} + 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - a^{5} c^{4} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}} \log\left({\left(3024 \, c^{4} d^{8} e^{5} + 10908 \, a c^{3} d^{6} e^{7} + 13509 \, a^{2} c^{2} d^{4} e^{9} + 6250 \, a^{3} c d^{2} e^{11} + 625 \, a^{4} e^{13}\right)} \sqrt{e x + d} - {\left(126 \, a^{3} c^{4} d^{4} e^{6} + 255 \, a^{4} c^{3} d^{2} e^{8} + 125 \, a^{5} c^{2} e^{10} - {\left(12 \, a^{5} c^{8} d^{3} + 13 \, a^{6} c^{7} d e^{2}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - a^{5} c^{4} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9}}}}{a^{5} c^{4}}}\right) - 4 \, {\left(11 \, a^{2} c d^{2} e + 5 \, a^{3} e^{3} - 2 \, {\left(3 \, c^{3} d^{3} + 4 \, a c^{2} d e^{2}\right)} x^{3} - {\left(a c^{2} d^{2} e - 9 \, a^{2} c e^{3}\right)} x^{2} - 2 \, {\left(5 \, a c^{2} d^{3} - 2 \, a^{2} c d e^{2}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{2} c^{4} x^{4} + 2 \, a^{3} c^{3} x^{2} + a^{4} c^{2}\right)}}"," ",0,"1/64*((a^2*c^4*x^4 + 2*a^3*c^3*x^2 + a^4*c^2)*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + a^5*c^4*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))*log((3024*c^4*d^8*e^5 + 10908*a*c^3*d^6*e^7 + 13509*a^2*c^2*d^4*e^9 + 6250*a^3*c*d^2*e^11 + 625*a^4*e^13)*sqrt(e*x + d) + (126*a^3*c^4*d^4*e^6 + 255*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 + (12*a^5*c^8*d^3 + 13*a^6*c^7*d*e^2)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + a^5*c^4*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))) - (a^2*c^4*x^4 + 2*a^3*c^3*x^2 + a^4*c^2)*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + a^5*c^4*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))*log((3024*c^4*d^8*e^5 + 10908*a*c^3*d^6*e^7 + 13509*a^2*c^2*d^4*e^9 + 6250*a^3*c*d^2*e^11 + 625*a^4*e^13)*sqrt(e*x + d) - (126*a^3*c^4*d^4*e^6 + 255*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 + (12*a^5*c^8*d^3 + 13*a^6*c^7*d*e^2)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + a^5*c^4*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))) + (a^2*c^4*x^4 + 2*a^3*c^3*x^2 + a^4*c^2)*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - a^5*c^4*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))*log((3024*c^4*d^8*e^5 + 10908*a*c^3*d^6*e^7 + 13509*a^2*c^2*d^4*e^9 + 6250*a^3*c*d^2*e^11 + 625*a^4*e^13)*sqrt(e*x + d) + (126*a^3*c^4*d^4*e^6 + 255*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 - (12*a^5*c^8*d^3 + 13*a^6*c^7*d*e^2)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - a^5*c^4*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))) - (a^2*c^4*x^4 + 2*a^3*c^3*x^2 + a^4*c^2)*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - a^5*c^4*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))*log((3024*c^4*d^8*e^5 + 10908*a*c^3*d^6*e^7 + 13509*a^2*c^2*d^4*e^9 + 6250*a^3*c*d^2*e^11 + 625*a^4*e^13)*sqrt(e*x + d) - (126*a^3*c^4*d^4*e^6 + 255*a^4*c^3*d^2*e^8 + 125*a^5*c^2*e^10 - (12*a^5*c^8*d^3 + 13*a^6*c^7*d*e^2)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - a^5*c^4*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9)))/(a^5*c^4))) - 4*(11*a^2*c*d^2*e + 5*a^3*e^3 - 2*(3*c^3*d^3 + 4*a*c^2*d*e^2)*x^3 - (a*c^2*d^2*e - 9*a^2*c*e^3)*x^2 - 2*(5*a*c^2*d^3 - 2*a^2*c*d*e^2)*x)*sqrt(e*x + d))/(a^2*c^4*x^4 + 2*a^3*c^3*x^2 + a^4*c^2)","B",0
644,1,1037,0,0.450961," ","integrate((e*x+d)^(5/2)/(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{-\frac{a^{5} c^{3} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}} + 16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4}}{a^{5} c^{3}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} + 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} + 27 \, {\left(2 \, a^{3} c^{2} d e^{6} - {\left(4 \, a^{5} c^{6} d^{2} + a^{6} c^{5} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}}\right)} \sqrt{-\frac{a^{5} c^{3} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}} + 16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4}}{a^{5} c^{3}}}\right) - 3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{-\frac{a^{5} c^{3} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}} + 16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4}}{a^{5} c^{3}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} + 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} - 27 \, {\left(2 \, a^{3} c^{2} d e^{6} - {\left(4 \, a^{5} c^{6} d^{2} + a^{6} c^{5} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}}\right)} \sqrt{-\frac{a^{5} c^{3} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}} + 16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4}}{a^{5} c^{3}}}\right) + 3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{a^{5} c^{3} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}} - 16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} - 5 \, a^{2} d e^{4}}{a^{5} c^{3}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} + 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} + 27 \, {\left(2 \, a^{3} c^{2} d e^{6} + {\left(4 \, a^{5} c^{6} d^{2} + a^{6} c^{5} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}}\right)} \sqrt{\frac{a^{5} c^{3} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}} - 16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} - 5 \, a^{2} d e^{4}}{a^{5} c^{3}}}\right) - 3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{\frac{a^{5} c^{3} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}} - 16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} - 5 \, a^{2} d e^{4}}{a^{5} c^{3}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} + 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} - 27 \, {\left(2 \, a^{3} c^{2} d e^{6} + {\left(4 \, a^{5} c^{6} d^{2} + a^{6} c^{5} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}}\right)} \sqrt{\frac{a^{5} c^{3} \sqrt{-\frac{e^{10}}{a^{5} c^{7}}} - 16 \, c^{2} d^{5} - 20 \, a c d^{3} e^{2} - 5 \, a^{2} d e^{4}}{a^{5} c^{3}}}\right) + 4 \, {\left(a c d e x^{2} - 7 \, a^{2} d e + 3 \, {\left(2 \, c^{2} d^{2} + a c e^{2}\right)} x^{3} + {\left(10 \, a c d^{2} - a^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}}"," ",0,"1/64*(3*(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt(-(a^5*c^3*sqrt(-e^10/(a^5*c^7)) + 16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4)/(a^5*c^3))*log(27*(16*c^2*d^4*e^5 + 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) + 27*(2*a^3*c^2*d*e^6 - (4*a^5*c^6*d^2 + a^6*c^5*e^2)*sqrt(-e^10/(a^5*c^7)))*sqrt(-(a^5*c^3*sqrt(-e^10/(a^5*c^7)) + 16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4)/(a^5*c^3))) - 3*(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt(-(a^5*c^3*sqrt(-e^10/(a^5*c^7)) + 16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4)/(a^5*c^3))*log(27*(16*c^2*d^4*e^5 + 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) - 27*(2*a^3*c^2*d*e^6 - (4*a^5*c^6*d^2 + a^6*c^5*e^2)*sqrt(-e^10/(a^5*c^7)))*sqrt(-(a^5*c^3*sqrt(-e^10/(a^5*c^7)) + 16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4)/(a^5*c^3))) + 3*(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt((a^5*c^3*sqrt(-e^10/(a^5*c^7)) - 16*c^2*d^5 - 20*a*c*d^3*e^2 - 5*a^2*d*e^4)/(a^5*c^3))*log(27*(16*c^2*d^4*e^5 + 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) + 27*(2*a^3*c^2*d*e^6 + (4*a^5*c^6*d^2 + a^6*c^5*e^2)*sqrt(-e^10/(a^5*c^7)))*sqrt((a^5*c^3*sqrt(-e^10/(a^5*c^7)) - 16*c^2*d^5 - 20*a*c*d^3*e^2 - 5*a^2*d*e^4)/(a^5*c^3))) - 3*(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt((a^5*c^3*sqrt(-e^10/(a^5*c^7)) - 16*c^2*d^5 - 20*a*c*d^3*e^2 - 5*a^2*d*e^4)/(a^5*c^3))*log(27*(16*c^2*d^4*e^5 + 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) - 27*(2*a^3*c^2*d*e^6 + (4*a^5*c^6*d^2 + a^6*c^5*e^2)*sqrt(-e^10/(a^5*c^7)))*sqrt((a^5*c^3*sqrt(-e^10/(a^5*c^7)) - 16*c^2*d^5 - 20*a*c*d^3*e^2 - 5*a^2*d*e^4)/(a^5*c^3))) + 4*(a*c*d*e*x^2 - 7*a^2*d*e + 3*(2*c^2*d^2 + a*c*e^2)*x^3 + (10*a*c*d^2 - a^2*e^2)*x)*sqrt(e*x + d))/(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)","A",0
645,1,1752,0,0.473912," ","integrate((e*x+d)^(3/2)/(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{-\frac{16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + {\left(a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} + 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} + 27 \, {\left(2 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8} + {\left(4 \, a^{5} c^{6} d^{5} + 7 \, a^{6} c^{5} d^{3} e^{2} + 3 \, a^{7} c^{4} d e^{4}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}\right)} \sqrt{-\frac{16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + {\left(a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}}}\right) - 3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{-\frac{16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + {\left(a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} + 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} - 27 \, {\left(2 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8} + {\left(4 \, a^{5} c^{6} d^{5} + 7 \, a^{6} c^{5} d^{3} e^{2} + 3 \, a^{7} c^{4} d e^{4}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}\right)} \sqrt{-\frac{16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} + {\left(a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}}}\right) + 3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{-\frac{16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - {\left(a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} + 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} + 27 \, {\left(2 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8} - {\left(4 \, a^{5} c^{6} d^{5} + 7 \, a^{6} c^{5} d^{3} e^{2} + 3 \, a^{7} c^{4} d e^{4}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}\right)} \sqrt{-\frac{16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - {\left(a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}}}\right) - 3 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)} \sqrt{-\frac{16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - {\left(a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}}} \log\left(27 \, {\left(16 \, c^{2} d^{4} e^{5} + 12 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} \sqrt{e x + d} - 27 \, {\left(2 \, a^{3} c^{2} d^{2} e^{6} + a^{4} c e^{8} - {\left(4 \, a^{5} c^{6} d^{5} + 7 \, a^{6} c^{5} d^{3} e^{2} + 3 \, a^{7} c^{4} d e^{4}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}\right)} \sqrt{-\frac{16 \, c^{2} d^{5} + 20 \, a c d^{3} e^{2} + 5 \, a^{2} d e^{4} - {\left(a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}\right)} \sqrt{-\frac{e^{10}}{a^{5} c^{7} d^{4} + 2 \, a^{6} c^{6} d^{2} e^{2} + a^{7} c^{5} e^{4}}}}{a^{5} c^{3} d^{2} + a^{6} c^{2} e^{2}}}\right) + 4 \, {\left(6 \, c^{2} d x^{3} + a c e x^{2} + 10 \, a c d x - 3 \, a^{2} e\right)} \sqrt{e x + d}}{64 \, {\left(a^{2} c^{3} x^{4} + 2 \, a^{3} c^{2} x^{2} + a^{4} c\right)}}"," ",0,"1/64*(3*(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt(-(16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4 + (a^5*c^3*d^2 + a^6*c^2*e^2)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 + a^6*c^2*e^2))*log(27*(16*c^2*d^4*e^5 + 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) + 27*(2*a^3*c^2*d^2*e^6 + a^4*c*e^8 + (4*a^5*c^6*d^5 + 7*a^6*c^5*d^3*e^2 + 3*a^7*c^4*d*e^4)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))*sqrt(-(16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4 + (a^5*c^3*d^2 + a^6*c^2*e^2)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 + a^6*c^2*e^2))) - 3*(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt(-(16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4 + (a^5*c^3*d^2 + a^6*c^2*e^2)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 + a^6*c^2*e^2))*log(27*(16*c^2*d^4*e^5 + 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) - 27*(2*a^3*c^2*d^2*e^6 + a^4*c*e^8 + (4*a^5*c^6*d^5 + 7*a^6*c^5*d^3*e^2 + 3*a^7*c^4*d*e^4)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))*sqrt(-(16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4 + (a^5*c^3*d^2 + a^6*c^2*e^2)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 + a^6*c^2*e^2))) + 3*(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt(-(16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4 - (a^5*c^3*d^2 + a^6*c^2*e^2)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 + a^6*c^2*e^2))*log(27*(16*c^2*d^4*e^5 + 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) + 27*(2*a^3*c^2*d^2*e^6 + a^4*c*e^8 - (4*a^5*c^6*d^5 + 7*a^6*c^5*d^3*e^2 + 3*a^7*c^4*d*e^4)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))*sqrt(-(16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4 - (a^5*c^3*d^2 + a^6*c^2*e^2)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 + a^6*c^2*e^2))) - 3*(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)*sqrt(-(16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4 - (a^5*c^3*d^2 + a^6*c^2*e^2)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 + a^6*c^2*e^2))*log(27*(16*c^2*d^4*e^5 + 12*a*c*d^2*e^7 + a^2*e^9)*sqrt(e*x + d) - 27*(2*a^3*c^2*d^2*e^6 + a^4*c*e^8 - (4*a^5*c^6*d^5 + 7*a^6*c^5*d^3*e^2 + 3*a^7*c^4*d*e^4)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))*sqrt(-(16*c^2*d^5 + 20*a*c*d^3*e^2 + 5*a^2*d*e^4 - (a^5*c^3*d^2 + a^6*c^2*e^2)*sqrt(-e^10/(a^5*c^7*d^4 + 2*a^6*c^6*d^2*e^2 + a^7*c^5*e^4)))/(a^5*c^3*d^2 + a^6*c^2*e^2))) + 4*(6*c^2*d*x^3 + a*c*e*x^2 + 10*a*c*d*x - 3*a^2*e)*sqrt(e*x + d))/(a^2*c^3*x^4 + 2*a^3*c^2*x^2 + a^4*c)","B",0
646,1,3770,0,0.705333," ","integrate((e*x+d)^(1/2)/(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(a^{4} c d^{2} + a^{5} e^{2} + {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} x^{2}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + {\left(a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}}} \log\left({\left(3024 \, c^{3} d^{6} e^{5} + 7884 \, a c^{2} d^{4} e^{7} + 5625 \, a^{2} c d^{2} e^{9} + 625 \, a^{3} e^{11}\right)} \sqrt{e x + d} + {\left(126 \, a^{3} c^{3} d^{5} e^{6} + 318 \, a^{4} c^{2} d^{3} e^{8} + 200 \, a^{5} c d e^{10} - {\left(12 \, a^{5} c^{7} d^{10} + 55 \, a^{6} c^{6} d^{8} e^{2} + 98 \, a^{7} c^{5} d^{6} e^{4} + 84 \, a^{8} c^{4} d^{4} e^{6} + 34 \, a^{9} c^{3} d^{2} e^{8} + 5 \, a^{10} c^{2} e^{10}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + {\left(a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}}}\right) - {\left(a^{4} c d^{2} + a^{5} e^{2} + {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} x^{2}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + {\left(a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}}} \log\left({\left(3024 \, c^{3} d^{6} e^{5} + 7884 \, a c^{2} d^{4} e^{7} + 5625 \, a^{2} c d^{2} e^{9} + 625 \, a^{3} e^{11}\right)} \sqrt{e x + d} - {\left(126 \, a^{3} c^{3} d^{5} e^{6} + 318 \, a^{4} c^{2} d^{3} e^{8} + 200 \, a^{5} c d e^{10} - {\left(12 \, a^{5} c^{7} d^{10} + 55 \, a^{6} c^{6} d^{8} e^{2} + 98 \, a^{7} c^{5} d^{6} e^{4} + 84 \, a^{8} c^{4} d^{4} e^{6} + 34 \, a^{9} c^{3} d^{2} e^{8} + 5 \, a^{10} c^{2} e^{10}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + {\left(a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}}}\right) + {\left(a^{4} c d^{2} + a^{5} e^{2} + {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} x^{2}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - {\left(a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}}} \log\left({\left(3024 \, c^{3} d^{6} e^{5} + 7884 \, a c^{2} d^{4} e^{7} + 5625 \, a^{2} c d^{2} e^{9} + 625 \, a^{3} e^{11}\right)} \sqrt{e x + d} + {\left(126 \, a^{3} c^{3} d^{5} e^{6} + 318 \, a^{4} c^{2} d^{3} e^{8} + 200 \, a^{5} c d e^{10} + {\left(12 \, a^{5} c^{7} d^{10} + 55 \, a^{6} c^{6} d^{8} e^{2} + 98 \, a^{7} c^{5} d^{6} e^{4} + 84 \, a^{8} c^{4} d^{4} e^{6} + 34 \, a^{9} c^{3} d^{2} e^{8} + 5 \, a^{10} c^{2} e^{10}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - {\left(a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}}}\right) - {\left(a^{4} c d^{2} + a^{5} e^{2} + {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} x^{2}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - {\left(a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}}} \log\left({\left(3024 \, c^{3} d^{6} e^{5} + 7884 \, a c^{2} d^{4} e^{7} + 5625 \, a^{2} c d^{2} e^{9} + 625 \, a^{3} e^{11}\right)} \sqrt{e x + d} - {\left(126 \, a^{3} c^{3} d^{5} e^{6} + 318 \, a^{4} c^{2} d^{3} e^{8} + 200 \, a^{5} c d e^{10} + {\left(12 \, a^{5} c^{7} d^{10} + 55 \, a^{6} c^{6} d^{8} e^{2} + 98 \, a^{7} c^{5} d^{6} e^{4} + 84 \, a^{8} c^{4} d^{4} e^{6} + 34 \, a^{9} c^{3} d^{2} e^{8} + 5 \, a^{10} c^{2} e^{10}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}\right)} \sqrt{-\frac{144 \, c^{3} d^{7} + 420 \, a c^{2} d^{5} e^{2} + 385 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} - {\left(a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}\right)} \sqrt{-\frac{441 \, c^{2} d^{4} e^{10} + 1050 \, a c d^{2} e^{12} + 625 \, a^{2} e^{14}}{a^{5} c^{9} d^{12} + 6 \, a^{6} c^{8} d^{10} e^{2} + 15 \, a^{7} c^{7} d^{8} e^{4} + 20 \, a^{8} c^{6} d^{6} e^{6} + 15 \, a^{9} c^{5} d^{4} e^{8} + 6 \, a^{10} c^{4} d^{2} e^{10} + a^{11} c^{3} e^{12}}}}{a^{5} c^{4} d^{6} + 3 \, a^{6} c^{3} d^{4} e^{2} + 3 \, a^{7} c^{2} d^{2} e^{4} + a^{8} c e^{6}}}\right) + 4 \, {\left(a c d e x^{2} + a^{2} d e + {\left(6 \, c^{2} d^{2} + 5 \, a c e^{2}\right)} x^{3} + {\left(10 \, a c d^{2} + 9 \, a^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{4} c d^{2} + a^{5} e^{2} + {\left(a^{2} c^{3} d^{2} + a^{3} c^{2} e^{2}\right)} x^{4} + 2 \, {\left(a^{3} c^{2} d^{2} + a^{4} c e^{2}\right)} x^{2}\right)}}"," ",0,"1/64*((a^4*c*d^2 + a^5*e^2 + (a^2*c^3*d^2 + a^3*c^2*e^2)*x^4 + 2*(a^3*c^2*d^2 + a^4*c*e^2)*x^2)*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + (a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6))*log((3024*c^3*d^6*e^5 + 7884*a*c^2*d^4*e^7 + 5625*a^2*c*d^2*e^9 + 625*a^3*e^11)*sqrt(e*x + d) + (126*a^3*c^3*d^5*e^6 + 318*a^4*c^2*d^3*e^8 + 200*a^5*c*d*e^10 - (12*a^5*c^7*d^10 + 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*e^4 + 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 + 5*a^10*c^2*e^10)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + (a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6))) - (a^4*c*d^2 + a^5*e^2 + (a^2*c^3*d^2 + a^3*c^2*e^2)*x^4 + 2*(a^3*c^2*d^2 + a^4*c*e^2)*x^2)*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + (a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6))*log((3024*c^3*d^6*e^5 + 7884*a*c^2*d^4*e^7 + 5625*a^2*c*d^2*e^9 + 625*a^3*e^11)*sqrt(e*x + d) - (126*a^3*c^3*d^5*e^6 + 318*a^4*c^2*d^3*e^8 + 200*a^5*c*d*e^10 - (12*a^5*c^7*d^10 + 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*e^4 + 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 + 5*a^10*c^2*e^10)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + (a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6))) + (a^4*c*d^2 + a^5*e^2 + (a^2*c^3*d^2 + a^3*c^2*e^2)*x^4 + 2*(a^3*c^2*d^2 + a^4*c*e^2)*x^2)*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - (a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6))*log((3024*c^3*d^6*e^5 + 7884*a*c^2*d^4*e^7 + 5625*a^2*c*d^2*e^9 + 625*a^3*e^11)*sqrt(e*x + d) + (126*a^3*c^3*d^5*e^6 + 318*a^4*c^2*d^3*e^8 + 200*a^5*c*d*e^10 + (12*a^5*c^7*d^10 + 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*e^4 + 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 + 5*a^10*c^2*e^10)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - (a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6))) - (a^4*c*d^2 + a^5*e^2 + (a^2*c^3*d^2 + a^3*c^2*e^2)*x^4 + 2*(a^3*c^2*d^2 + a^4*c*e^2)*x^2)*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - (a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6))*log((3024*c^3*d^6*e^5 + 7884*a*c^2*d^4*e^7 + 5625*a^2*c*d^2*e^9 + 625*a^3*e^11)*sqrt(e*x + d) - (126*a^3*c^3*d^5*e^6 + 318*a^4*c^2*d^3*e^8 + 200*a^5*c*d*e^10 + (12*a^5*c^7*d^10 + 55*a^6*c^6*d^8*e^2 + 98*a^7*c^5*d^6*e^4 + 84*a^8*c^4*d^4*e^6 + 34*a^9*c^3*d^2*e^8 + 5*a^10*c^2*e^10)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))*sqrt(-(144*c^3*d^7 + 420*a*c^2*d^5*e^2 + 385*a^2*c*d^3*e^4 + 105*a^3*d*e^6 - (a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6)*sqrt(-(441*c^2*d^4*e^10 + 1050*a*c*d^2*e^12 + 625*a^2*e^14)/(a^5*c^9*d^12 + 6*a^6*c^8*d^10*e^2 + 15*a^7*c^7*d^8*e^4 + 20*a^8*c^6*d^6*e^6 + 15*a^9*c^5*d^4*e^8 + 6*a^10*c^4*d^2*e^10 + a^11*c^3*e^12)))/(a^5*c^4*d^6 + 3*a^6*c^3*d^4*e^2 + 3*a^7*c^2*d^2*e^4 + a^8*c*e^6))) + 4*(a*c*d*e*x^2 + a^2*d*e + (6*c^2*d^2 + 5*a*c*e^2)*x^3 + (10*a*c*d^2 + 9*a^2*e^2)*x)*sqrt(e*x + d))/(a^4*c*d^2 + a^5*e^2 + (a^2*c^3*d^2 + a^3*c^2*e^2)*x^4 + 2*(a^3*c^2*d^2 + a^4*c*e^2)*x^2)","B",0
647,1,5779,0,1.793491," ","integrate(1/(c*x^2+a)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left(a^{4} c^{2} d^{4} + 2 \, a^{5} c d^{2} e^{2} + a^{6} e^{4} + {\left(a^{2} c^{4} d^{4} + 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(a^{3} c^{3} d^{4} + 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4}\right)} x^{2}\right)} \sqrt{-\frac{16 \, c^{4} d^{9} + 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} + 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} + {\left(a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}}} \log\left(27 \, {\left(336 \, c^{4} d^{8} e^{5} + 1788 \, a c^{3} d^{6} e^{7} + 4189 \, a^{2} c^{2} d^{4} e^{9} + 4802 \, a^{3} c d^{2} e^{11} + 2401 \, a^{4} e^{13}\right)} \sqrt{e x + d} + 27 \, {\left(42 \, a^{3} c^{4} d^{8} e^{6} + 213 \, a^{4} c^{3} d^{6} e^{8} + 515 \, a^{5} c^{2} d^{4} e^{10} + 623 \, a^{6} c d^{2} e^{12} + 343 \, a^{7} e^{14} + {\left(4 \, a^{5} c^{8} d^{15} + 31 \, a^{6} c^{7} d^{13} e^{2} + 106 \, a^{7} c^{6} d^{11} e^{4} + 205 \, a^{8} c^{5} d^{9} e^{6} + 240 \, a^{9} c^{4} d^{7} e^{8} + 169 \, a^{10} c^{3} d^{5} e^{10} + 66 \, a^{11} c^{2} d^{3} e^{12} + 11 \, a^{12} c d e^{14}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}\right)} \sqrt{-\frac{16 \, c^{4} d^{9} + 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} + 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} + {\left(a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}}}\right) - 3 \, {\left(a^{4} c^{2} d^{4} + 2 \, a^{5} c d^{2} e^{2} + a^{6} e^{4} + {\left(a^{2} c^{4} d^{4} + 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(a^{3} c^{3} d^{4} + 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4}\right)} x^{2}\right)} \sqrt{-\frac{16 \, c^{4} d^{9} + 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} + 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} + {\left(a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}}} \log\left(27 \, {\left(336 \, c^{4} d^{8} e^{5} + 1788 \, a c^{3} d^{6} e^{7} + 4189 \, a^{2} c^{2} d^{4} e^{9} + 4802 \, a^{3} c d^{2} e^{11} + 2401 \, a^{4} e^{13}\right)} \sqrt{e x + d} - 27 \, {\left(42 \, a^{3} c^{4} d^{8} e^{6} + 213 \, a^{4} c^{3} d^{6} e^{8} + 515 \, a^{5} c^{2} d^{4} e^{10} + 623 \, a^{6} c d^{2} e^{12} + 343 \, a^{7} e^{14} + {\left(4 \, a^{5} c^{8} d^{15} + 31 \, a^{6} c^{7} d^{13} e^{2} + 106 \, a^{7} c^{6} d^{11} e^{4} + 205 \, a^{8} c^{5} d^{9} e^{6} + 240 \, a^{9} c^{4} d^{7} e^{8} + 169 \, a^{10} c^{3} d^{5} e^{10} + 66 \, a^{11} c^{2} d^{3} e^{12} + 11 \, a^{12} c d e^{14}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}\right)} \sqrt{-\frac{16 \, c^{4} d^{9} + 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} + 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} + {\left(a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}}}\right) + 3 \, {\left(a^{4} c^{2} d^{4} + 2 \, a^{5} c d^{2} e^{2} + a^{6} e^{4} + {\left(a^{2} c^{4} d^{4} + 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(a^{3} c^{3} d^{4} + 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4}\right)} x^{2}\right)} \sqrt{-\frac{16 \, c^{4} d^{9} + 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} + 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} - {\left(a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}}} \log\left(27 \, {\left(336 \, c^{4} d^{8} e^{5} + 1788 \, a c^{3} d^{6} e^{7} + 4189 \, a^{2} c^{2} d^{4} e^{9} + 4802 \, a^{3} c d^{2} e^{11} + 2401 \, a^{4} e^{13}\right)} \sqrt{e x + d} + 27 \, {\left(42 \, a^{3} c^{4} d^{8} e^{6} + 213 \, a^{4} c^{3} d^{6} e^{8} + 515 \, a^{5} c^{2} d^{4} e^{10} + 623 \, a^{6} c d^{2} e^{12} + 343 \, a^{7} e^{14} - {\left(4 \, a^{5} c^{8} d^{15} + 31 \, a^{6} c^{7} d^{13} e^{2} + 106 \, a^{7} c^{6} d^{11} e^{4} + 205 \, a^{8} c^{5} d^{9} e^{6} + 240 \, a^{9} c^{4} d^{7} e^{8} + 169 \, a^{10} c^{3} d^{5} e^{10} + 66 \, a^{11} c^{2} d^{3} e^{12} + 11 \, a^{12} c d e^{14}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}\right)} \sqrt{-\frac{16 \, c^{4} d^{9} + 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} + 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} - {\left(a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}}}\right) - 3 \, {\left(a^{4} c^{2} d^{4} + 2 \, a^{5} c d^{2} e^{2} + a^{6} e^{4} + {\left(a^{2} c^{4} d^{4} + 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(a^{3} c^{3} d^{4} + 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4}\right)} x^{2}\right)} \sqrt{-\frac{16 \, c^{4} d^{9} + 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} + 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} - {\left(a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}}} \log\left(27 \, {\left(336 \, c^{4} d^{8} e^{5} + 1788 \, a c^{3} d^{6} e^{7} + 4189 \, a^{2} c^{2} d^{4} e^{9} + 4802 \, a^{3} c d^{2} e^{11} + 2401 \, a^{4} e^{13}\right)} \sqrt{e x + d} - 27 \, {\left(42 \, a^{3} c^{4} d^{8} e^{6} + 213 \, a^{4} c^{3} d^{6} e^{8} + 515 \, a^{5} c^{2} d^{4} e^{10} + 623 \, a^{6} c d^{2} e^{12} + 343 \, a^{7} e^{14} - {\left(4 \, a^{5} c^{8} d^{15} + 31 \, a^{6} c^{7} d^{13} e^{2} + 106 \, a^{7} c^{6} d^{11} e^{4} + 205 \, a^{8} c^{5} d^{9} e^{6} + 240 \, a^{9} c^{4} d^{7} e^{8} + 169 \, a^{10} c^{3} d^{5} e^{10} + 66 \, a^{11} c^{2} d^{3} e^{12} + 11 \, a^{12} c d e^{14}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}\right)} \sqrt{-\frac{16 \, c^{4} d^{9} + 84 \, a c^{3} d^{7} e^{2} + 189 \, a^{2} c^{2} d^{5} e^{4} + 210 \, a^{3} c d^{3} e^{6} + 105 \, a^{4} d e^{8} - {\left(a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}\right)} \sqrt{-\frac{441 \, c^{4} d^{8} e^{10} + 2268 \, a c^{3} d^{6} e^{12} + 4974 \, a^{2} c^{2} d^{4} e^{14} + 5292 \, a^{3} c d^{2} e^{16} + 2401 \, a^{4} e^{18}}{a^{5} c^{11} d^{20} + 10 \, a^{6} c^{10} d^{18} e^{2} + 45 \, a^{7} c^{9} d^{16} e^{4} + 120 \, a^{8} c^{8} d^{14} e^{6} + 210 \, a^{9} c^{7} d^{12} e^{8} + 252 \, a^{10} c^{6} d^{10} e^{10} + 210 \, a^{11} c^{5} d^{8} e^{12} + 120 \, a^{12} c^{4} d^{6} e^{14} + 45 \, a^{13} c^{3} d^{4} e^{16} + 10 \, a^{14} c^{2} d^{2} e^{18} + a^{15} c e^{20}}}}{a^{5} c^{5} d^{10} + 5 \, a^{6} c^{4} d^{8} e^{2} + 10 \, a^{7} c^{3} d^{6} e^{4} + 10 \, a^{8} c^{2} d^{4} e^{6} + 5 \, a^{9} c d^{2} e^{8} + a^{10} e^{10}}}\right) + 4 \, {\left(5 \, a^{2} c d^{2} e + 11 \, a^{3} e^{3} + 6 \, {\left(c^{3} d^{3} + 2 \, a c^{2} d e^{2}\right)} x^{3} + {\left(a c^{2} d^{2} e + 7 \, a^{2} c e^{3}\right)} x^{2} + 2 \, {\left(5 \, a c^{2} d^{3} + 8 \, a^{2} c d e^{2}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{4} c^{2} d^{4} + 2 \, a^{5} c d^{2} e^{2} + a^{6} e^{4} + {\left(a^{2} c^{4} d^{4} + 2 \, a^{3} c^{3} d^{2} e^{2} + a^{4} c^{2} e^{4}\right)} x^{4} + 2 \, {\left(a^{3} c^{3} d^{4} + 2 \, a^{4} c^{2} d^{2} e^{2} + a^{5} c e^{4}\right)} x^{2}\right)}}"," ",0,"1/64*(3*(a^4*c^2*d^4 + 2*a^5*c*d^2*e^2 + a^6*e^4 + (a^2*c^4*d^4 + 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^4 + 2*(a^3*c^3*d^4 + 2*a^4*c^2*d^2*e^2 + a^5*c*e^4)*x^2)*sqrt(-(16*c^4*d^9 + 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 + 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 + (a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10))*log(27*(336*c^4*d^8*e^5 + 1788*a*c^3*d^6*e^7 + 4189*a^2*c^2*d^4*e^9 + 4802*a^3*c*d^2*e^11 + 2401*a^4*e^13)*sqrt(e*x + d) + 27*(42*a^3*c^4*d^8*e^6 + 213*a^4*c^3*d^6*e^8 + 515*a^5*c^2*d^4*e^10 + 623*a^6*c*d^2*e^12 + 343*a^7*e^14 + (4*a^5*c^8*d^15 + 31*a^6*c^7*d^13*e^2 + 106*a^7*c^6*d^11*e^4 + 205*a^8*c^5*d^9*e^6 + 240*a^9*c^4*d^7*e^8 + 169*a^10*c^3*d^5*e^10 + 66*a^11*c^2*d^3*e^12 + 11*a^12*c*d*e^14)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))*sqrt(-(16*c^4*d^9 + 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 + 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 + (a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10))) - 3*(a^4*c^2*d^4 + 2*a^5*c*d^2*e^2 + a^6*e^4 + (a^2*c^4*d^4 + 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^4 + 2*(a^3*c^3*d^4 + 2*a^4*c^2*d^2*e^2 + a^5*c*e^4)*x^2)*sqrt(-(16*c^4*d^9 + 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 + 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 + (a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10))*log(27*(336*c^4*d^8*e^5 + 1788*a*c^3*d^6*e^7 + 4189*a^2*c^2*d^4*e^9 + 4802*a^3*c*d^2*e^11 + 2401*a^4*e^13)*sqrt(e*x + d) - 27*(42*a^3*c^4*d^8*e^6 + 213*a^4*c^3*d^6*e^8 + 515*a^5*c^2*d^4*e^10 + 623*a^6*c*d^2*e^12 + 343*a^7*e^14 + (4*a^5*c^8*d^15 + 31*a^6*c^7*d^13*e^2 + 106*a^7*c^6*d^11*e^4 + 205*a^8*c^5*d^9*e^6 + 240*a^9*c^4*d^7*e^8 + 169*a^10*c^3*d^5*e^10 + 66*a^11*c^2*d^3*e^12 + 11*a^12*c*d*e^14)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))*sqrt(-(16*c^4*d^9 + 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 + 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 + (a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10))) + 3*(a^4*c^2*d^4 + 2*a^5*c*d^2*e^2 + a^6*e^4 + (a^2*c^4*d^4 + 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^4 + 2*(a^3*c^3*d^4 + 2*a^4*c^2*d^2*e^2 + a^5*c*e^4)*x^2)*sqrt(-(16*c^4*d^9 + 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 + 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 - (a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10))*log(27*(336*c^4*d^8*e^5 + 1788*a*c^3*d^6*e^7 + 4189*a^2*c^2*d^4*e^9 + 4802*a^3*c*d^2*e^11 + 2401*a^4*e^13)*sqrt(e*x + d) + 27*(42*a^3*c^4*d^8*e^6 + 213*a^4*c^3*d^6*e^8 + 515*a^5*c^2*d^4*e^10 + 623*a^6*c*d^2*e^12 + 343*a^7*e^14 - (4*a^5*c^8*d^15 + 31*a^6*c^7*d^13*e^2 + 106*a^7*c^6*d^11*e^4 + 205*a^8*c^5*d^9*e^6 + 240*a^9*c^4*d^7*e^8 + 169*a^10*c^3*d^5*e^10 + 66*a^11*c^2*d^3*e^12 + 11*a^12*c*d*e^14)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))*sqrt(-(16*c^4*d^9 + 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 + 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 - (a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10))) - 3*(a^4*c^2*d^4 + 2*a^5*c*d^2*e^2 + a^6*e^4 + (a^2*c^4*d^4 + 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^4 + 2*(a^3*c^3*d^4 + 2*a^4*c^2*d^2*e^2 + a^5*c*e^4)*x^2)*sqrt(-(16*c^4*d^9 + 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 + 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 - (a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10))*log(27*(336*c^4*d^8*e^5 + 1788*a*c^3*d^6*e^7 + 4189*a^2*c^2*d^4*e^9 + 4802*a^3*c*d^2*e^11 + 2401*a^4*e^13)*sqrt(e*x + d) - 27*(42*a^3*c^4*d^8*e^6 + 213*a^4*c^3*d^6*e^8 + 515*a^5*c^2*d^4*e^10 + 623*a^6*c*d^2*e^12 + 343*a^7*e^14 - (4*a^5*c^8*d^15 + 31*a^6*c^7*d^13*e^2 + 106*a^7*c^6*d^11*e^4 + 205*a^8*c^5*d^9*e^6 + 240*a^9*c^4*d^7*e^8 + 169*a^10*c^3*d^5*e^10 + 66*a^11*c^2*d^3*e^12 + 11*a^12*c*d*e^14)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))*sqrt(-(16*c^4*d^9 + 84*a*c^3*d^7*e^2 + 189*a^2*c^2*d^5*e^4 + 210*a^3*c*d^3*e^6 + 105*a^4*d*e^8 - (a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10)*sqrt(-(441*c^4*d^8*e^10 + 2268*a*c^3*d^6*e^12 + 4974*a^2*c^2*d^4*e^14 + 5292*a^3*c*d^2*e^16 + 2401*a^4*e^18)/(a^5*c^11*d^20 + 10*a^6*c^10*d^18*e^2 + 45*a^7*c^9*d^16*e^4 + 120*a^8*c^8*d^14*e^6 + 210*a^9*c^7*d^12*e^8 + 252*a^10*c^6*d^10*e^10 + 210*a^11*c^5*d^8*e^12 + 120*a^12*c^4*d^6*e^14 + 45*a^13*c^3*d^4*e^16 + 10*a^14*c^2*d^2*e^18 + a^15*c*e^20)))/(a^5*c^5*d^10 + 5*a^6*c^4*d^8*e^2 + 10*a^7*c^3*d^6*e^4 + 10*a^8*c^2*d^4*e^6 + 5*a^9*c*d^2*e^8 + a^10*e^10))) + 4*(5*a^2*c*d^2*e + 11*a^3*e^3 + 6*(c^3*d^3 + 2*a*c^2*d*e^2)*x^3 + (a*c^2*d^2*e + 7*a^2*c*e^3)*x^2 + 2*(5*a*c^2*d^3 + 8*a^2*c*d*e^2)*x)*sqrt(e*x + d))/(a^4*c^2*d^4 + 2*a^5*c*d^2*e^2 + a^6*e^4 + (a^2*c^4*d^4 + 2*a^3*c^3*d^2*e^2 + a^4*c^2*e^4)*x^4 + 2*(a^3*c^3*d^4 + 2*a^4*c^2*d^2*e^2 + a^5*c*e^4)*x^2)","B",0
648,1,282,0,0.416774," ","integrate((2+3*x)^(1/2)/(x^2+1),x, algorithm=""fricas"")","\frac{1}{156} \cdot 13^{\frac{1}{4}} \sqrt{4 \, \sqrt{13} + 26} {\left(2 \, \sqrt{13} - 13\right)} \log\left(\frac{1}{13} \cdot 13^{\frac{3}{4}} \sqrt{3 \, x + 2} \sqrt{4 \, \sqrt{13} + 26} + 3 \, x + \sqrt{13} + 2\right) - \frac{1}{156} \cdot 13^{\frac{1}{4}} \sqrt{4 \, \sqrt{13} + 26} {\left(2 \, \sqrt{13} - 13\right)} \log\left(-\frac{1}{13} \cdot 13^{\frac{3}{4}} \sqrt{3 \, x + 2} \sqrt{4 \, \sqrt{13} + 26} + 3 \, x + \sqrt{13} + 2\right) - \frac{1}{13} \cdot 13^{\frac{3}{4}} \sqrt{4 \, \sqrt{13} + 26} \arctan\left(-\frac{1}{39} \cdot 13^{\frac{3}{4}} \sqrt{3 \, x + 2} \sqrt{4 \, \sqrt{13} + 26} + \frac{1}{39} \cdot 13^{\frac{1}{4}} \sqrt{13^{\frac{3}{4}} \sqrt{3 \, x + 2} \sqrt{4 \, \sqrt{13} + 26} + 39 \, x + 13 \, \sqrt{13} + 26} \sqrt{4 \, \sqrt{13} + 26} - \frac{1}{3} \, \sqrt{13} - \frac{2}{3}\right) - \frac{1}{13} \cdot 13^{\frac{3}{4}} \sqrt{4 \, \sqrt{13} + 26} \arctan\left(-\frac{1}{39} \cdot 13^{\frac{3}{4}} \sqrt{3 \, x + 2} \sqrt{4 \, \sqrt{13} + 26} + \frac{1}{39} \cdot 13^{\frac{1}{4}} \sqrt{-13^{\frac{3}{4}} \sqrt{3 \, x + 2} \sqrt{4 \, \sqrt{13} + 26} + 39 \, x + 13 \, \sqrt{13} + 26} \sqrt{4 \, \sqrt{13} + 26} + \frac{1}{3} \, \sqrt{13} + \frac{2}{3}\right)"," ",0,"1/156*13^(1/4)*sqrt(4*sqrt(13) + 26)*(2*sqrt(13) - 13)*log(1/13*13^(3/4)*sqrt(3*x + 2)*sqrt(4*sqrt(13) + 26) + 3*x + sqrt(13) + 2) - 1/156*13^(1/4)*sqrt(4*sqrt(13) + 26)*(2*sqrt(13) - 13)*log(-1/13*13^(3/4)*sqrt(3*x + 2)*sqrt(4*sqrt(13) + 26) + 3*x + sqrt(13) + 2) - 1/13*13^(3/4)*sqrt(4*sqrt(13) + 26)*arctan(-1/39*13^(3/4)*sqrt(3*x + 2)*sqrt(4*sqrt(13) + 26) + 1/39*13^(1/4)*sqrt(13^(3/4)*sqrt(3*x + 2)*sqrt(4*sqrt(13) + 26) + 39*x + 13*sqrt(13) + 26)*sqrt(4*sqrt(13) + 26) - 1/3*sqrt(13) - 2/3) - 1/13*13^(3/4)*sqrt(4*sqrt(13) + 26)*arctan(-1/39*13^(3/4)*sqrt(3*x + 2)*sqrt(4*sqrt(13) + 26) + 1/39*13^(1/4)*sqrt(-13^(3/4)*sqrt(3*x + 2)*sqrt(4*sqrt(13) + 26) + 39*x + 13*sqrt(13) + 26)*sqrt(4*sqrt(13) + 26) + 1/3*sqrt(13) + 2/3)","A",0
649,1,925,0,0.452427," ","integrate((d*x+c)^(1/2)/(x^2+1),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(c^{2} + d^{2}\right)}^{\frac{3}{4}} \sqrt{d^{2}} \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} \arctan\left(-\frac{\sqrt{2} {\left(c^{2} + d^{2}\right)}^{\frac{3}{4}} \sqrt{d^{2}} \sqrt{d x + c} d \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} - \sqrt{2} {\left(c^{2} + d^{2}\right)}^{\frac{3}{4}} \sqrt{d^{2}} \sqrt{\frac{\sqrt{2} {\left(c^{2} + d^{2}\right)}^{\frac{3}{4}} \sqrt{d x + c} d^{3} \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} + c^{3} d^{2} + c d^{4} + {\left(c^{2} d^{3} + d^{5}\right)} x + {\left(c^{2} d^{2} + d^{4}\right)} \sqrt{c^{2} + d^{2}}}{c^{2} + d^{2}}} \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} + {\left(c^{2} + d^{2}\right)}^{\frac{3}{2}} \sqrt{d^{2}} + {\left(c^{3} + c d^{2}\right)} \sqrt{d^{2}}}{c^{2} d^{2} + d^{4}}\right) + 4 \, \sqrt{2} {\left(c^{2} + d^{2}\right)}^{\frac{3}{4}} \sqrt{d^{2}} \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} \arctan\left(-\frac{\sqrt{2} {\left(c^{2} + d^{2}\right)}^{\frac{3}{4}} \sqrt{d^{2}} \sqrt{d x + c} d \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} - \sqrt{2} {\left(c^{2} + d^{2}\right)}^{\frac{3}{4}} \sqrt{d^{2}} \sqrt{-\frac{\sqrt{2} {\left(c^{2} + d^{2}\right)}^{\frac{3}{4}} \sqrt{d x + c} d^{3} \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} - c^{3} d^{2} - c d^{4} - {\left(c^{2} d^{3} + d^{5}\right)} x - {\left(c^{2} d^{2} + d^{4}\right)} \sqrt{c^{2} + d^{2}}}{c^{2} + d^{2}}} \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} - {\left(c^{2} + d^{2}\right)}^{\frac{3}{2}} \sqrt{d^{2}} - {\left(c^{3} + c d^{2}\right)} \sqrt{d^{2}}}{c^{2} d^{2} + d^{4}}\right) + \sqrt{2} {\left(c^{2} + d^{2} - \sqrt{c^{2} + d^{2}} c\right)} {\left(c^{2} + d^{2}\right)}^{\frac{1}{4}} \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} \log\left(\frac{\sqrt{2} {\left(c^{2} + d^{2}\right)}^{\frac{3}{4}} \sqrt{d x + c} d^{3} \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} + c^{3} d^{2} + c d^{4} + {\left(c^{2} d^{3} + d^{5}\right)} x + {\left(c^{2} d^{2} + d^{4}\right)} \sqrt{c^{2} + d^{2}}}{c^{2} + d^{2}}\right) - \sqrt{2} {\left(c^{2} + d^{2} - \sqrt{c^{2} + d^{2}} c\right)} {\left(c^{2} + d^{2}\right)}^{\frac{1}{4}} \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} \log\left(-\frac{\sqrt{2} {\left(c^{2} + d^{2}\right)}^{\frac{3}{4}} \sqrt{d x + c} d^{3} \sqrt{\frac{c^{2} + d^{2} + \sqrt{c^{2} + d^{2}} c}{d^{2}}} - c^{3} d^{2} - c d^{4} - {\left(c^{2} d^{3} + d^{5}\right)} x - {\left(c^{2} d^{2} + d^{4}\right)} \sqrt{c^{2} + d^{2}}}{c^{2} + d^{2}}\right)}{4 \, {\left(c^{2} + d^{2}\right)}}"," ",0,"-1/4*(4*sqrt(2)*(c^2 + d^2)^(3/4)*sqrt(d^2)*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2)*arctan(-(sqrt(2)*(c^2 + d^2)^(3/4)*sqrt(d^2)*sqrt(d*x + c)*d*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2) - sqrt(2)*(c^2 + d^2)^(3/4)*sqrt(d^2)*sqrt((sqrt(2)*(c^2 + d^2)^(3/4)*sqrt(d*x + c)*d^3*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2) + c^3*d^2 + c*d^4 + (c^2*d^3 + d^5)*x + (c^2*d^2 + d^4)*sqrt(c^2 + d^2))/(c^2 + d^2))*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2) + (c^2 + d^2)^(3/2)*sqrt(d^2) + (c^3 + c*d^2)*sqrt(d^2))/(c^2*d^2 + d^4)) + 4*sqrt(2)*(c^2 + d^2)^(3/4)*sqrt(d^2)*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2)*arctan(-(sqrt(2)*(c^2 + d^2)^(3/4)*sqrt(d^2)*sqrt(d*x + c)*d*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2) - sqrt(2)*(c^2 + d^2)^(3/4)*sqrt(d^2)*sqrt(-(sqrt(2)*(c^2 + d^2)^(3/4)*sqrt(d*x + c)*d^3*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2) - c^3*d^2 - c*d^4 - (c^2*d^3 + d^5)*x - (c^2*d^2 + d^4)*sqrt(c^2 + d^2))/(c^2 + d^2))*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2) - (c^2 + d^2)^(3/2)*sqrt(d^2) - (c^3 + c*d^2)*sqrt(d^2))/(c^2*d^2 + d^4)) + sqrt(2)*(c^2 + d^2 - sqrt(c^2 + d^2)*c)*(c^2 + d^2)^(1/4)*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2)*log((sqrt(2)*(c^2 + d^2)^(3/4)*sqrt(d*x + c)*d^3*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2) + c^3*d^2 + c*d^4 + (c^2*d^3 + d^5)*x + (c^2*d^2 + d^4)*sqrt(c^2 + d^2))/(c^2 + d^2)) - sqrt(2)*(c^2 + d^2 - sqrt(c^2 + d^2)*c)*(c^2 + d^2)^(1/4)*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2)*log(-(sqrt(2)*(c^2 + d^2)^(3/4)*sqrt(d*x + c)*d^3*sqrt((c^2 + d^2 + sqrt(c^2 + d^2)*c)/d^2) - c^3*d^2 - c*d^4 - (c^2*d^3 + d^5)*x - (c^2*d^2 + d^4)*sqrt(c^2 + d^2))/(c^2 + d^2)))/(c^2 + d^2)","B",0
650,1,40,0,0.399751," ","integrate((2+3*x)^(1/2)/(-x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{5} \log\left(\frac{2 \, \sqrt{5} \sqrt{3 \, x + 2} + 3 \, x + 7}{x - 1}\right) - \arctan\left(\sqrt{3 \, x + 2}\right)"," ",0,"1/2*sqrt(5)*log((2*sqrt(5)*sqrt(3*x + 2) + 3*x + 7)/(x - 1)) - arctan(sqrt(3*x + 2))","A",0
651,1,295,0,0.432921," ","integrate((d*x+c)^(1/2)/(-x^2+1),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{c - d} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c - d} + 2 \, c - d}{x + 1}\right) + \frac{1}{2} \, \sqrt{c + d} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c + d} + 2 \, c + d}{x - 1}\right), -\sqrt{-c + d} \arctan\left(-\frac{\sqrt{d x + c} \sqrt{-c + d}}{c - d}\right) + \frac{1}{2} \, \sqrt{c + d} \log\left(\frac{d x + 2 \, \sqrt{d x + c} \sqrt{c + d} + 2 \, c + d}{x - 1}\right), -\sqrt{-c - d} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c - d}}{c + d}\right) + \frac{1}{2} \, \sqrt{c - d} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c - d} + 2 \, c - d}{x + 1}\right), -\sqrt{-c + d} \arctan\left(-\frac{\sqrt{d x + c} \sqrt{-c + d}}{c - d}\right) - \sqrt{-c - d} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c - d}}{c + d}\right)\right]"," ",0,"[1/2*sqrt(c - d)*log((d*x - 2*sqrt(d*x + c)*sqrt(c - d) + 2*c - d)/(x + 1)) + 1/2*sqrt(c + d)*log((d*x + 2*sqrt(d*x + c)*sqrt(c + d) + 2*c + d)/(x - 1)), -sqrt(-c + d)*arctan(-sqrt(d*x + c)*sqrt(-c + d)/(c - d)) + 1/2*sqrt(c + d)*log((d*x + 2*sqrt(d*x + c)*sqrt(c + d) + 2*c + d)/(x - 1)), -sqrt(-c - d)*arctan(sqrt(d*x + c)*sqrt(-c - d)/(c + d)) + 1/2*sqrt(c - d)*log((d*x - 2*sqrt(d*x + c)*sqrt(c - d) + 2*c - d)/(x + 1)), -sqrt(-c + d)*arctan(-sqrt(d*x + c)*sqrt(-c + d)/(c - d)) - sqrt(-c - d)*arctan(sqrt(d*x + c)*sqrt(-c - d)/(c + d))]","A",0
652,1,311,0,0.414908," ","integrate((2+3*x)^(1/2)/(b*x^2+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-\frac{3 \, a b \sqrt{-\frac{1}{a b^{3}}} + 2}{a b}} \log\left(a b^{2} \sqrt{-\frac{3 \, a b \sqrt{-\frac{1}{a b^{3}}} + 2}{a b}} \sqrt{-\frac{1}{a b^{3}}} + \sqrt{3 \, x + 2}\right) + \frac{1}{2} \, \sqrt{-\frac{3 \, a b \sqrt{-\frac{1}{a b^{3}}} + 2}{a b}} \log\left(-a b^{2} \sqrt{-\frac{3 \, a b \sqrt{-\frac{1}{a b^{3}}} + 2}{a b}} \sqrt{-\frac{1}{a b^{3}}} + \sqrt{3 \, x + 2}\right) + \frac{1}{2} \, \sqrt{\frac{3 \, a b \sqrt{-\frac{1}{a b^{3}}} - 2}{a b}} \log\left(a b^{2} \sqrt{\frac{3 \, a b \sqrt{-\frac{1}{a b^{3}}} - 2}{a b}} \sqrt{-\frac{1}{a b^{3}}} + \sqrt{3 \, x + 2}\right) - \frac{1}{2} \, \sqrt{\frac{3 \, a b \sqrt{-\frac{1}{a b^{3}}} - 2}{a b}} \log\left(-a b^{2} \sqrt{\frac{3 \, a b \sqrt{-\frac{1}{a b^{3}}} - 2}{a b}} \sqrt{-\frac{1}{a b^{3}}} + \sqrt{3 \, x + 2}\right)"," ",0,"-1/2*sqrt(-(3*a*b*sqrt(-1/(a*b^3)) + 2)/(a*b))*log(a*b^2*sqrt(-(3*a*b*sqrt(-1/(a*b^3)) + 2)/(a*b))*sqrt(-1/(a*b^3)) + sqrt(3*x + 2)) + 1/2*sqrt(-(3*a*b*sqrt(-1/(a*b^3)) + 2)/(a*b))*log(-a*b^2*sqrt(-(3*a*b*sqrt(-1/(a*b^3)) + 2)/(a*b))*sqrt(-1/(a*b^3)) + sqrt(3*x + 2)) + 1/2*sqrt((3*a*b*sqrt(-1/(a*b^3)) - 2)/(a*b))*log(a*b^2*sqrt((3*a*b*sqrt(-1/(a*b^3)) - 2)/(a*b))*sqrt(-1/(a*b^3)) + sqrt(3*x + 2)) - 1/2*sqrt((3*a*b*sqrt(-1/(a*b^3)) - 2)/(a*b))*log(-a*b^2*sqrt((3*a*b*sqrt(-1/(a*b^3)) - 2)/(a*b))*sqrt(-1/(a*b^3)) + sqrt(3*x + 2))","A",0
653,1,299,0,0.418133," ","integrate((2+3*x)^(1/2)/(-b*x^2+a),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{3 \, a b \sqrt{\frac{1}{a b^{3}}} + 2}{a b}} \log\left(a b^{2} \sqrt{\frac{3 \, a b \sqrt{\frac{1}{a b^{3}}} + 2}{a b}} \sqrt{\frac{1}{a b^{3}}} + \sqrt{3 \, x + 2}\right) - \frac{1}{2} \, \sqrt{\frac{3 \, a b \sqrt{\frac{1}{a b^{3}}} + 2}{a b}} \log\left(-a b^{2} \sqrt{\frac{3 \, a b \sqrt{\frac{1}{a b^{3}}} + 2}{a b}} \sqrt{\frac{1}{a b^{3}}} + \sqrt{3 \, x + 2}\right) - \frac{1}{2} \, \sqrt{-\frac{3 \, a b \sqrt{\frac{1}{a b^{3}}} - 2}{a b}} \log\left(a b^{2} \sqrt{-\frac{3 \, a b \sqrt{\frac{1}{a b^{3}}} - 2}{a b}} \sqrt{\frac{1}{a b^{3}}} + \sqrt{3 \, x + 2}\right) + \frac{1}{2} \, \sqrt{-\frac{3 \, a b \sqrt{\frac{1}{a b^{3}}} - 2}{a b}} \log\left(-a b^{2} \sqrt{-\frac{3 \, a b \sqrt{\frac{1}{a b^{3}}} - 2}{a b}} \sqrt{\frac{1}{a b^{3}}} + \sqrt{3 \, x + 2}\right)"," ",0,"1/2*sqrt((3*a*b*sqrt(1/(a*b^3)) + 2)/(a*b))*log(a*b^2*sqrt((3*a*b*sqrt(1/(a*b^3)) + 2)/(a*b))*sqrt(1/(a*b^3)) + sqrt(3*x + 2)) - 1/2*sqrt((3*a*b*sqrt(1/(a*b^3)) + 2)/(a*b))*log(-a*b^2*sqrt((3*a*b*sqrt(1/(a*b^3)) + 2)/(a*b))*sqrt(1/(a*b^3)) + sqrt(3*x + 2)) - 1/2*sqrt(-(3*a*b*sqrt(1/(a*b^3)) - 2)/(a*b))*log(a*b^2*sqrt(-(3*a*b*sqrt(1/(a*b^3)) - 2)/(a*b))*sqrt(1/(a*b^3)) + sqrt(3*x + 2)) + 1/2*sqrt(-(3*a*b*sqrt(1/(a*b^3)) - 2)/(a*b))*log(-a*b^2*sqrt(-(3*a*b*sqrt(1/(a*b^3)) - 2)/(a*b))*sqrt(1/(a*b^3)) + sqrt(3*x + 2))","B",0
654,1,260,0,0.425801," ","integrate((1+x)^(1/2)/(x^2+1),x, algorithm=""fricas"")","\frac{1}{8} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} \log\left(\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + x + \sqrt{2} + 1\right) - \frac{1}{8} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} \log\left(-\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + x + \sqrt{2} + 1\right) - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + \frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 2 \, x + 2 \, \sqrt{2} + 2} \sqrt{2 \, \sqrt{2} + 4} - \sqrt{2} - 1\right) - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + \frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{-2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 2 \, x + 2 \, \sqrt{2} + 2} \sqrt{2 \, \sqrt{2} + 4} + \sqrt{2} + 1\right)"," ",0,"1/8*2^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2)*log(1/2*2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + x + sqrt(2) + 1) - 1/8*2^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2)*log(-1/2*2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + x + sqrt(2) + 1) - 1/2*2^(3/4)*sqrt(2*sqrt(2) + 4)*arctan(-1/2*2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 1/2*2^(1/4)*sqrt(2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 2*x + 2*sqrt(2) + 2)*sqrt(2*sqrt(2) + 4) - sqrt(2) - 1) - 1/2*2^(3/4)*sqrt(2*sqrt(2) + 4)*arctan(-1/2*2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 1/2*2^(1/4)*sqrt(-2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 2*x + 2*sqrt(2) + 2)*sqrt(2*sqrt(2) + 4) + sqrt(2) + 1)","A",0
655,1,269,0,0.431310," ","integrate(1/(x^2+1)/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 1\right)} \log\left(2 \cdot 2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4\right) - \frac{1}{8} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 1\right)} \log\left(-2 \cdot 2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4\right) - \frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{4} \cdot 2^{\frac{3}{4}} \sqrt{2 \cdot 2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 4} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} - \sqrt{2} - 1\right) - \frac{1}{2} \cdot 2^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{4} \cdot 2^{\frac{3}{4}} \sqrt{-2 \cdot 2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 4} - \frac{1}{2} \cdot 2^{\frac{3}{4}} \sqrt{x + 1} \sqrt{2 \, \sqrt{2} + 4} + \sqrt{2} + 1\right)"," ",0,"1/8*2^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 1)*log(2*2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4) - 1/8*2^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 1)*log(-2*2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4) - 1/2*2^(1/4)*sqrt(2*sqrt(2) + 4)*arctan(1/4*2^(3/4)*sqrt(2*2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4)*sqrt(2*sqrt(2) + 4) - 1/2*2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) - sqrt(2) - 1) - 1/2*2^(1/4)*sqrt(2*sqrt(2) + 4)*arctan(1/4*2^(3/4)*sqrt(-2*2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4)*sqrt(2*sqrt(2) + 4) - 1/2*2^(3/4)*sqrt(x + 1)*sqrt(2*sqrt(2) + 4) + sqrt(2) + 1)","A",0
656,1,436,0,0.438118," ","integrate((-1+x)^(1/2)/(x^2+1)^3,x, algorithm=""fricas"")","-\frac{92 \cdot 278258^{\frac{1}{4}} \sqrt{2} {\left(x^{4} + 2 \, x^{2} + 1\right)} \sqrt{-393142 \, \sqrt{2} + 556516} \arctan\left(\frac{1}{109810067572} \cdot 278258^{\frac{3}{4}} \sqrt{46} \sqrt{373 \cdot 278258^{\frac{1}{4}} \sqrt{x - 1} {\left(11 \, \sqrt{2} + 14\right)} \sqrt{-393142 \, \sqrt{2} + 556516} + 6399934 \, x + 6399934 \, \sqrt{2} - 6399934} {\left(7 \, \sqrt{2} + 11\right)} \sqrt{-393142 \, \sqrt{2} + 556516} - \frac{1}{6399934} \cdot 278258^{\frac{3}{4}} \sqrt{x - 1} {\left(7 \, \sqrt{2} + 11\right)} \sqrt{-393142 \, \sqrt{2} + 556516} - \sqrt{2} + 1\right) + 92 \cdot 278258^{\frac{1}{4}} \sqrt{2} {\left(x^{4} + 2 \, x^{2} + 1\right)} \sqrt{-393142 \, \sqrt{2} + 556516} \arctan\left(\frac{1}{109810067572} \cdot 278258^{\frac{3}{4}} \sqrt{46} \sqrt{-373 \cdot 278258^{\frac{1}{4}} \sqrt{x - 1} {\left(11 \, \sqrt{2} + 14\right)} \sqrt{-393142 \, \sqrt{2} + 556516} + 6399934 \, x + 6399934 \, \sqrt{2} - 6399934} {\left(7 \, \sqrt{2} + 11\right)} \sqrt{-393142 \, \sqrt{2} + 556516} - \frac{1}{6399934} \cdot 278258^{\frac{3}{4}} \sqrt{x - 1} {\left(7 \, \sqrt{2} + 11\right)} \sqrt{-393142 \, \sqrt{2} + 556516} + \sqrt{2} - 1\right) + 278258^{\frac{1}{4}} {\left(746 \, x^{4} + 1492 \, x^{2} + 527 \, \sqrt{2} {\left(x^{4} + 2 \, x^{2} + 1\right)} + 746\right)} \sqrt{-393142 \, \sqrt{2} + 556516} \log\left(\frac{373}{46} \cdot 278258^{\frac{1}{4}} \sqrt{x - 1} {\left(11 \, \sqrt{2} + 14\right)} \sqrt{-393142 \, \sqrt{2} + 556516} + 139129 \, x + 139129 \, \sqrt{2} - 139129\right) - 278258^{\frac{1}{4}} {\left(746 \, x^{4} + 1492 \, x^{2} + 527 \, \sqrt{2} {\left(x^{4} + 2 \, x^{2} + 1\right)} + 746\right)} \sqrt{-393142 \, \sqrt{2} + 556516} \log\left(-\frac{373}{46} \cdot 278258^{\frac{1}{4}} \sqrt{x - 1} {\left(11 \, \sqrt{2} + 14\right)} \sqrt{-393142 \, \sqrt{2} + 556516} + 139129 \, x + 139129 \, \sqrt{2} - 139129\right) - 137264 \, {\left(11 \, x^{3} - x^{2} + 19 \, x - 1\right)} \sqrt{x - 1}}{4392448 \, {\left(x^{4} + 2 \, x^{2} + 1\right)}}"," ",0,"-1/4392448*(92*278258^(1/4)*sqrt(2)*(x^4 + 2*x^2 + 1)*sqrt(-393142*sqrt(2) + 556516)*arctan(1/109810067572*278258^(3/4)*sqrt(46)*sqrt(373*278258^(1/4)*sqrt(x - 1)*(11*sqrt(2) + 14)*sqrt(-393142*sqrt(2) + 556516) + 6399934*x + 6399934*sqrt(2) - 6399934)*(7*sqrt(2) + 11)*sqrt(-393142*sqrt(2) + 556516) - 1/6399934*278258^(3/4)*sqrt(x - 1)*(7*sqrt(2) + 11)*sqrt(-393142*sqrt(2) + 556516) - sqrt(2) + 1) + 92*278258^(1/4)*sqrt(2)*(x^4 + 2*x^2 + 1)*sqrt(-393142*sqrt(2) + 556516)*arctan(1/109810067572*278258^(3/4)*sqrt(46)*sqrt(-373*278258^(1/4)*sqrt(x - 1)*(11*sqrt(2) + 14)*sqrt(-393142*sqrt(2) + 556516) + 6399934*x + 6399934*sqrt(2) - 6399934)*(7*sqrt(2) + 11)*sqrt(-393142*sqrt(2) + 556516) - 1/6399934*278258^(3/4)*sqrt(x - 1)*(7*sqrt(2) + 11)*sqrt(-393142*sqrt(2) + 556516) + sqrt(2) - 1) + 278258^(1/4)*(746*x^4 + 1492*x^2 + 527*sqrt(2)*(x^4 + 2*x^2 + 1) + 746)*sqrt(-393142*sqrt(2) + 556516)*log(373/46*278258^(1/4)*sqrt(x - 1)*(11*sqrt(2) + 14)*sqrt(-393142*sqrt(2) + 556516) + 139129*x + 139129*sqrt(2) - 139129) - 278258^(1/4)*(746*x^4 + 1492*x^2 + 527*sqrt(2)*(x^4 + 2*x^2 + 1) + 746)*sqrt(-393142*sqrt(2) + 556516)*log(-373/46*278258^(1/4)*sqrt(x - 1)*(11*sqrt(2) + 14)*sqrt(-393142*sqrt(2) + 556516) + 139129*x + 139129*sqrt(2) - 139129) - 137264*(11*x^3 - x^2 + 19*x - 1)*sqrt(x - 1))/(x^4 + 2*x^2 + 1)","B",0
657,0,0,0,0.422806," ","integrate((e*x+d)^(3/2)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + a} {\left(e x + d\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(e*x + d)^(3/2), x)","F",0
658,0,0,0,0.428437," ","integrate((e*x+d)^(1/2)*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + a} \sqrt{e x + d}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d), x)","F",0
659,0,0,0,0.413795," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a}}{\sqrt{e x + d}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)/sqrt(e*x + d), x)","F",0
660,0,0,0,0.415999," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
661,0,0,0,0.419427," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
662,0,0,0,0.414726," ","integrate((c*x^2+a)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
663,0,0,0,0.413146," ","integrate((e*x+d)^(3/2)*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e x^{3} + c d x^{2} + a e x + a d\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}, x\right)"," ",0,"integral((c*e*x^3 + c*d*x^2 + a*e*x + a*d)*sqrt(c*x^2 + a)*sqrt(e*x + d), x)","F",0
664,0,0,0,0.404060," ","integrate((c*x^2+a)^(3/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x + d}, x\right)"," ",0,"integral((c*x^2 + a)^(3/2)*sqrt(e*x + d), x)","F",0
665,0,0,0,0.424739," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((c*x^2 + a)^(3/2)/sqrt(e*x + d), x)","F",0
666,0,0,0,0.406679," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c*x^2 + a)^(3/2)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
667,0,0,0,0.421801," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c*x^2 + a)^(3/2)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
668,0,0,0,0.421653," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((c*x^2 + a)^(3/2)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
669,0,0,0,0.429201," ","integrate((c*x^2+a)^(3/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{5} x^{5} + 5 \, d e^{4} x^{4} + 10 \, d^{2} e^{3} x^{3} + 10 \, d^{3} e^{2} x^{2} + 5 \, d^{4} e x + d^{5}}, x\right)"," ",0,"integral((c*x^2 + a)^(3/2)*sqrt(e*x + d)/(e^5*x^5 + 5*d*e^4*x^4 + 10*d^2*e^3*x^3 + 10*d^3*e^2*x^2 + 5*d^4*e*x + d^5), x)","F",0
670,0,0,0,0.422271," ","integrate((c*x^2+a)^(5/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} x^{4} + 2 \, a c x^{2} + a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}, x\right)"," ",0,"integral((c^2*x^4 + 2*a*c*x^2 + a^2)*sqrt(c*x^2 + a)*sqrt(e*x + d), x)","F",0
671,0,0,0,0.414592," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, a c x^{2} + a^{2}\right)} \sqrt{c x^{2} + a}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((c^2*x^4 + 2*a*c*x^2 + a^2)*sqrt(c*x^2 + a)/sqrt(e*x + d), x)","F",0
672,0,0,0,0.436321," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, a c x^{2} + a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c^2*x^4 + 2*a*c*x^2 + a^2)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
673,0,0,0,0.438088," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, a c x^{2} + a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c^2*x^4 + 2*a*c*x^2 + a^2)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
674,0,0,0,0.415747," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, a c x^{2} + a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((c^2*x^4 + 2*a*c*x^2 + a^2)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
675,0,0,0,0.440660," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, a c x^{2} + a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{5} x^{5} + 5 \, d e^{4} x^{4} + 10 \, d^{2} e^{3} x^{3} + 10 \, d^{3} e^{2} x^{2} + 5 \, d^{4} e x + d^{5}}, x\right)"," ",0,"integral((c^2*x^4 + 2*a*c*x^2 + a^2)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^5*x^5 + 5*d*e^4*x^4 + 10*d^2*e^3*x^3 + 10*d^3*e^2*x^2 + 5*d^4*e*x + d^5), x)","F",0
676,0,0,0,0.456342," ","integrate((c*x^2+a)^(5/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, a c x^{2} + a^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{e^{6} x^{6} + 6 \, d e^{5} x^{5} + 15 \, d^{2} e^{4} x^{4} + 20 \, d^{3} e^{3} x^{3} + 15 \, d^{4} e^{2} x^{2} + 6 \, d^{5} e x + d^{6}}, x\right)"," ",0,"integral((c^2*x^4 + 2*a*c*x^2 + a^2)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(e^6*x^6 + 6*d*e^5*x^5 + 15*d^2*e^4*x^4 + 20*d^3*e^3*x^3 + 15*d^4*e^2*x^2 + 6*d^5*e*x + d^6), x)","F",0
677,0,0,0,0.405727," ","integrate((e*x+d)^(7/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(e*x + d)/sqrt(c*x^2 + a), x)","F",0
678,0,0,0,0.411135," ","integrate((e*x+d)^(5/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(e*x + d)/sqrt(c*x^2 + a), x)","F",0
679,0,0,0,0.410128," ","integrate((e*x+d)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((e*x + d)^(3/2)/sqrt(c*x^2 + a), x)","F",0
680,0,0,0,0.415165," ","integrate((e*x+d)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x + d}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral(sqrt(e*x + d)/sqrt(c*x^2 + a), x)","F",0
681,0,0,0,0.416723," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c e x^{3} + c d x^{2} + a e x + a d}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c*e*x^3 + c*d*x^2 + a*e*x + a*d), x)","F",0
682,0,0,0,0.412777," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c e^{2} x^{4} + 2 \, c d e x^{3} + 2 \, a d e x + a d^{2} + {\left(c d^{2} + a e^{2}\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c*e^2*x^4 + 2*c*d*e*x^3 + 2*a*d*e*x + a*d^2 + (c*d^2 + a*e^2)*x^2), x)","F",0
683,0,0,0,0.421601," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c e^{3} x^{5} + 3 \, c d e^{2} x^{4} + 3 \, a d^{2} e x + a d^{3} + {\left(3 \, c d^{2} e + a e^{3}\right)} x^{3} + {\left(c d^{3} + 3 \, a d e^{2}\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c*e^3*x^5 + 3*c*d*e^2*x^4 + 3*a*d^2*e*x + a*d^3 + (3*c*d^2*e + a*e^3)*x^3 + (c*d^3 + 3*a*d*e^2)*x^2), x)","F",0
684,0,0,0,0.422696," ","integrate(1/(e*x+d)^(7/2)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c e^{4} x^{6} + 4 \, c d e^{3} x^{5} + 4 \, a d^{3} e x + a d^{4} + {\left(6 \, c d^{2} e^{2} + a e^{4}\right)} x^{4} + 4 \, {\left(c d^{3} e + a d e^{3}\right)} x^{3} + {\left(c d^{4} + 6 \, a d^{2} e^{2}\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c*e^4*x^6 + 4*c*d*e^3*x^5 + 4*a*d^3*e*x + a*d^4 + (6*c*d^2*e^2 + a*e^4)*x^4 + 4*(c*d^3*e + a*d*e^3)*x^3 + (c*d^4 + 6*a*d^2*e^2)*x^2), x)","F",0
685,0,0,0,0.425017," ","integrate((e*x+d)^(7/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
686,0,0,0,0.419351," ","integrate((e*x+d)^(5/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
687,0,0,0,0.418163," ","integrate((e*x+d)^(3/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(e x + d\right)}^{\frac{3}{2}}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(e*x + d)^(3/2)/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
688,0,0,0,0.408711," ","integrate((e*x+d)^(1/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
689,0,0,0,0.421110," ","integrate(1/(c*x^2+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{2} e x^{5} + c^{2} d x^{4} + 2 \, a c e x^{3} + 2 \, a c d x^{2} + a^{2} e x + a^{2} d}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^2*e*x^5 + c^2*d*x^4 + 2*a*c*e*x^3 + 2*a*c*d*x^2 + a^2*e*x + a^2*d), x)","F",0
690,0,0,0,0.420858," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{2} e^{2} x^{6} + 2 \, c^{2} d e x^{5} + 4 \, a c d e x^{3} + 2 \, a^{2} d e x + {\left(c^{2} d^{2} + 2 \, a c e^{2}\right)} x^{4} + a^{2} d^{2} + {\left(2 \, a c d^{2} + a^{2} e^{2}\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^2*e^2*x^6 + 2*c^2*d*e*x^5 + 4*a*c*d*e*x^3 + 2*a^2*d*e*x + (c^2*d^2 + 2*a*c*e^2)*x^4 + a^2*d^2 + (2*a*c*d^2 + a^2*e^2)*x^2), x)","F",0
691,0,0,0,0.445830," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{2} e^{3} x^{7} + 3 \, c^{2} d e^{2} x^{6} + 3 \, a^{2} d^{2} e x + {\left(3 \, c^{2} d^{2} e + 2 \, a c e^{3}\right)} x^{5} + a^{2} d^{3} + {\left(c^{2} d^{3} + 6 \, a c d e^{2}\right)} x^{4} + {\left(6 \, a c d^{2} e + a^{2} e^{3}\right)} x^{3} + {\left(2 \, a c d^{3} + 3 \, a^{2} d e^{2}\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^2*e^3*x^7 + 3*c^2*d*e^2*x^6 + 3*a^2*d^2*e*x + (3*c^2*d^2*e + 2*a*c*e^3)*x^5 + a^2*d^3 + (c^2*d^3 + 6*a*c*d*e^2)*x^4 + (6*a*c*d^2*e + a^2*e^3)*x^3 + (2*a*c*d^3 + 3*a^2*d*e^2)*x^2), x)","F",0
692,0,0,0,0.431870," ","integrate((e*x+d)^(9/2)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
693,0,0,0,0.416249," ","integrate((e*x+d)^(7/2)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
694,0,0,0,0.408571," ","integrate((e*x+d)^(5/2)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
695,0,0,0,0.407698," ","integrate((e*x+d)^(3/2)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(e x + d\right)}^{\frac{3}{2}}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(e*x + d)^(3/2)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
696,0,0,0,0.425967," ","integrate((e*x+d)^(1/2)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
697,0,0,0,0.421933," ","integrate(1/(c*x^2+a)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{3} e x^{7} + c^{3} d x^{6} + 3 \, a c^{2} e x^{5} + 3 \, a c^{2} d x^{4} + 3 \, a^{2} c e x^{3} + 3 \, a^{2} c d x^{2} + a^{3} e x + a^{3} d}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^3*e*x^7 + c^3*d*x^6 + 3*a*c^2*e*x^5 + 3*a*c^2*d*x^4 + 3*a^2*c*e*x^3 + 3*a^2*c*d*x^2 + a^3*e*x + a^3*d), x)","F",0
698,0,0,0,0.447495," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} \sqrt{e x + d}}{c^{3} e^{2} x^{8} + 2 \, c^{3} d e x^{7} + 6 \, a c^{2} d e x^{5} + 6 \, a^{2} c d e x^{3} + {\left(c^{3} d^{2} + 3 \, a c^{2} e^{2}\right)} x^{6} + 2 \, a^{3} d e x + a^{3} d^{2} + 3 \, {\left(a c^{2} d^{2} + a^{2} c e^{2}\right)} x^{4} + {\left(3 \, a^{2} c d^{2} + a^{3} e^{2}\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*sqrt(e*x + d)/(c^3*e^2*x^8 + 2*c^3*d*e*x^7 + 6*a*c^2*d*e*x^5 + 6*a^2*c*d*e*x^3 + (c^3*d^2 + 3*a*c^2*e^2)*x^6 + 2*a^3*d*e*x + a^3*d^2 + 3*(a*c^2*d^2 + a^2*c*e^2)*x^4 + (3*a^2*c*d^2 + a^3*e^2)*x^2), x)","F",0
699,1,337,0,40.916360," ","integrate(1/(e*x+d)/(3*e^2*x^2+d^2)^(1/3),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{3} d \sqrt{4^{\frac{1}{3}} {\left(d^{2}\right)}^{\frac{1}{3}}} \arctan\left(\frac{\sqrt{3} {\left(2 \cdot 4^{\frac{2}{3}} {\left(3 \, e^{2} x^{2} + d^{2}\right)}^{\frac{2}{3}} {\left(d^{2}\right)}^{\frac{2}{3}} {\left(e x - d\right)} + 4^{\frac{1}{3}} {\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(d^{2}\right)}^{\frac{1}{3}} + 4 \, {\left(d e^{2} x^{2} - 2 \, d^{2} e x + d^{3}\right)} {\left(3 \, e^{2} x^{2} + d^{2}\right)}^{\frac{1}{3}}\right)} \sqrt{4^{\frac{1}{3}} {\left(d^{2}\right)}^{\frac{1}{3}}}}{6 \, {\left(d e^{3} x^{3} - 9 \, d^{2} e^{2} x^{2} + 3 \, d^{3} e x - 3 \, d^{4}\right)}}\right) + 4^{\frac{2}{3}} {\left(d^{2}\right)}^{\frac{2}{3}} \log\left(\frac{4^{\frac{2}{3}} {\left(3 \, e^{2} x^{2} + d^{2}\right)}^{\frac{2}{3}} {\left(d^{2}\right)}^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(e^{2} x^{2} - 2 \, d e x + d^{2}\right)} {\left(d^{2}\right)}^{\frac{1}{3}} - 2 \, {\left(3 \, e^{2} x^{2} + d^{2}\right)}^{\frac{1}{3}} {\left(d e x - d^{2}\right)}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \cdot 4^{\frac{2}{3}} {\left(d^{2}\right)}^{\frac{2}{3}} \log\left(\frac{4^{\frac{1}{3}} {\left(d^{2}\right)}^{\frac{1}{3}} {\left(e x - d\right)} + 2 \, {\left(3 \, e^{2} x^{2} + d^{2}\right)}^{\frac{1}{3}} d}{e x + d}\right)}{24 \, d^{2} e}"," ",0,"-1/24*(4*sqrt(3)*d*sqrt(4^(1/3)*(d^2)^(1/3))*arctan(1/6*sqrt(3)*(2*4^(2/3)*(3*e^2*x^2 + d^2)^(2/3)*(d^2)^(2/3)*(e*x - d) + 4^(1/3)*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(d^2)^(1/3) + 4*(d*e^2*x^2 - 2*d^2*e*x + d^3)*(3*e^2*x^2 + d^2)^(1/3))*sqrt(4^(1/3)*(d^2)^(1/3))/(d*e^3*x^3 - 9*d^2*e^2*x^2 + 3*d^3*e*x - 3*d^4)) + 4^(2/3)*(d^2)^(2/3)*log((4^(2/3)*(3*e^2*x^2 + d^2)^(2/3)*(d^2)^(2/3) + 4^(1/3)*(e^2*x^2 - 2*d*e*x + d^2)*(d^2)^(1/3) - 2*(3*e^2*x^2 + d^2)^(1/3)*(d*e*x - d^2))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*4^(2/3)*(d^2)^(2/3)*log((4^(1/3)*(d^2)^(1/3)*(e*x - d) + 2*(3*e^2*x^2 + d^2)^(1/3)*d)/(e*x + d)))/(d^2*e)","B",0
700,0,0,0,0.419755," ","integrate((2+3*x)^3/(27*x^2+4)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}{{\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)/(27*x^2 + 4)^(1/3), x)","F",0
701,0,0,0,0.415622," ","integrate((2+3*x)^2/(27*x^2+4)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{9 \, x^{2} + 12 \, x + 4}{{\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)/(27*x^2 + 4)^(1/3), x)","F",0
702,0,0,0,0.392673," ","integrate((2+3*x)/(27*x^2+4)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{3 \, x + 2}{{\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((3*x + 2)/(27*x^2 + 4)^(1/3), x)","F",0
703,1,200,0,2.680955," ","integrate(1/(2+3*x)/(27*x^2+4)^(1/3),x, algorithm=""fricas"")","-\frac{1}{36} \, \sqrt{6} 2^{\frac{1}{6}} \arctan\left(\frac{2^{\frac{1}{6}} {\left(4 \, \sqrt{6} 2^{\frac{2}{3}} {\left(27 \, x^{2} + 4\right)}^{\frac{2}{3}} {\left(3 \, x - 2\right)} + \sqrt{6} 2^{\frac{1}{3}} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} + 4 \, \sqrt{6} {\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}} {\left(9 \, x^{2} - 12 \, x + 4\right)}\right)}}{18 \, {\left(9 \, x^{3} - 54 \, x^{2} + 12 \, x - 8\right)}}\right) - \frac{1}{72} \cdot 2^{\frac{2}{3}} \log\left(\frac{2 \cdot 2^{\frac{2}{3}} {\left(27 \, x^{2} + 4\right)}^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(9 \, x^{2} - 12 \, x + 4\right)} - 2 \, {\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}} {\left(3 \, x - 2\right)}}{9 \, x^{2} + 12 \, x + 4}\right) + \frac{1}{36} \cdot 2^{\frac{2}{3}} \log\left(\frac{2^{\frac{1}{3}} {\left(3 \, x - 2\right)} + 2 \, {\left(27 \, x^{2} + 4\right)}^{\frac{1}{3}}}{3 \, x + 2}\right)"," ",0,"-1/36*sqrt(6)*2^(1/6)*arctan(1/18*2^(1/6)*(4*sqrt(6)*2^(2/3)*(27*x^2 + 4)^(2/3)*(3*x - 2) + sqrt(6)*2^(1/3)*(27*x^3 + 54*x^2 + 36*x + 8) + 4*sqrt(6)*(27*x^2 + 4)^(1/3)*(9*x^2 - 12*x + 4))/(9*x^3 - 54*x^2 + 12*x - 8)) - 1/72*2^(2/3)*log((2*2^(2/3)*(27*x^2 + 4)^(2/3) + 2^(1/3)*(9*x^2 - 12*x + 4) - 2*(27*x^2 + 4)^(1/3)*(3*x - 2))/(9*x^2 + 12*x + 4)) + 1/36*2^(2/3)*log((2^(1/3)*(3*x - 2) + 2*(27*x^2 + 4)^(1/3))/(3*x + 2))","B",0
704,0,0,0,2.701761," ","integrate(1/(2+3*x)^2/(27*x^2+4)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{2} + 4\right)}^{\frac{2}{3}}}{243 \, x^{4} + 324 \, x^{3} + 144 \, x^{2} + 48 \, x + 16}, x\right)"," ",0,"integral((27*x^2 + 4)^(2/3)/(243*x^4 + 324*x^3 + 144*x^2 + 48*x + 16), x)","F",0
705,0,0,0,2.714218," ","integrate(1/(2+3*x)^3/(27*x^2+4)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{2} + 4\right)}^{\frac{2}{3}}}{729 \, x^{5} + 1458 \, x^{4} + 1080 \, x^{3} + 432 \, x^{2} + 144 \, x + 32}, x\right)"," ",0,"integral((27*x^2 + 4)^(2/3)/(729*x^5 + 1458*x^4 + 1080*x^3 + 432*x^2 + 144*x + 32), x)","F",0
706,0,0,0,0.425938," ","integrate((2+3*I*x)^3/(-27*x^2+4)^(1/3),x, algorithm=""fricas"")","\frac{630 \, x {\rm integral}\left(\frac{128 \, {\left(-27 \, x^{2} + 4\right)}^{\frac{2}{3}}}{63 \, {\left(27 \, x^{4} - 4 \, x^{2}\right)}}, x\right) + {\left(189 i \, x^{3} + 540 \, x^{2} - 588 i \, x - 320\right)} {\left(-27 \, x^{2} + 4\right)}^{\frac{2}{3}}}{630 \, x}"," ",0,"1/630*(630*x*integral(128/63*(-27*x^2 + 4)^(2/3)/(27*x^4 - 4*x^2), x) + (189*I*x^3 + 540*x^2 - 588*I*x - 320)*(-27*x^2 + 4)^(2/3))/x","F",0
707,0,0,0,0.424130," ","integrate((2+3*I*x)^2/(-27*x^2+4)^(1/3),x, algorithm=""fricas"")","\frac{21 \, x {\rm integral}\left(\frac{32 \, {\left(-27 \, x^{2} + 4\right)}^{\frac{2}{3}}}{21 \, {\left(27 \, x^{4} - 4 \, x^{2}\right)}}, x\right) + {\left(3 \, x^{2} - 7 i \, x - 8\right)} {\left(-27 \, x^{2} + 4\right)}^{\frac{2}{3}}}{21 \, x}"," ",0,"1/21*(21*x*integral(32/21*(-27*x^2 + 4)^(2/3)/(27*x^4 - 4*x^2), x) + (3*x^2 - 7*I*x - 8)*(-27*x^2 + 4)^(2/3))/x","F",0
708,0,0,0,0.414875," ","integrate((2+3*I*x)/(-27*x^2+4)^(1/3),x, algorithm=""fricas"")","\frac{36 \, x {\rm integral}\left(\frac{8 \, {\left(-27 \, x^{2} + 4\right)}^{\frac{2}{3}}}{9 \, {\left(27 \, x^{4} - 4 \, x^{2}\right)}}, x\right) + {\left(-27 \, x^{2} + 4\right)}^{\frac{2}{3}} {\left(-3 i \, x - 8\right)}}{36 \, x}"," ",0,"1/36*(36*x*integral(8/9*(-27*x^2 + 4)^(2/3)/(27*x^4 - 4*x^2), x) + (-27*x^2 + 4)^(2/3)*(-3*I*x - 8))/x","F",0
709,-1,0,0,0.000000," ","integrate(1/(2+3*I*x)/(-27*x^2+4)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
710,-1,0,0,0.000000," ","integrate(1/(2+3*I*x)^2/(-27*x^2+4)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
711,-1,0,0,0.000000," ","integrate(1/(2+3*I*x)^3/(-27*x^2+4)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
712,1,282,0,5.502781," ","integrate(1/(x^2+1)^(1/3)/(x+3^(1/2)),x, algorithm=""fricas"")","-\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \arctan\left(\frac{4^{\frac{1}{6}} \sqrt{3} {\left(6 \cdot 4^{\frac{2}{3}} {\left(x^{4} + 8 \, \sqrt{3} x^{3} - 18 \, x^{2} - 27\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(x^{6} + 99 \, x^{4} + 243 \, x^{2} + 12 \, \sqrt{3} {\left(x^{5} + 10 \, x^{3} + 9 \, x\right)} + 81\right)} + 4 \, {\left(21 \, x^{4} + 54 \, x^{2} + \sqrt{3} {\left(x^{5} - 42 \, x^{3} - 27 \, x\right)} + 81\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}\right)}}{6 \, {\left(x^{6} - 225 \, x^{4} - 405 \, x^{2} - 243\right)}}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \log\left(\frac{3 \cdot 4^{\frac{2}{3}} {\left(x^{2} - 2 \, \sqrt{3} x + 3\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(x^{4} + 18 \, x^{2} - 4 \, \sqrt{3} {\left(x^{3} + 3 \, x\right)} + 9\right)} + 2 \, {\left(9 \, x^{2} - \sqrt{3} {\left(x^{3} + 9 \, x\right)} + 9\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}}{x^{4} - 6 \, x^{2} + 9}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \log\left(\frac{4^{\frac{1}{3}} {\left(x^{2} - 2 \, \sqrt{3} x + 3\right)} + 2 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(\sqrt{3} x - 3\right)}}{x^{2} - 3}\right)"," ",0,"-1/6*4^(1/6)*sqrt(3)*arctan(1/6*4^(1/6)*sqrt(3)*(6*4^(2/3)*(x^4 + 8*sqrt(3)*x^3 - 18*x^2 - 27)*(x^2 + 1)^(2/3) + 4^(1/3)*(x^6 + 99*x^4 + 243*x^2 + 12*sqrt(3)*(x^5 + 10*x^3 + 9*x) + 81) + 4*(21*x^4 + 54*x^2 + sqrt(3)*(x^5 - 42*x^3 - 27*x) + 81)*(x^2 + 1)^(1/3))/(x^6 - 225*x^4 - 405*x^2 - 243)) - 1/24*4^(2/3)*log((3*4^(2/3)*(x^2 - 2*sqrt(3)*x + 3)*(x^2 + 1)^(2/3) + 4^(1/3)*(x^4 + 18*x^2 - 4*sqrt(3)*(x^3 + 3*x) + 9) + 2*(9*x^2 - sqrt(3)*(x^3 + 9*x) + 9)*(x^2 + 1)^(1/3))/(x^4 - 6*x^2 + 9)) + 1/12*4^(2/3)*log((4^(1/3)*(x^2 - 2*sqrt(3)*x + 3) + 2*(x^2 + 1)^(1/3)*(sqrt(3)*x - 3))/(x^2 - 3))","B",0
713,1,335,0,3.392247," ","integrate(1/(x^2+1)^(1/3)/(-x+3^(1/2)),x, algorithm=""fricas"")","\frac{1}{6} \cdot 4^{\frac{1}{6}} \sqrt{3} \left(-1\right)^{\frac{1}{3}} \arctan\left(\frac{4^{\frac{1}{6}} \sqrt{3} {\left(6 \cdot 4^{\frac{2}{3}} {\left(8 \, \sqrt{3} \left(-1\right)^{\frac{2}{3}} x^{3} - \left(-1\right)^{\frac{2}{3}} {\left(x^{4} - 18 \, x^{2} - 27\right)}\right)} {\left(x^{2} + 1\right)}^{\frac{2}{3}} - 4^{\frac{1}{3}} {\left(x^{6} + 99 \, x^{4} + 243 \, x^{2} - 12 \, \sqrt{3} {\left(x^{5} + 10 \, x^{3} + 9 \, x\right)} + 81\right)} - 4 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(\sqrt{3} \left(-1\right)^{\frac{1}{3}} {\left(x^{5} - 42 \, x^{3} - 27 \, x\right)} - 3 \, \left(-1\right)^{\frac{1}{3}} {\left(7 \, x^{4} + 18 \, x^{2} + 27\right)}\right)}\right)}}{6 \, {\left(x^{6} - 225 \, x^{4} - 405 \, x^{2} - 243\right)}}\right) - \frac{1}{24} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-\frac{3 \cdot 4^{\frac{2}{3}} {\left(x^{2} + 1\right)}^{\frac{2}{3}} {\left(2 \, \sqrt{3} \left(-1\right)^{\frac{1}{3}} x + \left(-1\right)^{\frac{1}{3}} {\left(x^{2} + 3\right)}\right)} - 4^{\frac{1}{3}} {\left(4 \, \sqrt{3} \left(-1\right)^{\frac{2}{3}} {\left(x^{3} + 3 \, x\right)} + \left(-1\right)^{\frac{2}{3}} {\left(x^{4} + 18 \, x^{2} + 9\right)}\right)} - 2 \, {\left(9 \, x^{2} + \sqrt{3} {\left(x^{3} + 9 \, x\right)} + 9\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}}{x^{4} - 6 \, x^{2} + 9}\right) + \frac{1}{12} \cdot 4^{\frac{2}{3}} \left(-1\right)^{\frac{1}{3}} \log\left(-\frac{4^{\frac{1}{3}} {\left(x^{2} + 2 \, \sqrt{3} x + 3\right)} + 2 \, {\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(\sqrt{3} \left(-1\right)^{\frac{1}{3}} x + 3 \, \left(-1\right)^{\frac{1}{3}}\right)}}{x^{2} - 3}\right)"," ",0,"1/6*4^(1/6)*sqrt(3)*(-1)^(1/3)*arctan(1/6*4^(1/6)*sqrt(3)*(6*4^(2/3)*(8*sqrt(3)*(-1)^(2/3)*x^3 - (-1)^(2/3)*(x^4 - 18*x^2 - 27))*(x^2 + 1)^(2/3) - 4^(1/3)*(x^6 + 99*x^4 + 243*x^2 - 12*sqrt(3)*(x^5 + 10*x^3 + 9*x) + 81) - 4*(x^2 + 1)^(1/3)*(sqrt(3)*(-1)^(1/3)*(x^5 - 42*x^3 - 27*x) - 3*(-1)^(1/3)*(7*x^4 + 18*x^2 + 27)))/(x^6 - 225*x^4 - 405*x^2 - 243)) - 1/24*4^(2/3)*(-1)^(1/3)*log(-(3*4^(2/3)*(x^2 + 1)^(2/3)*(2*sqrt(3)*(-1)^(1/3)*x + (-1)^(1/3)*(x^2 + 3)) - 4^(1/3)*(4*sqrt(3)*(-1)^(2/3)*(x^3 + 3*x) + (-1)^(2/3)*(x^4 + 18*x^2 + 9)) - 2*(9*x^2 + sqrt(3)*(x^3 + 9*x) + 9)*(x^2 + 1)^(1/3))/(x^4 - 6*x^2 + 9)) + 1/12*4^(2/3)*(-1)^(1/3)*log(-(4^(1/3)*(x^2 + 2*sqrt(3)*x + 3) + 2*(x^2 + 1)^(1/3)*(sqrt(3)*(-1)^(1/3)*x + 3*(-1)^(1/3)))/(x^2 - 3))","B",0
714,1,113,0,0.693661," ","integrate(1/(3-x)/(-x^2+1)^(1/3),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{3} \arctan\left(\frac{18031 \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(x + 1\right)} + \sqrt{3} {\left(5054 \, x^{2} - 8497 \, x + 23659\right)} + 57889 \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{6859 \, x^{2} + 240699 \, x - 220122}\right) + \frac{1}{8} \, \log\left(\frac{x^{2} + 6 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(x + 1\right)} - 6 \, x + 12 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 9}{x^{2} - 6 \, x + 9}\right)"," ",0,"-1/4*sqrt(3)*arctan((18031*sqrt(3)*(-x^2 + 1)^(1/3)*(x + 1) + sqrt(3)*(5054*x^2 - 8497*x + 23659) + 57889*sqrt(3)*(-x^2 + 1)^(2/3))/(6859*x^2 + 240699*x - 220122)) + 1/8*log((x^2 + 6*(-x^2 + 1)^(1/3)*(x + 1) - 6*x + 12*(-x^2 + 1)^(2/3) + 9)/(x^2 - 6*x + 9))","A",0
715,1,115,0,0.691941," ","integrate(1/(3+x)/(-x^2+1)^(1/3),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{3} \arctan\left(-\frac{18031 \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(x - 1\right)} - \sqrt{3} {\left(5054 \, x^{2} + 8497 \, x + 23659\right)} - 57889 \, \sqrt{3} {\left(-x^{2} + 1\right)}^{\frac{2}{3}}}{6859 \, x^{2} - 240699 \, x - 220122}\right) - \frac{1}{8} \, \log\left(\frac{x^{2} - 6 \, {\left(-x^{2} + 1\right)}^{\frac{1}{3}} {\left(x - 1\right)} + 6 \, x + 12 \, {\left(-x^{2} + 1\right)}^{\frac{2}{3}} + 9}{x^{2} + 6 \, x + 9}\right)"," ",0,"1/4*sqrt(3)*arctan(-(18031*sqrt(3)*(-x^2 + 1)^(1/3)*(x - 1) - sqrt(3)*(5054*x^2 + 8497*x + 23659) - 57889*sqrt(3)*(-x^2 + 1)^(2/3))/(6859*x^2 - 240699*x - 220122)) - 1/8*log((x^2 - 6*(-x^2 + 1)^(1/3)*(x - 1) + 6*x + 12*(-x^2 + 1)^(2/3) + 9)/(x^2 + 6*x + 9))","B",0
716,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(-9*e^2*x^2+d^2)^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
717,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x^2+c)^(1/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x^2+c)^(3/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,0,0,0,0.623400," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{\frac{3}{4}} \sqrt{e x + d}}{c e^{2} x^{4} + 2 \, c d e x^{3} + 2 \, a d e x + a d^{2} + {\left(c d^{2} + a e^{2}\right)} x^{2}}, x\right)"," ",0,"integral((c*x^2 + a)^(3/4)*sqrt(e*x + d)/(c*e^2*x^4 + 2*c*d*e*x^3 + 2*a*d*e*x + a*d^2 + (c*d^2 + a*e^2)*x^2), x)","F",0
720,-2,0,0,0.000000," ","integrate(1/(1+x)/(x^2+1)^(1/6),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   Not integrable (provided residues have no relations)","F(-2)",0
721,1,1250,0,0.437911," ","integrate((e*x+d)^m*(c*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} d e^{6} m^{6} + 27 \, a^{3} d e^{6} m^{5} + 720 \, c^{3} d^{7} + 3024 \, a c^{2} d^{5} e^{2} + 5040 \, a^{2} c d^{3} e^{4} + 5040 \, a^{3} d e^{6} + {\left(c^{3} e^{7} m^{6} + 21 \, c^{3} e^{7} m^{5} + 175 \, c^{3} e^{7} m^{4} + 735 \, c^{3} e^{7} m^{3} + 1624 \, c^{3} e^{7} m^{2} + 1764 \, c^{3} e^{7} m + 720 \, c^{3} e^{7}\right)} x^{7} + {\left(c^{3} d e^{6} m^{6} + 15 \, c^{3} d e^{6} m^{5} + 85 \, c^{3} d e^{6} m^{4} + 225 \, c^{3} d e^{6} m^{3} + 274 \, c^{3} d e^{6} m^{2} + 120 \, c^{3} d e^{6} m\right)} x^{6} + 3 \, {\left(a c^{2} e^{7} m^{6} + 1008 \, a c^{2} e^{7} - {\left(2 \, c^{3} d^{2} e^{5} - 23 \, a c^{2} e^{7}\right)} m^{5} - {\left(20 \, c^{3} d^{2} e^{5} - 207 \, a c^{2} e^{7}\right)} m^{4} - 5 \, {\left(14 \, c^{3} d^{2} e^{5} - 185 \, a c^{2} e^{7}\right)} m^{3} - 4 \, {\left(25 \, c^{3} d^{2} e^{5} - 536 \, a c^{2} e^{7}\right)} m^{2} - 12 \, {\left(4 \, c^{3} d^{2} e^{5} - 201 \, a c^{2} e^{7}\right)} m\right)} x^{5} + {\left(6 \, a^{2} c d^{3} e^{4} + 295 \, a^{3} d e^{6}\right)} m^{4} + 3 \, {\left(a c^{2} d e^{6} m^{6} + 19 \, a c^{2} d e^{6} m^{5} + {\left(10 \, c^{3} d^{3} e^{4} + 131 \, a c^{2} d e^{6}\right)} m^{4} + {\left(60 \, c^{3} d^{3} e^{4} + 401 \, a c^{2} d e^{6}\right)} m^{3} + 10 \, {\left(11 \, c^{3} d^{3} e^{4} + 54 \, a c^{2} d e^{6}\right)} m^{2} + 12 \, {\left(5 \, c^{3} d^{3} e^{4} + 21 \, a c^{2} d e^{6}\right)} m\right)} x^{4} + 3 \, {\left(44 \, a^{2} c d^{3} e^{4} + 555 \, a^{3} d e^{6}\right)} m^{3} + 3 \, {\left(a^{2} c e^{7} m^{6} + 1680 \, a^{2} c e^{7} - {\left(4 \, a c^{2} d^{2} e^{5} - 25 \, a^{2} c e^{7}\right)} m^{5} - {\left(64 \, a c^{2} d^{2} e^{5} - 247 \, a^{2} c e^{7}\right)} m^{4} - {\left(40 \, c^{3} d^{4} e^{3} + 332 \, a c^{2} d^{2} e^{5} - 1219 \, a^{2} c e^{7}\right)} m^{3} - 8 \, {\left(15 \, c^{3} d^{4} e^{3} + 76 \, a c^{2} d^{2} e^{5} - 389 \, a^{2} c e^{7}\right)} m^{2} - 4 \, {\left(20 \, c^{3} d^{4} e^{3} + 84 \, a c^{2} d^{2} e^{5} - 949 \, a^{2} c e^{7}\right)} m\right)} x^{3} + 2 \, {\left(36 \, a c^{2} d^{5} e^{2} + 537 \, a^{2} c d^{3} e^{4} + 2552 \, a^{3} d e^{6}\right)} m^{2} + 3 \, {\left(a^{2} c d e^{6} m^{6} + 23 \, a^{2} c d e^{6} m^{5} + 3 \, {\left(4 \, a c^{2} d^{3} e^{4} + 67 \, a^{2} c d e^{6}\right)} m^{4} + {\left(168 \, a c^{2} d^{3} e^{4} + 817 \, a^{2} c d e^{6}\right)} m^{3} + 2 \, {\left(60 \, c^{3} d^{5} e^{2} + 330 \, a c^{2} d^{3} e^{4} + 739 \, a^{2} c d e^{6}\right)} m^{2} + 24 \, {\left(5 \, c^{3} d^{5} e^{2} + 21 \, a c^{2} d^{3} e^{4} + 35 \, a^{2} c d e^{6}\right)} m\right)} x^{2} + 12 \, {\left(78 \, a c^{2} d^{5} e^{2} + 319 \, a^{2} c d^{3} e^{4} + 669 \, a^{3} d e^{6}\right)} m + {\left(a^{3} e^{7} m^{6} + 5040 \, a^{3} e^{7} - 3 \, {\left(2 \, a^{2} c d^{2} e^{5} - 9 \, a^{3} e^{7}\right)} m^{5} - {\left(132 \, a^{2} c d^{2} e^{5} - 295 \, a^{3} e^{7}\right)} m^{4} - 3 \, {\left(24 \, a c^{2} d^{4} e^{3} + 358 \, a^{2} c d^{2} e^{5} - 555 \, a^{3} e^{7}\right)} m^{3} - 4 \, {\left(234 \, a c^{2} d^{4} e^{3} + 957 \, a^{2} c d^{2} e^{5} - 1276 \, a^{3} e^{7}\right)} m^{2} - 36 \, {\left(20 \, c^{3} d^{6} e + 84 \, a c^{2} d^{4} e^{3} + 140 \, a^{2} c d^{2} e^{5} - 223 \, a^{3} e^{7}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{7} m^{7} + 28 \, e^{7} m^{6} + 322 \, e^{7} m^{5} + 1960 \, e^{7} m^{4} + 6769 \, e^{7} m^{3} + 13132 \, e^{7} m^{2} + 13068 \, e^{7} m + 5040 \, e^{7}}"," ",0,"(a^3*d*e^6*m^6 + 27*a^3*d*e^6*m^5 + 720*c^3*d^7 + 3024*a*c^2*d^5*e^2 + 5040*a^2*c*d^3*e^4 + 5040*a^3*d*e^6 + (c^3*e^7*m^6 + 21*c^3*e^7*m^5 + 175*c^3*e^7*m^4 + 735*c^3*e^7*m^3 + 1624*c^3*e^7*m^2 + 1764*c^3*e^7*m + 720*c^3*e^7)*x^7 + (c^3*d*e^6*m^6 + 15*c^3*d*e^6*m^5 + 85*c^3*d*e^6*m^4 + 225*c^3*d*e^6*m^3 + 274*c^3*d*e^6*m^2 + 120*c^3*d*e^6*m)*x^6 + 3*(a*c^2*e^7*m^6 + 1008*a*c^2*e^7 - (2*c^3*d^2*e^5 - 23*a*c^2*e^7)*m^5 - (20*c^3*d^2*e^5 - 207*a*c^2*e^7)*m^4 - 5*(14*c^3*d^2*e^5 - 185*a*c^2*e^7)*m^3 - 4*(25*c^3*d^2*e^5 - 536*a*c^2*e^7)*m^2 - 12*(4*c^3*d^2*e^5 - 201*a*c^2*e^7)*m)*x^5 + (6*a^2*c*d^3*e^4 + 295*a^3*d*e^6)*m^4 + 3*(a*c^2*d*e^6*m^6 + 19*a*c^2*d*e^6*m^5 + (10*c^3*d^3*e^4 + 131*a*c^2*d*e^6)*m^4 + (60*c^3*d^3*e^4 + 401*a*c^2*d*e^6)*m^3 + 10*(11*c^3*d^3*e^4 + 54*a*c^2*d*e^6)*m^2 + 12*(5*c^3*d^3*e^4 + 21*a*c^2*d*e^6)*m)*x^4 + 3*(44*a^2*c*d^3*e^4 + 555*a^3*d*e^6)*m^3 + 3*(a^2*c*e^7*m^6 + 1680*a^2*c*e^7 - (4*a*c^2*d^2*e^5 - 25*a^2*c*e^7)*m^5 - (64*a*c^2*d^2*e^5 - 247*a^2*c*e^7)*m^4 - (40*c^3*d^4*e^3 + 332*a*c^2*d^2*e^5 - 1219*a^2*c*e^7)*m^3 - 8*(15*c^3*d^4*e^3 + 76*a*c^2*d^2*e^5 - 389*a^2*c*e^7)*m^2 - 4*(20*c^3*d^4*e^3 + 84*a*c^2*d^2*e^5 - 949*a^2*c*e^7)*m)*x^3 + 2*(36*a*c^2*d^5*e^2 + 537*a^2*c*d^3*e^4 + 2552*a^3*d*e^6)*m^2 + 3*(a^2*c*d*e^6*m^6 + 23*a^2*c*d*e^6*m^5 + 3*(4*a*c^2*d^3*e^4 + 67*a^2*c*d*e^6)*m^4 + (168*a*c^2*d^3*e^4 + 817*a^2*c*d*e^6)*m^3 + 2*(60*c^3*d^5*e^2 + 330*a*c^2*d^3*e^4 + 739*a^2*c*d*e^6)*m^2 + 24*(5*c^3*d^5*e^2 + 21*a*c^2*d^3*e^4 + 35*a^2*c*d*e^6)*m)*x^2 + 12*(78*a*c^2*d^5*e^2 + 319*a^2*c*d^3*e^4 + 669*a^3*d*e^6)*m + (a^3*e^7*m^6 + 5040*a^3*e^7 - 3*(2*a^2*c*d^2*e^5 - 9*a^3*e^7)*m^5 - (132*a^2*c*d^2*e^5 - 295*a^3*e^7)*m^4 - 3*(24*a*c^2*d^4*e^3 + 358*a^2*c*d^2*e^5 - 555*a^3*e^7)*m^3 - 4*(234*a*c^2*d^4*e^3 + 957*a^2*c*d^2*e^5 - 1276*a^3*e^7)*m^2 - 36*(20*c^3*d^6*e + 84*a*c^2*d^4*e^3 + 140*a^2*c*d^2*e^5 - 223*a^3*e^7)*m)*x)*(e*x + d)^m/(e^7*m^7 + 28*e^7*m^6 + 322*e^7*m^5 + 1960*e^7*m^4 + 6769*e^7*m^3 + 13132*e^7*m^2 + 13068*e^7*m + 5040*e^7)","B",0
722,1,520,0,0.428005," ","integrate((e*x+d)^m*(c*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} d e^{4} m^{4} + 14 \, a^{2} d e^{4} m^{3} + 24 \, c^{2} d^{5} + 80 \, a c d^{3} e^{2} + 120 \, a^{2} d e^{4} + {\left(c^{2} e^{5} m^{4} + 10 \, c^{2} e^{5} m^{3} + 35 \, c^{2} e^{5} m^{2} + 50 \, c^{2} e^{5} m + 24 \, c^{2} e^{5}\right)} x^{5} + {\left(c^{2} d e^{4} m^{4} + 6 \, c^{2} d e^{4} m^{3} + 11 \, c^{2} d e^{4} m^{2} + 6 \, c^{2} d e^{4} m\right)} x^{4} + 2 \, {\left(a c e^{5} m^{4} + 40 \, a c e^{5} - 2 \, {\left(c^{2} d^{2} e^{3} - 6 \, a c e^{5}\right)} m^{3} - {\left(6 \, c^{2} d^{2} e^{3} - 49 \, a c e^{5}\right)} m^{2} - 2 \, {\left(2 \, c^{2} d^{2} e^{3} - 39 \, a c e^{5}\right)} m\right)} x^{3} + {\left(4 \, a c d^{3} e^{2} + 71 \, a^{2} d e^{4}\right)} m^{2} + 2 \, {\left(a c d e^{4} m^{4} + 10 \, a c d e^{4} m^{3} + {\left(6 \, c^{2} d^{3} e^{2} + 29 \, a c d e^{4}\right)} m^{2} + 2 \, {\left(3 \, c^{2} d^{3} e^{2} + 10 \, a c d e^{4}\right)} m\right)} x^{2} + 2 \, {\left(18 \, a c d^{3} e^{2} + 77 \, a^{2} d e^{4}\right)} m + {\left(a^{2} e^{5} m^{4} + 120 \, a^{2} e^{5} - 2 \, {\left(2 \, a c d^{2} e^{3} - 7 \, a^{2} e^{5}\right)} m^{3} - {\left(36 \, a c d^{2} e^{3} - 71 \, a^{2} e^{5}\right)} m^{2} - 2 \, {\left(12 \, c^{2} d^{4} e + 40 \, a c d^{2} e^{3} - 77 \, a^{2} e^{5}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{5} m^{5} + 15 \, e^{5} m^{4} + 85 \, e^{5} m^{3} + 225 \, e^{5} m^{2} + 274 \, e^{5} m + 120 \, e^{5}}"," ",0,"(a^2*d*e^4*m^4 + 14*a^2*d*e^4*m^3 + 24*c^2*d^5 + 80*a*c*d^3*e^2 + 120*a^2*d*e^4 + (c^2*e^5*m^4 + 10*c^2*e^5*m^3 + 35*c^2*e^5*m^2 + 50*c^2*e^5*m + 24*c^2*e^5)*x^5 + (c^2*d*e^4*m^4 + 6*c^2*d*e^4*m^3 + 11*c^2*d*e^4*m^2 + 6*c^2*d*e^4*m)*x^4 + 2*(a*c*e^5*m^4 + 40*a*c*e^5 - 2*(c^2*d^2*e^3 - 6*a*c*e^5)*m^3 - (6*c^2*d^2*e^3 - 49*a*c*e^5)*m^2 - 2*(2*c^2*d^2*e^3 - 39*a*c*e^5)*m)*x^3 + (4*a*c*d^3*e^2 + 71*a^2*d*e^4)*m^2 + 2*(a*c*d*e^4*m^4 + 10*a*c*d*e^4*m^3 + (6*c^2*d^3*e^2 + 29*a*c*d*e^4)*m^2 + 2*(3*c^2*d^3*e^2 + 10*a*c*d*e^4)*m)*x^2 + 2*(18*a*c*d^3*e^2 + 77*a^2*d*e^4)*m + (a^2*e^5*m^4 + 120*a^2*e^5 - 2*(2*a*c*d^2*e^3 - 7*a^2*e^5)*m^3 - (36*a*c*d^2*e^3 - 71*a^2*e^5)*m^2 - 2*(12*c^2*d^4*e + 40*a*c*d^2*e^3 - 77*a^2*e^5)*m)*x)*(e*x + d)^m/(e^5*m^5 + 15*e^5*m^4 + 85*e^5*m^3 + 225*e^5*m^2 + 274*e^5*m + 120*e^5)","B",0
723,1,149,0,0.416919," ","integrate((e*x+d)^m*(c*x^2+a),x, algorithm=""fricas"")","\frac{{\left(a d e^{2} m^{2} + 5 \, a d e^{2} m + 2 \, c d^{3} + 6 \, a d e^{2} + {\left(c e^{3} m^{2} + 3 \, c e^{3} m + 2 \, c e^{3}\right)} x^{3} + {\left(c d e^{2} m^{2} + c d e^{2} m\right)} x^{2} + {\left(a e^{3} m^{2} + 6 \, a e^{3} - {\left(2 \, c d^{2} e - 5 \, a e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{3} m^{3} + 6 \, e^{3} m^{2} + 11 \, e^{3} m + 6 \, e^{3}}"," ",0,"(a*d*e^2*m^2 + 5*a*d*e^2*m + 2*c*d^3 + 6*a*d*e^2 + (c*e^3*m^2 + 3*c*e^3*m + 2*c*e^3)*x^3 + (c*d*e^2*m^2 + c*d*e^2*m)*x^2 + (a*e^3*m^2 + 6*a*e^3 - (2*c*d^2*e - 5*a*e^3)*m)*x)*(e*x + d)^m/(e^3*m^3 + 6*e^3*m^2 + 11*e^3*m + 6*e^3)","B",0
724,0,0,0,0.411926," ","integrate((e*x+d)^m/(c*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c x^{2} + a}, x\right)"," ",0,"integral((e*x + d)^m/(c*x^2 + a), x)","F",0
725,0,0,0,0.429086," ","integrate((e*x+d)^m/(c*x^2+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral((e*x + d)^m/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
726,0,0,0,0.422890," ","integrate((e*x+d)^m/(c*x^2+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c^{3} x^{6} + 3 \, a c^{2} x^{4} + 3 \, a^{2} c x^{2} + a^{3}}, x\right)"," ",0,"integral((e*x + d)^m/(c^3*x^6 + 3*a*c^2*x^4 + 3*a^2*c*x^2 + a^3), x)","F",0
727,0,0,0,0.426634," ","integrate((e*x+d)^m*(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + a)^(3/2)*(e*x + d)^m, x)","F",0
728,0,0,0,0.423604," ","integrate((e*x+d)^m*(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + a} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(e*x + d)^m, x)","F",0
729,0,0,0,0.427021," ","integrate((e*x+d)^m/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{\sqrt{c x^{2} + a}}, x\right)"," ",0,"integral((e*x + d)^m/sqrt(c*x^2 + a), x)","F",0
730,0,0,0,0.424571," ","integrate((e*x+d)^m/(c*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + a} {\left(e x + d\right)}^{m}}{c^{2} x^{4} + 2 \, a c x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + a)*(e*x + d)^m/(c^2*x^4 + 2*a*c*x^2 + a^2), x)","F",0
731,0,0,0,0.425241," ","integrate((e*x+d)^m*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + a)^p*(e*x + d)^m, x)","F",0
732,0,0,0,0.412676," ","integrate((e*x+d)^3*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(c*x^2 + a)^p, x)","F",0
733,0,0,0,0.418447," ","integrate((e*x+d)^2*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(c*x^2 + a)^p, x)","F",0
734,0,0,0,0.413223," ","integrate((e*x+d)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)} {\left(c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x + d)*(c*x^2 + a)^p, x)","F",0
735,0,0,0,0.424953," ","integrate((c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((c*x^2 + a)^p, x)","F",0
736,0,0,0,0.418446," ","integrate((c*x^2+a)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{p}}{e x + d}, x\right)"," ",0,"integral((c*x^2 + a)^p/(e*x + d), x)","F",0
737,0,0,0,0.440647," ","integrate((c*x^2+a)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{p}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c*x^2 + a)^p/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
738,0,0,0,0.446023," ","integrate((c*x^2+a)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{p}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c*x^2 + a)^p/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
739,0,0,0,0.439436," ","integrate((c*x^2+a)^p/((e*x+d)^(2*p)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + a\right)}^{p}}{{\left(e x + d\right)}^{2 \, p}}, x\right)"," ",0,"integral((c*x^2 + a)^p/(e*x + d)^(2*p), x)","F",0
740,0,0,0,0.430852," ","integrate((e*x+d)^(-1-2*p)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 1}, x\right)"," ",0,"integral((c*x^2 + a)^p*(e*x + d)^(-2*p - 1), x)","F",0
741,0,0,0,0.434193," ","integrate((e*x+d)^(-2-2*p)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 2}, x\right)"," ",0,"integral((c*x^2 + a)^p*(e*x + d)^(-2*p - 2), x)","F",0
742,0,0,0,0.444163," ","integrate((e*x+d)^(-3-2*p)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}, x\right)"," ",0,"integral((c*x^2 + a)^p*(e*x + d)^(-2*p - 3), x)","F",0
743,0,0,0,0.439861," ","integrate((e*x+d)^(-4-2*p)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 4}, x\right)"," ",0,"integral((c*x^2 + a)^p*(e*x + d)^(-2*p - 4), x)","F",0
744,0,0,0,0.455334," ","integrate((e*x+d)^(-5-2*p)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 5}, x\right)"," ",0,"integral((c*x^2 + a)^p*(e*x + d)^(-2*p - 5), x)","F",0
745,0,0,0,0.472530," ","integrate((e*x+d)^(-6-2*p)*(c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 6}, x\right)"," ",0,"integral((c*x^2 + a)^p*(e*x + d)^(-2*p - 6), x)","F",0
746,0,0,0,0.428573," ","integrate((3-4*x)^n/(-x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{2} + 1} {\left(-4 \, x + 3\right)}^{n}}{x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-x^2 + 1)*(-4*x + 3)^n/(x^2 - 1), x)","F",0
747,1,65,0,0.402113," ","integrate((b*x+a)^6/(-b^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{6 \, b^{5} x^{5} + 45 \, a b^{4} x^{4} + 160 \, a^{2} b^{3} x^{3} + 390 \, a^{3} b^{2} x^{2} + 930 \, a^{4} b x + 960 \, a^{5} \log\left(b x - a\right)}{30 \, b}"," ",0,"-1/30*(6*b^5*x^5 + 45*a*b^4*x^4 + 160*a^2*b^3*x^3 + 390*a^3*b^2*x^2 + 930*a^4*b*x + 960*a^5*log(b*x - a))/b","A",0
748,1,54,0,0.393189," ","integrate((b*x+a)^5/(-b^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{3 \, b^{4} x^{4} + 20 \, a b^{3} x^{3} + 66 \, a^{2} b^{2} x^{2} + 180 \, a^{3} b x + 192 \, a^{4} \log\left(b x - a\right)}{12 \, b}"," ",0,"-1/12*(3*b^4*x^4 + 20*a*b^3*x^3 + 66*a^2*b^2*x^2 + 180*a^3*b*x + 192*a^4*log(b*x - a))/b","A",0
749,1,42,0,0.394315," ","integrate((b*x+a)^4/(-b^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{b^{3} x^{3} + 6 \, a b^{2} x^{2} + 21 \, a^{2} b x + 24 \, a^{3} \log\left(b x - a\right)}{3 \, b}"," ",0,"-1/3*(b^3*x^3 + 6*a*b^2*x^2 + 21*a^2*b*x + 24*a^3*log(b*x - a))/b","A",0
750,1,31,0,0.390914," ","integrate((b*x+a)^3/(-b^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{b^{2} x^{2} + 6 \, a b x + 8 \, a^{2} \log\left(b x - a\right)}{2 \, b}"," ",0,"-1/2*(b^2*x^2 + 6*a*b*x + 8*a^2*log(b*x - a))/b","A",0
751,1,20,0,0.396820," ","integrate((b*x+a)^2/(-b^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{b x + 2 \, a \log\left(b x - a\right)}{b}"," ",0,"-(b*x + 2*a*log(b*x - a))/b","A",0
752,1,13,0,0.404251," ","integrate((b*x+a)/(-b^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{\log\left(b x - a\right)}{b}"," ",0,"-log(b*x - a)/b","A",0
753,1,49,0,0.402057," ","integrate(1/(b*x+a)/(-b^2*x^2+a^2),x, algorithm=""fricas"")","\frac{{\left(b x + a\right)} \log\left(b x + a\right) - {\left(b x + a\right)} \log\left(b x - a\right) - 2 \, a}{4 \, {\left(a^{2} b^{2} x + a^{3} b\right)}}"," ",0,"1/4*((b*x + a)*log(b*x + a) - (b*x + a)*log(b*x - a) - 2*a)/(a^2*b^2*x + a^3*b)","A",0
754,1,89,0,0.402104," ","integrate(1/(b*x+a)^2/(-b^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{2 \, a b x + 4 \, a^{2} - {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(b x + a\right) + {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(b x - a\right)}{8 \, {\left(a^{3} b^{3} x^{2} + 2 \, a^{4} b^{2} x + a^{5} b\right)}}"," ",0,"-1/8*(2*a*b*x + 4*a^2 - (b^2*x^2 + 2*a*b*x + a^2)*log(b*x + a) + (b^2*x^2 + 2*a*b*x + a^2)*log(b*x - a))/(a^3*b^3*x^2 + 2*a^4*b^2*x + a^5*b)","A",0
755,1,134,0,0.395343," ","integrate(1/(b*x+a)^3/(-b^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{6 \, a b^{2} x^{2} + 18 \, a^{2} b x + 20 \, a^{3} - 3 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} \log\left(b x + a\right) + 3 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} \log\left(b x - a\right)}{48 \, {\left(a^{4} b^{4} x^{3} + 3 \, a^{5} b^{3} x^{2} + 3 \, a^{6} b^{2} x + a^{7} b\right)}}"," ",0,"-1/48*(6*a*b^2*x^2 + 18*a^2*b*x + 20*a^3 - 3*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*log(b*x + a) + 3*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*log(b*x - a))/(a^4*b^4*x^3 + 3*a^5*b^3*x^2 + 3*a^6*b^2*x + a^7*b)","B",0
756,1,178,0,0.393620," ","integrate(1/(b*x+a)^4/(-b^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{6 \, a b^{3} x^{3} + 24 \, a^{2} b^{2} x^{2} + 38 \, a^{3} b x + 32 \, a^{4} - 3 \, {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} \log\left(b x + a\right) + 3 \, {\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} \log\left(b x - a\right)}{96 \, {\left(a^{5} b^{5} x^{4} + 4 \, a^{6} b^{4} x^{3} + 6 \, a^{7} b^{3} x^{2} + 4 \, a^{8} b^{2} x + a^{9} b\right)}}"," ",0,"-1/96*(6*a*b^3*x^3 + 24*a^2*b^2*x^2 + 38*a^3*b*x + 32*a^4 - 3*(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*log(b*x + a) + 3*(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*log(b*x - a))/(a^5*b^5*x^4 + 4*a^6*b^4*x^3 + 6*a^7*b^3*x^2 + 4*a^8*b^2*x + a^9*b)","B",0
757,1,88,0,0.400269," ","integrate((b*x+a)^7/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{5} x^{5} + 25 \, a b^{4} x^{4} + 110 \, a^{2} b^{3} x^{3} + 450 \, a^{3} b^{2} x^{2} - 588 \, a^{4} b x - 384 \, a^{5} + 960 \, {\left(a^{4} b x - a^{5}\right)} \log\left(b x - a\right)}{12 \, {\left(b^{2} x - a b\right)}}"," ",0,"1/12*(3*b^5*x^5 + 25*a*b^4*x^4 + 110*a^2*b^3*x^3 + 450*a^3*b^2*x^2 - 588*a^4*b*x - 384*a^5 + 960*(a^4*b*x - a^5)*log(b*x - a))/(b^2*x - a*b)","A",0
758,1,76,0,0.393363," ","integrate((b*x+a)^6/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{b^{4} x^{4} + 8 \, a b^{3} x^{3} + 42 \, a^{2} b^{2} x^{2} - 51 \, a^{3} b x - 48 \, a^{4} + 96 \, {\left(a^{3} b x - a^{4}\right)} \log\left(b x - a\right)}{3 \, {\left(b^{2} x - a b\right)}}"," ",0,"1/3*(b^4*x^4 + 8*a*b^3*x^3 + 42*a^2*b^2*x^2 - 51*a^3*b*x - 48*a^4 + 96*(a^3*b*x - a^4)*log(b*x - a))/(b^2*x - a*b)","A",0
759,1,65,0,0.388118," ","integrate((b*x+a)^5/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{b^{3} x^{3} + 9 \, a b^{2} x^{2} - 10 \, a^{2} b x - 16 \, a^{3} + 24 \, {\left(a^{2} b x - a^{3}\right)} \log\left(b x - a\right)}{2 \, {\left(b^{2} x - a b\right)}}"," ",0,"1/2*(b^3*x^3 + 9*a*b^2*x^2 - 10*a^2*b*x - 16*a^3 + 24*(a^2*b*x - a^3)*log(b*x - a))/(b^2*x - a*b)","A",0
760,1,51,0,0.399276," ","integrate((b*x+a)^4/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{b^{2} x^{2} - a b x - 4 \, a^{2} + 4 \, {\left(a b x - a^{2}\right)} \log\left(b x - a\right)}{b^{2} x - a b}"," ",0,"(b^2*x^2 - a*b*x - 4*a^2 + 4*(a*b*x - a^2)*log(b*x - a))/(b^2*x - a*b)","A",0
761,1,33,0,0.392735," ","integrate((b*x+a)^3/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{{\left(b x - a\right)} \log\left(b x - a\right) - 2 \, a}{b^{2} x - a b}"," ",0,"((b*x - a)*log(b*x - a) - 2*a)/(b^2*x - a*b)","A",0
762,1,14,0,0.387912," ","integrate((b*x+a)^2/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{1}{b^{2} x - a b}"," ",0,"-1/(b^2*x - a*b)","A",0
763,1,54,0,0.405473," ","integrate((b*x+a)/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{{\left(b x - a\right)} \log\left(b x + a\right) - {\left(b x - a\right)} \log\left(b x - a\right) - 2 \, a}{4 \, {\left(a^{2} b^{2} x - a^{3} b\right)}}"," ",0,"1/4*((b*x - a)*log(b*x + a) - (b*x - a)*log(b*x - a) - 2*a)/(a^2*b^2*x - a^3*b)","A",0
764,1,136,0,0.402818," ","integrate(1/(b*x+a)/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{6 \, a b^{2} x^{2} + 6 \, a^{2} b x - 4 \, a^{3} - 3 \, {\left(b^{3} x^{3} + a b^{2} x^{2} - a^{2} b x - a^{3}\right)} \log\left(b x + a\right) + 3 \, {\left(b^{3} x^{3} + a b^{2} x^{2} - a^{2} b x - a^{3}\right)} \log\left(b x - a\right)}{16 \, {\left(a^{4} b^{4} x^{3} + a^{5} b^{3} x^{2} - a^{6} b^{2} x - a^{7} b\right)}}"," ",0,"-1/16*(6*a*b^2*x^2 + 6*a^2*b*x - 4*a^3 - 3*(b^3*x^3 + a*b^2*x^2 - a^2*b*x - a^3)*log(b*x + a) + 3*(b^3*x^3 + a*b^2*x^2 - a^2*b*x - a^3)*log(b*x - a))/(a^4*b^4*x^3 + a^5*b^3*x^2 - a^6*b^2*x - a^7*b)","B",0
765,1,150,0,0.399925," ","integrate(1/(b*x+a)^2/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{6 \, a b^{3} x^{3} + 12 \, a^{2} b^{2} x^{2} + 2 \, a^{3} b x - 8 \, a^{4} - 3 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{3} - 2 \, a^{3} b x - a^{4}\right)} \log\left(b x + a\right) + 3 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{3} - 2 \, a^{3} b x - a^{4}\right)} \log\left(b x - a\right)}{24 \, {\left(a^{5} b^{5} x^{4} + 2 \, a^{6} b^{4} x^{3} - 2 \, a^{8} b^{2} x - a^{9} b\right)}}"," ",0,"-1/24*(6*a*b^3*x^3 + 12*a^2*b^2*x^2 + 2*a^3*b*x - 8*a^4 - 3*(b^4*x^4 + 2*a*b^3*x^3 - 2*a^3*b*x - a^4)*log(b*x + a) + 3*(b^4*x^4 + 2*a*b^3*x^3 - 2*a^3*b*x - a^4)*log(b*x - a))/(a^5*b^5*x^4 + 2*a^6*b^4*x^3 - 2*a^8*b^2*x - a^9*b)","A",0
766,1,227,0,0.405821," ","integrate(1/(b*x+a)^3/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","-\frac{30 \, a b^{4} x^{4} + 90 \, a^{2} b^{3} x^{3} + 70 \, a^{3} b^{2} x^{2} - 30 \, a^{4} b x - 64 \, a^{5} - 15 \, {\left(b^{5} x^{5} + 3 \, a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{3} - 2 \, a^{3} b^{2} x^{2} - 3 \, a^{4} b x - a^{5}\right)} \log\left(b x + a\right) + 15 \, {\left(b^{5} x^{5} + 3 \, a b^{4} x^{4} + 2 \, a^{2} b^{3} x^{3} - 2 \, a^{3} b^{2} x^{2} - 3 \, a^{4} b x - a^{5}\right)} \log\left(b x - a\right)}{192 \, {\left(a^{6} b^{6} x^{5} + 3 \, a^{7} b^{5} x^{4} + 2 \, a^{8} b^{4} x^{3} - 2 \, a^{9} b^{3} x^{2} - 3 \, a^{10} b^{2} x - a^{11} b\right)}}"," ",0,"-1/192*(30*a*b^4*x^4 + 90*a^2*b^3*x^3 + 70*a^3*b^2*x^2 - 30*a^4*b*x - 64*a^5 - 15*(b^5*x^5 + 3*a*b^4*x^4 + 2*a^2*b^3*x^3 - 2*a^3*b^2*x^2 - 3*a^4*b*x - a^5)*log(b*x + a) + 15*(b^5*x^5 + 3*a*b^4*x^4 + 2*a^2*b^3*x^3 - 2*a^3*b^2*x^2 - 3*a^4*b*x - a^5)*log(b*x - a))/(a^6*b^6*x^5 + 3*a^7*b^5*x^4 + 2*a^8*b^4*x^3 - 2*a^9*b^3*x^2 - 3*a^10*b^2*x - a^11*b)","B",0
767,1,106,0,0.409224," ","integrate((b*x+a)^8/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{b^{5} x^{5} + 10 \, a b^{4} x^{4} + 70 \, a^{2} b^{3} x^{3} - 174 \, a^{3} b^{2} x^{2} - 147 \, a^{4} b x + 192 \, a^{5} + 240 \, {\left(a^{3} b^{2} x^{2} - 2 \, a^{4} b x + a^{5}\right)} \log\left(b x - a\right)}{3 \, {\left(b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"-1/3*(b^5*x^5 + 10*a*b^4*x^4 + 70*a^2*b^3*x^3 - 174*a^3*b^2*x^2 - 147*a^4*b*x + 192*a^5 + 240*(a^3*b^2*x^2 - 2*a^4*b*x + a^5)*log(b*x - a))/(b^3*x^2 - 2*a*b^2*x + a^2*b)","A",0
768,1,95,0,0.393767," ","integrate((b*x+a)^7/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{b^{4} x^{4} + 12 \, a b^{3} x^{3} - 27 \, a^{2} b^{2} x^{2} - 50 \, a^{3} b x + 48 \, a^{4} + 48 \, {\left(a^{2} b^{2} x^{2} - 2 \, a^{3} b x + a^{4}\right)} \log\left(b x - a\right)}{2 \, {\left(b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"-1/2*(b^4*x^4 + 12*a*b^3*x^3 - 27*a^2*b^2*x^2 - 50*a^3*b*x + 48*a^4 + 48*(a^2*b^2*x^2 - 2*a^3*b*x + a^4)*log(b*x - a))/(b^3*x^2 - 2*a*b^2*x + a^2*b)","A",0
769,1,82,0,0.395432," ","integrate((b*x+a)^6/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{b^{3} x^{3} - 2 \, a b^{2} x^{2} - 11 \, a^{2} b x + 8 \, a^{3} + 6 \, {\left(a b^{2} x^{2} - 2 \, a^{2} b x + a^{3}\right)} \log\left(b x - a\right)}{b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b}"," ",0,"-(b^3*x^3 - 2*a*b^2*x^2 - 11*a^2*b*x + 8*a^3 + 6*(a*b^2*x^2 - 2*a^2*b*x + a^3)*log(b*x - a))/(b^3*x^2 - 2*a*b^2*x + a^2*b)","A",0
770,1,60,0,0.398215," ","integrate((b*x+a)^5/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{4 \, a b x - 2 \, a^{2} - {\left(b^{2} x^{2} - 2 \, a b x + a^{2}\right)} \log\left(b x - a\right)}{b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b}"," ",0,"(4*a*b*x - 2*a^2 - (b^2*x^2 - 2*a*b*x + a^2)*log(b*x - a))/(b^3*x^2 - 2*a*b^2*x + a^2*b)","A",0
771,1,20,0,0.384360," ","integrate((b*x+a)^4/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{x}{b^{2} x^{2} - 2 \, a b x + a^{2}}"," ",0,"x/(b^2*x^2 - 2*a*b*x + a^2)","A",0
772,1,24,0,0.384352," ","integrate((b*x+a)^3/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{1}{2 \, {\left(b^{3} x^{2} - 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"1/2/(b^3*x^2 - 2*a*b^2*x + a^2*b)","A",0
773,1,89,0,0.401293," ","integrate((b*x+a)^2/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{2 \, a b x - 4 \, a^{2} - {\left(b^{2} x^{2} - 2 \, a b x + a^{2}\right)} \log\left(b x + a\right) + {\left(b^{2} x^{2} - 2 \, a b x + a^{2}\right)} \log\left(b x - a\right)}{8 \, {\left(a^{3} b^{3} x^{2} - 2 \, a^{4} b^{2} x + a^{5} b\right)}}"," ",0,"-1/8*(2*a*b*x - 4*a^2 - (b^2*x^2 - 2*a*b*x + a^2)*log(b*x + a) + (b^2*x^2 - 2*a*b*x + a^2)*log(b*x - a))/(a^3*b^3*x^2 - 2*a^4*b^2*x + a^5*b)","A",0
774,1,134,0,0.402911," ","integrate((b*x+a)/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{6 \, a b^{2} x^{2} - 6 \, a^{2} b x - 4 \, a^{3} - 3 \, {\left(b^{3} x^{3} - a b^{2} x^{2} - a^{2} b x + a^{3}\right)} \log\left(b x + a\right) + 3 \, {\left(b^{3} x^{3} - a b^{2} x^{2} - a^{2} b x + a^{3}\right)} \log\left(b x - a\right)}{16 \, {\left(a^{4} b^{4} x^{3} - a^{5} b^{3} x^{2} - a^{6} b^{2} x + a^{7} b\right)}}"," ",0,"-1/16*(6*a*b^2*x^2 - 6*a^2*b*x - 4*a^3 - 3*(b^3*x^3 - a*b^2*x^2 - a^2*b*x + a^3)*log(b*x + a) + 3*(b^3*x^3 - a*b^2*x^2 - a^2*b*x + a^3)*log(b*x - a))/(a^4*b^4*x^3 - a^5*b^3*x^2 - a^6*b^2*x + a^7*b)","B",0
775,1,216,0,0.412292," ","integrate(1/(b*x+a)/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{30 \, a b^{4} x^{4} + 30 \, a^{2} b^{3} x^{3} - 50 \, a^{3} b^{2} x^{2} - 50 \, a^{4} b x + 16 \, a^{5} - 15 \, {\left(b^{5} x^{5} + a b^{4} x^{4} - 2 \, a^{2} b^{3} x^{3} - 2 \, a^{3} b^{2} x^{2} + a^{4} b x + a^{5}\right)} \log\left(b x + a\right) + 15 \, {\left(b^{5} x^{5} + a b^{4} x^{4} - 2 \, a^{2} b^{3} x^{3} - 2 \, a^{3} b^{2} x^{2} + a^{4} b x + a^{5}\right)} \log\left(b x - a\right)}{96 \, {\left(a^{6} b^{6} x^{5} + a^{7} b^{5} x^{4} - 2 \, a^{8} b^{4} x^{3} - 2 \, a^{9} b^{3} x^{2} + a^{10} b^{2} x + a^{11} b\right)}}"," ",0,"-1/96*(30*a*b^4*x^4 + 30*a^2*b^3*x^3 - 50*a^3*b^2*x^2 - 50*a^4*b*x + 16*a^5 - 15*(b^5*x^5 + a*b^4*x^4 - 2*a^2*b^3*x^3 - 2*a^3*b^2*x^2 + a^4*b*x + a^5)*log(b*x + a) + 15*(b^5*x^5 + a*b^4*x^4 - 2*a^2*b^3*x^3 - 2*a^3*b^2*x^2 + a^4*b*x + a^5)*log(b*x - a))/(a^6*b^6*x^5 + a^7*b^5*x^4 - 2*a^8*b^4*x^3 - 2*a^9*b^3*x^2 + a^10*b^2*x + a^11*b)","B",0
776,1,266,0,0.407432," ","integrate(1/(b*x+a)^2/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","-\frac{30 \, a b^{5} x^{5} + 60 \, a^{2} b^{4} x^{4} - 20 \, a^{3} b^{3} x^{3} - 100 \, a^{4} b^{2} x^{2} - 34 \, a^{5} b x + 32 \, a^{6} - 15 \, {\left(b^{6} x^{6} + 2 \, a b^{5} x^{5} - a^{2} b^{4} x^{4} - 4 \, a^{3} b^{3} x^{3} - a^{4} b^{2} x^{2} + 2 \, a^{5} b x + a^{6}\right)} \log\left(b x + a\right) + 15 \, {\left(b^{6} x^{6} + 2 \, a b^{5} x^{5} - a^{2} b^{4} x^{4} - 4 \, a^{3} b^{3} x^{3} - a^{4} b^{2} x^{2} + 2 \, a^{5} b x + a^{6}\right)} \log\left(b x - a\right)}{128 \, {\left(a^{7} b^{7} x^{6} + 2 \, a^{8} b^{6} x^{5} - a^{9} b^{5} x^{4} - 4 \, a^{10} b^{4} x^{3} - a^{11} b^{3} x^{2} + 2 \, a^{12} b^{2} x + a^{13} b\right)}}"," ",0,"-1/128*(30*a*b^5*x^5 + 60*a^2*b^4*x^4 - 20*a^3*b^3*x^3 - 100*a^4*b^2*x^2 - 34*a^5*b*x + 32*a^6 - 15*(b^6*x^6 + 2*a*b^5*x^5 - a^2*b^4*x^4 - 4*a^3*b^3*x^3 - a^4*b^2*x^2 + 2*a^5*b*x + a^6)*log(b*x + a) + 15*(b^6*x^6 + 2*a*b^5*x^5 - a^2*b^4*x^4 - 4*a^3*b^3*x^3 - a^4*b^2*x^2 + 2*a^5*b*x + a^6)*log(b*x - a))/(a^7*b^7*x^6 + 2*a^8*b^6*x^5 - a^9*b^5*x^4 - 4*a^10*b^4*x^3 - a^11*b^3*x^2 + 2*a^12*b^2*x + a^13*b)","B",0
777,1,106,0,0.428848," ","integrate((b*x+a)^4*(-b^2*x^2+a^2)^(1/2),x, algorithm=""fricas"")","-\frac{630 \, a^{6} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) - {\left(40 \, b^{5} x^{5} + 192 \, a b^{4} x^{4} + 350 \, a^{2} b^{3} x^{3} + 256 \, a^{3} b^{2} x^{2} - 75 \, a^{4} b x - 448 \, a^{5}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{240 \, b}"," ",0,"-1/240*(630*a^6*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) - (40*b^5*x^5 + 192*a*b^4*x^4 + 350*a^2*b^3*x^3 + 256*a^3*b^2*x^2 - 75*a^4*b*x - 448*a^5)*sqrt(-b^2*x^2 + a^2))/b","A",0
778,1,95,0,0.406068," ","integrate((b*x+a)^3*(-b^2*x^2+a^2)^(1/2),x, algorithm=""fricas"")","-\frac{210 \, a^{5} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) - {\left(24 \, b^{4} x^{4} + 90 \, a b^{3} x^{3} + 112 \, a^{2} b^{2} x^{2} + 15 \, a^{3} b x - 136 \, a^{4}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{120 \, b}"," ",0,"-1/120*(210*a^5*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) - (24*b^4*x^4 + 90*a*b^3*x^3 + 112*a^2*b^2*x^2 + 15*a^3*b*x - 136*a^4)*sqrt(-b^2*x^2 + a^2))/b","A",0
779,1,84,0,0.406620," ","integrate((b*x+a)^2*(-b^2*x^2+a^2)^(1/2),x, algorithm=""fricas"")","-\frac{30 \, a^{4} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) - {\left(6 \, b^{3} x^{3} + 16 \, a b^{2} x^{2} + 9 \, a^{2} b x - 16 \, a^{3}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{24 \, b}"," ",0,"-1/24*(30*a^4*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) - (6*b^3*x^3 + 16*a*b^2*x^2 + 9*a^2*b*x - 16*a^3)*sqrt(-b^2*x^2 + a^2))/b","A",0
780,1,73,0,0.414708," ","integrate((b*x+a)*(-b^2*x^2+a^2)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, a^{3} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) - {\left(2 \, b^{2} x^{2} + 3 \, a b x - 2 \, a^{2}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{6 \, b}"," ",0,"-1/6*(6*a^3*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) - (2*b^2*x^2 + 3*a*b*x - 2*a^2)*sqrt(-b^2*x^2 + a^2))/b","A",0
781,1,52,0,0.410117," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) - \sqrt{-b^{2} x^{2} + a^{2}}}{b}"," ",0,"-(2*a*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) - sqrt(-b^2*x^2 + a^2))/b","A",0
782,1,66,0,0.422245," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(b x - {\left(b x + a\right)} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) + a + \sqrt{-b^{2} x^{2} + a^{2}}\right)}}{b^{2} x + a b}"," ",0,"-2*(b*x - (b*x + a)*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) + a + sqrt(-b^2*x^2 + a^2))/(b^2*x + a*b)","A",0
783,1,66,0,0.405926," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - \sqrt{-b^{2} x^{2} + a^{2}} {\left(b x - a\right)}}{3 \, {\left(a b^{3} x^{2} + 2 \, a^{2} b^{2} x + a^{3} b\right)}}"," ",0,"-1/3*(b^2*x^2 + 2*a*b*x + a^2 - sqrt(-b^2*x^2 + a^2)*(b*x - a))/(a*b^3*x^2 + 2*a^2*b^2*x + a^3*b)","B",0
784,1,104,0,0.419758," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^4,x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{3} + 12 \, a b^{2} x^{2} + 12 \, a^{2} b x + 4 \, a^{3} - {\left(b^{2} x^{2} + 3 \, a b x - 4 \, a^{2}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{15 \, {\left(a^{2} b^{4} x^{3} + 3 \, a^{3} b^{3} x^{2} + 3 \, a^{4} b^{2} x + a^{5} b\right)}}"," ",0,"-1/15*(4*b^3*x^3 + 12*a*b^2*x^2 + 12*a^2*b*x + 4*a^3 - (b^2*x^2 + 3*a*b*x - 4*a^2)*sqrt(-b^2*x^2 + a^2))/(a^2*b^4*x^3 + 3*a^3*b^3*x^2 + 3*a^4*b^2*x + a^5*b)","A",0
785,1,138,0,0.418393," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^5,x, algorithm=""fricas"")","-\frac{23 \, b^{4} x^{4} + 92 \, a b^{3} x^{3} + 138 \, a^{2} b^{2} x^{2} + 92 \, a^{3} b x + 23 \, a^{4} - {\left(2 \, b^{3} x^{3} + 8 \, a b^{2} x^{2} + 13 \, a^{2} b x - 23 \, a^{3}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{105 \, {\left(a^{3} b^{5} x^{4} + 4 \, a^{4} b^{4} x^{3} + 6 \, a^{5} b^{3} x^{2} + 4 \, a^{6} b^{2} x + a^{7} b\right)}}"," ",0,"-1/105*(23*b^4*x^4 + 92*a*b^3*x^3 + 138*a^2*b^2*x^2 + 92*a^3*b*x + 23*a^4 - (2*b^3*x^3 + 8*a*b^2*x^2 + 13*a^2*b*x - 23*a^3)*sqrt(-b^2*x^2 + a^2))/(a^3*b^5*x^4 + 4*a^4*b^4*x^3 + 6*a^5*b^3*x^2 + 4*a^6*b^2*x + a^7*b)","A",0
786,1,171,0,0.444238," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^6,x, algorithm=""fricas"")","-\frac{58 \, b^{5} x^{5} + 290 \, a b^{4} x^{4} + 580 \, a^{2} b^{3} x^{3} + 580 \, a^{3} b^{2} x^{2} + 290 \, a^{4} b x + 58 \, a^{5} - {\left(2 \, b^{4} x^{4} + 10 \, a b^{3} x^{3} + 21 \, a^{2} b^{2} x^{2} + 25 \, a^{3} b x - 58 \, a^{4}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{315 \, {\left(a^{4} b^{6} x^{5} + 5 \, a^{5} b^{5} x^{4} + 10 \, a^{6} b^{4} x^{3} + 10 \, a^{7} b^{3} x^{2} + 5 \, a^{8} b^{2} x + a^{9} b\right)}}"," ",0,"-1/315*(58*b^5*x^5 + 290*a*b^4*x^4 + 580*a^2*b^3*x^3 + 580*a^3*b^2*x^2 + 290*a^4*b*x + 58*a^5 - (2*b^4*x^4 + 10*a*b^3*x^3 + 21*a^2*b^2*x^2 + 25*a^3*b*x - 58*a^4)*sqrt(-b^2*x^2 + a^2))/(a^4*b^6*x^5 + 5*a^5*b^5*x^4 + 10*a^6*b^4*x^3 + 10*a^7*b^3*x^2 + 5*a^8*b^2*x + a^9*b)","A",0
787,1,204,0,0.484272," ","integrate((-b^2*x^2+a^2)^(1/2)/(b*x+a)^7,x, algorithm=""fricas"")","-\frac{547 \, b^{6} x^{6} + 3282 \, a b^{5} x^{5} + 8205 \, a^{2} b^{4} x^{4} + 10940 \, a^{3} b^{3} x^{3} + 8205 \, a^{4} b^{2} x^{2} + 3282 \, a^{5} b x + 547 \, a^{6} - {\left(8 \, b^{5} x^{5} + 48 \, a b^{4} x^{4} + 124 \, a^{2} b^{3} x^{3} + 184 \, a^{3} b^{2} x^{2} + 183 \, a^{4} b x - 547 \, a^{5}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{3465 \, {\left(a^{5} b^{7} x^{6} + 6 \, a^{6} b^{6} x^{5} + 15 \, a^{7} b^{5} x^{4} + 20 \, a^{8} b^{4} x^{3} + 15 \, a^{9} b^{3} x^{2} + 6 \, a^{10} b^{2} x + a^{11} b\right)}}"," ",0,"-1/3465*(547*b^6*x^6 + 3282*a*b^5*x^5 + 8205*a^2*b^4*x^4 + 10940*a^3*b^3*x^3 + 8205*a^4*b^2*x^2 + 3282*a^5*b*x + 547*a^6 - (8*b^5*x^5 + 48*a*b^4*x^4 + 124*a^2*b^3*x^3 + 184*a^3*b^2*x^2 + 183*a^4*b*x - 547*a^5)*sqrt(-b^2*x^2 + a^2))/(a^5*b^7*x^6 + 6*a^6*b^6*x^5 + 15*a^7*b^5*x^4 + 20*a^8*b^4*x^3 + 15*a^9*b^3*x^2 + 6*a^10*b^2*x + a^11*b)","A",0
788,1,116,0,0.417849," ","integrate((b*x+a)^3*(-b^2*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{630 \, a^{7} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) + {\left(80 \, b^{6} x^{6} + 280 \, a b^{5} x^{5} + 208 \, a^{2} b^{4} x^{4} - 350 \, a^{3} b^{3} x^{3} - 656 \, a^{4} b^{2} x^{2} - 245 \, a^{5} b x + 368 \, a^{6}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{560 \, b}"," ",0,"-1/560*(630*a^7*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) + (80*b^6*x^6 + 280*a*b^5*x^5 + 208*a^2*b^4*x^4 - 350*a^3*b^3*x^3 - 656*a^4*b^2*x^2 - 245*a^5*b*x + 368*a^6)*sqrt(-b^2*x^2 + a^2))/b","A",0
789,1,105,0,0.410933," ","integrate((b*x+a)^2*(-b^2*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{210 \, a^{6} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) + {\left(40 \, b^{5} x^{5} + 96 \, a b^{4} x^{4} - 10 \, a^{2} b^{3} x^{3} - 192 \, a^{3} b^{2} x^{2} - 135 \, a^{4} b x + 96 \, a^{5}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{240 \, b}"," ",0,"-1/240*(210*a^6*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) + (40*b^5*x^5 + 96*a*b^4*x^4 - 10*a^2*b^3*x^3 - 192*a^3*b^2*x^2 - 135*a^4*b*x + 96*a^5)*sqrt(-b^2*x^2 + a^2))/b","A",0
790,1,94,0,0.414697," ","integrate((b*x+a)*(-b^2*x^2+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{30 \, a^{5} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) + {\left(8 \, b^{4} x^{4} + 10 \, a b^{3} x^{3} - 16 \, a^{2} b^{2} x^{2} - 25 \, a^{3} b x + 8 \, a^{4}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{40 \, b}"," ",0,"-1/40*(30*a^5*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) + (8*b^4*x^4 + 10*a*b^3*x^3 - 16*a^2*b^2*x^2 - 25*a^3*b*x + 8*a^4)*sqrt(-b^2*x^2 + a^2))/b","A",0
791,1,72,0,0.412828," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a),x, algorithm=""fricas"")","-\frac{6 \, a^{3} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) + {\left(2 \, b^{2} x^{2} - 3 \, a b x - 2 \, a^{2}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{6 \, b}"," ",0,"-1/6*(6*a^3*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) + (2*b^2*x^2 - 3*a*b*x - 2*a^2)*sqrt(-b^2*x^2 + a^2))/b","A",0
792,1,60,0,0.404352," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{6 \, a^{2} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) + \sqrt{-b^{2} x^{2} + a^{2}} {\left(b x - 4 \, a\right)}}{2 \, b}"," ",0,"-1/2*(6*a^2*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) + sqrt(-b^2*x^2 + a^2)*(b*x - 4*a))/b","A",0
793,1,83,0,0.410391," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{5 \, a b x + 5 \, a^{2} - 6 \, {\left(a b x + a^{2}\right)} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) + \sqrt{-b^{2} x^{2} + a^{2}} {\left(b x + 5 \, a\right)}}{b^{2} x + a b}"," ",0,"-(5*a*b*x + 5*a^2 - 6*(a*b*x + a^2)*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) + sqrt(-b^2*x^2 + a^2)*(b*x + 5*a))/(b^2*x + a*b)","A",0
794,1,110,0,0.418458," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^4,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b^{2} x^{2} + 4 \, a b x + 2 \, a^{2} - 3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) + 2 \, \sqrt{-b^{2} x^{2} + a^{2}} {\left(2 \, b x + a\right)}\right)}}{3 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"2/3*(2*b^2*x^2 + 4*a*b*x + 2*a^2 - 3*(b^2*x^2 + 2*a*b*x + a^2)*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) + 2*sqrt(-b^2*x^2 + a^2)*(2*b*x + a))/(b^3*x^2 + 2*a*b^2*x + a^2*b)","A",0
795,1,96,0,0.404668," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^5,x, algorithm=""fricas"")","-\frac{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3} + {\left(b^{2} x^{2} - 2 \, a b x + a^{2}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{5 \, {\left(a b^{4} x^{3} + 3 \, a^{2} b^{3} x^{2} + 3 \, a^{3} b^{2} x + a^{4} b\right)}}"," ",0,"-1/5*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3 + (b^2*x^2 - 2*a*b*x + a^2)*sqrt(-b^2*x^2 + a^2))/(a*b^4*x^3 + 3*a^2*b^3*x^2 + 3*a^3*b^2*x + a^4*b)","B",0
796,1,136,0,0.424782," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^6,x, algorithm=""fricas"")","-\frac{6 \, b^{4} x^{4} + 24 \, a b^{3} x^{3} + 36 \, a^{2} b^{2} x^{2} + 24 \, a^{3} b x + 6 \, a^{4} + {\left(b^{3} x^{3} + 4 \, a b^{2} x^{2} - 11 \, a^{2} b x + 6 \, a^{3}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{35 \, {\left(a^{2} b^{5} x^{4} + 4 \, a^{3} b^{4} x^{3} + 6 \, a^{4} b^{3} x^{2} + 4 \, a^{5} b^{2} x + a^{6} b\right)}}"," ",0,"-1/35*(6*b^4*x^4 + 24*a*b^3*x^3 + 36*a^2*b^2*x^2 + 24*a^3*b*x + 6*a^4 + (b^3*x^3 + 4*a*b^2*x^2 - 11*a^2*b*x + 6*a^3)*sqrt(-b^2*x^2 + a^2))/(a^2*b^5*x^4 + 4*a^3*b^4*x^3 + 6*a^4*b^3*x^2 + 4*a^5*b^2*x + a^6*b)","B",0
797,1,170,0,0.428292," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^7,x, algorithm=""fricas"")","-\frac{47 \, b^{5} x^{5} + 235 \, a b^{4} x^{4} + 470 \, a^{2} b^{3} x^{3} + 470 \, a^{3} b^{2} x^{2} + 235 \, a^{4} b x + 47 \, a^{5} + {\left(2 \, b^{4} x^{4} + 10 \, a b^{3} x^{3} + 21 \, a^{2} b^{2} x^{2} - 80 \, a^{3} b x + 47 \, a^{4}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{315 \, {\left(a^{3} b^{6} x^{5} + 5 \, a^{4} b^{5} x^{4} + 10 \, a^{5} b^{4} x^{3} + 10 \, a^{6} b^{3} x^{2} + 5 \, a^{7} b^{2} x + a^{8} b\right)}}"," ",0,"-1/315*(47*b^5*x^5 + 235*a*b^4*x^4 + 470*a^2*b^3*x^3 + 470*a^3*b^2*x^2 + 235*a^4*b*x + 47*a^5 + (2*b^4*x^4 + 10*a*b^3*x^3 + 21*a^2*b^2*x^2 - 80*a^3*b*x + 47*a^4)*sqrt(-b^2*x^2 + a^2))/(a^3*b^6*x^5 + 5*a^4*b^5*x^4 + 10*a^5*b^4*x^3 + 10*a^6*b^3*x^2 + 5*a^7*b^2*x + a^8*b)","A",0
798,1,203,0,0.499049," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^8,x, algorithm=""fricas"")","-\frac{152 \, b^{6} x^{6} + 912 \, a b^{5} x^{5} + 2280 \, a^{2} b^{4} x^{4} + 3040 \, a^{3} b^{3} x^{3} + 2280 \, a^{4} b^{2} x^{2} + 912 \, a^{5} b x + 152 \, a^{6} + {\left(2 \, b^{5} x^{5} + 12 \, a b^{4} x^{4} + 31 \, a^{2} b^{3} x^{3} + 46 \, a^{3} b^{2} x^{2} - 243 \, a^{4} b x + 152 \, a^{5}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{1155 \, {\left(a^{4} b^{7} x^{6} + 6 \, a^{5} b^{6} x^{5} + 15 \, a^{6} b^{5} x^{4} + 20 \, a^{7} b^{4} x^{3} + 15 \, a^{8} b^{3} x^{2} + 6 \, a^{9} b^{2} x + a^{10} b\right)}}"," ",0,"-1/1155*(152*b^6*x^6 + 912*a*b^5*x^5 + 2280*a^2*b^4*x^4 + 3040*a^3*b^3*x^3 + 2280*a^4*b^2*x^2 + 912*a^5*b*x + 152*a^6 + (2*b^5*x^5 + 12*a*b^4*x^4 + 31*a^2*b^3*x^3 + 46*a^3*b^2*x^2 - 243*a^4*b*x + 152*a^5)*sqrt(-b^2*x^2 + a^2))/(a^4*b^7*x^6 + 6*a^5*b^6*x^5 + 15*a^6*b^5*x^4 + 20*a^7*b^4*x^3 + 15*a^8*b^3*x^2 + 6*a^9*b^2*x + a^10*b)","A",0
799,1,236,0,0.637316," ","integrate((-b^2*x^2+a^2)^(3/2)/(b*x+a)^9,x, algorithm=""fricas"")","-\frac{1763 \, b^{7} x^{7} + 12341 \, a b^{6} x^{6} + 37023 \, a^{2} b^{5} x^{5} + 61705 \, a^{3} b^{4} x^{4} + 61705 \, a^{4} b^{3} x^{3} + 37023 \, a^{5} b^{2} x^{2} + 12341 \, a^{6} b x + 1763 \, a^{7} + {\left(8 \, b^{6} x^{6} + 56 \, a b^{5} x^{5} + 172 \, a^{2} b^{4} x^{4} + 308 \, a^{3} b^{3} x^{3} + 367 \, a^{4} b^{2} x^{2} - 2674 \, a^{5} b x + 1763 \, a^{6}\right)} \sqrt{-b^{2} x^{2} + a^{2}}}{15015 \, {\left(a^{5} b^{8} x^{7} + 7 \, a^{6} b^{7} x^{6} + 21 \, a^{7} b^{6} x^{5} + 35 \, a^{8} b^{5} x^{4} + 35 \, a^{9} b^{4} x^{3} + 21 \, a^{10} b^{3} x^{2} + 7 \, a^{11} b^{2} x + a^{12} b\right)}}"," ",0,"-1/15015*(1763*b^7*x^7 + 12341*a*b^6*x^6 + 37023*a^2*b^5*x^5 + 61705*a^3*b^4*x^4 + 61705*a^4*b^3*x^3 + 37023*a^5*b^2*x^2 + 12341*a^6*b*x + 1763*a^7 + (8*b^6*x^6 + 56*a*b^5*x^5 + 172*a^2*b^4*x^4 + 308*a^3*b^3*x^3 + 367*a^4*b^2*x^2 - 2674*a^5*b*x + 1763*a^6)*sqrt(-b^2*x^2 + a^2))/(a^5*b^8*x^7 + 7*a^6*b^7*x^6 + 21*a^7*b^6*x^5 + 35*a^8*b^5*x^4 + 35*a^9*b^4*x^3 + 21*a^10*b^3*x^2 + 7*a^11*b^2*x + a^12*b)","A",0
800,1,160,0,0.426509," ","integrate((e*x+d)^3*(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{90090 \, d^{11} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(11520 \, e^{10} x^{10} + 38016 \, d e^{9} x^{9} - 1280 \, d^{2} e^{8} x^{8} - 131472 \, d^{3} e^{7} x^{7} - 110080 \, d^{4} e^{6} x^{6} + 142296 \, d^{5} e^{5} x^{5} + 222720 \, d^{6} e^{4} x^{4} - 12210 \, d^{7} e^{3} x^{3} - 167680 \, d^{8} e^{2} x^{2} - 81675 \, d^{9} e x + 44800 \, d^{10}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{126720 \, e}"," ",0,"-1/126720*(90090*d^11*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (11520*e^10*x^10 + 38016*d*e^9*x^9 - 1280*d^2*e^8*x^8 - 131472*d^3*e^7*x^7 - 110080*d^4*e^6*x^6 + 142296*d^5*e^5*x^5 + 222720*d^6*e^4*x^4 - 12210*d^7*e^3*x^3 - 167680*d^8*e^2*x^2 - 81675*d^9*e*x + 44800*d^10)*sqrt(-e^2*x^2 + d^2))/e","A",0
801,1,149,0,0.427787," ","integrate((e*x+d)^2*(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{6930 \, d^{10} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(1152 \, e^{9} x^{9} + 2560 \, d e^{8} x^{8} - 3024 \, d^{2} e^{7} x^{7} - 10240 \, d^{3} e^{6} x^{6} + 312 \, d^{4} e^{5} x^{5} + 15360 \, d^{5} e^{4} x^{4} + 6150 \, d^{6} e^{3} x^{3} - 10240 \, d^{7} e^{2} x^{2} - 8055 \, d^{8} e x + 2560 \, d^{9}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{11520 \, e}"," ",0,"-1/11520*(6930*d^10*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (1152*e^9*x^9 + 2560*d*e^8*x^8 - 3024*d^2*e^7*x^7 - 10240*d^3*e^6*x^6 + 312*d^4*e^5*x^5 + 15360*d^5*e^4*x^4 + 6150*d^6*e^3*x^3 - 10240*d^7*e^2*x^2 - 8055*d^8*e*x + 2560*d^9)*sqrt(-e^2*x^2 + d^2))/e","A",0
802,1,138,0,0.433334," ","integrate((e*x+d)*(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{630 \, d^{9} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(128 \, e^{8} x^{8} + 144 \, d e^{7} x^{7} - 512 \, d^{2} e^{6} x^{6} - 600 \, d^{3} e^{5} x^{5} + 768 \, d^{4} e^{4} x^{4} + 978 \, d^{5} e^{3} x^{3} - 512 \, d^{6} e^{2} x^{2} - 837 \, d^{7} e x + 128 \, d^{8}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{1152 \, e}"," ",0,"-1/1152*(630*d^9*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (128*e^8*x^8 + 144*d*e^7*x^7 - 512*d^2*e^6*x^6 - 600*d^3*e^5*x^5 + 768*d^4*e^4*x^4 + 978*d^5*e^3*x^3 - 512*d^6*e^2*x^2 - 837*d^7*e*x + 128*d^8)*sqrt(-e^2*x^2 + d^2))/e","A",0
803,1,116,0,0.423106," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d),x, algorithm=""fricas"")","-\frac{210 \, d^{7} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(48 \, e^{6} x^{6} - 56 \, d e^{5} x^{5} - 144 \, d^{2} e^{4} x^{4} + 182 \, d^{3} e^{3} x^{3} + 144 \, d^{4} e^{2} x^{2} - 231 \, d^{5} e x - 48 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{336 \, e}"," ",0,"-1/336*(210*d^7*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (48*e^6*x^6 - 56*d*e^5*x^5 - 144*d^2*e^4*x^4 + 182*d^3*e^3*x^3 + 144*d^4*e^2*x^2 - 231*d^5*e*x - 48*d^6)*sqrt(-e^2*x^2 + d^2))/e","A",0
804,1,105,0,0.422816," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{210 \, d^{6} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(40 \, e^{5} x^{5} - 96 \, d e^{4} x^{4} - 10 \, d^{2} e^{3} x^{3} + 192 \, d^{3} e^{2} x^{2} - 135 \, d^{4} e x - 96 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{240 \, e}"," ",0,"-1/240*(210*d^6*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (40*e^5*x^5 - 96*d*e^4*x^4 - 10*d^2*e^3*x^3 + 192*d^3*e^2*x^2 - 135*d^4*e*x - 96*d^5)*sqrt(-e^2*x^2 + d^2))/e","A",0
805,1,94,0,0.404697," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^3,x, algorithm=""fricas"")","-\frac{210 \, d^{5} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(24 \, e^{4} x^{4} - 90 \, d e^{3} x^{3} + 112 \, d^{2} e^{2} x^{2} - 15 \, d^{3} e x - 136 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{120 \, e}"," ",0,"-1/120*(210*d^5*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (24*e^4*x^4 - 90*d*e^3*x^3 + 112*d^2*e^2*x^2 - 15*d^3*e*x - 136*d^4)*sqrt(-e^2*x^2 + d^2))/e","A",0
806,1,83,0,0.414271," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{210 \, d^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(6 \, e^{3} x^{3} - 32 \, d e^{2} x^{2} + 81 \, d^{2} e x - 160 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, e}"," ",0,"-1/24*(210*d^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (6*e^3*x^3 - 32*d*e^2*x^2 + 81*d^2*e*x - 160*d^3)*sqrt(-e^2*x^2 + d^2))/e","A",0
807,1,110,0,0.427989," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{166 \, d^{3} e x + 166 \, d^{4} - 210 \, {\left(d^{3} e x + d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(2 \, e^{3} x^{3} - 13 \, d e^{2} x^{2} + 55 \, d^{2} e x + 166 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, {\left(e^{2} x + d e\right)}}"," ",0,"-1/6*(166*d^3*e*x + 166*d^4 - 210*(d^3*e*x + d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (2*e^3*x^3 - 13*d*e^2*x^2 + 55*d^2*e*x + 166*d^3)*sqrt(-e^2*x^2 + d^2))/(e^2*x + d*e)","A",0
808,1,144,0,0.430177," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^6,x, algorithm=""fricas"")","\frac{164 \, d^{2} e^{2} x^{2} + 328 \, d^{3} e x + 164 \, d^{4} - 210 \, {\left(d^{2} e^{2} x^{2} + 2 \, d^{3} e x + d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(3 \, e^{3} x^{3} - 30 \, d e^{2} x^{2} - 229 \, d^{2} e x - 164 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"1/6*(164*d^2*e^2*x^2 + 328*d^3*e*x + 164*d^4 - 210*(d^2*e^2*x^2 + 2*d^3*e*x + d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (3*e^3*x^3 - 30*d*e^2*x^2 - 229*d^2*e*x - 164*d^3)*sqrt(-e^2*x^2 + d^2))/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
809,1,172,0,0.430892," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{167 \, d e^{3} x^{3} + 501 \, d^{2} e^{2} x^{2} + 501 \, d^{3} e x + 167 \, d^{4} - 210 \, {\left(d e^{3} x^{3} + 3 \, d^{2} e^{2} x^{2} + 3 \, d^{3} e x + d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(15 \, e^{3} x^{3} + 277 \, d e^{2} x^{2} + 381 \, d^{2} e x + 167 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"-1/15*(167*d*e^3*x^3 + 501*d^2*e^2*x^2 + 501*d^3*e*x + 167*d^4 - 210*(d*e^3*x^3 + 3*d^2*e^2*x^2 + 3*d^3*e*x + d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (15*e^3*x^3 + 277*d*e^2*x^2 + 381*d^2*e*x + 167*d^3)*sqrt(-e^2*x^2 + d^2))/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","A",0
810,1,200,0,0.428901," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^8,x, algorithm=""fricas"")","\frac{2 \, {\left(76 \, e^{4} x^{4} + 304 \, d e^{3} x^{3} + 456 \, d^{2} e^{2} x^{2} + 304 \, d^{3} e x + 76 \, d^{4} - 105 \, {\left(e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + 4 \, {\left(44 \, e^{3} x^{3} + 71 \, d e^{2} x^{2} + 76 \, d^{2} e x + 19 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}\right)}}{105 \, {\left(e^{5} x^{4} + 4 \, d e^{4} x^{3} + 6 \, d^{2} e^{3} x^{2} + 4 \, d^{3} e^{2} x + d^{4} e\right)}}"," ",0,"2/105*(76*e^4*x^4 + 304*d*e^3*x^3 + 456*d^2*e^2*x^2 + 304*d^3*e*x + 76*d^4 - 105*(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + 4*(44*e^3*x^3 + 71*d*e^2*x^2 + 76*d^2*e*x + 19*d^3)*sqrt(-e^2*x^2 + d^2))/(e^5*x^4 + 4*d*e^4*x^3 + 6*d^2*e^3*x^2 + 4*d^3*e^2*x + d^4*e)","A",0
811,1,162,0,0.431762," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{e^{5} x^{5} + 5 \, d e^{4} x^{4} + 10 \, d^{2} e^{3} x^{3} + 10 \, d^{3} e^{2} x^{2} + 5 \, d^{4} e x + d^{5} + {\left(e^{4} x^{4} - 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} - 4 \, d^{3} e x + d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{9 \, {\left(d e^{6} x^{5} + 5 \, d^{2} e^{5} x^{4} + 10 \, d^{3} e^{4} x^{3} + 10 \, d^{4} e^{3} x^{2} + 5 \, d^{5} e^{2} x + d^{6} e\right)}}"," ",0,"-1/9*(e^5*x^5 + 5*d*e^4*x^4 + 10*d^2*e^3*x^3 + 10*d^3*e^2*x^2 + 5*d^4*e*x + d^5 + (e^4*x^4 - 4*d*e^3*x^3 + 6*d^2*e^2*x^2 - 4*d^3*e*x + d^4)*sqrt(-e^2*x^2 + d^2))/(d*e^6*x^5 + 5*d^2*e^5*x^4 + 10*d^3*e^4*x^3 + 10*d^4*e^3*x^2 + 5*d^5*e^2*x + d^6*e)","B",0
812,1,202,0,0.501551," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{10 \, e^{6} x^{6} + 60 \, d e^{5} x^{5} + 150 \, d^{2} e^{4} x^{4} + 200 \, d^{3} e^{3} x^{3} + 150 \, d^{4} e^{2} x^{2} + 60 \, d^{5} e x + 10 \, d^{6} + {\left(e^{5} x^{5} + 6 \, d e^{4} x^{4} - 34 \, d^{2} e^{3} x^{3} + 56 \, d^{3} e^{2} x^{2} - 39 \, d^{4} e x + 10 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{99 \, {\left(d^{2} e^{7} x^{6} + 6 \, d^{3} e^{6} x^{5} + 15 \, d^{4} e^{5} x^{4} + 20 \, d^{5} e^{4} x^{3} + 15 \, d^{6} e^{3} x^{2} + 6 \, d^{7} e^{2} x + d^{8} e\right)}}"," ",0,"-1/99*(10*e^6*x^6 + 60*d*e^5*x^5 + 150*d^2*e^4*x^4 + 200*d^3*e^3*x^3 + 150*d^4*e^2*x^2 + 60*d^5*e*x + 10*d^6 + (e^5*x^5 + 6*d*e^4*x^4 - 34*d^2*e^3*x^3 + 56*d^3*e^2*x^2 - 39*d^4*e*x + 10*d^5)*sqrt(-e^2*x^2 + d^2))/(d^2*e^7*x^6 + 6*d^3*e^6*x^5 + 15*d^4*e^5*x^4 + 20*d^5*e^4*x^3 + 15*d^6*e^3*x^2 + 6*d^7*e^2*x + d^8*e)","B",0
813,1,236,0,0.630021," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{119 \, e^{7} x^{7} + 833 \, d e^{6} x^{6} + 2499 \, d^{2} e^{5} x^{5} + 4165 \, d^{3} e^{4} x^{4} + 4165 \, d^{4} e^{3} x^{3} + 2499 \, d^{5} e^{2} x^{2} + 833 \, d^{6} e x + 119 \, d^{7} + {\left(2 \, e^{6} x^{6} + 14 \, d e^{5} x^{5} + 43 \, d^{2} e^{4} x^{4} - 352 \, d^{3} e^{3} x^{3} + 628 \, d^{4} e^{2} x^{2} - 454 \, d^{5} e x + 119 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{1287 \, {\left(d^{3} e^{8} x^{7} + 7 \, d^{4} e^{7} x^{6} + 21 \, d^{5} e^{6} x^{5} + 35 \, d^{6} e^{5} x^{4} + 35 \, d^{7} e^{4} x^{3} + 21 \, d^{8} e^{3} x^{2} + 7 \, d^{9} e^{2} x + d^{10} e\right)}}"," ",0,"-1/1287*(119*e^7*x^7 + 833*d*e^6*x^6 + 2499*d^2*e^5*x^5 + 4165*d^3*e^4*x^4 + 4165*d^4*e^3*x^3 + 2499*d^5*e^2*x^2 + 833*d^6*e*x + 119*d^7 + (2*e^6*x^6 + 14*d*e^5*x^5 + 43*d^2*e^4*x^4 - 352*d^3*e^3*x^3 + 628*d^4*e^2*x^2 - 454*d^5*e*x + 119*d^6)*sqrt(-e^2*x^2 + d^2))/(d^3*e^8*x^7 + 7*d^4*e^7*x^6 + 21*d^5*e^6*x^5 + 35*d^6*e^5*x^4 + 35*d^7*e^4*x^3 + 21*d^8*e^3*x^2 + 7*d^9*e^2*x + d^10*e)","B",0
814,1,269,0,0.815289," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^12,x, algorithm=""fricas"")","-\frac{548 \, e^{8} x^{8} + 4384 \, d e^{7} x^{7} + 15344 \, d^{2} e^{6} x^{6} + 30688 \, d^{3} e^{5} x^{5} + 38360 \, d^{4} e^{4} x^{4} + 30688 \, d^{5} e^{3} x^{3} + 15344 \, d^{6} e^{2} x^{2} + 4384 \, d^{7} e x + 548 \, d^{8} + {\left(2 \, e^{7} x^{7} + 16 \, d e^{6} x^{6} + 57 \, d^{2} e^{5} x^{5} + 120 \, d^{3} e^{4} x^{4} - 1440 \, d^{4} e^{3} x^{3} + 2748 \, d^{5} e^{2} x^{2} - 2051 \, d^{6} e x + 548 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6435 \, {\left(d^{4} e^{9} x^{8} + 8 \, d^{5} e^{8} x^{7} + 28 \, d^{6} e^{7} x^{6} + 56 \, d^{7} e^{6} x^{5} + 70 \, d^{8} e^{5} x^{4} + 56 \, d^{9} e^{4} x^{3} + 28 \, d^{10} e^{3} x^{2} + 8 \, d^{11} e^{2} x + d^{12} e\right)}}"," ",0,"-1/6435*(548*e^8*x^8 + 4384*d*e^7*x^7 + 15344*d^2*e^6*x^6 + 30688*d^3*e^5*x^5 + 38360*d^4*e^4*x^4 + 30688*d^5*e^3*x^3 + 15344*d^6*e^2*x^2 + 4384*d^7*e*x + 548*d^8 + (2*e^7*x^7 + 16*d*e^6*x^6 + 57*d^2*e^5*x^5 + 120*d^3*e^4*x^4 - 1440*d^4*e^3*x^3 + 2748*d^5*e^2*x^2 - 2051*d^6*e*x + 548*d^7)*sqrt(-e^2*x^2 + d^2))/(d^4*e^9*x^8 + 8*d^5*e^8*x^7 + 28*d^6*e^7*x^6 + 56*d^7*e^6*x^5 + 70*d^8*e^5*x^4 + 56*d^9*e^4*x^3 + 28*d^10*e^3*x^2 + 8*d^11*e^2*x + d^12*e)","B",0
815,1,302,0,1.052819," ","integrate((-e^2*x^2+d^2)^(7/2)/(e*x+d)^13,x, algorithm=""fricas"")","-\frac{8627 \, e^{9} x^{9} + 77643 \, d e^{8} x^{8} + 310572 \, d^{2} e^{7} x^{7} + 724668 \, d^{3} e^{6} x^{6} + 1087002 \, d^{4} e^{5} x^{5} + 1087002 \, d^{5} e^{4} x^{4} + 724668 \, d^{6} e^{3} x^{3} + 310572 \, d^{7} e^{2} x^{2} + 77643 \, d^{8} e x + 8627 \, d^{9} + {\left(8 \, e^{8} x^{8} + 72 \, d e^{7} x^{7} + 292 \, d^{2} e^{6} x^{6} + 708 \, d^{3} e^{5} x^{5} + 1155 \, d^{4} e^{4} x^{4} - 20508 \, d^{5} e^{3} x^{3} + 41398 \, d^{6} e^{2} x^{2} - 31752 \, d^{7} e x + 8627 \, d^{8}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{109395 \, {\left(d^{5} e^{10} x^{9} + 9 \, d^{6} e^{9} x^{8} + 36 \, d^{7} e^{8} x^{7} + 84 \, d^{8} e^{7} x^{6} + 126 \, d^{9} e^{6} x^{5} + 126 \, d^{10} e^{5} x^{4} + 84 \, d^{11} e^{4} x^{3} + 36 \, d^{12} e^{3} x^{2} + 9 \, d^{13} e^{2} x + d^{14} e\right)}}"," ",0,"-1/109395*(8627*e^9*x^9 + 77643*d*e^8*x^8 + 310572*d^2*e^7*x^7 + 724668*d^3*e^6*x^6 + 1087002*d^4*e^5*x^5 + 1087002*d^5*e^4*x^4 + 724668*d^6*e^3*x^3 + 310572*d^7*e^2*x^2 + 77643*d^8*e*x + 8627*d^9 + (8*e^8*x^8 + 72*d*e^7*x^7 + 292*d^2*e^6*x^6 + 708*d^3*e^5*x^5 + 1155*d^4*e^4*x^4 - 20508*d^5*e^3*x^3 + 41398*d^6*e^2*x^2 - 31752*d^7*e*x + 8627*d^8)*sqrt(-e^2*x^2 + d^2))/(d^5*e^10*x^9 + 9*d^6*e^9*x^8 + 36*d^7*e^8*x^7 + 84*d^8*e^7*x^6 + 126*d^9*e^6*x^5 + 126*d^10*e^5*x^4 + 84*d^11*e^4*x^3 + 36*d^12*e^3*x^2 + 9*d^13*e^2*x + d^14*e)","B",0
816,1,50,0,0.422747," ","integrate((-b^2*x^2+a^2)^(1/2)/(-b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a \arctan\left(-\frac{a - \sqrt{-b^{2} x^{2} + a^{2}}}{b x}\right) + \sqrt{-b^{2} x^{2} + a^{2}}}{b}"," ",0,"-(2*a*arctan(-(a - sqrt(-b^2*x^2 + a^2))/(b*x)) + sqrt(-b^2*x^2 + a^2))/b","A",0
817,1,238,0,0.427666," ","integrate((b*x+a)^2*(-a^2*c/b^2+c*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{4} \sqrt{c} \log\left(2 \, b^{2} c x^{2} - 2 \, b^{2} \sqrt{c} x \sqrt{\frac{b^{2} c x^{2} - a^{2} c}{b^{2}}} - a^{2} c\right) + 2 \, {\left(6 \, b^{4} x^{3} + 16 \, a b^{3} x^{2} + 9 \, a^{2} b^{2} x - 16 \, a^{3} b\right)} \sqrt{\frac{b^{2} c x^{2} - a^{2} c}{b^{2}}}}{48 \, b^{2}}, \frac{15 \, a^{4} \sqrt{-c} \arctan\left(\frac{b^{2} \sqrt{-c} x \sqrt{\frac{b^{2} c x^{2} - a^{2} c}{b^{2}}}}{b^{2} c x^{2} - a^{2} c}\right) + {\left(6 \, b^{4} x^{3} + 16 \, a b^{3} x^{2} + 9 \, a^{2} b^{2} x - 16 \, a^{3} b\right)} \sqrt{\frac{b^{2} c x^{2} - a^{2} c}{b^{2}}}}{24 \, b^{2}}\right]"," ",0,"[1/48*(15*a^4*sqrt(c)*log(2*b^2*c*x^2 - 2*b^2*sqrt(c)*x*sqrt((b^2*c*x^2 - a^2*c)/b^2) - a^2*c) + 2*(6*b^4*x^3 + 16*a*b^3*x^2 + 9*a^2*b^2*x - 16*a^3*b)*sqrt((b^2*c*x^2 - a^2*c)/b^2))/b^2, 1/24*(15*a^4*sqrt(-c)*arctan(b^2*sqrt(-c)*x*sqrt((b^2*c*x^2 - a^2*c)/b^2)/(b^2*c*x^2 - a^2*c)) + (6*b^4*x^3 + 16*a*b^3*x^2 + 9*a^2*b^2*x - 16*a^3*b)*sqrt((b^2*c*x^2 - a^2*c)/b^2))/b^2]","A",0
818,1,260,0,0.446053," ","integrate((b*x+a)^3*(-a^2*c/b^2+c*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, a^{5} \sqrt{c} \log\left(2 \, b^{2} c x^{2} - 2 \, b^{2} \sqrt{c} x \sqrt{\frac{b^{2} c x^{2} - a^{2} c}{b^{2}}} - a^{2} c\right) + 2 \, {\left(24 \, b^{5} x^{4} + 90 \, a b^{4} x^{3} + 112 \, a^{2} b^{3} x^{2} + 15 \, a^{3} b^{2} x - 136 \, a^{4} b\right)} \sqrt{\frac{b^{2} c x^{2} - a^{2} c}{b^{2}}}}{240 \, b^{2}}, \frac{105 \, a^{5} \sqrt{-c} \arctan\left(\frac{b^{2} \sqrt{-c} x \sqrt{\frac{b^{2} c x^{2} - a^{2} c}{b^{2}}}}{b^{2} c x^{2} - a^{2} c}\right) + {\left(24 \, b^{5} x^{4} + 90 \, a b^{4} x^{3} + 112 \, a^{2} b^{3} x^{2} + 15 \, a^{3} b^{2} x - 136 \, a^{4} b\right)} \sqrt{\frac{b^{2} c x^{2} - a^{2} c}{b^{2}}}}{120 \, b^{2}}\right]"," ",0,"[1/240*(105*a^5*sqrt(c)*log(2*b^2*c*x^2 - 2*b^2*sqrt(c)*x*sqrt((b^2*c*x^2 - a^2*c)/b^2) - a^2*c) + 2*(24*b^5*x^4 + 90*a*b^4*x^3 + 112*a^2*b^3*x^2 + 15*a^3*b^2*x - 136*a^4*b)*sqrt((b^2*c*x^2 - a^2*c)/b^2))/b^2, 1/120*(105*a^5*sqrt(-c)*arctan(b^2*sqrt(-c)*x*sqrt((b^2*c*x^2 - a^2*c)/b^2)/(b^2*c*x^2 - a^2*c)) + (24*b^5*x^4 + 90*a*b^4*x^3 + 112*a^2*b^3*x^2 + 15*a^3*b^2*x - 136*a^4*b)*sqrt((b^2*c*x^2 - a^2*c)/b^2))/b^2]","A",0
819,1,34,0,0.407818," ","integrate((1+x)*(x^2-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(2 \, x^{2} + 3 \, x - 2\right)} \sqrt{x^{2} - 1} + \frac{1}{2} \, \log\left(-x + \sqrt{x^{2} - 1}\right)"," ",0,"1/6*(2*x^2 + 3*x - 2)*sqrt(x^2 - 1) + 1/2*log(-x + sqrt(x^2 - 1))","A",0
820,1,40,0,0.393955," ","integrate((1+x)*(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(2 \, x^{2} + 3 \, x - 2\right)} \sqrt{-x^{2} + 1} - \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"1/6*(2*x^2 + 3*x - 2)*sqrt(-x^2 + 1) - arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
821,1,28,0,0.410810," ","integrate((-x^2+1)^(1/2)/(1+x),x, algorithm=""fricas"")","\sqrt{-x^{2} + 1} - 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"sqrt(-x^2 + 1) - 2*arctan((sqrt(-x^2 + 1) - 1)/x)","B",0
822,1,40,0,0.403891," ","integrate((1-x)*(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{6} \, {\left(2 \, x^{2} - 3 \, x - 2\right)} \sqrt{-x^{2} + 1} - \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-1/6*(2*x^2 - 3*x - 2)*sqrt(-x^2 + 1) - arctan((sqrt(-x^2 + 1) - 1)/x)","A",0
823,1,30,0,0.407993," ","integrate((-x^2+1)^(1/2)/(1-x),x, algorithm=""fricas"")","-\sqrt{-x^{2} + 1} - 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-sqrt(-x^2 + 1) - 2*arctan((sqrt(-x^2 + 1) - 1)/x)","B",0
824,1,41,0,0.395741," ","integrate((-x^2+1)^(1/2)/(1-x)^2,x, algorithm=""fricas"")","\frac{2 \, {\left({\left(x - 1\right)} \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right) + x - \sqrt{-x^{2} + 1} - 1\right)}}{x - 1}"," ",0,"2*((x - 1)*arctan((sqrt(-x^2 + 1) - 1)/x) + x - sqrt(-x^2 + 1) - 1)/(x - 1)","A",0
825,1,33,0,0.402472," ","integrate((-x^2+1)^(1/2)/(1-x)^3,x, algorithm=""fricas"")","\frac{x^{2} + \sqrt{-x^{2} + 1} {\left(x + 1\right)} - 2 \, x + 1}{3 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"1/3*(x^2 + sqrt(-x^2 + 1)*(x + 1) - 2*x + 1)/(x^2 - 2*x + 1)","B",0
826,1,94,0,0.419765," ","integrate((e*x+d)^5/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{630 \, d^{5} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(8 \, e^{4} x^{4} + 50 \, d e^{3} x^{3} + 144 \, d^{2} e^{2} x^{2} + 275 \, d^{3} e x + 488 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{40 \, e}"," ",0,"-1/40*(630*d^5*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (8*e^4*x^4 + 50*d*e^3*x^3 + 144*d^2*e^2*x^2 + 275*d^3*e*x + 488*d^4)*sqrt(-e^2*x^2 + d^2))/e","A",0
827,1,83,0,0.409535," ","integrate((e*x+d)^4/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{210 \, d^{4} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(6 \, e^{3} x^{3} + 32 \, d e^{2} x^{2} + 81 \, d^{2} e x + 160 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{24 \, e}"," ",0,"-1/24*(210*d^4*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (6*e^3*x^3 + 32*d*e^2*x^2 + 81*d^2*e*x + 160*d^3)*sqrt(-e^2*x^2 + d^2))/e","A",0
828,1,72,0,0.419492," ","integrate((e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{30 \, d^{3} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(2 \, e^{2} x^{2} + 9 \, d e x + 22 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, e}"," ",0,"-1/6*(30*d^3*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (2*e^2*x^2 + 9*d*e*x + 22*d^2)*sqrt(-e^2*x^2 + d^2))/e","A",0
829,1,60,0,0.409164," ","integrate((e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, d^{2} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + 4 \, d\right)}}{2 \, e}"," ",0,"-1/2*(6*d^2*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + sqrt(-e^2*x^2 + d^2)*(e*x + 4*d))/e","A",0
830,1,50,0,0.393819," ","integrate((e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, d \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + \sqrt{-e^{2} x^{2} + d^{2}}}{e}"," ",0,"-(2*d*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + sqrt(-e^2*x^2 + d^2))/e","A",0
831,1,35,0,0.400553," ","integrate(1/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{e x + d + \sqrt{-e^{2} x^{2} + d^{2}}}{d e^{2} x + d^{2} e}"," ",0,"-(e*x + d + sqrt(-e^2*x^2 + d^2))/(d*e^2*x + d^2*e)","A",0
832,1,70,0,0.394719," ","integrate(1/(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, e^{2} x^{2} + 4 \, d e x + 2 \, d^{2} + \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + 2 \, d\right)}}{3 \, {\left(d^{2} e^{3} x^{2} + 2 \, d^{3} e^{2} x + d^{4} e\right)}}"," ",0,"-1/3*(2*e^2*x^2 + 4*d*e*x + 2*d^2 + sqrt(-e^2*x^2 + d^2)*(e*x + 2*d))/(d^2*e^3*x^2 + 2*d^3*e^2*x + d^4*e)","A",0
833,1,104,0,0.403383," ","integrate(1/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{7 \, e^{3} x^{3} + 21 \, d e^{2} x^{2} + 21 \, d^{2} e x + 7 \, d^{3} + {\left(2 \, e^{2} x^{2} + 6 \, d e x + 7 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{4} x^{3} + 3 \, d^{4} e^{3} x^{2} + 3 \, d^{5} e^{2} x + d^{6} e\right)}}"," ",0,"-1/15*(7*e^3*x^3 + 21*d*e^2*x^2 + 21*d^2*e*x + 7*d^3 + (2*e^2*x^2 + 6*d*e*x + 7*d^2)*sqrt(-e^2*x^2 + d^2))/(d^3*e^4*x^3 + 3*d^4*e^3*x^2 + 3*d^5*e^2*x + d^6*e)","A",0
834,1,137,0,0.402301," ","integrate(1/(e*x+d)^4/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{12 \, e^{4} x^{4} + 48 \, d e^{3} x^{3} + 72 \, d^{2} e^{2} x^{2} + 48 \, d^{3} e x + 12 \, d^{4} + {\left(2 \, e^{3} x^{3} + 8 \, d e^{2} x^{2} + 13 \, d^{2} e x + 12 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{35 \, {\left(d^{4} e^{5} x^{4} + 4 \, d^{5} e^{4} x^{3} + 6 \, d^{6} e^{3} x^{2} + 4 \, d^{7} e^{2} x + d^{8} e\right)}}"," ",0,"-1/35*(12*e^4*x^4 + 48*d*e^3*x^3 + 72*d^2*e^2*x^2 + 48*d^3*e*x + 12*d^4 + (2*e^3*x^3 + 8*d*e^2*x^2 + 13*d^2*e*x + 12*d^3)*sqrt(-e^2*x^2 + d^2))/(d^4*e^5*x^4 + 4*d^5*e^4*x^3 + 6*d^6*e^3*x^2 + 4*d^7*e^2*x + d^8*e)","A",0
835,1,170,0,0.442049," ","integrate(1/(e*x+d)^5/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","-\frac{83 \, e^{5} x^{5} + 415 \, d e^{4} x^{4} + 830 \, d^{2} e^{3} x^{3} + 830 \, d^{3} e^{2} x^{2} + 415 \, d^{4} e x + 83 \, d^{5} + {\left(8 \, e^{4} x^{4} + 40 \, d e^{3} x^{3} + 84 \, d^{2} e^{2} x^{2} + 100 \, d^{3} e x + 83 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{315 \, {\left(d^{5} e^{6} x^{5} + 5 \, d^{6} e^{5} x^{4} + 10 \, d^{7} e^{4} x^{3} + 10 \, d^{8} e^{3} x^{2} + 5 \, d^{9} e^{2} x + d^{10} e\right)}}"," ",0,"-1/315*(83*e^5*x^5 + 415*d*e^4*x^4 + 830*d^2*e^3*x^3 + 830*d^3*e^2*x^2 + 415*d^4*e*x + 83*d^5 + (8*e^4*x^4 + 40*d*e^3*x^3 + 84*d^2*e^2*x^2 + 100*d^3*e*x + 83*d^4)*sqrt(-e^2*x^2 + d^2))/(d^5*e^6*x^5 + 5*d^6*e^5*x^4 + 10*d^7*e^4*x^3 + 10*d^8*e^3*x^2 + 5*d^9*e^2*x + d^10*e)","A",0
836,1,143,0,0.437514," ","integrate((e*x+d)^6/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{164 \, d^{2} e^{2} x^{2} - 328 \, d^{3} e x + 164 \, d^{4} + 210 \, {\left(d^{2} e^{2} x^{2} - 2 \, d^{3} e x + d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(3 \, e^{3} x^{3} + 30 \, d e^{2} x^{2} - 229 \, d^{2} e x + 164 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{6 \, {\left(e^{3} x^{2} - 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-1/6*(164*d^2*e^2*x^2 - 328*d^3*e*x + 164*d^4 + 210*(d^2*e^2*x^2 - 2*d^3*e*x + d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (3*e^3*x^3 + 30*d*e^2*x^2 - 229*d^2*e*x + 164*d^3)*sqrt(-e^2*x^2 + d^2))/(e^3*x^2 - 2*d*e^2*x + d^2*e)","A",0
837,1,128,0,0.422985," ","integrate((e*x+d)^5/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{23 \, d e^{2} x^{2} - 46 \, d^{2} e x + 23 \, d^{3} + 30 \, {\left(d e^{2} x^{2} - 2 \, d^{2} e x + d^{3}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(3 \, e^{2} x^{2} - 34 \, d e x + 23 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(e^{3} x^{2} - 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-1/3*(23*d*e^2*x^2 - 46*d^2*e*x + 23*d^3 + 30*(d*e^2*x^2 - 2*d^2*e*x + d^3)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (3*e^2*x^2 - 34*d*e*x + 23*d^2)*sqrt(-e^2*x^2 + d^2))/(e^3*x^2 - 2*d*e^2*x + d^2*e)","A",0
838,1,112,0,0.415849," ","integrate((e*x+d)^4/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, e^{2} x^{2} - 4 \, d e x + 2 \, d^{2} + 3 \, {\left(e^{2} x^{2} - 2 \, d e x + d^{2}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - 2 \, \sqrt{-e^{2} x^{2} + d^{2}} {\left(2 \, e x - d\right)}\right)}}{3 \, {\left(e^{3} x^{2} - 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-2/3*(2*e^2*x^2 - 4*d*e*x + 2*d^2 + 3*(e^2*x^2 - 2*d*e*x + d^2)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - 2*sqrt(-e^2*x^2 + d^2)*(2*e*x - d))/(e^3*x^2 - 2*d*e^2*x + d^2*e)","A",0
839,1,63,0,0.397674," ","integrate((e*x+d)^3/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","\frac{e^{2} x^{2} - 2 \, d e x + d^{2} + \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + d\right)}}{3 \, {\left(d e^{3} x^{2} - 2 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"1/3*(e^2*x^2 - 2*d*e*x + d^2 + sqrt(-e^2*x^2 + d^2)*(e*x + d))/(d*e^3*x^2 - 2*d^2*e^2*x + d^3*e)","B",0
840,1,71,0,0.397761," ","integrate((e*x+d)^2/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, e^{2} x^{2} - 4 \, d e x + 2 \, d^{2} - \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x - 2 \, d\right)}}{3 \, {\left(d^{2} e^{3} x^{2} - 2 \, d^{3} e^{2} x + d^{4} e\right)}}"," ",0,"1/3*(2*e^2*x^2 - 4*d*e*x + 2*d^2 - sqrt(-e^2*x^2 + d^2)*(e*x - 2*d))/(d^2*e^3*x^2 - 2*d^3*e^2*x + d^4*e)","A",0
841,1,102,0,0.409170," ","integrate((e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","\frac{e^{3} x^{3} - d e^{2} x^{2} - d^{2} e x + d^{3} - {\left(2 \, e^{2} x^{2} - 2 \, d e x - d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{3 \, {\left(d^{3} e^{4} x^{3} - d^{4} e^{3} x^{2} - d^{5} e^{2} x + d^{6} e\right)}}"," ",0,"1/3*(e^3*x^3 - d*e^2*x^2 - d^2*e*x + d^3 - (2*e^2*x^2 - 2*d*e*x - d^2)*sqrt(-e^2*x^2 + d^2))/(d^3*e^4*x^3 - d^4*e^3*x^2 - d^5*e^2*x + d^6*e)","B",0
842,1,168,0,0.428901," ","integrate(1/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, e^{5} x^{5} + 3 \, d e^{4} x^{4} - 6 \, d^{2} e^{3} x^{3} - 6 \, d^{3} e^{2} x^{2} + 3 \, d^{4} e x + 3 \, d^{5} + {\left(8 \, e^{4} x^{4} + 8 \, d e^{3} x^{3} - 12 \, d^{2} e^{2} x^{2} - 12 \, d^{3} e x + 3 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{5} e^{6} x^{5} + d^{6} e^{5} x^{4} - 2 \, d^{7} e^{4} x^{3} - 2 \, d^{8} e^{3} x^{2} + d^{9} e^{2} x + d^{10} e\right)}}"," ",0,"-1/15*(3*e^5*x^5 + 3*d*e^4*x^4 - 6*d^2*e^3*x^3 - 6*d^3*e^2*x^2 + 3*d^4*e*x + 3*d^5 + (8*e^4*x^4 + 8*d*e^3*x^3 - 12*d^2*e^2*x^2 - 12*d^3*e*x + 3*d^4)*sqrt(-e^2*x^2 + d^2))/(d^5*e^6*x^5 + d^6*e^5*x^4 - 2*d^7*e^4*x^3 - 2*d^8*e^3*x^2 + d^9*e^2*x + d^10*e)","B",0
843,1,203,0,0.446949," ","integrate(1/(e*x+d)^2/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{6 \, e^{6} x^{6} + 12 \, d e^{5} x^{5} - 6 \, d^{2} e^{4} x^{4} - 24 \, d^{3} e^{3} x^{3} - 6 \, d^{4} e^{2} x^{2} + 12 \, d^{5} e x + 6 \, d^{6} + {\left(8 \, e^{5} x^{5} + 16 \, d e^{4} x^{4} - 4 \, d^{2} e^{3} x^{3} - 24 \, d^{3} e^{2} x^{2} - 9 \, d^{4} e x + 6 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{21 \, {\left(d^{6} e^{7} x^{6} + 2 \, d^{7} e^{6} x^{5} - d^{8} e^{5} x^{4} - 4 \, d^{9} e^{4} x^{3} - d^{10} e^{3} x^{2} + 2 \, d^{11} e^{2} x + d^{12} e\right)}}"," ",0,"-1/21*(6*e^6*x^6 + 12*d*e^5*x^5 - 6*d^2*e^4*x^4 - 24*d^3*e^3*x^3 - 6*d^4*e^2*x^2 + 12*d^5*e*x + 6*d^6 + (8*e^5*x^5 + 16*d*e^4*x^4 - 4*d^2*e^3*x^3 - 24*d^3*e^2*x^2 - 9*d^4*e*x + 6*d^5)*sqrt(-e^2*x^2 + d^2))/(d^6*e^7*x^6 + 2*d^7*e^6*x^5 - d^8*e^5*x^4 - 4*d^9*e^4*x^3 - d^10*e^3*x^2 + 2*d^11*e^2*x + d^12*e)","B",0
844,1,234,0,0.538612," ","integrate(1/(e*x+d)^3/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{19 \, e^{7} x^{7} + 57 \, d e^{6} x^{6} + 19 \, d^{2} e^{5} x^{5} - 95 \, d^{3} e^{4} x^{4} - 95 \, d^{4} e^{3} x^{3} + 19 \, d^{5} e^{2} x^{2} + 57 \, d^{6} e x + 19 \, d^{7} + {\left(16 \, e^{6} x^{6} + 48 \, d e^{5} x^{5} + 24 \, d^{2} e^{4} x^{4} - 56 \, d^{3} e^{3} x^{3} - 66 \, d^{4} e^{2} x^{2} - 6 \, d^{5} e x + 19 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{63 \, {\left(d^{7} e^{8} x^{7} + 3 \, d^{8} e^{7} x^{6} + d^{9} e^{6} x^{5} - 5 \, d^{10} e^{5} x^{4} - 5 \, d^{11} e^{4} x^{3} + d^{12} e^{3} x^{2} + 3 \, d^{13} e^{2} x + d^{14} e\right)}}"," ",0,"-1/63*(19*e^7*x^7 + 57*d*e^6*x^6 + 19*d^2*e^5*x^5 - 95*d^3*e^4*x^4 - 95*d^4*e^3*x^3 + 19*d^5*e^2*x^2 + 57*d^6*e*x + 19*d^7 + (16*e^6*x^6 + 48*d*e^5*x^5 + 24*d^2*e^4*x^4 - 56*d^3*e^3*x^3 - 66*d^4*e^2*x^2 - 6*d^5*e*x + 19*d^6)*sqrt(-e^2*x^2 + d^2))/(d^7*e^8*x^7 + 3*d^8*e^7*x^6 + d^9*e^6*x^5 - 5*d^10*e^5*x^4 - 5*d^11*e^4*x^3 + d^12*e^3*x^2 + 3*d^13*e^2*x + d^14*e)","A",0
845,1,269,0,0.635350," ","integrate(1/(e*x+d)^4/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","-\frac{28 \, e^{8} x^{8} + 112 \, d e^{7} x^{7} + 112 \, d^{2} e^{6} x^{6} - 112 \, d^{3} e^{5} x^{5} - 280 \, d^{4} e^{4} x^{4} - 112 \, d^{5} e^{3} x^{3} + 112 \, d^{6} e^{2} x^{2} + 112 \, d^{7} e x + 28 \, d^{8} + {\left(16 \, e^{7} x^{7} + 64 \, d e^{6} x^{6} + 72 \, d^{2} e^{5} x^{5} - 32 \, d^{3} e^{4} x^{4} - 122 \, d^{4} e^{3} x^{3} - 72 \, d^{5} e^{2} x^{2} + 13 \, d^{6} e x + 28 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{99 \, {\left(d^{8} e^{9} x^{8} + 4 \, d^{9} e^{8} x^{7} + 4 \, d^{10} e^{7} x^{6} - 4 \, d^{11} e^{6} x^{5} - 10 \, d^{12} e^{5} x^{4} - 4 \, d^{13} e^{4} x^{3} + 4 \, d^{14} e^{3} x^{2} + 4 \, d^{15} e^{2} x + d^{16} e\right)}}"," ",0,"-1/99*(28*e^8*x^8 + 112*d*e^7*x^7 + 112*d^2*e^6*x^6 - 112*d^3*e^5*x^5 - 280*d^4*e^4*x^4 - 112*d^5*e^3*x^3 + 112*d^6*e^2*x^2 + 112*d^7*e*x + 28*d^8 + (16*e^7*x^7 + 64*d*e^6*x^6 + 72*d^2*e^5*x^5 - 32*d^3*e^4*x^4 - 122*d^4*e^3*x^3 - 72*d^5*e^2*x^2 + 13*d^6*e*x + 28*d^7)*sqrt(-e^2*x^2 + d^2))/(d^8*e^9*x^8 + 4*d^9*e^8*x^7 + 4*d^10*e^7*x^6 - 4*d^11*e^6*x^5 - 10*d^12*e^5*x^4 - 4*d^13*e^4*x^3 + 4*d^14*e^3*x^2 + 4*d^15*e^2*x + d^16*e)","A",0
846,1,201,0,0.476397," ","integrate((e*x+d)^9/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{5446 \, d^{3} e^{3} x^{3} - 16338 \, d^{4} e^{2} x^{2} + 16338 \, d^{5} e x - 5446 \, d^{6} + 6930 \, {\left(d^{3} e^{3} x^{3} - 3 \, d^{4} e^{2} x^{2} + 3 \, d^{5} e x - d^{6}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(10 \, e^{5} x^{5} + 105 \, d e^{4} x^{4} + 815 \, d^{2} e^{3} x^{3} - 8711 \, d^{3} e^{2} x^{2} + 12843 \, d^{4} e x - 5446 \, d^{5}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{30 \, {\left(e^{4} x^{3} - 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x - d^{3} e\right)}}"," ",0,"1/30*(5446*d^3*e^3*x^3 - 16338*d^4*e^2*x^2 + 16338*d^5*e*x - 5446*d^6 + 6930*(d^3*e^3*x^3 - 3*d^4*e^2*x^2 + 3*d^5*e*x - d^6)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (10*e^5*x^5 + 105*d*e^4*x^4 + 815*d^2*e^3*x^3 - 8711*d^3*e^2*x^2 + 12843*d^4*e*x - 5446*d^5)*sqrt(-e^2*x^2 + d^2))/(e^4*x^3 - 3*d*e^3*x^2 + 3*d^2*e^2*x - d^3*e)","A",0
847,1,190,0,0.434405," ","integrate((e*x+d)^8/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{496 \, d^{2} e^{3} x^{3} - 1488 \, d^{3} e^{2} x^{2} + 1488 \, d^{4} e x - 496 \, d^{5} + 630 \, {\left(d^{2} e^{3} x^{3} - 3 \, d^{3} e^{2} x^{2} + 3 \, d^{4} e x - d^{5}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(5 \, e^{4} x^{4} + 65 \, d e^{3} x^{3} - 801 \, d^{2} e^{2} x^{2} + 1163 \, d^{3} e x - 496 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{10 \, {\left(e^{4} x^{3} - 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x - d^{3} e\right)}}"," ",0,"1/10*(496*d^2*e^3*x^3 - 1488*d^3*e^2*x^2 + 1488*d^4*e*x - 496*d^5 + 630*(d^2*e^3*x^3 - 3*d^3*e^2*x^2 + 3*d^4*e*x - d^5)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (5*e^4*x^4 + 65*d*e^3*x^3 - 801*d^2*e^2*x^2 + 1163*d^3*e*x - 496*d^4)*sqrt(-e^2*x^2 + d^2))/(e^4*x^3 - 3*d*e^3*x^2 + 3*d^2*e^2*x - d^3*e)","A",0
848,1,175,0,0.430871," ","integrate((e*x+d)^7/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{167 \, d e^{3} x^{3} - 501 \, d^{2} e^{2} x^{2} + 501 \, d^{3} e x - 167 \, d^{4} + 210 \, {\left(d e^{3} x^{3} - 3 \, d^{2} e^{2} x^{2} + 3 \, d^{3} e x - d^{4}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) + {\left(15 \, e^{3} x^{3} - 277 \, d e^{2} x^{2} + 381 \, d^{2} e x - 167 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(e^{4} x^{3} - 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x - d^{3} e\right)}}"," ",0,"1/15*(167*d*e^3*x^3 - 501*d^2*e^2*x^2 + 501*d^3*e*x - 167*d^4 + 210*(d*e^3*x^3 - 3*d^2*e^2*x^2 + 3*d^3*e*x - d^4)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) + (15*e^3*x^3 - 277*d*e^2*x^2 + 381*d^2*e*x - 167*d^3)*sqrt(-e^2*x^2 + d^2))/(e^4*x^3 - 3*d*e^3*x^2 + 3*d^2*e^2*x - d^3*e)","A",0
849,1,159,0,0.435451," ","integrate((e*x+d)^6/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(13 \, e^{3} x^{3} - 39 \, d e^{2} x^{2} + 39 \, d^{2} e x - 13 \, d^{3} + 15 \, {\left(e^{3} x^{3} - 3 \, d e^{2} x^{2} + 3 \, d^{2} e x - d^{3}\right)} \arctan\left(-\frac{d - \sqrt{-e^{2} x^{2} + d^{2}}}{e x}\right) - {\left(23 \, e^{2} x^{2} - 24 \, d e x + 13 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}\right)}}{15 \, {\left(e^{4} x^{3} - 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x - d^{3} e\right)}}"," ",0,"2/15*(13*e^3*x^3 - 39*d*e^2*x^2 + 39*d^2*e*x - 13*d^3 + 15*(e^3*x^3 - 3*d*e^2*x^2 + 3*d^2*e*x - d^3)*arctan(-(d - sqrt(-e^2*x^2 + d^2))/(e*x)) - (23*e^2*x^2 - 24*d*e*x + 13*d^2)*sqrt(-e^2*x^2 + d^2))/(e^4*x^3 - 3*d*e^3*x^2 + 3*d^2*e^2*x - d^3*e)","A",0
850,1,100,0,0.409142," ","integrate((e*x+d)^5/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{e^{3} x^{3} - 3 \, d e^{2} x^{2} + 3 \, d^{2} e x - d^{3} - {\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d e^{4} x^{3} - 3 \, d^{2} e^{3} x^{2} + 3 \, d^{3} e^{2} x - d^{4} e\right)}}"," ",0,"1/5*(e^3*x^3 - 3*d*e^2*x^2 + 3*d^2*e*x - d^3 - (e^2*x^2 + 2*d*e*x + d^2)*sqrt(-e^2*x^2 + d^2))/(d*e^4*x^3 - 3*d^2*e^3*x^2 + 3*d^3*e^2*x - d^4*e)","B",0
851,1,104,0,0.412760," ","integrate((e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{4 \, e^{3} x^{3} - 12 \, d e^{2} x^{2} + 12 \, d^{2} e x - 4 \, d^{3} + {\left(e^{2} x^{2} - 3 \, d e x - 4 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{2} e^{4} x^{3} - 3 \, d^{3} e^{3} x^{2} + 3 \, d^{4} e^{2} x - d^{5} e\right)}}"," ",0,"1/15*(4*e^3*x^3 - 12*d*e^2*x^2 + 12*d^2*e*x - 4*d^3 + (e^2*x^2 - 3*d*e*x - 4*d^2)*sqrt(-e^2*x^2 + d^2))/(d^2*e^4*x^3 - 3*d^3*e^3*x^2 + 3*d^4*e^2*x - d^5*e)","A",0
852,1,106,0,0.411782," ","integrate((e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{7 \, e^{3} x^{3} - 21 \, d e^{2} x^{2} + 21 \, d^{2} e x - 7 \, d^{3} - {\left(2 \, e^{2} x^{2} - 6 \, d e x + 7 \, d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{3} e^{4} x^{3} - 3 \, d^{4} e^{3} x^{2} + 3 \, d^{5} e^{2} x - d^{6} e\right)}}"," ",0,"1/15*(7*e^3*x^3 - 21*d*e^2*x^2 + 21*d^2*e*x - 7*d^3 - (2*e^2*x^2 - 6*d*e*x + 7*d^2)*sqrt(-e^2*x^2 + d^2))/(d^3*e^4*x^3 - 3*d^4*e^3*x^2 + 3*d^5*e^2*x - d^6*e)","A",0
853,1,116,0,0.407679," ","integrate((e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{2 \, e^{4} x^{4} - 4 \, d e^{3} x^{3} + 4 \, d^{3} e x - 2 \, d^{4} - {\left(2 \, e^{3} x^{3} - 4 \, d e^{2} x^{2} + d^{2} e x + 2 \, d^{3}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{5 \, {\left(d^{4} e^{5} x^{4} - 2 \, d^{5} e^{4} x^{3} + 2 \, d^{7} e^{2} x - d^{8} e\right)}}"," ",0,"1/5*(2*e^4*x^4 - 4*d*e^3*x^3 + 4*d^3*e*x - 2*d^4 - (2*e^3*x^3 - 4*d*e^2*x^2 + d^2*e*x + 2*d^3)*sqrt(-e^2*x^2 + d^2))/(d^4*e^5*x^4 - 2*d^5*e^4*x^3 + 2*d^7*e^2*x - d^8*e)","A",0
854,1,171,0,0.425021," ","integrate((e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","\frac{3 \, e^{5} x^{5} - 3 \, d e^{4} x^{4} - 6 \, d^{2} e^{3} x^{3} + 6 \, d^{3} e^{2} x^{2} + 3 \, d^{4} e x - 3 \, d^{5} - {\left(8 \, e^{4} x^{4} - 8 \, d e^{3} x^{3} - 12 \, d^{2} e^{2} x^{2} + 12 \, d^{3} e x + 3 \, d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{15 \, {\left(d^{5} e^{6} x^{5} - d^{6} e^{5} x^{4} - 2 \, d^{7} e^{4} x^{3} + 2 \, d^{8} e^{3} x^{2} + d^{9} e^{2} x - d^{10} e\right)}}"," ",0,"1/15*(3*e^5*x^5 - 3*d*e^4*x^4 - 6*d^2*e^3*x^3 + 6*d^3*e^2*x^2 + 3*d^4*e*x - 3*d^5 - (8*e^4*x^4 - 8*d*e^3*x^3 - 12*d^2*e^2*x^2 + 12*d^3*e*x + 3*d^4)*sqrt(-e^2*x^2 + d^2))/(d^5*e^6*x^5 - d^6*e^5*x^4 - 2*d^7*e^4*x^3 + 2*d^8*e^3*x^2 + d^9*e^2*x - d^10*e)","B",0
855,1,236,0,0.529339," ","integrate(1/(e*x+d)/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{5 \, e^{7} x^{7} + 5 \, d e^{6} x^{6} - 15 \, d^{2} e^{5} x^{5} - 15 \, d^{3} e^{4} x^{4} + 15 \, d^{4} e^{3} x^{3} + 15 \, d^{5} e^{2} x^{2} - 5 \, d^{6} e x - 5 \, d^{7} + {\left(16 \, e^{6} x^{6} + 16 \, d e^{5} x^{5} - 40 \, d^{2} e^{4} x^{4} - 40 \, d^{3} e^{3} x^{3} + 30 \, d^{4} e^{2} x^{2} + 30 \, d^{5} e x - 5 \, d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{35 \, {\left(d^{7} e^{8} x^{7} + d^{8} e^{7} x^{6} - 3 \, d^{9} e^{6} x^{5} - 3 \, d^{10} e^{5} x^{4} + 3 \, d^{11} e^{4} x^{3} + 3 \, d^{12} e^{3} x^{2} - d^{13} e^{2} x - d^{14} e\right)}}"," ",0,"-1/35*(5*e^7*x^7 + 5*d*e^6*x^6 - 15*d^2*e^5*x^5 - 15*d^3*e^4*x^4 + 15*d^4*e^3*x^3 + 15*d^5*e^2*x^2 - 5*d^6*e*x - 5*d^7 + (16*e^6*x^6 + 16*d*e^5*x^5 - 40*d^2*e^4*x^4 - 40*d^3*e^3*x^3 + 30*d^4*e^2*x^2 + 30*d^5*e*x - 5*d^6)*sqrt(-e^2*x^2 + d^2))/(d^7*e^8*x^7 + d^8*e^7*x^6 - 3*d^9*e^6*x^5 - 3*d^10*e^5*x^4 + 3*d^11*e^4*x^3 + 3*d^12*e^3*x^2 - d^13*e^2*x - d^14*e)","B",0
856,1,248,0,0.649835," ","integrate(1/(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{10 \, e^{8} x^{8} + 20 \, d e^{7} x^{7} - 20 \, d^{2} e^{6} x^{6} - 60 \, d^{3} e^{5} x^{5} + 60 \, d^{5} e^{3} x^{3} + 20 \, d^{6} e^{2} x^{2} - 20 \, d^{7} e x - 10 \, d^{8} + {\left(16 \, e^{7} x^{7} + 32 \, d e^{6} x^{6} - 24 \, d^{2} e^{5} x^{5} - 80 \, d^{3} e^{4} x^{4} - 10 \, d^{4} e^{3} x^{3} + 60 \, d^{5} e^{2} x^{2} + 25 \, d^{6} e x - 10 \, d^{7}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{45 \, {\left(d^{8} e^{9} x^{8} + 2 \, d^{9} e^{8} x^{7} - 2 \, d^{10} e^{7} x^{6} - 6 \, d^{11} e^{6} x^{5} + 6 \, d^{13} e^{4} x^{3} + 2 \, d^{14} e^{3} x^{2} - 2 \, d^{15} e^{2} x - d^{16} e\right)}}"," ",0,"-1/45*(10*e^8*x^8 + 20*d*e^7*x^7 - 20*d^2*e^6*x^6 - 60*d^3*e^5*x^5 + 60*d^5*e^3*x^3 + 20*d^6*e^2*x^2 - 20*d^7*e*x - 10*d^8 + (16*e^7*x^7 + 32*d*e^6*x^6 - 24*d^2*e^5*x^5 - 80*d^3*e^4*x^4 - 10*d^4*e^3*x^3 + 60*d^5*e^2*x^2 + 25*d^6*e*x - 10*d^7)*sqrt(-e^2*x^2 + d^2))/(d^8*e^9*x^8 + 2*d^9*e^8*x^7 - 2*d^10*e^7*x^6 - 6*d^11*e^6*x^5 + 6*d^13*e^4*x^3 + 2*d^14*e^3*x^2 - 2*d^15*e^2*x - d^16*e)","B",0
857,1,259,0,0.863458," ","integrate(1/(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{125 \, e^{9} x^{9} + 375 \, d e^{8} x^{8} - 1000 \, d^{3} e^{6} x^{6} - 750 \, d^{4} e^{5} x^{5} + 750 \, d^{5} e^{4} x^{4} + 1000 \, d^{6} e^{3} x^{3} - 375 \, d^{8} e x - 125 \, d^{9} + {\left(128 \, e^{8} x^{8} + 384 \, d e^{7} x^{7} + 64 \, d^{2} e^{6} x^{6} - 832 \, d^{3} e^{5} x^{5} - 720 \, d^{4} e^{4} x^{4} + 400 \, d^{5} e^{3} x^{3} + 680 \, d^{6} e^{2} x^{2} + 120 \, d^{7} e x - 125 \, d^{8}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{495 \, {\left(d^{9} e^{10} x^{9} + 3 \, d^{10} e^{9} x^{8} - 8 \, d^{12} e^{7} x^{6} - 6 \, d^{13} e^{6} x^{5} + 6 \, d^{14} e^{5} x^{4} + 8 \, d^{15} e^{4} x^{3} - 3 \, d^{17} e^{2} x - d^{18} e\right)}}"," ",0,"-1/495*(125*e^9*x^9 + 375*d*e^8*x^8 - 1000*d^3*e^6*x^6 - 750*d^4*e^5*x^5 + 750*d^5*e^4*x^4 + 1000*d^6*e^3*x^3 - 375*d^8*e*x - 125*d^9 + (128*e^8*x^8 + 384*d*e^7*x^7 + 64*d^2*e^6*x^6 - 832*d^3*e^5*x^5 - 720*d^4*e^4*x^4 + 400*d^5*e^3*x^3 + 680*d^6*e^2*x^2 + 120*d^7*e*x - 125*d^8)*sqrt(-e^2*x^2 + d^2))/(d^9*e^10*x^9 + 3*d^10*e^9*x^8 - 8*d^12*e^7*x^6 - 6*d^13*e^6*x^5 + 6*d^14*e^5*x^4 + 8*d^15*e^4*x^3 - 3*d^17*e^2*x - d^18*e)","A",0
858,1,314,0,1.191813," ","integrate(1/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{180 \, e^{10} x^{10} + 720 \, d e^{9} x^{9} + 540 \, d^{2} e^{8} x^{8} - 1440 \, d^{3} e^{7} x^{7} - 2520 \, d^{4} e^{6} x^{6} + 2520 \, d^{6} e^{4} x^{4} + 1440 \, d^{7} e^{3} x^{3} - 540 \, d^{8} e^{2} x^{2} - 720 \, d^{9} e x - 180 \, d^{10} + {\left(128 \, e^{9} x^{9} + 512 \, d e^{8} x^{8} + 448 \, d^{2} e^{7} x^{7} - 768 \, d^{3} e^{6} x^{6} - 1552 \, d^{4} e^{5} x^{5} - 320 \, d^{5} e^{4} x^{4} + 1080 \, d^{6} e^{3} x^{3} + 800 \, d^{7} e^{2} x^{2} - 5 \, d^{8} e x - 180 \, d^{9}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{715 \, {\left(d^{10} e^{11} x^{10} + 4 \, d^{11} e^{10} x^{9} + 3 \, d^{12} e^{9} x^{8} - 8 \, d^{13} e^{8} x^{7} - 14 \, d^{14} e^{7} x^{6} + 14 \, d^{16} e^{5} x^{4} + 8 \, d^{17} e^{4} x^{3} - 3 \, d^{18} e^{3} x^{2} - 4 \, d^{19} e^{2} x - d^{20} e\right)}}"," ",0,"-1/715*(180*e^10*x^10 + 720*d*e^9*x^9 + 540*d^2*e^8*x^8 - 1440*d^3*e^7*x^7 - 2520*d^4*e^6*x^6 + 2520*d^6*e^4*x^4 + 1440*d^7*e^3*x^3 - 540*d^8*e^2*x^2 - 720*d^9*e*x - 180*d^10 + (128*e^9*x^9 + 512*d*e^8*x^8 + 448*d^2*e^7*x^7 - 768*d^3*e^6*x^6 - 1552*d^4*e^5*x^5 - 320*d^5*e^4*x^4 + 1080*d^6*e^3*x^3 + 800*d^7*e^2*x^2 - 5*d^8*e*x - 180*d^9)*sqrt(-e^2*x^2 + d^2))/(d^10*e^11*x^10 + 4*d^11*e^10*x^9 + 3*d^12*e^9*x^8 - 8*d^13*e^8*x^7 - 14*d^14*e^7*x^6 + 14*d^16*e^5*x^4 + 8*d^17*e^4*x^3 - 3*d^18*e^3*x^2 - 4*d^19*e^2*x - d^20*e)","A",0
859,1,369,0,1.650834," ","integrate(1/(e*x+d)^5/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","-\frac{503 \, e^{11} x^{11} + 2515 \, d e^{10} x^{10} + 3521 \, d^{2} e^{9} x^{9} - 2515 \, d^{3} e^{8} x^{8} - 11066 \, d^{4} e^{7} x^{7} - 7042 \, d^{5} e^{6} x^{6} + 7042 \, d^{6} e^{5} x^{5} + 11066 \, d^{7} e^{4} x^{4} + 2515 \, d^{8} e^{3} x^{3} - 3521 \, d^{9} e^{2} x^{2} - 2515 \, d^{10} e x - 503 \, d^{11} + {\left(256 \, e^{10} x^{10} + 1280 \, d e^{9} x^{9} + 1920 \, d^{2} e^{8} x^{8} - 640 \, d^{3} e^{7} x^{7} - 4640 \, d^{4} e^{6} x^{6} - 3744 \, d^{5} e^{5} x^{5} + 1520 \, d^{6} e^{4} x^{4} + 3760 \, d^{7} e^{3} x^{3} + 1590 \, d^{8} e^{2} x^{2} - 370 \, d^{9} e x - 503 \, d^{10}\right)} \sqrt{-e^{2} x^{2} + d^{2}}}{2145 \, {\left(d^{11} e^{12} x^{11} + 5 \, d^{12} e^{11} x^{10} + 7 \, d^{13} e^{10} x^{9} - 5 \, d^{14} e^{9} x^{8} - 22 \, d^{15} e^{8} x^{7} - 14 \, d^{16} e^{7} x^{6} + 14 \, d^{17} e^{6} x^{5} + 22 \, d^{18} e^{5} x^{4} + 5 \, d^{19} e^{4} x^{3} - 7 \, d^{20} e^{3} x^{2} - 5 \, d^{21} e^{2} x - d^{22} e\right)}}"," ",0,"-1/2145*(503*e^11*x^11 + 2515*d*e^10*x^10 + 3521*d^2*e^9*x^9 - 2515*d^3*e^8*x^8 - 11066*d^4*e^7*x^7 - 7042*d^5*e^6*x^6 + 7042*d^6*e^5*x^5 + 11066*d^7*e^4*x^4 + 2515*d^8*e^3*x^3 - 3521*d^9*e^2*x^2 - 2515*d^10*e*x - 503*d^11 + (256*e^10*x^10 + 1280*d*e^9*x^9 + 1920*d^2*e^8*x^8 - 640*d^3*e^7*x^7 - 4640*d^4*e^6*x^6 - 3744*d^5*e^5*x^5 + 1520*d^6*e^4*x^4 + 3760*d^7*e^3*x^3 + 1590*d^8*e^2*x^2 - 370*d^9*e*x - 503*d^10)*sqrt(-e^2*x^2 + d^2))/(d^11*e^12*x^11 + 5*d^12*e^11*x^10 + 7*d^13*e^10*x^9 - 5*d^14*e^9*x^8 - 22*d^15*e^8*x^7 - 14*d^16*e^7*x^6 + 14*d^17*e^6*x^5 + 22*d^18*e^5*x^4 + 5*d^19*e^4*x^3 - 7*d^20*e^3*x^2 - 5*d^21*e^2*x - d^22*e)","A",0
860,1,30,0,0.404445," ","integrate((1+x)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","-\sqrt{-x^{2} + 1} - 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"-sqrt(-x^2 + 1) - 2*arctan((sqrt(-x^2 + 1) - 1)/x)","B",0
861,1,28,0,0.410273," ","integrate((1-x)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\sqrt{-x^{2} + 1} - 2 \, \arctan\left(\frac{\sqrt{-x^{2} + 1} - 1}{x}\right)"," ",0,"sqrt(-x^2 + 1) - 2*arctan((sqrt(-x^2 + 1) - 1)/x)","B",0
862,1,78,0,0.393915," ","integrate((e*x+d)^(5/2)*(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, e^{4} x^{4} + 130 \, d e^{3} x^{3} + 156 \, d^{2} e^{2} x^{2} - 2 \, d^{3} e x - 319 \, d^{4}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{315 \, {\left(e^{2} x + d e\right)}}"," ",0,"2/315*(35*e^4*x^4 + 130*d*e^3*x^3 + 156*d^2*e^2*x^2 - 2*d^3*e*x - 319*d^4)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(e^2*x + d*e)","A",0
863,1,67,0,0.400440," ","integrate((e*x+d)^(3/2)*(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, e^{3} x^{3} + 39 \, d e^{2} x^{2} + 17 \, d^{2} e x - 71 \, d^{3}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{105 \, {\left(e^{2} x + d e\right)}}"," ",0,"2/105*(15*e^3*x^3 + 39*d*e^2*x^2 + 17*d^2*e*x - 71*d^3)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(e^2*x + d*e)","A",0
864,1,56,0,0.410942," ","integrate((e*x+d)^(1/2)*(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(3 \, e^{2} x^{2} + 4 \, d e x - 7 \, d^{2}\right)} \sqrt{e x + d}}{15 \, {\left(e^{2} x + d e\right)}}"," ",0,"2/15*sqrt(-c*e^2*x^2 + c*d^2)*(3*e^2*x^2 + 4*d*e*x - 7*d^2)*sqrt(e*x + d)/(e^2*x + d*e)","A",0
865,1,44,0,0.405243," ","integrate((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} {\left(e x - d\right)}}{3 \, {\left(e^{2} x + d e\right)}}"," ",0,"2/3*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*(e*x - d)/(e^2*x + d*e)","A",0
866,1,237,0,0.426604," ","integrate((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{c d} {\left(e x + d\right)} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} + 2 \, \sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{c d} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{e^{2} x + d e}, -\frac{2 \, {\left(\sqrt{2} \sqrt{-c d} {\left(e x + d\right)} \arctan\left(\frac{\sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{-c d} \sqrt{e x + d}}{c e^{2} x^{2} - c d^{2}}\right) - \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}\right)}}{e^{2} x + d e}\right]"," ",0,"[(sqrt(2)*sqrt(c*d)*(e*x + d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 + 2*sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(c*d)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d))/(e^2*x + d*e), -2*(sqrt(2)*sqrt(-c*d)*(e*x + d)*arctan(sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(-c*d)*sqrt(e*x + d)/(c*e^2*x^2 - c*d^2)) - sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d))/(e^2*x + d*e)]","A",0
867,1,292,0,0.420814," ","integrate((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{1}{2}} {\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{\frac{c}{d}} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} - 4 \, \sqrt{\frac{1}{2}} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{\frac{c}{d}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}, \frac{\sqrt{\frac{1}{2}} {\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{-\frac{c}{d}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{-\frac{c}{d}}}{c e^{2} x^{2} - c d^{2}}\right) - \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}\right]"," ",0,"[1/2*(sqrt(1/2)*(e^2*x^2 + 2*d*e*x + d^2)*sqrt(c/d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 - 4*sqrt(1/2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(c/d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d))/(e^3*x^2 + 2*d*e^2*x + d^2*e), (sqrt(1/2)*(e^2*x^2 + 2*d*e*x + d^2)*sqrt(-c/d)*arctan(2*sqrt(1/2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(-c/d)/(c*e^2*x^2 - c*d^2)) - sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d))/(e^3*x^2 + 2*d*e^2*x + d^2*e)]","A",0
868,1,356,0,0.414610," ","integrate((-c*e^2*x^2+c*d^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{1}{2}} {\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{\frac{c}{d}} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} - 4 \, \sqrt{\frac{1}{2}} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{\frac{c}{d}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} {\left(e x - 3 \, d\right)}}{16 \, {\left(d e^{4} x^{3} + 3 \, d^{2} e^{3} x^{2} + 3 \, d^{3} e^{2} x + d^{4} e\right)}}, \frac{\sqrt{\frac{1}{2}} {\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{-\frac{c}{d}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{-\frac{c}{d}}}{c e^{2} x^{2} - c d^{2}}\right) + \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} {\left(e x - 3 \, d\right)}}{8 \, {\left(d e^{4} x^{3} + 3 \, d^{2} e^{3} x^{2} + 3 \, d^{3} e^{2} x + d^{4} e\right)}}\right]"," ",0,"[1/16*(sqrt(1/2)*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c/d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 - 4*sqrt(1/2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(c/d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*(e*x - 3*d))/(d*e^4*x^3 + 3*d^2*e^3*x^2 + 3*d^3*e^2*x + d^4*e), 1/8*(sqrt(1/2)*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(-c/d)*arctan(2*sqrt(1/2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(-c/d)/(c*e^2*x^2 - c*d^2)) + sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*(e*x - 3*d))/(d*e^4*x^3 + 3*d^2*e^3*x^2 + 3*d^3*e^2*x + d^4*e)]","A",0
869,1,107,0,0.392098," ","integrate((e*x+d)^(5/2)*(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(1155 \, c e^{6} x^{6} + 3990 \, c d e^{5} x^{5} + 2765 \, c d^{2} e^{4} x^{4} - 5420 \, c d^{3} e^{3} x^{3} - 9507 \, c d^{4} e^{2} x^{2} - 2666 \, c d^{5} e x + 9683 \, c d^{6}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{15015 \, {\left(e^{2} x + d e\right)}}"," ",0,"-2/15015*(1155*c*e^6*x^6 + 3990*c*d*e^5*x^5 + 2765*c*d^2*e^4*x^4 - 5420*c*d^3*e^3*x^3 - 9507*c*d^4*e^2*x^2 - 2666*c*d^5*e*x + 9683*c*d^6)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(e^2*x + d*e)","A",0
870,1,95,0,0.408792," ","integrate((e*x+d)^(3/2)*(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(105 \, c e^{5} x^{5} + 245 \, c d e^{4} x^{4} - 50 \, c d^{2} e^{3} x^{3} - 522 \, c d^{3} e^{2} x^{2} - 311 \, c d^{4} e x + 533 \, c d^{5}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{1155 \, {\left(e^{2} x + d e\right)}}"," ",0,"-2/1155*(105*c*e^5*x^5 + 245*c*d*e^4*x^4 - 50*c*d^2*e^3*x^3 - 522*c*d^3*e^2*x^2 - 311*c*d^4*e*x + 533*c*d^5)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(e^2*x + d*e)","A",0
871,1,83,0,0.402229," ","integrate((e*x+d)^(1/2)*(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, c e^{4} x^{4} + 40 \, c d e^{3} x^{3} - 78 \, c d^{2} e^{2} x^{2} - 104 \, c d^{3} e x + 107 \, c d^{4}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{315 \, {\left(e^{2} x + d e\right)}}"," ",0,"-2/315*(35*c*e^4*x^4 + 40*c*d*e^3*x^3 - 78*c*d^2*e^2*x^2 - 104*c*d^3*e*x + 107*c*d^4)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(e^2*x + d*e)","A",0
872,1,71,0,0.402476," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, c e^{3} x^{3} - c d e^{2} x^{2} - 13 \, c d^{2} e x + 9 \, c d^{3}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{35 \, {\left(e^{2} x + d e\right)}}"," ",0,"-2/35*(5*c*e^3*x^3 - c*d*e^2*x^2 - 13*c*d^2*e*x + 9*c*d^3)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(e^2*x + d*e)","A",0
873,1,57,0,0.412387," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(c e^{2} x^{2} - 2 \, c d e x + c d^{2}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{5 \, {\left(e^{2} x + d e\right)}}"," ",0,"-2/5*(c*e^2*x^2 - 2*c*d*e*x + c*d^2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(e^2*x + d*e)","A",0
874,1,269,0,0.429119," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, \sqrt{2} {\left(c d e x + c d^{2}\right)} \sqrt{c d} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} + 2 \, \sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{c d} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(c e x - 7 \, c d\right)} \sqrt{e x + d}\right)}}{3 \, {\left(e^{2} x + d e\right)}}, -\frac{2 \, {\left(6 \, \sqrt{2} {\left(c d e x + c d^{2}\right)} \sqrt{-c d} \arctan\left(\frac{\sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{-c d} \sqrt{e x + d}}{c e^{2} x^{2} - c d^{2}}\right) + \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(c e x - 7 \, c d\right)} \sqrt{e x + d}\right)}}{3 \, {\left(e^{2} x + d e\right)}}\right]"," ",0,"[2/3*(3*sqrt(2)*(c*d*e*x + c*d^2)*sqrt(c*d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 + 2*sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(c*d)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - sqrt(-c*e^2*x^2 + c*d^2)*(c*e*x - 7*c*d)*sqrt(e*x + d))/(e^2*x + d*e), -2/3*(6*sqrt(2)*(c*d*e*x + c*d^2)*sqrt(-c*d)*arctan(sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(-c*d)*sqrt(e*x + d)/(c*e^2*x^2 - c*d^2)) + sqrt(-c*e^2*x^2 + c*d^2)*(c*e*x - 7*c*d)*sqrt(e*x + d))/(e^2*x + d*e)]","A",0
875,1,309,0,0.427988," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)} \sqrt{c d} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} - 2 \, \sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{c d} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(c e x + 2 \, c d\right)} \sqrt{e x + d}}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}, \frac{3 \, \sqrt{2} {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)} \sqrt{-c d} \arctan\left(\frac{\sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{-c d} \sqrt{e x + d}}{c e^{2} x^{2} - c d^{2}}\right) - 2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(c e x + 2 \, c d\right)} \sqrt{e x + d}}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}\right]"," ",0,"[1/2*(3*sqrt(2)*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*sqrt(c*d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 - 2*sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(c*d)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 4*sqrt(-c*e^2*x^2 + c*d^2)*(c*e*x + 2*c*d)*sqrt(e*x + d))/(e^3*x^2 + 2*d*e^2*x + d^2*e), (3*sqrt(2)*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*sqrt(-c*d)*arctan(sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(-c*d)*sqrt(e*x + d)/(c*e^2*x^2 - c*d^2)) - 2*sqrt(-c*e^2*x^2 + c*d^2)*(c*e*x + 2*c*d)*sqrt(e*x + d))/(e^3*x^2 + 2*d*e^2*x + d^2*e)]","A",0
876,1,367,0,0.435839," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{2}} {\left(c e^{3} x^{3} + 3 \, c d e^{2} x^{2} + 3 \, c d^{2} e x + c d^{3}\right)} \sqrt{\frac{c}{d}} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} + 4 \, \sqrt{\frac{1}{2}} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{\frac{c}{d}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(5 \, c e x + c d\right)} \sqrt{e x + d}}{8 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}, -\frac{3 \, \sqrt{\frac{1}{2}} {\left(c e^{3} x^{3} + 3 \, c d e^{2} x^{2} + 3 \, c d^{2} e x + c d^{3}\right)} \sqrt{-\frac{c}{d}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{-\frac{c}{d}}}{c e^{2} x^{2} - c d^{2}}\right) - \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(5 \, c e x + c d\right)} \sqrt{e x + d}}{4 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}\right]"," ",0,"[1/8*(3*sqrt(1/2)*(c*e^3*x^3 + 3*c*d*e^2*x^2 + 3*c*d^2*e*x + c*d^3)*sqrt(c/d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 + 4*sqrt(1/2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(c/d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(-c*e^2*x^2 + c*d^2)*(5*c*e*x + c*d)*sqrt(e*x + d))/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e), -1/4*(3*sqrt(1/2)*(c*e^3*x^3 + 3*c*d*e^2*x^2 + 3*c*d^2*e*x + c*d^3)*sqrt(-c/d)*arctan(2*sqrt(1/2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(-c/d)/(c*e^2*x^2 - c*d^2)) - sqrt(-c*e^2*x^2 + c*d^2)*(5*c*e*x + c*d)*sqrt(e*x + d))/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)]","A",0
877,1,444,0,0.415516," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{2}} {\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + 6 \, c d^{2} e^{2} x^{2} + 4 \, c d^{3} e x + c d^{4}\right)} \sqrt{\frac{c}{d}} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} + 4 \, \sqrt{\frac{1}{2}} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{\frac{c}{d}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(3 \, c e^{2} x^{2} - 22 \, c d e x + 7 \, c d^{2}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{96 \, {\left(d e^{5} x^{4} + 4 \, d^{2} e^{4} x^{3} + 6 \, d^{3} e^{3} x^{2} + 4 \, d^{4} e^{2} x + d^{5} e\right)}}, -\frac{3 \, \sqrt{\frac{1}{2}} {\left(c e^{4} x^{4} + 4 \, c d e^{3} x^{3} + 6 \, c d^{2} e^{2} x^{2} + 4 \, c d^{3} e x + c d^{4}\right)} \sqrt{-\frac{c}{d}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{-\frac{c}{d}}}{c e^{2} x^{2} - c d^{2}}\right) + {\left(3 \, c e^{2} x^{2} - 22 \, c d e x + 7 \, c d^{2}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{48 \, {\left(d e^{5} x^{4} + 4 \, d^{2} e^{4} x^{3} + 6 \, d^{3} e^{3} x^{2} + 4 \, d^{4} e^{2} x + d^{5} e\right)}}\right]"," ",0,"[1/96*(3*sqrt(1/2)*(c*e^4*x^4 + 4*c*d*e^3*x^3 + 6*c*d^2*e^2*x^2 + 4*c*d^3*e*x + c*d^4)*sqrt(c/d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 + 4*sqrt(1/2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(c/d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(3*c*e^2*x^2 - 22*c*d*e*x + 7*c*d^2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d))/(d*e^5*x^4 + 4*d^2*e^4*x^3 + 6*d^3*e^3*x^2 + 4*d^4*e^2*x + d^5*e), -1/48*(3*sqrt(1/2)*(c*e^4*x^4 + 4*c*d*e^3*x^3 + 6*c*d^2*e^2*x^2 + 4*c*d^3*e*x + c*d^4)*sqrt(-c/d)*arctan(2*sqrt(1/2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(-c/d)/(c*e^2*x^2 - c*d^2)) + (3*c*e^2*x^2 - 22*c*d*e*x + 7*c*d^2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d))/(d*e^5*x^4 + 4*d^2*e^4*x^3 + 6*d^3*e^3*x^2 + 4*d^4*e^2*x + d^5*e)]","A",0
878,1,518,0,0.441205," ","integrate((-c*e^2*x^2+c*d^2)^(3/2)/(e*x+d)^(13/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{\frac{1}{2}} {\left(c e^{5} x^{5} + 5 \, c d e^{4} x^{4} + 10 \, c d^{2} e^{3} x^{3} + 10 \, c d^{3} e^{2} x^{2} + 5 \, c d^{4} e x + c d^{5}\right)} \sqrt{\frac{c}{d}} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} + 4 \, \sqrt{\frac{1}{2}} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{\frac{c}{d}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(3 \, c e^{3} x^{3} + 13 \, c d e^{2} x^{2} - 79 \, c d^{2} e x + 39 \, c d^{3}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{512 \, {\left(d^{2} e^{6} x^{5} + 5 \, d^{3} e^{5} x^{4} + 10 \, d^{4} e^{4} x^{3} + 10 \, d^{5} e^{3} x^{2} + 5 \, d^{6} e^{2} x + d^{7} e\right)}}, -\frac{3 \, \sqrt{\frac{1}{2}} {\left(c e^{5} x^{5} + 5 \, c d e^{4} x^{4} + 10 \, c d^{2} e^{3} x^{3} + 10 \, c d^{3} e^{2} x^{2} + 5 \, c d^{4} e x + c d^{5}\right)} \sqrt{-\frac{c}{d}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{-\frac{c}{d}}}{c e^{2} x^{2} - c d^{2}}\right) + {\left(3 \, c e^{3} x^{3} + 13 \, c d e^{2} x^{2} - 79 \, c d^{2} e x + 39 \, c d^{3}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{256 \, {\left(d^{2} e^{6} x^{5} + 5 \, d^{3} e^{5} x^{4} + 10 \, d^{4} e^{4} x^{3} + 10 \, d^{5} e^{3} x^{2} + 5 \, d^{6} e^{2} x + d^{7} e\right)}}\right]"," ",0,"[1/512*(3*sqrt(1/2)*(c*e^5*x^5 + 5*c*d*e^4*x^4 + 10*c*d^2*e^3*x^3 + 10*c*d^3*e^2*x^2 + 5*c*d^4*e*x + c*d^5)*sqrt(c/d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 + 4*sqrt(1/2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(c/d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(3*c*e^3*x^3 + 13*c*d*e^2*x^2 - 79*c*d^2*e*x + 39*c*d^3)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d))/(d^2*e^6*x^5 + 5*d^3*e^5*x^4 + 10*d^4*e^4*x^3 + 10*d^5*e^3*x^2 + 5*d^6*e^2*x + d^7*e), -1/256*(3*sqrt(1/2)*(c*e^5*x^5 + 5*c*d*e^4*x^4 + 10*c*d^2*e^3*x^3 + 10*c*d^3*e^2*x^2 + 5*c*d^4*e*x + c*d^5)*sqrt(-c/d)*arctan(2*sqrt(1/2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(-c/d)/(c*e^2*x^2 - c*d^2)) + (3*c*e^3*x^3 + 13*c*d*e^2*x^2 - 79*c*d^2*e*x + 39*c*d^3)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d))/(d^2*e^6*x^5 + 5*d^3*e^5*x^4 + 10*d^4*e^4*x^3 + 10*d^5*e^3*x^2 + 5*d^6*e^2*x + d^7*e)]","A",0
879,1,69,0,0.403944," ","integrate((e*x+d)^(7/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, e^{3} x^{3} + 27 \, d e^{2} x^{2} + 71 \, d^{2} e x + 177 \, d^{3}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{35 \, {\left(c e^{2} x + c d e\right)}}"," ",0,"-2/35*(5*e^3*x^3 + 27*d*e^2*x^2 + 71*d^2*e*x + 177*d^3)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(c*e^2*x + c*d*e)","A",0
880,1,58,0,0.392457," ","integrate((e*x+d)^(5/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(3 \, e^{2} x^{2} + 14 \, d e x + 43 \, d^{2}\right)} \sqrt{e x + d}}{15 \, {\left(c e^{2} x + c d e\right)}}"," ",0,"-2/15*sqrt(-c*e^2*x^2 + c*d^2)*(3*e^2*x^2 + 14*d*e*x + 43*d^2)*sqrt(e*x + d)/(c*e^2*x + c*d*e)","A",0
881,1,46,0,0.388669," ","integrate((e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(e x + 5 \, d\right)} \sqrt{e x + d}}{3 \, {\left(c e^{2} x + c d e\right)}}"," ",0,"-2/3*sqrt(-c*e^2*x^2 + c*d^2)*(e*x + 5*d)*sqrt(e*x + d)/(c*e^2*x + c*d*e)","A",0
882,1,39,0,0.397392," ","integrate((e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{c e^{2} x + c d e}"," ",0,"-2*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(c*e^2*x + c*d*e)","A",0
883,1,169,0,0.412184," ","integrate(1/(e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{\frac{1}{c d}} \log\left(-\frac{e^{2} x^{2} - 2 \, d e x + 2 \, \sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{\frac{1}{c d}} - 3 \, d^{2}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, e}, -\frac{\sqrt{2} \sqrt{-\frac{1}{c d}} \arctan\left(\frac{\sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d \sqrt{-\frac{1}{c d}}}{e^{2} x^{2} - d^{2}}\right)}{e}\right]"," ",0,"[1/2*sqrt(2)*sqrt(1/(c*d))*log(-(e^2*x^2 - 2*d*e*x + 2*sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(1/(c*d)) - 3*d^2)/(e^2*x^2 + 2*d*e*x + d^2))/e, -sqrt(2)*sqrt(-1/(c*d))*arctan(sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d*sqrt(-1/(c*d))/(e^2*x^2 - d^2))/e]","A",0
884,1,300,0,0.409685," ","integrate(1/(e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c d} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} + 2 \, \sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{c d} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d}{8 \, {\left(c d^{2} e^{3} x^{2} + 2 \, c d^{3} e^{2} x + c d^{4} e\right)}}, -\frac{\sqrt{2} {\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{-c d} \arctan\left(\frac{\sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{-c d} \sqrt{e x + d}}{c e^{2} x^{2} - c d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d}{4 \, {\left(c d^{2} e^{3} x^{2} + 2 \, c d^{3} e^{2} x + c d^{4} e\right)}}\right]"," ",0,"[1/8*(sqrt(2)*(e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 + 2*sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(c*d)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 4*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d)/(c*d^2*e^3*x^2 + 2*c*d^3*e^2*x + c*d^4*e), -1/4*(sqrt(2)*(e^2*x^2 + 2*d*e*x + d^2)*sqrt(-c*d)*arctan(sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(-c*d)*sqrt(e*x + d)/(c*e^2*x^2 - c*d^2)) + 2*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d)/(c*d^2*e^3*x^2 + 2*c*d^3*e^2*x + c*d^4*e)]","A",0
885,1,368,0,0.423596," ","integrate(1/(e*x+d)^(5/2)/(-c*e^2*x^2+c*d^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c d} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} + 2 \, \sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{c d} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(3 \, d e x + 7 \, d^{2}\right)} \sqrt{e x + d}}{64 \, {\left(c d^{3} e^{4} x^{3} + 3 \, c d^{4} e^{3} x^{2} + 3 \, c d^{5} e^{2} x + c d^{6} e\right)}}, -\frac{3 \, \sqrt{2} {\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{-c d} \arctan\left(\frac{\sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{-c d} \sqrt{e x + d}}{c e^{2} x^{2} - c d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(3 \, d e x + 7 \, d^{2}\right)} \sqrt{e x + d}}{32 \, {\left(c d^{3} e^{4} x^{3} + 3 \, c d^{4} e^{3} x^{2} + 3 \, c d^{5} e^{2} x + c d^{6} e\right)}}\right]"," ",0,"[1/64*(3*sqrt(2)*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 + 2*sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(c*d)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 4*sqrt(-c*e^2*x^2 + c*d^2)*(3*d*e*x + 7*d^2)*sqrt(e*x + d))/(c*d^3*e^4*x^3 + 3*c*d^4*e^3*x^2 + 3*c*d^5*e^2*x + c*d^6*e), -1/32*(3*sqrt(2)*(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(-c*d)*arctan(sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(-c*d)*sqrt(e*x + d)/(c*e^2*x^2 - c*d^2)) + 2*sqrt(-c*e^2*x^2 + c*d^2)*(3*d*e*x + 7*d^2)*sqrt(e*x + d))/(c*d^3*e^4*x^3 + 3*c*d^4*e^3*x^2 + 3*c*d^5*e^2*x + c*d^6*e)]","A",0
886,1,77,0,0.392848," ","integrate((e*x+d)^(9/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(e^{3} x^{3} + 7 \, d e^{2} x^{2} + 43 \, d^{2} e x - 91 \, d^{3}\right)} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{5 \, {\left(c^{2} e^{3} x^{2} - c^{2} d^{2} e\right)}}"," ",0,"2/5*(e^3*x^3 + 7*d*e^2*x^2 + 43*d^2*e*x - 91*d^3)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(c^2*e^3*x^2 - c^2*d^2*e)","A",0
887,1,66,0,0.391248," ","integrate((e*x+d)^(7/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(e^{2} x^{2} + 10 \, d e x - 23 \, d^{2}\right)} \sqrt{e x + d}}{3 \, {\left(c^{2} e^{3} x^{2} - c^{2} d^{2} e\right)}}"," ",0,"2/3*sqrt(-c*e^2*x^2 + c*d^2)*(e^2*x^2 + 10*d*e*x - 23*d^2)*sqrt(e*x + d)/(c^2*e^3*x^2 - c^2*d^2*e)","A",0
888,1,55,0,0.400079," ","integrate((e*x+d)^(5/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} {\left(e x - 3 \, d\right)}}{c^{2} e^{3} x^{2} - c^{2} d^{2} e}"," ",0,"2*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*(e*x - 3*d)/(c^2*e^3*x^2 - c^2*d^2*e)","A",0
889,1,48,0,0.385909," ","integrate((e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d}}{c^{2} e^{3} x^{2} - c^{2} d^{2} e}"," ",0,"-2*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)/(c^2*e^3*x^2 - c^2*d^2*e)","A",0
890,1,284,0,0.415816," ","integrate((e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(e^{2} x^{2} - d^{2}\right)} \sqrt{c d} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} + 2 \, \sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{c d} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d}{4 \, {\left(c^{2} d^{2} e^{3} x^{2} - c^{2} d^{4} e\right)}}, -\frac{\sqrt{2} {\left(e^{2} x^{2} - d^{2}\right)} \sqrt{-c d} \arctan\left(\frac{\sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{-c d} \sqrt{e x + d}}{c e^{2} x^{2} - c d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{e x + d} d}{2 \, {\left(c^{2} d^{2} e^{3} x^{2} - c^{2} d^{4} e\right)}}\right]"," ",0,"[1/4*(sqrt(2)*(e^2*x^2 - d^2)*sqrt(c*d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 + 2*sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(c*d)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 4*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d)/(c^2*d^2*e^3*x^2 - c^2*d^4*e), -1/2*(sqrt(2)*(e^2*x^2 - d^2)*sqrt(-c*d)*arctan(sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(-c*d)*sqrt(e*x + d)/(c*e^2*x^2 - c*d^2)) + 2*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(e*x + d)*d)/(c^2*d^2*e^3*x^2 - c^2*d^4*e)]","A",0
891,1,382,0,0.415845," ","integrate(1/(e*x+d)^(1/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(e^{3} x^{3} + d e^{2} x^{2} - d^{2} e x - d^{3}\right)} \sqrt{c d} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} + 2 \, \sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{c d} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(3 \, d e x + d^{2}\right)} \sqrt{e x + d}}{16 \, {\left(c^{2} d^{3} e^{4} x^{3} + c^{2} d^{4} e^{3} x^{2} - c^{2} d^{5} e^{2} x - c^{2} d^{6} e\right)}}, -\frac{3 \, \sqrt{2} {\left(e^{3} x^{3} + d e^{2} x^{2} - d^{2} e x - d^{3}\right)} \sqrt{-c d} \arctan\left(\frac{\sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{-c d} \sqrt{e x + d}}{c e^{2} x^{2} - c d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(3 \, d e x + d^{2}\right)} \sqrt{e x + d}}{8 \, {\left(c^{2} d^{3} e^{4} x^{3} + c^{2} d^{4} e^{3} x^{2} - c^{2} d^{5} e^{2} x - c^{2} d^{6} e\right)}}\right]"," ",0,"[1/16*(3*sqrt(2)*(e^3*x^3 + d*e^2*x^2 - d^2*e*x - d^3)*sqrt(c*d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 + 2*sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(c*d)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 4*sqrt(-c*e^2*x^2 + c*d^2)*(3*d*e*x + d^2)*sqrt(e*x + d))/(c^2*d^3*e^4*x^3 + c^2*d^4*e^3*x^2 - c^2*d^5*e^2*x - c^2*d^6*e), -1/8*(3*sqrt(2)*(e^3*x^3 + d*e^2*x^2 - d^2*e*x - d^3)*sqrt(-c*d)*arctan(sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(-c*d)*sqrt(e*x + d)/(c*e^2*x^2 - c*d^2)) + 2*sqrt(-c*e^2*x^2 + c*d^2)*(3*d*e*x + d^2)*sqrt(e*x + d))/(c^2*d^3*e^4*x^3 + c^2*d^4*e^3*x^2 - c^2*d^5*e^2*x - c^2*d^6*e)]","A",0
892,1,412,0,0.414809," ","integrate(1/(e*x+d)^(3/2)/(-c*e^2*x^2+c*d^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{2} {\left(e^{4} x^{4} + 2 \, d e^{3} x^{3} - 2 \, d^{3} e x - d^{4}\right)} \sqrt{c d} \log\left(-\frac{c e^{2} x^{2} - 2 \, c d e x - 3 \, c d^{2} + 2 \, \sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{c d} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(15 \, d e^{2} x^{2} + 20 \, d^{2} e x - 3 \, d^{3}\right)} \sqrt{e x + d}}{128 \, {\left(c^{2} d^{4} e^{5} x^{4} + 2 \, c^{2} d^{5} e^{4} x^{3} - 2 \, c^{2} d^{7} e^{2} x - c^{2} d^{8} e\right)}}, -\frac{15 \, \sqrt{2} {\left(e^{4} x^{4} + 2 \, d e^{3} x^{3} - 2 \, d^{3} e x - d^{4}\right)} \sqrt{-c d} \arctan\left(\frac{\sqrt{2} \sqrt{-c e^{2} x^{2} + c d^{2}} \sqrt{-c d} \sqrt{e x + d}}{c e^{2} x^{2} - c d^{2}}\right) + 2 \, \sqrt{-c e^{2} x^{2} + c d^{2}} {\left(15 \, d e^{2} x^{2} + 20 \, d^{2} e x - 3 \, d^{3}\right)} \sqrt{e x + d}}{64 \, {\left(c^{2} d^{4} e^{5} x^{4} + 2 \, c^{2} d^{5} e^{4} x^{3} - 2 \, c^{2} d^{7} e^{2} x - c^{2} d^{8} e\right)}}\right]"," ",0,"[1/128*(15*sqrt(2)*(e^4*x^4 + 2*d*e^3*x^3 - 2*d^3*e*x - d^4)*sqrt(c*d)*log(-(c*e^2*x^2 - 2*c*d*e*x - 3*c*d^2 + 2*sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(c*d)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 4*sqrt(-c*e^2*x^2 + c*d^2)*(15*d*e^2*x^2 + 20*d^2*e*x - 3*d^3)*sqrt(e*x + d))/(c^2*d^4*e^5*x^4 + 2*c^2*d^5*e^4*x^3 - 2*c^2*d^7*e^2*x - c^2*d^8*e), -1/64*(15*sqrt(2)*(e^4*x^4 + 2*d*e^3*x^3 - 2*d^3*e*x - d^4)*sqrt(-c*d)*arctan(sqrt(2)*sqrt(-c*e^2*x^2 + c*d^2)*sqrt(-c*d)*sqrt(e*x + d)/(c*e^2*x^2 - c*d^2)) + 2*sqrt(-c*e^2*x^2 + c*d^2)*(15*d*e^2*x^2 + 20*d^2*e*x - 3*d^3)*sqrt(e*x + d))/(c^2*d^4*e^5*x^4 + 2*c^2*d^5*e^4*x^3 - 2*c^2*d^7*e^2*x - c^2*d^8*e)]","A",0
893,1,30,0,0.386957," ","integrate(1/(-1+x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-x^{2} + 1} \sqrt{x - 1}}{x^{2} - 1}\right)"," ",0,"sqrt(2)*arctan(sqrt(2)*sqrt(-x^2 + 1)*sqrt(x - 1)/(x^2 - 1))","A",0
894,1,62,0,0.389045," ","integrate((e*x+2)^(5/2)*(-3*e^2*x^2+12)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, e^{4} x^{4} + 260 \, e^{3} x^{3} + 624 \, e^{2} x^{2} - 16 \, e x - 5104\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{315 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"2/315*(35*e^4*x^4 + 260*e^3*x^3 + 624*e^2*x^2 - 16*e*x - 5104)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
895,1,54,0,0.397449," ","integrate((e*x+2)^(3/2)*(-3*e^2*x^2+12)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, e^{3} x^{3} + 78 \, e^{2} x^{2} + 68 \, e x - 568\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{105 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"2/105*(15*e^3*x^3 + 78*e^2*x^2 + 68*e*x - 568)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
896,1,46,0,0.408087," ","integrate((e*x+2)^(1/2)*(-3*e^2*x^2+12)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, e^{2} x^{2} + 8 \, e x - 28\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{15 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"2/15*(3*e^2*x^2 + 8*e*x - 28)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
897,1,37,0,0.406168," ","integrate((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} {\left(e x - 2\right)}}{3 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"2/3*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)*(e*x - 2)/(e^2*x + 2*e)","B",0
898,1,99,0,0.414813," ","integrate((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{3} {\left(e x + 2\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) + \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}\right)}}{e^{2} x + 2 \, e}"," ",0,"2*(sqrt(3)*(e*x + 2)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) + sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2))/(e^2*x + 2*e)","B",0
899,1,116,0,0.393322," ","integrate((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{3} {\left(e^{2} x^{2} + 4 \, e x + 4\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x - 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) - 4 \, \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{4 \, {\left(e^{3} x^{2} + 4 \, e^{2} x + 4 \, e\right)}}"," ",0,"1/4*(sqrt(3)*(e^2*x^2 + 4*e*x + 4)*log(-(3*e^2*x^2 - 12*e*x - 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) - 4*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2))/(e^3*x^2 + 4*e^2*x + 4*e)","B",0
900,1,137,0,0.405665," ","integrate((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(7/2),x, algorithm=""fricas"")","\frac{\sqrt{3} {\left(e^{3} x^{3} + 6 \, e^{2} x^{2} + 12 \, e x + 8\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x - 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) + 4 \, \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} {\left(e x - 6\right)}}{64 \, {\left(e^{4} x^{3} + 6 \, e^{3} x^{2} + 12 \, e^{2} x + 8 \, e\right)}}"," ",0,"1/64*(sqrt(3)*(e^3*x^3 + 6*e^2*x^2 + 12*e*x + 8)*log(-(3*e^2*x^2 - 12*e*x - 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) + 4*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)*(e*x - 6))/(e^4*x^3 + 6*e^3*x^2 + 12*e^2*x + 8*e)","B",0
901,1,78,0,0.403149," ","integrate((e*x+2)^(5/2)*(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(1155 \, e^{6} x^{6} + 7980 \, e^{5} x^{5} + 11060 \, e^{4} x^{4} - 43360 \, e^{3} x^{3} - 152112 \, e^{2} x^{2} - 85312 \, e x + 619712\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{5005 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"-2/5005*(1155*e^6*x^6 + 7980*e^5*x^5 + 11060*e^4*x^4 - 43360*e^3*x^3 - 152112*e^2*x^2 - 85312*e*x + 619712)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
902,1,70,0,0.396106," ","integrate((e*x+2)^(3/2)*(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(105 \, e^{5} x^{5} + 490 \, e^{4} x^{4} - 200 \, e^{3} x^{3} - 4176 \, e^{2} x^{2} - 4976 \, e x + 17056\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{385 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"-2/385*(105*e^5*x^5 + 490*e^4*x^4 - 200*e^3*x^3 - 4176*e^2*x^2 - 4976*e*x + 17056)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
903,1,62,0,0.384475," ","integrate((e*x+2)^(1/2)*(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, e^{4} x^{4} + 80 \, e^{3} x^{3} - 312 \, e^{2} x^{2} - 832 \, e x + 1712\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{105 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"-2/105*(35*e^4*x^4 + 80*e^3*x^3 - 312*e^2*x^2 - 832*e*x + 1712)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
904,1,54,0,0.396166," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, {\left(5 \, e^{3} x^{3} - 2 \, e^{2} x^{2} - 52 \, e x + 72\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{35 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"-6/35*(5*e^3*x^3 - 2*e^2*x^2 - 52*e*x + 72)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
905,1,45,0,0.383457," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(3/2),x, algorithm=""fricas"")","-\frac{6 \, {\left(e^{2} x^{2} - 4 \, e x + 4\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{5 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"-6/5*(e^2*x^2 - 4*e*x + 4)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","B",0
906,1,106,0,0.399394," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(12 \, \sqrt{3} {\left(e x + 2\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) - \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} {\left(e x - 14\right)}\right)}}{e^{2} x + 2 \, e}"," ",0,"2*(12*sqrt(3)*(e*x + 2)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) - sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)*(e*x - 14))/(e^2*x + 2*e)","B",0
907,1,122,0,0.413866," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(7/2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, \sqrt{3} {\left(e^{2} x^{2} + 4 \, e x + 4\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x - 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) - 2 \, \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 4\right)} \sqrt{e x + 2}\right)}}{e^{3} x^{2} + 4 \, e^{2} x + 4 \, e}"," ",0,"3*(3*sqrt(3)*(e^2*x^2 + 4*e*x + 4)*log(-(3*e^2*x^2 - 12*e*x - 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) - 2*sqrt(-3*e^2*x^2 + 12)*(e*x + 4)*sqrt(e*x + 2))/(e^3*x^2 + 4*e^2*x + 4*e)","B",0
908,1,139,0,0.409876," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(9/2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, \sqrt{3} {\left(e^{3} x^{3} + 6 \, e^{2} x^{2} + 12 \, e x + 8\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) + 4 \, \sqrt{-3 \, e^{2} x^{2} + 12} {\left(5 \, e x + 2\right)} \sqrt{e x + 2}\right)}}{16 \, {\left(e^{4} x^{3} + 6 \, e^{3} x^{2} + 12 \, e^{2} x + 8 \, e\right)}}"," ",0,"3/16*(3*sqrt(3)*(e^3*x^3 + 6*e^2*x^2 + 12*e*x + 8)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) + 4*sqrt(-3*e^2*x^2 + 12)*(5*e*x + 2)*sqrt(e*x + 2))/(e^4*x^3 + 6*e^3*x^2 + 12*e^2*x + 8*e)","B",0
909,1,163,0,0.398964," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(11/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{3} {\left(e^{4} x^{4} + 8 \, e^{3} x^{3} + 24 \, e^{2} x^{2} + 32 \, e x + 16\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) - 4 \, {\left(3 \, e^{2} x^{2} - 44 \, e x + 28\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{128 \, {\left(e^{5} x^{4} + 8 \, e^{4} x^{3} + 24 \, e^{3} x^{2} + 32 \, e^{2} x + 16 \, e\right)}}"," ",0,"1/128*(3*sqrt(3)*(e^4*x^4 + 8*e^3*x^3 + 24*e^2*x^2 + 32*e*x + 16)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) - 4*(3*e^2*x^2 - 44*e*x + 28)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2))/(e^5*x^4 + 8*e^4*x^3 + 24*e^3*x^2 + 32*e^2*x + 16*e)","A",0
910,1,187,0,0.418320," ","integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(13/2),x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, \sqrt{3} {\left(e^{5} x^{5} + 10 \, e^{4} x^{4} + 40 \, e^{3} x^{3} + 80 \, e^{2} x^{2} + 80 \, e x + 32\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) - 4 \, {\left(3 \, e^{3} x^{3} + 26 \, e^{2} x^{2} - 316 \, e x + 312\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}\right)}}{4096 \, {\left(e^{6} x^{5} + 10 \, e^{5} x^{4} + 40 \, e^{4} x^{3} + 80 \, e^{3} x^{2} + 80 \, e^{2} x + 32 \, e\right)}}"," ",0,"3/4096*(3*sqrt(3)*(e^5*x^5 + 10*e^4*x^4 + 40*e^3*x^3 + 80*e^2*x^2 + 80*e*x + 32)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) - 4*(3*e^3*x^3 + 26*e^2*x^2 - 316*e*x + 312)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2))/(e^6*x^5 + 10*e^5*x^4 + 40*e^4*x^3 + 80*e^3*x^2 + 80*e^2*x + 32*e)","A",0
911,1,54,0,0.407826," ","integrate((e*x+2)^(7/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, e^{3} x^{3} + 54 \, e^{2} x^{2} + 284 \, e x + 1416\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{105 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"-2/105*(5*e^3*x^3 + 54*e^2*x^2 + 284*e*x + 1416)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
912,1,46,0,0.391015," ","integrate((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, e^{2} x^{2} + 28 \, e x + 172\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{45 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"-2/45*(3*e^2*x^2 + 28*e*x + 172)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
913,1,37,0,0.400294," ","integrate((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 10\right)} \sqrt{e x + 2}}{9 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"-2/9*sqrt(-3*e^2*x^2 + 12)*(e*x + 10)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
914,1,32,0,0.397281," ","integrate((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{3 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"-2/3*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^2*x + 2*e)","A",0
915,1,64,0,0.408772," ","integrate(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{3} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right)}{6 \, e}"," ",0,"1/6*sqrt(3)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4))/e","B",0
916,1,116,0,0.415436," ","integrate(1/(e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{3} {\left(e^{2} x^{2} + 4 \, e x + 4\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) - 4 \, \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{48 \, {\left(e^{3} x^{2} + 4 \, e^{2} x + 4 \, e\right)}}"," ",0,"1/48*(sqrt(3)*(e^2*x^2 + 4*e*x + 4)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) - 4*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2))/(e^3*x^2 + 4*e^2*x + 4*e)","B",0
917,1,139,0,0.407048," ","integrate(1/(e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{3} {\left(e^{3} x^{3} + 6 \, e^{2} x^{2} + 12 \, e x + 8\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) - 4 \, \sqrt{-3 \, e^{2} x^{2} + 12} {\left(3 \, e x + 14\right)} \sqrt{e x + 2}}{768 \, {\left(e^{4} x^{3} + 6 \, e^{3} x^{2} + 12 \, e^{2} x + 8 \, e\right)}}"," ",0,"1/768*(3*sqrt(3)*(e^3*x^3 + 6*e^2*x^2 + 12*e*x + 8)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) - 4*sqrt(-3*e^2*x^2 + 12)*(3*e*x + 14)*sqrt(e*x + 2))/(e^4*x^3 + 6*e^3*x^2 + 12*e^2*x + 8*e)","B",0
918,1,64,0,0.403099," ","integrate((e*x+2)^(11/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, e^{4} x^{4} + 72 \, e^{3} x^{3} + 568 \, e^{2} x^{2} + 5664 \, e x - 23216\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{315 \, {\left(e^{3} x^{2} - 4 \, e\right)}}"," ",0,"2/315*(5*e^4*x^4 + 72*e^3*x^3 + 568*e^2*x^2 + 5664*e*x - 23216)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^3*x^2 - 4*e)","A",0
919,1,55,0,0.400519," ","integrate((e*x+2)^(9/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(e^{3} x^{3} + 14 \, e^{2} x^{2} + 172 \, e x - 728\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{45 \, {\left(e^{3} x^{2} - 4 \, e\right)}}"," ",0,"2/45*(e^3*x^3 + 14*e^2*x^2 + 172*e*x - 728)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^3*x^2 - 4*e)","A",0
920,1,47,0,0.398993," ","integrate((e*x+2)^(7/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(e^{2} x^{2} + 20 \, e x - 92\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{27 \, {\left(e^{3} x^{2} - 4 \, e\right)}}"," ",0,"2/27*(e^2*x^2 + 20*e*x - 92)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^3*x^2 - 4*e)","A",0
921,1,39,0,0.387545," ","integrate((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} {\left(e x - 6\right)}}{9 \, {\left(e^{3} x^{2} - 4 \, e\right)}}"," ",0,"2/9*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)*(e*x - 6)/(e^3*x^2 - 4*e)","A",0
922,1,34,0,0.385256," ","integrate((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{9 \, {\left(e^{3} x^{2} - 4 \, e\right)}}"," ",0,"-2/9*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2)/(e^3*x^2 - 4*e)","B",0
923,1,106,0,0.407362," ","integrate((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{3} {\left(e^{2} x^{2} - 4\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) - 4 \, \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{72 \, {\left(e^{3} x^{2} - 4 \, e\right)}}"," ",0,"1/72*(sqrt(3)*(e^2*x^2 - 4)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) - 4*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2))/(e^3*x^2 - 4*e)","B",0
924,1,139,0,0.407917," ","integrate(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{3} {\left(e^{3} x^{3} + 2 \, e^{2} x^{2} - 4 \, e x - 8\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) - 4 \, \sqrt{-3 \, e^{2} x^{2} + 12} {\left(3 \, e x + 2\right)} \sqrt{e x + 2}}{576 \, {\left(e^{4} x^{3} + 2 \, e^{3} x^{2} - 4 \, e^{2} x - 8 \, e\right)}}"," ",0,"1/576*(3*sqrt(3)*(e^3*x^3 + 2*e^2*x^2 - 4*e*x - 8)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) - 4*sqrt(-3*e^2*x^2 + 12)*(3*e*x + 2)*sqrt(e*x + 2))/(e^4*x^3 + 2*e^3*x^2 - 4*e^2*x - 8*e)","B",0
925,1,147,0,0.418485," ","integrate(1/(e*x+2)^(3/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{3} {\left(e^{4} x^{4} + 4 \, e^{3} x^{3} - 16 \, e x - 16\right)} \log\left(-\frac{3 \, e^{2} x^{2} - 12 \, e x + 4 \, \sqrt{3} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2} - 36}{e^{2} x^{2} + 4 \, e x + 4}\right) - 4 \, {\left(15 \, e^{2} x^{2} + 40 \, e x - 12\right)} \sqrt{-3 \, e^{2} x^{2} + 12} \sqrt{e x + 2}}{9216 \, {\left(e^{5} x^{4} + 4 \, e^{4} x^{3} - 16 \, e^{2} x - 16 \, e\right)}}"," ",0,"1/9216*(15*sqrt(3)*(e^4*x^4 + 4*e^3*x^3 - 16*e*x - 16)*log(-(3*e^2*x^2 - 12*e*x + 4*sqrt(3)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2) - 36)/(e^2*x^2 + 4*e*x + 4)) - 4*(15*e^2*x^2 + 40*e*x - 12)*sqrt(-3*e^2*x^2 + 12)*sqrt(e*x + 2))/(e^5*x^4 + 4*e^4*x^3 - 16*e^2*x - 16*e)","A",0
926,1,27,0,0.394569," ","integrate(1/(1+x)/(1-x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(\frac{x + 2 \, \sqrt{2} \sqrt{-x + 1} - 3}{x + 1}\right)"," ",0,"1/2*sqrt(2)*log((x + 2*sqrt(2)*sqrt(-x + 1) - 3)/(x + 1))","A",0
927,1,45,0,0.404650," ","integrate(1/(1+x)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(-\frac{x^{2} + 2 \, \sqrt{2} \sqrt{-x^{2} + 1} \sqrt{x + 1} - 2 \, x - 3}{x^{2} + 2 \, x + 1}\right)"," ",0,"1/2*sqrt(2)*log(-(x^2 + 2*sqrt(2)*sqrt(-x^2 + 1)*sqrt(x + 1) - 2*x - 3)/(x^2 + 2*x + 1))","B",0
928,1,35,0,0.398330," ","integrate(1/(a*x+1)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(\frac{a x + 2 \, \sqrt{2} \sqrt{-a x + 1} - 3}{a x + 1}\right)}{2 \, a}"," ",0,"1/2*sqrt(2)*log((a*x + 2*sqrt(2)*sqrt(-a*x + 1) - 3)/(a*x + 1))/a","A",0
929,1,63,0,0.403881," ","integrate(1/(a*x+1)^(1/2)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{a^{2} x^{2} - 2 \, a x + 2 \, \sqrt{2} \sqrt{-a^{2} x^{2} + 1} \sqrt{a x + 1} - 3}{a^{2} x^{2} + 2 \, a x + 1}\right)}{2 \, a}"," ",0,"1/2*sqrt(2)*log(-(a^2*x^2 - 2*a*x + 2*sqrt(2)*sqrt(-a^2*x^2 + 1)*sqrt(a*x + 1) - 3)/(a^2*x^2 + 2*a*x + 1))/a","B",0
930,1,542,0,0.441675," ","integrate((e*x+2)^(1/2)*(-3*e^2*x^2+12)^(1/4),x, algorithm=""fricas"")","\frac{12 \cdot 3^{\frac{1}{4}} \sqrt{2} e \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{3^{\frac{3}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} - 3^{\frac{3}{4}} \sqrt{2} {\left(e^{4} x + 2 \, e^{3}\right)} \sqrt{\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}} \frac{1}{e^{4}}^{\frac{3}{4}} + 3 \, e x + 6}{3 \, {\left(e x + 2\right)}}\right) + 12 \cdot 3^{\frac{1}{4}} \sqrt{2} e \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{3^{\frac{3}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} - 3^{\frac{3}{4}} \sqrt{2} {\left(e^{4} x + 2 \, e^{3}\right)} \sqrt{-\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}} \frac{1}{e^{4}}^{\frac{3}{4}} - 3 \, e x - 6}{3 \, {\left(e x + 2\right)}}\right) - 3 \cdot 3^{\frac{1}{4}} \sqrt{2} e \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}\right) + 3 \cdot 3^{\frac{1}{4}} \sqrt{2} e \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(-\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}\right) + 2 \, {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} {\left(e x + 1\right)}}{4 \, e}"," ",0,"1/4*(12*3^(1/4)*sqrt(2)*e*(e^(-4))^(1/4)*arctan(-1/3*(3^(3/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) - 3^(3/4)*sqrt(2)*(e^4*x + 2*e^3)*sqrt((3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12))/(e*x + 2))*(e^(-4))^(3/4) + 3*e*x + 6)/(e*x + 2)) + 12*3^(1/4)*sqrt(2)*e*(e^(-4))^(1/4)*arctan(-1/3*(3^(3/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) - 3^(3/4)*sqrt(2)*(e^4*x + 2*e^3)*sqrt(-(3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12))/(e*x + 2))*(e^(-4))^(3/4) - 3*e*x - 6)/(e*x + 2)) - 3*3^(1/4)*sqrt(2)*e*(e^(-4))^(1/4)*log((3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12))/(e*x + 2)) + 3*3^(1/4)*sqrt(2)*e*(e^(-4))^(1/4)*log(-(3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12))/(e*x + 2)) + 2*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*(e*x + 1))/e","B",0
931,1,536,0,0.438722," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(1/2),x, algorithm=""fricas"")","\frac{4 \cdot 3^{\frac{1}{4}} \sqrt{2} e \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{3^{\frac{3}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} - 3^{\frac{3}{4}} \sqrt{2} {\left(e^{4} x + 2 \, e^{3}\right)} \sqrt{\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}} \frac{1}{e^{4}}^{\frac{3}{4}} + 3 \, e x + 6}{3 \, {\left(e x + 2\right)}}\right) + 4 \cdot 3^{\frac{1}{4}} \sqrt{2} e \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{3^{\frac{3}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} - 3^{\frac{3}{4}} \sqrt{2} {\left(e^{4} x + 2 \, e^{3}\right)} \sqrt{-\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}} \frac{1}{e^{4}}^{\frac{3}{4}} - 3 \, e x - 6}{3 \, {\left(e x + 2\right)}}\right) - 3^{\frac{1}{4}} \sqrt{2} e \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}\right) + 3^{\frac{1}{4}} \sqrt{2} e \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(-\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}\right) + 2 \, {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2}}{2 \, e}"," ",0,"1/2*(4*3^(1/4)*sqrt(2)*e*(e^(-4))^(1/4)*arctan(-1/3*(3^(3/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) - 3^(3/4)*sqrt(2)*(e^4*x + 2*e^3)*sqrt((3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12))/(e*x + 2))*(e^(-4))^(3/4) + 3*e*x + 6)/(e*x + 2)) + 4*3^(1/4)*sqrt(2)*e*(e^(-4))^(1/4)*arctan(-1/3*(3^(3/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) - 3^(3/4)*sqrt(2)*(e^4*x + 2*e^3)*sqrt(-(3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12))/(e*x + 2))*(e^(-4))^(3/4) - 3*e*x - 6)/(e*x + 2)) - 3^(1/4)*sqrt(2)*e*(e^(-4))^(1/4)*log((3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12))/(e*x + 2)) + 3^(1/4)*sqrt(2)*e*(e^(-4))^(1/4)*log(-(3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12))/(e*x + 2)) + 2*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2))/e","B",0
932,1,576,0,0.439064," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(3/2),x, algorithm=""fricas"")","-\frac{4 \cdot 3^{\frac{1}{4}} \sqrt{2} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{3^{\frac{3}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} - 3^{\frac{3}{4}} \sqrt{2} {\left(e^{4} x + 2 \, e^{3}\right)} \sqrt{\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}} \frac{1}{e^{4}}^{\frac{3}{4}} + 3 \, e x + 6}{3 \, {\left(e x + 2\right)}}\right) + 4 \cdot 3^{\frac{1}{4}} \sqrt{2} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{3^{\frac{3}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} - 3^{\frac{3}{4}} \sqrt{2} {\left(e^{4} x + 2 \, e^{3}\right)} \sqrt{-\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}} \frac{1}{e^{4}}^{\frac{3}{4}} - 3 \, e x - 6}{3 \, {\left(e x + 2\right)}}\right) - 3^{\frac{1}{4}} \sqrt{2} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}\right) + 3^{\frac{1}{4}} \sqrt{2} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(-\frac{3^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - \sqrt{3} {\left(e^{3} x + 2 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12}}{e x + 2}\right) + 8 \, {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2}}{2 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"-1/2*(4*3^(1/4)*sqrt(2)*(e^2*x + 2*e)*(e^(-4))^(1/4)*arctan(-1/3*(3^(3/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) - 3^(3/4)*sqrt(2)*(e^4*x + 2*e^3)*sqrt((3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12))/(e*x + 2))*(e^(-4))^(3/4) + 3*e*x + 6)/(e*x + 2)) + 4*3^(1/4)*sqrt(2)*(e^2*x + 2*e)*(e^(-4))^(1/4)*arctan(-1/3*(3^(3/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) - 3^(3/4)*sqrt(2)*(e^4*x + 2*e^3)*sqrt(-(3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12))/(e*x + 2))*(e^(-4))^(3/4) - 3*e*x - 6)/(e*x + 2)) - 3^(1/4)*sqrt(2)*(e^2*x + 2*e)*(e^(-4))^(1/4)*log((3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12))/(e*x + 2)) + 3^(1/4)*sqrt(2)*(e^2*x + 2*e)*(e^(-4))^(1/4)*log(-(3^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - sqrt(3)*(e^3*x + 2*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12))/(e*x + 2)) + 8*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2))/(e^2*x + 2*e)","B",0
933,1,45,0,0.402906," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2} {\left(e x - 2\right)}}{5 \, {\left(e^{3} x^{2} + 4 \, e^{2} x + 4 \, e\right)}}"," ",0,"1/5*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)*(e*x - 2)/(e^3*x^2 + 4*e^2*x + 4*e)","A",0
934,1,61,0,0.400988," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(7/2),x, algorithm=""fricas"")","\frac{{\left(e^{2} x^{2} + 5 \, e x - 14\right)} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2}}{45 \, {\left(e^{4} x^{3} + 6 \, e^{3} x^{2} + 12 \, e^{2} x + 8 \, e\right)}}"," ",0,"1/45*(e^2*x^2 + 5*e*x - 14)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)/(e^4*x^3 + 6*e^3*x^2 + 12*e^2*x + 8*e)","A",0
935,1,78,0,0.400029," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(9/2),x, algorithm=""fricas"")","\frac{{\left(2 \, e^{3} x^{3} + 14 \, e^{2} x^{2} + 37 \, e x - 146\right)} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2}}{585 \, {\left(e^{5} x^{4} + 8 \, e^{4} x^{3} + 24 \, e^{3} x^{2} + 32 \, e^{2} x + 16 \, e\right)}}"," ",0,"1/585*(2*e^3*x^3 + 14*e^2*x^2 + 37*e*x - 146)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)/(e^5*x^4 + 8*e^4*x^3 + 24*e^3*x^2 + 32*e^2*x + 16*e)","A",0
936,1,94,0,0.400222," ","integrate((-3*e^2*x^2+12)^(1/4)/(e*x+2)^(11/2),x, algorithm=""fricas"")","\frac{{\left(2 \, e^{4} x^{4} + 18 \, e^{3} x^{3} + 65 \, e^{2} x^{2} + 123 \, e x - 682\right)} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{1}{4}} \sqrt{e x + 2}}{3315 \, {\left(e^{6} x^{5} + 10 \, e^{5} x^{4} + 40 \, e^{4} x^{3} + 80 \, e^{3} x^{2} + 80 \, e^{2} x + 32 \, e\right)}}"," ",0,"1/3315*(2*e^4*x^4 + 18*e^3*x^3 + 65*e^2*x^2 + 123*e*x - 682)*(-3*e^2*x^2 + 12)^(1/4)*sqrt(e*x + 2)/(e^6*x^5 + 10*e^5*x^4 + 40*e^4*x^3 + 80*e^3*x^2 + 80*e^2*x + 32*e)","A",0
937,1,661,0,0.457732," ","integrate((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""fricas"")","\frac{180 \cdot 27^{\frac{1}{4}} \sqrt{2} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{27^{\frac{3}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} + 27 \, e^{2} x^{2} - 27^{\frac{3}{4}} \sqrt{2} {\left(e^{5} x^{2} - 4 \, e^{3}\right)} \sqrt{\frac{27^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + 3 \, \sqrt{3} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - 3 \, \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}}{e^{2} x^{2} - 4}} \frac{1}{e^{4}}^{\frac{3}{4}} - 108}{27 \, {\left(e^{2} x^{2} - 4\right)}}\right) + 180 \cdot 27^{\frac{1}{4}} \sqrt{2} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{27^{\frac{3}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} - 27 \, e^{2} x^{2} - 27^{\frac{3}{4}} \sqrt{2} {\left(e^{5} x^{2} - 4 \, e^{3}\right)} \sqrt{-\frac{27^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - 3 \, \sqrt{3} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + 3 \, \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}}{e^{2} x^{2} - 4}} \frac{1}{e^{4}}^{\frac{3}{4}} + 108}{27 \, {\left(e^{2} x^{2} - 4\right)}}\right) - 45 \cdot 27^{\frac{1}{4}} \sqrt{2} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(\frac{27^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + 3 \, \sqrt{3} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - 3 \, \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}}{e^{2} x^{2} - 4}\right) + 45 \cdot 27^{\frac{1}{4}} \sqrt{2} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(-\frac{27^{\frac{1}{4}} \sqrt{2} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - 3 \, \sqrt{3} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + 3 \, \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}}{e^{2} x^{2} - 4}\right) - 2 \, {\left(2 \, e^{2} x^{2} + 17 \, e x + 71\right)} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2}}{36 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"1/36*(180*27^(1/4)*sqrt(2)*(e^2*x + 2*e)*(e^(-4))^(1/4)*arctan(-1/27*(27^(3/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) + 27*e^2*x^2 - 27^(3/4)*sqrt(2)*(e^5*x^2 - 4*e^3)*sqrt((27^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + 3*sqrt(3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) - 3*sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4))*(e^(-4))^(3/4) - 108)/(e^2*x^2 - 4)) + 180*27^(1/4)*sqrt(2)*(e^2*x + 2*e)*(e^(-4))^(1/4)*arctan(-1/27*(27^(3/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) - 27*e^2*x^2 - 27^(3/4)*sqrt(2)*(e^5*x^2 - 4*e^3)*sqrt(-(27^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - 3*sqrt(3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) + 3*sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4))*(e^(-4))^(3/4) + 108)/(e^2*x^2 - 4)) - 45*27^(1/4)*sqrt(2)*(e^2*x + 2*e)*(e^(-4))^(1/4)*log((27^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + 3*sqrt(3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) - 3*sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4)) + 45*27^(1/4)*sqrt(2)*(e^2*x + 2*e)*(e^(-4))^(1/4)*log(-(27^(1/4)*sqrt(2)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - 3*sqrt(3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) + 3*sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4)) - 2*(2*e^2*x^2 + 17*e*x + 71)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2))/(e^2*x + 2*e)","B",0
938,1,656,0,0.449977," ","integrate((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""fricas"")","\frac{60 \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} + e^{2} x^{2} - \sqrt{3} \sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(e^{5} x^{2} - 4 \, e^{3}\right)} \sqrt{\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}}{e^{2} x^{2} - 4}} \frac{1}{e^{4}}^{\frac{3}{4}} - 4}{e^{2} x^{2} - 4}\right) + 60 \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} - e^{2} x^{2} - \sqrt{3} \sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(e^{5} x^{2} - 4 \, e^{3}\right)} \sqrt{-\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}}{e^{2} x^{2} - 4}} \frac{1}{e^{4}}^{\frac{3}{4}} + 4}{e^{2} x^{2} - 4}\right) - 15 \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(\frac{3 \, {\left(\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}\right)}}{e^{2} x^{2} - 4}\right) + 15 \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(-\frac{3 \, {\left(\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}\right)}}{e^{2} x^{2} - 4}\right) - 2 \, {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} {\left(e x + 7\right)} \sqrt{e x + 2}}{12 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"1/12*(60*sqrt(2)*(1/3)^(1/4)*(e^2*x + 2*e)*(e^(-4))^(1/4)*arctan(-(sqrt(2)*(1/3)^(3/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) + e^2*x^2 - sqrt(3)*sqrt(2)*(1/3)^(3/4)*(e^5*x^2 - 4*e^3)*sqrt((sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4))*(e^(-4))^(3/4) - 4)/(e^2*x^2 - 4)) + 60*sqrt(2)*(1/3)^(1/4)*(e^2*x + 2*e)*(e^(-4))^(1/4)*arctan(-(sqrt(2)*(1/3)^(3/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) - e^2*x^2 - sqrt(3)*sqrt(2)*(1/3)^(3/4)*(e^5*x^2 - 4*e^3)*sqrt(-(sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4))*(e^(-4))^(3/4) + 4)/(e^2*x^2 - 4)) - 15*sqrt(2)*(1/3)^(1/4)*(e^2*x + 2*e)*(e^(-4))^(1/4)*log(3*(sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4)) + 15*sqrt(2)*(1/3)^(1/4)*(e^2*x + 2*e)*(e^(-4))^(1/4)*log(-3*(sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4)) - 2*(-3*e^2*x^2 + 12)^(3/4)*(e*x + 7)*sqrt(e*x + 2))/(e^2*x + 2*e)","B",0
939,1,651,0,0.447773," ","integrate((e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} + e^{2} x^{2} - \sqrt{3} \sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(e^{5} x^{2} - 4 \, e^{3}\right)} \sqrt{\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}}{e^{2} x^{2} - 4}} \frac{1}{e^{4}}^{\frac{3}{4}} - 4}{e^{2} x^{2} - 4}\right) + 12 \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} - e^{2} x^{2} - \sqrt{3} \sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(e^{5} x^{2} - 4 \, e^{3}\right)} \sqrt{-\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}}{e^{2} x^{2} - 4}} \frac{1}{e^{4}}^{\frac{3}{4}} + 4}{e^{2} x^{2} - 4}\right) - 3 \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(\frac{3 \, {\left(\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}\right)}}{e^{2} x^{2} - 4}\right) + 3 \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(e^{2} x + 2 \, e\right)} \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(-\frac{3 \, {\left(\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}\right)}}{e^{2} x^{2} - 4}\right) - 2 \, {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2}}{6 \, {\left(e^{2} x + 2 \, e\right)}}"," ",0,"1/6*(12*sqrt(2)*(1/3)^(1/4)*(e^2*x + 2*e)*(e^(-4))^(1/4)*arctan(-(sqrt(2)*(1/3)^(3/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) + e^2*x^2 - sqrt(3)*sqrt(2)*(1/3)^(3/4)*(e^5*x^2 - 4*e^3)*sqrt((sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4))*(e^(-4))^(3/4) - 4)/(e^2*x^2 - 4)) + 12*sqrt(2)*(1/3)^(1/4)*(e^2*x + 2*e)*(e^(-4))^(1/4)*arctan(-(sqrt(2)*(1/3)^(3/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) - e^2*x^2 - sqrt(3)*sqrt(2)*(1/3)^(3/4)*(e^5*x^2 - 4*e^3)*sqrt(-(sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4))*(e^(-4))^(3/4) + 4)/(e^2*x^2 - 4)) - 3*sqrt(2)*(1/3)^(1/4)*(e^2*x + 2*e)*(e^(-4))^(1/4)*log(3*(sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4)) + 3*sqrt(2)*(1/3)^(1/4)*(e^2*x + 2*e)*(e^(-4))^(1/4)*log(-3*(sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4)) - 2*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2))/(e^2*x + 2*e)","B",0
940,1,581,0,0.439451," ","integrate(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""fricas"")","2 \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} + e^{2} x^{2} - \sqrt{3} \sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(e^{5} x^{2} - 4 \, e^{3}\right)} \sqrt{\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}}{e^{2} x^{2} - 4}} \frac{1}{e^{4}}^{\frac{3}{4}} - 4}{e^{2} x^{2} - 4}\right) + 2 \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} \frac{1}{e^{4}}^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e^{3} \frac{1}{e^{4}}^{\frac{3}{4}} - e^{2} x^{2} - \sqrt{3} \sqrt{2} \left(\frac{1}{3}\right)^{\frac{3}{4}} {\left(e^{5} x^{2} - 4 \, e^{3}\right)} \sqrt{-\frac{\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}}{e^{2} x^{2} - 4}} \frac{1}{e^{4}}^{\frac{3}{4}} + 4}{e^{2} x^{2} - 4}\right) - \frac{1}{2} \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(\frac{3 \, {\left(\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} + 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} - \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}\right)}}{e^{2} x^{2} - 4}\right) + \frac{1}{2} \, \sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} \frac{1}{e^{4}}^{\frac{1}{4}} \log\left(-\frac{3 \, {\left(\sqrt{2} \left(\frac{1}{3}\right)^{\frac{1}{4}} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2} e \frac{1}{e^{4}}^{\frac{1}{4}} - 3 \, \sqrt{\frac{1}{3}} {\left(e^{4} x^{2} - 4 \, e^{2}\right)} \sqrt{\frac{1}{e^{4}}} + \sqrt{-3 \, e^{2} x^{2} + 12} {\left(e x + 2\right)}\right)}}{e^{2} x^{2} - 4}\right)"," ",0,"2*sqrt(2)*(1/3)^(1/4)*(e^(-4))^(1/4)*arctan(-(sqrt(2)*(1/3)^(3/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) + e^2*x^2 - sqrt(3)*sqrt(2)*(1/3)^(3/4)*(e^5*x^2 - 4*e^3)*sqrt((sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4))*(e^(-4))^(3/4) - 4)/(e^2*x^2 - 4)) + 2*sqrt(2)*(1/3)^(1/4)*(e^(-4))^(1/4)*arctan(-(sqrt(2)*(1/3)^(3/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e^3*(e^(-4))^(3/4) - e^2*x^2 - sqrt(3)*sqrt(2)*(1/3)^(3/4)*(e^5*x^2 - 4*e^3)*sqrt(-(sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4))*(e^(-4))^(3/4) + 4)/(e^2*x^2 - 4)) - 1/2*sqrt(2)*(1/3)^(1/4)*(e^(-4))^(1/4)*log(3*(sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) + 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) - sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4)) + 1/2*sqrt(2)*(1/3)^(1/4)*(e^(-4))^(1/4)*log(-3*(sqrt(2)*(1/3)^(1/4)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)*e*(e^(-4))^(1/4) - 3*sqrt(1/3)*(e^4*x^2 - 4*e^2)*sqrt(e^(-4)) + sqrt(-3*e^2*x^2 + 12)*(e*x + 2))/(e^2*x^2 - 4))","B",0
941,1,40,0,0.391105," ","integrate(1/(e*x+2)^(3/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2}}{9 \, {\left(e^{3} x^{2} + 4 \, e^{2} x + 4 \, e\right)}}"," ",0,"-1/9*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)/(e^3*x^2 + 4*e^2*x + 4*e)","A",0
942,1,53,0,0.411926," ","integrate(1/(e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} {\left(e x + 5\right)} \sqrt{e x + 2}}{63 \, {\left(e^{4} x^{3} + 6 \, e^{3} x^{2} + 12 \, e^{2} x + 8 \, e\right)}}"," ",0,"-1/63*(-3*e^2*x^2 + 12)^(3/4)*(e*x + 5)*sqrt(e*x + 2)/(e^4*x^3 + 6*e^3*x^2 + 12*e^2*x + 8*e)","A",0
943,1,70,0,0.398515," ","integrate(1/(e*x+2)^(7/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(2 \, e^{2} x^{2} + 14 \, e x + 41\right)} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2}}{693 \, {\left(e^{5} x^{4} + 8 \, e^{4} x^{3} + 24 \, e^{3} x^{2} + 32 \, e^{2} x + 16 \, e\right)}}"," ",0,"-1/693*(2*e^2*x^2 + 14*e*x + 41)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)/(e^5*x^4 + 8*e^4*x^3 + 24*e^3*x^2 + 32*e^2*x + 16*e)","A",0
944,1,86,0,0.424084," ","integrate(1/(e*x+2)^(9/2)/(-3*e^2*x^2+12)^(1/4),x, algorithm=""fricas"")","-\frac{{\left(2 \, e^{3} x^{3} + 18 \, e^{2} x^{2} + 69 \, e x + 159\right)} {\left(-3 \, e^{2} x^{2} + 12\right)}^{\frac{3}{4}} \sqrt{e x + 2}}{3465 \, {\left(e^{6} x^{5} + 10 \, e^{5} x^{4} + 40 \, e^{4} x^{3} + 80 \, e^{3} x^{2} + 80 \, e^{2} x + 32 \, e\right)}}"," ",0,"-1/3465*(2*e^3*x^3 + 18*e^2*x^2 + 69*e*x + 159)*(-3*e^2*x^2 + 12)^(3/4)*sqrt(e*x + 2)/(e^6*x^5 + 10*e^5*x^4 + 40*e^4*x^3 + 80*e^3*x^2 + 80*e^2*x + 32*e)","A",0
945,1,317,0,0.416637," ","integrate((b*x+a)^m*(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","\frac{{\left(a^{7} m^{3} + 21 \, a^{7} m^{2} + 152 \, a^{7} m - {\left(b^{7} m^{3} + 15 \, b^{7} m^{2} + 74 \, b^{7} m + 120 \, b^{7}\right)} x^{7} + 384 \, a^{7} - {\left(a b^{6} m^{3} + 9 \, a b^{6} m^{2} + 20 \, a b^{6} m\right)} x^{6} + 3 \, {\left(a^{2} b^{5} m^{3} + 19 \, a^{2} b^{5} m^{2} + 102 \, a^{2} b^{5} m + 168 \, a^{2} b^{5}\right)} x^{5} + 3 \, {\left(a^{3} b^{4} m^{3} + 13 \, a^{3} b^{4} m^{2} + 32 \, a^{3} b^{4} m\right)} x^{4} - 3 \, {\left(a^{4} b^{3} m^{3} + 23 \, a^{4} b^{3} m^{2} + 162 \, a^{4} b^{3} m + 280 \, a^{4} b^{3}\right)} x^{3} - 3 \, {\left(a^{5} b^{2} m^{3} + 17 \, a^{5} b^{2} m^{2} + 76 \, a^{5} b^{2} m\right)} x^{2} + {\left(a^{6} b m^{3} + 27 \, a^{6} b m^{2} + 254 \, a^{6} b m + 840 \, a^{6} b\right)} x\right)} {\left(b x + a\right)}^{m}}{b m^{4} + 22 \, b m^{3} + 179 \, b m^{2} + 638 \, b m + 840 \, b}"," ",0,"(a^7*m^3 + 21*a^7*m^2 + 152*a^7*m - (b^7*m^3 + 15*b^7*m^2 + 74*b^7*m + 120*b^7)*x^7 + 384*a^7 - (a*b^6*m^3 + 9*a*b^6*m^2 + 20*a*b^6*m)*x^6 + 3*(a^2*b^5*m^3 + 19*a^2*b^5*m^2 + 102*a^2*b^5*m + 168*a^2*b^5)*x^5 + 3*(a^3*b^4*m^3 + 13*a^3*b^4*m^2 + 32*a^3*b^4*m)*x^4 - 3*(a^4*b^3*m^3 + 23*a^4*b^3*m^2 + 162*a^4*b^3*m + 280*a^4*b^3)*x^3 - 3*(a^5*b^2*m^3 + 17*a^5*b^2*m^2 + 76*a^5*b^2*m)*x^2 + (a^6*b*m^3 + 27*a^6*b*m^2 + 254*a^6*b*m + 840*a^6*b)*x)*(b*x + a)^m/(b*m^4 + 22*b*m^3 + 179*b*m^2 + 638*b*m + 840*b)","B",0
946,1,173,0,0.424681," ","integrate((b*x+a)^m*(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","\frac{{\left(a^{5} m^{2} + 11 \, a^{5} m + {\left(b^{5} m^{2} + 7 \, b^{5} m + 12 \, b^{5}\right)} x^{5} + 32 \, a^{5} + {\left(a b^{4} m^{2} + 3 \, a b^{4} m\right)} x^{4} - 2 \, {\left(a^{2} b^{3} m^{2} + 11 \, a^{2} b^{3} m + 20 \, a^{2} b^{3}\right)} x^{3} - 2 \, {\left(a^{3} b^{2} m^{2} + 7 \, a^{3} b^{2} m\right)} x^{2} + {\left(a^{4} b m^{2} + 15 \, a^{4} b m + 60 \, a^{4} b\right)} x\right)} {\left(b x + a\right)}^{m}}{b m^{3} + 12 \, b m^{2} + 47 \, b m + 60 \, b}"," ",0,"(a^5*m^2 + 11*a^5*m + (b^5*m^2 + 7*b^5*m + 12*b^5)*x^5 + 32*a^5 + (a*b^4*m^2 + 3*a*b^4*m)*x^4 - 2*(a^2*b^3*m^2 + 11*a^2*b^3*m + 20*a^2*b^3)*x^3 - 2*(a^3*b^2*m^2 + 7*a^3*b^2*m)*x^2 + (a^4*b*m^2 + 15*a^4*b*m + 60*a^4*b)*x)*(b*x + a)^m/(b*m^3 + 12*b*m^2 + 47*b*m + 60*b)","B",0
947,1,76,0,0.412127," ","integrate((b*x+a)^m*(-b^2*x^2+a^2),x, algorithm=""fricas"")","-\frac{{\left(a b^{2} m x^{2} - a^{3} m + {\left(b^{3} m + 2 \, b^{3}\right)} x^{3} - 4 \, a^{3} - {\left(a^{2} b m + 6 \, a^{2} b\right)} x\right)} {\left(b x + a\right)}^{m}}{b m^{2} + 5 \, b m + 6 \, b}"," ",0,"-(a*b^2*m*x^2 - a^3*m + (b^3*m + 2*b^3)*x^3 - 4*a^3 - (a^2*b*m + 6*a^2*b)*x)*(b*x + a)^m/(b*m^2 + 5*b*m + 6*b)","A",0
948,0,0,0,0.418480," ","integrate((b*x+a)^m/(-b^2*x^2+a^2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x + a\right)}^{m}}{b^{2} x^{2} - a^{2}}, x\right)"," ",0,"integral(-(b*x + a)^m/(b^2*x^2 - a^2), x)","F",0
949,0,0,0,0.427689," ","integrate((b*x+a)^m/(-b^2*x^2+a^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m}}{b^{4} x^{4} - 2 \, a^{2} b^{2} x^{2} + a^{4}}, x\right)"," ",0,"integral((b*x + a)^m/(b^4*x^4 - 2*a^2*b^2*x^2 + a^4), x)","F",0
950,0,0,0,0.428205," ","integrate((b*x+a)^m/(-b^2*x^2+a^2)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x + a\right)}^{m}}{b^{6} x^{6} - 3 \, a^{2} b^{4} x^{4} + 3 \, a^{4} b^{2} x^{2} - a^{6}}, x\right)"," ",0,"integral(-(b*x + a)^m/(b^6*x^6 - 3*a^2*b^4*x^4 + 3*a^4*b^2*x^2 - a^6), x)","F",0
951,0,0,0,0.425829," ","integrate((e*x+d)^m*(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(e^{6} x^{6} - 3 \, d^{2} e^{4} x^{4} + 3 \, d^{4} e^{2} x^{2} - d^{6}\right)} \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral(-(e^6*x^6 - 3*d^2*e^4*x^4 + 3*d^4*e^2*x^2 - d^6)*sqrt(-e^2*x^2 + d^2)*(e*x + d)^m, x)","F",0
952,0,0,0,0.421983," ","integrate((e*x+d)^m*(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{4} x^{4} - 2 \, d^{2} e^{2} x^{2} + d^{4}\right)} \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((e^4*x^4 - 2*d^2*e^2*x^2 + d^4)*sqrt(-e^2*x^2 + d^2)*(e*x + d)^m, x)","F",0
953,0,0,0,0.421674," ","integrate((e*x+d)^m*(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(e^{2} x^{2} - d^{2}\right)} \sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral(-(e^2*x^2 - d^2)*sqrt(-e^2*x^2 + d^2)*(e*x + d)^m, x)","F",0
954,0,0,0,0.412603," ","integrate((e*x+d)^m*(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral(sqrt(-e^2*x^2 + d^2)*(e*x + d)^m, x)","F",0
955,0,0,0,0.410903," ","integrate((e*x+d)^m/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + d\right)}^{m}}{e^{2} x^{2} - d^{2}}, x\right)"," ",0,"integral(-sqrt(-e^2*x^2 + d^2)*(e*x + d)^m/(e^2*x^2 - d^2), x)","F",0
956,0,0,0,0.415585," ","integrate((e*x+d)^m/(-e^2*x^2+d^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + d\right)}^{m}}{e^{4} x^{4} - 2 \, d^{2} e^{2} x^{2} + d^{4}}, x\right)"," ",0,"integral(sqrt(-e^2*x^2 + d^2)*(e*x + d)^m/(e^4*x^4 - 2*d^2*e^2*x^2 + d^4), x)","F",0
957,0,0,0,0.434307," ","integrate((e*x+d)^m/(-e^2*x^2+d^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + d\right)}^{m}}{e^{6} x^{6} - 3 \, d^{2} e^{4} x^{4} + 3 \, d^{4} e^{2} x^{2} - d^{6}}, x\right)"," ",0,"integral(-sqrt(-e^2*x^2 + d^2)*(e*x + d)^m/(e^6*x^6 - 3*d^2*e^4*x^4 + 3*d^4*e^2*x^2 - d^6), x)","F",0
958,0,0,0,0.417011," ","integrate((e*x+d)^m/(-e^2*x^2+d^2)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-e^{2} x^{2} + d^{2}} {\left(e x + d\right)}^{m}}{e^{8} x^{8} - 4 \, d^{2} e^{6} x^{6} + 6 \, d^{4} e^{4} x^{4} - 4 \, d^{6} e^{2} x^{2} + d^{8}}, x\right)"," ",0,"integral(sqrt(-e^2*x^2 + d^2)*(e*x + d)^m/(e^8*x^8 - 4*d^2*e^6*x^6 + 6*d^4*e^4*x^4 - 4*d^6*e^2*x^2 + d^8), x)","F",0
959,0,0,0,0.427640," ","integrate((b*x+a)^m*(-b^2*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(-b^{2} x^{2} + a^{2}\right)}^{p} {\left(b x + a\right)}^{m}, x\right)"," ",0,"integral((-b^2*x^2 + a^2)^p*(b*x + a)^m, x)","F",0
960,0,0,0,0.404370," ","integrate((e*x+d)^3*(1-e^2*x^2/d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \left(-\frac{e^{2} x^{2} - d^{2}}{d^{2}}\right)^{p}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(-(e^2*x^2 - d^2)/d^2)^p, x)","F",0
961,0,0,0,0.430368," ","integrate((e*x+d)^2*(1-e^2*x^2/d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \left(-\frac{e^{2} x^{2} - d^{2}}{d^{2}}\right)^{p}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(-(e^2*x^2 - d^2)/d^2)^p, x)","F",0
962,0,0,0,0.410931," ","integrate((e*x+d)*(1-e^2*x^2/d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)} \left(-\frac{e^{2} x^{2} - d^{2}}{d^{2}}\right)^{p}, x\right)"," ",0,"integral((e*x + d)*(-(e^2*x^2 - d^2)/d^2)^p, x)","F",0
963,0,0,0,0.414024," ","integrate((1-e^2*x^2/d^2)^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(-\frac{e^{2} x^{2} - d^{2}}{d^{2}}\right)^{p}, x\right)"," ",0,"integral((-(e^2*x^2 - d^2)/d^2)^p, x)","F",0
964,0,0,0,0.408172," ","integrate((1-e^2*x^2/d^2)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(-\frac{e^{2} x^{2} - d^{2}}{d^{2}}\right)^{p}}{e x + d}, x\right)"," ",0,"integral((-(e^2*x^2 - d^2)/d^2)^p/(e*x + d), x)","F",0
965,0,0,0,0.425642," ","integrate((1-e^2*x^2/d^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(-\frac{e^{2} x^{2} - d^{2}}{d^{2}}\right)^{p}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((-(e^2*x^2 - d^2)/d^2)^p/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
966,0,0,0,0.425251," ","integrate((1-e^2*x^2/d^2)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(-\frac{e^{2} x^{2} - d^{2}}{d^{2}}\right)^{p}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((-(e^2*x^2 - d^2)/d^2)^p/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
967,0,0,0,0.396095," ","integrate((b*x+a)^3*(-b^2*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}, x\right)"," ",0,"integral((b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*(-b^2*x^2 + a^2)^p, x)","F",0
968,0,0,0,0.409686," ","integrate((b*x+a)^2*(-b^2*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*(-b^2*x^2 + a^2)^p, x)","F",0
969,0,0,0,0.401098," ","integrate((b*x+a)*(-b^2*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}, x\right)"," ",0,"integral((b*x + a)*(-b^2*x^2 + a^2)^p, x)","F",0
970,0,0,0,0.428537," ","integrate((-b^2*x^2+a^2)^p/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{b x + a}, x\right)"," ",0,"integral((-b^2*x^2 + a^2)^p/(b*x + a), x)","F",0
971,0,0,0,0.420264," ","integrate((-b^2*x^2+a^2)^p/(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right)"," ",0,"integral((-b^2*x^2 + a^2)^p/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
972,0,0,0,0.415871," ","integrate((-b^2*x^2+a^2)^p/(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}, x\right)"," ",0,"integral((-b^2*x^2 + a^2)^p/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3), x)","F",0
973,0,0,0,0.423558," ","integrate((b*x+a)^(3/2)*(-b^2*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{\frac{3}{2}} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^(3/2)*(-b^2*x^2 + a^2)^p, x)","F",0
974,0,0,0,0.427925," ","integrate((b*x+a)^(1/2)*(-b^2*x^2+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b x + a} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}, x\right)"," ",0,"integral(sqrt(b*x + a)*(-b^2*x^2 + a^2)^p, x)","F",0
975,0,0,0,0.418357," ","integrate((-b^2*x^2+a^2)^p/(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{\sqrt{b x + a}}, x\right)"," ",0,"integral((-b^2*x^2 + a^2)^p/sqrt(b*x + a), x)","F",0
976,0,0,0,0.440610," ","integrate((-b^2*x^2+a^2)^p/(b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right)"," ",0,"integral(sqrt(b*x + a)*(-b^2*x^2 + a^2)^p/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
977,1,36,0,0.427528," ","integrate(-a*(-b^2*x^2+a^2)^p+(b*x+a)*(-b^2*x^2+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(b^{2} x^{2} - a^{2}\right)} {\left(-b^{2} x^{2} + a^{2}\right)}^{p}}{2 \, {\left(b p + b\right)}}"," ",0,"1/2*(b^2*x^2 - a^2)*(-b^2*x^2 + a^2)^p/(b*p + b)","A",0
978,1,47,0,0.341014," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e^{4} c + x^{4} e^{3} d c + 2 x^{3} e^{2} d^{2} c + 2 x^{2} e d^{3} c + x d^{4} c"," ",0,"1/5*x^5*e^4*c + x^4*e^3*d*c + 2*x^3*e^2*d^2*c + 2*x^2*e*d^3*c + x*d^4*c","B",0
979,1,35,0,0.341842," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","\frac{1}{4} x^{4} e^{3} c + x^{3} e^{2} d c + \frac{3}{2} x^{2} e d^{2} c + x d^{3} c"," ",0,"1/4*x^4*e^3*c + x^3*e^2*d*c + 3/2*x^2*e*d^2*c + x*d^3*c","B",0
980,1,23,0,0.362449," ","integrate(c*e^2*x^2+2*c*d*e*x+c*d^2,x, algorithm=""fricas"")","\frac{1}{3} x^{3} e^{2} c + x^{2} e d c + x d^{2} c"," ",0,"1/3*x^3*e^2*c + x^2*e*d*c + x*d^2*c","A",0
981,1,12,0,0.381931," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d),x, algorithm=""fricas"")","\frac{1}{2} \, c e x^{2} + c d x"," ",0,"1/2*c*e*x^2 + c*d*x","A",0
982,1,3,0,0.360069," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^2,x, algorithm=""fricas"")","c x"," ",0,"c*x","A",0
983,1,11,0,0.395817," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{c \log\left(e x + d\right)}{e}"," ",0,"c*log(e*x + d)/e","A",0
984,1,14,0,0.375082," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{c}{e^{2} x + d e}"," ",0,"-c/(e^2*x + d*e)","A",0
985,1,25,0,0.372489," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{c}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-1/2*c/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
986,1,36,0,0.389528," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{c}{3 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"-1/3*c/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","B",0
987,1,85,0,0.353458," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{6} c^{2} + x^{6} e^{5} d c^{2} + 3 x^{5} e^{4} d^{2} c^{2} + 5 x^{4} e^{3} d^{3} c^{2} + 5 x^{3} e^{2} d^{4} c^{2} + 3 x^{2} e d^{5} c^{2} + x d^{6} c^{2}"," ",0,"1/7*x^7*e^6*c^2 + x^6*e^5*d*c^2 + 3*x^5*e^4*d^2*c^2 + 5*x^4*e^3*d^3*c^2 + 5*x^3*e^2*d^4*c^2 + 3*x^2*e*d^5*c^2 + x*d^6*c^2","B",0
988,1,71,0,0.354493," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{5} c^{2} + x^{5} e^{4} d c^{2} + \frac{5}{2} x^{4} e^{3} d^{2} c^{2} + \frac{10}{3} x^{3} e^{2} d^{3} c^{2} + \frac{5}{2} x^{2} e d^{4} c^{2} + x d^{5} c^{2}"," ",0,"1/6*x^6*e^5*c^2 + x^5*e^4*d*c^2 + 5/2*x^4*e^3*d^2*c^2 + 10/3*x^3*e^2*d^3*c^2 + 5/2*x^2*e*d^4*c^2 + x*d^5*c^2","B",0
989,1,57,0,0.361360," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","\frac{1}{5} x^{5} e^{4} c^{2} + x^{4} e^{3} d c^{2} + 2 x^{3} e^{2} d^{2} c^{2} + 2 x^{2} e d^{3} c^{2} + x d^{4} c^{2}"," ",0,"1/5*x^5*e^4*c^2 + x^4*e^3*d*c^2 + 2*x^3*e^2*d^2*c^2 + 2*x^2*e*d^3*c^2 + x*d^4*c^2","B",0
990,1,43,0,0.380661," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d),x, algorithm=""fricas"")","\frac{1}{4} \, c^{2} e^{3} x^{4} + c^{2} d e^{2} x^{3} + \frac{3}{2} \, c^{2} d^{2} e x^{2} + c^{2} d^{3} x"," ",0,"1/4*c^2*e^3*x^4 + c^2*d*e^2*x^3 + 3/2*c^2*d^2*e*x^2 + c^2*d^3*x","B",0
991,1,29,0,0.382301," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{1}{3} \, c^{2} e^{2} x^{3} + c^{2} d e x^{2} + c^{2} d^{2} x"," ",0,"1/3*c^2*e^2*x^3 + c^2*d*e*x^2 + c^2*d^2*x","A",0
992,1,16,0,0.383870," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{1}{2} \, c^{2} e x^{2} + c^{2} d x"," ",0,"1/2*c^2*e*x^2 + c^2*d*x","A",0
993,1,5,0,0.380366," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^4,x, algorithm=""fricas"")","c^{2} x"," ",0,"c^2*x","A",0
994,1,13,0,0.378623," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{c^{2} \log\left(e x + d\right)}{e}"," ",0,"c^2*log(e*x + d)/e","A",0
995,1,16,0,0.384895," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{c^{2}}{e^{2} x + d e}"," ",0,"-c^2/(e^2*x + d*e)","A",0
996,1,27,0,0.382043," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{c^{2}}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"-1/2*c^2/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
997,1,38,0,0.374827," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^2/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{c^{2}}{3 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"-1/3*c^2/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","B",0
998,1,37,0,0.394042," ","integrate((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","\frac{e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x}{4 \, c}"," ",0,"1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)/c","B",0
999,1,26,0,0.369005," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","\frac{e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x}{3 \, c}"," ",0,"1/3*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)/c","A",0
1000,1,15,0,0.386456," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","\frac{e x^{2} + 2 \, d x}{2 \, c}"," ",0,"1/2*(e*x^2 + 2*d*x)/c","A",0
1001,1,5,0,0.368737," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","\frac{x}{c}"," ",0,"x/c","A",0
1002,1,13,0,0.384800," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","\frac{\log\left(e x + d\right)}{c e}"," ",0,"log(e*x + d)/(c*e)","A",0
1003,1,15,0,0.378675," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","-\frac{1}{c e^{2} x + c d e}"," ",0,"-1/(c*e^2*x + c*d*e)","A",0
1004,1,27,0,0.380531," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(c e^{3} x^{2} + 2 \, c d e^{2} x + c d^{2} e\right)}}"," ",0,"-1/2/(c*e^3*x^2 + 2*c*d*e^2*x + c*d^2*e)","A",0
1005,1,39,0,0.370523," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","-\frac{1}{3 \, {\left(c e^{4} x^{3} + 3 \, c d e^{3} x^{2} + 3 \, c d^{2} e^{2} x + c d^{3} e\right)}}"," ",0,"-1/3/(c*e^4*x^3 + 3*c*d*e^3*x^2 + 3*c*d^2*e^2*x + c*d^3*e)","B",0
1006,1,51,0,0.386222," ","integrate(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(c e^{5} x^{4} + 4 \, c d e^{4} x^{3} + 6 \, c d^{2} e^{3} x^{2} + 4 \, c d^{3} e^{2} x + c d^{4} e\right)}}"," ",0,"-1/4/(c*e^5*x^4 + 4*c*d*e^4*x^3 + 6*c*d^2*e^3*x^2 + 4*c*d^3*e^2*x + c*d^4*e)","B",0
1007,1,37,0,0.372628," ","integrate((e*x+d)^7/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","\frac{e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x}{4 \, c^{2}}"," ",0,"1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)/c^2","B",0
1008,1,26,0,0.365854," ","integrate((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","\frac{e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x}{3 \, c^{2}}"," ",0,"1/3*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)/c^2","A",0
1009,1,15,0,0.389595," ","integrate((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","\frac{e x^{2} + 2 \, d x}{2 \, c^{2}}"," ",0,"1/2*(e*x^2 + 2*d*x)/c^2","A",0
1010,1,5,0,0.375971," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","\frac{x}{c^{2}}"," ",0,"x/c^2","A",0
1011,1,13,0,0.391539," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","\frac{\log\left(e x + d\right)}{c^{2} e}"," ",0,"log(e*x + d)/(c^2*e)","A",0
1012,1,19,0,0.397378," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","-\frac{1}{c^{2} e^{2} x + c^{2} d e}"," ",0,"-1/(c^2*e^2*x + c^2*d*e)","A",0
1013,1,33,0,0.377976," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(c^{2} e^{3} x^{2} + 2 \, c^{2} d e^{2} x + c^{2} d^{2} e\right)}}"," ",0,"-1/2/(c^2*e^3*x^2 + 2*c^2*d*e^2*x + c^2*d^2*e)","B",0
1014,1,47,0,0.378182," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","-\frac{1}{3 \, {\left(c^{2} e^{4} x^{3} + 3 \, c^{2} d e^{3} x^{2} + 3 \, c^{2} d^{2} e^{2} x + c^{2} d^{3} e\right)}}"," ",0,"-1/3/(c^2*e^4*x^3 + 3*c^2*d*e^3*x^2 + 3*c^2*d^2*e^2*x + c^2*d^3*e)","B",0
1015,1,61,0,0.389177," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(c^{2} e^{5} x^{4} + 4 \, c^{2} d e^{4} x^{3} + 6 \, c^{2} d^{2} e^{3} x^{2} + 4 \, c^{2} d^{3} e^{2} x + c^{2} d^{4} e\right)}}"," ",0,"-1/4/(c^2*e^5*x^4 + 4*c^2*d*e^4*x^3 + 6*c^2*d^2*e^3*x^2 + 4*c^2*d^3*e^2*x + c^2*d^4*e)","B",0
1016,1,75,0,0.376571," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","-\frac{1}{5 \, {\left(c^{2} e^{6} x^{5} + 5 \, c^{2} d e^{5} x^{4} + 10 \, c^{2} d^{2} e^{4} x^{3} + 10 \, c^{2} d^{3} e^{3} x^{2} + 5 \, c^{2} d^{4} e^{2} x + c^{2} d^{5} e\right)}}"," ",0,"-1/5/(c^2*e^6*x^5 + 5*c^2*d*e^5*x^4 + 10*c^2*d^2*e^4*x^3 + 10*c^2*d^3*e^3*x^2 + 5*c^2*d^4*e^2*x + c^2*d^5*e)","B",0
1017,1,37,0,0.380199," ","integrate((e*x+d)^9/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","\frac{e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x}{4 \, c^{3}}"," ",0,"1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)/c^3","B",0
1018,1,26,0,0.376092," ","integrate((e*x+d)^8/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","\frac{e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x}{3 \, c^{3}}"," ",0,"1/3*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)/c^3","A",0
1019,1,15,0,0.377300," ","integrate((e*x+d)^7/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","\frac{e x^{2} + 2 \, d x}{2 \, c^{3}}"," ",0,"1/2*(e*x^2 + 2*d*x)/c^3","A",0
1020,1,5,0,0.376566," ","integrate((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","\frac{x}{c^{3}}"," ",0,"x/c^3","A",0
1021,1,13,0,0.377043," ","integrate((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","\frac{\log\left(e x + d\right)}{c^{3} e}"," ",0,"log(e*x + d)/(c^3*e)","A",0
1022,1,19,0,0.377334," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","-\frac{1}{c^{3} e^{2} x + c^{3} d e}"," ",0,"-1/(c^3*e^2*x + c^3*d*e)","A",0
1023,1,33,0,0.378711," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(c^{3} e^{3} x^{2} + 2 \, c^{3} d e^{2} x + c^{3} d^{2} e\right)}}"," ",0,"-1/2/(c^3*e^3*x^2 + 2*c^3*d*e^2*x + c^3*d^2*e)","B",0
1024,1,47,0,0.395316," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","-\frac{1}{3 \, {\left(c^{3} e^{4} x^{3} + 3 \, c^{3} d e^{3} x^{2} + 3 \, c^{3} d^{2} e^{2} x + c^{3} d^{3} e\right)}}"," ",0,"-1/3/(c^3*e^4*x^3 + 3*c^3*d*e^3*x^2 + 3*c^3*d^2*e^2*x + c^3*d^3*e)","B",0
1025,1,61,0,0.381191," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(c^{3} e^{5} x^{4} + 4 \, c^{3} d e^{4} x^{3} + 6 \, c^{3} d^{2} e^{3} x^{2} + 4 \, c^{3} d^{3} e^{2} x + c^{3} d^{4} e\right)}}"," ",0,"-1/4/(c^3*e^5*x^4 + 4*c^3*d*e^4*x^3 + 6*c^3*d^2*e^3*x^2 + 4*c^3*d^3*e^2*x + c^3*d^4*e)","B",0
1026,1,75,0,0.374661," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","-\frac{1}{5 \, {\left(c^{3} e^{6} x^{5} + 5 \, c^{3} d e^{5} x^{4} + 10 \, c^{3} d^{2} e^{4} x^{3} + 10 \, c^{3} d^{3} e^{3} x^{2} + 5 \, c^{3} d^{4} e^{2} x + c^{3} d^{5} e\right)}}"," ",0,"-1/5/(c^3*e^6*x^5 + 5*c^3*d*e^5*x^4 + 10*c^3*d^2*e^4*x^3 + 10*c^3*d^3*e^3*x^2 + 5*c^3*d^4*e^2*x + c^3*d^5*e)","B",0
1027,1,89,0,0.378160," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","-\frac{1}{6 \, {\left(c^{3} e^{7} x^{6} + 6 \, c^{3} d e^{6} x^{5} + 15 \, c^{3} d^{2} e^{5} x^{4} + 20 \, c^{3} d^{3} e^{4} x^{3} + 15 \, c^{3} d^{4} e^{3} x^{2} + 6 \, c^{3} d^{5} e^{2} x + c^{3} d^{6} e\right)}}"," ",0,"-1/6/(c^3*e^7*x^6 + 6*c^3*d*e^6*x^5 + 15*c^3*d^2*e^5*x^4 + 20*c^3*d^3*e^4*x^3 + 15*c^3*d^4*e^3*x^2 + 6*c^3*d^5*e^2*x + c^3*d^6*e)","B",0
1028,1,103,0,0.381083," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","-\frac{1}{7 \, {\left(c^{3} e^{8} x^{7} + 7 \, c^{3} d e^{7} x^{6} + 21 \, c^{3} d^{2} e^{6} x^{5} + 35 \, c^{3} d^{3} e^{5} x^{4} + 35 \, c^{3} d^{4} e^{4} x^{3} + 21 \, c^{3} d^{5} e^{3} x^{2} + 7 \, c^{3} d^{6} e^{2} x + c^{3} d^{7} e\right)}}"," ",0,"-1/7/(c^3*e^8*x^7 + 7*c^3*d*e^7*x^6 + 21*c^3*d^2*e^6*x^5 + 35*c^3*d^3*e^5*x^4 + 35*c^3*d^4*e^4*x^3 + 21*c^3*d^5*e^3*x^2 + 7*c^3*d^6*e^2*x + c^3*d^7*e)","B",0
1029,1,74,0,0.390800," ","integrate((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(e^{4} x^{5} + 5 \, d e^{3} x^{4} + 10 \, d^{2} e^{2} x^{3} + 10 \, d^{3} e x^{2} + 5 \, d^{4} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{5 \, {\left(e x + d\right)}}"," ",0,"1/5*(e^4*x^5 + 5*d*e^3*x^4 + 10*d^2*e^2*x^3 + 10*d^3*e*x^2 + 5*d^4*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1030,1,63,0,0.386718," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{4 \, {\left(e x + d\right)}}"," ",0,"1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","A",0
1031,1,52,0,0.396990," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x\right)}}{3 \, {\left(e x + d\right)}}"," ",0,"1/3*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)/(e*x + d)","A",0
1032,1,41,0,0.393558," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e x^{2} + 2 \, d x\right)}}{2 \, {\left(e x + d\right)}}"," ",0,"1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x^2 + 2*d*x)/(e*x + d)","A",0
1033,1,31,0,0.394766," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} x}{e x + d}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*x/(e*x + d)","A",0
1034,1,40,0,0.401682," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} \log\left(e x + d\right)}{e^{2} x + d e}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*log(e*x + d)/(e^2*x + d*e)","A",0
1035,1,46,0,0.406204," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}"," ",0,"-sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
1036,1,57,0,0.399364," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{2 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"-1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","A",0
1037,1,68,0,0.406257," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{3 \, {\left(e^{5} x^{4} + 4 \, d e^{4} x^{3} + 6 \, d^{2} e^{3} x^{2} + 4 \, d^{3} e^{2} x + d^{4} e\right)}}"," ",0,"-1/3*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e^5*x^4 + 4*d*e^4*x^3 + 6*d^2*e^3*x^2 + 4*d^3*e^2*x + d^4*e)","B",0
1038,1,79,0,0.390218," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{4 \, {\left(e^{6} x^{5} + 5 \, d e^{5} x^{4} + 10 \, d^{2} e^{4} x^{3} + 10 \, d^{3} e^{3} x^{2} + 5 \, d^{4} e^{2} x + d^{5} e\right)}}"," ",0,"-1/4*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e^6*x^5 + 5*d*e^5*x^4 + 10*d^2*e^4*x^3 + 10*d^3*e^3*x^2 + 5*d^4*e^2*x + d^5*e)","B",0
1039,1,103,0,0.397702," ","integrate((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(c e^{6} x^{7} + 7 \, c d e^{5} x^{6} + 21 \, c d^{2} e^{4} x^{5} + 35 \, c d^{3} e^{3} x^{4} + 35 \, c d^{4} e^{2} x^{3} + 21 \, c d^{5} e x^{2} + 7 \, c d^{6} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{7 \, {\left(e x + d\right)}}"," ",0,"1/7*(c*e^6*x^7 + 7*c*d*e^5*x^6 + 21*c*d^2*e^4*x^5 + 35*c*d^3*e^3*x^4 + 35*c*d^4*e^2*x^3 + 21*c*d^5*e*x^2 + 7*c*d^6*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1040,1,91,0,0.403132," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(c e^{5} x^{6} + 6 \, c d e^{4} x^{5} + 15 \, c d^{2} e^{3} x^{4} + 20 \, c d^{3} e^{2} x^{3} + 15 \, c d^{4} e x^{2} + 6 \, c d^{5} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{6 \, {\left(e x + d\right)}}"," ",0,"1/6*(c*e^5*x^6 + 6*c*d*e^4*x^5 + 15*c*d^2*e^3*x^4 + 20*c*d^3*e^2*x^3 + 15*c*d^4*e*x^2 + 6*c*d^5*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1041,1,79,0,0.388794," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(c e^{4} x^{5} + 5 \, c d e^{3} x^{4} + 10 \, c d^{2} e^{2} x^{3} + 10 \, c d^{3} e x^{2} + 5 \, c d^{4} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{5 \, {\left(e x + d\right)}}"," ",0,"1/5*(c*e^4*x^5 + 5*c*d*e^3*x^4 + 10*c*d^2*e^2*x^3 + 10*c*d^3*e*x^2 + 5*c*d^4*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1042,1,67,0,0.384239," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(c e^{3} x^{4} + 4 \, c d e^{2} x^{3} + 6 \, c d^{2} e x^{2} + 4 \, c d^{3} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{4 \, {\left(e x + d\right)}}"," ",0,"1/4*(c*e^3*x^4 + 4*c*d*e^2*x^3 + 6*c*d^2*e*x^2 + 4*c*d^3*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1043,1,55,0,0.384576," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\frac{{\left(c e^{2} x^{3} + 3 \, c d e x^{2} + 3 \, c d^{2} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{3 \, {\left(e x + d\right)}}"," ",0,"1/3*(c*e^2*x^3 + 3*c*d*e*x^2 + 3*c*d^2*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1044,1,43,0,0.399158," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(c e x^{2} + 2 \, c d x\right)}}{2 \, {\left(e x + d\right)}}"," ",0,"1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(c*e*x^2 + 2*c*d*x)/(e*x + d)","A",0
1045,1,32,0,0.388789," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} c x}{e x + d}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*c*x/(e*x + d)","A",0
1046,1,41,0,0.404657," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} c \log\left(e x + d\right)}{e^{2} x + d e}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*c*log(e*x + d)/(e^2*x + d*e)","A",0
1047,1,47,0,0.407137," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} c}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}"," ",0,"-sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*c/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
1048,1,58,0,0.400293," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} c}{2 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"-1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*c/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","A",0
1049,1,69,0,0.396102," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} c}{3 \, {\left(e^{5} x^{4} + 4 \, d e^{4} x^{3} + 6 \, d^{2} e^{3} x^{2} + 4 \, d^{3} e^{2} x + d^{4} e\right)}}"," ",0,"-1/3*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*c/(e^5*x^4 + 4*d*e^4*x^3 + 6*d^2*e^3*x^2 + 4*d^3*e^2*x + d^4*e)","B",0
1050,1,145,0,0.394022," ","integrate((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(c^{2} e^{8} x^{9} + 9 \, c^{2} d e^{7} x^{8} + 36 \, c^{2} d^{2} e^{6} x^{7} + 84 \, c^{2} d^{3} e^{5} x^{6} + 126 \, c^{2} d^{4} e^{4} x^{5} + 126 \, c^{2} d^{5} e^{3} x^{4} + 84 \, c^{2} d^{6} e^{2} x^{3} + 36 \, c^{2} d^{7} e x^{2} + 9 \, c^{2} d^{8} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{9 \, {\left(e x + d\right)}}"," ",0,"1/9*(c^2*e^8*x^9 + 9*c^2*d*e^7*x^8 + 36*c^2*d^2*e^6*x^7 + 84*c^2*d^3*e^5*x^6 + 126*c^2*d^4*e^4*x^5 + 126*c^2*d^5*e^3*x^4 + 84*c^2*d^6*e^2*x^3 + 36*c^2*d^7*e*x^2 + 9*c^2*d^8*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1051,1,131,0,0.392462," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(c^{2} e^{7} x^{8} + 8 \, c^{2} d e^{6} x^{7} + 28 \, c^{2} d^{2} e^{5} x^{6} + 56 \, c^{2} d^{3} e^{4} x^{5} + 70 \, c^{2} d^{4} e^{3} x^{4} + 56 \, c^{2} d^{5} e^{2} x^{3} + 28 \, c^{2} d^{6} e x^{2} + 8 \, c^{2} d^{7} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{8 \, {\left(e x + d\right)}}"," ",0,"1/8*(c^2*e^7*x^8 + 8*c^2*d*e^6*x^7 + 28*c^2*d^2*e^5*x^6 + 56*c^2*d^3*e^4*x^5 + 70*c^2*d^4*e^3*x^4 + 56*c^2*d^5*e^2*x^3 + 28*c^2*d^6*e*x^2 + 8*c^2*d^7*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1052,1,117,0,0.401858," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(c^{2} e^{6} x^{7} + 7 \, c^{2} d e^{5} x^{6} + 21 \, c^{2} d^{2} e^{4} x^{5} + 35 \, c^{2} d^{3} e^{3} x^{4} + 35 \, c^{2} d^{4} e^{2} x^{3} + 21 \, c^{2} d^{5} e x^{2} + 7 \, c^{2} d^{6} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{7 \, {\left(e x + d\right)}}"," ",0,"1/7*(c^2*e^6*x^7 + 7*c^2*d*e^5*x^6 + 21*c^2*d^2*e^4*x^5 + 35*c^2*d^3*e^3*x^4 + 35*c^2*d^4*e^2*x^3 + 21*c^2*d^5*e*x^2 + 7*c^2*d^6*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1053,1,103,0,0.393268," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(c^{2} e^{5} x^{6} + 6 \, c^{2} d e^{4} x^{5} + 15 \, c^{2} d^{2} e^{3} x^{4} + 20 \, c^{2} d^{3} e^{2} x^{3} + 15 \, c^{2} d^{4} e x^{2} + 6 \, c^{2} d^{5} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{6 \, {\left(e x + d\right)}}"," ",0,"1/6*(c^2*e^5*x^6 + 6*c^2*d*e^4*x^5 + 15*c^2*d^2*e^3*x^4 + 20*c^2*d^3*e^2*x^3 + 15*c^2*d^4*e*x^2 + 6*c^2*d^5*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1054,1,89,0,0.396214," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\frac{{\left(c^{2} e^{4} x^{5} + 5 \, c^{2} d e^{3} x^{4} + 10 \, c^{2} d^{2} e^{2} x^{3} + 10 \, c^{2} d^{3} e x^{2} + 5 \, c^{2} d^{4} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{5 \, {\left(e x + d\right)}}"," ",0,"1/5*(c^2*e^4*x^5 + 5*c^2*d*e^3*x^4 + 10*c^2*d^2*e^2*x^3 + 10*c^2*d^3*e*x^2 + 5*c^2*d^4*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1055,1,75,0,0.396022," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{{\left(c^{2} e^{3} x^{4} + 4 \, c^{2} d e^{2} x^{3} + 6 \, c^{2} d^{2} e x^{2} + 4 \, c^{2} d^{3} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{4 \, {\left(e x + d\right)}}"," ",0,"1/4*(c^2*e^3*x^4 + 4*c^2*d*e^2*x^3 + 6*c^2*d^2*e*x^2 + 4*c^2*d^3*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1056,1,61,0,0.391968," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{{\left(c^{2} e^{2} x^{3} + 3 \, c^{2} d e x^{2} + 3 \, c^{2} d^{2} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{3 \, {\left(e x + d\right)}}"," ",0,"1/3*(c^2*e^2*x^3 + 3*c^2*d*e*x^2 + 3*c^2*d^2*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","B",0
1057,1,47,0,0.396911," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{{\left(c^{2} e x^{2} + 2 \, c^{2} d x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{2 \, {\left(e x + d\right)}}"," ",0,"1/2*(c^2*e*x^2 + 2*c^2*d*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(e*x + d)","A",0
1058,1,34,0,0.397335," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} c^{2} x}{e x + d}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*c^2*x/(e*x + d)","A",0
1059,1,43,0,0.406087," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^6,x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} c^{2} \log\left(e x + d\right)}{e^{2} x + d e}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*c^2*log(e*x + d)/(e^2*x + d*e)","A",0
1060,1,49,0,0.388152," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} c^{2}}{e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e}"," ",0,"-sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*c^2/(e^3*x^2 + 2*d*e^2*x + d^2*e)","A",0
1061,1,60,0,0.404038," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} c^{2}}{2 \, {\left(e^{4} x^{3} + 3 \, d e^{3} x^{2} + 3 \, d^{2} e^{2} x + d^{3} e\right)}}"," ",0,"-1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*c^2/(e^4*x^3 + 3*d*e^3*x^2 + 3*d^2*e^2*x + d^3*e)","A",0
1062,1,66,0,0.405792," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{4 \, {\left(c e x + c d\right)}}"," ",0,"1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c*e*x + c*d)","A",0
1063,1,55,0,0.389873," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x\right)}}{3 \, {\left(c e x + c d\right)}}"," ",0,"1/3*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)/(c*e*x + c*d)","A",0
1064,1,44,0,0.402949," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e x^{2} + 2 \, d x\right)}}{2 \, {\left(c e x + c d\right)}}"," ",0,"1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x^2 + 2*d*x)/(c*e*x + c*d)","A",0
1065,1,34,0,0.391230," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} x}{c e x + c d}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*x/(c*e*x + c*d)","A",0
1066,1,42,0,0.398933," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} \log\left(e x + d\right)}{c e^{2} x + c d e}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*log(e*x + d)/(c*e^2*x + c*d*e)","A",0
1067,1,49,0,0.395684," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{c e^{3} x^{2} + 2 \, c d e^{2} x + c d^{2} e}"," ",0,"-sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c*e^3*x^2 + 2*c*d*e^2*x + c*d^2*e)","A",0
1068,1,61,0,0.405138," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{2 \, {\left(c e^{4} x^{3} + 3 \, c d e^{3} x^{2} + 3 \, c d^{2} e^{2} x + c d^{3} e\right)}}"," ",0,"-1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c*e^4*x^3 + 3*c*d*e^3*x^2 + 3*c*d^2*e^2*x + c*d^3*e)","A",0
1069,1,73,0,0.392078," ","integrate(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{3 \, {\left(c e^{5} x^{4} + 4 \, c d e^{4} x^{3} + 6 \, c d^{2} e^{3} x^{2} + 4 \, c d^{3} e^{2} x + c d^{4} e\right)}}"," ",0,"-1/3*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c*e^5*x^4 + 4*c*d*e^4*x^3 + 6*c*d^2*e^3*x^2 + 4*c*d^3*e^2*x + c*d^4*e)","B",0
1070,1,85,0,0.387320," ","integrate(1/(e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{4 \, {\left(c e^{6} x^{5} + 5 \, c d e^{5} x^{4} + 10 \, c d^{2} e^{4} x^{3} + 10 \, c d^{3} e^{3} x^{2} + 5 \, c d^{4} e^{2} x + c d^{5} e\right)}}"," ",0,"-1/4*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c*e^6*x^5 + 5*c*d*e^5*x^4 + 10*c*d^2*e^4*x^3 + 10*c*d^3*e^3*x^2 + 5*c*d^4*e^2*x + c*d^5*e)","B",0
1071,1,48,0,0.398374," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e x^{2} + 2 \, d x\right)}}{2 \, {\left(c^{2} e x + c^{2} d\right)}}"," ",0,"1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x^2 + 2*d*x)/(c^2*e*x + c^2*d)","A",0
1072,1,38,0,0.407549," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} x}{c^{2} e x + c^{2} d}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*x/(c^2*e*x + c^2*d)","A",0
1073,1,46,0,0.388392," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} \log\left(e x + d\right)}{c^{2} e^{2} x + c^{2} d e}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*log(e*x + d)/(c^2*e^2*x + c^2*d*e)","A",0
1074,1,55,0,0.387642," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{c^{2} e^{3} x^{2} + 2 \, c^{2} d e^{2} x + c^{2} d^{2} e}"," ",0,"-sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^2*e^3*x^2 + 2*c^2*d*e^2*x + c^2*d^2*e)","A",0
1075,1,69,0,0.391859," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{2 \, {\left(c^{2} e^{4} x^{3} + 3 \, c^{2} d e^{3} x^{2} + 3 \, c^{2} d^{2} e^{2} x + c^{2} d^{3} e\right)}}"," ",0,"-1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^2*e^4*x^3 + 3*c^2*d*e^3*x^2 + 3*c^2*d^2*e^2*x + c^2*d^3*e)","A",0
1076,1,83,0,0.388537," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{3 \, {\left(c^{2} e^{5} x^{4} + 4 \, c^{2} d e^{4} x^{3} + 6 \, c^{2} d^{2} e^{3} x^{2} + 4 \, c^{2} d^{3} e^{2} x + c^{2} d^{4} e\right)}}"," ",0,"-1/3*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^2*e^5*x^4 + 4*c^2*d*e^4*x^3 + 6*c^2*d^2*e^3*x^2 + 4*c^2*d^3*e^2*x + c^2*d^4*e)","B",0
1077,1,97,0,0.398405," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{4 \, {\left(c^{2} e^{6} x^{5} + 5 \, c^{2} d e^{5} x^{4} + 10 \, c^{2} d^{2} e^{4} x^{3} + 10 \, c^{2} d^{3} e^{3} x^{2} + 5 \, c^{2} d^{4} e^{2} x + c^{2} d^{5} e\right)}}"," ",0,"-1/4*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^2*e^6*x^5 + 5*c^2*d*e^5*x^4 + 10*c^2*d^2*e^4*x^3 + 10*c^2*d^3*e^3*x^2 + 5*c^2*d^4*e^2*x + c^2*d^5*e)","B",0
1078,1,111,0,0.400425," ","integrate(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{5 \, {\left(c^{2} e^{7} x^{6} + 6 \, c^{2} d e^{6} x^{5} + 15 \, c^{2} d^{2} e^{5} x^{4} + 20 \, c^{2} d^{3} e^{4} x^{3} + 15 \, c^{2} d^{4} e^{3} x^{2} + 6 \, c^{2} d^{5} e^{2} x + c^{2} d^{6} e\right)}}"," ",0,"-1/5*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^2*e^7*x^6 + 6*c^2*d*e^6*x^5 + 15*c^2*d^2*e^5*x^4 + 20*c^2*d^3*e^4*x^3 + 15*c^2*d^4*e^3*x^2 + 6*c^2*d^5*e^2*x + c^2*d^6*e)","B",0
1079,1,48,0,0.412170," ","integrate((e*x+d)^6/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e x^{2} + 2 \, d x\right)}}{2 \, {\left(c^{3} e x + c^{3} d\right)}}"," ",0,"1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x^2 + 2*d*x)/(c^3*e*x + c^3*d)","A",0
1080,1,38,0,0.403349," ","integrate((e*x+d)^5/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} x}{c^{3} e x + c^{3} d}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*x/(c^3*e*x + c^3*d)","A",0
1081,1,46,0,0.389955," ","integrate((e*x+d)^4/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} \log\left(e x + d\right)}{c^{3} e^{2} x + c^{3} d e}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*log(e*x + d)/(c^3*e^2*x + c^3*d*e)","A",0
1082,1,55,0,0.392739," ","integrate((e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{c^{3} e^{3} x^{2} + 2 \, c^{3} d e^{2} x + c^{3} d^{2} e}"," ",0,"-sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^3*e^3*x^2 + 2*c^3*d*e^2*x + c^3*d^2*e)","A",0
1083,1,69,0,0.383250," ","integrate((e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{2 \, {\left(c^{3} e^{4} x^{3} + 3 \, c^{3} d e^{3} x^{2} + 3 \, c^{3} d^{2} e^{2} x + c^{3} d^{3} e\right)}}"," ",0,"-1/2*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^3*e^4*x^3 + 3*c^3*d*e^3*x^2 + 3*c^3*d^2*e^2*x + c^3*d^3*e)","A",0
1084,1,83,0,0.418567," ","integrate((e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{3 \, {\left(c^{3} e^{5} x^{4} + 4 \, c^{3} d e^{4} x^{3} + 6 \, c^{3} d^{2} e^{3} x^{2} + 4 \, c^{3} d^{3} e^{2} x + c^{3} d^{4} e\right)}}"," ",0,"-1/3*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^3*e^5*x^4 + 4*c^3*d*e^4*x^3 + 6*c^3*d^2*e^3*x^2 + 4*c^3*d^3*e^2*x + c^3*d^4*e)","B",0
1085,1,97,0,0.397933," ","integrate(1/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{4 \, {\left(c^{3} e^{6} x^{5} + 5 \, c^{3} d e^{5} x^{4} + 10 \, c^{3} d^{2} e^{4} x^{3} + 10 \, c^{3} d^{3} e^{3} x^{2} + 5 \, c^{3} d^{4} e^{2} x + c^{3} d^{5} e\right)}}"," ",0,"-1/4*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^3*e^6*x^5 + 5*c^3*d*e^5*x^4 + 10*c^3*d^2*e^4*x^3 + 10*c^3*d^3*e^3*x^2 + 5*c^3*d^4*e^2*x + c^3*d^5*e)","B",0
1086,1,111,0,0.385449," ","integrate(1/(e*x+d)/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{5 \, {\left(c^{3} e^{7} x^{6} + 6 \, c^{3} d e^{6} x^{5} + 15 \, c^{3} d^{2} e^{5} x^{4} + 20 \, c^{3} d^{3} e^{4} x^{3} + 15 \, c^{3} d^{4} e^{3} x^{2} + 6 \, c^{3} d^{5} e^{2} x + c^{3} d^{6} e\right)}}"," ",0,"-1/5*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^3*e^7*x^6 + 6*c^3*d*e^6*x^5 + 15*c^3*d^2*e^5*x^4 + 20*c^3*d^3*e^4*x^3 + 15*c^3*d^4*e^3*x^2 + 6*c^3*d^5*e^2*x + c^3*d^6*e)","B",0
1087,1,125,0,0.395612," ","integrate(1/(e*x+d)^2/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{6 \, {\left(c^{3} e^{8} x^{7} + 7 \, c^{3} d e^{7} x^{6} + 21 \, c^{3} d^{2} e^{6} x^{5} + 35 \, c^{3} d^{3} e^{5} x^{4} + 35 \, c^{3} d^{4} e^{4} x^{3} + 21 \, c^{3} d^{5} e^{3} x^{2} + 7 \, c^{3} d^{6} e^{2} x + c^{3} d^{7} e\right)}}"," ",0,"-1/6*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^3*e^8*x^7 + 7*c^3*d*e^7*x^6 + 21*c^3*d^2*e^6*x^5 + 35*c^3*d^3*e^5*x^4 + 35*c^3*d^4*e^4*x^3 + 21*c^3*d^5*e^3*x^2 + 7*c^3*d^6*e^2*x + c^3*d^7*e)","B",0
1088,1,139,0,0.408953," ","integrate(1/(e*x+d)^3/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}}}{7 \, {\left(c^{3} e^{9} x^{8} + 8 \, c^{3} d e^{8} x^{7} + 28 \, c^{3} d^{2} e^{7} x^{6} + 56 \, c^{3} d^{3} e^{6} x^{5} + 70 \, c^{3} d^{4} e^{5} x^{4} + 56 \, c^{3} d^{5} e^{4} x^{3} + 28 \, c^{3} d^{6} e^{3} x^{2} + 8 \, c^{3} d^{7} e^{2} x + c^{3} d^{8} e\right)}}"," ",0,"-1/7*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)/(c^3*e^9*x^8 + 8*c^3*d*e^8*x^7 + 28*c^3*d^2*e^7*x^6 + 56*c^3*d^3*e^6*x^5 + 70*c^3*d^4*e^5*x^4 + 56*c^3*d^5*e^4*x^3 + 28*c^3*d^6*e^3*x^2 + 8*c^3*d^7*e^2*x + c^3*d^8*e)","B",0
1089,1,85,0,0.414936," ","integrate((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","\frac{{\left(c^{2} e^{5} x^{5} + 5 \, c^{2} d e^{4} x^{4} + 10 \, c^{2} d^{2} e^{3} x^{3} + 10 \, c^{2} d^{3} e^{2} x^{2} + 5 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} {\left(e x + d\right)}^{m}}{e m + 5 \, e}"," ",0,"(c^2*e^5*x^5 + 5*c^2*d*e^4*x^4 + 10*c^2*d^2*e^3*x^3 + 10*c^2*d^3*e^2*x^2 + 5*c^2*d^4*e*x + c^2*d^5)*(e*x + d)^m/(e*m + 5*e)","B",0
1090,1,49,0,0.421670," ","integrate((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","\frac{{\left(c e^{3} x^{3} + 3 \, c d e^{2} x^{2} + 3 \, c d^{2} e x + c d^{3}\right)} {\left(e x + d\right)}^{m}}{e m + 3 \, e}"," ",0,"(c*e^3*x^3 + 3*c*d*e^2*x^2 + 3*c*d^2*e*x + c*d^3)*(e*x + d)^m/(e*m + 3*e)","B",0
1091,1,36,0,0.412583," ","integrate((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2),x, algorithm=""fricas"")","\frac{{\left(e x + d\right)}^{m}}{c d e m - c d e + {\left(c e^{2} m - c e^{2}\right)} x}"," ",0,"(e*x + d)^m/(c*d*e*m - c*d*e + (c*e^2*m - c*e^2)*x)","A",0
1092,1,100,0,0.420238," ","integrate((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^2,x, algorithm=""fricas"")","\frac{{\left(e x + d\right)}^{m}}{c^{2} d^{3} e m - 3 \, c^{2} d^{3} e + {\left(c^{2} e^{4} m - 3 \, c^{2} e^{4}\right)} x^{3} + 3 \, {\left(c^{2} d e^{3} m - 3 \, c^{2} d e^{3}\right)} x^{2} + 3 \, {\left(c^{2} d^{2} e^{2} m - 3 \, c^{2} d^{2} e^{2}\right)} x}"," ",0,"(e*x + d)^m/(c^2*d^3*e*m - 3*c^2*d^3*e + (c^2*e^4*m - 3*c^2*e^4)*x^3 + 3*(c^2*d*e^3*m - 3*c^2*d*e^3)*x^2 + 3*(c^2*d^2*e^2*m - 3*c^2*d^2*e^2)*x)","B",0
1093,1,156,0,0.432309," ","integrate((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^3,x, algorithm=""fricas"")","\frac{{\left(e x + d\right)}^{m}}{c^{3} d^{5} e m - 5 \, c^{3} d^{5} e + {\left(c^{3} e^{6} m - 5 \, c^{3} e^{6}\right)} x^{5} + 5 \, {\left(c^{3} d e^{5} m - 5 \, c^{3} d e^{5}\right)} x^{4} + 10 \, {\left(c^{3} d^{2} e^{4} m - 5 \, c^{3} d^{2} e^{4}\right)} x^{3} + 10 \, {\left(c^{3} d^{3} e^{3} m - 5 \, c^{3} d^{3} e^{3}\right)} x^{2} + 5 \, {\left(c^{3} d^{4} e^{2} m - 5 \, c^{3} d^{4} e^{2}\right)} x}"," ",0,"(e*x + d)^m/(c^3*d^5*e*m - 5*c^3*d^5*e + (c^3*e^6*m - 5*c^3*e^6)*x^5 + 5*(c^3*d*e^5*m - 5*c^3*d*e^5)*x^4 + 10*(c^3*d^2*e^4*m - 5*c^3*d^2*e^4)*x^3 + 10*(c^3*d^3*e^3*m - 5*c^3*d^3*e^3)*x^2 + 5*(c^3*d^4*e^2*m - 5*c^3*d^4*e^2)*x)","B",0
1094,1,71,0,0.412572," ","integrate((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(c e^{3} x^{3} + 3 \, c d e^{2} x^{2} + 3 \, c d^{2} e x + c d^{3}\right)} \sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e x + d\right)}^{m}}{e m + 4 \, e}"," ",0,"(c*e^3*x^3 + 3*c*d*e^2*x^2 + 3*c*d^2*e*x + c*d^3)*sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x + d)^m/(e*m + 4*e)","A",0
1095,1,44,0,0.435376," ","integrate((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e x + d\right)} {\left(e x + d\right)}^{m}}{e m + 2 \, e}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x + d)*(e*x + d)^m/(e*m + 2*e)","A",0
1096,1,45,0,0.429587," ","integrate((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e x + d\right)}^{m}}{c e^{2} m x + c d e m}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x + d)^m/(c*e^2*m*x + c*d*e*m)","A",0
1097,1,122,0,0.422781," ","integrate((e*x+d)^m/(c*e^2*x^2+2*c*d*e*x+c*d^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{c e^{2} x^{2} + 2 \, c d e x + c d^{2}} {\left(e x + d\right)}^{m}}{c^{2} d^{3} e m - 2 \, c^{2} d^{3} e + {\left(c^{2} e^{4} m - 2 \, c^{2} e^{4}\right)} x^{3} + 3 \, {\left(c^{2} d e^{3} m - 2 \, c^{2} d e^{3}\right)} x^{2} + 3 \, {\left(c^{2} d^{2} e^{2} m - 2 \, c^{2} d^{2} e^{2}\right)} x}"," ",0,"sqrt(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*(e*x + d)^m/(c^2*d^3*e*m - 2*c^2*d^3*e + (c^2*e^4*m - 2*c^2*e^4)*x^3 + 3*(c^2*d*e^3*m - 2*c^2*d*e^3)*x^2 + 3*(c^2*d^2*e^2*m - 2*c^2*d^2*e^2)*x)","B",0
1098,1,39,0,0.436073," ","integrate((e*x+d)^m*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""fricas"")","\frac{{\left(e x + d\right)} {\left(e x + d\right)}^{m} e^{\left(2 \, p \log\left(e x + d\right) + p \log\left(c\right)\right)}}{e m + 2 \, e p + e}"," ",0,"(e*x + d)*(e*x + d)^m*e^(2*p*log(e*x + d) + p*log(c))/(e*m + 2*e*p + e)","A",0
1099,1,30,0,0.435416," ","integrate((e*x+d)^p/((c*e^2*x^2+2*c*d*e*x+c*d^2)^p),x, algorithm=""fricas"")","-\frac{e x + d}{{\left(e p - e\right)} {\left(e x + d\right)}^{p} c^{p}}"," ",0,"-(e*x + d)/((e*p - e)*(e*x + d)^p*c^p)","A",0
1100,1,71,0,0.422589," ","integrate((e*x+d)^3*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""fricas"")","\frac{{\left(e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}\right)} {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}{2 \, {\left(e p + 2 \, e\right)}}"," ",0,"1/2*(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4)*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p/(e*p + 2*e)","A",0
1101,1,60,0,0.424345," ","integrate((e*x+d)^2*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""fricas"")","\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}{2 \, e p + 3 \, e}"," ",0,"(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p/(2*e*p + 3*e)","A",0
1102,1,47,0,0.421214," ","integrate((e*x+d)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""fricas"")","\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}{2 \, {\left(e p + e\right)}}"," ",0,"1/2*(e^2*x^2 + 2*d*e*x + d^2)*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p/(e*p + e)","A",0
1103,1,36,0,0.411515," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""fricas"")","\frac{{\left(e x + d\right)} {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}{2 \, e p + e}"," ",0,"(e*x + d)*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p/(2*e*p + e)","A",0
1104,1,30,0,0.423171," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^p/(e*x+d),x, algorithm=""fricas"")","\frac{{\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}{2 \, e p}"," ",0,"1/2*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p/(e*p)","A",0
1105,1,49,0,0.421073," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","\frac{{\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}{2 \, d e p - d e + {\left(2 \, e^{2} p - e^{2}\right)} x}"," ",0,"(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p/(2*d*e*p - d*e + (2*e^2*p - e^2)*x)","A",0
1106,1,70,0,0.416933," ","integrate((c*e^2*x^2+2*c*d*e*x+c*d^2)^p/(e*x+d)^3,x, algorithm=""fricas"")","\frac{{\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)}^{p}}{2 \, {\left(d^{2} e p - d^{2} e + {\left(e^{3} p - e^{3}\right)} x^{2} + 2 \, {\left(d e^{2} p - d e^{2}\right)} x\right)}}"," ",0,"1/2*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)^p/(d^2*e*p - d^2*e + (e^3*p - e^3)*x^2 + 2*(d*e^2*p - d*e^2)*x)","A",0
1107,1,13,0,0.407932," ","integrate((e*x+d)^(-1-2*p)*(c*e^2*x^2+2*c*d*e*x+c*d^2)^p,x, algorithm=""fricas"")","\frac{c^{p} \log\left(e x + d\right)}{e}"," ",0,"c^p*log(e*x + d)/e","A",0
1108,1,15,0,0.408527," ","integrate((e*x+d)^(-1+2*p)/((c*e^2*x^2+2*c*d*e*x+c*d^2)^p),x, algorithm=""fricas"")","\frac{\log\left(e x + d\right)}{c^{p} e}"," ",0,"log(e*x + d)/(c^p*e)","A",0
1109,1,137,0,0.350754," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{16}{7} x^{7} d^{4} c^{5} + 8 x^{6} d^{4} c^{4} b + \frac{56}{5} x^{5} d^{4} c^{3} b^{2} + \frac{16}{5} x^{5} d^{4} c^{4} a + 8 x^{4} d^{4} c^{2} b^{3} + 8 x^{4} d^{4} c^{3} b a + 3 x^{3} d^{4} c b^{4} + 8 x^{3} d^{4} c^{2} b^{2} a + \frac{1}{2} x^{2} d^{4} b^{5} + 4 x^{2} d^{4} c b^{3} a + x d^{4} b^{4} a"," ",0,"16/7*x^7*d^4*c^5 + 8*x^6*d^4*c^4*b + 56/5*x^5*d^4*c^3*b^2 + 16/5*x^5*d^4*c^4*a + 8*x^4*d^4*c^2*b^3 + 8*x^4*d^4*c^3*b*a + 3*x^3*d^4*c*b^4 + 8*x^3*d^4*c^2*b^2*a + 1/2*x^2*d^4*b^5 + 4*x^2*d^4*c*b^3*a + x*d^4*b^4*a","B",0
1110,1,108,0,0.351112," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{4}{3} x^{6} d^{3} c^{4} + 4 x^{5} d^{3} c^{3} b + \frac{9}{2} x^{4} d^{3} c^{2} b^{2} + 2 x^{4} d^{3} c^{3} a + \frac{7}{3} x^{3} d^{3} c b^{3} + 4 x^{3} d^{3} c^{2} b a + \frac{1}{2} x^{2} d^{3} b^{4} + 3 x^{2} d^{3} c b^{2} a + x d^{3} b^{3} a"," ",0,"4/3*x^6*d^3*c^4 + 4*x^5*d^3*c^3*b + 9/2*x^4*d^3*c^2*b^2 + 2*x^4*d^3*c^3*a + 7/3*x^3*d^3*c*b^3 + 4*x^3*d^3*c^2*b*a + 1/2*x^2*d^3*b^4 + 3*x^2*d^3*c*b^2*a + x*d^3*b^3*a","B",0
1111,1,79,0,0.355772," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{4}{5} x^{5} d^{2} c^{3} + 2 x^{4} d^{2} c^{2} b + \frac{5}{3} x^{3} d^{2} c b^{2} + \frac{4}{3} x^{3} d^{2} c^{2} a + \frac{1}{2} x^{2} d^{2} b^{3} + 2 x^{2} d^{2} c b a + x d^{2} b^{2} a"," ",0,"4/5*x^5*d^2*c^3 + 2*x^4*d^2*c^2*b + 5/3*x^3*d^2*c*b^2 + 4/3*x^3*d^2*c^2*a + 1/2*x^2*d^2*b^3 + 2*x^2*d^2*c*b*a + x*d^2*b^2*a","A",0
1112,1,38,0,0.352636," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{2} x^{4} d c^{2} + x^{3} d c b + \frac{1}{2} x^{2} d b^{2} + x^{2} d c a + x d b a"," ",0,"1/2*x^4*d*c^2 + x^3*d*c*b + 1/2*x^2*d*b^2 + x^2*d*c*a + x*d*b*a","B",0
1113,1,39,0,0.393796," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d),x, algorithm=""fricas"")","\frac{2 \, c^{2} x^{2} + 2 \, b c x - {\left(b^{2} - 4 \, a c\right)} \log\left(2 \, c x + b\right)}{8 \, c^{2} d}"," ",0,"1/8*(2*c^2*x^2 + 2*b*c*x - (b^2 - 4*a*c)*log(2*c*x + b))/(c^2*d)","A",0
1114,1,43,0,0.385835," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^2,x, algorithm=""fricas"")","\frac{4 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 4 \, a c}{8 \, {\left(2 \, c^{3} d^{2} x + b c^{2} d^{2}\right)}}"," ",0,"1/8*(4*c^2*x^2 + 2*b*c*x + b^2 - 4*a*c)/(2*c^3*d^2*x + b*c^2*d^2)","A",0
1115,1,70,0,0.394066," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^3,x, algorithm=""fricas"")","\frac{b^{2} - 4 \, a c + 2 \, {\left(4 \, c^{2} x^{2} + 4 \, b c x + b^{2}\right)} \log\left(2 \, c x + b\right)}{16 \, {\left(4 \, c^{4} d^{3} x^{2} + 4 \, b c^{3} d^{3} x + b^{2} c^{2} d^{3}\right)}}"," ",0,"1/16*(b^2 - 4*a*c + 2*(4*c^2*x^2 + 4*b*c*x + b^2)*log(2*c*x + b))/(4*c^4*d^3*x^2 + 4*b*c^3*d^3*x + b^2*c^2*d^3)","A",0
1116,1,71,0,0.393986," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^4,x, algorithm=""fricas"")","-\frac{6 \, c^{2} x^{2} + 6 \, b c x + b^{2} + 2 \, a c}{12 \, {\left(8 \, c^{5} d^{4} x^{3} + 12 \, b c^{4} d^{4} x^{2} + 6 \, b^{2} c^{3} d^{4} x + b^{3} c^{2} d^{4}\right)}}"," ",0,"-1/12*(6*c^2*x^2 + 6*b*c*x + b^2 + 2*a*c)/(8*c^5*d^4*x^3 + 12*b*c^4*d^4*x^2 + 6*b^2*c^3*d^4*x + b^3*c^2*d^4)","A",0
1117,1,85,0,0.381438," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^5,x, algorithm=""fricas"")","-\frac{8 \, c^{2} x^{2} + 8 \, b c x + b^{2} + 4 \, a c}{32 \, {\left(16 \, c^{6} d^{5} x^{4} + 32 \, b c^{5} d^{5} x^{3} + 24 \, b^{2} c^{4} d^{5} x^{2} + 8 \, b^{3} c^{3} d^{5} x + b^{4} c^{2} d^{5}\right)}}"," ",0,"-1/32*(8*c^2*x^2 + 8*b*c*x + b^2 + 4*a*c)/(16*c^6*d^5*x^4 + 32*b*c^5*d^5*x^3 + 24*b^2*c^4*d^5*x^2 + 8*b^3*c^3*d^5*x + b^4*c^2*d^5)","B",0
1118,1,99,0,0.405367," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^6,x, algorithm=""fricas"")","-\frac{10 \, c^{2} x^{2} + 10 \, b c x + b^{2} + 6 \, a c}{60 \, {\left(32 \, c^{7} d^{6} x^{5} + 80 \, b c^{6} d^{6} x^{4} + 80 \, b^{2} c^{5} d^{6} x^{3} + 40 \, b^{3} c^{4} d^{6} x^{2} + 10 \, b^{4} c^{3} d^{6} x + b^{5} c^{2} d^{6}\right)}}"," ",0,"-1/60*(10*c^2*x^2 + 10*b*c*x + b^2 + 6*a*c)/(32*c^7*d^6*x^5 + 80*b*c^6*d^6*x^4 + 80*b^2*c^5*d^6*x^3 + 40*b^3*c^4*d^6*x^2 + 10*b^4*c^3*d^6*x + b^5*c^2*d^6)","B",0
1119,1,113,0,0.397733," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^7,x, algorithm=""fricas"")","-\frac{12 \, c^{2} x^{2} + 12 \, b c x + b^{2} + 8 \, a c}{96 \, {\left(64 \, c^{8} d^{7} x^{6} + 192 \, b c^{7} d^{7} x^{5} + 240 \, b^{2} c^{6} d^{7} x^{4} + 160 \, b^{3} c^{5} d^{7} x^{3} + 60 \, b^{4} c^{4} d^{7} x^{2} + 12 \, b^{5} c^{3} d^{7} x + b^{6} c^{2} d^{7}\right)}}"," ",0,"-1/96*(12*c^2*x^2 + 12*b*c*x + b^2 + 8*a*c)/(64*c^8*d^7*x^6 + 192*b*c^7*d^7*x^5 + 240*b^2*c^6*d^7*x^4 + 160*b^3*c^5*d^7*x^3 + 60*b^4*c^4*d^7*x^2 + 12*b^5*c^3*d^7*x + b^6*c^2*d^7)","B",0
1120,1,127,0,0.396112," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^8,x, algorithm=""fricas"")","-\frac{14 \, c^{2} x^{2} + 14 \, b c x + b^{2} + 10 \, a c}{140 \, {\left(128 \, c^{9} d^{8} x^{7} + 448 \, b c^{8} d^{8} x^{6} + 672 \, b^{2} c^{7} d^{8} x^{5} + 560 \, b^{3} c^{6} d^{8} x^{4} + 280 \, b^{4} c^{5} d^{8} x^{3} + 84 \, b^{5} c^{4} d^{8} x^{2} + 14 \, b^{6} c^{3} d^{8} x + b^{7} c^{2} d^{8}\right)}}"," ",0,"-1/140*(14*c^2*x^2 + 14*b*c*x + b^2 + 10*a*c)/(128*c^9*d^8*x^7 + 448*b*c^8*d^8*x^6 + 672*b^2*c^7*d^8*x^5 + 560*b^3*c^6*d^8*x^4 + 280*b^4*c^5*d^8*x^3 + 84*b^5*c^4*d^8*x^2 + 14*b^6*c^3*d^8*x + b^7*c^2*d^8)","B",0
1121,1,286,0,0.344992," ","integrate((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{16}{5} x^{10} d^{5} c^{7} + 16 x^{9} d^{5} c^{6} b + 34 x^{8} d^{5} c^{5} b^{2} + 8 x^{8} d^{5} c^{6} a + 40 x^{7} d^{5} c^{4} b^{3} + 32 x^{7} d^{5} c^{5} b a + \frac{85}{3} x^{6} d^{5} c^{3} b^{4} + \frac{160}{3} x^{6} d^{5} c^{4} b^{2} a + \frac{16}{3} x^{6} d^{5} c^{5} a^{2} + \frac{61}{5} x^{5} d^{5} c^{2} b^{5} + 48 x^{5} d^{5} c^{3} b^{3} a + 16 x^{5} d^{5} c^{4} b a^{2} + 3 x^{4} d^{5} c b^{6} + 25 x^{4} d^{5} c^{2} b^{4} a + 20 x^{4} d^{5} c^{3} b^{2} a^{2} + \frac{1}{3} x^{3} d^{5} b^{7} + \frac{22}{3} x^{3} d^{5} c b^{5} a + \frac{40}{3} x^{3} d^{5} c^{2} b^{3} a^{2} + x^{2} d^{5} b^{6} a + 5 x^{2} d^{5} c b^{4} a^{2} + x d^{5} b^{5} a^{2}"," ",0,"16/5*x^10*d^5*c^7 + 16*x^9*d^5*c^6*b + 34*x^8*d^5*c^5*b^2 + 8*x^8*d^5*c^6*a + 40*x^7*d^5*c^4*b^3 + 32*x^7*d^5*c^5*b*a + 85/3*x^6*d^5*c^3*b^4 + 160/3*x^6*d^5*c^4*b^2*a + 16/3*x^6*d^5*c^5*a^2 + 61/5*x^5*d^5*c^2*b^5 + 48*x^5*d^5*c^3*b^3*a + 16*x^5*d^5*c^4*b*a^2 + 3*x^4*d^5*c*b^6 + 25*x^4*d^5*c^2*b^4*a + 20*x^4*d^5*c^3*b^2*a^2 + 1/3*x^3*d^5*b^7 + 22/3*x^3*d^5*c*b^5*a + 40/3*x^3*d^5*c^2*b^3*a^2 + x^2*d^5*b^6*a + 5*x^2*d^5*c*b^4*a^2 + x*d^5*b^5*a^2","B",0
1122,1,240,0,0.359772," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{16}{9} x^{9} d^{4} c^{6} + 8 x^{8} d^{4} c^{5} b + \frac{104}{7} x^{7} d^{4} c^{4} b^{2} + \frac{32}{7} x^{7} d^{4} c^{5} a + \frac{44}{3} x^{6} d^{4} c^{3} b^{3} + 16 x^{6} d^{4} c^{4} b a + \frac{41}{5} x^{5} d^{4} c^{2} b^{4} + \frac{112}{5} x^{5} d^{4} c^{3} b^{2} a + \frac{16}{5} x^{5} d^{4} c^{4} a^{2} + \frac{5}{2} x^{4} d^{4} c b^{5} + 16 x^{4} d^{4} c^{2} b^{3} a + 8 x^{4} d^{4} c^{3} b a^{2} + \frac{1}{3} x^{3} d^{4} b^{6} + 6 x^{3} d^{4} c b^{4} a + 8 x^{3} d^{4} c^{2} b^{2} a^{2} + x^{2} d^{4} b^{5} a + 4 x^{2} d^{4} c b^{3} a^{2} + x d^{4} b^{4} a^{2}"," ",0,"16/9*x^9*d^4*c^6 + 8*x^8*d^4*c^5*b + 104/7*x^7*d^4*c^4*b^2 + 32/7*x^7*d^4*c^5*a + 44/3*x^6*d^4*c^3*b^3 + 16*x^6*d^4*c^4*b*a + 41/5*x^5*d^4*c^2*b^4 + 112/5*x^5*d^4*c^3*b^2*a + 16/5*x^5*d^4*c^4*a^2 + 5/2*x^4*d^4*c*b^5 + 16*x^4*d^4*c^2*b^3*a + 8*x^4*d^4*c^3*b*a^2 + 1/3*x^3*d^4*b^6 + 6*x^3*d^4*c*b^4*a + 8*x^3*d^4*c^2*b^2*a^2 + x^2*d^4*b^5*a + 4*x^2*d^4*c*b^3*a^2 + x*d^4*b^4*a^2","B",0
1123,1,193,0,0.356524," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","x^{8} d^{3} c^{5} + 4 x^{7} d^{3} c^{4} b + \frac{19}{3} x^{6} d^{3} c^{3} b^{2} + \frac{8}{3} x^{6} d^{3} c^{4} a + 5 x^{5} d^{3} c^{2} b^{3} + 8 x^{5} d^{3} c^{3} b a + 2 x^{4} d^{3} c b^{4} + 9 x^{4} d^{3} c^{2} b^{2} a + 2 x^{4} d^{3} c^{3} a^{2} + \frac{1}{3} x^{3} d^{3} b^{5} + \frac{14}{3} x^{3} d^{3} c b^{3} a + 4 x^{3} d^{3} c^{2} b a^{2} + x^{2} d^{3} b^{4} a + 3 x^{2} d^{3} c b^{2} a^{2} + x d^{3} b^{3} a^{2}"," ",0,"x^8*d^3*c^5 + 4*x^7*d^3*c^4*b + 19/3*x^6*d^3*c^3*b^2 + 8/3*x^6*d^3*c^4*a + 5*x^5*d^3*c^2*b^3 + 8*x^5*d^3*c^3*b*a + 2*x^4*d^3*c*b^4 + 9*x^4*d^3*c^2*b^2*a + 2*x^4*d^3*c^3*a^2 + 1/3*x^3*d^3*b^5 + 14/3*x^3*d^3*c*b^3*a + 4*x^3*d^3*c^2*b*a^2 + x^2*d^3*b^4*a + 3*x^2*d^3*c*b^2*a^2 + x*d^3*b^3*a^2","B",0
1124,1,148,0,0.345891," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{4}{7} x^{7} d^{2} c^{4} + 2 x^{6} d^{2} c^{3} b + \frac{13}{5} x^{5} d^{2} c^{2} b^{2} + \frac{8}{5} x^{5} d^{2} c^{3} a + \frac{3}{2} x^{4} d^{2} c b^{3} + 4 x^{4} d^{2} c^{2} b a + \frac{1}{3} x^{3} d^{2} b^{4} + \frac{10}{3} x^{3} d^{2} c b^{2} a + \frac{4}{3} x^{3} d^{2} c^{2} a^{2} + x^{2} d^{2} b^{3} a + 2 x^{2} d^{2} c b a^{2} + x d^{2} b^{2} a^{2}"," ",0,"4/7*x^7*d^2*c^4 + 2*x^6*d^2*c^3*b + 13/5*x^5*d^2*c^2*b^2 + 8/5*x^5*d^2*c^3*a + 3/2*x^4*d^2*c*b^3 + 4*x^4*d^2*c^2*b*a + 1/3*x^3*d^2*b^4 + 10/3*x^3*d^2*c*b^2*a + 4/3*x^3*d^2*c^2*a^2 + x^2*d^2*b^3*a + 2*x^2*d^2*c*b*a^2 + x*d^2*b^2*a^2","B",0
1125,1,80,0,0.371597," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{3} x^{6} d c^{3} + x^{5} d c^{2} b + x^{4} d c b^{2} + x^{4} d c^{2} a + \frac{1}{3} x^{3} d b^{3} + 2 x^{3} d c b a + x^{2} d b^{2} a + x^{2} d c a^{2} + x d b a^{2}"," ",0,"1/3*x^6*d*c^3 + x^5*d*c^2*b + x^4*d*c*b^2 + x^4*d*c^2*a + 1/3*x^3*d*b^3 + 2*x^3*d*c*b*a + x^2*d*b^2*a + x^2*d*c*a^2 + x*d*b*a^2","B",0
1126,1,88,0,0.396297," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d),x, algorithm=""fricas"")","\frac{4 \, c^{4} x^{4} + 8 \, b c^{3} x^{3} + 2 \, {\left(b^{2} c^{2} + 8 \, a c^{3}\right)} x^{2} - 2 \, {\left(b^{3} c - 8 \, a b c^{2}\right)} x + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \log\left(2 \, c x + b\right)}{32 \, c^{3} d}"," ",0,"1/32*(4*c^4*x^4 + 8*b*c^3*x^3 + 2*(b^2*c^2 + 8*a*c^3)*x^2 - 2*(b^3*c - 8*a*b*c^2)*x + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*log(2*c*x + b))/(c^3*d)","A",0
1127,1,85,0,0.406135," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^2,x, algorithm=""fricas"")","\frac{16 \, c^{4} x^{4} + 32 \, b c^{3} x^{3} + 96 \, a c^{3} x^{2} - 3 \, b^{4} + 24 \, a b^{2} c - 48 \, a^{2} c^{2} - 6 \, {\left(b^{3} c - 8 \, a b c^{2}\right)} x}{96 \, {\left(2 \, c^{4} d^{2} x + b c^{3} d^{2}\right)}}"," ",0,"1/96*(16*c^4*x^4 + 32*b*c^3*x^3 + 96*a*c^3*x^2 - 3*b^4 + 24*a*b^2*c - 48*a^2*c^2 - 6*(b^3*c - 8*a*b*c^2)*x)/(2*c^4*d^2*x + b*c^3*d^2)","A",0
1128,1,147,0,0.393574," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^3,x, algorithm=""fricas"")","\frac{16 \, c^{4} x^{4} + 32 \, b c^{3} x^{3} + 20 \, b^{2} c^{2} x^{2} + 4 \, b^{3} c x - b^{4} + 8 \, a b^{2} c - 16 \, a^{2} c^{2} - 4 \, {\left(b^{4} - 4 \, a b^{2} c + 4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \log\left(2 \, c x + b\right)}{64 \, {\left(4 \, c^{5} d^{3} x^{2} + 4 \, b c^{4} d^{3} x + b^{2} c^{3} d^{3}\right)}}"," ",0,"1/64*(16*c^4*x^4 + 32*b*c^3*x^3 + 20*b^2*c^2*x^2 + 4*b^3*c*x - b^4 + 8*a*b^2*c - 16*a^2*c^2 - 4*(b^4 - 4*a*b^2*c + 4*(b^2*c^2 - 4*a*c^3)*x^2 + 4*(b^3*c - 4*a*b*c^2)*x)*log(2*c*x + b))/(4*c^5*d^3*x^2 + 4*b*c^4*d^3*x + b^2*c^3*d^3)","B",0
1129,1,125,0,0.393498," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^4,x, algorithm=""fricas"")","\frac{48 \, c^{4} x^{4} + 72 \, b c^{3} x^{3} + 5 \, b^{4} - 16 \, a b^{2} c - 16 \, a^{2} c^{2} + 12 \, {\left(5 \, b^{2} c^{2} - 8 \, a c^{3}\right)} x^{2} + 6 \, {\left(5 \, b^{3} c - 16 \, a b c^{2}\right)} x}{96 \, {\left(8 \, c^{6} d^{4} x^{3} + 12 \, b c^{5} d^{4} x^{2} + 6 \, b^{2} c^{4} d^{4} x + b^{3} c^{3} d^{4}\right)}}"," ",0,"1/96*(48*c^4*x^4 + 72*b*c^3*x^3 + 5*b^4 - 16*a*b^2*c - 16*a^2*c^2 + 12*(5*b^2*c^2 - 8*a*c^3)*x^2 + 6*(5*b^3*c - 16*a*b*c^2)*x)/(8*c^6*d^4*x^3 + 12*b*c^5*d^4*x^2 + 6*b^2*c^4*d^4*x + b^3*c^3*d^4)","B",0
1130,1,168,0,0.405684," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^5,x, algorithm=""fricas"")","\frac{3 \, b^{4} - 8 \, a b^{2} c - 16 \, a^{2} c^{2} + 16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x + 4 \, {\left(16 \, c^{4} x^{4} + 32 \, b c^{3} x^{3} + 24 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x + b^{4}\right)} \log\left(2 \, c x + b\right)}{128 \, {\left(16 \, c^{7} d^{5} x^{4} + 32 \, b c^{6} d^{5} x^{3} + 24 \, b^{2} c^{5} d^{5} x^{2} + 8 \, b^{3} c^{4} d^{5} x + b^{4} c^{3} d^{5}\right)}}"," ",0,"1/128*(3*b^4 - 8*a*b^2*c - 16*a^2*c^2 + 16*(b^2*c^2 - 4*a*c^3)*x^2 + 16*(b^3*c - 4*a*b*c^2)*x + 4*(16*c^4*x^4 + 32*b*c^3*x^3 + 24*b^2*c^2*x^2 + 8*b^3*c*x + b^4)*log(2*c*x + b))/(16*c^7*d^5*x^4 + 32*b*c^6*d^5*x^3 + 24*b^2*c^5*d^5*x^2 + 8*b^3*c^4*d^5*x + b^4*c^3*d^5)","B",0
1131,1,149,0,0.397362," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^6,x, algorithm=""fricas"")","-\frac{30 \, c^{4} x^{4} + 60 \, b c^{3} x^{3} + b^{4} + 2 \, a b^{2} c + 6 \, a^{2} c^{2} + 20 \, {\left(2 \, b^{2} c^{2} + a c^{3}\right)} x^{2} + 10 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} x}{60 \, {\left(32 \, c^{8} d^{6} x^{5} + 80 \, b c^{7} d^{6} x^{4} + 80 \, b^{2} c^{6} d^{6} x^{3} + 40 \, b^{3} c^{5} d^{6} x^{2} + 10 \, b^{4} c^{4} d^{6} x + b^{5} c^{3} d^{6}\right)}}"," ",0,"-1/60*(30*c^4*x^4 + 60*b*c^3*x^3 + b^4 + 2*a*b^2*c + 6*a^2*c^2 + 20*(2*b^2*c^2 + a*c^3)*x^2 + 10*(b^3*c + 2*a*b*c^2)*x)/(32*c^8*d^6*x^5 + 80*b*c^7*d^6*x^4 + 80*b^2*c^6*d^6*x^3 + 40*b^3*c^5*d^6*x^2 + 10*b^4*c^4*d^6*x + b^5*c^3*d^6)","B",0
1132,1,164,0,0.393170," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^7,x, algorithm=""fricas"")","-\frac{48 \, c^{4} x^{4} + 96 \, b c^{3} x^{3} + b^{4} + 4 \, a b^{2} c + 16 \, a^{2} c^{2} + 12 \, {\left(5 \, b^{2} c^{2} + 4 \, a c^{3}\right)} x^{2} + 12 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} x}{192 \, {\left(64 \, c^{9} d^{7} x^{6} + 192 \, b c^{8} d^{7} x^{5} + 240 \, b^{2} c^{7} d^{7} x^{4} + 160 \, b^{3} c^{6} d^{7} x^{3} + 60 \, b^{4} c^{5} d^{7} x^{2} + 12 \, b^{5} c^{4} d^{7} x + b^{6} c^{3} d^{7}\right)}}"," ",0,"-1/192*(48*c^4*x^4 + 96*b*c^3*x^3 + b^4 + 4*a*b^2*c + 16*a^2*c^2 + 12*(5*b^2*c^2 + 4*a*c^3)*x^2 + 12*(b^3*c + 4*a*b*c^2)*x)/(64*c^9*d^7*x^6 + 192*b*c^8*d^7*x^5 + 240*b^2*c^7*d^7*x^4 + 160*b^3*c^6*d^7*x^3 + 60*b^4*c^5*d^7*x^2 + 12*b^5*c^4*d^7*x + b^6*c^3*d^7)","B",0
1133,1,176,0,0.395244," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^8,x, algorithm=""fricas"")","-\frac{70 \, c^{4} x^{4} + 140 \, b c^{3} x^{3} + b^{4} + 6 \, a b^{2} c + 30 \, a^{2} c^{2} + 84 \, {\left(b^{2} c^{2} + a c^{3}\right)} x^{2} + 14 \, {\left(b^{3} c + 6 \, a b c^{2}\right)} x}{420 \, {\left(128 \, c^{10} d^{8} x^{7} + 448 \, b c^{9} d^{8} x^{6} + 672 \, b^{2} c^{8} d^{8} x^{5} + 560 \, b^{3} c^{7} d^{8} x^{4} + 280 \, b^{4} c^{6} d^{8} x^{3} + 84 \, b^{5} c^{5} d^{8} x^{2} + 14 \, b^{6} c^{4} d^{8} x + b^{7} c^{3} d^{8}\right)}}"," ",0,"-1/420*(70*c^4*x^4 + 140*b*c^3*x^3 + b^4 + 6*a*b^2*c + 30*a^2*c^2 + 84*(b^2*c^2 + a*c^3)*x^2 + 14*(b^3*c + 6*a*b*c^2)*x)/(128*c^10*d^8*x^7 + 448*b*c^9*d^8*x^6 + 672*b^2*c^8*d^8*x^5 + 560*b^3*c^7*d^8*x^4 + 280*b^4*c^6*d^8*x^3 + 84*b^5*c^5*d^8*x^2 + 14*b^6*c^4*d^8*x + b^7*c^3*d^8)","B",0
1134,1,192,0,0.394520," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^9,x, algorithm=""fricas"")","-\frac{96 \, c^{4} x^{4} + 192 \, b c^{3} x^{3} + b^{4} + 8 \, a b^{2} c + 48 \, a^{2} c^{2} + 16 \, {\left(7 \, b^{2} c^{2} + 8 \, a c^{3}\right)} x^{2} + 16 \, {\left(b^{3} c + 8 \, a b c^{2}\right)} x}{768 \, {\left(256 \, c^{11} d^{9} x^{8} + 1024 \, b c^{10} d^{9} x^{7} + 1792 \, b^{2} c^{9} d^{9} x^{6} + 1792 \, b^{3} c^{8} d^{9} x^{5} + 1120 \, b^{4} c^{7} d^{9} x^{4} + 448 \, b^{5} c^{6} d^{9} x^{3} + 112 \, b^{6} c^{5} d^{9} x^{2} + 16 \, b^{7} c^{4} d^{9} x + b^{8} c^{3} d^{9}\right)}}"," ",0,"-1/768*(96*c^4*x^4 + 192*b*c^3*x^3 + b^4 + 8*a*b^2*c + 48*a^2*c^2 + 16*(7*b^2*c^2 + 8*a*c^3)*x^2 + 16*(b^3*c + 8*a*b*c^2)*x)/(256*c^11*d^9*x^8 + 1024*b*c^10*d^9*x^7 + 1792*b^2*c^9*d^9*x^6 + 1792*b^3*c^8*d^9*x^5 + 1120*b^4*c^7*d^9*x^4 + 448*b^5*c^6*d^9*x^3 + 112*b^6*c^5*d^9*x^2 + 16*b^7*c^4*d^9*x + b^8*c^3*d^9)","B",0
1135,1,206,0,0.406035," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^10,x, algorithm=""fricas"")","-\frac{126 \, c^{4} x^{4} + 252 \, b c^{3} x^{3} + b^{4} + 10 \, a b^{2} c + 70 \, a^{2} c^{2} + 36 \, {\left(4 \, b^{2} c^{2} + 5 \, a c^{3}\right)} x^{2} + 18 \, {\left(b^{3} c + 10 \, a b c^{2}\right)} x}{1260 \, {\left(512 \, c^{12} d^{10} x^{9} + 2304 \, b c^{11} d^{10} x^{8} + 4608 \, b^{2} c^{10} d^{10} x^{7} + 5376 \, b^{3} c^{9} d^{10} x^{6} + 4032 \, b^{4} c^{8} d^{10} x^{5} + 2016 \, b^{5} c^{7} d^{10} x^{4} + 672 \, b^{6} c^{6} d^{10} x^{3} + 144 \, b^{7} c^{5} d^{10} x^{2} + 18 \, b^{8} c^{4} d^{10} x + b^{9} c^{3} d^{10}\right)}}"," ",0,"-1/1260*(126*c^4*x^4 + 252*b*c^3*x^3 + b^4 + 10*a*b^2*c + 70*a^2*c^2 + 36*(4*b^2*c^2 + 5*a*c^3)*x^2 + 18*(b^3*c + 10*a*b*c^2)*x)/(512*c^12*d^10*x^9 + 2304*b*c^11*d^10*x^8 + 4608*b^2*c^10*d^10*x^7 + 5376*b^3*c^9*d^10*x^6 + 4032*b^4*c^8*d^10*x^5 + 2016*b^5*c^7*d^10*x^4 + 672*b^6*c^6*d^10*x^3 + 144*b^7*c^5*d^10*x^2 + 18*b^8*c^4*d^10*x + b^9*c^3*d^10)","B",0
1136,1,220,0,0.382586," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^11,x, algorithm=""fricas"")","-\frac{160 \, c^{4} x^{4} + 320 \, b c^{3} x^{3} + b^{4} + 12 \, a b^{2} c + 96 \, a^{2} c^{2} + 60 \, {\left(3 \, b^{2} c^{2} + 4 \, a c^{3}\right)} x^{2} + 20 \, {\left(b^{3} c + 12 \, a b c^{2}\right)} x}{1920 \, {\left(1024 \, c^{13} d^{11} x^{10} + 5120 \, b c^{12} d^{11} x^{9} + 11520 \, b^{2} c^{11} d^{11} x^{8} + 15360 \, b^{3} c^{10} d^{11} x^{7} + 13440 \, b^{4} c^{9} d^{11} x^{6} + 8064 \, b^{5} c^{8} d^{11} x^{5} + 3360 \, b^{6} c^{7} d^{11} x^{4} + 960 \, b^{7} c^{6} d^{11} x^{3} + 180 \, b^{8} c^{5} d^{11} x^{2} + 20 \, b^{9} c^{4} d^{11} x + b^{10} c^{3} d^{11}\right)}}"," ",0,"-1/1920*(160*c^4*x^4 + 320*b*c^3*x^3 + b^4 + 12*a*b^2*c + 96*a^2*c^2 + 60*(3*b^2*c^2 + 4*a*c^3)*x^2 + 20*(b^3*c + 12*a*b*c^2)*x)/(1024*c^13*d^11*x^10 + 5120*b*c^12*d^11*x^9 + 11520*b^2*c^11*d^11*x^8 + 15360*b^3*c^10*d^11*x^7 + 13440*b^4*c^9*d^11*x^6 + 8064*b^5*c^8*d^11*x^5 + 3360*b^6*c^7*d^11*x^4 + 960*b^7*c^6*d^11*x^3 + 180*b^8*c^5*d^11*x^2 + 20*b^9*c^4*d^11*x + b^10*c^3*d^11)","B",0
1137,1,424,0,0.336346," ","integrate((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{8}{3} x^{12} d^{5} c^{8} + 16 x^{11} d^{5} c^{7} b + \frac{208}{5} x^{10} d^{5} c^{6} b^{2} + \frac{48}{5} x^{10} d^{5} c^{7} a + \frac{184}{3} x^{9} d^{5} c^{5} b^{3} + 48 x^{9} d^{5} c^{6} b a + \frac{225}{4} x^{8} d^{5} c^{4} b^{4} + 102 x^{8} d^{5} c^{5} b^{2} a + 12 x^{8} d^{5} c^{6} a^{2} + 33 x^{7} d^{5} c^{3} b^{5} + 120 x^{7} d^{5} c^{4} b^{3} a + 48 x^{7} d^{5} c^{5} b a^{2} + \frac{73}{6} x^{6} d^{5} c^{2} b^{6} + 85 x^{6} d^{5} c^{3} b^{4} a + 80 x^{6} d^{5} c^{4} b^{2} a^{2} + \frac{16}{3} x^{6} d^{5} c^{5} a^{3} + \frac{13}{5} x^{5} d^{5} c b^{7} + \frac{183}{5} x^{5} d^{5} c^{2} b^{5} a + 72 x^{5} d^{5} c^{3} b^{3} a^{2} + 16 x^{5} d^{5} c^{4} b a^{3} + \frac{1}{4} x^{4} d^{5} b^{8} + 9 x^{4} d^{5} c b^{6} a + \frac{75}{2} x^{4} d^{5} c^{2} b^{4} a^{2} + 20 x^{4} d^{5} c^{3} b^{2} a^{3} + x^{3} d^{5} b^{7} a + 11 x^{3} d^{5} c b^{5} a^{2} + \frac{40}{3} x^{3} d^{5} c^{2} b^{3} a^{3} + \frac{3}{2} x^{2} d^{5} b^{6} a^{2} + 5 x^{2} d^{5} c b^{4} a^{3} + x d^{5} b^{5} a^{3}"," ",0,"8/3*x^12*d^5*c^8 + 16*x^11*d^5*c^7*b + 208/5*x^10*d^5*c^6*b^2 + 48/5*x^10*d^5*c^7*a + 184/3*x^9*d^5*c^5*b^3 + 48*x^9*d^5*c^6*b*a + 225/4*x^8*d^5*c^4*b^4 + 102*x^8*d^5*c^5*b^2*a + 12*x^8*d^5*c^6*a^2 + 33*x^7*d^5*c^3*b^5 + 120*x^7*d^5*c^4*b^3*a + 48*x^7*d^5*c^5*b*a^2 + 73/6*x^6*d^5*c^2*b^6 + 85*x^6*d^5*c^3*b^4*a + 80*x^6*d^5*c^4*b^2*a^2 + 16/3*x^6*d^5*c^5*a^3 + 13/5*x^5*d^5*c*b^7 + 183/5*x^5*d^5*c^2*b^5*a + 72*x^5*d^5*c^3*b^3*a^2 + 16*x^5*d^5*c^4*b*a^3 + 1/4*x^4*d^5*b^8 + 9*x^4*d^5*c*b^6*a + 75/2*x^4*d^5*c^2*b^4*a^2 + 20*x^4*d^5*c^3*b^2*a^3 + x^3*d^5*b^7*a + 11*x^3*d^5*c*b^5*a^2 + 40/3*x^3*d^5*c^2*b^3*a^3 + 3/2*x^2*d^5*b^6*a^2 + 5*x^2*d^5*c*b^4*a^3 + x*d^5*b^5*a^3","B",0
1138,1,361,0,0.362487," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{16}{11} x^{11} d^{4} c^{7} + 8 x^{10} d^{4} c^{6} b + \frac{56}{3} x^{9} d^{4} c^{5} b^{2} + \frac{16}{3} x^{9} d^{4} c^{6} a + 24 x^{8} d^{4} c^{4} b^{3} + 24 x^{8} d^{4} c^{5} b a + \frac{129}{7} x^{7} d^{4} c^{3} b^{4} + \frac{312}{7} x^{7} d^{4} c^{4} b^{2} a + \frac{48}{7} x^{7} d^{4} c^{5} a^{2} + \frac{17}{2} x^{6} d^{4} c^{2} b^{5} + 44 x^{6} d^{4} c^{3} b^{3} a + 24 x^{6} d^{4} c^{4} b a^{2} + \frac{11}{5} x^{5} d^{4} c b^{6} + \frac{123}{5} x^{5} d^{4} c^{2} b^{4} a + \frac{168}{5} x^{5} d^{4} c^{3} b^{2} a^{2} + \frac{16}{5} x^{5} d^{4} c^{4} a^{3} + \frac{1}{4} x^{4} d^{4} b^{7} + \frac{15}{2} x^{4} d^{4} c b^{5} a + 24 x^{4} d^{4} c^{2} b^{3} a^{2} + 8 x^{4} d^{4} c^{3} b a^{3} + x^{3} d^{4} b^{6} a + 9 x^{3} d^{4} c b^{4} a^{2} + 8 x^{3} d^{4} c^{2} b^{2} a^{3} + \frac{3}{2} x^{2} d^{4} b^{5} a^{2} + 4 x^{2} d^{4} c b^{3} a^{3} + x d^{4} b^{4} a^{3}"," ",0,"16/11*x^11*d^4*c^7 + 8*x^10*d^4*c^6*b + 56/3*x^9*d^4*c^5*b^2 + 16/3*x^9*d^4*c^6*a + 24*x^8*d^4*c^4*b^3 + 24*x^8*d^4*c^5*b*a + 129/7*x^7*d^4*c^3*b^4 + 312/7*x^7*d^4*c^4*b^2*a + 48/7*x^7*d^4*c^5*a^2 + 17/2*x^6*d^4*c^2*b^5 + 44*x^6*d^4*c^3*b^3*a + 24*x^6*d^4*c^4*b*a^2 + 11/5*x^5*d^4*c*b^6 + 123/5*x^5*d^4*c^2*b^4*a + 168/5*x^5*d^4*c^3*b^2*a^2 + 16/5*x^5*d^4*c^4*a^3 + 1/4*x^4*d^4*b^7 + 15/2*x^4*d^4*c*b^5*a + 24*x^4*d^4*c^2*b^3*a^2 + 8*x^4*d^4*c^3*b*a^3 + x^3*d^4*b^6*a + 9*x^3*d^4*c*b^4*a^2 + 8*x^3*d^4*c^2*b^2*a^3 + 3/2*x^2*d^4*b^5*a^2 + 4*x^2*d^4*c*b^3*a^3 + x*d^4*b^4*a^3","B",0
1139,1,298,0,0.361460," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{4}{5} x^{10} d^{3} c^{6} + 4 x^{9} d^{3} c^{5} b + \frac{33}{4} x^{8} d^{3} c^{4} b^{2} + 3 x^{8} d^{3} c^{5} a + 9 x^{7} d^{3} c^{3} b^{3} + 12 x^{7} d^{3} c^{4} b a + \frac{11}{2} x^{6} d^{3} c^{2} b^{4} + 19 x^{6} d^{3} c^{3} b^{2} a + 4 x^{6} d^{3} c^{4} a^{2} + \frac{9}{5} x^{5} d^{3} c b^{5} + 15 x^{5} d^{3} c^{2} b^{3} a + 12 x^{5} d^{3} c^{3} b a^{2} + \frac{1}{4} x^{4} d^{3} b^{6} + 6 x^{4} d^{3} c b^{4} a + \frac{27}{2} x^{4} d^{3} c^{2} b^{2} a^{2} + 2 x^{4} d^{3} c^{3} a^{3} + x^{3} d^{3} b^{5} a + 7 x^{3} d^{3} c b^{3} a^{2} + 4 x^{3} d^{3} c^{2} b a^{3} + \frac{3}{2} x^{2} d^{3} b^{4} a^{2} + 3 x^{2} d^{3} c b^{2} a^{3} + x d^{3} b^{3} a^{3}"," ",0,"4/5*x^10*d^3*c^6 + 4*x^9*d^3*c^5*b + 33/4*x^8*d^3*c^4*b^2 + 3*x^8*d^3*c^5*a + 9*x^7*d^3*c^3*b^3 + 12*x^7*d^3*c^4*b*a + 11/2*x^6*d^3*c^2*b^4 + 19*x^6*d^3*c^3*b^2*a + 4*x^6*d^3*c^4*a^2 + 9/5*x^5*d^3*c*b^5 + 15*x^5*d^3*c^2*b^3*a + 12*x^5*d^3*c^3*b*a^2 + 1/4*x^4*d^3*b^6 + 6*x^4*d^3*c*b^4*a + 27/2*x^4*d^3*c^2*b^2*a^2 + 2*x^4*d^3*c^3*a^3 + x^3*d^3*b^5*a + 7*x^3*d^3*c*b^3*a^2 + 4*x^3*d^3*c^2*b*a^3 + 3/2*x^2*d^3*b^4*a^2 + 3*x^2*d^3*c*b^2*a^3 + x*d^3*b^3*a^3","B",0
1140,1,235,0,0.346101," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{4}{9} x^{9} d^{2} c^{5} + 2 x^{8} d^{2} c^{4} b + \frac{25}{7} x^{7} d^{2} c^{3} b^{2} + \frac{12}{7} x^{7} d^{2} c^{4} a + \frac{19}{6} x^{6} d^{2} c^{2} b^{3} + 6 x^{6} d^{2} c^{3} b a + \frac{7}{5} x^{5} d^{2} c b^{4} + \frac{39}{5} x^{5} d^{2} c^{2} b^{2} a + \frac{12}{5} x^{5} d^{2} c^{3} a^{2} + \frac{1}{4} x^{4} d^{2} b^{5} + \frac{9}{2} x^{4} d^{2} c b^{3} a + 6 x^{4} d^{2} c^{2} b a^{2} + x^{3} d^{2} b^{4} a + 5 x^{3} d^{2} c b^{2} a^{2} + \frac{4}{3} x^{3} d^{2} c^{2} a^{3} + \frac{3}{2} x^{2} d^{2} b^{3} a^{2} + 2 x^{2} d^{2} c b a^{3} + x d^{2} b^{2} a^{3}"," ",0,"4/9*x^9*d^2*c^5 + 2*x^8*d^2*c^4*b + 25/7*x^7*d^2*c^3*b^2 + 12/7*x^7*d^2*c^4*a + 19/6*x^6*d^2*c^2*b^3 + 6*x^6*d^2*c^3*b*a + 7/5*x^5*d^2*c*b^4 + 39/5*x^5*d^2*c^2*b^2*a + 12/5*x^5*d^2*c^3*a^2 + 1/4*x^4*d^2*b^5 + 9/2*x^4*d^2*c*b^3*a + 6*x^4*d^2*c^2*b*a^2 + x^3*d^2*b^4*a + 5*x^3*d^2*c*b^2*a^2 + 4/3*x^3*d^2*c^2*a^3 + 3/2*x^2*d^2*b^3*a^2 + 2*x^2*d^2*c*b*a^3 + x*d^2*b^2*a^3","B",0
1141,1,140,0,0.361497," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{4} x^{8} d c^{4} + x^{7} d c^{3} b + \frac{3}{2} x^{6} d c^{2} b^{2} + x^{6} d c^{3} a + x^{5} d c b^{3} + 3 x^{5} d c^{2} b a + \frac{1}{4} x^{4} d b^{4} + 3 x^{4} d c b^{2} a + \frac{3}{2} x^{4} d c^{2} a^{2} + x^{3} d b^{3} a + 3 x^{3} d c b a^{2} + \frac{3}{2} x^{2} d b^{2} a^{2} + x^{2} d c a^{3} + x d b a^{3}"," ",0,"1/4*x^8*d*c^4 + x^7*d*c^3*b + 3/2*x^6*d*c^2*b^2 + x^6*d*c^3*a + x^5*d*c*b^3 + 3*x^5*d*c^2*b*a + 1/4*x^4*d*b^4 + 3*x^4*d*c*b^2*a + 3/2*x^4*d*c^2*a^2 + x^3*d*b^3*a + 3*x^3*d*c*b*a^2 + 3/2*x^2*d*b^2*a^2 + x^2*d*c*a^3 + x*d*b*a^3","B",0
1142,1,162,0,0.383561," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d),x, algorithm=""fricas"")","\frac{32 \, c^{6} x^{6} + 96 \, b c^{5} x^{5} + 12 \, {\left(7 \, b^{2} c^{4} + 12 \, a c^{5}\right)} x^{4} + 8 \, {\left(b^{3} c^{3} + 36 \, a b c^{4}\right)} x^{3} - 6 \, {\left(b^{4} c^{2} - 12 \, a b^{2} c^{3} - 48 \, a^{2} c^{4}\right)} x^{2} + 6 \, {\left(b^{5} c - 12 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} x - 3 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \log\left(2 \, c x + b\right)}{384 \, c^{4} d}"," ",0,"1/384*(32*c^6*x^6 + 96*b*c^5*x^5 + 12*(7*b^2*c^4 + 12*a*c^5)*x^4 + 8*(b^3*c^3 + 36*a*b*c^4)*x^3 - 6*(b^4*c^2 - 12*a*b^2*c^3 - 48*a^2*c^4)*x^2 + 6*(b^5*c - 12*a*b^3*c^2 + 48*a^2*b*c^3)*x - 3*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*log(2*c*x + b))/(c^4*d)","A",0
1143,1,138,0,0.384912," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^2,x, algorithm=""fricas"")","\frac{64 \, c^{6} x^{6} + 192 \, b c^{5} x^{5} + 640 \, a b c^{4} x^{3} + 960 \, a^{2} c^{4} x^{2} + 5 \, b^{6} - 60 \, a b^{4} c + 240 \, a^{2} b^{2} c^{2} - 320 \, a^{3} c^{3} + 160 \, {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} x^{4} + 10 \, {\left(b^{5} c - 12 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} x}{640 \, {\left(2 \, c^{5} d^{2} x + b c^{4} d^{2}\right)}}"," ",0,"1/640*(64*c^6*x^6 + 192*b*c^5*x^5 + 640*a*b*c^4*x^3 + 960*a^2*c^4*x^2 + 5*b^6 - 60*a*b^4*c + 240*a^2*b^2*c^2 - 320*a^3*c^3 + 160*(b^2*c^4 + 2*a*c^5)*x^4 + 10*(b^5*c - 12*a*b^3*c^2 + 48*a^2*b*c^3)*x)/(2*c^5*d^2*x + b*c^4*d^2)","A",0
1144,1,252,0,0.399822," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^3,x, algorithm=""fricas"")","\frac{32 \, c^{6} x^{6} + 96 \, b c^{5} x^{5} + b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3} + 24 \, {\left(3 \, b^{2} c^{4} + 8 \, a c^{5}\right)} x^{4} - 16 \, {\left(b^{3} c^{3} - 24 \, a b c^{4}\right)} x^{3} - 16 \, {\left(2 \, b^{4} c^{2} - 15 \, a b^{2} c^{3}\right)} x^{2} - 8 \, {\left(b^{5} c - 6 \, a b^{3} c^{2}\right)} x + 6 \, {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 4 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + 4 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x\right)} \log\left(2 \, c x + b\right)}{256 \, {\left(4 \, c^{6} d^{3} x^{2} + 4 \, b c^{5} d^{3} x + b^{2} c^{4} d^{3}\right)}}"," ",0,"1/256*(32*c^6*x^6 + 96*b*c^5*x^5 + b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3 + 24*(3*b^2*c^4 + 8*a*c^5)*x^4 - 16*(b^3*c^3 - 24*a*b*c^4)*x^3 - 16*(2*b^4*c^2 - 15*a*b^2*c^3)*x^2 - 8*(b^5*c - 6*a*b^3*c^2)*x + 6*(b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2 + 4*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + 4*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x)*log(2*c*x + b))/(4*c^6*d^3*x^2 + 4*b*c^5*d^3*x + b^2*c^4*d^3)","B",0
1145,1,198,0,0.395280," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^4,x, algorithm=""fricas"")","\frac{16 \, c^{6} x^{6} + 48 \, b c^{5} x^{5} - 2 \, b^{6} + 15 \, a b^{4} c - 24 \, a^{2} b^{2} c^{2} - 16 \, a^{3} c^{3} + 24 \, {\left(b^{2} c^{4} + 6 \, a c^{5}\right)} x^{4} - 8 \, {\left(2 \, b^{3} c^{3} - 27 \, a b c^{4}\right)} x^{3} - 12 \, {\left(2 \, b^{4} c^{2} - 15 \, a b^{2} c^{3} + 12 \, a^{2} c^{4}\right)} x^{2} - 6 \, {\left(2 \, b^{5} c - 15 \, a b^{3} c^{2} + 24 \, a^{2} b c^{3}\right)} x}{96 \, {\left(8 \, c^{7} d^{4} x^{3} + 12 \, b c^{6} d^{4} x^{2} + 6 \, b^{2} c^{5} d^{4} x + b^{3} c^{4} d^{4}\right)}}"," ",0,"1/96*(16*c^6*x^6 + 48*b*c^5*x^5 - 2*b^6 + 15*a*b^4*c - 24*a^2*b^2*c^2 - 16*a^3*c^3 + 24*(b^2*c^4 + 6*a*c^5)*x^4 - 8*(2*b^3*c^3 - 27*a*b*c^4)*x^3 - 12*(2*b^4*c^2 - 15*a*b^2*c^3 + 12*a^2*c^4)*x^2 - 6*(2*b^5*c - 15*a*b^3*c^2 + 24*a^2*b*c^3)*x)/(8*c^7*d^4*x^3 + 12*b*c^6*d^4*x^2 + 6*b^2*c^5*d^4*x + b^3*c^4*d^4)","B",0
1146,1,291,0,0.402177," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^5,x, algorithm=""fricas"")","\frac{128 \, c^{6} x^{6} + 384 \, b c^{5} x^{5} + 448 \, b^{2} c^{4} x^{4} + 256 \, b^{3} c^{3} x^{3} - 5 \, b^{6} + 36 \, a b^{4} c - 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3} + 48 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} x^{2} - 16 \, {\left(b^{5} c - 12 \, a b^{3} c^{2} + 24 \, a^{2} b c^{3}\right)} x - 12 \, {\left(b^{6} - 4 \, a b^{4} c + 16 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} + 32 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3} + 24 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} x^{2} + 8 \, {\left(b^{5} c - 4 \, a b^{3} c^{2}\right)} x\right)} \log\left(2 \, c x + b\right)}{512 \, {\left(16 \, c^{8} d^{5} x^{4} + 32 \, b c^{7} d^{5} x^{3} + 24 \, b^{2} c^{6} d^{5} x^{2} + 8 \, b^{3} c^{5} d^{5} x + b^{4} c^{4} d^{5}\right)}}"," ",0,"1/512*(128*c^6*x^6 + 384*b*c^5*x^5 + 448*b^2*c^4*x^4 + 256*b^3*c^3*x^3 - 5*b^6 + 36*a*b^4*c - 48*a^2*b^2*c^2 - 64*a^3*c^3 + 48*(b^4*c^2 + 4*a*b^2*c^3 - 8*a^2*c^4)*x^2 - 16*(b^5*c - 12*a*b^3*c^2 + 24*a^2*b*c^3)*x - 12*(b^6 - 4*a*b^4*c + 16*(b^2*c^4 - 4*a*c^5)*x^4 + 32*(b^3*c^3 - 4*a*b*c^4)*x^3 + 24*(b^4*c^2 - 4*a*b^2*c^3)*x^2 + 8*(b^5*c - 4*a*b^3*c^2)*x)*log(2*c*x + b))/(16*c^8*d^5*x^4 + 32*b*c^7*d^5*x^3 + 24*b^2*c^6*d^5*x^2 + 8*b^3*c^5*d^5*x + b^4*c^4*d^5)","B",0
1147,1,227,0,0.395355," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^6,x, algorithm=""fricas"")","\frac{320 \, c^{6} x^{6} + 800 \, b c^{5} x^{5} + 11 \, b^{6} - 32 \, a b^{4} c - 32 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3} + 80 \, {\left(13 \, b^{2} c^{4} - 12 \, a c^{5}\right)} x^{4} + 80 \, {\left(11 \, b^{3} c^{3} - 24 \, a b c^{4}\right)} x^{3} + 40 \, {\left(11 \, b^{4} c^{2} - 32 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} x^{2} + 10 \, {\left(11 \, b^{5} c - 32 \, a b^{3} c^{2} - 32 \, a^{2} b c^{3}\right)} x}{640 \, {\left(32 \, c^{9} d^{6} x^{5} + 80 \, b c^{8} d^{6} x^{4} + 80 \, b^{2} c^{7} d^{6} x^{3} + 40 \, b^{3} c^{6} d^{6} x^{2} + 10 \, b^{4} c^{5} d^{6} x + b^{5} c^{4} d^{6}\right)}}"," ",0,"1/640*(320*c^6*x^6 + 800*b*c^5*x^5 + 11*b^6 - 32*a*b^4*c - 32*a^2*b^2*c^2 - 64*a^3*c^3 + 80*(13*b^2*c^4 - 12*a*c^5)*x^4 + 80*(11*b^3*c^3 - 24*a*b*c^4)*x^3 + 40*(11*b^4*c^2 - 32*a*b^2*c^3 - 8*a^2*c^4)*x^2 + 10*(11*b^5*c - 32*a*b^3*c^2 - 32*a^2*b*c^3)*x)/(32*c^9*d^6*x^5 + 80*b*c^8*d^6*x^4 + 80*b^2*c^7*d^6*x^3 + 40*b^3*c^6*d^6*x^2 + 10*b^4*c^5*d^6*x + b^5*c^4*d^6)","B",0
1148,1,292,0,0.404377," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^7,x, algorithm=""fricas"")","\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 + 12 \, {\left(64 \, c^{6} x^{6} + 192 \, b c^{5} x^{5} + 240 \, b^{2} c^{4} x^{4} + 160 \, b^{3} c^{3} x^{3} + 60 \, b^{4} c^{2} x^{2} + 12 \, b^{5} c x + b^{6}\right)} \log\left(2 \, c x + b\right)}{1536 \, {\left(64 \, c^{10} d^{7} x^{6} + 192 \, b c^{9} d^{7} x^{5} + 240 \, b^{2} c^{8} d^{7} x^{4} + 160 \, b^{3} c^{7} d^{7} x^{3} + 60 \, b^{4} c^{6} d^{7} x^{2} + 12 \, b^{5} c^{5} d^{7} x + b^{6} c^{4} d^{7}\right)}}"," ",0,"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 + 12*(64*c^6*x^6 + 192*b*c^5*x^5 + 240*b^2*c^4*x^4 + 160*b^3*c^3*x^3 + 60*b^4*c^2*x^2 + 12*b^5*c*x + b^6)*log(2*c*x + b))/(64*c^10*d^7*x^6 + 192*b*c^9*d^7*x^5 + 240*b^2*c^8*d^7*x^4 + 160*b^3*c^7*d^7*x^3 + 60*b^4*c^6*d^7*x^2 + 12*b^5*c^5*d^7*x + b^6*c^4*d^7)","B",0
1149,1,248,0,0.392200," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^8,x, algorithm=""fricas"")","-\frac{140 \, c^{6} x^{6} + 420 \, b c^{5} x^{5} + b^{6} + 2 \, a b^{4} c + 6 \, a^{2} b^{2} c^{2} + 20 \, a^{3} c^{3} + 70 \, {\left(7 \, b^{2} c^{4} + 2 \, a c^{5}\right)} x^{4} + 280 \, {\left(b^{3} c^{3} + a b c^{4}\right)} x^{3} + 84 \, {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} x^{2} + 14 \, {\left(b^{5} c + 2 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} x}{280 \, {\left(128 \, c^{11} d^{8} x^{7} + 448 \, b c^{10} d^{8} x^{6} + 672 \, b^{2} c^{9} d^{8} x^{5} + 560 \, b^{3} c^{8} d^{8} x^{4} + 280 \, b^{4} c^{7} d^{8} x^{3} + 84 \, b^{5} c^{6} d^{8} x^{2} + 14 \, b^{6} c^{5} d^{8} x + b^{7} c^{4} d^{8}\right)}}"," ",0,"-1/280*(140*c^6*x^6 + 420*b*c^5*x^5 + b^6 + 2*a*b^4*c + 6*a^2*b^2*c^2 + 20*a^3*c^3 + 70*(7*b^2*c^4 + 2*a*c^5)*x^4 + 280*(b^3*c^3 + a*b*c^4)*x^3 + 84*(b^4*c^2 + 2*a*b^2*c^3 + a^2*c^4)*x^2 + 14*(b^5*c + 2*a*b^3*c^2 + 6*a^2*b*c^3)*x)/(128*c^11*d^8*x^7 + 448*b*c^10*d^8*x^6 + 672*b^2*c^9*d^8*x^5 + 560*b^3*c^8*d^8*x^4 + 280*b^4*c^7*d^8*x^3 + 84*b^5*c^6*d^8*x^2 + 14*b^6*c^5*d^8*x + b^7*c^4*d^8)","B",0
1150,1,266,0,0.395753," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^9,x, algorithm=""fricas"")","-\frac{256 \, c^{6} x^{6} + 768 \, b c^{5} x^{5} + b^{6} + 4 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2} + 64 \, a^{3} c^{3} + 96 \, {\left(9 \, b^{2} c^{4} + 4 \, a c^{5}\right)} x^{4} + 64 \, {\left(7 \, b^{3} c^{3} + 12 \, a b c^{4}\right)} x^{3} + 16 \, {\left(7 \, b^{4} c^{2} + 28 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + 16 \, {\left(b^{5} c + 4 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}{1024 \, {\left(256 \, c^{12} d^{9} x^{8} + 1024 \, b c^{11} d^{9} x^{7} + 1792 \, b^{2} c^{10} d^{9} x^{6} + 1792 \, b^{3} c^{9} d^{9} x^{5} + 1120 \, b^{4} c^{8} d^{9} x^{4} + 448 \, b^{5} c^{7} d^{9} x^{3} + 112 \, b^{6} c^{6} d^{9} x^{2} + 16 \, b^{7} c^{5} d^{9} x + b^{8} c^{4} d^{9}\right)}}"," ",0,"-1/1024*(256*c^6*x^6 + 768*b*c^5*x^5 + b^6 + 4*a*b^4*c + 16*a^2*b^2*c^2 + 64*a^3*c^3 + 96*(9*b^2*c^4 + 4*a*c^5)*x^4 + 64*(7*b^3*c^3 + 12*a*b*c^4)*x^3 + 16*(7*b^4*c^2 + 28*a*b^2*c^3 + 16*a^2*c^4)*x^2 + 16*(b^5*c + 4*a*b^3*c^2 + 16*a^2*b*c^3)*x)/(256*c^12*d^9*x^8 + 1024*b*c^11*d^9*x^7 + 1792*b^2*c^10*d^9*x^6 + 1792*b^3*c^9*d^9*x^5 + 1120*b^4*c^8*d^9*x^4 + 448*b^5*c^7*d^9*x^3 + 112*b^6*c^6*d^9*x^2 + 16*b^7*c^5*d^9*x + b^8*c^4*d^9)","B",0
1151,1,280,0,0.390886," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^10,x, algorithm=""fricas"")","-\frac{420 \, c^{6} x^{6} + 1260 \, b c^{5} x^{5} + b^{6} + 6 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2} + 140 \, a^{3} c^{3} + 126 \, {\left(11 \, b^{2} c^{4} + 6 \, a c^{5}\right)} x^{4} + 168 \, {\left(4 \, b^{3} c^{3} + 9 \, a b c^{4}\right)} x^{3} + 36 \, {\left(4 \, b^{4} c^{2} + 24 \, a b^{2} c^{3} + 15 \, a^{2} c^{4}\right)} x^{2} + 18 \, {\left(b^{5} c + 6 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} x}{2520 \, {\left(512 \, c^{13} d^{10} x^{9} + 2304 \, b c^{12} d^{10} x^{8} + 4608 \, b^{2} c^{11} d^{10} x^{7} + 5376 \, b^{3} c^{10} d^{10} x^{6} + 4032 \, b^{4} c^{9} d^{10} x^{5} + 2016 \, b^{5} c^{8} d^{10} x^{4} + 672 \, b^{6} c^{7} d^{10} x^{3} + 144 \, b^{7} c^{6} d^{10} x^{2} + 18 \, b^{8} c^{5} d^{10} x + b^{9} c^{4} d^{10}\right)}}"," ",0,"-1/2520*(420*c^6*x^6 + 1260*b*c^5*x^5 + b^6 + 6*a*b^4*c + 30*a^2*b^2*c^2 + 140*a^3*c^3 + 126*(11*b^2*c^4 + 6*a*c^5)*x^4 + 168*(4*b^3*c^3 + 9*a*b*c^4)*x^3 + 36*(4*b^4*c^2 + 24*a*b^2*c^3 + 15*a^2*c^4)*x^2 + 18*(b^5*c + 6*a*b^3*c^2 + 30*a^2*b*c^3)*x)/(512*c^13*d^10*x^9 + 2304*b*c^12*d^10*x^8 + 4608*b^2*c^11*d^10*x^7 + 5376*b^3*c^10*d^10*x^6 + 4032*b^4*c^9*d^10*x^5 + 2016*b^5*c^8*d^10*x^4 + 672*b^6*c^7*d^10*x^3 + 144*b^7*c^6*d^10*x^2 + 18*b^8*c^5*d^10*x + b^9*c^4*d^10)","B",0
1152,1,294,0,0.389957," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^11,x, algorithm=""fricas"")","-\frac{640 \, c^{6} x^{6} + 1920 \, b c^{5} x^{5} + b^{6} + 8 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3} + 160 \, {\left(13 \, b^{2} c^{4} + 8 \, a c^{5}\right)} x^{4} + 320 \, {\left(3 \, b^{3} c^{3} + 8 \, a b c^{4}\right)} x^{3} + 60 \, {\left(3 \, b^{4} c^{2} + 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + 20 \, {\left(b^{5} c + 8 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} x}{5120 \, {\left(1024 \, c^{14} d^{11} x^{10} + 5120 \, b c^{13} d^{11} x^{9} + 11520 \, b^{2} c^{12} d^{11} x^{8} + 15360 \, b^{3} c^{11} d^{11} x^{7} + 13440 \, b^{4} c^{10} d^{11} x^{6} + 8064 \, b^{5} c^{9} d^{11} x^{5} + 3360 \, b^{6} c^{8} d^{11} x^{4} + 960 \, b^{7} c^{7} d^{11} x^{3} + 180 \, b^{8} c^{6} d^{11} x^{2} + 20 \, b^{9} c^{5} d^{11} x + b^{10} c^{4} d^{11}\right)}}"," ",0,"-1/5120*(640*c^6*x^6 + 1920*b*c^5*x^5 + b^6 + 8*a*b^4*c + 48*a^2*b^2*c^2 + 256*a^3*c^3 + 160*(13*b^2*c^4 + 8*a*c^5)*x^4 + 320*(3*b^3*c^3 + 8*a*b*c^4)*x^3 + 60*(3*b^4*c^2 + 24*a*b^2*c^3 + 16*a^2*c^4)*x^2 + 20*(b^5*c + 8*a*b^3*c^2 + 48*a^2*b*c^3)*x)/(1024*c^14*d^11*x^10 + 5120*b*c^13*d^11*x^9 + 11520*b^2*c^12*d^11*x^8 + 15360*b^3*c^11*d^11*x^7 + 13440*b^4*c^10*d^11*x^6 + 8064*b^5*c^9*d^11*x^5 + 3360*b^6*c^8*d^11*x^4 + 960*b^7*c^7*d^11*x^3 + 180*b^8*c^6*d^11*x^2 + 20*b^9*c^5*d^11*x + b^10*c^4*d^11)","B",0
1153,1,306,0,0.386440," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^12,x, algorithm=""fricas"")","-\frac{924 \, c^{6} x^{6} + 2772 \, b c^{5} x^{5} + b^{6} + 10 \, a b^{4} c + 70 \, a^{2} b^{2} c^{2} + 420 \, a^{3} c^{3} + 990 \, {\left(3 \, b^{2} c^{4} + 2 \, a c^{5}\right)} x^{4} + 1320 \, {\left(b^{3} c^{3} + 3 \, a b c^{4}\right)} x^{3} + 220 \, {\left(b^{4} c^{2} + 10 \, a b^{2} c^{3} + 7 \, a^{2} c^{4}\right)} x^{2} + 22 \, {\left(b^{5} c + 10 \, a b^{3} c^{2} + 70 \, a^{2} b c^{3}\right)} x}{9240 \, {\left(2048 \, c^{15} d^{12} x^{11} + 11264 \, b c^{14} d^{12} x^{10} + 28160 \, b^{2} c^{13} d^{12} x^{9} + 42240 \, b^{3} c^{12} d^{12} x^{8} + 42240 \, b^{4} c^{11} d^{12} x^{7} + 29568 \, b^{5} c^{10} d^{12} x^{6} + 14784 \, b^{6} c^{9} d^{12} x^{5} + 5280 \, b^{7} c^{8} d^{12} x^{4} + 1320 \, b^{8} c^{7} d^{12} x^{3} + 220 \, b^{9} c^{6} d^{12} x^{2} + 22 \, b^{10} c^{5} d^{12} x + b^{11} c^{4} d^{12}\right)}}"," ",0,"-1/9240*(924*c^6*x^6 + 2772*b*c^5*x^5 + b^6 + 10*a*b^4*c + 70*a^2*b^2*c^2 + 420*a^3*c^3 + 990*(3*b^2*c^4 + 2*a*c^5)*x^4 + 1320*(b^3*c^3 + 3*a*b*c^4)*x^3 + 220*(b^4*c^2 + 10*a*b^2*c^3 + 7*a^2*c^4)*x^2 + 22*(b^5*c + 10*a*b^3*c^2 + 70*a^2*b*c^3)*x)/(2048*c^15*d^12*x^11 + 11264*b*c^14*d^12*x^10 + 28160*b^2*c^13*d^12*x^9 + 42240*b^3*c^12*d^12*x^8 + 42240*b^4*c^11*d^12*x^7 + 29568*b^5*c^10*d^12*x^6 + 14784*b^6*c^9*d^12*x^5 + 5280*b^7*c^8*d^12*x^4 + 1320*b^8*c^7*d^12*x^3 + 220*b^9*c^6*d^12*x^2 + 22*b^10*c^5*d^12*x + b^11*c^4*d^12)","B",0
1154,1,536,0,0.429116," ","integrate((2*c*d*x+b*d)^8/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{256}{7} \, c^{7} d^{8} x^{7} + 128 \, b c^{6} d^{8} x^{6} + \frac{256}{5} \, {\left(4 \, b^{2} c^{5} - a c^{6}\right)} d^{8} x^{5} + 64 \, {\left(3 \, b^{3} c^{4} - 2 \, a b c^{5}\right)} d^{8} x^{4} + \frac{32}{3} \, {\left(11 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{8} x^{3} + 16 \, {\left(3 \, b^{5} c^{2} - 8 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{8} x^{2} - {\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^{8} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 16 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} d^{8} x, \frac{256}{7} \, c^{7} d^{8} x^{7} + 128 \, b c^{6} d^{8} x^{6} + \frac{256}{5} \, {\left(4 \, b^{2} c^{5} - a c^{6}\right)} d^{8} x^{5} + 64 \, {\left(3 \, b^{3} c^{4} - 2 \, a b c^{5}\right)} d^{8} x^{4} + \frac{32}{3} \, {\left(11 \, b^{4} c^{3} - 16 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{8} x^{3} + 16 \, {\left(3 \, b^{5} c^{2} - 8 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{8} x^{2} - 2 \, {\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^{8} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 16 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} d^{8} x\right]"," ",0,"[256/7*c^7*d^8*x^7 + 128*b*c^6*d^8*x^6 + 256/5*(4*b^2*c^5 - a*c^6)*d^8*x^5 + 64*(3*b^3*c^4 - 2*a*b*c^5)*d^8*x^4 + 32/3*(11*b^4*c^3 - 16*a*b^2*c^4 + 8*a^2*c^5)*d^8*x^3 + 16*(3*b^5*c^2 - 8*a*b^3*c^3 + 8*a^2*b*c^4)*d^8*x^2 - (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^8*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 16*(b^6*c - 6*a*b^4*c^2 + 16*a^2*b^2*c^3 - 16*a^3*c^4)*d^8*x, 256/7*c^7*d^8*x^7 + 128*b*c^6*d^8*x^6 + 256/5*(4*b^2*c^5 - a*c^6)*d^8*x^5 + 64*(3*b^3*c^4 - 2*a*b*c^5)*d^8*x^4 + 32/3*(11*b^4*c^3 - 16*a*b^2*c^4 + 8*a^2*c^5)*d^8*x^3 + 16*(3*b^5*c^2 - 8*a*b^3*c^3 + 8*a^2*b*c^4)*d^8*x^2 - 2*(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^8*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 16*(b^6*c - 6*a*b^4*c^2 + 16*a^2*b^2*c^3 - 16*a^3*c^4)*d^8*x]","B",0
1155,1,181,0,0.392333," ","integrate((2*c*d*x+b*d)^7/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{64}{3} \, c^{6} d^{7} x^{6} + 64 \, b c^{5} d^{7} x^{5} + 8 \, {\left(11 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d^{7} x^{4} + \frac{16}{3} \, {\left(13 \, b^{3} c^{3} - 12 \, a b c^{4}\right)} d^{7} x^{3} + 4 \, {\left(9 \, b^{4} c^{2} - 20 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} x^{2} + 4 \, {\left(3 \, b^{5} c - 12 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{7} x + {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{7} \log\left(c x^{2} + b x + a\right)"," ",0,"64/3*c^6*d^7*x^6 + 64*b*c^5*d^7*x^5 + 8*(11*b^2*c^4 - 4*a*c^5)*d^7*x^4 + 16/3*(13*b^3*c^3 - 12*a*b*c^4)*d^7*x^3 + 4*(9*b^4*c^2 - 20*a*b^2*c^3 + 16*a^2*c^4)*d^7*x^2 + 4*(3*b^5*c - 12*a*b^3*c^2 + 16*a^2*b*c^3)*d^7*x + (b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^7*log(c*x^2 + b*x + a)","B",0
1156,1,356,0,0.409766," ","integrate((2*c*d*x+b*d)^6/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{64}{5} \, c^{5} d^{6} x^{5} + 32 \, b c^{4} d^{6} x^{4} + \frac{16}{3} \, {\left(7 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} x^{3} + 8 \, {\left(3 \, b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} x^{2} + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} d^{6} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 4 \, {\left(3 \, b^{4} c - 12 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{6} x, \frac{64}{5} \, c^{5} d^{6} x^{5} + 32 \, b c^{4} d^{6} x^{4} + \frac{16}{3} \, {\left(7 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} x^{3} + 8 \, {\left(3 \, b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} x^{2} - 2 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} d^{6} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 4 \, {\left(3 \, b^{4} c - 12 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{6} x\right]"," ",0,"[64/5*c^5*d^6*x^5 + 32*b*c^4*d^6*x^4 + 16/3*(7*b^2*c^3 - 4*a*c^4)*d^6*x^3 + 8*(3*b^3*c^2 - 4*a*b*c^3)*d^6*x^2 + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(b^2 - 4*a*c)*d^6*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 4*(3*b^4*c - 12*a*b^2*c^2 + 16*a^2*c^3)*d^6*x, 64/5*c^5*d^6*x^5 + 32*b*c^4*d^6*x^4 + 16/3*(7*b^2*c^3 - 4*a*c^4)*d^6*x^3 + 8*(3*b^3*c^2 - 4*a*b*c^3)*d^6*x^2 - 2*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-b^2 + 4*a*c)*d^6*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 4*(3*b^4*c - 12*a*b^2*c^2 + 16*a^2*c^3)*d^6*x]","A",0
1157,1,99,0,0.383398," ","integrate((2*c*d*x+b*d)^5/(c*x^2+b*x+a),x, algorithm=""fricas"")","8 \, c^{4} d^{5} x^{4} + 16 \, b c^{3} d^{5} x^{3} + 16 \, {\left(b^{2} c^{2} - a c^{3}\right)} d^{5} x^{2} + 8 \, {\left(b^{3} c - 2 \, a b c^{2}\right)} d^{5} x + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{5} \log\left(c x^{2} + b x + a\right)"," ",0,"8*c^4*d^5*x^4 + 16*b*c^3*d^5*x^3 + 16*(b^2*c^2 - a*c^3)*d^5*x^2 + 8*(b^3*c - 2*a*b*c^2)*d^5*x + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^5*log(c*x^2 + b*x + a)","A",0
1158,1,208,0,0.427476," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{16}{3} \, c^{3} d^{4} x^{3} + 8 \, b c^{2} d^{4} x^{2} - {\left(b^{2} - 4 \, a c\right)}^{\frac{3}{2}} d^{4} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 8 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{4} x, \frac{16}{3} \, c^{3} d^{4} x^{3} + 8 \, b c^{2} d^{4} x^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} \sqrt{-b^{2} + 4 \, a c} d^{4} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 8 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{4} x\right]"," ",0,"[16/3*c^3*d^4*x^3 + 8*b*c^2*d^4*x^2 - (b^2 - 4*a*c)^(3/2)*d^4*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 8*(b^2*c - 2*a*c^2)*d^4*x, 16/3*c^3*d^4*x^3 + 8*b*c^2*d^4*x^2 - 2*(b^2 - 4*a*c)*sqrt(-b^2 + 4*a*c)*d^4*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 8*(b^2*c - 2*a*c^2)*d^4*x]","A",0
1159,1,43,0,0.385723," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","4 \, c^{2} d^{3} x^{2} + 4 \, b c d^{3} x + {\left(b^{2} - 4 \, a c\right)} d^{3} \log\left(c x^{2} + b x + a\right)"," ",0,"4*c^2*d^3*x^2 + 4*b*c*d^3*x + (b^2 - 4*a*c)*d^3*log(c*x^2 + b*x + a)","A",0
1160,1,132,0,0.410462," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[4 \, c d^{2} x + \sqrt{b^{2} - 4 \, a c} d^{2} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right), 4 \, c d^{2} x - 2 \, \sqrt{-b^{2} + 4 \, a c} d^{2} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)\right]"," ",0,"[4*c*d^2*x + sqrt(b^2 - 4*a*c)*d^2*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)), 4*c*d^2*x - 2*sqrt(-b^2 + 4*a*c)*d^2*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c))]","A",0
1161,1,13,0,0.386928," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","d \log\left(c x^{2} + b x + a\right)"," ",0,"d*log(c*x^2 + b*x + a)","A",0
1162,1,35,0,0.397942," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{\log\left(c x^{2} + b x + a\right) - 2 \, \log\left(2 \, c x + b\right)}{{\left(b^{2} - 4 \, a c\right)} d}"," ",0,"(log(c*x^2 + b*x + a) - 2*log(2*c*x + b))/((b^2 - 4*a*c)*d)","A",0
1163,1,256,0,0.416793," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[-\frac{\sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, b^{2} + 8 \, a c}{2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} x + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2}}, -\frac{2 \, {\left(\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - b^{2} + 4 \, a c\right)}}{2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} x + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2}}\right]"," ",0,"[-(sqrt(b^2 - 4*a*c)*(2*c*x + b)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*b^2 + 8*a*c)/(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2*x + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2), -2*(sqrt(-b^2 + 4*a*c)*(2*c*x + b)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - b^2 + 4*a*c)/(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2*x + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2)]","B",0
1164,1,156,0,0.395026," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{b^{2} - 4 \, a c + {\left(4 \, c^{2} x^{2} + 4 \, b c x + b^{2}\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(4 \, c^{2} x^{2} + 4 \, b c x + b^{2}\right)} \log\left(2 \, c x + b\right)}{4 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{3} x^{2} + 4 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} x + {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} d^{3}}"," ",0,"(b^2 - 4*a*c + (4*c^2*x^2 + 4*b*c*x + b^2)*log(c*x^2 + b*x + a) - 2*(4*c^2*x^2 + 4*b*c*x + b^2)*log(2*c*x + b))/(4*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^3*x^2 + 4*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^3*x + (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*d^3)","B",0
1165,1,627,0,0.425158," ","integrate(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{8 \, b^{4} - 40 \, a b^{2} c + 32 \, a^{2} c^{2} + 24 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + 3 \, {\left(8 \, c^{3} x^{3} + 12 \, b c^{2} x^{2} + 6 \, b^{2} c x + b^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 24 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x}{3 \, {\left(8 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{4} x^{3} + 12 \, {\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)} d^{4} x^{2} + 6 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{4} x + {\left(b^{9} - 12 \, a b^{7} c + 48 \, a^{2} b^{5} c^{2} - 64 \, a^{3} b^{3} c^{3}\right)} d^{4}\right)}}, \frac{2 \, {\left(4 \, b^{4} - 20 \, a b^{2} c + 16 \, a^{2} c^{2} + 12 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} - 3 \, {\left(8 \, c^{3} x^{3} + 12 \, b c^{2} x^{2} + 6 \, b^{2} c x + b^{3}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 12 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)}}{3 \, {\left(8 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{4} x^{3} + 12 \, {\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)} d^{4} x^{2} + 6 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} d^{4} x + {\left(b^{9} - 12 \, a b^{7} c + 48 \, a^{2} b^{5} c^{2} - 64 \, a^{3} b^{3} c^{3}\right)} d^{4}\right)}}\right]"," ",0,"[1/3*(8*b^4 - 40*a*b^2*c + 32*a^2*c^2 + 24*(b^2*c^2 - 4*a*c^3)*x^2 + 3*(8*c^3*x^3 + 12*b*c^2*x^2 + 6*b^2*c*x + b^3)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 24*(b^3*c - 4*a*b*c^2)*x)/(8*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^4*x^3 + 12*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^4*x^2 + 6*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^4*x + (b^9 - 12*a*b^7*c + 48*a^2*b^5*c^2 - 64*a^3*b^3*c^3)*d^4), 2/3*(4*b^4 - 20*a*b^2*c + 16*a^2*c^2 + 12*(b^2*c^2 - 4*a*c^3)*x^2 - 3*(8*c^3*x^3 + 12*b*c^2*x^2 + 6*b^2*c*x + b^3)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 12*(b^3*c - 4*a*b*c^2)*x)/(8*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^4*x^3 + 12*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^4*x^2 + 6*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*d^4*x + (b^9 - 12*a*b^7*c + 48*a^2*b^5*c^2 - 64*a^3*b^3*c^3)*d^4)]","B",0
1166,1,753,0,0.424663," ","integrate((2*c*d*x+b*d)^8/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{768 \, c^{7} d^{8} x^{7} + 2688 \, b c^{6} d^{8} x^{6} + 896 \, {\left(5 \, b^{2} c^{5} - 2 \, a c^{6}\right)} d^{8} x^{5} + 4480 \, {\left(b^{3} c^{4} - a b c^{5}\right)} d^{8} x^{4} + 1120 \, {\left(3 \, b^{4} c^{3} - 8 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{8} x^{3} + 480 \, {\left(3 \, b^{5} c^{2} - 12 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{8} x^{2} - 30 \, {\left(b^{6} c - 60 \, a b^{4} c^{2} + 304 \, a^{2} b^{2} c^{3} - 448 \, a^{3} c^{4}\right)} d^{8} x - 15 \, {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{8} + 210 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{8} x + {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d^{8}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{15 \, {\left(c x^{2} + b x + a\right)}}, \frac{768 \, c^{7} d^{8} x^{7} + 2688 \, b c^{6} d^{8} x^{6} + 896 \, {\left(5 \, b^{2} c^{5} - 2 \, a c^{6}\right)} d^{8} x^{5} + 4480 \, {\left(b^{3} c^{4} - a b c^{5}\right)} d^{8} x^{4} + 1120 \, {\left(3 \, b^{4} c^{3} - 8 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{8} x^{3} + 480 \, {\left(3 \, b^{5} c^{2} - 12 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{8} x^{2} - 30 \, {\left(b^{6} c - 60 \, a b^{4} c^{2} + 304 \, a^{2} b^{2} c^{3} - 448 \, a^{3} c^{4}\right)} d^{8} x - 15 \, {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{8} - 420 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{8} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{8} x + {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d^{8}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{15 \, {\left(c x^{2} + b x + a\right)}}\right]"," ",0,"[1/15*(768*c^7*d^8*x^7 + 2688*b*c^6*d^8*x^6 + 896*(5*b^2*c^5 - 2*a*c^6)*d^8*x^5 + 4480*(b^3*c^4 - a*b*c^5)*d^8*x^4 + 1120*(3*b^4*c^3 - 8*a*b^2*c^4 + 8*a^2*c^5)*d^8*x^3 + 480*(3*b^5*c^2 - 12*a*b^3*c^3 + 16*a^2*b*c^4)*d^8*x^2 - 30*(b^6*c - 60*a*b^4*c^2 + 304*a^2*b^2*c^3 - 448*a^3*c^4)*d^8*x - 15*(b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^8 + 210*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^8*x + (a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d^8)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(c*x^2 + b*x + a), 1/15*(768*c^7*d^8*x^7 + 2688*b*c^6*d^8*x^6 + 896*(5*b^2*c^5 - 2*a*c^6)*d^8*x^5 + 4480*(b^3*c^4 - a*b*c^5)*d^8*x^4 + 1120*(3*b^4*c^3 - 8*a*b^2*c^4 + 8*a^2*c^5)*d^8*x^3 + 480*(3*b^5*c^2 - 12*a*b^3*c^3 + 16*a^2*b*c^4)*d^8*x^2 - 30*(b^6*c - 60*a*b^4*c^2 + 304*a^2*b^2*c^3 - 448*a^3*c^4)*d^8*x - 15*(b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^8 - 420*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^8*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^8*x + (a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d^8)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(c*x^2 + b*x + a)]","B",0
1167,1,283,0,0.405043," ","integrate((2*c*d*x+b*d)^7/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{32 \, c^{6} d^{7} x^{6} + 96 \, b c^{5} d^{7} x^{5} + 48 \, {\left(3 \, b^{2} c^{4} - 2 \, a c^{5}\right)} d^{7} x^{4} + 64 \, {\left(2 \, b^{3} c^{3} - 3 \, a b c^{4}\right)} d^{7} x^{3} + 16 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{7} x^{2} + 16 \, {\left(3 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} d^{7} x - {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{7} + 12 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{7} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{7} x + {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d^{7}\right)} \log\left(c x^{2} + b x + a\right)}{c x^{2} + b x + a}"," ",0,"(32*c^6*d^7*x^6 + 96*b*c^5*d^7*x^5 + 48*(3*b^2*c^4 - 2*a*c^5)*d^7*x^4 + 64*(2*b^3*c^3 - 3*a*b*c^4)*d^7*x^3 + 16*(3*b^4*c^2 - 3*a*b^2*c^3 - 8*a^2*c^4)*d^7*x^2 + 16*(3*a*b^3*c^2 - 8*a^2*b*c^3)*d^7*x - (b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^7 + 12*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^7*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^7*x + (a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d^7)*log(c*x^2 + b*x + a))/(c*x^2 + b*x + a)","B",0
1168,1,504,0,0.430555," ","integrate((2*c*d*x+b*d)^6/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{64 \, c^{5} d^{6} x^{5} + 160 \, b c^{4} d^{6} x^{4} + 80 \, {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} x^{3} + 144 \, {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d^{6} x^{2} - 6 \, {\left(b^{4} c - 32 \, a b^{2} c^{2} + 80 \, a^{2} c^{3}\right)} d^{6} x - 3 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{6} - 30 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{6} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{6} x + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{6}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{3 \, {\left(c x^{2} + b x + a\right)}}, \frac{64 \, c^{5} d^{6} x^{5} + 160 \, b c^{4} d^{6} x^{4} + 80 \, {\left(3 \, b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} x^{3} + 144 \, {\left(b^{3} c^{2} - 2 \, a b c^{3}\right)} d^{6} x^{2} - 6 \, {\left(b^{4} c - 32 \, a b^{2} c^{2} + 80 \, a^{2} c^{3}\right)} d^{6} x - 3 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{6} - 60 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{6} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{6} x + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{6}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{3 \, {\left(c x^{2} + b x + a\right)}}\right]"," ",0,"[1/3*(64*c^5*d^6*x^5 + 160*b*c^4*d^6*x^4 + 80*(3*b^2*c^3 - 4*a*c^4)*d^6*x^3 + 144*(b^3*c^2 - 2*a*b*c^3)*d^6*x^2 - 6*(b^4*c - 32*a*b^2*c^2 + 80*a^2*c^3)*d^6*x - 3*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^6 - 30*((b^2*c^2 - 4*a*c^3)*d^6*x^2 + (b^3*c - 4*a*b*c^2)*d^6*x + (a*b^2*c - 4*a^2*c^2)*d^6)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(c*x^2 + b*x + a), 1/3*(64*c^5*d^6*x^5 + 160*b*c^4*d^6*x^4 + 80*(3*b^2*c^3 - 4*a*c^4)*d^6*x^3 + 144*(b^3*c^2 - 2*a*b*c^3)*d^6*x^2 - 6*(b^4*c - 32*a*b^2*c^2 + 80*a^2*c^3)*d^6*x - 3*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^6 - 60*((b^2*c^2 - 4*a*c^3)*d^6*x^2 + (b^3*c - 4*a*b*c^2)*d^6*x + (a*b^2*c - 4*a^2*c^2)*d^6)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(c*x^2 + b*x + a)]","B",0
1169,1,165,0,0.402979," ","integrate((2*c*d*x+b*d)^5/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{16 \, c^{4} d^{5} x^{4} + 32 \, b c^{3} d^{5} x^{3} + 16 \, a b c^{2} d^{5} x + 16 \, {\left(b^{2} c^{2} + a c^{3}\right)} d^{5} x^{2} - {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{5} + 8 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{5} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{5} x + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{5}\right)} \log\left(c x^{2} + b x + a\right)}{c x^{2} + b x + a}"," ",0,"(16*c^4*d^5*x^4 + 32*b*c^3*d^5*x^3 + 16*a*b*c^2*d^5*x + 16*(b^2*c^2 + a*c^3)*d^5*x^2 - (b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^5 + 8*((b^2*c^2 - 4*a*c^3)*d^5*x^2 + (b^3*c - 4*a*b*c^2)*d^5*x + (a*b^2*c - 4*a^2*c^2)*d^5)*log(c*x^2 + b*x + a))/(c*x^2 + b*x + a)","B",0
1170,1,297,0,0.398695," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{16 \, c^{3} d^{4} x^{3} + 16 \, b c^{2} d^{4} x^{2} - 2 \, {\left(b^{2} c - 12 \, a c^{2}\right)} d^{4} x - {\left(b^{3} - 4 \, a b c\right)} d^{4} + 6 \, {\left(c^{2} d^{4} x^{2} + b c d^{4} x + a c d^{4}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{c x^{2} + b x + a}, \frac{16 \, c^{3} d^{4} x^{3} + 16 \, b c^{2} d^{4} x^{2} - 2 \, {\left(b^{2} c - 12 \, a c^{2}\right)} d^{4} x - {\left(b^{3} - 4 \, a b c\right)} d^{4} - 12 \, {\left(c^{2} d^{4} x^{2} + b c d^{4} x + a c d^{4}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{c x^{2} + b x + a}\right]"," ",0,"[(16*c^3*d^4*x^3 + 16*b*c^2*d^4*x^2 - 2*(b^2*c - 12*a*c^2)*d^4*x - (b^3 - 4*a*b*c)*d^4 + 6*(c^2*d^4*x^2 + b*c*d^4*x + a*c*d^4)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(c*x^2 + b*x + a), (16*c^3*d^4*x^3 + 16*b*c^2*d^4*x^2 - 2*(b^2*c - 12*a*c^2)*d^4*x - (b^3 - 4*a*b*c)*d^4 - 12*(c^2*d^4*x^2 + b*c*d^4*x + a*c*d^4)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(c*x^2 + b*x + a)]","A",0
1171,1,64,0,0.401407," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(b^{2} - 4 \, a c\right)} d^{3} - 4 \, {\left(c^{2} d^{3} x^{2} + b c d^{3} x + a c d^{3}\right)} \log\left(c x^{2} + b x + a\right)}{c x^{2} + b x + a}"," ",0,"-((b^2 - 4*a*c)*d^3 - 4*(c^2*d^3*x^2 + b*c*d^3*x + a*c*d^3)*log(c*x^2 + b*x + a))/(c*x^2 + b*x + a)","A",0
1172,1,309,0,0.423301," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} x + {\left(b^{3} - 4 \, a b c\right)} d^{2} - 2 \, {\left(c^{2} d^{2} x^{2} + b c d^{2} x + a c d^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x}, -\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} x + {\left(b^{3} - 4 \, a b c\right)} d^{2} + 4 \, {\left(c^{2} d^{2} x^{2} + b c d^{2} x + a c d^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x}\right]"," ",0,"[-(2*(b^2*c - 4*a*c^2)*d^2*x + (b^3 - 4*a*b*c)*d^2 - 2*(c^2*d^2*x^2 + b*c*d^2*x + a*c*d^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x), -(2*(b^2*c - 4*a*c^2)*d^2*x + (b^3 - 4*a*b*c)*d^2 + 4*(c^2*d^2*x^2 + b*c*d^2*x + a*c*d^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)]","B",0
1173,1,15,0,0.396092," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{d}{c x^{2} + b x + a}"," ",0,"-d/(c*x^2 + b*x + a)","A",0
1174,1,141,0,0.396294," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{2} - 4 \, a c + 4 \, {\left(c^{2} x^{2} + b c x + a c\right)} \log\left(c x^{2} + b x + a\right) - 8 \, {\left(c^{2} x^{2} + b c x + a c\right)} \log\left(2 \, c x + b\right)}{{\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} d}"," ",0,"-(b^2 - 4*a*c + 4*(c^2*x^2 + b*c*x + a*c)*log(c*x^2 + b*x + a) - 8*(c^2*x^2 + b*c*x + a*c)*log(2*c*x + b))/((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*d)","A",0
1175,1,644,0,0.424399," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{b^{4} + 4 \, a b^{2} c - 32 \, a^{2} c^{2} + 12 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} - 6 \, {\left(2 \, c^{3} x^{3} + 3 \, b c^{2} x^{2} + a b c + {\left(b^{2} c + 2 \, a c^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 12 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x}{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)} d^{2} x^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2} x^{2} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} x + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d^{2}}, -\frac{b^{4} + 4 \, a b^{2} c - 32 \, a^{2} c^{2} + 12 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} - 12 \, {\left(2 \, c^{3} x^{3} + 3 \, b c^{2} x^{2} + a b c + {\left(b^{2} c + 2 \, a c^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 12 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x}{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)} d^{2} x^{3} + 3 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2} x^{2} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} x + {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d^{2}}\right]"," ",0,"[-(b^4 + 4*a*b^2*c - 32*a^2*c^2 + 12*(b^2*c^2 - 4*a*c^3)*x^2 - 6*(2*c^3*x^3 + 3*b*c^2*x^2 + a*b*c + (b^2*c + 2*a*c^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 12*(b^3*c - 4*a*b*c^2)*x)/(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*x^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2*x^2 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*x + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2), -(b^4 + 4*a*b^2*c - 32*a^2*c^2 + 12*(b^2*c^2 - 4*a*c^3)*x^2 - 12*(2*c^3*x^3 + 3*b*c^2*x^2 + a*b*c + (b^2*c + 2*a*c^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 12*(b^3*c - 4*a*b*c^2)*x)/(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*x^3 + 3*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2*x^2 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*x + (a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2)]","B",0
1176,1,409,0,0.406332," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\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 + 8 \, {\left(4 \, c^{4} x^{4} + 8 \, b c^{3} x^{3} + a b^{2} c + {\left(5 \, b^{2} c^{2} + 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c + 4 \, a b c^{2}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 16 \, {\left(4 \, c^{4} x^{4} + 8 \, b c^{3} x^{3} + a b^{2} c + {\left(5 \, b^{2} c^{2} + 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c + 4 \, a b c^{2}\right)} x\right)} \log\left(2 \, c x + b\right)}{4 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{3} x^{4} + 8 \, {\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)} d^{3} x^{3} + {\left(5 \, b^{8} c - 56 \, a b^{6} c^{2} + 192 \, a^{2} b^{4} c^{3} - 128 \, a^{3} b^{2} c^{4} - 256 \, a^{4} c^{5}\right)} d^{3} x^{2} + {\left(b^{9} - 8 \, a b^{7} c + 128 \, a^{3} b^{3} c^{3} - 256 \, a^{4} b c^{4}\right)} d^{3} x + {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} d^{3}}"," ",0,"-(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 + 8*(4*c^4*x^4 + 8*b*c^3*x^3 + a*b^2*c + (5*b^2*c^2 + 4*a*c^3)*x^2 + (b^3*c + 4*a*b*c^2)*x)*log(c*x^2 + b*x + a) - 16*(4*c^4*x^4 + 8*b*c^3*x^3 + a*b^2*c + (5*b^2*c^2 + 4*a*c^3)*x^2 + (b^3*c + 4*a*b*c^2)*x)*log(2*c*x + b))/(4*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^3*x^4 + 8*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3*x^3 + (5*b^8*c - 56*a*b^6*c^2 + 192*a^2*b^4*c^3 - 128*a^3*b^2*c^4 - 256*a^4*c^5)*d^3*x^2 + (b^9 - 8*a*b^7*c + 128*a^3*b^3*c^3 - 256*a^4*b*c^4)*d^3*x + (a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*d^3)","B",0
1177,1,1185,0,0.418525," ","integrate((2*c*d*x+b*d)^10/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{2048 \, c^{9} d^{10} x^{9} + 9216 \, b c^{8} d^{10} x^{8} + 1536 \, {\left(13 \, b^{2} c^{7} - 4 \, a c^{8}\right)} d^{10} x^{7} + 5376 \, {\left(5 \, b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{10} x^{6} + 5376 \, {\left(5 \, b^{4} c^{5} - 10 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} d^{10} x^{5} + 6400 \, {\left(3 \, b^{5} c^{4} - 10 \, a b^{3} c^{5} + 12 \, a^{2} b c^{6}\right)} d^{10} x^{4} + 20 \, {\left(303 \, b^{6} c^{3} - 436 \, a b^{4} c^{4} - 2736 \, a^{2} b^{2} c^{5} + 6720 \, a^{3} c^{6}\right)} d^{10} x^{3} - 10 \, {\left(51 \, b^{7} c^{2} - 1892 \, a b^{5} c^{3} + 9488 \, a^{2} b^{3} c^{4} - 14016 \, a^{3} b c^{5}\right)} d^{10} x^{2} - 20 \, {\left(9 \, b^{8} c - 93 \, a b^{6} c^{2} - 68 \, a^{2} b^{4} c^{3} + 2064 \, a^{3} b^{2} c^{4} - 4032 \, a^{4} c^{5}\right)} d^{10} x - 5 \, {\left(b^{9} + 18 \, a b^{7} c - 312 \, a^{2} b^{5} c^{2} + 1376 \, a^{3} b^{3} c^{3} - 1920 \, a^{4} b c^{4}\right)} d^{10} + 1260 \, {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{10} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{10} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} d^{10} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} d^{10} x + {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{10}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{10 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}, \frac{2048 \, c^{9} d^{10} x^{9} + 9216 \, b c^{8} d^{10} x^{8} + 1536 \, {\left(13 \, b^{2} c^{7} - 4 \, a c^{8}\right)} d^{10} x^{7} + 5376 \, {\left(5 \, b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{10} x^{6} + 5376 \, {\left(5 \, b^{4} c^{5} - 10 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} d^{10} x^{5} + 6400 \, {\left(3 \, b^{5} c^{4} - 10 \, a b^{3} c^{5} + 12 \, a^{2} b c^{6}\right)} d^{10} x^{4} + 20 \, {\left(303 \, b^{6} c^{3} - 436 \, a b^{4} c^{4} - 2736 \, a^{2} b^{2} c^{5} + 6720 \, a^{3} c^{6}\right)} d^{10} x^{3} - 10 \, {\left(51 \, b^{7} c^{2} - 1892 \, a b^{5} c^{3} + 9488 \, a^{2} b^{3} c^{4} - 14016 \, a^{3} b c^{5}\right)} d^{10} x^{2} - 20 \, {\left(9 \, b^{8} c - 93 \, a b^{6} c^{2} - 68 \, a^{2} b^{4} c^{3} + 2064 \, a^{3} b^{2} c^{4} - 4032 \, a^{4} c^{5}\right)} d^{10} x - 5 \, {\left(b^{9} + 18 \, a b^{7} c - 312 \, a^{2} b^{5} c^{2} + 1376 \, a^{3} b^{3} c^{3} - 1920 \, a^{4} b c^{4}\right)} d^{10} - 2520 \, {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{10} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{10} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} d^{10} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} d^{10} x + {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{10}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{10 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}\right]"," ",0,"[1/10*(2048*c^9*d^10*x^9 + 9216*b*c^8*d^10*x^8 + 1536*(13*b^2*c^7 - 4*a*c^8)*d^10*x^7 + 5376*(5*b^3*c^6 - 4*a*b*c^7)*d^10*x^6 + 5376*(5*b^4*c^5 - 10*a*b^2*c^6 + 8*a^2*c^7)*d^10*x^5 + 6400*(3*b^5*c^4 - 10*a*b^3*c^5 + 12*a^2*b*c^6)*d^10*x^4 + 20*(303*b^6*c^3 - 436*a*b^4*c^4 - 2736*a^2*b^2*c^5 + 6720*a^3*c^6)*d^10*x^3 - 10*(51*b^7*c^2 - 1892*a*b^5*c^3 + 9488*a^2*b^3*c^4 - 14016*a^3*b*c^5)*d^10*x^2 - 20*(9*b^8*c - 93*a*b^6*c^2 - 68*a^2*b^4*c^3 + 2064*a^3*b^2*c^4 - 4032*a^4*c^5)*d^10*x - 5*(b^9 + 18*a*b^7*c - 312*a^2*b^5*c^2 + 1376*a^3*b^3*c^3 - 1920*a^4*b*c^4)*d^10 + 1260*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^10*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^10*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*d^10*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*d^10*x + (a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^10)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), 1/10*(2048*c^9*d^10*x^9 + 9216*b*c^8*d^10*x^8 + 1536*(13*b^2*c^7 - 4*a*c^8)*d^10*x^7 + 5376*(5*b^3*c^6 - 4*a*b*c^7)*d^10*x^6 + 5376*(5*b^4*c^5 - 10*a*b^2*c^6 + 8*a^2*c^7)*d^10*x^5 + 6400*(3*b^5*c^4 - 10*a*b^3*c^5 + 12*a^2*b*c^6)*d^10*x^4 + 20*(303*b^6*c^3 - 436*a*b^4*c^4 - 2736*a^2*b^2*c^5 + 6720*a^3*c^6)*d^10*x^3 - 10*(51*b^7*c^2 - 1892*a*b^5*c^3 + 9488*a^2*b^3*c^4 - 14016*a^3*b*c^5)*d^10*x^2 - 20*(9*b^8*c - 93*a*b^6*c^2 - 68*a^2*b^4*c^3 + 2064*a^3*b^2*c^4 - 4032*a^4*c^5)*d^10*x - 5*(b^9 + 18*a*b^7*c - 312*a^2*b^5*c^2 + 1376*a^3*b^3*c^3 - 1920*a^4*b*c^4)*d^10 - 2520*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^10*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^10*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*d^10*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*d^10*x + (a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^10)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)]","B",0
1178,1,490,0,0.390875," ","integrate((2*c*d*x+b*d)^9/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{256 \, c^{8} d^{9} x^{8} + 1024 \, b c^{7} d^{9} x^{7} + 1024 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{9} x^{6} + 512 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{9} x^{5} + 256 \, {\left(7 \, b^{4} c^{4} - 8 \, a b^{2} c^{5} - 11 \, a^{2} c^{6}\right)} d^{9} x^{4} + 512 \, {\left(b^{5} c^{3} + 2 \, a b^{3} c^{4} - 11 \, a^{2} b c^{5}\right)} d^{9} x^{3} - 32 \, {\left(b^{6} c^{2} - 44 \, a b^{4} c^{3} + 120 \, a^{2} b^{2} c^{4} - 16 \, a^{3} c^{5}\right)} d^{9} x^{2} - 32 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 32 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b c^{4}\right)} d^{9} x - {\left(b^{8} + 16 \, a b^{6} c - 288 \, a^{2} b^{4} c^{2} + 1280 \, a^{3} b^{2} c^{3} - 1792 \, a^{4} c^{4}\right)} d^{9} + 192 \, {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{9} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{9} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} d^{9} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} d^{9} x + {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{9}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"1/2*(256*c^8*d^9*x^8 + 1024*b*c^7*d^9*x^7 + 1024*(2*b^2*c^6 - a*c^7)*d^9*x^6 + 512*(5*b^3*c^5 - 6*a*b*c^6)*d^9*x^5 + 256*(7*b^4*c^4 - 8*a*b^2*c^5 - 11*a^2*c^6)*d^9*x^4 + 512*(b^5*c^3 + 2*a*b^3*c^4 - 11*a^2*b*c^5)*d^9*x^3 - 32*(b^6*c^2 - 44*a*b^4*c^3 + 120*a^2*b^2*c^4 - 16*a^3*c^5)*d^9*x^2 - 32*(b^7*c - 12*a*b^5*c^2 + 32*a^2*b^3*c^3 - 16*a^3*b*c^4)*d^9*x - (b^8 + 16*a*b^6*c - 288*a^2*b^4*c^2 + 1280*a^3*b^2*c^3 - 1792*a^4*c^4)*d^9 + 192*((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^9*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^9*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*d^9*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*d^9*x + (a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^9)*log(c*x^2 + b*x + a))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1179,1,868,0,0.413861," ","integrate((2*c*d*x+b*d)^8/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{512 \, c^{7} d^{8} x^{7} + 1792 \, b c^{6} d^{8} x^{6} + 3584 \, {\left(b^{2} c^{5} - a c^{6}\right)} d^{8} x^{5} + 256 \, {\left(15 \, b^{3} c^{4} - 26 \, a b c^{5}\right)} d^{8} x^{4} + 4 \, {\left(345 \, b^{4} c^{3} + 312 \, a b^{2} c^{4} - 2800 \, a^{2} c^{5}\right)} d^{8} x^{3} - 6 \, {\left(39 \, b^{5} c^{2} - 824 \, a b^{3} c^{3} + 2032 \, a^{2} b c^{4}\right)} d^{8} x^{2} - 12 \, {\left(7 \, b^{6} c - 45 \, a b^{4} c^{2} - 104 \, a^{2} b^{2} c^{3} + 560 \, a^{3} c^{4}\right)} d^{8} x - 3 \, {\left(b^{7} + 14 \, a b^{5} c - 160 \, a^{2} b^{3} c^{2} + 352 \, a^{3} b c^{3}\right)} d^{8} - 420 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} x^{4} + 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{8} x^{3} + {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{8} x^{2} + 2 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{8} x + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{8}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{6 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}, \frac{512 \, c^{7} d^{8} x^{7} + 1792 \, b c^{6} d^{8} x^{6} + 3584 \, {\left(b^{2} c^{5} - a c^{6}\right)} d^{8} x^{5} + 256 \, {\left(15 \, b^{3} c^{4} - 26 \, a b c^{5}\right)} d^{8} x^{4} + 4 \, {\left(345 \, b^{4} c^{3} + 312 \, a b^{2} c^{4} - 2800 \, a^{2} c^{5}\right)} d^{8} x^{3} - 6 \, {\left(39 \, b^{5} c^{2} - 824 \, a b^{3} c^{3} + 2032 \, a^{2} b c^{4}\right)} d^{8} x^{2} - 12 \, {\left(7 \, b^{6} c - 45 \, a b^{4} c^{2} - 104 \, a^{2} b^{2} c^{3} + 560 \, a^{3} c^{4}\right)} d^{8} x - 3 \, {\left(b^{7} + 14 \, a b^{5} c - 160 \, a^{2} b^{3} c^{2} + 352 \, a^{3} b c^{3}\right)} d^{8} - 840 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{8} x^{4} + 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{8} x^{3} + {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{8} x^{2} + 2 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{8} x + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{8}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{6 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}\right]"," ",0,"[1/6*(512*c^7*d^8*x^7 + 1792*b*c^6*d^8*x^6 + 3584*(b^2*c^5 - a*c^6)*d^8*x^5 + 256*(15*b^3*c^4 - 26*a*b*c^5)*d^8*x^4 + 4*(345*b^4*c^3 + 312*a*b^2*c^4 - 2800*a^2*c^5)*d^8*x^3 - 6*(39*b^5*c^2 - 824*a*b^3*c^3 + 2032*a^2*b*c^4)*d^8*x^2 - 12*(7*b^6*c - 45*a*b^4*c^2 - 104*a^2*b^2*c^3 + 560*a^3*c^4)*d^8*x - 3*(b^7 + 14*a*b^5*c - 160*a^2*b^3*c^2 + 352*a^3*b*c^3)*d^8 - 420*((b^2*c^4 - 4*a*c^5)*d^8*x^4 + 2*(b^3*c^3 - 4*a*b*c^4)*d^8*x^3 + (b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*d^8*x^2 + 2*(a*b^3*c^2 - 4*a^2*b*c^3)*d^8*x + (a^2*b^2*c^2 - 4*a^3*c^3)*d^8)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), 1/6*(512*c^7*d^8*x^7 + 1792*b*c^6*d^8*x^6 + 3584*(b^2*c^5 - a*c^6)*d^8*x^5 + 256*(15*b^3*c^4 - 26*a*b*c^5)*d^8*x^4 + 4*(345*b^4*c^3 + 312*a*b^2*c^4 - 2800*a^2*c^5)*d^8*x^3 - 6*(39*b^5*c^2 - 824*a*b^3*c^3 + 2032*a^2*b*c^4)*d^8*x^2 - 12*(7*b^6*c - 45*a*b^4*c^2 - 104*a^2*b^2*c^3 + 560*a^3*c^4)*d^8*x - 3*(b^7 + 14*a*b^5*c - 160*a^2*b^3*c^2 + 352*a^3*b*c^3)*d^8 - 840*((b^2*c^4 - 4*a*c^5)*d^8*x^4 + 2*(b^3*c^3 - 4*a*b*c^4)*d^8*x^3 + (b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*d^8*x^2 + 2*(a*b^3*c^2 - 4*a^2*b*c^3)*d^8*x + (a^2*b^2*c^2 - 4*a^3*c^3)*d^8)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)]","B",0
1180,1,346,0,0.390307," ","integrate((2*c*d*x+b*d)^7/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{128 \, c^{6} d^{7} x^{6} + 384 \, b c^{5} d^{7} x^{5} + 128 \, {\left(3 \, b^{2} c^{4} + 2 \, a c^{5}\right)} d^{7} x^{4} + 128 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{7} x^{3} - 8 \, {\left(3 \, b^{4} c^{2} - 56 \, a b^{2} c^{3} + 32 \, a^{2} c^{4}\right)} d^{7} x^{2} - 8 \, {\left(3 \, b^{5} c - 24 \, a b^{3} c^{2} + 32 \, a^{2} b c^{3}\right)} d^{7} x - {\left(b^{6} + 12 \, a b^{4} c - 144 \, a^{2} b^{2} c^{2} + 320 \, a^{3} c^{3}\right)} d^{7} + 96 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{7} x^{4} + 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} x^{3} + {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d^{7} x^{2} + 2 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{7} x + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{7}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"1/2*(128*c^6*d^7*x^6 + 384*b*c^5*d^7*x^5 + 128*(3*b^2*c^4 + 2*a*c^5)*d^7*x^4 + 128*(b^3*c^3 + 4*a*b*c^4)*d^7*x^3 - 8*(3*b^4*c^2 - 56*a*b^2*c^3 + 32*a^2*c^4)*d^7*x^2 - 8*(3*b^5*c - 24*a*b^3*c^2 + 32*a^2*b*c^3)*d^7*x - (b^6 + 12*a*b^4*c - 144*a^2*b^2*c^2 + 320*a^3*c^3)*d^7 + 96*((b^2*c^4 - 4*a*c^5)*d^7*x^4 + 2*(b^3*c^3 - 4*a*b*c^4)*d^7*x^3 + (b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*d^7*x^2 + 2*(a*b^3*c^2 - 4*a^2*b*c^3)*d^7*x + (a^2*b^2*c^2 - 4*a^3*c^3)*d^7)*log(c*x^2 + b*x + a))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1181,1,571,0,0.402769," ","integrate((2*c*d*x+b*d)^6/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{128 \, c^{5} d^{6} x^{5} + 256 \, b c^{4} d^{6} x^{4} + 4 \, {\left(23 \, b^{2} c^{3} + 100 \, a c^{4}\right)} d^{6} x^{3} - 2 \, {\left(27 \, b^{3} c^{2} - 236 \, a b c^{3}\right)} d^{6} x^{2} - 4 \, {\left(5 \, b^{4} c - 13 \, a b^{2} c^{2} - 60 \, a^{2} c^{3}\right)} d^{6} x - {\left(b^{5} + 10 \, a b^{3} c - 56 \, a^{2} b c^{2}\right)} d^{6} + 60 \, {\left(c^{4} d^{6} x^{4} + 2 \, b c^{3} d^{6} x^{3} + 2 \, a b c^{2} d^{6} x + a^{2} c^{2} d^{6} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}, \frac{128 \, c^{5} d^{6} x^{5} + 256 \, b c^{4} d^{6} x^{4} + 4 \, {\left(23 \, b^{2} c^{3} + 100 \, a c^{4}\right)} d^{6} x^{3} - 2 \, {\left(27 \, b^{3} c^{2} - 236 \, a b c^{3}\right)} d^{6} x^{2} - 4 \, {\left(5 \, b^{4} c - 13 \, a b^{2} c^{2} - 60 \, a^{2} c^{3}\right)} d^{6} x - {\left(b^{5} + 10 \, a b^{3} c - 56 \, a^{2} b c^{2}\right)} d^{6} - 120 \, {\left(c^{4} d^{6} x^{4} + 2 \, b c^{3} d^{6} x^{3} + 2 \, a b c^{2} d^{6} x + a^{2} c^{2} d^{6} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}\right]"," ",0,"[1/2*(128*c^5*d^6*x^5 + 256*b*c^4*d^6*x^4 + 4*(23*b^2*c^3 + 100*a*c^4)*d^6*x^3 - 2*(27*b^3*c^2 - 236*a*b*c^3)*d^6*x^2 - 4*(5*b^4*c - 13*a*b^2*c^2 - 60*a^2*c^3)*d^6*x - (b^5 + 10*a*b^3*c - 56*a^2*b*c^2)*d^6 + 60*(c^4*d^6*x^4 + 2*b*c^3*d^6*x^3 + 2*a*b*c^2*d^6*x + a^2*c^2*d^6 + (b^2*c^2 + 2*a*c^3)*d^6*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), 1/2*(128*c^5*d^6*x^5 + 256*b*c^4*d^6*x^4 + 4*(23*b^2*c^3 + 100*a*c^4)*d^6*x^3 - 2*(27*b^3*c^2 - 236*a*b*c^3)*d^6*x^2 - 4*(5*b^4*c - 13*a*b^2*c^2 - 60*a^2*c^3)*d^6*x - (b^5 + 10*a*b^3*c - 56*a^2*b*c^2)*d^6 - 120*(c^4*d^6*x^4 + 2*b*c^3*d^6*x^3 + 2*a*b*c^2*d^6*x + a^2*c^2*d^6 + (b^2*c^2 + 2*a*c^3)*d^6*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)]","B",0
1182,1,182,0,0.395642," ","integrate((2*c*d*x+b*d)^5/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{5} x^{2} + 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{5} x + {\left(b^{4} + 8 \, a b^{2} c - 48 \, a^{2} c^{2}\right)} d^{5} - 32 \, {\left(c^{4} d^{5} x^{4} + 2 \, b c^{3} d^{5} x^{3} + 2 \, a b c^{2} d^{5} x + a^{2} c^{2} d^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} x^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"-1/2*(16*(b^2*c^2 - 4*a*c^3)*d^5*x^2 + 16*(b^3*c - 4*a*b*c^2)*d^5*x + (b^4 + 8*a*b^2*c - 48*a^2*c^2)*d^5 - 32*(c^4*d^5*x^4 + 2*b*c^3*d^5*x^3 + 2*a*b*c^2*d^5*x + a^2*c^2*d^5 + (b^2*c^2 + 2*a*c^3)*d^5*x^2)*log(c*x^2 + b*x + a))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1183,1,625,0,0.417114," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{20 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} x^{3} + 30 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} x^{2} + 12 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} x + {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{4} - 12 \, {\left(c^{4} d^{4} x^{4} + 2 \, b c^{3} d^{4} x^{3} + 2 \, a b c^{2} d^{4} x + a^{2} c^{2} d^{4} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)}}, -\frac{20 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} x^{3} + 30 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} x^{2} + 12 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} x + {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{4} + 24 \, {\left(c^{4} d^{4} x^{4} + 2 \, b c^{3} d^{4} x^{3} + 2 \, a b c^{2} d^{4} x + a^{2} c^{2} d^{4} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)}}\right]"," ",0,"[-1/2*(20*(b^2*c^3 - 4*a*c^4)*d^4*x^3 + 30*(b^3*c^2 - 4*a*b*c^3)*d^4*x^2 + 12*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*x + (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^4 - 12*(c^4*d^4*x^4 + 2*b*c^3*d^4*x^3 + 2*a*b*c^2*d^4*x + a^2*c^2*d^4 + (b^2*c^2 + 2*a*c^3)*d^4*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x), -1/2*(20*(b^2*c^3 - 4*a*c^4)*d^4*x^3 + 30*(b^3*c^2 - 4*a*b*c^3)*d^4*x^2 + 12*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*x + (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^4 + 24*(c^4*d^4*x^4 + 2*b*c^3*d^4*x^3 + 2*a*b*c^2*d^4*x + a^2*c^2*d^4 + (b^2*c^2 + 2*a*c^3)*d^4*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)]","B",0
1184,1,71,0,0.377543," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{8 \, c^{2} d^{3} x^{2} + 8 \, b c d^{3} x + {\left(b^{2} + 4 \, a c\right)} d^{3}}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"-1/2*(8*c^2*d^3*x^2 + 8*b*c*d^3*x + (b^2 + 4*a*c)*d^3)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1185,1,713,0,0.430120," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} x^{3} + 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} x^{2} + 4 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} x + {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d^{2} + 4 \, {\left(c^{4} d^{2} x^{4} + 2 \, b c^{3} d^{2} x^{3} + 2 \, a b c^{2} d^{2} x + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{2 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}, -\frac{4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} x^{3} + 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} x^{2} + 4 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} x + {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d^{2} - 8 \, {\left(c^{4} d^{2} x^{4} + 2 \, b c^{3} d^{2} x^{3} + 2 \, a b c^{2} d^{2} x + a^{2} c^{2} d^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{2 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}\right]"," ",0,"[-1/2*(4*(b^2*c^3 - 4*a*c^4)*d^2*x^3 + 6*(b^3*c^2 - 4*a*b*c^3)*d^2*x^2 + 4*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*x + (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d^2 + 4*(c^4*d^2*x^4 + 2*b*c^3*d^2*x^3 + 2*a*b*c^2*d^2*x + a^2*c^2*d^2 + (b^2*c^2 + 2*a*c^3)*d^2*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x), -1/2*(4*(b^2*c^3 - 4*a*c^4)*d^2*x^3 + 6*(b^3*c^2 - 4*a*b*c^3)*d^2*x^2 + 4*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*x + (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d^2 - 8*(c^4*d^2*x^4 + 2*b*c^3*d^2*x^3 + 2*a*b*c^2*d^2*x + a^2*c^2*d^2 + (b^2*c^2 + 2*a*c^3)*d^2*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)]","B",0
1186,1,40,0,0.381498," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{d}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"-1/2*d/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1187,1,386,0,0.399215," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\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 - 32 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{3} + 2 \, a b c^{2} x + a^{2} c^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{2}\right)} \log\left(c x^{2} + b x + a\right) + 64 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{3} + 2 \, a b c^{2} x + a^{2} c^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{2}\right)} \log\left(2 \, c x + b\right)}{2 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d\right)}}"," ",0,"-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 - 32*(c^4*x^4 + 2*b*c^3*x^3 + 2*a*b*c^2*x + a^2*c^2 + (b^2*c^2 + 2*a*c^3)*x^2)*log(c*x^2 + b*x + a) + 64*(c^4*x^4 + 2*b*c^3*x^3 + 2*a*b*c^2*x + a^2*c^2 + (b^2*c^2 + 2*a*c^3)*x^2)*log(2*c*x + b))/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*d)","B",0
1188,1,1170,0,0.420059," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{b^{6} - 22 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3} - 120 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} - 240 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3} - 10 \, {\left(13 \, b^{4} c^{2} - 32 \, a b^{2} c^{3} - 80 \, a^{2} c^{4}\right)} x^{2} + 60 \, {\left(2 \, c^{5} x^{5} + 5 \, b c^{4} x^{4} + a^{2} b c^{2} + 4 \, {\left(b^{2} c^{3} + a c^{4}\right)} x^{3} + {\left(b^{3} c^{2} + 6 \, a b c^{3}\right)} x^{2} + 2 \, {\left(a b^{2} c^{2} + a^{2} c^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 10 \, {\left(b^{5} c + 16 \, a b^{3} c^{2} - 80 \, a^{2} b c^{3}\right)} x}{2 \, {\left(2 \, {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} d^{2} x^{5} + 5 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} d^{2} x^{4} + 4 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} d^{2} x^{3} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} d^{2} x^{2} + 2 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} d^{2} x + {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} d^{2}\right)}}, -\frac{b^{6} - 22 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3} - 120 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} - 240 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3} - 10 \, {\left(13 \, b^{4} c^{2} - 32 \, a b^{2} c^{3} - 80 \, a^{2} c^{4}\right)} x^{2} + 120 \, {\left(2 \, c^{5} x^{5} + 5 \, b c^{4} x^{4} + a^{2} b c^{2} + 4 \, {\left(b^{2} c^{3} + a c^{4}\right)} x^{3} + {\left(b^{3} c^{2} + 6 \, a b c^{3}\right)} x^{2} + 2 \, {\left(a b^{2} c^{2} + a^{2} c^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 10 \, {\left(b^{5} c + 16 \, a b^{3} c^{2} - 80 \, a^{2} b c^{3}\right)} x}{2 \, {\left(2 \, {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} d^{2} x^{5} + 5 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} d^{2} x^{4} + 4 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} d^{2} x^{3} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} d^{2} x^{2} + 2 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} d^{2} x + {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} d^{2}\right)}}\right]"," ",0,"[-1/2*(b^6 - 22*a*b^4*c + 8*a^2*b^2*c^2 + 256*a^3*c^3 - 120*(b^2*c^4 - 4*a*c^5)*x^4 - 240*(b^3*c^3 - 4*a*b*c^4)*x^3 - 10*(13*b^4*c^2 - 32*a*b^2*c^3 - 80*a^2*c^4)*x^2 + 60*(2*c^5*x^5 + 5*b*c^4*x^4 + a^2*b*c^2 + 4*(b^2*c^3 + a*c^4)*x^3 + (b^3*c^2 + 6*a*b*c^3)*x^2 + 2*(a*b^2*c^2 + a^2*c^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 10*(b^5*c + 16*a*b^3*c^2 - 80*a^2*b*c^3)*x)/(2*(b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*d^2*x^5 + 5*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*d^2*x^4 + 4*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*d^2*x^3 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*d^2*x^2 + 2*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*d^2*x + (a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*d^2), -1/2*(b^6 - 22*a*b^4*c + 8*a^2*b^2*c^2 + 256*a^3*c^3 - 120*(b^2*c^4 - 4*a*c^5)*x^4 - 240*(b^3*c^3 - 4*a*b*c^4)*x^3 - 10*(13*b^4*c^2 - 32*a*b^2*c^3 - 80*a^2*c^4)*x^2 + 120*(2*c^5*x^5 + 5*b*c^4*x^4 + a^2*b*c^2 + 4*(b^2*c^3 + a*c^4)*x^3 + (b^3*c^2 + 6*a*b*c^3)*x^2 + 2*(a*b^2*c^2 + a^2*c^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 10*(b^5*c + 16*a*b^3*c^2 - 80*a^2*b*c^3)*x)/(2*(b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*d^2*x^5 + 5*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*d^2*x^4 + 4*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*d^2*x^3 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*d^2*x^2 + 2*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*d^2*x + (a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*d^2)]","B",0
1189,1,809,0,0.426898," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{b^{6} - 24 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 128 \, a^{3} c^{3} - 96 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{4} - 192 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{3} - 36 \, {\left(3 \, b^{4} c^{2} - 8 \, a b^{2} c^{3} - 16 \, a^{2} c^{4}\right)} x^{2} - 12 \, {\left(b^{5} c + 8 \, a b^{3} c^{2} - 48 \, a^{2} b c^{3}\right)} x - 96 \, {\left(4 \, c^{6} x^{6} + 12 \, b c^{5} x^{5} + a^{2} b^{2} c^{2} + {\left(13 \, b^{2} c^{4} + 8 \, a c^{5}\right)} x^{4} + 2 \, {\left(3 \, b^{3} c^{3} + 8 \, a b c^{4}\right)} x^{3} + {\left(b^{4} c^{2} + 10 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 192 \, {\left(4 \, c^{6} x^{6} + 12 \, b c^{5} x^{5} + a^{2} b^{2} c^{2} + {\left(13 \, b^{2} c^{4} + 8 \, a c^{5}\right)} x^{4} + 2 \, {\left(3 \, b^{3} c^{3} + 8 \, a b c^{4}\right)} x^{3} + {\left(b^{4} c^{2} + 10 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} x\right)} \log\left(2 \, c x + b\right)}{2 \, {\left(4 \, {\left(b^{8} c^{4} - 16 \, a b^{6} c^{5} + 96 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} + 256 \, a^{4} c^{8}\right)} d^{3} x^{6} + 12 \, {\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} d^{3} x^{5} + {\left(13 \, b^{10} c^{2} - 200 \, a b^{8} c^{3} + 1120 \, a^{2} b^{6} c^{4} - 2560 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} + 2048 \, a^{5} c^{7}\right)} d^{3} x^{4} + 2 \, {\left(3 \, b^{11} c - 40 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 1280 \, a^{4} b^{3} c^{5} + 2048 \, a^{5} b c^{6}\right)} d^{3} x^{3} + {\left(b^{12} - 6 \, a b^{10} c - 60 \, a^{2} b^{8} c^{2} + 640 \, a^{3} b^{6} c^{3} - 1920 \, a^{4} b^{4} c^{4} + 1536 \, a^{5} b^{2} c^{5} + 1024 \, a^{6} c^{6}\right)} d^{3} x^{2} + 2 \, {\left(a b^{11} - 14 \, a^{2} b^{9} c + 64 \, a^{3} b^{7} c^{2} - 64 \, a^{4} b^{5} c^{3} - 256 \, a^{5} b^{3} c^{4} + 512 \, a^{6} b c^{5}\right)} d^{3} x + {\left(a^{2} b^{10} - 16 \, a^{3} b^{8} c + 96 \, a^{4} b^{6} c^{2} - 256 \, a^{5} b^{4} c^{3} + 256 \, a^{6} b^{2} c^{4}\right)} d^{3}\right)}}"," ",0,"-1/2*(b^6 - 24*a*b^4*c + 48*a^2*b^2*c^2 + 128*a^3*c^3 - 96*(b^2*c^4 - 4*a*c^5)*x^4 - 192*(b^3*c^3 - 4*a*b*c^4)*x^3 - 36*(3*b^4*c^2 - 8*a*b^2*c^3 - 16*a^2*c^4)*x^2 - 12*(b^5*c + 8*a*b^3*c^2 - 48*a^2*b*c^3)*x - 96*(4*c^6*x^6 + 12*b*c^5*x^5 + a^2*b^2*c^2 + (13*b^2*c^4 + 8*a*c^5)*x^4 + 2*(3*b^3*c^3 + 8*a*b*c^4)*x^3 + (b^4*c^2 + 10*a*b^2*c^3 + 4*a^2*c^4)*x^2 + 2*(a*b^3*c^2 + 2*a^2*b*c^3)*x)*log(c*x^2 + b*x + a) + 192*(4*c^6*x^6 + 12*b*c^5*x^5 + a^2*b^2*c^2 + (13*b^2*c^4 + 8*a*c^5)*x^4 + 2*(3*b^3*c^3 + 8*a*b*c^4)*x^3 + (b^4*c^2 + 10*a*b^2*c^3 + 4*a^2*c^4)*x^2 + 2*(a*b^3*c^2 + 2*a^2*b*c^3)*x)*log(2*c*x + b))/(4*(b^8*c^4 - 16*a*b^6*c^5 + 96*a^2*b^4*c^6 - 256*a^3*b^2*c^7 + 256*a^4*c^8)*d^3*x^6 + 12*(b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*d^3*x^5 + (13*b^10*c^2 - 200*a*b^8*c^3 + 1120*a^2*b^6*c^4 - 2560*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 + 2048*a^5*c^7)*d^3*x^4 + 2*(3*b^11*c - 40*a*b^9*c^2 + 160*a^2*b^7*c^3 - 1280*a^4*b^3*c^5 + 2048*a^5*b*c^6)*d^3*x^3 + (b^12 - 6*a*b^10*c - 60*a^2*b^8*c^2 + 640*a^3*b^6*c^3 - 1920*a^4*b^4*c^4 + 1536*a^5*b^2*c^5 + 1024*a^6*c^6)*d^3*x^2 + 2*(a*b^11 - 14*a^2*b^9*c + 64*a^3*b^7*c^2 - 64*a^4*b^5*c^3 - 256*a^5*b^3*c^4 + 512*a^6*b*c^5)*d^3*x + (a^2*b^10 - 16*a^3*b^8*c + 96*a^4*b^6*c^2 - 256*a^5*b^4*c^3 + 256*a^6*b^2*c^4)*d^3)","B",0
1190,1,2077,0,0.446061," ","integrate(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{3 \, b^{8} - 90 \, a b^{6} c - 328 \, a^{2} b^{4} c^{2} + 2816 \, a^{3} b^{2} c^{3} - 1024 \, a^{4} c^{4} - 3360 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} x^{6} - 10080 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} x^{5} - 5600 \, {\left(2 \, b^{4} c^{4} - 7 \, a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} x^{4} - 5600 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} x^{3} - 14 \, {\left(83 \, b^{6} c^{2} + 204 \, a b^{4} c^{3} - 2016 \, a^{2} b^{2} c^{4} - 512 \, a^{3} c^{5}\right)} x^{2} - 420 \, {\left(8 \, c^{7} x^{7} + 28 \, b c^{6} x^{6} + a^{2} b^{3} c^{2} + 2 \, {\left(19 \, b^{2} c^{5} + 8 \, a c^{6}\right)} x^{5} + 5 \, {\left(5 \, b^{3} c^{4} + 8 \, a b c^{5}\right)} x^{4} + 4 \, {\left(2 \, b^{4} c^{3} + 9 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} x^{3} + {\left(b^{5} c^{2} + 14 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} x^{2} + 2 \, {\left(a b^{4} c^{2} + 3 \, a^{2} b^{2} c^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 14 \, {\left(3 \, b^{7} c + 124 \, a b^{5} c^{2} - 416 \, a^{2} b^{3} c^{3} - 512 \, a^{3} b c^{4}\right)} x}{6 \, {\left(8 \, {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} d^{4} x^{7} + 28 \, {\left(b^{11} c^{4} - 20 \, a b^{9} c^{5} + 160 \, a^{2} b^{7} c^{6} - 640 \, a^{3} b^{5} c^{7} + 1280 \, a^{4} b^{3} c^{8} - 1024 \, a^{5} b c^{9}\right)} d^{4} x^{6} + 2 \, {\left(19 \, b^{12} c^{3} - 372 \, a b^{10} c^{4} + 2880 \, a^{2} b^{8} c^{5} - 10880 \, a^{3} b^{6} c^{6} + 19200 \, a^{4} b^{4} c^{7} - 9216 \, a^{5} b^{2} c^{8} - 8192 \, a^{6} c^{9}\right)} d^{4} x^{5} + 5 \, {\left(5 \, b^{13} c^{2} - 92 \, a b^{11} c^{3} + 640 \, a^{2} b^{9} c^{4} - 1920 \, a^{3} b^{7} c^{5} + 1280 \, a^{4} b^{5} c^{6} + 5120 \, a^{5} b^{3} c^{7} - 8192 \, a^{6} b c^{8}\right)} d^{4} x^{4} + 4 \, {\left(2 \, b^{14} c - 31 \, a b^{12} c^{2} + 142 \, a^{2} b^{10} c^{3} + 120 \, a^{3} b^{8} c^{4} - 2880 \, a^{4} b^{6} c^{5} + 8192 \, a^{5} b^{4} c^{6} - 6656 \, a^{6} b^{2} c^{7} - 2048 \, a^{7} c^{8}\right)} d^{4} x^{3} + {\left(b^{15} - 6 \, a b^{13} c - 108 \, a^{2} b^{11} c^{2} + 1360 \, a^{3} b^{9} c^{3} - 5760 \, a^{4} b^{7} c^{4} + 9216 \, a^{5} b^{5} c^{5} + 1024 \, a^{6} b^{3} c^{6} - 12288 \, a^{7} b c^{7}\right)} d^{4} x^{2} + 2 \, {\left(a b^{14} - 17 \, a^{2} b^{12} c + 100 \, a^{3} b^{10} c^{2} - 160 \, a^{4} b^{8} c^{3} - 640 \, a^{5} b^{6} c^{4} + 2816 \, a^{6} b^{4} c^{5} - 3072 \, a^{7} b^{2} c^{6}\right)} d^{4} x + {\left(a^{2} b^{13} - 20 \, a^{3} b^{11} c + 160 \, a^{4} b^{9} c^{2} - 640 \, a^{5} b^{7} c^{3} + 1280 \, a^{6} b^{5} c^{4} - 1024 \, a^{7} b^{3} c^{5}\right)} d^{4}\right)}}, -\frac{3 \, b^{8} - 90 \, a b^{6} c - 328 \, a^{2} b^{4} c^{2} + 2816 \, a^{3} b^{2} c^{3} - 1024 \, a^{4} c^{4} - 3360 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} x^{6} - 10080 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} x^{5} - 5600 \, {\left(2 \, b^{4} c^{4} - 7 \, a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} x^{4} - 5600 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} x^{3} - 14 \, {\left(83 \, b^{6} c^{2} + 204 \, a b^{4} c^{3} - 2016 \, a^{2} b^{2} c^{4} - 512 \, a^{3} c^{5}\right)} x^{2} + 840 \, {\left(8 \, c^{7} x^{7} + 28 \, b c^{6} x^{6} + a^{2} b^{3} c^{2} + 2 \, {\left(19 \, b^{2} c^{5} + 8 \, a c^{6}\right)} x^{5} + 5 \, {\left(5 \, b^{3} c^{4} + 8 \, a b c^{5}\right)} x^{4} + 4 \, {\left(2 \, b^{4} c^{3} + 9 \, a b^{2} c^{4} + 2 \, a^{2} c^{5}\right)} x^{3} + {\left(b^{5} c^{2} + 14 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} x^{2} + 2 \, {\left(a b^{4} c^{2} + 3 \, a^{2} b^{2} c^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 14 \, {\left(3 \, b^{7} c + 124 \, a b^{5} c^{2} - 416 \, a^{2} b^{3} c^{3} - 512 \, a^{3} b c^{4}\right)} x}{6 \, {\left(8 \, {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} d^{4} x^{7} + 28 \, {\left(b^{11} c^{4} - 20 \, a b^{9} c^{5} + 160 \, a^{2} b^{7} c^{6} - 640 \, a^{3} b^{5} c^{7} + 1280 \, a^{4} b^{3} c^{8} - 1024 \, a^{5} b c^{9}\right)} d^{4} x^{6} + 2 \, {\left(19 \, b^{12} c^{3} - 372 \, a b^{10} c^{4} + 2880 \, a^{2} b^{8} c^{5} - 10880 \, a^{3} b^{6} c^{6} + 19200 \, a^{4} b^{4} c^{7} - 9216 \, a^{5} b^{2} c^{8} - 8192 \, a^{6} c^{9}\right)} d^{4} x^{5} + 5 \, {\left(5 \, b^{13} c^{2} - 92 \, a b^{11} c^{3} + 640 \, a^{2} b^{9} c^{4} - 1920 \, a^{3} b^{7} c^{5} + 1280 \, a^{4} b^{5} c^{6} + 5120 \, a^{5} b^{3} c^{7} - 8192 \, a^{6} b c^{8}\right)} d^{4} x^{4} + 4 \, {\left(2 \, b^{14} c - 31 \, a b^{12} c^{2} + 142 \, a^{2} b^{10} c^{3} + 120 \, a^{3} b^{8} c^{4} - 2880 \, a^{4} b^{6} c^{5} + 8192 \, a^{5} b^{4} c^{6} - 6656 \, a^{6} b^{2} c^{7} - 2048 \, a^{7} c^{8}\right)} d^{4} x^{3} + {\left(b^{15} - 6 \, a b^{13} c - 108 \, a^{2} b^{11} c^{2} + 1360 \, a^{3} b^{9} c^{3} - 5760 \, a^{4} b^{7} c^{4} + 9216 \, a^{5} b^{5} c^{5} + 1024 \, a^{6} b^{3} c^{6} - 12288 \, a^{7} b c^{7}\right)} d^{4} x^{2} + 2 \, {\left(a b^{14} - 17 \, a^{2} b^{12} c + 100 \, a^{3} b^{10} c^{2} - 160 \, a^{4} b^{8} c^{3} - 640 \, a^{5} b^{6} c^{4} + 2816 \, a^{6} b^{4} c^{5} - 3072 \, a^{7} b^{2} c^{6}\right)} d^{4} x + {\left(a^{2} b^{13} - 20 \, a^{3} b^{11} c + 160 \, a^{4} b^{9} c^{2} - 640 \, a^{5} b^{7} c^{3} + 1280 \, a^{6} b^{5} c^{4} - 1024 \, a^{7} b^{3} c^{5}\right)} d^{4}\right)}}\right]"," ",0,"[-1/6*(3*b^8 - 90*a*b^6*c - 328*a^2*b^4*c^2 + 2816*a^3*b^2*c^3 - 1024*a^4*c^4 - 3360*(b^2*c^6 - 4*a*c^7)*x^6 - 10080*(b^3*c^5 - 4*a*b*c^6)*x^5 - 5600*(2*b^4*c^4 - 7*a*b^2*c^5 - 4*a^2*c^6)*x^4 - 5600*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*x^3 - 14*(83*b^6*c^2 + 204*a*b^4*c^3 - 2016*a^2*b^2*c^4 - 512*a^3*c^5)*x^2 - 420*(8*c^7*x^7 + 28*b*c^6*x^6 + a^2*b^3*c^2 + 2*(19*b^2*c^5 + 8*a*c^6)*x^5 + 5*(5*b^3*c^4 + 8*a*b*c^5)*x^4 + 4*(2*b^4*c^3 + 9*a*b^2*c^4 + 2*a^2*c^5)*x^3 + (b^5*c^2 + 14*a*b^3*c^3 + 12*a^2*b*c^4)*x^2 + 2*(a*b^4*c^2 + 3*a^2*b^2*c^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 14*(3*b^7*c + 124*a*b^5*c^2 - 416*a^2*b^3*c^3 - 512*a^3*b*c^4)*x)/(8*(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*d^4*x^7 + 28*(b^11*c^4 - 20*a*b^9*c^5 + 160*a^2*b^7*c^6 - 640*a^3*b^5*c^7 + 1280*a^4*b^3*c^8 - 1024*a^5*b*c^9)*d^4*x^6 + 2*(19*b^12*c^3 - 372*a*b^10*c^4 + 2880*a^2*b^8*c^5 - 10880*a^3*b^6*c^6 + 19200*a^4*b^4*c^7 - 9216*a^5*b^2*c^8 - 8192*a^6*c^9)*d^4*x^5 + 5*(5*b^13*c^2 - 92*a*b^11*c^3 + 640*a^2*b^9*c^4 - 1920*a^3*b^7*c^5 + 1280*a^4*b^5*c^6 + 5120*a^5*b^3*c^7 - 8192*a^6*b*c^8)*d^4*x^4 + 4*(2*b^14*c - 31*a*b^12*c^2 + 142*a^2*b^10*c^3 + 120*a^3*b^8*c^4 - 2880*a^4*b^6*c^5 + 8192*a^5*b^4*c^6 - 6656*a^6*b^2*c^7 - 2048*a^7*c^8)*d^4*x^3 + (b^15 - 6*a*b^13*c - 108*a^2*b^11*c^2 + 1360*a^3*b^9*c^3 - 5760*a^4*b^7*c^4 + 9216*a^5*b^5*c^5 + 1024*a^6*b^3*c^6 - 12288*a^7*b*c^7)*d^4*x^2 + 2*(a*b^14 - 17*a^2*b^12*c + 100*a^3*b^10*c^2 - 160*a^4*b^8*c^3 - 640*a^5*b^6*c^4 + 2816*a^6*b^4*c^5 - 3072*a^7*b^2*c^6)*d^4*x + (a^2*b^13 - 20*a^3*b^11*c + 160*a^4*b^9*c^2 - 640*a^5*b^7*c^3 + 1280*a^6*b^5*c^4 - 1024*a^7*b^3*c^5)*d^4), -1/6*(3*b^8 - 90*a*b^6*c - 328*a^2*b^4*c^2 + 2816*a^3*b^2*c^3 - 1024*a^4*c^4 - 3360*(b^2*c^6 - 4*a*c^7)*x^6 - 10080*(b^3*c^5 - 4*a*b*c^6)*x^5 - 5600*(2*b^4*c^4 - 7*a*b^2*c^5 - 4*a^2*c^6)*x^4 - 5600*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*x^3 - 14*(83*b^6*c^2 + 204*a*b^4*c^3 - 2016*a^2*b^2*c^4 - 512*a^3*c^5)*x^2 + 840*(8*c^7*x^7 + 28*b*c^6*x^6 + a^2*b^3*c^2 + 2*(19*b^2*c^5 + 8*a*c^6)*x^5 + 5*(5*b^3*c^4 + 8*a*b*c^5)*x^4 + 4*(2*b^4*c^3 + 9*a*b^2*c^4 + 2*a^2*c^5)*x^3 + (b^5*c^2 + 14*a*b^3*c^3 + 12*a^2*b*c^4)*x^2 + 2*(a*b^4*c^2 + 3*a^2*b^2*c^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 14*(3*b^7*c + 124*a*b^5*c^2 - 416*a^2*b^3*c^3 - 512*a^3*b*c^4)*x)/(8*(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*d^4*x^7 + 28*(b^11*c^4 - 20*a*b^9*c^5 + 160*a^2*b^7*c^6 - 640*a^3*b^5*c^7 + 1280*a^4*b^3*c^8 - 1024*a^5*b*c^9)*d^4*x^6 + 2*(19*b^12*c^3 - 372*a*b^10*c^4 + 2880*a^2*b^8*c^5 - 10880*a^3*b^6*c^6 + 19200*a^4*b^4*c^7 - 9216*a^5*b^2*c^8 - 8192*a^6*c^9)*d^4*x^5 + 5*(5*b^13*c^2 - 92*a*b^11*c^3 + 640*a^2*b^9*c^4 - 1920*a^3*b^7*c^5 + 1280*a^4*b^5*c^6 + 5120*a^5*b^3*c^7 - 8192*a^6*b*c^8)*d^4*x^4 + 4*(2*b^14*c - 31*a*b^12*c^2 + 142*a^2*b^10*c^3 + 120*a^3*b^8*c^4 - 2880*a^4*b^6*c^5 + 8192*a^5*b^4*c^6 - 6656*a^6*b^2*c^7 - 2048*a^7*c^8)*d^4*x^3 + (b^15 - 6*a*b^13*c - 108*a^2*b^11*c^2 + 1360*a^3*b^9*c^3 - 5760*a^4*b^7*c^4 + 9216*a^5*b^5*c^5 + 1024*a^6*b^3*c^6 - 12288*a^7*b*c^7)*d^4*x^2 + 2*(a*b^14 - 17*a^2*b^12*c + 100*a^3*b^10*c^2 - 160*a^4*b^8*c^3 - 640*a^5*b^6*c^4 + 2816*a^6*b^4*c^5 - 3072*a^7*b^2*c^6)*d^4*x + (a^2*b^13 - 20*a^3*b^11*c + 160*a^4*b^9*c^2 - 640*a^5*b^7*c^3 + 1280*a^6*b^5*c^4 - 1024*a^7*b^3*c^5)*d^4)]","B",0
1191,1,473,0,0.456136," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{c} d^{4} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(256 \, c^{6} d^{4} x^{5} + 640 \, b c^{5} d^{4} x^{4} + 16 \, {\left(39 \, b^{2} c^{4} + 4 \, a c^{5}\right)} d^{4} x^{3} + 8 \, {\left(37 \, b^{3} c^{3} + 12 \, a b c^{4}\right)} d^{4} x^{2} + 2 \, {\left(31 \, b^{4} c^{2} + 48 \, a b^{2} c^{3} - 48 \, a^{2} c^{4}\right)} d^{4} x + {\left(3 \, b^{5} c + 32 \, a b^{3} c^{2} - 48 \, a^{2} b c^{3}\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{2}}, \frac{3 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-c} d^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(256 \, c^{6} d^{4} x^{5} + 640 \, b c^{5} d^{4} x^{4} + 16 \, {\left(39 \, b^{2} c^{4} + 4 \, a c^{5}\right)} d^{4} x^{3} + 8 \, {\left(37 \, b^{3} c^{3} + 12 \, a b c^{4}\right)} d^{4} x^{2} + 2 \, {\left(31 \, b^{4} c^{2} + 48 \, a b^{2} c^{3} - 48 \, a^{2} c^{4}\right)} d^{4} x + {\left(3 \, b^{5} c + 32 \, a b^{3} c^{2} - 48 \, a^{2} b c^{3}\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}}{192 \, c^{2}}\right]"," ",0,"[-1/384*(3*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(c)*d^4*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(256*c^6*d^4*x^5 + 640*b*c^5*d^4*x^4 + 16*(39*b^2*c^4 + 4*a*c^5)*d^4*x^3 + 8*(37*b^3*c^3 + 12*a*b*c^4)*d^4*x^2 + 2*(31*b^4*c^2 + 48*a*b^2*c^3 - 48*a^2*c^4)*d^4*x + (3*b^5*c + 32*a*b^3*c^2 - 48*a^2*b*c^3)*d^4)*sqrt(c*x^2 + b*x + a))/c^2, 1/192*(3*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-c)*d^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(256*c^6*d^4*x^5 + 640*b*c^5*d^4*x^4 + 16*(39*b^2*c^4 + 4*a*c^5)*d^4*x^3 + 8*(37*b^3*c^3 + 12*a*b*c^4)*d^4*x^2 + 2*(31*b^4*c^2 + 48*a*b^2*c^3 - 48*a^2*c^4)*d^4*x + (3*b^5*c + 32*a*b^3*c^2 - 48*a^2*b*c^3)*d^4)*sqrt(c*x^2 + b*x + a))/c^2]","A",0
1192,1,91,0,0.415437," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(12 \, c^{3} d^{3} x^{4} + 24 \, b c^{2} d^{3} x^{3} + {\left(17 \, b^{2} c + 4 \, a c^{2}\right)} d^{3} x^{2} + {\left(5 \, b^{3} + 4 \, a b c\right)} d^{3} x + {\left(5 \, a b^{2} - 8 \, a^{2} c\right)} d^{3}\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/15*(12*c^3*d^3*x^4 + 24*b*c^2*d^3*x^3 + (17*b^2*c + 4*a*c^2)*d^3*x^2 + (5*b^3 + 4*a*b*c)*d^3*x + (5*a*b^2 - 8*a^2*c)*d^3)*sqrt(c*x^2 + b*x + a)","A",0
1193,1,309,0,0.440367," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{c} d^{2} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(16 \, c^{4} d^{2} x^{3} + 24 \, b c^{3} d^{2} x^{2} + 2 \, {\left(5 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{2} x + {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{2}\right)} \sqrt{c x^{2} + b x + a}}{64 \, c^{2}}, \frac{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} d^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(16 \, c^{4} d^{2} x^{3} + 24 \, b c^{3} d^{2} x^{2} + 2 \, {\left(5 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{2} x + {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{2}\right)} \sqrt{c x^{2} + b x + a}}{32 \, c^{2}}\right]"," ",0,"[1/64*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(c)*d^2*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(16*c^4*d^2*x^3 + 24*b*c^3*d^2*x^2 + 2*(5*b^2*c^2 + 4*a*c^3)*d^2*x + (b^3*c + 4*a*b*c^2)*d^2)*sqrt(c*x^2 + b*x + a))/c^2, 1/32*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*d^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(16*c^4*d^2*x^3 + 24*b*c^3*d^2*x^2 + 2*(5*b^2*c^2 + 4*a*c^3)*d^2*x + (b^3*c + 4*a*b*c^2)*d^2)*sqrt(c*x^2 + b*x + a))/c^2]","A",0
1194,1,28,0,0.400011," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(c d x^{2} + b d x + a d\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/3*(c*d*x^2 + b*d*x + a*d)*sqrt(c*x^2 + b*x + a)","A",0
1195,1,182,0,0.464419," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{b^{2} - 4 \, a c}{c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{c x^{2} + b x + a} c \sqrt{-\frac{b^{2} - 4 \, a c}{c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, \sqrt{c x^{2} + b x + a}}{8 \, c d}, \frac{\sqrt{\frac{b^{2} - 4 \, a c}{c}} \arctan\left(\frac{\sqrt{\frac{b^{2} - 4 \, a c}{c}}}{2 \, \sqrt{c x^{2} + b x + a}}\right) + 2 \, \sqrt{c x^{2} + b x + a}}{4 \, c d}\right]"," ",0,"[1/8*(sqrt(-(b^2 - 4*a*c)/c)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(c*x^2 + b*x + a)*c*sqrt(-(b^2 - 4*a*c)/c))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*sqrt(c*x^2 + b*x + a))/(c*d), 1/4*(sqrt((b^2 - 4*a*c)/c)*arctan(1/2*sqrt((b^2 - 4*a*c)/c)/sqrt(c*x^2 + b*x + a)) + 2*sqrt(c*x^2 + b*x + a))/(c*d)]","A",0
1196,1,189,0,0.463977," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, c x + b\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, \sqrt{c x^{2} + b x + a} c}{8 \, {\left(2 \, c^{3} d^{2} x + b c^{2} d^{2}\right)}}, -\frac{{\left(2 \, c x + b\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, \sqrt{c x^{2} + b x + a} c}{4 \, {\left(2 \, c^{3} d^{2} x + b c^{2} d^{2}\right)}}\right]"," ",0,"[1/8*((2*c*x + b)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*sqrt(c*x^2 + b*x + a)*c)/(2*c^3*d^2*x + b*c^2*d^2), -1/4*((2*c*x + b)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*sqrt(c*x^2 + b*x + a)*c)/(2*c^3*d^2*x + b*c^2*d^2)]","A",0
1197,1,378,0,0.518847," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, c^{2} x^{2} + 4 \, b c x + b^{2}\right)} \sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(4 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} x^{2} + 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} x + {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d^{3}\right)}}, -\frac{{\left(4 \, c^{2} x^{2} + 4 \, b c x + b^{2}\right)} \sqrt{b^{2} c - 4 \, a c^{2}} \arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(4 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} x^{2} + 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} x + {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d^{3}\right)}}\right]"," ",0,"[-1/16*((4*c^2*x^2 + 4*b*c*x + b^2)*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*(b^2*c^4 - 4*a*c^5)*d^3*x^2 + 4*(b^3*c^3 - 4*a*b*c^4)*d^3*x + (b^4*c^2 - 4*a*b^2*c^3)*d^3), -1/8*((4*c^2*x^2 + 4*b*c*x + b^2)*sqrt(b^2*c - 4*a*c^2)*arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c)) + 2*(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*(b^2*c^4 - 4*a*c^5)*d^3*x^2 + 4*(b^3*c^3 - 4*a*b*c^4)*d^3*x + (b^4*c^2 - 4*a*b^2*c^3)*d^3)]","B",0
1198,1,98,0,0.707438," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^4,x, algorithm=""fricas"")","\frac{2 \, {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{3 \, {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} x^{3} + 12 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} x^{2} + 6 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{4} x + {\left(b^{5} - 4 \, a b^{3} c\right)} d^{4}\right)}}"," ",0,"2/3*(c*x^2 + b*x + a)^(3/2)/(8*(b^2*c^3 - 4*a*c^4)*d^4*x^3 + 12*(b^3*c^2 - 4*a*b*c^3)*d^4*x^2 + 6*(b^4*c - 4*a*b^2*c^2)*d^4*x + (b^5 - 4*a*b^3*c)*d^4)","B",0
1199,1,728,0,1.147166," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^5,x, algorithm=""fricas"")","\left[\frac{{\left(16 \, c^{4} x^{4} + 32 \, b c^{3} x^{3} + 24 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x + b^{4}\right)} \sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c + 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) - 4 \, {\left(b^{4} c - 12 \, a b^{2} c^{2} + 32 \, a^{2} c^{3} - 4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} - 4 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{64 \, {\left(16 \, {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{5} x^{4} + 32 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{5} x^{3} + 24 \, {\left(b^{6} c^{4} - 8 \, a b^{4} c^{5} + 16 \, a^{2} b^{2} c^{6}\right)} d^{5} x^{2} + 8 \, {\left(b^{7} c^{3} - 8 \, a b^{5} c^{4} + 16 \, a^{2} b^{3} c^{5}\right)} d^{5} x + {\left(b^{8} c^{2} - 8 \, a b^{6} c^{3} + 16 \, a^{2} b^{4} c^{4}\right)} d^{5}\right)}}, -\frac{{\left(16 \, c^{4} x^{4} + 32 \, b c^{3} x^{3} + 24 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x + b^{4}\right)} \sqrt{b^{2} c - 4 \, a c^{2}} \arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(b^{4} c - 12 \, a b^{2} c^{2} + 32 \, a^{2} c^{3} - 4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} - 4 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{32 \, {\left(16 \, {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{5} x^{4} + 32 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{5} x^{3} + 24 \, {\left(b^{6} c^{4} - 8 \, a b^{4} c^{5} + 16 \, a^{2} b^{2} c^{6}\right)} d^{5} x^{2} + 8 \, {\left(b^{7} c^{3} - 8 \, a b^{5} c^{4} + 16 \, a^{2} b^{3} c^{5}\right)} d^{5} x + {\left(b^{8} c^{2} - 8 \, a b^{6} c^{3} + 16 \, a^{2} b^{4} c^{4}\right)} d^{5}\right)}}\right]"," ",0,"[1/64*((16*c^4*x^4 + 32*b*c^3*x^3 + 24*b^2*c^2*x^2 + 8*b^3*c*x + b^4)*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c + 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2)) - 4*(b^4*c - 12*a*b^2*c^2 + 32*a^2*c^3 - 4*(b^2*c^3 - 4*a*c^4)*x^2 - 4*(b^3*c^2 - 4*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/(16*(b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^5*x^4 + 32*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^5*x^3 + 24*(b^6*c^4 - 8*a*b^4*c^5 + 16*a^2*b^2*c^6)*d^5*x^2 + 8*(b^7*c^3 - 8*a*b^5*c^4 + 16*a^2*b^3*c^5)*d^5*x + (b^8*c^2 - 8*a*b^6*c^3 + 16*a^2*b^4*c^4)*d^5), -1/32*((16*c^4*x^4 + 32*b*c^3*x^3 + 24*b^2*c^2*x^2 + 8*b^3*c*x + b^4)*sqrt(b^2*c - 4*a*c^2)*arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c)) + 2*(b^4*c - 12*a*b^2*c^2 + 32*a^2*c^3 - 4*(b^2*c^3 - 4*a*c^4)*x^2 - 4*(b^3*c^2 - 4*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/(16*(b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^5*x^4 + 32*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^5*x^3 + 24*(b^6*c^4 - 8*a*b^4*c^5 + 16*a^2*b^2*c^6)*d^5*x^2 + 8*(b^7*c^3 - 8*a*b^5*c^4 + 16*a^2*b^3*c^5)*d^5*x + (b^8*c^2 - 8*a*b^6*c^3 + 16*a^2*b^4*c^4)*d^5)]","B",0
1200,1,274,0,2.090307," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^6,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{3} x^{4} + 16 \, b c^{2} x^{3} + 5 \, a b^{2} - 12 \, a^{2} c + {\left(13 \, b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(5 \, b^{3} - 4 \, a b c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15 \, {\left(32 \, {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{6} x^{5} + 80 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{6} x^{4} + 80 \, {\left(b^{6} c^{3} - 8 \, a b^{4} c^{4} + 16 \, a^{2} b^{2} c^{5}\right)} d^{6} x^{3} + 40 \, {\left(b^{7} c^{2} - 8 \, a b^{5} c^{3} + 16 \, a^{2} b^{3} c^{4}\right)} d^{6} x^{2} + 10 \, {\left(b^{8} c - 8 \, a b^{6} c^{2} + 16 \, a^{2} b^{4} c^{3}\right)} d^{6} x + {\left(b^{9} - 8 \, a b^{7} c + 16 \, a^{2} b^{5} c^{2}\right)} d^{6}\right)}}"," ",0,"2/15*(8*c^3*x^4 + 16*b*c^2*x^3 + 5*a*b^2 - 12*a^2*c + (13*b^2*c - 4*a*c^2)*x^2 + (5*b^3 - 4*a*b*c)*x)*sqrt(c*x^2 + b*x + a)/(32*(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^6*x^5 + 80*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^6*x^4 + 80*(b^6*c^3 - 8*a*b^4*c^4 + 16*a^2*b^2*c^5)*d^6*x^3 + 40*(b^7*c^2 - 8*a*b^5*c^3 + 16*a^2*b^3*c^4)*d^6*x^2 + 10*(b^8*c - 8*a*b^6*c^2 + 16*a^2*b^4*c^3)*d^6*x + (b^9 - 8*a*b^7*c + 16*a^2*b^5*c^2)*d^6)","B",0
1201,1,1220,0,3.749813," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^7,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(64 \, c^{6} x^{6} + 192 \, b c^{5} x^{5} + 240 \, b^{2} c^{4} x^{4} + 160 \, b^{3} c^{3} x^{3} + 60 \, b^{4} c^{2} x^{2} + 12 \, b^{5} c x + b^{6}\right)} \sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, {\left(3 \, b^{6} c - 68 \, a b^{4} c^{2} + 352 \, a^{2} b^{2} c^{3} - 512 \, a^{3} c^{4} - 48 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{4} - 96 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{3} - 16 \, {\left(5 \, b^{4} c^{3} - 22 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} x^{2} - 32 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, {\left(64 \, {\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{7} x^{6} + 192 \, {\left(b^{7} c^{7} - 12 \, a b^{5} c^{8} + 48 \, a^{2} b^{3} c^{9} - 64 \, a^{3} b c^{10}\right)} d^{7} x^{5} + 240 \, {\left(b^{8} c^{6} - 12 \, a b^{6} c^{7} + 48 \, a^{2} b^{4} c^{8} - 64 \, a^{3} b^{2} c^{9}\right)} d^{7} x^{4} + 160 \, {\left(b^{9} c^{5} - 12 \, a b^{7} c^{6} + 48 \, a^{2} b^{5} c^{7} - 64 \, a^{3} b^{3} c^{8}\right)} d^{7} x^{3} + 60 \, {\left(b^{10} c^{4} - 12 \, a b^{8} c^{5} + 48 \, a^{2} b^{6} c^{6} - 64 \, a^{3} b^{4} c^{7}\right)} d^{7} x^{2} + 12 \, {\left(b^{11} c^{3} - 12 \, a b^{9} c^{4} + 48 \, a^{2} b^{7} c^{5} - 64 \, a^{3} b^{5} c^{6}\right)} d^{7} x + {\left(b^{12} c^{2} - 12 \, a b^{10} c^{3} + 48 \, a^{2} b^{8} c^{4} - 64 \, a^{3} b^{6} c^{5}\right)} d^{7}\right)}}, -\frac{3 \, {\left(64 \, c^{6} x^{6} + 192 \, b c^{5} x^{5} + 240 \, b^{2} c^{4} x^{4} + 160 \, b^{3} c^{3} x^{3} + 60 \, b^{4} c^{2} x^{2} + 12 \, b^{5} c x + b^{6}\right)} \sqrt{b^{2} c - 4 \, a c^{2}} \arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(3 \, b^{6} c - 68 \, a b^{4} c^{2} + 352 \, a^{2} b^{2} c^{3} - 512 \, a^{3} c^{4} - 48 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{4} - 96 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{3} - 16 \, {\left(5 \, b^{4} c^{3} - 22 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} x^{2} - 32 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{192 \, {\left(64 \, {\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{7} x^{6} + 192 \, {\left(b^{7} c^{7} - 12 \, a b^{5} c^{8} + 48 \, a^{2} b^{3} c^{9} - 64 \, a^{3} b c^{10}\right)} d^{7} x^{5} + 240 \, {\left(b^{8} c^{6} - 12 \, a b^{6} c^{7} + 48 \, a^{2} b^{4} c^{8} - 64 \, a^{3} b^{2} c^{9}\right)} d^{7} x^{4} + 160 \, {\left(b^{9} c^{5} - 12 \, a b^{7} c^{6} + 48 \, a^{2} b^{5} c^{7} - 64 \, a^{3} b^{3} c^{8}\right)} d^{7} x^{3} + 60 \, {\left(b^{10} c^{4} - 12 \, a b^{8} c^{5} + 48 \, a^{2} b^{6} c^{6} - 64 \, a^{3} b^{4} c^{7}\right)} d^{7} x^{2} + 12 \, {\left(b^{11} c^{3} - 12 \, a b^{9} c^{4} + 48 \, a^{2} b^{7} c^{5} - 64 \, a^{3} b^{5} c^{6}\right)} d^{7} x + {\left(b^{12} c^{2} - 12 \, a b^{10} c^{3} + 48 \, a^{2} b^{8} c^{4} - 64 \, a^{3} b^{6} c^{5}\right)} d^{7}\right)}}\right]"," ",0,"[-1/384*(3*(64*c^6*x^6 + 192*b*c^5*x^5 + 240*b^2*c^4*x^4 + 160*b^3*c^3*x^3 + 60*b^4*c^2*x^2 + 12*b^5*c*x + b^6)*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*(3*b^6*c - 68*a*b^4*c^2 + 352*a^2*b^2*c^3 - 512*a^3*c^4 - 48*(b^2*c^5 - 4*a*c^6)*x^4 - 96*(b^3*c^4 - 4*a*b*c^5)*x^3 - 16*(5*b^4*c^3 - 22*a*b^2*c^4 + 8*a^2*c^5)*x^2 - 32*(b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*x)*sqrt(c*x^2 + b*x + a))/(64*(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^7*x^6 + 192*(b^7*c^7 - 12*a*b^5*c^8 + 48*a^2*b^3*c^9 - 64*a^3*b*c^10)*d^7*x^5 + 240*(b^8*c^6 - 12*a*b^6*c^7 + 48*a^2*b^4*c^8 - 64*a^3*b^2*c^9)*d^7*x^4 + 160*(b^9*c^5 - 12*a*b^7*c^6 + 48*a^2*b^5*c^7 - 64*a^3*b^3*c^8)*d^7*x^3 + 60*(b^10*c^4 - 12*a*b^8*c^5 + 48*a^2*b^6*c^6 - 64*a^3*b^4*c^7)*d^7*x^2 + 12*(b^11*c^3 - 12*a*b^9*c^4 + 48*a^2*b^7*c^5 - 64*a^3*b^5*c^6)*d^7*x + (b^12*c^2 - 12*a*b^10*c^3 + 48*a^2*b^8*c^4 - 64*a^3*b^6*c^5)*d^7), -1/192*(3*(64*c^6*x^6 + 192*b*c^5*x^5 + 240*b^2*c^4*x^4 + 160*b^3*c^3*x^3 + 60*b^4*c^2*x^2 + 12*b^5*c*x + b^6)*sqrt(b^2*c - 4*a*c^2)*arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c)) + 2*(3*b^6*c - 68*a*b^4*c^2 + 352*a^2*b^2*c^3 - 512*a^3*c^4 - 48*(b^2*c^5 - 4*a*c^6)*x^4 - 96*(b^3*c^4 - 4*a*b*c^5)*x^3 - 16*(5*b^4*c^3 - 22*a*b^2*c^4 + 8*a^2*c^5)*x^2 - 32*(b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*x)*sqrt(c*x^2 + b*x + a))/(64*(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^7*x^6 + 192*(b^7*c^7 - 12*a*b^5*c^8 + 48*a^2*b^3*c^9 - 64*a^3*b*c^10)*d^7*x^5 + 240*(b^8*c^6 - 12*a*b^6*c^7 + 48*a^2*b^4*c^8 - 64*a^3*b^2*c^9)*d^7*x^4 + 160*(b^9*c^5 - 12*a*b^7*c^6 + 48*a^2*b^5*c^7 - 64*a^3*b^3*c^8)*d^7*x^3 + 60*(b^10*c^4 - 12*a*b^8*c^5 + 48*a^2*b^6*c^6 - 64*a^3*b^4*c^7)*d^7*x^2 + 12*(b^11*c^3 - 12*a*b^9*c^4 + 48*a^2*b^7*c^5 - 64*a^3*b^5*c^6)*d^7*x + (b^12*c^2 - 12*a*b^10*c^3 + 48*a^2*b^8*c^4 - 64*a^3*b^6*c^5)*d^7)]","B",0
1202,1,251,0,0.446605," ","integrate((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(560 \, c^{6} d^{5} x^{8} + 2240 \, b c^{5} d^{5} x^{7} + 40 \, {\left(93 \, b^{2} c^{4} + 20 \, a c^{5}\right)} d^{5} x^{6} + 40 \, {\left(83 \, b^{3} c^{3} + 60 \, a b c^{4}\right)} d^{5} x^{5} + {\left(1703 \, b^{4} c^{2} + 2976 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d^{5} x^{4} + 2 \, {\left(243 \, b^{5} c + 976 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} d^{5} x^{3} + {\left(63 \, b^{6} + 702 \, a b^{4} c + 120 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{5} x^{2} + 2 \, {\left(63 \, a b^{5} + 36 \, a^{2} b^{3} c - 32 \, a^{3} b c^{2}\right)} d^{5} x + {\left(63 \, a^{2} b^{4} - 144 \, a^{3} b^{2} c + 128 \, a^{4} c^{2}\right)} d^{5}\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/315*(560*c^6*d^5*x^8 + 2240*b*c^5*d^5*x^7 + 40*(93*b^2*c^4 + 20*a*c^5)*d^5*x^6 + 40*(83*b^3*c^3 + 60*a*b*c^4)*d^5*x^5 + (1703*b^4*c^2 + 2976*a*b^2*c^3 + 48*a^2*c^4)*d^5*x^4 + 2*(243*b^5*c + 976*a*b^3*c^2 + 48*a^2*b*c^3)*d^5*x^3 + (63*b^6 + 702*a*b^4*c + 120*a^2*b^2*c^2 - 64*a^3*c^3)*d^5*x^2 + 2*(63*a*b^5 + 36*a^2*b^3*c - 32*a^3*b*c^2)*d^5*x + (63*a^2*b^4 - 144*a^3*b^2*c + 128*a^4*c^2)*d^5)*sqrt(c*x^2 + b*x + a)","B",0
1203,1,677,0,0.476571," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\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{c} d^{4} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2048 \, c^{8} d^{4} x^{7} + 7168 \, b c^{7} d^{4} x^{6} + 768 \, {\left(13 \, b^{2} c^{6} + 4 \, a c^{7}\right)} d^{4} x^{5} + 640 \, {\left(11 \, b^{3} c^{5} + 12 \, a b c^{6}\right)} d^{4} x^{4} + 16 \, {\left(161 \, b^{4} c^{4} + 472 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{4} x^{3} + 24 \, {\left(17 \, b^{5} c^{3} + 152 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{4} x^{2} + 2 \, {\left(b^{6} c^{2} + 396 \, a b^{4} c^{3} + 240 \, a^{2} b^{2} c^{4} - 192 \, a^{3} c^{5}\right)} d^{4} x - {\left(3 \, b^{7} c - 44 \, a b^{5} c^{2} - 176 \, a^{2} b^{3} c^{3} + 192 \, a^{3} b c^{4}\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}}{4096 \, c^{3}}, -\frac{3 \, {\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{-c} d^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(2048 \, c^{8} d^{4} x^{7} + 7168 \, b c^{7} d^{4} x^{6} + 768 \, {\left(13 \, b^{2} c^{6} + 4 \, a c^{7}\right)} d^{4} x^{5} + 640 \, {\left(11 \, b^{3} c^{5} + 12 \, a b c^{6}\right)} d^{4} x^{4} + 16 \, {\left(161 \, b^{4} c^{4} + 472 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{4} x^{3} + 24 \, {\left(17 \, b^{5} c^{3} + 152 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{4} x^{2} + 2 \, {\left(b^{6} c^{2} + 396 \, a b^{4} c^{3} + 240 \, a^{2} b^{2} c^{4} - 192 \, a^{3} c^{5}\right)} d^{4} x - {\left(3 \, b^{7} c - 44 \, a b^{5} c^{2} - 176 \, a^{2} b^{3} c^{3} + 192 \, a^{3} b c^{4}\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}}{2048 \, c^{3}}\right]"," ",0,"[1/4096*(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)*sqrt(c)*d^4*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(2048*c^8*d^4*x^7 + 7168*b*c^7*d^4*x^6 + 768*(13*b^2*c^6 + 4*a*c^7)*d^4*x^5 + 640*(11*b^3*c^5 + 12*a*b*c^6)*d^4*x^4 + 16*(161*b^4*c^4 + 472*a*b^2*c^5 + 16*a^2*c^6)*d^4*x^3 + 24*(17*b^5*c^3 + 152*a*b^3*c^4 + 16*a^2*b*c^5)*d^4*x^2 + 2*(b^6*c^2 + 396*a*b^4*c^3 + 240*a^2*b^2*c^4 - 192*a^3*c^5)*d^4*x - (3*b^7*c - 44*a*b^5*c^2 - 176*a^2*b^3*c^3 + 192*a^3*b*c^4)*d^4)*sqrt(c*x^2 + b*x + a))/c^3, -1/2048*(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)*sqrt(-c)*d^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(2048*c^8*d^4*x^7 + 7168*b*c^7*d^4*x^6 + 768*(13*b^2*c^6 + 4*a*c^7)*d^4*x^5 + 640*(11*b^3*c^5 + 12*a*b*c^6)*d^4*x^4 + 16*(161*b^4*c^4 + 472*a*b^2*c^5 + 16*a^2*c^6)*d^4*x^3 + 24*(17*b^5*c^3 + 152*a*b^3*c^4 + 16*a^2*b*c^5)*d^4*x^2 + 2*(b^6*c^2 + 396*a*b^4*c^3 + 240*a^2*b^2*c^4 - 192*a^3*c^5)*d^4*x - (3*b^7*c - 44*a*b^5*c^2 - 176*a^2*b^3*c^3 + 192*a^3*b*c^4)*d^4)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
1204,1,149,0,0.429312," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2}{35} \, {\left(20 \, c^{4} d^{3} x^{6} + 60 \, b c^{3} d^{3} x^{5} + {\left(67 \, b^{2} c^{2} + 32 \, a c^{3}\right)} d^{3} x^{4} + 2 \, {\left(17 \, b^{3} c + 32 \, a b c^{2}\right)} d^{3} x^{3} + {\left(7 \, b^{4} + 46 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} x^{2} + 2 \, {\left(7 \, a b^{3} + 2 \, a^{2} b c\right)} d^{3} x + {\left(7 \, a^{2} b^{2} - 8 \, a^{3} c\right)} d^{3}\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/35*(20*c^4*d^3*x^6 + 60*b*c^3*d^3*x^5 + (67*b^2*c^2 + 32*a*c^3)*d^3*x^4 + 2*(17*b^3*c + 32*a*b*c^2)*d^3*x^3 + (7*b^4 + 46*a*b^2*c + 4*a^2*c^2)*d^3*x^2 + 2*(7*a*b^3 + 2*a^2*b*c)*d^3*x + (7*a^2*b^2 - 8*a^3*c)*d^3)*sqrt(c*x^2 + b*x + a)","B",0
1205,1,473,0,0.443216," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{c} d^{2} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(256 \, c^{6} d^{2} x^{5} + 640 \, b c^{5} d^{2} x^{4} + 16 \, {\left(33 \, b^{2} c^{4} + 28 \, a c^{5}\right)} d^{2} x^{3} + 8 \, {\left(19 \, b^{3} c^{3} + 84 \, a b c^{4}\right)} d^{2} x^{2} + 2 \, {\left(b^{4} c^{2} + 144 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d^{2} x - {\left(3 \, b^{5} c - 32 \, a b^{3} c^{2} - 48 \, a^{2} b c^{3}\right)} d^{2}\right)} \sqrt{c x^{2} + b x + a}}{1536 \, c^{3}}, -\frac{3 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-c} d^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(256 \, c^{6} d^{2} x^{5} + 640 \, b c^{5} d^{2} x^{4} + 16 \, {\left(33 \, b^{2} c^{4} + 28 \, a c^{5}\right)} d^{2} x^{3} + 8 \, {\left(19 \, b^{3} c^{3} + 84 \, a b c^{4}\right)} d^{2} x^{2} + 2 \, {\left(b^{4} c^{2} + 144 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d^{2} x - {\left(3 \, b^{5} c - 32 \, a b^{3} c^{2} - 48 \, a^{2} b c^{3}\right)} d^{2}\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{3}}\right]"," ",0,"[-1/1536*(3*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(c)*d^2*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(256*c^6*d^2*x^5 + 640*b*c^5*d^2*x^4 + 16*(33*b^2*c^4 + 28*a*c^5)*d^2*x^3 + 8*(19*b^3*c^3 + 84*a*b*c^4)*d^2*x^2 + 2*(b^4*c^2 + 144*a*b^2*c^3 + 48*a^2*c^4)*d^2*x - (3*b^5*c - 32*a*b^3*c^2 - 48*a^2*b*c^3)*d^2)*sqrt(c*x^2 + b*x + a))/c^3, -1/768*(3*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-c)*d^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(256*c^6*d^2*x^5 + 640*b*c^5*d^2*x^4 + 16*(33*b^2*c^4 + 28*a*c^5)*d^2*x^3 + 8*(19*b^3*c^3 + 84*a*b*c^4)*d^2*x^2 + 2*(b^4*c^2 + 144*a*b^2*c^3 + 48*a^2*c^4)*d^2*x - (3*b^5*c - 32*a*b^3*c^2 - 48*a^2*b*c^3)*d^2)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
1206,1,55,0,0.422102," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2}{5} \, {\left(c^{2} d x^{4} + 2 \, b c d x^{3} + 2 \, a b d x + {\left(b^{2} + 2 \, a c\right)} d x^{2} + a^{2} d\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/5*(c^2*d*x^4 + 2*b*c*d*x^3 + 2*a*b*d*x + (b^2 + 2*a*c)*d*x^2 + a^2*d)*sqrt(c*x^2 + b*x + a)","B",0
1207,1,246,0,0.502236," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{2} - 4 \, a c\right)} \sqrt{-\frac{b^{2} - 4 \, a c}{c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{c x^{2} + b x + a} c \sqrt{-\frac{b^{2} - 4 \, a c}{c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) - 4 \, {\left(4 \, c^{2} x^{2} + 4 \, b c x - 3 \, b^{2} + 16 \, a c\right)} \sqrt{c x^{2} + b x + a}}{96 \, c^{2} d}, -\frac{3 \, {\left(b^{2} - 4 \, a c\right)} \sqrt{\frac{b^{2} - 4 \, a c}{c}} \arctan\left(\frac{\sqrt{\frac{b^{2} - 4 \, a c}{c}}}{2 \, \sqrt{c x^{2} + b x + a}}\right) - 2 \, {\left(4 \, c^{2} x^{2} + 4 \, b c x - 3 \, b^{2} + 16 \, a c\right)} \sqrt{c x^{2} + b x + a}}{48 \, c^{2} d}\right]"," ",0,"[-1/96*(3*(b^2 - 4*a*c)*sqrt(-(b^2 - 4*a*c)/c)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(c*x^2 + b*x + a)*c*sqrt(-(b^2 - 4*a*c)/c))/(4*c^2*x^2 + 4*b*c*x + b^2)) - 4*(4*c^2*x^2 + 4*b*c*x - 3*b^2 + 16*a*c)*sqrt(c*x^2 + b*x + a))/(c^2*d), -1/48*(3*(b^2 - 4*a*c)*sqrt((b^2 - 4*a*c)/c)*arctan(1/2*sqrt((b^2 - 4*a*c)/c)/sqrt(c*x^2 + b*x + a)) - 2*(4*c^2*x^2 + 4*b*c*x - 3*b^2 + 16*a*c)*sqrt(c*x^2 + b*x + a))/(c^2*d)]","A",0
1208,1,281,0,0.517756," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} - 4 \, a b c + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(4 \, c^{3} x^{2} + 4 \, b c^{2} x + 3 \, b^{2} c - 8 \, a c^{2}\right)} \sqrt{c x^{2} + b x + a}}{64 \, {\left(2 \, c^{4} d^{2} x + b c^{3} d^{2}\right)}}, \frac{3 \, {\left(b^{3} - 4 \, a b c + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(4 \, c^{3} x^{2} + 4 \, b c^{2} x + 3 \, b^{2} c - 8 \, a c^{2}\right)} \sqrt{c x^{2} + b x + a}}{32 \, {\left(2 \, c^{4} d^{2} x + b c^{3} d^{2}\right)}}\right]"," ",0,"[-1/64*(3*(b^3 - 4*a*b*c + 2*(b^2*c - 4*a*c^2)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(4*c^3*x^2 + 4*b*c^2*x + 3*b^2*c - 8*a*c^2)*sqrt(c*x^2 + b*x + a))/(2*c^4*d^2*x + b*c^3*d^2), 1/32*(3*(b^3 - 4*a*b*c + 2*(b^2*c - 4*a*c^2)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(4*c^3*x^2 + 4*b*c^2*x + 3*b^2*c - 8*a*c^2)*sqrt(c*x^2 + b*x + a))/(2*c^4*d^2*x + b*c^3*d^2)]","A",0
1209,1,320,0,0.589483," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, c^{2} x^{2} + 4 \, b c x + b^{2}\right)} \sqrt{-\frac{b^{2} - 4 \, a c}{c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{c x^{2} + b x + a} c \sqrt{-\frac{b^{2} - 4 \, a c}{c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, {\left(8 \, c^{2} x^{2} + 8 \, b c x + 3 \, b^{2} - 4 \, a c\right)} \sqrt{c x^{2} + b x + a}}{64 \, {\left(4 \, c^{4} d^{3} x^{2} + 4 \, b c^{3} d^{3} x + b^{2} c^{2} d^{3}\right)}}, \frac{3 \, {\left(4 \, c^{2} x^{2} + 4 \, b c x + b^{2}\right)} \sqrt{\frac{b^{2} - 4 \, a c}{c}} \arctan\left(\frac{\sqrt{\frac{b^{2} - 4 \, a c}{c}}}{2 \, \sqrt{c x^{2} + b x + a}}\right) + 2 \, {\left(8 \, c^{2} x^{2} + 8 \, b c x + 3 \, b^{2} - 4 \, a c\right)} \sqrt{c x^{2} + b x + a}}{32 \, {\left(4 \, c^{4} d^{3} x^{2} + 4 \, b c^{3} d^{3} x + b^{2} c^{2} d^{3}\right)}}\right]"," ",0,"[1/64*(3*(4*c^2*x^2 + 4*b*c*x + b^2)*sqrt(-(b^2 - 4*a*c)/c)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(c*x^2 + b*x + a)*c*sqrt(-(b^2 - 4*a*c)/c))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*(8*c^2*x^2 + 8*b*c*x + 3*b^2 - 4*a*c)*sqrt(c*x^2 + b*x + a))/(4*c^4*d^3*x^2 + 4*b*c^3*d^3*x + b^2*c^2*d^3), 1/32*(3*(4*c^2*x^2 + 4*b*c*x + b^2)*sqrt((b^2 - 4*a*c)/c)*arctan(1/2*sqrt((b^2 - 4*a*c)/c)/sqrt(c*x^2 + b*x + a)) + 2*(8*c^2*x^2 + 8*b*c*x + 3*b^2 - 4*a*c)*sqrt(c*x^2 + b*x + a))/(4*c^4*d^3*x^2 + 4*b*c^3*d^3*x + b^2*c^2*d^3)]","A",0
1210,1,345,0,0.831412," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, c^{3} x^{3} + 12 \, b c^{2} x^{2} + 6 \, b^{2} c x + b^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(16 \, c^{3} x^{2} + 16 \, b c^{2} x + 3 \, b^{2} c + 4 \, a c^{2}\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(8 \, c^{6} d^{4} x^{3} + 12 \, b c^{5} d^{4} x^{2} + 6 \, b^{2} c^{4} d^{4} x + b^{3} c^{3} d^{4}\right)}}, -\frac{3 \, {\left(8 \, c^{3} x^{3} + 12 \, b c^{2} x^{2} + 6 \, b^{2} c x + b^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(16 \, c^{3} x^{2} + 16 \, b c^{2} x + 3 \, b^{2} c + 4 \, a c^{2}\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(8 \, c^{6} d^{4} x^{3} + 12 \, b c^{5} d^{4} x^{2} + 6 \, b^{2} c^{4} d^{4} x + b^{3} c^{3} d^{4}\right)}}\right]"," ",0,"[1/96*(3*(8*c^3*x^3 + 12*b*c^2*x^2 + 6*b^2*c*x + b^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(16*c^3*x^2 + 16*b*c^2*x + 3*b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(8*c^6*d^4*x^3 + 12*b*c^5*d^4*x^2 + 6*b^2*c^4*d^4*x + b^3*c^3*d^4), -1/48*(3*(8*c^3*x^3 + 12*b*c^2*x^2 + 6*b^2*c*x + b^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(16*c^3*x^2 + 16*b*c^2*x + 3*b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(8*c^6*d^4*x^3 + 12*b*c^5*d^4*x^2 + 6*b^2*c^4*d^4*x + b^3*c^3*d^4)]","A",0
1211,1,622,0,1.162122," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^5,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(16 \, c^{4} x^{4} + 32 \, b c^{3} x^{3} + 24 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x + b^{4}\right)} \sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, {\left(3 \, b^{4} c - 4 \, a b^{2} c^{2} - 32 \, a^{2} c^{3} + 20 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + 20 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{256 \, {\left(16 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{5} x^{4} + 32 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{5} x^{3} + 24 \, {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} d^{5} x^{2} + 8 \, {\left(b^{5} c^{4} - 4 \, a b^{3} c^{5}\right)} d^{5} x + {\left(b^{6} c^{3} - 4 \, a b^{4} c^{4}\right)} d^{5}\right)}}, -\frac{3 \, {\left(16 \, c^{4} x^{4} + 32 \, b c^{3} x^{3} + 24 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x + b^{4}\right)} \sqrt{b^{2} c - 4 \, a c^{2}} \arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(3 \, b^{4} c - 4 \, a b^{2} c^{2} - 32 \, a^{2} c^{3} + 20 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + 20 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{128 \, {\left(16 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{5} x^{4} + 32 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{5} x^{3} + 24 \, {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} d^{5} x^{2} + 8 \, {\left(b^{5} c^{4} - 4 \, a b^{3} c^{5}\right)} d^{5} x + {\left(b^{6} c^{3} - 4 \, a b^{4} c^{4}\right)} d^{5}\right)}}\right]"," ",0,"[-1/256*(3*(16*c^4*x^4 + 32*b*c^3*x^3 + 24*b^2*c^2*x^2 + 8*b^3*c*x + b^4)*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*(3*b^4*c - 4*a*b^2*c^2 - 32*a^2*c^3 + 20*(b^2*c^3 - 4*a*c^4)*x^2 + 20*(b^3*c^2 - 4*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/(16*(b^2*c^7 - 4*a*c^8)*d^5*x^4 + 32*(b^3*c^6 - 4*a*b*c^7)*d^5*x^3 + 24*(b^4*c^5 - 4*a*b^2*c^6)*d^5*x^2 + 8*(b^5*c^4 - 4*a*b^3*c^5)*d^5*x + (b^6*c^3 - 4*a*b^4*c^4)*d^5), -1/128*(3*(16*c^4*x^4 + 32*b*c^3*x^3 + 24*b^2*c^2*x^2 + 8*b^3*c*x + b^4)*sqrt(b^2*c - 4*a*c^2)*arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c)) + 2*(3*b^4*c - 4*a*b^2*c^2 - 32*a^2*c^3 + 20*(b^2*c^3 - 4*a*c^4)*x^2 + 20*(b^3*c^2 - 4*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/(16*(b^2*c^7 - 4*a*c^8)*d^5*x^4 + 32*(b^3*c^6 - 4*a*b*c^7)*d^5*x^3 + 24*(b^4*c^5 - 4*a*b^2*c^6)*d^5*x^2 + 8*(b^5*c^4 - 4*a*b^3*c^5)*d^5*x + (b^6*c^3 - 4*a*b^4*c^4)*d^5)]","B",0
1212,1,183,0,2.089969," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^6,x, algorithm=""fricas"")","\frac{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a}}{5 \, {\left(32 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{6} x^{5} + 80 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{6} x^{4} + 80 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{6} x^{3} + 40 \, {\left(b^{5} c^{2} - 4 \, a b^{3} c^{3}\right)} d^{6} x^{2} + 10 \, {\left(b^{6} c - 4 \, a b^{4} c^{2}\right)} d^{6} x + {\left(b^{7} - 4 \, a b^{5} c\right)} d^{6}\right)}}"," ",0,"2/5*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)/(32*(b^2*c^5 - 4*a*c^6)*d^6*x^5 + 80*(b^3*c^4 - 4*a*b*c^5)*d^6*x^4 + 80*(b^4*c^3 - 4*a*b^2*c^4)*d^6*x^3 + 40*(b^5*c^2 - 4*a*b^3*c^3)*d^6*x^2 + 10*(b^6*c - 4*a*b^4*c^2)*d^6*x + (b^7 - 4*a*b^5*c)*d^6)","B",0
1213,1,1064,0,3.830062," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^7,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(64 \, c^{6} x^{6} + 192 \, b c^{5} x^{5} + 240 \, b^{2} c^{4} x^{4} + 160 \, b^{3} c^{3} x^{3} + 60 \, b^{4} c^{2} x^{2} + 12 \, b^{5} c x + b^{6}\right)} \sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c + 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) - 4 \, {\left(3 \, b^{6} c - 4 \, a b^{4} c^{2} - 160 \, a^{2} b^{2} c^{3} + 512 \, a^{3} c^{4} - 48 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{4} - 96 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{3} - 16 \, {\left(b^{4} c^{3} + 10 \, a b^{2} c^{4} - 56 \, a^{2} c^{5}\right)} x^{2} + 32 \, {\left(b^{5} c^{2} - 11 \, a b^{3} c^{3} + 28 \, a^{2} b c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1536 \, {\left(64 \, {\left(b^{4} c^{9} - 8 \, a b^{2} c^{10} + 16 \, a^{2} c^{11}\right)} d^{7} x^{6} + 192 \, {\left(b^{5} c^{8} - 8 \, a b^{3} c^{9} + 16 \, a^{2} b c^{10}\right)} d^{7} x^{5} + 240 \, {\left(b^{6} c^{7} - 8 \, a b^{4} c^{8} + 16 \, a^{2} b^{2} c^{9}\right)} d^{7} x^{4} + 160 \, {\left(b^{7} c^{6} - 8 \, a b^{5} c^{7} + 16 \, a^{2} b^{3} c^{8}\right)} d^{7} x^{3} + 60 \, {\left(b^{8} c^{5} - 8 \, a b^{6} c^{6} + 16 \, a^{2} b^{4} c^{7}\right)} d^{7} x^{2} + 12 \, {\left(b^{9} c^{4} - 8 \, a b^{7} c^{5} + 16 \, a^{2} b^{5} c^{6}\right)} d^{7} x + {\left(b^{10} c^{3} - 8 \, a b^{8} c^{4} + 16 \, a^{2} b^{6} c^{5}\right)} d^{7}\right)}}, -\frac{3 \, {\left(64 \, c^{6} x^{6} + 192 \, b c^{5} x^{5} + 240 \, b^{2} c^{4} x^{4} + 160 \, b^{3} c^{3} x^{3} + 60 \, b^{4} c^{2} x^{2} + 12 \, b^{5} c x + b^{6}\right)} \sqrt{b^{2} c - 4 \, a c^{2}} \arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(3 \, b^{6} c - 4 \, a b^{4} c^{2} - 160 \, a^{2} b^{2} c^{3} + 512 \, a^{3} c^{4} - 48 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{4} - 96 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{3} - 16 \, {\left(b^{4} c^{3} + 10 \, a b^{2} c^{4} - 56 \, a^{2} c^{5}\right)} x^{2} + 32 \, {\left(b^{5} c^{2} - 11 \, a b^{3} c^{3} + 28 \, a^{2} b c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, {\left(64 \, {\left(b^{4} c^{9} - 8 \, a b^{2} c^{10} + 16 \, a^{2} c^{11}\right)} d^{7} x^{6} + 192 \, {\left(b^{5} c^{8} - 8 \, a b^{3} c^{9} + 16 \, a^{2} b c^{10}\right)} d^{7} x^{5} + 240 \, {\left(b^{6} c^{7} - 8 \, a b^{4} c^{8} + 16 \, a^{2} b^{2} c^{9}\right)} d^{7} x^{4} + 160 \, {\left(b^{7} c^{6} - 8 \, a b^{5} c^{7} + 16 \, a^{2} b^{3} c^{8}\right)} d^{7} x^{3} + 60 \, {\left(b^{8} c^{5} - 8 \, a b^{6} c^{6} + 16 \, a^{2} b^{4} c^{7}\right)} d^{7} x^{2} + 12 \, {\left(b^{9} c^{4} - 8 \, a b^{7} c^{5} + 16 \, a^{2} b^{5} c^{6}\right)} d^{7} x + {\left(b^{10} c^{3} - 8 \, a b^{8} c^{4} + 16 \, a^{2} b^{6} c^{5}\right)} d^{7}\right)}}\right]"," ",0,"[1/1536*(3*(64*c^6*x^6 + 192*b*c^5*x^5 + 240*b^2*c^4*x^4 + 160*b^3*c^3*x^3 + 60*b^4*c^2*x^2 + 12*b^5*c*x + b^6)*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c + 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2)) - 4*(3*b^6*c - 4*a*b^4*c^2 - 160*a^2*b^2*c^3 + 512*a^3*c^4 - 48*(b^2*c^5 - 4*a*c^6)*x^4 - 96*(b^3*c^4 - 4*a*b*c^5)*x^3 - 16*(b^4*c^3 + 10*a*b^2*c^4 - 56*a^2*c^5)*x^2 + 32*(b^5*c^2 - 11*a*b^3*c^3 + 28*a^2*b*c^4)*x)*sqrt(c*x^2 + b*x + a))/(64*(b^4*c^9 - 8*a*b^2*c^10 + 16*a^2*c^11)*d^7*x^6 + 192*(b^5*c^8 - 8*a*b^3*c^9 + 16*a^2*b*c^10)*d^7*x^5 + 240*(b^6*c^7 - 8*a*b^4*c^8 + 16*a^2*b^2*c^9)*d^7*x^4 + 160*(b^7*c^6 - 8*a*b^5*c^7 + 16*a^2*b^3*c^8)*d^7*x^3 + 60*(b^8*c^5 - 8*a*b^6*c^6 + 16*a^2*b^4*c^7)*d^7*x^2 + 12*(b^9*c^4 - 8*a*b^7*c^5 + 16*a^2*b^5*c^6)*d^7*x + (b^10*c^3 - 8*a*b^8*c^4 + 16*a^2*b^6*c^5)*d^7), -1/768*(3*(64*c^6*x^6 + 192*b*c^5*x^5 + 240*b^2*c^4*x^4 + 160*b^3*c^3*x^3 + 60*b^4*c^2*x^2 + 12*b^5*c*x + b^6)*sqrt(b^2*c - 4*a*c^2)*arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c)) + 2*(3*b^6*c - 4*a*b^4*c^2 - 160*a^2*b^2*c^3 + 512*a^3*c^4 - 48*(b^2*c^5 - 4*a*c^6)*x^4 - 96*(b^3*c^4 - 4*a*b*c^5)*x^3 - 16*(b^4*c^3 + 10*a*b^2*c^4 - 56*a^2*c^5)*x^2 + 32*(b^5*c^2 - 11*a*b^3*c^3 + 28*a^2*b*c^4)*x)*sqrt(c*x^2 + b*x + a))/(64*(b^4*c^9 - 8*a*b^2*c^10 + 16*a^2*c^11)*d^7*x^6 + 192*(b^5*c^8 - 8*a*b^3*c^9 + 16*a^2*b*c^10)*d^7*x^5 + 240*(b^6*c^7 - 8*a*b^4*c^8 + 16*a^2*b^2*c^9)*d^7*x^4 + 160*(b^7*c^6 - 8*a*b^5*c^7 + 16*a^2*b^3*c^8)*d^7*x^3 + 60*(b^8*c^5 - 8*a*b^6*c^6 + 16*a^2*b^4*c^7)*d^7*x^2 + 12*(b^9*c^4 - 8*a*b^7*c^5 + 16*a^2*b^5*c^6)*d^7*x + (b^10*c^3 - 8*a*b^8*c^4 + 16*a^2*b^6*c^5)*d^7)]","B",0
1214,1,398,0,9.683667," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^8,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{4} x^{6} + 24 \, b c^{3} x^{5} + {\left(31 \, b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + 7 \, a^{2} b^{2} - 20 \, a^{3} c + 2 \, {\left(11 \, b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(7 \, b^{4} + 10 \, a b^{2} c - 32 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(7 \, a b^{3} - 16 \, a^{2} b c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{35 \, {\left(128 \, {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} d^{8} x^{7} + 448 \, {\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} d^{8} x^{6} + 672 \, {\left(b^{6} c^{5} - 8 \, a b^{4} c^{6} + 16 \, a^{2} b^{2} c^{7}\right)} d^{8} x^{5} + 560 \, {\left(b^{7} c^{4} - 8 \, a b^{5} c^{5} + 16 \, a^{2} b^{3} c^{6}\right)} d^{8} x^{4} + 280 \, {\left(b^{8} c^{3} - 8 \, a b^{6} c^{4} + 16 \, a^{2} b^{4} c^{5}\right)} d^{8} x^{3} + 84 \, {\left(b^{9} c^{2} - 8 \, a b^{7} c^{3} + 16 \, a^{2} b^{5} c^{4}\right)} d^{8} x^{2} + 14 \, {\left(b^{10} c - 8 \, a b^{8} c^{2} + 16 \, a^{2} b^{6} c^{3}\right)} d^{8} x + {\left(b^{11} - 8 \, a b^{9} c + 16 \, a^{2} b^{7} c^{2}\right)} d^{8}\right)}}"," ",0,"2/35*(8*c^4*x^6 + 24*b*c^3*x^5 + (31*b^2*c^2 - 4*a*c^3)*x^4 + 7*a^2*b^2 - 20*a^3*c + 2*(11*b^3*c - 4*a*b*c^2)*x^3 + (7*b^4 + 10*a*b^2*c - 32*a^2*c^2)*x^2 + 2*(7*a*b^3 - 16*a^2*b*c)*x)*sqrt(c*x^2 + b*x + a)/(128*(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*d^8*x^7 + 448*(b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*d^8*x^6 + 672*(b^6*c^5 - 8*a*b^4*c^6 + 16*a^2*b^2*c^7)*d^8*x^5 + 560*(b^7*c^4 - 8*a*b^5*c^5 + 16*a^2*b^3*c^6)*d^8*x^4 + 280*(b^8*c^3 - 8*a*b^6*c^4 + 16*a^2*b^4*c^5)*d^8*x^3 + 84*(b^9*c^2 - 8*a*b^7*c^3 + 16*a^2*b^5*c^4)*d^8*x^2 + 14*(b^10*c - 8*a*b^8*c^2 + 16*a^2*b^6*c^3)*d^8*x + (b^11 - 8*a*b^9*c + 16*a^2*b^7*c^2)*d^8)","B",0
1215,1,1646,0,16.865283," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^9,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(256 \, c^{8} x^{8} + 1024 \, b c^{7} x^{7} + 1792 \, b^{2} c^{6} x^{6} + 1792 \, b^{3} c^{5} x^{5} + 1120 \, b^{4} c^{4} x^{4} + 448 \, b^{5} c^{3} x^{3} + 112 \, b^{6} c^{2} x^{2} + 16 \, b^{7} c x + b^{8}\right)} \sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, {\left(3 \, b^{8} c - 4 \, a b^{6} c^{2} - 416 \, a^{2} b^{4} c^{3} + 2560 \, a^{3} b^{2} c^{4} - 4096 \, a^{4} c^{5} - 192 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} x^{6} - 576 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} x^{5} - 16 \, {\left(47 \, b^{4} c^{5} - 196 \, a b^{2} c^{6} + 32 \, a^{2} c^{7}\right)} x^{4} - 32 \, {\left(17 \, b^{5} c^{4} - 76 \, a b^{3} c^{5} + 32 \, a^{2} b c^{6}\right)} x^{3} - 12 \, {\left(11 \, b^{6} c^{3} + 4 \, a b^{4} c^{4} - 320 \, a^{2} b^{2} c^{5} + 512 \, a^{3} c^{6}\right)} x^{2} + 4 \, {\left(11 \, b^{7} c^{2} - 220 \, a b^{5} c^{3} + 1088 \, a^{2} b^{3} c^{4} - 1536 \, a^{3} b c^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4096 \, {\left(256 \, {\left(b^{6} c^{11} - 12 \, a b^{4} c^{12} + 48 \, a^{2} b^{2} c^{13} - 64 \, a^{3} c^{14}\right)} d^{9} x^{8} + 1024 \, {\left(b^{7} c^{10} - 12 \, a b^{5} c^{11} + 48 \, a^{2} b^{3} c^{12} - 64 \, a^{3} b c^{13}\right)} d^{9} x^{7} + 1792 \, {\left(b^{8} c^{9} - 12 \, a b^{6} c^{10} + 48 \, a^{2} b^{4} c^{11} - 64 \, a^{3} b^{2} c^{12}\right)} d^{9} x^{6} + 1792 \, {\left(b^{9} c^{8} - 12 \, a b^{7} c^{9} + 48 \, a^{2} b^{5} c^{10} - 64 \, a^{3} b^{3} c^{11}\right)} d^{9} x^{5} + 1120 \, {\left(b^{10} c^{7} - 12 \, a b^{8} c^{8} + 48 \, a^{2} b^{6} c^{9} - 64 \, a^{3} b^{4} c^{10}\right)} d^{9} x^{4} + 448 \, {\left(b^{11} c^{6} - 12 \, a b^{9} c^{7} + 48 \, a^{2} b^{7} c^{8} - 64 \, a^{3} b^{5} c^{9}\right)} d^{9} x^{3} + 112 \, {\left(b^{12} c^{5} - 12 \, a b^{10} c^{6} + 48 \, a^{2} b^{8} c^{7} - 64 \, a^{3} b^{6} c^{8}\right)} d^{9} x^{2} + 16 \, {\left(b^{13} c^{4} - 12 \, a b^{11} c^{5} + 48 \, a^{2} b^{9} c^{6} - 64 \, a^{3} b^{7} c^{7}\right)} d^{9} x + {\left(b^{14} c^{3} - 12 \, a b^{12} c^{4} + 48 \, a^{2} b^{10} c^{5} - 64 \, a^{3} b^{8} c^{6}\right)} d^{9}\right)}}, -\frac{3 \, {\left(256 \, c^{8} x^{8} + 1024 \, b c^{7} x^{7} + 1792 \, b^{2} c^{6} x^{6} + 1792 \, b^{3} c^{5} x^{5} + 1120 \, b^{4} c^{4} x^{4} + 448 \, b^{5} c^{3} x^{3} + 112 \, b^{6} c^{2} x^{2} + 16 \, b^{7} c x + b^{8}\right)} \sqrt{b^{2} c - 4 \, a c^{2}} \arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(3 \, b^{8} c - 4 \, a b^{6} c^{2} - 416 \, a^{2} b^{4} c^{3} + 2560 \, a^{3} b^{2} c^{4} - 4096 \, a^{4} c^{5} - 192 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} x^{6} - 576 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} x^{5} - 16 \, {\left(47 \, b^{4} c^{5} - 196 \, a b^{2} c^{6} + 32 \, a^{2} c^{7}\right)} x^{4} - 32 \, {\left(17 \, b^{5} c^{4} - 76 \, a b^{3} c^{5} + 32 \, a^{2} b c^{6}\right)} x^{3} - 12 \, {\left(11 \, b^{6} c^{3} + 4 \, a b^{4} c^{4} - 320 \, a^{2} b^{2} c^{5} + 512 \, a^{3} c^{6}\right)} x^{2} + 4 \, {\left(11 \, b^{7} c^{2} - 220 \, a b^{5} c^{3} + 1088 \, a^{2} b^{3} c^{4} - 1536 \, a^{3} b c^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2048 \, {\left(256 \, {\left(b^{6} c^{11} - 12 \, a b^{4} c^{12} + 48 \, a^{2} b^{2} c^{13} - 64 \, a^{3} c^{14}\right)} d^{9} x^{8} + 1024 \, {\left(b^{7} c^{10} - 12 \, a b^{5} c^{11} + 48 \, a^{2} b^{3} c^{12} - 64 \, a^{3} b c^{13}\right)} d^{9} x^{7} + 1792 \, {\left(b^{8} c^{9} - 12 \, a b^{6} c^{10} + 48 \, a^{2} b^{4} c^{11} - 64 \, a^{3} b^{2} c^{12}\right)} d^{9} x^{6} + 1792 \, {\left(b^{9} c^{8} - 12 \, a b^{7} c^{9} + 48 \, a^{2} b^{5} c^{10} - 64 \, a^{3} b^{3} c^{11}\right)} d^{9} x^{5} + 1120 \, {\left(b^{10} c^{7} - 12 \, a b^{8} c^{8} + 48 \, a^{2} b^{6} c^{9} - 64 \, a^{3} b^{4} c^{10}\right)} d^{9} x^{4} + 448 \, {\left(b^{11} c^{6} - 12 \, a b^{9} c^{7} + 48 \, a^{2} b^{7} c^{8} - 64 \, a^{3} b^{5} c^{9}\right)} d^{9} x^{3} + 112 \, {\left(b^{12} c^{5} - 12 \, a b^{10} c^{6} + 48 \, a^{2} b^{8} c^{7} - 64 \, a^{3} b^{6} c^{8}\right)} d^{9} x^{2} + 16 \, {\left(b^{13} c^{4} - 12 \, a b^{11} c^{5} + 48 \, a^{2} b^{9} c^{6} - 64 \, a^{3} b^{7} c^{7}\right)} d^{9} x + {\left(b^{14} c^{3} - 12 \, a b^{12} c^{4} + 48 \, a^{2} b^{10} c^{5} - 64 \, a^{3} b^{8} c^{6}\right)} d^{9}\right)}}\right]"," ",0,"[-1/4096*(3*(256*c^8*x^8 + 1024*b*c^7*x^7 + 1792*b^2*c^6*x^6 + 1792*b^3*c^5*x^5 + 1120*b^4*c^4*x^4 + 448*b^5*c^3*x^3 + 112*b^6*c^2*x^2 + 16*b^7*c*x + b^8)*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*(3*b^8*c - 4*a*b^6*c^2 - 416*a^2*b^4*c^3 + 2560*a^3*b^2*c^4 - 4096*a^4*c^5 - 192*(b^2*c^7 - 4*a*c^8)*x^6 - 576*(b^3*c^6 - 4*a*b*c^7)*x^5 - 16*(47*b^4*c^5 - 196*a*b^2*c^6 + 32*a^2*c^7)*x^4 - 32*(17*b^5*c^4 - 76*a*b^3*c^5 + 32*a^2*b*c^6)*x^3 - 12*(11*b^6*c^3 + 4*a*b^4*c^4 - 320*a^2*b^2*c^5 + 512*a^3*c^6)*x^2 + 4*(11*b^7*c^2 - 220*a*b^5*c^3 + 1088*a^2*b^3*c^4 - 1536*a^3*b*c^5)*x)*sqrt(c*x^2 + b*x + a))/(256*(b^6*c^11 - 12*a*b^4*c^12 + 48*a^2*b^2*c^13 - 64*a^3*c^14)*d^9*x^8 + 1024*(b^7*c^10 - 12*a*b^5*c^11 + 48*a^2*b^3*c^12 - 64*a^3*b*c^13)*d^9*x^7 + 1792*(b^8*c^9 - 12*a*b^6*c^10 + 48*a^2*b^4*c^11 - 64*a^3*b^2*c^12)*d^9*x^6 + 1792*(b^9*c^8 - 12*a*b^7*c^9 + 48*a^2*b^5*c^10 - 64*a^3*b^3*c^11)*d^9*x^5 + 1120*(b^10*c^7 - 12*a*b^8*c^8 + 48*a^2*b^6*c^9 - 64*a^3*b^4*c^10)*d^9*x^4 + 448*(b^11*c^6 - 12*a*b^9*c^7 + 48*a^2*b^7*c^8 - 64*a^3*b^5*c^9)*d^9*x^3 + 112*(b^12*c^5 - 12*a*b^10*c^6 + 48*a^2*b^8*c^7 - 64*a^3*b^6*c^8)*d^9*x^2 + 16*(b^13*c^4 - 12*a*b^11*c^5 + 48*a^2*b^9*c^6 - 64*a^3*b^7*c^7)*d^9*x + (b^14*c^3 - 12*a*b^12*c^4 + 48*a^2*b^10*c^5 - 64*a^3*b^8*c^6)*d^9), -1/2048*(3*(256*c^8*x^8 + 1024*b*c^7*x^7 + 1792*b^2*c^6*x^6 + 1792*b^3*c^5*x^5 + 1120*b^4*c^4*x^4 + 448*b^5*c^3*x^3 + 112*b^6*c^2*x^2 + 16*b^7*c*x + b^8)*sqrt(b^2*c - 4*a*c^2)*arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c)) + 2*(3*b^8*c - 4*a*b^6*c^2 - 416*a^2*b^4*c^3 + 2560*a^3*b^2*c^4 - 4096*a^4*c^5 - 192*(b^2*c^7 - 4*a*c^8)*x^6 - 576*(b^3*c^6 - 4*a*b*c^7)*x^5 - 16*(47*b^4*c^5 - 196*a*b^2*c^6 + 32*a^2*c^7)*x^4 - 32*(17*b^5*c^4 - 76*a*b^3*c^5 + 32*a^2*b*c^6)*x^3 - 12*(11*b^6*c^3 + 4*a*b^4*c^4 - 320*a^2*b^2*c^5 + 512*a^3*c^6)*x^2 + 4*(11*b^7*c^2 - 220*a*b^5*c^3 + 1088*a^2*b^3*c^4 - 1536*a^3*b*c^5)*x)*sqrt(c*x^2 + b*x + a))/(256*(b^6*c^11 - 12*a*b^4*c^12 + 48*a^2*b^2*c^13 - 64*a^3*c^14)*d^9*x^8 + 1024*(b^7*c^10 - 12*a*b^5*c^11 + 48*a^2*b^3*c^12 - 64*a^3*b*c^13)*d^9*x^7 + 1792*(b^8*c^9 - 12*a*b^6*c^10 + 48*a^2*b^4*c^11 - 64*a^3*b^2*c^12)*d^9*x^6 + 1792*(b^9*c^8 - 12*a*b^7*c^9 + 48*a^2*b^5*c^10 - 64*a^3*b^3*c^11)*d^9*x^5 + 1120*(b^10*c^7 - 12*a*b^8*c^8 + 48*a^2*b^6*c^9 - 64*a^3*b^4*c^10)*d^9*x^4 + 448*(b^11*c^6 - 12*a*b^9*c^7 + 48*a^2*b^7*c^8 - 64*a^3*b^5*c^9)*d^9*x^3 + 112*(b^12*c^5 - 12*a*b^10*c^6 + 48*a^2*b^8*c^7 - 64*a^3*b^6*c^8)*d^9*x^2 + 16*(b^13*c^4 - 12*a*b^11*c^5 + 48*a^2*b^9*c^6 - 64*a^3*b^7*c^7)*d^9*x + (b^14*c^3 - 12*a*b^12*c^4 + 48*a^2*b^10*c^5 - 64*a^3*b^8*c^6)*d^9)]","B",0
1216,1,676,0,27.150283," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^10,x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, c^{6} x^{8} + 512 \, b c^{5} x^{7} + 16 \, {\left(57 \, b^{2} c^{4} - 4 \, a c^{5}\right)} x^{6} + 63 \, a^{2} b^{4} - 360 \, a^{3} b^{2} c + 560 \, a^{4} c^{2} + 16 \, {\left(59 \, b^{3} c^{3} - 12 \, a b c^{4}\right)} x^{5} + {\left(623 \, b^{4} c^{2} - 264 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(135 \, b^{5} c - 104 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} x^{3} + {\left(63 \, b^{6} + 54 \, a b^{4} c - 528 \, a^{2} b^{2} c^{2} + 800 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(63 \, a b^{5} - 288 \, a^{2} b^{3} c + 400 \, a^{3} b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{315 \, {\left(512 \, {\left(b^{6} c^{9} - 12 \, a b^{4} c^{10} + 48 \, a^{2} b^{2} c^{11} - 64 \, a^{3} c^{12}\right)} d^{10} x^{9} + 2304 \, {\left(b^{7} c^{8} - 12 \, a b^{5} c^{9} + 48 \, a^{2} b^{3} c^{10} - 64 \, a^{3} b c^{11}\right)} d^{10} x^{8} + 4608 \, {\left(b^{8} c^{7} - 12 \, a b^{6} c^{8} + 48 \, a^{2} b^{4} c^{9} - 64 \, a^{3} b^{2} c^{10}\right)} d^{10} x^{7} + 5376 \, {\left(b^{9} c^{6} - 12 \, a b^{7} c^{7} + 48 \, a^{2} b^{5} c^{8} - 64 \, a^{3} b^{3} c^{9}\right)} d^{10} x^{6} + 4032 \, {\left(b^{10} c^{5} - 12 \, a b^{8} c^{6} + 48 \, a^{2} b^{6} c^{7} - 64 \, a^{3} b^{4} c^{8}\right)} d^{10} x^{5} + 2016 \, {\left(b^{11} c^{4} - 12 \, a b^{9} c^{5} + 48 \, a^{2} b^{7} c^{6} - 64 \, a^{3} b^{5} c^{7}\right)} d^{10} x^{4} + 672 \, {\left(b^{12} c^{3} - 12 \, a b^{10} c^{4} + 48 \, a^{2} b^{8} c^{5} - 64 \, a^{3} b^{6} c^{6}\right)} d^{10} x^{3} + 144 \, {\left(b^{13} c^{2} - 12 \, a b^{11} c^{3} + 48 \, a^{2} b^{9} c^{4} - 64 \, a^{3} b^{7} c^{5}\right)} d^{10} x^{2} + 18 \, {\left(b^{14} c - 12 \, a b^{12} c^{2} + 48 \, a^{2} b^{10} c^{3} - 64 \, a^{3} b^{8} c^{4}\right)} d^{10} x + {\left(b^{15} - 12 \, a b^{13} c + 48 \, a^{2} b^{11} c^{2} - 64 \, a^{3} b^{9} c^{3}\right)} d^{10}\right)}}"," ",0,"2/315*(128*c^6*x^8 + 512*b*c^5*x^7 + 16*(57*b^2*c^4 - 4*a*c^5)*x^6 + 63*a^2*b^4 - 360*a^3*b^2*c + 560*a^4*c^2 + 16*(59*b^3*c^3 - 12*a*b*c^4)*x^5 + (623*b^4*c^2 - 264*a*b^2*c^3 + 48*a^2*c^4)*x^4 + 2*(135*b^5*c - 104*a*b^3*c^2 + 48*a^2*b*c^3)*x^3 + (63*b^6 + 54*a*b^4*c - 528*a^2*b^2*c^2 + 800*a^3*c^3)*x^2 + 2*(63*a*b^5 - 288*a^2*b^3*c + 400*a^3*b*c^2)*x)*sqrt(c*x^2 + b*x + a)/(512*(b^6*c^9 - 12*a*b^4*c^10 + 48*a^2*b^2*c^11 - 64*a^3*c^12)*d^10*x^9 + 2304*(b^7*c^8 - 12*a*b^5*c^9 + 48*a^2*b^3*c^10 - 64*a^3*b*c^11)*d^10*x^8 + 4608*(b^8*c^7 - 12*a*b^6*c^8 + 48*a^2*b^4*c^9 - 64*a^3*b^2*c^10)*d^10*x^7 + 5376*(b^9*c^6 - 12*a*b^7*c^7 + 48*a^2*b^5*c^8 - 64*a^3*b^3*c^9)*d^10*x^6 + 4032*(b^10*c^5 - 12*a*b^8*c^6 + 48*a^2*b^6*c^7 - 64*a^3*b^4*c^8)*d^10*x^5 + 2016*(b^11*c^4 - 12*a*b^9*c^5 + 48*a^2*b^7*c^6 - 64*a^3*b^5*c^7)*d^10*x^4 + 672*(b^12*c^3 - 12*a*b^10*c^4 + 48*a^2*b^8*c^5 - 64*a^3*b^6*c^6)*d^10*x^3 + 144*(b^13*c^2 - 12*a*b^11*c^3 + 48*a^2*b^9*c^4 - 64*a^3*b^7*c^5)*d^10*x^2 + 18*(b^14*c - 12*a*b^12*c^2 + 48*a^2*b^10*c^3 - 64*a^3*b^8*c^4)*d^10*x + (b^15 - 12*a*b^13*c + 48*a^2*b^11*c^2 - 64*a^3*b^9*c^3)*d^10)","B",0
1217,1,338,0,0.490558," ","integrate((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2}{693} \, {\left(1008 \, c^{7} d^{5} x^{10} + 5040 \, b c^{6} d^{5} x^{9} + 56 \, {\left(191 \, b^{2} c^{5} + 46 \, a c^{6}\right)} d^{5} x^{8} + 448 \, {\left(28 \, b^{3} c^{4} + 23 \, a b c^{5}\right)} d^{5} x^{7} + {\left(8835 \, b^{4} c^{3} + 17128 \, a b^{2} c^{4} + 1808 \, a^{2} c^{5}\right)} d^{5} x^{6} + {\left(3769 \, b^{5} c^{2} + 15320 \, a b^{3} c^{3} + 5424 \, a^{2} b c^{4}\right)} d^{5} x^{5} + {\left(913 \, b^{6} c + 7889 \, a b^{4} c^{2} + 6744 \, a^{2} b^{2} c^{3} + 48 \, a^{3} c^{4}\right)} d^{5} x^{4} + {\left(99 \, b^{7} + 2266 \, a b^{5} c + 4448 \, a^{2} b^{3} c^{2} + 96 \, a^{3} b c^{3}\right)} d^{5} x^{3} + {\left(297 \, a b^{6} + 1617 \, a^{2} b^{4} c + 136 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} d^{5} x^{2} + {\left(297 \, a^{2} b^{5} + 88 \, a^{3} b^{3} c - 64 \, a^{4} b c^{2}\right)} d^{5} x + {\left(99 \, a^{3} b^{4} - 176 \, a^{4} b^{2} c + 128 \, a^{5} c^{2}\right)} d^{5}\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/693*(1008*c^7*d^5*x^10 + 5040*b*c^6*d^5*x^9 + 56*(191*b^2*c^5 + 46*a*c^6)*d^5*x^8 + 448*(28*b^3*c^4 + 23*a*b*c^5)*d^5*x^7 + (8835*b^4*c^3 + 17128*a*b^2*c^4 + 1808*a^2*c^5)*d^5*x^6 + (3769*b^5*c^2 + 15320*a*b^3*c^3 + 5424*a^2*b*c^4)*d^5*x^5 + (913*b^6*c + 7889*a*b^4*c^2 + 6744*a^2*b^2*c^3 + 48*a^3*c^4)*d^5*x^4 + (99*b^7 + 2266*a*b^5*c + 4448*a^2*b^3*c^2 + 96*a^3*b*c^3)*d^5*x^3 + (297*a*b^6 + 1617*a^2*b^4*c + 136*a^3*b^2*c^2 - 64*a^4*c^3)*d^5*x^2 + (297*a^2*b^5 + 88*a^3*b^3*c - 64*a^4*b*c^2)*d^5*x + (99*a^3*b^4 - 176*a^4*b^2*c + 128*a^5*c^2)*d^5)*sqrt(c*x^2 + b*x + a)","B",0
1218,1,923,0,0.504424," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} \sqrt{c} d^{4} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(65536 \, c^{10} d^{4} x^{9} + 294912 \, b c^{9} d^{4} x^{8} + 6144 \, {\left(89 \, b^{2} c^{8} + 28 \, a c^{9}\right)} d^{4} x^{7} + 21504 \, {\left(25 \, b^{3} c^{7} + 28 \, a b c^{8}\right)} d^{4} x^{6} + 256 \, {\left(1165 \, b^{4} c^{6} + 3280 \, a b^{2} c^{7} + 496 \, a^{2} c^{8}\right)} d^{4} x^{5} + 128 \, {\left(701 \, b^{5} c^{5} + 4640 \, a b^{3} c^{6} + 2480 \, a^{2} b c^{7}\right)} d^{4} x^{4} + 16 \, {\left(731 \, b^{6} c^{4} + 13660 \, a b^{4} c^{5} + 19600 \, a^{2} b^{2} c^{6} + 320 \, a^{3} c^{7}\right)} d^{4} x^{3} + 8 \, {\left(b^{7} c^{3} + 4372 \, a b^{5} c^{4} + 19120 \, a^{2} b^{3} c^{5} + 960 \, a^{3} b c^{6}\right)} d^{4} x^{2} - 2 \, {\left(5 \, b^{8} c^{2} - 88 \, a b^{6} c^{3} - 16960 \, a^{2} b^{4} c^{4} - 5760 \, a^{3} b^{2} c^{5} + 3840 \, a^{4} c^{6}\right)} d^{4} x + {\left(15 \, b^{9} c - 280 \, a b^{7} c^{2} + 2048 \, a^{2} b^{5} c^{3} + 4480 \, a^{3} b^{3} c^{4} - 3840 \, a^{4} b c^{5}\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}}{163840 \, c^{4}}, \frac{15 \, {\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} \sqrt{-c} d^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(65536 \, c^{10} d^{4} x^{9} + 294912 \, b c^{9} d^{4} x^{8} + 6144 \, {\left(89 \, b^{2} c^{8} + 28 \, a c^{9}\right)} d^{4} x^{7} + 21504 \, {\left(25 \, b^{3} c^{7} + 28 \, a b c^{8}\right)} d^{4} x^{6} + 256 \, {\left(1165 \, b^{4} c^{6} + 3280 \, a b^{2} c^{7} + 496 \, a^{2} c^{8}\right)} d^{4} x^{5} + 128 \, {\left(701 \, b^{5} c^{5} + 4640 \, a b^{3} c^{6} + 2480 \, a^{2} b c^{7}\right)} d^{4} x^{4} + 16 \, {\left(731 \, b^{6} c^{4} + 13660 \, a b^{4} c^{5} + 19600 \, a^{2} b^{2} c^{6} + 320 \, a^{3} c^{7}\right)} d^{4} x^{3} + 8 \, {\left(b^{7} c^{3} + 4372 \, a b^{5} c^{4} + 19120 \, a^{2} b^{3} c^{5} + 960 \, a^{3} b c^{6}\right)} d^{4} x^{2} - 2 \, {\left(5 \, b^{8} c^{2} - 88 \, a b^{6} c^{3} - 16960 \, a^{2} b^{4} c^{4} - 5760 \, a^{3} b^{2} c^{5} + 3840 \, a^{4} c^{6}\right)} d^{4} x + {\left(15 \, b^{9} c - 280 \, a b^{7} c^{2} + 2048 \, a^{2} b^{5} c^{3} + 4480 \, a^{3} b^{3} c^{4} - 3840 \, a^{4} b c^{5}\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}}{81920 \, c^{4}}\right]"," ",0,"[-1/163840*(15*(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*sqrt(c)*d^4*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(65536*c^10*d^4*x^9 + 294912*b*c^9*d^4*x^8 + 6144*(89*b^2*c^8 + 28*a*c^9)*d^4*x^7 + 21504*(25*b^3*c^7 + 28*a*b*c^8)*d^4*x^6 + 256*(1165*b^4*c^6 + 3280*a*b^2*c^7 + 496*a^2*c^8)*d^4*x^5 + 128*(701*b^5*c^5 + 4640*a*b^3*c^6 + 2480*a^2*b*c^7)*d^4*x^4 + 16*(731*b^6*c^4 + 13660*a*b^4*c^5 + 19600*a^2*b^2*c^6 + 320*a^3*c^7)*d^4*x^3 + 8*(b^7*c^3 + 4372*a*b^5*c^4 + 19120*a^2*b^3*c^5 + 960*a^3*b*c^6)*d^4*x^2 - 2*(5*b^8*c^2 - 88*a*b^6*c^3 - 16960*a^2*b^4*c^4 - 5760*a^3*b^2*c^5 + 3840*a^4*c^6)*d^4*x + (15*b^9*c - 280*a*b^7*c^2 + 2048*a^2*b^5*c^3 + 4480*a^3*b^3*c^4 - 3840*a^4*b*c^5)*d^4)*sqrt(c*x^2 + b*x + a))/c^4, 1/81920*(15*(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*sqrt(-c)*d^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(65536*c^10*d^4*x^9 + 294912*b*c^9*d^4*x^8 + 6144*(89*b^2*c^8 + 28*a*c^9)*d^4*x^7 + 21504*(25*b^3*c^7 + 28*a*b*c^8)*d^4*x^6 + 256*(1165*b^4*c^6 + 3280*a*b^2*c^7 + 496*a^2*c^8)*d^4*x^5 + 128*(701*b^5*c^5 + 4640*a*b^3*c^6 + 2480*a^2*b*c^7)*d^4*x^4 + 16*(731*b^6*c^4 + 13660*a*b^4*c^5 + 19600*a^2*b^2*c^6 + 320*a^3*c^7)*d^4*x^3 + 8*(b^7*c^3 + 4372*a*b^5*c^4 + 19120*a^2*b^3*c^5 + 960*a^3*b*c^6)*d^4*x^2 - 2*(5*b^8*c^2 - 88*a*b^6*c^3 - 16960*a^2*b^4*c^4 - 5760*a^3*b^2*c^5 + 3840*a^4*c^6)*d^4*x + (15*b^9*c - 280*a*b^7*c^2 + 2048*a^2*b^5*c^3 + 4480*a^3*b^3*c^4 - 3840*a^4*b*c^5)*d^4)*sqrt(c*x^2 + b*x + a))/c^4]","B",0
1219,1,215,0,0.452997," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2}{63} \, {\left(28 \, c^{5} d^{3} x^{8} + 112 \, b c^{4} d^{3} x^{7} + {\left(177 \, b^{2} c^{3} + 76 \, a c^{4}\right)} d^{3} x^{6} + {\left(139 \, b^{3} c^{2} + 228 \, a b c^{3}\right)} d^{3} x^{5} + 5 \, {\left(11 \, b^{4} c + 51 \, a b^{2} c^{2} + 12 \, a^{2} c^{3}\right)} d^{3} x^{4} + {\left(9 \, b^{5} + 130 \, a b^{3} c + 120 \, a^{2} b c^{2}\right)} d^{3} x^{3} + {\left(27 \, a b^{4} + 87 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{3} x^{2} + {\left(27 \, a^{2} b^{3} + 4 \, a^{3} b c\right)} d^{3} x + {\left(9 \, a^{3} b^{2} - 8 \, a^{4} c\right)} d^{3}\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/63*(28*c^5*d^3*x^8 + 112*b*c^4*d^3*x^7 + (177*b^2*c^3 + 76*a*c^4)*d^3*x^6 + (139*b^3*c^2 + 228*a*b*c^3)*d^3*x^5 + 5*(11*b^4*c + 51*a*b^2*c^2 + 12*a^2*c^3)*d^3*x^4 + (9*b^5 + 130*a*b^3*c + 120*a^2*b*c^2)*d^3*x^3 + (27*a*b^4 + 87*a^2*b^2*c + 4*a^3*c^2)*d^3*x^2 + (27*a^2*b^3 + 4*a^3*b*c)*d^3*x + (9*a^3*b^2 - 8*a^4*c)*d^3)*sqrt(c*x^2 + b*x + a)","B",0
1220,1,675,0,0.475819," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\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{c} d^{2} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(6144 \, c^{8} d^{2} x^{7} + 21504 \, b c^{7} d^{2} x^{6} + 256 \, {\left(109 \, b^{2} c^{6} + 68 \, a c^{7}\right)} d^{2} x^{5} + 640 \, {\left(25 \, b^{3} c^{5} + 68 \, a b c^{6}\right)} d^{2} x^{4} + 16 \, {\left(219 \, b^{4} c^{4} + 2248 \, a b^{2} c^{5} + 944 \, a^{2} c^{6}\right)} d^{2} x^{3} + 8 \, {\left(b^{5} c^{3} + 1304 \, a b^{3} c^{4} + 2832 \, a^{2} b c^{5}\right)} d^{2} x^{2} - 2 \, {\left(5 \, b^{6} c^{2} - 68 \, a b^{4} c^{3} - 4944 \, a^{2} b^{2} c^{4} - 960 \, a^{3} c^{5}\right)} d^{2} x + {\left(15 \, b^{7} c - 220 \, a b^{5} c^{2} + 1168 \, a^{2} b^{3} c^{3} + 960 \, a^{3} b c^{4}\right)} d^{2}\right)} \sqrt{c x^{2} + b x + a}}{49152 \, c^{4}}, \frac{15 \, {\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{-c} d^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(6144 \, c^{8} d^{2} x^{7} + 21504 \, b c^{7} d^{2} x^{6} + 256 \, {\left(109 \, b^{2} c^{6} + 68 \, a c^{7}\right)} d^{2} x^{5} + 640 \, {\left(25 \, b^{3} c^{5} + 68 \, a b c^{6}\right)} d^{2} x^{4} + 16 \, {\left(219 \, b^{4} c^{4} + 2248 \, a b^{2} c^{5} + 944 \, a^{2} c^{6}\right)} d^{2} x^{3} + 8 \, {\left(b^{5} c^{3} + 1304 \, a b^{3} c^{4} + 2832 \, a^{2} b c^{5}\right)} d^{2} x^{2} - 2 \, {\left(5 \, b^{6} c^{2} - 68 \, a b^{4} c^{3} - 4944 \, a^{2} b^{2} c^{4} - 960 \, a^{3} c^{5}\right)} d^{2} x + {\left(15 \, b^{7} c - 220 \, a b^{5} c^{2} + 1168 \, a^{2} b^{3} c^{3} + 960 \, a^{3} b c^{4}\right)} d^{2}\right)} \sqrt{c x^{2} + b x + a}}{24576 \, c^{4}}\right]"," ",0,"[1/49152*(15*(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(c)*d^2*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(6144*c^8*d^2*x^7 + 21504*b*c^7*d^2*x^6 + 256*(109*b^2*c^6 + 68*a*c^7)*d^2*x^5 + 640*(25*b^3*c^5 + 68*a*b*c^6)*d^2*x^4 + 16*(219*b^4*c^4 + 2248*a*b^2*c^5 + 944*a^2*c^6)*d^2*x^3 + 8*(b^5*c^3 + 1304*a*b^3*c^4 + 2832*a^2*b*c^5)*d^2*x^2 - 2*(5*b^6*c^2 - 68*a*b^4*c^3 - 4944*a^2*b^2*c^4 - 960*a^3*c^5)*d^2*x + (15*b^7*c - 220*a*b^5*c^2 + 1168*a^2*b^3*c^3 + 960*a^3*b*c^4)*d^2)*sqrt(c*x^2 + b*x + a))/c^4, 1/24576*(15*(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(-c)*d^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(6144*c^8*d^2*x^7 + 21504*b*c^7*d^2*x^6 + 256*(109*b^2*c^6 + 68*a*c^7)*d^2*x^5 + 640*(25*b^3*c^5 + 68*a*b*c^6)*d^2*x^4 + 16*(219*b^4*c^4 + 2248*a*b^2*c^5 + 944*a^2*c^6)*d^2*x^3 + 8*(b^5*c^3 + 1304*a*b^3*c^4 + 2832*a^2*b*c^5)*d^2*x^2 - 2*(5*b^6*c^2 - 68*a*b^4*c^3 - 4944*a^2*b^2*c^4 - 960*a^3*c^5)*d^2*x + (15*b^7*c - 220*a*b^5*c^2 + 1168*a^2*b^3*c^3 + 960*a^3*b*c^4)*d^2)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
1221,1,94,0,0.429747," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2}{7} \, {\left(c^{3} d x^{6} + 3 \, b c^{2} d x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} d x^{4} + 3 \, a^{2} b d x + {\left(b^{3} + 6 \, a b c\right)} d x^{3} + a^{3} d + 3 \, {\left(a b^{2} + a^{2} c\right)} d x^{2}\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/7*(c^3*d*x^6 + 3*b*c^2*d*x^5 + 3*(b^2*c + a*c^2)*d*x^4 + 3*a^2*b*d*x + (b^3 + 6*a*b*c)*d*x^3 + a^3*d + 3*(a*b^2 + a^2*c)*d*x^2)*sqrt(c*x^2 + b*x + a)","B",0
1222,1,372,0,0.552559," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-\frac{b^{2} - 4 \, a c}{c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{c x^{2} + b x + a} c \sqrt{-\frac{b^{2} - 4 \, a c}{c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, {\left(48 \, c^{4} x^{4} + 96 \, b c^{3} x^{3} + 15 \, b^{4} - 140 \, a b^{2} c + 368 \, a^{2} c^{2} + 4 \, {\left(7 \, b^{2} c^{2} + 44 \, a c^{3}\right)} x^{2} - 4 \, {\left(5 \, b^{3} c - 44 \, a b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1920 \, c^{3} d}, \frac{15 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{\frac{b^{2} - 4 \, a c}{c}} \arctan\left(\frac{\sqrt{\frac{b^{2} - 4 \, a c}{c}}}{2 \, \sqrt{c x^{2} + b x + a}}\right) + 2 \, {\left(48 \, c^{4} x^{4} + 96 \, b c^{3} x^{3} + 15 \, b^{4} - 140 \, a b^{2} c + 368 \, a^{2} c^{2} + 4 \, {\left(7 \, b^{2} c^{2} + 44 \, a c^{3}\right)} x^{2} - 4 \, {\left(5 \, b^{3} c - 44 \, a b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{960 \, c^{3} d}\right]"," ",0,"[1/1920*(15*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-(b^2 - 4*a*c)/c)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(c*x^2 + b*x + a)*c*sqrt(-(b^2 - 4*a*c)/c))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*(48*c^4*x^4 + 96*b*c^3*x^3 + 15*b^4 - 140*a*b^2*c + 368*a^2*c^2 + 4*(7*b^2*c^2 + 44*a*c^3)*x^2 - 4*(5*b^3*c - 44*a*b*c^2)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d), 1/960*(15*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt((b^2 - 4*a*c)/c)*arctan(1/2*sqrt((b^2 - 4*a*c)/c)/sqrt(c*x^2 + b*x + a)) + 2*(48*c^4*x^4 + 96*b*c^3*x^3 + 15*b^4 - 140*a*b^2*c + 368*a^2*c^2 + 4*(7*b^2*c^2 + 44*a*c^3)*x^2 - 4*(5*b^3*c - 44*a*b*c^2)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d)]","A",0
1223,1,427,0,0.586135," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(32 \, c^{5} x^{4} + 64 \, b c^{4} x^{3} - 15 \, b^{4} c + 100 \, a b^{2} c^{2} - 128 \, a^{2} c^{3} + 12 \, {\left(b^{2} c^{3} + 12 \, a c^{4}\right)} x^{2} - 4 \, {\left(5 \, b^{3} c^{2} - 36 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1024 \, {\left(2 \, c^{5} d^{2} x + b c^{4} d^{2}\right)}}, -\frac{15 \, {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2} + 2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(32 \, c^{5} x^{4} + 64 \, b c^{4} x^{3} - 15 \, b^{4} c + 100 \, a b^{2} c^{2} - 128 \, a^{2} c^{3} + 12 \, {\left(b^{2} c^{3} + 12 \, a c^{4}\right)} x^{2} - 4 \, {\left(5 \, b^{3} c^{2} - 36 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{512 \, {\left(2 \, c^{5} d^{2} x + b c^{4} d^{2}\right)}}\right]"," ",0,"[1/1024*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(32*c^5*x^4 + 64*b*c^4*x^3 - 15*b^4*c + 100*a*b^2*c^2 - 128*a^2*c^3 + 12*(b^2*c^3 + 12*a*c^4)*x^2 - 4*(5*b^3*c^2 - 36*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/(2*c^5*d^2*x + b*c^4*d^2), -1/512*(15*(b^5 - 8*a*b^3*c + 16*a^2*b*c^2 + 2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(32*c^5*x^4 + 64*b*c^4*x^3 - 15*b^4*c + 100*a*b^2*c^2 - 128*a^2*c^3 + 12*(b^2*c^3 + 12*a*c^4)*x^2 - 4*(5*b^3*c^2 - 36*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/(2*c^5*d^2*x + b*c^4*d^2)]","A",0
1224,1,480,0,0.711780," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{4} - 4 \, a b^{2} c + 4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \sqrt{-\frac{b^{2} - 4 \, a c}{c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{c x^{2} + b x + a} c \sqrt{-\frac{b^{2} - 4 \, a c}{c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) - 4 \, {\left(32 \, c^{4} x^{4} + 64 \, b c^{3} x^{3} - 15 \, b^{4} + 80 \, a b^{2} c - 48 \, a^{2} c^{2} - 8 \, {\left(b^{2} c^{2} - 28 \, a c^{3}\right)} x^{2} - 8 \, {\left(5 \, b^{3} c - 28 \, a b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, {\left(4 \, c^{5} d^{3} x^{2} + 4 \, b c^{4} d^{3} x + b^{2} c^{3} d^{3}\right)}}, -\frac{15 \, {\left(b^{4} - 4 \, a b^{2} c + 4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \sqrt{\frac{b^{2} - 4 \, a c}{c}} \arctan\left(\frac{\sqrt{\frac{b^{2} - 4 \, a c}{c}}}{2 \, \sqrt{c x^{2} + b x + a}}\right) - 2 \, {\left(32 \, c^{4} x^{4} + 64 \, b c^{3} x^{3} - 15 \, b^{4} + 80 \, a b^{2} c - 48 \, a^{2} c^{2} - 8 \, {\left(b^{2} c^{2} - 28 \, a c^{3}\right)} x^{2} - 8 \, {\left(5 \, b^{3} c - 28 \, a b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, {\left(4 \, c^{5} d^{3} x^{2} + 4 \, b c^{4} d^{3} x + b^{2} c^{3} d^{3}\right)}}\right]"," ",0,"[-1/768*(15*(b^4 - 4*a*b^2*c + 4*(b^2*c^2 - 4*a*c^3)*x^2 + 4*(b^3*c - 4*a*b*c^2)*x)*sqrt(-(b^2 - 4*a*c)/c)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(c*x^2 + b*x + a)*c*sqrt(-(b^2 - 4*a*c)/c))/(4*c^2*x^2 + 4*b*c*x + b^2)) - 4*(32*c^4*x^4 + 64*b*c^3*x^3 - 15*b^4 + 80*a*b^2*c - 48*a^2*c^2 - 8*(b^2*c^2 - 28*a*c^3)*x^2 - 8*(5*b^3*c - 28*a*b*c^2)*x)*sqrt(c*x^2 + b*x + a))/(4*c^5*d^3*x^2 + 4*b*c^4*d^3*x + b^2*c^3*d^3), -1/384*(15*(b^4 - 4*a*b^2*c + 4*(b^2*c^2 - 4*a*c^3)*x^2 + 4*(b^3*c - 4*a*b*c^2)*x)*sqrt((b^2 - 4*a*c)/c)*arctan(1/2*sqrt((b^2 - 4*a*c)/c)/sqrt(c*x^2 + b*x + a)) - 2*(32*c^4*x^4 + 64*b*c^3*x^3 - 15*b^4 + 80*a*b^2*c - 48*a^2*c^2 - 8*(b^2*c^2 - 28*a*c^3)*x^2 - 8*(5*b^3*c - 28*a*b*c^2)*x)*sqrt(c*x^2 + b*x + a))/(4*c^5*d^3*x^2 + 4*b*c^4*d^3*x + b^2*c^3*d^3)]","A",0
1225,1,529,0,1.094609," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^4,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{5} - 4 \, a b^{3} c + 8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} + 12 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} + 6 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(48 \, c^{5} x^{4} + 96 \, b c^{4} x^{3} + 15 \, b^{4} c - 40 \, a b^{2} c^{2} - 32 \, a^{2} c^{3} + 32 \, {\left(4 \, b^{2} c^{3} - 7 \, a c^{4}\right)} x^{2} + 16 \, {\left(5 \, b^{3} c^{2} - 14 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, {\left(8 \, c^{7} d^{4} x^{3} + 12 \, b c^{6} d^{4} x^{2} + 6 \, b^{2} c^{5} d^{4} x + b^{3} c^{4} d^{4}\right)}}, \frac{15 \, {\left(b^{5} - 4 \, a b^{3} c + 8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} + 12 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} + 6 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(48 \, c^{5} x^{4} + 96 \, b c^{4} x^{3} + 15 \, b^{4} c - 40 \, a b^{2} c^{2} - 32 \, a^{2} c^{3} + 32 \, {\left(4 \, b^{2} c^{3} - 7 \, a c^{4}\right)} x^{2} + 16 \, {\left(5 \, b^{3} c^{2} - 14 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, {\left(8 \, c^{7} d^{4} x^{3} + 12 \, b c^{6} d^{4} x^{2} + 6 \, b^{2} c^{5} d^{4} x + b^{3} c^{4} d^{4}\right)}}\right]"," ",0,"[-1/768*(15*(b^5 - 4*a*b^3*c + 8*(b^2*c^3 - 4*a*c^4)*x^3 + 12*(b^3*c^2 - 4*a*b*c^3)*x^2 + 6*(b^4*c - 4*a*b^2*c^2)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(48*c^5*x^4 + 96*b*c^4*x^3 + 15*b^4*c - 40*a*b^2*c^2 - 32*a^2*c^3 + 32*(4*b^2*c^3 - 7*a*c^4)*x^2 + 16*(5*b^3*c^2 - 14*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/(8*c^7*d^4*x^3 + 12*b*c^6*d^4*x^2 + 6*b^2*c^5*d^4*x + b^3*c^4*d^4), 1/384*(15*(b^5 - 4*a*b^3*c + 8*(b^2*c^3 - 4*a*c^4)*x^3 + 12*(b^3*c^2 - 4*a*b*c^3)*x^2 + 6*(b^4*c - 4*a*b^2*c^2)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(48*c^5*x^4 + 96*b*c^4*x^3 + 15*b^4*c - 40*a*b^2*c^2 - 32*a^2*c^3 + 32*(4*b^2*c^3 - 7*a*c^4)*x^2 + 16*(5*b^3*c^2 - 14*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/(8*c^7*d^4*x^3 + 12*b*c^6*d^4*x^2 + 6*b^2*c^5*d^4*x + b^3*c^4*d^4)]","B",0
1226,1,524,0,1.534225," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(16 \, c^{4} x^{4} + 32 \, b c^{3} x^{3} + 24 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x + b^{4}\right)} \sqrt{-\frac{b^{2} - 4 \, a c}{c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{c x^{2} + b x + a} c \sqrt{-\frac{b^{2} - 4 \, a c}{c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, {\left(128 \, c^{4} x^{4} + 256 \, b c^{3} x^{3} + 15 \, b^{4} - 20 \, a b^{2} c - 32 \, a^{2} c^{2} + 12 \, {\left(19 \, b^{2} c^{2} - 12 \, a c^{3}\right)} x^{2} + 4 \, {\left(25 \, b^{3} c - 36 \, a b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1024 \, {\left(16 \, c^{7} d^{5} x^{4} + 32 \, b c^{6} d^{5} x^{3} + 24 \, b^{2} c^{5} d^{5} x^{2} + 8 \, b^{3} c^{4} d^{5} x + b^{4} c^{3} d^{5}\right)}}, \frac{15 \, {\left(16 \, c^{4} x^{4} + 32 \, b c^{3} x^{3} + 24 \, b^{2} c^{2} x^{2} + 8 \, b^{3} c x + b^{4}\right)} \sqrt{\frac{b^{2} - 4 \, a c}{c}} \arctan\left(\frac{\sqrt{\frac{b^{2} - 4 \, a c}{c}}}{2 \, \sqrt{c x^{2} + b x + a}}\right) + 2 \, {\left(128 \, c^{4} x^{4} + 256 \, b c^{3} x^{3} + 15 \, b^{4} - 20 \, a b^{2} c - 32 \, a^{2} c^{2} + 12 \, {\left(19 \, b^{2} c^{2} - 12 \, a c^{3}\right)} x^{2} + 4 \, {\left(25 \, b^{3} c - 36 \, a b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{512 \, {\left(16 \, c^{7} d^{5} x^{4} + 32 \, b c^{6} d^{5} x^{3} + 24 \, b^{2} c^{5} d^{5} x^{2} + 8 \, b^{3} c^{4} d^{5} x + b^{4} c^{3} d^{5}\right)}}\right]"," ",0,"[1/1024*(15*(16*c^4*x^4 + 32*b*c^3*x^3 + 24*b^2*c^2*x^2 + 8*b^3*c*x + b^4)*sqrt(-(b^2 - 4*a*c)/c)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(c*x^2 + b*x + a)*c*sqrt(-(b^2 - 4*a*c)/c))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*(128*c^4*x^4 + 256*b*c^3*x^3 + 15*b^4 - 20*a*b^2*c - 32*a^2*c^2 + 12*(19*b^2*c^2 - 12*a*c^3)*x^2 + 4*(25*b^3*c - 36*a*b*c^2)*x)*sqrt(c*x^2 + b*x + a))/(16*c^7*d^5*x^4 + 32*b*c^6*d^5*x^3 + 24*b^2*c^5*d^5*x^2 + 8*b^3*c^4*d^5*x + b^4*c^3*d^5), 1/512*(15*(16*c^4*x^4 + 32*b*c^3*x^3 + 24*b^2*c^2*x^2 + 8*b^3*c*x + b^4)*sqrt((b^2 - 4*a*c)/c)*arctan(1/2*sqrt((b^2 - 4*a*c)/c)/sqrt(c*x^2 + b*x + a)) + 2*(128*c^4*x^4 + 256*b*c^3*x^3 + 15*b^4 - 20*a*b^2*c - 32*a^2*c^2 + 12*(19*b^2*c^2 - 12*a*c^3)*x^2 + 4*(25*b^3*c - 36*a*b*c^2)*x)*sqrt(c*x^2 + b*x + a))/(16*c^7*d^5*x^4 + 32*b*c^6*d^5*x^3 + 24*b^2*c^5*d^5*x^2 + 8*b^3*c^4*d^5*x + b^4*c^3*d^5)]","A",0
1227,1,549,0,2.515647," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(32 \, c^{5} x^{5} + 80 \, b c^{4} x^{4} + 80 \, b^{2} c^{3} x^{3} + 40 \, b^{3} c^{2} x^{2} + 10 \, b^{4} c x + b^{5}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(368 \, c^{5} x^{4} + 736 \, b c^{4} x^{3} + 15 \, b^{4} c + 20 \, a b^{2} c^{2} + 48 \, a^{2} c^{3} + 4 \, {\left(127 \, b^{2} c^{3} + 44 \, a c^{4}\right)} x^{2} + 4 \, {\left(35 \, b^{3} c^{2} + 44 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1920 \, {\left(32 \, c^{9} d^{6} x^{5} + 80 \, b c^{8} d^{6} x^{4} + 80 \, b^{2} c^{7} d^{6} x^{3} + 40 \, b^{3} c^{6} d^{6} x^{2} + 10 \, b^{4} c^{5} d^{6} x + b^{5} c^{4} d^{6}\right)}}, -\frac{15 \, {\left(32 \, c^{5} x^{5} + 80 \, b c^{4} x^{4} + 80 \, b^{2} c^{3} x^{3} + 40 \, b^{3} c^{2} x^{2} + 10 \, b^{4} c x + b^{5}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(368 \, c^{5} x^{4} + 736 \, b c^{4} x^{3} + 15 \, b^{4} c + 20 \, a b^{2} c^{2} + 48 \, a^{2} c^{3} + 4 \, {\left(127 \, b^{2} c^{3} + 44 \, a c^{4}\right)} x^{2} + 4 \, {\left(35 \, b^{3} c^{2} + 44 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{960 \, {\left(32 \, c^{9} d^{6} x^{5} + 80 \, b c^{8} d^{6} x^{4} + 80 \, b^{2} c^{7} d^{6} x^{3} + 40 \, b^{3} c^{6} d^{6} x^{2} + 10 \, b^{4} c^{5} d^{6} x + b^{5} c^{4} d^{6}\right)}}\right]"," ",0,"[1/1920*(15*(32*c^5*x^5 + 80*b*c^4*x^4 + 80*b^2*c^3*x^3 + 40*b^3*c^2*x^2 + 10*b^4*c*x + b^5)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(368*c^5*x^4 + 736*b*c^4*x^3 + 15*b^4*c + 20*a*b^2*c^2 + 48*a^2*c^3 + 4*(127*b^2*c^3 + 44*a*c^4)*x^2 + 4*(35*b^3*c^2 + 44*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/(32*c^9*d^6*x^5 + 80*b*c^8*d^6*x^4 + 80*b^2*c^7*d^6*x^3 + 40*b^3*c^6*d^6*x^2 + 10*b^4*c^5*d^6*x + b^5*c^4*d^6), -1/960*(15*(32*c^5*x^5 + 80*b*c^4*x^4 + 80*b^2*c^3*x^3 + 40*b^3*c^2*x^2 + 10*b^4*c*x + b^5)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(368*c^5*x^4 + 736*b*c^4*x^3 + 15*b^4*c + 20*a*b^2*c^2 + 48*a^2*c^3 + 4*(127*b^2*c^3 + 44*a*c^4)*x^2 + 4*(35*b^3*c^2 + 44*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/(32*c^9*d^6*x^5 + 80*b*c^8*d^6*x^4 + 80*b^2*c^7*d^6*x^3 + 40*b^3*c^6*d^6*x^2 + 10*b^4*c^5*d^6*x + b^5*c^4*d^6)]","B",0
1228,1,914,0,3.835668," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^7,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(64 \, c^{6} x^{6} + 192 \, b c^{5} x^{5} + 240 \, b^{2} c^{4} x^{4} + 160 \, b^{3} c^{3} x^{3} + 60 \, b^{4} c^{2} x^{2} + 12 \, b^{5} c x + b^{6}\right)} \sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, {\left(15 \, b^{6} c - 20 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} - 512 \, a^{3} c^{4} + 528 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{4} + 1056 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{3} + 16 \, {\left(43 \, b^{4} c^{3} - 146 \, a b^{2} c^{4} - 104 \, a^{2} c^{5}\right)} x^{2} + 32 \, {\left(5 \, b^{5} c^{2} - 7 \, a b^{3} c^{3} - 52 \, a^{2} b c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6144 \, {\left(64 \, {\left(b^{2} c^{10} - 4 \, a c^{11}\right)} d^{7} x^{6} + 192 \, {\left(b^{3} c^{9} - 4 \, a b c^{10}\right)} d^{7} x^{5} + 240 \, {\left(b^{4} c^{8} - 4 \, a b^{2} c^{9}\right)} d^{7} x^{4} + 160 \, {\left(b^{5} c^{7} - 4 \, a b^{3} c^{8}\right)} d^{7} x^{3} + 60 \, {\left(b^{6} c^{6} - 4 \, a b^{4} c^{7}\right)} d^{7} x^{2} + 12 \, {\left(b^{7} c^{5} - 4 \, a b^{5} c^{6}\right)} d^{7} x + {\left(b^{8} c^{4} - 4 \, a b^{6} c^{5}\right)} d^{7}\right)}}, -\frac{15 \, {\left(64 \, c^{6} x^{6} + 192 \, b c^{5} x^{5} + 240 \, b^{2} c^{4} x^{4} + 160 \, b^{3} c^{3} x^{3} + 60 \, b^{4} c^{2} x^{2} + 12 \, b^{5} c x + b^{6}\right)} \sqrt{b^{2} c - 4 \, a c^{2}} \arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(15 \, b^{6} c - 20 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} - 512 \, a^{3} c^{4} + 528 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{4} + 1056 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{3} + 16 \, {\left(43 \, b^{4} c^{3} - 146 \, a b^{2} c^{4} - 104 \, a^{2} c^{5}\right)} x^{2} + 32 \, {\left(5 \, b^{5} c^{2} - 7 \, a b^{3} c^{3} - 52 \, a^{2} b c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3072 \, {\left(64 \, {\left(b^{2} c^{10} - 4 \, a c^{11}\right)} d^{7} x^{6} + 192 \, {\left(b^{3} c^{9} - 4 \, a b c^{10}\right)} d^{7} x^{5} + 240 \, {\left(b^{4} c^{8} - 4 \, a b^{2} c^{9}\right)} d^{7} x^{4} + 160 \, {\left(b^{5} c^{7} - 4 \, a b^{3} c^{8}\right)} d^{7} x^{3} + 60 \, {\left(b^{6} c^{6} - 4 \, a b^{4} c^{7}\right)} d^{7} x^{2} + 12 \, {\left(b^{7} c^{5} - 4 \, a b^{5} c^{6}\right)} d^{7} x + {\left(b^{8} c^{4} - 4 \, a b^{6} c^{5}\right)} d^{7}\right)}}\right]"," ",0,"[-1/6144*(15*(64*c^6*x^6 + 192*b*c^5*x^5 + 240*b^2*c^4*x^4 + 160*b^3*c^3*x^3 + 60*b^4*c^2*x^2 + 12*b^5*c*x + b^6)*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*(15*b^6*c - 20*a*b^4*c^2 - 32*a^2*b^2*c^3 - 512*a^3*c^4 + 528*(b^2*c^5 - 4*a*c^6)*x^4 + 1056*(b^3*c^4 - 4*a*b*c^5)*x^3 + 16*(43*b^4*c^3 - 146*a*b^2*c^4 - 104*a^2*c^5)*x^2 + 32*(5*b^5*c^2 - 7*a*b^3*c^3 - 52*a^2*b*c^4)*x)*sqrt(c*x^2 + b*x + a))/(64*(b^2*c^10 - 4*a*c^11)*d^7*x^6 + 192*(b^3*c^9 - 4*a*b*c^10)*d^7*x^5 + 240*(b^4*c^8 - 4*a*b^2*c^9)*d^7*x^4 + 160*(b^5*c^7 - 4*a*b^3*c^8)*d^7*x^3 + 60*(b^6*c^6 - 4*a*b^4*c^7)*d^7*x^2 + 12*(b^7*c^5 - 4*a*b^5*c^6)*d^7*x + (b^8*c^4 - 4*a*b^6*c^5)*d^7), -1/3072*(15*(64*c^6*x^6 + 192*b*c^5*x^5 + 240*b^2*c^4*x^4 + 160*b^3*c^3*x^3 + 60*b^4*c^2*x^2 + 12*b^5*c*x + b^6)*sqrt(b^2*c - 4*a*c^2)*arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c)) + 2*(15*b^6*c - 20*a*b^4*c^2 - 32*a^2*b^2*c^3 - 512*a^3*c^4 + 528*(b^2*c^5 - 4*a*c^6)*x^4 + 1056*(b^3*c^4 - 4*a*b*c^5)*x^3 + 16*(43*b^4*c^3 - 146*a*b^2*c^4 - 104*a^2*c^5)*x^2 + 32*(5*b^5*c^2 - 7*a*b^3*c^3 - 52*a^2*b*c^4)*x)*sqrt(c*x^2 + b*x + a))/(64*(b^2*c^10 - 4*a*c^11)*d^7*x^6 + 192*(b^3*c^9 - 4*a*b*c^10)*d^7*x^5 + 240*(b^4*c^8 - 4*a*b^2*c^9)*d^7*x^4 + 160*(b^5*c^7 - 4*a*b^3*c^8)*d^7*x^3 + 60*(b^6*c^6 - 4*a*b^4*c^7)*d^7*x^2 + 12*(b^7*c^5 - 4*a*b^5*c^6)*d^7*x + (b^8*c^4 - 4*a*b^6*c^5)*d^7)]","B",0
1229,1,270,0,9.705054," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^8,x, algorithm=""fricas"")","\frac{2 \, {\left(c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}\right)} \sqrt{c x^{2} + b x + a}}{7 \, {\left(128 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{8} x^{7} + 448 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{8} x^{6} + 672 \, {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} d^{8} x^{5} + 560 \, {\left(b^{5} c^{4} - 4 \, a b^{3} c^{5}\right)} d^{8} x^{4} + 280 \, {\left(b^{6} c^{3} - 4 \, a b^{4} c^{4}\right)} d^{8} x^{3} + 84 \, {\left(b^{7} c^{2} - 4 \, a b^{5} c^{3}\right)} d^{8} x^{2} + 14 \, {\left(b^{8} c - 4 \, a b^{6} c^{2}\right)} d^{8} x + {\left(b^{9} - 4 \, a b^{7} c\right)} d^{8}\right)}}"," ",0,"2/7*(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2)*sqrt(c*x^2 + b*x + a)/(128*(b^2*c^7 - 4*a*c^8)*d^8*x^7 + 448*(b^3*c^6 - 4*a*b*c^7)*d^8*x^6 + 672*(b^4*c^5 - 4*a*b^2*c^6)*d^8*x^5 + 560*(b^5*c^4 - 4*a*b^3*c^5)*d^8*x^4 + 280*(b^6*c^3 - 4*a*b^4*c^4)*d^8*x^3 + 84*(b^7*c^2 - 4*a*b^5*c^3)*d^8*x^2 + 14*(b^8*c - 4*a*b^6*c^2)*d^8*x + (b^9 - 4*a*b^7*c)*d^8)","B",0
1230,1,1448,0,16.928177," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^9,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(256 \, c^{8} x^{8} + 1024 \, b c^{7} x^{7} + 1792 \, b^{2} c^{6} x^{6} + 1792 \, b^{3} c^{5} x^{5} + 1120 \, b^{4} c^{4} x^{4} + 448 \, b^{5} c^{3} x^{3} + 112 \, b^{6} c^{2} x^{2} + 16 \, b^{7} c x + b^{8}\right)} \sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c + 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) - 4 \, {\left(15 \, b^{8} c - 20 \, a b^{6} c^{2} - 32 \, a^{2} b^{4} c^{3} - 3584 \, a^{3} b^{2} c^{4} + 12288 \, a^{4} c^{5} - 960 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} x^{6} - 2880 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} x^{5} - 16 \, {\left(107 \, b^{4} c^{5} + 44 \, a b^{2} c^{6} - 1888 \, a^{2} c^{7}\right)} x^{4} + 32 \, {\left(43 \, b^{5} c^{4} - 644 \, a b^{3} c^{5} + 1888 \, a^{2} b c^{6}\right)} x^{3} + 4 \, {\left(347 \, b^{6} c^{3} - 3132 \, a b^{4} c^{4} + 4800 \, a^{2} b^{2} c^{5} + 8704 \, a^{3} c^{6}\right)} x^{2} + 4 \, {\left(55 \, b^{7} c^{2} - 76 \, a b^{5} c^{3} - 2752 \, a^{2} b^{3} c^{4} + 8704 \, a^{3} b c^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{49152 \, {\left(256 \, {\left(b^{4} c^{12} - 8 \, a b^{2} c^{13} + 16 \, a^{2} c^{14}\right)} d^{9} x^{8} + 1024 \, {\left(b^{5} c^{11} - 8 \, a b^{3} c^{12} + 16 \, a^{2} b c^{13}\right)} d^{9} x^{7} + 1792 \, {\left(b^{6} c^{10} - 8 \, a b^{4} c^{11} + 16 \, a^{2} b^{2} c^{12}\right)} d^{9} x^{6} + 1792 \, {\left(b^{7} c^{9} - 8 \, a b^{5} c^{10} + 16 \, a^{2} b^{3} c^{11}\right)} d^{9} x^{5} + 1120 \, {\left(b^{8} c^{8} - 8 \, a b^{6} c^{9} + 16 \, a^{2} b^{4} c^{10}\right)} d^{9} x^{4} + 448 \, {\left(b^{9} c^{7} - 8 \, a b^{7} c^{8} + 16 \, a^{2} b^{5} c^{9}\right)} d^{9} x^{3} + 112 \, {\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 16 \, a^{2} b^{6} c^{8}\right)} d^{9} x^{2} + 16 \, {\left(b^{11} c^{5} - 8 \, a b^{9} c^{6} + 16 \, a^{2} b^{7} c^{7}\right)} d^{9} x + {\left(b^{12} c^{4} - 8 \, a b^{10} c^{5} + 16 \, a^{2} b^{8} c^{6}\right)} d^{9}\right)}}, -\frac{15 \, {\left(256 \, c^{8} x^{8} + 1024 \, b c^{7} x^{7} + 1792 \, b^{2} c^{6} x^{6} + 1792 \, b^{3} c^{5} x^{5} + 1120 \, b^{4} c^{4} x^{4} + 448 \, b^{5} c^{3} x^{3} + 112 \, b^{6} c^{2} x^{2} + 16 \, b^{7} c x + b^{8}\right)} \sqrt{b^{2} c - 4 \, a c^{2}} \arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(15 \, b^{8} c - 20 \, a b^{6} c^{2} - 32 \, a^{2} b^{4} c^{3} - 3584 \, a^{3} b^{2} c^{4} + 12288 \, a^{4} c^{5} - 960 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} x^{6} - 2880 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} x^{5} - 16 \, {\left(107 \, b^{4} c^{5} + 44 \, a b^{2} c^{6} - 1888 \, a^{2} c^{7}\right)} x^{4} + 32 \, {\left(43 \, b^{5} c^{4} - 644 \, a b^{3} c^{5} + 1888 \, a^{2} b c^{6}\right)} x^{3} + 4 \, {\left(347 \, b^{6} c^{3} - 3132 \, a b^{4} c^{4} + 4800 \, a^{2} b^{2} c^{5} + 8704 \, a^{3} c^{6}\right)} x^{2} + 4 \, {\left(55 \, b^{7} c^{2} - 76 \, a b^{5} c^{3} - 2752 \, a^{2} b^{3} c^{4} + 8704 \, a^{3} b c^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{24576 \, {\left(256 \, {\left(b^{4} c^{12} - 8 \, a b^{2} c^{13} + 16 \, a^{2} c^{14}\right)} d^{9} x^{8} + 1024 \, {\left(b^{5} c^{11} - 8 \, a b^{3} c^{12} + 16 \, a^{2} b c^{13}\right)} d^{9} x^{7} + 1792 \, {\left(b^{6} c^{10} - 8 \, a b^{4} c^{11} + 16 \, a^{2} b^{2} c^{12}\right)} d^{9} x^{6} + 1792 \, {\left(b^{7} c^{9} - 8 \, a b^{5} c^{10} + 16 \, a^{2} b^{3} c^{11}\right)} d^{9} x^{5} + 1120 \, {\left(b^{8} c^{8} - 8 \, a b^{6} c^{9} + 16 \, a^{2} b^{4} c^{10}\right)} d^{9} x^{4} + 448 \, {\left(b^{9} c^{7} - 8 \, a b^{7} c^{8} + 16 \, a^{2} b^{5} c^{9}\right)} d^{9} x^{3} + 112 \, {\left(b^{10} c^{6} - 8 \, a b^{8} c^{7} + 16 \, a^{2} b^{6} c^{8}\right)} d^{9} x^{2} + 16 \, {\left(b^{11} c^{5} - 8 \, a b^{9} c^{6} + 16 \, a^{2} b^{7} c^{7}\right)} d^{9} x + {\left(b^{12} c^{4} - 8 \, a b^{10} c^{5} + 16 \, a^{2} b^{8} c^{6}\right)} d^{9}\right)}}\right]"," ",0,"[1/49152*(15*(256*c^8*x^8 + 1024*b*c^7*x^7 + 1792*b^2*c^6*x^6 + 1792*b^3*c^5*x^5 + 1120*b^4*c^4*x^4 + 448*b^5*c^3*x^3 + 112*b^6*c^2*x^2 + 16*b^7*c*x + b^8)*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c + 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2)) - 4*(15*b^8*c - 20*a*b^6*c^2 - 32*a^2*b^4*c^3 - 3584*a^3*b^2*c^4 + 12288*a^4*c^5 - 960*(b^2*c^7 - 4*a*c^8)*x^6 - 2880*(b^3*c^6 - 4*a*b*c^7)*x^5 - 16*(107*b^4*c^5 + 44*a*b^2*c^6 - 1888*a^2*c^7)*x^4 + 32*(43*b^5*c^4 - 644*a*b^3*c^5 + 1888*a^2*b*c^6)*x^3 + 4*(347*b^6*c^3 - 3132*a*b^4*c^4 + 4800*a^2*b^2*c^5 + 8704*a^3*c^6)*x^2 + 4*(55*b^7*c^2 - 76*a*b^5*c^3 - 2752*a^2*b^3*c^4 + 8704*a^3*b*c^5)*x)*sqrt(c*x^2 + b*x + a))/(256*(b^4*c^12 - 8*a*b^2*c^13 + 16*a^2*c^14)*d^9*x^8 + 1024*(b^5*c^11 - 8*a*b^3*c^12 + 16*a^2*b*c^13)*d^9*x^7 + 1792*(b^6*c^10 - 8*a*b^4*c^11 + 16*a^2*b^2*c^12)*d^9*x^6 + 1792*(b^7*c^9 - 8*a*b^5*c^10 + 16*a^2*b^3*c^11)*d^9*x^5 + 1120*(b^8*c^8 - 8*a*b^6*c^9 + 16*a^2*b^4*c^10)*d^9*x^4 + 448*(b^9*c^7 - 8*a*b^7*c^8 + 16*a^2*b^5*c^9)*d^9*x^3 + 112*(b^10*c^6 - 8*a*b^8*c^7 + 16*a^2*b^6*c^8)*d^9*x^2 + 16*(b^11*c^5 - 8*a*b^9*c^6 + 16*a^2*b^7*c^7)*d^9*x + (b^12*c^4 - 8*a*b^10*c^5 + 16*a^2*b^8*c^6)*d^9), -1/24576*(15*(256*c^8*x^8 + 1024*b*c^7*x^7 + 1792*b^2*c^6*x^6 + 1792*b^3*c^5*x^5 + 1120*b^4*c^4*x^4 + 448*b^5*c^3*x^3 + 112*b^6*c^2*x^2 + 16*b^7*c*x + b^8)*sqrt(b^2*c - 4*a*c^2)*arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c)) + 2*(15*b^8*c - 20*a*b^6*c^2 - 32*a^2*b^4*c^3 - 3584*a^3*b^2*c^4 + 12288*a^4*c^5 - 960*(b^2*c^7 - 4*a*c^8)*x^6 - 2880*(b^3*c^6 - 4*a*b*c^7)*x^5 - 16*(107*b^4*c^5 + 44*a*b^2*c^6 - 1888*a^2*c^7)*x^4 + 32*(43*b^5*c^4 - 644*a*b^3*c^5 + 1888*a^2*b*c^6)*x^3 + 4*(347*b^6*c^3 - 3132*a*b^4*c^4 + 4800*a^2*b^2*c^5 + 8704*a^3*c^6)*x^2 + 4*(55*b^7*c^2 - 76*a*b^5*c^3 - 2752*a^2*b^3*c^4 + 8704*a^3*b*c^5)*x)*sqrt(c*x^2 + b*x + a))/(256*(b^4*c^12 - 8*a*b^2*c^13 + 16*a^2*c^14)*d^9*x^8 + 1024*(b^5*c^11 - 8*a*b^3*c^12 + 16*a^2*b*c^13)*d^9*x^7 + 1792*(b^6*c^10 - 8*a*b^4*c^11 + 16*a^2*b^2*c^12)*d^9*x^6 + 1792*(b^7*c^9 - 8*a*b^5*c^10 + 16*a^2*b^3*c^11)*d^9*x^5 + 1120*(b^8*c^8 - 8*a*b^6*c^9 + 16*a^2*b^4*c^10)*d^9*x^4 + 448*(b^9*c^7 - 8*a*b^7*c^8 + 16*a^2*b^5*c^9)*d^9*x^3 + 112*(b^10*c^6 - 8*a*b^8*c^7 + 16*a^2*b^6*c^8)*d^9*x^2 + 16*(b^11*c^5 - 8*a*b^9*c^6 + 16*a^2*b^7*c^7)*d^9*x + (b^12*c^4 - 8*a*b^10*c^5 + 16*a^2*b^8*c^6)*d^9)]","B",0
1231,1,530,0,28.169010," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^10,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{5} x^{8} + 32 \, b c^{4} x^{7} + {\left(57 \, b^{2} c^{3} - 4 \, a c^{4}\right)} x^{6} + {\left(59 \, b^{3} c^{2} - 12 \, a b c^{3}\right)} x^{5} + 9 \, a^{3} b^{2} - 28 \, a^{4} c + 5 \, {\left(7 \, b^{4} c + 3 \, a b^{2} c^{2} - 12 \, a^{2} c^{3}\right)} x^{4} + {\left(9 \, b^{5} + 50 \, a b^{3} c - 120 \, a^{2} b c^{2}\right)} x^{3} + {\left(27 \, a b^{4} - 33 \, a^{2} b^{2} c - 76 \, a^{3} c^{2}\right)} x^{2} + {\left(27 \, a^{2} b^{3} - 76 \, a^{3} b c\right)} x\right)} \sqrt{c x^{2} + b x + a}}{63 \, {\left(512 \, {\left(b^{4} c^{9} - 8 \, a b^{2} c^{10} + 16 \, a^{2} c^{11}\right)} d^{10} x^{9} + 2304 \, {\left(b^{5} c^{8} - 8 \, a b^{3} c^{9} + 16 \, a^{2} b c^{10}\right)} d^{10} x^{8} + 4608 \, {\left(b^{6} c^{7} - 8 \, a b^{4} c^{8} + 16 \, a^{2} b^{2} c^{9}\right)} d^{10} x^{7} + 5376 \, {\left(b^{7} c^{6} - 8 \, a b^{5} c^{7} + 16 \, a^{2} b^{3} c^{8}\right)} d^{10} x^{6} + 4032 \, {\left(b^{8} c^{5} - 8 \, a b^{6} c^{6} + 16 \, a^{2} b^{4} c^{7}\right)} d^{10} x^{5} + 2016 \, {\left(b^{9} c^{4} - 8 \, a b^{7} c^{5} + 16 \, a^{2} b^{5} c^{6}\right)} d^{10} x^{4} + 672 \, {\left(b^{10} c^{3} - 8 \, a b^{8} c^{4} + 16 \, a^{2} b^{6} c^{5}\right)} d^{10} x^{3} + 144 \, {\left(b^{11} c^{2} - 8 \, a b^{9} c^{3} + 16 \, a^{2} b^{7} c^{4}\right)} d^{10} x^{2} + 18 \, {\left(b^{12} c - 8 \, a b^{10} c^{2} + 16 \, a^{2} b^{8} c^{3}\right)} d^{10} x + {\left(b^{13} - 8 \, a b^{11} c + 16 \, a^{2} b^{9} c^{2}\right)} d^{10}\right)}}"," ",0,"2/63*(8*c^5*x^8 + 32*b*c^4*x^7 + (57*b^2*c^3 - 4*a*c^4)*x^6 + (59*b^3*c^2 - 12*a*b*c^3)*x^5 + 9*a^3*b^2 - 28*a^4*c + 5*(7*b^4*c + 3*a*b^2*c^2 - 12*a^2*c^3)*x^4 + (9*b^5 + 50*a*b^3*c - 120*a^2*b*c^2)*x^3 + (27*a*b^4 - 33*a^2*b^2*c - 76*a^3*c^2)*x^2 + (27*a^2*b^3 - 76*a^3*b*c)*x)*sqrt(c*x^2 + b*x + a)/(512*(b^4*c^9 - 8*a*b^2*c^10 + 16*a^2*c^11)*d^10*x^9 + 2304*(b^5*c^8 - 8*a*b^3*c^9 + 16*a^2*b*c^10)*d^10*x^8 + 4608*(b^6*c^7 - 8*a*b^4*c^8 + 16*a^2*b^2*c^9)*d^10*x^7 + 5376*(b^7*c^6 - 8*a*b^5*c^7 + 16*a^2*b^3*c^8)*d^10*x^6 + 4032*(b^8*c^5 - 8*a*b^6*c^6 + 16*a^2*b^4*c^7)*d^10*x^5 + 2016*(b^9*c^4 - 8*a*b^7*c^5 + 16*a^2*b^5*c^6)*d^10*x^4 + 672*(b^10*c^3 - 8*a*b^8*c^4 + 16*a^2*b^6*c^5)*d^10*x^3 + 144*(b^11*c^2 - 8*a*b^9*c^3 + 16*a^2*b^7*c^4)*d^10*x^2 + 18*(b^12*c - 8*a*b^10*c^2 + 16*a^2*b^8*c^3)*d^10*x + (b^13 - 8*a*b^11*c + 16*a^2*b^9*c^2)*d^10)","B",0
1232,1,2114,0,43.699483," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^11,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(1024 \, c^{10} x^{10} + 5120 \, b c^{9} x^{9} + 11520 \, b^{2} c^{8} x^{8} + 15360 \, b^{3} c^{7} x^{7} + 13440 \, b^{4} c^{6} x^{6} + 8064 \, b^{5} c^{5} x^{5} + 3360 \, b^{6} c^{4} x^{4} + 960 \, b^{7} c^{3} x^{3} + 180 \, b^{8} c^{2} x^{2} + 20 \, b^{9} c x + b^{10}\right)} \sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, {\left(15 \, b^{10} c - 20 \, a b^{8} c^{2} - 32 \, a^{2} b^{6} c^{3} - 11776 \, a^{3} b^{4} c^{4} + 77824 \, a^{4} b^{2} c^{5} - 131072 \, a^{5} c^{6} - 3840 \, {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} x^{8} - 15360 \, {\left(b^{3} c^{8} - 4 \, a b c^{9}\right)} x^{7} - 640 \, {\left(43 \, b^{4} c^{7} - 176 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} x^{6} - 1920 \, {\left(15 \, b^{5} c^{6} - 64 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} x^{5} - 128 \, {\left(119 \, b^{6} c^{5} - 303 \, a b^{4} c^{6} - 1188 \, a^{2} b^{2} c^{7} + 1984 \, a^{3} c^{8}\right)} x^{4} - 128 \, {\left(3 \, b^{7} c^{4} + 434 \, a b^{5} c^{5} - 2776 \, a^{2} b^{3} c^{6} + 3968 \, a^{3} b c^{7}\right)} x^{3} + 24 \, {\left(97 \, b^{8} c^{3} - 1600 \, a b^{6} c^{4} + 6128 \, a^{2} b^{4} c^{5} - 1536 \, a^{3} b^{2} c^{6} - 14336 \, a^{4} c^{7}\right)} x^{2} + 8 \, {\left(35 \, b^{9} c^{2} - 48 \, a b^{7} c^{3} - 4464 \, a^{2} b^{5} c^{4} + 27136 \, a^{3} b^{3} c^{5} - 43008 \, a^{4} b c^{6}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{163840 \, {\left(1024 \, {\left(b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}\right)} d^{11} x^{10} + 5120 \, {\left(b^{7} c^{13} - 12 \, a b^{5} c^{14} + 48 \, a^{2} b^{3} c^{15} - 64 \, a^{3} b c^{16}\right)} d^{11} x^{9} + 11520 \, {\left(b^{8} c^{12} - 12 \, a b^{6} c^{13} + 48 \, a^{2} b^{4} c^{14} - 64 \, a^{3} b^{2} c^{15}\right)} d^{11} x^{8} + 15360 \, {\left(b^{9} c^{11} - 12 \, a b^{7} c^{12} + 48 \, a^{2} b^{5} c^{13} - 64 \, a^{3} b^{3} c^{14}\right)} d^{11} x^{7} + 13440 \, {\left(b^{10} c^{10} - 12 \, a b^{8} c^{11} + 48 \, a^{2} b^{6} c^{12} - 64 \, a^{3} b^{4} c^{13}\right)} d^{11} x^{6} + 8064 \, {\left(b^{11} c^{9} - 12 \, a b^{9} c^{10} + 48 \, a^{2} b^{7} c^{11} - 64 \, a^{3} b^{5} c^{12}\right)} d^{11} x^{5} + 3360 \, {\left(b^{12} c^{8} - 12 \, a b^{10} c^{9} + 48 \, a^{2} b^{8} c^{10} - 64 \, a^{3} b^{6} c^{11}\right)} d^{11} x^{4} + 960 \, {\left(b^{13} c^{7} - 12 \, a b^{11} c^{8} + 48 \, a^{2} b^{9} c^{9} - 64 \, a^{3} b^{7} c^{10}\right)} d^{11} x^{3} + 180 \, {\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 48 \, a^{2} b^{10} c^{8} - 64 \, a^{3} b^{8} c^{9}\right)} d^{11} x^{2} + 20 \, {\left(b^{15} c^{5} - 12 \, a b^{13} c^{6} + 48 \, a^{2} b^{11} c^{7} - 64 \, a^{3} b^{9} c^{8}\right)} d^{11} x + {\left(b^{16} c^{4} - 12 \, a b^{14} c^{5} + 48 \, a^{2} b^{12} c^{6} - 64 \, a^{3} b^{10} c^{7}\right)} d^{11}\right)}}, -\frac{15 \, {\left(1024 \, c^{10} x^{10} + 5120 \, b c^{9} x^{9} + 11520 \, b^{2} c^{8} x^{8} + 15360 \, b^{3} c^{7} x^{7} + 13440 \, b^{4} c^{6} x^{6} + 8064 \, b^{5} c^{5} x^{5} + 3360 \, b^{6} c^{4} x^{4} + 960 \, b^{7} c^{3} x^{3} + 180 \, b^{8} c^{2} x^{2} + 20 \, b^{9} c x + b^{10}\right)} \sqrt{b^{2} c - 4 \, a c^{2}} \arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(15 \, b^{10} c - 20 \, a b^{8} c^{2} - 32 \, a^{2} b^{6} c^{3} - 11776 \, a^{3} b^{4} c^{4} + 77824 \, a^{4} b^{2} c^{5} - 131072 \, a^{5} c^{6} - 3840 \, {\left(b^{2} c^{9} - 4 \, a c^{10}\right)} x^{8} - 15360 \, {\left(b^{3} c^{8} - 4 \, a b c^{9}\right)} x^{7} - 640 \, {\left(43 \, b^{4} c^{7} - 176 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} x^{6} - 1920 \, {\left(15 \, b^{5} c^{6} - 64 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} x^{5} - 128 \, {\left(119 \, b^{6} c^{5} - 303 \, a b^{4} c^{6} - 1188 \, a^{2} b^{2} c^{7} + 1984 \, a^{3} c^{8}\right)} x^{4} - 128 \, {\left(3 \, b^{7} c^{4} + 434 \, a b^{5} c^{5} - 2776 \, a^{2} b^{3} c^{6} + 3968 \, a^{3} b c^{7}\right)} x^{3} + 24 \, {\left(97 \, b^{8} c^{3} - 1600 \, a b^{6} c^{4} + 6128 \, a^{2} b^{4} c^{5} - 1536 \, a^{3} b^{2} c^{6} - 14336 \, a^{4} c^{7}\right)} x^{2} + 8 \, {\left(35 \, b^{9} c^{2} - 48 \, a b^{7} c^{3} - 4464 \, a^{2} b^{5} c^{4} + 27136 \, a^{3} b^{3} c^{5} - 43008 \, a^{4} b c^{6}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{81920 \, {\left(1024 \, {\left(b^{6} c^{14} - 12 \, a b^{4} c^{15} + 48 \, a^{2} b^{2} c^{16} - 64 \, a^{3} c^{17}\right)} d^{11} x^{10} + 5120 \, {\left(b^{7} c^{13} - 12 \, a b^{5} c^{14} + 48 \, a^{2} b^{3} c^{15} - 64 \, a^{3} b c^{16}\right)} d^{11} x^{9} + 11520 \, {\left(b^{8} c^{12} - 12 \, a b^{6} c^{13} + 48 \, a^{2} b^{4} c^{14} - 64 \, a^{3} b^{2} c^{15}\right)} d^{11} x^{8} + 15360 \, {\left(b^{9} c^{11} - 12 \, a b^{7} c^{12} + 48 \, a^{2} b^{5} c^{13} - 64 \, a^{3} b^{3} c^{14}\right)} d^{11} x^{7} + 13440 \, {\left(b^{10} c^{10} - 12 \, a b^{8} c^{11} + 48 \, a^{2} b^{6} c^{12} - 64 \, a^{3} b^{4} c^{13}\right)} d^{11} x^{6} + 8064 \, {\left(b^{11} c^{9} - 12 \, a b^{9} c^{10} + 48 \, a^{2} b^{7} c^{11} - 64 \, a^{3} b^{5} c^{12}\right)} d^{11} x^{5} + 3360 \, {\left(b^{12} c^{8} - 12 \, a b^{10} c^{9} + 48 \, a^{2} b^{8} c^{10} - 64 \, a^{3} b^{6} c^{11}\right)} d^{11} x^{4} + 960 \, {\left(b^{13} c^{7} - 12 \, a b^{11} c^{8} + 48 \, a^{2} b^{9} c^{9} - 64 \, a^{3} b^{7} c^{10}\right)} d^{11} x^{3} + 180 \, {\left(b^{14} c^{6} - 12 \, a b^{12} c^{7} + 48 \, a^{2} b^{10} c^{8} - 64 \, a^{3} b^{8} c^{9}\right)} d^{11} x^{2} + 20 \, {\left(b^{15} c^{5} - 12 \, a b^{13} c^{6} + 48 \, a^{2} b^{11} c^{7} - 64 \, a^{3} b^{9} c^{8}\right)} d^{11} x + {\left(b^{16} c^{4} - 12 \, a b^{14} c^{5} + 48 \, a^{2} b^{12} c^{6} - 64 \, a^{3} b^{10} c^{7}\right)} d^{11}\right)}}\right]"," ",0,"[-1/163840*(15*(1024*c^10*x^10 + 5120*b*c^9*x^9 + 11520*b^2*c^8*x^8 + 15360*b^3*c^7*x^7 + 13440*b^4*c^6*x^6 + 8064*b^5*c^5*x^5 + 3360*b^6*c^4*x^4 + 960*b^7*c^3*x^3 + 180*b^8*c^2*x^2 + 20*b^9*c*x + b^10)*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*(15*b^10*c - 20*a*b^8*c^2 - 32*a^2*b^6*c^3 - 11776*a^3*b^4*c^4 + 77824*a^4*b^2*c^5 - 131072*a^5*c^6 - 3840*(b^2*c^9 - 4*a*c^10)*x^8 - 15360*(b^3*c^8 - 4*a*b*c^9)*x^7 - 640*(43*b^4*c^7 - 176*a*b^2*c^8 + 16*a^2*c^9)*x^6 - 1920*(15*b^5*c^6 - 64*a*b^3*c^7 + 16*a^2*b*c^8)*x^5 - 128*(119*b^6*c^5 - 303*a*b^4*c^6 - 1188*a^2*b^2*c^7 + 1984*a^3*c^8)*x^4 - 128*(3*b^7*c^4 + 434*a*b^5*c^5 - 2776*a^2*b^3*c^6 + 3968*a^3*b*c^7)*x^3 + 24*(97*b^8*c^3 - 1600*a*b^6*c^4 + 6128*a^2*b^4*c^5 - 1536*a^3*b^2*c^6 - 14336*a^4*c^7)*x^2 + 8*(35*b^9*c^2 - 48*a*b^7*c^3 - 4464*a^2*b^5*c^4 + 27136*a^3*b^3*c^5 - 43008*a^4*b*c^6)*x)*sqrt(c*x^2 + b*x + a))/(1024*(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)*d^11*x^10 + 5120*(b^7*c^13 - 12*a*b^5*c^14 + 48*a^2*b^3*c^15 - 64*a^3*b*c^16)*d^11*x^9 + 11520*(b^8*c^12 - 12*a*b^6*c^13 + 48*a^2*b^4*c^14 - 64*a^3*b^2*c^15)*d^11*x^8 + 15360*(b^9*c^11 - 12*a*b^7*c^12 + 48*a^2*b^5*c^13 - 64*a^3*b^3*c^14)*d^11*x^7 + 13440*(b^10*c^10 - 12*a*b^8*c^11 + 48*a^2*b^6*c^12 - 64*a^3*b^4*c^13)*d^11*x^6 + 8064*(b^11*c^9 - 12*a*b^9*c^10 + 48*a^2*b^7*c^11 - 64*a^3*b^5*c^12)*d^11*x^5 + 3360*(b^12*c^8 - 12*a*b^10*c^9 + 48*a^2*b^8*c^10 - 64*a^3*b^6*c^11)*d^11*x^4 + 960*(b^13*c^7 - 12*a*b^11*c^8 + 48*a^2*b^9*c^9 - 64*a^3*b^7*c^10)*d^11*x^3 + 180*(b^14*c^6 - 12*a*b^12*c^7 + 48*a^2*b^10*c^8 - 64*a^3*b^8*c^9)*d^11*x^2 + 20*(b^15*c^5 - 12*a*b^13*c^6 + 48*a^2*b^11*c^7 - 64*a^3*b^9*c^8)*d^11*x + (b^16*c^4 - 12*a*b^14*c^5 + 48*a^2*b^12*c^6 - 64*a^3*b^10*c^7)*d^11), -1/81920*(15*(1024*c^10*x^10 + 5120*b*c^9*x^9 + 11520*b^2*c^8*x^8 + 15360*b^3*c^7*x^7 + 13440*b^4*c^6*x^6 + 8064*b^5*c^5*x^5 + 3360*b^6*c^4*x^4 + 960*b^7*c^3*x^3 + 180*b^8*c^2*x^2 + 20*b^9*c*x + b^10)*sqrt(b^2*c - 4*a*c^2)*arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c)) + 2*(15*b^10*c - 20*a*b^8*c^2 - 32*a^2*b^6*c^3 - 11776*a^3*b^4*c^4 + 77824*a^4*b^2*c^5 - 131072*a^5*c^6 - 3840*(b^2*c^9 - 4*a*c^10)*x^8 - 15360*(b^3*c^8 - 4*a*b*c^9)*x^7 - 640*(43*b^4*c^7 - 176*a*b^2*c^8 + 16*a^2*c^9)*x^6 - 1920*(15*b^5*c^6 - 64*a*b^3*c^7 + 16*a^2*b*c^8)*x^5 - 128*(119*b^6*c^5 - 303*a*b^4*c^6 - 1188*a^2*b^2*c^7 + 1984*a^3*c^8)*x^4 - 128*(3*b^7*c^4 + 434*a*b^5*c^5 - 2776*a^2*b^3*c^6 + 3968*a^3*b*c^7)*x^3 + 24*(97*b^8*c^3 - 1600*a*b^6*c^4 + 6128*a^2*b^4*c^5 - 1536*a^3*b^2*c^6 - 14336*a^4*c^7)*x^2 + 8*(35*b^9*c^2 - 48*a*b^7*c^3 - 4464*a^2*b^5*c^4 + 27136*a^3*b^3*c^5 - 43008*a^4*b*c^6)*x)*sqrt(c*x^2 + b*x + a))/(1024*(b^6*c^14 - 12*a*b^4*c^15 + 48*a^2*b^2*c^16 - 64*a^3*c^17)*d^11*x^10 + 5120*(b^7*c^13 - 12*a*b^5*c^14 + 48*a^2*b^3*c^15 - 64*a^3*b*c^16)*d^11*x^9 + 11520*(b^8*c^12 - 12*a*b^6*c^13 + 48*a^2*b^4*c^14 - 64*a^3*b^2*c^15)*d^11*x^8 + 15360*(b^9*c^11 - 12*a*b^7*c^12 + 48*a^2*b^5*c^13 - 64*a^3*b^3*c^14)*d^11*x^7 + 13440*(b^10*c^10 - 12*a*b^8*c^11 + 48*a^2*b^6*c^12 - 64*a^3*b^4*c^13)*d^11*x^6 + 8064*(b^11*c^9 - 12*a*b^9*c^10 + 48*a^2*b^7*c^11 - 64*a^3*b^5*c^12)*d^11*x^5 + 3360*(b^12*c^8 - 12*a*b^10*c^9 + 48*a^2*b^8*c^10 - 64*a^3*b^6*c^11)*d^11*x^4 + 960*(b^13*c^7 - 12*a*b^11*c^8 + 48*a^2*b^9*c^9 - 64*a^3*b^7*c^10)*d^11*x^3 + 180*(b^14*c^6 - 12*a*b^12*c^7 + 48*a^2*b^10*c^8 - 64*a^3*b^8*c^9)*d^11*x^2 + 20*(b^15*c^5 - 12*a*b^13*c^6 + 48*a^2*b^11*c^7 - 64*a^3*b^9*c^8)*d^11*x + (b^16*c^4 - 12*a*b^14*c^5 + 48*a^2*b^12*c^6 - 64*a^3*b^10*c^7)*d^11)]","B",0
1233,1,851,0,87.437557," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^12,x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, c^{7} x^{10} + 640 \, b c^{6} x^{9} + 16 \, {\left(91 \, b^{2} c^{5} - 4 \, a c^{6}\right)} x^{8} + 64 \, {\left(31 \, b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{7} + 99 \, a^{3} b^{4} - 616 \, a^{4} b^{2} c + 1008 \, a^{5} c^{2} + {\left(1795 \, b^{4} c^{3} - 472 \, a b^{2} c^{4} + 48 \, a^{2} c^{5}\right)} x^{6} + {\left(1129 \, b^{5} c^{2} - 520 \, a b^{3} c^{3} + 144 \, a^{2} b c^{4}\right)} x^{5} + {\left(473 \, b^{6} c - 31 \, a b^{4} c^{2} - 1176 \, a^{2} b^{2} c^{3} + 1808 \, a^{3} c^{4}\right)} x^{4} + {\left(99 \, b^{7} + 506 \, a b^{5} c - 2592 \, a^{2} b^{3} c^{2} + 3616 \, a^{3} b c^{3}\right)} x^{3} + {\left(297 \, a b^{6} - 1023 \, a^{2} b^{4} c + 136 \, a^{3} b^{2} c^{2} + 2576 \, a^{4} c^{3}\right)} x^{2} + {\left(297 \, a^{2} b^{5} - 1672 \, a^{3} b^{3} c + 2576 \, a^{4} b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{693 \, {\left(2048 \, {\left(b^{6} c^{11} - 12 \, a b^{4} c^{12} + 48 \, a^{2} b^{2} c^{13} - 64 \, a^{3} c^{14}\right)} d^{12} x^{11} + 11264 \, {\left(b^{7} c^{10} - 12 \, a b^{5} c^{11} + 48 \, a^{2} b^{3} c^{12} - 64 \, a^{3} b c^{13}\right)} d^{12} x^{10} + 28160 \, {\left(b^{8} c^{9} - 12 \, a b^{6} c^{10} + 48 \, a^{2} b^{4} c^{11} - 64 \, a^{3} b^{2} c^{12}\right)} d^{12} x^{9} + 42240 \, {\left(b^{9} c^{8} - 12 \, a b^{7} c^{9} + 48 \, a^{2} b^{5} c^{10} - 64 \, a^{3} b^{3} c^{11}\right)} d^{12} x^{8} + 42240 \, {\left(b^{10} c^{7} - 12 \, a b^{8} c^{8} + 48 \, a^{2} b^{6} c^{9} - 64 \, a^{3} b^{4} c^{10}\right)} d^{12} x^{7} + 29568 \, {\left(b^{11} c^{6} - 12 \, a b^{9} c^{7} + 48 \, a^{2} b^{7} c^{8} - 64 \, a^{3} b^{5} c^{9}\right)} d^{12} x^{6} + 14784 \, {\left(b^{12} c^{5} - 12 \, a b^{10} c^{6} + 48 \, a^{2} b^{8} c^{7} - 64 \, a^{3} b^{6} c^{8}\right)} d^{12} x^{5} + 5280 \, {\left(b^{13} c^{4} - 12 \, a b^{11} c^{5} + 48 \, a^{2} b^{9} c^{6} - 64 \, a^{3} b^{7} c^{7}\right)} d^{12} x^{4} + 1320 \, {\left(b^{14} c^{3} - 12 \, a b^{12} c^{4} + 48 \, a^{2} b^{10} c^{5} - 64 \, a^{3} b^{8} c^{6}\right)} d^{12} x^{3} + 220 \, {\left(b^{15} c^{2} - 12 \, a b^{13} c^{3} + 48 \, a^{2} b^{11} c^{4} - 64 \, a^{3} b^{9} c^{5}\right)} d^{12} x^{2} + 22 \, {\left(b^{16} c - 12 \, a b^{14} c^{2} + 48 \, a^{2} b^{12} c^{3} - 64 \, a^{3} b^{10} c^{4}\right)} d^{12} x + {\left(b^{17} - 12 \, a b^{15} c + 48 \, a^{2} b^{13} c^{2} - 64 \, a^{3} b^{11} c^{3}\right)} d^{12}\right)}}"," ",0,"2/693*(128*c^7*x^10 + 640*b*c^6*x^9 + 16*(91*b^2*c^5 - 4*a*c^6)*x^8 + 64*(31*b^3*c^4 - 4*a*b*c^5)*x^7 + 99*a^3*b^4 - 616*a^4*b^2*c + 1008*a^5*c^2 + (1795*b^4*c^3 - 472*a*b^2*c^4 + 48*a^2*c^5)*x^6 + (1129*b^5*c^2 - 520*a*b^3*c^3 + 144*a^2*b*c^4)*x^5 + (473*b^6*c - 31*a*b^4*c^2 - 1176*a^2*b^2*c^3 + 1808*a^3*c^4)*x^4 + (99*b^7 + 506*a*b^5*c - 2592*a^2*b^3*c^2 + 3616*a^3*b*c^3)*x^3 + (297*a*b^6 - 1023*a^2*b^4*c + 136*a^3*b^2*c^2 + 2576*a^4*c^3)*x^2 + (297*a^2*b^5 - 1672*a^3*b^3*c + 2576*a^4*b*c^2)*x)*sqrt(c*x^2 + b*x + a)/(2048*(b^6*c^11 - 12*a*b^4*c^12 + 48*a^2*b^2*c^13 - 64*a^3*c^14)*d^12*x^11 + 11264*(b^7*c^10 - 12*a*b^5*c^11 + 48*a^2*b^3*c^12 - 64*a^3*b*c^13)*d^12*x^10 + 28160*(b^8*c^9 - 12*a*b^6*c^10 + 48*a^2*b^4*c^11 - 64*a^3*b^2*c^12)*d^12*x^9 + 42240*(b^9*c^8 - 12*a*b^7*c^9 + 48*a^2*b^5*c^10 - 64*a^3*b^3*c^11)*d^12*x^8 + 42240*(b^10*c^7 - 12*a*b^8*c^8 + 48*a^2*b^6*c^9 - 64*a^3*b^4*c^10)*d^12*x^7 + 29568*(b^11*c^6 - 12*a*b^9*c^7 + 48*a^2*b^7*c^8 - 64*a^3*b^5*c^9)*d^12*x^6 + 14784*(b^12*c^5 - 12*a*b^10*c^6 + 48*a^2*b^8*c^7 - 64*a^3*b^6*c^8)*d^12*x^5 + 5280*(b^13*c^4 - 12*a*b^11*c^5 + 48*a^2*b^9*c^6 - 64*a^3*b^7*c^7)*d^12*x^4 + 1320*(b^14*c^3 - 12*a*b^12*c^4 + 48*a^2*b^10*c^5 - 64*a^3*b^8*c^6)*d^12*x^3 + 220*(b^15*c^2 - 12*a*b^13*c^3 + 48*a^2*b^11*c^4 - 64*a^3*b^9*c^5)*d^12*x^2 + 22*(b^16*c - 12*a*b^14*c^2 + 48*a^2*b^12*c^3 - 64*a^3*b^10*c^4)*d^12*x + (b^17 - 12*a*b^15*c + 48*a^2*b^13*c^2 - 64*a^3*b^11*c^3)*d^12)","B",0
1234,1,313,0,0.453506," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{c} d^{4} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(16 \, c^{4} d^{4} x^{3} + 24 \, b c^{3} d^{4} x^{2} + 6 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} x + {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}}{16 \, c}, -\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} d^{4} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(16 \, c^{4} d^{4} x^{3} + 24 \, b c^{3} d^{4} x^{2} + 6 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} x + {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}}{8 \, c}\right]"," ",0,"[1/16*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(c)*d^4*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(16*c^4*d^4*x^3 + 24*b*c^3*d^4*x^2 + 6*(3*b^2*c^2 - 4*a*c^3)*d^4*x + (5*b^3*c - 12*a*b*c^2)*d^4)*sqrt(c*x^2 + b*x + a))/c, -1/8*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*d^4*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(16*c^4*d^4*x^3 + 24*b*c^3*d^4*x^2 + 6*(3*b^2*c^2 - 4*a*c^3)*d^4*x + (5*b^3*c - 12*a*b*c^2)*d^4)*sqrt(c*x^2 + b*x + a))/c]","A",0
1235,1,48,0,0.428258," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(4 \, c^{2} d^{3} x^{2} + 4 \, b c d^{3} x + {\left(3 \, b^{2} - 8 \, a c\right)} d^{3}\right)} \sqrt{c x^{2} + b x + a}"," ",0,"2/3*(4*c^2*d^3*x^2 + 4*b*c*d^3*x + (3*b^2 - 8*a*c)*d^3)*sqrt(c*x^2 + b*x + a)","A",0
1236,1,195,0,0.439860," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{c} d^{2} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, c^{2} d^{2} x + b c d^{2}\right)} \sqrt{c x^{2} + b x + a}}{4 \, c}, -\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{-c} d^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(2 \, c^{2} d^{2} x + b c d^{2}\right)} \sqrt{c x^{2} + b x + a}}{2 \, c}\right]"," ",0,"[-1/4*((b^2 - 4*a*c)*sqrt(c)*d^2*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(2*c^2*d^2*x + b*c*d^2)*sqrt(c*x^2 + b*x + a))/c, -1/2*((b^2 - 4*a*c)*sqrt(-c)*d^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(2*c^2*d^2*x + b*c*d^2)*sqrt(c*x^2 + b*x + a))/c]","A",0
1237,1,15,0,0.411817," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{c x^{2} + b x + a} d"," ",0,"2*sqrt(c*x^2 + b*x + a)*d","A",0
1238,1,174,0,0.433158," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d}, -\frac{\arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{\sqrt{b^{2} c - 4 \, a c^{2}} d}\right]"," ",0,"[-1/2*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2))/((b^2*c - 4*a*c^2)*d), -arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c))/(sqrt(b^2*c - 4*a*c^2)*d)]","A",0
1239,1,48,0,0.451121," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c x^{2} + b x + a}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} x + {\left(b^{3} - 4 \, a b c\right)} d^{2}}"," ",0,"2*sqrt(c*x^2 + b*x + a)/(2*(b^2*c - 4*a*c^2)*d^2*x + (b^3 - 4*a*b*c)*d^2)","A",0
1240,1,440,0,0.554268," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, c^{2} x^{2} + 4 \, b c x + b^{2}\right)} \sqrt{-b^{2} c + 4 \, a c^{2}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c + 4 \, \sqrt{-b^{2} c + 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + 4 \, {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(4 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} x^{2} + 4 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{3} x + {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d^{3}\right)}}, -\frac{{\left(4 \, c^{2} x^{2} + 4 \, b c x + b^{2}\right)} \sqrt{b^{2} c - 4 \, a c^{2}} \arctan\left(\frac{\sqrt{b^{2} c - 4 \, a c^{2}} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(4 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} x^{2} + 4 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{3} x + {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d^{3}\right)}}\right]"," ",0,"[1/4*((4*c^2*x^2 + 4*b*c*x + b^2)*sqrt(-b^2*c + 4*a*c^2)*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c + 4*sqrt(-b^2*c + 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*c^2*x^2 + 4*b*c*x + b^2)) + 4*(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*x^2 + 4*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^3*x + (b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d^3), -1/2*((4*c^2*x^2 + 4*b*c*x + b^2)*sqrt(b^2*c - 4*a*c^2)*arctan(1/2*sqrt(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a)/(c^2*x^2 + b*c*x + a*c)) - 2*(b^2*c - 4*a*c^2)*sqrt(c*x^2 + b*x + a))/(4*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*x^2 + 4*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^3*x + (b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d^3)]","B",0
1241,1,165,0,0.803724," ","integrate(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{2} x^{2} + 8 \, b c x + 3 \, b^{2} - 4 \, a c\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(8 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} x^{3} + 12 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{4} x^{2} + 6 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d^{4} x + {\left(b^{7} - 8 \, a b^{5} c + 16 \, a^{2} b^{3} c^{2}\right)} d^{4}\right)}}"," ",0,"2/3*(8*c^2*x^2 + 8*b*c*x + 3*b^2 - 4*a*c)*sqrt(c*x^2 + b*x + a)/(8*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^4*x^3 + 12*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^4*x^2 + 6*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d^4*x + (b^7 - 8*a*b^5*c + 16*a^2*b^3*c^2)*d^4)","B",0
1242,1,357,0,0.564437," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} x^{2} + {\left(b^{3} - 4 \, a b c\right)} d^{4} x + {\left(a b^{2} - 4 \, a^{2} c\right)} d^{4}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 2 \, {\left(4 \, c^{3} d^{4} x^{3} + 6 \, b c^{2} d^{4} x^{2} + 12 \, a c^{2} d^{4} x - {\left(b^{3} - 6 \, a b c\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}}{c x^{2} + b x + a}, -\frac{2 \, {\left(3 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} x^{2} + {\left(b^{3} - 4 \, a b c\right)} d^{4} x + {\left(a b^{2} - 4 \, a^{2} c\right)} d^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - {\left(4 \, c^{3} d^{4} x^{3} + 6 \, b c^{2} d^{4} x^{2} + 12 \, a c^{2} d^{4} x - {\left(b^{3} - 6 \, a b c\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}\right)}}{c x^{2} + b x + a}\right]"," ",0,"[-(3*((b^2*c - 4*a*c^2)*d^4*x^2 + (b^3 - 4*a*b*c)*d^4*x + (a*b^2 - 4*a^2*c)*d^4)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 2*(4*c^3*d^4*x^3 + 6*b*c^2*d^4*x^2 + 12*a*c^2*d^4*x - (b^3 - 6*a*b*c)*d^4)*sqrt(c*x^2 + b*x + a))/(c*x^2 + b*x + a), -2*(3*((b^2*c - 4*a*c^2)*d^4*x^2 + (b^3 - 4*a*b*c)*d^4*x + (a*b^2 - 4*a^2*c)*d^4)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - (4*c^3*d^4*x^3 + 6*b*c^2*d^4*x^2 + 12*a*c^2*d^4*x - (b^3 - 6*a*b*c)*d^4)*sqrt(c*x^2 + b*x + a))/(c*x^2 + b*x + a)]","A",0
1243,1,47,0,0.481746," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, c^{2} d^{3} x^{2} + 4 \, b c d^{3} x - {\left(b^{2} - 8 \, a c\right)} d^{3}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"2*(4*c^2*d^3*x^2 + 4*b*c*d^3*x - (b^2 - 8*a*c)*d^3)/sqrt(c*x^2 + b*x + a)","A",0
1244,1,225,0,0.489590," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(c d^{2} x^{2} + b d^{2} x + a d^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - {\left(2 \, c d^{2} x + b d^{2}\right)} \sqrt{c x^{2} + b x + a}\right)}}{c x^{2} + b x + a}, -\frac{2 \, {\left(2 \, {\left(c d^{2} x^{2} + b d^{2} x + a d^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(2 \, c d^{2} x + b d^{2}\right)} \sqrt{c x^{2} + b x + a}\right)}}{c x^{2} + b x + a}\right]"," ",0,"[2*((c*d^2*x^2 + b*d^2*x + a*d^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - (2*c*d^2*x + b*d^2)*sqrt(c*x^2 + b*x + a))/(c*x^2 + b*x + a), -2*(2*(c*d^2*x^2 + b*d^2*x + a*d^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + (2*c*d^2*x + b*d^2)*sqrt(c*x^2 + b*x + a))/(c*x^2 + b*x + a)]","A",0
1245,1,15,0,0.437721," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, d}{\sqrt{c x^{2} + b x + a}}"," ",0,"-2*d/sqrt(c*x^2 + b*x + a)","A",0
1246,1,311,0,0.545820," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left({\left(c x^{2} + b x + a\right)} \sqrt{-\frac{c}{b^{2} - 4 \, a c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c + 4 \, \sqrt{c x^{2} + b x + a} {\left(b^{2} - 4 \, a c\right)} \sqrt{-\frac{c}{b^{2} - 4 \, a c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + \sqrt{c x^{2} + b x + a}\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d x^{2} + {\left(b^{3} - 4 \, a b c\right)} d x + {\left(a b^{2} - 4 \, a^{2} c\right)} d}, -\frac{2 \, {\left(2 \, {\left(c x^{2} + b x + a\right)} \sqrt{\frac{c}{b^{2} - 4 \, a c}} \arctan\left(-\frac{\sqrt{c x^{2} + b x + a} {\left(b^{2} - 4 \, a c\right)} \sqrt{\frac{c}{b^{2} - 4 \, a c}}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + \sqrt{c x^{2} + b x + a}\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d x^{2} + {\left(b^{3} - 4 \, a b c\right)} d x + {\left(a b^{2} - 4 \, a^{2} c\right)} d}\right]"," ",0,"[-2*((c*x^2 + b*x + a)*sqrt(-c/(b^2 - 4*a*c))*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c + 4*sqrt(c*x^2 + b*x + a)*(b^2 - 4*a*c)*sqrt(-c/(b^2 - 4*a*c)))/(4*c^2*x^2 + 4*b*c*x + b^2)) + sqrt(c*x^2 + b*x + a))/((b^2*c - 4*a*c^2)*d*x^2 + (b^3 - 4*a*b*c)*d*x + (a*b^2 - 4*a^2*c)*d), -2*(2*(c*x^2 + b*x + a)*sqrt(c/(b^2 - 4*a*c))*arctan(-1/2*sqrt(c*x^2 + b*x + a)*(b^2 - 4*a*c)*sqrt(c/(b^2 - 4*a*c))/(c^2*x^2 + b*c*x + a*c)) + sqrt(c*x^2 + b*x + a))/((b^2*c - 4*a*c^2)*d*x^2 + (b^3 - 4*a*b*c)*d*x + (a*b^2 - 4*a^2*c)*d)]","A",0
1247,1,155,0,0.677680," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, c^{2} x^{2} + 8 \, b c x + b^{2} + 4 \, a c\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} x^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} x^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2} x + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}}"," ",0,"-2*(8*c^2*x^2 + 8*b*c*x + b^2 + 4*a*c)*sqrt(c*x^2 + b*x + a)/(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*x^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*x^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2*x + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)","B",0
1248,1,702,0,1.249615," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(4 \, c^{3} x^{4} + 8 \, b c^{2} x^{3} + a b^{2} + {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} + 4 \, a b c\right)} x\right)} \sqrt{-\frac{c}{b^{2} - 4 \, a c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{c x^{2} + b x + a} {\left(b^{2} - 4 \, a c\right)} \sqrt{-\frac{c}{b^{2} - 4 \, a c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) - 2 \, {\left(6 \, c^{2} x^{2} + 6 \, b c x + b^{2} + 2 \, a c\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} x^{4} + 8 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{3} x^{3} + {\left(5 \, b^{6} c - 36 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d^{3} x^{2} + {\left(b^{7} - 4 \, a b^{5} c - 16 \, a^{2} b^{3} c^{2} + 64 \, a^{3} b c^{3}\right)} d^{3} x + {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} d^{3}}, -\frac{2 \, {\left(3 \, {\left(4 \, c^{3} x^{4} + 8 \, b c^{2} x^{3} + a b^{2} + {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} + 4 \, a b c\right)} x\right)} \sqrt{\frac{c}{b^{2} - 4 \, a c}} \arctan\left(-\frac{\sqrt{c x^{2} + b x + a} {\left(b^{2} - 4 \, a c\right)} \sqrt{\frac{c}{b^{2} - 4 \, a c}}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(6 \, c^{2} x^{2} + 6 \, b c x + b^{2} + 2 \, a c\right)} \sqrt{c x^{2} + b x + a}\right)}}{4 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} x^{4} + 8 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{3} x^{3} + {\left(5 \, b^{6} c - 36 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d^{3} x^{2} + {\left(b^{7} - 4 \, a b^{5} c - 16 \, a^{2} b^{3} c^{2} + 64 \, a^{3} b c^{3}\right)} d^{3} x + {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} d^{3}}\right]"," ",0,"[(3*(4*c^3*x^4 + 8*b*c^2*x^3 + a*b^2 + (5*b^2*c + 4*a*c^2)*x^2 + (b^3 + 4*a*b*c)*x)*sqrt(-c/(b^2 - 4*a*c))*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(c*x^2 + b*x + a)*(b^2 - 4*a*c)*sqrt(-c/(b^2 - 4*a*c)))/(4*c^2*x^2 + 4*b*c*x + b^2)) - 2*(6*c^2*x^2 + 6*b*c*x + b^2 + 2*a*c)*sqrt(c*x^2 + b*x + a))/(4*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*x^4 + 8*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^3*x^3 + (5*b^6*c - 36*a*b^4*c^2 + 48*a^2*b^2*c^3 + 64*a^3*c^4)*d^3*x^2 + (b^7 - 4*a*b^5*c - 16*a^2*b^3*c^2 + 64*a^3*b*c^3)*d^3*x + (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*d^3), -2*(3*(4*c^3*x^4 + 8*b*c^2*x^3 + a*b^2 + (5*b^2*c + 4*a*c^2)*x^2 + (b^3 + 4*a*b*c)*x)*sqrt(c/(b^2 - 4*a*c))*arctan(-1/2*sqrt(c*x^2 + b*x + a)*(b^2 - 4*a*c)*sqrt(c/(b^2 - 4*a*c))/(c^2*x^2 + b*c*x + a*c)) + (6*c^2*x^2 + 6*b*c*x + b^2 + 2*a*c)*sqrt(c*x^2 + b*x + a))/(4*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*x^4 + 8*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^3*x^3 + (5*b^6*c - 36*a*b^4*c^2 + 48*a^2*b^2*c^3 + 64*a^3*c^4)*d^3*x^2 + (b^7 - 4*a*b^5*c - 16*a^2*b^3*c^2 + 64*a^3*b*c^3)*d^3*x + (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*d^3)]","B",0
1249,1,381,0,2.238973," ","integrate(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, c^{4} x^{4} + 256 \, b c^{3} x^{3} + 3 \, b^{4} + 24 \, a b^{2} c - 16 \, a^{2} c^{2} + 16 \, {\left(11 \, b^{2} c^{2} + 4 \, a c^{3}\right)} x^{2} + 16 \, {\left(3 \, b^{3} c + 4 \, a b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(8 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{4} x^{5} + 20 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{4} x^{4} + 2 \, {\left(9 \, b^{8} c^{2} - 104 \, a b^{6} c^{3} + 384 \, a^{2} b^{4} c^{4} - 384 \, a^{3} b^{2} c^{5} - 256 \, a^{4} c^{6}\right)} d^{4} x^{3} + {\left(7 \, b^{9} c - 72 \, a b^{7} c^{2} + 192 \, a^{2} b^{5} c^{3} + 128 \, a^{3} b^{3} c^{4} - 768 \, a^{4} b c^{5}\right)} d^{4} x^{2} + {\left(b^{10} - 6 \, a b^{8} c - 24 \, a^{2} b^{6} c^{2} + 224 \, a^{3} b^{4} c^{3} - 384 \, a^{4} b^{2} c^{4}\right)} d^{4} x + {\left(a b^{9} - 12 \, a^{2} b^{7} c + 48 \, a^{3} b^{5} c^{2} - 64 \, a^{4} b^{3} c^{3}\right)} d^{4}\right)}}"," ",0,"-2/3*(128*c^4*x^4 + 256*b*c^3*x^3 + 3*b^4 + 24*a*b^2*c - 16*a^2*c^2 + 16*(11*b^2*c^2 + 4*a*c^3)*x^2 + 16*(3*b^3*c + 4*a*b*c^2)*x)*sqrt(c*x^2 + b*x + a)/(8*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^4*x^5 + 20*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^4*x^4 + 2*(9*b^8*c^2 - 104*a*b^6*c^3 + 384*a^2*b^4*c^4 - 384*a^3*b^2*c^5 - 256*a^4*c^6)*d^4*x^3 + (7*b^9*c - 72*a*b^7*c^2 + 192*a^2*b^5*c^3 + 128*a^3*b^3*c^4 - 768*a^4*b*c^5)*d^4*x^2 + (b^10 - 6*a*b^8*c - 24*a^2*b^6*c^2 + 224*a^3*b^4*c^3 - 384*a^4*b^2*c^4)*d^4*x + (a*b^9 - 12*a^2*b^7*c + 48*a^3*b^5*c^2 - 64*a^4*b^3*c^3)*d^4)","B",0
1250,1,693,0,1.120353," ","integrate((2*c*d*x+b*d)^6/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(30 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} x^{4} + 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} x^{3} + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{6} x^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{6} x + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{6}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - {\left(48 \, c^{5} d^{6} x^{5} + 120 \, b c^{4} d^{6} x^{4} + 40 \, {\left(b^{2} c^{3} + 8 \, a c^{4}\right)} d^{6} x^{3} - 60 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d^{6} x^{2} - 30 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{6} x - {\left(b^{5} + 20 \, a b^{3} c - 120 \, a^{2} b c^{2}\right)} d^{6}\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}, -\frac{2 \, {\left(60 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} x^{4} + 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} x^{3} + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{6} x^{2} + 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{6} x + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{6}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - {\left(48 \, c^{5} d^{6} x^{5} + 120 \, b c^{4} d^{6} x^{4} + 40 \, {\left(b^{2} c^{3} + 8 \, a c^{4}\right)} d^{6} x^{3} - 60 \, {\left(b^{3} c^{2} - 8 \, a b c^{3}\right)} d^{6} x^{2} - 30 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{6} x - {\left(b^{5} + 20 \, a b^{3} c - 120 \, a^{2} b c^{2}\right)} d^{6}\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}\right]"," ",0,"[-2/3*(30*((b^2*c^3 - 4*a*c^4)*d^6*x^4 + 2*(b^3*c^2 - 4*a*b*c^3)*d^6*x^3 + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^6*x^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*d^6*x + (a^2*b^2*c - 4*a^3*c^2)*d^6)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - (48*c^5*d^6*x^5 + 120*b*c^4*d^6*x^4 + 40*(b^2*c^3 + 8*a*c^4)*d^6*x^3 - 60*(b^3*c^2 - 8*a*b*c^3)*d^6*x^2 - 30*(b^4*c - 4*a*b^2*c^2 - 8*a^2*c^3)*d^6*x - (b^5 + 20*a*b^3*c - 120*a^2*b*c^2)*d^6)*sqrt(c*x^2 + b*x + a))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), -2/3*(60*((b^2*c^3 - 4*a*c^4)*d^6*x^4 + 2*(b^3*c^2 - 4*a*b*c^3)*d^6*x^3 + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^6*x^2 + 2*(a*b^3*c - 4*a^2*b*c^2)*d^6*x + (a^2*b^2*c - 4*a^3*c^2)*d^6)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - (48*c^5*d^6*x^5 + 120*b*c^4*d^6*x^4 + 40*(b^2*c^3 + 8*a*c^4)*d^6*x^3 - 60*(b^3*c^2 - 8*a*b*c^3)*d^6*x^2 - 30*(b^4*c - 4*a*b^2*c^2 - 8*a^2*c^3)*d^6*x - (b^5 + 20*a*b^3*c - 120*a^2*b*c^2)*d^6)*sqrt(c*x^2 + b*x + a))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)]","B",0
1251,1,140,0,0.905570," ","integrate((2*c*d*x+b*d)^5/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(48 \, c^{4} d^{5} x^{4} + 96 \, b c^{3} d^{5} x^{3} + 24 \, {\left(b^{2} c^{2} + 8 \, a c^{3}\right)} d^{5} x^{2} - 24 \, {\left(b^{3} c - 8 \, a b c^{2}\right)} d^{5} x - {\left(b^{4} + 16 \, a b^{2} c - 128 \, a^{2} c^{2}\right)} d^{5}\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"2/3*(48*c^4*d^5*x^4 + 96*b*c^3*d^5*x^3 + 24*(b^2*c^2 + 8*a*c^3)*d^5*x^2 - 24*(b^3*c - 8*a*b*c^2)*d^5*x - (b^4 + 16*a*b^2*c - 128*a^2*c^2)*d^5)*sqrt(c*x^2 + b*x + a)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","A",0
1252,1,440,0,0.846803," ","integrate((2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(12 \, {\left(c^{3} d^{4} x^{4} + 2 \, b c^{2} d^{4} x^{3} + 2 \, a b c d^{4} x + a^{2} c d^{4} + {\left(b^{2} c + 2 \, a c^{2}\right)} d^{4} x^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - {\left(32 \, c^{3} d^{4} x^{3} + 48 \, b c^{2} d^{4} x^{2} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{4} x + {\left(b^{3} + 12 \, a b c\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}, -\frac{2 \, {\left(24 \, {\left(c^{3} d^{4} x^{4} + 2 \, b c^{2} d^{4} x^{3} + 2 \, a b c d^{4} x + a^{2} c d^{4} + {\left(b^{2} c + 2 \, a c^{2}\right)} d^{4} x^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(32 \, c^{3} d^{4} x^{3} + 48 \, b c^{2} d^{4} x^{2} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{4} x + {\left(b^{3} + 12 \, a b c\right)} d^{4}\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}\right]"," ",0,"[2/3*(12*(c^3*d^4*x^4 + 2*b*c^2*d^4*x^3 + 2*a*b*c*d^4*x + a^2*c*d^4 + (b^2*c + 2*a*c^2)*d^4*x^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - (32*c^3*d^4*x^3 + 48*b*c^2*d^4*x^2 + 6*(3*b^2*c + 4*a*c^2)*d^4*x + (b^3 + 12*a*b*c)*d^4)*sqrt(c*x^2 + b*x + a))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), -2/3*(24*(c^3*d^4*x^4 + 2*b*c^2*d^4*x^3 + 2*a*b*c*d^4*x + a^2*c*d^4 + (b^2*c + 2*a*c^2)*d^4*x^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + (32*c^3*d^4*x^3 + 48*b*c^2*d^4*x^2 + 6*(3*b^2*c + 4*a*c^2)*d^4*x + (b^3 + 12*a*b*c)*d^4)*sqrt(c*x^2 + b*x + a))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)]","B",0
1253,1,83,0,0.707676," ","integrate((2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(12 \, c^{2} d^{3} x^{2} + 12 \, b c d^{3} x + {\left(b^{2} + 8 \, a c\right)} d^{3}\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"-2/3*(12*c^2*d^3*x^2 + 12*b*c*d^3*x + (b^2 + 8*a*c)*d^3)*sqrt(c*x^2 + b*x + a)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","A",0
1254,1,146,0,0.699216," ","integrate((2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, c^{3} d^{2} x^{3} + 12 \, b c^{2} d^{2} x^{2} + 6 \, b^{2} c d^{2} x + b^{3} d^{2}\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)}}"," ",0,"-2/3*(8*c^3*d^2*x^3 + 12*b*c^2*d^2*x^2 + 6*b^2*c*d^2*x + b^3*d^2)*sqrt(c*x^2 + b*x + a)/((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)","B",0
1255,1,52,0,0.653069," ","integrate((2*c*d*x+b*d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x + a} d}{3 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"-2/3*sqrt(c*x^2 + b*x + a)*d/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1256,1,620,0,0.939829," ","integrate(1/(2*c*d*x+b*d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(12 \, {\left(c^{3} x^{4} + 2 \, b c^{2} x^{3} + 2 \, a b c x + a^{2} c + {\left(b^{2} c + 2 \, a c^{2}\right)} x^{2}\right)} \sqrt{-\frac{c}{b^{2} - 4 \, a c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c + 4 \, \sqrt{c x^{2} + b x + a} {\left(b^{2} - 4 \, a c\right)} \sqrt{-\frac{c}{b^{2} - 4 \, a c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) + {\left(12 \, c^{2} x^{2} + 12 \, b c x - b^{2} + 16 \, a c\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} d\right)}}, \frac{2 \, {\left(24 \, {\left(c^{3} x^{4} + 2 \, b c^{2} x^{3} + 2 \, a b c x + a^{2} c + {\left(b^{2} c + 2 \, a c^{2}\right)} x^{2}\right)} \sqrt{\frac{c}{b^{2} - 4 \, a c}} \arctan\left(-\frac{\sqrt{c x^{2} + b x + a} {\left(b^{2} - 4 \, a c\right)} \sqrt{\frac{c}{b^{2} - 4 \, a c}}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(12 \, c^{2} x^{2} + 12 \, b c x - b^{2} + 16 \, a c\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} d\right)}}\right]"," ",0,"[2/3*(12*(c^3*x^4 + 2*b*c^2*x^3 + 2*a*b*c*x + a^2*c + (b^2*c + 2*a*c^2)*x^2)*sqrt(-c/(b^2 - 4*a*c))*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c + 4*sqrt(c*x^2 + b*x + a)*(b^2 - 4*a*c)*sqrt(-c/(b^2 - 4*a*c)))/(4*c^2*x^2 + 4*b*c*x + b^2)) + (12*c^2*x^2 + 12*b*c*x - b^2 + 16*a*c)*sqrt(c*x^2 + b*x + a))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*d), 2/3*(24*(c^3*x^4 + 2*b*c^2*x^3 + 2*a*b*c*x + a^2*c + (b^2*c + 2*a*c^2)*x^2)*sqrt(c/(b^2 - 4*a*c))*arctan(-1/2*sqrt(c*x^2 + b*x + a)*(b^2 - 4*a*c)*sqrt(c/(b^2 - 4*a*c))/(c^2*x^2 + b*c*x + a*c)) + (12*c^2*x^2 + 12*b*c*x - b^2 + 16*a*c)*sqrt(c*x^2 + b*x + a))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*d)]","B",0
1257,1,374,0,2.083987," ","integrate(1/(2*c*d*x+b*d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, c^{4} x^{4} + 256 \, b c^{3} x^{3} - b^{4} + 24 \, a b^{2} c + 48 \, a^{2} c^{2} + 48 \, {\left(3 \, b^{2} c^{2} + 4 \, a c^{3}\right)} x^{2} + 16 \, {\left(b^{3} c + 12 \, a b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(2 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{2} x^{5} + 5 \, {\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)} d^{2} x^{4} + 4 \, {\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)} d^{2} x^{3} + {\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)} d^{2} x^{2} + 2 \, {\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)} d^{2} x + {\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)} d^{2}\right)}}"," ",0,"2/3*(128*c^4*x^4 + 256*b*c^3*x^3 - b^4 + 24*a*b^2*c + 48*a^2*c^2 + 48*(3*b^2*c^2 + 4*a*c^3)*x^2 + 16*(b^3*c + 12*a*b*c^2)*x)*sqrt(c*x^2 + b*x + a)/(2*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^2*x^5 + 5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2*x^4 + 4*(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)*d^2*x^3 + (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)*d^2*x^2 + 2*(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)*d^2*x + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2)","B",0
1258,1,1287,0,3.582304," ","integrate(1/(2*c*d*x+b*d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(30 \, {\left(4 \, c^{5} x^{6} + 12 \, b c^{4} x^{5} + a^{2} b^{2} c + {\left(13 \, b^{2} c^{3} + 8 \, a c^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{3} c^{2} + 8 \, a b c^{3}\right)} x^{3} + {\left(b^{4} c + 10 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} x^{2} + 2 \, {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} x\right)} \sqrt{-\frac{c}{b^{2} - 4 \, a c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c - 4 \, \sqrt{c x^{2} + b x + a} {\left(b^{2} - 4 \, a c\right)} \sqrt{-\frac{c}{b^{2} - 4 \, a c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right) - {\left(120 \, c^{4} x^{4} + 240 \, b c^{3} x^{3} - b^{4} + 28 \, a b^{2} c + 24 \, a^{2} c^{2} + 20 \, {\left(7 \, b^{2} c^{2} + 8 \, a c^{3}\right)} x^{2} + 20 \, {\left(b^{3} c + 8 \, a b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left(4 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{3} x^{6} + 12 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{3} x^{5} + {\left(13 \, b^{8} c^{2} - 148 \, a b^{6} c^{3} + 528 \, a^{2} b^{4} c^{4} - 448 \, a^{3} b^{2} c^{5} - 512 \, a^{4} c^{6}\right)} d^{3} x^{4} + 2 \, {\left(3 \, b^{9} c - 28 \, a b^{7} c^{2} + 48 \, a^{2} b^{5} c^{3} + 192 \, a^{3} b^{3} c^{4} - 512 \, a^{4} b c^{5}\right)} d^{3} x^{3} + {\left(b^{10} - 2 \, a b^{8} c - 68 \, a^{2} b^{6} c^{2} + 368 \, a^{3} b^{4} c^{3} - 448 \, a^{4} b^{2} c^{4} - 256 \, a^{5} c^{5}\right)} d^{3} x^{2} + 2 \, {\left(a b^{9} - 10 \, a^{2} b^{7} c + 24 \, a^{3} b^{5} c^{2} + 32 \, a^{4} b^{3} c^{3} - 128 \, a^{5} b c^{4}\right)} d^{3} x + {\left(a^{2} b^{8} - 12 \, a^{3} b^{6} c + 48 \, a^{4} b^{4} c^{2} - 64 \, a^{5} b^{2} c^{3}\right)} d^{3}\right)}}, \frac{2 \, {\left(60 \, {\left(4 \, c^{5} x^{6} + 12 \, b c^{4} x^{5} + a^{2} b^{2} c + {\left(13 \, b^{2} c^{3} + 8 \, a c^{4}\right)} x^{4} + 2 \, {\left(3 \, b^{3} c^{2} + 8 \, a b c^{3}\right)} x^{3} + {\left(b^{4} c + 10 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} x^{2} + 2 \, {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} x\right)} \sqrt{\frac{c}{b^{2} - 4 \, a c}} \arctan\left(-\frac{\sqrt{c x^{2} + b x + a} {\left(b^{2} - 4 \, a c\right)} \sqrt{\frac{c}{b^{2} - 4 \, a c}}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(120 \, c^{4} x^{4} + 240 \, b c^{3} x^{3} - b^{4} + 28 \, a b^{2} c + 24 \, a^{2} c^{2} + 20 \, {\left(7 \, b^{2} c^{2} + 8 \, a c^{3}\right)} x^{2} + 20 \, {\left(b^{3} c + 8 \, a b c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}\right)}}{3 \, {\left(4 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{3} x^{6} + 12 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{3} x^{5} + {\left(13 \, b^{8} c^{2} - 148 \, a b^{6} c^{3} + 528 \, a^{2} b^{4} c^{4} - 448 \, a^{3} b^{2} c^{5} - 512 \, a^{4} c^{6}\right)} d^{3} x^{4} + 2 \, {\left(3 \, b^{9} c - 28 \, a b^{7} c^{2} + 48 \, a^{2} b^{5} c^{3} + 192 \, a^{3} b^{3} c^{4} - 512 \, a^{4} b c^{5}\right)} d^{3} x^{3} + {\left(b^{10} - 2 \, a b^{8} c - 68 \, a^{2} b^{6} c^{2} + 368 \, a^{3} b^{4} c^{3} - 448 \, a^{4} b^{2} c^{4} - 256 \, a^{5} c^{5}\right)} d^{3} x^{2} + 2 \, {\left(a b^{9} - 10 \, a^{2} b^{7} c + 24 \, a^{3} b^{5} c^{2} + 32 \, a^{4} b^{3} c^{3} - 128 \, a^{5} b c^{4}\right)} d^{3} x + {\left(a^{2} b^{8} - 12 \, a^{3} b^{6} c + 48 \, a^{4} b^{4} c^{2} - 64 \, a^{5} b^{2} c^{3}\right)} d^{3}\right)}}\right]"," ",0,"[-2/3*(30*(4*c^5*x^6 + 12*b*c^4*x^5 + a^2*b^2*c + (13*b^2*c^3 + 8*a*c^4)*x^4 + 2*(3*b^3*c^2 + 8*a*b*c^3)*x^3 + (b^4*c + 10*a*b^2*c^2 + 4*a^2*c^3)*x^2 + 2*(a*b^3*c + 2*a^2*b*c^2)*x)*sqrt(-c/(b^2 - 4*a*c))*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c - 4*sqrt(c*x^2 + b*x + a)*(b^2 - 4*a*c)*sqrt(-c/(b^2 - 4*a*c)))/(4*c^2*x^2 + 4*b*c*x + b^2)) - (120*c^4*x^4 + 240*b*c^3*x^3 - b^4 + 28*a*b^2*c + 24*a^2*c^2 + 20*(7*b^2*c^2 + 8*a*c^3)*x^2 + 20*(b^3*c + 8*a*b*c^2)*x)*sqrt(c*x^2 + b*x + a))/(4*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^3*x^6 + 12*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^3*x^5 + (13*b^8*c^2 - 148*a*b^6*c^3 + 528*a^2*b^4*c^4 - 448*a^3*b^2*c^5 - 512*a^4*c^6)*d^3*x^4 + 2*(3*b^9*c - 28*a*b^7*c^2 + 48*a^2*b^5*c^3 + 192*a^3*b^3*c^4 - 512*a^4*b*c^5)*d^3*x^3 + (b^10 - 2*a*b^8*c - 68*a^2*b^6*c^2 + 368*a^3*b^4*c^3 - 448*a^4*b^2*c^4 - 256*a^5*c^5)*d^3*x^2 + 2*(a*b^9 - 10*a^2*b^7*c + 24*a^3*b^5*c^2 + 32*a^4*b^3*c^3 - 128*a^5*b*c^4)*d^3*x + (a^2*b^8 - 12*a^3*b^6*c + 48*a^4*b^4*c^2 - 64*a^5*b^2*c^3)*d^3), 2/3*(60*(4*c^5*x^6 + 12*b*c^4*x^5 + a^2*b^2*c + (13*b^2*c^3 + 8*a*c^4)*x^4 + 2*(3*b^3*c^2 + 8*a*b*c^3)*x^3 + (b^4*c + 10*a*b^2*c^2 + 4*a^2*c^3)*x^2 + 2*(a*b^3*c + 2*a^2*b*c^2)*x)*sqrt(c/(b^2 - 4*a*c))*arctan(-1/2*sqrt(c*x^2 + b*x + a)*(b^2 - 4*a*c)*sqrt(c/(b^2 - 4*a*c))/(c^2*x^2 + b*c*x + a*c)) + (120*c^4*x^4 + 240*b*c^3*x^3 - b^4 + 28*a*b^2*c + 24*a^2*c^2 + 20*(7*b^2*c^2 + 8*a*c^3)*x^2 + 20*(b^3*c + 8*a*b*c^2)*x)*sqrt(c*x^2 + b*x + a))/(4*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^3*x^6 + 12*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^3*x^5 + (13*b^8*c^2 - 148*a*b^6*c^3 + 528*a^2*b^4*c^4 - 448*a^3*b^2*c^5 - 512*a^4*c^6)*d^3*x^4 + 2*(3*b^9*c - 28*a*b^7*c^2 + 48*a^2*b^5*c^3 + 192*a^3*b^3*c^4 - 512*a^4*b*c^5)*d^3*x^3 + (b^10 - 2*a*b^8*c - 68*a^2*b^6*c^2 + 368*a^3*b^4*c^3 - 448*a^4*b^2*c^4 - 256*a^5*c^5)*d^3*x^2 + 2*(a*b^9 - 10*a^2*b^7*c + 24*a^3*b^5*c^2 + 32*a^4*b^3*c^3 - 128*a^5*b*c^4)*d^3*x + (a^2*b^8 - 12*a^3*b^6*c + 48*a^4*b^4*c^2 - 64*a^5*b^2*c^3)*d^3)]","B",0
1259,1,677,0,6.870238," ","integrate(1/(2*c*d*x+b*d)^4/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1024 \, c^{6} x^{6} + 3072 \, b c^{5} x^{5} - b^{6} + 36 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3} + 384 \, {\left(9 \, b^{2} c^{4} + 4 \, a c^{5}\right)} x^{4} + 256 \, {\left(7 \, b^{3} c^{3} + 12 \, a b c^{4}\right)} x^{3} + 24 \, {\left(17 \, b^{4} c^{2} + 88 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + 24 \, {\left(b^{5} c + 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(8 \, {\left(b^{8} c^{5} - 16 \, a b^{6} c^{6} + 96 \, a^{2} b^{4} c^{7} - 256 \, a^{3} b^{2} c^{8} + 256 \, a^{4} c^{9}\right)} d^{4} x^{7} + 28 \, {\left(b^{9} c^{4} - 16 \, a b^{7} c^{5} + 96 \, a^{2} b^{5} c^{6} - 256 \, a^{3} b^{3} c^{7} + 256 \, a^{4} b c^{8}\right)} d^{4} x^{6} + 2 \, {\left(19 \, b^{10} c^{3} - 296 \, a b^{8} c^{4} + 1696 \, a^{2} b^{6} c^{5} - 4096 \, a^{3} b^{4} c^{6} + 2816 \, a^{4} b^{2} c^{7} + 2048 \, a^{5} c^{8}\right)} d^{4} x^{5} + 5 \, {\left(5 \, b^{11} c^{2} - 72 \, a b^{9} c^{3} + 352 \, a^{2} b^{7} c^{4} - 512 \, a^{3} b^{5} c^{5} - 768 \, a^{4} b^{3} c^{6} + 2048 \, a^{5} b c^{7}\right)} d^{4} x^{4} + 4 \, {\left(2 \, b^{12} c - 23 \, a b^{10} c^{2} + 50 \, a^{2} b^{8} c^{3} + 320 \, a^{3} b^{6} c^{4} - 1600 \, a^{4} b^{4} c^{5} + 1792 \, a^{5} b^{2} c^{6} + 512 \, a^{6} c^{7}\right)} d^{4} x^{3} + {\left(b^{13} - 2 \, a b^{11} c - 116 \, a^{2} b^{9} c^{2} + 896 \, a^{3} b^{7} c^{3} - 2176 \, a^{4} b^{5} c^{4} + 512 \, a^{5} b^{3} c^{5} + 3072 \, a^{6} b c^{6}\right)} d^{4} x^{2} + 2 \, {\left(a b^{12} - 13 \, a^{2} b^{10} c + 48 \, a^{3} b^{8} c^{2} + 32 \, a^{4} b^{6} c^{3} - 512 \, a^{5} b^{4} c^{4} + 768 \, a^{6} b^{2} c^{5}\right)} d^{4} x + {\left(a^{2} b^{11} - 16 \, a^{3} b^{9} c + 96 \, a^{4} b^{7} c^{2} - 256 \, a^{5} b^{5} c^{3} + 256 \, a^{6} b^{3} c^{4}\right)} d^{4}\right)}}"," ",0,"2/3*(1024*c^6*x^6 + 3072*b*c^5*x^5 - b^6 + 36*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3 + 384*(9*b^2*c^4 + 4*a*c^5)*x^4 + 256*(7*b^3*c^3 + 12*a*b*c^4)*x^3 + 24*(17*b^4*c^2 + 88*a*b^2*c^3 + 16*a^2*c^4)*x^2 + 24*(b^5*c + 24*a*b^3*c^2 + 16*a^2*b*c^3)*x)*sqrt(c*x^2 + b*x + a)/(8*(b^8*c^5 - 16*a*b^6*c^6 + 96*a^2*b^4*c^7 - 256*a^3*b^2*c^8 + 256*a^4*c^9)*d^4*x^7 + 28*(b^9*c^4 - 16*a*b^7*c^5 + 96*a^2*b^5*c^6 - 256*a^3*b^3*c^7 + 256*a^4*b*c^8)*d^4*x^6 + 2*(19*b^10*c^3 - 296*a*b^8*c^4 + 1696*a^2*b^6*c^5 - 4096*a^3*b^4*c^6 + 2816*a^4*b^2*c^7 + 2048*a^5*c^8)*d^4*x^5 + 5*(5*b^11*c^2 - 72*a*b^9*c^3 + 352*a^2*b^7*c^4 - 512*a^3*b^5*c^5 - 768*a^4*b^3*c^6 + 2048*a^5*b*c^7)*d^4*x^4 + 4*(2*b^12*c - 23*a*b^10*c^2 + 50*a^2*b^8*c^3 + 320*a^3*b^6*c^4 - 1600*a^4*b^4*c^5 + 1792*a^5*b^2*c^6 + 512*a^6*c^7)*d^4*x^3 + (b^13 - 2*a*b^11*c - 116*a^2*b^9*c^2 + 896*a^3*b^7*c^3 - 2176*a^4*b^5*c^4 + 512*a^5*b^3*c^5 + 3072*a^6*b*c^6)*d^4*x^2 + 2*(a*b^12 - 13*a^2*b^10*c + 48*a^3*b^8*c^2 + 32*a^4*b^6*c^3 - 512*a^5*b^4*c^4 + 768*a^6*b^2*c^5)*d^4*x + (a^2*b^11 - 16*a^3*b^9*c + 96*a^4*b^7*c^2 - 256*a^5*b^5*c^3 + 256*a^6*b^3*c^4)*d^4)","B",0
1260,1,66,0,0.409163," ","integrate(1/(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{\log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\right) - \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} - 1\right)}{b}"," ",0,"-(log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1) - log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) - 1))/b","B",0
1261,1,122,0,0.396258," ","integrate((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{{\left(56 \, c^{5} d^{2} x^{5} + 140 \, b c^{4} d^{2} x^{4} + 2 \, {\left(59 \, b^{2} c^{3} + 44 \, a c^{4}\right)} d^{2} x^{3} + {\left(37 \, b^{3} c^{2} + 132 \, a b c^{3}\right)} d^{2} x^{2} + {\left(b^{4} c + 66 \, a b^{2} c^{2}\right)} d^{2} x - {\left(b^{5} - 11 \, a b^{3} c\right)} d^{2}\right)} \sqrt{2 \, c d x + b d}}{77 \, c^{2}}"," ",0,"1/77*(56*c^5*d^2*x^5 + 140*b*c^4*d^2*x^4 + 2*(59*b^2*c^3 + 44*a*c^4)*d^2*x^3 + (37*b^3*c^2 + 132*a*b*c^3)*d^2*x^2 + (b^4*c + 66*a*b^2*c^2)*d^2*x - (b^5 - 11*a*b^3*c)*d^2)*sqrt(2*c*d*x + b*d)/c^2","B",0
1262,1,87,0,0.405994," ","integrate((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{{\left(20 \, c^{4} d x^{4} + 40 \, b c^{3} d x^{3} + 3 \, {\left(7 \, b^{2} c^{2} + 12 \, a c^{3}\right)} d x^{2} + {\left(b^{3} c + 36 \, a b c^{2}\right)} d x - {\left(b^{4} - 9 \, a b^{2} c\right)} d\right)} \sqrt{2 \, c d x + b d}}{45 \, c^{2}}"," ",0,"1/45*(20*c^4*d*x^4 + 40*b*c^3*d*x^3 + 3*(7*b^2*c^2 + 12*a*c^3)*d*x^2 + (b^3*c + 36*a*b*c^2)*d*x - (b^4 - 9*a*b^2*c)*d)*sqrt(2*c*d*x + b*d)/c^2","A",0
1263,1,58,0,0.397971," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{{\left(6 \, c^{3} x^{3} + 9 \, b c^{2} x^{2} - b^{3} + 7 \, a b c + {\left(b^{2} c + 14 \, a c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{21 \, c^{2}}"," ",0,"1/21*(6*c^3*x^3 + 9*b*c^2*x^2 - b^3 + 7*a*b*c + (b^2*c + 14*a*c^2)*x)*sqrt(2*c*d*x + b*d)/c^2","A",0
1264,1,40,0,0.399412," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^(1/2),x, algorithm=""fricas"")","\frac{{\left(c^{2} x^{2} + b c x - b^{2} + 5 \, a c\right)} \sqrt{2 \, c d x + b d}}{5 \, c^{2} d}"," ",0,"1/5*(c^2*x^2 + b*c*x - b^2 + 5*a*c)*sqrt(2*c*d*x + b*d)/(c^2*d)","A",0
1265,1,52,0,0.380848," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^(3/2),x, algorithm=""fricas"")","\frac{{\left(c^{2} x^{2} + b c x + b^{2} - 3 \, a c\right)} \sqrt{2 \, c d x + b d}}{3 \, {\left(2 \, c^{3} d^{2} x + b c^{2} d^{2}\right)}}"," ",0,"1/3*(c^2*x^2 + b*c*x + b^2 - 3*a*c)*sqrt(2*c*d*x + b*d)/(2*c^3*d^2*x + b*c^2*d^2)","A",0
1266,1,68,0,0.401242," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, c^{2} x^{2} + 3 \, b c x + b^{2} - a c\right)} \sqrt{2 \, c d x + b d}}{3 \, {\left(4 \, c^{4} d^{3} x^{2} + 4 \, b c^{3} d^{3} x + b^{2} c^{2} d^{3}\right)}}"," ",0,"1/3*(3*c^2*x^2 + 3*b*c*x + b^2 - a*c)*sqrt(2*c*d*x + b*d)/(4*c^4*d^3*x^2 + 4*b*c^3*d^3*x + b^2*c^2*d^3)","A",0
1267,1,81,0,0.393035," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(5 \, c^{2} x^{2} + 5 \, b c x + b^{2} + a c\right)} \sqrt{2 \, c d x + b d}}{5 \, {\left(8 \, c^{5} d^{4} x^{3} + 12 \, b c^{4} d^{4} x^{2} + 6 \, b^{2} c^{3} d^{4} x + b^{3} c^{2} d^{4}\right)}}"," ",0,"-1/5*(5*c^2*x^2 + 5*b*c*x + b^2 + a*c)*sqrt(2*c*d*x + b*d)/(8*c^5*d^4*x^3 + 12*b*c^4*d^4*x^2 + 6*b^2*c^3*d^4*x + b^3*c^2*d^4)","A",0
1268,1,96,0,0.401168," ","integrate((c*x^2+b*x+a)/(2*c*d*x+b*d)^(9/2),x, algorithm=""fricas"")","-\frac{{\left(7 \, c^{2} x^{2} + 7 \, b c x + b^{2} + 3 \, a c\right)} \sqrt{2 \, c d x + b d}}{21 \, {\left(16 \, c^{6} d^{5} x^{4} + 32 \, b c^{5} d^{5} x^{3} + 24 \, b^{2} c^{4} d^{5} x^{2} + 8 \, b^{3} c^{3} d^{5} x + b^{4} c^{2} d^{5}\right)}}"," ",0,"-1/21*(7*c^2*x^2 + 7*b*c*x + b^2 + 3*a*c)*sqrt(2*c*d*x + b*d)/(16*c^6*d^5*x^4 + 32*b*c^5*d^5*x^3 + 24*b^2*c^4*d^5*x^2 + 8*b^3*c^3*d^5*x + b^4*c^2*d^5)","B",0
1269,1,164,0,0.392585," ","integrate((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(180 \, c^{6} d x^{6} + 540 \, b c^{5} d x^{5} + 5 \, {\left(109 \, b^{2} c^{4} + 104 \, a c^{5}\right)} d x^{4} + 10 \, {\left(19 \, b^{3} c^{3} + 104 \, a b c^{4}\right)} d x^{3} + 3 \, {\left(b^{4} c^{2} + 182 \, a b^{2} c^{3} + 156 \, a^{2} c^{4}\right)} d x^{2} - 2 \, {\left(b^{5} c - 13 \, a b^{3} c^{2} - 234 \, a^{2} b c^{3}\right)} d x + {\left(2 \, b^{6} - 26 \, a b^{4} c + 117 \, a^{2} b^{2} c^{2}\right)} d\right)} \sqrt{2 \, c d x + b d}}{585 \, c^{3}}"," ",0,"1/585*(180*c^6*d*x^6 + 540*b*c^5*d*x^5 + 5*(109*b^2*c^4 + 104*a*c^5)*d*x^4 + 10*(19*b^3*c^3 + 104*a*b*c^4)*d*x^3 + 3*(b^4*c^2 + 182*a*b^2*c^3 + 156*a^2*c^4)*d*x^2 - 2*(b^5*c - 13*a*b^3*c^2 - 234*a^2*b*c^3)*d*x + (2*b^6 - 26*a*b^4*c + 117*a^2*b^2*c^2)*d)*sqrt(2*c*d*x + b*d)/c^3","B",0
1270,1,121,0,0.401850," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(42 \, c^{5} x^{5} + 105 \, b c^{4} x^{4} + 2 \, b^{5} - 22 \, a b^{3} c + 77 \, a^{2} b c^{2} + 12 \, {\left(6 \, b^{2} c^{3} + 11 \, a c^{4}\right)} x^{3} + 3 \, {\left(b^{3} c^{2} + 66 \, a b c^{3}\right)} x^{2} - 2 \, {\left(b^{4} c - 11 \, a b^{2} c^{2} - 77 \, a^{2} c^{3}\right)} x\right)} \sqrt{2 \, c d x + b d}}{231 \, c^{3}}"," ",0,"1/231*(42*c^5*x^5 + 105*b*c^4*x^4 + 2*b^5 - 22*a*b^3*c + 77*a^2*b*c^2 + 12*(6*b^2*c^3 + 11*a*c^4)*x^3 + 3*(b^3*c^2 + 66*a*b*c^3)*x^2 - 2*(b^4*c - 11*a*b^2*c^2 - 77*a^2*c^3)*x)*sqrt(2*c*d*x + b*d)/c^3","A",0
1271,1,92,0,0.389366," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(1/2),x, algorithm=""fricas"")","\frac{{\left(5 \, c^{4} x^{4} + 10 \, b c^{3} x^{3} + 2 \, b^{4} - 18 \, a b^{2} c + 45 \, a^{2} c^{2} + 3 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} x^{2} - 2 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{45 \, c^{3} d}"," ",0,"1/45*(5*c^4*x^4 + 10*b*c^3*x^3 + 2*b^4 - 18*a*b^2*c + 45*a^2*c^2 + 3*(b^2*c^2 + 6*a*c^3)*x^2 - 2*(b^3*c - 9*a*b*c^2)*x)*sqrt(2*c*d*x + b*d)/(c^3*d)","A",0
1272,1,105,0,0.387766," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, c^{4} x^{4} + 6 \, b c^{3} x^{3} - 2 \, b^{4} + 14 \, a b^{2} c - 21 \, a^{2} c^{2} + {\left(b^{2} c^{2} + 14 \, a c^{3}\right)} x^{2} - 2 \, {\left(b^{3} c - 7 \, a b c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{21 \, {\left(2 \, c^{4} d^{2} x + b c^{3} d^{2}\right)}}"," ",0,"1/21*(3*c^4*x^4 + 6*b*c^3*x^3 - 2*b^4 + 14*a*b^2*c - 21*a^2*c^2 + (b^2*c^2 + 14*a*c^3)*x^2 - 2*(b^3*c - 7*a*b*c^2)*x)*sqrt(2*c*d*x + b*d)/(2*c^4*d^2*x + b*c^3*d^2)","A",0
1273,1,120,0,0.395127," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(5/2),x, algorithm=""fricas"")","\frac{{\left(3 \, c^{4} x^{4} + 6 \, b c^{3} x^{3} - 2 \, b^{4} + 10 \, a b^{2} c - 5 \, a^{2} c^{2} - 3 \, {\left(b^{2} c^{2} - 10 \, a c^{3}\right)} x^{2} - 6 \, {\left(b^{3} c - 5 \, a b c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{15 \, {\left(4 \, c^{5} d^{3} x^{2} + 4 \, b c^{4} d^{3} x + b^{2} c^{3} d^{3}\right)}}"," ",0,"1/15*(3*c^4*x^4 + 6*b*c^3*x^3 - 2*b^4 + 10*a*b^2*c - 5*a^2*c^2 - 3*(b^2*c^2 - 10*a*c^3)*x^2 - 6*(b^3*c - 5*a*b*c^2)*x)*sqrt(2*c*d*x + b*d)/(4*c^5*d^3*x^2 + 4*b*c^4*d^3*x + b^2*c^3*d^3)","A",0
1274,1,134,0,0.394490," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(7/2),x, algorithm=""fricas"")","\frac{{\left(5 \, c^{4} x^{4} + 10 \, b c^{3} x^{3} + 2 \, b^{4} - 6 \, a b^{2} c - 3 \, a^{2} c^{2} + 15 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} x^{2} + 10 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{15 \, {\left(8 \, c^{6} d^{4} x^{3} + 12 \, b c^{5} d^{4} x^{2} + 6 \, b^{2} c^{4} d^{4} x + b^{3} c^{3} d^{4}\right)}}"," ",0,"1/15*(5*c^4*x^4 + 10*b*c^3*x^3 + 2*b^4 - 6*a*b^2*c - 3*a^2*c^2 + 15*(b^2*c^2 - 2*a*c^3)*x^2 + 10*(b^3*c - 3*a*b*c^2)*x)*sqrt(2*c*d*x + b*d)/(8*c^6*d^4*x^3 + 12*b*c^5*d^4*x^2 + 6*b^2*c^4*d^4*x + b^3*c^3*d^4)","A",0
1275,1,149,0,0.392578," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(9/2),x, algorithm=""fricas"")","\frac{{\left(21 \, c^{4} x^{4} + 42 \, b c^{3} x^{3} + 2 \, b^{4} - 2 \, a b^{2} c - 3 \, a^{2} c^{2} + 7 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} x^{2} + 14 \, {\left(b^{3} c - a b c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{21 \, {\left(16 \, c^{7} d^{5} x^{4} + 32 \, b c^{6} d^{5} x^{3} + 24 \, b^{2} c^{5} d^{5} x^{2} + 8 \, b^{3} c^{4} d^{5} x + b^{4} c^{3} d^{5}\right)}}"," ",0,"1/21*(21*c^4*x^4 + 42*b*c^3*x^3 + 2*b^4 - 2*a*b^2*c - 3*a^2*c^2 + 7*(5*b^2*c^2 - 2*a*c^3)*x^2 + 14*(b^3*c - a*b*c^2)*x)*sqrt(2*c*d*x + b*d)/(16*c^7*d^5*x^4 + 32*b*c^6*d^5*x^3 + 24*b^2*c^5*d^5*x^2 + 8*b^3*c^4*d^5*x + b^4*c^3*d^5)","A",0
1276,1,162,0,0.386167," ","integrate((c*x^2+b*x+a)^2/(2*c*d*x+b*d)^(11/2),x, algorithm=""fricas"")","-\frac{{\left(45 \, c^{4} x^{4} + 90 \, b c^{3} x^{3} + 2 \, b^{4} + 2 \, a b^{2} c + 5 \, a^{2} c^{2} + 9 \, {\left(7 \, b^{2} c^{2} + 2 \, a c^{3}\right)} x^{2} + 18 \, {\left(b^{3} c + a b c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{45 \, {\left(32 \, c^{8} d^{6} x^{5} + 80 \, b c^{7} d^{6} x^{4} + 80 \, b^{2} c^{6} d^{6} x^{3} + 40 \, b^{3} c^{5} d^{6} x^{2} + 10 \, b^{4} c^{4} d^{6} x + b^{5} c^{3} d^{6}\right)}}"," ",0,"-1/45*(45*c^4*x^4 + 90*b*c^3*x^3 + 2*b^4 + 2*a*b^2*c + 5*a^2*c^2 + 9*(7*b^2*c^2 + 2*a*c^3)*x^2 + 18*(b^3*c + a*b*c^2)*x)*sqrt(2*c*d*x + b*d)/(32*c^8*d^6*x^5 + 80*b*c^7*d^6*x^4 + 80*b^2*c^6*d^6*x^3 + 40*b^3*c^5*d^6*x^2 + 10*b^4*c^4*d^6*x + b^5*c^3*d^6)","B",0
1277,1,205,0,0.404288," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left(154 \, c^{7} x^{7} + 539 \, b c^{6} x^{6} - 2 \, b^{7} + 30 \, a b^{5} c - 165 \, a^{2} b^{3} c^{2} + 385 \, a^{3} b c^{3} + 21 \, {\left(31 \, b^{2} c^{5} + 30 \, a c^{6}\right)} x^{5} + 35 \, {\left(8 \, b^{3} c^{4} + 45 \, a b c^{5}\right)} x^{4} + 5 \, {\left(b^{4} c^{3} + 216 \, a b^{2} c^{4} + 198 \, a^{2} c^{5}\right)} x^{3} - 3 \, {\left(b^{5} c^{2} - 15 \, a b^{3} c^{3} - 495 \, a^{2} b c^{4}\right)} x^{2} + {\left(2 \, b^{6} c - 30 \, a b^{4} c^{2} + 165 \, a^{2} b^{2} c^{3} + 770 \, a^{3} c^{4}\right)} x\right)} \sqrt{2 \, c d x + b d}}{1155 \, c^{4}}"," ",0,"1/1155*(154*c^7*x^7 + 539*b*c^6*x^6 - 2*b^7 + 30*a*b^5*c - 165*a^2*b^3*c^2 + 385*a^3*b*c^3 + 21*(31*b^2*c^5 + 30*a*c^6)*x^5 + 35*(8*b^3*c^4 + 45*a*b*c^5)*x^4 + 5*(b^4*c^3 + 216*a*b^2*c^4 + 198*a^2*c^5)*x^3 - 3*(b^5*c^2 - 15*a*b^3*c^3 - 495*a^2*b*c^4)*x^2 + (2*b^6*c - 30*a*b^4*c^2 + 165*a^2*b^2*c^3 + 770*a^3*c^4)*x)*sqrt(2*c*d*x + b*d)/c^4","A",0
1278,1,165,0,0.405646," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(1/2),x, algorithm=""fricas"")","\frac{{\left(15 \, c^{6} x^{6} + 45 \, b c^{5} x^{5} - 2 \, b^{6} + 26 \, a b^{4} c - 117 \, a^{2} b^{2} c^{2} + 195 \, a^{3} c^{3} + 5 \, {\left(8 \, b^{2} c^{4} + 13 \, a c^{5}\right)} x^{4} + 5 \, {\left(b^{3} c^{3} + 26 \, a b c^{4}\right)} x^{3} - 3 \, {\left(b^{4} c^{2} - 13 \, a b^{2} c^{3} - 39 \, a^{2} c^{4}\right)} x^{2} + {\left(2 \, b^{5} c - 26 \, a b^{3} c^{2} + 117 \, a^{2} b c^{3}\right)} x\right)} \sqrt{2 \, c d x + b d}}{195 \, c^{4} d}"," ",0,"1/195*(15*c^6*x^6 + 45*b*c^5*x^5 - 2*b^6 + 26*a*b^4*c - 117*a^2*b^2*c^2 + 195*a^3*c^3 + 5*(8*b^2*c^4 + 13*a*c^5)*x^4 + 5*(b^3*c^3 + 26*a*b*c^4)*x^3 - 3*(b^4*c^2 - 13*a*b^2*c^3 - 39*a^2*c^4)*x^2 + (2*b^5*c - 26*a*b^3*c^2 + 117*a^2*b*c^3)*x)*sqrt(2*c*d*x + b*d)/(c^4*d)","A",0
1279,1,178,0,0.410160," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(3/2),x, algorithm=""fricas"")","\frac{{\left(7 \, c^{6} x^{6} + 21 \, b c^{5} x^{5} + 2 \, b^{6} - 22 \, a b^{4} c + 77 \, a^{2} b^{2} c^{2} - 77 \, a^{3} c^{3} + 3 \, {\left(6 \, b^{2} c^{4} + 11 \, a c^{5}\right)} x^{4} + {\left(b^{3} c^{3} + 66 \, a b c^{4}\right)} x^{3} - {\left(b^{4} c^{2} - 11 \, a b^{2} c^{3} - 77 \, a^{2} c^{4}\right)} x^{2} + {\left(2 \, b^{5} c - 22 \, a b^{3} c^{2} + 77 \, a^{2} b c^{3}\right)} x\right)} \sqrt{2 \, c d x + b d}}{77 \, {\left(2 \, c^{5} d^{2} x + b c^{4} d^{2}\right)}}"," ",0,"1/77*(7*c^6*x^6 + 21*b*c^5*x^5 + 2*b^6 - 22*a*b^4*c + 77*a^2*b^2*c^2 - 77*a^3*c^3 + 3*(6*b^2*c^4 + 11*a*c^5)*x^4 + (b^3*c^3 + 66*a*b*c^4)*x^3 - (b^4*c^2 - 11*a*b^2*c^3 - 77*a^2*c^4)*x^2 + (2*b^5*c - 22*a*b^3*c^2 + 77*a^2*b*c^3)*x)*sqrt(2*c*d*x + b*d)/(2*c^5*d^2*x + b*c^4*d^2)","A",0
1280,1,194,0,0.396950," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(5/2),x, algorithm=""fricas"")","\frac{{\left(5 \, c^{6} x^{6} + 15 \, b c^{5} x^{5} + 2 \, b^{6} - 18 \, a b^{4} c + 45 \, a^{2} b^{2} c^{2} - 15 \, a^{3} c^{3} + 3 \, {\left(4 \, b^{2} c^{4} + 9 \, a c^{5}\right)} x^{4} - {\left(b^{3} c^{3} - 54 \, a b c^{4}\right)} x^{3} + 3 \, {\left(b^{4} c^{2} - 9 \, a b^{2} c^{3} + 45 \, a^{2} c^{4}\right)} x^{2} + 3 \, {\left(2 \, b^{5} c - 18 \, a b^{3} c^{2} + 45 \, a^{2} b c^{3}\right)} x\right)} \sqrt{2 \, c d x + b d}}{45 \, {\left(4 \, c^{6} d^{3} x^{2} + 4 \, b c^{5} d^{3} x + b^{2} c^{4} d^{3}\right)}}"," ",0,"1/45*(5*c^6*x^6 + 15*b*c^5*x^5 + 2*b^6 - 18*a*b^4*c + 45*a^2*b^2*c^2 - 15*a^3*c^3 + 3*(4*b^2*c^4 + 9*a*c^5)*x^4 - (b^3*c^3 - 54*a*b*c^4)*x^3 + 3*(b^4*c^2 - 9*a*b^2*c^3 + 45*a^2*c^4)*x^2 + 3*(2*b^5*c - 18*a*b^3*c^2 + 45*a^2*b*c^3)*x)*sqrt(2*c*d*x + b*d)/(4*c^6*d^3*x^2 + 4*b*c^5*d^3*x + b^2*c^4*d^3)","A",0
1281,1,208,0,0.395896," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(7/2),x, algorithm=""fricas"")","\frac{{\left(5 \, c^{6} x^{6} + 15 \, b c^{5} x^{5} - 2 \, b^{6} + 14 \, a b^{4} c - 21 \, a^{2} b^{2} c^{2} - 7 \, a^{3} c^{3} + 5 \, {\left(2 \, b^{2} c^{4} + 7 \, a c^{5}\right)} x^{4} - 5 \, {\left(b^{3} c^{3} - 14 \, a b c^{4}\right)} x^{3} - 15 \, {\left(b^{4} c^{2} - 7 \, a b^{2} c^{3} + 7 \, a^{2} c^{4}\right)} x^{2} - 5 \, {\left(2 \, b^{5} c - 14 \, a b^{3} c^{2} + 21 \, a^{2} b c^{3}\right)} x\right)} \sqrt{2 \, c d x + b d}}{35 \, {\left(8 \, c^{7} d^{4} x^{3} + 12 \, b c^{6} d^{4} x^{2} + 6 \, b^{2} c^{5} d^{4} x + b^{3} c^{4} d^{4}\right)}}"," ",0,"1/35*(5*c^6*x^6 + 15*b*c^5*x^5 - 2*b^6 + 14*a*b^4*c - 21*a^2*b^2*c^2 - 7*a^3*c^3 + 5*(2*b^2*c^4 + 7*a*c^5)*x^4 - 5*(b^3*c^3 - 14*a*b*c^4)*x^3 - 15*(b^4*c^2 - 7*a*b^2*c^3 + 7*a^2*c^4)*x^2 - 5*(2*b^5*c - 14*a*b^3*c^2 + 21*a^2*b*c^3)*x)*sqrt(2*c*d*x + b*d)/(8*c^7*d^4*x^3 + 12*b*c^6*d^4*x^2 + 6*b^2*c^5*d^4*x + b^3*c^4*d^4)","A",0
1282,1,210,0,0.408621," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(9/2),x, algorithm=""fricas"")","\frac{{\left(7 \, c^{6} x^{6} + 21 \, b c^{5} x^{5} + 105 \, a c^{5} x^{4} - 2 \, b^{6} + 10 \, a b^{4} c - 5 \, a^{2} b^{2} c^{2} - 5 \, a^{3} c^{3} - 35 \, {\left(b^{3} c^{3} - 6 \, a b c^{4}\right)} x^{3} - 35 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + a^{2} c^{4}\right)} x^{2} - 7 \, {\left(2 \, b^{5} c - 10 \, a b^{3} c^{2} + 5 \, a^{2} b c^{3}\right)} x\right)} \sqrt{2 \, c d x + b d}}{35 \, {\left(16 \, c^{8} d^{5} x^{4} + 32 \, b c^{7} d^{5} x^{3} + 24 \, b^{2} c^{6} d^{5} x^{2} + 8 \, b^{3} c^{5} d^{5} x + b^{4} c^{4} d^{5}\right)}}"," ",0,"1/35*(7*c^6*x^6 + 21*b*c^5*x^5 + 105*a*c^5*x^4 - 2*b^6 + 10*a*b^4*c - 5*a^2*b^2*c^2 - 5*a^3*c^3 - 35*(b^3*c^3 - 6*a*b*c^4)*x^3 - 35*(b^4*c^2 - 5*a*b^2*c^3 + a^2*c^4)*x^2 - 7*(2*b^5*c - 10*a*b^3*c^2 + 5*a^2*b*c^3)*x)*sqrt(2*c*d*x + b*d)/(16*c^8*d^5*x^4 + 32*b*c^7*d^5*x^3 + 24*b^2*c^6*d^5*x^2 + 8*b^3*c^5*d^5*x + b^4*c^4*d^5)","A",0
1283,1,238,0,0.414928," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(11/2),x, algorithm=""fricas"")","\frac{{\left(15 \, c^{6} x^{6} + 45 \, b c^{5} x^{5} + 2 \, b^{6} - 6 \, a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 5 \, a^{3} c^{3} + 45 \, {\left(2 \, b^{2} c^{4} - 3 \, a c^{5}\right)} x^{4} + 15 \, {\left(7 \, b^{3} c^{3} - 18 \, a b c^{4}\right)} x^{3} + 9 \, {\left(7 \, b^{4} c^{2} - 21 \, a b^{2} c^{3} - 3 \, a^{2} c^{4}\right)} x^{2} + 9 \, {\left(2 \, b^{5} c - 6 \, a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} x\right)} \sqrt{2 \, c d x + b d}}{45 \, {\left(32 \, c^{9} d^{6} x^{5} + 80 \, b c^{8} d^{6} x^{4} + 80 \, b^{2} c^{7} d^{6} x^{3} + 40 \, b^{3} c^{6} d^{6} x^{2} + 10 \, b^{4} c^{5} d^{6} x + b^{5} c^{4} d^{6}\right)}}"," ",0,"1/45*(15*c^6*x^6 + 45*b*c^5*x^5 + 2*b^6 - 6*a*b^4*c - 3*a^2*b^2*c^2 - 5*a^3*c^3 + 45*(2*b^2*c^4 - 3*a*c^5)*x^4 + 15*(7*b^3*c^3 - 18*a*b*c^4)*x^3 + 9*(7*b^4*c^2 - 21*a*b^2*c^3 - 3*a^2*c^4)*x^2 + 9*(2*b^5*c - 6*a*b^3*c^2 - 3*a^2*b*c^3)*x)*sqrt(2*c*d*x + b*d)/(32*c^9*d^6*x^5 + 80*b*c^8*d^6*x^4 + 80*b^2*c^7*d^6*x^3 + 40*b^3*c^6*d^6*x^2 + 10*b^4*c^5*d^6*x + b^5*c^4*d^6)","B",0
1284,1,252,0,0.407214," ","integrate((c*x^2+b*x+a)^3/(2*c*d*x+b*d)^(13/2),x, algorithm=""fricas"")","\frac{{\left(77 \, c^{6} x^{6} + 231 \, b c^{5} x^{5} + 2 \, b^{6} - 2 \, a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 7 \, a^{3} c^{3} + 77 \, {\left(4 \, b^{2} c^{4} - a c^{5}\right)} x^{4} + 77 \, {\left(3 \, b^{3} c^{3} - 2 \, a b c^{4}\right)} x^{3} + 33 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{2} c^{3} - a^{2} c^{4}\right)} x^{2} + 11 \, {\left(2 \, b^{5} c - 2 \, a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} x\right)} \sqrt{2 \, c d x + b d}}{77 \, {\left(64 \, c^{10} d^{7} x^{6} + 192 \, b c^{9} d^{7} x^{5} + 240 \, b^{2} c^{8} d^{7} x^{4} + 160 \, b^{3} c^{7} d^{7} x^{3} + 60 \, b^{4} c^{6} d^{7} x^{2} + 12 \, b^{5} c^{5} d^{7} x + b^{6} c^{4} d^{7}\right)}}"," ",0,"1/77*(77*c^6*x^6 + 231*b*c^5*x^5 + 2*b^6 - 2*a*b^4*c - 3*a^2*b^2*c^2 - 7*a^3*c^3 + 77*(4*b^2*c^4 - a*c^5)*x^4 + 77*(3*b^3*c^3 - 2*a*b*c^4)*x^3 + 33*(3*b^4*c^2 - 3*a*b^2*c^3 - a^2*c^4)*x^2 + 11*(2*b^5*c - 2*a*b^3*c^2 - 3*a^2*b*c^3)*x)*sqrt(2*c*d*x + b*d)/(64*c^10*d^7*x^6 + 192*b*c^9*d^7*x^5 + 240*b^2*c^8*d^7*x^4 + 160*b^3*c^7*d^7*x^3 + 60*b^4*c^6*d^7*x^2 + 12*b^5*c^5*d^7*x + b^6*c^4*d^7)","B",0
1285,1,1241,0,0.462804," ","integrate((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{4}{45} \, {\left(80 \, c^{4} d^{5} x^{4} + 160 \, b c^{3} d^{5} x^{3} + 12 \, {\left(13 \, b^{2} c^{2} - 12 \, a c^{3}\right)} d^{5} x^{2} + 4 \, {\left(19 \, b^{3} c - 36 \, a b c^{2}\right)} d^{5} x + {\left(59 \, b^{4} - 396 \, a b^{2} c + 720 \, a^{2} c^{2}\right)} d^{5}\right)} \sqrt{2 \, c d x + b d} - 4 \, \left({\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{22}\right)^{\frac{1}{4}} \arctan\left(\frac{\left({\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{22}\right)^{\frac{3}{4}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{2 \, c d x + b d} d^{5} - \left({\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{22}\right)^{\frac{3}{4}} \sqrt{2 \, {\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)} d^{11} x + {\left(b^{9} - 16 \, a b^{7} c + 96 \, a^{2} b^{5} c^{2} - 256 \, a^{3} b^{3} c^{3} + 256 \, a^{4} b c^{4}\right)} d^{11} + \sqrt{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{22}}}}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{22}}\right) - \left({\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{22}\right)^{\frac{1}{4}} \log\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{2 \, c d x + b d} d^{5} + \left({\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{22}\right)^{\frac{1}{4}}\right) + \left({\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{22}\right)^{\frac{1}{4}} \log\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{2 \, c d x + b d} d^{5} - \left({\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{22}\right)^{\frac{1}{4}}\right)"," ",0,"4/45*(80*c^4*d^5*x^4 + 160*b*c^3*d^5*x^3 + 12*(13*b^2*c^2 - 12*a*c^3)*d^5*x^2 + 4*(19*b^3*c - 36*a*b*c^2)*d^5*x + (59*b^4 - 396*a*b^2*c + 720*a^2*c^2)*d^5)*sqrt(2*c*d*x + b*d) - 4*((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^22)^(1/4)*arctan((((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^22)^(3/4)*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(2*c*d*x + b*d)*d^5 - ((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^22)^(3/4)*sqrt(2*(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)*d^11*x + (b^9 - 16*a*b^7*c + 96*a^2*b^5*c^2 - 256*a^3*b^3*c^3 + 256*a^4*b*c^4)*d^11 + sqrt((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^22)))/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^22)) - ((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^22)^(1/4)*log((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(2*c*d*x + b*d)*d^5 + ((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^22)^(1/4)) + ((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^22)^(1/4)*log((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(2*c*d*x + b*d)*d^5 - ((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^22)^(1/4))","B",0
1286,1,1320,0,0.476437," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{8}{21} \, {\left(12 \, c^{3} d^{4} x^{3} + 18 \, b c^{2} d^{4} x^{2} + 4 \, {\left(4 \, b^{2} c - 7 \, a c^{2}\right)} d^{4} x + {\left(5 \, b^{3} - 14 \, a b c\right)} d^{4}\right)} \sqrt{2 \, c d x + b d} - 4 \, \left({\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{18}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left({\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{18}\right)^{\frac{1}{4}} {\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} \sqrt{2 \, c d x + b d} d^{13} + \sqrt{2 \, {\left(b^{20} c - 40 \, a b^{18} c^{2} + 720 \, a^{2} b^{16} c^{3} - 7680 \, a^{3} b^{14} c^{4} + 53760 \, a^{4} b^{12} c^{5} - 258048 \, a^{5} b^{10} c^{6} + 860160 \, a^{6} b^{8} c^{7} - 1966080 \, a^{7} b^{6} c^{8} + 2949120 \, a^{8} b^{4} c^{9} - 2621440 \, a^{9} b^{2} c^{10} + 1048576 \, a^{10} c^{11}\right)} d^{27} x + {\left(b^{21} - 40 \, a b^{19} c + 720 \, a^{2} b^{17} c^{2} - 7680 \, a^{3} b^{15} c^{3} + 53760 \, a^{4} b^{13} c^{4} - 258048 \, a^{5} b^{11} c^{5} + 860160 \, a^{6} b^{9} c^{6} - 1966080 \, a^{7} b^{7} c^{7} + 2949120 \, a^{8} b^{5} c^{8} - 2621440 \, a^{9} b^{3} c^{9} + 1048576 \, a^{10} b c^{10}\right)} d^{27} + \sqrt{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{18}} {\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{18}} \left({\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{18}\right)^{\frac{1}{4}}}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{18}}\right) + \left({\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{18}\right)^{\frac{1}{4}} \log\left(-{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} \sqrt{2 \, c d x + b d} d^{13} + \left({\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{18}\right)^{\frac{3}{4}}\right) - \left({\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{18}\right)^{\frac{1}{4}} \log\left(-{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} \sqrt{2 \, c d x + b d} d^{13} - \left({\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{18}\right)^{\frac{3}{4}}\right)"," ",0,"8/21*(12*c^3*d^4*x^3 + 18*b*c^2*d^4*x^2 + 4*(4*b^2*c - 7*a*c^2)*d^4*x + (5*b^3 - 14*a*b*c)*d^4)*sqrt(2*c*d*x + b*d) - 4*((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^18)^(1/4)*arctan(-(((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^18)^(1/4)*(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*sqrt(2*c*d*x + b*d)*d^13 + sqrt(2*(b^20*c - 40*a*b^18*c^2 + 720*a^2*b^16*c^3 - 7680*a^3*b^14*c^4 + 53760*a^4*b^12*c^5 - 258048*a^5*b^10*c^6 + 860160*a^6*b^8*c^7 - 1966080*a^7*b^6*c^8 + 2949120*a^8*b^4*c^9 - 2621440*a^9*b^2*c^10 + 1048576*a^10*c^11)*d^27*x + (b^21 - 40*a*b^19*c + 720*a^2*b^17*c^2 - 7680*a^3*b^15*c^3 + 53760*a^4*b^13*c^4 - 258048*a^5*b^11*c^5 + 860160*a^6*b^9*c^6 - 1966080*a^7*b^7*c^7 + 2949120*a^8*b^5*c^8 - 2621440*a^9*b^3*c^9 + 1048576*a^10*b*c^10)*d^27 + sqrt((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^18)*(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^18)*((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^18)^(1/4))/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^18)) + ((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^18)^(1/4)*log(-(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*sqrt(2*c*d*x + b*d)*d^13 + ((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^18)^(3/4)) - ((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^18)^(1/4)*log(-(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*sqrt(2*c*d*x + b*d)*d^13 - ((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^18)^(3/4))","B",0
1287,1,712,0,0.437220," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{8}{5} \, {\left(2 \, c^{2} d^{3} x^{2} + 2 \, b c d^{3} x + {\left(3 \, b^{2} - 10 \, a c\right)} d^{3}\right)} \sqrt{2 \, c d x + b d} + 4 \, \left({\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{14}\right)^{\frac{1}{4}} \arctan\left(-\frac{\left({\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{14}\right)^{\frac{3}{4}} \sqrt{2 \, c d x + b d} {\left(b^{2} - 4 \, a c\right)} d^{3} + \left({\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{14}\right)^{\frac{3}{4}} \sqrt{2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{7} x + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{7} + \sqrt{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{14}}}}{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{14}}\right) + \left({\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{14}\right)^{\frac{1}{4}} \log\left(-\sqrt{2 \, c d x + b d} {\left(b^{2} - 4 \, a c\right)} d^{3} + \left({\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{14}\right)^{\frac{1}{4}}\right) - \left({\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{14}\right)^{\frac{1}{4}} \log\left(-\sqrt{2 \, c d x + b d} {\left(b^{2} - 4 \, a c\right)} d^{3} - \left({\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{14}\right)^{\frac{1}{4}}\right)"," ",0,"8/5*(2*c^2*d^3*x^2 + 2*b*c*d^3*x + (3*b^2 - 10*a*c)*d^3)*sqrt(2*c*d*x + b*d) + 4*((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^14)^(1/4)*arctan(-(((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^14)^(3/4)*sqrt(2*c*d*x + b*d)*(b^2 - 4*a*c)*d^3 + ((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^14)^(3/4)*sqrt(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^7*x + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^7 + sqrt((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^14)))/((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^14)) + ((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^14)^(1/4)*log(-sqrt(2*c*d*x + b*d)*(b^2 - 4*a*c)*d^3 + ((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^14)^(1/4)) - ((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^14)^(1/4)*log(-sqrt(2*c*d*x + b*d)*(b^2 - 4*a*c)*d^3 - ((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^14)^(1/4))","B",0
1288,1,602,0,0.440561," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{4}{3} \, {\left(2 \, c d^{2} x + b d^{2}\right)} \sqrt{2 \, c d x + b d} + 4 \, \left({\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{10}\right)^{\frac{1}{4}} \arctan\left(\frac{\left({\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{10}\right)^{\frac{1}{4}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{2 \, c d x + b d} d^{7} - \sqrt{2 \, {\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)} d^{15} x + {\left(b^{9} - 16 \, a b^{7} c + 96 \, a^{2} b^{5} c^{2} - 256 \, a^{3} b^{3} c^{3} + 256 \, a^{4} b c^{4}\right)} d^{15} + \sqrt{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{10}} {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{10}} \left({\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{10}\right)^{\frac{1}{4}}}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{10}}\right) - \left({\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{10}\right)^{\frac{1}{4}} \log\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{2 \, c d x + b d} d^{7} + \left({\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{10}\right)^{\frac{3}{4}}\right) + \left({\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{10}\right)^{\frac{1}{4}} \log\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{2 \, c d x + b d} d^{7} - \left({\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{10}\right)^{\frac{3}{4}}\right)"," ",0,"4/3*(2*c*d^2*x + b*d^2)*sqrt(2*c*d*x + b*d) + 4*((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^10)^(1/4)*arctan((((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^10)^(1/4)*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(2*c*d*x + b*d)*d^7 - sqrt(2*(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)*d^15*x + (b^9 - 16*a*b^7*c + 96*a^2*b^5*c^2 - 256*a^3*b^3*c^3 + 256*a^4*b*c^4)*d^15 + sqrt((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^10)*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^10)*((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^10)^(1/4))/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^10)) - ((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^10)^(1/4)*log((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(2*c*d*x + b*d)*d^7 + ((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^10)^(3/4)) + ((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^10)^(1/4)*log((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(2*c*d*x + b*d)*d^7 - ((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^10)^(3/4))","B",0
1289,1,210,0,0.425712," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","4 \, \sqrt{2 \, c d x + b d} d - 4 \, \left({\left(b^{2} - 4 \, a c\right)} d^{6}\right)^{\frac{1}{4}} \arctan\left(\frac{\left({\left(b^{2} - 4 \, a c\right)} d^{6}\right)^{\frac{3}{4}} \sqrt{2 \, c d x + b d} d - \left({\left(b^{2} - 4 \, a c\right)} d^{6}\right)^{\frac{3}{4}} \sqrt{2 \, c d^{3} x + b d^{3} + \sqrt{{\left(b^{2} - 4 \, a c\right)} d^{6}}}}{{\left(b^{2} - 4 \, a c\right)} d^{6}}\right) - \left({\left(b^{2} - 4 \, a c\right)} d^{6}\right)^{\frac{1}{4}} \log\left(\sqrt{2 \, c d x + b d} d + \left({\left(b^{2} - 4 \, a c\right)} d^{6}\right)^{\frac{1}{4}}\right) + \left({\left(b^{2} - 4 \, a c\right)} d^{6}\right)^{\frac{1}{4}} \log\left(\sqrt{2 \, c d x + b d} d - \left({\left(b^{2} - 4 \, a c\right)} d^{6}\right)^{\frac{1}{4}}\right)"," ",0,"4*sqrt(2*c*d*x + b*d)*d - 4*((b^2 - 4*a*c)*d^6)^(1/4)*arctan((((b^2 - 4*a*c)*d^6)^(3/4)*sqrt(2*c*d*x + b*d)*d - ((b^2 - 4*a*c)*d^6)^(3/4)*sqrt(2*c*d^3*x + b*d^3 + sqrt((b^2 - 4*a*c)*d^6)))/((b^2 - 4*a*c)*d^6)) - ((b^2 - 4*a*c)*d^6)^(1/4)*log(sqrt(2*c*d*x + b*d)*d + ((b^2 - 4*a*c)*d^6)^(1/4)) + ((b^2 - 4*a*c)*d^6)^(1/4)*log(sqrt(2*c*d*x + b*d)*d - ((b^2 - 4*a*c)*d^6)^(1/4))","B",0
1290,1,232,0,0.424921," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-4 \, \left(\frac{d^{2}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2 \, c d x + b d} d \left(\frac{d^{2}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} - \sqrt{2 \, c d^{3} x + b d^{3} + {\left(b^{2} - 4 \, a c\right)} d^{2} \sqrt{\frac{d^{2}}{b^{2} - 4 \, a c}}} \left(\frac{d^{2}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}}}{d^{2}}\right) - \left(\frac{d^{2}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} \log\left({\left(b^{2} - 4 \, a c\right)} \left(\frac{d^{2}}{b^{2} - 4 \, a c}\right)^{\frac{3}{4}} + \sqrt{2 \, c d x + b d} d\right) + \left(\frac{d^{2}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} \log\left(-{\left(b^{2} - 4 \, a c\right)} \left(\frac{d^{2}}{b^{2} - 4 \, a c}\right)^{\frac{3}{4}} + \sqrt{2 \, c d x + b d} d\right)"," ",0,"-4*(d^2/(b^2 - 4*a*c))^(1/4)*arctan(-(sqrt(2*c*d*x + b*d)*d*(d^2/(b^2 - 4*a*c))^(1/4) - sqrt(2*c*d^3*x + b*d^3 + (b^2 - 4*a*c)*d^2*sqrt(d^2/(b^2 - 4*a*c)))*(d^2/(b^2 - 4*a*c))^(1/4))/d^2) - (d^2/(b^2 - 4*a*c))^(1/4)*log((b^2 - 4*a*c)*(d^2/(b^2 - 4*a*c))^(3/4) + sqrt(2*c*d*x + b*d)*d) + (d^2/(b^2 - 4*a*c))^(1/4)*log(-(b^2 - 4*a*c)*(d^2/(b^2 - 4*a*c))^(3/4) + sqrt(2*c*d*x + b*d)*d)","B",0
1291,1,447,0,0.430736," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","4 \, \left(\frac{1}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{2}}\right)^{\frac{1}{4}} \arctan\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{2}}} + 2 \, c d x + b d} d \left(\frac{1}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{2}}\right)^{\frac{3}{4}} - {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{2 \, c d x + b d} d \left(\frac{1}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{2}}\right)^{\frac{3}{4}}\right) - \left(\frac{1}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{2}}\right)^{\frac{1}{4}} \log\left({\left(b^{2} - 4 \, a c\right)} d \left(\frac{1}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{2}}\right)^{\frac{1}{4}} + \sqrt{2 \, c d x + b d}\right) + \left(\frac{1}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{2}}\right)^{\frac{1}{4}} \log\left(-{\left(b^{2} - 4 \, a c\right)} d \left(\frac{1}{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{2}}\right)^{\frac{1}{4}} + \sqrt{2 \, c d x + b d}\right)"," ",0,"4*(1/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^2))^(1/4)*arctan((b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt((b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^2*sqrt(1/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^2)) + 2*c*d*x + b*d)*d*(1/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^2))^(3/4) - (b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(2*c*d*x + b*d)*d*(1/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^2))^(3/4)) - (1/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^2))^(1/4)*log((b^2 - 4*a*c)*d*(1/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^2))^(1/4) + sqrt(2*c*d*x + b*d)) + (1/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^2))^(1/4)*log(-(b^2 - 4*a*c)*d*(1/((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^2))^(1/4) + sqrt(2*c*d*x + b*d))","B",0
1292,1,826,0,0.448345," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{4 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \left(\frac{1}{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{{\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{4} \sqrt{\frac{1}{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{6}}} + 2 \, c d x + b d} {\left(b^{2} - 4 \, a c\right)} d \left(\frac{1}{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{6}}\right)^{\frac{1}{4}} + \sqrt{2 \, c d x + b d} {\left(b^{2} - 4 \, a c\right)} d \left(\frac{1}{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{6}}\right)^{\frac{1}{4}}\right) - {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \left(\frac{1}{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{6}}\right)^{\frac{1}{4}} \log\left({\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)} d^{5} \left(\frac{1}{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{6}}\right)^{\frac{3}{4}} + \sqrt{2 \, c d x + b d}\right) + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} x + {\left(b^{3} - 4 \, a b c\right)} d^{2}\right)} \left(\frac{1}{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{6}}\right)^{\frac{1}{4}} \log\left(-{\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)} d^{5} \left(\frac{1}{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{6}}\right)^{\frac{3}{4}} + \sqrt{2 \, c d x + b d}\right) + 4 \, \sqrt{2 \, c d x + b d}}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} x + {\left(b^{3} - 4 \, a b c\right)} d^{2}}"," ",0,"(4*(2*(b^2*c - 4*a*c^2)*d^2*x + (b^3 - 4*a*b*c)*d^2)*(1/((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^6))^(1/4)*arctan(-sqrt((b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^4*sqrt(1/((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^6)) + 2*c*d*x + b*d)*(b^2 - 4*a*c)*d*(1/((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^6))^(1/4) + sqrt(2*c*d*x + b*d)*(b^2 - 4*a*c)*d*(1/((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^6))^(1/4)) - (2*(b^2*c - 4*a*c^2)*d^2*x + (b^3 - 4*a*b*c)*d^2)*(1/((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^6))^(1/4)*log((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)*d^5*(1/((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^6))^(3/4) + sqrt(2*c*d*x + b*d)) + (2*(b^2*c - 4*a*c^2)*d^2*x + (b^3 - 4*a*b*c)*d^2)*(1/((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^6))^(1/4)*log(-(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)*d^5*(1/((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^6))^(3/4) + sqrt(2*c*d*x + b*d)) + 4*sqrt(2*c*d*x + b*d))/(2*(b^2*c - 4*a*c^2)*d^2*x + (b^3 - 4*a*b*c)*d^2)","B",0
1293,1,1163,0,0.446312," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{12 \, {\left(4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} x^{2} + 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} x + {\left(b^{4} - 4 \, a b^{2} c\right)} d^{3}\right)} \left(\frac{1}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} \sqrt{{\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)} d^{6} \sqrt{\frac{1}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{10}}} + 2 \, c d x + b d} d^{7} \left(\frac{1}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{10}}\right)^{\frac{3}{4}} + {\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} \sqrt{2 \, c d x + b d} d^{7} \left(\frac{1}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{10}}\right)^{\frac{3}{4}}\right) + 3 \, {\left(4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} x^{2} + 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} x + {\left(b^{4} - 4 \, a b^{2} c\right)} d^{3}\right)} \left(\frac{1}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{10}}\right)^{\frac{1}{4}} \log\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} \left(\frac{1}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{10}}\right)^{\frac{1}{4}} + \sqrt{2 \, c d x + b d}\right) - 3 \, {\left(4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} x^{2} + 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} x + {\left(b^{4} - 4 \, a b^{2} c\right)} d^{3}\right)} \left(\frac{1}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{10}}\right)^{\frac{1}{4}} \log\left(-{\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} \left(\frac{1}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{10}}\right)^{\frac{1}{4}} + \sqrt{2 \, c d x + b d}\right) - 4 \, \sqrt{2 \, c d x + b d}}{3 \, {\left(4 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} x^{2} + 4 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} x + {\left(b^{4} - 4 \, a b^{2} c\right)} d^{3}\right)}}"," ",0,"-1/3*(12*(4*(b^2*c^2 - 4*a*c^3)*d^3*x^2 + 4*(b^3*c - 4*a*b*c^2)*d^3*x + (b^4 - 4*a*b^2*c)*d^3)*(1/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^10))^(1/4)*arctan(-(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*sqrt((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)*d^6*sqrt(1/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^10)) + 2*c*d*x + b*d)*d^7*(1/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^10))^(3/4) + (b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*sqrt(2*c*d*x + b*d)*d^7*(1/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^10))^(3/4)) + 3*(4*(b^2*c^2 - 4*a*c^3)*d^3*x^2 + 4*(b^3*c - 4*a*b*c^2)*d^3*x + (b^4 - 4*a*b^2*c)*d^3)*(1/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^10))^(1/4)*log((b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^3*(1/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^10))^(1/4) + sqrt(2*c*d*x + b*d)) - 3*(4*(b^2*c^2 - 4*a*c^3)*d^3*x^2 + 4*(b^3*c - 4*a*b*c^2)*d^3*x + (b^4 - 4*a*b^2*c)*d^3)*(1/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^10))^(1/4)*log(-(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^3*(1/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^10))^(1/4) + sqrt(2*c*d*x + b*d)) - 4*sqrt(2*c*d*x + b*d))/(4*(b^2*c^2 - 4*a*c^3)*d^3*x^2 + 4*(b^3*c - 4*a*b*c^2)*d^3*x + (b^4 - 4*a*b^2*c)*d^3)","B",0
1294,1,1693,0,0.474595," ","integrate(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{20 \, {\left(8 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} x^{3} + 12 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{4} x^{2} + 6 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d^{4} x + {\left(b^{7} - 8 \, a b^{5} c + 16 \, a^{2} b^{3} c^{2}\right)} d^{4}\right)} \left(\frac{1}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{14}}\right)^{\frac{1}{4}} \arctan\left(\sqrt{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{8} \sqrt{\frac{1}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{14}}} + 2 \, c d x + b d} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} \left(\frac{1}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{14}}\right)^{\frac{1}{4}} - {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{2 \, c d x + b d} d^{3} \left(\frac{1}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{14}}\right)^{\frac{1}{4}}\right) + 5 \, {\left(8 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} x^{3} + 12 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{4} x^{2} + 6 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d^{4} x + {\left(b^{7} - 8 \, a b^{5} c + 16 \, a^{2} b^{3} c^{2}\right)} d^{4}\right)} \left(\frac{1}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{14}}\right)^{\frac{1}{4}} \log\left({\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{11} \left(\frac{1}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{14}}\right)^{\frac{3}{4}} + \sqrt{2 \, c d x + b d}\right) - 5 \, {\left(8 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} x^{3} + 12 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{4} x^{2} + 6 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d^{4} x + {\left(b^{7} - 8 \, a b^{5} c + 16 \, a^{2} b^{3} c^{2}\right)} d^{4}\right)} \left(\frac{1}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{14}}\right)^{\frac{1}{4}} \log\left(-{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{11} \left(\frac{1}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{14}}\right)^{\frac{3}{4}} + \sqrt{2 \, c d x + b d}\right) - 8 \, {\left(10 \, c^{2} x^{2} + 10 \, b c x + 3 \, b^{2} - 2 \, a c\right)} \sqrt{2 \, c d x + b d}}{5 \, {\left(8 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} x^{3} + 12 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{4} x^{2} + 6 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d^{4} x + {\left(b^{7} - 8 \, a b^{5} c + 16 \, a^{2} b^{3} c^{2}\right)} d^{4}\right)}}"," ",0,"-1/5*(20*(8*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^4*x^3 + 12*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^4*x^2 + 6*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d^4*x + (b^7 - 8*a*b^5*c + 16*a^2*b^3*c^2)*d^4)*(1/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^14))^(1/4)*arctan(sqrt((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*d^8*sqrt(1/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^14)) + 2*c*d*x + b*d)*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^3*(1/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^14))^(1/4) - (b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(2*c*d*x + b*d)*d^3*(1/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^14))^(1/4)) + 5*(8*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^4*x^3 + 12*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^4*x^2 + 6*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d^4*x + (b^7 - 8*a*b^5*c + 16*a^2*b^3*c^2)*d^4)*(1/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^14))^(1/4)*log((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^11*(1/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^14))^(3/4) + sqrt(2*c*d*x + b*d)) - 5*(8*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^4*x^3 + 12*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^4*x^2 + 6*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d^4*x + (b^7 - 8*a*b^5*c + 16*a^2*b^3*c^2)*d^4)*(1/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^14))^(1/4)*log(-(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^11*(1/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^14))^(3/4) + sqrt(2*c*d*x + b*d)) - 8*(10*c^2*x^2 + 10*b*c*x + 3*b^2 - 2*a*c)*sqrt(2*c*d*x + b*d))/(8*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^4*x^3 + 12*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^4*x^2 + 6*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d^4*x + (b^7 - 8*a*b^5*c + 16*a^2*b^3*c^2)*d^4)","B",0
1295,1,1445,0,0.466741," ","integrate((2*c*d*x+b*d)^(15/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{2340 \, \left({\left(b^{18} c^{4} - 36 \, a b^{16} c^{5} + 576 \, a^{2} b^{14} c^{6} - 5376 \, a^{3} b^{12} c^{7} + 32256 \, a^{4} b^{10} c^{8} - 129024 \, a^{5} b^{8} c^{9} + 344064 \, a^{6} b^{6} c^{10} - 589824 \, a^{7} b^{4} c^{11} + 589824 \, a^{8} b^{2} c^{12} - 262144 \, a^{9} c^{13}\right)} d^{30}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \arctan\left(\frac{\left({\left(b^{18} c^{4} - 36 \, a b^{16} c^{5} + 576 \, a^{2} b^{14} c^{6} - 5376 \, a^{3} b^{12} c^{7} + 32256 \, a^{4} b^{10} c^{8} - 129024 \, a^{5} b^{8} c^{9} + 344064 \, a^{6} b^{6} c^{10} - 589824 \, a^{7} b^{4} c^{11} + 589824 \, a^{8} b^{2} c^{12} - 262144 \, a^{9} c^{13}\right)} d^{30}\right)^{\frac{3}{4}} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{2 \, c d x + b d} d^{7} - \left({\left(b^{18} c^{4} - 36 \, a b^{16} c^{5} + 576 \, a^{2} b^{14} c^{6} - 5376 \, a^{3} b^{12} c^{7} + 32256 \, a^{4} b^{10} c^{8} - 129024 \, a^{5} b^{8} c^{9} + 344064 \, a^{6} b^{6} c^{10} - 589824 \, a^{7} b^{4} c^{11} + 589824 \, a^{8} b^{2} c^{12} - 262144 \, a^{9} c^{13}\right)} d^{30}\right)^{\frac{3}{4}} \sqrt{2 \, {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} d^{15} x + {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} d^{15} + \sqrt{{\left(b^{18} c^{4} - 36 \, a b^{16} c^{5} + 576 \, a^{2} b^{14} c^{6} - 5376 \, a^{3} b^{12} c^{7} + 32256 \, a^{4} b^{10} c^{8} - 129024 \, a^{5} b^{8} c^{9} + 344064 \, a^{6} b^{6} c^{10} - 589824 \, a^{7} b^{4} c^{11} + 589824 \, a^{8} b^{2} c^{12} - 262144 \, a^{9} c^{13}\right)} d^{30}}}}{{\left(b^{18} c^{4} - 36 \, a b^{16} c^{5} + 576 \, a^{2} b^{14} c^{6} - 5376 \, a^{3} b^{12} c^{7} + 32256 \, a^{4} b^{10} c^{8} - 129024 \, a^{5} b^{8} c^{9} + 344064 \, a^{6} b^{6} c^{10} - 589824 \, a^{7} b^{4} c^{11} + 589824 \, a^{8} b^{2} c^{12} - 262144 \, a^{9} c^{13}\right)} d^{30}}\right) + 585 \, \left({\left(b^{18} c^{4} - 36 \, a b^{16} c^{5} + 576 \, a^{2} b^{14} c^{6} - 5376 \, a^{3} b^{12} c^{7} + 32256 \, a^{4} b^{10} c^{8} - 129024 \, a^{5} b^{8} c^{9} + 344064 \, a^{6} b^{6} c^{10} - 589824 \, a^{7} b^{4} c^{11} + 589824 \, a^{8} b^{2} c^{12} - 262144 \, a^{9} c^{13}\right)} d^{30}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(13 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{2 \, c d x + b d} d^{7} + 13 \, \left({\left(b^{18} c^{4} - 36 \, a b^{16} c^{5} + 576 \, a^{2} b^{14} c^{6} - 5376 \, a^{3} b^{12} c^{7} + 32256 \, a^{4} b^{10} c^{8} - 129024 \, a^{5} b^{8} c^{9} + 344064 \, a^{6} b^{6} c^{10} - 589824 \, a^{7} b^{4} c^{11} + 589824 \, a^{8} b^{2} c^{12} - 262144 \, a^{9} c^{13}\right)} d^{30}\right)^{\frac{1}{4}}\right) - 585 \, \left({\left(b^{18} c^{4} - 36 \, a b^{16} c^{5} + 576 \, a^{2} b^{14} c^{6} - 5376 \, a^{3} b^{12} c^{7} + 32256 \, a^{4} b^{10} c^{8} - 129024 \, a^{5} b^{8} c^{9} + 344064 \, a^{6} b^{6} c^{10} - 589824 \, a^{7} b^{4} c^{11} + 589824 \, a^{8} b^{2} c^{12} - 262144 \, a^{9} c^{13}\right)} d^{30}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(13 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{2 \, c d x + b d} d^{7} - 13 \, \left({\left(b^{18} c^{4} - 36 \, a b^{16} c^{5} + 576 \, a^{2} b^{14} c^{6} - 5376 \, a^{3} b^{12} c^{7} + 32256 \, a^{4} b^{10} c^{8} - 129024 \, a^{5} b^{8} c^{9} + 344064 \, a^{6} b^{6} c^{10} - 589824 \, a^{7} b^{4} c^{11} + 589824 \, a^{8} b^{2} c^{12} - 262144 \, a^{9} c^{13}\right)} d^{30}\right)^{\frac{1}{4}}\right) - {\left(1280 \, c^{6} d^{7} x^{6} + 3840 \, b c^{5} d^{7} x^{5} + 256 \, {\left(22 \, b^{2} c^{4} - 13 \, a c^{5}\right)} d^{7} x^{4} + 256 \, {\left(19 \, b^{3} c^{3} - 26 \, a b c^{4}\right)} d^{7} x^{3} + 96 \, {\left(45 \, b^{4} c^{2} - 208 \, a b^{2} c^{3} + 312 \, a^{2} c^{4}\right)} d^{7} x^{2} + 32 \, {\left(79 \, b^{5} c - 520 \, a b^{3} c^{2} + 936 \, a^{2} b c^{3}\right)} d^{7} x - {\left(45 \, b^{6} - 3068 \, a b^{4} c + 20592 \, a^{2} b^{2} c^{2} - 37440 \, a^{3} c^{3}\right)} d^{7}\right)} \sqrt{2 \, c d x + b d}}{45 \, {\left(c x^{2} + b x + a\right)}}"," ",0,"-1/45*(2340*((b^18*c^4 - 36*a*b^16*c^5 + 576*a^2*b^14*c^6 - 5376*a^3*b^12*c^7 + 32256*a^4*b^10*c^8 - 129024*a^5*b^8*c^9 + 344064*a^6*b^6*c^10 - 589824*a^7*b^4*c^11 + 589824*a^8*b^2*c^12 - 262144*a^9*c^13)*d^30)^(1/4)*(c*x^2 + b*x + a)*arctan((((b^18*c^4 - 36*a*b^16*c^5 + 576*a^2*b^14*c^6 - 5376*a^3*b^12*c^7 + 32256*a^4*b^10*c^8 - 129024*a^5*b^8*c^9 + 344064*a^6*b^6*c^10 - 589824*a^7*b^4*c^11 + 589824*a^8*b^2*c^12 - 262144*a^9*c^13)*d^30)^(3/4)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(2*c*d*x + b*d)*d^7 - ((b^18*c^4 - 36*a*b^16*c^5 + 576*a^2*b^14*c^6 - 5376*a^3*b^12*c^7 + 32256*a^4*b^10*c^8 - 129024*a^5*b^8*c^9 + 344064*a^6*b^6*c^10 - 589824*a^7*b^4*c^11 + 589824*a^8*b^2*c^12 - 262144*a^9*c^13)*d^30)^(3/4)*sqrt(2*(b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*d^15*x + (b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*d^15 + sqrt((b^18*c^4 - 36*a*b^16*c^5 + 576*a^2*b^14*c^6 - 5376*a^3*b^12*c^7 + 32256*a^4*b^10*c^8 - 129024*a^5*b^8*c^9 + 344064*a^6*b^6*c^10 - 589824*a^7*b^4*c^11 + 589824*a^8*b^2*c^12 - 262144*a^9*c^13)*d^30)))/((b^18*c^4 - 36*a*b^16*c^5 + 576*a^2*b^14*c^6 - 5376*a^3*b^12*c^7 + 32256*a^4*b^10*c^8 - 129024*a^5*b^8*c^9 + 344064*a^6*b^6*c^10 - 589824*a^7*b^4*c^11 + 589824*a^8*b^2*c^12 - 262144*a^9*c^13)*d^30)) + 585*((b^18*c^4 - 36*a*b^16*c^5 + 576*a^2*b^14*c^6 - 5376*a^3*b^12*c^7 + 32256*a^4*b^10*c^8 - 129024*a^5*b^8*c^9 + 344064*a^6*b^6*c^10 - 589824*a^7*b^4*c^11 + 589824*a^8*b^2*c^12 - 262144*a^9*c^13)*d^30)^(1/4)*(c*x^2 + b*x + a)*log(13*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(2*c*d*x + b*d)*d^7 + 13*((b^18*c^4 - 36*a*b^16*c^5 + 576*a^2*b^14*c^6 - 5376*a^3*b^12*c^7 + 32256*a^4*b^10*c^8 - 129024*a^5*b^8*c^9 + 344064*a^6*b^6*c^10 - 589824*a^7*b^4*c^11 + 589824*a^8*b^2*c^12 - 262144*a^9*c^13)*d^30)^(1/4)) - 585*((b^18*c^4 - 36*a*b^16*c^5 + 576*a^2*b^14*c^6 - 5376*a^3*b^12*c^7 + 32256*a^4*b^10*c^8 - 129024*a^5*b^8*c^9 + 344064*a^6*b^6*c^10 - 589824*a^7*b^4*c^11 + 589824*a^8*b^2*c^12 - 262144*a^9*c^13)*d^30)^(1/4)*(c*x^2 + b*x + a)*log(13*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(2*c*d*x + b*d)*d^7 - 13*((b^18*c^4 - 36*a*b^16*c^5 + 576*a^2*b^14*c^6 - 5376*a^3*b^12*c^7 + 32256*a^4*b^10*c^8 - 129024*a^5*b^8*c^9 + 344064*a^6*b^6*c^10 - 589824*a^7*b^4*c^11 + 589824*a^8*b^2*c^12 - 262144*a^9*c^13)*d^30)^(1/4)) - (1280*c^6*d^7*x^6 + 3840*b*c^5*d^7*x^5 + 256*(22*b^2*c^4 - 13*a*c^5)*d^7*x^4 + 256*(19*b^3*c^3 - 26*a*b*c^4)*d^7*x^3 + 96*(45*b^4*c^2 - 208*a*b^2*c^3 + 312*a^2*c^4)*d^7*x^2 + 32*(79*b^5*c - 520*a*b^3*c^2 + 936*a^2*b*c^3)*d^7*x - (45*b^6 - 3068*a*b^4*c + 20592*a^2*b^2*c^2 - 37440*a^3*c^3)*d^7)*sqrt(2*c*d*x + b*d))/(c*x^2 + b*x + a)","B",0
1296,1,1523,0,0.486567," ","integrate((2*c*d*x+b*d)^(13/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{924 \, \left({\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{26}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \arctan\left(-\frac{\left({\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{26}\right)^{\frac{1}{4}} {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{2 \, c d x + b d} d^{19} + \sqrt{2 \, {\left(b^{20} c^{7} - 40 \, a b^{18} c^{8} + 720 \, a^{2} b^{16} c^{9} - 7680 \, a^{3} b^{14} c^{10} + 53760 \, a^{4} b^{12} c^{11} - 258048 \, a^{5} b^{10} c^{12} + 860160 \, a^{6} b^{8} c^{13} - 1966080 \, a^{7} b^{6} c^{14} + 2949120 \, a^{8} b^{4} c^{15} - 2621440 \, a^{9} b^{2} c^{16} + 1048576 \, a^{10} c^{17}\right)} d^{39} x + {\left(b^{21} c^{6} - 40 \, a b^{19} c^{7} + 720 \, a^{2} b^{17} c^{8} - 7680 \, a^{3} b^{15} c^{9} + 53760 \, a^{4} b^{13} c^{10} - 258048 \, a^{5} b^{11} c^{11} + 860160 \, a^{6} b^{9} c^{12} - 1966080 \, a^{7} b^{7} c^{13} + 2949120 \, a^{8} b^{5} c^{14} - 2621440 \, a^{9} b^{3} c^{15} + 1048576 \, a^{10} b c^{16}\right)} d^{39} + \sqrt{{\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{26}} {\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{26}} \left({\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{26}\right)^{\frac{1}{4}}}{{\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{26}}\right) - 231 \, \left({\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{26}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(-1331 \, {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{2 \, c d x + b d} d^{19} + 1331 \, \left({\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{26}\right)^{\frac{3}{4}}\right) + 231 \, \left({\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{26}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(-1331 \, {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{2 \, c d x + b d} d^{19} - 1331 \, \left({\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{26}\right)^{\frac{3}{4}}\right) - {\left(384 \, c^{5} d^{6} x^{5} + 960 \, b c^{4} d^{6} x^{4} + 32 \, {\left(41 \, b^{2} c^{3} - 44 \, a c^{4}\right)} d^{6} x^{3} + 48 \, {\left(21 \, b^{3} c^{2} - 44 \, a b c^{3}\right)} d^{6} x^{2} + 2 \, {\left(115 \, b^{4} c + 88 \, a b^{2} c^{2} - 1232 \, a^{2} c^{3}\right)} d^{6} x - {\left(21 \, b^{5} - 440 \, a b^{3} c + 1232 \, a^{2} b c^{2}\right)} d^{6}\right)} \sqrt{2 \, c d x + b d}}{21 \, {\left(c x^{2} + b x + a\right)}}"," ",0,"-1/21*(924*((b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^26)^(1/4)*(c*x^2 + b*x + a)*arctan(-(((b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^26)^(1/4)*(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt(2*c*d*x + b*d)*d^19 + sqrt(2*(b^20*c^7 - 40*a*b^18*c^8 + 720*a^2*b^16*c^9 - 7680*a^3*b^14*c^10 + 53760*a^4*b^12*c^11 - 258048*a^5*b^10*c^12 + 860160*a^6*b^8*c^13 - 1966080*a^7*b^6*c^14 + 2949120*a^8*b^4*c^15 - 2621440*a^9*b^2*c^16 + 1048576*a^10*c^17)*d^39*x + (b^21*c^6 - 40*a*b^19*c^7 + 720*a^2*b^17*c^8 - 7680*a^3*b^15*c^9 + 53760*a^4*b^13*c^10 - 258048*a^5*b^11*c^11 + 860160*a^6*b^9*c^12 - 1966080*a^7*b^7*c^13 + 2949120*a^8*b^5*c^14 - 2621440*a^9*b^3*c^15 + 1048576*a^10*b*c^16)*d^39 + sqrt((b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^26)*(b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^26)*((b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^26)^(1/4))/((b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^26)) - 231*((b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^26)^(1/4)*(c*x^2 + b*x + a)*log(-1331*(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt(2*c*d*x + b*d)*d^19 + 1331*((b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^26)^(3/4)) + 231*((b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^26)^(1/4)*(c*x^2 + b*x + a)*log(-1331*(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt(2*c*d*x + b*d)*d^19 - 1331*((b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^26)^(3/4)) - (384*c^5*d^6*x^5 + 960*b*c^4*d^6*x^4 + 32*(41*b^2*c^3 - 44*a*c^4)*d^6*x^3 + 48*(21*b^3*c^2 - 44*a*b*c^3)*d^6*x^2 + 2*(115*b^4*c + 88*a*b^2*c^2 - 1232*a^2*c^3)*d^6*x - (21*b^5 - 440*a*b^3*c + 1232*a^2*b*c^2)*d^6)*sqrt(2*c*d*x + b*d))/(c*x^2 + b*x + a)","B",0
1297,1,891,0,0.454182," ","integrate((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{180 \, \left({\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{22}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \arctan\left(-\frac{\left({\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{22}\right)^{\frac{3}{4}} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{2 \, c d x + b d} d^{5} + \left({\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{22}\right)^{\frac{3}{4}} \sqrt{2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{11} x + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{11} + \sqrt{{\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{22}}}}{{\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{22}}\right) + 45 \, \left({\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{22}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(-9 \, {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{2 \, c d x + b d} d^{5} + 9 \, \left({\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{22}\right)^{\frac{1}{4}}\right) - 45 \, \left({\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{22}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(-9 \, {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{2 \, c d x + b d} d^{5} - 9 \, \left({\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{22}\right)^{\frac{1}{4}}\right) + {\left(64 \, c^{4} d^{5} x^{4} + 128 \, b c^{3} d^{5} x^{3} + 48 \, {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} d^{5} x^{2} + 16 \, {\left(11 \, b^{3} c - 36 \, a b c^{2}\right)} d^{5} x - {\left(5 \, b^{4} - 216 \, a b^{2} c + 720 \, a^{2} c^{2}\right)} d^{5}\right)} \sqrt{2 \, c d x + b d}}{5 \, {\left(c x^{2} + b x + a\right)}}"," ",0,"1/5*(180*((b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^22)^(1/4)*(c*x^2 + b*x + a)*arctan(-(((b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^22)^(3/4)*(b^2*c - 4*a*c^2)*sqrt(2*c*d*x + b*d)*d^5 + ((b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^22)^(3/4)*sqrt(2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^11*x + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^11 + sqrt((b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^22)))/((b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^22)) + 45*((b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^22)^(1/4)*(c*x^2 + b*x + a)*log(-9*(b^2*c - 4*a*c^2)*sqrt(2*c*d*x + b*d)*d^5 + 9*((b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^22)^(1/4)) - 45*((b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^22)^(1/4)*(c*x^2 + b*x + a)*log(-9*(b^2*c - 4*a*c^2)*sqrt(2*c*d*x + b*d)*d^5 - 9*((b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^22)^(1/4)) + (64*c^4*d^5*x^4 + 128*b*c^3*d^5*x^3 + 48*(5*b^2*c^2 - 12*a*c^3)*d^5*x^2 + 16*(11*b^3*c - 36*a*b*c^2)*d^5*x - (5*b^4 - 216*a*b^2*c + 720*a^2*c^2)*d^5)*sqrt(2*c*d*x + b*d))/(c*x^2 + b*x + a)","B",0
1298,1,782,0,0.451183," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{84 \, \left({\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{18}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \arctan\left(\frac{\left({\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{18}\right)^{\frac{1}{4}} {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{2 \, c d x + b d} d^{13} - \sqrt{2 \, {\left(b^{8} c^{7} - 16 \, a b^{6} c^{8} + 96 \, a^{2} b^{4} c^{9} - 256 \, a^{3} b^{2} c^{10} + 256 \, a^{4} c^{11}\right)} d^{27} x + {\left(b^{9} c^{6} - 16 \, a b^{7} c^{7} + 96 \, a^{2} b^{5} c^{8} - 256 \, a^{3} b^{3} c^{9} + 256 \, a^{4} b c^{10}\right)} d^{27} + \sqrt{{\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{18}} {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{18}} \left({\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{18}\right)^{\frac{1}{4}}}{{\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{18}}\right) - 21 \, \left({\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{18}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(343 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{2 \, c d x + b d} d^{13} + 343 \, \left({\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{18}\right)^{\frac{3}{4}}\right) + 21 \, \left({\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{18}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(343 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{2 \, c d x + b d} d^{13} - 343 \, \left({\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{18}\right)^{\frac{3}{4}}\right) + {\left(32 \, c^{3} d^{4} x^{3} + 48 \, b c^{2} d^{4} x^{2} + 2 \, {\left(5 \, b^{2} c + 28 \, a c^{2}\right)} d^{4} x - {\left(3 \, b^{3} - 28 \, a b c\right)} d^{4}\right)} \sqrt{2 \, c d x + b d}}{3 \, {\left(c x^{2} + b x + a\right)}}"," ",0,"1/3*(84*((b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^18)^(1/4)*(c*x^2 + b*x + a)*arctan((((b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^18)^(1/4)*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(2*c*d*x + b*d)*d^13 - sqrt(2*(b^8*c^7 - 16*a*b^6*c^8 + 96*a^2*b^4*c^9 - 256*a^3*b^2*c^10 + 256*a^4*c^11)*d^27*x + (b^9*c^6 - 16*a*b^7*c^7 + 96*a^2*b^5*c^8 - 256*a^3*b^3*c^9 + 256*a^4*b*c^10)*d^27 + sqrt((b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^18)*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^18)*((b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^18)^(1/4))/((b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^18)) - 21*((b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^18)^(1/4)*(c*x^2 + b*x + a)*log(343*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(2*c*d*x + b*d)*d^13 + 343*((b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^18)^(3/4)) + 21*((b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^18)^(1/4)*(c*x^2 + b*x + a)*log(343*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(2*c*d*x + b*d)*d^13 - 343*((b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^18)^(3/4)) + (32*c^3*d^4*x^3 + 48*b*c^2*d^4*x^2 + 2*(5*b^2*c + 28*a*c^2)*d^4*x - (3*b^3 - 28*a*b*c)*d^4)*sqrt(2*c*d*x + b*d))/(c*x^2 + b*x + a)","B",0
1299,1,359,0,0.441667," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{20 \, \left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{14}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \arctan\left(\frac{\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{14}\right)^{\frac{3}{4}} \sqrt{2 \, c d x + b d} c d^{3} - \left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{14}\right)^{\frac{3}{4}} \sqrt{2 \, c^{3} d^{7} x + b c^{2} d^{7} + \sqrt{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{14}}}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{14}}\right) + 5 \, \left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{14}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(5 \, \sqrt{2 \, c d x + b d} c d^{3} + 5 \, \left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{14}\right)^{\frac{1}{4}}\right) - 5 \, \left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{14}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(5 \, \sqrt{2 \, c d x + b d} c d^{3} - 5 \, \left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{14}\right)^{\frac{1}{4}}\right) - {\left(16 \, c^{2} d^{3} x^{2} + 16 \, b c d^{3} x - {\left(b^{2} - 20 \, a c\right)} d^{3}\right)} \sqrt{2 \, c d x + b d}}{c x^{2} + b x + a}"," ",0,"-(20*((b^2*c^4 - 4*a*c^5)*d^14)^(1/4)*(c*x^2 + b*x + a)*arctan((((b^2*c^4 - 4*a*c^5)*d^14)^(3/4)*sqrt(2*c*d*x + b*d)*c*d^3 - ((b^2*c^4 - 4*a*c^5)*d^14)^(3/4)*sqrt(2*c^3*d^7*x + b*c^2*d^7 + sqrt((b^2*c^4 - 4*a*c^5)*d^14)))/((b^2*c^4 - 4*a*c^5)*d^14)) + 5*((b^2*c^4 - 4*a*c^5)*d^14)^(1/4)*(c*x^2 + b*x + a)*log(5*sqrt(2*c*d*x + b*d)*c*d^3 + 5*((b^2*c^4 - 4*a*c^5)*d^14)^(1/4)) - 5*((b^2*c^4 - 4*a*c^5)*d^14)^(1/4)*(c*x^2 + b*x + a)*log(5*sqrt(2*c*d*x + b*d)*c*d^3 - 5*((b^2*c^4 - 4*a*c^5)*d^14)^(1/4)) - (16*c^2*d^3*x^2 + 16*b*c*d^3*x - (b^2 - 20*a*c)*d^3)*sqrt(2*c*d*x + b*d))/(c*x^2 + b*x + a)","B",0
1300,1,358,0,0.445564," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{12 \, \left(\frac{c^{4} d^{10}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \arctan\left(-\frac{\left(\frac{c^{4} d^{10}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} \sqrt{2 \, c d x + b d} c^{3} d^{7} - \sqrt{2 \, c^{7} d^{15} x + b c^{6} d^{15} + \sqrt{\frac{c^{4} d^{10}}{b^{2} - 4 \, a c}} {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{10}} \left(\frac{c^{4} d^{10}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}}}{c^{4} d^{10}}\right) + 3 \, \left(\frac{c^{4} d^{10}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(27 \, \sqrt{2 \, c d x + b d} c^{3} d^{7} + 27 \, \left(\frac{c^{4} d^{10}}{b^{2} - 4 \, a c}\right)^{\frac{3}{4}} {\left(b^{2} - 4 \, a c\right)}\right) - 3 \, \left(\frac{c^{4} d^{10}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(27 \, \sqrt{2 \, c d x + b d} c^{3} d^{7} - 27 \, \left(\frac{c^{4} d^{10}}{b^{2} - 4 \, a c}\right)^{\frac{3}{4}} {\left(b^{2} - 4 \, a c\right)}\right) + {\left(2 \, c d^{2} x + b d^{2}\right)} \sqrt{2 \, c d x + b d}}{c x^{2} + b x + a}"," ",0,"-(12*(c^4*d^10/(b^2 - 4*a*c))^(1/4)*(c*x^2 + b*x + a)*arctan(-((c^4*d^10/(b^2 - 4*a*c))^(1/4)*sqrt(2*c*d*x + b*d)*c^3*d^7 - sqrt(2*c^7*d^15*x + b*c^6*d^15 + sqrt(c^4*d^10/(b^2 - 4*a*c))*(b^2*c^4 - 4*a*c^5)*d^10)*(c^4*d^10/(b^2 - 4*a*c))^(1/4))/(c^4*d^10)) + 3*(c^4*d^10/(b^2 - 4*a*c))^(1/4)*(c*x^2 + b*x + a)*log(27*sqrt(2*c*d*x + b*d)*c^3*d^7 + 27*(c^4*d^10/(b^2 - 4*a*c))^(3/4)*(b^2 - 4*a*c)) - 3*(c^4*d^10/(b^2 - 4*a*c))^(1/4)*(c*x^2 + b*x + a)*log(27*sqrt(2*c*d*x + b*d)*c^3*d^7 - 27*(c^4*d^10/(b^2 - 4*a*c))^(3/4)*(b^2 - 4*a*c)) + (2*c*d^2*x + b*d^2)*sqrt(2*c*d*x + b*d))/(c*x^2 + b*x + a)","B",0
1301,1,549,0,0.444614," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, \left(\frac{c^{4} d^{6}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \arctan\left(-\frac{\left(\frac{c^{4} d^{6}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{3}{4}} {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} \sqrt{2 \, c d x + b d} d - \left(\frac{c^{4} d^{6}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{3}{4}} \sqrt{2 \, c^{3} d^{3} x + b c^{2} d^{3} + \sqrt{\frac{c^{4} d^{6}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}{c^{4} d^{6}}\right) - \left(\frac{c^{4} d^{6}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(\sqrt{2 \, c d x + b d} c d + \left(\frac{c^{4} d^{6}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{1}{4}} {\left(b^{2} - 4 \, a c\right)}\right) + \left(\frac{c^{4} d^{6}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{1}{4}} {\left(c x^{2} + b x + a\right)} \log\left(\sqrt{2 \, c d x + b d} c d - \left(\frac{c^{4} d^{6}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{1}{4}} {\left(b^{2} - 4 \, a c\right)}\right) - \sqrt{2 \, c d x + b d} d}{c x^{2} + b x + a}"," ",0,"(4*(c^4*d^6/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(1/4)*(c*x^2 + b*x + a)*arctan(-((c^4*d^6/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(3/4)*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*sqrt(2*c*d*x + b*d)*d - (c^4*d^6/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(3/4)*sqrt(2*c^3*d^3*x + b*c^2*d^3 + sqrt(c^4*d^6/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*(b^4 - 8*a*b^2*c + 16*a^2*c^2))*(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c^4*d^6)) - (c^4*d^6/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(1/4)*(c*x^2 + b*x + a)*log(sqrt(2*c*d*x + b*d)*c*d + (c^4*d^6/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(1/4)*(b^2 - 4*a*c)) + (c^4*d^6/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(1/4)*(c*x^2 + b*x + a)*log(sqrt(2*c*d*x + b*d)*c*d - (c^4*d^6/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(1/4)*(b^2 - 4*a*c)) - sqrt(2*c*d*x + b*d)*d)/(c*x^2 + b*x + a)","B",0
1302,1,915,0,0.454326," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, \left(\frac{c^{4} d^{2}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{1}{4}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \arctan\left(\frac{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \left(\frac{c^{4} d^{2}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{1}{4}} \sqrt{2 \, c d x + b d} d - \sqrt{2 \, c^{7} d^{3} x + b c^{6} d^{3} + {\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{\frac{c^{4} d^{2}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}} d^{2}} \left(\frac{c^{4} d^{2}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{1}{4}} {\left(b^{2} - 4 \, a c\right)}}{c^{4} d^{2}}\right) - \left(\frac{c^{4} d^{2}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{1}{4}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \log\left(\sqrt{2 \, c d x + b d} c^{3} d + {\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(\frac{c^{4} d^{2}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{3}{4}}\right) + \left(\frac{c^{4} d^{2}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{1}{4}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \log\left(\sqrt{2 \, c d x + b d} c^{3} d - {\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(\frac{c^{4} d^{2}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{3}{4}}\right) + \sqrt{2 \, c d x + b d} {\left(2 \, c x + b\right)}}{a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x}"," ",0,"-(4*(c^4*d^2/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(1/4)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*arctan(((b^2*c^3 - 4*a*c^4)*(c^4*d^2/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(1/4)*sqrt(2*c*d*x + b*d)*d - sqrt(2*c^7*d^3*x + b*c^6*d^3 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*sqrt(c^4*d^2/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))*d^2)*(c^4*d^2/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(1/4)*(b^2 - 4*a*c))/(c^4*d^2)) - (c^4*d^2/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(1/4)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*log(sqrt(2*c*d*x + b*d)*c^3*d + (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^4*d^2/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(3/4)) + (c^4*d^2/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(1/4)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*log(sqrt(2*c*d*x + b*d)*c^3*d - (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^4*d^2/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(3/4)) + sqrt(2*c*d*x + b*d)*(2*c*x + b))/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)","B",0
1303,1,1147,0,0.461853," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{12 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d x^{2} + {\left(b^{3} - 4 \, a b c\right)} d x + {\left(a b^{2} - 4 \, a^{2} c\right)} d\right)} \left(\frac{c^{4}}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{2}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} \sqrt{2 \, c^{3} d x + b c^{2} d + {\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{\frac{c^{4}}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{2}}} d^{2}} \left(\frac{c^{4}}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{2}}\right)^{\frac{3}{4}} d - {\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} \sqrt{2 \, c d x + b d} \left(\frac{c^{4}}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{2}}\right)^{\frac{3}{4}} d}{c^{4}}\right) + 3 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d x^{2} + {\left(b^{3} - 4 \, a b c\right)} d x + {\left(a b^{2} - 4 \, a^{2} c\right)} d\right)} \left(\frac{c^{4}}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{2}}\right)^{\frac{1}{4}} \log\left(3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \left(\frac{c^{4}}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{2}}\right)^{\frac{1}{4}} d + 3 \, \sqrt{2 \, c d x + b d} c\right) - 3 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d x^{2} + {\left(b^{3} - 4 \, a b c\right)} d x + {\left(a b^{2} - 4 \, a^{2} c\right)} d\right)} \left(\frac{c^{4}}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{2}}\right)^{\frac{1}{4}} \log\left(-3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \left(\frac{c^{4}}{{\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{2}}\right)^{\frac{1}{4}} d + 3 \, \sqrt{2 \, c d x + b d} c\right) - \sqrt{2 \, c d x + b d}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d x^{2} + {\left(b^{3} - 4 \, a b c\right)} d x + {\left(a b^{2} - 4 \, a^{2} c\right)} d}"," ",0,"(12*((b^2*c - 4*a*c^2)*d*x^2 + (b^3 - 4*a*b*c)*d*x + (a*b^2 - 4*a^2*c)*d)*(c^4/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^2))^(1/4)*arctan(-((b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*sqrt(2*c^3*d*x + b*c^2*d + (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(c^4/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^2))*d^2)*(c^4/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^2))^(3/4)*d - (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*sqrt(2*c*d*x + b*d)*(c^4/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^2))^(3/4)*d)/c^4) + 3*((b^2*c - 4*a*c^2)*d*x^2 + (b^3 - 4*a*b*c)*d*x + (a*b^2 - 4*a^2*c)*d)*(c^4/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^2))^(1/4)*log(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c^4/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^2))^(1/4)*d + 3*sqrt(2*c*d*x + b*d)*c) - 3*((b^2*c - 4*a*c^2)*d*x^2 + (b^3 - 4*a*b*c)*d*x + (a*b^2 - 4*a^2*c)*d)*(c^4/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^2))^(1/4)*log(-3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*(c^4/((b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^2))^(1/4)*d + 3*sqrt(2*c*d*x + b*d)*c) - sqrt(2*c*d*x + b*d))/((b^2*c - 4*a*c^2)*d*x^2 + (b^3 - 4*a*b*c)*d*x + (a*b^2 - 4*a^2*c)*d)","B",0
1304,1,1710,0,0.480843," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{20 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} x^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} x^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2} x + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} \left(\frac{c^{4}}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{6}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2 \, c^{7} d x + b c^{6} d + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{4} \sqrt{\frac{c^{4}}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{6}}}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d \left(\frac{c^{4}}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{6}}\right)^{\frac{1}{4}} - {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} \sqrt{2 \, c d x + b d} d \left(\frac{c^{4}}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{6}}\right)^{\frac{1}{4}}}{c^{4}}\right) + 5 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} x^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} x^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2} x + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} \left(\frac{c^{4}}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{6}}\right)^{\frac{1}{4}} \log\left(125 \, {\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{5} \left(\frac{c^{4}}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{6}}\right)^{\frac{3}{4}} + 125 \, \sqrt{2 \, c d x + b d} c^{3}\right) - 5 \, {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} x^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} x^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2} x + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}\right)} \left(\frac{c^{4}}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{6}}\right)^{\frac{1}{4}} \log\left(-125 \, {\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} d^{5} \left(\frac{c^{4}}{{\left(b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}\right)} d^{6}}\right)^{\frac{3}{4}} + 125 \, \sqrt{2 \, c d x + b d} c^{3}\right) - {\left(20 \, c^{2} x^{2} + 20 \, b c x + b^{2} + 16 \, a c\right)} \sqrt{2 \, c d x + b d}}{2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} x^{3} + 3 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} x^{2} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d^{2} x + {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{2}}"," ",0,"(20*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*x^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*x^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2*x + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*(c^4/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^6))^(1/4)*arctan((sqrt(2*c^7*d*x + b*c^6*d + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^4*sqrt(c^4/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^6)))*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d*(c^4/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^6))^(1/4) - (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*sqrt(2*c*d*x + b*d)*d*(c^4/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^6))^(1/4))/c^4) + 5*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*x^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*x^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2*x + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*(c^4/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^6))^(1/4)*log(125*(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^5*(c^4/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^6))^(3/4) + 125*sqrt(2*c*d*x + b*d)*c^3) - 5*(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*x^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*x^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2*x + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)*(c^4/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^6))^(1/4)*log(-125*(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*d^5*(c^4/((b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9)*d^6))^(3/4) + 125*sqrt(2*c*d*x + b*d)*c^3) - (20*c^2*x^2 + 20*b*c*x + b^2 + 16*a*c)*sqrt(2*c*d*x + b*d))/(2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*x^3 + 3*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*x^2 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d^2*x + (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d^2)","B",0
1305,1,2167,0,0.500298," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{84 \, {\left(4 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} x^{4} + 8 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{3} x^{3} + {\left(5 \, b^{6} c - 36 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d^{3} x^{2} + {\left(b^{7} - 4 \, a b^{5} c - 16 \, a^{2} b^{3} c^{2} + 64 \, a^{3} b c^{3}\right)} d^{3} x + {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} d^{3}\right)} \left(\frac{c^{4}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{10}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{16} - 32 \, a b^{14} c + 448 \, a^{2} b^{12} c^{2} - 3584 \, a^{3} b^{10} c^{3} + 17920 \, a^{4} b^{8} c^{4} - 57344 \, a^{5} b^{6} c^{5} + 114688 \, a^{6} b^{4} c^{6} - 131072 \, a^{7} b^{2} c^{7} + 65536 \, a^{8} c^{8}\right)} \sqrt{{\left(b^{12} - 24 \, a b^{10} c + 240 \, a^{2} b^{8} c^{2} - 1280 \, a^{3} b^{6} c^{3} + 3840 \, a^{4} b^{4} c^{4} - 6144 \, a^{5} b^{2} c^{5} + 4096 \, a^{6} c^{6}\right)} d^{6} \sqrt{\frac{c^{4}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{10}}} + 2 \, c^{3} d x + b c^{2} d} d^{7} \left(\frac{c^{4}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{10}}\right)^{\frac{3}{4}} - {\left(b^{16} c - 32 \, a b^{14} c^{2} + 448 \, a^{2} b^{12} c^{3} - 3584 \, a^{3} b^{10} c^{4} + 17920 \, a^{4} b^{8} c^{5} - 57344 \, a^{5} b^{6} c^{6} + 114688 \, a^{6} b^{4} c^{7} - 131072 \, a^{7} b^{2} c^{8} + 65536 \, a^{8} c^{9}\right)} \sqrt{2 \, c d x + b d} d^{7} \left(\frac{c^{4}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{10}}\right)^{\frac{3}{4}}}{c^{4}}\right) - 21 \, {\left(4 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} x^{4} + 8 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{3} x^{3} + {\left(5 \, b^{6} c - 36 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d^{3} x^{2} + {\left(b^{7} - 4 \, a b^{5} c - 16 \, a^{2} b^{3} c^{2} + 64 \, a^{3} b c^{3}\right)} d^{3} x + {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} d^{3}\right)} \left(\frac{c^{4}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{10}}\right)^{\frac{1}{4}} \log\left(7 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{3} \left(\frac{c^{4}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{10}}\right)^{\frac{1}{4}} + 7 \, \sqrt{2 \, c d x + b d} c\right) + 21 \, {\left(4 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} x^{4} + 8 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{3} x^{3} + {\left(5 \, b^{6} c - 36 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d^{3} x^{2} + {\left(b^{7} - 4 \, a b^{5} c - 16 \, a^{2} b^{3} c^{2} + 64 \, a^{3} b c^{3}\right)} d^{3} x + {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} d^{3}\right)} \left(\frac{c^{4}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{10}}\right)^{\frac{1}{4}} \log\left(-7 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{3} \left(\frac{c^{4}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{10}}\right)^{\frac{1}{4}} + 7 \, \sqrt{2 \, c d x + b d} c\right) + {\left(28 \, c^{2} x^{2} + 28 \, b c x + 3 \, b^{2} + 16 \, a c\right)} \sqrt{2 \, c d x + b d}}{3 \, {\left(4 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} x^{4} + 8 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{3} x^{3} + {\left(5 \, b^{6} c - 36 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d^{3} x^{2} + {\left(b^{7} - 4 \, a b^{5} c - 16 \, a^{2} b^{3} c^{2} + 64 \, a^{3} b c^{3}\right)} d^{3} x + {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} d^{3}\right)}}"," ",0,"-1/3*(84*(4*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*x^4 + 8*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^3*x^3 + (5*b^6*c - 36*a*b^4*c^2 + 48*a^2*b^2*c^3 + 64*a^3*c^4)*d^3*x^2 + (b^7 - 4*a*b^5*c - 16*a^2*b^3*c^2 + 64*a^3*b*c^3)*d^3*x + (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*d^3)*(c^4/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^10))^(1/4)*arctan(((b^16 - 32*a*b^14*c + 448*a^2*b^12*c^2 - 3584*a^3*b^10*c^3 + 17920*a^4*b^8*c^4 - 57344*a^5*b^6*c^5 + 114688*a^6*b^4*c^6 - 131072*a^7*b^2*c^7 + 65536*a^8*c^8)*sqrt((b^12 - 24*a*b^10*c + 240*a^2*b^8*c^2 - 1280*a^3*b^6*c^3 + 3840*a^4*b^4*c^4 - 6144*a^5*b^2*c^5 + 4096*a^6*c^6)*d^6*sqrt(c^4/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^10)) + 2*c^3*d*x + b*c^2*d)*d^7*(c^4/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^10))^(3/4) - (b^16*c - 32*a*b^14*c^2 + 448*a^2*b^12*c^3 - 3584*a^3*b^10*c^4 + 17920*a^4*b^8*c^5 - 57344*a^5*b^6*c^6 + 114688*a^6*b^4*c^7 - 131072*a^7*b^2*c^8 + 65536*a^8*c^9)*sqrt(2*c*d*x + b*d)*d^7*(c^4/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^10))^(3/4))/c^4) - 21*(4*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*x^4 + 8*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^3*x^3 + (5*b^6*c - 36*a*b^4*c^2 + 48*a^2*b^2*c^3 + 64*a^3*c^4)*d^3*x^2 + (b^7 - 4*a*b^5*c - 16*a^2*b^3*c^2 + 64*a^3*b*c^3)*d^3*x + (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*d^3)*(c^4/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^10))^(1/4)*log(7*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^3*(c^4/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^10))^(1/4) + 7*sqrt(2*c*d*x + b*d)*c) + 21*(4*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*x^4 + 8*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^3*x^3 + (5*b^6*c - 36*a*b^4*c^2 + 48*a^2*b^2*c^3 + 64*a^3*c^4)*d^3*x^2 + (b^7 - 4*a*b^5*c - 16*a^2*b^3*c^2 + 64*a^3*b*c^3)*d^3*x + (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*d^3)*(c^4/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^10))^(1/4)*log(-7*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^3*(c^4/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^10))^(1/4) + 7*sqrt(2*c*d*x + b*d)*c) + (28*c^2*x^2 + 28*b*c*x + 3*b^2 + 16*a*c)*sqrt(2*c*d*x + b*d))/(4*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*x^4 + 8*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^3*x^3 + (5*b^6*c - 36*a*b^4*c^2 + 48*a^2*b^2*c^3 + 64*a^3*c^4)*d^3*x^2 + (b^7 - 4*a*b^5*c - 16*a^2*b^3*c^2 + 64*a^3*b*c^3)*d^3*x + (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*d^3)","B",0
1306,1,2919,0,0.530881," ","integrate(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{180 \, {\left(8 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{4} x^{5} + 20 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{4} x^{4} + 2 \, {\left(9 \, b^{8} c^{2} - 104 \, a b^{6} c^{3} + 384 \, a^{2} b^{4} c^{4} - 384 \, a^{3} b^{2} c^{5} - 256 \, a^{4} c^{6}\right)} d^{4} x^{3} + {\left(7 \, b^{9} c - 72 \, a b^{7} c^{2} + 192 \, a^{2} b^{5} c^{3} + 128 \, a^{3} b^{3} c^{4} - 768 \, a^{4} b c^{5}\right)} d^{4} x^{2} + {\left(b^{10} - 6 \, a b^{8} c - 24 \, a^{2} b^{6} c^{2} + 224 \, a^{3} b^{4} c^{3} - 384 \, a^{4} b^{2} c^{4}\right)} d^{4} x + {\left(a b^{9} - 12 \, a^{2} b^{7} c + 48 \, a^{3} b^{5} c^{2} - 64 \, a^{4} b^{3} c^{3}\right)} d^{4}\right)} \left(\frac{c^{4}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{14}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{{\left(b^{14} c^{4} - 28 \, a b^{12} c^{5} + 336 \, a^{2} b^{10} c^{6} - 2240 \, a^{3} b^{8} c^{7} + 8960 \, a^{4} b^{6} c^{8} - 21504 \, a^{5} b^{4} c^{9} + 28672 \, a^{6} b^{2} c^{10} - 16384 \, a^{7} c^{11}\right)} d^{8} \sqrt{\frac{c^{4}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{14}}} + 2 \, c^{7} d x + b c^{6} d} {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} d^{3} \left(\frac{c^{4}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{14}}\right)^{\frac{1}{4}} - {\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{2 \, c d x + b d} d^{3} \left(\frac{c^{4}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{14}}\right)^{\frac{1}{4}}}{c^{4}}\right) - 45 \, {\left(8 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{4} x^{5} + 20 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{4} x^{4} + 2 \, {\left(9 \, b^{8} c^{2} - 104 \, a b^{6} c^{3} + 384 \, a^{2} b^{4} c^{4} - 384 \, a^{3} b^{2} c^{5} - 256 \, a^{4} c^{6}\right)} d^{4} x^{3} + {\left(7 \, b^{9} c - 72 \, a b^{7} c^{2} + 192 \, a^{2} b^{5} c^{3} + 128 \, a^{3} b^{3} c^{4} - 768 \, a^{4} b c^{5}\right)} d^{4} x^{2} + {\left(b^{10} - 6 \, a b^{8} c - 24 \, a^{2} b^{6} c^{2} + 224 \, a^{3} b^{4} c^{3} - 384 \, a^{4} b^{2} c^{4}\right)} d^{4} x + {\left(a b^{9} - 12 \, a^{2} b^{7} c + 48 \, a^{3} b^{5} c^{2} - 64 \, a^{4} b^{3} c^{3}\right)} d^{4}\right)} \left(\frac{c^{4}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{14}}\right)^{\frac{1}{4}} \log\left(729 \, {\left(b^{20} - 40 \, a b^{18} c + 720 \, a^{2} b^{16} c^{2} - 7680 \, a^{3} b^{14} c^{3} + 53760 \, a^{4} b^{12} c^{4} - 258048 \, a^{5} b^{10} c^{5} + 860160 \, a^{6} b^{8} c^{6} - 1966080 \, a^{7} b^{6} c^{7} + 2949120 \, a^{8} b^{4} c^{8} - 2621440 \, a^{9} b^{2} c^{9} + 1048576 \, a^{10} c^{10}\right)} d^{11} \left(\frac{c^{4}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{14}}\right)^{\frac{3}{4}} + 729 \, \sqrt{2 \, c d x + b d} c^{3}\right) + 45 \, {\left(8 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{4} x^{5} + 20 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{4} x^{4} + 2 \, {\left(9 \, b^{8} c^{2} - 104 \, a b^{6} c^{3} + 384 \, a^{2} b^{4} c^{4} - 384 \, a^{3} b^{2} c^{5} - 256 \, a^{4} c^{6}\right)} d^{4} x^{3} + {\left(7 \, b^{9} c - 72 \, a b^{7} c^{2} + 192 \, a^{2} b^{5} c^{3} + 128 \, a^{3} b^{3} c^{4} - 768 \, a^{4} b c^{5}\right)} d^{4} x^{2} + {\left(b^{10} - 6 \, a b^{8} c - 24 \, a^{2} b^{6} c^{2} + 224 \, a^{3} b^{4} c^{3} - 384 \, a^{4} b^{2} c^{4}\right)} d^{4} x + {\left(a b^{9} - 12 \, a^{2} b^{7} c + 48 \, a^{3} b^{5} c^{2} - 64 \, a^{4} b^{3} c^{3}\right)} d^{4}\right)} \left(\frac{c^{4}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{14}}\right)^{\frac{1}{4}} \log\left(-729 \, {\left(b^{20} - 40 \, a b^{18} c + 720 \, a^{2} b^{16} c^{2} - 7680 \, a^{3} b^{14} c^{3} + 53760 \, a^{4} b^{12} c^{4} - 258048 \, a^{5} b^{10} c^{5} + 860160 \, a^{6} b^{8} c^{6} - 1966080 \, a^{7} b^{6} c^{7} + 2949120 \, a^{8} b^{4} c^{8} - 2621440 \, a^{9} b^{2} c^{9} + 1048576 \, a^{10} c^{10}\right)} d^{11} \left(\frac{c^{4}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{14}}\right)^{\frac{3}{4}} + 729 \, \sqrt{2 \, c d x + b d} c^{3}\right) + {\left(720 \, c^{4} x^{4} + 1440 \, b c^{3} x^{3} + 5 \, b^{4} + 176 \, a b^{2} c - 64 \, a^{2} c^{2} + 72 \, {\left(13 \, b^{2} c^{2} + 8 \, a c^{3}\right)} x^{2} + 72 \, {\left(3 \, b^{3} c + 8 \, a b c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{5 \, {\left(8 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{4} x^{5} + 20 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{4} x^{4} + 2 \, {\left(9 \, b^{8} c^{2} - 104 \, a b^{6} c^{3} + 384 \, a^{2} b^{4} c^{4} - 384 \, a^{3} b^{2} c^{5} - 256 \, a^{4} c^{6}\right)} d^{4} x^{3} + {\left(7 \, b^{9} c - 72 \, a b^{7} c^{2} + 192 \, a^{2} b^{5} c^{3} + 128 \, a^{3} b^{3} c^{4} - 768 \, a^{4} b c^{5}\right)} d^{4} x^{2} + {\left(b^{10} - 6 \, a b^{8} c - 24 \, a^{2} b^{6} c^{2} + 224 \, a^{3} b^{4} c^{3} - 384 \, a^{4} b^{2} c^{4}\right)} d^{4} x + {\left(a b^{9} - 12 \, a^{2} b^{7} c + 48 \, a^{3} b^{5} c^{2} - 64 \, a^{4} b^{3} c^{3}\right)} d^{4}\right)}}"," ",0,"-1/5*(180*(8*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^4*x^5 + 20*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^4*x^4 + 2*(9*b^8*c^2 - 104*a*b^6*c^3 + 384*a^2*b^4*c^4 - 384*a^3*b^2*c^5 - 256*a^4*c^6)*d^4*x^3 + (7*b^9*c - 72*a*b^7*c^2 + 192*a^2*b^5*c^3 + 128*a^3*b^3*c^4 - 768*a^4*b*c^5)*d^4*x^2 + (b^10 - 6*a*b^8*c - 24*a^2*b^6*c^2 + 224*a^3*b^4*c^3 - 384*a^4*b^2*c^4)*d^4*x + (a*b^9 - 12*a^2*b^7*c + 48*a^3*b^5*c^2 - 64*a^4*b^3*c^3)*d^4)*(c^4/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^14))^(1/4)*arctan(-(sqrt((b^14*c^4 - 28*a*b^12*c^5 + 336*a^2*b^10*c^6 - 2240*a^3*b^8*c^7 + 8960*a^4*b^6*c^8 - 21504*a^5*b^4*c^9 + 28672*a^6*b^2*c^10 - 16384*a^7*c^11)*d^8*sqrt(c^4/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^14)) + 2*c^7*d*x + b*c^6*d)*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*d^3*(c^4/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^14))^(1/4) - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt(2*c*d*x + b*d)*d^3*(c^4/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^14))^(1/4))/c^4) - 45*(8*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^4*x^5 + 20*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^4*x^4 + 2*(9*b^8*c^2 - 104*a*b^6*c^3 + 384*a^2*b^4*c^4 - 384*a^3*b^2*c^5 - 256*a^4*c^6)*d^4*x^3 + (7*b^9*c - 72*a*b^7*c^2 + 192*a^2*b^5*c^3 + 128*a^3*b^3*c^4 - 768*a^4*b*c^5)*d^4*x^2 + (b^10 - 6*a*b^8*c - 24*a^2*b^6*c^2 + 224*a^3*b^4*c^3 - 384*a^4*b^2*c^4)*d^4*x + (a*b^9 - 12*a^2*b^7*c + 48*a^3*b^5*c^2 - 64*a^4*b^3*c^3)*d^4)*(c^4/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^14))^(1/4)*log(729*(b^20 - 40*a*b^18*c + 720*a^2*b^16*c^2 - 7680*a^3*b^14*c^3 + 53760*a^4*b^12*c^4 - 258048*a^5*b^10*c^5 + 860160*a^6*b^8*c^6 - 1966080*a^7*b^6*c^7 + 2949120*a^8*b^4*c^8 - 2621440*a^9*b^2*c^9 + 1048576*a^10*c^10)*d^11*(c^4/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^14))^(3/4) + 729*sqrt(2*c*d*x + b*d)*c^3) + 45*(8*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^4*x^5 + 20*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^4*x^4 + 2*(9*b^8*c^2 - 104*a*b^6*c^3 + 384*a^2*b^4*c^4 - 384*a^3*b^2*c^5 - 256*a^4*c^6)*d^4*x^3 + (7*b^9*c - 72*a*b^7*c^2 + 192*a^2*b^5*c^3 + 128*a^3*b^3*c^4 - 768*a^4*b*c^5)*d^4*x^2 + (b^10 - 6*a*b^8*c - 24*a^2*b^6*c^2 + 224*a^3*b^4*c^3 - 384*a^4*b^2*c^4)*d^4*x + (a*b^9 - 12*a^2*b^7*c + 48*a^3*b^5*c^2 - 64*a^4*b^3*c^3)*d^4)*(c^4/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^14))^(1/4)*log(-729*(b^20 - 40*a*b^18*c + 720*a^2*b^16*c^2 - 7680*a^3*b^14*c^3 + 53760*a^4*b^12*c^4 - 258048*a^5*b^10*c^5 + 860160*a^6*b^8*c^6 - 1966080*a^7*b^6*c^7 + 2949120*a^8*b^4*c^8 - 2621440*a^9*b^2*c^9 + 1048576*a^10*c^10)*d^11*(c^4/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^14))^(3/4) + 729*sqrt(2*c*d*x + b*d)*c^3) + (720*c^4*x^4 + 1440*b*c^3*x^3 + 5*b^4 + 176*a*b^2*c - 64*a^2*c^2 + 72*(13*b^2*c^2 + 8*a*c^3)*x^2 + 72*(3*b^3*c + 8*a*b*c^2)*x)*sqrt(2*c*d*x + b*d))/(8*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^4*x^5 + 20*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^4*x^4 + 2*(9*b^8*c^2 - 104*a*b^6*c^3 + 384*a^2*b^4*c^4 - 384*a^3*b^2*c^5 - 256*a^4*c^6)*d^4*x^3 + (7*b^9*c - 72*a*b^7*c^2 + 192*a^2*b^5*c^3 + 128*a^3*b^3*c^4 - 768*a^4*b*c^5)*d^4*x^2 + (b^10 - 6*a*b^8*c - 24*a^2*b^6*c^2 + 224*a^3*b^4*c^3 - 384*a^4*b^2*c^4)*d^4*x + (a*b^9 - 12*a^2*b^7*c + 48*a^3*b^5*c^2 - 64*a^4*b^3*c^3)*d^4)","B",0
1307,1,1713,0,0.488481," ","integrate((2*c*d*x+b*d)^(17/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{4620 \, \left({\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} d^{34}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \arctan\left(-\frac{\left({\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} d^{34}\right)^{\frac{1}{4}} {\left(b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}\right)} \sqrt{2 \, c d x + b d} d^{25} + \sqrt{2 \, {\left(b^{20} c^{13} - 40 \, a b^{18} c^{14} + 720 \, a^{2} b^{16} c^{15} - 7680 \, a^{3} b^{14} c^{16} + 53760 \, a^{4} b^{12} c^{17} - 258048 \, a^{5} b^{10} c^{18} + 860160 \, a^{6} b^{8} c^{19} - 1966080 \, a^{7} b^{6} c^{20} + 2949120 \, a^{8} b^{4} c^{21} - 2621440 \, a^{9} b^{2} c^{22} + 1048576 \, a^{10} c^{23}\right)} d^{51} x + {\left(b^{21} c^{12} - 40 \, a b^{19} c^{13} + 720 \, a^{2} b^{17} c^{14} - 7680 \, a^{3} b^{15} c^{15} + 53760 \, a^{4} b^{13} c^{16} - 258048 \, a^{5} b^{11} c^{17} + 860160 \, a^{6} b^{9} c^{18} - 1966080 \, a^{7} b^{7} c^{19} + 2949120 \, a^{8} b^{5} c^{20} - 2621440 \, a^{9} b^{3} c^{21} + 1048576 \, a^{10} b c^{22}\right)} d^{51} + \sqrt{{\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} d^{34}} {\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} d^{34}} \left({\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} d^{34}\right)^{\frac{1}{4}}}{{\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} d^{34}}\right) - 1155 \, \left({\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} d^{34}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(-4492125 \, {\left(b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}\right)} \sqrt{2 \, c d x + b d} d^{25} + 4492125 \, \left({\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} d^{34}\right)^{\frac{3}{4}}\right) + 1155 \, \left({\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} d^{34}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(-4492125 \, {\left(b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}\right)} \sqrt{2 \, c d x + b d} d^{25} - 4492125 \, \left({\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} d^{34}\right)^{\frac{3}{4}}\right) - {\left(1024 \, c^{7} d^{8} x^{7} + 3584 \, b c^{6} d^{8} x^{6} + 512 \, {\left(13 \, b^{2} c^{5} - 10 \, a c^{6}\right)} d^{8} x^{5} + 2560 \, {\left(3 \, b^{3} c^{4} - 5 \, a b c^{5}\right)} d^{8} x^{4} + 10 \, {\left(423 \, b^{4} c^{3} - 312 \, a b^{2} c^{4} - 1936 \, a^{2} c^{5}\right)} d^{8} x^{3} + {\left(457 \, b^{5} c^{2} + 8120 \, a b^{3} c^{3} - 29040 \, a^{2} b c^{4}\right)} d^{8} x^{2} - {\left(203 \, b^{6} c - 3350 \, a b^{4} c^{2} + 5280 \, a^{2} b^{2} c^{3} + 12320 \, a^{3} c^{4}\right)} d^{8} x - {\left(7 \, b^{7} + 105 \, a b^{5} c - 2200 \, a^{2} b^{3} c^{2} + 6160 \, a^{3} b c^{3}\right)} d^{8}\right)} \sqrt{2 \, c d x + b d}}{14 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"-1/14*(4620*((b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*d^34)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*arctan(-(((b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*d^34)^(1/4)*(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)*sqrt(2*c*d*x + b*d)*d^25 + sqrt(2*(b^20*c^13 - 40*a*b^18*c^14 + 720*a^2*b^16*c^15 - 7680*a^3*b^14*c^16 + 53760*a^4*b^12*c^17 - 258048*a^5*b^10*c^18 + 860160*a^6*b^8*c^19 - 1966080*a^7*b^6*c^20 + 2949120*a^8*b^4*c^21 - 2621440*a^9*b^2*c^22 + 1048576*a^10*c^23)*d^51*x + (b^21*c^12 - 40*a*b^19*c^13 + 720*a^2*b^17*c^14 - 7680*a^3*b^15*c^15 + 53760*a^4*b^13*c^16 - 258048*a^5*b^11*c^17 + 860160*a^6*b^9*c^18 - 1966080*a^7*b^7*c^19 + 2949120*a^8*b^5*c^20 - 2621440*a^9*b^3*c^21 + 1048576*a^10*b*c^22)*d^51 + sqrt((b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*d^34)*(b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*d^34)*((b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*d^34)^(1/4))/((b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*d^34)) - 1155*((b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*d^34)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(-4492125*(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)*sqrt(2*c*d*x + b*d)*d^25 + 4492125*((b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*d^34)^(3/4)) + 1155*((b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*d^34)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(-4492125*(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)*sqrt(2*c*d*x + b*d)*d^25 - 4492125*((b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*d^34)^(3/4)) - (1024*c^7*d^8*x^7 + 3584*b*c^6*d^8*x^6 + 512*(13*b^2*c^5 - 10*a*c^6)*d^8*x^5 + 2560*(3*b^3*c^4 - 5*a*b*c^5)*d^8*x^4 + 10*(423*b^4*c^3 - 312*a*b^2*c^4 - 1936*a^2*c^5)*d^8*x^3 + (457*b^5*c^2 + 8120*a*b^3*c^3 - 29040*a^2*b*c^4)*d^8*x^2 - (203*b^6*c - 3350*a*b^4*c^2 + 5280*a^2*b^2*c^3 + 12320*a^3*c^4)*d^8*x - (7*b^7 + 105*a*b^5*c - 2200*a^2*b^3*c^2 + 6160*a^3*b*c^3)*d^8)*sqrt(2*c*d*x + b*d))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1308,1,1077,0,0.459933," ","integrate((2*c*d*x+b*d)^(15/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{2340 \, \left({\left(b^{10} c^{8} - 20 \, a b^{8} c^{9} + 160 \, a^{2} b^{6} c^{10} - 640 \, a^{3} b^{4} c^{11} + 1280 \, a^{4} b^{2} c^{12} - 1024 \, a^{5} c^{13}\right)} d^{30}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \arctan\left(-\frac{\left({\left(b^{10} c^{8} - 20 \, a b^{8} c^{9} + 160 \, a^{2} b^{6} c^{10} - 640 \, a^{3} b^{4} c^{11} + 1280 \, a^{4} b^{2} c^{12} - 1024 \, a^{5} c^{13}\right)} d^{30}\right)^{\frac{3}{4}} {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{2 \, c d x + b d} d^{7} + \left({\left(b^{10} c^{8} - 20 \, a b^{8} c^{9} + 160 \, a^{2} b^{6} c^{10} - 640 \, a^{3} b^{4} c^{11} + 1280 \, a^{4} b^{2} c^{12} - 1024 \, a^{5} c^{13}\right)} d^{30}\right)^{\frac{3}{4}} \sqrt{2 \, {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{15} x + {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{15} + \sqrt{{\left(b^{10} c^{8} - 20 \, a b^{8} c^{9} + 160 \, a^{2} b^{6} c^{10} - 640 \, a^{3} b^{4} c^{11} + 1280 \, a^{4} b^{2} c^{12} - 1024 \, a^{5} c^{13}\right)} d^{30}}}}{{\left(b^{10} c^{8} - 20 \, a b^{8} c^{9} + 160 \, a^{2} b^{6} c^{10} - 640 \, a^{3} b^{4} c^{11} + 1280 \, a^{4} b^{2} c^{12} - 1024 \, a^{5} c^{13}\right)} d^{30}}\right) + 585 \, \left({\left(b^{10} c^{8} - 20 \, a b^{8} c^{9} + 160 \, a^{2} b^{6} c^{10} - 640 \, a^{3} b^{4} c^{11} + 1280 \, a^{4} b^{2} c^{12} - 1024 \, a^{5} c^{13}\right)} d^{30}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(-117 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{2 \, c d x + b d} d^{7} + 117 \, \left({\left(b^{10} c^{8} - 20 \, a b^{8} c^{9} + 160 \, a^{2} b^{6} c^{10} - 640 \, a^{3} b^{4} c^{11} + 1280 \, a^{4} b^{2} c^{12} - 1024 \, a^{5} c^{13}\right)} d^{30}\right)^{\frac{1}{4}}\right) - 585 \, \left({\left(b^{10} c^{8} - 20 \, a b^{8} c^{9} + 160 \, a^{2} b^{6} c^{10} - 640 \, a^{3} b^{4} c^{11} + 1280 \, a^{4} b^{2} c^{12} - 1024 \, a^{5} c^{13}\right)} d^{30}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(-117 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{2 \, c d x + b d} d^{7} - 117 \, \left({\left(b^{10} c^{8} - 20 \, a b^{8} c^{9} + 160 \, a^{2} b^{6} c^{10} - 640 \, a^{3} b^{4} c^{11} + 1280 \, a^{4} b^{2} c^{12} - 1024 \, a^{5} c^{13}\right)} d^{30}\right)^{\frac{1}{4}}\right) + {\left(512 \, c^{6} d^{7} x^{6} + 1536 \, b c^{5} d^{7} x^{5} + 512 \, {\left(7 \, b^{2} c^{4} - 13 \, a c^{5}\right)} d^{7} x^{4} + 512 \, {\left(9 \, b^{3} c^{3} - 26 \, a b c^{4}\right)} d^{7} x^{3} + 3 \, {\left(641 \, b^{4} c^{2} - 520 \, a b^{2} c^{3} - 5616 \, a^{2} c^{4}\right)} d^{7} x^{2} - {\left(125 \, b^{5} c - 5096 \, a b^{3} c^{2} + 16848 \, a^{2} b c^{3}\right)} d^{7} x - {\left(5 \, b^{6} + 65 \, a b^{4} c - 2808 \, a^{2} b^{2} c^{2} + 9360 \, a^{3} c^{3}\right)} d^{7}\right)} \sqrt{2 \, c d x + b d}}{10 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"1/10*(2340*((b^10*c^8 - 20*a*b^8*c^9 + 160*a^2*b^6*c^10 - 640*a^3*b^4*c^11 + 1280*a^4*b^2*c^12 - 1024*a^5*c^13)*d^30)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*arctan(-(((b^10*c^8 - 20*a*b^8*c^9 + 160*a^2*b^6*c^10 - 640*a^3*b^4*c^11 + 1280*a^4*b^2*c^12 - 1024*a^5*c^13)*d^30)^(3/4)*(b^2*c^2 - 4*a*c^3)*sqrt(2*c*d*x + b*d)*d^7 + ((b^10*c^8 - 20*a*b^8*c^9 + 160*a^2*b^6*c^10 - 640*a^3*b^4*c^11 + 1280*a^4*b^2*c^12 - 1024*a^5*c^13)*d^30)^(3/4)*sqrt(2*(b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^15*x + (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^15 + sqrt((b^10*c^8 - 20*a*b^8*c^9 + 160*a^2*b^6*c^10 - 640*a^3*b^4*c^11 + 1280*a^4*b^2*c^12 - 1024*a^5*c^13)*d^30)))/((b^10*c^8 - 20*a*b^8*c^9 + 160*a^2*b^6*c^10 - 640*a^3*b^4*c^11 + 1280*a^4*b^2*c^12 - 1024*a^5*c^13)*d^30)) + 585*((b^10*c^8 - 20*a*b^8*c^9 + 160*a^2*b^6*c^10 - 640*a^3*b^4*c^11 + 1280*a^4*b^2*c^12 - 1024*a^5*c^13)*d^30)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(-117*(b^2*c^2 - 4*a*c^3)*sqrt(2*c*d*x + b*d)*d^7 + 117*((b^10*c^8 - 20*a*b^8*c^9 + 160*a^2*b^6*c^10 - 640*a^3*b^4*c^11 + 1280*a^4*b^2*c^12 - 1024*a^5*c^13)*d^30)^(1/4)) - 585*((b^10*c^8 - 20*a*b^8*c^9 + 160*a^2*b^6*c^10 - 640*a^3*b^4*c^11 + 1280*a^4*b^2*c^12 - 1024*a^5*c^13)*d^30)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(-117*(b^2*c^2 - 4*a*c^3)*sqrt(2*c*d*x + b*d)*d^7 - 117*((b^10*c^8 - 20*a*b^8*c^9 + 160*a^2*b^6*c^10 - 640*a^3*b^4*c^11 + 1280*a^4*b^2*c^12 - 1024*a^5*c^13)*d^30)^(1/4)) + (512*c^6*d^7*x^6 + 1536*b*c^5*d^7*x^5 + 512*(7*b^2*c^4 - 13*a*c^5)*d^7*x^4 + 512*(9*b^3*c^3 - 26*a*b*c^4)*d^7*x^3 + 3*(641*b^4*c^2 - 520*a*b^2*c^3 - 5616*a^2*c^4)*d^7*x^2 - (125*b^5*c - 5096*a*b^3*c^2 + 16848*a^2*b*c^3)*d^7*x - (5*b^6 + 65*a*b^4*c - 2808*a^2*b^2*c^2 + 9360*a^3*c^3)*d^7)*sqrt(2*c*d*x + b*d))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1309,1,951,0,0.466495," ","integrate((2*c*d*x+b*d)^(13/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{924 \, \left({\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{26}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \arctan\left(\frac{\left({\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{26}\right)^{\frac{1}{4}} {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} \sqrt{2 \, c d x + b d} d^{19} - \sqrt{2 \, {\left(b^{8} c^{13} - 16 \, a b^{6} c^{14} + 96 \, a^{2} b^{4} c^{15} - 256 \, a^{3} b^{2} c^{16} + 256 \, a^{4} c^{17}\right)} d^{39} x + {\left(b^{9} c^{12} - 16 \, a b^{7} c^{13} + 96 \, a^{2} b^{5} c^{14} - 256 \, a^{3} b^{3} c^{15} + 256 \, a^{4} b c^{16}\right)} d^{39} + \sqrt{{\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{26}} {\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{26}} \left({\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{26}\right)^{\frac{1}{4}}}{{\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{26}}\right) - 231 \, \left({\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{26}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(456533 \, {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} \sqrt{2 \, c d x + b d} d^{19} + 456533 \, \left({\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{26}\right)^{\frac{3}{4}}\right) + 231 \, \left({\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{26}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(456533 \, {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} \sqrt{2 \, c d x + b d} d^{19} - 456533 \, \left({\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{26}\right)^{\frac{3}{4}}\right) + {\left(256 \, c^{5} d^{6} x^{5} + 640 \, b c^{4} d^{6} x^{4} + 2 \, {\left(199 \, b^{2} c^{3} + 484 \, a c^{4}\right)} d^{6} x^{3} - {\left(43 \, b^{3} c^{2} - 1452 \, a b c^{3}\right)} d^{6} x^{2} - {\left(63 \, b^{4} c - 418 \, a b^{2} c^{2} - 616 \, a^{2} c^{3}\right)} d^{6} x - {\left(3 \, b^{5} + 33 \, a b^{3} c - 308 \, a^{2} b c^{2}\right)} d^{6}\right)} \sqrt{2 \, c d x + b d}}{6 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"1/6*(924*((b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^26)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*arctan((((b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^26)^(1/4)*(b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*sqrt(2*c*d*x + b*d)*d^19 - sqrt(2*(b^8*c^13 - 16*a*b^6*c^14 + 96*a^2*b^4*c^15 - 256*a^3*b^2*c^16 + 256*a^4*c^17)*d^39*x + (b^9*c^12 - 16*a*b^7*c^13 + 96*a^2*b^5*c^14 - 256*a^3*b^3*c^15 + 256*a^4*b*c^16)*d^39 + sqrt((b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^26)*(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^26)*((b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^26)^(1/4))/((b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^26)) - 231*((b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^26)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(456533*(b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*sqrt(2*c*d*x + b*d)*d^19 + 456533*((b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^26)^(3/4)) + 231*((b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^26)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(456533*(b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*sqrt(2*c*d*x + b*d)*d^19 - 456533*((b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^26)^(3/4)) + (256*c^5*d^6*x^5 + 640*b*c^4*d^6*x^4 + 2*(199*b^2*c^3 + 484*a*c^4)*d^6*x^3 - (43*b^3*c^2 - 1452*a*b*c^3)*d^6*x^2 - (63*b^4*c - 418*a*b^2*c^2 - 616*a^2*c^3)*d^6*x - (3*b^5 + 33*a*b^3*c - 308*a^2*b*c^2)*d^6)*sqrt(2*c*d*x + b*d))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1310,1,523,0,0.442485," ","integrate((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{180 \, \left({\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{22}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \arctan\left(\frac{\left({\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{22}\right)^{\frac{3}{4}} \sqrt{2 \, c d x + b d} c^{2} d^{5} - \left({\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{22}\right)^{\frac{3}{4}} \sqrt{2 \, c^{5} d^{11} x + b c^{4} d^{11} + \sqrt{{\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{22}}}}{{\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{22}}\right) + 45 \, \left({\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{22}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(45 \, \sqrt{2 \, c d x + b d} c^{2} d^{5} + 45 \, \left({\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{22}\right)^{\frac{1}{4}}\right) - 45 \, \left({\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{22}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(45 \, \sqrt{2 \, c d x + b d} c^{2} d^{5} - 45 \, \left({\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{22}\right)^{\frac{1}{4}}\right) - {\left(128 \, c^{4} d^{5} x^{4} + 256 \, b c^{3} d^{5} x^{3} + 3 \, {\left(37 \, b^{2} c^{2} + 108 \, a c^{3}\right)} d^{5} x^{2} - {\left(17 \, b^{3} c - 324 \, a b c^{2}\right)} d^{5} x - {\left(b^{4} + 9 \, a b^{2} c - 180 \, a^{2} c^{2}\right)} d^{5}\right)} \sqrt{2 \, c d x + b d}}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"-1/2*(180*((b^2*c^8 - 4*a*c^9)*d^22)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*arctan((((b^2*c^8 - 4*a*c^9)*d^22)^(3/4)*sqrt(2*c*d*x + b*d)*c^2*d^5 - ((b^2*c^8 - 4*a*c^9)*d^22)^(3/4)*sqrt(2*c^5*d^11*x + b*c^4*d^11 + sqrt((b^2*c^8 - 4*a*c^9)*d^22)))/((b^2*c^8 - 4*a*c^9)*d^22)) + 45*((b^2*c^8 - 4*a*c^9)*d^22)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(45*sqrt(2*c*d*x + b*d)*c^2*d^5 + 45*((b^2*c^8 - 4*a*c^9)*d^22)^(1/4)) - 45*((b^2*c^8 - 4*a*c^9)*d^22)^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(45*sqrt(2*c*d*x + b*d)*c^2*d^5 - 45*((b^2*c^8 - 4*a*c^9)*d^22)^(1/4)) - (128*c^4*d^5*x^4 + 256*b*c^3*d^5*x^3 + 3*(37*b^2*c^2 + 108*a*c^3)*d^5*x^2 - (17*b^3*c - 324*a*b*c^2)*d^5*x - (b^4 + 9*a*b^2*c - 180*a^2*c^2)*d^5)*sqrt(2*c*d*x + b*d))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1311,1,500,0,0.447777," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{84 \, \left(\frac{c^{8} d^{18}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \arctan\left(-\frac{\left(\frac{c^{8} d^{18}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} \sqrt{2 \, c d x + b d} c^{6} d^{13} - \sqrt{2 \, c^{13} d^{27} x + b c^{12} d^{27} + \sqrt{\frac{c^{8} d^{18}}{b^{2} - 4 \, a c}} {\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{18}} \left(\frac{c^{8} d^{18}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}}}{c^{8} d^{18}}\right) + 21 \, \left(\frac{c^{8} d^{18}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(9261 \, \sqrt{2 \, c d x + b d} c^{6} d^{13} + 9261 \, \left(\frac{c^{8} d^{18}}{b^{2} - 4 \, a c}\right)^{\frac{3}{4}} {\left(b^{2} - 4 \, a c\right)}\right) - 21 \, \left(\frac{c^{8} d^{18}}{b^{2} - 4 \, a c}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(9261 \, \sqrt{2 \, c d x + b d} c^{6} d^{13} - 9261 \, \left(\frac{c^{8} d^{18}}{b^{2} - 4 \, a c}\right)^{\frac{3}{4}} {\left(b^{2} - 4 \, a c\right)}\right) + {\left(22 \, c^{3} d^{4} x^{3} + 33 \, b c^{2} d^{4} x^{2} + {\left(13 \, b^{2} c + 14 \, a c^{2}\right)} d^{4} x + {\left(b^{3} + 7 \, a b c\right)} d^{4}\right)} \sqrt{2 \, c d x + b d}}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"-1/2*(84*(c^8*d^18/(b^2 - 4*a*c))^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*arctan(-((c^8*d^18/(b^2 - 4*a*c))^(1/4)*sqrt(2*c*d*x + b*d)*c^6*d^13 - sqrt(2*c^13*d^27*x + b*c^12*d^27 + sqrt(c^8*d^18/(b^2 - 4*a*c))*(b^2*c^8 - 4*a*c^9)*d^18)*(c^8*d^18/(b^2 - 4*a*c))^(1/4))/(c^8*d^18)) + 21*(c^8*d^18/(b^2 - 4*a*c))^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(9261*sqrt(2*c*d*x + b*d)*c^6*d^13 + 9261*(c^8*d^18/(b^2 - 4*a*c))^(3/4)*(b^2 - 4*a*c)) - 21*(c^8*d^18/(b^2 - 4*a*c))^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(9261*sqrt(2*c*d*x + b*d)*c^6*d^13 - 9261*(c^8*d^18/(b^2 - 4*a*c))^(3/4)*(b^2 - 4*a*c)) + (22*c^3*d^4*x^3 + 33*b*c^2*d^4*x^2 + (13*b^2*c + 14*a*c^2)*d^4*x + (b^3 + 7*a*b*c)*d^4)*sqrt(2*c*d*x + b*d))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1312,1,697,0,0.431196," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{20 \, \left(\frac{c^{8} d^{14}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \arctan\left(-\frac{\left(\frac{c^{8} d^{14}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{3}{4}} {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} \sqrt{2 \, c d x + b d} d^{3} - \left(\frac{c^{8} d^{14}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{3}{4}} \sqrt{2 \, c^{5} d^{7} x + b c^{4} d^{7} + \sqrt{\frac{c^{8} d^{14}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}{c^{8} d^{14}}\right) - 5 \, \left(\frac{c^{8} d^{14}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(5 \, \sqrt{2 \, c d x + b d} c^{2} d^{3} + 5 \, \left(\frac{c^{8} d^{14}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{1}{4}} {\left(b^{2} - 4 \, a c\right)}\right) + 5 \, \left(\frac{c^{8} d^{14}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{1}{4}} {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \log\left(5 \, \sqrt{2 \, c d x + b d} c^{2} d^{3} - 5 \, \left(\frac{c^{8} d^{14}}{b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}}\right)^{\frac{1}{4}} {\left(b^{2} - 4 \, a c\right)}\right) - {\left(9 \, c^{2} d^{3} x^{2} + 9 \, b c d^{3} x + {\left(b^{2} + 5 \, a c\right)} d^{3}\right)} \sqrt{2 \, c d x + b d}}{2 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)}}"," ",0,"1/2*(20*(c^8*d^14/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*arctan(-((c^8*d^14/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(3/4)*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*sqrt(2*c*d*x + b*d)*d^3 - (c^8*d^14/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(3/4)*sqrt(2*c^5*d^7*x + b*c^4*d^7 + sqrt(c^8*d^14/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))*(b^4 - 8*a*b^2*c + 16*a^2*c^2))*(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c^8*d^14)) - 5*(c^8*d^14/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(5*sqrt(2*c*d*x + b*d)*c^2*d^3 + 5*(c^8*d^14/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(1/4)*(b^2 - 4*a*c)) + 5*(c^8*d^14/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(1/4)*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*log(5*sqrt(2*c*d*x + b*d)*c^2*d^3 - 5*(c^8*d^14/(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3))^(1/4)*(b^2 - 4*a*c)) - (9*c^2*d^3*x^2 + 9*b*c*d^3*x + (b^2 + 5*a*c)*d^3)*sqrt(2*c*d*x + b*d))/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)","B",0
1313,1,1174,0,0.454509," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{12 \, \left(\frac{c^{8} d^{10}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{1}{4}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \arctan\left(\frac{\left(\frac{c^{8} d^{10}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{1}{4}} {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} \sqrt{2 \, c d x + b d} d^{7} - \sqrt{2 \, c^{13} d^{15} x + b c^{12} d^{15} + \sqrt{\frac{c^{8} d^{10}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}} {\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{10}} \left(\frac{c^{8} d^{10}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{1}{4}} {\left(b^{2} - 4 \, a c\right)}}{c^{8} d^{10}}\right) - 3 \, \left(\frac{c^{8} d^{10}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{1}{4}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \log\left(27 \, \sqrt{2 \, c d x + b d} c^{6} d^{7} + 27 \, \left(\frac{c^{8} d^{10}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{3}{4}} {\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)}\right) + 3 \, \left(\frac{c^{8} d^{10}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{1}{4}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \log\left(27 \, \sqrt{2 \, c d x + b d} c^{6} d^{7} - 27 \, \left(\frac{c^{8} d^{10}}{b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}}\right)^{\frac{3}{4}} {\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)}\right) + {\left(6 \, c^{3} d^{2} x^{3} + 9 \, b c^{2} d^{2} x^{2} + {\left(5 \, b^{2} c - 2 \, a c^{2}\right)} d^{2} x + {\left(b^{3} - a b c\right)} d^{2}\right)} \sqrt{2 \, c d x + b d}}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)}}"," ",0,"-1/2*(12*(c^8*d^10/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(1/4)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*arctan(((c^8*d^10/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(1/4)*(b^2*c^6 - 4*a*c^7)*sqrt(2*c*d*x + b*d)*d^7 - sqrt(2*c^13*d^15*x + b*c^12*d^15 + sqrt(c^8*d^10/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))*(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^10)*(c^8*d^10/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(1/4)*(b^2 - 4*a*c))/(c^8*d^10)) - 3*(c^8*d^10/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(1/4)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*log(27*sqrt(2*c*d*x + b*d)*c^6*d^7 + 27*(c^8*d^10/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(3/4)*(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)) + 3*(c^8*d^10/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(1/4)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*log(27*sqrt(2*c*d*x + b*d)*c^6*d^7 - 27*(c^8*d^10/(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5))^(3/4)*(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)) + (6*c^3*d^2*x^3 + 9*b*c^2*d^2*x^2 + (5*b^2*c - 2*a*c^2)*d^2*x + (b^3 - a*b*c)*d^2)*sqrt(2*c*d*x + b*d))/((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)","B",0
1314,1,1360,0,0.453941," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{12 \, \left(\frac{c^{8} d^{6}}{b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}}\right)^{\frac{1}{4}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \arctan\left(\frac{\left(\frac{c^{8} d^{6}}{b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}}\right)^{\frac{3}{4}} {\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} \sqrt{2 \, c d x + b d} d - \left(\frac{c^{8} d^{6}}{b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}}\right)^{\frac{3}{4}} {\left(b^{10} - 20 \, a b^{8} c + 160 \, a^{2} b^{6} c^{2} - 640 \, a^{3} b^{4} c^{3} + 1280 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} \sqrt{2 \, c^{5} d^{3} x + b c^{4} d^{3} + \sqrt{\frac{c^{8} d^{6}}{b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}}} {\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)}}}{c^{8} d^{6}}\right) + 3 \, \left(\frac{c^{8} d^{6}}{b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}}\right)^{\frac{1}{4}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \log\left(3 \, \sqrt{2 \, c d x + b d} c^{2} d + 3 \, \left(\frac{c^{8} d^{6}}{b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}}\right)^{\frac{1}{4}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}\right) - 3 \, \left(\frac{c^{8} d^{6}}{b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}}\right)^{\frac{1}{4}} {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \log\left(3 \, \sqrt{2 \, c d x + b d} c^{2} d - 3 \, \left(\frac{c^{8} d^{6}}{b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}}\right)^{\frac{1}{4}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}\right) - {\left(c^{2} d x^{2} + b c d x + {\left(b^{2} - 3 \, a c\right)} d\right)} \sqrt{2 \, c d x + b d}}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} x^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)}}"," ",0,"1/2*(12*(c^8*d^6/(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7))^(1/4)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*arctan(((c^8*d^6/(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7))^(3/4)*(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*sqrt(2*c*d*x + b*d)*d - (c^8*d^6/(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7))^(3/4)*(b^10 - 20*a*b^8*c + 160*a^2*b^6*c^2 - 640*a^3*b^4*c^3 + 1280*a^4*b^2*c^4 - 1024*a^5*c^5)*sqrt(2*c^5*d^3*x + b*c^4*d^3 + sqrt(c^8*d^6/(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7))*(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^8*d^6)) + 3*(c^8*d^6/(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7))^(1/4)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*log(3*sqrt(2*c*d*x + b*d)*c^2*d + 3*(c^8*d^6/(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7))^(1/4)*(b^4 - 8*a*b^2*c + 16*a^2*c^2)) - 3*(c^8*d^6/(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7))^(1/4)*((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)*log(3*sqrt(2*c*d*x + b*d)*c^2*d - 3*(c^8*d^6/(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7))^(1/4)*(b^4 - 8*a*b^2*c + 16*a^2*c^2)) - (c^2*d*x^2 + b*c*d*x + (b^2 - 3*a*c)*d)*sqrt(2*c*d*x + b*d))/((b^2*c^2 - 4*a*c^3)*x^4 + a^2*b^2 - 4*a^3*c + 2*(b^3*c - 4*a*b*c^2)*x^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*x^2 + 2*(a*b^3 - 4*a^2*b*c)*x)","B",0
1315,1,1796,0,0.467794," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{20 \, \left(\frac{c^{8} d^{2}}{b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}}\right)^{\frac{1}{4}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \arctan\left(-\frac{{\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} \left(\frac{c^{8} d^{2}}{b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}}\right)^{\frac{1}{4}} \sqrt{2 \, c d x + b d} d - \sqrt{2 \, c^{13} d^{3} x + b c^{12} d^{3} + {\left(b^{10} c^{8} - 20 \, a b^{8} c^{9} + 160 \, a^{2} b^{6} c^{10} - 640 \, a^{3} b^{4} c^{11} + 1280 \, a^{4} b^{2} c^{12} - 1024 \, a^{5} c^{13}\right)} \sqrt{\frac{c^{8} d^{2}}{b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}}} d^{2}} \left(\frac{c^{8} d^{2}}{b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}}\right)^{\frac{1}{4}} {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)}}{c^{8} d^{2}}\right) + 5 \, \left(\frac{c^{8} d^{2}}{b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}}\right)^{\frac{1}{4}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \log\left(125 \, \sqrt{2 \, c d x + b d} c^{6} d + 125 \, {\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} \left(\frac{c^{8} d^{2}}{b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}}\right)^{\frac{3}{4}}\right) - 5 \, \left(\frac{c^{8} d^{2}}{b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}}\right)^{\frac{1}{4}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \log\left(125 \, \sqrt{2 \, c d x + b d} c^{6} d - 125 \, {\left(b^{14} - 28 \, a b^{12} c + 336 \, a^{2} b^{10} c^{2} - 2240 \, a^{3} b^{8} c^{3} + 8960 \, a^{4} b^{6} c^{4} - 21504 \, a^{5} b^{4} c^{5} + 28672 \, a^{6} b^{2} c^{6} - 16384 \, a^{7} c^{7}\right)} \left(\frac{c^{8} d^{2}}{b^{18} - 36 \, a b^{16} c + 576 \, a^{2} b^{14} c^{2} - 5376 \, a^{3} b^{12} c^{3} + 32256 \, a^{4} b^{10} c^{4} - 129024 \, a^{5} b^{8} c^{5} + 344064 \, a^{6} b^{6} c^{6} - 589824 \, a^{7} b^{4} c^{7} + 589824 \, a^{8} b^{2} c^{8} - 262144 \, a^{9} c^{9}}\right)^{\frac{3}{4}}\right) - {\left(10 \, c^{3} x^{3} + 15 \, b c^{2} x^{2} - b^{3} + 9 \, a b c + 3 \, {\left(b^{2} c + 6 \, a c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{2 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"-1/2*(20*(c^8*d^2/(b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9))^(1/4)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*arctan(-((b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*(c^8*d^2/(b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9))^(1/4)*sqrt(2*c*d*x + b*d)*d - sqrt(2*c^13*d^3*x + b*c^12*d^3 + (b^10*c^8 - 20*a*b^8*c^9 + 160*a^2*b^6*c^10 - 640*a^3*b^4*c^11 + 1280*a^4*b^2*c^12 - 1024*a^5*c^13)*sqrt(c^8*d^2/(b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9))*d^2)*(c^8*d^2/(b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9))^(1/4)*(b^4 - 8*a*b^2*c + 16*a^2*c^2))/(c^8*d^2)) + 5*(c^8*d^2/(b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9))^(1/4)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*log(125*sqrt(2*c*d*x + b*d)*c^6*d + 125*(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*(c^8*d^2/(b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9))^(3/4)) - 5*(c^8*d^2/(b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9))^(1/4)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*log(125*sqrt(2*c*d*x + b*d)*c^6*d - 125*(b^14 - 28*a*b^12*c + 336*a^2*b^10*c^2 - 2240*a^3*b^8*c^3 + 8960*a^4*b^6*c^4 - 21504*a^5*b^4*c^5 + 28672*a^6*b^2*c^6 - 16384*a^7*c^7)*(c^8*d^2/(b^18 - 36*a*b^16*c + 576*a^2*b^14*c^2 - 5376*a^3*b^12*c^3 + 32256*a^4*b^10*c^4 - 129024*a^5*b^8*c^5 + 344064*a^6*b^6*c^6 - 589824*a^7*b^4*c^7 + 589824*a^8*b^2*c^8 - 262144*a^9*c^9))^(3/4)) - (10*c^3*x^3 + 15*b*c^2*x^2 - b^3 + 9*a*b*c + 3*(b^2*c + 6*a*c^2)*x)*sqrt(2*c*d*x + b*d))/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
1316,1,2021,0,0.480202," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{84 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} d\right)} \left(\frac{c^{8}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(b^{16} - 32 \, a b^{14} c + 448 \, a^{2} b^{12} c^{2} - 3584 \, a^{3} b^{10} c^{3} + 17920 \, a^{4} b^{8} c^{4} - 57344 \, a^{5} b^{6} c^{5} + 114688 \, a^{6} b^{4} c^{6} - 131072 \, a^{7} b^{2} c^{7} + 65536 \, a^{8} c^{8}\right)} \sqrt{2 \, c^{5} d x + b c^{4} d + {\left(b^{12} - 24 \, a b^{10} c + 240 \, a^{2} b^{8} c^{2} - 1280 \, a^{3} b^{6} c^{3} + 3840 \, a^{4} b^{4} c^{4} - 6144 \, a^{5} b^{2} c^{5} + 4096 \, a^{6} c^{6}\right)} \sqrt{\frac{c^{8}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{2}}} d^{2}} \left(\frac{c^{8}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{2}}\right)^{\frac{3}{4}} d - {\left(b^{16} c^{2} - 32 \, a b^{14} c^{3} + 448 \, a^{2} b^{12} c^{4} - 3584 \, a^{3} b^{10} c^{5} + 17920 \, a^{4} b^{8} c^{6} - 57344 \, a^{5} b^{6} c^{7} + 114688 \, a^{6} b^{4} c^{8} - 131072 \, a^{7} b^{2} c^{9} + 65536 \, a^{8} c^{10}\right)} \left(\frac{c^{8}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{2}}\right)^{\frac{3}{4}} \sqrt{2 \, c d x + b d} d}{c^{8}}\right) - 21 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} d\right)} \left(\frac{c^{8}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{2}}\right)^{\frac{1}{4}} \log\left(21 \, \sqrt{2 \, c d x + b d} c^{2} + 21 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \left(\frac{c^{8}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{2}}\right)^{\frac{1}{4}} d\right) + 21 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} d\right)} \left(\frac{c^{8}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{2}}\right)^{\frac{1}{4}} \log\left(21 \, \sqrt{2 \, c d x + b d} c^{2} - 21 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \left(\frac{c^{8}}{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} d^{2}}\right)^{\frac{1}{4}} d\right) + {\left(7 \, c^{2} x^{2} + 7 \, b c x - b^{2} + 11 \, a c\right)} \sqrt{2 \, c d x + b d}}{2 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} d x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} d\right)}}"," ",0,"1/2*(84*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*d)*(c^8/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^2))^(1/4)*arctan(((b^16 - 32*a*b^14*c + 448*a^2*b^12*c^2 - 3584*a^3*b^10*c^3 + 17920*a^4*b^8*c^4 - 57344*a^5*b^6*c^5 + 114688*a^6*b^4*c^6 - 131072*a^7*b^2*c^7 + 65536*a^8*c^8)*sqrt(2*c^5*d*x + b*c^4*d + (b^12 - 24*a*b^10*c + 240*a^2*b^8*c^2 - 1280*a^3*b^6*c^3 + 3840*a^4*b^4*c^4 - 6144*a^5*b^2*c^5 + 4096*a^6*c^6)*sqrt(c^8/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^2))*d^2)*(c^8/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^2))^(3/4)*d - (b^16*c^2 - 32*a*b^14*c^3 + 448*a^2*b^12*c^4 - 3584*a^3*b^10*c^5 + 17920*a^4*b^8*c^6 - 57344*a^5*b^6*c^7 + 114688*a^6*b^4*c^8 - 131072*a^7*b^2*c^9 + 65536*a^8*c^10)*(c^8/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^2))^(3/4)*sqrt(2*c*d*x + b*d)*d)/c^8) - 21*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*d)*(c^8/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^2))^(1/4)*log(21*sqrt(2*c*d*x + b*d)*c^2 + 21*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*(c^8/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^2))^(1/4)*d) + 21*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*d)*(c^8/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^2))^(1/4)*log(21*sqrt(2*c*d*x + b*d)*c^2 - 21*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*(c^8/((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*d^2))^(1/4)*d) + (7*c^2*x^2 + 7*b*c*x - b^2 + 11*a*c)*sqrt(2*c*d*x + b*d))/((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*d*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*d)","B",0
1317,1,2890,0,0.525670," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{180 \, {\left(2 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{2} x^{5} + 5 \, {\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)} d^{2} x^{4} + 4 \, {\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)} d^{2} x^{3} + {\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)} d^{2} x^{2} + 2 \, {\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)} d^{2} x + {\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)} d^{2}\right)} \left(\frac{c^{8}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{6}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2 \, c^{13} d x + b c^{12} d + {\left(b^{14} c^{8} - 28 \, a b^{12} c^{9} + 336 \, a^{2} b^{10} c^{10} - 2240 \, a^{3} b^{8} c^{11} + 8960 \, a^{4} b^{6} c^{12} - 21504 \, a^{5} b^{4} c^{13} + 28672 \, a^{6} b^{2} c^{14} - 16384 \, a^{7} c^{15}\right)} \sqrt{\frac{c^{8}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{6}}} d^{4}} {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \left(\frac{c^{8}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{6}}\right)^{\frac{1}{4}} d - {\left(b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}\right)} \sqrt{2 \, c d x + b d} \left(\frac{c^{8}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{6}}\right)^{\frac{1}{4}} d}{c^{8}}\right) - 45 \, {\left(2 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{2} x^{5} + 5 \, {\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)} d^{2} x^{4} + 4 \, {\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)} d^{2} x^{3} + {\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)} d^{2} x^{2} + 2 \, {\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)} d^{2} x + {\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)} d^{2}\right)} \left(\frac{c^{8}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{6}}\right)^{\frac{1}{4}} \log\left(91125 \, {\left(b^{20} - 40 \, a b^{18} c + 720 \, a^{2} b^{16} c^{2} - 7680 \, a^{3} b^{14} c^{3} + 53760 \, a^{4} b^{12} c^{4} - 258048 \, a^{5} b^{10} c^{5} + 860160 \, a^{6} b^{8} c^{6} - 1966080 \, a^{7} b^{6} c^{7} + 2949120 \, a^{8} b^{4} c^{8} - 2621440 \, a^{9} b^{2} c^{9} + 1048576 \, a^{10} c^{10}\right)} \left(\frac{c^{8}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{6}}\right)^{\frac{3}{4}} d^{5} + 91125 \, \sqrt{2 \, c d x + b d} c^{6}\right) + 45 \, {\left(2 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{2} x^{5} + 5 \, {\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)} d^{2} x^{4} + 4 \, {\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)} d^{2} x^{3} + {\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)} d^{2} x^{2} + 2 \, {\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)} d^{2} x + {\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)} d^{2}\right)} \left(\frac{c^{8}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{6}}\right)^{\frac{1}{4}} \log\left(-91125 \, {\left(b^{20} - 40 \, a b^{18} c + 720 \, a^{2} b^{16} c^{2} - 7680 \, a^{3} b^{14} c^{3} + 53760 \, a^{4} b^{12} c^{4} - 258048 \, a^{5} b^{10} c^{5} + 860160 \, a^{6} b^{8} c^{6} - 1966080 \, a^{7} b^{6} c^{7} + 2949120 \, a^{8} b^{4} c^{8} - 2621440 \, a^{9} b^{2} c^{9} + 1048576 \, a^{10} c^{10}\right)} \left(\frac{c^{8}}{{\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{6}}\right)^{\frac{3}{4}} d^{5} + 91125 \, \sqrt{2 \, c d x + b d} c^{6}\right) + {\left(180 \, c^{4} x^{4} + 360 \, b c^{3} x^{3} - b^{4} + 17 \, a b^{2} c + 128 \, a^{2} c^{2} + 27 \, {\left(7 \, b^{2} c^{2} + 12 \, a c^{3}\right)} x^{2} + 9 \, {\left(b^{3} c + 36 \, a b c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{2 \, {\left(2 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{2} x^{5} + 5 \, {\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)} d^{2} x^{4} + 4 \, {\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)} d^{2} x^{3} + {\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)} d^{2} x^{2} + 2 \, {\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)} d^{2} x + {\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)} d^{2}\right)}}"," ",0,"1/2*(180*(2*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^2*x^5 + 5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2*x^4 + 4*(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)*d^2*x^3 + (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)*d^2*x^2 + 2*(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)*d^2*x + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2)*(c^8/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^6))^(1/4)*arctan(-(sqrt(2*c^13*d*x + b*c^12*d + (b^14*c^8 - 28*a*b^12*c^9 + 336*a^2*b^10*c^10 - 2240*a^3*b^8*c^11 + 8960*a^4*b^6*c^12 - 21504*a^5*b^4*c^13 + 28672*a^6*b^2*c^14 - 16384*a^7*c^15)*sqrt(c^8/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^6))*d^4)*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*(c^8/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^6))^(1/4)*d - (b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)*sqrt(2*c*d*x + b*d)*(c^8/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^6))^(1/4)*d)/c^8) - 45*(2*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^2*x^5 + 5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2*x^4 + 4*(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)*d^2*x^3 + (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)*d^2*x^2 + 2*(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)*d^2*x + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2)*(c^8/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^6))^(1/4)*log(91125*(b^20 - 40*a*b^18*c + 720*a^2*b^16*c^2 - 7680*a^3*b^14*c^3 + 53760*a^4*b^12*c^4 - 258048*a^5*b^10*c^5 + 860160*a^6*b^8*c^6 - 1966080*a^7*b^6*c^7 + 2949120*a^8*b^4*c^8 - 2621440*a^9*b^2*c^9 + 1048576*a^10*c^10)*(c^8/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^6))^(3/4)*d^5 + 91125*sqrt(2*c*d*x + b*d)*c^6) + 45*(2*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^2*x^5 + 5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2*x^4 + 4*(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)*d^2*x^3 + (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)*d^2*x^2 + 2*(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)*d^2*x + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2)*(c^8/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^6))^(1/4)*log(-91125*(b^20 - 40*a*b^18*c + 720*a^2*b^16*c^2 - 7680*a^3*b^14*c^3 + 53760*a^4*b^12*c^4 - 258048*a^5*b^10*c^5 + 860160*a^6*b^8*c^6 - 1966080*a^7*b^6*c^7 + 2949120*a^8*b^4*c^8 - 2621440*a^9*b^2*c^9 + 1048576*a^10*c^10)*(c^8/((b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^6))^(3/4)*d^5 + 91125*sqrt(2*c*d*x + b*d)*c^6) + (180*c^4*x^4 + 360*b*c^3*x^3 - b^4 + 17*a*b^2*c + 128*a^2*c^2 + 27*(7*b^2*c^2 + 12*a*c^3)*x^2 + 9*(b^3*c + 36*a*b*c^2)*x)*sqrt(2*c*d*x + b*d))/(2*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^2*x^5 + 5*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2*x^4 + 4*(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)*d^2*x^3 + (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)*d^2*x^2 + 2*(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)*d^2*x + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*d^2)","B",0
1318,1,3401,0,0.537650," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{924 \, {\left(4 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{3} x^{6} + 12 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{3} x^{5} + {\left(13 \, b^{8} c^{2} - 148 \, a b^{6} c^{3} + 528 \, a^{2} b^{4} c^{4} - 448 \, a^{3} b^{2} c^{5} - 512 \, a^{4} c^{6}\right)} d^{3} x^{4} + 2 \, {\left(3 \, b^{9} c - 28 \, a b^{7} c^{2} + 48 \, a^{2} b^{5} c^{3} + 192 \, a^{3} b^{3} c^{4} - 512 \, a^{4} b c^{5}\right)} d^{3} x^{3} + {\left(b^{10} - 2 \, a b^{8} c - 68 \, a^{2} b^{6} c^{2} + 368 \, a^{3} b^{4} c^{3} - 448 \, a^{4} b^{2} c^{4} - 256 \, a^{5} c^{5}\right)} d^{3} x^{2} + 2 \, {\left(a b^{9} - 10 \, a^{2} b^{7} c + 24 \, a^{3} b^{5} c^{2} + 32 \, a^{4} b^{3} c^{3} - 128 \, a^{5} b c^{4}\right)} d^{3} x + {\left(a^{2} b^{8} - 12 \, a^{3} b^{6} c + 48 \, a^{4} b^{4} c^{2} - 64 \, a^{5} b^{2} c^{3}\right)} d^{3}\right)} \left(\frac{c^{8}}{{\left(b^{30} - 60 \, a b^{28} c + 1680 \, a^{2} b^{26} c^{2} - 29120 \, a^{3} b^{24} c^{3} + 349440 \, a^{4} b^{22} c^{4} - 3075072 \, a^{5} b^{20} c^{5} + 20500480 \, a^{6} b^{18} c^{6} - 105431040 \, a^{7} b^{16} c^{7} + 421724160 \, a^{8} b^{14} c^{8} - 1312030720 \, a^{9} b^{12} c^{9} + 3148873728 \, a^{10} b^{10} c^{10} - 5725224960 \, a^{11} b^{8} c^{11} + 7633633280 \, a^{12} b^{6} c^{12} - 7046430720 \, a^{13} b^{4} c^{13} + 4026531840 \, a^{14} b^{2} c^{14} - 1073741824 \, a^{15} c^{15}\right)} d^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(b^{22} - 44 \, a b^{20} c + 880 \, a^{2} b^{18} c^{2} - 10560 \, a^{3} b^{16} c^{3} + 84480 \, a^{4} b^{14} c^{4} - 473088 \, a^{5} b^{12} c^{5} + 1892352 \, a^{6} b^{10} c^{6} - 5406720 \, a^{7} b^{8} c^{7} + 10813440 \, a^{8} b^{6} c^{8} - 14417920 \, a^{9} b^{4} c^{9} + 11534336 \, a^{10} b^{2} c^{10} - 4194304 \, a^{11} c^{11}\right)} \sqrt{{\left(b^{16} - 32 \, a b^{14} c + 448 \, a^{2} b^{12} c^{2} - 3584 \, a^{3} b^{10} c^{3} + 17920 \, a^{4} b^{8} c^{4} - 57344 \, a^{5} b^{6} c^{5} + 114688 \, a^{6} b^{4} c^{6} - 131072 \, a^{7} b^{2} c^{7} + 65536 \, a^{8} c^{8}\right)} d^{6} \sqrt{\frac{c^{8}}{{\left(b^{30} - 60 \, a b^{28} c + 1680 \, a^{2} b^{26} c^{2} - 29120 \, a^{3} b^{24} c^{3} + 349440 \, a^{4} b^{22} c^{4} - 3075072 \, a^{5} b^{20} c^{5} + 20500480 \, a^{6} b^{18} c^{6} - 105431040 \, a^{7} b^{16} c^{7} + 421724160 \, a^{8} b^{14} c^{8} - 1312030720 \, a^{9} b^{12} c^{9} + 3148873728 \, a^{10} b^{10} c^{10} - 5725224960 \, a^{11} b^{8} c^{11} + 7633633280 \, a^{12} b^{6} c^{12} - 7046430720 \, a^{13} b^{4} c^{13} + 4026531840 \, a^{14} b^{2} c^{14} - 1073741824 \, a^{15} c^{15}\right)} d^{10}}} + 2 \, c^{5} d x + b c^{4} d} d^{7} \left(\frac{c^{8}}{{\left(b^{30} - 60 \, a b^{28} c + 1680 \, a^{2} b^{26} c^{2} - 29120 \, a^{3} b^{24} c^{3} + 349440 \, a^{4} b^{22} c^{4} - 3075072 \, a^{5} b^{20} c^{5} + 20500480 \, a^{6} b^{18} c^{6} - 105431040 \, a^{7} b^{16} c^{7} + 421724160 \, a^{8} b^{14} c^{8} - 1312030720 \, a^{9} b^{12} c^{9} + 3148873728 \, a^{10} b^{10} c^{10} - 5725224960 \, a^{11} b^{8} c^{11} + 7633633280 \, a^{12} b^{6} c^{12} - 7046430720 \, a^{13} b^{4} c^{13} + 4026531840 \, a^{14} b^{2} c^{14} - 1073741824 \, a^{15} c^{15}\right)} d^{10}}\right)^{\frac{3}{4}} - {\left(b^{22} c^{2} - 44 \, a b^{20} c^{3} + 880 \, a^{2} b^{18} c^{4} - 10560 \, a^{3} b^{16} c^{5} + 84480 \, a^{4} b^{14} c^{6} - 473088 \, a^{5} b^{12} c^{7} + 1892352 \, a^{6} b^{10} c^{8} - 5406720 \, a^{7} b^{8} c^{9} + 10813440 \, a^{8} b^{6} c^{10} - 14417920 \, a^{9} b^{4} c^{11} + 11534336 \, a^{10} b^{2} c^{12} - 4194304 \, a^{11} c^{13}\right)} \sqrt{2 \, c d x + b d} d^{7} \left(\frac{c^{8}}{{\left(b^{30} - 60 \, a b^{28} c + 1680 \, a^{2} b^{26} c^{2} - 29120 \, a^{3} b^{24} c^{3} + 349440 \, a^{4} b^{22} c^{4} - 3075072 \, a^{5} b^{20} c^{5} + 20500480 \, a^{6} b^{18} c^{6} - 105431040 \, a^{7} b^{16} c^{7} + 421724160 \, a^{8} b^{14} c^{8} - 1312030720 \, a^{9} b^{12} c^{9} + 3148873728 \, a^{10} b^{10} c^{10} - 5725224960 \, a^{11} b^{8} c^{11} + 7633633280 \, a^{12} b^{6} c^{12} - 7046430720 \, a^{13} b^{4} c^{13} + 4026531840 \, a^{14} b^{2} c^{14} - 1073741824 \, a^{15} c^{15}\right)} d^{10}}\right)^{\frac{3}{4}}}{c^{8}}\right) + 231 \, {\left(4 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{3} x^{6} + 12 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{3} x^{5} + {\left(13 \, b^{8} c^{2} - 148 \, a b^{6} c^{3} + 528 \, a^{2} b^{4} c^{4} - 448 \, a^{3} b^{2} c^{5} - 512 \, a^{4} c^{6}\right)} d^{3} x^{4} + 2 \, {\left(3 \, b^{9} c - 28 \, a b^{7} c^{2} + 48 \, a^{2} b^{5} c^{3} + 192 \, a^{3} b^{3} c^{4} - 512 \, a^{4} b c^{5}\right)} d^{3} x^{3} + {\left(b^{10} - 2 \, a b^{8} c - 68 \, a^{2} b^{6} c^{2} + 368 \, a^{3} b^{4} c^{3} - 448 \, a^{4} b^{2} c^{4} - 256 \, a^{5} c^{5}\right)} d^{3} x^{2} + 2 \, {\left(a b^{9} - 10 \, a^{2} b^{7} c + 24 \, a^{3} b^{5} c^{2} + 32 \, a^{4} b^{3} c^{3} - 128 \, a^{5} b c^{4}\right)} d^{3} x + {\left(a^{2} b^{8} - 12 \, a^{3} b^{6} c + 48 \, a^{4} b^{4} c^{2} - 64 \, a^{5} b^{2} c^{3}\right)} d^{3}\right)} \left(\frac{c^{8}}{{\left(b^{30} - 60 \, a b^{28} c + 1680 \, a^{2} b^{26} c^{2} - 29120 \, a^{3} b^{24} c^{3} + 349440 \, a^{4} b^{22} c^{4} - 3075072 \, a^{5} b^{20} c^{5} + 20500480 \, a^{6} b^{18} c^{6} - 105431040 \, a^{7} b^{16} c^{7} + 421724160 \, a^{8} b^{14} c^{8} - 1312030720 \, a^{9} b^{12} c^{9} + 3148873728 \, a^{10} b^{10} c^{10} - 5725224960 \, a^{11} b^{8} c^{11} + 7633633280 \, a^{12} b^{6} c^{12} - 7046430720 \, a^{13} b^{4} c^{13} + 4026531840 \, a^{14} b^{2} c^{14} - 1073741824 \, a^{15} c^{15}\right)} d^{10}}\right)^{\frac{1}{4}} \log\left(77 \, {\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)} d^{3} \left(\frac{c^{8}}{{\left(b^{30} - 60 \, a b^{28} c + 1680 \, a^{2} b^{26} c^{2} - 29120 \, a^{3} b^{24} c^{3} + 349440 \, a^{4} b^{22} c^{4} - 3075072 \, a^{5} b^{20} c^{5} + 20500480 \, a^{6} b^{18} c^{6} - 105431040 \, a^{7} b^{16} c^{7} + 421724160 \, a^{8} b^{14} c^{8} - 1312030720 \, a^{9} b^{12} c^{9} + 3148873728 \, a^{10} b^{10} c^{10} - 5725224960 \, a^{11} b^{8} c^{11} + 7633633280 \, a^{12} b^{6} c^{12} - 7046430720 \, a^{13} b^{4} c^{13} + 4026531840 \, a^{14} b^{2} c^{14} - 1073741824 \, a^{15} c^{15}\right)} d^{10}}\right)^{\frac{1}{4}} + 77 \, \sqrt{2 \, c d x + b d} c^{2}\right) - 231 \, {\left(4 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{3} x^{6} + 12 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{3} x^{5} + {\left(13 \, b^{8} c^{2} - 148 \, a b^{6} c^{3} + 528 \, a^{2} b^{4} c^{4} - 448 \, a^{3} b^{2} c^{5} - 512 \, a^{4} c^{6}\right)} d^{3} x^{4} + 2 \, {\left(3 \, b^{9} c - 28 \, a b^{7} c^{2} + 48 \, a^{2} b^{5} c^{3} + 192 \, a^{3} b^{3} c^{4} - 512 \, a^{4} b c^{5}\right)} d^{3} x^{3} + {\left(b^{10} - 2 \, a b^{8} c - 68 \, a^{2} b^{6} c^{2} + 368 \, a^{3} b^{4} c^{3} - 448 \, a^{4} b^{2} c^{4} - 256 \, a^{5} c^{5}\right)} d^{3} x^{2} + 2 \, {\left(a b^{9} - 10 \, a^{2} b^{7} c + 24 \, a^{3} b^{5} c^{2} + 32 \, a^{4} b^{3} c^{3} - 128 \, a^{5} b c^{4}\right)} d^{3} x + {\left(a^{2} b^{8} - 12 \, a^{3} b^{6} c + 48 \, a^{4} b^{4} c^{2} - 64 \, a^{5} b^{2} c^{3}\right)} d^{3}\right)} \left(\frac{c^{8}}{{\left(b^{30} - 60 \, a b^{28} c + 1680 \, a^{2} b^{26} c^{2} - 29120 \, a^{3} b^{24} c^{3} + 349440 \, a^{4} b^{22} c^{4} - 3075072 \, a^{5} b^{20} c^{5} + 20500480 \, a^{6} b^{18} c^{6} - 105431040 \, a^{7} b^{16} c^{7} + 421724160 \, a^{8} b^{14} c^{8} - 1312030720 \, a^{9} b^{12} c^{9} + 3148873728 \, a^{10} b^{10} c^{10} - 5725224960 \, a^{11} b^{8} c^{11} + 7633633280 \, a^{12} b^{6} c^{12} - 7046430720 \, a^{13} b^{4} c^{13} + 4026531840 \, a^{14} b^{2} c^{14} - 1073741824 \, a^{15} c^{15}\right)} d^{10}}\right)^{\frac{1}{4}} \log\left(-77 \, {\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)} d^{3} \left(\frac{c^{8}}{{\left(b^{30} - 60 \, a b^{28} c + 1680 \, a^{2} b^{26} c^{2} - 29120 \, a^{3} b^{24} c^{3} + 349440 \, a^{4} b^{22} c^{4} - 3075072 \, a^{5} b^{20} c^{5} + 20500480 \, a^{6} b^{18} c^{6} - 105431040 \, a^{7} b^{16} c^{7} + 421724160 \, a^{8} b^{14} c^{8} - 1312030720 \, a^{9} b^{12} c^{9} + 3148873728 \, a^{10} b^{10} c^{10} - 5725224960 \, a^{11} b^{8} c^{11} + 7633633280 \, a^{12} b^{6} c^{12} - 7046430720 \, a^{13} b^{4} c^{13} + 4026531840 \, a^{14} b^{2} c^{14} - 1073741824 \, a^{15} c^{15}\right)} d^{10}}\right)^{\frac{1}{4}} + 77 \, \sqrt{2 \, c d x + b d} c^{2}\right) - {\left(308 \, c^{4} x^{4} + 616 \, b c^{3} x^{3} - 3 \, b^{4} + 57 \, a b^{2} c + 128 \, a^{2} c^{2} + 11 \, {\left(31 \, b^{2} c^{2} + 44 \, a c^{3}\right)} x^{2} + 11 \, {\left(3 \, b^{3} c + 44 \, a b c^{2}\right)} x\right)} \sqrt{2 \, c d x + b d}}{6 \, {\left(4 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{3} x^{6} + 12 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{3} x^{5} + {\left(13 \, b^{8} c^{2} - 148 \, a b^{6} c^{3} + 528 \, a^{2} b^{4} c^{4} - 448 \, a^{3} b^{2} c^{5} - 512 \, a^{4} c^{6}\right)} d^{3} x^{4} + 2 \, {\left(3 \, b^{9} c - 28 \, a b^{7} c^{2} + 48 \, a^{2} b^{5} c^{3} + 192 \, a^{3} b^{3} c^{4} - 512 \, a^{4} b c^{5}\right)} d^{3} x^{3} + {\left(b^{10} - 2 \, a b^{8} c - 68 \, a^{2} b^{6} c^{2} + 368 \, a^{3} b^{4} c^{3} - 448 \, a^{4} b^{2} c^{4} - 256 \, a^{5} c^{5}\right)} d^{3} x^{2} + 2 \, {\left(a b^{9} - 10 \, a^{2} b^{7} c + 24 \, a^{3} b^{5} c^{2} + 32 \, a^{4} b^{3} c^{3} - 128 \, a^{5} b c^{4}\right)} d^{3} x + {\left(a^{2} b^{8} - 12 \, a^{3} b^{6} c + 48 \, a^{4} b^{4} c^{2} - 64 \, a^{5} b^{2} c^{3}\right)} d^{3}\right)}}"," ",0,"-1/6*(924*(4*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^3*x^6 + 12*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^3*x^5 + (13*b^8*c^2 - 148*a*b^6*c^3 + 528*a^2*b^4*c^4 - 448*a^3*b^2*c^5 - 512*a^4*c^6)*d^3*x^4 + 2*(3*b^9*c - 28*a*b^7*c^2 + 48*a^2*b^5*c^3 + 192*a^3*b^3*c^4 - 512*a^4*b*c^5)*d^3*x^3 + (b^10 - 2*a*b^8*c - 68*a^2*b^6*c^2 + 368*a^3*b^4*c^3 - 448*a^4*b^2*c^4 - 256*a^5*c^5)*d^3*x^2 + 2*(a*b^9 - 10*a^2*b^7*c + 24*a^3*b^5*c^2 + 32*a^4*b^3*c^3 - 128*a^5*b*c^4)*d^3*x + (a^2*b^8 - 12*a^3*b^6*c + 48*a^4*b^4*c^2 - 64*a^5*b^2*c^3)*d^3)*(c^8/((b^30 - 60*a*b^28*c + 1680*a^2*b^26*c^2 - 29120*a^3*b^24*c^3 + 349440*a^4*b^22*c^4 - 3075072*a^5*b^20*c^5 + 20500480*a^6*b^18*c^6 - 105431040*a^7*b^16*c^7 + 421724160*a^8*b^14*c^8 - 1312030720*a^9*b^12*c^9 + 3148873728*a^10*b^10*c^10 - 5725224960*a^11*b^8*c^11 + 7633633280*a^12*b^6*c^12 - 7046430720*a^13*b^4*c^13 + 4026531840*a^14*b^2*c^14 - 1073741824*a^15*c^15)*d^10))^(1/4)*arctan(-((b^22 - 44*a*b^20*c + 880*a^2*b^18*c^2 - 10560*a^3*b^16*c^3 + 84480*a^4*b^14*c^4 - 473088*a^5*b^12*c^5 + 1892352*a^6*b^10*c^6 - 5406720*a^7*b^8*c^7 + 10813440*a^8*b^6*c^8 - 14417920*a^9*b^4*c^9 + 11534336*a^10*b^2*c^10 - 4194304*a^11*c^11)*sqrt((b^16 - 32*a*b^14*c + 448*a^2*b^12*c^2 - 3584*a^3*b^10*c^3 + 17920*a^4*b^8*c^4 - 57344*a^5*b^6*c^5 + 114688*a^6*b^4*c^6 - 131072*a^7*b^2*c^7 + 65536*a^8*c^8)*d^6*sqrt(c^8/((b^30 - 60*a*b^28*c + 1680*a^2*b^26*c^2 - 29120*a^3*b^24*c^3 + 349440*a^4*b^22*c^4 - 3075072*a^5*b^20*c^5 + 20500480*a^6*b^18*c^6 - 105431040*a^7*b^16*c^7 + 421724160*a^8*b^14*c^8 - 1312030720*a^9*b^12*c^9 + 3148873728*a^10*b^10*c^10 - 5725224960*a^11*b^8*c^11 + 7633633280*a^12*b^6*c^12 - 7046430720*a^13*b^4*c^13 + 4026531840*a^14*b^2*c^14 - 1073741824*a^15*c^15)*d^10)) + 2*c^5*d*x + b*c^4*d)*d^7*(c^8/((b^30 - 60*a*b^28*c + 1680*a^2*b^26*c^2 - 29120*a^3*b^24*c^3 + 349440*a^4*b^22*c^4 - 3075072*a^5*b^20*c^5 + 20500480*a^6*b^18*c^6 - 105431040*a^7*b^16*c^7 + 421724160*a^8*b^14*c^8 - 1312030720*a^9*b^12*c^9 + 3148873728*a^10*b^10*c^10 - 5725224960*a^11*b^8*c^11 + 7633633280*a^12*b^6*c^12 - 7046430720*a^13*b^4*c^13 + 4026531840*a^14*b^2*c^14 - 1073741824*a^15*c^15)*d^10))^(3/4) - (b^22*c^2 - 44*a*b^20*c^3 + 880*a^2*b^18*c^4 - 10560*a^3*b^16*c^5 + 84480*a^4*b^14*c^6 - 473088*a^5*b^12*c^7 + 1892352*a^6*b^10*c^8 - 5406720*a^7*b^8*c^9 + 10813440*a^8*b^6*c^10 - 14417920*a^9*b^4*c^11 + 11534336*a^10*b^2*c^12 - 4194304*a^11*c^13)*sqrt(2*c*d*x + b*d)*d^7*(c^8/((b^30 - 60*a*b^28*c + 1680*a^2*b^26*c^2 - 29120*a^3*b^24*c^3 + 349440*a^4*b^22*c^4 - 3075072*a^5*b^20*c^5 + 20500480*a^6*b^18*c^6 - 105431040*a^7*b^16*c^7 + 421724160*a^8*b^14*c^8 - 1312030720*a^9*b^12*c^9 + 3148873728*a^10*b^10*c^10 - 5725224960*a^11*b^8*c^11 + 7633633280*a^12*b^6*c^12 - 7046430720*a^13*b^4*c^13 + 4026531840*a^14*b^2*c^14 - 1073741824*a^15*c^15)*d^10))^(3/4))/c^8) + 231*(4*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^3*x^6 + 12*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^3*x^5 + (13*b^8*c^2 - 148*a*b^6*c^3 + 528*a^2*b^4*c^4 - 448*a^3*b^2*c^5 - 512*a^4*c^6)*d^3*x^4 + 2*(3*b^9*c - 28*a*b^7*c^2 + 48*a^2*b^5*c^3 + 192*a^3*b^3*c^4 - 512*a^4*b*c^5)*d^3*x^3 + (b^10 - 2*a*b^8*c - 68*a^2*b^6*c^2 + 368*a^3*b^4*c^3 - 448*a^4*b^2*c^4 - 256*a^5*c^5)*d^3*x^2 + 2*(a*b^9 - 10*a^2*b^7*c + 24*a^3*b^5*c^2 + 32*a^4*b^3*c^3 - 128*a^5*b*c^4)*d^3*x + (a^2*b^8 - 12*a^3*b^6*c + 48*a^4*b^4*c^2 - 64*a^5*b^2*c^3)*d^3)*(c^8/((b^30 - 60*a*b^28*c + 1680*a^2*b^26*c^2 - 29120*a^3*b^24*c^3 + 349440*a^4*b^22*c^4 - 3075072*a^5*b^20*c^5 + 20500480*a^6*b^18*c^6 - 105431040*a^7*b^16*c^7 + 421724160*a^8*b^14*c^8 - 1312030720*a^9*b^12*c^9 + 3148873728*a^10*b^10*c^10 - 5725224960*a^11*b^8*c^11 + 7633633280*a^12*b^6*c^12 - 7046430720*a^13*b^4*c^13 + 4026531840*a^14*b^2*c^14 - 1073741824*a^15*c^15)*d^10))^(1/4)*log(77*(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)*d^3*(c^8/((b^30 - 60*a*b^28*c + 1680*a^2*b^26*c^2 - 29120*a^3*b^24*c^3 + 349440*a^4*b^22*c^4 - 3075072*a^5*b^20*c^5 + 20500480*a^6*b^18*c^6 - 105431040*a^7*b^16*c^7 + 421724160*a^8*b^14*c^8 - 1312030720*a^9*b^12*c^9 + 3148873728*a^10*b^10*c^10 - 5725224960*a^11*b^8*c^11 + 7633633280*a^12*b^6*c^12 - 7046430720*a^13*b^4*c^13 + 4026531840*a^14*b^2*c^14 - 1073741824*a^15*c^15)*d^10))^(1/4) + 77*sqrt(2*c*d*x + b*d)*c^2) - 231*(4*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^3*x^6 + 12*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^3*x^5 + (13*b^8*c^2 - 148*a*b^6*c^3 + 528*a^2*b^4*c^4 - 448*a^3*b^2*c^5 - 512*a^4*c^6)*d^3*x^4 + 2*(3*b^9*c - 28*a*b^7*c^2 + 48*a^2*b^5*c^3 + 192*a^3*b^3*c^4 - 512*a^4*b*c^5)*d^3*x^3 + (b^10 - 2*a*b^8*c - 68*a^2*b^6*c^2 + 368*a^3*b^4*c^3 - 448*a^4*b^2*c^4 - 256*a^5*c^5)*d^3*x^2 + 2*(a*b^9 - 10*a^2*b^7*c + 24*a^3*b^5*c^2 + 32*a^4*b^3*c^3 - 128*a^5*b*c^4)*d^3*x + (a^2*b^8 - 12*a^3*b^6*c + 48*a^4*b^4*c^2 - 64*a^5*b^2*c^3)*d^3)*(c^8/((b^30 - 60*a*b^28*c + 1680*a^2*b^26*c^2 - 29120*a^3*b^24*c^3 + 349440*a^4*b^22*c^4 - 3075072*a^5*b^20*c^5 + 20500480*a^6*b^18*c^6 - 105431040*a^7*b^16*c^7 + 421724160*a^8*b^14*c^8 - 1312030720*a^9*b^12*c^9 + 3148873728*a^10*b^10*c^10 - 5725224960*a^11*b^8*c^11 + 7633633280*a^12*b^6*c^12 - 7046430720*a^13*b^4*c^13 + 4026531840*a^14*b^2*c^14 - 1073741824*a^15*c^15)*d^10))^(1/4)*log(-77*(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)*d^3*(c^8/((b^30 - 60*a*b^28*c + 1680*a^2*b^26*c^2 - 29120*a^3*b^24*c^3 + 349440*a^4*b^22*c^4 - 3075072*a^5*b^20*c^5 + 20500480*a^6*b^18*c^6 - 105431040*a^7*b^16*c^7 + 421724160*a^8*b^14*c^8 - 1312030720*a^9*b^12*c^9 + 3148873728*a^10*b^10*c^10 - 5725224960*a^11*b^8*c^11 + 7633633280*a^12*b^6*c^12 - 7046430720*a^13*b^4*c^13 + 4026531840*a^14*b^2*c^14 - 1073741824*a^15*c^15)*d^10))^(1/4) + 77*sqrt(2*c*d*x + b*d)*c^2) - (308*c^4*x^4 + 616*b*c^3*x^3 - 3*b^4 + 57*a*b^2*c + 128*a^2*c^2 + 11*(31*b^2*c^2 + 44*a*c^3)*x^2 + 11*(3*b^3*c + 44*a*b*c^2)*x)*sqrt(2*c*d*x + b*d))/(4*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^3*x^6 + 12*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^3*x^5 + (13*b^8*c^2 - 148*a*b^6*c^3 + 528*a^2*b^4*c^4 - 448*a^3*b^2*c^5 - 512*a^4*c^6)*d^3*x^4 + 2*(3*b^9*c - 28*a*b^7*c^2 + 48*a^2*b^5*c^3 + 192*a^3*b^3*c^4 - 512*a^4*b*c^5)*d^3*x^3 + (b^10 - 2*a*b^8*c - 68*a^2*b^6*c^2 + 368*a^3*b^4*c^3 - 448*a^4*b^2*c^4 - 256*a^5*c^5)*d^3*x^2 + 2*(a*b^9 - 10*a^2*b^7*c + 24*a^3*b^5*c^2 + 32*a^4*b^3*c^3 - 128*a^5*b*c^4)*d^3*x + (a^2*b^8 - 12*a^3*b^6*c + 48*a^4*b^4*c^2 - 64*a^5*b^2*c^3)*d^3)","B",0
1319,1,4347,0,0.574101," ","integrate(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{2340 \, {\left(8 \, {\left(b^{8} c^{5} - 16 \, a b^{6} c^{6} + 96 \, a^{2} b^{4} c^{7} - 256 \, a^{3} b^{2} c^{8} + 256 \, a^{4} c^{9}\right)} d^{4} x^{7} + 28 \, {\left(b^{9} c^{4} - 16 \, a b^{7} c^{5} + 96 \, a^{2} b^{5} c^{6} - 256 \, a^{3} b^{3} c^{7} + 256 \, a^{4} b c^{8}\right)} d^{4} x^{6} + 2 \, {\left(19 \, b^{10} c^{3} - 296 \, a b^{8} c^{4} + 1696 \, a^{2} b^{6} c^{5} - 4096 \, a^{3} b^{4} c^{6} + 2816 \, a^{4} b^{2} c^{7} + 2048 \, a^{5} c^{8}\right)} d^{4} x^{5} + 5 \, {\left(5 \, b^{11} c^{2} - 72 \, a b^{9} c^{3} + 352 \, a^{2} b^{7} c^{4} - 512 \, a^{3} b^{5} c^{5} - 768 \, a^{4} b^{3} c^{6} + 2048 \, a^{5} b c^{7}\right)} d^{4} x^{4} + 4 \, {\left(2 \, b^{12} c - 23 \, a b^{10} c^{2} + 50 \, a^{2} b^{8} c^{3} + 320 \, a^{3} b^{6} c^{4} - 1600 \, a^{4} b^{4} c^{5} + 1792 \, a^{5} b^{2} c^{6} + 512 \, a^{6} c^{7}\right)} d^{4} x^{3} + {\left(b^{13} - 2 \, a b^{11} c - 116 \, a^{2} b^{9} c^{2} + 896 \, a^{3} b^{7} c^{3} - 2176 \, a^{4} b^{5} c^{4} + 512 \, a^{5} b^{3} c^{5} + 3072 \, a^{6} b c^{6}\right)} d^{4} x^{2} + 2 \, {\left(a b^{12} - 13 \, a^{2} b^{10} c + 48 \, a^{3} b^{8} c^{2} + 32 \, a^{4} b^{6} c^{3} - 512 \, a^{5} b^{4} c^{4} + 768 \, a^{6} b^{2} c^{5}\right)} d^{4} x + {\left(a^{2} b^{11} - 16 \, a^{3} b^{9} c + 96 \, a^{4} b^{7} c^{2} - 256 \, a^{5} b^{5} c^{3} + 256 \, a^{6} b^{3} c^{4}\right)} d^{4}\right)} \left(\frac{c^{8}}{{\left(b^{34} - 68 \, a b^{32} c + 2176 \, a^{2} b^{30} c^{2} - 43520 \, a^{3} b^{28} c^{3} + 609280 \, a^{4} b^{26} c^{4} - 6336512 \, a^{5} b^{24} c^{5} + 50692096 \, a^{6} b^{22} c^{6} - 318636032 \, a^{7} b^{20} c^{7} + 1593180160 \, a^{8} b^{18} c^{8} - 6372720640 \, a^{9} b^{16} c^{9} + 20392706048 \, a^{10} b^{14} c^{10} - 51908706304 \, a^{11} b^{12} c^{11} + 103817412608 \, a^{12} b^{10} c^{12} - 159719096320 \, a^{13} b^{8} c^{13} + 182536110080 \, a^{14} b^{6} c^{14} - 146028888064 \, a^{15} b^{4} c^{15} + 73014444032 \, a^{16} b^{2} c^{16} - 17179869184 \, a^{17} c^{17}\right)} d^{14}}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2 \, c^{13} d x + b c^{12} d + {\left(b^{18} c^{8} - 36 \, a b^{16} c^{9} + 576 \, a^{2} b^{14} c^{10} - 5376 \, a^{3} b^{12} c^{11} + 32256 \, a^{4} b^{10} c^{12} - 129024 \, a^{5} b^{8} c^{13} + 344064 \, a^{6} b^{6} c^{14} - 589824 \, a^{7} b^{4} c^{15} + 589824 \, a^{8} b^{2} c^{16} - 262144 \, a^{9} c^{17}\right)} d^{8} \sqrt{\frac{c^{8}}{{\left(b^{34} - 68 \, a b^{32} c + 2176 \, a^{2} b^{30} c^{2} - 43520 \, a^{3} b^{28} c^{3} + 609280 \, a^{4} b^{26} c^{4} - 6336512 \, a^{5} b^{24} c^{5} + 50692096 \, a^{6} b^{22} c^{6} - 318636032 \, a^{7} b^{20} c^{7} + 1593180160 \, a^{8} b^{18} c^{8} - 6372720640 \, a^{9} b^{16} c^{9} + 20392706048 \, a^{10} b^{14} c^{10} - 51908706304 \, a^{11} b^{12} c^{11} + 103817412608 \, a^{12} b^{10} c^{12} - 159719096320 \, a^{13} b^{8} c^{13} + 182536110080 \, a^{14} b^{6} c^{14} - 146028888064 \, a^{15} b^{4} c^{15} + 73014444032 \, a^{16} b^{2} c^{16} - 17179869184 \, a^{17} c^{17}\right)} d^{14}}}} {\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)} d^{3} \left(\frac{c^{8}}{{\left(b^{34} - 68 \, a b^{32} c + 2176 \, a^{2} b^{30} c^{2} - 43520 \, a^{3} b^{28} c^{3} + 609280 \, a^{4} b^{26} c^{4} - 6336512 \, a^{5} b^{24} c^{5} + 50692096 \, a^{6} b^{22} c^{6} - 318636032 \, a^{7} b^{20} c^{7} + 1593180160 \, a^{8} b^{18} c^{8} - 6372720640 \, a^{9} b^{16} c^{9} + 20392706048 \, a^{10} b^{14} c^{10} - 51908706304 \, a^{11} b^{12} c^{11} + 103817412608 \, a^{12} b^{10} c^{12} - 159719096320 \, a^{13} b^{8} c^{13} + 182536110080 \, a^{14} b^{6} c^{14} - 146028888064 \, a^{15} b^{4} c^{15} + 73014444032 \, a^{16} b^{2} c^{16} - 17179869184 \, a^{17} c^{17}\right)} d^{14}}\right)^{\frac{1}{4}} - {\left(b^{8} c^{6} - 16 \, a b^{6} c^{7} + 96 \, a^{2} b^{4} c^{8} - 256 \, a^{3} b^{2} c^{9} + 256 \, a^{4} c^{10}\right)} \sqrt{2 \, c d x + b d} d^{3} \left(\frac{c^{8}}{{\left(b^{34} - 68 \, a b^{32} c + 2176 \, a^{2} b^{30} c^{2} - 43520 \, a^{3} b^{28} c^{3} + 609280 \, a^{4} b^{26} c^{4} - 6336512 \, a^{5} b^{24} c^{5} + 50692096 \, a^{6} b^{22} c^{6} - 318636032 \, a^{7} b^{20} c^{7} + 1593180160 \, a^{8} b^{18} c^{8} - 6372720640 \, a^{9} b^{16} c^{9} + 20392706048 \, a^{10} b^{14} c^{10} - 51908706304 \, a^{11} b^{12} c^{11} + 103817412608 \, a^{12} b^{10} c^{12} - 159719096320 \, a^{13} b^{8} c^{13} + 182536110080 \, a^{14} b^{6} c^{14} - 146028888064 \, a^{15} b^{4} c^{15} + 73014444032 \, a^{16} b^{2} c^{16} - 17179869184 \, a^{17} c^{17}\right)} d^{14}}\right)^{\frac{1}{4}}}{c^{8}}\right) + 585 \, {\left(8 \, {\left(b^{8} c^{5} - 16 \, a b^{6} c^{6} + 96 \, a^{2} b^{4} c^{7} - 256 \, a^{3} b^{2} c^{8} + 256 \, a^{4} c^{9}\right)} d^{4} x^{7} + 28 \, {\left(b^{9} c^{4} - 16 \, a b^{7} c^{5} + 96 \, a^{2} b^{5} c^{6} - 256 \, a^{3} b^{3} c^{7} + 256 \, a^{4} b c^{8}\right)} d^{4} x^{6} + 2 \, {\left(19 \, b^{10} c^{3} - 296 \, a b^{8} c^{4} + 1696 \, a^{2} b^{6} c^{5} - 4096 \, a^{3} b^{4} c^{6} + 2816 \, a^{4} b^{2} c^{7} + 2048 \, a^{5} c^{8}\right)} d^{4} x^{5} + 5 \, {\left(5 \, b^{11} c^{2} - 72 \, a b^{9} c^{3} + 352 \, a^{2} b^{7} c^{4} - 512 \, a^{3} b^{5} c^{5} - 768 \, a^{4} b^{3} c^{6} + 2048 \, a^{5} b c^{7}\right)} d^{4} x^{4} + 4 \, {\left(2 \, b^{12} c - 23 \, a b^{10} c^{2} + 50 \, a^{2} b^{8} c^{3} + 320 \, a^{3} b^{6} c^{4} - 1600 \, a^{4} b^{4} c^{5} + 1792 \, a^{5} b^{2} c^{6} + 512 \, a^{6} c^{7}\right)} d^{4} x^{3} + {\left(b^{13} - 2 \, a b^{11} c - 116 \, a^{2} b^{9} c^{2} + 896 \, a^{3} b^{7} c^{3} - 2176 \, a^{4} b^{5} c^{4} + 512 \, a^{5} b^{3} c^{5} + 3072 \, a^{6} b c^{6}\right)} d^{4} x^{2} + 2 \, {\left(a b^{12} - 13 \, a^{2} b^{10} c + 48 \, a^{3} b^{8} c^{2} + 32 \, a^{4} b^{6} c^{3} - 512 \, a^{5} b^{4} c^{4} + 768 \, a^{6} b^{2} c^{5}\right)} d^{4} x + {\left(a^{2} b^{11} - 16 \, a^{3} b^{9} c + 96 \, a^{4} b^{7} c^{2} - 256 \, a^{5} b^{5} c^{3} + 256 \, a^{6} b^{3} c^{4}\right)} d^{4}\right)} \left(\frac{c^{8}}{{\left(b^{34} - 68 \, a b^{32} c + 2176 \, a^{2} b^{30} c^{2} - 43520 \, a^{3} b^{28} c^{3} + 609280 \, a^{4} b^{26} c^{4} - 6336512 \, a^{5} b^{24} c^{5} + 50692096 \, a^{6} b^{22} c^{6} - 318636032 \, a^{7} b^{20} c^{7} + 1593180160 \, a^{8} b^{18} c^{8} - 6372720640 \, a^{9} b^{16} c^{9} + 20392706048 \, a^{10} b^{14} c^{10} - 51908706304 \, a^{11} b^{12} c^{11} + 103817412608 \, a^{12} b^{10} c^{12} - 159719096320 \, a^{13} b^{8} c^{13} + 182536110080 \, a^{14} b^{6} c^{14} - 146028888064 \, a^{15} b^{4} c^{15} + 73014444032 \, a^{16} b^{2} c^{16} - 17179869184 \, a^{17} c^{17}\right)} d^{14}}\right)^{\frac{1}{4}} \log\left(1601613 \, {\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{11} \left(\frac{c^{8}}{{\left(b^{34} - 68 \, a b^{32} c + 2176 \, a^{2} b^{30} c^{2} - 43520 \, a^{3} b^{28} c^{3} + 609280 \, a^{4} b^{26} c^{4} - 6336512 \, a^{5} b^{24} c^{5} + 50692096 \, a^{6} b^{22} c^{6} - 318636032 \, a^{7} b^{20} c^{7} + 1593180160 \, a^{8} b^{18} c^{8} - 6372720640 \, a^{9} b^{16} c^{9} + 20392706048 \, a^{10} b^{14} c^{10} - 51908706304 \, a^{11} b^{12} c^{11} + 103817412608 \, a^{12} b^{10} c^{12} - 159719096320 \, a^{13} b^{8} c^{13} + 182536110080 \, a^{14} b^{6} c^{14} - 146028888064 \, a^{15} b^{4} c^{15} + 73014444032 \, a^{16} b^{2} c^{16} - 17179869184 \, a^{17} c^{17}\right)} d^{14}}\right)^{\frac{3}{4}} + 1601613 \, \sqrt{2 \, c d x + b d} c^{6}\right) - 585 \, {\left(8 \, {\left(b^{8} c^{5} - 16 \, a b^{6} c^{6} + 96 \, a^{2} b^{4} c^{7} - 256 \, a^{3} b^{2} c^{8} + 256 \, a^{4} c^{9}\right)} d^{4} x^{7} + 28 \, {\left(b^{9} c^{4} - 16 \, a b^{7} c^{5} + 96 \, a^{2} b^{5} c^{6} - 256 \, a^{3} b^{3} c^{7} + 256 \, a^{4} b c^{8}\right)} d^{4} x^{6} + 2 \, {\left(19 \, b^{10} c^{3} - 296 \, a b^{8} c^{4} + 1696 \, a^{2} b^{6} c^{5} - 4096 \, a^{3} b^{4} c^{6} + 2816 \, a^{4} b^{2} c^{7} + 2048 \, a^{5} c^{8}\right)} d^{4} x^{5} + 5 \, {\left(5 \, b^{11} c^{2} - 72 \, a b^{9} c^{3} + 352 \, a^{2} b^{7} c^{4} - 512 \, a^{3} b^{5} c^{5} - 768 \, a^{4} b^{3} c^{6} + 2048 \, a^{5} b c^{7}\right)} d^{4} x^{4} + 4 \, {\left(2 \, b^{12} c - 23 \, a b^{10} c^{2} + 50 \, a^{2} b^{8} c^{3} + 320 \, a^{3} b^{6} c^{4} - 1600 \, a^{4} b^{4} c^{5} + 1792 \, a^{5} b^{2} c^{6} + 512 \, a^{6} c^{7}\right)} d^{4} x^{3} + {\left(b^{13} - 2 \, a b^{11} c - 116 \, a^{2} b^{9} c^{2} + 896 \, a^{3} b^{7} c^{3} - 2176 \, a^{4} b^{5} c^{4} + 512 \, a^{5} b^{3} c^{5} + 3072 \, a^{6} b c^{6}\right)} d^{4} x^{2} + 2 \, {\left(a b^{12} - 13 \, a^{2} b^{10} c + 48 \, a^{3} b^{8} c^{2} + 32 \, a^{4} b^{6} c^{3} - 512 \, a^{5} b^{4} c^{4} + 768 \, a^{6} b^{2} c^{5}\right)} d^{4} x + {\left(a^{2} b^{11} - 16 \, a^{3} b^{9} c + 96 \, a^{4} b^{7} c^{2} - 256 \, a^{5} b^{5} c^{3} + 256 \, a^{6} b^{3} c^{4}\right)} d^{4}\right)} \left(\frac{c^{8}}{{\left(b^{34} - 68 \, a b^{32} c + 2176 \, a^{2} b^{30} c^{2} - 43520 \, a^{3} b^{28} c^{3} + 609280 \, a^{4} b^{26} c^{4} - 6336512 \, a^{5} b^{24} c^{5} + 50692096 \, a^{6} b^{22} c^{6} - 318636032 \, a^{7} b^{20} c^{7} + 1593180160 \, a^{8} b^{18} c^{8} - 6372720640 \, a^{9} b^{16} c^{9} + 20392706048 \, a^{10} b^{14} c^{10} - 51908706304 \, a^{11} b^{12} c^{11} + 103817412608 \, a^{12} b^{10} c^{12} - 159719096320 \, a^{13} b^{8} c^{13} + 182536110080 \, a^{14} b^{6} c^{14} - 146028888064 \, a^{15} b^{4} c^{15} + 73014444032 \, a^{16} b^{2} c^{16} - 17179869184 \, a^{17} c^{17}\right)} d^{14}}\right)^{\frac{1}{4}} \log\left(-1601613 \, {\left(b^{26} - 52 \, a b^{24} c + 1248 \, a^{2} b^{22} c^{2} - 18304 \, a^{3} b^{20} c^{3} + 183040 \, a^{4} b^{18} c^{4} - 1317888 \, a^{5} b^{16} c^{5} + 7028736 \, a^{6} b^{14} c^{6} - 28114944 \, a^{7} b^{12} c^{7} + 84344832 \, a^{8} b^{10} c^{8} - 187432960 \, a^{9} b^{8} c^{9} + 299892736 \, a^{10} b^{6} c^{10} - 327155712 \, a^{11} b^{4} c^{11} + 218103808 \, a^{12} b^{2} c^{12} - 67108864 \, a^{13} c^{13}\right)} d^{11} \left(\frac{c^{8}}{{\left(b^{34} - 68 \, a b^{32} c + 2176 \, a^{2} b^{30} c^{2} - 43520 \, a^{3} b^{28} c^{3} + 609280 \, a^{4} b^{26} c^{4} - 6336512 \, a^{5} b^{24} c^{5} + 50692096 \, a^{6} b^{22} c^{6} - 318636032 \, a^{7} b^{20} c^{7} + 1593180160 \, a^{8} b^{18} c^{8} - 6372720640 \, a^{9} b^{16} c^{9} + 20392706048 \, a^{10} b^{14} c^{10} - 51908706304 \, a^{11} b^{12} c^{11} + 103817412608 \, a^{12} b^{10} c^{12} - 159719096320 \, a^{13} b^{8} c^{13} + 182536110080 \, a^{14} b^{6} c^{14} - 146028888064 \, a^{15} b^{4} c^{15} + 73014444032 \, a^{16} b^{2} c^{16} - 17179869184 \, a^{17} c^{17}\right)} d^{14}}\right)^{\frac{3}{4}} + 1601613 \, \sqrt{2 \, c d x + b d} c^{6}\right) - {\left(9360 \, c^{6} x^{6} + 28080 \, b c^{5} x^{5} - 5 \, b^{6} + 125 \, a b^{4} c + 2048 \, a^{2} b^{2} c^{2} - 512 \, a^{3} c^{3} + 2808 \, {\left(11 \, b^{2} c^{4} + 6 \, a c^{5}\right)} x^{4} + 3744 \, {\left(4 \, b^{3} c^{3} + 9 \, a b c^{4}\right)} x^{3} + 13 \, {\left(221 \, b^{4} c^{2} + 1688 \, a b^{2} c^{3} + 512 \, a^{2} c^{4}\right)} x^{2} + 13 \, {\left(5 \, b^{5} c + 392 \, a b^{3} c^{2} + 512 \, a^{2} b c^{3}\right)} x\right)} \sqrt{2 \, c d x + b d}}{10 \, {\left(8 \, {\left(b^{8} c^{5} - 16 \, a b^{6} c^{6} + 96 \, a^{2} b^{4} c^{7} - 256 \, a^{3} b^{2} c^{8} + 256 \, a^{4} c^{9}\right)} d^{4} x^{7} + 28 \, {\left(b^{9} c^{4} - 16 \, a b^{7} c^{5} + 96 \, a^{2} b^{5} c^{6} - 256 \, a^{3} b^{3} c^{7} + 256 \, a^{4} b c^{8}\right)} d^{4} x^{6} + 2 \, {\left(19 \, b^{10} c^{3} - 296 \, a b^{8} c^{4} + 1696 \, a^{2} b^{6} c^{5} - 4096 \, a^{3} b^{4} c^{6} + 2816 \, a^{4} b^{2} c^{7} + 2048 \, a^{5} c^{8}\right)} d^{4} x^{5} + 5 \, {\left(5 \, b^{11} c^{2} - 72 \, a b^{9} c^{3} + 352 \, a^{2} b^{7} c^{4} - 512 \, a^{3} b^{5} c^{5} - 768 \, a^{4} b^{3} c^{6} + 2048 \, a^{5} b c^{7}\right)} d^{4} x^{4} + 4 \, {\left(2 \, b^{12} c - 23 \, a b^{10} c^{2} + 50 \, a^{2} b^{8} c^{3} + 320 \, a^{3} b^{6} c^{4} - 1600 \, a^{4} b^{4} c^{5} + 1792 \, a^{5} b^{2} c^{6} + 512 \, a^{6} c^{7}\right)} d^{4} x^{3} + {\left(b^{13} - 2 \, a b^{11} c - 116 \, a^{2} b^{9} c^{2} + 896 \, a^{3} b^{7} c^{3} - 2176 \, a^{4} b^{5} c^{4} + 512 \, a^{5} b^{3} c^{5} + 3072 \, a^{6} b c^{6}\right)} d^{4} x^{2} + 2 \, {\left(a b^{12} - 13 \, a^{2} b^{10} c + 48 \, a^{3} b^{8} c^{2} + 32 \, a^{4} b^{6} c^{3} - 512 \, a^{5} b^{4} c^{4} + 768 \, a^{6} b^{2} c^{5}\right)} d^{4} x + {\left(a^{2} b^{11} - 16 \, a^{3} b^{9} c + 96 \, a^{4} b^{7} c^{2} - 256 \, a^{5} b^{5} c^{3} + 256 \, a^{6} b^{3} c^{4}\right)} d^{4}\right)}}"," ",0,"-1/10*(2340*(8*(b^8*c^5 - 16*a*b^6*c^6 + 96*a^2*b^4*c^7 - 256*a^3*b^2*c^8 + 256*a^4*c^9)*d^4*x^7 + 28*(b^9*c^4 - 16*a*b^7*c^5 + 96*a^2*b^5*c^6 - 256*a^3*b^3*c^7 + 256*a^4*b*c^8)*d^4*x^6 + 2*(19*b^10*c^3 - 296*a*b^8*c^4 + 1696*a^2*b^6*c^5 - 4096*a^3*b^4*c^6 + 2816*a^4*b^2*c^7 + 2048*a^5*c^8)*d^4*x^5 + 5*(5*b^11*c^2 - 72*a*b^9*c^3 + 352*a^2*b^7*c^4 - 512*a^3*b^5*c^5 - 768*a^4*b^3*c^6 + 2048*a^5*b*c^7)*d^4*x^4 + 4*(2*b^12*c - 23*a*b^10*c^2 + 50*a^2*b^8*c^3 + 320*a^3*b^6*c^4 - 1600*a^4*b^4*c^5 + 1792*a^5*b^2*c^6 + 512*a^6*c^7)*d^4*x^3 + (b^13 - 2*a*b^11*c - 116*a^2*b^9*c^2 + 896*a^3*b^7*c^3 - 2176*a^4*b^5*c^4 + 512*a^5*b^3*c^5 + 3072*a^6*b*c^6)*d^4*x^2 + 2*(a*b^12 - 13*a^2*b^10*c + 48*a^3*b^8*c^2 + 32*a^4*b^6*c^3 - 512*a^5*b^4*c^4 + 768*a^6*b^2*c^5)*d^4*x + (a^2*b^11 - 16*a^3*b^9*c + 96*a^4*b^7*c^2 - 256*a^5*b^5*c^3 + 256*a^6*b^3*c^4)*d^4)*(c^8/((b^34 - 68*a*b^32*c + 2176*a^2*b^30*c^2 - 43520*a^3*b^28*c^3 + 609280*a^4*b^26*c^4 - 6336512*a^5*b^24*c^5 + 50692096*a^6*b^22*c^6 - 318636032*a^7*b^20*c^7 + 1593180160*a^8*b^18*c^8 - 6372720640*a^9*b^16*c^9 + 20392706048*a^10*b^14*c^10 - 51908706304*a^11*b^12*c^11 + 103817412608*a^12*b^10*c^12 - 159719096320*a^13*b^8*c^13 + 182536110080*a^14*b^6*c^14 - 146028888064*a^15*b^4*c^15 + 73014444032*a^16*b^2*c^16 - 17179869184*a^17*c^17)*d^14))^(1/4)*arctan((sqrt(2*c^13*d*x + b*c^12*d + (b^18*c^8 - 36*a*b^16*c^9 + 576*a^2*b^14*c^10 - 5376*a^3*b^12*c^11 + 32256*a^4*b^10*c^12 - 129024*a^5*b^8*c^13 + 344064*a^6*b^6*c^14 - 589824*a^7*b^4*c^15 + 589824*a^8*b^2*c^16 - 262144*a^9*c^17)*d^8*sqrt(c^8/((b^34 - 68*a*b^32*c + 2176*a^2*b^30*c^2 - 43520*a^3*b^28*c^3 + 609280*a^4*b^26*c^4 - 6336512*a^5*b^24*c^5 + 50692096*a^6*b^22*c^6 - 318636032*a^7*b^20*c^7 + 1593180160*a^8*b^18*c^8 - 6372720640*a^9*b^16*c^9 + 20392706048*a^10*b^14*c^10 - 51908706304*a^11*b^12*c^11 + 103817412608*a^12*b^10*c^12 - 159719096320*a^13*b^8*c^13 + 182536110080*a^14*b^6*c^14 - 146028888064*a^15*b^4*c^15 + 73014444032*a^16*b^2*c^16 - 17179869184*a^17*c^17)*d^14)))*(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)*d^3*(c^8/((b^34 - 68*a*b^32*c + 2176*a^2*b^30*c^2 - 43520*a^3*b^28*c^3 + 609280*a^4*b^26*c^4 - 6336512*a^5*b^24*c^5 + 50692096*a^6*b^22*c^6 - 318636032*a^7*b^20*c^7 + 1593180160*a^8*b^18*c^8 - 6372720640*a^9*b^16*c^9 + 20392706048*a^10*b^14*c^10 - 51908706304*a^11*b^12*c^11 + 103817412608*a^12*b^10*c^12 - 159719096320*a^13*b^8*c^13 + 182536110080*a^14*b^6*c^14 - 146028888064*a^15*b^4*c^15 + 73014444032*a^16*b^2*c^16 - 17179869184*a^17*c^17)*d^14))^(1/4) - (b^8*c^6 - 16*a*b^6*c^7 + 96*a^2*b^4*c^8 - 256*a^3*b^2*c^9 + 256*a^4*c^10)*sqrt(2*c*d*x + b*d)*d^3*(c^8/((b^34 - 68*a*b^32*c + 2176*a^2*b^30*c^2 - 43520*a^3*b^28*c^3 + 609280*a^4*b^26*c^4 - 6336512*a^5*b^24*c^5 + 50692096*a^6*b^22*c^6 - 318636032*a^7*b^20*c^7 + 1593180160*a^8*b^18*c^8 - 6372720640*a^9*b^16*c^9 + 20392706048*a^10*b^14*c^10 - 51908706304*a^11*b^12*c^11 + 103817412608*a^12*b^10*c^12 - 159719096320*a^13*b^8*c^13 + 182536110080*a^14*b^6*c^14 - 146028888064*a^15*b^4*c^15 + 73014444032*a^16*b^2*c^16 - 17179869184*a^17*c^17)*d^14))^(1/4))/c^8) + 585*(8*(b^8*c^5 - 16*a*b^6*c^6 + 96*a^2*b^4*c^7 - 256*a^3*b^2*c^8 + 256*a^4*c^9)*d^4*x^7 + 28*(b^9*c^4 - 16*a*b^7*c^5 + 96*a^2*b^5*c^6 - 256*a^3*b^3*c^7 + 256*a^4*b*c^8)*d^4*x^6 + 2*(19*b^10*c^3 - 296*a*b^8*c^4 + 1696*a^2*b^6*c^5 - 4096*a^3*b^4*c^6 + 2816*a^4*b^2*c^7 + 2048*a^5*c^8)*d^4*x^5 + 5*(5*b^11*c^2 - 72*a*b^9*c^3 + 352*a^2*b^7*c^4 - 512*a^3*b^5*c^5 - 768*a^4*b^3*c^6 + 2048*a^5*b*c^7)*d^4*x^4 + 4*(2*b^12*c - 23*a*b^10*c^2 + 50*a^2*b^8*c^3 + 320*a^3*b^6*c^4 - 1600*a^4*b^4*c^5 + 1792*a^5*b^2*c^6 + 512*a^6*c^7)*d^4*x^3 + (b^13 - 2*a*b^11*c - 116*a^2*b^9*c^2 + 896*a^3*b^7*c^3 - 2176*a^4*b^5*c^4 + 512*a^5*b^3*c^5 + 3072*a^6*b*c^6)*d^4*x^2 + 2*(a*b^12 - 13*a^2*b^10*c + 48*a^3*b^8*c^2 + 32*a^4*b^6*c^3 - 512*a^5*b^4*c^4 + 768*a^6*b^2*c^5)*d^4*x + (a^2*b^11 - 16*a^3*b^9*c + 96*a^4*b^7*c^2 - 256*a^5*b^5*c^3 + 256*a^6*b^3*c^4)*d^4)*(c^8/((b^34 - 68*a*b^32*c + 2176*a^2*b^30*c^2 - 43520*a^3*b^28*c^3 + 609280*a^4*b^26*c^4 - 6336512*a^5*b^24*c^5 + 50692096*a^6*b^22*c^6 - 318636032*a^7*b^20*c^7 + 1593180160*a^8*b^18*c^8 - 6372720640*a^9*b^16*c^9 + 20392706048*a^10*b^14*c^10 - 51908706304*a^11*b^12*c^11 + 103817412608*a^12*b^10*c^12 - 159719096320*a^13*b^8*c^13 + 182536110080*a^14*b^6*c^14 - 146028888064*a^15*b^4*c^15 + 73014444032*a^16*b^2*c^16 - 17179869184*a^17*c^17)*d^14))^(1/4)*log(1601613*(b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^11*(c^8/((b^34 - 68*a*b^32*c + 2176*a^2*b^30*c^2 - 43520*a^3*b^28*c^3 + 609280*a^4*b^26*c^4 - 6336512*a^5*b^24*c^5 + 50692096*a^6*b^22*c^6 - 318636032*a^7*b^20*c^7 + 1593180160*a^8*b^18*c^8 - 6372720640*a^9*b^16*c^9 + 20392706048*a^10*b^14*c^10 - 51908706304*a^11*b^12*c^11 + 103817412608*a^12*b^10*c^12 - 159719096320*a^13*b^8*c^13 + 182536110080*a^14*b^6*c^14 - 146028888064*a^15*b^4*c^15 + 73014444032*a^16*b^2*c^16 - 17179869184*a^17*c^17)*d^14))^(3/4) + 1601613*sqrt(2*c*d*x + b*d)*c^6) - 585*(8*(b^8*c^5 - 16*a*b^6*c^6 + 96*a^2*b^4*c^7 - 256*a^3*b^2*c^8 + 256*a^4*c^9)*d^4*x^7 + 28*(b^9*c^4 - 16*a*b^7*c^5 + 96*a^2*b^5*c^6 - 256*a^3*b^3*c^7 + 256*a^4*b*c^8)*d^4*x^6 + 2*(19*b^10*c^3 - 296*a*b^8*c^4 + 1696*a^2*b^6*c^5 - 4096*a^3*b^4*c^6 + 2816*a^4*b^2*c^7 + 2048*a^5*c^8)*d^4*x^5 + 5*(5*b^11*c^2 - 72*a*b^9*c^3 + 352*a^2*b^7*c^4 - 512*a^3*b^5*c^5 - 768*a^4*b^3*c^6 + 2048*a^5*b*c^7)*d^4*x^4 + 4*(2*b^12*c - 23*a*b^10*c^2 + 50*a^2*b^8*c^3 + 320*a^3*b^6*c^4 - 1600*a^4*b^4*c^5 + 1792*a^5*b^2*c^6 + 512*a^6*c^7)*d^4*x^3 + (b^13 - 2*a*b^11*c - 116*a^2*b^9*c^2 + 896*a^3*b^7*c^3 - 2176*a^4*b^5*c^4 + 512*a^5*b^3*c^5 + 3072*a^6*b*c^6)*d^4*x^2 + 2*(a*b^12 - 13*a^2*b^10*c + 48*a^3*b^8*c^2 + 32*a^4*b^6*c^3 - 512*a^5*b^4*c^4 + 768*a^6*b^2*c^5)*d^4*x + (a^2*b^11 - 16*a^3*b^9*c + 96*a^4*b^7*c^2 - 256*a^5*b^5*c^3 + 256*a^6*b^3*c^4)*d^4)*(c^8/((b^34 - 68*a*b^32*c + 2176*a^2*b^30*c^2 - 43520*a^3*b^28*c^3 + 609280*a^4*b^26*c^4 - 6336512*a^5*b^24*c^5 + 50692096*a^6*b^22*c^6 - 318636032*a^7*b^20*c^7 + 1593180160*a^8*b^18*c^8 - 6372720640*a^9*b^16*c^9 + 20392706048*a^10*b^14*c^10 - 51908706304*a^11*b^12*c^11 + 103817412608*a^12*b^10*c^12 - 159719096320*a^13*b^8*c^13 + 182536110080*a^14*b^6*c^14 - 146028888064*a^15*b^4*c^15 + 73014444032*a^16*b^2*c^16 - 17179869184*a^17*c^17)*d^14))^(1/4)*log(-1601613*(b^26 - 52*a*b^24*c + 1248*a^2*b^22*c^2 - 18304*a^3*b^20*c^3 + 183040*a^4*b^18*c^4 - 1317888*a^5*b^16*c^5 + 7028736*a^6*b^14*c^6 - 28114944*a^7*b^12*c^7 + 84344832*a^8*b^10*c^8 - 187432960*a^9*b^8*c^9 + 299892736*a^10*b^6*c^10 - 327155712*a^11*b^4*c^11 + 218103808*a^12*b^2*c^12 - 67108864*a^13*c^13)*d^11*(c^8/((b^34 - 68*a*b^32*c + 2176*a^2*b^30*c^2 - 43520*a^3*b^28*c^3 + 609280*a^4*b^26*c^4 - 6336512*a^5*b^24*c^5 + 50692096*a^6*b^22*c^6 - 318636032*a^7*b^20*c^7 + 1593180160*a^8*b^18*c^8 - 6372720640*a^9*b^16*c^9 + 20392706048*a^10*b^14*c^10 - 51908706304*a^11*b^12*c^11 + 103817412608*a^12*b^10*c^12 - 159719096320*a^13*b^8*c^13 + 182536110080*a^14*b^6*c^14 - 146028888064*a^15*b^4*c^15 + 73014444032*a^16*b^2*c^16 - 17179869184*a^17*c^17)*d^14))^(3/4) + 1601613*sqrt(2*c*d*x + b*d)*c^6) - (9360*c^6*x^6 + 28080*b*c^5*x^5 - 5*b^6 + 125*a*b^4*c + 2048*a^2*b^2*c^2 - 512*a^3*c^3 + 2808*(11*b^2*c^4 + 6*a*c^5)*x^4 + 3744*(4*b^3*c^3 + 9*a*b*c^4)*x^3 + 13*(221*b^4*c^2 + 1688*a*b^2*c^3 + 512*a^2*c^4)*x^2 + 13*(5*b^5*c + 392*a*b^3*c^2 + 512*a^2*b*c^3)*x)*sqrt(2*c*d*x + b*d))/(8*(b^8*c^5 - 16*a*b^6*c^6 + 96*a^2*b^4*c^7 - 256*a^3*b^2*c^8 + 256*a^4*c^9)*d^4*x^7 + 28*(b^9*c^4 - 16*a*b^7*c^5 + 96*a^2*b^5*c^6 - 256*a^3*b^3*c^7 + 256*a^4*b*c^8)*d^4*x^6 + 2*(19*b^10*c^3 - 296*a*b^8*c^4 + 1696*a^2*b^6*c^5 - 4096*a^3*b^4*c^6 + 2816*a^4*b^2*c^7 + 2048*a^5*c^8)*d^4*x^5 + 5*(5*b^11*c^2 - 72*a*b^9*c^3 + 352*a^2*b^7*c^4 - 512*a^3*b^5*c^5 - 768*a^4*b^3*c^6 + 2048*a^5*b*c^7)*d^4*x^4 + 4*(2*b^12*c - 23*a*b^10*c^2 + 50*a^2*b^8*c^3 + 320*a^3*b^6*c^4 - 1600*a^4*b^4*c^5 + 1792*a^5*b^2*c^6 + 512*a^6*c^7)*d^4*x^3 + (b^13 - 2*a*b^11*c - 116*a^2*b^9*c^2 + 896*a^3*b^7*c^3 - 2176*a^4*b^5*c^4 + 512*a^5*b^3*c^5 + 3072*a^6*b*c^6)*d^4*x^2 + 2*(a*b^12 - 13*a^2*b^10*c + 48*a^3*b^8*c^2 + 32*a^4*b^6*c^3 - 512*a^5*b^4*c^4 + 768*a^6*b^2*c^5)*d^4*x + (a^2*b^11 - 16*a^3*b^9*c + 96*a^4*b^7*c^2 - 256*a^5*b^5*c^3 + 256*a^6*b^3*c^4)*d^4)","B",0
1320,1,200,0,0.415959," ","integrate((1+2*x)^(7/2)/(x^2+x+1),x, algorithm=""fricas"")","-6 \cdot 3^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1} - \frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} - 1\right) - 6 \cdot 3^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1} - \frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 1\right) + \frac{3}{2} \cdot 3^{\frac{1}{4}} \sqrt{2} \log\left(3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) - \frac{3}{2} \cdot 3^{\frac{1}{4}} \sqrt{2} \log\left(-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) + \frac{8}{5} \, {\left(2 \, x^{2} + 2 \, x - 7\right)} \sqrt{2 \, x + 1}"," ",0,"-6*3^(1/4)*sqrt(2)*arctan(1/3*3^(3/4)*sqrt(2)*sqrt(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 1/3*3^(3/4)*sqrt(2)*sqrt(2*x + 1) - 1) - 6*3^(1/4)*sqrt(2)*arctan(1/3*3^(3/4)*sqrt(2)*sqrt(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 1/3*3^(3/4)*sqrt(2)*sqrt(2*x + 1) + 1) + 3/2*3^(1/4)*sqrt(2)*log(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 3/2*3^(1/4)*sqrt(2)*log(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) + 8/5*(2*x^2 + 2*x - 7)*sqrt(2*x + 1)","A",0
1321,1,199,0,0.416728," ","integrate((1+2*x)^(5/2)/(x^2+x+1),x, algorithm=""fricas"")","2 \cdot 27^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{9} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 18 \, x + 9 \, \sqrt{3} + 9} - \frac{1}{3} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} - 1\right) + 2 \cdot 27^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{27} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{-9 \cdot 27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 162 \, x + 81 \, \sqrt{3} + 81} - \frac{1}{3} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 1\right) + \frac{1}{2} \cdot 27^{\frac{1}{4}} \sqrt{2} \log\left(9 \cdot 27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 162 \, x + 81 \, \sqrt{3} + 81\right) - \frac{1}{2} \cdot 27^{\frac{1}{4}} \sqrt{2} \log\left(-9 \cdot 27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 162 \, x + 81 \, \sqrt{3} + 81\right) + \frac{4}{3} \, {\left(2 \, x + 1\right)}^{\frac{3}{2}}"," ",0,"2*27^(1/4)*sqrt(2)*arctan(1/9*27^(1/4)*sqrt(2)*sqrt(27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 18*x + 9*sqrt(3) + 9) - 1/3*27^(1/4)*sqrt(2)*sqrt(2*x + 1) - 1) + 2*27^(1/4)*sqrt(2)*arctan(1/27*27^(1/4)*sqrt(2)*sqrt(-9*27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 162*x + 81*sqrt(3) + 81) - 1/3*27^(1/4)*sqrt(2)*sqrt(2*x + 1) + 1) + 1/2*27^(1/4)*sqrt(2)*log(9*27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 162*x + 81*sqrt(3) + 81) - 1/2*27^(1/4)*sqrt(2)*log(-9*27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 162*x + 81*sqrt(3) + 81) + 4/3*(2*x + 1)^(3/2)","A",0
1322,1,190,0,0.421195," ","integrate((1+2*x)^(3/2)/(x^2+x+1),x, algorithm=""fricas"")","2 \cdot 3^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1} - \frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} - 1\right) + 2 \cdot 3^{\frac{1}{4}} \sqrt{2} \arctan\left(\frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1} - \frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 1\right) - \frac{1}{2} \cdot 3^{\frac{1}{4}} \sqrt{2} \log\left(3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) + \frac{1}{2} \cdot 3^{\frac{1}{4}} \sqrt{2} \log\left(-3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1\right) + 4 \, \sqrt{2 \, x + 1}"," ",0,"2*3^(1/4)*sqrt(2)*arctan(1/3*3^(3/4)*sqrt(2)*sqrt(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 1/3*3^(3/4)*sqrt(2)*sqrt(2*x + 1) - 1) + 2*3^(1/4)*sqrt(2)*arctan(1/3*3^(3/4)*sqrt(2)*sqrt(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 1/3*3^(3/4)*sqrt(2)*sqrt(2*x + 1) + 1) - 1/2*3^(1/4)*sqrt(2)*log(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) + 1/2*3^(1/4)*sqrt(2)*log(-3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) + 4*sqrt(2*x + 1)","A",0
1323,1,188,0,0.428123," ","integrate((1+2*x)^(1/2)/(x^2+x+1),x, algorithm=""fricas"")","-\frac{2}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1} - \frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} - 1\right) - \frac{2}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{-4 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 8 \, x + 4 \, \sqrt{3} + 4} - \frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 1\right) - \frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} \log\left(4 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 8 \, x + 4 \, \sqrt{3} + 4\right) + \frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} \log\left(-4 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 8 \, x + 4 \, \sqrt{3} + 4\right)"," ",0,"-2/3*3^(3/4)*sqrt(2)*arctan(1/3*3^(3/4)*sqrt(2)*sqrt(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 1/3*3^(3/4)*sqrt(2)*sqrt(2*x + 1) - 1) - 2/3*3^(3/4)*sqrt(2)*arctan(1/6*3^(3/4)*sqrt(2)*sqrt(-4*3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 8*x + 4*sqrt(3) + 4) - 1/3*3^(3/4)*sqrt(2)*sqrt(2*x + 1) + 1) - 1/6*3^(3/4)*sqrt(2)*log(4*3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 8*x + 4*sqrt(3) + 4) + 1/6*3^(3/4)*sqrt(2)*log(-4*3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 8*x + 4*sqrt(3) + 4)","A",0
1324,1,190,0,0.438062," ","integrate(1/(1+2*x)^(1/2)/(x^2+x+1),x, algorithm=""fricas"")","-\frac{2}{27} \cdot 27^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{9} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 18 \, x + 9 \, \sqrt{3} + 9} - \frac{1}{3} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} - 1\right) - \frac{2}{27} \cdot 27^{\frac{3}{4}} \sqrt{2} \arctan\left(\frac{1}{54} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{-36 \cdot 27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 648 \, x + 324 \, \sqrt{3} + 324} - \frac{1}{3} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 1\right) + \frac{1}{54} \cdot 27^{\frac{3}{4}} \sqrt{2} \log\left(36 \cdot 27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 648 \, x + 324 \, \sqrt{3} + 324\right) - \frac{1}{54} \cdot 27^{\frac{3}{4}} \sqrt{2} \log\left(-36 \cdot 27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 648 \, x + 324 \, \sqrt{3} + 324\right)"," ",0,"-2/27*27^(3/4)*sqrt(2)*arctan(1/9*27^(1/4)*sqrt(2)*sqrt(27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 18*x + 9*sqrt(3) + 9) - 1/3*27^(1/4)*sqrt(2)*sqrt(2*x + 1) - 1) - 2/27*27^(3/4)*sqrt(2)*arctan(1/54*27^(1/4)*sqrt(2)*sqrt(-36*27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 648*x + 324*sqrt(3) + 324) - 1/3*27^(1/4)*sqrt(2)*sqrt(2*x + 1) + 1) + 1/54*27^(3/4)*sqrt(2)*log(36*27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 648*x + 324*sqrt(3) + 324) - 1/54*27^(3/4)*sqrt(2)*log(-36*27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 648*x + 324*sqrt(3) + 324)","A",0
1325,1,225,0,0.416885," ","integrate(1/(1+2*x)^(3/2)/(x^2+x+1),x, algorithm=""fricas"")","\frac{4 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(2 \, x + 1\right)} \arctan\left(\frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 2 \, x + \sqrt{3} + 1} - \frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} - 1\right) + 4 \cdot 3^{\frac{3}{4}} \sqrt{2} {\left(2 \, x + 1\right)} \arctan\left(\frac{1}{6} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{-4 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 8 \, x + 4 \, \sqrt{3} + 4} - \frac{1}{3} \cdot 3^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 1\right) + 3^{\frac{3}{4}} \sqrt{2} {\left(2 \, x + 1\right)} \log\left(4 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 8 \, x + 4 \, \sqrt{3} + 4\right) - 3^{\frac{3}{4}} \sqrt{2} {\left(2 \, x + 1\right)} \log\left(-4 \cdot 3^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 8 \, x + 4 \, \sqrt{3} + 4\right) - 24 \, \sqrt{2 \, x + 1}}{18 \, {\left(2 \, x + 1\right)}}"," ",0,"1/18*(4*3^(3/4)*sqrt(2)*(2*x + 1)*arctan(1/3*3^(3/4)*sqrt(2)*sqrt(3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 2*x + sqrt(3) + 1) - 1/3*3^(3/4)*sqrt(2)*sqrt(2*x + 1) - 1) + 4*3^(3/4)*sqrt(2)*(2*x + 1)*arctan(1/6*3^(3/4)*sqrt(2)*sqrt(-4*3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 8*x + 4*sqrt(3) + 4) - 1/3*3^(3/4)*sqrt(2)*sqrt(2*x + 1) + 1) + 3^(3/4)*sqrt(2)*(2*x + 1)*log(4*3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 8*x + 4*sqrt(3) + 4) - 3^(3/4)*sqrt(2)*(2*x + 1)*log(-4*3^(1/4)*sqrt(2)*sqrt(2*x + 1) + 8*x + 4*sqrt(3) + 4) - 24*sqrt(2*x + 1))/(2*x + 1)","A",0
1326,1,252,0,0.414180," ","integrate(1/(1+2*x)^(5/2)/(x^2+x+1),x, algorithm=""fricas"")","\frac{4 \cdot 27^{\frac{3}{4}} \sqrt{2} {\left(4 \, x^{2} + 4 \, x + 1\right)} \arctan\left(\frac{1}{9} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 18 \, x + 9 \, \sqrt{3} + 9} - \frac{1}{3} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} - 1\right) + 4 \cdot 27^{\frac{3}{4}} \sqrt{2} {\left(4 \, x^{2} + 4 \, x + 1\right)} \arctan\left(\frac{1}{54} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{-36 \cdot 27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 648 \, x + 324 \, \sqrt{3} + 324} - \frac{1}{3} \cdot 27^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 1\right) - 27^{\frac{3}{4}} \sqrt{2} {\left(4 \, x^{2} + 4 \, x + 1\right)} \log\left(36 \cdot 27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 648 \, x + 324 \, \sqrt{3} + 324\right) + 27^{\frac{3}{4}} \sqrt{2} {\left(4 \, x^{2} + 4 \, x + 1\right)} \log\left(-36 \cdot 27^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} + 648 \, x + 324 \, \sqrt{3} + 324\right) - 72 \, \sqrt{2 \, x + 1}}{162 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}}"," ",0,"1/162*(4*27^(3/4)*sqrt(2)*(4*x^2 + 4*x + 1)*arctan(1/9*27^(1/4)*sqrt(2)*sqrt(27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 18*x + 9*sqrt(3) + 9) - 1/3*27^(1/4)*sqrt(2)*sqrt(2*x + 1) - 1) + 4*27^(3/4)*sqrt(2)*(4*x^2 + 4*x + 1)*arctan(1/54*27^(1/4)*sqrt(2)*sqrt(-36*27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 648*x + 324*sqrt(3) + 324) - 1/3*27^(1/4)*sqrt(2)*sqrt(2*x + 1) + 1) - 27^(3/4)*sqrt(2)*(4*x^2 + 4*x + 1)*log(36*27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 648*x + 324*sqrt(3) + 324) + 27^(3/4)*sqrt(2)*(4*x^2 + 4*x + 1)*log(-36*27^(3/4)*sqrt(2)*sqrt(2*x + 1) + 648*x + 324*sqrt(3) + 324) - 72*sqrt(2*x + 1))/(4*x^2 + 4*x + 1)","B",0
1327,0,0,0,0.417734," ","integrate((2*c*d*x+b*d)^(7/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(8 \, c^{3} d^{3} x^{3} + 12 \, b c^{2} d^{3} x^{2} + 6 \, b^{2} c d^{3} x + b^{3} d^{3}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral((8*c^3*d^3*x^3 + 12*b*c^2*d^3*x^2 + 6*b^2*c*d^3*x + b^3*d^3)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1328,0,0,0,0.404640," ","integrate((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, c d x + b d\right)}^{\frac{3}{2}} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral((2*c*d*x + b*d)^(3/2)*sqrt(c*x^2 + b*x + a), x)","F",0
1329,0,0,0,0.419554," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a}}{\sqrt{2 \, c d x + b d}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)/sqrt(2*c*d*x + b*d), x)","F",0
1330,0,0,0,0.426152," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{8 \, c^{3} d^{3} x^{3} + 12 \, b c^{2} d^{3} x^{2} + 6 \, b^{2} c d^{3} x + b^{3} d^{3}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(8*c^3*d^3*x^3 + 12*b*c^2*d^3*x^2 + 6*b^2*c*d^3*x + b^3*d^3), x)","F",0
1331,0,0,0,0.427802," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{32 \, c^{5} d^{5} x^{5} + 80 \, b c^{4} d^{5} x^{4} + 80 \, b^{2} c^{3} d^{5} x^{3} + 40 \, b^{3} c^{2} d^{5} x^{2} + 10 \, b^{4} c d^{5} x + b^{5} d^{5}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(32*c^5*d^5*x^5 + 80*b*c^4*d^5*x^4 + 80*b^2*c^3*d^5*x^3 + 40*b^3*c^2*d^5*x^2 + 10*b^4*c*d^5*x + b^5*d^5), x)","F",0
1332,0,0,0,0.430250," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{128 \, c^{7} d^{7} x^{7} + 448 \, b c^{6} d^{7} x^{6} + 672 \, b^{2} c^{5} d^{7} x^{5} + 560 \, b^{3} c^{4} d^{7} x^{4} + 280 \, b^{4} c^{3} d^{7} x^{3} + 84 \, b^{5} c^{2} d^{7} x^{2} + 14 \, b^{6} c d^{7} x + b^{7} d^{7}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(128*c^7*d^7*x^7 + 448*b*c^6*d^7*x^6 + 672*b^2*c^5*d^7*x^5 + 560*b^3*c^4*d^7*x^4 + 280*b^4*c^3*d^7*x^3 + 84*b^5*c^2*d^7*x^2 + 14*b^6*c*d^7*x + b^7*d^7), x)","F",0
1333,0,0,0,0.420255," ","integrate((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, c^{2} d^{2} x^{2} + 4 \, b c d^{2} x + b^{2} d^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral((4*c^2*d^2*x^2 + 4*b*c*d^2*x + b^2*d^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1334,0,0,0,0.404388," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1335,0,0,0,0.420364," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} d^{2} x^{2} + 4 \, b c d^{2} x + b^{2} d^{2}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(4*c^2*d^2*x^2 + 4*b*c*d^2*x + b^2*d^2), x)","F",0
1336,0,0,0,0.416081," ","integrate((c*x^2+b*x+a)^(1/2)/(2*c*d*x+b*d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{16 \, c^{4} d^{4} x^{4} + 32 \, b c^{3} d^{4} x^{3} + 24 \, b^{2} c^{2} d^{4} x^{2} + 8 \, b^{3} c d^{4} x + b^{4} d^{4}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(16*c^4*d^4*x^4 + 32*b*c^3*d^4*x^3 + 24*b^2*c^2*d^4*x^2 + 8*b^3*c*d^4*x + b^4*d^4), x)","F",0
1337,0,0,0,0.427040," ","integrate((2*c*d*x+b*d)^(7/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(8 \, c^{4} d^{3} x^{5} + 20 \, b c^{3} d^{3} x^{4} + a b^{3} d^{3} + 2 \, {\left(9 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{3} x^{3} + {\left(7 \, b^{3} c + 12 \, a b c^{2}\right)} d^{3} x^{2} + {\left(b^{4} + 6 \, a b^{2} c\right)} d^{3} x\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral((8*c^4*d^3*x^5 + 20*b*c^3*d^3*x^4 + a*b^3*d^3 + 2*(9*b^2*c^2 + 4*a*c^3)*d^3*x^3 + (7*b^3*c + 12*a*b*c^2)*d^3*x^2 + (b^4 + 6*a*b^2*c)*d^3*x)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1338,0,0,0,0.413449," ","integrate((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, c^{2} d x^{3} + 3 \, b c d x^{2} + a b d + {\left(b^{2} + 2 \, a c\right)} d x\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral((2*c^2*d*x^3 + 3*b*c*d*x^2 + a*b*d + (b^2 + 2*a*c)*d*x)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1339,0,0,0,0.423682," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{\sqrt{2 \, c d x + b d}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/2)/sqrt(2*c*d*x + b*d), x)","F",0
1340,0,0,0,0.413730," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{8 \, c^{3} d^{3} x^{3} + 12 \, b c^{2} d^{3} x^{2} + 6 \, b^{2} c d^{3} x + b^{3} d^{3}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(3/2)/(8*c^3*d^3*x^3 + 12*b*c^2*d^3*x^2 + 6*b^2*c*d^3*x + b^3*d^3), x)","F",0
1341,0,0,0,0.421780," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{32 \, c^{5} d^{5} x^{5} + 80 \, b c^{4} d^{5} x^{4} + 80 \, b^{2} c^{3} d^{5} x^{3} + 40 \, b^{3} c^{2} d^{5} x^{2} + 10 \, b^{4} c d^{5} x + b^{5} d^{5}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(3/2)/(32*c^5*d^5*x^5 + 80*b*c^4*d^5*x^4 + 80*b^2*c^3*d^5*x^3 + 40*b^3*c^2*d^5*x^2 + 10*b^4*c*d^5*x + b^5*d^5), x)","F",0
1342,0,0,0,0.440161," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{128 \, c^{7} d^{7} x^{7} + 448 \, b c^{6} d^{7} x^{6} + 672 \, b^{2} c^{5} d^{7} x^{5} + 560 \, b^{3} c^{4} d^{7} x^{4} + 280 \, b^{4} c^{3} d^{7} x^{3} + 84 \, b^{5} c^{2} d^{7} x^{2} + 14 \, b^{6} c d^{7} x + b^{7} d^{7}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(3/2)/(128*c^7*d^7*x^7 + 448*b*c^6*d^7*x^6 + 672*b^2*c^5*d^7*x^5 + 560*b^3*c^4*d^7*x^4 + 280*b^4*c^3*d^7*x^3 + 84*b^5*c^2*d^7*x^2 + 14*b^6*c*d^7*x + b^7*d^7), x)","F",0
1343,0,0,0,0.449597," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(17/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{512 \, c^{9} d^{9} x^{9} + 2304 \, b c^{8} d^{9} x^{8} + 4608 \, b^{2} c^{7} d^{9} x^{7} + 5376 \, b^{3} c^{6} d^{9} x^{6} + 4032 \, b^{4} c^{5} d^{9} x^{5} + 2016 \, b^{5} c^{4} d^{9} x^{4} + 672 \, b^{6} c^{3} d^{9} x^{3} + 144 \, b^{7} c^{2} d^{9} x^{2} + 18 \, b^{8} c d^{9} x + b^{9} d^{9}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(3/2)/(512*c^9*d^9*x^9 + 2304*b*c^8*d^9*x^8 + 4608*b^2*c^7*d^9*x^7 + 5376*b^3*c^6*d^9*x^6 + 4032*b^4*c^5*d^9*x^5 + 2016*b^5*c^4*d^9*x^4 + 672*b^6*c^3*d^9*x^3 + 144*b^7*c^2*d^9*x^2 + 18*b^8*c*d^9*x + b^9*d^9), x)","F",0
1344,0,0,0,0.428927," ","integrate((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, c^{3} d^{2} x^{4} + 8 \, b c^{2} d^{2} x^{3} + a b^{2} d^{2} + {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} x^{2} + {\left(b^{3} + 4 \, a b c\right)} d^{2} x\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral((4*c^3*d^2*x^4 + 8*b*c^2*d^2*x^3 + a*b^2*d^2 + (5*b^2*c + 4*a*c^2)*d^2*x^2 + (b^3 + 4*a*b*c)*d^2*x)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1345,0,0,0,0.424825," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(3/2), x)","F",0
1346,0,0,0,0.426831," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{4 \, c^{2} d^{2} x^{2} + 4 \, b c d^{2} x + b^{2} d^{2}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(3/2)/(4*c^2*d^2*x^2 + 4*b*c*d^2*x + b^2*d^2), x)","F",0
1347,0,0,0,0.436986," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{16 \, c^{4} d^{4} x^{4} + 32 \, b c^{3} d^{4} x^{3} + 24 \, b^{2} c^{2} d^{4} x^{2} + 8 \, b^{3} c d^{4} x + b^{4} d^{4}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(3/2)/(16*c^4*d^4*x^4 + 32*b*c^3*d^4*x^3 + 24*b^2*c^2*d^4*x^2 + 8*b^3*c*d^4*x + b^4*d^4), x)","F",0
1348,0,0,0,0.425484," ","integrate((c*x^2+b*x+a)^(3/2)/(2*c*d*x+b*d)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} {\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{64 \, c^{6} d^{6} x^{6} + 192 \, b c^{5} d^{6} x^{5} + 240 \, b^{2} c^{4} d^{6} x^{4} + 160 \, b^{3} c^{3} d^{6} x^{3} + 60 \, b^{4} c^{2} d^{6} x^{2} + 12 \, b^{5} c d^{6} x + b^{6} d^{6}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*(c*x^2 + b*x + a)^(3/2)/(64*c^6*d^6*x^6 + 192*b*c^5*d^6*x^5 + 240*b^2*c^4*d^6*x^4 + 160*b^3*c^3*d^6*x^3 + 60*b^4*c^2*d^6*x^2 + 12*b^5*c*d^6*x + b^6*d^6), x)","F",0
1349,0,0,0,0.434775," ","integrate((2*c*d*x+b*d)^(7/2)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(8 \, c^{5} d^{3} x^{7} + 28 \, b c^{4} d^{3} x^{6} + 2 \, {\left(19 \, b^{2} c^{3} + 8 \, a c^{4}\right)} d^{3} x^{5} + a^{2} b^{3} d^{3} + 5 \, {\left(5 \, b^{3} c^{2} + 8 \, a b c^{3}\right)} d^{3} x^{4} + 4 \, {\left(2 \, b^{4} c + 9 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{3} x^{3} + {\left(b^{5} + 14 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} d^{3} x^{2} + 2 \, {\left(a b^{4} + 3 \, a^{2} b^{2} c\right)} d^{3} x\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral((8*c^5*d^3*x^7 + 28*b*c^4*d^3*x^6 + 2*(19*b^2*c^3 + 8*a*c^4)*d^3*x^5 + a^2*b^3*d^3 + 5*(5*b^3*c^2 + 8*a*b*c^3)*d^3*x^4 + 4*(2*b^4*c + 9*a*b^2*c^2 + 2*a^2*c^3)*d^3*x^3 + (b^5 + 14*a*b^3*c + 12*a^2*b*c^2)*d^3*x^2 + 2*(a*b^4 + 3*a^2*b^2*c)*d^3*x)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1350,0,0,0,0.426661," ","integrate((2*c*d*x+b*d)^(3/2)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, c^{3} d x^{5} + 5 \, b c^{2} d x^{4} + 4 \, {\left(b^{2} c + a c^{2}\right)} d x^{3} + a^{2} b d + {\left(b^{3} + 6 \, a b c\right)} d x^{2} + 2 \, {\left(a b^{2} + a^{2} c\right)} d x\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral((2*c^3*d*x^5 + 5*b*c^2*d*x^4 + 4*(b^2*c + a*c^2)*d*x^3 + a^2*b*d + (b^3 + 6*a*b*c)*d*x^2 + 2*(a*b^2 + a^2*c)*d*x)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1351,0,0,0,0.418998," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a}}{\sqrt{2 \, c d x + b d}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)/sqrt(2*c*d*x + b*d), x)","F",0
1352,0,0,0,0.438411," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{8 \, c^{3} d^{3} x^{3} + 12 \, b c^{2} d^{3} x^{2} + 6 \, b^{2} c d^{3} x + b^{3} d^{3}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(8*c^3*d^3*x^3 + 12*b*c^2*d^3*x^2 + 6*b^2*c*d^3*x + b^3*d^3), x)","F",0
1353,0,0,0,0.447949," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{32 \, c^{5} d^{5} x^{5} + 80 \, b c^{4} d^{5} x^{4} + 80 \, b^{2} c^{3} d^{5} x^{3} + 40 \, b^{3} c^{2} d^{5} x^{2} + 10 \, b^{4} c d^{5} x + b^{5} d^{5}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(32*c^5*d^5*x^5 + 80*b*c^4*d^5*x^4 + 80*b^2*c^3*d^5*x^3 + 40*b^3*c^2*d^5*x^2 + 10*b^4*c*d^5*x + b^5*d^5), x)","F",0
1354,0,0,0,0.447521," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(13/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{128 \, c^{7} d^{7} x^{7} + 448 \, b c^{6} d^{7} x^{6} + 672 \, b^{2} c^{5} d^{7} x^{5} + 560 \, b^{3} c^{4} d^{7} x^{4} + 280 \, b^{4} c^{3} d^{7} x^{3} + 84 \, b^{5} c^{2} d^{7} x^{2} + 14 \, b^{6} c d^{7} x + b^{7} d^{7}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(128*c^7*d^7*x^7 + 448*b*c^6*d^7*x^6 + 672*b^2*c^5*d^7*x^5 + 560*b^3*c^4*d^7*x^4 + 280*b^4*c^3*d^7*x^3 + 84*b^5*c^2*d^7*x^2 + 14*b^6*c*d^7*x + b^7*d^7), x)","F",0
1355,0,0,0,0.460179," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(17/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{512 \, c^{9} d^{9} x^{9} + 2304 \, b c^{8} d^{9} x^{8} + 4608 \, b^{2} c^{7} d^{9} x^{7} + 5376 \, b^{3} c^{6} d^{9} x^{6} + 4032 \, b^{4} c^{5} d^{9} x^{5} + 2016 \, b^{5} c^{4} d^{9} x^{4} + 672 \, b^{6} c^{3} d^{9} x^{3} + 144 \, b^{7} c^{2} d^{9} x^{2} + 18 \, b^{8} c d^{9} x + b^{9} d^{9}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(512*c^9*d^9*x^9 + 2304*b*c^8*d^9*x^8 + 4608*b^2*c^7*d^9*x^7 + 5376*b^3*c^6*d^9*x^6 + 4032*b^4*c^5*d^9*x^5 + 2016*b^5*c^4*d^9*x^4 + 672*b^6*c^3*d^9*x^3 + 144*b^7*c^2*d^9*x^2 + 18*b^8*c*d^9*x + b^9*d^9), x)","F",0
1356,0,0,0,0.485988," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(21/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{2048 \, c^{11} d^{11} x^{11} + 11264 \, b c^{10} d^{11} x^{10} + 28160 \, b^{2} c^{9} d^{11} x^{9} + 42240 \, b^{3} c^{8} d^{11} x^{8} + 42240 \, b^{4} c^{7} d^{11} x^{7} + 29568 \, b^{5} c^{6} d^{11} x^{6} + 14784 \, b^{6} c^{5} d^{11} x^{5} + 5280 \, b^{7} c^{4} d^{11} x^{4} + 1320 \, b^{8} c^{3} d^{11} x^{3} + 220 \, b^{9} c^{2} d^{11} x^{2} + 22 \, b^{10} c d^{11} x + b^{11} d^{11}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(2048*c^11*d^11*x^11 + 11264*b*c^10*d^11*x^10 + 28160*b^2*c^9*d^11*x^9 + 42240*b^3*c^8*d^11*x^8 + 42240*b^4*c^7*d^11*x^7 + 29568*b^5*c^6*d^11*x^6 + 14784*b^6*c^5*d^11*x^5 + 5280*b^7*c^4*d^11*x^4 + 1320*b^8*c^3*d^11*x^3 + 220*b^9*c^2*d^11*x^2 + 22*b^10*c*d^11*x + b^11*d^11), x)","F",0
1357,0,0,0,0.440529," ","integrate((2*c*d*x+b*d)^(5/2)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, c^{4} d^{2} x^{6} + 12 \, b c^{3} d^{2} x^{5} + {\left(13 \, b^{2} c^{2} + 8 \, a c^{3}\right)} d^{2} x^{4} + a^{2} b^{2} d^{2} + 2 \, {\left(3 \, b^{3} c + 8 \, a b c^{2}\right)} d^{2} x^{3} + {\left(b^{4} + 10 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} x^{2} + 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} d^{2} x\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral((4*c^4*d^2*x^6 + 12*b*c^3*d^2*x^5 + (13*b^2*c^2 + 8*a*c^3)*d^2*x^4 + a^2*b^2*d^2 + 2*(3*b^3*c + 8*a*b*c^2)*d^2*x^3 + (b^4 + 10*a*b^2*c + 4*a^2*c^2)*d^2*x^2 + 2*(a*b^3 + 2*a^2*b*c)*d^2*x)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1358,0,0,0,0.417027," ","integrate((2*c*d*x+b*d)^(1/2)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a), x)","F",0
1359,0,0,0,0.440756," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{4 \, c^{2} d^{2} x^{2} + 4 \, b c d^{2} x + b^{2} d^{2}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(4*c^2*d^2*x^2 + 4*b*c*d^2*x + b^2*d^2), x)","F",0
1360,0,0,0,0.439933," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{16 \, c^{4} d^{4} x^{4} + 32 \, b c^{3} d^{4} x^{3} + 24 \, b^{2} c^{2} d^{4} x^{2} + 8 \, b^{3} c d^{4} x + b^{4} d^{4}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(16*c^4*d^4*x^4 + 32*b*c^3*d^4*x^3 + 24*b^2*c^2*d^4*x^2 + 8*b^3*c*d^4*x + b^4*d^4), x)","F",0
1361,0,0,0,0.460995," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{64 \, c^{6} d^{6} x^{6} + 192 \, b c^{5} d^{6} x^{5} + 240 \, b^{2} c^{4} d^{6} x^{4} + 160 \, b^{3} c^{3} d^{6} x^{3} + 60 \, b^{4} c^{2} d^{6} x^{2} + 12 \, b^{5} c d^{6} x + b^{6} d^{6}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(64*c^6*d^6*x^6 + 192*b*c^5*d^6*x^5 + 240*b^2*c^4*d^6*x^4 + 160*b^3*c^3*d^6*x^3 + 60*b^4*c^2*d^6*x^2 + 12*b^5*c*d^6*x + b^6*d^6), x)","F",0
1362,0,0,0,0.458313," ","integrate((c*x^2+b*x+a)^(5/2)/(2*c*d*x+b*d)^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{256 \, c^{8} d^{8} x^{8} + 1024 \, b c^{7} d^{8} x^{7} + 1792 \, b^{2} c^{6} d^{8} x^{6} + 1792 \, b^{3} c^{5} d^{8} x^{5} + 1120 \, b^{4} c^{4} d^{8} x^{4} + 448 \, b^{5} c^{3} d^{8} x^{3} + 112 \, b^{6} c^{2} d^{8} x^{2} + 16 \, b^{7} c d^{8} x + b^{8} d^{8}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(256*c^8*d^8*x^8 + 1024*b*c^7*d^8*x^7 + 1792*b^2*c^6*d^8*x^6 + 1792*b^3*c^5*d^8*x^5 + 1120*b^4*c^4*d^8*x^4 + 448*b^5*c^3*d^8*x^3 + 112*b^6*c^2*d^8*x^2 + 16*b^7*c*d^8*x + b^8*d^8), x)","F",0
1363,0,0,0,0.423243," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(8 \, c^{3} d^{3} x^{3} + 12 \, b c^{2} d^{3} x^{2} + 6 \, b^{2} c d^{3} x + b^{3} d^{3}\right)} \sqrt{2 \, c d x + b d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((8*c^3*d^3*x^3 + 12*b*c^2*d^3*x^2 + 6*b^2*c*d^3*x + b^3*d^3)*sqrt(2*c*d*x + b*d)/sqrt(c*x^2 + b*x + a), x)","F",0
1364,0,0,0,0.407848," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^(3/2)/sqrt(c*x^2 + b*x + a), x)","F",0
1365,0,0,0,0.419590," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{2 \, c^{2} d x^{3} + 3 \, b c d x^{2} + a b d + {\left(b^{2} + 2 \, a c\right)} d x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(2*c^2*d*x^3 + 3*b*c*d*x^2 + a*b*d + (b^2 + 2*a*c)*d*x), x)","F",0
1366,0,0,0,0.423190," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{8 \, c^{4} d^{3} x^{5} + 20 \, b c^{3} d^{3} x^{4} + a b^{3} d^{3} + 2 \, {\left(9 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{3} x^{3} + {\left(7 \, b^{3} c + 12 \, a b c^{2}\right)} d^{3} x^{2} + {\left(b^{4} + 6 \, a b^{2} c\right)} d^{3} x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(8*c^4*d^3*x^5 + 20*b*c^3*d^3*x^4 + a*b^3*d^3 + 2*(9*b^2*c^2 + 4*a*c^3)*d^3*x^3 + (7*b^3*c + 12*a*b*c^2)*d^3*x^2 + (b^4 + 6*a*b^2*c)*d^3*x), x)","F",0
1367,0,0,0,0.437468," ","integrate(1/(2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{32 \, c^{6} d^{5} x^{7} + 112 \, b c^{5} d^{5} x^{6} + a b^{5} d^{5} + 32 \, {\left(5 \, b^{2} c^{4} + a c^{5}\right)} d^{5} x^{5} + 40 \, {\left(3 \, b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{5} x^{4} + 10 \, {\left(5 \, b^{4} c^{2} + 8 \, a b^{2} c^{3}\right)} d^{5} x^{3} + {\left(11 \, b^{5} c + 40 \, a b^{3} c^{2}\right)} d^{5} x^{2} + {\left(b^{6} + 10 \, a b^{4} c\right)} d^{5} x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(32*c^6*d^5*x^7 + 112*b*c^5*d^5*x^6 + a*b^5*d^5 + 32*(5*b^2*c^4 + a*c^5)*d^5*x^5 + 40*(3*b^3*c^3 + 2*a*b*c^4)*d^5*x^4 + 10*(5*b^4*c^2 + 8*a*b^2*c^3)*d^5*x^3 + (11*b^5*c + 40*a*b^3*c^2)*d^5*x^2 + (b^6 + 10*a*b^4*c)*d^5*x), x)","F",0
1368,0,0,0,0.436939," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(16 \, c^{4} d^{4} x^{4} + 32 \, b c^{3} d^{4} x^{3} + 24 \, b^{2} c^{2} d^{4} x^{2} + 8 \, b^{3} c d^{4} x + b^{4} d^{4}\right)} \sqrt{2 \, c d x + b d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((16*c^4*d^4*x^4 + 32*b*c^3*d^4*x^3 + 24*b^2*c^2*d^4*x^2 + 8*b^3*c*d^4*x + b^4*d^4)*sqrt(2*c*d*x + b*d)/sqrt(c*x^2 + b*x + a), x)","F",0
1369,0,0,0,0.432101," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, c^{2} d^{2} x^{2} + 4 \, b c d^{2} x + b^{2} d^{2}\right)} \sqrt{2 \, c d x + b d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((4*c^2*d^2*x^2 + 4*b*c*d^2*x + b^2*d^2)*sqrt(2*c*d*x + b*d)/sqrt(c*x^2 + b*x + a), x)","F",0
1370,0,0,0,0.408913," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)/sqrt(c*x^2 + b*x + a), x)","F",0
1371,0,0,0,0.418791," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{4 \, c^{3} d^{2} x^{4} + 8 \, b c^{2} d^{2} x^{3} + a b^{2} d^{2} + {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} x^{2} + {\left(b^{3} + 4 \, a b c\right)} d^{2} x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(4*c^3*d^2*x^4 + 8*b*c^2*d^2*x^3 + a*b^2*d^2 + (5*b^2*c + 4*a*c^2)*d^2*x^2 + (b^3 + 4*a*b*c)*d^2*x), x)","F",0
1372,0,0,0,0.421281," ","integrate(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{16 \, c^{5} d^{4} x^{6} + 48 \, b c^{4} d^{4} x^{5} + a b^{4} d^{4} + 8 \, {\left(7 \, b^{2} c^{3} + 2 \, a c^{4}\right)} d^{4} x^{4} + 32 \, {\left(b^{3} c^{2} + a b c^{3}\right)} d^{4} x^{3} + 3 \, {\left(3 \, b^{4} c + 8 \, a b^{2} c^{2}\right)} d^{4} x^{2} + {\left(b^{5} + 8 \, a b^{3} c\right)} d^{4} x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(16*c^5*d^4*x^6 + 48*b*c^4*d^4*x^5 + a*b^4*d^4 + 8*(7*b^2*c^3 + 2*a*c^4)*d^4*x^4 + 32*(b^3*c^2 + a*b*c^3)*d^4*x^3 + 3*(3*b^4*c + 8*a*b^2*c^2)*d^4*x^2 + (b^5 + 8*a*b^3*c)*d^4*x), x)","F",0
1373,0,0,0,0.413100," ","integrate((3-2*x)^(3/2)/(x^2-3*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-2 \, x + 3\right)}^{\frac{3}{2}}}{\sqrt{x^{2} - 3 \, x + 1}}, x\right)"," ",0,"integral((-2*x + 3)^(3/2)/sqrt(x^2 - 3*x + 1), x)","F",0
1374,0,0,0,0.401208," ","integrate(1/(3-2*x)^(1/2)/(x^2-3*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} - 3 \, x + 1} \sqrt{-2 \, x + 3}}{2 \, x^{3} - 9 \, x^{2} + 11 \, x - 3}, x\right)"," ",0,"integral(-sqrt(x^2 - 3*x + 1)*sqrt(-2*x + 3)/(2*x^3 - 9*x^2 + 11*x - 3), x)","F",0
1375,0,0,0,0.412519," ","integrate(1/(3-2*x)^(5/2)/(x^2-3*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{x^{2} - 3 \, x + 1} \sqrt{-2 \, x + 3}}{8 \, x^{5} - 60 \, x^{4} + 170 \, x^{3} - 225 \, x^{2} + 135 \, x - 27}, x\right)"," ",0,"integral(-sqrt(x^2 - 3*x + 1)*sqrt(-2*x + 3)/(8*x^5 - 60*x^4 + 170*x^3 - 225*x^2 + 135*x - 27), x)","F",0
1376,0,0,0,0.422588," ","integrate((3-2*x)^(5/2)/(x^2-3*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, x^{2} - 12 \, x + 9\right)} \sqrt{-2 \, x + 3}}{\sqrt{x^{2} - 3 \, x + 1}}, x\right)"," ",0,"integral((4*x^2 - 12*x + 9)*sqrt(-2*x + 3)/sqrt(x^2 - 3*x + 1), x)","F",0
1377,0,0,0,0.413115," ","integrate((3-2*x)^(1/2)/(x^2-3*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-2 \, x + 3}}{\sqrt{x^{2} - 3 \, x + 1}}, x\right)"," ",0,"integral(sqrt(-2*x + 3)/sqrt(x^2 - 3*x + 1), x)","F",0
1378,0,0,0,0.420169," ","integrate(1/(3-2*x)^(3/2)/(x^2-3*x+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{2} - 3 \, x + 1} \sqrt{-2 \, x + 3}}{4 \, x^{4} - 24 \, x^{3} + 49 \, x^{2} - 39 \, x + 9}, x\right)"," ",0,"integral(sqrt(x^2 - 3*x + 1)*sqrt(-2*x + 3)/(4*x^4 - 24*x^3 + 49*x^2 - 39*x + 9), x)","F",0
1379,0,0,0,0.438750," ","integrate((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(32 \, c^{5} d^{5} x^{5} + 80 \, b c^{4} d^{5} x^{4} + 80 \, b^{2} c^{3} d^{5} x^{3} + 40 \, b^{3} c^{2} d^{5} x^{2} + 10 \, b^{4} c d^{5} x + b^{5} d^{5}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((32*c^5*d^5*x^5 + 80*b*c^4*d^5*x^4 + 80*b^2*c^3*d^5*x^3 + 40*b^3*c^2*d^5*x^2 + 10*b^4*c*d^5*x + b^5*d^5)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1380,0,0,0,0.416608," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(8 \, c^{3} d^{3} x^{3} + 12 \, b c^{2} d^{3} x^{2} + 6 \, b^{2} c d^{3} x + b^{3} d^{3}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((8*c^3*d^3*x^3 + 12*b*c^2*d^3*x^2 + 6*b^2*c*d^3*x + b^3*d^3)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1381,0,0,0,0.420467," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}} \sqrt{c x^{2} + b x + a}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^(3/2)*sqrt(c*x^2 + b*x + a)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1382,0,0,0,0.425441," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{2 \, c^{3} d x^{5} + 5 \, b c^{2} d x^{4} + 4 \, {\left(b^{2} c + a c^{2}\right)} d x^{3} + a^{2} b d + {\left(b^{3} + 6 \, a b c\right)} d x^{2} + 2 \, {\left(a b^{2} + a^{2} c\right)} d x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(2*c^3*d*x^5 + 5*b*c^2*d*x^4 + 4*(b^2*c + a*c^2)*d*x^3 + a^2*b*d + (b^3 + 6*a*b*c)*d*x^2 + 2*(a*b^2 + a^2*c)*d*x), x)","F",0
1383,0,0,0,0.444006," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{8 \, c^{5} d^{3} x^{7} + 28 \, b c^{4} d^{3} x^{6} + 2 \, {\left(19 \, b^{2} c^{3} + 8 \, a c^{4}\right)} d^{3} x^{5} + a^{2} b^{3} d^{3} + 5 \, {\left(5 \, b^{3} c^{2} + 8 \, a b c^{3}\right)} d^{3} x^{4} + 4 \, {\left(2 \, b^{4} c + 9 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{3} x^{3} + {\left(b^{5} + 14 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} d^{3} x^{2} + 2 \, {\left(a b^{4} + 3 \, a^{2} b^{2} c\right)} d^{3} x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(8*c^5*d^3*x^7 + 28*b*c^4*d^3*x^6 + 2*(19*b^2*c^3 + 8*a*c^4)*d^3*x^5 + a^2*b^3*d^3 + 5*(5*b^3*c^2 + 8*a*b*c^3)*d^3*x^4 + 4*(2*b^4*c + 9*a*b^2*c^2 + 2*a^2*c^3)*d^3*x^3 + (b^5 + 14*a*b^3*c + 12*a^2*b*c^2)*d^3*x^2 + 2*(a*b^4 + 3*a^2*b^2*c)*d^3*x), x)","F",0
1384,0,0,0,0.425851," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(16 \, c^{4} d^{4} x^{4} + 32 \, b c^{3} d^{4} x^{3} + 24 \, b^{2} c^{2} d^{4} x^{2} + 8 \, b^{3} c d^{4} x + b^{4} d^{4}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((16*c^4*d^4*x^4 + 32*b*c^3*d^4*x^3 + 24*b^2*c^2*d^4*x^2 + 8*b^3*c*d^4*x + b^4*d^4)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1385,0,0,0,0.442613," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, c^{2} d^{2} x^{2} + 4 \, b c d^{2} x + b^{2} d^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((4*c^2*d^2*x^2 + 4*b*c*d^2*x + b^2*d^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1386,0,0,0,0.424083," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1387,0,0,0,0.426058," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{4 \, c^{4} d^{2} x^{6} + 12 \, b c^{3} d^{2} x^{5} + {\left(13 \, b^{2} c^{2} + 8 \, a c^{3}\right)} d^{2} x^{4} + a^{2} b^{2} d^{2} + 2 \, {\left(3 \, b^{3} c + 8 \, a b c^{2}\right)} d^{2} x^{3} + {\left(b^{4} + 10 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} x^{2} + 2 \, {\left(a b^{3} + 2 \, a^{2} b c\right)} d^{2} x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(4*c^4*d^2*x^6 + 12*b*c^3*d^2*x^5 + (13*b^2*c^2 + 8*a*c^3)*d^2*x^4 + a^2*b^2*d^2 + 2*(3*b^3*c + 8*a*b*c^2)*d^2*x^3 + (b^4 + 10*a*b^2*c + 4*a^2*c^2)*d^2*x^2 + 2*(a*b^3 + 2*a^2*b*c)*d^2*x), x)","F",0
1388,0,0,0,0.433242," ","integrate(1/(2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{16 \, c^{6} d^{4} x^{8} + 64 \, b c^{5} d^{4} x^{7} + 8 \, {\left(13 \, b^{2} c^{4} + 4 \, a c^{5}\right)} d^{4} x^{6} + a^{2} b^{4} d^{4} + 8 \, {\left(11 \, b^{3} c^{3} + 12 \, a b c^{4}\right)} d^{4} x^{5} + {\left(41 \, b^{4} c^{2} + 112 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} x^{4} + 2 \, {\left(5 \, b^{5} c + 32 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{4} x^{3} + {\left(b^{6} + 18 \, a b^{4} c + 24 \, a^{2} b^{2} c^{2}\right)} d^{4} x^{2} + 2 \, {\left(a b^{5} + 4 \, a^{2} b^{3} c\right)} d^{4} x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(16*c^6*d^4*x^8 + 64*b*c^5*d^4*x^7 + 8*(13*b^2*c^4 + 4*a*c^5)*d^4*x^6 + a^2*b^4*d^4 + 8*(11*b^3*c^3 + 12*a*b*c^4)*d^4*x^5 + (41*b^4*c^2 + 112*a*b^2*c^3 + 16*a^2*c^4)*d^4*x^4 + 2*(5*b^5*c + 32*a*b^3*c^2 + 16*a^2*b*c^3)*d^4*x^3 + (b^6 + 18*a*b^4*c + 24*a^2*b^2*c^2)*d^4*x^2 + 2*(a*b^5 + 4*a^2*b^3*c)*d^4*x), x)","F",0
1389,0,0,0,0.454759," ","integrate((2*c*d*x+b*d)^(15/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(128 \, c^{7} d^{7} x^{7} + 448 \, b c^{6} d^{7} x^{6} + 672 \, b^{2} c^{5} d^{7} x^{5} + 560 \, b^{3} c^{4} d^{7} x^{4} + 280 \, b^{4} c^{3} d^{7} x^{3} + 84 \, b^{5} c^{2} d^{7} x^{2} + 14 \, b^{6} c d^{7} x + b^{7} d^{7}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((128*c^7*d^7*x^7 + 448*b*c^6*d^7*x^6 + 672*b^2*c^5*d^7*x^5 + 560*b^3*c^4*d^7*x^4 + 280*b^4*c^3*d^7*x^3 + 84*b^5*c^2*d^7*x^2 + 14*b^6*c*d^7*x + b^7*d^7)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1390,0,0,0,0.457370," ","integrate((2*c*d*x+b*d)^(11/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(32 \, c^{5} d^{5} x^{5} + 80 \, b c^{4} d^{5} x^{4} + 80 \, b^{2} c^{3} d^{5} x^{3} + 40 \, b^{3} c^{2} d^{5} x^{2} + 10 \, b^{4} c d^{5} x + b^{5} d^{5}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((32*c^5*d^5*x^5 + 80*b*c^4*d^5*x^4 + 80*b^2*c^3*d^5*x^3 + 40*b^3*c^2*d^5*x^2 + 10*b^4*c*d^5*x + b^5*d^5)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1391,0,0,0,0.434965," ","integrate((2*c*d*x+b*d)^(7/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(8 \, c^{3} d^{3} x^{3} + 12 \, b c^{2} d^{3} x^{2} + 6 \, b^{2} c d^{3} x + b^{3} d^{3}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((8*c^3*d^3*x^3 + 12*b*c^2*d^3*x^2 + 6*b^2*c*d^3*x + b^3*d^3)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1392,0,0,0,0.444344," ","integrate((2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{\frac{3}{2}} \sqrt{c x^{2} + b x + a}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^(3/2)*sqrt(c*x^2 + b*x + a)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1393,0,0,0,0.418621," ","integrate(1/(2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{2 \, c^{4} d x^{7} + 7 \, b c^{3} d x^{6} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d x^{5} + 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d x^{4} + a^{3} b d + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d x^{3} + 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d x^{2} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(2*c^4*d*x^7 + 7*b*c^3*d*x^6 + 3*(3*b^2*c^2 + 2*a*c^3)*d*x^5 + 5*(b^3*c + 3*a*b*c^2)*d*x^4 + a^3*b*d + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*x^3 + 3*(a*b^3 + 3*a^2*b*c)*d*x^2 + (3*a^2*b^2 + 2*a^3*c)*d*x), x)","F",0
1394,0,0,0,0.438773," ","integrate(1/(2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{8 \, c^{6} d^{3} x^{9} + 36 \, b c^{5} d^{3} x^{8} + 6 \, {\left(11 \, b^{2} c^{4} + 4 \, a c^{5}\right)} d^{3} x^{7} + 21 \, {\left(3 \, b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{3} x^{6} + a^{3} b^{3} d^{3} + 3 \, {\left(11 \, b^{4} c^{2} + 38 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} x^{5} + 3 \, {\left(3 \, b^{5} c + 25 \, a b^{3} c^{2} + 20 \, a^{2} b c^{3}\right)} d^{3} x^{4} + {\left(b^{6} + 24 \, a b^{4} c + 54 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d^{3} x^{3} + 3 \, {\left(a b^{5} + 7 \, a^{2} b^{3} c + 4 \, a^{3} b c^{2}\right)} d^{3} x^{2} + 3 \, {\left(a^{2} b^{4} + 2 \, a^{3} b^{2} c\right)} d^{3} x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(8*c^6*d^3*x^9 + 36*b*c^5*d^3*x^8 + 6*(11*b^2*c^4 + 4*a*c^5)*d^3*x^7 + 21*(3*b^3*c^3 + 4*a*b*c^4)*d^3*x^6 + a^3*b^3*d^3 + 3*(11*b^4*c^2 + 38*a*b^2*c^3 + 8*a^2*c^4)*d^3*x^5 + 3*(3*b^5*c + 25*a*b^3*c^2 + 20*a^2*b*c^3)*d^3*x^4 + (b^6 + 24*a*b^4*c + 54*a^2*b^2*c^2 + 8*a^3*c^3)*d^3*x^3 + 3*(a*b^5 + 7*a^2*b^3*c + 4*a^3*b*c^2)*d^3*x^2 + 3*(a^2*b^4 + 2*a^3*b^2*c)*d^3*x), x)","F",0
1395,0,0,0,0.459584," ","integrate((2*c*d*x+b*d)^(13/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(64 \, c^{6} d^{6} x^{6} + 192 \, b c^{5} d^{6} x^{5} + 240 \, b^{2} c^{4} d^{6} x^{4} + 160 \, b^{3} c^{3} d^{6} x^{3} + 60 \, b^{4} c^{2} d^{6} x^{2} + 12 \, b^{5} c d^{6} x + b^{6} d^{6}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((64*c^6*d^6*x^6 + 192*b*c^5*d^6*x^5 + 240*b^2*c^4*d^6*x^4 + 160*b^3*c^3*d^6*x^3 + 60*b^4*c^2*d^6*x^2 + 12*b^5*c*d^6*x + b^6*d^6)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1396,0,0,0,0.444474," ","integrate((2*c*d*x+b*d)^(9/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(16 \, c^{4} d^{4} x^{4} + 32 \, b c^{3} d^{4} x^{3} + 24 \, b^{2} c^{2} d^{4} x^{2} + 8 \, b^{3} c d^{4} x + b^{4} d^{4}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((16*c^4*d^4*x^4 + 32*b*c^3*d^4*x^3 + 24*b^2*c^2*d^4*x^2 + 8*b^3*c*d^4*x + b^4*d^4)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1397,0,0,0,0.431375," ","integrate((2*c*d*x+b*d)^(5/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(4 \, c^{2} d^{2} x^{2} + 4 \, b c d^{2} x + b^{2} d^{2}\right)} \sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((4*c^2*d^2*x^2 + 4*b*c*d^2*x + b^2*d^2)*sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1398,0,0,0,0.435167," ","integrate((2*c*d*x+b*d)^(1/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1399,0,0,0,0.433158," ","integrate(1/(2*c*d*x+b*d)^(3/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{2 \, c d x + b d} \sqrt{c x^{2} + b x + a}}{4 \, c^{5} d^{2} x^{8} + 16 \, b c^{4} d^{2} x^{7} + {\left(25 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{2} x^{6} + {\left(19 \, b^{3} c^{2} + 36 \, a b c^{3}\right)} d^{2} x^{5} + a^{3} b^{2} d^{2} + {\left(7 \, b^{4} c + 39 \, a b^{2} c^{2} + 12 \, a^{2} c^{3}\right)} d^{2} x^{4} + {\left(b^{5} + 18 \, a b^{3} c + 24 \, a^{2} b c^{2}\right)} d^{2} x^{3} + {\left(3 \, a b^{4} + 15 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} x^{2} + {\left(3 \, a^{2} b^{3} + 4 \, a^{3} b c\right)} d^{2} x}, x\right)"," ",0,"integral(sqrt(2*c*d*x + b*d)*sqrt(c*x^2 + b*x + a)/(4*c^5*d^2*x^8 + 16*b*c^4*d^2*x^7 + (25*b^2*c^3 + 12*a*c^4)*d^2*x^6 + (19*b^3*c^2 + 36*a*b*c^3)*d^2*x^5 + a^3*b^2*d^2 + (7*b^4*c + 39*a*b^2*c^2 + 12*a^2*c^3)*d^2*x^4 + (b^5 + 18*a*b^3*c + 24*a^2*b*c^2)*d^2*x^3 + (3*a*b^4 + 15*a^2*b^2*c + 4*a^3*c^2)*d^2*x^2 + (3*a^2*b^3 + 4*a^3*b*c)*d^2*x), x)","F",0
1400,0,0,0,0.424463," ","integrate((d*e*x+c*e)^(11/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d^{5} e^{5} x^{5} + 5 \, c d^{4} e^{5} x^{4} + 10 \, c^{2} d^{3} e^{5} x^{3} + 10 \, c^{3} d^{2} e^{5} x^{2} + 5 \, c^{4} d e^{5} x + c^{5} e^{5}\right)} \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}, x\right)"," ",0,"integral(-(d^5*e^5*x^5 + 5*c*d^4*e^5*x^4 + 10*c^2*d^3*e^5*x^3 + 10*c^3*d^2*e^5*x^2 + 5*c^4*d*e^5*x + c^5*e^5)*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
1401,0,0,0,0.427388," ","integrate((d*e*x+c*e)^(7/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d^{3} e^{3} x^{3} + 3 \, c d^{2} e^{3} x^{2} + 3 \, c^{2} d e^{3} x + c^{3} e^{3}\right)} \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}, x\right)"," ",0,"integral(-(d^3*e^3*x^3 + 3*c*d^2*e^3*x^2 + 3*c^2*d*e^3*x + c^3*e^3)*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
1402,0,0,0,0.419188," ","integrate((d*e*x+c*e)^(3/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} {\left(d e x + c e\right)}^{\frac{3}{2}}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*(d*e*x + c*e)^(3/2)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
1403,0,0,0,0.413519," ","integrate(1/(d*e*x+c*e)^(1/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{3} e x^{3} + 3 \, c d^{2} e x^{2} + {\left(3 \, c^{2} - 1\right)} d e x + {\left(c^{3} - c\right)} e}, x\right)"," ",0,"integral(-sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^3*e*x^3 + 3*c*d^2*e*x^2 + (3*c^2 - 1)*d*e*x + (c^3 - c)*e), x)","F",0
1404,0,0,0,0.424378," ","integrate(1/(d*e*x+c*e)^(5/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + {\left(10 \, c^{2} - 1\right)} d^{3} e^{3} x^{3} + {\left(10 \, c^{3} - 3 \, c\right)} d^{2} e^{3} x^{2} + {\left(5 \, c^{4} - 3 \, c^{2}\right)} d e^{3} x + {\left(c^{5} - c^{3}\right)} e^{3}}, x\right)"," ",0,"integral(-sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + (10*c^2 - 1)*d^3*e^3*x^3 + (10*c^3 - 3*c)*d^2*e^3*x^2 + (5*c^4 - 3*c^2)*d*e^3*x + (c^5 - c^3)*e^3), x)","F",0
1405,0,0,0,0.436196," ","integrate(1/(d*e*x+c*e)^(9/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{7} e^{5} x^{7} + 7 \, c d^{6} e^{5} x^{6} + {\left(21 \, c^{2} - 1\right)} d^{5} e^{5} x^{5} + 5 \, {\left(7 \, c^{3} - c\right)} d^{4} e^{5} x^{4} + 5 \, {\left(7 \, c^{4} - 2 \, c^{2}\right)} d^{3} e^{5} x^{3} + {\left(21 \, c^{5} - 10 \, c^{3}\right)} d^{2} e^{5} x^{2} + {\left(7 \, c^{6} - 5 \, c^{4}\right)} d e^{5} x + {\left(c^{7} - c^{5}\right)} e^{5}}, x\right)"," ",0,"integral(-sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^7*e^5*x^7 + 7*c*d^6*e^5*x^6 + (21*c^2 - 1)*d^5*e^5*x^5 + 5*(7*c^3 - c)*d^4*e^5*x^4 + 5*(7*c^4 - 2*c^2)*d^3*e^5*x^3 + (21*c^5 - 10*c^3)*d^2*e^5*x^2 + (7*c^6 - 5*c^4)*d*e^5*x + (c^7 - c^5)*e^5), x)","F",0
1406,0,0,0,0.439479," ","integrate(1/(d*e*x+c*e)^(13/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{9} e^{7} x^{9} + 9 \, c d^{8} e^{7} x^{8} + {\left(36 \, c^{2} - 1\right)} d^{7} e^{7} x^{7} + 7 \, {\left(12 \, c^{3} - c\right)} d^{6} e^{7} x^{6} + 21 \, {\left(6 \, c^{4} - c^{2}\right)} d^{5} e^{7} x^{5} + 7 \, {\left(18 \, c^{5} - 5 \, c^{3}\right)} d^{4} e^{7} x^{4} + 7 \, {\left(12 \, c^{6} - 5 \, c^{4}\right)} d^{3} e^{7} x^{3} + 3 \, {\left(12 \, c^{7} - 7 \, c^{5}\right)} d^{2} e^{7} x^{2} + {\left(9 \, c^{8} - 7 \, c^{6}\right)} d e^{7} x + {\left(c^{9} - c^{7}\right)} e^{7}}, x\right)"," ",0,"integral(-sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^9*e^7*x^9 + 9*c*d^8*e^7*x^8 + (36*c^2 - 1)*d^7*e^7*x^7 + 7*(12*c^3 - c)*d^6*e^7*x^6 + 21*(6*c^4 - c^2)*d^5*e^7*x^5 + 7*(18*c^5 - 5*c^3)*d^4*e^7*x^4 + 7*(12*c^6 - 5*c^4)*d^3*e^7*x^3 + 3*(12*c^7 - 7*c^5)*d^2*e^7*x^2 + (9*c^8 - 7*c^6)*d*e^7*x + (c^9 - c^7)*e^7), x)","F",0
1407,0,0,0,0.421408," ","integrate((d*e*x+c*e)^(9/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d^{4} e^{4} x^{4} + 4 \, c d^{3} e^{4} x^{3} + 6 \, c^{2} d^{2} e^{4} x^{2} + 4 \, c^{3} d e^{4} x + c^{4} e^{4}\right)} \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}, x\right)"," ",0,"integral(-(d^4*e^4*x^4 + 4*c*d^3*e^4*x^3 + 6*c^2*d^2*e^4*x^2 + 4*c^3*d*e^4*x + c^4*e^4)*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
1408,0,0,0,0.431765," ","integrate((d*e*x+c*e)^(5/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d^{2} e^{2} x^{2} + 2 \, c d e^{2} x + c^{2} e^{2}\right)} \sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}, x\right)"," ",0,"integral(-(d^2*e^2*x^2 + 2*c*d*e^2*x + c^2*e^2)*sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
1409,0,0,0,0.431123," ","integrate((d*e*x+c*e)^(1/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)","F",0
1410,0,0,0,0.432847," ","integrate(1/(d*e*x+c*e)^(3/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{4} e^{2} x^{4} + 4 \, c d^{3} e^{2} x^{3} + {\left(6 \, c^{2} - 1\right)} d^{2} e^{2} x^{2} + 2 \, {\left(2 \, c^{3} - c\right)} d e^{2} x + {\left(c^{4} - c^{2}\right)} e^{2}}, x\right)"," ",0,"integral(-sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^4*e^2*x^4 + 4*c*d^3*e^2*x^3 + (6*c^2 - 1)*d^2*e^2*x^2 + 2*(2*c^3 - c)*d*e^2*x + (c^4 - c^2)*e^2), x)","F",0
1411,0,0,0,0.434416," ","integrate(1/(d*e*x+c*e)^(7/2)/(-d^2*x^2-2*c*d*x-c^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-d^{2} x^{2} - 2 \, c d x - c^{2} + 1} \sqrt{d e x + c e}}{d^{6} e^{4} x^{6} + 6 \, c d^{5} e^{4} x^{5} + {\left(15 \, c^{2} - 1\right)} d^{4} e^{4} x^{4} + 4 \, {\left(5 \, c^{3} - c\right)} d^{3} e^{4} x^{3} + 3 \, {\left(5 \, c^{4} - 2 \, c^{2}\right)} d^{2} e^{4} x^{2} + 2 \, {\left(3 \, c^{5} - 2 \, c^{3}\right)} d e^{4} x + {\left(c^{6} - c^{4}\right)} e^{4}}, x\right)"," ",0,"integral(-sqrt(-d^2*x^2 - 2*c*d*x - c^2 + 1)*sqrt(d*e*x + c*e)/(d^6*e^4*x^6 + 6*c*d^5*e^4*x^5 + (15*c^2 - 1)*d^4*e^4*x^4 + 4*(5*c^3 - c)*d^3*e^4*x^3 + 3*(5*c^4 - 2*c^2)*d^2*e^4*x^2 + 2*(3*c^5 - 2*c^3)*d*e^4*x + (c^6 - c^4)*e^4), x)","F",0
1412,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(11/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1413,1,194,0,0.481955," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(17/3),x, algorithm=""fricas"")","\frac{3 \, {\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} {\left(2 \, c d x + b d\right)}^{\frac{1}{3}} {\left(c x^{2} + b x + a\right)}^{\frac{1}{3}}}{7 \, {\left(32 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{6} x^{5} + 80 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{6} x^{4} + 80 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{6} x^{3} + 40 \, {\left(b^{5} c^{2} - 4 \, a b^{3} c^{3}\right)} d^{6} x^{2} + 10 \, {\left(b^{6} c - 4 \, a b^{4} c^{2}\right)} d^{6} x + {\left(b^{7} - 4 \, a b^{5} c\right)} d^{6}\right)}}"," ",0,"3/7*(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*(2*c*d*x + b*d)^(1/3)*(c*x^2 + b*x + a)^(1/3)/(32*(b^2*c^5 - 4*a*c^6)*d^6*x^5 + 80*(b^3*c^4 - 4*a*b*c^5)*d^6*x^4 + 80*(b^4*c^3 - 4*a*b^2*c^4)*d^6*x^3 + 40*(b^5*c^2 - 4*a*b^3*c^3)*d^6*x^2 + 10*(b^6*c - 4*a*b^4*c^2)*d^6*x + (b^7 - 4*a*b^5*c)*d^6)","B",0
1414,1,409,0,0.542105," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(23/3),x, algorithm=""fricas"")","\frac{3 \, {\left(6 \, c^{4} x^{6} + 18 \, b c^{3} x^{5} + {\left(23 \, b^{2} c^{2} - 2 \, a c^{3}\right)} x^{4} + 5 \, a^{2} b^{2} - 14 \, a^{3} c + 4 \, {\left(4 \, b^{3} c - a b c^{2}\right)} x^{3} + {\left(5 \, b^{4} + 8 \, a b^{2} c - 22 \, a^{2} c^{2}\right)} x^{2} + 2 \, {\left(5 \, a b^{3} - 11 \, a^{2} b c\right)} x\right)} {\left(2 \, c d x + b d\right)}^{\frac{1}{3}} {\left(c x^{2} + b x + a\right)}^{\frac{1}{3}}}{35 \, {\left(128 \, {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} d^{8} x^{7} + 448 \, {\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} d^{8} x^{6} + 672 \, {\left(b^{6} c^{5} - 8 \, a b^{4} c^{6} + 16 \, a^{2} b^{2} c^{7}\right)} d^{8} x^{5} + 560 \, {\left(b^{7} c^{4} - 8 \, a b^{5} c^{5} + 16 \, a^{2} b^{3} c^{6}\right)} d^{8} x^{4} + 280 \, {\left(b^{8} c^{3} - 8 \, a b^{6} c^{4} + 16 \, a^{2} b^{4} c^{5}\right)} d^{8} x^{3} + 84 \, {\left(b^{9} c^{2} - 8 \, a b^{7} c^{3} + 16 \, a^{2} b^{5} c^{4}\right)} d^{8} x^{2} + 14 \, {\left(b^{10} c - 8 \, a b^{8} c^{2} + 16 \, a^{2} b^{6} c^{3}\right)} d^{8} x + {\left(b^{11} - 8 \, a b^{9} c + 16 \, a^{2} b^{7} c^{2}\right)} d^{8}\right)}}"," ",0,"3/35*(6*c^4*x^6 + 18*b*c^3*x^5 + (23*b^2*c^2 - 2*a*c^3)*x^4 + 5*a^2*b^2 - 14*a^3*c + 4*(4*b^3*c - a*b*c^2)*x^3 + (5*b^4 + 8*a*b^2*c - 22*a^2*c^2)*x^2 + 2*(5*a*b^3 - 11*a^2*b*c)*x)*(2*c*d*x + b*d)^(1/3)*(c*x^2 + b*x + a)^(1/3)/(128*(b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*d^8*x^7 + 448*(b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*d^8*x^6 + 672*(b^6*c^5 - 8*a*b^4*c^6 + 16*a^2*b^2*c^7)*d^8*x^5 + 560*(b^7*c^4 - 8*a*b^5*c^5 + 16*a^2*b^3*c^6)*d^8*x^4 + 280*(b^8*c^3 - 8*a*b^6*c^4 + 16*a^2*b^4*c^5)*d^8*x^3 + 84*(b^9*c^2 - 8*a*b^7*c^3 + 16*a^2*b^5*c^4)*d^8*x^2 + 14*(b^10*c - 8*a*b^8*c^2 + 16*a^2*b^6*c^3)*d^8*x + (b^11 - 8*a*b^9*c + 16*a^2*b^7*c^2)*d^8)","B",0
1415,1,687,0,0.701327," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(29/3),x, algorithm=""fricas"")","\frac{3 \, {\left(144 \, c^{6} x^{8} + 576 \, b c^{5} x^{7} + 12 \, {\left(85 \, b^{2} c^{4} - 4 \, a c^{5}\right)} x^{6} + 65 \, a^{2} b^{4} - 364 \, a^{3} b^{2} c + 560 \, a^{4} c^{2} + 36 \, {\left(29 \, b^{3} c^{3} - 4 \, a b c^{4}\right)} x^{5} + {\left(677 \, b^{4} c^{2} - 196 \, a b^{2} c^{3} + 32 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(143 \, b^{5} c - 76 \, a b^{3} c^{2} + 32 \, a^{2} b c^{3}\right)} x^{3} + {\left(65 \, b^{6} + 78 \, a b^{4} c - 540 \, a^{2} b^{2} c^{2} + 784 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(65 \, a b^{5} - 286 \, a^{2} b^{3} c + 392 \, a^{3} b c^{2}\right)} x\right)} {\left(2 \, c d x + b d\right)}^{\frac{1}{3}} {\left(c x^{2} + b x + a\right)}^{\frac{1}{3}}}{455 \, {\left(512 \, {\left(b^{6} c^{9} - 12 \, a b^{4} c^{10} + 48 \, a^{2} b^{2} c^{11} - 64 \, a^{3} c^{12}\right)} d^{10} x^{9} + 2304 \, {\left(b^{7} c^{8} - 12 \, a b^{5} c^{9} + 48 \, a^{2} b^{3} c^{10} - 64 \, a^{3} b c^{11}\right)} d^{10} x^{8} + 4608 \, {\left(b^{8} c^{7} - 12 \, a b^{6} c^{8} + 48 \, a^{2} b^{4} c^{9} - 64 \, a^{3} b^{2} c^{10}\right)} d^{10} x^{7} + 5376 \, {\left(b^{9} c^{6} - 12 \, a b^{7} c^{7} + 48 \, a^{2} b^{5} c^{8} - 64 \, a^{3} b^{3} c^{9}\right)} d^{10} x^{6} + 4032 \, {\left(b^{10} c^{5} - 12 \, a b^{8} c^{6} + 48 \, a^{2} b^{6} c^{7} - 64 \, a^{3} b^{4} c^{8}\right)} d^{10} x^{5} + 2016 \, {\left(b^{11} c^{4} - 12 \, a b^{9} c^{5} + 48 \, a^{2} b^{7} c^{6} - 64 \, a^{3} b^{5} c^{7}\right)} d^{10} x^{4} + 672 \, {\left(b^{12} c^{3} - 12 \, a b^{10} c^{4} + 48 \, a^{2} b^{8} c^{5} - 64 \, a^{3} b^{6} c^{6}\right)} d^{10} x^{3} + 144 \, {\left(b^{13} c^{2} - 12 \, a b^{11} c^{3} + 48 \, a^{2} b^{9} c^{4} - 64 \, a^{3} b^{7} c^{5}\right)} d^{10} x^{2} + 18 \, {\left(b^{14} c - 12 \, a b^{12} c^{2} + 48 \, a^{2} b^{10} c^{3} - 64 \, a^{3} b^{8} c^{4}\right)} d^{10} x + {\left(b^{15} - 12 \, a b^{13} c + 48 \, a^{2} b^{11} c^{2} - 64 \, a^{3} b^{9} c^{3}\right)} d^{10}\right)}}"," ",0,"3/455*(144*c^6*x^8 + 576*b*c^5*x^7 + 12*(85*b^2*c^4 - 4*a*c^5)*x^6 + 65*a^2*b^4 - 364*a^3*b^2*c + 560*a^4*c^2 + 36*(29*b^3*c^3 - 4*a*b*c^4)*x^5 + (677*b^4*c^2 - 196*a*b^2*c^3 + 32*a^2*c^4)*x^4 + 2*(143*b^5*c - 76*a*b^3*c^2 + 32*a^2*b*c^3)*x^3 + (65*b^6 + 78*a*b^4*c - 540*a^2*b^2*c^2 + 784*a^3*c^3)*x^2 + 2*(65*a*b^5 - 286*a^2*b^3*c + 392*a^3*b*c^2)*x)*(2*c*d*x + b*d)^(1/3)*(c*x^2 + b*x + a)^(1/3)/(512*(b^6*c^9 - 12*a*b^4*c^10 + 48*a^2*b^2*c^11 - 64*a^3*c^12)*d^10*x^9 + 2304*(b^7*c^8 - 12*a*b^5*c^9 + 48*a^2*b^3*c^10 - 64*a^3*b*c^11)*d^10*x^8 + 4608*(b^8*c^7 - 12*a*b^6*c^8 + 48*a^2*b^4*c^9 - 64*a^3*b^2*c^10)*d^10*x^7 + 5376*(b^9*c^6 - 12*a*b^7*c^7 + 48*a^2*b^5*c^8 - 64*a^3*b^3*c^9)*d^10*x^6 + 4032*(b^10*c^5 - 12*a*b^8*c^6 + 48*a^2*b^6*c^7 - 64*a^3*b^4*c^8)*d^10*x^5 + 2016*(b^11*c^4 - 12*a*b^9*c^5 + 48*a^2*b^7*c^6 - 64*a^3*b^5*c^7)*d^10*x^4 + 672*(b^12*c^3 - 12*a*b^10*c^4 + 48*a^2*b^8*c^5 - 64*a^3*b^6*c^6)*d^10*x^3 + 144*(b^13*c^2 - 12*a*b^11*c^3 + 48*a^2*b^9*c^4 - 64*a^3*b^7*c^5)*d^10*x^2 + 18*(b^14*c - 12*a*b^12*c^2 + 48*a^2*b^10*c^3 - 64*a^3*b^8*c^4)*d^10*x + (b^15 - 12*a*b^13*c + 48*a^2*b^11*c^2 - 64*a^3*b^9*c^3)*d^10)","B",0
1416,0,0,0,0.429094," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{{\left(2 \, c d x + b d\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(4/3)/(2*c*d*x + b*d)^(2/3), x)","F",0
1417,0,0,0,0.440144," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(8/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{\frac{1}{3}} {\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{8 \, c^{3} d^{3} x^{3} + 12 \, b c^{2} d^{3} x^{2} + 6 \, b^{2} c d^{3} x + b^{3} d^{3}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^(1/3)*(c*x^2 + b*x + a)^(4/3)/(8*c^3*d^3*x^3 + 12*b*c^2*d^3*x^2 + 6*b^2*c*d^3*x + b^3*d^3), x)","F",0
1418,0,0,0,0.453488," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(14/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{\frac{1}{3}} {\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{32 \, c^{5} d^{5} x^{5} + 80 \, b c^{4} d^{5} x^{4} + 80 \, b^{2} c^{3} d^{5} x^{3} + 40 \, b^{3} c^{2} d^{5} x^{2} + 10 \, b^{4} c d^{5} x + b^{5} d^{5}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^(1/3)*(c*x^2 + b*x + a)^(4/3)/(32*c^5*d^5*x^5 + 80*b*c^4*d^5*x^4 + 80*b^2*c^3*d^5*x^3 + 40*b^3*c^2*d^5*x^2 + 10*b^4*c*d^5*x + b^5*d^5), x)","F",0
1419,0,0,0,0.534291," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(20/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{\frac{1}{3}} {\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{128 \, c^{7} d^{7} x^{7} + 448 \, b c^{6} d^{7} x^{6} + 672 \, b^{2} c^{5} d^{7} x^{5} + 560 \, b^{3} c^{4} d^{7} x^{4} + 280 \, b^{4} c^{3} d^{7} x^{3} + 84 \, b^{5} c^{2} d^{7} x^{2} + 14 \, b^{6} c d^{7} x + b^{7} d^{7}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^(1/3)*(c*x^2 + b*x + a)^(4/3)/(128*c^7*d^7*x^7 + 448*b*c^6*d^7*x^6 + 672*b^2*c^5*d^7*x^5 + 560*b^3*c^4*d^7*x^4 + 280*b^4*c^3*d^7*x^3 + 84*b^5*c^2*d^7*x^2 + 14*b^6*c*d^7*x + b^7*d^7), x)","F",0
1420,0,0,0,0.437042," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{\frac{2}{3}} {\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{4 \, c^{2} d^{2} x^{2} + 4 \, b c d^{2} x + b^{2} d^{2}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^(2/3)*(c*x^2 + b*x + a)^(4/3)/(4*c^2*d^2*x^2 + 4*b*c*d^2*x + b^2*d^2), x)","F",0
1421,0,0,0,0.457226," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(10/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{\frac{2}{3}} {\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{16 \, c^{4} d^{4} x^{4} + 32 \, b c^{3} d^{4} x^{3} + 24 \, b^{2} c^{2} d^{4} x^{2} + 8 \, b^{3} c d^{4} x + b^{4} d^{4}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^(2/3)*(c*x^2 + b*x + a)^(4/3)/(16*c^4*d^4*x^4 + 32*b*c^3*d^4*x^3 + 24*b^2*c^2*d^4*x^2 + 8*b^3*c*d^4*x + b^4*d^4), x)","F",0
1422,0,0,0,0.477105," ","integrate((c*x^2+b*x+a)^(4/3)/(2*c*d*x+b*d)^(16/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{\frac{2}{3}} {\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}}{64 \, c^{6} d^{6} x^{6} + 192 \, b c^{5} d^{6} x^{5} + 240 \, b^{2} c^{4} d^{6} x^{4} + 160 \, b^{3} c^{3} d^{6} x^{3} + 60 \, b^{4} c^{2} d^{6} x^{2} + 12 \, b^{5} c d^{6} x + b^{6} d^{6}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^(2/3)*(c*x^2 + b*x + a)^(4/3)/(64*c^6*d^6*x^6 + 192*b*c^5*d^6*x^5 + 240*b^2*c^4*d^6*x^4 + 160*b^3*c^3*d^6*x^3 + 60*b^4*c^2*d^6*x^2 + 12*b^5*c*d^6*x + b^6*d^6), x)","F",0
1423,1,691,0,0.417767," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left(4 \, a^{3} b c^{3} m^{3} + 8 \, {\left(c^{7} m^{3} + 9 \, c^{7} m^{2} + 23 \, c^{7} m + 15 \, c^{7}\right)} x^{7} - 3 \, b^{7} + 42 \, a b^{5} c - 210 \, a^{2} b^{3} c^{2} + 420 \, a^{3} b c^{3} + 28 \, {\left(b c^{6} m^{3} + 9 \, b c^{6} m^{2} + 23 \, b c^{6} m + 15 \, b c^{6}\right)} x^{6} + 12 \, {\left(42 \, b^{2} c^{5} + 42 \, a c^{6} + {\left(3 \, b^{2} c^{5} + 2 \, a c^{6}\right)} m^{3} + 2 \, {\left(13 \, b^{2} c^{5} + 11 \, a c^{6}\right)} m^{2} + {\left(65 \, b^{2} c^{5} + 62 \, a c^{6}\right)} m\right)} x^{5} + 10 \, {\left(21 \, b^{3} c^{4} + 126 \, a b c^{5} + 2 \, {\left(b^{3} c^{4} + 3 \, a b c^{5}\right)} m^{3} + 3 \, {\left(5 \, b^{3} c^{4} + 22 \, a b c^{5}\right)} m^{2} + 2 \, {\left(17 \, b^{3} c^{4} + 93 \, a b c^{5}\right)} m\right)} x^{4} + 4 \, {\left(210 \, a b^{2} c^{4} + 210 \, a^{2} c^{5} + {\left(b^{4} c^{3} + 12 \, a b^{2} c^{4} + 6 \, a^{2} c^{5}\right)} m^{3} + 3 \, {\left(b^{4} c^{3} + 42 \, a b^{2} c^{4} + 26 \, a^{2} c^{5}\right)} m^{2} + 2 \, {\left(b^{4} c^{3} + 162 \, a b^{2} c^{4} + 141 \, a^{2} c^{5}\right)} m\right)} x^{3} - 6 \, {\left(a^{2} b^{3} c^{2} - 10 \, a^{3} b c^{3}\right)} m^{2} + 6 \, {\left(210 \, a^{2} b c^{4} + 2 \, {\left(a b^{3} c^{3} + 3 \, a^{2} b c^{4}\right)} m^{3} - {\left(b^{5} c^{2} - 16 \, a b^{3} c^{3} - 78 \, a^{2} b c^{4}\right)} m^{2} - {\left(b^{5} c^{2} - 14 \, a b^{3} c^{3} - 282 \, a^{2} b c^{4}\right)} m\right)} x^{2} + 2 \, {\left(3 \, a b^{5} c - 36 \, a^{2} b^{3} c^{2} + 142 \, a^{3} b c^{3}\right)} m + 2 \, {\left(420 \, a^{3} c^{4} + 2 \, {\left(3 \, a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} m^{3} - 6 \, {\left(a b^{4} c^{2} - 12 \, a^{2} b^{2} c^{3} - 10 \, a^{3} c^{4}\right)} m^{2} + {\left(3 \, b^{6} c - 42 \, a b^{4} c^{2} + 210 \, a^{2} b^{2} c^{3} + 284 \, a^{3} c^{4}\right)} m\right)} x\right)} {\left(2 \, c d x + b d\right)}^{m}}{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*(4*a^3*b*c^3*m^3 + 8*(c^7*m^3 + 9*c^7*m^2 + 23*c^7*m + 15*c^7)*x^7 - 3*b^7 + 42*a*b^5*c - 210*a^2*b^3*c^2 + 420*a^3*b*c^3 + 28*(b*c^6*m^3 + 9*b*c^6*m^2 + 23*b*c^6*m + 15*b*c^6)*x^6 + 12*(42*b^2*c^5 + 42*a*c^6 + (3*b^2*c^5 + 2*a*c^6)*m^3 + 2*(13*b^2*c^5 + 11*a*c^6)*m^2 + (65*b^2*c^5 + 62*a*c^6)*m)*x^5 + 10*(21*b^3*c^4 + 126*a*b*c^5 + 2*(b^3*c^4 + 3*a*b*c^5)*m^3 + 3*(5*b^3*c^4 + 22*a*b*c^5)*m^2 + 2*(17*b^3*c^4 + 93*a*b*c^5)*m)*x^4 + 4*(210*a*b^2*c^4 + 210*a^2*c^5 + (b^4*c^3 + 12*a*b^2*c^4 + 6*a^2*c^5)*m^3 + 3*(b^4*c^3 + 42*a*b^2*c^4 + 26*a^2*c^5)*m^2 + 2*(b^4*c^3 + 162*a*b^2*c^4 + 141*a^2*c^5)*m)*x^3 - 6*(a^2*b^3*c^2 - 10*a^3*b*c^3)*m^2 + 6*(210*a^2*b*c^4 + 2*(a*b^3*c^3 + 3*a^2*b*c^4)*m^3 - (b^5*c^2 - 16*a*b^3*c^3 - 78*a^2*b*c^4)*m^2 - (b^5*c^2 - 14*a*b^3*c^3 - 282*a^2*b*c^4)*m)*x^2 + 2*(3*a*b^5*c - 36*a^2*b^3*c^2 + 142*a^3*b*c^3)*m + 2*(420*a^3*c^4 + 2*(3*a^2*b^2*c^3 + 2*a^3*c^4)*m^3 - 6*(a*b^4*c^2 - 12*a^2*b^2*c^3 - 10*a^3*c^4)*m^2 + (3*b^6*c - 42*a*b^4*c^2 + 210*a^2*b^2*c^3 + 284*a^3*c^4)*m)*x)*(2*c*d*x + b*d)^m/(c^4*m^4 + 16*c^4*m^3 + 86*c^4*m^2 + 176*c^4*m + 105*c^4)","B",0
1424,1,307,0,0.416191," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} b c^{2} m^{2} + 4 \, {\left(c^{5} m^{2} + 4 \, c^{5} m + 3 \, c^{5}\right)} x^{5} + b^{5} - 10 \, a b^{3} c + 30 \, a^{2} b c^{2} + 10 \, {\left(b c^{4} m^{2} + 4 \, b c^{4} m + 3 \, b c^{4}\right)} x^{4} + 4 \, {\left(5 \, b^{2} c^{3} + 10 \, a c^{4} + 2 \, {\left(b^{2} c^{3} + a c^{4}\right)} m^{2} + {\left(7 \, b^{2} c^{3} + 12 \, a c^{4}\right)} m\right)} x^{3} + 2 \, {\left(30 \, a b c^{3} + {\left(b^{3} c^{2} + 6 \, a b c^{3}\right)} m^{2} + {\left(b^{3} c^{2} + 36 \, a b c^{3}\right)} m\right)} x^{2} - 2 \, {\left(a b^{3} c - 8 \, a^{2} b c^{2}\right)} m + 2 \, {\left(30 \, a^{2} c^{3} + 2 \, {\left(a b^{2} c^{2} + a^{2} c^{3}\right)} m^{2} - {\left(b^{4} c - 10 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} m\right)} x\right)} {\left(2 \, c d x + b d\right)}^{m}}{4 \, {\left(c^{3} m^{3} + 9 \, c^{3} m^{2} + 23 \, c^{3} m + 15 \, c^{3}\right)}}"," ",0,"1/4*(2*a^2*b*c^2*m^2 + 4*(c^5*m^2 + 4*c^5*m + 3*c^5)*x^5 + b^5 - 10*a*b^3*c + 30*a^2*b*c^2 + 10*(b*c^4*m^2 + 4*b*c^4*m + 3*b*c^4)*x^4 + 4*(5*b^2*c^3 + 10*a*c^4 + 2*(b^2*c^3 + a*c^4)*m^2 + (7*b^2*c^3 + 12*a*c^4)*m)*x^3 + 2*(30*a*b*c^3 + (b^3*c^2 + 6*a*b*c^3)*m^2 + (b^3*c^2 + 36*a*b*c^3)*m)*x^2 - 2*(a*b^3*c - 8*a^2*b*c^2)*m + 2*(30*a^2*c^3 + 2*(a*b^2*c^2 + a^2*c^3)*m^2 - (b^4*c - 10*a*b^2*c^2 - 16*a^2*c^3)*m)*x)*(2*c*d*x + b*d)^m/(c^3*m^3 + 9*c^3*m^2 + 23*c^3*m + 15*c^3)","B",0
1425,1,106,0,0.419208," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{{\left(2 \, a b c m + 4 \, {\left(c^{3} m + c^{3}\right)} x^{3} - b^{3} + 6 \, a b c + 6 \, {\left(b c^{2} m + b c^{2}\right)} x^{2} + 2 \, {\left(6 \, a c^{2} + {\left(b^{2} c + 2 \, a c^{2}\right)} m\right)} x\right)} {\left(2 \, c d x + b d\right)}^{m}}{4 \, {\left(c^{2} m^{2} + 4 \, c^{2} m + 3 \, c^{2}\right)}}"," ",0,"1/4*(2*a*b*c*m + 4*(c^3*m + c^3)*x^3 - b^3 + 6*a*b*c + 6*(b*c^2*m + b*c^2)*x^2 + 2*(6*a*c^2 + (b^2*c + 2*a*c^2)*m)*x)*(2*c*d*x + b*d)^m/(c^2*m^2 + 4*c^2*m + 3*c^2)","A",0
1426,0,0,0,0.404069," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{m}}{c x^{2} + b x + a}, x\right)"," ",0,"integral((2*c*d*x + b*d)^m/(c*x^2 + b*x + a), x)","F",0
1427,0,0,0,0.433926," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^m/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1428,0,0,0,0.415120," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{m}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^m/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1429,0,0,0,0.414314," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a} {\left(2 \, c d x + b d\right)}^{m}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)*(2*c*d*x + b*d)^m, x)","F",0
1430,0,0,0,0.437160," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(2 \, c d x + b d\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/2)*(2*c*d*x + b*d)^m, x)","F",0
1431,0,0,0,0.422827," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} {\left(2 \, c d x + b d\right)}^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*d*x + b*d)^m, x)","F",0
1432,0,0,0,0.434824," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, c d x + b d\right)}^{m}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((2*c*d*x + b*d)^m/sqrt(c*x^2 + b*x + a), x)","F",0
1433,0,0,0,0.425600," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c d x + b d\right)}^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*d*x + b*d)^m/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
1434,0,0,0,0.426105," ","integrate((2*c*d*x+b*d)^m/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c d x + b d\right)}^{m}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(2*c*d*x + b*d)^m/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
1435,0,0,0,0.445016," ","integrate((2*c*d*x+b*d)^m*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, c d x + b d\right)}^{m} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((2*c*d*x + b*d)^m*(c*x^2 + b*x + a)^p, x)","F",0
1436,1,401,0,0.431358," ","integrate((2*c*d*x+b*d)^5*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","\frac{{\left(a b^{4} d^{5} p^{2} + {\left(5 \, a b^{4} - 8 \, a^{2} b^{2} c\right)} d^{5} p + 16 \, {\left(c^{5} d^{5} p^{2} + 3 \, c^{5} d^{5} p + 2 \, c^{5} d^{5}\right)} x^{6} + 2 \, {\left(3 \, a b^{4} - 12 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} d^{5} + 48 \, {\left(b c^{4} d^{5} p^{2} + 3 \, b c^{4} d^{5} p + 2 \, b c^{4} d^{5}\right)} x^{5} + 8 \, {\left(15 \, b^{2} c^{3} d^{5} + {\left(7 \, b^{2} c^{3} + 2 \, a c^{4}\right)} d^{5} p^{2} + 2 \, {\left(11 \, b^{2} c^{3} + a c^{4}\right)} d^{5} p\right)} x^{4} + 16 \, {\left(5 \, b^{3} c^{2} d^{5} + 2 \, {\left(b^{3} c^{2} + a b c^{3}\right)} d^{5} p^{2} + {\left(7 \, b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{5} p\right)} x^{3} + {\left(30 \, b^{4} c d^{5} + 3 \, {\left(3 \, b^{4} c + 8 \, a b^{2} c^{2}\right)} d^{5} p^{2} + {\left(37 \, b^{4} c + 40 \, a b^{2} c^{2} - 32 \, a^{2} c^{3}\right)} d^{5} p\right)} x^{2} + {\left(6 \, b^{5} d^{5} + {\left(b^{5} + 8 \, a b^{3} c\right)} d^{5} p^{2} + {\left(5 \, b^{5} + 24 \, a b^{3} c - 32 \, a^{2} b c^{2}\right)} d^{5} p\right)} x\right)} {\left(c x^{2} + b x + a\right)}^{p}}{p^{3} + 6 \, p^{2} + 11 \, p + 6}"," ",0,"(a*b^4*d^5*p^2 + (5*a*b^4 - 8*a^2*b^2*c)*d^5*p + 16*(c^5*d^5*p^2 + 3*c^5*d^5*p + 2*c^5*d^5)*x^6 + 2*(3*a*b^4 - 12*a^2*b^2*c + 16*a^3*c^2)*d^5 + 48*(b*c^4*d^5*p^2 + 3*b*c^4*d^5*p + 2*b*c^4*d^5)*x^5 + 8*(15*b^2*c^3*d^5 + (7*b^2*c^3 + 2*a*c^4)*d^5*p^2 + 2*(11*b^2*c^3 + a*c^4)*d^5*p)*x^4 + 16*(5*b^3*c^2*d^5 + 2*(b^3*c^2 + a*b*c^3)*d^5*p^2 + (7*b^3*c^2 + 2*a*b*c^3)*d^5*p)*x^3 + (30*b^4*c*d^5 + 3*(3*b^4*c + 8*a*b^2*c^2)*d^5*p^2 + (37*b^4*c + 40*a*b^2*c^2 - 32*a^2*c^3)*d^5*p)*x^2 + (6*b^5*d^5 + (b^5 + 8*a*b^3*c)*d^5*p^2 + (5*b^5 + 24*a*b^3*c - 32*a^2*b*c^2)*d^5*p)*x)*(c*x^2 + b*x + a)^p/(p^3 + 6*p^2 + 11*p + 6)","B",0
1437,0,0,0,0.431377," ","integrate((2*c*d*x+b*d)^4*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(16 \, c^{4} d^{4} x^{4} + 32 \, b c^{3} d^{4} x^{3} + 24 \, b^{2} c^{2} d^{4} x^{2} + 8 \, b^{3} c d^{4} x + b^{4} d^{4}\right)} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((16*c^4*d^4*x^4 + 32*b*c^3*d^4*x^3 + 24*b^2*c^2*d^4*x^2 + 8*b^3*c*d^4*x + b^4*d^4)*(c*x^2 + b*x + a)^p, x)","F",0
1438,1,151,0,0.420366," ","integrate((2*c*d*x+b*d)^3*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","\frac{{\left(a b^{2} d^{3} p + 4 \, {\left(c^{3} d^{3} p + c^{3} d^{3}\right)} x^{4} + 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{3} + 8 \, {\left(b c^{2} d^{3} p + b c^{2} d^{3}\right)} x^{3} + {\left(6 \, b^{2} c d^{3} + {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} d^{3} p\right)} x^{2} + {\left(2 \, b^{3} d^{3} + {\left(b^{3} + 4 \, a b c\right)} d^{3} p\right)} x\right)} {\left(c x^{2} + b x + a\right)}^{p}}{p^{2} + 3 \, p + 2}"," ",0,"(a*b^2*d^3*p + 4*(c^3*d^3*p + c^3*d^3)*x^4 + 2*(a*b^2 - 2*a^2*c)*d^3 + 8*(b*c^2*d^3*p + b*c^2*d^3)*x^3 + (6*b^2*c*d^3 + (5*b^2*c + 4*a*c^2)*d^3*p)*x^2 + (2*b^3*d^3 + (b^3 + 4*a*b*c)*d^3*p)*x)*(c*x^2 + b*x + a)^p/(p^2 + 3*p + 2)","B",0
1439,0,0,0,0.420119," ","integrate((2*c*d*x+b*d)^2*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(4 \, c^{2} d^{2} x^{2} + 4 \, b c d^{2} x + b^{2} d^{2}\right)} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((4*c^2*d^2*x^2 + 4*b*c*d^2*x + b^2*d^2)*(c*x^2 + b*x + a)^p, x)","F",0
1440,1,32,0,0.425878," ","integrate((2*c*d*x+b*d)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","\frac{{\left(c d x^{2} + b d x + a d\right)} {\left(c x^{2} + b x + a\right)}^{p}}{p + 1}"," ",0,"(c*d*x^2 + b*d*x + a*d)*(c*x^2 + b*x + a)^p/(p + 1)","A",0
1441,0,0,0,0.426044," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{2 \, c d x + b d}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/(2*c*d*x + b*d), x)","F",0
1442,0,0,0,0.433297," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{4 \, c^{2} d^{2} x^{2} + 4 \, b c d^{2} x + b^{2} d^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/(4*c^2*d^2*x^2 + 4*b*c*d^2*x + b^2*d^2), x)","F",0
1443,0,0,0,0.441019," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{8 \, c^{3} d^{3} x^{3} + 12 \, b c^{2} d^{3} x^{2} + 6 \, b^{2} c d^{3} x + b^{3} d^{3}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/(8*c^3*d^3*x^3 + 12*b*c^2*d^3*x^2 + 6*b^2*c*d^3*x + b^3*d^3), x)","F",0
1444,0,0,0,0.436473," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{16 \, c^{4} d^{4} x^{4} + 32 \, b c^{3} d^{4} x^{3} + 24 \, b^{2} c^{2} d^{4} x^{2} + 8 \, b^{3} c d^{4} x + b^{4} d^{4}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/(16*c^4*d^4*x^4 + 32*b*c^3*d^4*x^3 + 24*b^2*c^2*d^4*x^2 + 8*b^3*c*d^4*x + b^4*d^4), x)","F",0
1445,0,0,0,0.422162," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{32 \, c^{5} d^{5} x^{5} + 80 \, b c^{4} d^{5} x^{4} + 80 \, b^{2} c^{3} d^{5} x^{3} + 40 \, b^{3} c^{2} d^{5} x^{2} + 10 \, b^{4} c d^{5} x + b^{5} d^{5}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/(32*c^5*d^5*x^5 + 80*b*c^4*d^5*x^4 + 80*b^2*c^3*d^5*x^3 + 40*b^3*c^2*d^5*x^2 + 10*b^4*c*d^5*x + b^5*d^5), x)","F",0
1446,0,0,0,0.444947," ","integrate((c*x^2+b*x+a)^p/(2*c*d*x+b*d)^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{64 \, c^{6} d^{6} x^{6} + 192 \, b c^{5} d^{6} x^{5} + 240 \, b^{2} c^{4} d^{6} x^{4} + 160 \, b^{3} c^{3} d^{6} x^{3} + 60 \, b^{4} c^{2} d^{6} x^{2} + 12 \, b^{5} c d^{6} x + b^{6} d^{6}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/(64*c^6*d^6*x^6 + 192*b*c^5*d^6*x^5 + 240*b^2*c^4*d^6*x^4 + 160*b^3*c^3*d^6*x^3 + 60*b^4*c^2*d^6*x^2 + 12*b^5*c*d^6*x + b^6*d^6), x)","F",0
1447,1,12,0,0.402057," ","integrate((1+x)/(x^2+2*x-3)^(2/3),x, algorithm=""fricas"")","\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
1448,1,15,0,0.424330," ","integrate((c*x+b)/(c*x^2+2*b*x+a)^(3/7),x, algorithm=""fricas"")","\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
1449,1,24,0,0.416470," ","integrate((1+x)^m*(x^2+2*x+1)^n,x, algorithm=""fricas"")","\frac{{\left(x + 1\right)}^{m} {\left(x + 1\right)}^{2 \, n} {\left(x + 1\right)}}{m + 2 \, n + 1}"," ",0,"(x + 1)^m*(x + 1)^(2*n)*(x + 1)/(m + 2*n + 1)","A",0
1450,1,63,0,0.419757," ","integrate((1/2*b*e/c+e*x)^m*(1/4/c*b^2+b*x+c*x^2)^n,x, algorithm=""fricas"")","\frac{{\left(2 \, c x + b\right)} \left(\frac{2 \, c e x + b e}{2 \, c}\right)^{m} e^{\left(2 \, n \log\left(\frac{2 \, c e x + b e}{2 \, c}\right) + n \log\left(\frac{c}{e^{2}}\right)\right)}}{2 \, {\left(c m + 2 \, c n + c\right)}}"," ",0,"1/2*(2*c*x + b)*(1/2*(2*c*e*x + b*e)/c)^m*e^(2*n*log(1/2*(2*c*e*x + b*e)/c) + n*log(c/e^2))/(c*m + 2*c*n + c)","A",0
1451,1,170,0,0.354457," ","integrate((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{4} b^{2} + \frac{2}{3} x^{6} e^{3} d b^{2} + \frac{1}{3} x^{6} e^{4} b a + \frac{6}{5} x^{5} e^{2} d^{2} b^{2} + \frac{8}{5} x^{5} e^{3} d b a + \frac{1}{5} x^{5} e^{4} a^{2} + x^{4} e d^{3} b^{2} + 3 x^{4} e^{2} d^{2} b a + x^{4} e^{3} d a^{2} + \frac{1}{3} x^{3} d^{4} b^{2} + \frac{8}{3} x^{3} e d^{3} b a + 2 x^{3} e^{2} d^{2} a^{2} + x^{2} d^{4} b a + 2 x^{2} e d^{3} a^{2} + x d^{4} a^{2}"," ",0,"1/7*x^7*e^4*b^2 + 2/3*x^6*e^3*d*b^2 + 1/3*x^6*e^4*b*a + 6/5*x^5*e^2*d^2*b^2 + 8/5*x^5*e^3*d*b*a + 1/5*x^5*e^4*a^2 + x^4*e*d^3*b^2 + 3*x^4*e^2*d^2*b*a + x^4*e^3*d*a^2 + 1/3*x^3*d^4*b^2 + 8/3*x^3*e*d^3*b*a + 2*x^3*e^2*d^2*a^2 + x^2*d^4*b*a + 2*x^2*e*d^3*a^2 + x*d^4*a^2","B",0
1452,1,130,0,0.354729," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{3} b^{2} + \frac{3}{5} x^{5} e^{2} d b^{2} + \frac{2}{5} x^{5} e^{3} b a + \frac{3}{4} x^{4} e d^{2} b^{2} + \frac{3}{2} x^{4} e^{2} d b a + \frac{1}{4} x^{4} e^{3} a^{2} + \frac{1}{3} x^{3} d^{3} b^{2} + 2 x^{3} e d^{2} b a + x^{3} e^{2} d a^{2} + x^{2} d^{3} b a + \frac{3}{2} x^{2} e d^{2} a^{2} + x d^{3} a^{2}"," ",0,"1/6*x^6*e^3*b^2 + 3/5*x^5*e^2*d*b^2 + 2/5*x^5*e^3*b*a + 3/4*x^4*e*d^2*b^2 + 3/2*x^4*e^2*d*b*a + 1/4*x^4*e^3*a^2 + 1/3*x^3*d^3*b^2 + 2*x^3*e*d^2*b*a + x^3*e^2*d*a^2 + x^2*d^3*b*a + 3/2*x^2*e*d^2*a^2 + x*d^3*a^2","B",0
1453,1,89,0,0.347154," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e^{2} b^{2} + \frac{1}{2} x^{4} e d b^{2} + \frac{1}{2} x^{4} e^{2} b a + \frac{1}{3} x^{3} d^{2} b^{2} + \frac{4}{3} x^{3} e d b a + \frac{1}{3} x^{3} e^{2} a^{2} + x^{2} d^{2} b a + x^{2} e d a^{2} + x d^{2} a^{2}"," ",0,"1/5*x^5*e^2*b^2 + 1/2*x^4*e*d*b^2 + 1/2*x^4*e^2*b*a + 1/3*x^3*d^2*b^2 + 4/3*x^3*e*d*b*a + 1/3*x^3*e^2*a^2 + x^2*d^2*b*a + x^2*e*d*a^2 + x*d^2*a^2","A",0
1454,1,49,0,0.348448," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{1}{4} x^{4} e b^{2} + \frac{1}{3} x^{3} d b^{2} + \frac{2}{3} x^{3} e b a + x^{2} d b a + \frac{1}{2} x^{2} e a^{2} + x d a^{2}"," ",0,"1/4*x^4*e*b^2 + 1/3*x^3*d*b^2 + 2/3*x^3*e*b*a + x^2*d*b*a + 1/2*x^2*e*a^2 + x*d*a^2","A",0
1455,1,20,0,0.348778," ","integrate(b^2*x^2+2*a*b*x+a^2,x, algorithm=""fricas"")","\frac{1}{3} x^{3} b^{2} + x^{2} b a + x a^{2}"," ",0,"1/3*x^3*b^2 + x^2*b*a + x*a^2","A",0
1456,1,62,0,0.393444," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d),x, algorithm=""fricas"")","\frac{b^{2} e^{2} x^{2} - 2 \, {\left(b^{2} d e - 2 \, a b e^{2}\right)} x + 2 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \log\left(e x + d\right)}{2 \, e^{3}}"," ",0,"1/2*(b^2*e^2*x^2 - 2*(b^2*d*e - 2*a*b*e^2)*x + 2*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*log(e*x + d))/e^3","A",0
1457,1,92,0,0.390935," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{b^{2} e^{2} x^{2} + b^{2} d e x - b^{2} d^{2} + 2 \, a b d e - a^{2} e^{2} - 2 \, {\left(b^{2} d^{2} - a b d e + {\left(b^{2} d e - a b e^{2}\right)} x\right)} \log\left(e x + d\right)}{e^{4} x + d e^{3}}"," ",0,"(b^2*e^2*x^2 + b^2*d*e*x - b^2*d^2 + 2*a*b*d*e - a^2*e^2 - 2*(b^2*d^2 - a*b*d*e + (b^2*d*e - a*b*e^2)*x)*log(e*x + d))/(e^4*x + d*e^3)","A",0
1458,1,100,0,0.385137," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{3 \, b^{2} d^{2} - 2 \, a b d e - a^{2} e^{2} + 4 \, {\left(b^{2} d e - a b e^{2}\right)} x + 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, b^{2} d e x + b^{2} d^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"1/2*(3*b^2*d^2 - 2*a*b*d*e - a^2*e^2 + 4*(b^2*d*e - a*b*e^2)*x + 2*(b^2*e^2*x^2 + 2*b^2*d*e*x + b^2*d^2)*log(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
1459,1,84,0,0.390395," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{3 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + a b d e + a^{2} e^{2} + 3 \, {\left(b^{2} d e + a b e^{2}\right)} x}{3 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/3*(3*b^2*e^2*x^2 + b^2*d^2 + a*b*d*e + a^2*e^2 + 3*(b^2*d*e + a*b*e^2)*x)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","B",0
1460,1,98,0,0.389704," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{6 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 2 \, a b d e + 3 \, a^{2} e^{2} + 4 \, {\left(b^{2} d e + 2 \, a b e^{2}\right)} x}{12 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/12*(6*b^2*e^2*x^2 + b^2*d^2 + 2*a*b*d*e + 3*a^2*e^2 + 4*(b^2*d*e + 2*a*b*e^2)*x)/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)","A",0
1461,1,109,0,0.370451," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{10 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 3 \, a b d e + 6 \, a^{2} e^{2} + 5 \, {\left(b^{2} d e + 3 \, a b e^{2}\right)} x}{30 \, {\left(e^{8} x^{5} + 5 \, d e^{7} x^{4} + 10 \, d^{2} e^{6} x^{3} + 10 \, d^{3} e^{5} x^{2} + 5 \, d^{4} e^{4} x + d^{5} e^{3}\right)}}"," ",0,"-1/30*(10*b^2*e^2*x^2 + b^2*d^2 + 3*a*b*d*e + 6*a^2*e^2 + 5*(b^2*d*e + 3*a*b*e^2)*x)/(e^8*x^5 + 5*d*e^7*x^4 + 10*d^2*e^6*x^3 + 10*d^3*e^5*x^2 + 5*d^4*e^4*x + d^5*e^3)","A",0
1462,1,120,0,0.389759," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{15 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + 4 \, a b d e + 10 \, a^{2} e^{2} + 6 \, {\left(b^{2} d e + 4 \, a b e^{2}\right)} x}{60 \, {\left(e^{9} x^{6} + 6 \, d e^{8} x^{5} + 15 \, d^{2} e^{7} x^{4} + 20 \, d^{3} e^{6} x^{3} + 15 \, d^{4} e^{5} x^{2} + 6 \, d^{5} e^{4} x + d^{6} e^{3}\right)}}"," ",0,"-1/60*(15*b^2*e^2*x^2 + b^2*d^2 + 4*a*b*d*e + 10*a^2*e^2 + 6*(b^2*d*e + 4*a*b*e^2)*x)/(e^9*x^6 + 6*d*e^8*x^5 + 15*d^2*e^7*x^4 + 20*d^3*e^6*x^3 + 15*d^4*e^5*x^2 + 6*d^5*e^4*x + d^6*e^3)","B",0
1463,1,470,0,0.344649," ","integrate((e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{6} b^{4} + \frac{3}{5} x^{10} e^{5} d b^{4} + \frac{2}{5} x^{10} e^{6} b^{3} a + \frac{5}{3} x^{9} e^{4} d^{2} b^{4} + \frac{8}{3} x^{9} e^{5} d b^{3} a + \frac{2}{3} x^{9} e^{6} b^{2} a^{2} + \frac{5}{2} x^{8} e^{3} d^{3} b^{4} + \frac{15}{2} x^{8} e^{4} d^{2} b^{3} a + \frac{9}{2} x^{8} e^{5} d b^{2} a^{2} + \frac{1}{2} x^{8} e^{6} b a^{3} + \frac{15}{7} x^{7} e^{2} d^{4} b^{4} + \frac{80}{7} x^{7} e^{3} d^{3} b^{3} a + \frac{90}{7} x^{7} e^{4} d^{2} b^{2} a^{2} + \frac{24}{7} x^{7} e^{5} d b a^{3} + \frac{1}{7} x^{7} e^{6} a^{4} + x^{6} e d^{5} b^{4} + 10 x^{6} e^{2} d^{4} b^{3} a + 20 x^{6} e^{3} d^{3} b^{2} a^{2} + 10 x^{6} e^{4} d^{2} b a^{3} + x^{6} e^{5} d a^{4} + \frac{1}{5} x^{5} d^{6} b^{4} + \frac{24}{5} x^{5} e d^{5} b^{3} a + 18 x^{5} e^{2} d^{4} b^{2} a^{2} + 16 x^{5} e^{3} d^{3} b a^{3} + 3 x^{5} e^{4} d^{2} a^{4} + x^{4} d^{6} b^{3} a + 9 x^{4} e d^{5} b^{2} a^{2} + 15 x^{4} e^{2} d^{4} b a^{3} + 5 x^{4} e^{3} d^{3} a^{4} + 2 x^{3} d^{6} b^{2} a^{2} + 8 x^{3} e d^{5} b a^{3} + 5 x^{3} e^{2} d^{4} a^{4} + 2 x^{2} d^{6} b a^{3} + 3 x^{2} e d^{5} a^{4} + x d^{6} a^{4}"," ",0,"1/11*x^11*e^6*b^4 + 3/5*x^10*e^5*d*b^4 + 2/5*x^10*e^6*b^3*a + 5/3*x^9*e^4*d^2*b^4 + 8/3*x^9*e^5*d*b^3*a + 2/3*x^9*e^6*b^2*a^2 + 5/2*x^8*e^3*d^3*b^4 + 15/2*x^8*e^4*d^2*b^3*a + 9/2*x^8*e^5*d*b^2*a^2 + 1/2*x^8*e^6*b*a^3 + 15/7*x^7*e^2*d^4*b^4 + 80/7*x^7*e^3*d^3*b^3*a + 90/7*x^7*e^4*d^2*b^2*a^2 + 24/7*x^7*e^5*d*b*a^3 + 1/7*x^7*e^6*a^4 + x^6*e*d^5*b^4 + 10*x^6*e^2*d^4*b^3*a + 20*x^6*e^3*d^3*b^2*a^2 + 10*x^6*e^4*d^2*b*a^3 + x^6*e^5*d*a^4 + 1/5*x^5*d^6*b^4 + 24/5*x^5*e*d^5*b^3*a + 18*x^5*e^2*d^4*b^2*a^2 + 16*x^5*e^3*d^3*b*a^3 + 3*x^5*e^4*d^2*a^4 + x^4*d^6*b^3*a + 9*x^4*e*d^5*b^2*a^2 + 15*x^4*e^2*d^4*b*a^3 + 5*x^4*e^3*d^3*a^4 + 2*x^3*d^6*b^2*a^2 + 8*x^3*e*d^5*b*a^3 + 5*x^3*e^2*d^4*a^4 + 2*x^2*d^6*b*a^3 + 3*x^2*e*d^5*a^4 + x*d^6*a^4","B",0
1464,1,396,0,0.344611," ","integrate((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{5} b^{4} + \frac{5}{9} x^{9} e^{4} d b^{4} + \frac{4}{9} x^{9} e^{5} b^{3} a + \frac{5}{4} x^{8} e^{3} d^{2} b^{4} + \frac{5}{2} x^{8} e^{4} d b^{3} a + \frac{3}{4} x^{8} e^{5} b^{2} a^{2} + \frac{10}{7} x^{7} e^{2} d^{3} b^{4} + \frac{40}{7} x^{7} e^{3} d^{2} b^{3} a + \frac{30}{7} x^{7} e^{4} d b^{2} a^{2} + \frac{4}{7} x^{7} e^{5} b a^{3} + \frac{5}{6} x^{6} e d^{4} b^{4} + \frac{20}{3} x^{6} e^{2} d^{3} b^{3} a + 10 x^{6} e^{3} d^{2} b^{2} a^{2} + \frac{10}{3} x^{6} e^{4} d b a^{3} + \frac{1}{6} x^{6} e^{5} a^{4} + \frac{1}{5} x^{5} d^{5} b^{4} + 4 x^{5} e d^{4} b^{3} a + 12 x^{5} e^{2} d^{3} b^{2} a^{2} + 8 x^{5} e^{3} d^{2} b a^{3} + x^{5} e^{4} d a^{4} + x^{4} d^{5} b^{3} a + \frac{15}{2} x^{4} e d^{4} b^{2} a^{2} + 10 x^{4} e^{2} d^{3} b a^{3} + \frac{5}{2} x^{4} e^{3} d^{2} a^{4} + 2 x^{3} d^{5} b^{2} a^{2} + \frac{20}{3} x^{3} e d^{4} b a^{3} + \frac{10}{3} x^{3} e^{2} d^{3} a^{4} + 2 x^{2} d^{5} b a^{3} + \frac{5}{2} x^{2} e d^{4} a^{4} + x d^{5} a^{4}"," ",0,"1/10*x^10*e^5*b^4 + 5/9*x^9*e^4*d*b^4 + 4/9*x^9*e^5*b^3*a + 5/4*x^8*e^3*d^2*b^4 + 5/2*x^8*e^4*d*b^3*a + 3/4*x^8*e^5*b^2*a^2 + 10/7*x^7*e^2*d^3*b^4 + 40/7*x^7*e^3*d^2*b^3*a + 30/7*x^7*e^4*d*b^2*a^2 + 4/7*x^7*e^5*b*a^3 + 5/6*x^6*e*d^4*b^4 + 20/3*x^6*e^2*d^3*b^3*a + 10*x^6*e^3*d^2*b^2*a^2 + 10/3*x^6*e^4*d*b*a^3 + 1/6*x^6*e^5*a^4 + 1/5*x^5*d^5*b^4 + 4*x^5*e*d^4*b^3*a + 12*x^5*e^2*d^3*b^2*a^2 + 8*x^5*e^3*d^2*b*a^3 + x^5*e^4*d*a^4 + x^4*d^5*b^3*a + 15/2*x^4*e*d^4*b^2*a^2 + 10*x^4*e^2*d^3*b*a^3 + 5/2*x^4*e^3*d^2*a^4 + 2*x^3*d^5*b^2*a^2 + 20/3*x^3*e*d^4*b*a^3 + 10/3*x^3*e^2*d^3*a^4 + 2*x^2*d^5*b*a^3 + 5/2*x^2*e*d^4*a^4 + x*d^5*a^4","B",0
1465,1,321,0,0.341485," ","integrate((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{4} b^{4} + \frac{1}{2} x^{8} e^{3} d b^{4} + \frac{1}{2} x^{8} e^{4} b^{3} a + \frac{6}{7} x^{7} e^{2} d^{2} b^{4} + \frac{16}{7} x^{7} e^{3} d b^{3} a + \frac{6}{7} x^{7} e^{4} b^{2} a^{2} + \frac{2}{3} x^{6} e d^{3} b^{4} + 4 x^{6} e^{2} d^{2} b^{3} a + 4 x^{6} e^{3} d b^{2} a^{2} + \frac{2}{3} x^{6} e^{4} b a^{3} + \frac{1}{5} x^{5} d^{4} b^{4} + \frac{16}{5} x^{5} e d^{3} b^{3} a + \frac{36}{5} x^{5} e^{2} d^{2} b^{2} a^{2} + \frac{16}{5} x^{5} e^{3} d b a^{3} + \frac{1}{5} x^{5} e^{4} a^{4} + x^{4} d^{4} b^{3} a + 6 x^{4} e d^{3} b^{2} a^{2} + 6 x^{4} e^{2} d^{2} b a^{3} + x^{4} e^{3} d a^{4} + 2 x^{3} d^{4} b^{2} a^{2} + \frac{16}{3} x^{3} e d^{3} b a^{3} + 2 x^{3} e^{2} d^{2} a^{4} + 2 x^{2} d^{4} b a^{3} + 2 x^{2} e d^{3} a^{4} + x d^{4} a^{4}"," ",0,"1/9*x^9*e^4*b^4 + 1/2*x^8*e^3*d*b^4 + 1/2*x^8*e^4*b^3*a + 6/7*x^7*e^2*d^2*b^4 + 16/7*x^7*e^3*d*b^3*a + 6/7*x^7*e^4*b^2*a^2 + 2/3*x^6*e*d^3*b^4 + 4*x^6*e^2*d^2*b^3*a + 4*x^6*e^3*d*b^2*a^2 + 2/3*x^6*e^4*b*a^3 + 1/5*x^5*d^4*b^4 + 16/5*x^5*e*d^3*b^3*a + 36/5*x^5*e^2*d^2*b^2*a^2 + 16/5*x^5*e^3*d*b*a^3 + 1/5*x^5*e^4*a^4 + x^4*d^4*b^3*a + 6*x^4*e*d^3*b^2*a^2 + 6*x^4*e^2*d^2*b*a^3 + x^4*e^3*d*a^4 + 2*x^3*d^4*b^2*a^2 + 16/3*x^3*e*d^3*b*a^3 + 2*x^3*e^2*d^2*a^4 + 2*x^2*d^4*b*a^3 + 2*x^2*e*d^3*a^4 + x*d^4*a^4","B",0
1466,1,245,0,0.353287," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{3} b^{4} + \frac{3}{7} x^{7} e^{2} d b^{4} + \frac{4}{7} x^{7} e^{3} b^{3} a + \frac{1}{2} x^{6} e d^{2} b^{4} + 2 x^{6} e^{2} d b^{3} a + x^{6} e^{3} b^{2} a^{2} + \frac{1}{5} x^{5} d^{3} b^{4} + \frac{12}{5} x^{5} e d^{2} b^{3} a + \frac{18}{5} x^{5} e^{2} d b^{2} a^{2} + \frac{4}{5} x^{5} e^{3} b a^{3} + x^{4} d^{3} b^{3} a + \frac{9}{2} x^{4} e d^{2} b^{2} a^{2} + 3 x^{4} e^{2} d b a^{3} + \frac{1}{4} x^{4} e^{3} a^{4} + 2 x^{3} d^{3} b^{2} a^{2} + 4 x^{3} e d^{2} b a^{3} + x^{3} e^{2} d a^{4} + 2 x^{2} d^{3} b a^{3} + \frac{3}{2} x^{2} e d^{2} a^{4} + x d^{3} a^{4}"," ",0,"1/8*x^8*e^3*b^4 + 3/7*x^7*e^2*d*b^4 + 4/7*x^7*e^3*b^3*a + 1/2*x^6*e*d^2*b^4 + 2*x^6*e^2*d*b^3*a + x^6*e^3*b^2*a^2 + 1/5*x^5*d^3*b^4 + 12/5*x^5*e*d^2*b^3*a + 18/5*x^5*e^2*d*b^2*a^2 + 4/5*x^5*e^3*b*a^3 + x^4*d^3*b^3*a + 9/2*x^4*e*d^2*b^2*a^2 + 3*x^4*e^2*d*b*a^3 + 1/4*x^4*e^3*a^4 + 2*x^3*d^3*b^2*a^2 + 4*x^3*e*d^2*b*a^3 + x^3*e^2*d*a^4 + 2*x^2*d^3*b*a^3 + 3/2*x^2*e*d^2*a^4 + x*d^3*a^4","B",0
1467,1,170,0,0.353899," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{2} b^{4} + \frac{1}{3} x^{6} e d b^{4} + \frac{2}{3} x^{6} e^{2} b^{3} a + \frac{1}{5} x^{5} d^{2} b^{4} + \frac{8}{5} x^{5} e d b^{3} a + \frac{6}{5} x^{5} e^{2} b^{2} a^{2} + x^{4} d^{2} b^{3} a + 3 x^{4} e d b^{2} a^{2} + x^{4} e^{2} b a^{3} + 2 x^{3} d^{2} b^{2} a^{2} + \frac{8}{3} x^{3} e d b a^{3} + \frac{1}{3} x^{3} e^{2} a^{4} + 2 x^{2} d^{2} b a^{3} + x^{2} e d a^{4} + x d^{2} a^{4}"," ",0,"1/7*x^7*e^2*b^4 + 1/3*x^6*e*d*b^4 + 2/3*x^6*e^2*b^3*a + 1/5*x^5*d^2*b^4 + 8/5*x^5*e*d*b^3*a + 6/5*x^5*e^2*b^2*a^2 + x^4*d^2*b^3*a + 3*x^4*e*d*b^2*a^2 + x^4*e^2*b*a^3 + 2*x^3*d^2*b^2*a^2 + 8/3*x^3*e*d*b*a^3 + 1/3*x^3*e^2*a^4 + 2*x^2*d^2*b*a^3 + x^2*e*d*a^4 + x*d^2*a^4","B",0
1468,1,97,0,0.355832," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} e b^{4} + \frac{1}{5} x^{5} d b^{4} + \frac{4}{5} x^{5} e b^{3} a + x^{4} d b^{3} a + \frac{3}{2} x^{4} e b^{2} a^{2} + 2 x^{3} d b^{2} a^{2} + \frac{4}{3} x^{3} e b a^{3} + 2 x^{2} d b a^{3} + \frac{1}{2} x^{2} e a^{4} + x d a^{4}"," ",0,"1/6*x^6*e*b^4 + 1/5*x^5*d*b^4 + 4/5*x^5*e*b^3*a + x^4*d*b^3*a + 3/2*x^4*e*b^2*a^2 + 2*x^3*d*b^2*a^2 + 4/3*x^3*e*b*a^3 + 2*x^2*d*b*a^3 + 1/2*x^2*e*a^4 + x*d*a^4","B",0
1469,1,42,0,0.351285," ","integrate((b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{1}{5} x^{5} b^{4} + x^{4} b^{3} a + 2 x^{3} b^{2} a^{2} + 2 x^{2} b a^{3} + x a^{4}"," ",0,"1/5*x^5*b^4 + x^4*b^3*a + 2*x^3*b^2*a^2 + 2*x^2*b*a^3 + x*a^4","B",0
1470,1,179,0,0.387291," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d),x, algorithm=""fricas"")","\frac{3 \, b^{4} e^{4} x^{4} - 4 \, {\left(b^{4} d e^{3} - 4 \, a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(b^{4} d^{2} e^{2} - 4 \, a b^{3} d e^{3} + 6 \, a^{2} b^{2} e^{4}\right)} x^{2} - 12 \, {\left(b^{4} d^{3} e - 4 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} - 4 \, a^{3} b e^{4}\right)} x + 12 \, {\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)} \log\left(e x + d\right)}{12 \, e^{5}}"," ",0,"1/12*(3*b^4*e^4*x^4 - 4*(b^4*d*e^3 - 4*a*b^3*e^4)*x^3 + 6*(b^4*d^2*e^2 - 4*a*b^3*d*e^3 + 6*a^2*b^2*e^4)*x^2 - 12*(b^4*d^3*e - 4*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 - 4*a^3*b*e^4)*x + 12*(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)*log(e*x + d))/e^5","A",0
1471,1,267,0,0.388062," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{b^{4} e^{4} x^{4} - 3 \, b^{4} d^{4} + 12 \, a b^{3} d^{3} e - 18 \, a^{2} b^{2} d^{2} e^{2} + 12 \, a^{3} b d e^{3} - 3 \, a^{4} e^{4} - 2 \, {\left(b^{4} d e^{3} - 3 \, a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(b^{4} d^{2} e^{2} - 3 \, a b^{3} d e^{3} + 3 \, a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(3 \, b^{4} d^{3} e - 8 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3}\right)} x - 12 \, {\left(b^{4} d^{4} - 3 \, a b^{3} d^{3} e + 3 \, a^{2} b^{2} d^{2} e^{2} - a^{3} b d e^{3} + {\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)} \log\left(e x + d\right)}{3 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"1/3*(b^4*e^4*x^4 - 3*b^4*d^4 + 12*a*b^3*d^3*e - 18*a^2*b^2*d^2*e^2 + 12*a^3*b*d*e^3 - 3*a^4*e^4 - 2*(b^4*d*e^3 - 3*a*b^3*e^4)*x^3 + 6*(b^4*d^2*e^2 - 3*a*b^3*d*e^3 + 3*a^2*b^2*e^4)*x^2 + 3*(3*b^4*d^3*e - 8*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3)*x - 12*(b^4*d^4 - 3*a*b^3*d^3*e + 3*a^2*b^2*d^2*e^2 - a^3*b*d*e^3 + (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)*log(e*x + d))/(e^6*x + d*e^5)","B",0
1472,1,291,0,0.390767," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{b^{4} e^{4} x^{4} + 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} - 4 \, {\left(b^{4} d e^{3} - 2 \, a b^{3} e^{4}\right)} x^{3} - {\left(11 \, b^{4} d^{2} e^{2} - 16 \, a b^{3} d e^{3}\right)} x^{2} + 2 \, {\left(b^{4} d^{3} e - 8 \, a b^{3} d^{2} e^{2} + 12 \, a^{2} b^{2} d e^{3} - 4 \, a^{3} b e^{4}\right)} x + 12 \, {\left(b^{4} d^{4} - 2 \, a b^{3} d^{3} e + a^{2} b^{2} d^{2} e^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(b^{4} d^{3} e - 2 \, a b^{3} d^{2} e^{2} + a^{2} b^{2} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"1/2*(b^4*e^4*x^4 + 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 - 4*(b^4*d*e^3 - 2*a*b^3*e^4)*x^3 - (11*b^4*d^2*e^2 - 16*a*b^3*d*e^3)*x^2 + 2*(b^4*d^3*e - 8*a*b^3*d^2*e^2 + 12*a^2*b^2*d*e^3 - 4*a^3*b*e^4)*x + 12*(b^4*d^4 - 2*a*b^3*d^3*e + a^2*b^2*d^2*e^2 + (b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(b^4*d^3*e - 2*a*b^3*d^2*e^2 + a^2*b^2*d*e^3)*x)*log(e*x + d))/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","B",0
1473,1,292,0,0.381286," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, b^{4} e^{4} x^{4} + 9 \, b^{4} d e^{3} x^{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} - 9 \, {\left(b^{4} d^{2} e^{2} - 4 \, a b^{3} d e^{3} + 2 \, a^{2} b^{2} e^{4}\right)} x^{2} - 3 \, {\left(9 \, b^{4} d^{3} e - 18 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} + 2 \, a^{3} b e^{4}\right)} x - 12 \, {\left(b^{4} d^{4} - a b^{3} d^{3} e + {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(b^{4} d^{2} e^{2} - a b^{3} d e^{3}\right)} x^{2} + 3 \, {\left(b^{4} d^{3} e - a b^{3} d^{2} e^{2}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"1/3*(3*b^4*e^4*x^4 + 9*b^4*d*e^3*x^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 - 9*(b^4*d^2*e^2 - 4*a*b^3*d*e^3 + 2*a^2*b^2*e^4)*x^2 - 3*(9*b^4*d^3*e - 18*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 + 2*a^3*b*e^4)*x - 12*(b^4*d^4 - a*b^3*d^3*e + (b^4*d*e^3 - a*b^3*e^4)*x^3 + 3*(b^4*d^2*e^2 - a*b^3*d*e^3)*x^2 + 3*(b^4*d^3*e - a*b^3*d^2*e^2)*x)*log(e*x + d))/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","B",0
1474,1,268,0,0.404593," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{25 \, b^{4} d^{4} - 12 \, a b^{3} d^{3} e - 6 \, a^{2} b^{2} d^{2} e^{2} - 4 \, a^{3} b d e^{3} - 3 \, a^{4} e^{4} + 48 \, {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 36 \, {\left(3 \, b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} - a^{2} b^{2} e^{4}\right)} x^{2} + 8 \, {\left(11 \, b^{4} d^{3} e - 6 \, a b^{3} d^{2} e^{2} - 3 \, a^{2} b^{2} d e^{3} - 2 \, a^{3} b e^{4}\right)} x + 12 \, {\left(b^{4} e^{4} x^{4} + 4 \, b^{4} d e^{3} x^{3} + 6 \, b^{4} d^{2} e^{2} x^{2} + 4 \, b^{4} d^{3} e x + b^{4} d^{4}\right)} \log\left(e x + d\right)}{12 \, {\left(e^{9} x^{4} + 4 \, d e^{8} x^{3} + 6 \, d^{2} e^{7} x^{2} + 4 \, d^{3} e^{6} x + d^{4} e^{5}\right)}}"," ",0,"1/12*(25*b^4*d^4 - 12*a*b^3*d^3*e - 6*a^2*b^2*d^2*e^2 - 4*a^3*b*d*e^3 - 3*a^4*e^4 + 48*(b^4*d*e^3 - a*b^3*e^4)*x^3 + 36*(3*b^4*d^2*e^2 - 2*a*b^3*d*e^3 - a^2*b^2*e^4)*x^2 + 8*(11*b^4*d^3*e - 6*a*b^3*d^2*e^2 - 3*a^2*b^2*d*e^3 - 2*a^3*b*e^4)*x + 12*(b^4*e^4*x^4 + 4*b^4*d*e^3*x^3 + 6*b^4*d^2*e^2*x^2 + 4*b^4*d^3*e*x + b^4*d^4)*log(e*x + d))/(e^9*x^4 + 4*d*e^8*x^3 + 6*d^2*e^7*x^2 + 4*d^3*e^6*x + d^4*e^5)","B",0
1475,1,215,0,0.388688," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{5 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + a b^{3} d^{3} e + a^{2} b^{2} d^{2} e^{2} + a^{3} b d e^{3} + a^{4} e^{4} + 10 \, {\left(b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{3} + 10 \, {\left(b^{4} d^{2} e^{2} + a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 5 \, {\left(b^{4} d^{3} e + a b^{3} d^{2} e^{2} + a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x}{5 \, {\left(e^{10} x^{5} + 5 \, d e^{9} x^{4} + 10 \, d^{2} e^{8} x^{3} + 10 \, d^{3} e^{7} x^{2} + 5 \, d^{4} e^{6} x + d^{5} e^{5}\right)}}"," ",0,"-1/5*(5*b^4*e^4*x^4 + b^4*d^4 + a*b^3*d^3*e + a^2*b^2*d^2*e^2 + a^3*b*d*e^3 + a^4*e^4 + 10*(b^4*d*e^3 + a*b^3*e^4)*x^3 + 10*(b^4*d^2*e^2 + a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 5*(b^4*d^3*e + a*b^3*d^2*e^2 + a^2*b^2*d*e^3 + a^3*b*e^4)*x)/(e^10*x^5 + 5*d*e^9*x^4 + 10*d^2*e^8*x^3 + 10*d^3*e^7*x^2 + 5*d^4*e^6*x + d^5*e^5)","B",0
1476,1,236,0,0.397344," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{15 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 2 \, a b^{3} d^{3} e + 3 \, a^{2} b^{2} d^{2} e^{2} + 4 \, a^{3} b d e^{3} + 5 \, a^{4} e^{4} + 20 \, {\left(b^{4} d e^{3} + 2 \, a b^{3} e^{4}\right)} x^{3} + 15 \, {\left(b^{4} d^{2} e^{2} + 2 \, a b^{3} d e^{3} + 3 \, a^{2} b^{2} e^{4}\right)} x^{2} + 6 \, {\left(b^{4} d^{3} e + 2 \, a b^{3} d^{2} e^{2} + 3 \, a^{2} b^{2} d e^{3} + 4 \, a^{3} b e^{4}\right)} x}{30 \, {\left(e^{11} x^{6} + 6 \, d e^{10} x^{5} + 15 \, d^{2} e^{9} x^{4} + 20 \, d^{3} e^{8} x^{3} + 15 \, d^{4} e^{7} x^{2} + 6 \, d^{5} e^{6} x + d^{6} e^{5}\right)}}"," ",0,"-1/30*(15*b^4*e^4*x^4 + b^4*d^4 + 2*a*b^3*d^3*e + 3*a^2*b^2*d^2*e^2 + 4*a^3*b*d*e^3 + 5*a^4*e^4 + 20*(b^4*d*e^3 + 2*a*b^3*e^4)*x^3 + 15*(b^4*d^2*e^2 + 2*a*b^3*d*e^3 + 3*a^2*b^2*e^4)*x^2 + 6*(b^4*d^3*e + 2*a*b^3*d^2*e^2 + 3*a^2*b^2*d*e^3 + 4*a^3*b*e^4)*x)/(e^11*x^6 + 6*d*e^10*x^5 + 15*d^2*e^9*x^4 + 20*d^3*e^8*x^3 + 15*d^4*e^7*x^2 + 6*d^5*e^6*x + d^6*e^5)","B",0
1477,1,247,0,0.391935," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{35 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 3 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} + 10 \, a^{3} b d e^{3} + 15 \, a^{4} e^{4} + 35 \, {\left(b^{4} d e^{3} + 3 \, a b^{3} e^{4}\right)} x^{3} + 21 \, {\left(b^{4} d^{2} e^{2} + 3 \, a b^{3} d e^{3} + 6 \, a^{2} b^{2} e^{4}\right)} x^{2} + 7 \, {\left(b^{4} d^{3} e + 3 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} + 10 \, a^{3} b e^{4}\right)} x}{105 \, {\left(e^{12} x^{7} + 7 \, d e^{11} x^{6} + 21 \, d^{2} e^{10} x^{5} + 35 \, d^{3} e^{9} x^{4} + 35 \, d^{4} e^{8} x^{3} + 21 \, d^{5} e^{7} x^{2} + 7 \, d^{6} e^{6} x + d^{7} e^{5}\right)}}"," ",0,"-1/105*(35*b^4*e^4*x^4 + b^4*d^4 + 3*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 + 10*a^3*b*d*e^3 + 15*a^4*e^4 + 35*(b^4*d*e^3 + 3*a*b^3*e^4)*x^3 + 21*(b^4*d^2*e^2 + 3*a*b^3*d*e^3 + 6*a^2*b^2*e^4)*x^2 + 7*(b^4*d^3*e + 3*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 + 10*a^3*b*e^4)*x)/(e^12*x^7 + 7*d*e^11*x^6 + 21*d^2*e^10*x^5 + 35*d^3*e^9*x^4 + 35*d^4*e^8*x^3 + 21*d^5*e^7*x^2 + 7*d^6*e^6*x + d^7*e^5)","B",0
1478,1,258,0,0.390865," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{70 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 4 \, a b^{3} d^{3} e + 10 \, a^{2} b^{2} d^{2} e^{2} + 20 \, a^{3} b d e^{3} + 35 \, a^{4} e^{4} + 56 \, {\left(b^{4} d e^{3} + 4 \, a b^{3} e^{4}\right)} x^{3} + 28 \, {\left(b^{4} d^{2} e^{2} + 4 \, a b^{3} d e^{3} + 10 \, a^{2} b^{2} e^{4}\right)} x^{2} + 8 \, {\left(b^{4} d^{3} e + 4 \, a b^{3} d^{2} e^{2} + 10 \, a^{2} b^{2} d e^{3} + 20 \, a^{3} b e^{4}\right)} x}{280 \, {\left(e^{13} x^{8} + 8 \, d e^{12} x^{7} + 28 \, d^{2} e^{11} x^{6} + 56 \, d^{3} e^{10} x^{5} + 70 \, d^{4} e^{9} x^{4} + 56 \, d^{5} e^{8} x^{3} + 28 \, d^{6} e^{7} x^{2} + 8 \, d^{7} e^{6} x + d^{8} e^{5}\right)}}"," ",0,"-1/280*(70*b^4*e^4*x^4 + b^4*d^4 + 4*a*b^3*d^3*e + 10*a^2*b^2*d^2*e^2 + 20*a^3*b*d*e^3 + 35*a^4*e^4 + 56*(b^4*d*e^3 + 4*a*b^3*e^4)*x^3 + 28*(b^4*d^2*e^2 + 4*a*b^3*d*e^3 + 10*a^2*b^2*e^4)*x^2 + 8*(b^4*d^3*e + 4*a*b^3*d^2*e^2 + 10*a^2*b^2*d*e^3 + 20*a^3*b*e^4)*x)/(e^13*x^8 + 8*d*e^12*x^7 + 28*d^2*e^11*x^6 + 56*d^3*e^10*x^5 + 70*d^4*e^9*x^4 + 56*d^5*e^8*x^3 + 28*d^6*e^7*x^2 + 8*d^7*e^6*x + d^8*e^5)","B",0
1479,1,269,0,0.389164," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{126 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 5 \, a b^{3} d^{3} e + 15 \, a^{2} b^{2} d^{2} e^{2} + 35 \, a^{3} b d e^{3} + 70 \, a^{4} e^{4} + 84 \, {\left(b^{4} d e^{3} + 5 \, a b^{3} e^{4}\right)} x^{3} + 36 \, {\left(b^{4} d^{2} e^{2} + 5 \, a b^{3} d e^{3} + 15 \, a^{2} b^{2} e^{4}\right)} x^{2} + 9 \, {\left(b^{4} d^{3} e + 5 \, a b^{3} d^{2} e^{2} + 15 \, a^{2} b^{2} d e^{3} + 35 \, a^{3} b e^{4}\right)} x}{630 \, {\left(e^{14} x^{9} + 9 \, d e^{13} x^{8} + 36 \, d^{2} e^{12} x^{7} + 84 \, d^{3} e^{11} x^{6} + 126 \, d^{4} e^{10} x^{5} + 126 \, d^{5} e^{9} x^{4} + 84 \, d^{6} e^{8} x^{3} + 36 \, d^{7} e^{7} x^{2} + 9 \, d^{8} e^{6} x + d^{9} e^{5}\right)}}"," ",0,"-1/630*(126*b^4*e^4*x^4 + b^4*d^4 + 5*a*b^3*d^3*e + 15*a^2*b^2*d^2*e^2 + 35*a^3*b*d*e^3 + 70*a^4*e^4 + 84*(b^4*d*e^3 + 5*a*b^3*e^4)*x^3 + 36*(b^4*d^2*e^2 + 5*a*b^3*d*e^3 + 15*a^2*b^2*e^4)*x^2 + 9*(b^4*d^3*e + 5*a*b^3*d^2*e^2 + 15*a^2*b^2*d*e^3 + 35*a^3*b*e^4)*x)/(e^14*x^9 + 9*d*e^13*x^8 + 36*d^2*e^12*x^7 + 84*d^3*e^11*x^6 + 126*d^4*e^10*x^5 + 126*d^5*e^9*x^4 + 84*d^6*e^8*x^3 + 36*d^7*e^7*x^2 + 9*d^8*e^6*x + d^9*e^5)","B",0
1480,1,280,0,0.380740," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{210 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + 6 \, a b^{3} d^{3} e + 21 \, a^{2} b^{2} d^{2} e^{2} + 56 \, a^{3} b d e^{3} + 126 \, a^{4} e^{4} + 120 \, {\left(b^{4} d e^{3} + 6 \, a b^{3} e^{4}\right)} x^{3} + 45 \, {\left(b^{4} d^{2} e^{2} + 6 \, a b^{3} d e^{3} + 21 \, a^{2} b^{2} e^{4}\right)} x^{2} + 10 \, {\left(b^{4} d^{3} e + 6 \, a b^{3} d^{2} e^{2} + 21 \, a^{2} b^{2} d e^{3} + 56 \, a^{3} b e^{4}\right)} x}{1260 \, {\left(e^{15} x^{10} + 10 \, d e^{14} x^{9} + 45 \, d^{2} e^{13} x^{8} + 120 \, d^{3} e^{12} x^{7} + 210 \, d^{4} e^{11} x^{6} + 252 \, d^{5} e^{10} x^{5} + 210 \, d^{6} e^{9} x^{4} + 120 \, d^{7} e^{8} x^{3} + 45 \, d^{8} e^{7} x^{2} + 10 \, d^{9} e^{6} x + d^{10} e^{5}\right)}}"," ",0,"-1/1260*(210*b^4*e^4*x^4 + b^4*d^4 + 6*a*b^3*d^3*e + 21*a^2*b^2*d^2*e^2 + 56*a^3*b*d*e^3 + 126*a^4*e^4 + 120*(b^4*d*e^3 + 6*a*b^3*e^4)*x^3 + 45*(b^4*d^2*e^2 + 6*a*b^3*d*e^3 + 21*a^2*b^2*e^4)*x^2 + 10*(b^4*d^3*e + 6*a*b^3*d^2*e^2 + 21*a^2*b^2*d*e^3 + 56*a^3*b*e^4)*x)/(e^15*x^10 + 10*d*e^14*x^9 + 45*d^2*e^13*x^8 + 120*d^3*e^12*x^7 + 210*d^4*e^11*x^6 + 252*d^5*e^10*x^5 + 210*d^6*e^9*x^4 + 120*d^7*e^8*x^3 + 45*d^8*e^7*x^2 + 10*d^9*e^6*x + d^10*e^5)","B",0
1481,1,906,0,0.361882," ","integrate((e*x+d)^8*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{15} x^{15} e^{8} b^{6} + \frac{4}{7} x^{14} e^{7} d b^{6} + \frac{3}{7} x^{14} e^{8} b^{5} a + \frac{28}{13} x^{13} e^{6} d^{2} b^{6} + \frac{48}{13} x^{13} e^{7} d b^{5} a + \frac{15}{13} x^{13} e^{8} b^{4} a^{2} + \frac{14}{3} x^{12} e^{5} d^{3} b^{6} + 14 x^{12} e^{6} d^{2} b^{5} a + 10 x^{12} e^{7} d b^{4} a^{2} + \frac{5}{3} x^{12} e^{8} b^{3} a^{3} + \frac{70}{11} x^{11} e^{4} d^{4} b^{6} + \frac{336}{11} x^{11} e^{5} d^{3} b^{5} a + \frac{420}{11} x^{11} e^{6} d^{2} b^{4} a^{2} + \frac{160}{11} x^{11} e^{7} d b^{3} a^{3} + \frac{15}{11} x^{11} e^{8} b^{2} a^{4} + \frac{28}{5} x^{10} e^{3} d^{5} b^{6} + 42 x^{10} e^{4} d^{4} b^{5} a + 84 x^{10} e^{5} d^{3} b^{4} a^{2} + 56 x^{10} e^{6} d^{2} b^{3} a^{3} + 12 x^{10} e^{7} d b^{2} a^{4} + \frac{3}{5} x^{10} e^{8} b a^{5} + \frac{28}{9} x^{9} e^{2} d^{6} b^{6} + \frac{112}{3} x^{9} e^{3} d^{5} b^{5} a + \frac{350}{3} x^{9} e^{4} d^{4} b^{4} a^{2} + \frac{1120}{9} x^{9} e^{5} d^{3} b^{3} a^{3} + \frac{140}{3} x^{9} e^{6} d^{2} b^{2} a^{4} + \frac{16}{3} x^{9} e^{7} d b a^{5} + \frac{1}{9} x^{9} e^{8} a^{6} + x^{8} e d^{7} b^{6} + 21 x^{8} e^{2} d^{6} b^{5} a + 105 x^{8} e^{3} d^{5} b^{4} a^{2} + 175 x^{8} e^{4} d^{4} b^{3} a^{3} + 105 x^{8} e^{5} d^{3} b^{2} a^{4} + 21 x^{8} e^{6} d^{2} b a^{5} + x^{8} e^{7} d a^{6} + \frac{1}{7} x^{7} d^{8} b^{6} + \frac{48}{7} x^{7} e d^{7} b^{5} a + 60 x^{7} e^{2} d^{6} b^{4} a^{2} + 160 x^{7} e^{3} d^{5} b^{3} a^{3} + 150 x^{7} e^{4} d^{4} b^{2} a^{4} + 48 x^{7} e^{5} d^{3} b a^{5} + 4 x^{7} e^{6} d^{2} a^{6} + x^{6} d^{8} b^{5} a + 20 x^{6} e d^{7} b^{4} a^{2} + \frac{280}{3} x^{6} e^{2} d^{6} b^{3} a^{3} + 140 x^{6} e^{3} d^{5} b^{2} a^{4} + 70 x^{6} e^{4} d^{4} b a^{5} + \frac{28}{3} x^{6} e^{5} d^{3} a^{6} + 3 x^{5} d^{8} b^{4} a^{2} + 32 x^{5} e d^{7} b^{3} a^{3} + 84 x^{5} e^{2} d^{6} b^{2} a^{4} + \frac{336}{5} x^{5} e^{3} d^{5} b a^{5} + 14 x^{5} e^{4} d^{4} a^{6} + 5 x^{4} d^{8} b^{3} a^{3} + 30 x^{4} e d^{7} b^{2} a^{4} + 42 x^{4} e^{2} d^{6} b a^{5} + 14 x^{4} e^{3} d^{5} a^{6} + 5 x^{3} d^{8} b^{2} a^{4} + 16 x^{3} e d^{7} b a^{5} + \frac{28}{3} x^{3} e^{2} d^{6} a^{6} + 3 x^{2} d^{8} b a^{5} + 4 x^{2} e d^{7} a^{6} + x d^{8} a^{6}"," ",0,"1/15*x^15*e^8*b^6 + 4/7*x^14*e^7*d*b^6 + 3/7*x^14*e^8*b^5*a + 28/13*x^13*e^6*d^2*b^6 + 48/13*x^13*e^7*d*b^5*a + 15/13*x^13*e^8*b^4*a^2 + 14/3*x^12*e^5*d^3*b^6 + 14*x^12*e^6*d^2*b^5*a + 10*x^12*e^7*d*b^4*a^2 + 5/3*x^12*e^8*b^3*a^3 + 70/11*x^11*e^4*d^4*b^6 + 336/11*x^11*e^5*d^3*b^5*a + 420/11*x^11*e^6*d^2*b^4*a^2 + 160/11*x^11*e^7*d*b^3*a^3 + 15/11*x^11*e^8*b^2*a^4 + 28/5*x^10*e^3*d^5*b^6 + 42*x^10*e^4*d^4*b^5*a + 84*x^10*e^5*d^3*b^4*a^2 + 56*x^10*e^6*d^2*b^3*a^3 + 12*x^10*e^7*d*b^2*a^4 + 3/5*x^10*e^8*b*a^5 + 28/9*x^9*e^2*d^6*b^6 + 112/3*x^9*e^3*d^5*b^5*a + 350/3*x^9*e^4*d^4*b^4*a^2 + 1120/9*x^9*e^5*d^3*b^3*a^3 + 140/3*x^9*e^6*d^2*b^2*a^4 + 16/3*x^9*e^7*d*b*a^5 + 1/9*x^9*e^8*a^6 + x^8*e*d^7*b^6 + 21*x^8*e^2*d^6*b^5*a + 105*x^8*e^3*d^5*b^4*a^2 + 175*x^8*e^4*d^4*b^3*a^3 + 105*x^8*e^5*d^3*b^2*a^4 + 21*x^8*e^6*d^2*b*a^5 + x^8*e^7*d*a^6 + 1/7*x^7*d^8*b^6 + 48/7*x^7*e*d^7*b^5*a + 60*x^7*e^2*d^6*b^4*a^2 + 160*x^7*e^3*d^5*b^3*a^3 + 150*x^7*e^4*d^4*b^2*a^4 + 48*x^7*e^5*d^3*b*a^5 + 4*x^7*e^6*d^2*a^6 + x^6*d^8*b^5*a + 20*x^6*e*d^7*b^4*a^2 + 280/3*x^6*e^2*d^6*b^3*a^3 + 140*x^6*e^3*d^5*b^2*a^4 + 70*x^6*e^4*d^4*b*a^5 + 28/3*x^6*e^5*d^3*a^6 + 3*x^5*d^8*b^4*a^2 + 32*x^5*e*d^7*b^3*a^3 + 84*x^5*e^2*d^6*b^2*a^4 + 336/5*x^5*e^3*d^5*b*a^5 + 14*x^5*e^4*d^4*a^6 + 5*x^4*d^8*b^3*a^3 + 30*x^4*e*d^7*b^2*a^4 + 42*x^4*e^2*d^6*b*a^5 + 14*x^4*e^3*d^5*a^6 + 5*x^3*d^8*b^2*a^4 + 16*x^3*e*d^7*b*a^5 + 28/3*x^3*e^2*d^6*a^6 + 3*x^2*d^8*b*a^5 + 4*x^2*e*d^7*a^6 + x*d^8*a^6","B",0
1482,1,798,0,0.354500," ","integrate((e*x+d)^7*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{14} x^{14} e^{7} b^{6} + \frac{7}{13} x^{13} e^{6} d b^{6} + \frac{6}{13} x^{13} e^{7} b^{5} a + \frac{7}{4} x^{12} e^{5} d^{2} b^{6} + \frac{7}{2} x^{12} e^{6} d b^{5} a + \frac{5}{4} x^{12} e^{7} b^{4} a^{2} + \frac{35}{11} x^{11} e^{4} d^{3} b^{6} + \frac{126}{11} x^{11} e^{5} d^{2} b^{5} a + \frac{105}{11} x^{11} e^{6} d b^{4} a^{2} + \frac{20}{11} x^{11} e^{7} b^{3} a^{3} + \frac{7}{2} x^{10} e^{3} d^{4} b^{6} + 21 x^{10} e^{4} d^{3} b^{5} a + \frac{63}{2} x^{10} e^{5} d^{2} b^{4} a^{2} + 14 x^{10} e^{6} d b^{3} a^{3} + \frac{3}{2} x^{10} e^{7} b^{2} a^{4} + \frac{7}{3} x^{9} e^{2} d^{5} b^{6} + \frac{70}{3} x^{9} e^{3} d^{4} b^{5} a + \frac{175}{3} x^{9} e^{4} d^{3} b^{4} a^{2} + \frac{140}{3} x^{9} e^{5} d^{2} b^{3} a^{3} + \frac{35}{3} x^{9} e^{6} d b^{2} a^{4} + \frac{2}{3} x^{9} e^{7} b a^{5} + \frac{7}{8} x^{8} e d^{6} b^{6} + \frac{63}{4} x^{8} e^{2} d^{5} b^{5} a + \frac{525}{8} x^{8} e^{3} d^{4} b^{4} a^{2} + \frac{175}{2} x^{8} e^{4} d^{3} b^{3} a^{3} + \frac{315}{8} x^{8} e^{5} d^{2} b^{2} a^{4} + \frac{21}{4} x^{8} e^{6} d b a^{5} + \frac{1}{8} x^{8} e^{7} a^{6} + \frac{1}{7} x^{7} d^{7} b^{6} + 6 x^{7} e d^{6} b^{5} a + 45 x^{7} e^{2} d^{5} b^{4} a^{2} + 100 x^{7} e^{3} d^{4} b^{3} a^{3} + 75 x^{7} e^{4} d^{3} b^{2} a^{4} + 18 x^{7} e^{5} d^{2} b a^{5} + x^{7} e^{6} d a^{6} + x^{6} d^{7} b^{5} a + \frac{35}{2} x^{6} e d^{6} b^{4} a^{2} + 70 x^{6} e^{2} d^{5} b^{3} a^{3} + \frac{175}{2} x^{6} e^{3} d^{4} b^{2} a^{4} + 35 x^{6} e^{4} d^{3} b a^{5} + \frac{7}{2} x^{6} e^{5} d^{2} a^{6} + 3 x^{5} d^{7} b^{4} a^{2} + 28 x^{5} e d^{6} b^{3} a^{3} + 63 x^{5} e^{2} d^{5} b^{2} a^{4} + 42 x^{5} e^{3} d^{4} b a^{5} + 7 x^{5} e^{4} d^{3} a^{6} + 5 x^{4} d^{7} b^{3} a^{3} + \frac{105}{4} x^{4} e d^{6} b^{2} a^{4} + \frac{63}{2} x^{4} e^{2} d^{5} b a^{5} + \frac{35}{4} x^{4} e^{3} d^{4} a^{6} + 5 x^{3} d^{7} b^{2} a^{4} + 14 x^{3} e d^{6} b a^{5} + 7 x^{3} e^{2} d^{5} a^{6} + 3 x^{2} d^{7} b a^{5} + \frac{7}{2} x^{2} e d^{6} a^{6} + x d^{7} a^{6}"," ",0,"1/14*x^14*e^7*b^6 + 7/13*x^13*e^6*d*b^6 + 6/13*x^13*e^7*b^5*a + 7/4*x^12*e^5*d^2*b^6 + 7/2*x^12*e^6*d*b^5*a + 5/4*x^12*e^7*b^4*a^2 + 35/11*x^11*e^4*d^3*b^6 + 126/11*x^11*e^5*d^2*b^5*a + 105/11*x^11*e^6*d*b^4*a^2 + 20/11*x^11*e^7*b^3*a^3 + 7/2*x^10*e^3*d^4*b^6 + 21*x^10*e^4*d^3*b^5*a + 63/2*x^10*e^5*d^2*b^4*a^2 + 14*x^10*e^6*d*b^3*a^3 + 3/2*x^10*e^7*b^2*a^4 + 7/3*x^9*e^2*d^5*b^6 + 70/3*x^9*e^3*d^4*b^5*a + 175/3*x^9*e^4*d^3*b^4*a^2 + 140/3*x^9*e^5*d^2*b^3*a^3 + 35/3*x^9*e^6*d*b^2*a^4 + 2/3*x^9*e^7*b*a^5 + 7/8*x^8*e*d^6*b^6 + 63/4*x^8*e^2*d^5*b^5*a + 525/8*x^8*e^3*d^4*b^4*a^2 + 175/2*x^8*e^4*d^3*b^3*a^3 + 315/8*x^8*e^5*d^2*b^2*a^4 + 21/4*x^8*e^6*d*b*a^5 + 1/8*x^8*e^7*a^6 + 1/7*x^7*d^7*b^6 + 6*x^7*e*d^6*b^5*a + 45*x^7*e^2*d^5*b^4*a^2 + 100*x^7*e^3*d^4*b^3*a^3 + 75*x^7*e^4*d^3*b^2*a^4 + 18*x^7*e^5*d^2*b*a^5 + x^7*e^6*d*a^6 + x^6*d^7*b^5*a + 35/2*x^6*e*d^6*b^4*a^2 + 70*x^6*e^2*d^5*b^3*a^3 + 175/2*x^6*e^3*d^4*b^2*a^4 + 35*x^6*e^4*d^3*b*a^5 + 7/2*x^6*e^5*d^2*a^6 + 3*x^5*d^7*b^4*a^2 + 28*x^5*e*d^6*b^3*a^3 + 63*x^5*e^2*d^5*b^2*a^4 + 42*x^5*e^3*d^4*b*a^5 + 7*x^5*e^4*d^3*a^6 + 5*x^4*d^7*b^3*a^3 + 105/4*x^4*e*d^6*b^2*a^4 + 63/2*x^4*e^2*d^5*b*a^5 + 35/4*x^4*e^3*d^4*a^6 + 5*x^3*d^7*b^2*a^4 + 14*x^3*e*d^6*b*a^5 + 7*x^3*e^2*d^5*a^6 + 3*x^2*d^7*b*a^5 + 7/2*x^2*e*d^6*a^6 + x*d^7*a^6","B",0
1483,1,689,0,0.354299," ","integrate((e*x+d)^6*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{6} b^{6} + \frac{1}{2} x^{12} e^{5} d b^{6} + \frac{1}{2} x^{12} e^{6} b^{5} a + \frac{15}{11} x^{11} e^{4} d^{2} b^{6} + \frac{36}{11} x^{11} e^{5} d b^{5} a + \frac{15}{11} x^{11} e^{6} b^{4} a^{2} + 2 x^{10} e^{3} d^{3} b^{6} + 9 x^{10} e^{4} d^{2} b^{5} a + 9 x^{10} e^{5} d b^{4} a^{2} + 2 x^{10} e^{6} b^{3} a^{3} + \frac{5}{3} x^{9} e^{2} d^{4} b^{6} + \frac{40}{3} x^{9} e^{3} d^{3} b^{5} a + 25 x^{9} e^{4} d^{2} b^{4} a^{2} + \frac{40}{3} x^{9} e^{5} d b^{3} a^{3} + \frac{5}{3} x^{9} e^{6} b^{2} a^{4} + \frac{3}{4} x^{8} e d^{5} b^{6} + \frac{45}{4} x^{8} e^{2} d^{4} b^{5} a + \frac{75}{2} x^{8} e^{3} d^{3} b^{4} a^{2} + \frac{75}{2} x^{8} e^{4} d^{2} b^{3} a^{3} + \frac{45}{4} x^{8} e^{5} d b^{2} a^{4} + \frac{3}{4} x^{8} e^{6} b a^{5} + \frac{1}{7} x^{7} d^{6} b^{6} + \frac{36}{7} x^{7} e d^{5} b^{5} a + \frac{225}{7} x^{7} e^{2} d^{4} b^{4} a^{2} + \frac{400}{7} x^{7} e^{3} d^{3} b^{3} a^{3} + \frac{225}{7} x^{7} e^{4} d^{2} b^{2} a^{4} + \frac{36}{7} x^{7} e^{5} d b a^{5} + \frac{1}{7} x^{7} e^{6} a^{6} + x^{6} d^{6} b^{5} a + 15 x^{6} e d^{5} b^{4} a^{2} + 50 x^{6} e^{2} d^{4} b^{3} a^{3} + 50 x^{6} e^{3} d^{3} b^{2} a^{4} + 15 x^{6} e^{4} d^{2} b a^{5} + x^{6} e^{5} d a^{6} + 3 x^{5} d^{6} b^{4} a^{2} + 24 x^{5} e d^{5} b^{3} a^{3} + 45 x^{5} e^{2} d^{4} b^{2} a^{4} + 24 x^{5} e^{3} d^{3} b a^{5} + 3 x^{5} e^{4} d^{2} a^{6} + 5 x^{4} d^{6} b^{3} a^{3} + \frac{45}{2} x^{4} e d^{5} b^{2} a^{4} + \frac{45}{2} x^{4} e^{2} d^{4} b a^{5} + 5 x^{4} e^{3} d^{3} a^{6} + 5 x^{3} d^{6} b^{2} a^{4} + 12 x^{3} e d^{5} b a^{5} + 5 x^{3} e^{2} d^{4} a^{6} + 3 x^{2} d^{6} b a^{5} + 3 x^{2} e d^{5} a^{6} + x d^{6} a^{6}"," ",0,"1/13*x^13*e^6*b^6 + 1/2*x^12*e^5*d*b^6 + 1/2*x^12*e^6*b^5*a + 15/11*x^11*e^4*d^2*b^6 + 36/11*x^11*e^5*d*b^5*a + 15/11*x^11*e^6*b^4*a^2 + 2*x^10*e^3*d^3*b^6 + 9*x^10*e^4*d^2*b^5*a + 9*x^10*e^5*d*b^4*a^2 + 2*x^10*e^6*b^3*a^3 + 5/3*x^9*e^2*d^4*b^6 + 40/3*x^9*e^3*d^3*b^5*a + 25*x^9*e^4*d^2*b^4*a^2 + 40/3*x^9*e^5*d*b^3*a^3 + 5/3*x^9*e^6*b^2*a^4 + 3/4*x^8*e*d^5*b^6 + 45/4*x^8*e^2*d^4*b^5*a + 75/2*x^8*e^3*d^3*b^4*a^2 + 75/2*x^8*e^4*d^2*b^3*a^3 + 45/4*x^8*e^5*d*b^2*a^4 + 3/4*x^8*e^6*b*a^5 + 1/7*x^7*d^6*b^6 + 36/7*x^7*e*d^5*b^5*a + 225/7*x^7*e^2*d^4*b^4*a^2 + 400/7*x^7*e^3*d^3*b^3*a^3 + 225/7*x^7*e^4*d^2*b^2*a^4 + 36/7*x^7*e^5*d*b*a^5 + 1/7*x^7*e^6*a^6 + x^6*d^6*b^5*a + 15*x^6*e*d^5*b^4*a^2 + 50*x^6*e^2*d^4*b^3*a^3 + 50*x^6*e^3*d^3*b^2*a^4 + 15*x^6*e^4*d^2*b*a^5 + x^6*e^5*d*a^6 + 3*x^5*d^6*b^4*a^2 + 24*x^5*e*d^5*b^3*a^3 + 45*x^5*e^2*d^4*b^2*a^4 + 24*x^5*e^3*d^3*b*a^5 + 3*x^5*e^4*d^2*a^6 + 5*x^4*d^6*b^3*a^3 + 45/2*x^4*e*d^5*b^2*a^4 + 45/2*x^4*e^2*d^4*b*a^5 + 5*x^4*e^3*d^3*a^6 + 5*x^3*d^6*b^2*a^4 + 12*x^3*e*d^5*b*a^5 + 5*x^3*e^2*d^4*a^6 + 3*x^2*d^6*b*a^5 + 3*x^2*e*d^5*a^6 + x*d^6*a^6","B",0
1484,1,579,0,0.357309," ","integrate((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{5} b^{6} + \frac{5}{11} x^{11} e^{4} d b^{6} + \frac{6}{11} x^{11} e^{5} b^{5} a + x^{10} e^{3} d^{2} b^{6} + 3 x^{10} e^{4} d b^{5} a + \frac{3}{2} x^{10} e^{5} b^{4} a^{2} + \frac{10}{9} x^{9} e^{2} d^{3} b^{6} + \frac{20}{3} x^{9} e^{3} d^{2} b^{5} a + \frac{25}{3} x^{9} e^{4} d b^{4} a^{2} + \frac{20}{9} x^{9} e^{5} b^{3} a^{3} + \frac{5}{8} x^{8} e d^{4} b^{6} + \frac{15}{2} x^{8} e^{2} d^{3} b^{5} a + \frac{75}{4} x^{8} e^{3} d^{2} b^{4} a^{2} + \frac{25}{2} x^{8} e^{4} d b^{3} a^{3} + \frac{15}{8} x^{8} e^{5} b^{2} a^{4} + \frac{1}{7} x^{7} d^{5} b^{6} + \frac{30}{7} x^{7} e d^{4} b^{5} a + \frac{150}{7} x^{7} e^{2} d^{3} b^{4} a^{2} + \frac{200}{7} x^{7} e^{3} d^{2} b^{3} a^{3} + \frac{75}{7} x^{7} e^{4} d b^{2} a^{4} + \frac{6}{7} x^{7} e^{5} b a^{5} + x^{6} d^{5} b^{5} a + \frac{25}{2} x^{6} e d^{4} b^{4} a^{2} + \frac{100}{3} x^{6} e^{2} d^{3} b^{3} a^{3} + 25 x^{6} e^{3} d^{2} b^{2} a^{4} + 5 x^{6} e^{4} d b a^{5} + \frac{1}{6} x^{6} e^{5} a^{6} + 3 x^{5} d^{5} b^{4} a^{2} + 20 x^{5} e d^{4} b^{3} a^{3} + 30 x^{5} e^{2} d^{3} b^{2} a^{4} + 12 x^{5} e^{3} d^{2} b a^{5} + x^{5} e^{4} d a^{6} + 5 x^{4} d^{5} b^{3} a^{3} + \frac{75}{4} x^{4} e d^{4} b^{2} a^{4} + 15 x^{4} e^{2} d^{3} b a^{5} + \frac{5}{2} x^{4} e^{3} d^{2} a^{6} + 5 x^{3} d^{5} b^{2} a^{4} + 10 x^{3} e d^{4} b a^{5} + \frac{10}{3} x^{3} e^{2} d^{3} a^{6} + 3 x^{2} d^{5} b a^{5} + \frac{5}{2} x^{2} e d^{4} a^{6} + x d^{5} a^{6}"," ",0,"1/12*x^12*e^5*b^6 + 5/11*x^11*e^4*d*b^6 + 6/11*x^11*e^5*b^5*a + x^10*e^3*d^2*b^6 + 3*x^10*e^4*d*b^5*a + 3/2*x^10*e^5*b^4*a^2 + 10/9*x^9*e^2*d^3*b^6 + 20/3*x^9*e^3*d^2*b^5*a + 25/3*x^9*e^4*d*b^4*a^2 + 20/9*x^9*e^5*b^3*a^3 + 5/8*x^8*e*d^4*b^6 + 15/2*x^8*e^2*d^3*b^5*a + 75/4*x^8*e^3*d^2*b^4*a^2 + 25/2*x^8*e^4*d*b^3*a^3 + 15/8*x^8*e^5*b^2*a^4 + 1/7*x^7*d^5*b^6 + 30/7*x^7*e*d^4*b^5*a + 150/7*x^7*e^2*d^3*b^4*a^2 + 200/7*x^7*e^3*d^2*b^3*a^3 + 75/7*x^7*e^4*d*b^2*a^4 + 6/7*x^7*e^5*b*a^5 + x^6*d^5*b^5*a + 25/2*x^6*e*d^4*b^4*a^2 + 100/3*x^6*e^2*d^3*b^3*a^3 + 25*x^6*e^3*d^2*b^2*a^4 + 5*x^6*e^4*d*b*a^5 + 1/6*x^6*e^5*a^6 + 3*x^5*d^5*b^4*a^2 + 20*x^5*e*d^4*b^3*a^3 + 30*x^5*e^2*d^3*b^2*a^4 + 12*x^5*e^3*d^2*b*a^5 + x^5*e^4*d*a^6 + 5*x^4*d^5*b^3*a^3 + 75/4*x^4*e*d^4*b^2*a^4 + 15*x^4*e^2*d^3*b*a^5 + 5/2*x^4*e^3*d^2*a^6 + 5*x^3*d^5*b^2*a^4 + 10*x^3*e*d^4*b*a^5 + 10/3*x^3*e^2*d^3*a^6 + 3*x^2*d^5*b*a^5 + 5/2*x^2*e*d^4*a^6 + x*d^5*a^6","B",0
1485,1,470,0,0.356376," ","integrate((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{4} b^{6} + \frac{2}{5} x^{10} e^{3} d b^{6} + \frac{3}{5} x^{10} e^{4} b^{5} a + \frac{2}{3} x^{9} e^{2} d^{2} b^{6} + \frac{8}{3} x^{9} e^{3} d b^{5} a + \frac{5}{3} x^{9} e^{4} b^{4} a^{2} + \frac{1}{2} x^{8} e d^{3} b^{6} + \frac{9}{2} x^{8} e^{2} d^{2} b^{5} a + \frac{15}{2} x^{8} e^{3} d b^{4} a^{2} + \frac{5}{2} x^{8} e^{4} b^{3} a^{3} + \frac{1}{7} x^{7} d^{4} b^{6} + \frac{24}{7} x^{7} e d^{3} b^{5} a + \frac{90}{7} x^{7} e^{2} d^{2} b^{4} a^{2} + \frac{80}{7} x^{7} e^{3} d b^{3} a^{3} + \frac{15}{7} x^{7} e^{4} b^{2} a^{4} + x^{6} d^{4} b^{5} a + 10 x^{6} e d^{3} b^{4} a^{2} + 20 x^{6} e^{2} d^{2} b^{3} a^{3} + 10 x^{6} e^{3} d b^{2} a^{4} + x^{6} e^{4} b a^{5} + 3 x^{5} d^{4} b^{4} a^{2} + 16 x^{5} e d^{3} b^{3} a^{3} + 18 x^{5} e^{2} d^{2} b^{2} a^{4} + \frac{24}{5} x^{5} e^{3} d b a^{5} + \frac{1}{5} x^{5} e^{4} a^{6} + 5 x^{4} d^{4} b^{3} a^{3} + 15 x^{4} e d^{3} b^{2} a^{4} + 9 x^{4} e^{2} d^{2} b a^{5} + x^{4} e^{3} d a^{6} + 5 x^{3} d^{4} b^{2} a^{4} + 8 x^{3} e d^{3} b a^{5} + 2 x^{3} e^{2} d^{2} a^{6} + 3 x^{2} d^{4} b a^{5} + 2 x^{2} e d^{3} a^{6} + x d^{4} a^{6}"," ",0,"1/11*x^11*e^4*b^6 + 2/5*x^10*e^3*d*b^6 + 3/5*x^10*e^4*b^5*a + 2/3*x^9*e^2*d^2*b^6 + 8/3*x^9*e^3*d*b^5*a + 5/3*x^9*e^4*b^4*a^2 + 1/2*x^8*e*d^3*b^6 + 9/2*x^8*e^2*d^2*b^5*a + 15/2*x^8*e^3*d*b^4*a^2 + 5/2*x^8*e^4*b^3*a^3 + 1/7*x^7*d^4*b^6 + 24/7*x^7*e*d^3*b^5*a + 90/7*x^7*e^2*d^2*b^4*a^2 + 80/7*x^7*e^3*d*b^3*a^3 + 15/7*x^7*e^4*b^2*a^4 + x^6*d^4*b^5*a + 10*x^6*e*d^3*b^4*a^2 + 20*x^6*e^2*d^2*b^3*a^3 + 10*x^6*e^3*d*b^2*a^4 + x^6*e^4*b*a^5 + 3*x^5*d^4*b^4*a^2 + 16*x^5*e*d^3*b^3*a^3 + 18*x^5*e^2*d^2*b^2*a^4 + 24/5*x^5*e^3*d*b*a^5 + 1/5*x^5*e^4*a^6 + 5*x^4*d^4*b^3*a^3 + 15*x^4*e*d^3*b^2*a^4 + 9*x^4*e^2*d^2*b*a^5 + x^4*e^3*d*a^6 + 5*x^3*d^4*b^2*a^4 + 8*x^3*e*d^3*b*a^5 + 2*x^3*e^2*d^2*a^6 + 3*x^2*d^4*b*a^5 + 2*x^2*e*d^3*a^6 + x*d^4*a^6","B",0
1486,1,362,0,0.348085," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{3} b^{6} + \frac{1}{3} x^{9} e^{2} d b^{6} + \frac{2}{3} x^{9} e^{3} b^{5} a + \frac{3}{8} x^{8} e d^{2} b^{6} + \frac{9}{4} x^{8} e^{2} d b^{5} a + \frac{15}{8} x^{8} e^{3} b^{4} a^{2} + \frac{1}{7} x^{7} d^{3} b^{6} + \frac{18}{7} x^{7} e d^{2} b^{5} a + \frac{45}{7} x^{7} e^{2} d b^{4} a^{2} + \frac{20}{7} x^{7} e^{3} b^{3} a^{3} + x^{6} d^{3} b^{5} a + \frac{15}{2} x^{6} e d^{2} b^{4} a^{2} + 10 x^{6} e^{2} d b^{3} a^{3} + \frac{5}{2} x^{6} e^{3} b^{2} a^{4} + 3 x^{5} d^{3} b^{4} a^{2} + 12 x^{5} e d^{2} b^{3} a^{3} + 9 x^{5} e^{2} d b^{2} a^{4} + \frac{6}{5} x^{5} e^{3} b a^{5} + 5 x^{4} d^{3} b^{3} a^{3} + \frac{45}{4} x^{4} e d^{2} b^{2} a^{4} + \frac{9}{2} x^{4} e^{2} d b a^{5} + \frac{1}{4} x^{4} e^{3} a^{6} + 5 x^{3} d^{3} b^{2} a^{4} + 6 x^{3} e d^{2} b a^{5} + x^{3} e^{2} d a^{6} + 3 x^{2} d^{3} b a^{5} + \frac{3}{2} x^{2} e d^{2} a^{6} + x d^{3} a^{6}"," ",0,"1/10*x^10*e^3*b^6 + 1/3*x^9*e^2*d*b^6 + 2/3*x^9*e^3*b^5*a + 3/8*x^8*e*d^2*b^6 + 9/4*x^8*e^2*d*b^5*a + 15/8*x^8*e^3*b^4*a^2 + 1/7*x^7*d^3*b^6 + 18/7*x^7*e*d^2*b^5*a + 45/7*x^7*e^2*d*b^4*a^2 + 20/7*x^7*e^3*b^3*a^3 + x^6*d^3*b^5*a + 15/2*x^6*e*d^2*b^4*a^2 + 10*x^6*e^2*d*b^3*a^3 + 5/2*x^6*e^3*b^2*a^4 + 3*x^5*d^3*b^4*a^2 + 12*x^5*e*d^2*b^3*a^3 + 9*x^5*e^2*d*b^2*a^4 + 6/5*x^5*e^3*b*a^5 + 5*x^4*d^3*b^3*a^3 + 45/4*x^4*e*d^2*b^2*a^4 + 9/2*x^4*e^2*d*b*a^5 + 1/4*x^4*e^3*a^6 + 5*x^3*d^3*b^2*a^4 + 6*x^3*e*d^2*b*a^5 + x^3*e^2*d*a^6 + 3*x^2*d^3*b*a^5 + 3/2*x^2*e*d^2*a^6 + x*d^3*a^6","B",0
1487,1,253,0,0.347109," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{2} b^{6} + \frac{1}{4} x^{8} e d b^{6} + \frac{3}{4} x^{8} e^{2} b^{5} a + \frac{1}{7} x^{7} d^{2} b^{6} + \frac{12}{7} x^{7} e d b^{5} a + \frac{15}{7} x^{7} e^{2} b^{4} a^{2} + x^{6} d^{2} b^{5} a + 5 x^{6} e d b^{4} a^{2} + \frac{10}{3} x^{6} e^{2} b^{3} a^{3} + 3 x^{5} d^{2} b^{4} a^{2} + 8 x^{5} e d b^{3} a^{3} + 3 x^{5} e^{2} b^{2} a^{4} + 5 x^{4} d^{2} b^{3} a^{3} + \frac{15}{2} x^{4} e d b^{2} a^{4} + \frac{3}{2} x^{4} e^{2} b a^{5} + 5 x^{3} d^{2} b^{2} a^{4} + 4 x^{3} e d b a^{5} + \frac{1}{3} x^{3} e^{2} a^{6} + 3 x^{2} d^{2} b a^{5} + x^{2} e d a^{6} + x d^{2} a^{6}"," ",0,"1/9*x^9*e^2*b^6 + 1/4*x^8*e*d*b^6 + 3/4*x^8*e^2*b^5*a + 1/7*x^7*d^2*b^6 + 12/7*x^7*e*d*b^5*a + 15/7*x^7*e^2*b^4*a^2 + x^6*d^2*b^5*a + 5*x^6*e*d*b^4*a^2 + 10/3*x^6*e^2*b^3*a^3 + 3*x^5*d^2*b^4*a^2 + 8*x^5*e*d*b^3*a^3 + 3*x^5*e^2*b^2*a^4 + 5*x^4*d^2*b^3*a^3 + 15/2*x^4*e*d*b^2*a^4 + 3/2*x^4*e^2*b*a^5 + 5*x^3*d^2*b^2*a^4 + 4*x^3*e*d*b*a^5 + 1/3*x^3*e^2*a^6 + 3*x^2*d^2*b*a^5 + x^2*e*d*a^6 + x*d^2*a^6","B",0
1488,1,145,0,0.338384," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e b^{6} + \frac{1}{7} x^{7} d b^{6} + \frac{6}{7} x^{7} e b^{5} a + x^{6} d b^{5} a + \frac{5}{2} x^{6} e b^{4} a^{2} + 3 x^{5} d b^{4} a^{2} + 4 x^{5} e b^{3} a^{3} + 5 x^{4} d b^{3} a^{3} + \frac{15}{4} x^{4} e b^{2} a^{4} + 5 x^{3} d b^{2} a^{4} + 2 x^{3} e b a^{5} + 3 x^{2} d b a^{5} + \frac{1}{2} x^{2} e a^{6} + x d a^{6}"," ",0,"1/8*x^8*e*b^6 + 1/7*x^7*d*b^6 + 6/7*x^7*e*b^5*a + x^6*d*b^5*a + 5/2*x^6*e*b^4*a^2 + 3*x^5*d*b^4*a^2 + 4*x^5*e*b^3*a^3 + 5*x^4*d*b^3*a^3 + 15/4*x^4*e*b^2*a^4 + 5*x^3*d*b^2*a^4 + 2*x^3*e*b*a^5 + 3*x^2*d*b*a^5 + 1/2*x^2*e*a^6 + x*d*a^6","B",0
1489,1,64,0,0.358161," ","integrate((b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{1}{7} x^{7} b^{6} + x^{6} b^{5} a + 3 x^{5} b^{4} a^{2} + 5 x^{4} b^{3} a^{3} + 5 x^{3} b^{2} a^{4} + 3 x^{2} b a^{5} + x a^{6}"," ",0,"1/7*x^7*b^6 + x^6*b^5*a + 3*x^5*b^4*a^2 + 5*x^4*b^3*a^3 + 5*x^3*b^2*a^4 + 3*x^2*b*a^5 + x*a^6","B",0
1490,1,351,0,0.383164," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d),x, algorithm=""fricas"")","\frac{10 \, b^{6} e^{6} x^{6} - 12 \, {\left(b^{6} d e^{5} - 6 \, a b^{5} e^{6}\right)} x^{5} + 15 \, {\left(b^{6} d^{2} e^{4} - 6 \, a b^{5} d e^{5} + 15 \, a^{2} b^{4} e^{6}\right)} x^{4} - 20 \, {\left(b^{6} d^{3} e^{3} - 6 \, a b^{5} d^{2} e^{4} + 15 \, a^{2} b^{4} d e^{5} - 20 \, a^{3} b^{3} e^{6}\right)} x^{3} + 30 \, {\left(b^{6} d^{4} e^{2} - 6 \, a b^{5} d^{3} e^{3} + 15 \, a^{2} b^{4} d^{2} e^{4} - 20 \, a^{3} b^{3} d e^{5} + 15 \, a^{4} b^{2} e^{6}\right)} x^{2} - 60 \, {\left(b^{6} d^{5} e - 6 \, a b^{5} d^{4} e^{2} + 15 \, a^{2} b^{4} d^{3} e^{3} - 20 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5} - 6 \, a^{5} b e^{6}\right)} x + 60 \, {\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)} \log\left(e x + d\right)}{60 \, e^{7}}"," ",0,"1/60*(10*b^6*e^6*x^6 - 12*(b^6*d*e^5 - 6*a*b^5*e^6)*x^5 + 15*(b^6*d^2*e^4 - 6*a*b^5*d*e^5 + 15*a^2*b^4*e^6)*x^4 - 20*(b^6*d^3*e^3 - 6*a*b^5*d^2*e^4 + 15*a^2*b^4*d*e^5 - 20*a^3*b^3*e^6)*x^3 + 30*(b^6*d^4*e^2 - 6*a*b^5*d^3*e^3 + 15*a^2*b^4*d^2*e^4 - 20*a^3*b^3*d*e^5 + 15*a^4*b^2*e^6)*x^2 - 60*(b^6*d^5*e - 6*a*b^5*d^4*e^2 + 15*a^2*b^4*d^3*e^3 - 20*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5 - 6*a^5*b*e^6)*x + 60*(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)*log(e*x + d))/e^7","B",0
1491,1,496,0,0.390540," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^2,x, algorithm=""fricas"")","\frac{2 \, b^{6} e^{6} x^{6} - 10 \, b^{6} d^{6} + 60 \, a b^{5} d^{5} e - 150 \, a^{2} b^{4} d^{4} e^{2} + 200 \, a^{3} b^{3} d^{3} e^{3} - 150 \, a^{4} b^{2} d^{2} e^{4} + 60 \, a^{5} b d e^{5} - 10 \, a^{6} e^{6} - 3 \, {\left(b^{6} d e^{5} - 5 \, a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(b^{6} d^{2} e^{4} - 5 \, a b^{5} d e^{5} + 10 \, a^{2} b^{4} e^{6}\right)} x^{4} - 10 \, {\left(b^{6} d^{3} e^{3} - 5 \, a b^{5} d^{2} e^{4} + 10 \, a^{2} b^{4} d e^{5} - 10 \, a^{3} b^{3} e^{6}\right)} x^{3} + 30 \, {\left(b^{6} d^{4} e^{2} - 5 \, a b^{5} d^{3} e^{3} + 10 \, a^{2} b^{4} d^{2} e^{4} - 10 \, a^{3} b^{3} d e^{5} + 5 \, a^{4} b^{2} e^{6}\right)} x^{2} + 10 \, {\left(5 \, b^{6} d^{5} e - 24 \, a b^{5} d^{4} e^{2} + 45 \, a^{2} b^{4} d^{3} e^{3} - 40 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5}\right)} x - 60 \, {\left(b^{6} d^{6} - 5 \, a b^{5} d^{5} e + 10 \, 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} - a^{5} b d e^{5} + {\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)} \log\left(e x + d\right)}{10 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"1/10*(2*b^6*e^6*x^6 - 10*b^6*d^6 + 60*a*b^5*d^5*e - 150*a^2*b^4*d^4*e^2 + 200*a^3*b^3*d^3*e^3 - 150*a^4*b^2*d^2*e^4 + 60*a^5*b*d*e^5 - 10*a^6*e^6 - 3*(b^6*d*e^5 - 5*a*b^5*e^6)*x^5 + 5*(b^6*d^2*e^4 - 5*a*b^5*d*e^5 + 10*a^2*b^4*e^6)*x^4 - 10*(b^6*d^3*e^3 - 5*a*b^5*d^2*e^4 + 10*a^2*b^4*d*e^5 - 10*a^3*b^3*e^6)*x^3 + 30*(b^6*d^4*e^2 - 5*a*b^5*d^3*e^3 + 10*a^2*b^4*d^2*e^4 - 10*a^3*b^3*d*e^5 + 5*a^4*b^2*e^6)*x^2 + 10*(5*b^6*d^5*e - 24*a*b^5*d^4*e^2 + 45*a^2*b^4*d^3*e^3 - 40*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5)*x - 60*(b^6*d^6 - 5*a*b^5*d^5*e + 10*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 - a^5*b*d*e^5 + (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)*log(e*x + d))/(e^8*x + d*e^7)","B",0
1492,1,548,0,0.410607," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{b^{6} e^{6} x^{6} + 22 \, b^{6} d^{6} - 108 \, a b^{5} d^{5} e + 210 \, a^{2} b^{4} d^{4} e^{2} - 200 \, a^{3} b^{3} d^{3} e^{3} + 90 \, a^{4} b^{2} d^{2} e^{4} - 12 \, a^{5} b d e^{5} - 2 \, a^{6} e^{6} - 2 \, {\left(b^{6} d e^{5} - 4 \, a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(b^{6} d^{2} e^{4} - 4 \, a b^{5} d e^{5} + 6 \, a^{2} b^{4} e^{6}\right)} x^{4} - 20 \, {\left(b^{6} d^{3} e^{3} - 4 \, a b^{5} d^{2} e^{4} + 6 \, a^{2} b^{4} d e^{5} - 4 \, a^{3} b^{3} e^{6}\right)} x^{3} - 2 \, {\left(34 \, b^{6} d^{4} e^{2} - 126 \, a b^{5} d^{3} e^{3} + 165 \, a^{2} b^{4} d^{2} e^{4} - 80 \, a^{3} b^{3} d e^{5}\right)} x^{2} - 4 \, {\left(4 \, b^{6} d^{5} e - 6 \, a b^{5} d^{4} e^{2} - 15 \, a^{2} b^{4} d^{3} e^{3} + 40 \, a^{3} b^{3} d^{2} e^{4} - 30 \, a^{4} b^{2} d e^{5} + 6 \, a^{5} b e^{6}\right)} x + 60 \, {\left(b^{6} d^{6} - 4 \, a b^{5} d^{5} e + 6 \, a^{2} b^{4} d^{4} e^{2} - 4 \, a^{3} b^{3} d^{3} e^{3} + a^{4} b^{2} d^{2} e^{4} + {\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} + 2 \, {\left(b^{6} d^{5} e - 4 \, a b^{5} d^{4} e^{2} + 6 \, a^{2} b^{4} d^{3} e^{3} - 4 \, a^{3} b^{3} d^{2} e^{4} + a^{4} b^{2} d e^{5}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"1/4*(b^6*e^6*x^6 + 22*b^6*d^6 - 108*a*b^5*d^5*e + 210*a^2*b^4*d^4*e^2 - 200*a^3*b^3*d^3*e^3 + 90*a^4*b^2*d^2*e^4 - 12*a^5*b*d*e^5 - 2*a^6*e^6 - 2*(b^6*d*e^5 - 4*a*b^5*e^6)*x^5 + 5*(b^6*d^2*e^4 - 4*a*b^5*d*e^5 + 6*a^2*b^4*e^6)*x^4 - 20*(b^6*d^3*e^3 - 4*a*b^5*d^2*e^4 + 6*a^2*b^4*d*e^5 - 4*a^3*b^3*e^6)*x^3 - 2*(34*b^6*d^4*e^2 - 126*a*b^5*d^3*e^3 + 165*a^2*b^4*d^2*e^4 - 80*a^3*b^3*d*e^5)*x^2 - 4*(4*b^6*d^5*e - 6*a*b^5*d^4*e^2 - 15*a^2*b^4*d^3*e^3 + 40*a^3*b^3*d^2*e^4 - 30*a^4*b^2*d*e^5 + 6*a^5*b*e^6)*x + 60*(b^6*d^6 - 4*a*b^5*d^5*e + 6*a^2*b^4*d^4*e^2 - 4*a^3*b^3*d^3*e^3 + a^4*b^2*d^2*e^4 + (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 + 2*(b^6*d^5*e - 4*a*b^5*d^4*e^2 + 6*a^2*b^4*d^3*e^3 - 4*a^3*b^3*d^2*e^4 + a^4*b^2*d*e^5)*x)*log(e*x + d))/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","B",0
1493,1,576,0,0.399821," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{b^{6} e^{6} x^{6} - 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} - 3 \, {\left(b^{6} d e^{5} - 3 \, a b^{5} e^{6}\right)} x^{5} + 15 \, {\left(b^{6} d^{2} e^{4} - 3 \, a b^{5} d e^{5} + 3 \, a^{2} b^{4} e^{6}\right)} x^{4} + {\left(73 \, b^{6} d^{3} e^{3} - 189 \, a b^{5} d^{2} e^{4} + 135 \, a^{2} b^{4} d e^{5}\right)} x^{3} + 3 \, {\left(13 \, b^{6} d^{4} e^{2} - 9 \, a b^{5} d^{3} e^{3} - 45 \, a^{2} b^{4} d^{2} e^{4} + 60 \, a^{3} b^{3} d e^{5} - 15 \, a^{4} b^{2} e^{6}\right)} x^{2} - 3 \, {\left(17 \, b^{6} d^{5} e - 81 \, a b^{5} d^{4} e^{2} + 135 \, a^{2} b^{4} d^{3} e^{3} - 90 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5} + 3 \, a^{5} b e^{6}\right)} x - 60 \, {\left(b^{6} d^{6} - 3 \, a b^{5} d^{5} e + 3 \, a^{2} b^{4} d^{4} e^{2} - a^{3} b^{3} d^{3} e^{3} + {\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)} x^{3} + 3 \, {\left(b^{6} d^{4} e^{2} - 3 \, a b^{5} d^{3} e^{3} + 3 \, a^{2} b^{4} d^{2} e^{4} - a^{3} b^{3} d e^{5}\right)} x^{2} + 3 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 3 \, a^{2} b^{4} d^{3} e^{3} - a^{3} b^{3} d^{2} e^{4}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"1/3*(b^6*e^6*x^6 - 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 - 3*(b^6*d*e^5 - 3*a*b^5*e^6)*x^5 + 15*(b^6*d^2*e^4 - 3*a*b^5*d*e^5 + 3*a^2*b^4*e^6)*x^4 + (73*b^6*d^3*e^3 - 189*a*b^5*d^2*e^4 + 135*a^2*b^4*d*e^5)*x^3 + 3*(13*b^6*d^4*e^2 - 9*a*b^5*d^3*e^3 - 45*a^2*b^4*d^2*e^4 + 60*a^3*b^3*d*e^5 - 15*a^4*b^2*e^6)*x^2 - 3*(17*b^6*d^5*e - 81*a*b^5*d^4*e^2 + 135*a^2*b^4*d^3*e^3 - 90*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5 + 3*a^5*b*e^6)*x - 60*(b^6*d^6 - 3*a*b^5*d^5*e + 3*a^2*b^4*d^4*e^2 - a^3*b^3*d^3*e^3 + (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)*x^3 + 3*(b^6*d^4*e^2 - 3*a*b^5*d^3*e^3 + 3*a^2*b^4*d^2*e^4 - a^3*b^3*d*e^5)*x^2 + 3*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 3*a^2*b^4*d^3*e^3 - a^3*b^3*d^2*e^4)*x)*log(e*x + d))/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","B",0
1494,1,571,0,0.409613," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^5,x, algorithm=""fricas"")","\frac{2 \, b^{6} e^{6} x^{6} + 57 \, b^{6} d^{6} - 154 \, a b^{5} d^{5} e + 125 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} - 5 \, a^{4} b^{2} d^{2} e^{4} - 2 \, a^{5} b d e^{5} - a^{6} e^{6} - 12 \, {\left(b^{6} d e^{5} - 2 \, a b^{5} e^{6}\right)} x^{5} - 4 \, {\left(17 \, b^{6} d^{2} e^{4} - 24 \, a b^{5} d e^{5}\right)} x^{4} - 16 \, {\left(2 \, b^{6} d^{3} e^{3} + 6 \, a b^{5} d^{2} e^{4} - 15 \, a^{2} b^{4} d e^{5} + 5 \, a^{3} b^{3} e^{6}\right)} x^{3} + 6 \, {\left(22 \, b^{6} d^{4} e^{2} - 84 \, a b^{5} d^{3} e^{3} + 90 \, a^{2} b^{4} d^{2} e^{4} - 20 \, a^{3} b^{3} d e^{5} - 5 \, a^{4} b^{2} e^{6}\right)} x^{2} + 4 \, {\left(42 \, b^{6} d^{5} e - 124 \, a b^{5} d^{4} e^{2} + 110 \, a^{2} b^{4} d^{3} e^{3} - 20 \, a^{3} b^{3} d^{2} e^{4} - 5 \, a^{4} b^{2} d e^{5} - 2 \, a^{5} b e^{6}\right)} x + 60 \, {\left(b^{6} d^{6} - 2 \, a b^{5} d^{5} e + a^{2} b^{4} d^{4} e^{2} + {\left(b^{6} d^{2} e^{4} - 2 \, a b^{5} d e^{5} + a^{2} b^{4} e^{6}\right)} x^{4} + 4 \, {\left(b^{6} d^{3} e^{3} - 2 \, a b^{5} d^{2} e^{4} + a^{2} b^{4} d e^{5}\right)} x^{3} + 6 \, {\left(b^{6} d^{4} e^{2} - 2 \, a b^{5} d^{3} e^{3} + a^{2} b^{4} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(b^{6} d^{5} e - 2 \, a b^{5} d^{4} e^{2} + a^{2} b^{4} d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(e^{11} x^{4} + 4 \, d e^{10} x^{3} + 6 \, d^{2} e^{9} x^{2} + 4 \, d^{3} e^{8} x + d^{4} e^{7}\right)}}"," ",0,"1/4*(2*b^6*e^6*x^6 + 57*b^6*d^6 - 154*a*b^5*d^5*e + 125*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 - 5*a^4*b^2*d^2*e^4 - 2*a^5*b*d*e^5 - a^6*e^6 - 12*(b^6*d*e^5 - 2*a*b^5*e^6)*x^5 - 4*(17*b^6*d^2*e^4 - 24*a*b^5*d*e^5)*x^4 - 16*(2*b^6*d^3*e^3 + 6*a*b^5*d^2*e^4 - 15*a^2*b^4*d*e^5 + 5*a^3*b^3*e^6)*x^3 + 6*(22*b^6*d^4*e^2 - 84*a*b^5*d^3*e^3 + 90*a^2*b^4*d^2*e^4 - 20*a^3*b^3*d*e^5 - 5*a^4*b^2*e^6)*x^2 + 4*(42*b^6*d^5*e - 124*a*b^5*d^4*e^2 + 110*a^2*b^4*d^3*e^3 - 20*a^3*b^3*d^2*e^4 - 5*a^4*b^2*d*e^5 - 2*a^5*b*e^6)*x + 60*(b^6*d^6 - 2*a*b^5*d^5*e + a^2*b^4*d^4*e^2 + (b^6*d^2*e^4 - 2*a*b^5*d*e^5 + a^2*b^4*e^6)*x^4 + 4*(b^6*d^3*e^3 - 2*a*b^5*d^2*e^4 + a^2*b^4*d*e^5)*x^3 + 6*(b^6*d^4*e^2 - 2*a*b^5*d^3*e^3 + a^2*b^4*d^2*e^4)*x^2 + 4*(b^6*d^5*e - 2*a*b^5*d^4*e^2 + a^2*b^4*d^3*e^3)*x)*log(e*x + d))/(e^11*x^4 + 4*d*e^10*x^3 + 6*d^2*e^9*x^2 + 4*d^3*e^8*x + d^4*e^7)","B",0
1495,1,542,0,0.404884," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^6,x, algorithm=""fricas"")","\frac{10 \, b^{6} e^{6} x^{6} + 50 \, b^{6} d e^{5} x^{5} - 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} - 50 \, {\left(b^{6} d^{2} e^{4} - 6 \, a b^{5} d e^{5} + 3 \, a^{2} b^{4} e^{6}\right)} x^{4} - 100 \, {\left(4 \, 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(12 \, 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(75 \, 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 - 60 \, {\left(b^{6} d^{6} - a b^{5} d^{5} e + {\left(b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(b^{6} d^{2} e^{4} - a b^{5} d e^{5}\right)} x^{4} + 10 \, {\left(b^{6} d^{3} e^{3} - a b^{5} d^{2} e^{4}\right)} x^{3} + 10 \, {\left(b^{6} d^{4} e^{2} - a b^{5} d^{3} e^{3}\right)} x^{2} + 5 \, {\left(b^{6} d^{5} e - a b^{5} d^{4} e^{2}\right)} x\right)} \log\left(e x + d\right)}{10 \, {\left(e^{12} x^{5} + 5 \, d e^{11} x^{4} + 10 \, d^{2} e^{10} x^{3} + 10 \, d^{3} e^{9} x^{2} + 5 \, d^{4} e^{8} x + d^{5} e^{7}\right)}}"," ",0,"1/10*(10*b^6*e^6*x^6 + 50*b^6*d*e^5*x^5 - 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 - 50*(b^6*d^2*e^4 - 6*a*b^5*d*e^5 + 3*a^2*b^4*e^6)*x^4 - 100*(4*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*(12*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*(75*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 - 60*(b^6*d^6 - a*b^5*d^5*e + (b^6*d*e^5 - a*b^5*e^6)*x^5 + 5*(b^6*d^2*e^4 - a*b^5*d*e^5)*x^4 + 10*(b^6*d^3*e^3 - a*b^5*d^2*e^4)*x^3 + 10*(b^6*d^4*e^2 - a*b^5*d^3*e^3)*x^2 + 5*(b^6*d^5*e - a*b^5*d^4*e^2)*x)*log(e*x + d))/(e^12*x^5 + 5*d*e^11*x^4 + 10*d^2*e^10*x^3 + 10*d^3*e^9*x^2 + 5*d^4*e^8*x + d^5*e^7)","B",0
1496,1,492,0,0.396088," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^7,x, algorithm=""fricas"")","\frac{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} + 360 \, {\left(b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 450 \, {\left(3 \, b^{6} d^{2} e^{4} - 2 \, a b^{5} d e^{5} - a^{2} b^{4} e^{6}\right)} x^{4} + 200 \, {\left(11 \, b^{6} d^{3} e^{3} - 6 \, a b^{5} d^{2} e^{4} - 3 \, a^{2} b^{4} d e^{5} - 2 \, a^{3} b^{3} e^{6}\right)} x^{3} + 75 \, {\left(25 \, b^{6} d^{4} e^{2} - 12 \, a b^{5} d^{3} e^{3} - 6 \, a^{2} b^{4} d^{2} e^{4} - 4 \, a^{3} b^{3} d e^{5} - 3 \, a^{4} b^{2} e^{6}\right)} x^{2} + 6 \, {\left(137 \, b^{6} d^{5} e - 60 \, a b^{5} d^{4} e^{2} - 30 \, a^{2} b^{4} d^{3} e^{3} - 20 \, a^{3} b^{3} d^{2} e^{4} - 15 \, a^{4} b^{2} d e^{5} - 12 \, a^{5} b e^{6}\right)} x + 60 \, {\left(b^{6} e^{6} x^{6} + 6 \, b^{6} d e^{5} x^{5} + 15 \, b^{6} d^{2} e^{4} x^{4} + 20 \, b^{6} d^{3} e^{3} x^{3} + 15 \, b^{6} d^{4} e^{2} x^{2} + 6 \, b^{6} d^{5} e x + b^{6} d^{6}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{13} x^{6} + 6 \, d e^{12} x^{5} + 15 \, d^{2} e^{11} x^{4} + 20 \, d^{3} e^{10} x^{3} + 15 \, d^{4} e^{9} x^{2} + 6 \, d^{5} e^{8} x + d^{6} e^{7}\right)}}"," ",0,"1/60*(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 + 360*(b^6*d*e^5 - a*b^5*e^6)*x^5 + 450*(3*b^6*d^2*e^4 - 2*a*b^5*d*e^5 - a^2*b^4*e^6)*x^4 + 200*(11*b^6*d^3*e^3 - 6*a*b^5*d^2*e^4 - 3*a^2*b^4*d*e^5 - 2*a^3*b^3*e^6)*x^3 + 75*(25*b^6*d^4*e^2 - 12*a*b^5*d^3*e^3 - 6*a^2*b^4*d^2*e^4 - 4*a^3*b^3*d*e^5 - 3*a^4*b^2*e^6)*x^2 + 6*(137*b^6*d^5*e - 60*a*b^5*d^4*e^2 - 30*a^2*b^4*d^3*e^3 - 20*a^3*b^3*d^2*e^4 - 15*a^4*b^2*d*e^5 - 12*a^5*b*e^6)*x + 60*(b^6*e^6*x^6 + 6*b^6*d*e^5*x^5 + 15*b^6*d^2*e^4*x^4 + 20*b^6*d^3*e^3*x^3 + 15*b^6*d^4*e^2*x^2 + 6*b^6*d^5*e*x + b^6*d^6)*log(e*x + d))/(e^13*x^6 + 6*d*e^12*x^5 + 15*d^2*e^11*x^4 + 20*d^3*e^10*x^3 + 15*d^4*e^9*x^2 + 6*d^5*e^8*x + d^6*e^7)","B",0
1497,1,398,0,0.378598," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{7 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + a b^{5} d^{5} e + a^{2} b^{4} d^{4} e^{2} + a^{3} b^{3} d^{3} e^{3} + a^{4} b^{2} d^{2} e^{4} + a^{5} b d e^{5} + a^{6} e^{6} + 21 \, {\left(b^{6} d e^{5} + a b^{5} e^{6}\right)} x^{5} + 35 \, {\left(b^{6} d^{2} e^{4} + a b^{5} d e^{5} + a^{2} b^{4} e^{6}\right)} x^{4} + 35 \, {\left(b^{6} d^{3} e^{3} + a b^{5} d^{2} e^{4} + a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + 21 \, {\left(b^{6} d^{4} e^{2} + a b^{5} d^{3} e^{3} + a^{2} b^{4} d^{2} e^{4} + a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + 7 \, {\left(b^{6} d^{5} e + a b^{5} d^{4} e^{2} + a^{2} b^{4} d^{3} e^{3} + a^{3} b^{3} d^{2} e^{4} + a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x}{7 \, {\left(e^{14} x^{7} + 7 \, d e^{13} x^{6} + 21 \, d^{2} e^{12} x^{5} + 35 \, d^{3} e^{11} x^{4} + 35 \, d^{4} e^{10} x^{3} + 21 \, d^{5} e^{9} x^{2} + 7 \, d^{6} e^{8} x + d^{7} e^{7}\right)}}"," ",0,"-1/7*(7*b^6*e^6*x^6 + b^6*d^6 + a*b^5*d^5*e + a^2*b^4*d^4*e^2 + a^3*b^3*d^3*e^3 + a^4*b^2*d^2*e^4 + a^5*b*d*e^5 + a^6*e^6 + 21*(b^6*d*e^5 + a*b^5*e^6)*x^5 + 35*(b^6*d^2*e^4 + a*b^5*d*e^5 + a^2*b^4*e^6)*x^4 + 35*(b^6*d^3*e^3 + a*b^5*d^2*e^4 + a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 + 21*(b^6*d^4*e^2 + a*b^5*d^3*e^3 + a^2*b^4*d^2*e^4 + a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + 7*(b^6*d^5*e + a*b^5*d^4*e^2 + a^2*b^4*d^3*e^3 + a^3*b^3*d^2*e^4 + a^4*b^2*d*e^5 + a^5*b*e^6)*x)/(e^14*x^7 + 7*d*e^13*x^6 + 21*d^2*e^12*x^5 + 35*d^3*e^11*x^4 + 35*d^4*e^10*x^3 + 21*d^5*e^9*x^2 + 7*d^6*e^8*x + d^7*e^7)","B",0
1498,1,430,0,0.380417," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{28 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 2 \, a b^{5} d^{5} e + 3 \, a^{2} b^{4} d^{4} e^{2} + 4 \, a^{3} b^{3} d^{3} e^{3} + 5 \, a^{4} b^{2} d^{2} e^{4} + 6 \, a^{5} b d e^{5} + 7 \, a^{6} e^{6} + 56 \, {\left(b^{6} d e^{5} + 2 \, a b^{5} e^{6}\right)} x^{5} + 70 \, {\left(b^{6} d^{2} e^{4} + 2 \, a b^{5} d e^{5} + 3 \, a^{2} b^{4} e^{6}\right)} x^{4} + 56 \, {\left(b^{6} d^{3} e^{3} + 2 \, a b^{5} d^{2} e^{4} + 3 \, a^{2} b^{4} d e^{5} + 4 \, a^{3} b^{3} e^{6}\right)} x^{3} + 28 \, {\left(b^{6} d^{4} e^{2} + 2 \, a b^{5} d^{3} e^{3} + 3 \, a^{2} b^{4} d^{2} e^{4} + 4 \, a^{3} b^{3} d e^{5} + 5 \, a^{4} b^{2} e^{6}\right)} x^{2} + 8 \, {\left(b^{6} d^{5} e + 2 \, a b^{5} d^{4} e^{2} + 3 \, a^{2} b^{4} d^{3} e^{3} + 4 \, a^{3} b^{3} d^{2} e^{4} + 5 \, a^{4} b^{2} d e^{5} + 6 \, a^{5} b e^{6}\right)} x}{56 \, {\left(e^{15} x^{8} + 8 \, d e^{14} x^{7} + 28 \, d^{2} e^{13} x^{6} + 56 \, d^{3} e^{12} x^{5} + 70 \, d^{4} e^{11} x^{4} + 56 \, d^{5} e^{10} x^{3} + 28 \, d^{6} e^{9} x^{2} + 8 \, d^{7} e^{8} x + d^{8} e^{7}\right)}}"," ",0,"-1/56*(28*b^6*e^6*x^6 + b^6*d^6 + 2*a*b^5*d^5*e + 3*a^2*b^4*d^4*e^2 + 4*a^3*b^3*d^3*e^3 + 5*a^4*b^2*d^2*e^4 + 6*a^5*b*d*e^5 + 7*a^6*e^6 + 56*(b^6*d*e^5 + 2*a*b^5*e^6)*x^5 + 70*(b^6*d^2*e^4 + 2*a*b^5*d*e^5 + 3*a^2*b^4*e^6)*x^4 + 56*(b^6*d^3*e^3 + 2*a*b^5*d^2*e^4 + 3*a^2*b^4*d*e^5 + 4*a^3*b^3*e^6)*x^3 + 28*(b^6*d^4*e^2 + 2*a*b^5*d^3*e^3 + 3*a^2*b^4*d^2*e^4 + 4*a^3*b^3*d*e^5 + 5*a^4*b^2*e^6)*x^2 + 8*(b^6*d^5*e + 2*a*b^5*d^4*e^2 + 3*a^2*b^4*d^3*e^3 + 4*a^3*b^3*d^2*e^4 + 5*a^4*b^2*d*e^5 + 6*a^5*b*e^6)*x)/(e^15*x^8 + 8*d*e^14*x^7 + 28*d^2*e^13*x^6 + 56*d^3*e^12*x^5 + 70*d^4*e^11*x^4 + 56*d^5*e^10*x^3 + 28*d^6*e^9*x^2 + 8*d^7*e^8*x + d^8*e^7)","B",0
1499,1,441,0,0.380439," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{84 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 3 \, a b^{5} d^{5} e + 6 \, a^{2} b^{4} d^{4} e^{2} + 10 \, a^{3} b^{3} d^{3} e^{3} + 15 \, a^{4} b^{2} d^{2} e^{4} + 21 \, a^{5} b d e^{5} + 28 \, a^{6} e^{6} + 126 \, {\left(b^{6} d e^{5} + 3 \, a b^{5} e^{6}\right)} x^{5} + 126 \, {\left(b^{6} d^{2} e^{4} + 3 \, a b^{5} d e^{5} + 6 \, a^{2} b^{4} e^{6}\right)} x^{4} + 84 \, {\left(b^{6} d^{3} e^{3} + 3 \, a b^{5} d^{2} e^{4} + 6 \, a^{2} b^{4} d e^{5} + 10 \, a^{3} b^{3} e^{6}\right)} x^{3} + 36 \, {\left(b^{6} d^{4} e^{2} + 3 \, a b^{5} d^{3} e^{3} + 6 \, a^{2} b^{4} d^{2} e^{4} + 10 \, a^{3} b^{3} d e^{5} + 15 \, a^{4} b^{2} e^{6}\right)} x^{2} + 9 \, {\left(b^{6} d^{5} e + 3 \, a b^{5} d^{4} e^{2} + 6 \, a^{2} b^{4} d^{3} e^{3} + 10 \, a^{3} b^{3} d^{2} e^{4} + 15 \, a^{4} b^{2} d e^{5} + 21 \, a^{5} b e^{6}\right)} x}{252 \, {\left(e^{16} x^{9} + 9 \, d e^{15} x^{8} + 36 \, d^{2} e^{14} x^{7} + 84 \, d^{3} e^{13} x^{6} + 126 \, d^{4} e^{12} x^{5} + 126 \, d^{5} e^{11} x^{4} + 84 \, d^{6} e^{10} x^{3} + 36 \, d^{7} e^{9} x^{2} + 9 \, d^{8} e^{8} x + d^{9} e^{7}\right)}}"," ",0,"-1/252*(84*b^6*e^6*x^6 + b^6*d^6 + 3*a*b^5*d^5*e + 6*a^2*b^4*d^4*e^2 + 10*a^3*b^3*d^3*e^3 + 15*a^4*b^2*d^2*e^4 + 21*a^5*b*d*e^5 + 28*a^6*e^6 + 126*(b^6*d*e^5 + 3*a*b^5*e^6)*x^5 + 126*(b^6*d^2*e^4 + 3*a*b^5*d*e^5 + 6*a^2*b^4*e^6)*x^4 + 84*(b^6*d^3*e^3 + 3*a*b^5*d^2*e^4 + 6*a^2*b^4*d*e^5 + 10*a^3*b^3*e^6)*x^3 + 36*(b^6*d^4*e^2 + 3*a*b^5*d^3*e^3 + 6*a^2*b^4*d^2*e^4 + 10*a^3*b^3*d*e^5 + 15*a^4*b^2*e^6)*x^2 + 9*(b^6*d^5*e + 3*a*b^5*d^4*e^2 + 6*a^2*b^4*d^3*e^3 + 10*a^3*b^3*d^2*e^4 + 15*a^4*b^2*d*e^5 + 21*a^5*b*e^6)*x)/(e^16*x^9 + 9*d*e^15*x^8 + 36*d^2*e^14*x^7 + 84*d^3*e^13*x^6 + 126*d^4*e^12*x^5 + 126*d^5*e^11*x^4 + 84*d^6*e^10*x^3 + 36*d^7*e^9*x^2 + 9*d^8*e^8*x + d^9*e^7)","B",0
1500,1,452,0,0.386785," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{210 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 4 \, a b^{5} d^{5} e + 10 \, a^{2} b^{4} d^{4} e^{2} + 20 \, a^{3} b^{3} d^{3} e^{3} + 35 \, a^{4} b^{2} d^{2} e^{4} + 56 \, a^{5} b d e^{5} + 84 \, a^{6} e^{6} + 252 \, {\left(b^{6} d e^{5} + 4 \, a b^{5} e^{6}\right)} x^{5} + 210 \, {\left(b^{6} d^{2} e^{4} + 4 \, a b^{5} d e^{5} + 10 \, a^{2} b^{4} e^{6}\right)} x^{4} + 120 \, {\left(b^{6} d^{3} e^{3} + 4 \, a b^{5} d^{2} e^{4} + 10 \, a^{2} b^{4} d e^{5} + 20 \, a^{3} b^{3} e^{6}\right)} x^{3} + 45 \, {\left(b^{6} d^{4} e^{2} + 4 \, a b^{5} d^{3} e^{3} + 10 \, a^{2} b^{4} d^{2} e^{4} + 20 \, a^{3} b^{3} d e^{5} + 35 \, a^{4} b^{2} e^{6}\right)} x^{2} + 10 \, {\left(b^{6} d^{5} e + 4 \, a b^{5} d^{4} e^{2} + 10 \, a^{2} b^{4} d^{3} e^{3} + 20 \, a^{3} b^{3} d^{2} e^{4} + 35 \, a^{4} b^{2} d e^{5} + 56 \, a^{5} b e^{6}\right)} x}{840 \, {\left(e^{17} x^{10} + 10 \, d e^{16} x^{9} + 45 \, d^{2} e^{15} x^{8} + 120 \, d^{3} e^{14} x^{7} + 210 \, d^{4} e^{13} x^{6} + 252 \, d^{5} e^{12} x^{5} + 210 \, d^{6} e^{11} x^{4} + 120 \, d^{7} e^{10} x^{3} + 45 \, d^{8} e^{9} x^{2} + 10 \, d^{9} e^{8} x + d^{10} e^{7}\right)}}"," ",0,"-1/840*(210*b^6*e^6*x^6 + b^6*d^6 + 4*a*b^5*d^5*e + 10*a^2*b^4*d^4*e^2 + 20*a^3*b^3*d^3*e^3 + 35*a^4*b^2*d^2*e^4 + 56*a^5*b*d*e^5 + 84*a^6*e^6 + 252*(b^6*d*e^5 + 4*a*b^5*e^6)*x^5 + 210*(b^6*d^2*e^4 + 4*a*b^5*d*e^5 + 10*a^2*b^4*e^6)*x^4 + 120*(b^6*d^3*e^3 + 4*a*b^5*d^2*e^4 + 10*a^2*b^4*d*e^5 + 20*a^3*b^3*e^6)*x^3 + 45*(b^6*d^4*e^2 + 4*a*b^5*d^3*e^3 + 10*a^2*b^4*d^2*e^4 + 20*a^3*b^3*d*e^5 + 35*a^4*b^2*e^6)*x^2 + 10*(b^6*d^5*e + 4*a*b^5*d^4*e^2 + 10*a^2*b^4*d^3*e^3 + 20*a^3*b^3*d^2*e^4 + 35*a^4*b^2*d*e^5 + 56*a^5*b*e^6)*x)/(e^17*x^10 + 10*d*e^16*x^9 + 45*d^2*e^15*x^8 + 120*d^3*e^14*x^7 + 210*d^4*e^13*x^6 + 252*d^5*e^12*x^5 + 210*d^6*e^11*x^4 + 120*d^7*e^10*x^3 + 45*d^8*e^9*x^2 + 10*d^9*e^8*x + d^10*e^7)","B",0
1501,1,463,0,0.391131," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^12,x, algorithm=""fricas"")","-\frac{462 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 5 \, a b^{5} d^{5} e + 15 \, a^{2} b^{4} d^{4} e^{2} + 35 \, a^{3} b^{3} d^{3} e^{3} + 70 \, a^{4} b^{2} d^{2} e^{4} + 126 \, a^{5} b d e^{5} + 210 \, a^{6} e^{6} + 462 \, {\left(b^{6} d e^{5} + 5 \, a b^{5} e^{6}\right)} x^{5} + 330 \, {\left(b^{6} d^{2} e^{4} + 5 \, a b^{5} d e^{5} + 15 \, a^{2} b^{4} e^{6}\right)} x^{4} + 165 \, {\left(b^{6} d^{3} e^{3} + 5 \, a b^{5} d^{2} e^{4} + 15 \, a^{2} b^{4} d e^{5} + 35 \, a^{3} b^{3} e^{6}\right)} x^{3} + 55 \, {\left(b^{6} d^{4} e^{2} + 5 \, a b^{5} d^{3} e^{3} + 15 \, a^{2} b^{4} d^{2} e^{4} + 35 \, a^{3} b^{3} d e^{5} + 70 \, a^{4} b^{2} e^{6}\right)} x^{2} + 11 \, {\left(b^{6} d^{5} e + 5 \, a b^{5} d^{4} e^{2} + 15 \, a^{2} b^{4} d^{3} e^{3} + 35 \, a^{3} b^{3} d^{2} e^{4} + 70 \, a^{4} b^{2} d e^{5} + 126 \, a^{5} b e^{6}\right)} x}{2310 \, {\left(e^{18} x^{11} + 11 \, d e^{17} x^{10} + 55 \, d^{2} e^{16} x^{9} + 165 \, d^{3} e^{15} x^{8} + 330 \, d^{4} e^{14} x^{7} + 462 \, d^{5} e^{13} x^{6} + 462 \, d^{6} e^{12} x^{5} + 330 \, d^{7} e^{11} x^{4} + 165 \, d^{8} e^{10} x^{3} + 55 \, d^{9} e^{9} x^{2} + 11 \, d^{10} e^{8} x + d^{11} e^{7}\right)}}"," ",0,"-1/2310*(462*b^6*e^6*x^6 + b^6*d^6 + 5*a*b^5*d^5*e + 15*a^2*b^4*d^4*e^2 + 35*a^3*b^3*d^3*e^3 + 70*a^4*b^2*d^2*e^4 + 126*a^5*b*d*e^5 + 210*a^6*e^6 + 462*(b^6*d*e^5 + 5*a*b^5*e^6)*x^5 + 330*(b^6*d^2*e^4 + 5*a*b^5*d*e^5 + 15*a^2*b^4*e^6)*x^4 + 165*(b^6*d^3*e^3 + 5*a*b^5*d^2*e^4 + 15*a^2*b^4*d*e^5 + 35*a^3*b^3*e^6)*x^3 + 55*(b^6*d^4*e^2 + 5*a*b^5*d^3*e^3 + 15*a^2*b^4*d^2*e^4 + 35*a^3*b^3*d*e^5 + 70*a^4*b^2*e^6)*x^2 + 11*(b^6*d^5*e + 5*a*b^5*d^4*e^2 + 15*a^2*b^4*d^3*e^3 + 35*a^3*b^3*d^2*e^4 + 70*a^4*b^2*d*e^5 + 126*a^5*b*e^6)*x)/(e^18*x^11 + 11*d*e^17*x^10 + 55*d^2*e^16*x^9 + 165*d^3*e^15*x^8 + 330*d^4*e^14*x^7 + 462*d^5*e^13*x^6 + 462*d^6*e^12*x^5 + 330*d^7*e^11*x^4 + 165*d^8*e^10*x^3 + 55*d^9*e^9*x^2 + 11*d^10*e^8*x + d^11*e^7)","B",0
1502,1,474,0,0.385352," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^13,x, algorithm=""fricas"")","-\frac{924 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 6 \, a b^{5} d^{5} e + 21 \, a^{2} b^{4} d^{4} e^{2} + 56 \, a^{3} b^{3} d^{3} e^{3} + 126 \, a^{4} b^{2} d^{2} e^{4} + 252 \, a^{5} b d e^{5} + 462 \, a^{6} e^{6} + 792 \, {\left(b^{6} d e^{5} + 6 \, a b^{5} e^{6}\right)} x^{5} + 495 \, {\left(b^{6} d^{2} e^{4} + 6 \, a b^{5} d e^{5} + 21 \, a^{2} b^{4} e^{6}\right)} x^{4} + 220 \, {\left(b^{6} d^{3} e^{3} + 6 \, a b^{5} d^{2} e^{4} + 21 \, a^{2} b^{4} d e^{5} + 56 \, a^{3} b^{3} e^{6}\right)} x^{3} + 66 \, {\left(b^{6} d^{4} e^{2} + 6 \, a b^{5} d^{3} e^{3} + 21 \, a^{2} b^{4} d^{2} e^{4} + 56 \, a^{3} b^{3} d e^{5} + 126 \, a^{4} b^{2} e^{6}\right)} x^{2} + 12 \, {\left(b^{6} d^{5} e + 6 \, a b^{5} d^{4} e^{2} + 21 \, a^{2} b^{4} d^{3} e^{3} + 56 \, a^{3} b^{3} d^{2} e^{4} + 126 \, a^{4} b^{2} d e^{5} + 252 \, a^{5} b e^{6}\right)} x}{5544 \, {\left(e^{19} x^{12} + 12 \, d e^{18} x^{11} + 66 \, d^{2} e^{17} x^{10} + 220 \, d^{3} e^{16} x^{9} + 495 \, d^{4} e^{15} x^{8} + 792 \, d^{5} e^{14} x^{7} + 924 \, d^{6} e^{13} x^{6} + 792 \, d^{7} e^{12} x^{5} + 495 \, d^{8} e^{11} x^{4} + 220 \, d^{9} e^{10} x^{3} + 66 \, d^{10} e^{9} x^{2} + 12 \, d^{11} e^{8} x + d^{12} e^{7}\right)}}"," ",0,"-1/5544*(924*b^6*e^6*x^6 + b^6*d^6 + 6*a*b^5*d^5*e + 21*a^2*b^4*d^4*e^2 + 56*a^3*b^3*d^3*e^3 + 126*a^4*b^2*d^2*e^4 + 252*a^5*b*d*e^5 + 462*a^6*e^6 + 792*(b^6*d*e^5 + 6*a*b^5*e^6)*x^5 + 495*(b^6*d^2*e^4 + 6*a*b^5*d*e^5 + 21*a^2*b^4*e^6)*x^4 + 220*(b^6*d^3*e^3 + 6*a*b^5*d^2*e^4 + 21*a^2*b^4*d*e^5 + 56*a^3*b^3*e^6)*x^3 + 66*(b^6*d^4*e^2 + 6*a*b^5*d^3*e^3 + 21*a^2*b^4*d^2*e^4 + 56*a^3*b^3*d*e^5 + 126*a^4*b^2*e^6)*x^2 + 12*(b^6*d^5*e + 6*a*b^5*d^4*e^2 + 21*a^2*b^4*d^3*e^3 + 56*a^3*b^3*d^2*e^4 + 126*a^4*b^2*d*e^5 + 252*a^5*b*e^6)*x)/(e^19*x^12 + 12*d*e^18*x^11 + 66*d^2*e^17*x^10 + 220*d^3*e^16*x^9 + 495*d^4*e^15*x^8 + 792*d^5*e^14*x^7 + 924*d^6*e^13*x^6 + 792*d^7*e^12*x^5 + 495*d^8*e^11*x^4 + 220*d^9*e^10*x^3 + 66*d^10*e^9*x^2 + 12*d^11*e^8*x + d^12*e^7)","B",0
1503,1,485,0,0.384758," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^14,x, algorithm=""fricas"")","-\frac{1716 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 7 \, a b^{5} d^{5} e + 28 \, a^{2} b^{4} d^{4} e^{2} + 84 \, a^{3} b^{3} d^{3} e^{3} + 210 \, a^{4} b^{2} d^{2} e^{4} + 462 \, a^{5} b d e^{5} + 924 \, a^{6} e^{6} + 1287 \, {\left(b^{6} d e^{5} + 7 \, a b^{5} e^{6}\right)} x^{5} + 715 \, {\left(b^{6} d^{2} e^{4} + 7 \, a b^{5} d e^{5} + 28 \, a^{2} b^{4} e^{6}\right)} x^{4} + 286 \, {\left(b^{6} d^{3} e^{3} + 7 \, a b^{5} d^{2} e^{4} + 28 \, a^{2} b^{4} d e^{5} + 84 \, a^{3} b^{3} e^{6}\right)} x^{3} + 78 \, {\left(b^{6} d^{4} e^{2} + 7 \, a b^{5} d^{3} e^{3} + 28 \, a^{2} b^{4} d^{2} e^{4} + 84 \, a^{3} b^{3} d e^{5} + 210 \, a^{4} b^{2} e^{6}\right)} x^{2} + 13 \, {\left(b^{6} d^{5} e + 7 \, a b^{5} d^{4} e^{2} + 28 \, a^{2} b^{4} d^{3} e^{3} + 84 \, a^{3} b^{3} d^{2} e^{4} + 210 \, a^{4} b^{2} d e^{5} + 462 \, a^{5} b e^{6}\right)} x}{12012 \, {\left(e^{20} x^{13} + 13 \, d e^{19} x^{12} + 78 \, d^{2} e^{18} x^{11} + 286 \, d^{3} e^{17} x^{10} + 715 \, d^{4} e^{16} x^{9} + 1287 \, d^{5} e^{15} x^{8} + 1716 \, d^{6} e^{14} x^{7} + 1716 \, d^{7} e^{13} x^{6} + 1287 \, d^{8} e^{12} x^{5} + 715 \, d^{9} e^{11} x^{4} + 286 \, d^{10} e^{10} x^{3} + 78 \, d^{11} e^{9} x^{2} + 13 \, d^{12} e^{8} x + d^{13} e^{7}\right)}}"," ",0,"-1/12012*(1716*b^6*e^6*x^6 + b^6*d^6 + 7*a*b^5*d^5*e + 28*a^2*b^4*d^4*e^2 + 84*a^3*b^3*d^3*e^3 + 210*a^4*b^2*d^2*e^4 + 462*a^5*b*d*e^5 + 924*a^6*e^6 + 1287*(b^6*d*e^5 + 7*a*b^5*e^6)*x^5 + 715*(b^6*d^2*e^4 + 7*a*b^5*d*e^5 + 28*a^2*b^4*e^6)*x^4 + 286*(b^6*d^3*e^3 + 7*a*b^5*d^2*e^4 + 28*a^2*b^4*d*e^5 + 84*a^3*b^3*e^6)*x^3 + 78*(b^6*d^4*e^2 + 7*a*b^5*d^3*e^3 + 28*a^2*b^4*d^2*e^4 + 84*a^3*b^3*d*e^5 + 210*a^4*b^2*e^6)*x^2 + 13*(b^6*d^5*e + 7*a*b^5*d^4*e^2 + 28*a^2*b^4*d^3*e^3 + 84*a^3*b^3*d^2*e^4 + 210*a^4*b^2*d*e^5 + 462*a^5*b*e^6)*x)/(e^20*x^13 + 13*d*e^19*x^12 + 78*d^2*e^18*x^11 + 286*d^3*e^17*x^10 + 715*d^4*e^16*x^9 + 1287*d^5*e^15*x^8 + 1716*d^6*e^14*x^7 + 1716*d^7*e^13*x^6 + 1287*d^8*e^12*x^5 + 715*d^9*e^11*x^4 + 286*d^10*e^10*x^3 + 78*d^11*e^9*x^2 + 13*d^12*e^8*x + d^13*e^7)","B",0
1504,1,496,0,0.381162," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^15,x, algorithm=""fricas"")","-\frac{3003 \, b^{6} e^{6} x^{6} + b^{6} d^{6} + 8 \, a b^{5} d^{5} e + 36 \, a^{2} b^{4} d^{4} e^{2} + 120 \, a^{3} b^{3} d^{3} e^{3} + 330 \, a^{4} b^{2} d^{2} e^{4} + 792 \, a^{5} b d e^{5} + 1716 \, a^{6} e^{6} + 2002 \, {\left(b^{6} d e^{5} + 8 \, a b^{5} e^{6}\right)} x^{5} + 1001 \, {\left(b^{6} d^{2} e^{4} + 8 \, a b^{5} d e^{5} + 36 \, a^{2} b^{4} e^{6}\right)} x^{4} + 364 \, {\left(b^{6} d^{3} e^{3} + 8 \, a b^{5} d^{2} e^{4} + 36 \, a^{2} b^{4} d e^{5} + 120 \, a^{3} b^{3} e^{6}\right)} x^{3} + 91 \, {\left(b^{6} d^{4} e^{2} + 8 \, a b^{5} d^{3} e^{3} + 36 \, a^{2} b^{4} d^{2} e^{4} + 120 \, a^{3} b^{3} d e^{5} + 330 \, a^{4} b^{2} e^{6}\right)} x^{2} + 14 \, {\left(b^{6} d^{5} e + 8 \, a b^{5} d^{4} e^{2} + 36 \, a^{2} b^{4} d^{3} e^{3} + 120 \, a^{3} b^{3} d^{2} e^{4} + 330 \, a^{4} b^{2} d e^{5} + 792 \, a^{5} b e^{6}\right)} x}{24024 \, {\left(e^{21} x^{14} + 14 \, d e^{20} x^{13} + 91 \, d^{2} e^{19} x^{12} + 364 \, d^{3} e^{18} x^{11} + 1001 \, d^{4} e^{17} x^{10} + 2002 \, d^{5} e^{16} x^{9} + 3003 \, d^{6} e^{15} x^{8} + 3432 \, d^{7} e^{14} x^{7} + 3003 \, d^{8} e^{13} x^{6} + 2002 \, d^{9} e^{12} x^{5} + 1001 \, d^{10} e^{11} x^{4} + 364 \, d^{11} e^{10} x^{3} + 91 \, d^{12} e^{9} x^{2} + 14 \, d^{13} e^{8} x + d^{14} e^{7}\right)}}"," ",0,"-1/24024*(3003*b^6*e^6*x^6 + b^6*d^6 + 8*a*b^5*d^5*e + 36*a^2*b^4*d^4*e^2 + 120*a^3*b^3*d^3*e^3 + 330*a^4*b^2*d^2*e^4 + 792*a^5*b*d*e^5 + 1716*a^6*e^6 + 2002*(b^6*d*e^5 + 8*a*b^5*e^6)*x^5 + 1001*(b^6*d^2*e^4 + 8*a*b^5*d*e^5 + 36*a^2*b^4*e^6)*x^4 + 364*(b^6*d^3*e^3 + 8*a*b^5*d^2*e^4 + 36*a^2*b^4*d*e^5 + 120*a^3*b^3*e^6)*x^3 + 91*(b^6*d^4*e^2 + 8*a*b^5*d^3*e^3 + 36*a^2*b^4*d^2*e^4 + 120*a^3*b^3*d*e^5 + 330*a^4*b^2*e^6)*x^2 + 14*(b^6*d^5*e + 8*a*b^5*d^4*e^2 + 36*a^2*b^4*d^3*e^3 + 120*a^3*b^3*d^2*e^4 + 330*a^4*b^2*d*e^5 + 792*a^5*b*e^6)*x)/(e^21*x^14 + 14*d*e^20*x^13 + 91*d^2*e^19*x^12 + 364*d^3*e^18*x^11 + 1001*d^4*e^17*x^10 + 2002*d^5*e^16*x^9 + 3003*d^6*e^15*x^8 + 3432*d^7*e^14*x^7 + 3003*d^8*e^13*x^6 + 2002*d^9*e^12*x^5 + 1001*d^10*e^11*x^4 + 364*d^11*e^10*x^3 + 91*d^12*e^9*x^2 + 14*d^13*e^8*x + d^14*e^7)","B",0
1505,1,375,0,0.392339," ","integrate((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{3 \, b^{5} e^{5} x^{5} - 12 \, b^{5} d^{5} + 60 \, a b^{4} d^{4} e - 120 \, a^{2} b^{3} d^{3} e^{2} + 120 \, a^{3} b^{2} d^{2} e^{3} - 60 \, a^{4} b d e^{4} + 12 \, a^{5} e^{5} + 5 \, {\left(4 \, b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 10 \, {\left(6 \, b^{5} d^{2} e^{3} - 4 \, a b^{4} d e^{4} + a^{2} b^{3} e^{5}\right)} x^{3} + 30 \, {\left(4 \, b^{5} d^{3} e^{2} - 6 \, a b^{4} d^{2} e^{3} + 4 \, a^{2} b^{3} d e^{4} - a^{3} b^{2} e^{5}\right)} x^{2} + 12 \, {\left(10 \, a b^{4} d^{3} e^{2} - 20 \, a^{2} b^{3} d^{2} e^{3} + 15 \, a^{3} b^{2} d e^{4} - 4 \, a^{4} b e^{5}\right)} x + 60 \, {\left(a b^{4} d^{4} e - 4 \, a^{2} b^{3} d^{3} e^{2} + 6 \, a^{3} b^{2} d^{2} e^{3} - 4 \, a^{4} b d e^{4} + a^{5} e^{5} + {\left(b^{5} d^{4} e - 4 \, a b^{4} d^{3} e^{2} + 6 \, a^{2} b^{3} d^{2} e^{3} - 4 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{7} x + a b^{6}\right)}}"," ",0,"1/12*(3*b^5*e^5*x^5 - 12*b^5*d^5 + 60*a*b^4*d^4*e - 120*a^2*b^3*d^3*e^2 + 120*a^3*b^2*d^2*e^3 - 60*a^4*b*d*e^4 + 12*a^5*e^5 + 5*(4*b^5*d*e^4 - a*b^4*e^5)*x^4 + 10*(6*b^5*d^2*e^3 - 4*a*b^4*d*e^4 + a^2*b^3*e^5)*x^3 + 30*(4*b^5*d^3*e^2 - 6*a*b^4*d^2*e^3 + 4*a^2*b^3*d*e^4 - a^3*b^2*e^5)*x^2 + 12*(10*a*b^4*d^3*e^2 - 20*a^2*b^3*d^2*e^3 + 15*a^3*b^2*d*e^4 - 4*a^4*b*e^5)*x + 60*(a*b^4*d^4*e - 4*a^2*b^3*d^3*e^2 + 6*a^3*b^2*d^2*e^3 - 4*a^4*b*d*e^4 + a^5*e^5 + (b^5*d^4*e - 4*a*b^4*d^3*e^2 + 6*a^2*b^3*d^2*e^3 - 4*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*log(b*x + a))/(b^7*x + a*b^6)","B",0
1506,1,268,0,0.393192," ","integrate((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{b^{4} e^{4} x^{4} - 3 \, b^{4} d^{4} + 12 \, a b^{3} d^{3} e - 18 \, a^{2} b^{2} d^{2} e^{2} + 12 \, a^{3} b d e^{3} - 3 \, a^{4} e^{4} + 2 \, {\left(3 \, b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(3 \, b^{4} d^{2} e^{2} - 3 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(6 \, a b^{3} d^{2} e^{2} - 8 \, a^{2} b^{2} d e^{3} + 3 \, a^{3} b e^{4}\right)} x + 12 \, {\left(a b^{3} d^{3} e - 3 \, a^{2} b^{2} d^{2} e^{2} + 3 \, a^{3} b d e^{3} - a^{4} e^{4} + {\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)} \log\left(b x + a\right)}{3 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"1/3*(b^4*e^4*x^4 - 3*b^4*d^4 + 12*a*b^3*d^3*e - 18*a^2*b^2*d^2*e^2 + 12*a^3*b*d*e^3 - 3*a^4*e^4 + 2*(3*b^4*d*e^3 - a*b^3*e^4)*x^3 + 6*(3*b^4*d^2*e^2 - 3*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 3*(6*a*b^3*d^2*e^2 - 8*a^2*b^2*d*e^3 + 3*a^3*b*e^4)*x + 12*(a*b^3*d^3*e - 3*a^2*b^2*d^2*e^2 + 3*a^3*b*d*e^3 - a^4*e^4 + (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)*log(b*x + a))/(b^6*x + a*b^5)","B",0
1507,1,173,0,0.404496," ","integrate((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{b^{3} e^{3} x^{3} - 2 \, b^{3} d^{3} + 6 \, a b^{2} d^{2} e - 6 \, a^{2} b d e^{2} + 2 \, a^{3} e^{3} + 3 \, {\left(2 \, b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} d e^{2} - 2 \, a^{2} b e^{3}\right)} x + 6 \, {\left(a b^{2} d^{2} e - 2 \, a^{2} b d e^{2} + a^{3} e^{3} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"1/2*(b^3*e^3*x^3 - 2*b^3*d^3 + 6*a*b^2*d^2*e - 6*a^2*b*d*e^2 + 2*a^3*e^3 + 3*(2*b^3*d*e^2 - a*b^2*e^3)*x^2 + 2*(3*a*b^2*d*e^2 - 2*a^2*b*e^3)*x + 6*(a*b^2*d^2*e - 2*a^2*b*d*e^2 + a^3*e^3 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x)*log(b*x + a))/(b^5*x + a*b^4)","B",0
1508,1,92,0,0.396199," ","integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{b^{2} e^{2} x^{2} + a b e^{2} x - b^{2} d^{2} + 2 \, a b d e - a^{2} e^{2} + 2 \, {\left(a b d e - a^{2} e^{2} + {\left(b^{2} d e - a b e^{2}\right)} x\right)} \log\left(b x + a\right)}{b^{4} x + a b^{3}}"," ",0,"(b^2*e^2*x^2 + a*b*e^2*x - b^2*d^2 + 2*a*b*d*e - a^2*e^2 + 2*(a*b*d*e - a^2*e^2 + (b^2*d*e - a*b*e^2)*x)*log(b*x + a))/(b^4*x + a*b^3)","A",0
1509,1,39,0,0.388088," ","integrate((e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{b d - a e - {\left(b e x + a e\right)} \log\left(b x + a\right)}{b^{3} x + a b^{2}}"," ",0,"-(b*d - a*e - (b*e*x + a*e)*log(b*x + a))/(b^3*x + a*b^2)","A",0
1510,1,13,0,0.364789," ","integrate(1/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{1}{b^{2} x + a b}"," ",0,"-1/(b^2*x + a*b)","A",0
1511,1,93,0,0.401471," ","integrate(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{b d - a e + {\left(b e x + a e\right)} \log\left(b x + a\right) - {\left(b e x + a e\right)} \log\left(e x + d\right)}{a b^{2} d^{2} - 2 \, a^{2} b d e + a^{3} e^{2} + {\left(b^{3} d^{2} - 2 \, a b^{2} d e + a^{2} b e^{2}\right)} x}"," ",0,"-(b*d - a*e + (b*e*x + a*e)*log(b*x + a) - (b*e*x + a*e)*log(e*x + d))/(a*b^2*d^2 - 2*a^2*b*d*e + a^3*e^2 + (b^3*d^2 - 2*a*b^2*d*e + a^2*b*e^2)*x)","A",0
1512,1,241,0,0.391040," ","integrate(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\frac{b^{2} d^{2} - a^{2} e^{2} + 2 \, {\left(b^{2} d e - a b e^{2}\right)} x + 2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} e^{2} x^{2} + a b d e + {\left(b^{2} d e + a b e^{2}\right)} x\right)} \log\left(e x + d\right)}{a b^{3} d^{4} - 3 \, a^{2} b^{2} d^{3} e + 3 \, a^{3} b d^{2} e^{2} - a^{4} d e^{3} + {\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^{2} + {\left(b^{4} d^{4} - 2 \, a b^{3} d^{3} e + 2 \, a^{3} b d e^{3} - a^{4} e^{4}\right)} x}"," ",0,"-(b^2*d^2 - a^2*e^2 + 2*(b^2*d*e - a*b*e^2)*x + 2*(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)*log(b*x + a) - 2*(b^2*e^2*x^2 + a*b*d*e + (b^2*d*e + a*b*e^2)*x)*log(e*x + d))/(a*b^3*d^4 - 3*a^2*b^2*d^3*e + 3*a^3*b*d^2*e^2 - a^4*d*e^3 + (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^2 + (b^4*d^4 - 2*a*b^3*d^3*e + 2*a^3*b*d*e^3 - a^4*e^4)*x)","B",0
1513,1,495,0,0.417454," ","integrate(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\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 + 6 \, {\left(b^{3} e^{3} x^{3} + a b^{2} d^{2} e + {\left(2 \, b^{3} d e^{2} + a b^{2} e^{3}\right)} x^{2} + {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(b^{3} e^{3} x^{3} + a b^{2} d^{2} e + {\left(2 \, b^{3} d e^{2} + a b^{2} e^{3}\right)} x^{2} + {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a b^{4} d^{6} - 4 \, a^{2} b^{3} d^{5} e + 6 \, a^{3} b^{2} d^{4} e^{2} - 4 \, a^{4} b d^{3} e^{3} + a^{5} d^{2} e^{4} + {\left(b^{5} d^{4} e^{2} - 4 \, a b^{4} d^{3} e^{3} + 6 \, a^{2} b^{3} d^{2} e^{4} - 4 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} x^{3} + {\left(2 \, b^{5} d^{5} e - 7 \, a b^{4} d^{4} e^{2} + 8 \, a^{2} b^{3} d^{3} e^{3} - 2 \, a^{3} b^{2} d^{2} e^{4} - 2 \, a^{4} b d e^{5} + a^{5} e^{6}\right)} x^{2} + {\left(b^{5} d^{6} - 2 \, a b^{4} d^{5} e - 2 \, a^{2} b^{3} d^{4} e^{2} + 8 \, a^{3} b^{2} d^{3} e^{3} - 7 \, a^{4} b d^{2} e^{4} + 2 \, a^{5} d e^{5}\right)} x\right)}}"," ",0,"-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 + 6*(b^3*e^3*x^3 + a*b^2*d^2*e + (2*b^3*d*e^2 + a*b^2*e^3)*x^2 + (b^3*d^2*e + 2*a*b^2*d*e^2)*x)*log(b*x + a) - 6*(b^3*e^3*x^3 + a*b^2*d^2*e + (2*b^3*d*e^2 + a*b^2*e^3)*x^2 + (b^3*d^2*e + 2*a*b^2*d*e^2)*x)*log(e*x + d))/(a*b^4*d^6 - 4*a^2*b^3*d^5*e + 6*a^3*b^2*d^4*e^2 - 4*a^4*b*d^3*e^3 + a^5*d^2*e^4 + (b^5*d^4*e^2 - 4*a*b^4*d^3*e^3 + 6*a^2*b^3*d^2*e^4 - 4*a^3*b^2*d*e^5 + a^4*b*e^6)*x^3 + (2*b^5*d^5*e - 7*a*b^4*d^4*e^2 + 8*a^2*b^3*d^3*e^3 - 2*a^3*b^2*d^2*e^4 - 2*a^4*b*d*e^5 + a^5*e^6)*x^2 + (b^5*d^6 - 2*a*b^4*d^5*e - 2*a^2*b^3*d^4*e^2 + 8*a^3*b^2*d^3*e^3 - 7*a^4*b*d^2*e^4 + 2*a^5*d*e^5)*x)","B",0
1514,1,753,0,0.414335," ","integrate(1/(e*x+d)^4/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","-\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 + 12 \, {\left(b^{4} e^{4} x^{4} + a b^{3} d^{3} e + {\left(3 \, b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(b^{4} d^{2} e^{2} + a b^{3} d e^{3}\right)} x^{2} + {\left(b^{4} d^{3} e + 3 \, a b^{3} d^{2} e^{2}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(b^{4} e^{4} x^{4} + a b^{3} d^{3} e + {\left(3 \, b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(b^{4} d^{2} e^{2} + a b^{3} d e^{3}\right)} x^{2} + {\left(b^{4} d^{3} e + 3 \, a b^{3} d^{2} e^{2}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(a b^{5} d^{8} - 5 \, a^{2} b^{4} d^{7} e + 10 \, a^{3} b^{3} d^{6} e^{2} - 10 \, a^{4} b^{2} d^{5} e^{3} + 5 \, a^{5} b d^{4} e^{4} - a^{6} d^{3} e^{5} + {\left(b^{6} d^{5} e^{3} - 5 \, a b^{5} d^{4} e^{4} + 10 \, a^{2} b^{4} d^{3} e^{5} - 10 \, a^{3} b^{3} d^{2} e^{6} + 5 \, a^{4} b^{2} d e^{7} - a^{5} b e^{8}\right)} x^{4} + {\left(3 \, b^{6} d^{6} e^{2} - 14 \, a b^{5} d^{5} e^{3} + 25 \, a^{2} b^{4} d^{4} e^{4} - 20 \, a^{3} b^{3} d^{3} e^{5} + 5 \, a^{4} b^{2} d^{2} e^{6} + 2 \, a^{5} b d e^{7} - a^{6} e^{8}\right)} x^{3} + 3 \, {\left(b^{6} d^{7} e - 4 \, a b^{5} d^{6} e^{2} + 5 \, a^{2} b^{4} d^{5} e^{3} - 5 \, a^{4} b^{2} d^{3} e^{5} + 4 \, a^{5} b d^{2} e^{6} - a^{6} d e^{7}\right)} x^{2} + {\left(b^{6} d^{8} - 2 \, a b^{5} d^{7} e - 5 \, a^{2} b^{4} d^{6} e^{2} + 20 \, a^{3} b^{3} d^{5} e^{3} - 25 \, a^{4} b^{2} d^{4} e^{4} + 14 \, a^{5} b d^{3} e^{5} - 3 \, a^{6} d^{2} e^{6}\right)} x\right)}}"," ",0,"-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 + 12*(b^4*e^4*x^4 + a*b^3*d^3*e + (3*b^4*d*e^3 + a*b^3*e^4)*x^3 + 3*(b^4*d^2*e^2 + a*b^3*d*e^3)*x^2 + (b^4*d^3*e + 3*a*b^3*d^2*e^2)*x)*log(b*x + a) - 12*(b^4*e^4*x^4 + a*b^3*d^3*e + (3*b^4*d*e^3 + a*b^3*e^4)*x^3 + 3*(b^4*d^2*e^2 + a*b^3*d*e^3)*x^2 + (b^4*d^3*e + 3*a*b^3*d^2*e^2)*x)*log(e*x + d))/(a*b^5*d^8 - 5*a^2*b^4*d^7*e + 10*a^3*b^3*d^6*e^2 - 10*a^4*b^2*d^5*e^3 + 5*a^5*b*d^4*e^4 - a^6*d^3*e^5 + (b^6*d^5*e^3 - 5*a*b^5*d^4*e^4 + 10*a^2*b^4*d^3*e^5 - 10*a^3*b^3*d^2*e^6 + 5*a^4*b^2*d*e^7 - a^5*b*e^8)*x^4 + (3*b^6*d^6*e^2 - 14*a*b^5*d^5*e^3 + 25*a^2*b^4*d^4*e^4 - 20*a^3*b^3*d^3*e^5 + 5*a^4*b^2*d^2*e^6 + 2*a^5*b*d*e^7 - a^6*e^8)*x^3 + 3*(b^6*d^7*e - 4*a*b^5*d^6*e^2 + 5*a^2*b^4*d^5*e^3 - 5*a^4*b^2*d^3*e^5 + 4*a^5*b*d^2*e^6 - a^6*d*e^7)*x^2 + (b^6*d^8 - 2*a*b^5*d^7*e - 5*a^2*b^4*d^6*e^2 + 20*a^3*b^3*d^5*e^3 - 25*a^4*b^2*d^4*e^4 + 14*a^5*b*d^3*e^5 - 3*a^6*d^2*e^6)*x)","B",0
1515,1,577,0,0.386485," ","integrate((e*x+d)^6/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{b^{6} e^{6} x^{6} - 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} + 3 \, {\left(3 \, b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 15 \, {\left(3 \, b^{6} d^{2} e^{4} - 3 \, a b^{5} d e^{5} + a^{2} b^{4} e^{6}\right)} x^{4} + {\left(135 \, a b^{5} d^{2} e^{4} - 189 \, a^{2} b^{4} d e^{5} + 73 \, a^{3} b^{3} e^{6}\right)} x^{3} - 3 \, {\left(15 \, b^{6} d^{4} e^{2} - 60 \, a b^{5} d^{3} e^{3} + 45 \, a^{2} b^{4} d^{2} e^{4} + 9 \, a^{3} b^{3} d e^{5} - 13 \, a^{4} b^{2} e^{6}\right)} x^{2} - 3 \, {\left(3 \, b^{6} d^{5} e + 15 \, a b^{5} d^{4} e^{2} - 90 \, a^{2} b^{4} d^{3} e^{3} + 135 \, a^{3} b^{3} d^{2} e^{4} - 81 \, a^{4} b^{2} d e^{5} + 17 \, a^{5} b e^{6}\right)} x + 60 \, {\left(a^{3} b^{3} d^{3} e^{3} - 3 \, a^{4} b^{2} d^{2} e^{4} + 3 \, a^{5} b d e^{5} - a^{6} e^{6} + {\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)} x^{3} + 3 \, {\left(a b^{5} d^{3} e^{3} - 3 \, a^{2} b^{4} d^{2} e^{4} + 3 \, a^{3} b^{3} d e^{5} - a^{4} b^{2} e^{6}\right)} x^{2} + 3 \, {\left(a^{2} b^{4} d^{3} e^{3} - 3 \, a^{3} b^{3} d^{2} e^{4} + 3 \, a^{4} b^{2} d e^{5} - a^{5} b e^{6}\right)} x\right)} \log\left(b x + a\right)}{3 \, {\left(b^{10} x^{3} + 3 \, a b^{9} x^{2} + 3 \, a^{2} b^{8} x + a^{3} b^{7}\right)}}"," ",0,"1/3*(b^6*e^6*x^6 - 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 + 3*(3*b^6*d*e^5 - a*b^5*e^6)*x^5 + 15*(3*b^6*d^2*e^4 - 3*a*b^5*d*e^5 + a^2*b^4*e^6)*x^4 + (135*a*b^5*d^2*e^4 - 189*a^2*b^4*d*e^5 + 73*a^3*b^3*e^6)*x^3 - 3*(15*b^6*d^4*e^2 - 60*a*b^5*d^3*e^3 + 45*a^2*b^4*d^2*e^4 + 9*a^3*b^3*d*e^5 - 13*a^4*b^2*e^6)*x^2 - 3*(3*b^6*d^5*e + 15*a*b^5*d^4*e^2 - 90*a^2*b^4*d^3*e^3 + 135*a^3*b^3*d^2*e^4 - 81*a^4*b^2*d*e^5 + 17*a^5*b*e^6)*x + 60*(a^3*b^3*d^3*e^3 - 3*a^4*b^2*d^2*e^4 + 3*a^5*b*d*e^5 - a^6*e^6 + (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)*x^3 + 3*(a*b^5*d^3*e^3 - 3*a^2*b^4*d^2*e^4 + 3*a^3*b^3*d*e^5 - a^4*b^2*e^6)*x^2 + 3*(a^2*b^4*d^3*e^3 - 3*a^3*b^3*d^2*e^4 + 3*a^4*b^2*d*e^5 - a^5*b*e^6)*x)*log(b*x + a))/(b^10*x^3 + 3*a*b^9*x^2 + 3*a^2*b^8*x + a^3*b^7)","B",0
1516,1,426,0,0.392086," ","integrate((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{5} e^{5} x^{5} - 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} + 15 \, {\left(2 \, b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 9 \, {\left(10 \, a b^{4} d e^{4} - 7 \, a^{2} b^{3} e^{5}\right)} x^{3} - 3 \, {\left(20 \, b^{5} d^{3} e^{2} - 60 \, a b^{4} d^{2} e^{3} + 30 \, a^{2} b^{3} d e^{4} + 3 \, a^{3} b^{2} e^{5}\right)} x^{2} - 3 \, {\left(5 \, b^{5} d^{4} e + 20 \, a b^{4} d^{3} e^{2} - 90 \, a^{2} b^{3} d^{2} e^{3} + 90 \, a^{3} b^{2} d e^{4} - 27 \, a^{4} b e^{5}\right)} x + 60 \, {\left(a^{3} b^{2} d^{2} e^{3} - 2 \, a^{4} b d e^{4} + a^{5} e^{5} + {\left(b^{5} d^{2} e^{3} - 2 \, a b^{4} d e^{4} + a^{2} b^{3} e^{5}\right)} x^{3} + 3 \, {\left(a b^{4} d^{2} e^{3} - 2 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{3} d^{2} e^{3} - 2 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{9} x^{3} + 3 \, a b^{8} x^{2} + 3 \, a^{2} b^{7} x + a^{3} b^{6}\right)}}"," ",0,"1/6*(3*b^5*e^5*x^5 - 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 + 15*(2*b^5*d*e^4 - a*b^4*e^5)*x^4 + 9*(10*a*b^4*d*e^4 - 7*a^2*b^3*e^5)*x^3 - 3*(20*b^5*d^3*e^2 - 60*a*b^4*d^2*e^3 + 30*a^2*b^3*d*e^4 + 3*a^3*b^2*e^5)*x^2 - 3*(5*b^5*d^4*e + 20*a*b^4*d^3*e^2 - 90*a^2*b^3*d^2*e^3 + 90*a^3*b^2*d*e^4 - 27*a^4*b*e^5)*x + 60*(a^3*b^2*d^2*e^3 - 2*a^4*b*d*e^4 + a^5*e^5 + (b^5*d^2*e^3 - 2*a*b^4*d*e^4 + a^2*b^3*e^5)*x^3 + 3*(a*b^4*d^2*e^3 - 2*a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^2 + 3*(a^2*b^3*d^2*e^3 - 2*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*log(b*x + a))/(b^9*x^3 + 3*a*b^8*x^2 + 3*a^2*b^7*x + a^3*b^6)","B",0
1517,1,292,0,0.406277," ","integrate((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{4} e^{4} x^{4} + 9 \, a b^{3} e^{4} x^{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} - 9 \, {\left(2 \, b^{4} d^{2} e^{2} - 4 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} - 3 \, {\left(2 \, b^{4} d^{3} e + 6 \, a b^{3} d^{2} e^{2} - 18 \, a^{2} b^{2} d e^{3} + 9 \, a^{3} b e^{4}\right)} x + 12 \, {\left(a^{3} b d e^{3} - a^{4} e^{4} + {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(a b^{3} d e^{3} - a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x\right)} \log\left(b x + a\right)}{3 \, {\left(b^{8} x^{3} + 3 \, a b^{7} x^{2} + 3 \, a^{2} b^{6} x + a^{3} b^{5}\right)}}"," ",0,"1/3*(3*b^4*e^4*x^4 + 9*a*b^3*e^4*x^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 - 9*(2*b^4*d^2*e^2 - 4*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 - 3*(2*b^4*d^3*e + 6*a*b^3*d^2*e^2 - 18*a^2*b^2*d*e^3 + 9*a^3*b*e^4)*x + 12*(a^3*b*d*e^3 - a^4*e^4 + (b^4*d*e^3 - a*b^3*e^4)*x^3 + 3*(a*b^3*d*e^3 - a^2*b^2*e^4)*x^2 + 3*(a^2*b^2*d*e^3 - a^3*b*e^4)*x)*log(b*x + a))/(b^8*x^3 + 3*a*b^7*x^2 + 3*a^2*b^6*x + a^3*b^5)","B",0
1518,1,176,0,0.388114," ","integrate((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\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} + 18 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 9 \, {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2} - 3 \, a^{2} b e^{3}\right)} x - 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \log\left(b x + a\right)}{6 \, {\left(b^{7} x^{3} + 3 \, a b^{6} x^{2} + 3 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}"," ",0,"-1/6*(2*b^3*d^3 + 3*a*b^2*d^2*e + 6*a^2*b*d*e^2 - 11*a^3*e^3 + 18*(b^3*d*e^2 - a*b^2*e^3)*x^2 + 9*(b^3*d^2*e + 2*a*b^2*d*e^2 - 3*a^2*b*e^3)*x - 6*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*log(b*x + a))/(b^7*x^3 + 3*a*b^6*x^2 + 3*a^2*b^5*x + a^3*b^4)","B",0
1519,1,84,0,0.389172," ","integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{3 \, b^{2} e^{2} x^{2} + b^{2} d^{2} + a b d e + a^{2} e^{2} + 3 \, {\left(b^{2} d e + a b e^{2}\right)} x}{3 \, {\left(b^{6} x^{3} + 3 \, a b^{5} x^{2} + 3 \, a^{2} b^{4} x + a^{3} b^{3}\right)}}"," ",0,"-1/3*(3*b^2*e^2*x^2 + b^2*d^2 + a*b*d*e + a^2*e^2 + 3*(b^2*d*e + a*b*e^2)*x)/(b^6*x^3 + 3*a*b^5*x^2 + 3*a^2*b^4*x + a^3*b^3)","B",0
1520,1,50,0,0.384022," ","integrate((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{3 \, b e x + 2 \, b d + a e}{6 \, {\left(b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x + a^{3} b^{2}\right)}}"," ",0,"-1/6*(3*b*e*x + 2*b*d + a*e)/(b^5*x^3 + 3*a*b^4*x^2 + 3*a^2*b^3*x + a^3*b^2)","A",0
1521,1,35,0,0.392071," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{1}{3 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)}}"," ",0,"-1/3/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b)","B",0
1522,1,425,0,0.401117," ","integrate(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\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^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(a^{3} b^{4} d^{4} - 4 \, a^{4} b^{3} d^{3} e + 6 \, a^{5} b^{2} d^{2} e^{2} - 4 \, a^{6} b d e^{3} + a^{7} e^{4} + {\left(b^{7} d^{4} - 4 \, a b^{6} d^{3} e + 6 \, a^{2} b^{5} d^{2} e^{2} - 4 \, a^{3} b^{4} d e^{3} + a^{4} b^{3} e^{4}\right)} x^{3} + 3 \, {\left(a b^{6} d^{4} - 4 \, a^{2} b^{5} d^{3} e + 6 \, a^{3} b^{4} d^{2} e^{2} - 4 \, a^{4} b^{3} d e^{3} + a^{5} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} d^{4} - 4 \, a^{3} b^{4} d^{3} e + 6 \, a^{4} b^{3} d^{2} e^{2} - 4 \, a^{5} b^{2} d e^{3} + a^{6} b e^{4}\right)} x\right)}}"," ",0,"-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 + 6*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*log(b*x + a) - 6*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*log(e*x + d))/(a^3*b^4*d^4 - 4*a^4*b^3*d^3*e + 6*a^5*b^2*d^2*e^2 - 4*a^6*b*d*e^3 + a^7*e^4 + (b^7*d^4 - 4*a*b^6*d^3*e + 6*a^2*b^5*d^2*e^2 - 4*a^3*b^4*d*e^3 + a^4*b^3*e^4)*x^3 + 3*(a*b^6*d^4 - 4*a^2*b^5*d^3*e + 6*a^3*b^4*d^2*e^2 - 4*a^4*b^3*d*e^3 + a^5*b^2*e^4)*x^2 + 3*(a^2*b^5*d^4 - 4*a^3*b^4*d^3*e + 6*a^4*b^3*d^2*e^2 - 4*a^5*b^2*d*e^3 + a^6*b*e^4)*x)","B",0
1523,1,751,0,0.408818," ","integrate(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\frac{b^{4} d^{4} - 6 \, a b^{3} d^{3} e + 18 \, a^{2} b^{2} d^{2} e^{2} - 10 \, a^{3} b d e^{3} - 3 \, a^{4} e^{4} + 12 \, {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(b^{4} d^{2} e^{2} + 4 \, a b^{3} d e^{3} - 5 \, a^{2} b^{2} e^{4}\right)} x^{2} - 2 \, {\left(b^{4} d^{3} e - 9 \, a b^{3} d^{2} e^{2} - 3 \, a^{2} b^{2} d e^{3} + 11 \, a^{3} b e^{4}\right)} x + 12 \, {\left(b^{4} e^{4} x^{4} + a^{3} b d e^{3} + {\left(b^{4} d e^{3} + 3 \, a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(b^{4} e^{4} x^{4} + a^{3} b d e^{3} + {\left(b^{4} d e^{3} + 3 \, a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(a^{3} b^{5} d^{6} - 5 \, a^{4} b^{4} d^{5} e + 10 \, a^{5} b^{3} d^{4} e^{2} - 10 \, a^{6} b^{2} d^{3} e^{3} + 5 \, a^{7} b d^{2} e^{4} - a^{8} d e^{5} + {\left(b^{8} d^{5} e - 5 \, a b^{7} d^{4} e^{2} + 10 \, a^{2} b^{6} d^{3} e^{3} - 10 \, a^{3} b^{5} d^{2} e^{4} + 5 \, a^{4} b^{4} d e^{5} - a^{5} b^{3} e^{6}\right)} x^{4} + {\left(b^{8} d^{6} - 2 \, a b^{7} d^{5} e - 5 \, a^{2} b^{6} d^{4} e^{2} + 20 \, a^{3} b^{5} d^{3} e^{3} - 25 \, a^{4} b^{4} d^{2} e^{4} + 14 \, a^{5} b^{3} d e^{5} - 3 \, a^{6} b^{2} e^{6}\right)} x^{3} + 3 \, {\left(a b^{7} d^{6} - 4 \, a^{2} b^{6} d^{5} e + 5 \, a^{3} b^{5} d^{4} e^{2} - 5 \, a^{5} b^{3} d^{2} e^{4} + 4 \, a^{6} b^{2} d e^{5} - a^{7} b e^{6}\right)} x^{2} + {\left(3 \, a^{2} b^{6} d^{6} - 14 \, a^{3} b^{5} d^{5} e + 25 \, a^{4} b^{4} d^{4} e^{2} - 20 \, a^{5} b^{3} d^{3} e^{3} + 5 \, a^{6} b^{2} d^{2} e^{4} + 2 \, a^{7} b d e^{5} - a^{8} e^{6}\right)} x\right)}}"," ",0,"-1/3*(b^4*d^4 - 6*a*b^3*d^3*e + 18*a^2*b^2*d^2*e^2 - 10*a^3*b*d*e^3 - 3*a^4*e^4 + 12*(b^4*d*e^3 - a*b^3*e^4)*x^3 + 6*(b^4*d^2*e^2 + 4*a*b^3*d*e^3 - 5*a^2*b^2*e^4)*x^2 - 2*(b^4*d^3*e - 9*a*b^3*d^2*e^2 - 3*a^2*b^2*d*e^3 + 11*a^3*b*e^4)*x + 12*(b^4*e^4*x^4 + a^3*b*d*e^3 + (b^4*d*e^3 + 3*a*b^3*e^4)*x^3 + 3*(a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + (3*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*log(b*x + a) - 12*(b^4*e^4*x^4 + a^3*b*d*e^3 + (b^4*d*e^3 + 3*a*b^3*e^4)*x^3 + 3*(a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + (3*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*log(e*x + d))/(a^3*b^5*d^6 - 5*a^4*b^4*d^5*e + 10*a^5*b^3*d^4*e^2 - 10*a^6*b^2*d^3*e^3 + 5*a^7*b*d^2*e^4 - a^8*d*e^5 + (b^8*d^5*e - 5*a*b^7*d^4*e^2 + 10*a^2*b^6*d^3*e^3 - 10*a^3*b^5*d^2*e^4 + 5*a^4*b^4*d*e^5 - a^5*b^3*e^6)*x^4 + (b^8*d^6 - 2*a*b^7*d^5*e - 5*a^2*b^6*d^4*e^2 + 20*a^3*b^5*d^3*e^3 - 25*a^4*b^4*d^2*e^4 + 14*a^5*b^3*d*e^5 - 3*a^6*b^2*e^6)*x^3 + 3*(a*b^7*d^6 - 4*a^2*b^6*d^5*e + 5*a^3*b^5*d^4*e^2 - 5*a^5*b^3*d^2*e^4 + 4*a^6*b^2*d*e^5 - a^7*b*e^6)*x^2 + (3*a^2*b^6*d^6 - 14*a^3*b^5*d^5*e + 25*a^4*b^4*d^4*e^2 - 20*a^5*b^3*d^3*e^3 + 5*a^6*b^2*d^2*e^4 + 2*a^7*b*d*e^5 - a^8*e^6)*x)","B",0
1524,1,1151,0,0.421333," ","integrate(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","-\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 + 60 \, {\left(b^{5} e^{5} x^{5} + a^{3} b^{2} d^{2} e^{3} + {\left(2 \, b^{5} d e^{4} + 3 \, a b^{4} e^{5}\right)} x^{4} + {\left(b^{5} d^{2} e^{3} + 6 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + {\left(3 \, a b^{4} d^{2} e^{3} + 6 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} d^{2} e^{3} + 2 \, a^{3} b^{2} d e^{4}\right)} x\right)} \log\left(b x + a\right) - 60 \, {\left(b^{5} e^{5} x^{5} + a^{3} b^{2} d^{2} e^{3} + {\left(2 \, b^{5} d e^{4} + 3 \, a b^{4} e^{5}\right)} x^{4} + {\left(b^{5} d^{2} e^{3} + 6 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + {\left(3 \, a b^{4} d^{2} e^{3} + 6 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} d^{2} e^{3} + 2 \, a^{3} b^{2} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(a^{3} b^{6} d^{8} - 6 \, a^{4} b^{5} d^{7} e + 15 \, a^{5} b^{4} d^{6} e^{2} - 20 \, a^{6} b^{3} d^{5} e^{3} + 15 \, a^{7} b^{2} d^{4} e^{4} - 6 \, a^{8} b d^{3} e^{5} + a^{9} d^{2} e^{6} + {\left(b^{9} d^{6} e^{2} - 6 \, a b^{8} d^{5} e^{3} + 15 \, a^{2} b^{7} d^{4} e^{4} - 20 \, a^{3} b^{6} d^{3} e^{5} + 15 \, a^{4} b^{5} d^{2} e^{6} - 6 \, a^{5} b^{4} d e^{7} + a^{6} b^{3} e^{8}\right)} x^{5} + {\left(2 \, b^{9} d^{7} e - 9 \, a b^{8} d^{6} e^{2} + 12 \, a^{2} b^{7} d^{5} e^{3} + 5 \, a^{3} b^{6} d^{4} e^{4} - 30 \, a^{4} b^{5} d^{3} e^{5} + 33 \, a^{5} b^{4} d^{2} e^{6} - 16 \, a^{6} b^{3} d e^{7} + 3 \, a^{7} b^{2} e^{8}\right)} x^{4} + {\left(b^{9} d^{8} - 18 \, a^{2} b^{7} d^{6} e^{2} + 52 \, a^{3} b^{6} d^{5} e^{3} - 60 \, a^{4} b^{5} d^{4} e^{4} + 24 \, a^{5} b^{4} d^{3} e^{5} + 10 \, a^{6} b^{3} d^{2} e^{6} - 12 \, a^{7} b^{2} d e^{7} + 3 \, a^{8} b e^{8}\right)} x^{3} + {\left(3 \, a b^{8} d^{8} - 12 \, a^{2} b^{7} d^{7} e + 10 \, a^{3} b^{6} d^{6} e^{2} + 24 \, a^{4} b^{5} d^{5} e^{3} - 60 \, a^{5} b^{4} d^{4} e^{4} + 52 \, a^{6} b^{3} d^{3} e^{5} - 18 \, a^{7} b^{2} d^{2} e^{6} + a^{9} e^{8}\right)} x^{2} + {\left(3 \, a^{2} b^{7} d^{8} - 16 \, a^{3} b^{6} d^{7} e + 33 \, a^{4} b^{5} d^{6} e^{2} - 30 \, a^{5} b^{4} d^{5} e^{3} + 5 \, a^{6} b^{3} d^{4} e^{4} + 12 \, a^{7} b^{2} d^{3} e^{5} - 9 \, a^{8} b d^{2} e^{6} + 2 \, a^{9} d e^{7}\right)} x\right)}}"," ",0,"-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 + 60*(b^5*e^5*x^5 + a^3*b^2*d^2*e^3 + (2*b^5*d*e^4 + 3*a*b^4*e^5)*x^4 + (b^5*d^2*e^3 + 6*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + (3*a*b^4*d^2*e^3 + 6*a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^2 + (3*a^2*b^3*d^2*e^3 + 2*a^3*b^2*d*e^4)*x)*log(b*x + a) - 60*(b^5*e^5*x^5 + a^3*b^2*d^2*e^3 + (2*b^5*d*e^4 + 3*a*b^4*e^5)*x^4 + (b^5*d^2*e^3 + 6*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + (3*a*b^4*d^2*e^3 + 6*a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^2 + (3*a^2*b^3*d^2*e^3 + 2*a^3*b^2*d*e^4)*x)*log(e*x + d))/(a^3*b^6*d^8 - 6*a^4*b^5*d^7*e + 15*a^5*b^4*d^6*e^2 - 20*a^6*b^3*d^5*e^3 + 15*a^7*b^2*d^4*e^4 - 6*a^8*b*d^3*e^5 + a^9*d^2*e^6 + (b^9*d^6*e^2 - 6*a*b^8*d^5*e^3 + 15*a^2*b^7*d^4*e^4 - 20*a^3*b^6*d^3*e^5 + 15*a^4*b^5*d^2*e^6 - 6*a^5*b^4*d*e^7 + a^6*b^3*e^8)*x^5 + (2*b^9*d^7*e - 9*a*b^8*d^6*e^2 + 12*a^2*b^7*d^5*e^3 + 5*a^3*b^6*d^4*e^4 - 30*a^4*b^5*d^3*e^5 + 33*a^5*b^4*d^2*e^6 - 16*a^6*b^3*d*e^7 + 3*a^7*b^2*e^8)*x^4 + (b^9*d^8 - 18*a^2*b^7*d^6*e^2 + 52*a^3*b^6*d^5*e^3 - 60*a^4*b^5*d^4*e^4 + 24*a^5*b^4*d^3*e^5 + 10*a^6*b^3*d^2*e^6 - 12*a^7*b^2*d*e^7 + 3*a^8*b*e^8)*x^3 + (3*a*b^8*d^8 - 12*a^2*b^7*d^7*e + 10*a^3*b^6*d^6*e^2 + 24*a^4*b^5*d^5*e^3 - 60*a^5*b^4*d^4*e^4 + 52*a^6*b^3*d^3*e^5 - 18*a^7*b^2*d^2*e^6 + a^9*e^8)*x^2 + (3*a^2*b^7*d^8 - 16*a^3*b^6*d^7*e + 33*a^4*b^5*d^6*e^2 - 30*a^5*b^4*d^5*e^3 + 5*a^6*b^3*d^4*e^4 + 12*a^7*b^2*d^3*e^5 - 9*a^8*b*d^2*e^6 + 2*a^9*d*e^7)*x)","B",0
1525,1,943,0,0.391114," ","integrate((e*x+d)^8/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{5 \, b^{8} e^{8} x^{8} - 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} + 20 \, {\left(3 \, b^{8} d e^{7} - a b^{7} e^{8}\right)} x^{7} + 140 \, {\left(3 \, b^{8} d^{2} e^{6} - 3 \, a b^{7} d e^{7} + a^{2} b^{6} e^{8}\right)} x^{6} + 25 \, {\left(84 \, a b^{7} d^{2} e^{6} - 120 \, a^{2} b^{6} d e^{7} + 47 \, a^{3} b^{5} e^{8}\right)} x^{5} - 25 \, {\left(42 \, b^{8} d^{4} e^{4} - 168 \, a b^{7} d^{3} e^{5} + 84 \, a^{2} b^{6} d^{2} e^{6} + 96 \, a^{3} b^{5} d e^{7} - 67 \, a^{4} b^{4} e^{8}\right)} x^{4} - 10 \, {\left(42 \, b^{8} d^{5} e^{3} + 210 \, a b^{7} d^{4} e^{4} - 1260 \, a^{2} b^{6} d^{3} e^{5} + 1680 \, a^{3} b^{5} d^{2} e^{6} - 780 \, a^{4} b^{4} d e^{7} + 85 \, a^{5} b^{3} e^{8}\right)} x^{3} - 10 \, {\left(14 \, b^{8} d^{6} e^{2} + 42 \, a b^{7} d^{5} e^{3} + 210 \, a^{2} b^{6} d^{4} e^{4} - 1540 \, a^{3} b^{5} d^{3} e^{5} + 2520 \, a^{4} b^{4} d^{2} e^{6} - 1620 \, a^{5} b^{3} d e^{7} + 365 \, a^{6} b^{2} e^{8}\right)} x^{2} - 5 \, {\left(6 \, b^{8} d^{7} e + 14 \, a b^{7} d^{6} e^{2} + 42 \, a^{2} b^{6} d^{5} e^{3} + 210 \, a^{3} b^{5} d^{4} e^{4} - 1750 \, a^{4} b^{4} d^{3} e^{5} + 3150 \, a^{5} b^{3} d^{2} e^{6} - 2250 \, a^{6} b^{2} d e^{7} + 575 \, a^{7} b e^{8}\right)} x + 840 \, {\left(a^{5} b^{3} d^{3} e^{5} - 3 \, a^{6} b^{2} d^{2} e^{6} + 3 \, a^{7} b d e^{7} - a^{8} e^{8} + {\left(b^{8} d^{3} e^{5} - 3 \, a b^{7} d^{2} e^{6} + 3 \, a^{2} b^{6} d e^{7} - a^{3} b^{5} e^{8}\right)} x^{5} + 5 \, {\left(a b^{7} d^{3} e^{5} - 3 \, a^{2} b^{6} d^{2} e^{6} + 3 \, a^{3} b^{5} d e^{7} - a^{4} b^{4} e^{8}\right)} x^{4} + 10 \, {\left(a^{2} b^{6} d^{3} e^{5} - 3 \, a^{3} b^{5} d^{2} e^{6} + 3 \, a^{4} b^{4} d e^{7} - a^{5} b^{3} e^{8}\right)} x^{3} + 10 \, {\left(a^{3} b^{5} d^{3} e^{5} - 3 \, a^{4} b^{4} d^{2} e^{6} + 3 \, a^{5} b^{3} d e^{7} - a^{6} b^{2} e^{8}\right)} x^{2} + 5 \, {\left(a^{4} b^{4} d^{3} e^{5} - 3 \, a^{5} b^{3} d^{2} e^{6} + 3 \, a^{6} b^{2} d e^{7} - a^{7} b e^{8}\right)} x\right)} \log\left(b x + a\right)}{15 \, {\left(b^{14} x^{5} + 5 \, a b^{13} x^{4} + 10 \, a^{2} b^{12} x^{3} + 10 \, a^{3} b^{11} x^{2} + 5 \, a^{4} b^{10} x + a^{5} b^{9}\right)}}"," ",0,"1/15*(5*b^8*e^8*x^8 - 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 + 20*(3*b^8*d*e^7 - a*b^7*e^8)*x^7 + 140*(3*b^8*d^2*e^6 - 3*a*b^7*d*e^7 + a^2*b^6*e^8)*x^6 + 25*(84*a*b^7*d^2*e^6 - 120*a^2*b^6*d*e^7 + 47*a^3*b^5*e^8)*x^5 - 25*(42*b^8*d^4*e^4 - 168*a*b^7*d^3*e^5 + 84*a^2*b^6*d^2*e^6 + 96*a^3*b^5*d*e^7 - 67*a^4*b^4*e^8)*x^4 - 10*(42*b^8*d^5*e^3 + 210*a*b^7*d^4*e^4 - 1260*a^2*b^6*d^3*e^5 + 1680*a^3*b^5*d^2*e^6 - 780*a^4*b^4*d*e^7 + 85*a^5*b^3*e^8)*x^3 - 10*(14*b^8*d^6*e^2 + 42*a*b^7*d^5*e^3 + 210*a^2*b^6*d^4*e^4 - 1540*a^3*b^5*d^3*e^5 + 2520*a^4*b^4*d^2*e^6 - 1620*a^5*b^3*d*e^7 + 365*a^6*b^2*e^8)*x^2 - 5*(6*b^8*d^7*e + 14*a*b^7*d^6*e^2 + 42*a^2*b^6*d^5*e^3 + 210*a^3*b^5*d^4*e^4 - 1750*a^4*b^4*d^3*e^5 + 3150*a^5*b^3*d^2*e^6 - 2250*a^6*b^2*d*e^7 + 575*a^7*b*e^8)*x + 840*(a^5*b^3*d^3*e^5 - 3*a^6*b^2*d^2*e^6 + 3*a^7*b*d*e^7 - a^8*e^8 + (b^8*d^3*e^5 - 3*a*b^7*d^2*e^6 + 3*a^2*b^6*d*e^7 - a^3*b^5*e^8)*x^5 + 5*(a*b^7*d^3*e^5 - 3*a^2*b^6*d^2*e^6 + 3*a^3*b^5*d*e^7 - a^4*b^4*e^8)*x^4 + 10*(a^2*b^6*d^3*e^5 - 3*a^3*b^5*d^2*e^6 + 3*a^4*b^4*d*e^7 - a^5*b^3*e^8)*x^3 + 10*(a^3*b^5*d^3*e^5 - 3*a^4*b^4*d^2*e^6 + 3*a^5*b^3*d*e^7 - a^6*b^2*e^8)*x^2 + 5*(a^4*b^4*d^3*e^5 - 3*a^5*b^3*d^2*e^6 + 3*a^6*b^2*d*e^7 - a^7*b*e^8)*x)*log(b*x + a))/(b^14*x^5 + 5*a*b^13*x^4 + 10*a^2*b^12*x^3 + 10*a^3*b^11*x^2 + 5*a^4*b^10*x + a^5*b^9)","B",0
1526,1,732,0,0.391714," ","integrate((e*x+d)^7/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{10 \, b^{7} e^{7} x^{7} - 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} + 70 \, {\left(2 \, b^{7} d e^{6} - a b^{6} e^{7}\right)} x^{6} + 100 \, {\left(7 \, a b^{6} d e^{6} - 5 \, a^{2} b^{5} e^{7}\right)} x^{5} - 100 \, {\left(7 \, b^{7} d^{3} e^{4} - 21 \, a b^{6} d^{2} e^{5} + 7 \, a^{2} b^{5} d e^{6} + 4 \, a^{3} b^{4} e^{7}\right)} x^{4} - 50 \, {\left(7 \, b^{7} d^{4} e^{3} + 28 \, a b^{6} d^{3} e^{4} - 126 \, a^{2} b^{5} d^{2} e^{5} + 112 \, a^{3} b^{4} d e^{6} - 26 \, a^{4} b^{3} e^{7}\right)} x^{3} - 10 \, {\left(14 \, b^{7} d^{5} e^{2} + 35 \, a b^{6} d^{4} e^{3} + 140 \, a^{2} b^{5} d^{3} e^{4} - 770 \, a^{3} b^{4} d^{2} e^{5} + 840 \, a^{4} b^{3} d e^{6} - 270 \, a^{5} b^{2} e^{7}\right)} x^{2} - 5 \, {\left(7 \, b^{7} d^{6} e + 14 \, a b^{6} d^{5} e^{2} + 35 \, a^{2} b^{5} d^{4} e^{3} + 140 \, a^{3} b^{4} d^{3} e^{4} - 875 \, a^{4} b^{3} d^{2} e^{5} + 1050 \, a^{5} b^{2} d e^{6} - 375 \, a^{6} b e^{7}\right)} x + 420 \, {\left(a^{5} b^{2} d^{2} e^{5} - 2 \, a^{6} b d e^{6} + a^{7} e^{7} + {\left(b^{7} d^{2} e^{5} - 2 \, a b^{6} d e^{6} + a^{2} b^{5} e^{7}\right)} x^{5} + 5 \, {\left(a b^{6} d^{2} e^{5} - 2 \, a^{2} b^{5} d e^{6} + a^{3} b^{4} e^{7}\right)} x^{4} + 10 \, {\left(a^{2} b^{5} d^{2} e^{5} - 2 \, a^{3} b^{4} d e^{6} + a^{4} b^{3} e^{7}\right)} x^{3} + 10 \, {\left(a^{3} b^{4} d^{2} e^{5} - 2 \, a^{4} b^{3} d e^{6} + a^{5} b^{2} e^{7}\right)} x^{2} + 5 \, {\left(a^{4} b^{3} d^{2} e^{5} - 2 \, a^{5} b^{2} d e^{6} + a^{6} b e^{7}\right)} x\right)} \log\left(b x + a\right)}{20 \, {\left(b^{13} x^{5} + 5 \, a b^{12} x^{4} + 10 \, a^{2} b^{11} x^{3} + 10 \, a^{3} b^{10} x^{2} + 5 \, a^{4} b^{9} x + a^{5} b^{8}\right)}}"," ",0,"1/20*(10*b^7*e^7*x^7 - 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 + 70*(2*b^7*d*e^6 - a*b^6*e^7)*x^6 + 100*(7*a*b^6*d*e^6 - 5*a^2*b^5*e^7)*x^5 - 100*(7*b^7*d^3*e^4 - 21*a*b^6*d^2*e^5 + 7*a^2*b^5*d*e^6 + 4*a^3*b^4*e^7)*x^4 - 50*(7*b^7*d^4*e^3 + 28*a*b^6*d^3*e^4 - 126*a^2*b^5*d^2*e^5 + 112*a^3*b^4*d*e^6 - 26*a^4*b^3*e^7)*x^3 - 10*(14*b^7*d^5*e^2 + 35*a*b^6*d^4*e^3 + 140*a^2*b^5*d^3*e^4 - 770*a^3*b^4*d^2*e^5 + 840*a^4*b^3*d*e^6 - 270*a^5*b^2*e^7)*x^2 - 5*(7*b^7*d^6*e + 14*a*b^6*d^5*e^2 + 35*a^2*b^5*d^4*e^3 + 140*a^3*b^4*d^3*e^4 - 875*a^4*b^3*d^2*e^5 + 1050*a^5*b^2*d*e^6 - 375*a^6*b*e^7)*x + 420*(a^5*b^2*d^2*e^5 - 2*a^6*b*d*e^6 + a^7*e^7 + (b^7*d^2*e^5 - 2*a*b^6*d*e^6 + a^2*b^5*e^7)*x^5 + 5*(a*b^6*d^2*e^5 - 2*a^2*b^5*d*e^6 + a^3*b^4*e^7)*x^4 + 10*(a^2*b^5*d^2*e^5 - 2*a^3*b^4*d*e^6 + a^4*b^3*e^7)*x^3 + 10*(a^3*b^4*d^2*e^5 - 2*a^4*b^3*d*e^6 + a^5*b^2*e^7)*x^2 + 5*(a^4*b^3*d^2*e^5 - 2*a^5*b^2*d*e^6 + a^6*b*e^7)*x)*log(b*x + a))/(b^13*x^5 + 5*a*b^12*x^4 + 10*a^2*b^11*x^3 + 10*a^3*b^10*x^2 + 5*a^4*b^9*x + a^5*b^8)","B",0
1527,1,542,0,0.402913," ","integrate((e*x+d)^6/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{10 \, b^{6} e^{6} x^{6} + 50 \, a b^{5} e^{6} x^{5} - 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} - 50 \, {\left(3 \, b^{6} d^{2} e^{4} - 6 \, 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} + 4 \, 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} + 12 \, 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} + 75 \, a^{5} b e^{6}\right)} x + 60 \, {\left(a^{5} b d e^{5} - a^{6} e^{6} + {\left(b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(a b^{5} d e^{5} - a^{2} b^{4} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{4} d e^{5} - a^{3} b^{3} e^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{3} d e^{5} - a^{4} b^{2} e^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{2} d e^{5} - a^{5} b e^{6}\right)} x\right)} \log\left(b x + a\right)}{10 \, {\left(b^{12} x^{5} + 5 \, a b^{11} x^{4} + 10 \, a^{2} b^{10} x^{3} + 10 \, a^{3} b^{9} x^{2} + 5 \, a^{4} b^{8} x + a^{5} b^{7}\right)}}"," ",0,"1/10*(10*b^6*e^6*x^6 + 50*a*b^5*e^6*x^5 - 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 - 50*(3*b^6*d^2*e^4 - 6*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 + 4*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 + 12*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 + 75*a^5*b*e^6)*x + 60*(a^5*b*d*e^5 - a^6*e^6 + (b^6*d*e^5 - a*b^5*e^6)*x^5 + 5*(a*b^5*d*e^5 - a^2*b^4*e^6)*x^4 + 10*(a^2*b^4*d*e^5 - a^3*b^3*e^6)*x^3 + 10*(a^3*b^3*d*e^5 - a^4*b^2*e^6)*x^2 + 5*(a^4*b^2*d*e^5 - a^5*b*e^6)*x)*log(b*x + a))/(b^12*x^5 + 5*a*b^11*x^4 + 10*a^2*b^10*x^3 + 10*a^3*b^9*x^2 + 5*a^4*b^8*x + a^5*b^7)","B",0
1528,1,372,0,0.407844," ","integrate((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\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} + 300 \, {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 300 \, {\left(b^{5} d^{2} e^{3} + 2 \, a b^{4} d e^{4} - 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + 100 \, {\left(2 \, b^{5} d^{3} e^{2} + 3 \, a b^{4} d^{2} e^{3} + 6 \, a^{2} b^{3} d e^{4} - 11 \, a^{3} b^{2} e^{5}\right)} x^{2} + 25 \, {\left(3 \, b^{5} d^{4} e + 4 \, a b^{4} d^{3} e^{2} + 6 \, a^{2} b^{3} d^{2} e^{3} + 12 \, a^{3} b^{2} d e^{4} - 25 \, a^{4} b e^{5}\right)} x - 60 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \log\left(b x + a\right)}{60 \, {\left(b^{11} x^{5} + 5 \, a b^{10} x^{4} + 10 \, a^{2} b^{9} x^{3} + 10 \, a^{3} b^{8} x^{2} + 5 \, a^{4} b^{7} x + a^{5} b^{6}\right)}}"," ",0,"-1/60*(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 + 300*(b^5*d*e^4 - a*b^4*e^5)*x^4 + 300*(b^5*d^2*e^3 + 2*a*b^4*d*e^4 - 3*a^2*b^3*e^5)*x^3 + 100*(2*b^5*d^3*e^2 + 3*a*b^4*d^2*e^3 + 6*a^2*b^3*d*e^4 - 11*a^3*b^2*e^5)*x^2 + 25*(3*b^5*d^4*e + 4*a*b^4*d^3*e^2 + 6*a^2*b^3*d^2*e^3 + 12*a^3*b^2*d*e^4 - 25*a^4*b*e^5)*x - 60*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*log(b*x + a))/(b^11*x^5 + 5*a*b^10*x^4 + 10*a^2*b^9*x^3 + 10*a^3*b^8*x^2 + 5*a^4*b^7*x + a^5*b^6)","B",0
1529,1,215,0,0.390928," ","integrate((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{5 \, b^{4} e^{4} x^{4} + b^{4} d^{4} + a b^{3} d^{3} e + a^{2} b^{2} d^{2} e^{2} + a^{3} b d e^{3} + a^{4} e^{4} + 10 \, {\left(b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{3} + 10 \, {\left(b^{4} d^{2} e^{2} + a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 5 \, {\left(b^{4} d^{3} e + a b^{3} d^{2} e^{2} + a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x}{5 \, {\left(b^{10} x^{5} + 5 \, a b^{9} x^{4} + 10 \, a^{2} b^{8} x^{3} + 10 \, a^{3} b^{7} x^{2} + 5 \, a^{4} b^{6} x + a^{5} b^{5}\right)}}"," ",0,"-1/5*(5*b^4*e^4*x^4 + b^4*d^4 + a*b^3*d^3*e + a^2*b^2*d^2*e^2 + a^3*b*d*e^3 + a^4*e^4 + 10*(b^4*d*e^3 + a*b^3*e^4)*x^3 + 10*(b^4*d^2*e^2 + a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 5*(b^4*d^3*e + a*b^3*d^2*e^2 + a^2*b^2*d*e^3 + a^3*b*e^4)*x)/(b^10*x^5 + 5*a*b^9*x^4 + 10*a^2*b^8*x^3 + 10*a^3*b^7*x^2 + 5*a^4*b^6*x + a^5*b^5)","B",0
1530,1,160,0,0.381382," ","integrate((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{10 \, b^{3} e^{3} x^{3} + 4 \, b^{3} d^{3} + 3 \, a b^{2} d^{2} e + 2 \, a^{2} b d e^{2} + a^{3} e^{3} + 10 \, {\left(2 \, b^{3} d e^{2} + a b^{2} e^{3}\right)} x^{2} + 5 \, {\left(3 \, b^{3} d^{2} e + 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x}{20 \, {\left(b^{9} x^{5} + 5 \, a b^{8} x^{4} + 10 \, a^{2} b^{7} x^{3} + 10 \, a^{3} b^{6} x^{2} + 5 \, a^{4} b^{5} x + a^{5} b^{4}\right)}}"," ",0,"-1/20*(10*b^3*e^3*x^3 + 4*b^3*d^3 + 3*a*b^2*d^2*e + 2*a^2*b*d*e^2 + a^3*e^3 + 10*(2*b^3*d*e^2 + a*b^2*e^3)*x^2 + 5*(3*b^3*d^2*e + 2*a*b^2*d*e^2 + a^2*b*e^3)*x)/(b^9*x^5 + 5*a*b^8*x^4 + 10*a^2*b^7*x^3 + 10*a^3*b^6*x^2 + 5*a^4*b^5*x + a^5*b^4)","B",0
1531,1,109,0,0.378208," ","integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{10 \, b^{2} e^{2} x^{2} + 6 \, b^{2} d^{2} + 3 \, a b d e + a^{2} e^{2} + 5 \, {\left(3 \, b^{2} d e + a b e^{2}\right)} x}{30 \, {\left(b^{8} x^{5} + 5 \, a b^{7} x^{4} + 10 \, a^{2} b^{6} x^{3} + 10 \, a^{3} b^{5} x^{2} + 5 \, a^{4} b^{4} x + a^{5} b^{3}\right)}}"," ",0,"-1/30*(10*b^2*e^2*x^2 + 6*b^2*d^2 + 3*a*b*d*e + a^2*e^2 + 5*(3*b^2*d*e + a*b*e^2)*x)/(b^8*x^5 + 5*a*b^7*x^4 + 10*a^2*b^6*x^3 + 10*a^3*b^5*x^2 + 5*a^4*b^4*x + a^5*b^3)","A",0
1532,1,72,0,0.386258," ","integrate((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{5 \, b e x + 4 \, b d + a e}{20 \, {\left(b^{7} x^{5} + 5 \, a b^{6} x^{4} + 10 \, a^{2} b^{5} x^{3} + 10 \, a^{3} b^{4} x^{2} + 5 \, a^{4} b^{3} x + a^{5} b^{2}\right)}}"," ",0,"-1/20*(5*b*e*x + 4*b*d + a*e)/(b^7*x^5 + 5*a*b^6*x^4 + 10*a^2*b^5*x^3 + 10*a^3*b^4*x^2 + 5*a^4*b^3*x + a^5*b^2)","B",0
1533,1,57,0,0.381250," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{1}{5 \, {\left(b^{6} x^{5} + 5 \, a b^{5} x^{4} + 10 \, a^{2} b^{4} x^{3} + 10 \, a^{3} b^{3} x^{2} + 5 \, a^{4} b^{2} x + a^{5} b\right)}}"," ",0,"-1/5/(b^6*x^5 + 5*a*b^5*x^4 + 10*a^2*b^4*x^3 + 10*a^3*b^3*x^2 + 5*a^4*b^2*x + a^5*b)","B",0
1534,1,923,0,0.418469," ","integrate(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\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^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \log\left(b x + a\right) - 60 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \log\left(e x + d\right)}{60 \, {\left(a^{5} b^{6} d^{6} - 6 \, a^{6} b^{5} d^{5} e + 15 \, a^{7} b^{4} d^{4} e^{2} - 20 \, a^{8} b^{3} d^{3} e^{3} + 15 \, a^{9} b^{2} d^{2} e^{4} - 6 \, a^{10} b d e^{5} + a^{11} e^{6} + {\left(b^{11} d^{6} - 6 \, a b^{10} d^{5} e + 15 \, a^{2} b^{9} d^{4} e^{2} - 20 \, a^{3} b^{8} d^{3} e^{3} + 15 \, a^{4} b^{7} d^{2} e^{4} - 6 \, a^{5} b^{6} d e^{5} + a^{6} b^{5} e^{6}\right)} x^{5} + 5 \, {\left(a b^{10} d^{6} - 6 \, a^{2} b^{9} d^{5} e + 15 \, a^{3} b^{8} d^{4} e^{2} - 20 \, a^{4} b^{7} d^{3} e^{3} + 15 \, a^{5} b^{6} d^{2} e^{4} - 6 \, a^{6} b^{5} d e^{5} + a^{7} b^{4} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{9} d^{6} - 6 \, a^{3} b^{8} d^{5} e + 15 \, a^{4} b^{7} d^{4} e^{2} - 20 \, a^{5} b^{6} d^{3} e^{3} + 15 \, a^{6} b^{5} d^{2} e^{4} - 6 \, a^{7} b^{4} d e^{5} + a^{8} b^{3} e^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{8} d^{6} - 6 \, a^{4} b^{7} d^{5} e + 15 \, a^{5} b^{6} d^{4} e^{2} - 20 \, a^{6} b^{5} d^{3} e^{3} + 15 \, a^{7} b^{4} d^{2} e^{4} - 6 \, a^{8} b^{3} d e^{5} + a^{9} b^{2} e^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{7} d^{6} - 6 \, a^{5} b^{6} d^{5} e + 15 \, a^{6} b^{5} d^{4} e^{2} - 20 \, a^{7} b^{4} d^{3} e^{3} + 15 \, a^{8} b^{3} d^{2} e^{4} - 6 \, a^{9} b^{2} d e^{5} + a^{10} b e^{6}\right)} x\right)}}"," ",0,"-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 + 60*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*log(b*x + a) - 60*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*log(e*x + d))/(a^5*b^6*d^6 - 6*a^6*b^5*d^5*e + 15*a^7*b^4*d^4*e^2 - 20*a^8*b^3*d^3*e^3 + 15*a^9*b^2*d^2*e^4 - 6*a^10*b*d*e^5 + a^11*e^6 + (b^11*d^6 - 6*a*b^10*d^5*e + 15*a^2*b^9*d^4*e^2 - 20*a^3*b^8*d^3*e^3 + 15*a^4*b^7*d^2*e^4 - 6*a^5*b^6*d*e^5 + a^6*b^5*e^6)*x^5 + 5*(a*b^10*d^6 - 6*a^2*b^9*d^5*e + 15*a^3*b^8*d^4*e^2 - 20*a^4*b^7*d^3*e^3 + 15*a^5*b^6*d^2*e^4 - 6*a^6*b^5*d*e^5 + a^7*b^4*e^6)*x^4 + 10*(a^2*b^9*d^6 - 6*a^3*b^8*d^5*e + 15*a^4*b^7*d^4*e^2 - 20*a^5*b^6*d^3*e^3 + 15*a^6*b^5*d^2*e^4 - 6*a^7*b^4*d*e^5 + a^8*b^3*e^6)*x^3 + 10*(a^3*b^8*d^6 - 6*a^4*b^7*d^5*e + 15*a^5*b^6*d^4*e^2 - 20*a^6*b^5*d^3*e^3 + 15*a^7*b^4*d^2*e^4 - 6*a^8*b^3*d*e^5 + a^9*b^2*e^6)*x^2 + 5*(a^4*b^7*d^6 - 6*a^5*b^6*d^5*e + 15*a^6*b^5*d^4*e^2 - 20*a^7*b^4*d^3*e^3 + 15*a^8*b^3*d^2*e^4 - 6*a^9*b^2*d*e^5 + a^10*b*e^6)*x)","B",0
1535,1,1420,0,0.438426," ","integrate(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\frac{2 \, b^{6} d^{6} - 15 \, a b^{5} d^{5} e + 50 \, a^{2} b^{4} d^{4} e^{2} - 100 \, a^{3} b^{3} d^{3} e^{3} + 150 \, a^{4} b^{2} d^{2} e^{4} - 77 \, a^{5} b d e^{5} - 10 \, a^{6} e^{6} + 60 \, {\left(b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 30 \, {\left(b^{6} d^{2} e^{4} + 8 \, a b^{5} d e^{5} - 9 \, a^{2} b^{4} e^{6}\right)} x^{4} - 10 \, {\left(b^{6} d^{3} e^{3} - 15 \, a b^{5} d^{2} e^{4} - 33 \, a^{2} b^{4} d e^{5} + 47 \, a^{3} b^{3} e^{6}\right)} x^{3} + 5 \, {\left(b^{6} d^{4} e^{2} - 10 \, a b^{5} d^{3} e^{3} + 60 \, a^{2} b^{4} d^{2} e^{4} + 26 \, a^{3} b^{3} d e^{5} - 77 \, a^{4} b^{2} e^{6}\right)} x^{2} - {\left(3 \, b^{6} d^{5} e - 25 \, a b^{5} d^{4} e^{2} + 100 \, a^{2} b^{4} d^{3} e^{3} - 300 \, a^{3} b^{3} d^{2} e^{4} + 85 \, a^{4} b^{2} d e^{5} + 137 \, a^{5} b e^{6}\right)} x + 60 \, {\left(b^{6} e^{6} x^{6} + a^{5} b d e^{5} + {\left(b^{6} d e^{5} + 5 \, a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(a b^{5} d e^{5} + 2 \, a^{2} b^{4} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + 5 \, {\left(2 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + {\left(5 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x\right)} \log\left(b x + a\right) - 60 \, {\left(b^{6} e^{6} x^{6} + a^{5} b d e^{5} + {\left(b^{6} d e^{5} + 5 \, a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(a b^{5} d e^{5} + 2 \, a^{2} b^{4} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + 5 \, {\left(2 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + {\left(5 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x\right)} \log\left(e x + d\right)}{10 \, {\left(a^{5} b^{7} d^{8} - 7 \, a^{6} b^{6} d^{7} e + 21 \, a^{7} b^{5} d^{6} e^{2} - 35 \, a^{8} b^{4} d^{5} e^{3} + 35 \, a^{9} b^{3} d^{4} e^{4} - 21 \, a^{10} b^{2} d^{3} e^{5} + 7 \, a^{11} b d^{2} e^{6} - a^{12} d e^{7} + {\left(b^{12} d^{7} e - 7 \, a b^{11} d^{6} e^{2} + 21 \, a^{2} b^{10} d^{5} e^{3} - 35 \, a^{3} b^{9} d^{4} e^{4} + 35 \, a^{4} b^{8} d^{3} e^{5} - 21 \, a^{5} b^{7} d^{2} e^{6} + 7 \, a^{6} b^{6} d e^{7} - a^{7} b^{5} e^{8}\right)} x^{6} + {\left(b^{12} d^{8} - 2 \, a b^{11} d^{7} e - 14 \, a^{2} b^{10} d^{6} e^{2} + 70 \, a^{3} b^{9} d^{5} e^{3} - 140 \, a^{4} b^{8} d^{4} e^{4} + 154 \, a^{5} b^{7} d^{3} e^{5} - 98 \, a^{6} b^{6} d^{2} e^{6} + 34 \, a^{7} b^{5} d e^{7} - 5 \, a^{8} b^{4} e^{8}\right)} x^{5} + 5 \, {\left(a b^{11} d^{8} - 5 \, a^{2} b^{10} d^{7} e + 7 \, a^{3} b^{9} d^{6} e^{2} + 7 \, a^{4} b^{8} d^{5} e^{3} - 35 \, a^{5} b^{7} d^{4} e^{4} + 49 \, a^{6} b^{6} d^{3} e^{5} - 35 \, a^{7} b^{5} d^{2} e^{6} + 13 \, a^{8} b^{4} d e^{7} - 2 \, a^{9} b^{3} e^{8}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{8} - 6 \, a^{3} b^{9} d^{7} e + 14 \, a^{4} b^{8} d^{6} e^{2} - 14 \, a^{5} b^{7} d^{5} e^{3} + 14 \, a^{7} b^{5} d^{3} e^{5} - 14 \, a^{8} b^{4} d^{2} e^{6} + 6 \, a^{9} b^{3} d e^{7} - a^{10} b^{2} e^{8}\right)} x^{3} + 5 \, {\left(2 \, a^{3} b^{9} d^{8} - 13 \, a^{4} b^{8} d^{7} e + 35 \, a^{5} b^{7} d^{6} e^{2} - 49 \, a^{6} b^{6} d^{5} e^{3} + 35 \, a^{7} b^{5} d^{4} e^{4} - 7 \, a^{8} b^{4} d^{3} e^{5} - 7 \, a^{9} b^{3} d^{2} e^{6} + 5 \, a^{10} b^{2} d e^{7} - a^{11} b e^{8}\right)} x^{2} + {\left(5 \, a^{4} b^{8} d^{8} - 34 \, a^{5} b^{7} d^{7} e + 98 \, a^{6} b^{6} d^{6} e^{2} - 154 \, a^{7} b^{5} d^{5} e^{3} + 140 \, a^{8} b^{4} d^{4} e^{4} - 70 \, a^{9} b^{3} d^{3} e^{5} + 14 \, a^{10} b^{2} d^{2} e^{6} + 2 \, a^{11} b d e^{7} - a^{12} e^{8}\right)} x\right)}}"," ",0,"-1/10*(2*b^6*d^6 - 15*a*b^5*d^5*e + 50*a^2*b^4*d^4*e^2 - 100*a^3*b^3*d^3*e^3 + 150*a^4*b^2*d^2*e^4 - 77*a^5*b*d*e^5 - 10*a^6*e^6 + 60*(b^6*d*e^5 - a*b^5*e^6)*x^5 + 30*(b^6*d^2*e^4 + 8*a*b^5*d*e^5 - 9*a^2*b^4*e^6)*x^4 - 10*(b^6*d^3*e^3 - 15*a*b^5*d^2*e^4 - 33*a^2*b^4*d*e^5 + 47*a^3*b^3*e^6)*x^3 + 5*(b^6*d^4*e^2 - 10*a*b^5*d^3*e^3 + 60*a^2*b^4*d^2*e^4 + 26*a^3*b^3*d*e^5 - 77*a^4*b^2*e^6)*x^2 - (3*b^6*d^5*e - 25*a*b^5*d^4*e^2 + 100*a^2*b^4*d^3*e^3 - 300*a^3*b^3*d^2*e^4 + 85*a^4*b^2*d*e^5 + 137*a^5*b*e^6)*x + 60*(b^6*e^6*x^6 + a^5*b*d*e^5 + (b^6*d*e^5 + 5*a*b^5*e^6)*x^5 + 5*(a*b^5*d*e^5 + 2*a^2*b^4*e^6)*x^4 + 10*(a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 + 5*(2*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + (5*a^4*b^2*d*e^5 + a^5*b*e^6)*x)*log(b*x + a) - 60*(b^6*e^6*x^6 + a^5*b*d*e^5 + (b^6*d*e^5 + 5*a*b^5*e^6)*x^5 + 5*(a*b^5*d*e^5 + 2*a^2*b^4*e^6)*x^4 + 10*(a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 + 5*(2*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + (5*a^4*b^2*d*e^5 + a^5*b*e^6)*x)*log(e*x + d))/(a^5*b^7*d^8 - 7*a^6*b^6*d^7*e + 21*a^7*b^5*d^6*e^2 - 35*a^8*b^4*d^5*e^3 + 35*a^9*b^3*d^4*e^4 - 21*a^10*b^2*d^3*e^5 + 7*a^11*b*d^2*e^6 - a^12*d*e^7 + (b^12*d^7*e - 7*a*b^11*d^6*e^2 + 21*a^2*b^10*d^5*e^3 - 35*a^3*b^9*d^4*e^4 + 35*a^4*b^8*d^3*e^5 - 21*a^5*b^7*d^2*e^6 + 7*a^6*b^6*d*e^7 - a^7*b^5*e^8)*x^6 + (b^12*d^8 - 2*a*b^11*d^7*e - 14*a^2*b^10*d^6*e^2 + 70*a^3*b^9*d^5*e^3 - 140*a^4*b^8*d^4*e^4 + 154*a^5*b^7*d^3*e^5 - 98*a^6*b^6*d^2*e^6 + 34*a^7*b^5*d*e^7 - 5*a^8*b^4*e^8)*x^5 + 5*(a*b^11*d^8 - 5*a^2*b^10*d^7*e + 7*a^3*b^9*d^6*e^2 + 7*a^4*b^8*d^5*e^3 - 35*a^5*b^7*d^4*e^4 + 49*a^6*b^6*d^3*e^5 - 35*a^7*b^5*d^2*e^6 + 13*a^8*b^4*d*e^7 - 2*a^9*b^3*e^8)*x^4 + 10*(a^2*b^10*d^8 - 6*a^3*b^9*d^7*e + 14*a^4*b^8*d^6*e^2 - 14*a^5*b^7*d^5*e^3 + 14*a^7*b^5*d^3*e^5 - 14*a^8*b^4*d^2*e^6 + 6*a^9*b^3*d*e^7 - a^10*b^2*e^8)*x^3 + 5*(2*a^3*b^9*d^8 - 13*a^4*b^8*d^7*e + 35*a^5*b^7*d^6*e^2 - 49*a^6*b^6*d^5*e^3 + 35*a^7*b^5*d^4*e^4 - 7*a^8*b^4*d^3*e^5 - 7*a^9*b^3*d^2*e^6 + 5*a^10*b^2*d*e^7 - a^11*b*e^8)*x^2 + (5*a^4*b^8*d^8 - 34*a^5*b^7*d^7*e + 98*a^6*b^6*d^6*e^2 - 154*a^7*b^5*d^5*e^3 + 140*a^8*b^4*d^4*e^4 - 70*a^9*b^3*d^3*e^5 + 14*a^10*b^2*d^2*e^6 + 2*a^11*b*d*e^7 - a^12*e^8)*x)","B",0
1536,1,2005,0,0.464373," ","integrate(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","-\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 + 420 \, {\left(b^{7} e^{7} x^{7} + a^{5} b^{2} d^{2} e^{5} + {\left(2 \, b^{7} d e^{6} + 5 \, a b^{6} e^{7}\right)} x^{6} + {\left(b^{7} d^{2} e^{5} + 10 \, a b^{6} d e^{6} + 10 \, a^{2} b^{5} e^{7}\right)} x^{5} + 5 \, {\left(a b^{6} d^{2} e^{5} + 4 \, a^{2} b^{5} d e^{6} + 2 \, a^{3} b^{4} e^{7}\right)} x^{4} + 5 \, {\left(2 \, a^{2} b^{5} d^{2} e^{5} + 4 \, a^{3} b^{4} d e^{6} + a^{4} b^{3} e^{7}\right)} x^{3} + {\left(10 \, a^{3} b^{4} d^{2} e^{5} + 10 \, a^{4} b^{3} d e^{6} + a^{5} b^{2} e^{7}\right)} x^{2} + {\left(5 \, a^{4} b^{3} d^{2} e^{5} + 2 \, a^{5} b^{2} d e^{6}\right)} x\right)} \log\left(b x + a\right) - 420 \, {\left(b^{7} e^{7} x^{7} + a^{5} b^{2} d^{2} e^{5} + {\left(2 \, b^{7} d e^{6} + 5 \, a b^{6} e^{7}\right)} x^{6} + {\left(b^{7} d^{2} e^{5} + 10 \, a b^{6} d e^{6} + 10 \, a^{2} b^{5} e^{7}\right)} x^{5} + 5 \, {\left(a b^{6} d^{2} e^{5} + 4 \, a^{2} b^{5} d e^{6} + 2 \, a^{3} b^{4} e^{7}\right)} x^{4} + 5 \, {\left(2 \, a^{2} b^{5} d^{2} e^{5} + 4 \, a^{3} b^{4} d e^{6} + a^{4} b^{3} e^{7}\right)} x^{3} + {\left(10 \, a^{3} b^{4} d^{2} e^{5} + 10 \, a^{4} b^{3} d e^{6} + a^{5} b^{2} e^{7}\right)} x^{2} + {\left(5 \, a^{4} b^{3} d^{2} e^{5} + 2 \, a^{5} b^{2} d e^{6}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(a^{5} b^{8} d^{10} - 8 \, a^{6} b^{7} d^{9} e + 28 \, a^{7} b^{6} d^{8} e^{2} - 56 \, a^{8} b^{5} d^{7} e^{3} + 70 \, a^{9} b^{4} d^{6} e^{4} - 56 \, a^{10} b^{3} d^{5} e^{5} + 28 \, a^{11} b^{2} d^{4} e^{6} - 8 \, a^{12} b d^{3} e^{7} + a^{13} d^{2} e^{8} + {\left(b^{13} d^{8} e^{2} - 8 \, a b^{12} d^{7} e^{3} + 28 \, a^{2} b^{11} d^{6} e^{4} - 56 \, a^{3} b^{10} d^{5} e^{5} + 70 \, a^{4} b^{9} d^{4} e^{6} - 56 \, a^{5} b^{8} d^{3} e^{7} + 28 \, a^{6} b^{7} d^{2} e^{8} - 8 \, a^{7} b^{6} d e^{9} + a^{8} b^{5} e^{10}\right)} x^{7} + {\left(2 \, b^{13} d^{9} e - 11 \, a b^{12} d^{8} e^{2} + 16 \, a^{2} b^{11} d^{7} e^{3} + 28 \, a^{3} b^{10} d^{6} e^{4} - 140 \, a^{4} b^{9} d^{5} e^{5} + 238 \, a^{5} b^{8} d^{4} e^{6} - 224 \, a^{6} b^{7} d^{3} e^{7} + 124 \, a^{7} b^{6} d^{2} e^{8} - 38 \, a^{8} b^{5} d e^{9} + 5 \, a^{9} b^{4} e^{10}\right)} x^{6} + {\left(b^{13} d^{10} + 2 \, a b^{12} d^{9} e - 42 \, a^{2} b^{11} d^{8} e^{2} + 144 \, a^{3} b^{10} d^{7} e^{3} - 210 \, a^{4} b^{9} d^{6} e^{4} + 84 \, a^{5} b^{8} d^{5} e^{5} + 168 \, a^{6} b^{7} d^{4} e^{6} - 288 \, a^{7} b^{6} d^{3} e^{7} + 201 \, a^{8} b^{5} d^{2} e^{8} - 70 \, a^{9} b^{4} d e^{9} + 10 \, a^{10} b^{3} e^{10}\right)} x^{5} + 5 \, {\left(a b^{12} d^{10} - 4 \, a^{2} b^{11} d^{9} e - 2 \, a^{3} b^{10} d^{8} e^{2} + 40 \, a^{4} b^{9} d^{7} e^{3} - 98 \, a^{5} b^{8} d^{6} e^{4} + 112 \, a^{6} b^{7} d^{5} e^{5} - 56 \, a^{7} b^{6} d^{4} e^{6} - 8 \, a^{8} b^{5} d^{3} e^{7} + 25 \, a^{9} b^{4} d^{2} e^{8} - 12 \, a^{10} b^{3} d e^{9} + 2 \, a^{11} b^{2} e^{10}\right)} x^{4} + 5 \, {\left(2 \, a^{2} b^{11} d^{10} - 12 \, a^{3} b^{10} d^{9} e + 25 \, a^{4} b^{9} d^{8} e^{2} - 8 \, a^{5} b^{8} d^{7} e^{3} - 56 \, a^{6} b^{7} d^{6} e^{4} + 112 \, a^{7} b^{6} d^{5} e^{5} - 98 \, a^{8} b^{5} d^{4} e^{6} + 40 \, a^{9} b^{4} d^{3} e^{7} - 2 \, a^{10} b^{3} d^{2} e^{8} - 4 \, a^{11} b^{2} d e^{9} + a^{12} b e^{10}\right)} x^{3} + {\left(10 \, a^{3} b^{10} d^{10} - 70 \, a^{4} b^{9} d^{9} e + 201 \, a^{5} b^{8} d^{8} e^{2} - 288 \, a^{6} b^{7} d^{7} e^{3} + 168 \, a^{7} b^{6} d^{6} e^{4} + 84 \, a^{8} b^{5} d^{5} e^{5} - 210 \, a^{9} b^{4} d^{4} e^{6} + 144 \, a^{10} b^{3} d^{3} e^{7} - 42 \, a^{11} b^{2} d^{2} e^{8} + 2 \, a^{12} b d e^{9} + a^{13} e^{10}\right)} x^{2} + {\left(5 \, a^{4} b^{9} d^{10} - 38 \, a^{5} b^{8} d^{9} e + 124 \, a^{6} b^{7} d^{8} e^{2} - 224 \, a^{7} b^{6} d^{7} e^{3} + 238 \, a^{8} b^{5} d^{6} e^{4} - 140 \, a^{9} b^{4} d^{5} e^{5} + 28 \, a^{10} b^{3} d^{4} e^{6} + 16 \, a^{11} b^{2} d^{3} e^{7} - 11 \, a^{12} b d^{2} e^{8} + 2 \, a^{13} d e^{9}\right)} x\right)}}"," ",0,"-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 + 420*(b^7*e^7*x^7 + a^5*b^2*d^2*e^5 + (2*b^7*d*e^6 + 5*a*b^6*e^7)*x^6 + (b^7*d^2*e^5 + 10*a*b^6*d*e^6 + 10*a^2*b^5*e^7)*x^5 + 5*(a*b^6*d^2*e^5 + 4*a^2*b^5*d*e^6 + 2*a^3*b^4*e^7)*x^4 + 5*(2*a^2*b^5*d^2*e^5 + 4*a^3*b^4*d*e^6 + a^4*b^3*e^7)*x^3 + (10*a^3*b^4*d^2*e^5 + 10*a^4*b^3*d*e^6 + a^5*b^2*e^7)*x^2 + (5*a^4*b^3*d^2*e^5 + 2*a^5*b^2*d*e^6)*x)*log(b*x + a) - 420*(b^7*e^7*x^7 + a^5*b^2*d^2*e^5 + (2*b^7*d*e^6 + 5*a*b^6*e^7)*x^6 + (b^7*d^2*e^5 + 10*a*b^6*d*e^6 + 10*a^2*b^5*e^7)*x^5 + 5*(a*b^6*d^2*e^5 + 4*a^2*b^5*d*e^6 + 2*a^3*b^4*e^7)*x^4 + 5*(2*a^2*b^5*d^2*e^5 + 4*a^3*b^4*d*e^6 + a^4*b^3*e^7)*x^3 + (10*a^3*b^4*d^2*e^5 + 10*a^4*b^3*d*e^6 + a^5*b^2*e^7)*x^2 + (5*a^4*b^3*d^2*e^5 + 2*a^5*b^2*d*e^6)*x)*log(e*x + d))/(a^5*b^8*d^10 - 8*a^6*b^7*d^9*e + 28*a^7*b^6*d^8*e^2 - 56*a^8*b^5*d^7*e^3 + 70*a^9*b^4*d^6*e^4 - 56*a^10*b^3*d^5*e^5 + 28*a^11*b^2*d^4*e^6 - 8*a^12*b*d^3*e^7 + a^13*d^2*e^8 + (b^13*d^8*e^2 - 8*a*b^12*d^7*e^3 + 28*a^2*b^11*d^6*e^4 - 56*a^3*b^10*d^5*e^5 + 70*a^4*b^9*d^4*e^6 - 56*a^5*b^8*d^3*e^7 + 28*a^6*b^7*d^2*e^8 - 8*a^7*b^6*d*e^9 + a^8*b^5*e^10)*x^7 + (2*b^13*d^9*e - 11*a*b^12*d^8*e^2 + 16*a^2*b^11*d^7*e^3 + 28*a^3*b^10*d^6*e^4 - 140*a^4*b^9*d^5*e^5 + 238*a^5*b^8*d^4*e^6 - 224*a^6*b^7*d^3*e^7 + 124*a^7*b^6*d^2*e^8 - 38*a^8*b^5*d*e^9 + 5*a^9*b^4*e^10)*x^6 + (b^13*d^10 + 2*a*b^12*d^9*e - 42*a^2*b^11*d^8*e^2 + 144*a^3*b^10*d^7*e^3 - 210*a^4*b^9*d^6*e^4 + 84*a^5*b^8*d^5*e^5 + 168*a^6*b^7*d^4*e^6 - 288*a^7*b^6*d^3*e^7 + 201*a^8*b^5*d^2*e^8 - 70*a^9*b^4*d*e^9 + 10*a^10*b^3*e^10)*x^5 + 5*(a*b^12*d^10 - 4*a^2*b^11*d^9*e - 2*a^3*b^10*d^8*e^2 + 40*a^4*b^9*d^7*e^3 - 98*a^5*b^8*d^6*e^4 + 112*a^6*b^7*d^5*e^5 - 56*a^7*b^6*d^4*e^6 - 8*a^8*b^5*d^3*e^7 + 25*a^9*b^4*d^2*e^8 - 12*a^10*b^3*d*e^9 + 2*a^11*b^2*e^10)*x^4 + 5*(2*a^2*b^11*d^10 - 12*a^3*b^10*d^9*e + 25*a^4*b^9*d^8*e^2 - 8*a^5*b^8*d^7*e^3 - 56*a^6*b^7*d^6*e^4 + 112*a^7*b^6*d^5*e^5 - 98*a^8*b^5*d^4*e^6 + 40*a^9*b^4*d^3*e^7 - 2*a^10*b^3*d^2*e^8 - 4*a^11*b^2*d*e^9 + a^12*b*e^10)*x^3 + (10*a^3*b^10*d^10 - 70*a^4*b^9*d^9*e + 201*a^5*b^8*d^8*e^2 - 288*a^6*b^7*d^7*e^3 + 168*a^7*b^6*d^6*e^4 + 84*a^8*b^5*d^5*e^5 - 210*a^9*b^4*d^4*e^6 + 144*a^10*b^3*d^3*e^7 - 42*a^11*b^2*d^2*e^8 + 2*a^12*b*d*e^9 + a^13*e^10)*x^2 + (5*a^4*b^9*d^10 - 38*a^5*b^8*d^9*e + 124*a^6*b^7*d^8*e^2 - 224*a^7*b^6*d^7*e^3 + 238*a^8*b^5*d^6*e^4 - 140*a^9*b^4*d^5*e^5 + 28*a^10*b^3*d^4*e^6 + 16*a^11*b^2*d^3*e^7 - 11*a^12*b*d^2*e^8 + 2*a^13*d*e^9)*x)","B",0
1537,1,83,0,0.340177," ","integrate((e*x+d)*(4*x^2+12*x+9)^3,x, algorithm=""fricas"")","8 x^{8} e + \frac{576}{7} x^{7} e + \frac{64}{7} x^{7} d + 360 x^{6} e + 96 x^{6} d + 864 x^{5} e + 432 x^{5} d + 1215 x^{4} e + 1080 x^{4} d + 972 x^{3} e + 1620 x^{3} d + \frac{729}{2} x^{2} e + 1458 x^{2} d + 729 x d"," ",0,"8*x^8*e + 576/7*x^7*e + 64/7*x^7*d + 360*x^6*e + 96*x^6*d + 864*x^5*e + 432*x^5*d + 1215*x^4*e + 1080*x^4*d + 972*x^3*e + 1620*x^3*d + 729/2*x^2*e + 1458*x^2*d + 729*x*d","B",0
1538,1,59,0,0.351222," ","integrate((e*x+d)*(4*x^2+12*x+9)^2,x, algorithm=""fricas"")","\frac{8}{3} x^{6} e + \frac{96}{5} x^{5} e + \frac{16}{5} x^{5} d + 54 x^{4} e + 24 x^{4} d + 72 x^{3} e + 72 x^{3} d + \frac{81}{2} x^{2} e + 108 x^{2} d + 81 x d"," ",0,"8/3*x^6*e + 96/5*x^5*e + 16/5*x^5*d + 54*x^4*e + 24*x^4*d + 72*x^3*e + 72*x^3*d + 81/2*x^2*e + 108*x^2*d + 81*x*d","B",0
1539,1,34,0,0.348845," ","integrate((e*x+d)*(4*x^2+12*x+9),x, algorithm=""fricas"")","x^{4} e + 4 x^{3} e + \frac{4}{3} x^{3} d + \frac{9}{2} x^{2} e + 6 x^{2} d + 9 x d"," ",0,"x^4*e + 4*x^3*e + 4/3*x^3*d + 9/2*x^2*e + 6*x^2*d + 9*x*d","A",0
1540,1,31,0,0.392783," ","integrate((e*x+d)/(4*x^2+12*x+9),x, algorithm=""fricas"")","\frac{{\left(2 \, e x + 3 \, e\right)} \log\left(2 \, x + 3\right) - 2 \, d + 3 \, e}{4 \, {\left(2 \, x + 3\right)}}"," ",0,"1/4*((2*e*x + 3*e)*log(2*x + 3) - 2*d + 3*e)/(2*x + 3)","A",0
1541,1,30,0,0.387427," ","integrate((e*x+d)/(4*x^2+12*x+9)^2,x, algorithm=""fricas"")","-\frac{6 \, e x + 4 \, d + 3 \, e}{24 \, {\left(8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right)}}"," ",0,"-1/24*(6*e*x + 4*d + 3*e)/(8*x^3 + 36*x^2 + 54*x + 27)","A",0
1542,1,40,0,0.369030," ","integrate((e*x+d)/(4*x^2+12*x+9)^3,x, algorithm=""fricas"")","-\frac{10 \, e x + 8 \, d + 3 \, e}{80 \, {\left(32 \, x^{5} + 240 \, x^{4} + 720 \, x^{3} + 1080 \, x^{2} + 810 \, x + 243\right)}}"," ",0,"-1/80*(10*e*x + 8*d + 3*e)/(32*x^5 + 240*x^4 + 720*x^3 + 1080*x^2 + 810*x + 243)","A",0
1543,1,96,0,0.412363," ","integrate((e*x+d)^4*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, b e^{4} x^{6} + a d^{4} x + \frac{1}{5} \, {\left(4 \, b d e^{3} + a e^{4}\right)} x^{5} + \frac{1}{2} \, {\left(3 \, b d^{2} e^{2} + 2 \, a d e^{3}\right)} x^{4} + \frac{2}{3} \, {\left(2 \, b d^{3} e + 3 \, a d^{2} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(b d^{4} + 4 \, a d^{3} e\right)} x^{2}"," ",0,"1/6*b*e^4*x^6 + a*d^4*x + 1/5*(4*b*d*e^3 + a*e^4)*x^5 + 1/2*(3*b*d^2*e^2 + 2*a*d*e^3)*x^4 + 2/3*(2*b*d^3*e + 3*a*d^2*e^2)*x^3 + 1/2*(b*d^4 + 4*a*d^3*e)*x^2","A",0
1544,1,69,0,0.395961," ","integrate((e*x+d)^3*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{5} \, b e^{3} x^{5} + a d^{3} x + \frac{1}{4} \, {\left(3 \, b d e^{2} + a e^{3}\right)} x^{4} + {\left(b d^{2} e + a d e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(b d^{3} + 3 \, a d^{2} e\right)} x^{2}"," ",0,"1/5*b*e^3*x^5 + a*d^3*x + 1/4*(3*b*d*e^2 + a*e^3)*x^4 + (b*d^2*e + a*d*e^2)*x^3 + 1/2*(b*d^3 + 3*a*d^2*e)*x^2","A",0
1545,1,48,0,0.388809," ","integrate((e*x+d)^2*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, b e^{2} x^{4} + a d^{2} x + \frac{1}{3} \, {\left(2 \, b d e + a e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(b d^{2} + 2 \, a d e\right)} x^{2}"," ",0,"1/4*b*e^2*x^4 + a*d^2*x + 1/3*(2*b*d*e + a*e^2)*x^3 + 1/2*(b*d^2 + 2*a*d*e)*x^2","A",0
1546,1,24,0,0.401006," ","integrate((e*x+d)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, b e x^{3} + a d x + \frac{1}{2} \, {\left(b d + a e\right)} x^{2}"," ",0,"1/3*b*e*x^3 + a*d*x + 1/2*(b*d + a*e)*x^2","A",0
1547,1,10,0,0.395481," ","integrate(((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, b x^{2} + a x"," ",0,"1/2*b*x^2 + a*x","A",0
1548,1,25,0,0.394248," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\frac{b e x - {\left(b d - a e\right)} \log\left(e x + d\right)}{e^{2}}"," ",0,"(b*e*x - (b*d - a*e)*log(e*x + d))/e^2","A",0
1549,1,37,0,0.394573," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{b d - a e + {\left(b e x + b d\right)} \log\left(e x + d\right)}{e^{3} x + d e^{2}}"," ",0,"(b*d - a*e + (b*e*x + b*d)*log(e*x + d))/(e^3*x + d*e^2)","A",0
1550,1,38,0,0.379411," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","-\frac{2 \, b e x + b d + a e}{2 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}"," ",0,"-1/2*(2*b*e*x + b*d + a*e)/(e^4*x^2 + 2*d*e^3*x + d^2*e^2)","A",0
1551,1,50,0,0.409357," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{3 \, b e x + b d + 2 \, a e}{6 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}}"," ",0,"-1/6*(3*b*e*x + b*d + 2*a*e)/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2)","A",0
1552,1,61,0,0.413600," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{4 \, b e x + b d + 3 \, a e}{12 \, {\left(e^{6} x^{4} + 4 \, d e^{5} x^{3} + 6 \, d^{2} e^{4} x^{2} + 4 \, d^{3} e^{3} x + d^{4} e^{2}\right)}}"," ",0,"-1/12*(4*b*e*x + b*d + 3*a*e)/(e^6*x^4 + 4*d*e^5*x^3 + 6*d^2*e^4*x^2 + 4*d^3*e^3*x + d^4*e^2)","A",0
1553,1,72,0,0.396268," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{5 \, b e x + b d + 4 \, a e}{20 \, {\left(e^{7} x^{5} + 5 \, d e^{6} x^{4} + 10 \, d^{2} e^{5} x^{3} + 10 \, d^{3} e^{4} x^{2} + 5 \, d^{4} e^{3} x + d^{5} e^{2}\right)}}"," ",0,"-1/20*(5*b*e*x + b*d + 4*a*e)/(e^7*x^5 + 5*d*e^6*x^4 + 10*d^2*e^5*x^3 + 10*d^3*e^4*x^2 + 5*d^4*e^3*x + d^5*e^2)","A",0
1554,1,277,0,0.391388," ","integrate((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{9} \, b^{3} e^{5} x^{9} + a^{3} d^{5} x + \frac{1}{8} \, {\left(5 \, b^{3} d e^{4} + 3 \, a b^{2} e^{5}\right)} x^{8} + \frac{1}{7} \, {\left(10 \, b^{3} d^{2} e^{3} + 15 \, a b^{2} d e^{4} + 3 \, a^{2} b e^{5}\right)} x^{7} + \frac{1}{6} \, {\left(10 \, b^{3} d^{3} e^{2} + 30 \, a b^{2} d^{2} e^{3} + 15 \, a^{2} b d e^{4} + a^{3} e^{5}\right)} x^{6} + {\left(b^{3} d^{4} e + 6 \, a b^{2} d^{3} e^{2} + 6 \, a^{2} b d^{2} e^{3} + a^{3} d e^{4}\right)} x^{5} + \frac{1}{4} \, {\left(b^{3} d^{5} + 15 \, a b^{2} d^{4} e + 30 \, a^{2} b d^{3} e^{2} + 10 \, a^{3} d^{2} e^{3}\right)} x^{4} + \frac{1}{3} \, {\left(3 \, a b^{2} d^{5} + 15 \, a^{2} b d^{4} e + 10 \, a^{3} d^{3} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(3 \, a^{2} b d^{5} + 5 \, a^{3} d^{4} e\right)} x^{2}"," ",0,"1/9*b^3*e^5*x^9 + a^3*d^5*x + 1/8*(5*b^3*d*e^4 + 3*a*b^2*e^5)*x^8 + 1/7*(10*b^3*d^2*e^3 + 15*a*b^2*d*e^4 + 3*a^2*b*e^5)*x^7 + 1/6*(10*b^3*d^3*e^2 + 30*a*b^2*d^2*e^3 + 15*a^2*b*d*e^4 + a^3*e^5)*x^6 + (b^3*d^4*e + 6*a*b^2*d^3*e^2 + 6*a^2*b*d^2*e^3 + a^3*d*e^4)*x^5 + 1/4*(b^3*d^5 + 15*a*b^2*d^4*e + 30*a^2*b*d^3*e^2 + 10*a^3*d^2*e^3)*x^4 + 1/3*(3*a*b^2*d^5 + 15*a^2*b*d^4*e + 10*a^3*d^3*e^2)*x^3 + 1/2*(3*a^2*b*d^5 + 5*a^3*d^4*e)*x^2","A",0
1555,1,225,0,0.409188," ","integrate((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{8} \, b^{3} e^{4} x^{8} + a^{3} d^{4} x + \frac{1}{7} \, {\left(4 \, b^{3} d e^{3} + 3 \, a b^{2} e^{4}\right)} x^{7} + \frac{1}{2} \, {\left(2 \, b^{3} d^{2} e^{2} + 4 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)} x^{6} + \frac{1}{5} \, {\left(4 \, b^{3} d^{3} e + 18 \, a b^{2} d^{2} e^{2} + 12 \, a^{2} b d e^{3} + a^{3} e^{4}\right)} x^{5} + \frac{1}{4} \, {\left(b^{3} d^{4} + 12 \, a b^{2} d^{3} e + 18 \, a^{2} b d^{2} e^{2} + 4 \, a^{3} d e^{3}\right)} x^{4} + {\left(a b^{2} d^{4} + 4 \, a^{2} b d^{3} e + 2 \, a^{3} d^{2} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(3 \, a^{2} b d^{4} + 4 \, a^{3} d^{3} e\right)} x^{2}"," ",0,"1/8*b^3*e^4*x^8 + a^3*d^4*x + 1/7*(4*b^3*d*e^3 + 3*a*b^2*e^4)*x^7 + 1/2*(2*b^3*d^2*e^2 + 4*a*b^2*d*e^3 + a^2*b*e^4)*x^6 + 1/5*(4*b^3*d^3*e + 18*a*b^2*d^2*e^2 + 12*a^2*b*d*e^3 + a^3*e^4)*x^5 + 1/4*(b^3*d^4 + 12*a*b^2*d^3*e + 18*a^2*b*d^2*e^2 + 4*a^3*d*e^3)*x^4 + (a*b^2*d^4 + 4*a^2*b*d^3*e + 2*a^3*d^2*e^2)*x^3 + 1/2*(3*a^2*b*d^4 + 4*a^3*d^3*e)*x^2","A",0
1556,1,167,0,0.403359," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{7} \, b^{3} e^{3} x^{7} + a^{3} d^{3} x + \frac{1}{2} \, {\left(b^{3} d e^{2} + a b^{2} e^{3}\right)} x^{6} + \frac{3}{5} \, {\left(b^{3} d^{2} e + 3 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(b^{3} d^{3} + 9 \, a b^{2} d^{2} e + 9 \, a^{2} b d e^{2} + a^{3} e^{3}\right)} x^{4} + {\left(a b^{2} d^{3} + 3 \, a^{2} b d^{2} e + a^{3} d e^{2}\right)} x^{3} + \frac{3}{2} \, {\left(a^{2} b d^{3} + a^{3} d^{2} e\right)} x^{2}"," ",0,"1/7*b^3*e^3*x^7 + a^3*d^3*x + 1/2*(b^3*d*e^2 + a*b^2*e^3)*x^6 + 3/5*(b^3*d^2*e + 3*a*b^2*d*e^2 + a^2*b*e^3)*x^5 + 1/4*(b^3*d^3 + 9*a*b^2*d^2*e + 9*a^2*b*d*e^2 + a^3*e^3)*x^4 + (a*b^2*d^3 + 3*a^2*b*d^2*e + a^3*d*e^2)*x^3 + 3/2*(a^2*b*d^3 + a^3*d^2*e)*x^2","A",0
1557,1,124,0,0.402512," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{6} \, b^{3} e^{2} x^{6} + a^{3} d^{2} x + \frac{1}{5} \, {\left(2 \, b^{3} d e + 3 \, a b^{2} e^{2}\right)} x^{5} + \frac{1}{4} \, {\left(b^{3} d^{2} + 6 \, a b^{2} d e + 3 \, a^{2} b e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(3 \, a b^{2} d^{2} + 6 \, a^{2} b d e + a^{3} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(3 \, a^{2} b d^{2} + 2 \, a^{3} d e\right)} x^{2}"," ",0,"1/6*b^3*e^2*x^6 + a^3*d^2*x + 1/5*(2*b^3*d*e + 3*a*b^2*e^2)*x^5 + 1/4*(b^3*d^2 + 6*a*b^2*d*e + 3*a^2*b*e^2)*x^4 + 1/3*(3*a*b^2*d^2 + 6*a^2*b*d*e + a^3*e^2)*x^3 + 1/2*(3*a^2*b*d^2 + 2*a^3*d*e)*x^2","A",0
1558,1,69,0,0.403751," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{5} \, b^{3} e x^{5} + a^{3} d x + \frac{1}{4} \, {\left(b^{3} d + 3 \, a b^{2} e\right)} x^{4} + {\left(a b^{2} d + a^{2} b e\right)} x^{3} + \frac{1}{2} \, {\left(3 \, a^{2} b d + a^{3} e\right)} x^{2}"," ",0,"1/5*b^3*e*x^5 + a^3*d*x + 1/4*(b^3*d + 3*a*b^2*e)*x^4 + (a*b^2*d + a^2*b*e)*x^3 + 1/2*(3*a^2*b*d + a^3*e)*x^2","A",0
1559,1,31,0,0.383358," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{4} \, b^{3} x^{4} + a b^{2} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} x"," ",0,"1/4*b^3*x^4 + a*b^2*x^3 + 3/2*a^2*b*x^2 + a^3*x","A",0
1560,1,115,0,0.406162," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\frac{2 \, b^{3} e^{3} x^{3} - 3 \, {\left(b^{3} d e^{2} - 3 \, a b^{2} e^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{2} e - 3 \, a b^{2} d e^{2} + 3 \, a^{2} b e^{3}\right)} x - 6 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \log\left(e x + d\right)}{6 \, e^{4}}"," ",0,"1/6*(2*b^3*e^3*x^3 - 3*(b^3*d*e^2 - 3*a*b^2*e^3)*x^2 + 6*(b^3*d^2*e - 3*a*b^2*d*e^2 + 3*a^2*b*e^3)*x - 6*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*log(e*x + d))/e^4","A",0
1561,1,172,0,0.405343," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{b^{3} e^{3} x^{3} + 2 \, b^{3} d^{3} - 6 \, a b^{2} d^{2} e + 6 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} - 3 \, {\left(b^{3} d e^{2} - 2 \, a b^{2} e^{3}\right)} x^{2} - 2 \, {\left(2 \, b^{3} d^{2} e - 3 \, a b^{2} d e^{2}\right)} x + 6 \, {\left(b^{3} d^{3} - 2 \, a b^{2} d^{2} e + a^{2} b d e^{2} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/2*(b^3*e^3*x^3 + 2*b^3*d^3 - 6*a*b^2*d^2*e + 6*a^2*b*d*e^2 - 2*a^3*e^3 - 3*(b^3*d*e^2 - 2*a*b^2*e^3)*x^2 - 2*(2*b^3*d^2*e - 3*a*b^2*d*e^2)*x + 6*(b^3*d^3 - 2*a*b^2*d^2*e + a^2*b*d*e^2 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x)*log(e*x + d))/(e^5*x + d*e^4)","A",0
1562,1,188,0,0.397693," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} e^{3} x^{3} + 4 \, b^{3} d e^{2} x^{2} - 5 \, b^{3} d^{3} + 9 \, a b^{2} d^{2} e - 3 \, a^{2} b d e^{2} - a^{3} e^{3} - 2 \, {\left(2 \, b^{3} d^{2} e - 6 \, a b^{2} d e^{2} + 3 \, a^{2} b e^{3}\right)} x - 6 \, {\left(b^{3} d^{3} - a b^{2} d^{2} e + {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(b^{3} d^{2} e - a b^{2} d e^{2}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"1/2*(2*b^3*e^3*x^3 + 4*b^3*d*e^2*x^2 - 5*b^3*d^3 + 9*a*b^2*d^2*e - 3*a^2*b*d*e^2 - a^3*e^3 - 2*(2*b^3*d^2*e - 6*a*b^2*d*e^2 + 3*a^2*b*e^3)*x - 6*(b^3*d^3 - a*b^2*d^2*e + (b^3*d*e^2 - a*b^2*e^3)*x^2 + 2*(b^3*d^2*e - a*b^2*d*e^2)*x)*log(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1563,1,177,0,0.406439," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{11 \, b^{3} d^{3} - 6 \, a b^{2} d^{2} e - 3 \, a^{2} b d e^{2} - 2 \, a^{3} e^{3} + 18 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 9 \, {\left(3 \, b^{3} d^{2} e - 2 \, a b^{2} d e^{2} - a^{2} b e^{3}\right)} x + 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, b^{3} d e^{2} x^{2} + 3 \, b^{3} d^{2} e x + b^{3} d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/6*(11*b^3*d^3 - 6*a*b^2*d^2*e - 3*a^2*b*d*e^2 - 2*a^3*e^3 + 18*(b^3*d*e^2 - a*b^2*e^3)*x^2 + 9*(3*b^3*d^2*e - 2*a*b^2*d*e^2 - a^2*b*e^3)*x + 6*(b^3*e^3*x^3 + 3*b^3*d*e^2*x^2 + 3*b^3*d^2*e*x + b^3*d^3)*log(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
1564,1,143,0,0.398162," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{4 \, b^{3} e^{3} x^{3} + b^{3} d^{3} + a b^{2} d^{2} e + 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} + 4 \, {\left(b^{3} d^{2} e + a b^{2} d e^{2} + a^{2} b e^{3}\right)} x}{4 \, {\left(e^{8} x^{4} + 4 \, d e^{7} x^{3} + 6 \, d^{2} e^{6} x^{2} + 4 \, d^{3} e^{5} x + d^{4} e^{4}\right)}}"," ",0,"-1/4*(4*b^3*e^3*x^3 + b^3*d^3 + a*b^2*d^2*e + a^2*b*d*e^2 + a^3*e^3 + 6*(b^3*d*e^2 + a*b^2*e^3)*x^2 + 4*(b^3*d^2*e + a*b^2*d*e^2 + a^2*b*e^3)*x)/(e^8*x^4 + 4*d*e^7*x^3 + 6*d^2*e^6*x^2 + 4*d^3*e^5*x + d^4*e^4)","B",0
1565,1,160,0,0.408451," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{10 \, b^{3} e^{3} x^{3} + b^{3} d^{3} + 2 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} + 4 \, a^{3} e^{3} + 10 \, {\left(b^{3} d e^{2} + 2 \, a b^{2} e^{3}\right)} x^{2} + 5 \, {\left(b^{3} d^{2} e + 2 \, a b^{2} d e^{2} + 3 \, a^{2} b e^{3}\right)} x}{20 \, {\left(e^{9} x^{5} + 5 \, d e^{8} x^{4} + 10 \, d^{2} e^{7} x^{3} + 10 \, d^{3} e^{6} x^{2} + 5 \, d^{4} e^{5} x + d^{5} e^{4}\right)}}"," ",0,"-1/20*(10*b^3*e^3*x^3 + b^3*d^3 + 2*a*b^2*d^2*e + 3*a^2*b*d*e^2 + 4*a^3*e^3 + 10*(b^3*d*e^2 + 2*a*b^2*e^3)*x^2 + 5*(b^3*d^2*e + 2*a*b^2*d*e^2 + 3*a^2*b*e^3)*x)/(e^9*x^5 + 5*d*e^8*x^4 + 10*d^2*e^7*x^3 + 10*d^3*e^6*x^2 + 5*d^4*e^5*x + d^5*e^4)","B",0
1566,1,171,0,0.403990," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{20 \, b^{3} e^{3} x^{3} + b^{3} d^{3} + 3 \, a b^{2} d^{2} e + 6 \, a^{2} b d e^{2} + 10 \, a^{3} e^{3} + 15 \, {\left(b^{3} d e^{2} + 3 \, a b^{2} e^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{2} e + 3 \, a b^{2} d e^{2} + 6 \, a^{2} b e^{3}\right)} x}{60 \, {\left(e^{10} x^{6} + 6 \, d e^{9} x^{5} + 15 \, d^{2} e^{8} x^{4} + 20 \, d^{3} e^{7} x^{3} + 15 \, d^{4} e^{6} x^{2} + 6 \, d^{5} e^{5} x + d^{6} e^{4}\right)}}"," ",0,"-1/60*(20*b^3*e^3*x^3 + b^3*d^3 + 3*a*b^2*d^2*e + 6*a^2*b*d*e^2 + 10*a^3*e^3 + 15*(b^3*d*e^2 + 3*a*b^2*e^3)*x^2 + 6*(b^3*d^2*e + 3*a*b^2*d*e^2 + 6*a^2*b*e^3)*x)/(e^10*x^6 + 6*d*e^9*x^5 + 15*d^2*e^8*x^4 + 20*d^3*e^7*x^3 + 15*d^4*e^6*x^2 + 6*d^5*e^5*x + d^6*e^4)","A",0
1567,1,182,0,0.404810," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{35 \, b^{3} e^{3} x^{3} + b^{3} d^{3} + 4 \, a b^{2} d^{2} e + 10 \, a^{2} b d e^{2} + 20 \, a^{3} e^{3} + 21 \, {\left(b^{3} d e^{2} + 4 \, a b^{2} e^{3}\right)} x^{2} + 7 \, {\left(b^{3} d^{2} e + 4 \, a b^{2} d e^{2} + 10 \, a^{2} b e^{3}\right)} x}{140 \, {\left(e^{11} x^{7} + 7 \, d e^{10} x^{6} + 21 \, d^{2} e^{9} x^{5} + 35 \, d^{3} e^{8} x^{4} + 35 \, d^{4} e^{7} x^{3} + 21 \, d^{5} e^{6} x^{2} + 7 \, d^{6} e^{5} x + d^{7} e^{4}\right)}}"," ",0,"-1/140*(35*b^3*e^3*x^3 + b^3*d^3 + 4*a*b^2*d^2*e + 10*a^2*b*d*e^2 + 20*a^3*e^3 + 21*(b^3*d*e^2 + 4*a*b^2*e^3)*x^2 + 7*(b^3*d^2*e + 4*a*b^2*d*e^2 + 10*a^2*b*e^3)*x)/(e^11*x^7 + 7*d*e^10*x^6 + 21*d^2*e^9*x^5 + 35*d^3*e^8*x^4 + 35*d^4*e^7*x^3 + 21*d^5*e^6*x^2 + 7*d^6*e^5*x + d^7*e^4)","A",0
1568,1,193,0,0.412637," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{56 \, b^{3} e^{3} x^{3} + b^{3} d^{3} + 5 \, a b^{2} d^{2} e + 15 \, a^{2} b d e^{2} + 35 \, a^{3} e^{3} + 28 \, {\left(b^{3} d e^{2} + 5 \, a b^{2} e^{3}\right)} x^{2} + 8 \, {\left(b^{3} d^{2} e + 5 \, a b^{2} d e^{2} + 15 \, a^{2} b e^{3}\right)} x}{280 \, {\left(e^{12} x^{8} + 8 \, d e^{11} x^{7} + 28 \, d^{2} e^{10} x^{6} + 56 \, d^{3} e^{9} x^{5} + 70 \, d^{4} e^{8} x^{4} + 56 \, d^{5} e^{7} x^{3} + 28 \, d^{6} e^{6} x^{2} + 8 \, d^{7} e^{5} x + d^{8} e^{4}\right)}}"," ",0,"-1/280*(56*b^3*e^3*x^3 + b^3*d^3 + 5*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 35*a^3*e^3 + 28*(b^3*d*e^2 + 5*a*b^2*e^3)*x^2 + 8*(b^3*d^2*e + 5*a*b^2*d*e^2 + 15*a^2*b*e^3)*x)/(e^12*x^8 + 8*d*e^11*x^7 + 28*d^2*e^10*x^6 + 56*d^3*e^9*x^5 + 70*d^4*e^8*x^4 + 56*d^5*e^7*x^3 + 28*d^6*e^6*x^2 + 8*d^7*e^5*x + d^8*e^4)","A",0
1569,1,427,0,0.405297," ","integrate((e*x+d)^5*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{11} \, b^{5} e^{5} x^{11} + a^{5} d^{5} x + \frac{1}{2} \, {\left(b^{5} d e^{4} + a b^{4} e^{5}\right)} x^{10} + \frac{5}{9} \, {\left(2 \, b^{5} d^{2} e^{3} + 5 \, a b^{4} d e^{4} + 2 \, a^{2} b^{3} e^{5}\right)} x^{9} + \frac{5}{4} \, {\left(b^{5} d^{3} e^{2} + 5 \, a b^{4} d^{2} e^{3} + 5 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{8} + \frac{5}{7} \, {\left(b^{5} d^{4} e + 10 \, a b^{4} d^{3} e^{2} + 20 \, a^{2} b^{3} d^{2} e^{3} + 10 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x^{7} + \frac{1}{6} \, {\left(b^{5} d^{5} + 25 \, a b^{4} d^{4} e + 100 \, a^{2} b^{3} d^{3} e^{2} + 100 \, a^{3} b^{2} d^{2} e^{3} + 25 \, a^{4} b d e^{4} + a^{5} e^{5}\right)} x^{6} + {\left(a b^{4} d^{5} + 10 \, a^{2} b^{3} d^{4} e + 20 \, a^{3} b^{2} d^{3} e^{2} + 10 \, a^{4} b d^{2} e^{3} + a^{5} d e^{4}\right)} x^{5} + \frac{5}{2} \, {\left(a^{2} b^{3} d^{5} + 5 \, a^{3} b^{2} d^{4} e + 5 \, a^{4} b d^{3} e^{2} + a^{5} d^{2} e^{3}\right)} x^{4} + \frac{5}{3} \, {\left(2 \, a^{3} b^{2} d^{5} + 5 \, a^{4} b d^{4} e + 2 \, a^{5} d^{3} e^{2}\right)} x^{3} + \frac{5}{2} \, {\left(a^{4} b d^{5} + a^{5} d^{4} e\right)} x^{2}"," ",0,"1/11*b^5*e^5*x^11 + a^5*d^5*x + 1/2*(b^5*d*e^4 + a*b^4*e^5)*x^10 + 5/9*(2*b^5*d^2*e^3 + 5*a*b^4*d*e^4 + 2*a^2*b^3*e^5)*x^9 + 5/4*(b^5*d^3*e^2 + 5*a*b^4*d^2*e^3 + 5*a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^8 + 5/7*(b^5*d^4*e + 10*a*b^4*d^3*e^2 + 20*a^2*b^3*d^2*e^3 + 10*a^3*b^2*d*e^4 + a^4*b*e^5)*x^7 + 1/6*(b^5*d^5 + 25*a*b^4*d^4*e + 100*a^2*b^3*d^3*e^2 + 100*a^3*b^2*d^2*e^3 + 25*a^4*b*d*e^4 + a^5*e^5)*x^6 + (a*b^4*d^5 + 10*a^2*b^3*d^4*e + 20*a^3*b^2*d^3*e^2 + 10*a^4*b*d^2*e^3 + a^5*d*e^4)*x^5 + 5/2*(a^2*b^3*d^5 + 5*a^3*b^2*d^4*e + 5*a^4*b*d^3*e^2 + a^5*d^2*e^3)*x^4 + 5/3*(2*a^3*b^2*d^5 + 5*a^4*b*d^4*e + 2*a^5*d^3*e^2)*x^3 + 5/2*(a^4*b*d^5 + a^5*d^4*e)*x^2","B",0
1570,1,360,0,0.406652," ","integrate((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{10} \, b^{5} e^{4} x^{10} + a^{5} d^{4} x + \frac{1}{9} \, {\left(4 \, b^{5} d e^{3} + 5 \, a b^{4} e^{4}\right)} x^{9} + \frac{1}{4} \, {\left(3 \, b^{5} d^{2} e^{2} + 10 \, a b^{4} d e^{3} + 5 \, a^{2} b^{3} e^{4}\right)} x^{8} + \frac{2}{7} \, {\left(2 \, b^{5} d^{3} e + 15 \, a b^{4} d^{2} e^{2} + 20 \, a^{2} b^{3} d e^{3} + 5 \, a^{3} b^{2} e^{4}\right)} x^{7} + \frac{1}{6} \, {\left(b^{5} d^{4} + 20 \, a b^{4} d^{3} e + 60 \, a^{2} b^{3} d^{2} e^{2} + 40 \, a^{3} b^{2} d e^{3} + 5 \, a^{4} b e^{4}\right)} x^{6} + \frac{1}{5} \, {\left(5 \, a b^{4} d^{4} + 40 \, a^{2} b^{3} d^{3} e + 60 \, a^{3} b^{2} d^{2} e^{2} + 20 \, a^{4} b d e^{3} + a^{5} e^{4}\right)} x^{5} + \frac{1}{2} \, {\left(5 \, a^{2} b^{3} d^{4} + 20 \, a^{3} b^{2} d^{3} e + 15 \, a^{4} b d^{2} e^{2} + 2 \, a^{5} d e^{3}\right)} x^{4} + \frac{2}{3} \, {\left(5 \, a^{3} b^{2} d^{4} + 10 \, a^{4} b d^{3} e + 3 \, a^{5} d^{2} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(5 \, a^{4} b d^{4} + 4 \, a^{5} d^{3} e\right)} x^{2}"," ",0,"1/10*b^5*e^4*x^10 + a^5*d^4*x + 1/9*(4*b^5*d*e^3 + 5*a*b^4*e^4)*x^9 + 1/4*(3*b^5*d^2*e^2 + 10*a*b^4*d*e^3 + 5*a^2*b^3*e^4)*x^8 + 2/7*(2*b^5*d^3*e + 15*a*b^4*d^2*e^2 + 20*a^2*b^3*d*e^3 + 5*a^3*b^2*e^4)*x^7 + 1/6*(b^5*d^4 + 20*a*b^4*d^3*e + 60*a^2*b^3*d^2*e^2 + 40*a^3*b^2*d*e^3 + 5*a^4*b*e^4)*x^6 + 1/5*(5*a*b^4*d^4 + 40*a^2*b^3*d^3*e + 60*a^3*b^2*d^2*e^2 + 20*a^4*b*d*e^3 + a^5*e^4)*x^5 + 1/2*(5*a^2*b^3*d^4 + 20*a^3*b^2*d^3*e + 15*a^4*b*d^2*e^2 + 2*a^5*d*e^3)*x^4 + 2/3*(5*a^3*b^2*d^4 + 10*a^4*b*d^3*e + 3*a^5*d^2*e^2)*x^3 + 1/2*(5*a^4*b*d^4 + 4*a^5*d^3*e)*x^2","B",0
1571,1,277,0,0.396985," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{9} \, b^{5} e^{3} x^{9} + a^{5} d^{3} x + \frac{1}{8} \, {\left(3 \, b^{5} d e^{2} + 5 \, a b^{4} e^{3}\right)} x^{8} + \frac{1}{7} \, {\left(3 \, b^{5} d^{2} e + 15 \, a b^{4} d e^{2} + 10 \, a^{2} b^{3} e^{3}\right)} x^{7} + \frac{1}{6} \, {\left(b^{5} d^{3} + 15 \, a b^{4} d^{2} e + 30 \, a^{2} b^{3} d e^{2} + 10 \, a^{3} b^{2} e^{3}\right)} x^{6} + {\left(a b^{4} d^{3} + 6 \, a^{2} b^{3} d^{2} e + 6 \, a^{3} b^{2} d e^{2} + a^{4} b e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(10 \, a^{2} b^{3} d^{3} + 30 \, a^{3} b^{2} d^{2} e + 15 \, a^{4} b d e^{2} + a^{5} e^{3}\right)} x^{4} + \frac{1}{3} \, {\left(10 \, a^{3} b^{2} d^{3} + 15 \, a^{4} b d^{2} e + 3 \, a^{5} d e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(5 \, a^{4} b d^{3} + 3 \, a^{5} d^{2} e\right)} x^{2}"," ",0,"1/9*b^5*e^3*x^9 + a^5*d^3*x + 1/8*(3*b^5*d*e^2 + 5*a*b^4*e^3)*x^8 + 1/7*(3*b^5*d^2*e + 15*a*b^4*d*e^2 + 10*a^2*b^3*e^3)*x^7 + 1/6*(b^5*d^3 + 15*a*b^4*d^2*e + 30*a^2*b^3*d*e^2 + 10*a^3*b^2*e^3)*x^6 + (a*b^4*d^3 + 6*a^2*b^3*d^2*e + 6*a^3*b^2*d*e^2 + a^4*b*e^3)*x^5 + 1/4*(10*a^2*b^3*d^3 + 30*a^3*b^2*d^2*e + 15*a^4*b*d*e^2 + a^5*e^3)*x^4 + 1/3*(10*a^3*b^2*d^3 + 15*a^4*b*d^2*e + 3*a^5*d*e^2)*x^3 + 1/2*(5*a^4*b*d^3 + 3*a^5*d^2*e)*x^2","B",0
1572,1,197,0,0.391517," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{8} \, b^{5} e^{2} x^{8} + a^{5} d^{2} x + \frac{1}{7} \, {\left(2 \, b^{5} d e + 5 \, a b^{4} e^{2}\right)} x^{7} + \frac{1}{6} \, {\left(b^{5} d^{2} + 10 \, a b^{4} d e + 10 \, a^{2} b^{3} e^{2}\right)} x^{6} + {\left(a b^{4} d^{2} + 4 \, a^{2} b^{3} d e + 2 \, a^{3} b^{2} e^{2}\right)} x^{5} + \frac{5}{4} \, {\left(2 \, a^{2} b^{3} d^{2} + 4 \, a^{3} b^{2} d e + a^{4} b e^{2}\right)} x^{4} + \frac{1}{3} \, {\left(10 \, a^{3} b^{2} d^{2} + 10 \, a^{4} b d e + a^{5} e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(5 \, a^{4} b d^{2} + 2 \, a^{5} d e\right)} x^{2}"," ",0,"1/8*b^5*e^2*x^8 + a^5*d^2*x + 1/7*(2*b^5*d*e + 5*a*b^4*e^2)*x^7 + 1/6*(b^5*d^2 + 10*a*b^4*d*e + 10*a^2*b^3*e^2)*x^6 + (a*b^4*d^2 + 4*a^2*b^3*d*e + 2*a^3*b^2*e^2)*x^5 + 5/4*(2*a^2*b^3*d^2 + 4*a^3*b^2*d*e + a^4*b*e^2)*x^4 + 1/3*(10*a^3*b^2*d^2 + 10*a^4*b*d*e + a^5*e^2)*x^3 + 1/2*(5*a^4*b*d^2 + 2*a^5*d*e)*x^2","B",0
1573,1,115,0,0.396359," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{7} \, b^{5} e x^{7} + a^{5} d x + \frac{1}{6} \, {\left(b^{5} d + 5 \, a b^{4} e\right)} x^{6} + {\left(a b^{4} d + 2 \, a^{2} b^{3} e\right)} x^{5} + \frac{5}{2} \, {\left(a^{2} b^{3} d + a^{3} b^{2} e\right)} x^{4} + \frac{5}{3} \, {\left(2 \, a^{3} b^{2} d + a^{4} b e\right)} x^{3} + \frac{1}{2} \, {\left(5 \, a^{4} b d + a^{5} e\right)} x^{2}"," ",0,"1/7*b^5*e*x^7 + a^5*d*x + 1/6*(b^5*d + 5*a*b^4*e)*x^6 + (a*b^4*d + 2*a^2*b^3*e)*x^5 + 5/2*(a^2*b^3*d + a^3*b^2*e)*x^4 + 5/3*(2*a^3*b^2*d + a^4*b*e)*x^3 + 1/2*(5*a^4*b*d + a^5*e)*x^2","A",0
1574,1,53,0,0.388459," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{1}{6} \, b^{5} x^{6} + a b^{4} x^{5} + \frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{10}{3} \, a^{3} b^{2} x^{3} + \frac{5}{2} \, a^{4} b x^{2} + a^{5} x"," ",0,"1/6*b^5*x^6 + a*b^4*x^5 + 5/2*a^2*b^3*x^4 + 10/3*a^3*b^2*x^3 + 5/2*a^4*b*x^2 + a^5*x","A",0
1575,1,259,0,0.394149," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\frac{12 \, b^{5} e^{5} x^{5} - 15 \, {\left(b^{5} d e^{4} - 5 \, a b^{4} e^{5}\right)} x^{4} + 20 \, {\left(b^{5} d^{2} e^{3} - 5 \, a b^{4} d e^{4} + 10 \, a^{2} b^{3} e^{5}\right)} x^{3} - 30 \, {\left(b^{5} d^{3} e^{2} - 5 \, a b^{4} d^{2} e^{3} + 10 \, a^{2} b^{3} d e^{4} - 10 \, a^{3} b^{2} e^{5}\right)} x^{2} + 60 \, {\left(b^{5} d^{4} e - 5 \, a b^{4} d^{3} e^{2} + 10 \, a^{2} b^{3} d^{2} e^{3} - 10 \, a^{3} b^{2} d e^{4} + 5 \, a^{4} b e^{5}\right)} x - 60 \, {\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)} \log\left(e x + d\right)}{60 \, e^{6}}"," ",0,"1/60*(12*b^5*e^5*x^5 - 15*(b^5*d*e^4 - 5*a*b^4*e^5)*x^4 + 20*(b^5*d^2*e^3 - 5*a*b^4*d*e^4 + 10*a^2*b^3*e^5)*x^3 - 30*(b^5*d^3*e^2 - 5*a*b^4*d^2*e^3 + 10*a^2*b^3*d*e^4 - 10*a^3*b^2*e^5)*x^2 + 60*(b^5*d^4*e - 5*a*b^4*d^3*e^2 + 10*a^2*b^3*d^2*e^3 - 10*a^3*b^2*d*e^4 + 5*a^4*b*e^5)*x - 60*(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)*log(e*x + d))/e^6","A",0
1576,1,373,0,0.395863," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{3 \, b^{5} e^{5} x^{5} + 12 \, b^{5} d^{5} - 60 \, a b^{4} d^{4} e + 120 \, a^{2} b^{3} d^{3} e^{2} - 120 \, a^{3} b^{2} d^{2} e^{3} + 60 \, a^{4} b d e^{4} - 12 \, a^{5} e^{5} - 5 \, {\left(b^{5} d e^{4} - 4 \, a b^{4} e^{5}\right)} x^{4} + 10 \, {\left(b^{5} d^{2} e^{3} - 4 \, a b^{4} d e^{4} + 6 \, a^{2} b^{3} e^{5}\right)} x^{3} - 30 \, {\left(b^{5} d^{3} e^{2} - 4 \, a b^{4} d^{2} e^{3} + 6 \, a^{2} b^{3} d e^{4} - 4 \, a^{3} b^{2} e^{5}\right)} x^{2} - 12 \, {\left(4 \, b^{5} d^{4} e - 15 \, a b^{4} d^{3} e^{2} + 20 \, a^{2} b^{3} d^{2} e^{3} - 10 \, a^{3} b^{2} d e^{4}\right)} x + 60 \, {\left(b^{5} d^{5} - 4 \, a b^{4} d^{4} e + 6 \, a^{2} b^{3} d^{3} e^{2} - 4 \, a^{3} b^{2} d^{2} e^{3} + a^{4} b d e^{4} + {\left(b^{5} d^{4} e - 4 \, a b^{4} d^{3} e^{2} + 6 \, a^{2} b^{3} d^{2} e^{3} - 4 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"1/12*(3*b^5*e^5*x^5 + 12*b^5*d^5 - 60*a*b^4*d^4*e + 120*a^2*b^3*d^3*e^2 - 120*a^3*b^2*d^2*e^3 + 60*a^4*b*d*e^4 - 12*a^5*e^5 - 5*(b^5*d*e^4 - 4*a*b^4*e^5)*x^4 + 10*(b^5*d^2*e^3 - 4*a*b^4*d*e^4 + 6*a^2*b^3*e^5)*x^3 - 30*(b^5*d^3*e^2 - 4*a*b^4*d^2*e^3 + 6*a^2*b^3*d*e^4 - 4*a^3*b^2*e^5)*x^2 - 12*(4*b^5*d^4*e - 15*a*b^4*d^3*e^2 + 20*a^2*b^3*d^2*e^3 - 10*a^3*b^2*d*e^4)*x + 60*(b^5*d^5 - 4*a*b^4*d^4*e + 6*a^2*b^3*d^3*e^2 - 4*a^3*b^2*d^2*e^3 + a^4*b*d*e^4 + (b^5*d^4*e - 4*a*b^4*d^3*e^2 + 6*a^2*b^3*d^2*e^3 - 4*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*log(e*x + d))/(e^7*x + d*e^6)","A",0
1577,1,416,0,0.404097," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, b^{5} e^{5} x^{5} - 27 \, b^{5} d^{5} + 105 \, a b^{4} d^{4} e - 150 \, a^{2} b^{3} d^{3} e^{2} + 90 \, a^{3} b^{2} d^{2} e^{3} - 15 \, a^{4} b d e^{4} - 3 \, a^{5} e^{5} - 5 \, {\left(b^{5} d e^{4} - 3 \, a b^{4} e^{5}\right)} x^{4} + 20 \, {\left(b^{5} d^{2} e^{3} - 3 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + 3 \, {\left(21 \, b^{5} d^{3} e^{2} - 55 \, a b^{4} d^{2} e^{3} + 40 \, a^{2} b^{3} d e^{4}\right)} x^{2} + 6 \, {\left(b^{5} d^{4} e + 5 \, a b^{4} d^{3} e^{2} - 20 \, a^{2} b^{3} d^{2} e^{3} + 20 \, a^{3} b^{2} d e^{4} - 5 \, a^{4} b e^{5}\right)} x - 60 \, {\left(b^{5} d^{5} - 3 \, a b^{4} d^{4} e + 3 \, a^{2} b^{3} d^{3} e^{2} - a^{3} b^{2} d^{2} e^{3} + {\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} + 2 \, {\left(b^{5} d^{4} e - 3 \, a b^{4} d^{3} e^{2} + 3 \, a^{2} b^{3} d^{2} e^{3} - a^{3} b^{2} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"1/6*(2*b^5*e^5*x^5 - 27*b^5*d^5 + 105*a*b^4*d^4*e - 150*a^2*b^3*d^3*e^2 + 90*a^3*b^2*d^2*e^3 - 15*a^4*b*d*e^4 - 3*a^5*e^5 - 5*(b^5*d*e^4 - 3*a*b^4*e^5)*x^4 + 20*(b^5*d^2*e^3 - 3*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + 3*(21*b^5*d^3*e^2 - 55*a*b^4*d^2*e^3 + 40*a^2*b^3*d*e^4)*x^2 + 6*(b^5*d^4*e + 5*a*b^4*d^3*e^2 - 20*a^2*b^3*d^2*e^3 + 20*a^3*b^2*d*e^4 - 5*a^4*b*e^5)*x - 60*(b^5*d^5 - 3*a*b^4*d^4*e + 3*a^2*b^3*d^3*e^2 - a^3*b^2*d^2*e^3 + (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 + 2*(b^5*d^4*e - 3*a*b^4*d^3*e^2 + 3*a^2*b^3*d^2*e^3 - a^3*b^2*d*e^4)*x)*log(e*x + d))/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","A",0
1578,1,425,0,0.403813," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, b^{5} e^{5} x^{5} + 47 \, b^{5} d^{5} - 130 \, a b^{4} d^{4} e + 110 \, a^{2} b^{3} d^{3} e^{2} - 20 \, a^{3} b^{2} d^{2} e^{3} - 5 \, a^{4} b d e^{4} - 2 \, a^{5} e^{5} - 15 \, {\left(b^{5} d e^{4} - 2 \, a b^{4} e^{5}\right)} x^{4} - 9 \, {\left(7 \, b^{5} d^{2} e^{3} - 10 \, a b^{4} d e^{4}\right)} x^{3} - 3 \, {\left(3 \, b^{5} d^{3} e^{2} + 30 \, a b^{4} d^{2} e^{3} - 60 \, a^{2} b^{3} d e^{4} + 20 \, a^{3} b^{2} e^{5}\right)} x^{2} + 3 \, {\left(27 \, b^{5} d^{4} e - 90 \, a b^{4} d^{3} e^{2} + 90 \, a^{2} b^{3} d^{2} e^{3} - 20 \, a^{3} b^{2} d e^{4} - 5 \, a^{4} b e^{5}\right)} x + 60 \, {\left(b^{5} d^{5} - 2 \, a b^{4} d^{4} e + a^{2} b^{3} d^{3} e^{2} + {\left(b^{5} d^{2} e^{3} - 2 \, a b^{4} d e^{4} + a^{2} b^{3} e^{5}\right)} x^{3} + 3 \, {\left(b^{5} d^{3} e^{2} - 2 \, a b^{4} d^{2} e^{3} + a^{2} b^{3} d e^{4}\right)} x^{2} + 3 \, {\left(b^{5} d^{4} e - 2 \, a b^{4} d^{3} e^{2} + a^{2} b^{3} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"1/6*(3*b^5*e^5*x^5 + 47*b^5*d^5 - 130*a*b^4*d^4*e + 110*a^2*b^3*d^3*e^2 - 20*a^3*b^2*d^2*e^3 - 5*a^4*b*d*e^4 - 2*a^5*e^5 - 15*(b^5*d*e^4 - 2*a*b^4*e^5)*x^4 - 9*(7*b^5*d^2*e^3 - 10*a*b^4*d*e^4)*x^3 - 3*(3*b^5*d^3*e^2 + 30*a*b^4*d^2*e^3 - 60*a^2*b^3*d*e^4 + 20*a^3*b^2*e^5)*x^2 + 3*(27*b^5*d^4*e - 90*a*b^4*d^3*e^2 + 90*a^2*b^3*d^2*e^3 - 20*a^3*b^2*d*e^4 - 5*a^4*b*e^5)*x + 60*(b^5*d^5 - 2*a*b^4*d^4*e + a^2*b^3*d^3*e^2 + (b^5*d^2*e^3 - 2*a*b^4*d*e^4 + a^2*b^3*e^5)*x^3 + 3*(b^5*d^3*e^2 - 2*a*b^4*d^2*e^3 + a^2*b^3*d*e^4)*x^2 + 3*(b^5*d^4*e - 2*a*b^4*d^3*e^2 + a^2*b^3*d^2*e^3)*x)*log(e*x + d))/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","A",0
1579,1,412,0,0.392906," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{12 \, b^{5} e^{5} x^{5} + 48 \, b^{5} d e^{4} x^{4} - 77 \, b^{5} d^{5} + 125 \, a b^{4} d^{4} e - 30 \, a^{2} b^{3} d^{3} e^{2} - 10 \, a^{3} b^{2} d^{2} e^{3} - 5 \, a^{4} b d e^{4} - 3 \, a^{5} e^{5} - 24 \, {\left(2 \, b^{5} d^{2} e^{3} - 10 \, a b^{4} d e^{4} + 5 \, a^{2} b^{3} e^{5}\right)} x^{3} - 12 \, {\left(21 \, b^{5} d^{3} e^{2} - 45 \, a b^{4} d^{2} e^{3} + 15 \, a^{2} b^{3} d e^{4} + 5 \, a^{3} b^{2} e^{5}\right)} x^{2} - 4 \, {\left(62 \, b^{5} d^{4} e - 110 \, a b^{4} d^{3} e^{2} + 30 \, a^{2} b^{3} d^{2} e^{3} + 10 \, a^{3} b^{2} d e^{4} + 5 \, a^{4} b e^{5}\right)} x - 60 \, {\left(b^{5} d^{5} - a b^{4} d^{4} e + {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 4 \, {\left(b^{5} d^{2} e^{3} - a b^{4} d e^{4}\right)} x^{3} + 6 \, {\left(b^{5} d^{3} e^{2} - a b^{4} d^{2} e^{3}\right)} x^{2} + 4 \, {\left(b^{5} d^{4} e - a b^{4} d^{3} e^{2}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{10} x^{4} + 4 \, d e^{9} x^{3} + 6 \, d^{2} e^{8} x^{2} + 4 \, d^{3} e^{7} x + d^{4} e^{6}\right)}}"," ",0,"1/12*(12*b^5*e^5*x^5 + 48*b^5*d*e^4*x^4 - 77*b^5*d^5 + 125*a*b^4*d^4*e - 30*a^2*b^3*d^3*e^2 - 10*a^3*b^2*d^2*e^3 - 5*a^4*b*d*e^4 - 3*a^5*e^5 - 24*(2*b^5*d^2*e^3 - 10*a*b^4*d*e^4 + 5*a^2*b^3*e^5)*x^3 - 12*(21*b^5*d^3*e^2 - 45*a*b^4*d^2*e^3 + 15*a^2*b^3*d*e^4 + 5*a^3*b^2*e^5)*x^2 - 4*(62*b^5*d^4*e - 110*a*b^4*d^3*e^2 + 30*a^2*b^3*d^2*e^3 + 10*a^3*b^2*d*e^4 + 5*a^4*b*e^5)*x - 60*(b^5*d^5 - a*b^4*d^4*e + (b^5*d*e^4 - a*b^4*e^5)*x^4 + 4*(b^5*d^2*e^3 - a*b^4*d*e^4)*x^3 + 6*(b^5*d^3*e^2 - a*b^4*d^2*e^3)*x^2 + 4*(b^5*d^4*e - a*b^4*d^3*e^2)*x)*log(e*x + d))/(e^10*x^4 + 4*d*e^9*x^3 + 6*d^2*e^8*x^2 + 4*d^3*e^7*x + d^4*e^6)","A",0
1580,1,373,0,0.401715," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^6,x, algorithm=""fricas"")","\frac{137 \, b^{5} d^{5} - 60 \, a b^{4} d^{4} e - 30 \, a^{2} b^{3} d^{3} e^{2} - 20 \, a^{3} b^{2} d^{2} e^{3} - 15 \, a^{4} b d e^{4} - 12 \, a^{5} e^{5} + 300 \, {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 300 \, {\left(3 \, b^{5} d^{2} e^{3} - 2 \, a b^{4} d e^{4} - a^{2} b^{3} e^{5}\right)} x^{3} + 100 \, {\left(11 \, b^{5} d^{3} e^{2} - 6 \, a b^{4} d^{2} e^{3} - 3 \, a^{2} b^{3} d e^{4} - 2 \, a^{3} b^{2} e^{5}\right)} x^{2} + 25 \, {\left(25 \, b^{5} d^{4} e - 12 \, a b^{4} d^{3} e^{2} - 6 \, a^{2} b^{3} d^{2} e^{3} - 4 \, a^{3} b^{2} d e^{4} - 3 \, a^{4} b e^{5}\right)} x + 60 \, {\left(b^{5} e^{5} x^{5} + 5 \, b^{5} d e^{4} x^{4} + 10 \, b^{5} d^{2} e^{3} x^{3} + 10 \, b^{5} d^{3} e^{2} x^{2} + 5 \, b^{5} d^{4} e x + b^{5} d^{5}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{11} x^{5} + 5 \, d e^{10} x^{4} + 10 \, d^{2} e^{9} x^{3} + 10 \, d^{3} e^{8} x^{2} + 5 \, d^{4} e^{7} x + d^{5} e^{6}\right)}}"," ",0,"1/60*(137*b^5*d^5 - 60*a*b^4*d^4*e - 30*a^2*b^3*d^3*e^2 - 20*a^3*b^2*d^2*e^3 - 15*a^4*b*d*e^4 - 12*a^5*e^5 + 300*(b^5*d*e^4 - a*b^4*e^5)*x^4 + 300*(3*b^5*d^2*e^3 - 2*a*b^4*d*e^4 - a^2*b^3*e^5)*x^3 + 100*(11*b^5*d^3*e^2 - 6*a*b^4*d^2*e^3 - 3*a^2*b^3*d*e^4 - 2*a^3*b^2*e^5)*x^2 + 25*(25*b^5*d^4*e - 12*a*b^4*d^3*e^2 - 6*a^2*b^3*d^2*e^3 - 4*a^3*b^2*d*e^4 - 3*a^4*b*e^5)*x + 60*(b^5*e^5*x^5 + 5*b^5*d*e^4*x^4 + 10*b^5*d^2*e^3*x^3 + 10*b^5*d^3*e^2*x^2 + 5*b^5*d^4*e*x + b^5*d^5)*log(e*x + d))/(e^11*x^5 + 5*d*e^10*x^4 + 10*d^2*e^9*x^3 + 10*d^3*e^8*x^2 + 5*d^4*e^7*x + d^5*e^6)","A",0
1581,1,300,0,0.403238," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{6 \, b^{5} e^{5} x^{5} + b^{5} d^{5} + a b^{4} d^{4} e + a^{2} b^{3} d^{3} e^{2} + a^{3} b^{2} d^{2} e^{3} + a^{4} b d e^{4} + a^{5} e^{5} + 15 \, {\left(b^{5} d e^{4} + a b^{4} e^{5}\right)} x^{4} + 20 \, {\left(b^{5} d^{2} e^{3} + a b^{4} d e^{4} + a^{2} b^{3} e^{5}\right)} x^{3} + 15 \, {\left(b^{5} d^{3} e^{2} + a b^{4} d^{2} e^{3} + a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{2} + 6 \, {\left(b^{5} d^{4} e + a b^{4} d^{3} e^{2} + a^{2} b^{3} d^{2} e^{3} + a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x}{6 \, {\left(e^{12} x^{6} + 6 \, d e^{11} x^{5} + 15 \, d^{2} e^{10} x^{4} + 20 \, d^{3} e^{9} x^{3} + 15 \, d^{4} e^{8} x^{2} + 6 \, d^{5} e^{7} x + d^{6} e^{6}\right)}}"," ",0,"-1/6*(6*b^5*e^5*x^5 + b^5*d^5 + a*b^4*d^4*e + a^2*b^3*d^3*e^2 + a^3*b^2*d^2*e^3 + a^4*b*d*e^4 + a^5*e^5 + 15*(b^5*d*e^4 + a*b^4*e^5)*x^4 + 20*(b^5*d^2*e^3 + a*b^4*d*e^4 + a^2*b^3*e^5)*x^3 + 15*(b^5*d^3*e^2 + a*b^4*d^2*e^3 + a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^2 + 6*(b^5*d^4*e + a*b^4*d^3*e^2 + a^2*b^3*d^2*e^3 + a^3*b^2*d*e^4 + a^4*b*e^5)*x)/(e^12*x^6 + 6*d*e^11*x^5 + 15*d^2*e^10*x^4 + 20*d^3*e^9*x^3 + 15*d^4*e^8*x^2 + 6*d^5*e^7*x + d^6*e^6)","B",0
1582,1,326,0,0.405096," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{21 \, b^{5} e^{5} x^{5} + b^{5} d^{5} + 2 \, a b^{4} d^{4} e + 3 \, a^{2} b^{3} d^{3} e^{2} + 4 \, a^{3} b^{2} d^{2} e^{3} + 5 \, a^{4} b d e^{4} + 6 \, a^{5} e^{5} + 35 \, {\left(b^{5} d e^{4} + 2 \, a b^{4} e^{5}\right)} x^{4} + 35 \, {\left(b^{5} d^{2} e^{3} + 2 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + 21 \, {\left(b^{5} d^{3} e^{2} + 2 \, a b^{4} d^{2} e^{3} + 3 \, a^{2} b^{3} d e^{4} + 4 \, a^{3} b^{2} e^{5}\right)} x^{2} + 7 \, {\left(b^{5} d^{4} e + 2 \, a b^{4} d^{3} e^{2} + 3 \, a^{2} b^{3} d^{2} e^{3} + 4 \, a^{3} b^{2} d e^{4} + 5 \, a^{4} b e^{5}\right)} x}{42 \, {\left(e^{13} x^{7} + 7 \, d e^{12} x^{6} + 21 \, d^{2} e^{11} x^{5} + 35 \, d^{3} e^{10} x^{4} + 35 \, d^{4} e^{9} x^{3} + 21 \, d^{5} e^{8} x^{2} + 7 \, d^{6} e^{7} x + d^{7} e^{6}\right)}}"," ",0,"-1/42*(21*b^5*e^5*x^5 + b^5*d^5 + 2*a*b^4*d^4*e + 3*a^2*b^3*d^3*e^2 + 4*a^3*b^2*d^2*e^3 + 5*a^4*b*d*e^4 + 6*a^5*e^5 + 35*(b^5*d*e^4 + 2*a*b^4*e^5)*x^4 + 35*(b^5*d^2*e^3 + 2*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + 21*(b^5*d^3*e^2 + 2*a*b^4*d^2*e^3 + 3*a^2*b^3*d*e^4 + 4*a^3*b^2*e^5)*x^2 + 7*(b^5*d^4*e + 2*a*b^4*d^3*e^2 + 3*a^2*b^3*d^2*e^3 + 4*a^3*b^2*d*e^4 + 5*a^4*b*e^5)*x)/(e^13*x^7 + 7*d*e^12*x^6 + 21*d^2*e^11*x^5 + 35*d^3*e^10*x^4 + 35*d^4*e^9*x^3 + 21*d^5*e^8*x^2 + 7*d^6*e^7*x + d^7*e^6)","B",0
1583,1,337,0,0.396025," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{56 \, b^{5} e^{5} x^{5} + b^{5} d^{5} + 3 \, a b^{4} d^{4} e + 6 \, a^{2} b^{3} d^{3} e^{2} + 10 \, a^{3} b^{2} d^{2} e^{3} + 15 \, a^{4} b d e^{4} + 21 \, a^{5} e^{5} + 70 \, {\left(b^{5} d e^{4} + 3 \, a b^{4} e^{5}\right)} x^{4} + 56 \, {\left(b^{5} d^{2} e^{3} + 3 \, a b^{4} d e^{4} + 6 \, a^{2} b^{3} e^{5}\right)} x^{3} + 28 \, {\left(b^{5} d^{3} e^{2} + 3 \, a b^{4} d^{2} e^{3} + 6 \, a^{2} b^{3} d e^{4} + 10 \, a^{3} b^{2} e^{5}\right)} x^{2} + 8 \, {\left(b^{5} d^{4} e + 3 \, a b^{4} d^{3} e^{2} + 6 \, a^{2} b^{3} d^{2} e^{3} + 10 \, a^{3} b^{2} d e^{4} + 15 \, a^{4} b e^{5}\right)} x}{168 \, {\left(e^{14} x^{8} + 8 \, d e^{13} x^{7} + 28 \, d^{2} e^{12} x^{6} + 56 \, d^{3} e^{11} x^{5} + 70 \, d^{4} e^{10} x^{4} + 56 \, d^{5} e^{9} x^{3} + 28 \, d^{6} e^{8} x^{2} + 8 \, d^{7} e^{7} x + d^{8} e^{6}\right)}}"," ",0,"-1/168*(56*b^5*e^5*x^5 + b^5*d^5 + 3*a*b^4*d^4*e + 6*a^2*b^3*d^3*e^2 + 10*a^3*b^2*d^2*e^3 + 15*a^4*b*d*e^4 + 21*a^5*e^5 + 70*(b^5*d*e^4 + 3*a*b^4*e^5)*x^4 + 56*(b^5*d^2*e^3 + 3*a*b^4*d*e^4 + 6*a^2*b^3*e^5)*x^3 + 28*(b^5*d^3*e^2 + 3*a*b^4*d^2*e^3 + 6*a^2*b^3*d*e^4 + 10*a^3*b^2*e^5)*x^2 + 8*(b^5*d^4*e + 3*a*b^4*d^3*e^2 + 6*a^2*b^3*d^2*e^3 + 10*a^3*b^2*d*e^4 + 15*a^4*b*e^5)*x)/(e^14*x^8 + 8*d*e^13*x^7 + 28*d^2*e^12*x^6 + 56*d^3*e^11*x^5 + 70*d^4*e^10*x^4 + 56*d^5*e^9*x^3 + 28*d^6*e^8*x^2 + 8*d^7*e^7*x + d^8*e^6)","B",0
1584,1,348,0,0.398118," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{126 \, b^{5} e^{5} x^{5} + b^{5} d^{5} + 4 \, a b^{4} d^{4} e + 10 \, a^{2} b^{3} d^{3} e^{2} + 20 \, a^{3} b^{2} d^{2} e^{3} + 35 \, a^{4} b d e^{4} + 56 \, a^{5} e^{5} + 126 \, {\left(b^{5} d e^{4} + 4 \, a b^{4} e^{5}\right)} x^{4} + 84 \, {\left(b^{5} d^{2} e^{3} + 4 \, a b^{4} d e^{4} + 10 \, a^{2} b^{3} e^{5}\right)} x^{3} + 36 \, {\left(b^{5} d^{3} e^{2} + 4 \, a b^{4} d^{2} e^{3} + 10 \, a^{2} b^{3} d e^{4} + 20 \, a^{3} b^{2} e^{5}\right)} x^{2} + 9 \, {\left(b^{5} d^{4} e + 4 \, a b^{4} d^{3} e^{2} + 10 \, a^{2} b^{3} d^{2} e^{3} + 20 \, a^{3} b^{2} d e^{4} + 35 \, a^{4} b e^{5}\right)} x}{504 \, {\left(e^{15} x^{9} + 9 \, d e^{14} x^{8} + 36 \, d^{2} e^{13} x^{7} + 84 \, d^{3} e^{12} x^{6} + 126 \, d^{4} e^{11} x^{5} + 126 \, d^{5} e^{10} x^{4} + 84 \, d^{6} e^{9} x^{3} + 36 \, d^{7} e^{8} x^{2} + 9 \, d^{8} e^{7} x + d^{9} e^{6}\right)}}"," ",0,"-1/504*(126*b^5*e^5*x^5 + b^5*d^5 + 4*a*b^4*d^4*e + 10*a^2*b^3*d^3*e^2 + 20*a^3*b^2*d^2*e^3 + 35*a^4*b*d*e^4 + 56*a^5*e^5 + 126*(b^5*d*e^4 + 4*a*b^4*e^5)*x^4 + 84*(b^5*d^2*e^3 + 4*a*b^4*d*e^4 + 10*a^2*b^3*e^5)*x^3 + 36*(b^5*d^3*e^2 + 4*a*b^4*d^2*e^3 + 10*a^2*b^3*d*e^4 + 20*a^3*b^2*e^5)*x^2 + 9*(b^5*d^4*e + 4*a*b^4*d^3*e^2 + 10*a^2*b^3*d^2*e^3 + 20*a^3*b^2*d*e^4 + 35*a^4*b*e^5)*x)/(e^15*x^9 + 9*d*e^14*x^8 + 36*d^2*e^13*x^7 + 84*d^3*e^12*x^6 + 126*d^4*e^11*x^5 + 126*d^5*e^10*x^4 + 84*d^6*e^9*x^3 + 36*d^7*e^8*x^2 + 9*d^8*e^7*x + d^9*e^6)","B",0
1585,1,359,0,0.404791," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{252 \, b^{5} e^{5} x^{5} + b^{5} d^{5} + 5 \, a b^{4} d^{4} e + 15 \, a^{2} b^{3} d^{3} e^{2} + 35 \, a^{3} b^{2} d^{2} e^{3} + 70 \, a^{4} b d e^{4} + 126 \, a^{5} e^{5} + 210 \, {\left(b^{5} d e^{4} + 5 \, a b^{4} e^{5}\right)} x^{4} + 120 \, {\left(b^{5} d^{2} e^{3} + 5 \, a b^{4} d e^{4} + 15 \, a^{2} b^{3} e^{5}\right)} x^{3} + 45 \, {\left(b^{5} d^{3} e^{2} + 5 \, a b^{4} d^{2} e^{3} + 15 \, a^{2} b^{3} d e^{4} + 35 \, a^{3} b^{2} e^{5}\right)} x^{2} + 10 \, {\left(b^{5} d^{4} e + 5 \, a b^{4} d^{3} e^{2} + 15 \, a^{2} b^{3} d^{2} e^{3} + 35 \, a^{3} b^{2} d e^{4} + 70 \, a^{4} b e^{5}\right)} x}{1260 \, {\left(e^{16} x^{10} + 10 \, d e^{15} x^{9} + 45 \, d^{2} e^{14} x^{8} + 120 \, d^{3} e^{13} x^{7} + 210 \, d^{4} e^{12} x^{6} + 252 \, d^{5} e^{11} x^{5} + 210 \, d^{6} e^{10} x^{4} + 120 \, d^{7} e^{9} x^{3} + 45 \, d^{8} e^{8} x^{2} + 10 \, d^{9} e^{7} x + d^{10} e^{6}\right)}}"," ",0,"-1/1260*(252*b^5*e^5*x^5 + b^5*d^5 + 5*a*b^4*d^4*e + 15*a^2*b^3*d^3*e^2 + 35*a^3*b^2*d^2*e^3 + 70*a^4*b*d*e^4 + 126*a^5*e^5 + 210*(b^5*d*e^4 + 5*a*b^4*e^5)*x^4 + 120*(b^5*d^2*e^3 + 5*a*b^4*d*e^4 + 15*a^2*b^3*e^5)*x^3 + 45*(b^5*d^3*e^2 + 5*a*b^4*d^2*e^3 + 15*a^2*b^3*d*e^4 + 35*a^3*b^2*e^5)*x^2 + 10*(b^5*d^4*e + 5*a*b^4*d^3*e^2 + 15*a^2*b^3*d^2*e^3 + 35*a^3*b^2*d*e^4 + 70*a^4*b*e^5)*x)/(e^16*x^10 + 10*d*e^15*x^9 + 45*d^2*e^14*x^8 + 120*d^3*e^13*x^7 + 210*d^4*e^12*x^6 + 252*d^5*e^11*x^5 + 210*d^6*e^10*x^4 + 120*d^7*e^9*x^3 + 45*d^8*e^8*x^2 + 10*d^9*e^7*x + d^10*e^6)","A",0
1586,1,370,0,0.410936," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^12,x, algorithm=""fricas"")","-\frac{462 \, b^{5} e^{5} x^{5} + b^{5} d^{5} + 6 \, a b^{4} d^{4} e + 21 \, a^{2} b^{3} d^{3} e^{2} + 56 \, a^{3} b^{2} d^{2} e^{3} + 126 \, a^{4} b d e^{4} + 252 \, a^{5} e^{5} + 330 \, {\left(b^{5} d e^{4} + 6 \, a b^{4} e^{5}\right)} x^{4} + 165 \, {\left(b^{5} d^{2} e^{3} + 6 \, a b^{4} d e^{4} + 21 \, a^{2} b^{3} e^{5}\right)} x^{3} + 55 \, {\left(b^{5} d^{3} e^{2} + 6 \, a b^{4} d^{2} e^{3} + 21 \, a^{2} b^{3} d e^{4} + 56 \, a^{3} b^{2} e^{5}\right)} x^{2} + 11 \, {\left(b^{5} d^{4} e + 6 \, a b^{4} d^{3} e^{2} + 21 \, a^{2} b^{3} d^{2} e^{3} + 56 \, a^{3} b^{2} d e^{4} + 126 \, a^{4} b e^{5}\right)} x}{2772 \, {\left(e^{17} x^{11} + 11 \, d e^{16} x^{10} + 55 \, d^{2} e^{15} x^{9} + 165 \, d^{3} e^{14} x^{8} + 330 \, d^{4} e^{13} x^{7} + 462 \, d^{5} e^{12} x^{6} + 462 \, d^{6} e^{11} x^{5} + 330 \, d^{7} e^{10} x^{4} + 165 \, d^{8} e^{9} x^{3} + 55 \, d^{9} e^{8} x^{2} + 11 \, d^{10} e^{7} x + d^{11} e^{6}\right)}}"," ",0,"-1/2772*(462*b^5*e^5*x^5 + b^5*d^5 + 6*a*b^4*d^4*e + 21*a^2*b^3*d^3*e^2 + 56*a^3*b^2*d^2*e^3 + 126*a^4*b*d*e^4 + 252*a^5*e^5 + 330*(b^5*d*e^4 + 6*a*b^4*e^5)*x^4 + 165*(b^5*d^2*e^3 + 6*a*b^4*d*e^4 + 21*a^2*b^3*e^5)*x^3 + 55*(b^5*d^3*e^2 + 6*a*b^4*d^2*e^3 + 21*a^2*b^3*d*e^4 + 56*a^3*b^2*e^5)*x^2 + 11*(b^5*d^4*e + 6*a*b^4*d^3*e^2 + 21*a^2*b^3*d^2*e^3 + 56*a^3*b^2*d*e^4 + 126*a^4*b*e^5)*x)/(e^17*x^11 + 11*d*e^16*x^10 + 55*d^2*e^15*x^9 + 165*d^3*e^14*x^8 + 330*d^4*e^13*x^7 + 462*d^5*e^12*x^6 + 462*d^6*e^11*x^5 + 330*d^7*e^10*x^4 + 165*d^8*e^9*x^3 + 55*d^9*e^8*x^2 + 11*d^10*e^7*x + d^11*e^6)","A",0
1587,1,181,0,0.397320," ","integrate((e*x+d)^4/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{3 \, b^{4} e^{4} x^{4} + 4 \, {\left(4 \, b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(6 \, b^{4} d^{2} e^{2} - 4 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 12 \, {\left(4 \, b^{4} d^{3} e - 6 \, a b^{3} d^{2} e^{2} + 4 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x + 12 \, {\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)} \log\left(b x + a\right)}{12 \, b^{5}}"," ",0,"1/12*(3*b^4*e^4*x^4 + 4*(4*b^4*d*e^3 - a*b^3*e^4)*x^3 + 6*(6*b^4*d^2*e^2 - 4*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 12*(4*b^4*d^3*e - 6*a*b^3*d^2*e^2 + 4*a^2*b^2*d*e^3 - a^3*b*e^4)*x + 12*(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)*log(b*x + a))/b^5","A",0
1588,1,116,0,0.402677," ","integrate((e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, b^{3} e^{3} x^{3} + 3 \, {\left(3 \, b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 6 \, {\left(3 \, b^{3} d^{2} e - 3 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x + 6 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*b^3*e^3*x^3 + 3*(3*b^3*d*e^2 - a*b^2*e^3)*x^2 + 6*(3*b^3*d^2*e - 3*a*b^2*d*e^2 + a^2*b*e^3)*x + 6*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*log(b*x + a))/b^4","A",0
1589,1,63,0,0.402300," ","integrate((e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b^{2} e^{2} x^{2} + 2 \, {\left(2 \, b^{2} d e - a b e^{2}\right)} x + 2 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(b^2*e^2*x^2 + 2*(2*b^2*d*e - a*b*e^2)*x + 2*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*log(b*x + a))/b^3","A",0
1590,1,24,0,0.402521," ","integrate((e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b e x + {\left(b d - a e\right)} \log\left(b x + a\right)}{b^{2}}"," ",0,"(b*e*x + (b*d - a*e)*log(b*x + a))/b^2","A",0
1591,1,10,0,0.380560," ","integrate(1/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(b x + a\right)}{b}"," ",0,"log(b*x + a)/b","A",0
1592,1,26,0,0.400862," ","integrate(1/(e*x+d)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(b x + a\right) - \log\left(e x + d\right)}{b d - a e}"," ",0,"(log(b*x + a) - log(e*x + d))/(b*d - a*e)","A",0
1593,1,92,0,0.407432," ","integrate(1/(e*x+d)^2/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{b d - a e + {\left(b e x + b d\right)} \log\left(b x + a\right) - {\left(b e x + b d\right)} \log\left(e x + d\right)}{b^{2} d^{3} - 2 \, a b d^{2} e + a^{2} d e^{2} + {\left(b^{2} d^{2} e - 2 \, a b d e^{2} + a^{2} e^{3}\right)} x}"," ",0,"(b*d - a*e + (b*e*x + b*d)*log(b*x + a) - (b*e*x + b*d)*log(e*x + d))/(b^2*d^3 - 2*a*b*d^2*e + a^2*d*e^2 + (b^2*d^2*e - 2*a*b*d*e^2 + a^2*e^3)*x)","A",0
1594,1,242,0,0.399290," ","integrate(1/(e*x+d)^3/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\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 + 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, b^{2} d e x + b^{2} d^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, b^{2} d e x + b^{2} d^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(b^{3} d^{5} - 3 \, a b^{2} d^{4} e + 3 \, a^{2} b d^{3} e^{2} - a^{3} d^{2} e^{3} + {\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)} x^{2} + 2 \, {\left(b^{3} d^{4} e - 3 \, a b^{2} d^{3} e^{2} + 3 \, a^{2} b d^{2} e^{3} - a^{3} d e^{4}\right)} x\right)}}"," ",0,"1/2*(3*b^2*d^2 - 4*a*b*d*e + a^2*e^2 + 2*(b^2*d*e - a*b*e^2)*x + 2*(b^2*e^2*x^2 + 2*b^2*d*e*x + b^2*d^2)*log(b*x + a) - 2*(b^2*e^2*x^2 + 2*b^2*d*e*x + b^2*d^2)*log(e*x + d))/(b^3*d^5 - 3*a*b^2*d^4*e + 3*a^2*b*d^3*e^2 - a^3*d^2*e^3 + (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)*x^2 + 2*(b^3*d^4*e - 3*a*b^2*d^3*e^2 + 3*a^2*b*d^2*e^3 - a^3*d*e^4)*x)","A",0
1595,1,425,0,0.426900," ","integrate(1/(e*x+d)^4/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\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 + 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, b^{3} d e^{2} x^{2} + 3 \, b^{3} d^{2} e x + b^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(b^{3} e^{3} x^{3} + 3 \, b^{3} d e^{2} x^{2} + 3 \, b^{3} d^{2} e x + b^{3} d^{3}\right)} \log\left(e x + d\right)}{6 \, {\left(b^{4} d^{7} - 4 \, a b^{3} d^{6} e + 6 \, a^{2} b^{2} d^{5} e^{2} - 4 \, a^{3} b d^{4} e^{3} + a^{4} d^{3} e^{4} + {\left(b^{4} d^{4} e^{3} - 4 \, a b^{3} d^{3} e^{4} + 6 \, a^{2} b^{2} d^{2} e^{5} - 4 \, a^{3} b d e^{6} + a^{4} e^{7}\right)} x^{3} + 3 \, {\left(b^{4} d^{5} e^{2} - 4 \, a b^{3} d^{4} e^{3} + 6 \, a^{2} b^{2} d^{3} e^{4} - 4 \, a^{3} b d^{2} e^{5} + a^{4} d e^{6}\right)} x^{2} + 3 \, {\left(b^{4} d^{6} e - 4 \, a b^{3} d^{5} e^{2} + 6 \, a^{2} b^{2} d^{4} e^{3} - 4 \, a^{3} b d^{3} e^{4} + a^{4} d^{2} e^{5}\right)} x\right)}}"," ",0,"1/6*(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 + 6*(b^3*e^3*x^3 + 3*b^3*d*e^2*x^2 + 3*b^3*d^2*e*x + b^3*d^3)*log(b*x + a) - 6*(b^3*e^3*x^3 + 3*b^3*d*e^2*x^2 + 3*b^3*d^2*e*x + b^3*d^3)*log(e*x + d))/(b^4*d^7 - 4*a*b^3*d^6*e + 6*a^2*b^2*d^5*e^2 - 4*a^3*b*d^4*e^3 + a^4*d^3*e^4 + (b^4*d^4*e^3 - 4*a*b^3*d^3*e^4 + 6*a^2*b^2*d^2*e^5 - 4*a^3*b*d*e^6 + a^4*e^7)*x^3 + 3*(b^4*d^5*e^2 - 4*a*b^3*d^4*e^3 + 6*a^2*b^2*d^3*e^4 - 4*a^3*b*d^2*e^5 + a^4*d*e^6)*x^2 + 3*(b^4*d^6*e - 4*a*b^3*d^5*e^2 + 6*a^2*b^2*d^4*e^3 - 4*a^3*b*d^3*e^4 + a^4*d^2*e^5)*x)","B",0
1596,1,292,0,0.396482," ","integrate((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{b^{4} e^{4} x^{4} - b^{4} d^{4} - 4 \, a b^{3} d^{3} e + 18 \, a^{2} b^{2} d^{2} e^{2} - 20 \, a^{3} b d e^{3} + 7 \, a^{4} e^{4} + 4 \, {\left(2 \, b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + {\left(16 \, a b^{3} d e^{3} - 11 \, a^{2} b^{2} e^{4}\right)} x^{2} - 2 \, {\left(4 \, b^{4} d^{3} e - 12 \, a b^{3} d^{2} e^{2} + 8 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x + 12 \, {\left(a^{2} b^{2} d^{2} e^{2} - 2 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} e^{2} - 2 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"1/2*(b^4*e^4*x^4 - b^4*d^4 - 4*a*b^3*d^3*e + 18*a^2*b^2*d^2*e^2 - 20*a^3*b*d*e^3 + 7*a^4*e^4 + 4*(2*b^4*d*e^3 - a*b^3*e^4)*x^3 + (16*a*b^3*d*e^3 - 11*a^2*b^2*e^4)*x^2 - 2*(4*b^4*d^3*e - 12*a*b^3*d^2*e^2 + 8*a^2*b^2*d*e^3 - a^3*b*e^4)*x + 12*(a^2*b^2*d^2*e^2 - 2*a^3*b*d*e^3 + a^4*e^4 + (b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(a*b^3*d^2*e^2 - 2*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*log(b*x + a))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","A",0
1597,1,188,0,0.390503," ","integrate((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, b^{3} e^{3} x^{3} + 4 \, a b^{2} e^{3} x^{2} - b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 9 \, a^{2} b d e^{2} - 5 \, a^{3} e^{3} - 2 \, {\left(3 \, b^{3} d^{2} e - 6 \, a b^{2} d e^{2} + 2 \, a^{2} b e^{3}\right)} x + 6 \, {\left(a^{2} b d e^{2} - a^{3} e^{3} + {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(a b^{2} d e^{2} - a^{2} b e^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/2*(2*b^3*e^3*x^3 + 4*a*b^2*e^3*x^2 - b^3*d^3 - 3*a*b^2*d^2*e + 9*a^2*b*d*e^2 - 5*a^3*e^3 - 2*(3*b^3*d^2*e - 6*a*b^2*d*e^2 + 2*a^2*b*e^3)*x + 6*(a^2*b*d*e^2 - a^3*e^3 + (b^3*d*e^2 - a*b^2*e^3)*x^2 + 2*(a*b^2*d*e^2 - a^2*b*e^3)*x)*log(b*x + a))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","A",0
1598,1,99,0,0.393135," ","integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{b^{2} d^{2} + 2 \, a b d e - 3 \, a^{2} e^{2} + 4 \, {\left(b^{2} d e - a b e^{2}\right)} x - 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"-1/2*(b^2*d^2 + 2*a*b*d*e - 3*a^2*e^2 + 4*(b^2*d*e - a*b*e^2)*x - 2*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*log(b*x + a))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
1599,1,38,0,0.386218," ","integrate((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, b e x + b d + a e}{2 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-1/2*(2*b*e*x + b*d + a*e)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
1600,1,24,0,0.402410," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"-1/2/(b^3*x^2 + 2*a*b^2*x + a^2*b)","A",0
1601,1,242,0,0.413697," ","integrate(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{b^{2} d^{2} - 4 \, a b d e + 3 \, a^{2} e^{2} - 2 \, {\left(b^{2} d e - a b e^{2}\right)} x - 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{3} d^{3} - 3 \, a^{3} b^{2} d^{2} e + 3 \, a^{4} b d e^{2} - a^{5} e^{3} + {\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)} x^{2} + 2 \, {\left(a b^{4} d^{3} - 3 \, a^{2} b^{3} d^{2} e + 3 \, a^{3} b^{2} d e^{2} - a^{4} b e^{3}\right)} x\right)}}"," ",0,"-1/2*(b^2*d^2 - 4*a*b*d*e + 3*a^2*e^2 - 2*(b^2*d*e - a*b*e^2)*x - 2*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*log(b*x + a) + 2*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*log(e*x + d))/(a^2*b^3*d^3 - 3*a^3*b^2*d^2*e + 3*a^4*b*d*e^2 - a^5*e^3 + (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^2 + 2*(a*b^4*d^3 - 3*a^2*b^3*d^2*e + 3*a^3*b^2*d*e^2 - a^4*b*e^3)*x)","B",0
1602,1,494,0,0.419028," ","integrate(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{b^{3} d^{3} - 6 \, a b^{2} d^{2} e + 3 \, 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(b^{3} d^{2} e + 2 \, a b^{2} d e^{2} - 3 \, a^{2} b e^{3}\right)} x - 6 \, {\left(b^{3} e^{3} x^{3} + a^{2} b d e^{2} + {\left(b^{3} d e^{2} + 2 \, a b^{2} e^{3}\right)} x^{2} + {\left(2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} e^{3} x^{3} + a^{2} b d e^{2} + {\left(b^{3} d e^{2} + 2 \, a b^{2} e^{3}\right)} x^{2} + {\left(2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{4} d^{5} - 4 \, a^{3} b^{3} d^{4} e + 6 \, a^{4} b^{2} d^{3} e^{2} - 4 \, a^{5} b d^{2} e^{3} + a^{6} d e^{4} + {\left(b^{6} d^{4} e - 4 \, a b^{5} d^{3} e^{2} + 6 \, a^{2} b^{4} d^{2} e^{3} - 4 \, a^{3} b^{3} d e^{4} + a^{4} b^{2} e^{5}\right)} x^{3} + {\left(b^{6} d^{5} - 2 \, a b^{5} d^{4} e - 2 \, a^{2} b^{4} d^{3} e^{2} + 8 \, a^{3} b^{3} d^{2} e^{3} - 7 \, a^{4} b^{2} d e^{4} + 2 \, a^{5} b e^{5}\right)} x^{2} + {\left(2 \, a b^{5} d^{5} - 7 \, a^{2} b^{4} d^{4} e + 8 \, a^{3} b^{3} d^{3} e^{2} - 2 \, a^{4} b^{2} d^{2} e^{3} - 2 \, a^{5} b d e^{4} + a^{6} e^{5}\right)} x\right)}}"," ",0,"-1/2*(b^3*d^3 - 6*a*b^2*d^2*e + 3*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*(b^3*d^2*e + 2*a*b^2*d*e^2 - 3*a^2*b*e^3)*x - 6*(b^3*e^3*x^3 + a^2*b*d*e^2 + (b^3*d*e^2 + 2*a*b^2*e^3)*x^2 + (2*a*b^2*d*e^2 + a^2*b*e^3)*x)*log(b*x + a) + 6*(b^3*e^3*x^3 + a^2*b*d*e^2 + (b^3*d*e^2 + 2*a*b^2*e^3)*x^2 + (2*a*b^2*d*e^2 + a^2*b*e^3)*x)*log(e*x + d))/(a^2*b^4*d^5 - 4*a^3*b^3*d^4*e + 6*a^4*b^2*d^3*e^2 - 4*a^5*b*d^2*e^3 + a^6*d*e^4 + (b^6*d^4*e - 4*a*b^5*d^3*e^2 + 6*a^2*b^4*d^2*e^3 - 4*a^3*b^3*d*e^4 + a^4*b^2*e^5)*x^3 + (b^6*d^5 - 2*a*b^5*d^4*e - 2*a^2*b^4*d^3*e^2 + 8*a^3*b^3*d^2*e^3 - 7*a^4*b^2*d*e^4 + 2*a^5*b*e^5)*x^2 + (2*a*b^5*d^5 - 7*a^2*b^4*d^4*e + 8*a^3*b^3*d^3*e^2 - 2*a^4*b^2*d^2*e^3 - 2*a^5*b*d*e^4 + a^6*e^5)*x)","B",0
1603,1,760,0,0.421198," ","integrate(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","-\frac{b^{4} d^{4} - 8 \, a b^{3} d^{3} e + 8 \, 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} - 18 \, {\left(b^{4} d^{2} e^{2} - a^{2} b^{2} e^{4}\right)} x^{2} - 4 \, {\left(b^{4} d^{3} e + 6 \, a b^{3} d^{2} e^{2} - 6 \, a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x - 12 \, {\left(b^{4} e^{4} x^{4} + a^{2} b^{2} d^{2} e^{2} + 2 \, {\left(b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{3} + {\left(b^{4} d^{2} e^{2} + 4 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} e^{2} + a^{2} b^{2} d e^{3}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(b^{4} e^{4} x^{4} + a^{2} b^{2} d^{2} e^{2} + 2 \, {\left(b^{4} d e^{3} + a b^{3} e^{4}\right)} x^{3} + {\left(b^{4} d^{2} e^{2} + 4 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} e^{2} + a^{2} b^{2} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} b^{5} d^{7} - 5 \, a^{3} b^{4} d^{6} e + 10 \, a^{4} b^{3} d^{5} e^{2} - 10 \, a^{5} b^{2} d^{4} e^{3} + 5 \, a^{6} b d^{3} e^{4} - a^{7} d^{2} e^{5} + {\left(b^{7} d^{5} e^{2} - 5 \, a b^{6} d^{4} e^{3} + 10 \, a^{2} b^{5} d^{3} e^{4} - 10 \, a^{3} b^{4} d^{2} e^{5} + 5 \, a^{4} b^{3} d e^{6} - a^{5} b^{2} e^{7}\right)} x^{4} + 2 \, {\left(b^{7} d^{6} e - 4 \, a b^{6} d^{5} e^{2} + 5 \, a^{2} b^{5} d^{4} e^{3} - 5 \, a^{4} b^{3} d^{2} e^{5} + 4 \, a^{5} b^{2} d e^{6} - a^{6} b e^{7}\right)} x^{3} + {\left(b^{7} d^{7} - a b^{6} d^{6} e - 9 \, a^{2} b^{5} d^{5} e^{2} + 25 \, a^{3} b^{4} d^{4} e^{3} - 25 \, a^{4} b^{3} d^{3} e^{4} + 9 \, a^{5} b^{2} d^{2} e^{5} + a^{6} b d e^{6} - a^{7} e^{7}\right)} x^{2} + 2 \, {\left(a b^{6} d^{7} - 4 \, a^{2} b^{5} d^{6} e + 5 \, a^{3} b^{4} d^{5} e^{2} - 5 \, a^{5} b^{2} d^{3} e^{4} + 4 \, a^{6} b d^{2} e^{5} - a^{7} d e^{6}\right)} x\right)}}"," ",0,"-1/2*(b^4*d^4 - 8*a*b^3*d^3*e + 8*a^3*b*d*e^3 - a^4*e^4 - 12*(b^4*d*e^3 - a*b^3*e^4)*x^3 - 18*(b^4*d^2*e^2 - a^2*b^2*e^4)*x^2 - 4*(b^4*d^3*e + 6*a*b^3*d^2*e^2 - 6*a^2*b^2*d*e^3 - a^3*b*e^4)*x - 12*(b^4*e^4*x^4 + a^2*b^2*d^2*e^2 + 2*(b^4*d*e^3 + a*b^3*e^4)*x^3 + (b^4*d^2*e^2 + 4*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(a*b^3*d^2*e^2 + a^2*b^2*d*e^3)*x)*log(b*x + a) + 12*(b^4*e^4*x^4 + a^2*b^2*d^2*e^2 + 2*(b^4*d*e^3 + a*b^3*e^4)*x^3 + (b^4*d^2*e^2 + 4*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(a*b^3*d^2*e^2 + a^2*b^2*d*e^3)*x)*log(e*x + d))/(a^2*b^5*d^7 - 5*a^3*b^4*d^6*e + 10*a^4*b^3*d^5*e^2 - 10*a^5*b^2*d^4*e^3 + 5*a^6*b*d^3*e^4 - a^7*d^2*e^5 + (b^7*d^5*e^2 - 5*a*b^6*d^4*e^3 + 10*a^2*b^5*d^3*e^4 - 10*a^3*b^4*d^2*e^5 + 5*a^4*b^3*d*e^6 - a^5*b^2*e^7)*x^4 + 2*(b^7*d^6*e - 4*a*b^6*d^5*e^2 + 5*a^2*b^5*d^4*e^3 - 5*a^4*b^3*d^2*e^5 + 4*a^5*b^2*d*e^6 - a^6*b*e^7)*x^3 + (b^7*d^7 - a*b^6*d^6*e - 9*a^2*b^5*d^5*e^2 + 25*a^3*b^4*d^4*e^3 - 25*a^4*b^3*d^3*e^4 + 9*a^5*b^2*d^2*e^5 + a^6*b*d*e^6 - a^7*e^7)*x^2 + 2*(a*b^6*d^7 - 4*a^2*b^5*d^6*e + 5*a^3*b^4*d^5*e^2 - 5*a^5*b^2*d^3*e^4 + 4*a^6*b*d^2*e^5 - a^7*d*e^6)*x)","B",0
1604,1,572,0,0.398278," ","integrate((e*x+d)^6/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, b^{6} e^{6} x^{6} - b^{6} d^{6} - 2 \, a b^{5} d^{5} e - 5 \, a^{2} b^{4} d^{4} e^{2} - 20 \, a^{3} b^{3} d^{3} e^{3} + 125 \, a^{4} b^{2} d^{2} e^{4} - 154 \, a^{5} b d e^{5} + 57 \, a^{6} e^{6} + 12 \, {\left(2 \, b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 4 \, {\left(24 \, a b^{5} d e^{5} - 17 \, a^{2} b^{4} e^{6}\right)} x^{4} - 16 \, {\left(5 \, b^{6} d^{3} e^{3} - 15 \, a b^{5} d^{2} e^{4} + 6 \, a^{2} b^{4} d e^{5} + 2 \, a^{3} b^{3} e^{6}\right)} x^{3} - 6 \, {\left(5 \, b^{6} d^{4} e^{2} + 20 \, a b^{5} d^{3} e^{3} - 90 \, a^{2} b^{4} d^{2} e^{4} + 84 \, a^{3} b^{3} d e^{5} - 22 \, a^{4} b^{2} e^{6}\right)} x^{2} - 4 \, {\left(2 \, b^{6} d^{5} e + 5 \, a b^{5} d^{4} e^{2} + 20 \, a^{2} b^{4} d^{3} e^{3} - 110 \, a^{3} b^{3} d^{2} e^{4} + 124 \, a^{4} b^{2} d e^{5} - 42 \, a^{5} b e^{6}\right)} x + 60 \, {\left(a^{4} b^{2} d^{2} e^{4} - 2 \, a^{5} b d e^{5} + a^{6} e^{6} + {\left(b^{6} d^{2} e^{4} - 2 \, a b^{5} d e^{5} + a^{2} b^{4} e^{6}\right)} x^{4} + 4 \, {\left(a b^{5} d^{2} e^{4} - 2 \, a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + 6 \, {\left(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} + 4 \, {\left(a^{3} b^{3} d^{2} e^{4} - 2 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x\right)} \log\left(b x + a\right)}{4 \, {\left(b^{11} x^{4} + 4 \, a b^{10} x^{3} + 6 \, a^{2} b^{9} x^{2} + 4 \, a^{3} b^{8} x + a^{4} b^{7}\right)}}"," ",0,"1/4*(2*b^6*e^6*x^6 - b^6*d^6 - 2*a*b^5*d^5*e - 5*a^2*b^4*d^4*e^2 - 20*a^3*b^3*d^3*e^3 + 125*a^4*b^2*d^2*e^4 - 154*a^5*b*d*e^5 + 57*a^6*e^6 + 12*(2*b^6*d*e^5 - a*b^5*e^6)*x^5 + 4*(24*a*b^5*d*e^5 - 17*a^2*b^4*e^6)*x^4 - 16*(5*b^6*d^3*e^3 - 15*a*b^5*d^2*e^4 + 6*a^2*b^4*d*e^5 + 2*a^3*b^3*e^6)*x^3 - 6*(5*b^6*d^4*e^2 + 20*a*b^5*d^3*e^3 - 90*a^2*b^4*d^2*e^4 + 84*a^3*b^3*d*e^5 - 22*a^4*b^2*e^6)*x^2 - 4*(2*b^6*d^5*e + 5*a*b^5*d^4*e^2 + 20*a^2*b^4*d^3*e^3 - 110*a^3*b^3*d^2*e^4 + 124*a^4*b^2*d*e^5 - 42*a^5*b*e^6)*x + 60*(a^4*b^2*d^2*e^4 - 2*a^5*b*d*e^5 + a^6*e^6 + (b^6*d^2*e^4 - 2*a*b^5*d*e^5 + a^2*b^4*e^6)*x^4 + 4*(a*b^5*d^2*e^4 - 2*a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^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 + 4*(a^3*b^3*d^2*e^4 - 2*a^4*b^2*d*e^5 + a^5*b*e^6)*x)*log(b*x + a))/(b^11*x^4 + 4*a*b^10*x^3 + 6*a^2*b^9*x^2 + 4*a^3*b^8*x + a^4*b^7)","B",0
1605,1,412,0,0.398203," ","integrate((e*x+d)^5/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{12 \, b^{5} e^{5} x^{5} + 48 \, a b^{4} e^{5} x^{4} - 3 \, b^{5} d^{5} - 5 \, a b^{4} d^{4} e - 10 \, a^{2} b^{3} d^{3} e^{2} - 30 \, a^{3} b^{2} d^{2} e^{3} + 125 \, a^{4} b d e^{4} - 77 \, a^{5} e^{5} - 24 \, {\left(5 \, b^{5} d^{2} e^{3} - 10 \, a b^{4} d e^{4} + 2 \, a^{2} b^{3} e^{5}\right)} x^{3} - 12 \, {\left(5 \, b^{5} d^{3} e^{2} + 15 \, a b^{4} d^{2} e^{3} - 45 \, a^{2} b^{3} d e^{4} + 21 \, a^{3} b^{2} e^{5}\right)} x^{2} - 4 \, {\left(5 \, b^{5} d^{4} e + 10 \, a b^{4} d^{3} e^{2} + 30 \, a^{2} b^{3} d^{2} e^{3} - 110 \, a^{3} b^{2} d e^{4} + 62 \, a^{4} b e^{5}\right)} x + 60 \, {\left(a^{4} b d e^{4} - a^{5} e^{5} + {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 4 \, {\left(a b^{4} d e^{4} - a^{2} b^{3} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{3} d e^{4} - a^{3} b^{2} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{2} d e^{4} - a^{4} b e^{5}\right)} x\right)} \log\left(b x + a\right)}{12 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}"," ",0,"1/12*(12*b^5*e^5*x^5 + 48*a*b^4*e^5*x^4 - 3*b^5*d^5 - 5*a*b^4*d^4*e - 10*a^2*b^3*d^3*e^2 - 30*a^3*b^2*d^2*e^3 + 125*a^4*b*d*e^4 - 77*a^5*e^5 - 24*(5*b^5*d^2*e^3 - 10*a*b^4*d*e^4 + 2*a^2*b^3*e^5)*x^3 - 12*(5*b^5*d^3*e^2 + 15*a*b^4*d^2*e^3 - 45*a^2*b^3*d*e^4 + 21*a^3*b^2*e^5)*x^2 - 4*(5*b^5*d^4*e + 10*a*b^4*d^3*e^2 + 30*a^2*b^3*d^2*e^3 - 110*a^3*b^2*d*e^4 + 62*a^4*b*e^5)*x + 60*(a^4*b*d*e^4 - a^5*e^5 + (b^5*d*e^4 - a*b^4*e^5)*x^4 + 4*(a*b^4*d*e^4 - a^2*b^3*e^5)*x^3 + 6*(a^2*b^3*d*e^4 - a^3*b^2*e^5)*x^2 + 4*(a^3*b^2*d*e^4 - a^4*b*e^5)*x)*log(b*x + a))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6)","B",0
1606,1,267,0,0.417013," ","integrate((e*x+d)^4/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, b^{4} d^{4} + 4 \, a b^{3} d^{3} e + 6 \, a^{2} b^{2} d^{2} e^{2} + 12 \, a^{3} b d e^{3} - 25 \, a^{4} e^{4} + 48 \, {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 36 \, {\left(b^{4} d^{2} e^{2} + 2 \, a b^{3} d e^{3} - 3 \, a^{2} b^{2} e^{4}\right)} x^{2} + 8 \, {\left(2 \, b^{4} d^{3} e + 3 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} - 11 \, a^{3} b e^{4}\right)} x - 12 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \log\left(b x + a\right)}{12 \, {\left(b^{9} x^{4} + 4 \, a b^{8} x^{3} + 6 \, a^{2} b^{7} x^{2} + 4 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}"," ",0,"-1/12*(3*b^4*d^4 + 4*a*b^3*d^3*e + 6*a^2*b^2*d^2*e^2 + 12*a^3*b*d*e^3 - 25*a^4*e^4 + 48*(b^4*d*e^3 - a*b^3*e^4)*x^3 + 36*(b^4*d^2*e^2 + 2*a*b^3*d*e^3 - 3*a^2*b^2*e^4)*x^2 + 8*(2*b^4*d^3*e + 3*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 - 11*a^3*b*e^4)*x - 12*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*log(b*x + a))/(b^9*x^4 + 4*a*b^8*x^3 + 6*a^2*b^7*x^2 + 4*a^3*b^6*x + a^4*b^5)","A",0
1607,1,143,0,0.410915," ","integrate((e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, b^{3} e^{3} x^{3} + b^{3} d^{3} + a b^{2} d^{2} e + 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} + 4 \, {\left(b^{3} d^{2} e + a b^{2} d e^{2} + a^{2} b e^{3}\right)} x}{4 \, {\left(b^{8} x^{4} + 4 \, a b^{7} x^{3} + 6 \, a^{2} b^{6} x^{2} + 4 \, a^{3} b^{5} x + a^{4} b^{4}\right)}}"," ",0,"-1/4*(4*b^3*e^3*x^3 + b^3*d^3 + a*b^2*d^2*e + a^2*b*d*e^2 + a^3*e^3 + 6*(b^3*d*e^2 + a*b^2*e^3)*x^2 + 4*(b^3*d^2*e + a*b^2*d*e^2 + a^2*b*e^3)*x)/(b^8*x^4 + 4*a*b^7*x^3 + 6*a^2*b^6*x^2 + 4*a^3*b^5*x + a^4*b^4)","B",0
1608,1,98,0,0.402714," ","integrate((e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{6 \, b^{2} e^{2} x^{2} + 3 \, b^{2} d^{2} + 2 \, a b d e + a^{2} e^{2} + 4 \, {\left(2 \, b^{2} d e + a b e^{2}\right)} x}{12 \, {\left(b^{7} x^{4} + 4 \, a b^{6} x^{3} + 6 \, a^{2} b^{5} x^{2} + 4 \, a^{3} b^{4} x + a^{4} b^{3}\right)}}"," ",0,"-1/12*(6*b^2*e^2*x^2 + 3*b^2*d^2 + 2*a*b*d*e + a^2*e^2 + 4*(2*b^2*d*e + a*b*e^2)*x)/(b^7*x^4 + 4*a*b^6*x^3 + 6*a^2*b^5*x^2 + 4*a^3*b^4*x + a^4*b^3)","A",0
1609,1,61,0,0.401769," ","integrate((e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, b e x + 3 \, b d + a e}{12 \, {\left(b^{6} x^{4} + 4 \, a b^{5} x^{3} + 6 \, a^{2} b^{4} x^{2} + 4 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}"," ",0,"-1/12*(4*b*e*x + 3*b*d + a*e)/(b^6*x^4 + 4*a*b^5*x^3 + 6*a^2*b^4*x^2 + 4*a^3*b^3*x + a^4*b^2)","A",0
1610,1,46,0,0.401033," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{1}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}}"," ",0,"-1/4/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b)","A",0
1611,1,657,0,0.421343," ","integrate(1/(e*x+d)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, b^{4} d^{4} - 16 \, a b^{3} d^{3} e + 36 \, a^{2} b^{2} d^{2} e^{2} - 48 \, a^{3} b d e^{3} + 25 \, a^{4} e^{4} - 12 \, {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(b^{4} d^{2} e^{2} - 8 \, a b^{3} d e^{3} + 7 \, a^{2} b^{2} e^{4}\right)} x^{2} - 4 \, {\left(b^{4} d^{3} e - 6 \, a b^{3} d^{2} e^{2} + 18 \, a^{2} b^{2} d e^{3} - 13 \, a^{3} b e^{4}\right)} x - 12 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \log\left(b x + a\right) + 12 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \log\left(e x + d\right)}{12 \, {\left(a^{4} b^{5} d^{5} - 5 \, a^{5} b^{4} d^{4} e + 10 \, a^{6} b^{3} d^{3} e^{2} - 10 \, a^{7} b^{2} d^{2} e^{3} + 5 \, a^{8} b d e^{4} - a^{9} e^{5} + {\left(b^{9} d^{5} - 5 \, a b^{8} d^{4} e + 10 \, a^{2} b^{7} d^{3} e^{2} - 10 \, a^{3} b^{6} d^{2} e^{3} + 5 \, a^{4} b^{5} d e^{4} - a^{5} b^{4} e^{5}\right)} x^{4} + 4 \, {\left(a b^{8} d^{5} - 5 \, a^{2} b^{7} d^{4} e + 10 \, a^{3} b^{6} d^{3} e^{2} - 10 \, a^{4} b^{5} d^{2} e^{3} + 5 \, a^{5} b^{4} d e^{4} - a^{6} b^{3} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} d^{5} - 5 \, a^{3} b^{6} d^{4} e + 10 \, a^{4} b^{5} d^{3} e^{2} - 10 \, a^{5} b^{4} d^{2} e^{3} + 5 \, a^{6} b^{3} d e^{4} - a^{7} b^{2} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} d^{5} - 5 \, a^{4} b^{5} d^{4} e + 10 \, a^{5} b^{4} d^{3} e^{2} - 10 \, a^{6} b^{3} d^{2} e^{3} + 5 \, a^{7} b^{2} d e^{4} - a^{8} b e^{5}\right)} x\right)}}"," ",0,"-1/12*(3*b^4*d^4 - 16*a*b^3*d^3*e + 36*a^2*b^2*d^2*e^2 - 48*a^3*b*d*e^3 + 25*a^4*e^4 - 12*(b^4*d*e^3 - a*b^3*e^4)*x^3 + 6*(b^4*d^2*e^2 - 8*a*b^3*d*e^3 + 7*a^2*b^2*e^4)*x^2 - 4*(b^4*d^3*e - 6*a*b^3*d^2*e^2 + 18*a^2*b^2*d*e^3 - 13*a^3*b*e^4)*x - 12*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*log(b*x + a) + 12*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*log(e*x + d))/(a^4*b^5*d^5 - 5*a^5*b^4*d^4*e + 10*a^6*b^3*d^3*e^2 - 10*a^7*b^2*d^2*e^3 + 5*a^8*b*d*e^4 - a^9*e^5 + (b^9*d^5 - 5*a*b^8*d^4*e + 10*a^2*b^7*d^3*e^2 - 10*a^3*b^6*d^2*e^3 + 5*a^4*b^5*d*e^4 - a^5*b^4*e^5)*x^4 + 4*(a*b^8*d^5 - 5*a^2*b^7*d^4*e + 10*a^3*b^6*d^3*e^2 - 10*a^4*b^5*d^2*e^3 + 5*a^5*b^4*d*e^4 - a^6*b^3*e^5)*x^3 + 6*(a^2*b^7*d^5 - 5*a^3*b^6*d^4*e + 10*a^4*b^5*d^3*e^2 - 10*a^5*b^4*d^2*e^3 + 5*a^6*b^3*d*e^4 - a^7*b^2*e^5)*x^2 + 4*(a^3*b^6*d^5 - 5*a^4*b^5*d^4*e + 10*a^5*b^4*d^3*e^2 - 10*a^6*b^3*d^2*e^3 + 5*a^7*b^2*d*e^4 - a^8*b*e^5)*x)","B",0
1612,1,1083,0,0.431576," ","integrate(1/(e*x+d)^2/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{3 \, b^{5} d^{5} - 20 \, a b^{4} d^{4} e + 60 \, a^{2} b^{3} d^{3} e^{2} - 120 \, a^{3} b^{2} d^{2} e^{3} + 65 \, a^{4} b d e^{4} + 12 \, 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} + 6 \, a b^{4} d e^{4} - 7 \, a^{2} b^{3} e^{5}\right)} x^{3} + 10 \, {\left(b^{5} d^{3} e^{2} - 12 \, a b^{4} d^{2} e^{3} - 15 \, a^{2} b^{3} d e^{4} + 26 \, a^{3} b^{2} e^{5}\right)} x^{2} - 5 \, {\left(b^{5} d^{4} e - 8 \, a b^{4} d^{3} e^{2} + 36 \, a^{2} b^{3} d^{2} e^{3} - 4 \, a^{3} b^{2} d e^{4} - 25 \, a^{4} b e^{5}\right)} x - 60 \, {\left(b^{5} e^{5} x^{5} + a^{4} b d e^{4} + {\left(b^{5} d e^{4} + 4 \, a b^{4} e^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{3} d e^{4} + 2 \, a^{3} b^{2} e^{5}\right)} x^{2} + {\left(4 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \log\left(b x + a\right) + 60 \, {\left(b^{5} e^{5} x^{5} + a^{4} b d e^{4} + {\left(b^{5} d e^{4} + 4 \, a b^{4} e^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{3} d e^{4} + 2 \, a^{3} b^{2} e^{5}\right)} x^{2} + {\left(4 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(a^{4} b^{6} d^{7} - 6 \, a^{5} b^{5} d^{6} e + 15 \, a^{6} b^{4} d^{5} e^{2} - 20 \, a^{7} b^{3} d^{4} e^{3} + 15 \, a^{8} b^{2} d^{3} e^{4} - 6 \, a^{9} b d^{2} e^{5} + a^{10} d e^{6} + {\left(b^{10} d^{6} e - 6 \, a b^{9} d^{5} e^{2} + 15 \, a^{2} b^{8} d^{4} e^{3} - 20 \, a^{3} b^{7} d^{3} e^{4} + 15 \, a^{4} b^{6} d^{2} e^{5} - 6 \, a^{5} b^{5} d e^{6} + a^{6} b^{4} e^{7}\right)} x^{5} + {\left(b^{10} d^{7} - 2 \, a b^{9} d^{6} e - 9 \, a^{2} b^{8} d^{5} e^{2} + 40 \, a^{3} b^{7} d^{4} e^{3} - 65 \, a^{4} b^{6} d^{3} e^{4} + 54 \, a^{5} b^{5} d^{2} e^{5} - 23 \, a^{6} b^{4} d e^{6} + 4 \, a^{7} b^{3} e^{7}\right)} x^{4} + 2 \, {\left(2 \, a b^{9} d^{7} - 9 \, a^{2} b^{8} d^{6} e + 12 \, a^{3} b^{7} d^{5} e^{2} + 5 \, a^{4} b^{6} d^{4} e^{3} - 30 \, a^{5} b^{5} d^{3} e^{4} + 33 \, a^{6} b^{4} d^{2} e^{5} - 16 \, a^{7} b^{3} d e^{6} + 3 \, a^{8} b^{2} e^{7}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{8} d^{7} - 16 \, a^{3} b^{7} d^{6} e + 33 \, a^{4} b^{6} d^{5} e^{2} - 30 \, a^{5} b^{5} d^{4} e^{3} + 5 \, a^{6} b^{4} d^{3} e^{4} + 12 \, a^{7} b^{3} d^{2} e^{5} - 9 \, a^{8} b^{2} d e^{6} + 2 \, a^{9} b e^{7}\right)} x^{2} + {\left(4 \, a^{3} b^{7} d^{7} - 23 \, a^{4} b^{6} d^{6} e + 54 \, a^{5} b^{5} d^{5} e^{2} - 65 \, a^{6} b^{4} d^{4} e^{3} + 40 \, a^{7} b^{3} d^{3} e^{4} - 9 \, a^{8} b^{2} d^{2} e^{5} - 2 \, a^{9} b d e^{6} + a^{10} e^{7}\right)} x\right)}}"," ",0,"-1/12*(3*b^5*d^5 - 20*a*b^4*d^4*e + 60*a^2*b^3*d^3*e^2 - 120*a^3*b^2*d^2*e^3 + 65*a^4*b*d*e^4 + 12*a^5*e^5 - 60*(b^5*d*e^4 - a*b^4*e^5)*x^4 - 30*(b^5*d^2*e^3 + 6*a*b^4*d*e^4 - 7*a^2*b^3*e^5)*x^3 + 10*(b^5*d^3*e^2 - 12*a*b^4*d^2*e^3 - 15*a^2*b^3*d*e^4 + 26*a^3*b^2*e^5)*x^2 - 5*(b^5*d^4*e - 8*a*b^4*d^3*e^2 + 36*a^2*b^3*d^2*e^3 - 4*a^3*b^2*d*e^4 - 25*a^4*b*e^5)*x - 60*(b^5*e^5*x^5 + a^4*b*d*e^4 + (b^5*d*e^4 + 4*a*b^4*e^5)*x^4 + 2*(2*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + 2*(3*a^2*b^3*d*e^4 + 2*a^3*b^2*e^5)*x^2 + (4*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*log(b*x + a) + 60*(b^5*e^5*x^5 + a^4*b*d*e^4 + (b^5*d*e^4 + 4*a*b^4*e^5)*x^4 + 2*(2*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + 2*(3*a^2*b^3*d*e^4 + 2*a^3*b^2*e^5)*x^2 + (4*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*log(e*x + d))/(a^4*b^6*d^7 - 6*a^5*b^5*d^6*e + 15*a^6*b^4*d^5*e^2 - 20*a^7*b^3*d^4*e^3 + 15*a^8*b^2*d^3*e^4 - 6*a^9*b*d^2*e^5 + a^10*d*e^6 + (b^10*d^6*e - 6*a*b^9*d^5*e^2 + 15*a^2*b^8*d^4*e^3 - 20*a^3*b^7*d^3*e^4 + 15*a^4*b^6*d^2*e^5 - 6*a^5*b^5*d*e^6 + a^6*b^4*e^7)*x^5 + (b^10*d^7 - 2*a*b^9*d^6*e - 9*a^2*b^8*d^5*e^2 + 40*a^3*b^7*d^4*e^3 - 65*a^4*b^6*d^3*e^4 + 54*a^5*b^5*d^2*e^5 - 23*a^6*b^4*d*e^6 + 4*a^7*b^3*e^7)*x^4 + 2*(2*a*b^9*d^7 - 9*a^2*b^8*d^6*e + 12*a^3*b^7*d^5*e^2 + 5*a^4*b^6*d^4*e^3 - 30*a^5*b^5*d^3*e^4 + 33*a^6*b^4*d^2*e^5 - 16*a^7*b^3*d*e^6 + 3*a^8*b^2*e^7)*x^3 + 2*(3*a^2*b^8*d^7 - 16*a^3*b^7*d^6*e + 33*a^4*b^6*d^5*e^2 - 30*a^5*b^5*d^4*e^3 + 5*a^6*b^4*d^3*e^4 + 12*a^7*b^3*d^2*e^5 - 9*a^8*b^2*d*e^6 + 2*a^9*b*e^7)*x^2 + (4*a^3*b^7*d^7 - 23*a^4*b^6*d^6*e + 54*a^5*b^5*d^5*e^2 - 65*a^6*b^4*d^4*e^3 + 40*a^7*b^3*d^3*e^4 - 9*a^8*b^2*d^2*e^5 - 2*a^9*b*d*e^6 + a^10*e^7)*x)","B",0
1613,1,1565,0,0.451756," ","integrate(1/(e*x+d)^3/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","-\frac{b^{6} d^{6} - 8 \, a b^{5} d^{5} e + 30 \, a^{2} b^{4} d^{4} e^{2} - 80 \, a^{3} b^{3} d^{3} e^{3} + 35 \, a^{4} b^{2} d^{2} e^{4} + 24 \, a^{5} b d e^{5} - 2 \, a^{6} e^{6} - 60 \, {\left(b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} - 30 \, {\left(3 \, b^{6} d^{2} e^{4} + 4 \, a b^{5} d e^{5} - 7 \, a^{2} b^{4} e^{6}\right)} x^{4} - 20 \, {\left(b^{6} d^{3} e^{3} + 15 \, a b^{5} d^{2} e^{4} - 3 \, a^{2} b^{4} d e^{5} - 13 \, a^{3} b^{3} e^{6}\right)} x^{3} + 5 \, {\left(b^{6} d^{4} e^{2} - 16 \, a b^{5} d^{3} e^{3} - 66 \, a^{2} b^{4} d^{2} e^{4} + 56 \, a^{3} b^{3} d e^{5} + 25 \, a^{4} b^{2} e^{6}\right)} x^{2} - 2 \, {\left(b^{6} d^{5} e - 10 \, a b^{5} d^{4} e^{2} + 60 \, a^{2} b^{4} d^{3} e^{3} + 50 \, a^{3} b^{3} d^{2} e^{4} - 95 \, a^{4} b^{2} d e^{5} - 6 \, a^{5} b e^{6}\right)} x - 60 \, {\left(b^{6} e^{6} x^{6} + a^{4} b^{2} d^{2} e^{4} + 2 \, {\left(b^{6} d e^{5} + 2 \, a b^{5} e^{6}\right)} x^{5} + {\left(b^{6} d^{2} e^{4} + 8 \, a b^{5} d e^{5} + 6 \, a^{2} b^{4} e^{6}\right)} x^{4} + 4 \, {\left(a b^{5} d^{2} e^{4} + 3 \, a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + {\left(6 \, a^{2} b^{4} d^{2} e^{4} + 8 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{3} d^{2} e^{4} + a^{4} b^{2} d e^{5}\right)} x\right)} \log\left(b x + a\right) + 60 \, {\left(b^{6} e^{6} x^{6} + a^{4} b^{2} d^{2} e^{4} + 2 \, {\left(b^{6} d e^{5} + 2 \, a b^{5} e^{6}\right)} x^{5} + {\left(b^{6} d^{2} e^{4} + 8 \, a b^{5} d e^{5} + 6 \, a^{2} b^{4} e^{6}\right)} x^{4} + 4 \, {\left(a b^{5} d^{2} e^{4} + 3 \, a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + {\left(6 \, a^{2} b^{4} d^{2} e^{4} + 8 \, a^{3} b^{3} d e^{5} + a^{4} b^{2} e^{6}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{3} d^{2} e^{4} + a^{4} b^{2} d e^{5}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(a^{4} b^{7} d^{9} - 7 \, a^{5} b^{6} d^{8} e + 21 \, a^{6} b^{5} d^{7} e^{2} - 35 \, a^{7} b^{4} d^{6} e^{3} + 35 \, a^{8} b^{3} d^{5} e^{4} - 21 \, a^{9} b^{2} d^{4} e^{5} + 7 \, a^{10} b d^{3} e^{6} - a^{11} d^{2} e^{7} + {\left(b^{11} d^{7} e^{2} - 7 \, a b^{10} d^{6} e^{3} + 21 \, a^{2} b^{9} d^{5} e^{4} - 35 \, a^{3} b^{8} d^{4} e^{5} + 35 \, a^{4} b^{7} d^{3} e^{6} - 21 \, a^{5} b^{6} d^{2} e^{7} + 7 \, a^{6} b^{5} d e^{8} - a^{7} b^{4} e^{9}\right)} x^{6} + 2 \, {\left(b^{11} d^{8} e - 5 \, a b^{10} d^{7} e^{2} + 7 \, a^{2} b^{9} d^{6} e^{3} + 7 \, a^{3} b^{8} d^{5} e^{4} - 35 \, a^{4} b^{7} d^{4} e^{5} + 49 \, a^{5} b^{6} d^{3} e^{6} - 35 \, a^{6} b^{5} d^{2} e^{7} + 13 \, a^{7} b^{4} d e^{8} - 2 \, a^{8} b^{3} e^{9}\right)} x^{5} + {\left(b^{11} d^{9} + a b^{10} d^{8} e - 29 \, a^{2} b^{9} d^{7} e^{2} + 91 \, a^{3} b^{8} d^{6} e^{3} - 119 \, a^{4} b^{7} d^{5} e^{4} + 49 \, a^{5} b^{6} d^{4} e^{5} + 49 \, a^{6} b^{5} d^{3} e^{6} - 71 \, a^{7} b^{4} d^{2} e^{7} + 34 \, a^{8} b^{3} d e^{8} - 6 \, a^{9} b^{2} e^{9}\right)} x^{4} + 4 \, {\left(a b^{10} d^{9} - 4 \, a^{2} b^{9} d^{8} e + a^{3} b^{8} d^{7} e^{2} + 21 \, a^{4} b^{7} d^{6} e^{3} - 49 \, a^{5} b^{6} d^{5} e^{4} + 49 \, a^{6} b^{5} d^{4} e^{5} - 21 \, a^{7} b^{4} d^{3} e^{6} - a^{8} b^{3} d^{2} e^{7} + 4 \, a^{9} b^{2} d e^{8} - a^{10} b e^{9}\right)} x^{3} + {\left(6 \, a^{2} b^{9} d^{9} - 34 \, a^{3} b^{8} d^{8} e + 71 \, a^{4} b^{7} d^{7} e^{2} - 49 \, a^{5} b^{6} d^{6} e^{3} - 49 \, a^{6} b^{5} d^{5} e^{4} + 119 \, a^{7} b^{4} d^{4} e^{5} - 91 \, a^{8} b^{3} d^{3} e^{6} + 29 \, a^{9} b^{2} d^{2} e^{7} - a^{10} b d e^{8} - a^{11} e^{9}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{8} d^{9} - 13 \, a^{4} b^{7} d^{8} e + 35 \, a^{5} b^{6} d^{7} e^{2} - 49 \, a^{6} b^{5} d^{6} e^{3} + 35 \, a^{7} b^{4} d^{5} e^{4} - 7 \, a^{8} b^{3} d^{4} e^{5} - 7 \, a^{9} b^{2} d^{3} e^{6} + 5 \, a^{10} b d^{2} e^{7} - a^{11} d e^{8}\right)} x\right)}}"," ",0,"-1/4*(b^6*d^6 - 8*a*b^5*d^5*e + 30*a^2*b^4*d^4*e^2 - 80*a^3*b^3*d^3*e^3 + 35*a^4*b^2*d^2*e^4 + 24*a^5*b*d*e^5 - 2*a^6*e^6 - 60*(b^6*d*e^5 - a*b^5*e^6)*x^5 - 30*(3*b^6*d^2*e^4 + 4*a*b^5*d*e^5 - 7*a^2*b^4*e^6)*x^4 - 20*(b^6*d^3*e^3 + 15*a*b^5*d^2*e^4 - 3*a^2*b^4*d*e^5 - 13*a^3*b^3*e^6)*x^3 + 5*(b^6*d^4*e^2 - 16*a*b^5*d^3*e^3 - 66*a^2*b^4*d^2*e^4 + 56*a^3*b^3*d*e^5 + 25*a^4*b^2*e^6)*x^2 - 2*(b^6*d^5*e - 10*a*b^5*d^4*e^2 + 60*a^2*b^4*d^3*e^3 + 50*a^3*b^3*d^2*e^4 - 95*a^4*b^2*d*e^5 - 6*a^5*b*e^6)*x - 60*(b^6*e^6*x^6 + a^4*b^2*d^2*e^4 + 2*(b^6*d*e^5 + 2*a*b^5*e^6)*x^5 + (b^6*d^2*e^4 + 8*a*b^5*d*e^5 + 6*a^2*b^4*e^6)*x^4 + 4*(a*b^5*d^2*e^4 + 3*a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 + (6*a^2*b^4*d^2*e^4 + 8*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + 2*(2*a^3*b^3*d^2*e^4 + a^4*b^2*d*e^5)*x)*log(b*x + a) + 60*(b^6*e^6*x^6 + a^4*b^2*d^2*e^4 + 2*(b^6*d*e^5 + 2*a*b^5*e^6)*x^5 + (b^6*d^2*e^4 + 8*a*b^5*d*e^5 + 6*a^2*b^4*e^6)*x^4 + 4*(a*b^5*d^2*e^4 + 3*a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^3 + (6*a^2*b^4*d^2*e^4 + 8*a^3*b^3*d*e^5 + a^4*b^2*e^6)*x^2 + 2*(2*a^3*b^3*d^2*e^4 + a^4*b^2*d*e^5)*x)*log(e*x + d))/(a^4*b^7*d^9 - 7*a^5*b^6*d^8*e + 21*a^6*b^5*d^7*e^2 - 35*a^7*b^4*d^6*e^3 + 35*a^8*b^3*d^5*e^4 - 21*a^9*b^2*d^4*e^5 + 7*a^10*b*d^3*e^6 - a^11*d^2*e^7 + (b^11*d^7*e^2 - 7*a*b^10*d^6*e^3 + 21*a^2*b^9*d^5*e^4 - 35*a^3*b^8*d^4*e^5 + 35*a^4*b^7*d^3*e^6 - 21*a^5*b^6*d^2*e^7 + 7*a^6*b^5*d*e^8 - a^7*b^4*e^9)*x^6 + 2*(b^11*d^8*e - 5*a*b^10*d^7*e^2 + 7*a^2*b^9*d^6*e^3 + 7*a^3*b^8*d^5*e^4 - 35*a^4*b^7*d^4*e^5 + 49*a^5*b^6*d^3*e^6 - 35*a^6*b^5*d^2*e^7 + 13*a^7*b^4*d*e^8 - 2*a^8*b^3*e^9)*x^5 + (b^11*d^9 + a*b^10*d^8*e - 29*a^2*b^9*d^7*e^2 + 91*a^3*b^8*d^6*e^3 - 119*a^4*b^7*d^5*e^4 + 49*a^5*b^6*d^4*e^5 + 49*a^6*b^5*d^3*e^6 - 71*a^7*b^4*d^2*e^7 + 34*a^8*b^3*d*e^8 - 6*a^9*b^2*e^9)*x^4 + 4*(a*b^10*d^9 - 4*a^2*b^9*d^8*e + a^3*b^8*d^7*e^2 + 21*a^4*b^7*d^6*e^3 - 49*a^5*b^6*d^5*e^4 + 49*a^6*b^5*d^4*e^5 - 21*a^7*b^4*d^3*e^6 - a^8*b^3*d^2*e^7 + 4*a^9*b^2*d*e^8 - a^10*b*e^9)*x^3 + (6*a^2*b^9*d^9 - 34*a^3*b^8*d^8*e + 71*a^4*b^7*d^7*e^2 - 49*a^5*b^6*d^6*e^3 - 49*a^6*b^5*d^5*e^4 + 119*a^7*b^4*d^4*e^5 - 91*a^8*b^3*d^3*e^6 + 29*a^9*b^2*d^2*e^7 - a^10*b*d*e^8 - a^11*e^9)*x^2 + 2*(2*a^3*b^8*d^9 - 13*a^4*b^7*d^8*e + 35*a^5*b^6*d^7*e^2 - 49*a^6*b^5*d^6*e^3 + 35*a^7*b^4*d^5*e^4 - 7*a^8*b^3*d^4*e^5 - 7*a^9*b^2*d^3*e^6 + 5*a^10*b*d^2*e^7 - a^11*d*e^8)*x)","B",0
1614,1,69,0,0.386746," ","integrate((e*x+d)*(4*x^2+12*x+9)^(5/2),x, algorithm=""fricas"")","\frac{32}{7} \, e x^{7} + \frac{8}{3} \, {\left(2 \, d + 15 \, e\right)} x^{6} + 48 \, {\left(d + 3 \, e\right)} x^{5} + 90 \, {\left(2 \, d + 3 \, e\right)} x^{4} + 90 \, {\left(4 \, d + 3 \, e\right)} x^{3} + \frac{81}{2} \, {\left(10 \, d + 3 \, e\right)} x^{2} + 243 \, d x"," ",0,"32/7*e*x^7 + 8/3*(2*d + 15*e)*x^6 + 48*(d + 3*e)*x^5 + 90*(2*d + 3*e)*x^4 + 90*(4*d + 3*e)*x^3 + 81/2*(10*d + 3*e)*x^2 + 243*d*x","A",0
1615,1,44,0,0.392175," ","integrate((e*x+d)*(4*x^2+12*x+9)^(3/2),x, algorithm=""fricas"")","\frac{8}{5} \, e x^{5} + {\left(2 \, d + 9 \, e\right)} x^{4} + 6 \, {\left(2 \, d + 3 \, e\right)} x^{3} + \frac{27}{2} \, {\left(2 \, d + e\right)} x^{2} + 27 \, d x"," ",0,"8/5*e*x^5 + (2*d + 9*e)*x^4 + 6*(2*d + 3*e)*x^3 + 27/2*(2*d + e)*x^2 + 27*d*x","A",0
1616,1,23,0,0.393556," ","integrate((e*x+d)*(4*x^2+12*x+9)^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, e x^{3} + \frac{1}{2} \, {\left(2 \, d + 3 \, e\right)} x^{2} + 3 \, d x"," ",0,"2/3*e*x^3 + 1/2*(2*d + 3*e)*x^2 + 3*d*x","A",0
1617,1,20,0,0.410741," ","integrate((e*x+d)/(4*x^2+12*x+9)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, e x + \frac{1}{4} \, {\left(2 \, d - 3 \, e\right)} \log\left(2 \, x + 3\right)"," ",0,"1/2*e*x + 1/4*(2*d - 3*e)*log(2*x + 3)","A",0
1618,1,25,0,0.408019," ","integrate((e*x+d)/(4*x^2+12*x+9)^(3/2),x, algorithm=""fricas"")","-\frac{4 \, e x + 2 \, d + 3 \, e}{8 \, {\left(4 \, x^{2} + 12 \, x + 9\right)}}"," ",0,"-1/8*(4*e*x + 2*d + 3*e)/(4*x^2 + 12*x + 9)","A",0
1619,1,35,0,0.397457," ","integrate((e*x+d)/(4*x^2+12*x+9)^(5/2),x, algorithm=""fricas"")","-\frac{8 \, e x + 6 \, d + 3 \, e}{48 \, {\left(16 \, x^{4} + 96 \, x^{3} + 216 \, x^{2} + 216 \, x + 81\right)}}"," ",0,"-1/48*(8*e*x + 6*d + 3*e)/(16*x^4 + 96*x^3 + 216*x^2 + 216*x + 81)","A",0
1620,1,45,0,0.397048," ","integrate((e*x+d)/(4*x^2+12*x+9)^(7/2),x, algorithm=""fricas"")","-\frac{12 \, e x + 10 \, d + 3 \, e}{120 \, {\left(64 \, x^{6} + 576 \, x^{5} + 2160 \, x^{4} + 4320 \, x^{3} + 4860 \, x^{2} + 2916 \, x + 729\right)}}"," ",0,"-1/120*(12*e*x + 10*d + 3*e)/(64*x^6 + 576*x^5 + 2160*x^4 + 4320*x^3 + 4860*x^2 + 2916*x + 729)","A",0
1621,1,212,0,0.400654," ","integrate((e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, {\left(99 \, b^{2} e^{6} x^{6} + 8 \, b^{2} d^{6} - 52 \, a b d^{5} e + 143 \, a^{2} d^{4} e^{2} + 18 \, {\left(20 \, b^{2} d e^{5} + 13 \, a b e^{6}\right)} x^{5} + {\left(458 \, b^{2} d^{2} e^{4} + 884 \, a b d e^{5} + 143 \, a^{2} e^{6}\right)} x^{4} + 4 \, {\left(53 \, b^{2} d^{3} e^{3} + 299 \, a b d^{2} e^{4} + 143 \, a^{2} d e^{5}\right)} x^{3} + 3 \, {\left(b^{2} d^{4} e^{2} + 208 \, a b d^{3} e^{3} + 286 \, a^{2} d^{2} e^{4}\right)} x^{2} - 2 \, {\left(2 \, b^{2} d^{5} e - 13 \, a b d^{4} e^{2} - 286 \, a^{2} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{1287 \, e^{3}}"," ",0,"2/1287*(99*b^2*e^6*x^6 + 8*b^2*d^6 - 52*a*b*d^5*e + 143*a^2*d^4*e^2 + 18*(20*b^2*d*e^5 + 13*a*b*e^6)*x^5 + (458*b^2*d^2*e^4 + 884*a*b*d*e^5 + 143*a^2*e^6)*x^4 + 4*(53*b^2*d^3*e^3 + 299*a*b*d^2*e^4 + 143*a^2*d*e^5)*x^3 + 3*(b^2*d^4*e^2 + 208*a*b*d^3*e^3 + 286*a^2*d^2*e^4)*x^2 - 2*(2*b^2*d^5*e - 13*a*b*d^4*e^2 - 286*a^2*d^3*e^3)*x)*sqrt(e*x + d)/e^3","B",0
1622,1,174,0,0.399441," ","integrate((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, b^{2} e^{5} x^{5} + 8 \, b^{2} d^{5} - 44 \, a b d^{4} e + 99 \, a^{2} d^{3} e^{2} + 7 \, {\left(23 \, b^{2} d e^{4} + 22 \, a b e^{5}\right)} x^{4} + {\left(113 \, b^{2} d^{2} e^{3} + 418 \, a b d e^{4} + 99 \, a^{2} e^{5}\right)} x^{3} + 3 \, {\left(b^{2} d^{3} e^{2} + 110 \, a b d^{2} e^{3} + 99 \, a^{2} d e^{4}\right)} x^{2} - {\left(4 \, b^{2} d^{4} e - 22 \, a b d^{3} e^{2} - 297 \, a^{2} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{693 \, e^{3}}"," ",0,"2/693*(63*b^2*e^5*x^5 + 8*b^2*d^5 - 44*a*b*d^4*e + 99*a^2*d^3*e^2 + 7*(23*b^2*d*e^4 + 22*a*b*e^5)*x^4 + (113*b^2*d^2*e^3 + 418*a*b*d*e^4 + 99*a^2*e^5)*x^3 + 3*(b^2*d^3*e^2 + 110*a*b*d^2*e^3 + 99*a^2*d*e^4)*x^2 - (4*b^2*d^4*e - 22*a*b*d^3*e^2 - 297*a^2*d^2*e^3)*x)*sqrt(e*x + d)/e^3","B",0
1623,1,137,0,0.402283," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{2} e^{4} x^{4} + 8 \, b^{2} d^{4} - 36 \, a b d^{3} e + 63 \, a^{2} d^{2} e^{2} + 10 \, {\left(5 \, b^{2} d e^{3} + 9 \, a b e^{4}\right)} x^{3} + 3 \, {\left(b^{2} d^{2} e^{2} + 48 \, a b d e^{3} + 21 \, a^{2} e^{4}\right)} x^{2} - 2 \, {\left(2 \, b^{2} d^{3} e - 9 \, a b d^{2} e^{2} - 63 \, a^{2} d e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{3}}"," ",0,"2/315*(35*b^2*e^4*x^4 + 8*b^2*d^4 - 36*a*b*d^3*e + 63*a^2*d^2*e^2 + 10*(5*b^2*d*e^3 + 9*a*b*e^4)*x^3 + 3*(b^2*d^2*e^2 + 48*a*b*d*e^3 + 21*a^2*e^4)*x^2 - 2*(2*b^2*d^3*e - 9*a*b*d^2*e^2 - 63*a^2*d*e^3)*x)*sqrt(e*x + d)/e^3","B",0
1624,1,99,0,0.404997," ","integrate((b^2*x^2+2*a*b*x+a^2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b^{2} e^{3} x^{3} + 8 \, b^{2} d^{3} - 28 \, a b d^{2} e + 35 \, a^{2} d e^{2} + 3 \, {\left(b^{2} d e^{2} + 14 \, a b e^{3}\right)} x^{2} - {\left(4 \, b^{2} d^{2} e - 14 \, a b d e^{2} - 35 \, a^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{3}}"," ",0,"2/105*(15*b^2*e^3*x^3 + 8*b^2*d^3 - 28*a*b*d^2*e + 35*a^2*d*e^2 + 3*(b^2*d*e^2 + 14*a*b*e^3)*x^2 - (4*b^2*d^2*e - 14*a*b*d*e^2 - 35*a^2*e^3)*x)*sqrt(e*x + d)/e^3","A",0
1625,1,64,0,0.397034," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} e^{2} x^{2} + 8 \, b^{2} d^{2} - 20 \, a b d e + 15 \, a^{2} e^{2} - 2 \, {\left(2 \, b^{2} d e - 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, e^{3}}"," ",0,"2/15*(3*b^2*e^2*x^2 + 8*b^2*d^2 - 20*a*b*d*e + 15*a^2*e^2 - 2*(2*b^2*d*e - 5*a*b*e^2)*x)*sqrt(e*x + d)/e^3","A",0
1626,1,73,0,0.386474," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} e^{2} x^{2} - 8 \, b^{2} d^{2} + 12 \, a b d e - 3 \, a^{2} e^{2} - 2 \, {\left(2 \, b^{2} d e - 3 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{4} x + d e^{3}\right)}}"," ",0,"2/3*(b^2*e^2*x^2 - 8*b^2*d^2 + 12*a*b*d*e - 3*a^2*e^2 - 2*(2*b^2*d*e - 3*a*b*e^2)*x)*sqrt(e*x + d)/(e^4*x + d*e^3)","A",0
1627,1,85,0,0.387745," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} e^{2} x^{2} + 8 \, b^{2} d^{2} - 4 \, a b d e - a^{2} e^{2} + 6 \, {\left(2 \, b^{2} d e - a b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"2/3*(3*b^2*e^2*x^2 + 8*b^2*d^2 - 4*a*b*d*e - a^2*e^2 + 6*(2*b^2*d*e - a*b*e^2)*x)*sqrt(e*x + d)/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
1628,1,95,0,0.402299," ","integrate((b^2*x^2+2*a*b*x+a^2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, b^{2} e^{2} x^{2} + 8 \, b^{2} d^{2} + 4 \, a b d e + 3 \, a^{2} e^{2} + 10 \, {\left(2 \, b^{2} d e + a b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-2/15*(15*b^2*e^2*x^2 + 8*b^2*d^2 + 4*a*b*d*e + 3*a^2*e^2 + 10*(2*b^2*d*e + a*b*e^2)*x)*sqrt(e*x + d)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
1629,1,444,0,0.397141," ","integrate((e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(6435 \, b^{4} e^{8} x^{8} + 128 \, b^{4} d^{8} - 1088 \, a b^{3} d^{7} e + 4080 \, a^{2} b^{2} d^{6} e^{2} - 8840 \, a^{3} b d^{5} e^{3} + 12155 \, a^{4} d^{4} e^{4} + 1716 \, {\left(13 \, b^{4} d e^{7} + 17 \, a b^{3} e^{8}\right)} x^{7} + 66 \, {\left(401 \, b^{4} d^{2} e^{6} + 1564 \, a b^{3} d e^{7} + 765 \, a^{2} b^{2} e^{8}\right)} x^{6} + 36 \, {\left(303 \, b^{4} d^{3} e^{5} + 3502 \, a b^{3} d^{2} e^{6} + 5100 \, a^{2} b^{2} d e^{7} + 1105 \, a^{3} b e^{8}\right)} x^{5} + 5 \, {\left(7 \, b^{4} d^{4} e^{4} + 10880 \, a b^{3} d^{3} e^{5} + 46716 \, a^{2} b^{2} d^{2} e^{6} + 30056 \, a^{3} b d e^{7} + 2431 \, a^{4} e^{8}\right)} x^{4} - 20 \, {\left(2 \, b^{4} d^{5} e^{3} - 17 \, a b^{3} d^{4} e^{4} - 5406 \, a^{2} b^{2} d^{3} e^{5} - 10166 \, a^{3} b d^{2} e^{6} - 2431 \, a^{4} d e^{7}\right)} x^{3} + 6 \, {\left(8 \, b^{4} d^{6} e^{2} - 68 \, a b^{3} d^{5} e^{3} + 255 \, a^{2} b^{2} d^{4} e^{4} + 17680 \, a^{3} b d^{3} e^{5} + 12155 \, a^{4} d^{2} e^{6}\right)} x^{2} - 4 \, {\left(16 \, b^{4} d^{7} e - 136 \, a b^{3} d^{6} e^{2} + 510 \, a^{2} b^{2} d^{5} e^{3} - 1105 \, a^{3} b d^{4} e^{4} - 12155 \, a^{4} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{109395 \, e^{5}}"," ",0,"2/109395*(6435*b^4*e^8*x^8 + 128*b^4*d^8 - 1088*a*b^3*d^7*e + 4080*a^2*b^2*d^6*e^2 - 8840*a^3*b*d^5*e^3 + 12155*a^4*d^4*e^4 + 1716*(13*b^4*d*e^7 + 17*a*b^3*e^8)*x^7 + 66*(401*b^4*d^2*e^6 + 1564*a*b^3*d*e^7 + 765*a^2*b^2*e^8)*x^6 + 36*(303*b^4*d^3*e^5 + 3502*a*b^3*d^2*e^6 + 5100*a^2*b^2*d*e^7 + 1105*a^3*b*e^8)*x^5 + 5*(7*b^4*d^4*e^4 + 10880*a*b^3*d^3*e^5 + 46716*a^2*b^2*d^2*e^6 + 30056*a^3*b*d*e^7 + 2431*a^4*e^8)*x^4 - 20*(2*b^4*d^5*e^3 - 17*a*b^3*d^4*e^4 - 5406*a^2*b^2*d^3*e^5 - 10166*a^3*b*d^2*e^6 - 2431*a^4*d*e^7)*x^3 + 6*(8*b^4*d^6*e^2 - 68*a*b^3*d^5*e^3 + 255*a^2*b^2*d^4*e^4 + 17680*a^3*b*d^3*e^5 + 12155*a^4*d^2*e^6)*x^2 - 4*(16*b^4*d^7*e - 136*a*b^3*d^6*e^2 + 510*a^2*b^2*d^5*e^3 - 1105*a^3*b*d^4*e^4 - 12155*a^4*d^3*e^5)*x)*sqrt(e*x + d)/e^5","B",0
1630,1,377,0,0.401530," ","integrate((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, b^{4} e^{7} x^{7} + 128 \, b^{4} d^{7} - 960 \, a b^{3} d^{6} e + 3120 \, a^{2} b^{2} d^{5} e^{2} - 5720 \, a^{3} b d^{4} e^{3} + 6435 \, a^{4} d^{3} e^{4} + 231 \, {\left(31 \, b^{4} d e^{6} + 60 \, a b^{3} e^{7}\right)} x^{6} + 63 \, {\left(71 \, b^{4} d^{2} e^{5} + 540 \, a b^{3} d e^{6} + 390 \, a^{2} b^{2} e^{7}\right)} x^{5} + 35 \, {\left(b^{4} d^{3} e^{4} + 636 \, a b^{3} d^{2} e^{5} + 1794 \, a^{2} b^{2} d e^{6} + 572 \, a^{3} b e^{7}\right)} x^{4} - 5 \, {\left(8 \, b^{4} d^{4} e^{3} - 60 \, a b^{3} d^{3} e^{4} - 8814 \, a^{2} b^{2} d^{2} e^{5} - 10868 \, a^{3} b d e^{6} - 1287 \, a^{4} e^{7}\right)} x^{3} + 3 \, {\left(16 \, b^{4} d^{5} e^{2} - 120 \, a b^{3} d^{4} e^{3} + 390 \, a^{2} b^{2} d^{3} e^{4} + 14300 \, a^{3} b d^{2} e^{5} + 6435 \, a^{4} d e^{6}\right)} x^{2} - {\left(64 \, b^{4} d^{6} e - 480 \, a b^{3} d^{5} e^{2} + 1560 \, a^{2} b^{2} d^{4} e^{3} - 2860 \, a^{3} b d^{3} e^{4} - 19305 \, a^{4} d^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{5}}"," ",0,"2/45045*(3003*b^4*e^7*x^7 + 128*b^4*d^7 - 960*a*b^3*d^6*e + 3120*a^2*b^2*d^5*e^2 - 5720*a^3*b*d^4*e^3 + 6435*a^4*d^3*e^4 + 231*(31*b^4*d*e^6 + 60*a*b^3*e^7)*x^6 + 63*(71*b^4*d^2*e^5 + 540*a*b^3*d*e^6 + 390*a^2*b^2*e^7)*x^5 + 35*(b^4*d^3*e^4 + 636*a*b^3*d^2*e^5 + 1794*a^2*b^2*d*e^6 + 572*a^3*b*e^7)*x^4 - 5*(8*b^4*d^4*e^3 - 60*a*b^3*d^3*e^4 - 8814*a^2*b^2*d^2*e^5 - 10868*a^3*b*d*e^6 - 1287*a^4*e^7)*x^3 + 3*(16*b^4*d^5*e^2 - 120*a*b^3*d^4*e^3 + 390*a^2*b^2*d^3*e^4 + 14300*a^3*b*d^2*e^5 + 6435*a^4*d*e^6)*x^2 - (64*b^4*d^6*e - 480*a*b^3*d^5*e^2 + 1560*a^2*b^2*d^4*e^3 - 2860*a^3*b*d^3*e^4 - 19305*a^4*d^2*e^5)*x)*sqrt(e*x + d)/e^5","B",0
1631,1,311,0,0.397085," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, b^{4} e^{6} x^{6} + 128 \, b^{4} d^{6} - 832 \, a b^{3} d^{5} e + 2288 \, a^{2} b^{2} d^{4} e^{2} - 3432 \, a^{3} b d^{3} e^{3} + 3003 \, a^{4} d^{2} e^{4} + 210 \, {\left(7 \, b^{4} d e^{5} + 26 \, a b^{3} e^{6}\right)} x^{5} + 35 \, {\left(b^{4} d^{2} e^{4} + 208 \, a b^{3} d e^{5} + 286 \, a^{2} b^{2} e^{6}\right)} x^{4} - 20 \, {\left(2 \, b^{4} d^{3} e^{3} - 13 \, a b^{3} d^{2} e^{4} - 715 \, a^{2} b^{2} d e^{5} - 429 \, a^{3} b e^{6}\right)} x^{3} + 3 \, {\left(16 \, b^{4} d^{4} e^{2} - 104 \, a b^{3} d^{3} e^{3} + 286 \, a^{2} b^{2} d^{2} e^{4} + 4576 \, a^{3} b d e^{5} + 1001 \, a^{4} e^{6}\right)} x^{2} - 2 \, {\left(32 \, b^{4} d^{5} e - 208 \, a b^{3} d^{4} e^{2} + 572 \, a^{2} b^{2} d^{3} e^{3} - 858 \, a^{3} b d^{2} e^{4} - 3003 \, a^{4} d e^{5}\right)} x\right)} \sqrt{e x + d}}{15015 \, e^{5}}"," ",0,"2/15015*(1155*b^4*e^6*x^6 + 128*b^4*d^6 - 832*a*b^3*d^5*e + 2288*a^2*b^2*d^4*e^2 - 3432*a^3*b*d^3*e^3 + 3003*a^4*d^2*e^4 + 210*(7*b^4*d*e^5 + 26*a*b^3*e^6)*x^5 + 35*(b^4*d^2*e^4 + 208*a*b^3*d*e^5 + 286*a^2*b^2*e^6)*x^4 - 20*(2*b^4*d^3*e^3 - 13*a*b^3*d^2*e^4 - 715*a^2*b^2*d*e^5 - 429*a^3*b*e^6)*x^3 + 3*(16*b^4*d^4*e^2 - 104*a*b^3*d^3*e^3 + 286*a^2*b^2*d^2*e^4 + 4576*a^3*b*d*e^5 + 1001*a^4*e^6)*x^2 - 2*(32*b^4*d^5*e - 208*a*b^3*d^4*e^2 + 572*a^2*b^2*d^3*e^3 - 858*a^3*b*d^2*e^4 - 3003*a^4*d*e^5)*x)*sqrt(e*x + d)/e^5","B",0
1632,1,245,0,0.392987," ","integrate((b^2*x^2+2*a*b*x+a^2)^2*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, b^{4} e^{5} x^{5} + 128 \, b^{4} d^{5} - 704 \, a b^{3} d^{4} e + 1584 \, a^{2} b^{2} d^{3} e^{2} - 1848 \, a^{3} b d^{2} e^{3} + 1155 \, a^{4} d e^{4} + 35 \, {\left(b^{4} d e^{4} + 44 \, a b^{3} e^{5}\right)} x^{4} - 10 \, {\left(4 \, b^{4} d^{2} e^{3} - 22 \, a b^{3} d e^{4} - 297 \, a^{2} b^{2} e^{5}\right)} x^{3} + 6 \, {\left(8 \, b^{4} d^{3} e^{2} - 44 \, a b^{3} d^{2} e^{3} + 99 \, a^{2} b^{2} d e^{4} + 462 \, a^{3} b e^{5}\right)} x^{2} - {\left(64 \, b^{4} d^{4} e - 352 \, a b^{3} d^{3} e^{2} + 792 \, a^{2} b^{2} d^{2} e^{3} - 924 \, a^{3} b d e^{4} - 1155 \, a^{4} e^{5}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{5}}"," ",0,"2/3465*(315*b^4*e^5*x^5 + 128*b^4*d^5 - 704*a*b^3*d^4*e + 1584*a^2*b^2*d^3*e^2 - 1848*a^3*b*d^2*e^3 + 1155*a^4*d*e^4 + 35*(b^4*d*e^4 + 44*a*b^3*e^5)*x^4 - 10*(4*b^4*d^2*e^3 - 22*a*b^3*d*e^4 - 297*a^2*b^2*e^5)*x^3 + 6*(8*b^4*d^3*e^2 - 44*a*b^3*d^2*e^3 + 99*a^2*b^2*d*e^4 + 462*a^3*b*e^5)*x^2 - (64*b^4*d^4*e - 352*a*b^3*d^3*e^2 + 792*a^2*b^2*d^2*e^3 - 924*a^3*b*d*e^4 - 1155*a^4*e^5)*x)*sqrt(e*x + d)/e^5","B",0
1633,1,182,0,0.396439," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} e^{4} x^{4} + 128 \, b^{4} d^{4} - 576 \, a b^{3} d^{3} e + 1008 \, a^{2} b^{2} d^{2} e^{2} - 840 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} - 20 \, {\left(2 \, b^{4} d e^{3} - 9 \, a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(8 \, b^{4} d^{2} e^{2} - 36 \, a b^{3} d e^{3} + 63 \, a^{2} b^{2} e^{4}\right)} x^{2} - 4 \, {\left(16 \, b^{4} d^{3} e - 72 \, a b^{3} d^{2} e^{2} + 126 \, a^{2} b^{2} d e^{3} - 105 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{5}}"," ",0,"2/315*(35*b^4*e^4*x^4 + 128*b^4*d^4 - 576*a*b^3*d^3*e + 1008*a^2*b^2*d^2*e^2 - 840*a^3*b*d*e^3 + 315*a^4*e^4 - 20*(2*b^4*d*e^3 - 9*a*b^3*e^4)*x^3 + 6*(8*b^4*d^2*e^2 - 36*a*b^3*d*e^3 + 63*a^2*b^2*e^4)*x^2 - 4*(16*b^4*d^3*e - 72*a*b^3*d^2*e^2 + 126*a^2*b^2*d*e^3 - 105*a^3*b*e^4)*x)*sqrt(e*x + d)/e^5","A",0
1634,1,192,0,0.395522," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{4} e^{4} x^{4} - 128 \, b^{4} d^{4} + 448 \, a b^{3} d^{3} e - 560 \, a^{2} b^{2} d^{2} e^{2} + 280 \, a^{3} b d e^{3} - 35 \, a^{4} e^{4} - 4 \, {\left(2 \, b^{4} d e^{3} - 7 \, a b^{3} e^{4}\right)} x^{3} + 2 \, {\left(8 \, b^{4} d^{2} e^{2} - 28 \, a b^{3} d e^{3} + 35 \, a^{2} b^{2} e^{4}\right)} x^{2} - 4 \, {\left(16 \, b^{4} d^{3} e - 56 \, a b^{3} d^{2} e^{2} + 70 \, a^{2} b^{2} d e^{3} - 35 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"2/35*(5*b^4*e^4*x^4 - 128*b^4*d^4 + 448*a*b^3*d^3*e - 560*a^2*b^2*d^2*e^2 + 280*a^3*b*d*e^3 - 35*a^4*e^4 - 4*(2*b^4*d*e^3 - 7*a*b^3*e^4)*x^3 + 2*(8*b^4*d^2*e^2 - 28*a*b^3*d*e^3 + 35*a^2*b^2*e^4)*x^2 - 4*(16*b^4*d^3*e - 56*a*b^3*d^2*e^2 + 70*a^2*b^2*d*e^3 - 35*a^3*b*e^4)*x)*sqrt(e*x + d)/(e^6*x + d*e^5)","A",0
1635,1,203,0,0.400113," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{4} e^{4} x^{4} + 128 \, b^{4} d^{4} - 320 \, a b^{3} d^{3} e + 240 \, a^{2} b^{2} d^{2} e^{2} - 40 \, a^{3} b d e^{3} - 5 \, a^{4} e^{4} - 4 \, {\left(2 \, b^{4} d e^{3} - 5 \, a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(8 \, b^{4} d^{2} e^{2} - 20 \, a b^{3} d e^{3} + 15 \, a^{2} b^{2} e^{4}\right)} x^{2} + 12 \, {\left(16 \, b^{4} d^{3} e - 40 \, a b^{3} d^{2} e^{2} + 30 \, a^{2} b^{2} d e^{3} - 5 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"2/15*(3*b^4*e^4*x^4 + 128*b^4*d^4 - 320*a*b^3*d^3*e + 240*a^2*b^2*d^2*e^2 - 40*a^3*b*d*e^3 - 5*a^4*e^4 - 4*(2*b^4*d*e^3 - 5*a*b^3*e^4)*x^3 + 6*(8*b^4*d^2*e^2 - 20*a*b^3*d*e^3 + 15*a^2*b^2*e^4)*x^2 + 12*(16*b^4*d^3*e - 40*a*b^3*d^2*e^2 + 30*a^2*b^2*d*e^3 - 5*a^3*b*e^4)*x)*sqrt(e*x + d)/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
1636,1,213,0,0.395141," ","integrate((b^2*x^2+2*a*b*x+a^2)^2/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{4} e^{4} x^{4} - 128 \, b^{4} d^{4} + 192 \, a b^{3} d^{3} e - 48 \, a^{2} b^{2} d^{2} e^{2} - 8 \, a^{3} b d e^{3} - 3 \, a^{4} e^{4} - 20 \, {\left(2 \, b^{4} d e^{3} - 3 \, a b^{3} e^{4}\right)} x^{3} - 30 \, {\left(8 \, b^{4} d^{2} e^{2} - 12 \, a b^{3} d e^{3} + 3 \, a^{2} b^{2} e^{4}\right)} x^{2} - 20 \, {\left(16 \, b^{4} d^{3} e - 24 \, a b^{3} d^{2} e^{2} + 6 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"2/15*(5*b^4*e^4*x^4 - 128*b^4*d^4 + 192*a*b^3*d^3*e - 48*a^2*b^2*d^2*e^2 - 8*a^3*b*d*e^3 - 3*a^4*e^4 - 20*(2*b^4*d*e^3 - 3*a*b^3*e^4)*x^3 - 30*(8*b^4*d^2*e^2 - 12*a*b^3*d*e^3 + 3*a^2*b^2*e^4)*x^2 - 20*(16*b^4*d^3*e - 24*a*b^3*d^2*e^2 + 6*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*sqrt(e*x + d)/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
1637,1,729,0,0.420344," ","integrate((e*x+d)^(7/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(138567 \, b^{6} e^{10} x^{10} + 1024 \, b^{6} d^{10} - 10752 \, a b^{5} d^{9} e + 51072 \, a^{2} b^{4} d^{8} e^{2} - 144704 \, a^{3} b^{3} d^{7} e^{3} + 271320 \, a^{4} b^{2} d^{6} e^{4} - 352716 \, a^{5} b d^{5} e^{5} + 323323 \, a^{6} d^{4} e^{6} + 14586 \, {\left(32 \, b^{6} d e^{9} + 63 \, a b^{5} e^{10}\right)} x^{9} + 3861 \, {\left(138 \, b^{6} d^{2} e^{8} + 812 \, a b^{5} d e^{9} + 665 \, a^{2} b^{4} e^{10}\right)} x^{8} + 1716 \, {\left(121 \, b^{6} d^{3} e^{7} + 2121 \, a b^{5} d^{2} e^{8} + 5187 \, a^{2} b^{4} d e^{9} + 2261 \, a^{3} b^{3} e^{10}\right)} x^{7} + 231 \, {\left(b^{6} d^{4} e^{6} + 6288 \, a b^{5} d^{3} e^{7} + 45714 \, a^{2} b^{4} d^{2} e^{8} + 59432 \, a^{3} b^{3} d e^{9} + 14535 \, a^{4} b^{2} e^{10}\right)} x^{6} - 126 \, {\left(2 \, b^{6} d^{5} e^{5} - 21 \, a b^{5} d^{4} e^{6} - 34542 \, a^{2} b^{4} d^{3} e^{7} - 133076 \, a^{3} b^{3} d^{2} e^{8} - 96900 \, a^{4} b^{2} d e^{9} - 12597 \, a^{5} b e^{10}\right)} x^{5} + 7 \, {\left(40 \, b^{6} d^{6} e^{4} - 420 \, a b^{5} d^{5} e^{5} + 1995 \, a^{2} b^{4} d^{4} e^{6} + 1033600 \, a^{3} b^{3} d^{3} e^{7} + 2219010 \, a^{4} b^{2} d^{2} e^{8} + 856596 \, a^{5} b d e^{9} + 46189 \, a^{6} e^{10}\right)} x^{4} - 4 \, {\left(80 \, b^{6} d^{7} e^{3} - 840 \, a b^{5} d^{6} e^{4} + 3990 \, a^{2} b^{4} d^{5} e^{5} - 11305 \, a^{3} b^{3} d^{4} e^{6} - 1797495 \, a^{4} b^{2} d^{3} e^{7} - 2028117 \, a^{5} b d^{2} e^{8} - 323323 \, a^{6} d e^{9}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{8} e^{2} - 1344 \, a b^{5} d^{7} e^{3} + 6384 \, a^{2} b^{4} d^{6} e^{4} - 18088 \, a^{3} b^{3} d^{5} e^{5} + 33915 \, a^{4} b^{2} d^{4} e^{6} + 1410864 \, a^{5} b d^{3} e^{7} + 646646 \, a^{6} d^{2} e^{8}\right)} x^{2} - 2 \, {\left(256 \, b^{6} d^{9} e - 2688 \, a b^{5} d^{8} e^{2} + 12768 \, a^{2} b^{4} d^{7} e^{3} - 36176 \, a^{3} b^{3} d^{6} e^{4} + 67830 \, a^{4} b^{2} d^{5} e^{5} - 88179 \, a^{5} b d^{4} e^{6} - 646646 \, a^{6} d^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{2909907 \, e^{7}}"," ",0,"2/2909907*(138567*b^6*e^10*x^10 + 1024*b^6*d^10 - 10752*a*b^5*d^9*e + 51072*a^2*b^4*d^8*e^2 - 144704*a^3*b^3*d^7*e^3 + 271320*a^4*b^2*d^6*e^4 - 352716*a^5*b*d^5*e^5 + 323323*a^6*d^4*e^6 + 14586*(32*b^6*d*e^9 + 63*a*b^5*e^10)*x^9 + 3861*(138*b^6*d^2*e^8 + 812*a*b^5*d*e^9 + 665*a^2*b^4*e^10)*x^8 + 1716*(121*b^6*d^3*e^7 + 2121*a*b^5*d^2*e^8 + 5187*a^2*b^4*d*e^9 + 2261*a^3*b^3*e^10)*x^7 + 231*(b^6*d^4*e^6 + 6288*a*b^5*d^3*e^7 + 45714*a^2*b^4*d^2*e^8 + 59432*a^3*b^3*d*e^9 + 14535*a^4*b^2*e^10)*x^6 - 126*(2*b^6*d^5*e^5 - 21*a*b^5*d^4*e^6 - 34542*a^2*b^4*d^3*e^7 - 133076*a^3*b^3*d^2*e^8 - 96900*a^4*b^2*d*e^9 - 12597*a^5*b*e^10)*x^5 + 7*(40*b^6*d^6*e^4 - 420*a*b^5*d^5*e^5 + 1995*a^2*b^4*d^4*e^6 + 1033600*a^3*b^3*d^3*e^7 + 2219010*a^4*b^2*d^2*e^8 + 856596*a^5*b*d*e^9 + 46189*a^6*e^10)*x^4 - 4*(80*b^6*d^7*e^3 - 840*a*b^5*d^6*e^4 + 3990*a^2*b^4*d^5*e^5 - 11305*a^3*b^3*d^4*e^6 - 1797495*a^4*b^2*d^3*e^7 - 2028117*a^5*b*d^2*e^8 - 323323*a^6*d*e^9)*x^3 + 3*(128*b^6*d^8*e^2 - 1344*a*b^5*d^7*e^3 + 6384*a^2*b^4*d^6*e^4 - 18088*a^3*b^3*d^5*e^5 + 33915*a^4*b^2*d^4*e^6 + 1410864*a^5*b*d^3*e^7 + 646646*a^6*d^2*e^8)*x^2 - 2*(256*b^6*d^9*e - 2688*a*b^5*d^8*e^2 + 12768*a^2*b^4*d^7*e^3 - 36176*a^3*b^3*d^6*e^4 + 67830*a^4*b^2*d^5*e^5 - 88179*a^5*b*d^4*e^6 - 646646*a^6*d^3*e^7)*x)*sqrt(e*x + d)/e^7","B",0
1638,1,635,0,0.409918," ","integrate((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(51051 \, b^{6} e^{9} x^{9} + 1024 \, b^{6} d^{9} - 9728 \, a b^{5} d^{8} e + 41344 \, a^{2} b^{4} d^{7} e^{2} - 103360 \, a^{3} b^{3} d^{6} e^{3} + 167960 \, a^{4} b^{2} d^{5} e^{4} - 184756 \, a^{5} b d^{4} e^{5} + 138567 \, a^{6} d^{3} e^{6} + 9009 \, {\left(13 \, b^{6} d e^{8} + 38 \, a b^{5} e^{9}\right)} x^{8} + 3003 \, {\left(23 \, b^{6} d^{2} e^{7} + 266 \, a b^{5} d e^{8} + 323 \, a^{2} b^{4} e^{9}\right)} x^{7} + 231 \, {\left(b^{6} d^{3} e^{6} + 2090 \, a b^{5} d^{2} e^{7} + 10013 \, a^{2} b^{4} d e^{8} + 6460 \, a^{3} b^{3} e^{9}\right)} x^{6} - 63 \, {\left(4 \, b^{6} d^{4} e^{5} - 38 \, a b^{5} d^{3} e^{6} - 22933 \, a^{2} b^{4} d^{2} e^{7} - 58140 \, a^{3} b^{3} d e^{8} - 20995 \, a^{4} b^{2} e^{9}\right)} x^{5} + 7 \, {\left(40 \, b^{6} d^{5} e^{4} - 380 \, a b^{5} d^{4} e^{5} + 1615 \, a^{2} b^{4} d^{3} e^{6} + 342380 \, a^{3} b^{3} d^{2} e^{7} + 482885 \, a^{4} b^{2} d e^{8} + 92378 \, a^{5} b e^{9}\right)} x^{4} - {\left(320 \, b^{6} d^{6} e^{3} - 3040 \, a b^{5} d^{5} e^{4} + 12920 \, a^{2} b^{4} d^{4} e^{5} - 32300 \, a^{3} b^{3} d^{3} e^{6} - 2372435 \, a^{4} b^{2} d^{2} e^{7} - 1755182 \, a^{5} b d e^{8} - 138567 \, a^{6} e^{9}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{7} e^{2} - 1216 \, a b^{5} d^{6} e^{3} + 5168 \, a^{2} b^{4} d^{5} e^{4} - 12920 \, a^{3} b^{3} d^{4} e^{5} + 20995 \, a^{4} b^{2} d^{3} e^{6} + 461890 \, a^{5} b d^{2} e^{7} + 138567 \, a^{6} d e^{8}\right)} x^{2} - {\left(512 \, b^{6} d^{8} e - 4864 \, a b^{5} d^{7} e^{2} + 20672 \, a^{2} b^{4} d^{6} e^{3} - 51680 \, a^{3} b^{3} d^{5} e^{4} + 83980 \, a^{4} b^{2} d^{4} e^{5} - 92378 \, a^{5} b d^{3} e^{6} - 415701 \, a^{6} d^{2} e^{7}\right)} x\right)} \sqrt{e x + d}}{969969 \, e^{7}}"," ",0,"2/969969*(51051*b^6*e^9*x^9 + 1024*b^6*d^9 - 9728*a*b^5*d^8*e + 41344*a^2*b^4*d^7*e^2 - 103360*a^3*b^3*d^6*e^3 + 167960*a^4*b^2*d^5*e^4 - 184756*a^5*b*d^4*e^5 + 138567*a^6*d^3*e^6 + 9009*(13*b^6*d*e^8 + 38*a*b^5*e^9)*x^8 + 3003*(23*b^6*d^2*e^7 + 266*a*b^5*d*e^8 + 323*a^2*b^4*e^9)*x^7 + 231*(b^6*d^3*e^6 + 2090*a*b^5*d^2*e^7 + 10013*a^2*b^4*d*e^8 + 6460*a^3*b^3*e^9)*x^6 - 63*(4*b^6*d^4*e^5 - 38*a*b^5*d^3*e^6 - 22933*a^2*b^4*d^2*e^7 - 58140*a^3*b^3*d*e^8 - 20995*a^4*b^2*e^9)*x^5 + 7*(40*b^6*d^5*e^4 - 380*a*b^5*d^4*e^5 + 1615*a^2*b^4*d^3*e^6 + 342380*a^3*b^3*d^2*e^7 + 482885*a^4*b^2*d*e^8 + 92378*a^5*b*e^9)*x^4 - (320*b^6*d^6*e^3 - 3040*a*b^5*d^5*e^4 + 12920*a^2*b^4*d^4*e^5 - 32300*a^3*b^3*d^3*e^6 - 2372435*a^4*b^2*d^2*e^7 - 1755182*a^5*b*d*e^8 - 138567*a^6*e^9)*x^3 + 3*(128*b^6*d^7*e^2 - 1216*a*b^5*d^6*e^3 + 5168*a^2*b^4*d^5*e^4 - 12920*a^3*b^3*d^4*e^5 + 20995*a^4*b^2*d^3*e^6 + 461890*a^5*b*d^2*e^7 + 138567*a^6*d*e^8)*x^2 - (512*b^6*d^8*e - 4864*a*b^5*d^7*e^2 + 20672*a^2*b^4*d^6*e^3 - 51680*a^3*b^3*d^5*e^4 + 83980*a^4*b^2*d^4*e^5 - 92378*a^5*b*d^3*e^6 - 415701*a^6*d^2*e^7)*x)*sqrt(e*x + d)/e^7","B",0
1639,1,541,0,0.403996," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(15015 \, b^{6} e^{8} x^{8} + 1024 \, b^{6} d^{8} - 8704 \, a b^{5} d^{7} e + 32640 \, a^{2} b^{4} d^{6} e^{2} - 70720 \, a^{3} b^{3} d^{5} e^{3} + 97240 \, a^{4} b^{2} d^{4} e^{4} - 87516 \, a^{5} b d^{3} e^{5} + 51051 \, a^{6} d^{2} e^{6} + 6006 \, {\left(3 \, b^{6} d e^{7} + 17 \, a b^{5} e^{8}\right)} x^{7} + 231 \, {\left(b^{6} d^{2} e^{6} + 544 \, a b^{5} d e^{7} + 1275 \, a^{2} b^{4} e^{8}\right)} x^{6} - 42 \, {\left(6 \, b^{6} d^{3} e^{5} - 51 \, a b^{5} d^{2} e^{6} - 8925 \, a^{2} b^{4} d e^{7} - 11050 \, a^{3} b^{3} e^{8}\right)} x^{5} + 35 \, {\left(8 \, b^{6} d^{4} e^{4} - 68 \, a b^{5} d^{3} e^{5} + 255 \, a^{2} b^{4} d^{2} e^{6} + 17680 \, a^{3} b^{3} d e^{7} + 12155 \, a^{4} b^{2} e^{8}\right)} x^{4} - 10 \, {\left(32 \, b^{6} d^{5} e^{3} - 272 \, a b^{5} d^{4} e^{4} + 1020 \, a^{2} b^{4} d^{3} e^{5} - 2210 \, a^{3} b^{3} d^{2} e^{6} - 60775 \, a^{4} b^{2} d e^{7} - 21879 \, a^{5} b e^{8}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{6} e^{2} - 1088 \, a b^{5} d^{5} e^{3} + 4080 \, a^{2} b^{4} d^{4} e^{4} - 8840 \, a^{3} b^{3} d^{3} e^{5} + 12155 \, a^{4} b^{2} d^{2} e^{6} + 116688 \, a^{5} b d e^{7} + 17017 \, a^{6} e^{8}\right)} x^{2} - 2 \, {\left(256 \, b^{6} d^{7} e - 2176 \, a b^{5} d^{6} e^{2} + 8160 \, a^{2} b^{4} d^{5} e^{3} - 17680 \, a^{3} b^{3} d^{4} e^{4} + 24310 \, a^{4} b^{2} d^{3} e^{5} - 21879 \, a^{5} b d^{2} e^{6} - 51051 \, a^{6} d e^{7}\right)} x\right)} \sqrt{e x + d}}{255255 \, e^{7}}"," ",0,"2/255255*(15015*b^6*e^8*x^8 + 1024*b^6*d^8 - 8704*a*b^5*d^7*e + 32640*a^2*b^4*d^6*e^2 - 70720*a^3*b^3*d^5*e^3 + 97240*a^4*b^2*d^4*e^4 - 87516*a^5*b*d^3*e^5 + 51051*a^6*d^2*e^6 + 6006*(3*b^6*d*e^7 + 17*a*b^5*e^8)*x^7 + 231*(b^6*d^2*e^6 + 544*a*b^5*d*e^7 + 1275*a^2*b^4*e^8)*x^6 - 42*(6*b^6*d^3*e^5 - 51*a*b^5*d^2*e^6 - 8925*a^2*b^4*d*e^7 - 11050*a^3*b^3*e^8)*x^5 + 35*(8*b^6*d^4*e^4 - 68*a*b^5*d^3*e^5 + 255*a^2*b^4*d^2*e^6 + 17680*a^3*b^3*d*e^7 + 12155*a^4*b^2*e^8)*x^4 - 10*(32*b^6*d^5*e^3 - 272*a*b^5*d^4*e^4 + 1020*a^2*b^4*d^3*e^5 - 2210*a^3*b^3*d^2*e^6 - 60775*a^4*b^2*d*e^7 - 21879*a^5*b*e^8)*x^3 + 3*(128*b^6*d^6*e^2 - 1088*a*b^5*d^5*e^3 + 4080*a^2*b^4*d^4*e^4 - 8840*a^3*b^3*d^3*e^5 + 12155*a^4*b^2*d^2*e^6 + 116688*a^5*b*d*e^7 + 17017*a^6*e^8)*x^2 - 2*(256*b^6*d^7*e - 2176*a*b^5*d^6*e^2 + 8160*a^2*b^4*d^5*e^3 - 17680*a^3*b^3*d^4*e^4 + 24310*a^4*b^2*d^3*e^5 - 21879*a^5*b*d^2*e^6 - 51051*a^6*d*e^7)*x)*sqrt(e*x + d)/e^7","B",0
1640,1,447,0,0.400509," ","integrate((b^2*x^2+2*a*b*x+a^2)^3*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, b^{6} e^{7} x^{7} + 1024 \, b^{6} d^{7} - 7680 \, a b^{5} d^{6} e + 24960 \, a^{2} b^{4} d^{5} e^{2} - 45760 \, a^{3} b^{3} d^{4} e^{3} + 51480 \, a^{4} b^{2} d^{3} e^{4} - 36036 \, a^{5} b d^{2} e^{5} + 15015 \, a^{6} d e^{6} + 231 \, {\left(b^{6} d e^{6} + 90 \, a b^{5} e^{7}\right)} x^{6} - 63 \, {\left(4 \, b^{6} d^{2} e^{5} - 30 \, a b^{5} d e^{6} - 975 \, a^{2} b^{4} e^{7}\right)} x^{5} + 35 \, {\left(8 \, b^{6} d^{3} e^{4} - 60 \, a b^{5} d^{2} e^{5} + 195 \, a^{2} b^{4} d e^{6} + 2860 \, a^{3} b^{3} e^{7}\right)} x^{4} - 5 \, {\left(64 \, b^{6} d^{4} e^{3} - 480 \, a b^{5} d^{3} e^{4} + 1560 \, a^{2} b^{4} d^{2} e^{5} - 2860 \, a^{3} b^{3} d e^{6} - 19305 \, a^{4} b^{2} e^{7}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{5} e^{2} - 960 \, a b^{5} d^{4} e^{3} + 3120 \, a^{2} b^{4} d^{3} e^{4} - 5720 \, a^{3} b^{3} d^{2} e^{5} + 6435 \, a^{4} b^{2} d e^{6} + 18018 \, a^{5} b e^{7}\right)} x^{2} - {\left(512 \, b^{6} d^{6} e - 3840 \, a b^{5} d^{5} e^{2} + 12480 \, a^{2} b^{4} d^{4} e^{3} - 22880 \, a^{3} b^{3} d^{3} e^{4} + 25740 \, a^{4} b^{2} d^{2} e^{5} - 18018 \, a^{5} b d e^{6} - 15015 \, a^{6} e^{7}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{7}}"," ",0,"2/45045*(3003*b^6*e^7*x^7 + 1024*b^6*d^7 - 7680*a*b^5*d^6*e + 24960*a^2*b^4*d^5*e^2 - 45760*a^3*b^3*d^4*e^3 + 51480*a^4*b^2*d^3*e^4 - 36036*a^5*b*d^2*e^5 + 15015*a^6*d*e^6 + 231*(b^6*d*e^6 + 90*a*b^5*e^7)*x^6 - 63*(4*b^6*d^2*e^5 - 30*a*b^5*d*e^6 - 975*a^2*b^4*e^7)*x^5 + 35*(8*b^6*d^3*e^4 - 60*a*b^5*d^2*e^5 + 195*a^2*b^4*d*e^6 + 2860*a^3*b^3*e^7)*x^4 - 5*(64*b^6*d^4*e^3 - 480*a*b^5*d^3*e^4 + 1560*a^2*b^4*d^2*e^5 - 2860*a^3*b^3*d*e^6 - 19305*a^4*b^2*e^7)*x^3 + 3*(128*b^6*d^5*e^2 - 960*a*b^5*d^4*e^3 + 3120*a^2*b^4*d^3*e^4 - 5720*a^3*b^3*d^2*e^5 + 6435*a^4*b^2*d*e^6 + 18018*a^5*b*e^7)*x^2 - (512*b^6*d^6*e - 3840*a*b^5*d^5*e^2 + 12480*a^2*b^4*d^4*e^3 - 22880*a^3*b^3*d^3*e^4 + 25740*a^4*b^2*d^2*e^5 - 18018*a^5*b*d*e^6 - 15015*a^6*e^7)*x)*sqrt(e*x + d)/e^7","B",0
1641,1,356,0,0.389325," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, b^{6} e^{6} x^{6} + 1024 \, b^{6} d^{6} - 6656 \, a b^{5} d^{5} e + 18304 \, a^{2} b^{4} d^{4} e^{2} - 27456 \, a^{3} b^{3} d^{3} e^{3} + 24024 \, a^{4} b^{2} d^{2} e^{4} - 12012 \, a^{5} b d e^{5} + 3003 \, a^{6} e^{6} - 126 \, {\left(2 \, b^{6} d e^{5} - 13 \, a b^{5} e^{6}\right)} x^{5} + 35 \, {\left(8 \, b^{6} d^{2} e^{4} - 52 \, a b^{5} d e^{5} + 143 \, a^{2} b^{4} e^{6}\right)} x^{4} - 20 \, {\left(16 \, b^{6} d^{3} e^{3} - 104 \, a b^{5} d^{2} e^{4} + 286 \, a^{2} b^{4} d e^{5} - 429 \, a^{3} b^{3} e^{6}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{4} e^{2} - 832 \, a b^{5} d^{3} e^{3} + 2288 \, a^{2} b^{4} d^{2} e^{4} - 3432 \, a^{3} b^{3} d e^{5} + 3003 \, a^{4} b^{2} e^{6}\right)} x^{2} - 2 \, {\left(256 \, b^{6} d^{5} e - 1664 \, a b^{5} d^{4} e^{2} + 4576 \, a^{2} b^{4} d^{3} e^{3} - 6864 \, a^{3} b^{3} d^{2} e^{4} + 6006 \, a^{4} b^{2} d e^{5} - 3003 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{3003 \, e^{7}}"," ",0,"2/3003*(231*b^6*e^6*x^6 + 1024*b^6*d^6 - 6656*a*b^5*d^5*e + 18304*a^2*b^4*d^4*e^2 - 27456*a^3*b^3*d^3*e^3 + 24024*a^4*b^2*d^2*e^4 - 12012*a^5*b*d*e^5 + 3003*a^6*e^6 - 126*(2*b^6*d*e^5 - 13*a*b^5*e^6)*x^5 + 35*(8*b^6*d^2*e^4 - 52*a*b^5*d*e^5 + 143*a^2*b^4*e^6)*x^4 - 20*(16*b^6*d^3*e^3 - 104*a*b^5*d^2*e^4 + 286*a^2*b^4*d*e^5 - 429*a^3*b^3*e^6)*x^3 + 3*(128*b^6*d^4*e^2 - 832*a*b^5*d^3*e^3 + 2288*a^2*b^4*d^2*e^4 - 3432*a^3*b^3*d*e^5 + 3003*a^4*b^2*e^6)*x^2 - 2*(256*b^6*d^5*e - 1664*a*b^5*d^4*e^2 + 4576*a^2*b^4*d^3*e^3 - 6864*a^3*b^3*d^2*e^4 + 6006*a^4*b^2*d*e^5 - 3003*a^5*b*e^6)*x)*sqrt(e*x + d)/e^7","B",0
1642,1,365,0,0.406741," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(21 \, b^{6} e^{6} x^{6} - 1024 \, b^{6} d^{6} + 5632 \, a b^{5} d^{5} e - 12672 \, a^{2} b^{4} d^{4} e^{2} + 14784 \, a^{3} b^{3} d^{3} e^{3} - 9240 \, a^{4} b^{2} d^{2} e^{4} + 2772 \, a^{5} b d e^{5} - 231 \, a^{6} e^{6} - 14 \, {\left(2 \, b^{6} d e^{5} - 11 \, a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(8 \, b^{6} d^{2} e^{4} - 44 \, a b^{5} d e^{5} + 99 \, a^{2} b^{4} e^{6}\right)} x^{4} - 4 \, {\left(16 \, b^{6} d^{3} e^{3} - 88 \, a b^{5} d^{2} e^{4} + 198 \, a^{2} b^{4} d e^{5} - 231 \, a^{3} b^{3} e^{6}\right)} x^{3} + {\left(128 \, b^{6} d^{4} e^{2} - 704 \, a b^{5} d^{3} e^{3} + 1584 \, a^{2} b^{4} d^{2} e^{4} - 1848 \, a^{3} b^{3} d e^{5} + 1155 \, a^{4} b^{2} e^{6}\right)} x^{2} - 2 \, {\left(256 \, b^{6} d^{5} e - 1408 \, a b^{5} d^{4} e^{2} + 3168 \, a^{2} b^{4} d^{3} e^{3} - 3696 \, a^{3} b^{3} d^{2} e^{4} + 2310 \, a^{4} b^{2} d e^{5} - 693 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{231 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"2/231*(21*b^6*e^6*x^6 - 1024*b^6*d^6 + 5632*a*b^5*d^5*e - 12672*a^2*b^4*d^4*e^2 + 14784*a^3*b^3*d^3*e^3 - 9240*a^4*b^2*d^2*e^4 + 2772*a^5*b*d*e^5 - 231*a^6*e^6 - 14*(2*b^6*d*e^5 - 11*a*b^5*e^6)*x^5 + 5*(8*b^6*d^2*e^4 - 44*a*b^5*d*e^5 + 99*a^2*b^4*e^6)*x^4 - 4*(16*b^6*d^3*e^3 - 88*a*b^5*d^2*e^4 + 198*a^2*b^4*d*e^5 - 231*a^3*b^3*e^6)*x^3 + (128*b^6*d^4*e^2 - 704*a*b^5*d^3*e^3 + 1584*a^2*b^4*d^2*e^4 - 1848*a^3*b^3*d*e^5 + 1155*a^4*b^2*e^6)*x^2 - 2*(256*b^6*d^5*e - 1408*a*b^5*d^4*e^2 + 3168*a^2*b^4*d^3*e^3 - 3696*a^3*b^3*d^2*e^4 + 2310*a^4*b^2*d*e^5 - 693*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^8*x + d*e^7)","B",0
1643,1,377,0,0.401734," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b^{6} e^{6} x^{6} + 1024 \, b^{6} d^{6} - 4608 \, a b^{5} d^{5} e + 8064 \, a^{2} b^{4} d^{4} e^{2} - 6720 \, a^{3} b^{3} d^{3} e^{3} + 2520 \, a^{4} b^{2} d^{2} e^{4} - 252 \, a^{5} b d e^{5} - 21 \, a^{6} e^{6} - 6 \, {\left(2 \, b^{6} d e^{5} - 9 \, a b^{5} e^{6}\right)} x^{5} + 3 \, {\left(8 \, b^{6} d^{2} e^{4} - 36 \, a b^{5} d e^{5} + 63 \, a^{2} b^{4} e^{6}\right)} x^{4} - 4 \, {\left(16 \, b^{6} d^{3} e^{3} - 72 \, a b^{5} d^{2} e^{4} + 126 \, a^{2} b^{4} d e^{5} - 105 \, a^{3} b^{3} e^{6}\right)} x^{3} + 3 \, {\left(128 \, b^{6} d^{4} e^{2} - 576 \, a b^{5} d^{3} e^{3} + 1008 \, a^{2} b^{4} d^{2} e^{4} - 840 \, a^{3} b^{3} d e^{5} + 315 \, a^{4} b^{2} e^{6}\right)} x^{2} + 6 \, {\left(256 \, b^{6} d^{5} e - 1152 \, a b^{5} d^{4} e^{2} + 2016 \, a^{2} b^{4} d^{3} e^{3} - 1680 \, a^{3} b^{3} d^{2} e^{4} + 630 \, a^{4} b^{2} d e^{5} - 63 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{63 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"2/63*(7*b^6*e^6*x^6 + 1024*b^6*d^6 - 4608*a*b^5*d^5*e + 8064*a^2*b^4*d^4*e^2 - 6720*a^3*b^3*d^3*e^3 + 2520*a^4*b^2*d^2*e^4 - 252*a^5*b*d*e^5 - 21*a^6*e^6 - 6*(2*b^6*d*e^5 - 9*a*b^5*e^6)*x^5 + 3*(8*b^6*d^2*e^4 - 36*a*b^5*d*e^5 + 63*a^2*b^4*e^6)*x^4 - 4*(16*b^6*d^3*e^3 - 72*a*b^5*d^2*e^4 + 126*a^2*b^4*d*e^5 - 105*a^3*b^3*e^6)*x^3 + 3*(128*b^6*d^4*e^2 - 576*a*b^5*d^3*e^3 + 1008*a^2*b^4*d^2*e^4 - 840*a^3*b^3*d*e^5 + 315*a^4*b^2*e^6)*x^2 + 6*(256*b^6*d^5*e - 1152*a*b^5*d^4*e^2 + 2016*a^2*b^4*d^3*e^3 - 1680*a^3*b^3*d^2*e^4 + 630*a^4*b^2*d*e^5 - 63*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","B",0
1644,1,388,0,0.395068," ","integrate((b^2*x^2+2*a*b*x+a^2)^3/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{6} e^{6} x^{6} - 1024 \, b^{6} d^{6} + 3584 \, a b^{5} d^{5} e - 4480 \, a^{2} b^{4} d^{4} e^{2} + 2240 \, a^{3} b^{3} d^{3} e^{3} - 280 \, a^{4} b^{2} d^{2} e^{4} - 28 \, a^{5} b d e^{5} - 7 \, a^{6} e^{6} - 6 \, {\left(2 \, b^{6} d e^{5} - 7 \, a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(8 \, b^{6} d^{2} e^{4} - 28 \, a b^{5} d e^{5} + 35 \, a^{2} b^{4} e^{6}\right)} x^{4} - 20 \, {\left(16 \, b^{6} d^{3} e^{3} - 56 \, a b^{5} d^{2} e^{4} + 70 \, a^{2} b^{4} d e^{5} - 35 \, a^{3} b^{3} e^{6}\right)} x^{3} - 15 \, {\left(128 \, b^{6} d^{4} e^{2} - 448 \, a b^{5} d^{3} e^{3} + 560 \, a^{2} b^{4} d^{2} e^{4} - 280 \, a^{3} b^{3} d e^{5} + 35 \, a^{4} b^{2} e^{6}\right)} x^{2} - 10 \, {\left(256 \, b^{6} d^{5} e - 896 \, a b^{5} d^{4} e^{2} + 1120 \, a^{2} b^{4} d^{3} e^{3} - 560 \, a^{3} b^{3} d^{2} e^{4} + 70 \, a^{4} b^{2} d e^{5} + 7 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"2/35*(5*b^6*e^6*x^6 - 1024*b^6*d^6 + 3584*a*b^5*d^5*e - 4480*a^2*b^4*d^4*e^2 + 2240*a^3*b^3*d^3*e^3 - 280*a^4*b^2*d^2*e^4 - 28*a^5*b*d*e^5 - 7*a^6*e^6 - 6*(2*b^6*d*e^5 - 7*a*b^5*e^6)*x^5 + 5*(8*b^6*d^2*e^4 - 28*a*b^5*d*e^5 + 35*a^2*b^4*e^6)*x^4 - 20*(16*b^6*d^3*e^3 - 56*a*b^5*d^2*e^4 + 70*a^2*b^4*d*e^5 - 35*a^3*b^3*e^6)*x^3 - 15*(128*b^6*d^4*e^2 - 448*a*b^5*d^3*e^3 + 560*a^2*b^4*d^2*e^4 - 280*a^3*b^3*d*e^5 + 35*a^4*b^2*e^6)*x^2 - 10*(256*b^6*d^5*e - 896*a*b^5*d^4*e^2 + 1120*a^2*b^4*d^3*e^3 - 560*a^3*b^3*d^2*e^4 + 70*a^4*b^2*d*e^5 + 7*a^5*b*e^6)*x)*sqrt(e*x + d)/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","B",0
1645,1,678,0,0.429949," ","integrate((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(a b^{3} d^{3} e - 3 \, a^{2} b^{2} d^{2} e^{2} + 3 \, a^{3} b d e^{3} - a^{4} e^{4} + {\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)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(10 \, b^{4} e^{4} x^{4} - 35 \, b^{4} d^{4} + 528 \, a b^{3} d^{3} e - 1218 \, a^{2} b^{2} d^{2} e^{2} + 1050 \, a^{3} b d e^{3} - 315 \, a^{4} e^{4} + 2 \, {\left(29 \, b^{4} d e^{3} - 9 \, a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(26 \, b^{4} d^{2} e^{2} - 23 \, a b^{3} d e^{3} + 7 \, a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(194 \, b^{4} d^{3} e - 426 \, a b^{3} d^{2} e^{2} + 357 \, a^{2} b^{2} d e^{3} - 105 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{70 \, {\left(b^{6} x + a b^{5}\right)}}, -\frac{315 \, {\left(a b^{3} d^{3} e - 3 \, a^{2} b^{2} d^{2} e^{2} + 3 \, a^{3} b d e^{3} - a^{4} e^{4} + {\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)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(10 \, b^{4} e^{4} x^{4} - 35 \, b^{4} d^{4} + 528 \, a b^{3} d^{3} e - 1218 \, a^{2} b^{2} d^{2} e^{2} + 1050 \, a^{3} b d e^{3} - 315 \, a^{4} e^{4} + 2 \, {\left(29 \, b^{4} d e^{3} - 9 \, a b^{3} e^{4}\right)} x^{3} + 6 \, {\left(26 \, b^{4} d^{2} e^{2} - 23 \, a b^{3} d e^{3} + 7 \, a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(194 \, b^{4} d^{3} e - 426 \, a b^{3} d^{2} e^{2} + 357 \, a^{2} b^{2} d e^{3} - 105 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(b^{6} x + a b^{5}\right)}}\right]"," ",0,"[-1/70*(315*(a*b^3*d^3*e - 3*a^2*b^2*d^2*e^2 + 3*a^3*b*d*e^3 - a^4*e^4 + (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)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(10*b^4*e^4*x^4 - 35*b^4*d^4 + 528*a*b^3*d^3*e - 1218*a^2*b^2*d^2*e^2 + 1050*a^3*b*d*e^3 - 315*a^4*e^4 + 2*(29*b^4*d*e^3 - 9*a*b^3*e^4)*x^3 + 6*(26*b^4*d^2*e^2 - 23*a*b^3*d*e^3 + 7*a^2*b^2*e^4)*x^2 + 2*(194*b^4*d^3*e - 426*a*b^3*d^2*e^2 + 357*a^2*b^2*d*e^3 - 105*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^6*x + a*b^5), -1/35*(315*(a*b^3*d^3*e - 3*a^2*b^2*d^2*e^2 + 3*a^3*b*d*e^3 - a^4*e^4 + (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)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (10*b^4*e^4*x^4 - 35*b^4*d^4 + 528*a*b^3*d^3*e - 1218*a^2*b^2*d^2*e^2 + 1050*a^3*b*d*e^3 - 315*a^4*e^4 + 2*(29*b^4*d*e^3 - 9*a*b^3*e^4)*x^3 + 6*(26*b^4*d^2*e^2 - 23*a*b^3*d*e^3 + 7*a^2*b^2*e^4)*x^2 + 2*(194*b^4*d^3*e - 426*a*b^3*d^2*e^2 + 357*a^2*b^2*d*e^3 - 105*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^6*x + a*b^5)]","B",0
1646,1,486,0,0.423241," ","integrate((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a b^{2} d^{2} e - 2 \, a^{2} b d e^{2} + a^{3} e^{3} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(6 \, b^{3} e^{3} x^{3} - 15 \, b^{3} d^{3} + 161 \, a b^{2} d^{2} e - 245 \, a^{2} b d e^{2} + 105 \, a^{3} e^{3} + 2 \, {\left(16 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(58 \, b^{3} d^{2} e - 84 \, a b^{2} d e^{2} + 35 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left(b^{5} x + a b^{4}\right)}}, -\frac{105 \, {\left(a b^{2} d^{2} e - 2 \, a^{2} b d e^{2} + a^{3} e^{3} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(6 \, b^{3} e^{3} x^{3} - 15 \, b^{3} d^{3} + 161 \, a b^{2} d^{2} e - 245 \, a^{2} b d e^{2} + 105 \, a^{3} e^{3} + 2 \, {\left(16 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(58 \, b^{3} d^{2} e - 84 \, a b^{2} d e^{2} + 35 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b^{5} x + a b^{4}\right)}}\right]"," ",0,"[1/30*(105*(a*b^2*d^2*e - 2*a^2*b*d*e^2 + a^3*e^3 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(6*b^3*e^3*x^3 - 15*b^3*d^3 + 161*a*b^2*d^2*e - 245*a^2*b*d*e^2 + 105*a^3*e^3 + 2*(16*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 + 2*(58*b^3*d^2*e - 84*a*b^2*d*e^2 + 35*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^5*x + a*b^4), -1/15*(105*(a*b^2*d^2*e - 2*a^2*b*d*e^2 + a^3*e^3 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (6*b^3*e^3*x^3 - 15*b^3*d^3 + 161*a*b^2*d^2*e - 245*a^2*b*d*e^2 + 105*a^3*e^3 + 2*(16*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 + 2*(58*b^3*d^2*e - 84*a*b^2*d*e^2 + 35*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^5*x + a*b^4)]","B",0
1647,1,330,0,0.421875," ","integrate((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(a b d e - a^{2} e^{2} + {\left(b^{2} d e - a b e^{2}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(2 \, b^{2} e^{2} x^{2} - 3 \, b^{2} d^{2} + 20 \, a b d e - 15 \, a^{2} e^{2} + 2 \, {\left(7 \, b^{2} d e - 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(b^{4} x + a b^{3}\right)}}, -\frac{15 \, {\left(a b d e - a^{2} e^{2} + {\left(b^{2} d e - a b e^{2}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(2 \, b^{2} e^{2} x^{2} - 3 \, b^{2} d^{2} + 20 \, a b d e - 15 \, a^{2} e^{2} + 2 \, {\left(7 \, b^{2} d e - 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(b^{4} x + a b^{3}\right)}}\right]"," ",0,"[-1/6*(15*(a*b*d*e - a^2*e^2 + (b^2*d*e - a*b*e^2)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(2*b^2*e^2*x^2 - 3*b^2*d^2 + 20*a*b*d*e - 15*a^2*e^2 + 2*(7*b^2*d*e - 5*a*b*e^2)*x)*sqrt(e*x + d))/(b^4*x + a*b^3), -1/3*(15*(a*b*d*e - a^2*e^2 + (b^2*d*e - a*b*e^2)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (2*b^2*e^2*x^2 - 3*b^2*d^2 + 20*a*b*d*e - 15*a^2*e^2 + 2*(7*b^2*d*e - 5*a*b*e^2)*x)*sqrt(e*x + d))/(b^4*x + a*b^3)]","A",0
1648,1,210,0,0.439342," ","integrate((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b e x + a e\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(2 \, b e x - b d + 3 \, a e\right)} \sqrt{e x + d}}{2 \, {\left(b^{3} x + a b^{2}\right)}}, -\frac{3 \, {\left(b e x + a e\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(2 \, b e x - b d + 3 \, a e\right)} \sqrt{e x + d}}{b^{3} x + a b^{2}}\right]"," ",0,"[1/2*(3*(b*e*x + a*e)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(2*b*e*x - b*d + 3*a*e)*sqrt(e*x + d))/(b^3*x + a*b^2), -(3*(b*e*x + a*e)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (2*b*e*x - b*d + 3*a*e)*sqrt(e*x + d))/(b^3*x + a*b^2)]","A",0
1649,1,232,0,0.426831," ","integrate((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b^{2} d - a b e} {\left(b e x + a e\right)} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(b^{2} d - a b e\right)} \sqrt{e x + d}}{2 \, {\left(a b^{3} d - a^{2} b^{2} e + {\left(b^{4} d - a b^{3} e\right)} x\right)}}, \frac{\sqrt{-b^{2} d + a b e} {\left(b e x + a e\right)} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(b^{2} d - a b e\right)} \sqrt{e x + d}}{a b^{3} d - a^{2} b^{2} e + {\left(b^{4} d - a b^{3} e\right)} x}\right]"," ",0,"[1/2*(sqrt(b^2*d - a*b*e)*(b*e*x + a*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(b^2*d - a*b*e)*sqrt(e*x + d))/(a*b^3*d - a^2*b^2*e + (b^4*d - a*b^3*e)*x), (sqrt(-b^2*d + a*b*e)*(b*e*x + a*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (b^2*d - a*b*e)*sqrt(e*x + d))/(a*b^3*d - a^2*b^2*e + (b^4*d - a*b^3*e)*x)]","A",0
1650,1,280,0,0.428945," ","integrate(1/(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{b^{2} d - a b e} {\left(b e x + a e\right)} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(b^{2} d - a b e\right)} \sqrt{e x + d}}{2 \, {\left(a b^{3} d^{2} - 2 \, a^{2} b^{2} d e + a^{3} b e^{2} + {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} x\right)}}, -\frac{\sqrt{-b^{2} d + a b e} {\left(b e x + a e\right)} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(b^{2} d - a b e\right)} \sqrt{e x + d}}{a b^{3} d^{2} - 2 \, a^{2} b^{2} d e + a^{3} b e^{2} + {\left(b^{4} d^{2} - 2 \, a b^{3} d e + a^{2} b^{2} e^{2}\right)} x}\right]"," ",0,"[-1/2*(sqrt(b^2*d - a*b*e)*(b*e*x + a*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(b^2*d - a*b*e)*sqrt(e*x + d))/(a*b^3*d^2 - 2*a^2*b^2*d*e + a^3*b*e^2 + (b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*x), -(sqrt(-b^2*d + a*b*e)*(b*e*x + a*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (b^2*d - a*b*e)*sqrt(e*x + d))/(a*b^3*d^2 - 2*a^2*b^2*d*e + a^3*b*e^2 + (b^4*d^2 - 2*a*b^3*d*e + a^2*b^2*e^2)*x)]","B",0
1651,1,423,0,0.421526," ","integrate(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b e^{2} x^{2} + a d e + {\left(b d e + a e^{2}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(3 \, b e x + b d + 2 \, a e\right)} \sqrt{e x + d}}{2 \, {\left(a b^{2} d^{3} - 2 \, a^{2} b d^{2} e + a^{3} d e^{2} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x^{2} + {\left(b^{3} d^{3} - a b^{2} d^{2} e - a^{2} b d e^{2} + a^{3} e^{3}\right)} x\right)}}, \frac{3 \, {\left(b e^{2} x^{2} + a d e + {\left(b d e + a e^{2}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3 \, b e x + b d + 2 \, a e\right)} \sqrt{e x + d}}{a b^{2} d^{3} - 2 \, a^{2} b d^{2} e + a^{3} d e^{2} + {\left(b^{3} d^{2} e - 2 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x^{2} + {\left(b^{3} d^{3} - a b^{2} d^{2} e - a^{2} b d e^{2} + a^{3} e^{3}\right)} x}\right]"," ",0,"[1/2*(3*(b*e^2*x^2 + a*d*e + (b*d*e + a*e^2)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(3*b*e*x + b*d + 2*a*e)*sqrt(e*x + d))/(a*b^2*d^3 - 2*a^2*b*d^2*e + a^3*d*e^2 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x^2 + (b^3*d^3 - a*b^2*d^2*e - a^2*b*d*e^2 + a^3*e^3)*x), (3*(b*e^2*x^2 + a*d*e + (b*d*e + a*e^2)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3*b*e*x + b*d + 2*a*e)*sqrt(e*x + d))/(a*b^2*d^3 - 2*a^2*b*d^2*e + a^3*d*e^2 + (b^3*d^2*e - 2*a*b^2*d*e^2 + a^2*b*e^3)*x^2 + (b^3*d^3 - a*b^2*d^2*e - a^2*b*d*e^2 + a^3*e^3)*x)]","B",0
1652,1,782,0,0.434993," ","integrate(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{2} e^{3} x^{3} + a b d^{2} e + {\left(2 \, b^{2} d e^{2} + a b e^{3}\right)} x^{2} + {\left(b^{2} d^{2} e + 2 \, a b d e^{2}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(15 \, b^{2} e^{2} x^{2} + 3 \, b^{2} d^{2} + 14 \, a b d e - 2 \, a^{2} e^{2} + 10 \, {\left(2 \, b^{2} d e + a b e^{2}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(a b^{3} d^{5} - 3 \, a^{2} b^{2} d^{4} e + 3 \, a^{3} b d^{3} e^{2} - a^{4} d^{2} e^{3} + {\left(b^{4} d^{3} e^{2} - 3 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4} - a^{3} b e^{5}\right)} x^{3} + {\left(2 \, b^{4} d^{4} e - 5 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3} + a^{3} b d e^{4} - a^{4} e^{5}\right)} x^{2} + {\left(b^{4} d^{5} - a b^{3} d^{4} e - 3 \, a^{2} b^{2} d^{3} e^{2} + 5 \, a^{3} b d^{2} e^{3} - 2 \, a^{4} d e^{4}\right)} x\right)}}, \frac{15 \, {\left(b^{2} e^{3} x^{3} + a b d^{2} e + {\left(2 \, b^{2} d e^{2} + a b e^{3}\right)} x^{2} + {\left(b^{2} d^{2} e + 2 \, a b d e^{2}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(15 \, b^{2} e^{2} x^{2} + 3 \, b^{2} d^{2} + 14 \, a b d e - 2 \, a^{2} e^{2} + 10 \, {\left(2 \, b^{2} d e + a b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(a b^{3} d^{5} - 3 \, a^{2} b^{2} d^{4} e + 3 \, a^{3} b d^{3} e^{2} - a^{4} d^{2} e^{3} + {\left(b^{4} d^{3} e^{2} - 3 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4} - a^{3} b e^{5}\right)} x^{3} + {\left(2 \, b^{4} d^{4} e - 5 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3} + a^{3} b d e^{4} - a^{4} e^{5}\right)} x^{2} + {\left(b^{4} d^{5} - a b^{3} d^{4} e - 3 \, a^{2} b^{2} d^{3} e^{2} + 5 \, a^{3} b d^{2} e^{3} - 2 \, a^{4} d e^{4}\right)} x\right)}}\right]"," ",0,"[-1/6*(15*(b^2*e^3*x^3 + a*b*d^2*e + (2*b^2*d*e^2 + a*b*e^3)*x^2 + (b^2*d^2*e + 2*a*b*d*e^2)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(15*b^2*e^2*x^2 + 3*b^2*d^2 + 14*a*b*d*e - 2*a^2*e^2 + 10*(2*b^2*d*e + a*b*e^2)*x)*sqrt(e*x + d))/(a*b^3*d^5 - 3*a^2*b^2*d^4*e + 3*a^3*b*d^3*e^2 - a^4*d^2*e^3 + (b^4*d^3*e^2 - 3*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4 - a^3*b*e^5)*x^3 + (2*b^4*d^4*e - 5*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3 + a^3*b*d*e^4 - a^4*e^5)*x^2 + (b^4*d^5 - a*b^3*d^4*e - 3*a^2*b^2*d^3*e^2 + 5*a^3*b*d^2*e^3 - 2*a^4*d*e^4)*x), 1/3*(15*(b^2*e^3*x^3 + a*b*d^2*e + (2*b^2*d*e^2 + a*b*e^3)*x^2 + (b^2*d^2*e + 2*a*b*d*e^2)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (15*b^2*e^2*x^2 + 3*b^2*d^2 + 14*a*b*d*e - 2*a^2*e^2 + 10*(2*b^2*d*e + a*b*e^2)*x)*sqrt(e*x + d))/(a*b^3*d^5 - 3*a^2*b^2*d^4*e + 3*a^3*b*d^3*e^2 - a^4*d^2*e^3 + (b^4*d^3*e^2 - 3*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4 - a^3*b*e^5)*x^3 + (2*b^4*d^4*e - 5*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3 + a^3*b*d*e^4 - a^4*e^5)*x^2 + (b^4*d^5 - a*b^3*d^4*e - 3*a^2*b^2*d^3*e^2 + 5*a^3*b*d^2*e^3 - 2*a^4*d*e^4)*x)]","B",0
1653,1,1218,0,0.443155," ","integrate(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} e^{4} x^{4} + a b^{2} d^{3} e + {\left(3 \, b^{3} d e^{3} + a b^{2} e^{4}\right)} x^{3} + 3 \, {\left(b^{3} d^{2} e^{2} + a b^{2} d e^{3}\right)} x^{2} + {\left(b^{3} d^{3} e + 3 \, a b^{2} d^{2} e^{2}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(105 \, b^{3} e^{3} x^{3} + 15 \, b^{3} d^{3} + 116 \, a b^{2} d^{2} e - 32 \, a^{2} b d e^{2} + 6 \, a^{3} e^{3} + 35 \, {\left(7 \, b^{3} d e^{2} + 2 \, a b^{2} e^{3}\right)} x^{2} + 7 \, {\left(23 \, b^{3} d^{2} e + 24 \, a b^{2} d e^{2} - 2 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left(a b^{4} d^{7} - 4 \, a^{2} b^{3} d^{6} e + 6 \, a^{3} b^{2} d^{5} e^{2} - 4 \, a^{4} b d^{4} e^{3} + a^{5} d^{3} e^{4} + {\left(b^{5} d^{4} e^{3} - 4 \, a b^{4} d^{3} e^{4} + 6 \, a^{2} b^{3} d^{2} e^{5} - 4 \, a^{3} b^{2} d e^{6} + a^{4} b e^{7}\right)} x^{4} + {\left(3 \, b^{5} d^{5} e^{2} - 11 \, a b^{4} d^{4} e^{3} + 14 \, a^{2} b^{3} d^{3} e^{4} - 6 \, a^{3} b^{2} d^{2} e^{5} - a^{4} b d e^{6} + a^{5} e^{7}\right)} x^{3} + 3 \, {\left(b^{5} d^{6} e - 3 \, a b^{4} d^{5} e^{2} + 2 \, a^{2} b^{3} d^{4} e^{3} + 2 \, a^{3} b^{2} d^{3} e^{4} - 3 \, a^{4} b d^{2} e^{5} + a^{5} d e^{6}\right)} x^{2} + {\left(b^{5} d^{7} - a b^{4} d^{6} e - 6 \, a^{2} b^{3} d^{5} e^{2} + 14 \, a^{3} b^{2} d^{4} e^{3} - 11 \, a^{4} b d^{3} e^{4} + 3 \, a^{5} d^{2} e^{5}\right)} x\right)}}, \frac{105 \, {\left(b^{3} e^{4} x^{4} + a b^{2} d^{3} e + {\left(3 \, b^{3} d e^{3} + a b^{2} e^{4}\right)} x^{3} + 3 \, {\left(b^{3} d^{2} e^{2} + a b^{2} d e^{3}\right)} x^{2} + {\left(b^{3} d^{3} e + 3 \, a b^{2} d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(105 \, b^{3} e^{3} x^{3} + 15 \, b^{3} d^{3} + 116 \, a b^{2} d^{2} e - 32 \, a^{2} b d e^{2} + 6 \, a^{3} e^{3} + 35 \, {\left(7 \, b^{3} d e^{2} + 2 \, a b^{2} e^{3}\right)} x^{2} + 7 \, {\left(23 \, b^{3} d^{2} e + 24 \, a b^{2} d e^{2} - 2 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(a b^{4} d^{7} - 4 \, a^{2} b^{3} d^{6} e + 6 \, a^{3} b^{2} d^{5} e^{2} - 4 \, a^{4} b d^{4} e^{3} + a^{5} d^{3} e^{4} + {\left(b^{5} d^{4} e^{3} - 4 \, a b^{4} d^{3} e^{4} + 6 \, a^{2} b^{3} d^{2} e^{5} - 4 \, a^{3} b^{2} d e^{6} + a^{4} b e^{7}\right)} x^{4} + {\left(3 \, b^{5} d^{5} e^{2} - 11 \, a b^{4} d^{4} e^{3} + 14 \, a^{2} b^{3} d^{3} e^{4} - 6 \, a^{3} b^{2} d^{2} e^{5} - a^{4} b d e^{6} + a^{5} e^{7}\right)} x^{3} + 3 \, {\left(b^{5} d^{6} e - 3 \, a b^{4} d^{5} e^{2} + 2 \, a^{2} b^{3} d^{4} e^{3} + 2 \, a^{3} b^{2} d^{3} e^{4} - 3 \, a^{4} b d^{2} e^{5} + a^{5} d e^{6}\right)} x^{2} + {\left(b^{5} d^{7} - a b^{4} d^{6} e - 6 \, a^{2} b^{3} d^{5} e^{2} + 14 \, a^{3} b^{2} d^{4} e^{3} - 11 \, a^{4} b d^{3} e^{4} + 3 \, a^{5} d^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[1/30*(105*(b^3*e^4*x^4 + a*b^2*d^3*e + (3*b^3*d*e^3 + a*b^2*e^4)*x^3 + 3*(b^3*d^2*e^2 + a*b^2*d*e^3)*x^2 + (b^3*d^3*e + 3*a*b^2*d^2*e^2)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(105*b^3*e^3*x^3 + 15*b^3*d^3 + 116*a*b^2*d^2*e - 32*a^2*b*d*e^2 + 6*a^3*e^3 + 35*(7*b^3*d*e^2 + 2*a*b^2*e^3)*x^2 + 7*(23*b^3*d^2*e + 24*a*b^2*d*e^2 - 2*a^2*b*e^3)*x)*sqrt(e*x + d))/(a*b^4*d^7 - 4*a^2*b^3*d^6*e + 6*a^3*b^2*d^5*e^2 - 4*a^4*b*d^4*e^3 + a^5*d^3*e^4 + (b^5*d^4*e^3 - 4*a*b^4*d^3*e^4 + 6*a^2*b^3*d^2*e^5 - 4*a^3*b^2*d*e^6 + a^4*b*e^7)*x^4 + (3*b^5*d^5*e^2 - 11*a*b^4*d^4*e^3 + 14*a^2*b^3*d^3*e^4 - 6*a^3*b^2*d^2*e^5 - a^4*b*d*e^6 + a^5*e^7)*x^3 + 3*(b^5*d^6*e - 3*a*b^4*d^5*e^2 + 2*a^2*b^3*d^4*e^3 + 2*a^3*b^2*d^3*e^4 - 3*a^4*b*d^2*e^5 + a^5*d*e^6)*x^2 + (b^5*d^7 - a*b^4*d^6*e - 6*a^2*b^3*d^5*e^2 + 14*a^3*b^2*d^4*e^3 - 11*a^4*b*d^3*e^4 + 3*a^5*d^2*e^5)*x), 1/15*(105*(b^3*e^4*x^4 + a*b^2*d^3*e + (3*b^3*d*e^3 + a*b^2*e^4)*x^3 + 3*(b^3*d^2*e^2 + a*b^2*d*e^3)*x^2 + (b^3*d^3*e + 3*a*b^2*d^2*e^2)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (105*b^3*e^3*x^3 + 15*b^3*d^3 + 116*a*b^2*d^2*e - 32*a^2*b*d*e^2 + 6*a^3*e^3 + 35*(7*b^3*d*e^2 + 2*a*b^2*e^3)*x^2 + 7*(23*b^3*d^2*e + 24*a*b^2*d*e^2 - 2*a^2*b*e^3)*x)*sqrt(e*x + d))/(a*b^4*d^7 - 4*a^2*b^3*d^6*e + 6*a^3*b^2*d^5*e^2 - 4*a^4*b*d^4*e^3 + a^5*d^3*e^4 + (b^5*d^4*e^3 - 4*a*b^4*d^3*e^4 + 6*a^2*b^3*d^2*e^5 - 4*a^3*b^2*d*e^6 + a^4*b*e^7)*x^4 + (3*b^5*d^5*e^2 - 11*a*b^4*d^4*e^3 + 14*a^2*b^3*d^3*e^4 - 6*a^3*b^2*d^2*e^5 - a^4*b*d*e^6 + a^5*e^7)*x^3 + 3*(b^5*d^6*e - 3*a*b^4*d^5*e^2 + 2*a^2*b^3*d^4*e^3 + 2*a^3*b^2*d^3*e^4 - 3*a^4*b*d^2*e^5 + a^5*d*e^6)*x^2 + (b^5*d^7 - a*b^4*d^6*e - 6*a^2*b^3*d^5*e^2 + 14*a^3*b^2*d^4*e^3 - 11*a^4*b*d^3*e^4 + 3*a^5*d^2*e^5)*x)]","B",0
1654,1,994,0,0.433040," ","integrate((e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(a^{3} b^{2} d^{2} e^{3} - 2 \, a^{4} b d e^{4} + a^{5} e^{5} + {\left(b^{5} d^{2} e^{3} - 2 \, a b^{4} d e^{4} + a^{2} b^{3} e^{5}\right)} x^{3} + 3 \, {\left(a b^{4} d^{2} e^{3} - 2 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{3} d^{2} e^{3} - 2 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(48 \, b^{5} e^{5} x^{5} - 40 \, b^{5} d^{5} - 110 \, a b^{4} d^{4} e - 495 \, a^{2} b^{3} d^{3} e^{2} + 5313 \, a^{3} b^{2} d^{2} e^{3} - 8085 \, a^{4} b d e^{4} + 3465 \, a^{5} e^{5} + 16 \, {\left(26 \, b^{5} d e^{4} - 11 \, a b^{4} e^{5}\right)} x^{4} + 16 \, {\left(173 \, b^{5} d^{2} e^{3} - 242 \, a b^{4} d e^{4} + 99 \, a^{2} b^{3} e^{5}\right)} x^{3} - 3 \, {\left(445 \, b^{5} d^{3} e^{2} - 4103 \, a b^{4} d^{2} e^{3} + 6039 \, a^{2} b^{3} d e^{4} - 2541 \, a^{3} b^{2} e^{5}\right)} x^{2} - 2 \, {\left(155 \, b^{5} d^{4} e + 715 \, a b^{4} d^{3} e^{2} - 7227 \, a^{2} b^{3} d^{2} e^{3} + 10857 \, a^{3} b^{2} d e^{4} - 4620 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{240 \, {\left(b^{9} x^{3} + 3 \, a b^{8} x^{2} + 3 \, a^{2} b^{7} x + a^{3} b^{6}\right)}}, -\frac{3465 \, {\left(a^{3} b^{2} d^{2} e^{3} - 2 \, a^{4} b d e^{4} + a^{5} e^{5} + {\left(b^{5} d^{2} e^{3} - 2 \, a b^{4} d e^{4} + a^{2} b^{3} e^{5}\right)} x^{3} + 3 \, {\left(a b^{4} d^{2} e^{3} - 2 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{3} d^{2} e^{3} - 2 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(48 \, b^{5} e^{5} x^{5} - 40 \, b^{5} d^{5} - 110 \, a b^{4} d^{4} e - 495 \, a^{2} b^{3} d^{3} e^{2} + 5313 \, a^{3} b^{2} d^{2} e^{3} - 8085 \, a^{4} b d e^{4} + 3465 \, a^{5} e^{5} + 16 \, {\left(26 \, b^{5} d e^{4} - 11 \, a b^{4} e^{5}\right)} x^{4} + 16 \, {\left(173 \, b^{5} d^{2} e^{3} - 242 \, a b^{4} d e^{4} + 99 \, a^{2} b^{3} e^{5}\right)} x^{3} - 3 \, {\left(445 \, b^{5} d^{3} e^{2} - 4103 \, a b^{4} d^{2} e^{3} + 6039 \, a^{2} b^{3} d e^{4} - 2541 \, a^{3} b^{2} e^{5}\right)} x^{2} - 2 \, {\left(155 \, b^{5} d^{4} e + 715 \, a b^{4} d^{3} e^{2} - 7227 \, a^{2} b^{3} d^{2} e^{3} + 10857 \, a^{3} b^{2} d e^{4} - 4620 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{120 \, {\left(b^{9} x^{3} + 3 \, a b^{8} x^{2} + 3 \, a^{2} b^{7} x + a^{3} b^{6}\right)}}\right]"," ",0,"[1/240*(3465*(a^3*b^2*d^2*e^3 - 2*a^4*b*d*e^4 + a^5*e^5 + (b^5*d^2*e^3 - 2*a*b^4*d*e^4 + a^2*b^3*e^5)*x^3 + 3*(a*b^4*d^2*e^3 - 2*a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^2 + 3*(a^2*b^3*d^2*e^3 - 2*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(48*b^5*e^5*x^5 - 40*b^5*d^5 - 110*a*b^4*d^4*e - 495*a^2*b^3*d^3*e^2 + 5313*a^3*b^2*d^2*e^3 - 8085*a^4*b*d*e^4 + 3465*a^5*e^5 + 16*(26*b^5*d*e^4 - 11*a*b^4*e^5)*x^4 + 16*(173*b^5*d^2*e^3 - 242*a*b^4*d*e^4 + 99*a^2*b^3*e^5)*x^3 - 3*(445*b^5*d^3*e^2 - 4103*a*b^4*d^2*e^3 + 6039*a^2*b^3*d*e^4 - 2541*a^3*b^2*e^5)*x^2 - 2*(155*b^5*d^4*e + 715*a*b^4*d^3*e^2 - 7227*a^2*b^3*d^2*e^3 + 10857*a^3*b^2*d*e^4 - 4620*a^4*b*e^5)*x)*sqrt(e*x + d))/(b^9*x^3 + 3*a*b^8*x^2 + 3*a^2*b^7*x + a^3*b^6), -1/120*(3465*(a^3*b^2*d^2*e^3 - 2*a^4*b*d*e^4 + a^5*e^5 + (b^5*d^2*e^3 - 2*a*b^4*d*e^4 + a^2*b^3*e^5)*x^3 + 3*(a*b^4*d^2*e^3 - 2*a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^2 + 3*(a^2*b^3*d^2*e^3 - 2*a^3*b^2*d*e^4 + a^4*b*e^5)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (48*b^5*e^5*x^5 - 40*b^5*d^5 - 110*a*b^4*d^4*e - 495*a^2*b^3*d^3*e^2 + 5313*a^3*b^2*d^2*e^3 - 8085*a^4*b*d*e^4 + 3465*a^5*e^5 + 16*(26*b^5*d*e^4 - 11*a*b^4*e^5)*x^4 + 16*(173*b^5*d^2*e^3 - 242*a*b^4*d*e^4 + 99*a^2*b^3*e^5)*x^3 - 3*(445*b^5*d^3*e^2 - 4103*a*b^4*d^2*e^3 + 6039*a^2*b^3*d*e^4 - 2541*a^3*b^2*e^5)*x^2 - 2*(155*b^5*d^4*e + 715*a*b^4*d^3*e^2 - 7227*a^2*b^3*d^2*e^3 + 10857*a^3*b^2*d*e^4 - 4620*a^4*b*e^5)*x)*sqrt(e*x + d))/(b^9*x^3 + 3*a*b^8*x^2 + 3*a^2*b^7*x + a^3*b^6)]","B",0
1655,1,730,0,0.435218," ","integrate((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(a^{3} b d e^{3} - a^{4} e^{4} + {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(a b^{3} d e^{3} - a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(16 \, b^{4} e^{4} x^{4} - 8 \, b^{4} d^{4} - 18 \, a b^{3} d^{3} e - 63 \, a^{2} b^{2} d^{2} e^{2} + 420 \, a^{3} b d e^{3} - 315 \, a^{4} e^{4} + 16 \, {\left(13 \, b^{4} d e^{3} - 9 \, a b^{3} e^{4}\right)} x^{3} - 3 \, {\left(55 \, b^{4} d^{2} e^{2} - 318 \, a b^{3} d e^{3} + 231 \, a^{2} b^{2} e^{4}\right)} x^{2} - 2 \, {\left(25 \, b^{4} d^{3} e + 90 \, a b^{3} d^{2} e^{2} - 567 \, a^{2} b^{2} d e^{3} + 420 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(b^{8} x^{3} + 3 \, a b^{7} x^{2} + 3 \, a^{2} b^{6} x + a^{3} b^{5}\right)}}, -\frac{315 \, {\left(a^{3} b d e^{3} - a^{4} e^{4} + {\left(b^{4} d e^{3} - a b^{3} e^{4}\right)} x^{3} + 3 \, {\left(a b^{3} d e^{3} - a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{2} d e^{3} - a^{3} b e^{4}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(16 \, b^{4} e^{4} x^{4} - 8 \, b^{4} d^{4} - 18 \, a b^{3} d^{3} e - 63 \, a^{2} b^{2} d^{2} e^{2} + 420 \, a^{3} b d e^{3} - 315 \, a^{4} e^{4} + 16 \, {\left(13 \, b^{4} d e^{3} - 9 \, a b^{3} e^{4}\right)} x^{3} - 3 \, {\left(55 \, b^{4} d^{2} e^{2} - 318 \, a b^{3} d e^{3} + 231 \, a^{2} b^{2} e^{4}\right)} x^{2} - 2 \, {\left(25 \, b^{4} d^{3} e + 90 \, a b^{3} d^{2} e^{2} - 567 \, a^{2} b^{2} d e^{3} + 420 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(b^{8} x^{3} + 3 \, a b^{7} x^{2} + 3 \, a^{2} b^{6} x + a^{3} b^{5}\right)}}\right]"," ",0,"[-1/48*(315*(a^3*b*d*e^3 - a^4*e^4 + (b^4*d*e^3 - a*b^3*e^4)*x^3 + 3*(a*b^3*d*e^3 - a^2*b^2*e^4)*x^2 + 3*(a^2*b^2*d*e^3 - a^3*b*e^4)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(16*b^4*e^4*x^4 - 8*b^4*d^4 - 18*a*b^3*d^3*e - 63*a^2*b^2*d^2*e^2 + 420*a^3*b*d*e^3 - 315*a^4*e^4 + 16*(13*b^4*d*e^3 - 9*a*b^3*e^4)*x^3 - 3*(55*b^4*d^2*e^2 - 318*a*b^3*d*e^3 + 231*a^2*b^2*e^4)*x^2 - 2*(25*b^4*d^3*e + 90*a*b^3*d^2*e^2 - 567*a^2*b^2*d*e^3 + 420*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^8*x^3 + 3*a*b^7*x^2 + 3*a^2*b^6*x + a^3*b^5), -1/24*(315*(a^3*b*d*e^3 - a^4*e^4 + (b^4*d*e^3 - a*b^3*e^4)*x^3 + 3*(a*b^3*d*e^3 - a^2*b^2*e^4)*x^2 + 3*(a^2*b^2*d*e^3 - a^3*b*e^4)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (16*b^4*e^4*x^4 - 8*b^4*d^4 - 18*a*b^3*d^3*e - 63*a^2*b^2*d^2*e^2 + 420*a^3*b*d*e^3 - 315*a^4*e^4 + 16*(13*b^4*d*e^3 - 9*a*b^3*e^4)*x^3 - 3*(55*b^4*d^2*e^2 - 318*a*b^3*d*e^3 + 231*a^2*b^2*e^4)*x^2 - 2*(25*b^4*d^3*e + 90*a*b^3*d^2*e^2 - 567*a^2*b^2*d*e^3 + 420*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^8*x^3 + 3*a*b^7*x^2 + 3*a^2*b^6*x + a^3*b^5)]","B",0
1656,1,498,0,0.427905," ","integrate((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(48 \, b^{3} e^{3} x^{3} - 8 \, b^{3} d^{3} - 14 \, a b^{2} d^{2} e - 35 \, a^{2} b d e^{2} + 105 \, a^{3} e^{3} - 3 \, {\left(29 \, b^{3} d e^{2} - 77 \, a b^{2} e^{3}\right)} x^{2} - 2 \, {\left(19 \, b^{3} d^{2} e + 49 \, a b^{2} d e^{2} - 140 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(b^{7} x^{3} + 3 \, a b^{6} x^{2} + 3 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}, -\frac{105 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(48 \, b^{3} e^{3} x^{3} - 8 \, b^{3} d^{3} - 14 \, a b^{2} d^{2} e - 35 \, a^{2} b d e^{2} + 105 \, a^{3} e^{3} - 3 \, {\left(29 \, b^{3} d e^{2} - 77 \, a b^{2} e^{3}\right)} x^{2} - 2 \, {\left(19 \, b^{3} d^{2} e + 49 \, a b^{2} d e^{2} - 140 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(b^{7} x^{3} + 3 \, a b^{6} x^{2} + 3 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}\right]"," ",0,"[1/48*(105*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(48*b^3*e^3*x^3 - 8*b^3*d^3 - 14*a*b^2*d^2*e - 35*a^2*b*d*e^2 + 105*a^3*e^3 - 3*(29*b^3*d*e^2 - 77*a*b^2*e^3)*x^2 - 2*(19*b^3*d^2*e + 49*a*b^2*d*e^2 - 140*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^7*x^3 + 3*a*b^6*x^2 + 3*a^2*b^5*x + a^3*b^4), -1/24*(105*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (48*b^3*e^3*x^3 - 8*b^3*d^3 - 14*a*b^2*d^2*e - 35*a^2*b*d*e^2 + 105*a^3*e^3 - 3*(29*b^3*d*e^2 - 77*a*b^2*e^3)*x^2 - 2*(19*b^3*d^2*e + 49*a*b^2*d*e^2 - 140*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^7*x^3 + 3*a*b^6*x^2 + 3*a^2*b^5*x + a^3*b^4)]","B",0
1657,1,563,0,0.434507," ","integrate((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(8 \, b^{4} d^{3} + 2 \, a b^{3} d^{2} e + 5 \, a^{2} b^{2} d e^{2} - 15 \, a^{3} b e^{3} + 33 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(13 \, b^{4} d^{2} e + 7 \, a b^{3} d e^{2} - 20 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d - a^{4} b^{4} e + {\left(b^{8} d - a b^{7} e\right)} x^{3} + 3 \, {\left(a b^{7} d - a^{2} b^{6} e\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d - a^{3} b^{5} e\right)} x\right)}}, \frac{15 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(8 \, b^{4} d^{3} + 2 \, a b^{3} d^{2} e + 5 \, a^{2} b^{2} d e^{2} - 15 \, a^{3} b e^{3} + 33 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(13 \, b^{4} d^{2} e + 7 \, a b^{3} d e^{2} - 20 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d - a^{4} b^{4} e + {\left(b^{8} d - a b^{7} e\right)} x^{3} + 3 \, {\left(a b^{7} d - a^{2} b^{6} e\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d - a^{3} b^{5} e\right)} x\right)}}\right]"," ",0,"[1/48*(15*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(8*b^4*d^3 + 2*a*b^3*d^2*e + 5*a^2*b^2*d*e^2 - 15*a^3*b*e^3 + 33*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(13*b^4*d^2*e + 7*a*b^3*d*e^2 - 20*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d - a^4*b^4*e + (b^8*d - a*b^7*e)*x^3 + 3*(a*b^7*d - a^2*b^6*e)*x^2 + 3*(a^2*b^6*d - a^3*b^5*e)*x), 1/24*(15*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (8*b^4*d^3 + 2*a*b^3*d^2*e + 5*a^2*b^2*d*e^2 - 15*a^3*b*e^3 + 33*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(13*b^4*d^2*e + 7*a*b^3*d*e^2 - 20*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d - a^4*b^4*e + (b^8*d - a*b^7*e)*x^3 + 3*(a*b^7*d - a^2*b^6*e)*x^2 + 3*(a^2*b^6*d - a^3*b^5*e)*x)]","B",0
1658,1,666,0,0.432406," ","integrate((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(8 \, b^{4} d^{3} - 10 \, a b^{3} d^{2} e - a^{2} b^{2} d e^{2} + 3 \, a^{3} b e^{3} + 3 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(7 \, b^{4} d^{2} e - 11 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d^{2} - 2 \, a^{4} b^{4} d e + a^{5} b^{3} e^{2} + {\left(b^{8} d^{2} - 2 \, a b^{7} d e + a^{2} b^{6} e^{2}\right)} x^{3} + 3 \, {\left(a b^{7} d^{2} - 2 \, a^{2} b^{6} d e + a^{3} b^{5} e^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{2} - 2 \, a^{3} b^{5} d e + a^{4} b^{4} e^{2}\right)} x\right)}}, -\frac{3 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(8 \, b^{4} d^{3} - 10 \, a b^{3} d^{2} e - a^{2} b^{2} d e^{2} + 3 \, a^{3} b e^{3} + 3 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(7 \, b^{4} d^{2} e - 11 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d^{2} - 2 \, a^{4} b^{4} d e + a^{5} b^{3} e^{2} + {\left(b^{8} d^{2} - 2 \, a b^{7} d e + a^{2} b^{6} e^{2}\right)} x^{3} + 3 \, {\left(a b^{7} d^{2} - 2 \, a^{2} b^{6} d e + a^{3} b^{5} e^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{2} - 2 \, a^{3} b^{5} d e + a^{4} b^{4} e^{2}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(8*b^4*d^3 - 10*a*b^3*d^2*e - a^2*b^2*d*e^2 + 3*a^3*b*e^3 + 3*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(7*b^4*d^2*e - 11*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^2 - 2*a^4*b^4*d*e + a^5*b^3*e^2 + (b^8*d^2 - 2*a*b^7*d*e + a^2*b^6*e^2)*x^3 + 3*(a*b^7*d^2 - 2*a^2*b^6*d*e + a^3*b^5*e^2)*x^2 + 3*(a^2*b^6*d^2 - 2*a^3*b^5*d*e + a^4*b^4*e^2)*x), -1/24*(3*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (8*b^4*d^3 - 10*a*b^3*d^2*e - a^2*b^2*d*e^2 + 3*a^3*b*e^3 + 3*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(7*b^4*d^2*e - 11*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^2 - 2*a^4*b^4*d*e + a^5*b^3*e^2 + (b^8*d^2 - 2*a*b^7*d*e + a^2*b^6*e^2)*x^3 + 3*(a*b^7*d^2 - 2*a^2*b^6*d*e + a^3*b^5*e^2)*x^2 + 3*(a^2*b^6*d^2 - 2*a^3*b^5*d*e + a^4*b^4*e^2)*x)]","B",0
1659,1,785,0,0.427993," ","integrate((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(8 \, b^{4} d^{3} - 22 \, a b^{3} d^{2} e + 17 \, a^{2} b^{2} d e^{2} - 3 \, a^{3} b e^{3} - 3 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(b^{4} d^{2} e - 5 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d^{3} - 3 \, a^{4} b^{4} d^{2} e + 3 \, a^{5} b^{3} d e^{2} - a^{6} b^{2} e^{3} + {\left(b^{8} d^{3} - 3 \, a b^{7} d^{2} e + 3 \, a^{2} b^{6} d e^{2} - a^{3} b^{5} e^{3}\right)} x^{3} + 3 \, {\left(a b^{7} d^{3} - 3 \, a^{2} b^{6} d^{2} e + 3 \, a^{3} b^{5} d e^{2} - a^{4} b^{4} e^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{3} - 3 \, a^{3} b^{5} d^{2} e + 3 \, a^{4} b^{4} d e^{2} - a^{5} b^{3} e^{3}\right)} x\right)}}, \frac{3 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(8 \, b^{4} d^{3} - 22 \, a b^{3} d^{2} e + 17 \, a^{2} b^{2} d e^{2} - 3 \, a^{3} b e^{3} - 3 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} + 2 \, {\left(b^{4} d^{2} e - 5 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d^{3} - 3 \, a^{4} b^{4} d^{2} e + 3 \, a^{5} b^{3} d e^{2} - a^{6} b^{2} e^{3} + {\left(b^{8} d^{3} - 3 \, a b^{7} d^{2} e + 3 \, a^{2} b^{6} d e^{2} - a^{3} b^{5} e^{3}\right)} x^{3} + 3 \, {\left(a b^{7} d^{3} - 3 \, a^{2} b^{6} d^{2} e + 3 \, a^{3} b^{5} d e^{2} - a^{4} b^{4} e^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{3} - 3 \, a^{3} b^{5} d^{2} e + 3 \, a^{4} b^{4} d e^{2} - a^{5} b^{3} e^{3}\right)} x\right)}}\right]"," ",0,"[1/48*(3*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(8*b^4*d^3 - 22*a*b^3*d^2*e + 17*a^2*b^2*d*e^2 - 3*a^3*b*e^3 - 3*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(b^4*d^2*e - 5*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^3 - 3*a^4*b^4*d^2*e + 3*a^5*b^3*d*e^2 - a^6*b^2*e^3 + (b^8*d^3 - 3*a*b^7*d^2*e + 3*a^2*b^6*d*e^2 - a^3*b^5*e^3)*x^3 + 3*(a*b^7*d^3 - 3*a^2*b^6*d^2*e + 3*a^3*b^5*d*e^2 - a^4*b^4*e^3)*x^2 + 3*(a^2*b^6*d^3 - 3*a^3*b^5*d^2*e + 3*a^4*b^4*d*e^2 - a^5*b^3*e^3)*x), 1/24*(3*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (8*b^4*d^3 - 22*a*b^3*d^2*e + 17*a^2*b^2*d*e^2 - 3*a^3*b*e^3 - 3*(b^4*d*e^2 - a*b^3*e^3)*x^2 + 2*(b^4*d^2*e - 5*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^3 - 3*a^4*b^4*d^2*e + 3*a^5*b^3*d*e^2 - a^6*b^2*e^3 + (b^8*d^3 - 3*a*b^7*d^2*e + 3*a^2*b^6*d*e^2 - a^3*b^5*e^3)*x^3 + 3*(a*b^7*d^3 - 3*a^2*b^6*d^2*e + 3*a^3*b^5*d*e^2 - a^4*b^4*e^3)*x^2 + 3*(a^2*b^6*d^3 - 3*a^3*b^5*d^2*e + 3*a^4*b^4*d*e^2 - a^5*b^3*e^3)*x)]","B",0
1660,1,884,0,0.442545," ","integrate(1/(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(8 \, b^{4} d^{3} - 34 \, a b^{3} d^{2} e + 59 \, a^{2} b^{2} d e^{2} - 33 \, a^{3} b e^{3} + 15 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} - 10 \, {\left(b^{4} d^{2} e - 5 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d^{4} - 4 \, a^{4} b^{4} d^{3} e + 6 \, a^{5} b^{3} d^{2} e^{2} - 4 \, a^{6} b^{2} d e^{3} + a^{7} b e^{4} + {\left(b^{8} d^{4} - 4 \, a b^{7} d^{3} e + 6 \, a^{2} b^{6} d^{2} e^{2} - 4 \, a^{3} b^{5} d e^{3} + a^{4} b^{4} e^{4}\right)} x^{3} + 3 \, {\left(a b^{7} d^{4} - 4 \, a^{2} b^{6} d^{3} e + 6 \, a^{3} b^{5} d^{2} e^{2} - 4 \, a^{4} b^{4} d e^{3} + a^{5} b^{3} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{4} - 4 \, a^{3} b^{5} d^{3} e + 6 \, a^{4} b^{4} d^{2} e^{2} - 4 \, a^{5} b^{3} d e^{3} + a^{6} b^{2} e^{4}\right)} x\right)}}, -\frac{15 \, {\left(b^{3} e^{3} x^{3} + 3 \, a b^{2} e^{3} x^{2} + 3 \, a^{2} b e^{3} x + a^{3} e^{3}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(8 \, b^{4} d^{3} - 34 \, a b^{3} d^{2} e + 59 \, a^{2} b^{2} d e^{2} - 33 \, a^{3} b e^{3} + 15 \, {\left(b^{4} d e^{2} - a b^{3} e^{3}\right)} x^{2} - 10 \, {\left(b^{4} d^{2} e - 5 \, a b^{3} d e^{2} + 4 \, a^{2} b^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d^{4} - 4 \, a^{4} b^{4} d^{3} e + 6 \, a^{5} b^{3} d^{2} e^{2} - 4 \, a^{6} b^{2} d e^{3} + a^{7} b e^{4} + {\left(b^{8} d^{4} - 4 \, a b^{7} d^{3} e + 6 \, a^{2} b^{6} d^{2} e^{2} - 4 \, a^{3} b^{5} d e^{3} + a^{4} b^{4} e^{4}\right)} x^{3} + 3 \, {\left(a b^{7} d^{4} - 4 \, a^{2} b^{6} d^{3} e + 6 \, a^{3} b^{5} d^{2} e^{2} - 4 \, a^{4} b^{4} d e^{3} + a^{5} b^{3} e^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} d^{4} - 4 \, a^{3} b^{5} d^{3} e + 6 \, a^{4} b^{4} d^{2} e^{2} - 4 \, a^{5} b^{3} d e^{3} + a^{6} b^{2} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/48*(15*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(8*b^4*d^3 - 34*a*b^3*d^2*e + 59*a^2*b^2*d*e^2 - 33*a^3*b*e^3 + 15*(b^4*d*e^2 - a*b^3*e^3)*x^2 - 10*(b^4*d^2*e - 5*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^4 - 4*a^4*b^4*d^3*e + 6*a^5*b^3*d^2*e^2 - 4*a^6*b^2*d*e^3 + a^7*b*e^4 + (b^8*d^4 - 4*a*b^7*d^3*e + 6*a^2*b^6*d^2*e^2 - 4*a^3*b^5*d*e^3 + a^4*b^4*e^4)*x^3 + 3*(a*b^7*d^4 - 4*a^2*b^6*d^3*e + 6*a^3*b^5*d^2*e^2 - 4*a^4*b^4*d*e^3 + a^5*b^3*e^4)*x^2 + 3*(a^2*b^6*d^4 - 4*a^3*b^5*d^3*e + 6*a^4*b^4*d^2*e^2 - 4*a^5*b^3*d*e^3 + a^6*b^2*e^4)*x), -1/24*(15*(b^3*e^3*x^3 + 3*a*b^2*e^3*x^2 + 3*a^2*b*e^3*x + a^3*e^3)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (8*b^4*d^3 - 34*a*b^3*d^2*e + 59*a^2*b^2*d*e^2 - 33*a^3*b*e^3 + 15*(b^4*d*e^2 - a*b^3*e^3)*x^2 - 10*(b^4*d^2*e - 5*a*b^3*d*e^2 + 4*a^2*b^2*e^3)*x)*sqrt(e*x + d))/(a^3*b^5*d^4 - 4*a^4*b^4*d^3*e + 6*a^5*b^3*d^2*e^2 - 4*a^6*b^2*d*e^3 + a^7*b*e^4 + (b^8*d^4 - 4*a*b^7*d^3*e + 6*a^2*b^6*d^2*e^2 - 4*a^3*b^5*d*e^3 + a^4*b^4*e^4)*x^3 + 3*(a*b^7*d^4 - 4*a^2*b^6*d^3*e + 6*a^3*b^5*d^2*e^2 - 4*a^4*b^4*d*e^3 + a^5*b^3*e^4)*x^2 + 3*(a^2*b^6*d^4 - 4*a^3*b^5*d^3*e + 6*a^4*b^4*d^2*e^2 - 4*a^5*b^3*d*e^3 + a^6*b^2*e^4)*x)]","B",0
1661,1,1204,0,0.445897," ","integrate(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} e^{4} x^{4} + a^{3} d e^{3} + {\left(b^{3} d e^{3} + 3 \, a b^{2} e^{4}\right)} x^{3} + 3 \, {\left(a b^{2} d e^{3} + a^{2} b e^{4}\right)} x^{2} + {\left(3 \, a^{2} b d e^{3} + a^{3} e^{4}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(105 \, b^{3} e^{3} x^{3} + 8 \, b^{3} d^{3} - 38 \, a b^{2} d^{2} e + 87 \, a^{2} b d e^{2} + 48 \, a^{3} e^{3} + 35 \, {\left(b^{3} d e^{2} + 8 \, a b^{2} e^{3}\right)} x^{2} - 7 \, {\left(2 \, b^{3} d^{2} e - 14 \, a b^{2} d e^{2} - 33 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{4} d^{5} - 4 \, a^{4} b^{3} d^{4} e + 6 \, a^{5} b^{2} d^{3} e^{2} - 4 \, a^{6} b d^{2} e^{3} + a^{7} d e^{4} + {\left(b^{7} d^{4} e - 4 \, a b^{6} d^{3} e^{2} + 6 \, a^{2} b^{5} d^{2} e^{3} - 4 \, a^{3} b^{4} d e^{4} + a^{4} b^{3} e^{5}\right)} x^{4} + {\left(b^{7} d^{5} - a b^{6} d^{4} e - 6 \, a^{2} b^{5} d^{3} e^{2} + 14 \, a^{3} b^{4} d^{2} e^{3} - 11 \, a^{4} b^{3} d e^{4} + 3 \, a^{5} b^{2} e^{5}\right)} x^{3} + 3 \, {\left(a b^{6} d^{5} - 3 \, a^{2} b^{5} d^{4} e + 2 \, a^{3} b^{4} d^{3} e^{2} + 2 \, a^{4} b^{3} d^{2} e^{3} - 3 \, a^{5} b^{2} d e^{4} + a^{6} b e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{5} d^{5} - 11 \, a^{3} b^{4} d^{4} e + 14 \, a^{4} b^{3} d^{3} e^{2} - 6 \, a^{5} b^{2} d^{2} e^{3} - a^{6} b d e^{4} + a^{7} e^{5}\right)} x\right)}}, \frac{105 \, {\left(b^{3} e^{4} x^{4} + a^{3} d e^{3} + {\left(b^{3} d e^{3} + 3 \, a b^{2} e^{4}\right)} x^{3} + 3 \, {\left(a b^{2} d e^{3} + a^{2} b e^{4}\right)} x^{2} + {\left(3 \, a^{2} b d e^{3} + a^{3} e^{4}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(105 \, b^{3} e^{3} x^{3} + 8 \, b^{3} d^{3} - 38 \, a b^{2} d^{2} e + 87 \, a^{2} b d e^{2} + 48 \, a^{3} e^{3} + 35 \, {\left(b^{3} d e^{2} + 8 \, a b^{2} e^{3}\right)} x^{2} - 7 \, {\left(2 \, b^{3} d^{2} e - 14 \, a b^{2} d e^{2} - 33 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{4} d^{5} - 4 \, a^{4} b^{3} d^{4} e + 6 \, a^{5} b^{2} d^{3} e^{2} - 4 \, a^{6} b d^{2} e^{3} + a^{7} d e^{4} + {\left(b^{7} d^{4} e - 4 \, a b^{6} d^{3} e^{2} + 6 \, a^{2} b^{5} d^{2} e^{3} - 4 \, a^{3} b^{4} d e^{4} + a^{4} b^{3} e^{5}\right)} x^{4} + {\left(b^{7} d^{5} - a b^{6} d^{4} e - 6 \, a^{2} b^{5} d^{3} e^{2} + 14 \, a^{3} b^{4} d^{2} e^{3} - 11 \, a^{4} b^{3} d e^{4} + 3 \, a^{5} b^{2} e^{5}\right)} x^{3} + 3 \, {\left(a b^{6} d^{5} - 3 \, a^{2} b^{5} d^{4} e + 2 \, a^{3} b^{4} d^{3} e^{2} + 2 \, a^{4} b^{3} d^{2} e^{3} - 3 \, a^{5} b^{2} d e^{4} + a^{6} b e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{5} d^{5} - 11 \, a^{3} b^{4} d^{4} e + 14 \, a^{4} b^{3} d^{3} e^{2} - 6 \, a^{5} b^{2} d^{2} e^{3} - a^{6} b d e^{4} + a^{7} e^{5}\right)} x\right)}}\right]"," ",0,"[1/48*(105*(b^3*e^4*x^4 + a^3*d*e^3 + (b^3*d*e^3 + 3*a*b^2*e^4)*x^3 + 3*(a*b^2*d*e^3 + a^2*b*e^4)*x^2 + (3*a^2*b*d*e^3 + a^3*e^4)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(105*b^3*e^3*x^3 + 8*b^3*d^3 - 38*a*b^2*d^2*e + 87*a^2*b*d*e^2 + 48*a^3*e^3 + 35*(b^3*d*e^2 + 8*a*b^2*e^3)*x^2 - 7*(2*b^3*d^2*e - 14*a*b^2*d*e^2 - 33*a^2*b*e^3)*x)*sqrt(e*x + d))/(a^3*b^4*d^5 - 4*a^4*b^3*d^4*e + 6*a^5*b^2*d^3*e^2 - 4*a^6*b*d^2*e^3 + a^7*d*e^4 + (b^7*d^4*e - 4*a*b^6*d^3*e^2 + 6*a^2*b^5*d^2*e^3 - 4*a^3*b^4*d*e^4 + a^4*b^3*e^5)*x^4 + (b^7*d^5 - a*b^6*d^4*e - 6*a^2*b^5*d^3*e^2 + 14*a^3*b^4*d^2*e^3 - 11*a^4*b^3*d*e^4 + 3*a^5*b^2*e^5)*x^3 + 3*(a*b^6*d^5 - 3*a^2*b^5*d^4*e + 2*a^3*b^4*d^3*e^2 + 2*a^4*b^3*d^2*e^3 - 3*a^5*b^2*d*e^4 + a^6*b*e^5)*x^2 + (3*a^2*b^5*d^5 - 11*a^3*b^4*d^4*e + 14*a^4*b^3*d^3*e^2 - 6*a^5*b^2*d^2*e^3 - a^6*b*d*e^4 + a^7*e^5)*x), 1/24*(105*(b^3*e^4*x^4 + a^3*d*e^3 + (b^3*d*e^3 + 3*a*b^2*e^4)*x^3 + 3*(a*b^2*d*e^3 + a^2*b*e^4)*x^2 + (3*a^2*b*d*e^3 + a^3*e^4)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (105*b^3*e^3*x^3 + 8*b^3*d^3 - 38*a*b^2*d^2*e + 87*a^2*b*d*e^2 + 48*a^3*e^3 + 35*(b^3*d*e^2 + 8*a*b^2*e^3)*x^2 - 7*(2*b^3*d^2*e - 14*a*b^2*d*e^2 - 33*a^2*b*e^3)*x)*sqrt(e*x + d))/(a^3*b^4*d^5 - 4*a^4*b^3*d^4*e + 6*a^5*b^2*d^3*e^2 - 4*a^6*b*d^2*e^3 + a^7*d*e^4 + (b^7*d^4*e - 4*a*b^6*d^3*e^2 + 6*a^2*b^5*d^2*e^3 - 4*a^3*b^4*d*e^4 + a^4*b^3*e^5)*x^4 + (b^7*d^5 - a*b^6*d^4*e - 6*a^2*b^5*d^3*e^2 + 14*a^3*b^4*d^2*e^3 - 11*a^4*b^3*d*e^4 + 3*a^5*b^2*e^5)*x^3 + 3*(a*b^6*d^5 - 3*a^2*b^5*d^4*e + 2*a^3*b^4*d^3*e^2 + 2*a^4*b^3*d^2*e^3 - 3*a^5*b^2*d*e^4 + a^6*b*e^5)*x^2 + (3*a^2*b^5*d^5 - 11*a^3*b^4*d^4*e + 14*a^4*b^3*d^3*e^2 - 6*a^5*b^2*d^2*e^3 - a^6*b*d*e^4 + a^7*e^5)*x)]","B",0
1662,1,1840,0,0.446419," ","integrate(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{3} b d^{2} e^{3} + {\left(2 \, b^{4} d e^{4} + 3 \, a b^{3} e^{5}\right)} x^{4} + {\left(b^{4} d^{2} e^{3} + 6 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} x^{3} + {\left(3 \, a b^{3} d^{2} e^{3} + 6 \, a^{2} b^{2} d e^{4} + a^{3} b e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{2} d^{2} e^{3} + 2 \, a^{3} b d e^{4}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(315 \, b^{4} e^{4} x^{4} + 8 \, b^{4} d^{4} - 50 \, a b^{3} d^{3} e + 165 \, a^{2} b^{2} d^{2} e^{2} + 208 \, a^{3} b d e^{3} - 16 \, a^{4} e^{4} + 420 \, {\left(b^{4} d e^{3} + 2 \, a b^{3} e^{4}\right)} x^{3} + 63 \, {\left(b^{4} d^{2} e^{2} + 18 \, a b^{3} d e^{3} + 11 \, a^{2} b^{2} e^{4}\right)} x^{2} - 18 \, {\left(b^{4} d^{3} e - 10 \, a b^{3} d^{2} e^{2} - 53 \, a^{2} b^{2} d e^{3} - 8 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{48 \, {\left(a^{3} b^{5} d^{7} - 5 \, a^{4} b^{4} d^{6} e + 10 \, a^{5} b^{3} d^{5} e^{2} - 10 \, a^{6} b^{2} d^{4} e^{3} + 5 \, a^{7} b d^{3} e^{4} - a^{8} d^{2} e^{5} + {\left(b^{8} d^{5} e^{2} - 5 \, a b^{7} d^{4} e^{3} + 10 \, a^{2} b^{6} d^{3} e^{4} - 10 \, a^{3} b^{5} d^{2} e^{5} + 5 \, a^{4} b^{4} d e^{6} - a^{5} b^{3} e^{7}\right)} x^{5} + {\left(2 \, b^{8} d^{6} e - 7 \, a b^{7} d^{5} e^{2} + 5 \, a^{2} b^{6} d^{4} e^{3} + 10 \, a^{3} b^{5} d^{3} e^{4} - 20 \, a^{4} b^{4} d^{2} e^{5} + 13 \, a^{5} b^{3} d e^{6} - 3 \, a^{6} b^{2} e^{7}\right)} x^{4} + {\left(b^{8} d^{7} + a b^{7} d^{6} e - 17 \, a^{2} b^{6} d^{5} e^{2} + 35 \, a^{3} b^{5} d^{4} e^{3} - 25 \, a^{4} b^{4} d^{3} e^{4} - a^{5} b^{3} d^{2} e^{5} + 9 \, a^{6} b^{2} d e^{6} - 3 \, a^{7} b e^{7}\right)} x^{3} + {\left(3 \, a b^{7} d^{7} - 9 \, a^{2} b^{6} d^{6} e + a^{3} b^{5} d^{5} e^{2} + 25 \, a^{4} b^{4} d^{4} e^{3} - 35 \, a^{5} b^{3} d^{3} e^{4} + 17 \, a^{6} b^{2} d^{2} e^{5} - a^{7} b d e^{6} - a^{8} e^{7}\right)} x^{2} + {\left(3 \, a^{2} b^{6} d^{7} - 13 \, a^{3} b^{5} d^{6} e + 20 \, a^{4} b^{4} d^{5} e^{2} - 10 \, a^{5} b^{3} d^{4} e^{3} - 5 \, a^{6} b^{2} d^{3} e^{4} + 7 \, a^{7} b d^{2} e^{5} - 2 \, a^{8} d e^{6}\right)} x\right)}}, \frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{3} b d^{2} e^{3} + {\left(2 \, b^{4} d e^{4} + 3 \, a b^{3} e^{5}\right)} x^{4} + {\left(b^{4} d^{2} e^{3} + 6 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} x^{3} + {\left(3 \, a b^{3} d^{2} e^{3} + 6 \, a^{2} b^{2} d e^{4} + a^{3} b e^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{2} d^{2} e^{3} + 2 \, a^{3} b d e^{4}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(315 \, b^{4} e^{4} x^{4} + 8 \, b^{4} d^{4} - 50 \, a b^{3} d^{3} e + 165 \, a^{2} b^{2} d^{2} e^{2} + 208 \, a^{3} b d e^{3} - 16 \, a^{4} e^{4} + 420 \, {\left(b^{4} d e^{3} + 2 \, a b^{3} e^{4}\right)} x^{3} + 63 \, {\left(b^{4} d^{2} e^{2} + 18 \, a b^{3} d e^{3} + 11 \, a^{2} b^{2} e^{4}\right)} x^{2} - 18 \, {\left(b^{4} d^{3} e - 10 \, a b^{3} d^{2} e^{2} - 53 \, a^{2} b^{2} d e^{3} - 8 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{3} b^{5} d^{7} - 5 \, a^{4} b^{4} d^{6} e + 10 \, a^{5} b^{3} d^{5} e^{2} - 10 \, a^{6} b^{2} d^{4} e^{3} + 5 \, a^{7} b d^{3} e^{4} - a^{8} d^{2} e^{5} + {\left(b^{8} d^{5} e^{2} - 5 \, a b^{7} d^{4} e^{3} + 10 \, a^{2} b^{6} d^{3} e^{4} - 10 \, a^{3} b^{5} d^{2} e^{5} + 5 \, a^{4} b^{4} d e^{6} - a^{5} b^{3} e^{7}\right)} x^{5} + {\left(2 \, b^{8} d^{6} e - 7 \, a b^{7} d^{5} e^{2} + 5 \, a^{2} b^{6} d^{4} e^{3} + 10 \, a^{3} b^{5} d^{3} e^{4} - 20 \, a^{4} b^{4} d^{2} e^{5} + 13 \, a^{5} b^{3} d e^{6} - 3 \, a^{6} b^{2} e^{7}\right)} x^{4} + {\left(b^{8} d^{7} + a b^{7} d^{6} e - 17 \, a^{2} b^{6} d^{5} e^{2} + 35 \, a^{3} b^{5} d^{4} e^{3} - 25 \, a^{4} b^{4} d^{3} e^{4} - a^{5} b^{3} d^{2} e^{5} + 9 \, a^{6} b^{2} d e^{6} - 3 \, a^{7} b e^{7}\right)} x^{3} + {\left(3 \, a b^{7} d^{7} - 9 \, a^{2} b^{6} d^{6} e + a^{3} b^{5} d^{5} e^{2} + 25 \, a^{4} b^{4} d^{4} e^{3} - 35 \, a^{5} b^{3} d^{3} e^{4} + 17 \, a^{6} b^{2} d^{2} e^{5} - a^{7} b d e^{6} - a^{8} e^{7}\right)} x^{2} + {\left(3 \, a^{2} b^{6} d^{7} - 13 \, a^{3} b^{5} d^{6} e + 20 \, a^{4} b^{4} d^{5} e^{2} - 10 \, a^{5} b^{3} d^{4} e^{3} - 5 \, a^{6} b^{2} d^{3} e^{4} + 7 \, a^{7} b d^{2} e^{5} - 2 \, a^{8} d e^{6}\right)} x\right)}}\right]"," ",0,"[-1/48*(315*(b^4*e^5*x^5 + a^3*b*d^2*e^3 + (2*b^4*d*e^4 + 3*a*b^3*e^5)*x^4 + (b^4*d^2*e^3 + 6*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*x^3 + (3*a*b^3*d^2*e^3 + 6*a^2*b^2*d*e^4 + a^3*b*e^5)*x^2 + (3*a^2*b^2*d^2*e^3 + 2*a^3*b*d*e^4)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(315*b^4*e^4*x^4 + 8*b^4*d^4 - 50*a*b^3*d^3*e + 165*a^2*b^2*d^2*e^2 + 208*a^3*b*d*e^3 - 16*a^4*e^4 + 420*(b^4*d*e^3 + 2*a*b^3*e^4)*x^3 + 63*(b^4*d^2*e^2 + 18*a*b^3*d*e^3 + 11*a^2*b^2*e^4)*x^2 - 18*(b^4*d^3*e - 10*a*b^3*d^2*e^2 - 53*a^2*b^2*d*e^3 - 8*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^3*b^5*d^7 - 5*a^4*b^4*d^6*e + 10*a^5*b^3*d^5*e^2 - 10*a^6*b^2*d^4*e^3 + 5*a^7*b*d^3*e^4 - a^8*d^2*e^5 + (b^8*d^5*e^2 - 5*a*b^7*d^4*e^3 + 10*a^2*b^6*d^3*e^4 - 10*a^3*b^5*d^2*e^5 + 5*a^4*b^4*d*e^6 - a^5*b^3*e^7)*x^5 + (2*b^8*d^6*e - 7*a*b^7*d^5*e^2 + 5*a^2*b^6*d^4*e^3 + 10*a^3*b^5*d^3*e^4 - 20*a^4*b^4*d^2*e^5 + 13*a^5*b^3*d*e^6 - 3*a^6*b^2*e^7)*x^4 + (b^8*d^7 + a*b^7*d^6*e - 17*a^2*b^6*d^5*e^2 + 35*a^3*b^5*d^4*e^3 - 25*a^4*b^4*d^3*e^4 - a^5*b^3*d^2*e^5 + 9*a^6*b^2*d*e^6 - 3*a^7*b*e^7)*x^3 + (3*a*b^7*d^7 - 9*a^2*b^6*d^6*e + a^3*b^5*d^5*e^2 + 25*a^4*b^4*d^4*e^3 - 35*a^5*b^3*d^3*e^4 + 17*a^6*b^2*d^2*e^5 - a^7*b*d*e^6 - a^8*e^7)*x^2 + (3*a^2*b^6*d^7 - 13*a^3*b^5*d^6*e + 20*a^4*b^4*d^5*e^2 - 10*a^5*b^3*d^4*e^3 - 5*a^6*b^2*d^3*e^4 + 7*a^7*b*d^2*e^5 - 2*a^8*d*e^6)*x), 1/24*(315*(b^4*e^5*x^5 + a^3*b*d^2*e^3 + (2*b^4*d*e^4 + 3*a*b^3*e^5)*x^4 + (b^4*d^2*e^3 + 6*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*x^3 + (3*a*b^3*d^2*e^3 + 6*a^2*b^2*d*e^4 + a^3*b*e^5)*x^2 + (3*a^2*b^2*d^2*e^3 + 2*a^3*b*d*e^4)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (315*b^4*e^4*x^4 + 8*b^4*d^4 - 50*a*b^3*d^3*e + 165*a^2*b^2*d^2*e^2 + 208*a^3*b*d*e^3 - 16*a^4*e^4 + 420*(b^4*d*e^3 + 2*a*b^3*e^4)*x^3 + 63*(b^4*d^2*e^2 + 18*a*b^3*d*e^3 + 11*a^2*b^2*e^4)*x^2 - 18*(b^4*d^3*e - 10*a*b^3*d^2*e^2 - 53*a^2*b^2*d*e^3 - 8*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^3*b^5*d^7 - 5*a^4*b^4*d^6*e + 10*a^5*b^3*d^5*e^2 - 10*a^6*b^2*d^4*e^3 + 5*a^7*b*d^3*e^4 - a^8*d^2*e^5 + (b^8*d^5*e^2 - 5*a*b^7*d^4*e^3 + 10*a^2*b^6*d^3*e^4 - 10*a^3*b^5*d^2*e^5 + 5*a^4*b^4*d*e^6 - a^5*b^3*e^7)*x^5 + (2*b^8*d^6*e - 7*a*b^7*d^5*e^2 + 5*a^2*b^6*d^4*e^3 + 10*a^3*b^5*d^3*e^4 - 20*a^4*b^4*d^2*e^5 + 13*a^5*b^3*d*e^6 - 3*a^6*b^2*e^7)*x^4 + (b^8*d^7 + a*b^7*d^6*e - 17*a^2*b^6*d^5*e^2 + 35*a^3*b^5*d^4*e^3 - 25*a^4*b^4*d^3*e^4 - a^5*b^3*d^2*e^5 + 9*a^6*b^2*d*e^6 - 3*a^7*b*e^7)*x^3 + (3*a*b^7*d^7 - 9*a^2*b^6*d^6*e + a^3*b^5*d^5*e^2 + 25*a^4*b^4*d^4*e^3 - 35*a^5*b^3*d^3*e^4 + 17*a^6*b^2*d^2*e^5 - a^7*b*d*e^6 - a^8*e^7)*x^2 + (3*a^2*b^6*d^7 - 13*a^3*b^5*d^6*e + 20*a^4*b^4*d^5*e^2 - 10*a^5*b^3*d^4*e^3 - 5*a^6*b^2*d^3*e^4 + 7*a^7*b*d^2*e^5 - 2*a^8*d*e^6)*x)]","B",0
1663,1,2550,0,0.471629," ","integrate(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(b^{5} e^{6} x^{6} + a^{3} b^{2} d^{3} e^{3} + 3 \, {\left(b^{5} d e^{5} + a b^{4} e^{6}\right)} x^{5} + 3 \, {\left(b^{5} d^{2} e^{4} + 3 \, a b^{4} d e^{5} + a^{2} b^{3} e^{6}\right)} x^{4} + {\left(b^{5} d^{3} e^{3} + 9 \, a b^{4} d^{2} e^{4} + 9 \, a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} x^{3} + 3 \, {\left(a b^{4} d^{3} e^{3} + 3 \, a^{2} b^{3} d^{2} e^{4} + a^{3} b^{2} d e^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{3} d^{3} e^{3} + a^{3} b^{2} d^{2} e^{4}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(3465 \, b^{5} e^{5} x^{5} + 40 \, b^{5} d^{5} - 310 \, a b^{4} d^{4} e + 1335 \, a^{2} b^{3} d^{3} e^{2} + 2768 \, a^{3} b^{2} d^{2} e^{3} - 416 \, a^{4} b d e^{4} + 48 \, a^{5} e^{5} + 1155 \, {\left(7 \, b^{5} d e^{4} + 8 \, a b^{4} e^{5}\right)} x^{4} + 231 \, {\left(23 \, b^{5} d^{2} e^{3} + 94 \, a b^{4} d e^{4} + 33 \, a^{2} b^{3} e^{5}\right)} x^{3} + 99 \, {\left(5 \, b^{5} d^{3} e^{2} + 146 \, a b^{4} d^{2} e^{3} + 183 \, a^{2} b^{3} d e^{4} + 16 \, a^{3} b^{2} e^{5}\right)} x^{2} - 11 \, {\left(10 \, b^{5} d^{4} e - 130 \, a b^{4} d^{3} e^{2} - 1119 \, a^{2} b^{3} d^{2} e^{3} - 352 \, a^{3} b^{2} d e^{4} + 16 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{240 \, {\left(a^{3} b^{6} d^{9} - 6 \, a^{4} b^{5} d^{8} e + 15 \, a^{5} b^{4} d^{7} e^{2} - 20 \, a^{6} b^{3} d^{6} e^{3} + 15 \, a^{7} b^{2} d^{5} e^{4} - 6 \, a^{8} b d^{4} e^{5} + a^{9} d^{3} e^{6} + {\left(b^{9} d^{6} e^{3} - 6 \, a b^{8} d^{5} e^{4} + 15 \, a^{2} b^{7} d^{4} e^{5} - 20 \, a^{3} b^{6} d^{3} e^{6} + 15 \, a^{4} b^{5} d^{2} e^{7} - 6 \, a^{5} b^{4} d e^{8} + a^{6} b^{3} e^{9}\right)} x^{6} + 3 \, {\left(b^{9} d^{7} e^{2} - 5 \, a b^{8} d^{6} e^{3} + 9 \, a^{2} b^{7} d^{5} e^{4} - 5 \, a^{3} b^{6} d^{4} e^{5} - 5 \, a^{4} b^{5} d^{3} e^{6} + 9 \, a^{5} b^{4} d^{2} e^{7} - 5 \, a^{6} b^{3} d e^{8} + a^{7} b^{2} e^{9}\right)} x^{5} + 3 \, {\left(b^{9} d^{8} e - 3 \, a b^{8} d^{7} e^{2} - 2 \, a^{2} b^{7} d^{6} e^{3} + 19 \, a^{3} b^{6} d^{5} e^{4} - 30 \, a^{4} b^{5} d^{4} e^{5} + 19 \, a^{5} b^{4} d^{3} e^{6} - 2 \, a^{6} b^{3} d^{2} e^{7} - 3 \, a^{7} b^{2} d e^{8} + a^{8} b e^{9}\right)} x^{4} + {\left(b^{9} d^{9} + 3 \, a b^{8} d^{8} e - 30 \, a^{2} b^{7} d^{7} e^{2} + 62 \, a^{3} b^{6} d^{6} e^{3} - 36 \, a^{4} b^{5} d^{5} e^{4} - 36 \, a^{5} b^{4} d^{4} e^{5} + 62 \, a^{6} b^{3} d^{3} e^{6} - 30 \, a^{7} b^{2} d^{2} e^{7} + 3 \, a^{8} b d e^{8} + a^{9} e^{9}\right)} x^{3} + 3 \, {\left(a b^{8} d^{9} - 3 \, a^{2} b^{7} d^{8} e - 2 \, a^{3} b^{6} d^{7} e^{2} + 19 \, a^{4} b^{5} d^{6} e^{3} - 30 \, a^{5} b^{4} d^{5} e^{4} + 19 \, a^{6} b^{3} d^{4} e^{5} - 2 \, a^{7} b^{2} d^{3} e^{6} - 3 \, a^{8} b d^{2} e^{7} + a^{9} d e^{8}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{9} - 5 \, a^{3} b^{6} d^{8} e + 9 \, a^{4} b^{5} d^{7} e^{2} - 5 \, a^{5} b^{4} d^{6} e^{3} - 5 \, a^{6} b^{3} d^{5} e^{4} + 9 \, a^{7} b^{2} d^{4} e^{5} - 5 \, a^{8} b d^{3} e^{6} + a^{9} d^{2} e^{7}\right)} x\right)}}, \frac{3465 \, {\left(b^{5} e^{6} x^{6} + a^{3} b^{2} d^{3} e^{3} + 3 \, {\left(b^{5} d e^{5} + a b^{4} e^{6}\right)} x^{5} + 3 \, {\left(b^{5} d^{2} e^{4} + 3 \, a b^{4} d e^{5} + a^{2} b^{3} e^{6}\right)} x^{4} + {\left(b^{5} d^{3} e^{3} + 9 \, a b^{4} d^{2} e^{4} + 9 \, a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} x^{3} + 3 \, {\left(a b^{4} d^{3} e^{3} + 3 \, a^{2} b^{3} d^{2} e^{4} + a^{3} b^{2} d e^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{3} d^{3} e^{3} + a^{3} b^{2} d^{2} e^{4}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3465 \, b^{5} e^{5} x^{5} + 40 \, b^{5} d^{5} - 310 \, a b^{4} d^{4} e + 1335 \, a^{2} b^{3} d^{3} e^{2} + 2768 \, a^{3} b^{2} d^{2} e^{3} - 416 \, a^{4} b d e^{4} + 48 \, a^{5} e^{5} + 1155 \, {\left(7 \, b^{5} d e^{4} + 8 \, a b^{4} e^{5}\right)} x^{4} + 231 \, {\left(23 \, b^{5} d^{2} e^{3} + 94 \, a b^{4} d e^{4} + 33 \, a^{2} b^{3} e^{5}\right)} x^{3} + 99 \, {\left(5 \, b^{5} d^{3} e^{2} + 146 \, a b^{4} d^{2} e^{3} + 183 \, a^{2} b^{3} d e^{4} + 16 \, a^{3} b^{2} e^{5}\right)} x^{2} - 11 \, {\left(10 \, b^{5} d^{4} e - 130 \, a b^{4} d^{3} e^{2} - 1119 \, a^{2} b^{3} d^{2} e^{3} - 352 \, a^{3} b^{2} d e^{4} + 16 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{120 \, {\left(a^{3} b^{6} d^{9} - 6 \, a^{4} b^{5} d^{8} e + 15 \, a^{5} b^{4} d^{7} e^{2} - 20 \, a^{6} b^{3} d^{6} e^{3} + 15 \, a^{7} b^{2} d^{5} e^{4} - 6 \, a^{8} b d^{4} e^{5} + a^{9} d^{3} e^{6} + {\left(b^{9} d^{6} e^{3} - 6 \, a b^{8} d^{5} e^{4} + 15 \, a^{2} b^{7} d^{4} e^{5} - 20 \, a^{3} b^{6} d^{3} e^{6} + 15 \, a^{4} b^{5} d^{2} e^{7} - 6 \, a^{5} b^{4} d e^{8} + a^{6} b^{3} e^{9}\right)} x^{6} + 3 \, {\left(b^{9} d^{7} e^{2} - 5 \, a b^{8} d^{6} e^{3} + 9 \, a^{2} b^{7} d^{5} e^{4} - 5 \, a^{3} b^{6} d^{4} e^{5} - 5 \, a^{4} b^{5} d^{3} e^{6} + 9 \, a^{5} b^{4} d^{2} e^{7} - 5 \, a^{6} b^{3} d e^{8} + a^{7} b^{2} e^{9}\right)} x^{5} + 3 \, {\left(b^{9} d^{8} e - 3 \, a b^{8} d^{7} e^{2} - 2 \, a^{2} b^{7} d^{6} e^{3} + 19 \, a^{3} b^{6} d^{5} e^{4} - 30 \, a^{4} b^{5} d^{4} e^{5} + 19 \, a^{5} b^{4} d^{3} e^{6} - 2 \, a^{6} b^{3} d^{2} e^{7} - 3 \, a^{7} b^{2} d e^{8} + a^{8} b e^{9}\right)} x^{4} + {\left(b^{9} d^{9} + 3 \, a b^{8} d^{8} e - 30 \, a^{2} b^{7} d^{7} e^{2} + 62 \, a^{3} b^{6} d^{6} e^{3} - 36 \, a^{4} b^{5} d^{5} e^{4} - 36 \, a^{5} b^{4} d^{4} e^{5} + 62 \, a^{6} b^{3} d^{3} e^{6} - 30 \, a^{7} b^{2} d^{2} e^{7} + 3 \, a^{8} b d e^{8} + a^{9} e^{9}\right)} x^{3} + 3 \, {\left(a b^{8} d^{9} - 3 \, a^{2} b^{7} d^{8} e - 2 \, a^{3} b^{6} d^{7} e^{2} + 19 \, a^{4} b^{5} d^{6} e^{3} - 30 \, a^{5} b^{4} d^{5} e^{4} + 19 \, a^{6} b^{3} d^{4} e^{5} - 2 \, a^{7} b^{2} d^{3} e^{6} - 3 \, a^{8} b d^{2} e^{7} + a^{9} d e^{8}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} d^{9} - 5 \, a^{3} b^{6} d^{8} e + 9 \, a^{4} b^{5} d^{7} e^{2} - 5 \, a^{5} b^{4} d^{6} e^{3} - 5 \, a^{6} b^{3} d^{5} e^{4} + 9 \, a^{7} b^{2} d^{4} e^{5} - 5 \, a^{8} b d^{3} e^{6} + a^{9} d^{2} e^{7}\right)} x\right)}}\right]"," ",0,"[1/240*(3465*(b^5*e^6*x^6 + a^3*b^2*d^3*e^3 + 3*(b^5*d*e^5 + a*b^4*e^6)*x^5 + 3*(b^5*d^2*e^4 + 3*a*b^4*d*e^5 + a^2*b^3*e^6)*x^4 + (b^5*d^3*e^3 + 9*a*b^4*d^2*e^4 + 9*a^2*b^3*d*e^5 + a^3*b^2*e^6)*x^3 + 3*(a*b^4*d^3*e^3 + 3*a^2*b^3*d^2*e^4 + a^3*b^2*d*e^5)*x^2 + 3*(a^2*b^3*d^3*e^3 + a^3*b^2*d^2*e^4)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(3465*b^5*e^5*x^5 + 40*b^5*d^5 - 310*a*b^4*d^4*e + 1335*a^2*b^3*d^3*e^2 + 2768*a^3*b^2*d^2*e^3 - 416*a^4*b*d*e^4 + 48*a^5*e^5 + 1155*(7*b^5*d*e^4 + 8*a*b^4*e^5)*x^4 + 231*(23*b^5*d^2*e^3 + 94*a*b^4*d*e^4 + 33*a^2*b^3*e^5)*x^3 + 99*(5*b^5*d^3*e^2 + 146*a*b^4*d^2*e^3 + 183*a^2*b^3*d*e^4 + 16*a^3*b^2*e^5)*x^2 - 11*(10*b^5*d^4*e - 130*a*b^4*d^3*e^2 - 1119*a^2*b^3*d^2*e^3 - 352*a^3*b^2*d*e^4 + 16*a^4*b*e^5)*x)*sqrt(e*x + d))/(a^3*b^6*d^9 - 6*a^4*b^5*d^8*e + 15*a^5*b^4*d^7*e^2 - 20*a^6*b^3*d^6*e^3 + 15*a^7*b^2*d^5*e^4 - 6*a^8*b*d^4*e^5 + a^9*d^3*e^6 + (b^9*d^6*e^3 - 6*a*b^8*d^5*e^4 + 15*a^2*b^7*d^4*e^5 - 20*a^3*b^6*d^3*e^6 + 15*a^4*b^5*d^2*e^7 - 6*a^5*b^4*d*e^8 + a^6*b^3*e^9)*x^6 + 3*(b^9*d^7*e^2 - 5*a*b^8*d^6*e^3 + 9*a^2*b^7*d^5*e^4 - 5*a^3*b^6*d^4*e^5 - 5*a^4*b^5*d^3*e^6 + 9*a^5*b^4*d^2*e^7 - 5*a^6*b^3*d*e^8 + a^7*b^2*e^9)*x^5 + 3*(b^9*d^8*e - 3*a*b^8*d^7*e^2 - 2*a^2*b^7*d^6*e^3 + 19*a^3*b^6*d^5*e^4 - 30*a^4*b^5*d^4*e^5 + 19*a^5*b^4*d^3*e^6 - 2*a^6*b^3*d^2*e^7 - 3*a^7*b^2*d*e^8 + a^8*b*e^9)*x^4 + (b^9*d^9 + 3*a*b^8*d^8*e - 30*a^2*b^7*d^7*e^2 + 62*a^3*b^6*d^6*e^3 - 36*a^4*b^5*d^5*e^4 - 36*a^5*b^4*d^4*e^5 + 62*a^6*b^3*d^3*e^6 - 30*a^7*b^2*d^2*e^7 + 3*a^8*b*d*e^8 + a^9*e^9)*x^3 + 3*(a*b^8*d^9 - 3*a^2*b^7*d^8*e - 2*a^3*b^6*d^7*e^2 + 19*a^4*b^5*d^6*e^3 - 30*a^5*b^4*d^5*e^4 + 19*a^6*b^3*d^4*e^5 - 2*a^7*b^2*d^3*e^6 - 3*a^8*b*d^2*e^7 + a^9*d*e^8)*x^2 + 3*(a^2*b^7*d^9 - 5*a^3*b^6*d^8*e + 9*a^4*b^5*d^7*e^2 - 5*a^5*b^4*d^6*e^3 - 5*a^6*b^3*d^5*e^4 + 9*a^7*b^2*d^4*e^5 - 5*a^8*b*d^3*e^6 + a^9*d^2*e^7)*x), 1/120*(3465*(b^5*e^6*x^6 + a^3*b^2*d^3*e^3 + 3*(b^5*d*e^5 + a*b^4*e^6)*x^5 + 3*(b^5*d^2*e^4 + 3*a*b^4*d*e^5 + a^2*b^3*e^6)*x^4 + (b^5*d^3*e^3 + 9*a*b^4*d^2*e^4 + 9*a^2*b^3*d*e^5 + a^3*b^2*e^6)*x^3 + 3*(a*b^4*d^3*e^3 + 3*a^2*b^3*d^2*e^4 + a^3*b^2*d*e^5)*x^2 + 3*(a^2*b^3*d^3*e^3 + a^3*b^2*d^2*e^4)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3465*b^5*e^5*x^5 + 40*b^5*d^5 - 310*a*b^4*d^4*e + 1335*a^2*b^3*d^3*e^2 + 2768*a^3*b^2*d^2*e^3 - 416*a^4*b*d*e^4 + 48*a^5*e^5 + 1155*(7*b^5*d*e^4 + 8*a*b^4*e^5)*x^4 + 231*(23*b^5*d^2*e^3 + 94*a*b^4*d*e^4 + 33*a^2*b^3*e^5)*x^3 + 99*(5*b^5*d^3*e^2 + 146*a*b^4*d^2*e^3 + 183*a^2*b^3*d*e^4 + 16*a^3*b^2*e^5)*x^2 - 11*(10*b^5*d^4*e - 130*a*b^4*d^3*e^2 - 1119*a^2*b^3*d^2*e^3 - 352*a^3*b^2*d*e^4 + 16*a^4*b*e^5)*x)*sqrt(e*x + d))/(a^3*b^6*d^9 - 6*a^4*b^5*d^8*e + 15*a^5*b^4*d^7*e^2 - 20*a^6*b^3*d^6*e^3 + 15*a^7*b^2*d^5*e^4 - 6*a^8*b*d^4*e^5 + a^9*d^3*e^6 + (b^9*d^6*e^3 - 6*a*b^8*d^5*e^4 + 15*a^2*b^7*d^4*e^5 - 20*a^3*b^6*d^3*e^6 + 15*a^4*b^5*d^2*e^7 - 6*a^5*b^4*d*e^8 + a^6*b^3*e^9)*x^6 + 3*(b^9*d^7*e^2 - 5*a*b^8*d^6*e^3 + 9*a^2*b^7*d^5*e^4 - 5*a^3*b^6*d^4*e^5 - 5*a^4*b^5*d^3*e^6 + 9*a^5*b^4*d^2*e^7 - 5*a^6*b^3*d*e^8 + a^7*b^2*e^9)*x^5 + 3*(b^9*d^8*e - 3*a*b^8*d^7*e^2 - 2*a^2*b^7*d^6*e^3 + 19*a^3*b^6*d^5*e^4 - 30*a^4*b^5*d^4*e^5 + 19*a^5*b^4*d^3*e^6 - 2*a^6*b^3*d^2*e^7 - 3*a^7*b^2*d*e^8 + a^8*b*e^9)*x^4 + (b^9*d^9 + 3*a*b^8*d^8*e - 30*a^2*b^7*d^7*e^2 + 62*a^3*b^6*d^6*e^3 - 36*a^4*b^5*d^5*e^4 - 36*a^5*b^4*d^4*e^5 + 62*a^6*b^3*d^3*e^6 - 30*a^7*b^2*d^2*e^7 + 3*a^8*b*d*e^8 + a^9*e^9)*x^3 + 3*(a*b^8*d^9 - 3*a^2*b^7*d^8*e - 2*a^3*b^6*d^7*e^2 + 19*a^4*b^5*d^6*e^3 - 30*a^5*b^4*d^5*e^4 + 19*a^6*b^3*d^4*e^5 - 2*a^7*b^2*d^3*e^6 - 3*a^8*b*d^2*e^7 + a^9*d*e^8)*x^2 + 3*(a^2*b^7*d^9 - 5*a^3*b^6*d^8*e + 9*a^4*b^5*d^7*e^2 - 5*a^5*b^4*d^6*e^3 - 5*a^6*b^3*d^5*e^4 + 9*a^7*b^2*d^4*e^5 - 5*a^8*b*d^3*e^6 + a^9*d^2*e^7)*x)]","B",0
1664,1,1606,0,0.445913," ","integrate((e*x+d)^(15/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{45045 \, {\left(a^{5} b^{2} d^{2} e^{5} - 2 \, a^{6} b d e^{6} + a^{7} e^{7} + {\left(b^{7} d^{2} e^{5} - 2 \, a b^{6} d e^{6} + a^{2} b^{5} e^{7}\right)} x^{5} + 5 \, {\left(a b^{6} d^{2} e^{5} - 2 \, a^{2} b^{5} d e^{6} + a^{3} b^{4} e^{7}\right)} x^{4} + 10 \, {\left(a^{2} b^{5} d^{2} e^{5} - 2 \, a^{3} b^{4} d e^{6} + a^{4} b^{3} e^{7}\right)} x^{3} + 10 \, {\left(a^{3} b^{4} d^{2} e^{5} - 2 \, a^{4} b^{3} d e^{6} + a^{5} b^{2} e^{7}\right)} x^{2} + 5 \, {\left(a^{4} b^{3} d^{2} e^{5} - 2 \, a^{5} b^{2} d e^{6} + a^{6} b e^{7}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(256 \, b^{7} e^{7} x^{7} - 128 \, b^{7} d^{7} - 240 \, a b^{6} d^{6} e - 520 \, a^{2} b^{5} d^{5} e^{2} - 1430 \, a^{3} b^{4} d^{4} e^{3} - 6435 \, a^{4} b^{3} d^{3} e^{4} + 69069 \, a^{5} b^{2} d^{2} e^{5} - 105105 \, a^{6} b d e^{6} + 45045 \, a^{7} e^{7} + 256 \, {\left(12 \, b^{7} d e^{6} - 5 \, a b^{6} e^{7}\right)} x^{6} + 256 \, {\left(116 \, b^{7} d^{2} e^{5} - 160 \, a b^{6} d e^{6} + 65 \, a^{2} b^{5} e^{7}\right)} x^{5} - 5 \, {\left(5327 \, b^{7} d^{3} e^{4} - 45677 \, a b^{6} d^{2} e^{5} + 66157 \, a^{2} b^{5} d e^{6} - 27599 \, a^{3} b^{4} e^{7}\right)} x^{4} - 10 \, {\left(1211 \, b^{7} d^{4} e^{3} + 5810 \, a b^{6} d^{3} e^{4} - 54392 \, a^{2} b^{5} d^{2} e^{5} + 80366 \, a^{3} b^{4} d e^{6} - 33891 \, a^{4} b^{3} e^{7}\right)} x^{3} - 2 \, {\left(2324 \, b^{7} d^{5} e^{2} + 6545 \, a b^{6} d^{4} e^{3} + 30485 \, a^{2} b^{5} d^{3} e^{4} - 302445 \, a^{3} b^{4} d^{2} e^{5} + 452595 \, a^{4} b^{3} d e^{6} - 192192 \, a^{5} b^{2} e^{7}\right)} x^{2} - 2 \, {\left(568 \, b^{7} d^{6} e + 1240 \, a b^{6} d^{5} e^{2} + 3445 \, a^{2} b^{5} d^{4} e^{3} + 15730 \, a^{3} b^{4} d^{3} e^{4} - 163020 \, a^{4} b^{3} d^{2} e^{5} + 246246 \, a^{5} b^{2} d e^{6} - 105105 \, a^{6} b e^{7}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(b^{13} x^{5} + 5 \, a b^{12} x^{4} + 10 \, a^{2} b^{11} x^{3} + 10 \, a^{3} b^{10} x^{2} + 5 \, a^{4} b^{9} x + a^{5} b^{8}\right)}}, -\frac{45045 \, {\left(a^{5} b^{2} d^{2} e^{5} - 2 \, a^{6} b d e^{6} + a^{7} e^{7} + {\left(b^{7} d^{2} e^{5} - 2 \, a b^{6} d e^{6} + a^{2} b^{5} e^{7}\right)} x^{5} + 5 \, {\left(a b^{6} d^{2} e^{5} - 2 \, a^{2} b^{5} d e^{6} + a^{3} b^{4} e^{7}\right)} x^{4} + 10 \, {\left(a^{2} b^{5} d^{2} e^{5} - 2 \, a^{3} b^{4} d e^{6} + a^{4} b^{3} e^{7}\right)} x^{3} + 10 \, {\left(a^{3} b^{4} d^{2} e^{5} - 2 \, a^{4} b^{3} d e^{6} + a^{5} b^{2} e^{7}\right)} x^{2} + 5 \, {\left(a^{4} b^{3} d^{2} e^{5} - 2 \, a^{5} b^{2} d e^{6} + a^{6} b e^{7}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(256 \, b^{7} e^{7} x^{7} - 128 \, b^{7} d^{7} - 240 \, a b^{6} d^{6} e - 520 \, a^{2} b^{5} d^{5} e^{2} - 1430 \, a^{3} b^{4} d^{4} e^{3} - 6435 \, a^{4} b^{3} d^{3} e^{4} + 69069 \, a^{5} b^{2} d^{2} e^{5} - 105105 \, a^{6} b d e^{6} + 45045 \, a^{7} e^{7} + 256 \, {\left(12 \, b^{7} d e^{6} - 5 \, a b^{6} e^{7}\right)} x^{6} + 256 \, {\left(116 \, b^{7} d^{2} e^{5} - 160 \, a b^{6} d e^{6} + 65 \, a^{2} b^{5} e^{7}\right)} x^{5} - 5 \, {\left(5327 \, b^{7} d^{3} e^{4} - 45677 \, a b^{6} d^{2} e^{5} + 66157 \, a^{2} b^{5} d e^{6} - 27599 \, a^{3} b^{4} e^{7}\right)} x^{4} - 10 \, {\left(1211 \, b^{7} d^{4} e^{3} + 5810 \, a b^{6} d^{3} e^{4} - 54392 \, a^{2} b^{5} d^{2} e^{5} + 80366 \, a^{3} b^{4} d e^{6} - 33891 \, a^{4} b^{3} e^{7}\right)} x^{3} - 2 \, {\left(2324 \, b^{7} d^{5} e^{2} + 6545 \, a b^{6} d^{4} e^{3} + 30485 \, a^{2} b^{5} d^{3} e^{4} - 302445 \, a^{3} b^{4} d^{2} e^{5} + 452595 \, a^{4} b^{3} d e^{6} - 192192 \, a^{5} b^{2} e^{7}\right)} x^{2} - 2 \, {\left(568 \, b^{7} d^{6} e + 1240 \, a b^{6} d^{5} e^{2} + 3445 \, a^{2} b^{5} d^{4} e^{3} + 15730 \, a^{3} b^{4} d^{3} e^{4} - 163020 \, a^{4} b^{3} d^{2} e^{5} + 246246 \, a^{5} b^{2} d e^{6} - 105105 \, a^{6} b e^{7}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(b^{13} x^{5} + 5 \, a b^{12} x^{4} + 10 \, a^{2} b^{11} x^{3} + 10 \, a^{3} b^{10} x^{2} + 5 \, a^{4} b^{9} x + a^{5} b^{8}\right)}}\right]"," ",0,"[1/1280*(45045*(a^5*b^2*d^2*e^5 - 2*a^6*b*d*e^6 + a^7*e^7 + (b^7*d^2*e^5 - 2*a*b^6*d*e^6 + a^2*b^5*e^7)*x^5 + 5*(a*b^6*d^2*e^5 - 2*a^2*b^5*d*e^6 + a^3*b^4*e^7)*x^4 + 10*(a^2*b^5*d^2*e^5 - 2*a^3*b^4*d*e^6 + a^4*b^3*e^7)*x^3 + 10*(a^3*b^4*d^2*e^5 - 2*a^4*b^3*d*e^6 + a^5*b^2*e^7)*x^2 + 5*(a^4*b^3*d^2*e^5 - 2*a^5*b^2*d*e^6 + a^6*b*e^7)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(256*b^7*e^7*x^7 - 128*b^7*d^7 - 240*a*b^6*d^6*e - 520*a^2*b^5*d^5*e^2 - 1430*a^3*b^4*d^4*e^3 - 6435*a^4*b^3*d^3*e^4 + 69069*a^5*b^2*d^2*e^5 - 105105*a^6*b*d*e^6 + 45045*a^7*e^7 + 256*(12*b^7*d*e^6 - 5*a*b^6*e^7)*x^6 + 256*(116*b^7*d^2*e^5 - 160*a*b^6*d*e^6 + 65*a^2*b^5*e^7)*x^5 - 5*(5327*b^7*d^3*e^4 - 45677*a*b^6*d^2*e^5 + 66157*a^2*b^5*d*e^6 - 27599*a^3*b^4*e^7)*x^4 - 10*(1211*b^7*d^4*e^3 + 5810*a*b^6*d^3*e^4 - 54392*a^2*b^5*d^2*e^5 + 80366*a^3*b^4*d*e^6 - 33891*a^4*b^3*e^7)*x^3 - 2*(2324*b^7*d^5*e^2 + 6545*a*b^6*d^4*e^3 + 30485*a^2*b^5*d^3*e^4 - 302445*a^3*b^4*d^2*e^5 + 452595*a^4*b^3*d*e^6 - 192192*a^5*b^2*e^7)*x^2 - 2*(568*b^7*d^6*e + 1240*a*b^6*d^5*e^2 + 3445*a^2*b^5*d^4*e^3 + 15730*a^3*b^4*d^3*e^4 - 163020*a^4*b^3*d^2*e^5 + 246246*a^5*b^2*d*e^6 - 105105*a^6*b*e^7)*x)*sqrt(e*x + d))/(b^13*x^5 + 5*a*b^12*x^4 + 10*a^2*b^11*x^3 + 10*a^3*b^10*x^2 + 5*a^4*b^9*x + a^5*b^8), -1/640*(45045*(a^5*b^2*d^2*e^5 - 2*a^6*b*d*e^6 + a^7*e^7 + (b^7*d^2*e^5 - 2*a*b^6*d*e^6 + a^2*b^5*e^7)*x^5 + 5*(a*b^6*d^2*e^5 - 2*a^2*b^5*d*e^6 + a^3*b^4*e^7)*x^4 + 10*(a^2*b^5*d^2*e^5 - 2*a^3*b^4*d*e^6 + a^4*b^3*e^7)*x^3 + 10*(a^3*b^4*d^2*e^5 - 2*a^4*b^3*d*e^6 + a^5*b^2*e^7)*x^2 + 5*(a^4*b^3*d^2*e^5 - 2*a^5*b^2*d*e^6 + a^6*b*e^7)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (256*b^7*e^7*x^7 - 128*b^7*d^7 - 240*a*b^6*d^6*e - 520*a^2*b^5*d^5*e^2 - 1430*a^3*b^4*d^4*e^3 - 6435*a^4*b^3*d^3*e^4 + 69069*a^5*b^2*d^2*e^5 - 105105*a^6*b*d*e^6 + 45045*a^7*e^7 + 256*(12*b^7*d*e^6 - 5*a*b^6*e^7)*x^6 + 256*(116*b^7*d^2*e^5 - 160*a*b^6*d*e^6 + 65*a^2*b^5*e^7)*x^5 - 5*(5327*b^7*d^3*e^4 - 45677*a*b^6*d^2*e^5 + 66157*a^2*b^5*d*e^6 - 27599*a^3*b^4*e^7)*x^4 - 10*(1211*b^7*d^4*e^3 + 5810*a*b^6*d^3*e^4 - 54392*a^2*b^5*d^2*e^5 + 80366*a^3*b^4*d*e^6 - 33891*a^4*b^3*e^7)*x^3 - 2*(2324*b^7*d^5*e^2 + 6545*a*b^6*d^4*e^3 + 30485*a^2*b^5*d^3*e^4 - 302445*a^3*b^4*d^2*e^5 + 452595*a^4*b^3*d*e^6 - 192192*a^5*b^2*e^7)*x^2 - 2*(568*b^7*d^6*e + 1240*a*b^6*d^5*e^2 + 3445*a^2*b^5*d^4*e^3 + 15730*a^3*b^4*d^3*e^4 - 163020*a^4*b^3*d^2*e^5 + 246246*a^5*b^2*d*e^6 - 105105*a^6*b*e^7)*x)*sqrt(e*x + d))/(b^13*x^5 + 5*a*b^12*x^4 + 10*a^2*b^11*x^3 + 10*a^3*b^10*x^2 + 5*a^4*b^9*x + a^5*b^8)]","B",0
1665,1,1234,0,0.452431," ","integrate((e*x+d)^(13/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{45045 \, {\left(a^{5} b d e^{5} - a^{6} e^{6} + {\left(b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(a b^{5} d e^{5} - a^{2} b^{4} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{4} d e^{5} - a^{3} b^{3} e^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{3} d e^{5} - a^{4} b^{2} e^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{2} d e^{5} - a^{5} b e^{6}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(1280 \, b^{6} e^{6} x^{6} - 384 \, b^{6} d^{6} - 624 \, a b^{5} d^{5} e - 1144 \, a^{2} b^{4} d^{4} e^{2} - 2574 \, a^{3} b^{3} d^{3} e^{3} - 9009 \, a^{4} b^{2} d^{2} e^{4} + 60060 \, a^{5} b d e^{5} - 45045 \, a^{6} e^{6} + 1280 \, {\left(19 \, b^{6} d e^{5} - 13 \, a b^{5} e^{6}\right)} x^{5} - 5 \, {\left(7119 \, b^{6} d^{2} e^{4} - 38558 \, a b^{5} d e^{5} + 27599 \, a^{2} b^{4} e^{6}\right)} x^{4} - 10 \, {\left(2107 \, b^{6} d^{3} e^{3} + 7917 \, a b^{5} d^{2} e^{4} - 46475 \, a^{2} b^{4} d e^{5} + 33891 \, a^{3} b^{3} e^{6}\right)} x^{3} - 2 \, {\left(5012 \, b^{6} d^{4} e^{2} + 11557 \, a b^{5} d^{3} e^{3} + 42042 \, a^{2} b^{4} d^{2} e^{4} - 260403 \, a^{3} b^{3} d e^{5} + 192192 \, a^{4} b^{2} e^{6}\right)} x^{2} - 2 \, {\left(1464 \, b^{6} d^{5} e + 2704 \, a b^{5} d^{4} e^{2} + 6149 \, a^{2} b^{4} d^{3} e^{3} + 21879 \, a^{3} b^{3} d^{2} e^{4} - 141141 \, a^{4} b^{2} d e^{5} + 105105 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(b^{12} x^{5} + 5 \, a b^{11} x^{4} + 10 \, a^{2} b^{10} x^{3} + 10 \, a^{3} b^{9} x^{2} + 5 \, a^{4} b^{8} x + a^{5} b^{7}\right)}}, -\frac{45045 \, {\left(a^{5} b d e^{5} - a^{6} e^{6} + {\left(b^{6} d e^{5} - a b^{5} e^{6}\right)} x^{5} + 5 \, {\left(a b^{5} d e^{5} - a^{2} b^{4} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{4} d e^{5} - a^{3} b^{3} e^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{3} d e^{5} - a^{4} b^{2} e^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{2} d e^{5} - a^{5} b e^{6}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(1280 \, b^{6} e^{6} x^{6} - 384 \, b^{6} d^{6} - 624 \, a b^{5} d^{5} e - 1144 \, a^{2} b^{4} d^{4} e^{2} - 2574 \, a^{3} b^{3} d^{3} e^{3} - 9009 \, a^{4} b^{2} d^{2} e^{4} + 60060 \, a^{5} b d e^{5} - 45045 \, a^{6} e^{6} + 1280 \, {\left(19 \, b^{6} d e^{5} - 13 \, a b^{5} e^{6}\right)} x^{5} - 5 \, {\left(7119 \, b^{6} d^{2} e^{4} - 38558 \, a b^{5} d e^{5} + 27599 \, a^{2} b^{4} e^{6}\right)} x^{4} - 10 \, {\left(2107 \, b^{6} d^{3} e^{3} + 7917 \, a b^{5} d^{2} e^{4} - 46475 \, a^{2} b^{4} d e^{5} + 33891 \, a^{3} b^{3} e^{6}\right)} x^{3} - 2 \, {\left(5012 \, b^{6} d^{4} e^{2} + 11557 \, a b^{5} d^{3} e^{3} + 42042 \, a^{2} b^{4} d^{2} e^{4} - 260403 \, a^{3} b^{3} d e^{5} + 192192 \, a^{4} b^{2} e^{6}\right)} x^{2} - 2 \, {\left(1464 \, b^{6} d^{5} e + 2704 \, a b^{5} d^{4} e^{2} + 6149 \, a^{2} b^{4} d^{3} e^{3} + 21879 \, a^{3} b^{3} d^{2} e^{4} - 141141 \, a^{4} b^{2} d e^{5} + 105105 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(b^{12} x^{5} + 5 \, a b^{11} x^{4} + 10 \, a^{2} b^{10} x^{3} + 10 \, a^{3} b^{9} x^{2} + 5 \, a^{4} b^{8} x + a^{5} b^{7}\right)}}\right]"," ",0,"[-1/3840*(45045*(a^5*b*d*e^5 - a^6*e^6 + (b^6*d*e^5 - a*b^5*e^6)*x^5 + 5*(a*b^5*d*e^5 - a^2*b^4*e^6)*x^4 + 10*(a^2*b^4*d*e^5 - a^3*b^3*e^6)*x^3 + 10*(a^3*b^3*d*e^5 - a^4*b^2*e^6)*x^2 + 5*(a^4*b^2*d*e^5 - a^5*b*e^6)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(1280*b^6*e^6*x^6 - 384*b^6*d^6 - 624*a*b^5*d^5*e - 1144*a^2*b^4*d^4*e^2 - 2574*a^3*b^3*d^3*e^3 - 9009*a^4*b^2*d^2*e^4 + 60060*a^5*b*d*e^5 - 45045*a^6*e^6 + 1280*(19*b^6*d*e^5 - 13*a*b^5*e^6)*x^5 - 5*(7119*b^6*d^2*e^4 - 38558*a*b^5*d*e^5 + 27599*a^2*b^4*e^6)*x^4 - 10*(2107*b^6*d^3*e^3 + 7917*a*b^5*d^2*e^4 - 46475*a^2*b^4*d*e^5 + 33891*a^3*b^3*e^6)*x^3 - 2*(5012*b^6*d^4*e^2 + 11557*a*b^5*d^3*e^3 + 42042*a^2*b^4*d^2*e^4 - 260403*a^3*b^3*d*e^5 + 192192*a^4*b^2*e^6)*x^2 - 2*(1464*b^6*d^5*e + 2704*a*b^5*d^4*e^2 + 6149*a^2*b^4*d^3*e^3 + 21879*a^3*b^3*d^2*e^4 - 141141*a^4*b^2*d*e^5 + 105105*a^5*b*e^6)*x)*sqrt(e*x + d))/(b^12*x^5 + 5*a*b^11*x^4 + 10*a^2*b^10*x^3 + 10*a^3*b^9*x^2 + 5*a^4*b^8*x + a^5*b^7), -1/1920*(45045*(a^5*b*d*e^5 - a^6*e^6 + (b^6*d*e^5 - a*b^5*e^6)*x^5 + 5*(a*b^5*d*e^5 - a^2*b^4*e^6)*x^4 + 10*(a^2*b^4*d*e^5 - a^3*b^3*e^6)*x^3 + 10*(a^3*b^3*d*e^5 - a^4*b^2*e^6)*x^2 + 5*(a^4*b^2*d*e^5 - a^5*b*e^6)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (1280*b^6*e^6*x^6 - 384*b^6*d^6 - 624*a*b^5*d^5*e - 1144*a^2*b^4*d^4*e^2 - 2574*a^3*b^3*d^3*e^3 - 9009*a^4*b^2*d^2*e^4 + 60060*a^5*b*d*e^5 - 45045*a^6*e^6 + 1280*(19*b^6*d*e^5 - 13*a*b^5*e^6)*x^5 - 5*(7119*b^6*d^2*e^4 - 38558*a*b^5*d*e^5 + 27599*a^2*b^4*e^6)*x^4 - 10*(2107*b^6*d^3*e^3 + 7917*a*b^5*d^2*e^4 - 46475*a^2*b^4*d*e^5 + 33891*a^3*b^3*e^6)*x^3 - 2*(5012*b^6*d^4*e^2 + 11557*a*b^5*d^3*e^3 + 42042*a^2*b^4*d^2*e^4 - 260403*a^3*b^3*d*e^5 + 192192*a^4*b^2*e^6)*x^2 - 2*(1464*b^6*d^5*e + 2704*a*b^5*d^4*e^2 + 6149*a^2*b^4*d^3*e^3 + 21879*a^3*b^3*d^2*e^4 - 141141*a^4*b^2*d*e^5 + 105105*a^5*b*e^6)*x)*sqrt(e*x + d))/(b^12*x^5 + 5*a*b^11*x^4 + 10*a^2*b^10*x^3 + 10*a^3*b^9*x^2 + 5*a^4*b^8*x + a^5*b^7)]","B",0
1666,1,890,0,0.433210," ","integrate((e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(1280 \, b^{5} e^{5} x^{5} - 128 \, b^{5} d^{5} - 176 \, a b^{4} d^{4} e - 264 \, a^{2} b^{3} d^{3} e^{2} - 462 \, a^{3} b^{2} d^{2} e^{3} - 1155 \, a^{4} b d e^{4} + 3465 \, a^{5} e^{5} - 5 \, {\left(843 \, b^{5} d e^{4} - 2123 \, a b^{4} e^{5}\right)} x^{4} - 10 \, {\left(359 \, b^{5} d^{2} e^{3} + 968 \, a b^{4} d e^{4} - 2607 \, a^{2} b^{3} e^{5}\right)} x^{3} - 2 \, {\left(1124 \, b^{5} d^{3} e^{2} + 2013 \, a b^{4} d^{2} e^{3} + 5247 \, a^{2} b^{3} d e^{4} - 14784 \, a^{3} b^{2} e^{5}\right)} x^{2} - 2 \, {\left(408 \, b^{5} d^{4} e + 616 \, a b^{4} d^{3} e^{2} + 1089 \, a^{2} b^{3} d^{2} e^{3} + 2772 \, a^{3} b^{2} d e^{4} - 8085 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(b^{11} x^{5} + 5 \, a b^{10} x^{4} + 10 \, a^{2} b^{9} x^{3} + 10 \, a^{3} b^{8} x^{2} + 5 \, a^{4} b^{7} x + a^{5} b^{6}\right)}}, -\frac{3465 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(1280 \, b^{5} e^{5} x^{5} - 128 \, b^{5} d^{5} - 176 \, a b^{4} d^{4} e - 264 \, a^{2} b^{3} d^{3} e^{2} - 462 \, a^{3} b^{2} d^{2} e^{3} - 1155 \, a^{4} b d e^{4} + 3465 \, a^{5} e^{5} - 5 \, {\left(843 \, b^{5} d e^{4} - 2123 \, a b^{4} e^{5}\right)} x^{4} - 10 \, {\left(359 \, b^{5} d^{2} e^{3} + 968 \, a b^{4} d e^{4} - 2607 \, a^{2} b^{3} e^{5}\right)} x^{3} - 2 \, {\left(1124 \, b^{5} d^{3} e^{2} + 2013 \, a b^{4} d^{2} e^{3} + 5247 \, a^{2} b^{3} d e^{4} - 14784 \, a^{3} b^{2} e^{5}\right)} x^{2} - 2 \, {\left(408 \, b^{5} d^{4} e + 616 \, a b^{4} d^{3} e^{2} + 1089 \, a^{2} b^{3} d^{2} e^{3} + 2772 \, a^{3} b^{2} d e^{4} - 8085 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(b^{11} x^{5} + 5 \, a b^{10} x^{4} + 10 \, a^{2} b^{9} x^{3} + 10 \, a^{3} b^{8} x^{2} + 5 \, a^{4} b^{7} x + a^{5} b^{6}\right)}}\right]"," ",0,"[1/1280*(3465*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(1280*b^5*e^5*x^5 - 128*b^5*d^5 - 176*a*b^4*d^4*e - 264*a^2*b^3*d^3*e^2 - 462*a^3*b^2*d^2*e^3 - 1155*a^4*b*d*e^4 + 3465*a^5*e^5 - 5*(843*b^5*d*e^4 - 2123*a*b^4*e^5)*x^4 - 10*(359*b^5*d^2*e^3 + 968*a*b^4*d*e^4 - 2607*a^2*b^3*e^5)*x^3 - 2*(1124*b^5*d^3*e^2 + 2013*a*b^4*d^2*e^3 + 5247*a^2*b^3*d*e^4 - 14784*a^3*b^2*e^5)*x^2 - 2*(408*b^5*d^4*e + 616*a*b^4*d^3*e^2 + 1089*a^2*b^3*d^2*e^3 + 2772*a^3*b^2*d*e^4 - 8085*a^4*b*e^5)*x)*sqrt(e*x + d))/(b^11*x^5 + 5*a*b^10*x^4 + 10*a^2*b^9*x^3 + 10*a^3*b^8*x^2 + 5*a^4*b^7*x + a^5*b^6), -1/640*(3465*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (1280*b^5*e^5*x^5 - 128*b^5*d^5 - 176*a*b^4*d^4*e - 264*a^2*b^3*d^3*e^2 - 462*a^3*b^2*d^2*e^3 - 1155*a^4*b*d*e^4 + 3465*a^5*e^5 - 5*(843*b^5*d*e^4 - 2123*a*b^4*e^5)*x^4 - 10*(359*b^5*d^2*e^3 + 968*a*b^4*d*e^4 - 2607*a^2*b^3*e^5)*x^3 - 2*(1124*b^5*d^3*e^2 + 2013*a*b^4*d^2*e^3 + 5247*a^2*b^3*d*e^4 - 14784*a^3*b^2*e^5)*x^2 - 2*(408*b^5*d^4*e + 616*a*b^4*d^3*e^2 + 1089*a^2*b^3*d^2*e^3 + 2772*a^3*b^2*d*e^4 - 8085*a^4*b*e^5)*x)*sqrt(e*x + d))/(b^11*x^5 + 5*a*b^10*x^4 + 10*a^2*b^9*x^3 + 10*a^3*b^8*x^2 + 5*a^4*b^7*x + a^5*b^6)]","B",0
1667,1,1003,0,0.430717," ","integrate((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(128 \, b^{6} d^{5} + 16 \, a b^{5} d^{4} e + 24 \, a^{2} b^{4} d^{3} e^{2} + 42 \, a^{3} b^{3} d^{2} e^{3} + 105 \, a^{4} b^{2} d e^{4} - 315 \, a^{5} b e^{5} + 965 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} + 10 \, {\left(149 \, b^{6} d^{2} e^{3} + 88 \, a b^{5} d e^{4} - 237 \, a^{2} b^{4} e^{5}\right)} x^{3} + 6 \, {\left(228 \, b^{6} d^{3} e^{2} + 61 \, a b^{5} d^{2} e^{3} + 159 \, a^{2} b^{4} d e^{4} - 448 \, a^{3} b^{3} e^{5}\right)} x^{2} + 2 \, {\left(328 \, b^{6} d^{4} e + 56 \, a b^{5} d^{3} e^{2} + 99 \, a^{2} b^{4} d^{2} e^{3} + 252 \, a^{3} b^{3} d e^{4} - 735 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(a^{5} b^{7} d - a^{6} b^{6} e + {\left(b^{12} d - a b^{11} e\right)} x^{5} + 5 \, {\left(a b^{11} d - a^{2} b^{10} e\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d - a^{3} b^{9} e\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d - a^{4} b^{8} e\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d - a^{5} b^{7} e\right)} x\right)}}, \frac{315 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(128 \, b^{6} d^{5} + 16 \, a b^{5} d^{4} e + 24 \, a^{2} b^{4} d^{3} e^{2} + 42 \, a^{3} b^{3} d^{2} e^{3} + 105 \, a^{4} b^{2} d e^{4} - 315 \, a^{5} b e^{5} + 965 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} + 10 \, {\left(149 \, b^{6} d^{2} e^{3} + 88 \, a b^{5} d e^{4} - 237 \, a^{2} b^{4} e^{5}\right)} x^{3} + 6 \, {\left(228 \, b^{6} d^{3} e^{2} + 61 \, a b^{5} d^{2} e^{3} + 159 \, a^{2} b^{4} d e^{4} - 448 \, a^{3} b^{3} e^{5}\right)} x^{2} + 2 \, {\left(328 \, b^{6} d^{4} e + 56 \, a b^{5} d^{3} e^{2} + 99 \, a^{2} b^{4} d^{2} e^{3} + 252 \, a^{3} b^{3} d e^{4} - 735 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(a^{5} b^{7} d - a^{6} b^{6} e + {\left(b^{12} d - a b^{11} e\right)} x^{5} + 5 \, {\left(a b^{11} d - a^{2} b^{10} e\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d - a^{3} b^{9} e\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d - a^{4} b^{8} e\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d - a^{5} b^{7} e\right)} x\right)}}\right]"," ",0,"[1/1280*(315*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(128*b^6*d^5 + 16*a*b^5*d^4*e + 24*a^2*b^4*d^3*e^2 + 42*a^3*b^3*d^2*e^3 + 105*a^4*b^2*d*e^4 - 315*a^5*b*e^5 + 965*(b^6*d*e^4 - a*b^5*e^5)*x^4 + 10*(149*b^6*d^2*e^3 + 88*a*b^5*d*e^4 - 237*a^2*b^4*e^5)*x^3 + 6*(228*b^6*d^3*e^2 + 61*a*b^5*d^2*e^3 + 159*a^2*b^4*d*e^4 - 448*a^3*b^3*e^5)*x^2 + 2*(328*b^6*d^4*e + 56*a*b^5*d^3*e^2 + 99*a^2*b^4*d^2*e^3 + 252*a^3*b^3*d*e^4 - 735*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d - a^6*b^6*e + (b^12*d - a*b^11*e)*x^5 + 5*(a*b^11*d - a^2*b^10*e)*x^4 + 10*(a^2*b^10*d - a^3*b^9*e)*x^3 + 10*(a^3*b^9*d - a^4*b^8*e)*x^2 + 5*(a^4*b^8*d - a^5*b^7*e)*x), 1/640*(315*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (128*b^6*d^5 + 16*a*b^5*d^4*e + 24*a^2*b^4*d^3*e^2 + 42*a^3*b^3*d^2*e^3 + 105*a^4*b^2*d*e^4 - 315*a^5*b*e^5 + 965*(b^6*d*e^4 - a*b^5*e^5)*x^4 + 10*(149*b^6*d^2*e^3 + 88*a*b^5*d*e^4 - 237*a^2*b^4*e^5)*x^3 + 6*(228*b^6*d^3*e^2 + 61*a*b^5*d^2*e^3 + 159*a^2*b^4*d*e^4 - 448*a^3*b^3*e^5)*x^2 + 2*(328*b^6*d^4*e + 56*a*b^5*d^3*e^2 + 99*a^2*b^4*d^2*e^3 + 252*a^3*b^3*d*e^4 - 735*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d - a^6*b^6*e + (b^12*d - a*b^11*e)*x^5 + 5*(a*b^11*d - a^2*b^10*e)*x^4 + 10*(a^2*b^10*d - a^3*b^9*e)*x^3 + 10*(a^3*b^9*d - a^4*b^8*e)*x^2 + 5*(a^4*b^8*d - a^5*b^7*e)*x)]","B",0
1668,1,1158,0,0.431661," ","integrate((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(384 \, b^{6} d^{5} - 432 \, a b^{5} d^{4} e - 8 \, a^{2} b^{4} d^{3} e^{2} - 14 \, a^{3} b^{3} d^{2} e^{3} - 35 \, a^{4} b^{2} d e^{4} + 105 \, a^{5} b e^{5} + 105 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} + 10 \, {\left(121 \, b^{6} d^{2} e^{3} - 200 \, a b^{5} d e^{4} + 79 \, a^{2} b^{4} e^{5}\right)} x^{3} + 2 \, {\left(1052 \, b^{6} d^{3} e^{2} - 1341 \, a b^{5} d^{2} e^{3} - 159 \, a^{2} b^{4} d e^{4} + 448 \, a^{3} b^{3} e^{5}\right)} x^{2} + 2 \, {\left(744 \, b^{6} d^{4} e - 872 \, a b^{5} d^{3} e^{2} - 33 \, a^{2} b^{4} d^{2} e^{3} - 84 \, a^{3} b^{3} d e^{4} + 245 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(a^{5} b^{7} d^{2} - 2 \, a^{6} b^{6} d e + a^{7} b^{5} e^{2} + {\left(b^{12} d^{2} - 2 \, a b^{11} d e + a^{2} b^{10} e^{2}\right)} x^{5} + 5 \, {\left(a b^{11} d^{2} - 2 \, a^{2} b^{10} d e + a^{3} b^{9} e^{2}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{2} - 2 \, a^{3} b^{9} d e + a^{4} b^{8} e^{2}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d^{2} - 2 \, a^{4} b^{8} d e + a^{5} b^{7} e^{2}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d^{2} - 2 \, a^{5} b^{7} d e + a^{6} b^{6} e^{2}\right)} x\right)}}, -\frac{105 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(384 \, b^{6} d^{5} - 432 \, a b^{5} d^{4} e - 8 \, a^{2} b^{4} d^{3} e^{2} - 14 \, a^{3} b^{3} d^{2} e^{3} - 35 \, a^{4} b^{2} d e^{4} + 105 \, a^{5} b e^{5} + 105 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} + 10 \, {\left(121 \, b^{6} d^{2} e^{3} - 200 \, a b^{5} d e^{4} + 79 \, a^{2} b^{4} e^{5}\right)} x^{3} + 2 \, {\left(1052 \, b^{6} d^{3} e^{2} - 1341 \, a b^{5} d^{2} e^{3} - 159 \, a^{2} b^{4} d e^{4} + 448 \, a^{3} b^{3} e^{5}\right)} x^{2} + 2 \, {\left(744 \, b^{6} d^{4} e - 872 \, a b^{5} d^{3} e^{2} - 33 \, a^{2} b^{4} d^{2} e^{3} - 84 \, a^{3} b^{3} d e^{4} + 245 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{5} b^{7} d^{2} - 2 \, a^{6} b^{6} d e + a^{7} b^{5} e^{2} + {\left(b^{12} d^{2} - 2 \, a b^{11} d e + a^{2} b^{10} e^{2}\right)} x^{5} + 5 \, {\left(a b^{11} d^{2} - 2 \, a^{2} b^{10} d e + a^{3} b^{9} e^{2}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{2} - 2 \, a^{3} b^{9} d e + a^{4} b^{8} e^{2}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d^{2} - 2 \, a^{4} b^{8} d e + a^{5} b^{7} e^{2}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d^{2} - 2 \, a^{5} b^{7} d e + a^{6} b^{6} e^{2}\right)} x\right)}}\right]"," ",0,"[-1/3840*(105*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(384*b^6*d^5 - 432*a*b^5*d^4*e - 8*a^2*b^4*d^3*e^2 - 14*a^3*b^3*d^2*e^3 - 35*a^4*b^2*d*e^4 + 105*a^5*b*e^5 + 105*(b^6*d*e^4 - a*b^5*e^5)*x^4 + 10*(121*b^6*d^2*e^3 - 200*a*b^5*d*e^4 + 79*a^2*b^4*e^5)*x^3 + 2*(1052*b^6*d^3*e^2 - 1341*a*b^5*d^2*e^3 - 159*a^2*b^4*d*e^4 + 448*a^3*b^3*e^5)*x^2 + 2*(744*b^6*d^4*e - 872*a*b^5*d^3*e^2 - 33*a^2*b^4*d^2*e^3 - 84*a^3*b^3*d*e^4 + 245*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d^2 - 2*a^6*b^6*d*e + a^7*b^5*e^2 + (b^12*d^2 - 2*a*b^11*d*e + a^2*b^10*e^2)*x^5 + 5*(a*b^11*d^2 - 2*a^2*b^10*d*e + a^3*b^9*e^2)*x^4 + 10*(a^2*b^10*d^2 - 2*a^3*b^9*d*e + a^4*b^8*e^2)*x^3 + 10*(a^3*b^9*d^2 - 2*a^4*b^8*d*e + a^5*b^7*e^2)*x^2 + 5*(a^4*b^8*d^2 - 2*a^5*b^7*d*e + a^6*b^6*e^2)*x), -1/1920*(105*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (384*b^6*d^5 - 432*a*b^5*d^4*e - 8*a^2*b^4*d^3*e^2 - 14*a^3*b^3*d^2*e^3 - 35*a^4*b^2*d*e^4 + 105*a^5*b*e^5 + 105*(b^6*d*e^4 - a*b^5*e^5)*x^4 + 10*(121*b^6*d^2*e^3 - 200*a*b^5*d*e^4 + 79*a^2*b^4*e^5)*x^3 + 2*(1052*b^6*d^3*e^2 - 1341*a*b^5*d^2*e^3 - 159*a^2*b^4*d*e^4 + 448*a^3*b^3*e^5)*x^2 + 2*(744*b^6*d^4*e - 872*a*b^5*d^3*e^2 - 33*a^2*b^4*d^2*e^3 - 84*a^3*b^3*d*e^4 + 245*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d^2 - 2*a^6*b^6*d*e + a^7*b^5*e^2 + (b^12*d^2 - 2*a*b^11*d*e + a^2*b^10*e^2)*x^5 + 5*(a*b^11*d^2 - 2*a^2*b^10*d*e + a^3*b^9*e^2)*x^4 + 10*(a^2*b^10*d^2 - 2*a^3*b^9*d*e + a^4*b^8*e^2)*x^3 + 10*(a^3*b^9*d^2 - 2*a^4*b^8*d*e + a^5*b^7*e^2)*x^2 + 5*(a^4*b^8*d^2 - 2*a^5*b^7*d*e + a^6*b^6*e^2)*x)]","B",0
1669,1,1337,0,0.440508," ","integrate((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(128 \, b^{6} d^{5} - 304 \, a b^{5} d^{4} e + 184 \, a^{2} b^{4} d^{3} e^{2} + 2 \, a^{3} b^{3} d^{2} e^{3} + 5 \, a^{4} b^{2} d e^{4} - 15 \, a^{5} b e^{5} - 15 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} + 10 \, {\left(b^{6} d^{2} e^{3} - 8 \, a b^{5} d e^{4} + 7 \, a^{2} b^{4} e^{5}\right)} x^{3} + 2 \, {\left(124 \, b^{6} d^{3} e^{2} - 357 \, a b^{5} d^{2} e^{3} + 297 \, a^{2} b^{4} d e^{4} - 64 \, a^{3} b^{3} e^{5}\right)} x^{2} + 2 \, {\left(168 \, b^{6} d^{4} e - 424 \, a b^{5} d^{3} e^{2} + 279 \, a^{2} b^{4} d^{2} e^{3} + 12 \, a^{3} b^{3} d e^{4} - 35 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(a^{5} b^{7} d^{3} - 3 \, a^{6} b^{6} d^{2} e + 3 \, a^{7} b^{5} d e^{2} - a^{8} b^{4} e^{3} + {\left(b^{12} d^{3} - 3 \, a b^{11} d^{2} e + 3 \, a^{2} b^{10} d e^{2} - a^{3} b^{9} e^{3}\right)} x^{5} + 5 \, {\left(a b^{11} d^{3} - 3 \, a^{2} b^{10} d^{2} e + 3 \, a^{3} b^{9} d e^{2} - a^{4} b^{8} e^{3}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{3} - 3 \, a^{3} b^{9} d^{2} e + 3 \, a^{4} b^{8} d e^{2} - a^{5} b^{7} e^{3}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d^{3} - 3 \, a^{4} b^{8} d^{2} e + 3 \, a^{5} b^{7} d e^{2} - a^{6} b^{6} e^{3}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d^{3} - 3 \, a^{5} b^{7} d^{2} e + 3 \, a^{6} b^{6} d e^{2} - a^{7} b^{5} e^{3}\right)} x\right)}}, \frac{15 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(128 \, b^{6} d^{5} - 304 \, a b^{5} d^{4} e + 184 \, a^{2} b^{4} d^{3} e^{2} + 2 \, a^{3} b^{3} d^{2} e^{3} + 5 \, a^{4} b^{2} d e^{4} - 15 \, a^{5} b e^{5} - 15 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} + 10 \, {\left(b^{6} d^{2} e^{3} - 8 \, a b^{5} d e^{4} + 7 \, a^{2} b^{4} e^{5}\right)} x^{3} + 2 \, {\left(124 \, b^{6} d^{3} e^{2} - 357 \, a b^{5} d^{2} e^{3} + 297 \, a^{2} b^{4} d e^{4} - 64 \, a^{3} b^{3} e^{5}\right)} x^{2} + 2 \, {\left(168 \, b^{6} d^{4} e - 424 \, a b^{5} d^{3} e^{2} + 279 \, a^{2} b^{4} d^{2} e^{3} + 12 \, a^{3} b^{3} d e^{4} - 35 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(a^{5} b^{7} d^{3} - 3 \, a^{6} b^{6} d^{2} e + 3 \, a^{7} b^{5} d e^{2} - a^{8} b^{4} e^{3} + {\left(b^{12} d^{3} - 3 \, a b^{11} d^{2} e + 3 \, a^{2} b^{10} d e^{2} - a^{3} b^{9} e^{3}\right)} x^{5} + 5 \, {\left(a b^{11} d^{3} - 3 \, a^{2} b^{10} d^{2} e + 3 \, a^{3} b^{9} d e^{2} - a^{4} b^{8} e^{3}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{3} - 3 \, a^{3} b^{9} d^{2} e + 3 \, a^{4} b^{8} d e^{2} - a^{5} b^{7} e^{3}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d^{3} - 3 \, a^{4} b^{8} d^{2} e + 3 \, a^{5} b^{7} d e^{2} - a^{6} b^{6} e^{3}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d^{3} - 3 \, a^{5} b^{7} d^{2} e + 3 \, a^{6} b^{6} d e^{2} - a^{7} b^{5} e^{3}\right)} x\right)}}\right]"," ",0,"[1/1280*(15*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(128*b^6*d^5 - 304*a*b^5*d^4*e + 184*a^2*b^4*d^3*e^2 + 2*a^3*b^3*d^2*e^3 + 5*a^4*b^2*d*e^4 - 15*a^5*b*e^5 - 15*(b^6*d*e^4 - a*b^5*e^5)*x^4 + 10*(b^6*d^2*e^3 - 8*a*b^5*d*e^4 + 7*a^2*b^4*e^5)*x^3 + 2*(124*b^6*d^3*e^2 - 357*a*b^5*d^2*e^3 + 297*a^2*b^4*d*e^4 - 64*a^3*b^3*e^5)*x^2 + 2*(168*b^6*d^4*e - 424*a*b^5*d^3*e^2 + 279*a^2*b^4*d^2*e^3 + 12*a^3*b^3*d*e^4 - 35*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d^3 - 3*a^6*b^6*d^2*e + 3*a^7*b^5*d*e^2 - a^8*b^4*e^3 + (b^12*d^3 - 3*a*b^11*d^2*e + 3*a^2*b^10*d*e^2 - a^3*b^9*e^3)*x^5 + 5*(a*b^11*d^3 - 3*a^2*b^10*d^2*e + 3*a^3*b^9*d*e^2 - a^4*b^8*e^3)*x^4 + 10*(a^2*b^10*d^3 - 3*a^3*b^9*d^2*e + 3*a^4*b^8*d*e^2 - a^5*b^7*e^3)*x^3 + 10*(a^3*b^9*d^3 - 3*a^4*b^8*d^2*e + 3*a^5*b^7*d*e^2 - a^6*b^6*e^3)*x^2 + 5*(a^4*b^8*d^3 - 3*a^5*b^7*d^2*e + 3*a^6*b^6*d*e^2 - a^7*b^5*e^3)*x), 1/640*(15*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (128*b^6*d^5 - 304*a*b^5*d^4*e + 184*a^2*b^4*d^3*e^2 + 2*a^3*b^3*d^2*e^3 + 5*a^4*b^2*d*e^4 - 15*a^5*b*e^5 - 15*(b^6*d*e^4 - a*b^5*e^5)*x^4 + 10*(b^6*d^2*e^3 - 8*a*b^5*d*e^4 + 7*a^2*b^4*e^5)*x^3 + 2*(124*b^6*d^3*e^2 - 357*a*b^5*d^2*e^3 + 297*a^2*b^4*d*e^4 - 64*a^3*b^3*e^5)*x^2 + 2*(168*b^6*d^4*e - 424*a*b^5*d^3*e^2 + 279*a^2*b^4*d^2*e^3 + 12*a^3*b^3*d*e^4 - 35*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d^3 - 3*a^6*b^6*d^2*e + 3*a^7*b^5*d*e^2 - a^8*b^4*e^3 + (b^12*d^3 - 3*a*b^11*d^2*e + 3*a^2*b^10*d*e^2 - a^3*b^9*e^3)*x^5 + 5*(a*b^11*d^3 - 3*a^2*b^10*d^2*e + 3*a^3*b^9*d*e^2 - a^4*b^8*e^3)*x^4 + 10*(a^2*b^10*d^3 - 3*a^3*b^9*d^2*e + 3*a^4*b^8*d*e^2 - a^5*b^7*e^3)*x^3 + 10*(a^3*b^9*d^3 - 3*a^4*b^8*d^2*e + 3*a^5*b^7*d*e^2 - a^6*b^6*e^3)*x^2 + 5*(a^4*b^8*d^3 - 3*a^5*b^7*d^2*e + 3*a^6*b^6*d*e^2 - a^7*b^5*e^3)*x)]","B",0
1670,1,1492,0,0.458548," ","integrate((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(128 \, b^{6} d^{5} - 464 \, a b^{5} d^{4} e + 584 \, a^{2} b^{4} d^{3} e^{2} - 258 \, a^{3} b^{3} d^{2} e^{3} - 5 \, a^{4} b^{2} d e^{4} + 15 \, a^{5} b e^{5} + 15 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} - 10 \, {\left(b^{6} d^{2} e^{3} - 8 \, a b^{5} d e^{4} + 7 \, a^{2} b^{4} e^{5}\right)} x^{3} + 2 \, {\left(4 \, b^{6} d^{3} e^{2} - 27 \, a b^{5} d^{2} e^{3} + 87 \, a^{2} b^{4} d e^{4} - 64 \, a^{3} b^{3} e^{5}\right)} x^{2} + 2 \, {\left(88 \, b^{6} d^{4} e - 344 \, a b^{5} d^{3} e^{2} + 489 \, a^{2} b^{4} d^{2} e^{3} - 268 \, a^{3} b^{3} d e^{4} + 35 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(a^{5} b^{7} d^{4} - 4 \, a^{6} b^{6} d^{3} e + 6 \, a^{7} b^{5} d^{2} e^{2} - 4 \, a^{8} b^{4} d e^{3} + a^{9} b^{3} e^{4} + {\left(b^{12} d^{4} - 4 \, a b^{11} d^{3} e + 6 \, a^{2} b^{10} d^{2} e^{2} - 4 \, a^{3} b^{9} d e^{3} + a^{4} b^{8} e^{4}\right)} x^{5} + 5 \, {\left(a b^{11} d^{4} - 4 \, a^{2} b^{10} d^{3} e + 6 \, a^{3} b^{9} d^{2} e^{2} - 4 \, a^{4} b^{8} d e^{3} + a^{5} b^{7} e^{4}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{4} - 4 \, a^{3} b^{9} d^{3} e + 6 \, a^{4} b^{8} d^{2} e^{2} - 4 \, a^{5} b^{7} d e^{3} + a^{6} b^{6} e^{4}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d^{4} - 4 \, a^{4} b^{8} d^{3} e + 6 \, a^{5} b^{7} d^{2} e^{2} - 4 \, a^{6} b^{6} d e^{3} + a^{7} b^{5} e^{4}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d^{4} - 4 \, a^{5} b^{7} d^{3} e + 6 \, a^{6} b^{6} d^{2} e^{2} - 4 \, a^{7} b^{5} d e^{3} + a^{8} b^{4} e^{4}\right)} x\right)}}, -\frac{15 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(128 \, b^{6} d^{5} - 464 \, a b^{5} d^{4} e + 584 \, a^{2} b^{4} d^{3} e^{2} - 258 \, a^{3} b^{3} d^{2} e^{3} - 5 \, a^{4} b^{2} d e^{4} + 15 \, a^{5} b e^{5} + 15 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} - 10 \, {\left(b^{6} d^{2} e^{3} - 8 \, a b^{5} d e^{4} + 7 \, a^{2} b^{4} e^{5}\right)} x^{3} + 2 \, {\left(4 \, b^{6} d^{3} e^{2} - 27 \, a b^{5} d^{2} e^{3} + 87 \, a^{2} b^{4} d e^{4} - 64 \, a^{3} b^{3} e^{5}\right)} x^{2} + 2 \, {\left(88 \, b^{6} d^{4} e - 344 \, a b^{5} d^{3} e^{2} + 489 \, a^{2} b^{4} d^{2} e^{3} - 268 \, a^{3} b^{3} d e^{4} + 35 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(a^{5} b^{7} d^{4} - 4 \, a^{6} b^{6} d^{3} e + 6 \, a^{7} b^{5} d^{2} e^{2} - 4 \, a^{8} b^{4} d e^{3} + a^{9} b^{3} e^{4} + {\left(b^{12} d^{4} - 4 \, a b^{11} d^{3} e + 6 \, a^{2} b^{10} d^{2} e^{2} - 4 \, a^{3} b^{9} d e^{3} + a^{4} b^{8} e^{4}\right)} x^{5} + 5 \, {\left(a b^{11} d^{4} - 4 \, a^{2} b^{10} d^{3} e + 6 \, a^{3} b^{9} d^{2} e^{2} - 4 \, a^{4} b^{8} d e^{3} + a^{5} b^{7} e^{4}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{4} - 4 \, a^{3} b^{9} d^{3} e + 6 \, a^{4} b^{8} d^{2} e^{2} - 4 \, a^{5} b^{7} d e^{3} + a^{6} b^{6} e^{4}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d^{4} - 4 \, a^{4} b^{8} d^{3} e + 6 \, a^{5} b^{7} d^{2} e^{2} - 4 \, a^{6} b^{6} d e^{3} + a^{7} b^{5} e^{4}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d^{4} - 4 \, a^{5} b^{7} d^{3} e + 6 \, a^{6} b^{6} d^{2} e^{2} - 4 \, a^{7} b^{5} d e^{3} + a^{8} b^{4} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/1280*(15*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(128*b^6*d^5 - 464*a*b^5*d^4*e + 584*a^2*b^4*d^3*e^2 - 258*a^3*b^3*d^2*e^3 - 5*a^4*b^2*d*e^4 + 15*a^5*b*e^5 + 15*(b^6*d*e^4 - a*b^5*e^5)*x^4 - 10*(b^6*d^2*e^3 - 8*a*b^5*d*e^4 + 7*a^2*b^4*e^5)*x^3 + 2*(4*b^6*d^3*e^2 - 27*a*b^5*d^2*e^3 + 87*a^2*b^4*d*e^4 - 64*a^3*b^3*e^5)*x^2 + 2*(88*b^6*d^4*e - 344*a*b^5*d^3*e^2 + 489*a^2*b^4*d^2*e^3 - 268*a^3*b^3*d*e^4 + 35*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d^4 - 4*a^6*b^6*d^3*e + 6*a^7*b^5*d^2*e^2 - 4*a^8*b^4*d*e^3 + a^9*b^3*e^4 + (b^12*d^4 - 4*a*b^11*d^3*e + 6*a^2*b^10*d^2*e^2 - 4*a^3*b^9*d*e^3 + a^4*b^8*e^4)*x^5 + 5*(a*b^11*d^4 - 4*a^2*b^10*d^3*e + 6*a^3*b^9*d^2*e^2 - 4*a^4*b^8*d*e^3 + a^5*b^7*e^4)*x^4 + 10*(a^2*b^10*d^4 - 4*a^3*b^9*d^3*e + 6*a^4*b^8*d^2*e^2 - 4*a^5*b^7*d*e^3 + a^6*b^6*e^4)*x^3 + 10*(a^3*b^9*d^4 - 4*a^4*b^8*d^3*e + 6*a^5*b^7*d^2*e^2 - 4*a^6*b^6*d*e^3 + a^7*b^5*e^4)*x^2 + 5*(a^4*b^8*d^4 - 4*a^5*b^7*d^3*e + 6*a^6*b^6*d^2*e^2 - 4*a^7*b^5*d*e^3 + a^8*b^4*e^4)*x), -1/640*(15*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (128*b^6*d^5 - 464*a*b^5*d^4*e + 584*a^2*b^4*d^3*e^2 - 258*a^3*b^3*d^2*e^3 - 5*a^4*b^2*d*e^4 + 15*a^5*b*e^5 + 15*(b^6*d*e^4 - a*b^5*e^5)*x^4 - 10*(b^6*d^2*e^3 - 8*a*b^5*d*e^4 + 7*a^2*b^4*e^5)*x^3 + 2*(4*b^6*d^3*e^2 - 27*a*b^5*d^2*e^3 + 87*a^2*b^4*d*e^4 - 64*a^3*b^3*e^5)*x^2 + 2*(88*b^6*d^4*e - 344*a*b^5*d^3*e^2 + 489*a^2*b^4*d^2*e^3 - 268*a^3*b^3*d*e^4 + 35*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d^4 - 4*a^6*b^6*d^3*e + 6*a^7*b^5*d^2*e^2 - 4*a^8*b^4*d*e^3 + a^9*b^3*e^4 + (b^12*d^4 - 4*a*b^11*d^3*e + 6*a^2*b^10*d^2*e^2 - 4*a^3*b^9*d*e^3 + a^4*b^8*e^4)*x^5 + 5*(a*b^11*d^4 - 4*a^2*b^10*d^3*e + 6*a^3*b^9*d^2*e^2 - 4*a^4*b^8*d*e^3 + a^5*b^7*e^4)*x^4 + 10*(a^2*b^10*d^4 - 4*a^3*b^9*d^3*e + 6*a^4*b^8*d^2*e^2 - 4*a^5*b^7*d*e^3 + a^6*b^6*e^4)*x^3 + 10*(a^3*b^9*d^4 - 4*a^4*b^8*d^3*e + 6*a^5*b^7*d^2*e^2 - 4*a^6*b^6*d*e^3 + a^7*b^5*e^4)*x^2 + 5*(a^4*b^8*d^4 - 4*a^5*b^7*d^3*e + 6*a^6*b^6*d^2*e^2 - 4*a^7*b^5*d*e^3 + a^8*b^4*e^4)*x)]","B",0
1671,1,1673,0,0.467885," ","integrate((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(384 \, b^{6} d^{5} - 1872 \, a b^{5} d^{4} e + 3592 \, a^{2} b^{4} d^{3} e^{2} - 3314 \, a^{3} b^{3} d^{2} e^{3} + 1315 \, a^{4} b^{2} d e^{4} - 105 \, a^{5} b e^{5} - 105 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} + 70 \, {\left(b^{6} d^{2} e^{3} - 8 \, a b^{5} d e^{4} + 7 \, a^{2} b^{4} e^{5}\right)} x^{3} - 14 \, {\left(4 \, b^{6} d^{3} e^{2} - 27 \, a b^{5} d^{2} e^{3} + 87 \, a^{2} b^{4} d e^{4} - 64 \, a^{3} b^{3} e^{5}\right)} x^{2} + 2 \, {\left(24 \, b^{6} d^{4} e - 152 \, a b^{5} d^{3} e^{2} + 417 \, a^{2} b^{4} d^{2} e^{3} - 684 \, a^{3} b^{3} d e^{4} + 395 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(a^{5} b^{7} d^{5} - 5 \, a^{6} b^{6} d^{4} e + 10 \, a^{7} b^{5} d^{3} e^{2} - 10 \, a^{8} b^{4} d^{2} e^{3} + 5 \, a^{9} b^{3} d e^{4} - a^{10} b^{2} e^{5} + {\left(b^{12} d^{5} - 5 \, a b^{11} d^{4} e + 10 \, a^{2} b^{10} d^{3} e^{2} - 10 \, a^{3} b^{9} d^{2} e^{3} + 5 \, a^{4} b^{8} d e^{4} - a^{5} b^{7} e^{5}\right)} x^{5} + 5 \, {\left(a b^{11} d^{5} - 5 \, a^{2} b^{10} d^{4} e + 10 \, a^{3} b^{9} d^{3} e^{2} - 10 \, a^{4} b^{8} d^{2} e^{3} + 5 \, a^{5} b^{7} d e^{4} - a^{6} b^{6} e^{5}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{5} - 5 \, a^{3} b^{9} d^{4} e + 10 \, a^{4} b^{8} d^{3} e^{2} - 10 \, a^{5} b^{7} d^{2} e^{3} + 5 \, a^{6} b^{6} d e^{4} - a^{7} b^{5} e^{5}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d^{5} - 5 \, a^{4} b^{8} d^{4} e + 10 \, a^{5} b^{7} d^{3} e^{2} - 10 \, a^{6} b^{6} d^{2} e^{3} + 5 \, a^{7} b^{5} d e^{4} - a^{8} b^{4} e^{5}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d^{5} - 5 \, a^{5} b^{7} d^{4} e + 10 \, a^{6} b^{6} d^{3} e^{2} - 10 \, a^{7} b^{5} d^{2} e^{3} + 5 \, a^{8} b^{4} d e^{4} - a^{9} b^{3} e^{5}\right)} x\right)}}, \frac{105 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(384 \, b^{6} d^{5} - 1872 \, a b^{5} d^{4} e + 3592 \, a^{2} b^{4} d^{3} e^{2} - 3314 \, a^{3} b^{3} d^{2} e^{3} + 1315 \, a^{4} b^{2} d e^{4} - 105 \, a^{5} b e^{5} - 105 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} + 70 \, {\left(b^{6} d^{2} e^{3} - 8 \, a b^{5} d e^{4} + 7 \, a^{2} b^{4} e^{5}\right)} x^{3} - 14 \, {\left(4 \, b^{6} d^{3} e^{2} - 27 \, a b^{5} d^{2} e^{3} + 87 \, a^{2} b^{4} d e^{4} - 64 \, a^{3} b^{3} e^{5}\right)} x^{2} + 2 \, {\left(24 \, b^{6} d^{4} e - 152 \, a b^{5} d^{3} e^{2} + 417 \, a^{2} b^{4} d^{2} e^{3} - 684 \, a^{3} b^{3} d e^{4} + 395 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{5} b^{7} d^{5} - 5 \, a^{6} b^{6} d^{4} e + 10 \, a^{7} b^{5} d^{3} e^{2} - 10 \, a^{8} b^{4} d^{2} e^{3} + 5 \, a^{9} b^{3} d e^{4} - a^{10} b^{2} e^{5} + {\left(b^{12} d^{5} - 5 \, a b^{11} d^{4} e + 10 \, a^{2} b^{10} d^{3} e^{2} - 10 \, a^{3} b^{9} d^{2} e^{3} + 5 \, a^{4} b^{8} d e^{4} - a^{5} b^{7} e^{5}\right)} x^{5} + 5 \, {\left(a b^{11} d^{5} - 5 \, a^{2} b^{10} d^{4} e + 10 \, a^{3} b^{9} d^{3} e^{2} - 10 \, a^{4} b^{8} d^{2} e^{3} + 5 \, a^{5} b^{7} d e^{4} - a^{6} b^{6} e^{5}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{5} - 5 \, a^{3} b^{9} d^{4} e + 10 \, a^{4} b^{8} d^{3} e^{2} - 10 \, a^{5} b^{7} d^{2} e^{3} + 5 \, a^{6} b^{6} d e^{4} - a^{7} b^{5} e^{5}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d^{5} - 5 \, a^{4} b^{8} d^{4} e + 10 \, a^{5} b^{7} d^{3} e^{2} - 10 \, a^{6} b^{6} d^{2} e^{3} + 5 \, a^{7} b^{5} d e^{4} - a^{8} b^{4} e^{5}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d^{5} - 5 \, a^{5} b^{7} d^{4} e + 10 \, a^{6} b^{6} d^{3} e^{2} - 10 \, a^{7} b^{5} d^{2} e^{3} + 5 \, a^{8} b^{4} d e^{4} - a^{9} b^{3} e^{5}\right)} x\right)}}\right]"," ",0,"[1/3840*(105*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(384*b^6*d^5 - 1872*a*b^5*d^4*e + 3592*a^2*b^4*d^3*e^2 - 3314*a^3*b^3*d^2*e^3 + 1315*a^4*b^2*d*e^4 - 105*a^5*b*e^5 - 105*(b^6*d*e^4 - a*b^5*e^5)*x^4 + 70*(b^6*d^2*e^3 - 8*a*b^5*d*e^4 + 7*a^2*b^4*e^5)*x^3 - 14*(4*b^6*d^3*e^2 - 27*a*b^5*d^2*e^3 + 87*a^2*b^4*d*e^4 - 64*a^3*b^3*e^5)*x^2 + 2*(24*b^6*d^4*e - 152*a*b^5*d^3*e^2 + 417*a^2*b^4*d^2*e^3 - 684*a^3*b^3*d*e^4 + 395*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d^5 - 5*a^6*b^6*d^4*e + 10*a^7*b^5*d^3*e^2 - 10*a^8*b^4*d^2*e^3 + 5*a^9*b^3*d*e^4 - a^10*b^2*e^5 + (b^12*d^5 - 5*a*b^11*d^4*e + 10*a^2*b^10*d^3*e^2 - 10*a^3*b^9*d^2*e^3 + 5*a^4*b^8*d*e^4 - a^5*b^7*e^5)*x^5 + 5*(a*b^11*d^5 - 5*a^2*b^10*d^4*e + 10*a^3*b^9*d^3*e^2 - 10*a^4*b^8*d^2*e^3 + 5*a^5*b^7*d*e^4 - a^6*b^6*e^5)*x^4 + 10*(a^2*b^10*d^5 - 5*a^3*b^9*d^4*e + 10*a^4*b^8*d^3*e^2 - 10*a^5*b^7*d^2*e^3 + 5*a^6*b^6*d*e^4 - a^7*b^5*e^5)*x^3 + 10*(a^3*b^9*d^5 - 5*a^4*b^8*d^4*e + 10*a^5*b^7*d^3*e^2 - 10*a^6*b^6*d^2*e^3 + 5*a^7*b^5*d*e^4 - a^8*b^4*e^5)*x^2 + 5*(a^4*b^8*d^5 - 5*a^5*b^7*d^4*e + 10*a^6*b^6*d^3*e^2 - 10*a^7*b^5*d^2*e^3 + 5*a^8*b^4*d*e^4 - a^9*b^3*e^5)*x), 1/1920*(105*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (384*b^6*d^5 - 1872*a*b^5*d^4*e + 3592*a^2*b^4*d^3*e^2 - 3314*a^3*b^3*d^2*e^3 + 1315*a^4*b^2*d*e^4 - 105*a^5*b*e^5 - 105*(b^6*d*e^4 - a*b^5*e^5)*x^4 + 70*(b^6*d^2*e^3 - 8*a*b^5*d*e^4 + 7*a^2*b^4*e^5)*x^3 - 14*(4*b^6*d^3*e^2 - 27*a*b^5*d^2*e^3 + 87*a^2*b^4*d*e^4 - 64*a^3*b^3*e^5)*x^2 + 2*(24*b^6*d^4*e - 152*a*b^5*d^3*e^2 + 417*a^2*b^4*d^2*e^3 - 684*a^3*b^3*d*e^4 + 395*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d^5 - 5*a^6*b^6*d^4*e + 10*a^7*b^5*d^3*e^2 - 10*a^8*b^4*d^2*e^3 + 5*a^9*b^3*d*e^4 - a^10*b^2*e^5 + (b^12*d^5 - 5*a*b^11*d^4*e + 10*a^2*b^10*d^3*e^2 - 10*a^3*b^9*d^2*e^3 + 5*a^4*b^8*d*e^4 - a^5*b^7*e^5)*x^5 + 5*(a*b^11*d^5 - 5*a^2*b^10*d^4*e + 10*a^3*b^9*d^3*e^2 - 10*a^4*b^8*d^2*e^3 + 5*a^5*b^7*d*e^4 - a^6*b^6*e^5)*x^4 + 10*(a^2*b^10*d^5 - 5*a^3*b^9*d^4*e + 10*a^4*b^8*d^3*e^2 - 10*a^5*b^7*d^2*e^3 + 5*a^6*b^6*d*e^4 - a^7*b^5*e^5)*x^3 + 10*(a^3*b^9*d^5 - 5*a^4*b^8*d^4*e + 10*a^5*b^7*d^3*e^2 - 10*a^6*b^6*d^2*e^3 + 5*a^7*b^5*d*e^4 - a^8*b^4*e^5)*x^2 + 5*(a^4*b^8*d^5 - 5*a^5*b^7*d^4*e + 10*a^6*b^6*d^3*e^2 - 10*a^7*b^5*d^2*e^3 + 5*a^8*b^4*d*e^4 - a^9*b^3*e^5)*x)]","B",0
1672,1,1824,0,0.449457," ","integrate(1/(e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(128 \, b^{6} d^{5} - 784 \, a b^{5} d^{4} e + 2024 \, a^{2} b^{4} d^{3} e^{2} - 2858 \, a^{3} b^{3} d^{2} e^{3} + 2455 \, a^{4} b^{2} d e^{4} - 965 \, a^{5} b e^{5} + 315 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} - 210 \, {\left(b^{6} d^{2} e^{3} - 8 \, a b^{5} d e^{4} + 7 \, a^{2} b^{4} e^{5}\right)} x^{3} + 42 \, {\left(4 \, b^{6} d^{3} e^{2} - 27 \, a b^{5} d^{2} e^{3} + 87 \, a^{2} b^{4} d e^{4} - 64 \, a^{3} b^{3} e^{5}\right)} x^{2} - 6 \, {\left(24 \, b^{6} d^{4} e - 152 \, a b^{5} d^{3} e^{2} + 417 \, a^{2} b^{4} d^{2} e^{3} - 684 \, a^{3} b^{3} d e^{4} + 395 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(a^{5} b^{7} d^{6} - 6 \, a^{6} b^{6} d^{5} e + 15 \, a^{7} b^{5} d^{4} e^{2} - 20 \, a^{8} b^{4} d^{3} e^{3} + 15 \, a^{9} b^{3} d^{2} e^{4} - 6 \, a^{10} b^{2} d e^{5} + a^{11} b e^{6} + {\left(b^{12} d^{6} - 6 \, a b^{11} d^{5} e + 15 \, a^{2} b^{10} d^{4} e^{2} - 20 \, a^{3} b^{9} d^{3} e^{3} + 15 \, a^{4} b^{8} d^{2} e^{4} - 6 \, a^{5} b^{7} d e^{5} + a^{6} b^{6} e^{6}\right)} x^{5} + 5 \, {\left(a b^{11} d^{6} - 6 \, a^{2} b^{10} d^{5} e + 15 \, a^{3} b^{9} d^{4} e^{2} - 20 \, a^{4} b^{8} d^{3} e^{3} + 15 \, a^{5} b^{7} d^{2} e^{4} - 6 \, a^{6} b^{6} d e^{5} + a^{7} b^{5} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{6} - 6 \, a^{3} b^{9} d^{5} e + 15 \, a^{4} b^{8} d^{4} e^{2} - 20 \, a^{5} b^{7} d^{3} e^{3} + 15 \, a^{6} b^{6} d^{2} e^{4} - 6 \, a^{7} b^{5} d e^{5} + a^{8} b^{4} e^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d^{6} - 6 \, a^{4} b^{8} d^{5} e + 15 \, a^{5} b^{7} d^{4} e^{2} - 20 \, a^{6} b^{6} d^{3} e^{3} + 15 \, a^{7} b^{5} d^{2} e^{4} - 6 \, a^{8} b^{4} d e^{5} + a^{9} b^{3} e^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d^{6} - 6 \, a^{5} b^{7} d^{5} e + 15 \, a^{6} b^{6} d^{4} e^{2} - 20 \, a^{7} b^{5} d^{3} e^{3} + 15 \, a^{8} b^{4} d^{2} e^{4} - 6 \, a^{9} b^{3} d e^{5} + a^{10} b^{2} e^{6}\right)} x\right)}}, -\frac{315 \, {\left(b^{5} e^{5} x^{5} + 5 \, a b^{4} e^{5} x^{4} + 10 \, a^{2} b^{3} e^{5} x^{3} + 10 \, a^{3} b^{2} e^{5} x^{2} + 5 \, a^{4} b e^{5} x + a^{5} e^{5}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(128 \, b^{6} d^{5} - 784 \, a b^{5} d^{4} e + 2024 \, a^{2} b^{4} d^{3} e^{2} - 2858 \, a^{3} b^{3} d^{2} e^{3} + 2455 \, a^{4} b^{2} d e^{4} - 965 \, a^{5} b e^{5} + 315 \, {\left(b^{6} d e^{4} - a b^{5} e^{5}\right)} x^{4} - 210 \, {\left(b^{6} d^{2} e^{3} - 8 \, a b^{5} d e^{4} + 7 \, a^{2} b^{4} e^{5}\right)} x^{3} + 42 \, {\left(4 \, b^{6} d^{3} e^{2} - 27 \, a b^{5} d^{2} e^{3} + 87 \, a^{2} b^{4} d e^{4} - 64 \, a^{3} b^{3} e^{5}\right)} x^{2} - 6 \, {\left(24 \, b^{6} d^{4} e - 152 \, a b^{5} d^{3} e^{2} + 417 \, a^{2} b^{4} d^{2} e^{3} - 684 \, a^{3} b^{3} d e^{4} + 395 \, a^{4} b^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(a^{5} b^{7} d^{6} - 6 \, a^{6} b^{6} d^{5} e + 15 \, a^{7} b^{5} d^{4} e^{2} - 20 \, a^{8} b^{4} d^{3} e^{3} + 15 \, a^{9} b^{3} d^{2} e^{4} - 6 \, a^{10} b^{2} d e^{5} + a^{11} b e^{6} + {\left(b^{12} d^{6} - 6 \, a b^{11} d^{5} e + 15 \, a^{2} b^{10} d^{4} e^{2} - 20 \, a^{3} b^{9} d^{3} e^{3} + 15 \, a^{4} b^{8} d^{2} e^{4} - 6 \, a^{5} b^{7} d e^{5} + a^{6} b^{6} e^{6}\right)} x^{5} + 5 \, {\left(a b^{11} d^{6} - 6 \, a^{2} b^{10} d^{5} e + 15 \, a^{3} b^{9} d^{4} e^{2} - 20 \, a^{4} b^{8} d^{3} e^{3} + 15 \, a^{5} b^{7} d^{2} e^{4} - 6 \, a^{6} b^{6} d e^{5} + a^{7} b^{5} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} d^{6} - 6 \, a^{3} b^{9} d^{5} e + 15 \, a^{4} b^{8} d^{4} e^{2} - 20 \, a^{5} b^{7} d^{3} e^{3} + 15 \, a^{6} b^{6} d^{2} e^{4} - 6 \, a^{7} b^{5} d e^{5} + a^{8} b^{4} e^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} d^{6} - 6 \, a^{4} b^{8} d^{5} e + 15 \, a^{5} b^{7} d^{4} e^{2} - 20 \, a^{6} b^{6} d^{3} e^{3} + 15 \, a^{7} b^{5} d^{2} e^{4} - 6 \, a^{8} b^{4} d e^{5} + a^{9} b^{3} e^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} d^{6} - 6 \, a^{5} b^{7} d^{5} e + 15 \, a^{6} b^{6} d^{4} e^{2} - 20 \, a^{7} b^{5} d^{3} e^{3} + 15 \, a^{8} b^{4} d^{2} e^{4} - 6 \, a^{9} b^{3} d e^{5} + a^{10} b^{2} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/1280*(315*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(128*b^6*d^5 - 784*a*b^5*d^4*e + 2024*a^2*b^4*d^3*e^2 - 2858*a^3*b^3*d^2*e^3 + 2455*a^4*b^2*d*e^4 - 965*a^5*b*e^5 + 315*(b^6*d*e^4 - a*b^5*e^5)*x^4 - 210*(b^6*d^2*e^3 - 8*a*b^5*d*e^4 + 7*a^2*b^4*e^5)*x^3 + 42*(4*b^6*d^3*e^2 - 27*a*b^5*d^2*e^3 + 87*a^2*b^4*d*e^4 - 64*a^3*b^3*e^5)*x^2 - 6*(24*b^6*d^4*e - 152*a*b^5*d^3*e^2 + 417*a^2*b^4*d^2*e^3 - 684*a^3*b^3*d*e^4 + 395*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d^6 - 6*a^6*b^6*d^5*e + 15*a^7*b^5*d^4*e^2 - 20*a^8*b^4*d^3*e^3 + 15*a^9*b^3*d^2*e^4 - 6*a^10*b^2*d*e^5 + a^11*b*e^6 + (b^12*d^6 - 6*a*b^11*d^5*e + 15*a^2*b^10*d^4*e^2 - 20*a^3*b^9*d^3*e^3 + 15*a^4*b^8*d^2*e^4 - 6*a^5*b^7*d*e^5 + a^6*b^6*e^6)*x^5 + 5*(a*b^11*d^6 - 6*a^2*b^10*d^5*e + 15*a^3*b^9*d^4*e^2 - 20*a^4*b^8*d^3*e^3 + 15*a^5*b^7*d^2*e^4 - 6*a^6*b^6*d*e^5 + a^7*b^5*e^6)*x^4 + 10*(a^2*b^10*d^6 - 6*a^3*b^9*d^5*e + 15*a^4*b^8*d^4*e^2 - 20*a^5*b^7*d^3*e^3 + 15*a^6*b^6*d^2*e^4 - 6*a^7*b^5*d*e^5 + a^8*b^4*e^6)*x^3 + 10*(a^3*b^9*d^6 - 6*a^4*b^8*d^5*e + 15*a^5*b^7*d^4*e^2 - 20*a^6*b^6*d^3*e^3 + 15*a^7*b^5*d^2*e^4 - 6*a^8*b^4*d*e^5 + a^9*b^3*e^6)*x^2 + 5*(a^4*b^8*d^6 - 6*a^5*b^7*d^5*e + 15*a^6*b^6*d^4*e^2 - 20*a^7*b^5*d^3*e^3 + 15*a^8*b^4*d^2*e^4 - 6*a^9*b^3*d*e^5 + a^10*b^2*e^6)*x), -1/640*(315*(b^5*e^5*x^5 + 5*a*b^4*e^5*x^4 + 10*a^2*b^3*e^5*x^3 + 10*a^3*b^2*e^5*x^2 + 5*a^4*b*e^5*x + a^5*e^5)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (128*b^6*d^5 - 784*a*b^5*d^4*e + 2024*a^2*b^4*d^3*e^2 - 2858*a^3*b^3*d^2*e^3 + 2455*a^4*b^2*d*e^4 - 965*a^5*b*e^5 + 315*(b^6*d*e^4 - a*b^5*e^5)*x^4 - 210*(b^6*d^2*e^3 - 8*a*b^5*d*e^4 + 7*a^2*b^4*e^5)*x^3 + 42*(4*b^6*d^3*e^2 - 27*a*b^5*d^2*e^3 + 87*a^2*b^4*d*e^4 - 64*a^3*b^3*e^5)*x^2 - 6*(24*b^6*d^4*e - 152*a*b^5*d^3*e^2 + 417*a^2*b^4*d^2*e^3 - 684*a^3*b^3*d*e^4 + 395*a^4*b^2*e^5)*x)*sqrt(e*x + d))/(a^5*b^7*d^6 - 6*a^6*b^6*d^5*e + 15*a^7*b^5*d^4*e^2 - 20*a^8*b^4*d^3*e^3 + 15*a^9*b^3*d^2*e^4 - 6*a^10*b^2*d*e^5 + a^11*b*e^6 + (b^12*d^6 - 6*a*b^11*d^5*e + 15*a^2*b^10*d^4*e^2 - 20*a^3*b^9*d^3*e^3 + 15*a^4*b^8*d^2*e^4 - 6*a^5*b^7*d*e^5 + a^6*b^6*e^6)*x^5 + 5*(a*b^11*d^6 - 6*a^2*b^10*d^5*e + 15*a^3*b^9*d^4*e^2 - 20*a^4*b^8*d^3*e^3 + 15*a^5*b^7*d^2*e^4 - 6*a^6*b^6*d*e^5 + a^7*b^5*e^6)*x^4 + 10*(a^2*b^10*d^6 - 6*a^3*b^9*d^5*e + 15*a^4*b^8*d^4*e^2 - 20*a^5*b^7*d^3*e^3 + 15*a^6*b^6*d^2*e^4 - 6*a^7*b^5*d*e^5 + a^8*b^4*e^6)*x^3 + 10*(a^3*b^9*d^6 - 6*a^4*b^8*d^5*e + 15*a^5*b^7*d^4*e^2 - 20*a^6*b^6*d^3*e^3 + 15*a^7*b^5*d^2*e^4 - 6*a^8*b^4*d*e^5 + a^9*b^3*e^6)*x^2 + 5*(a^4*b^8*d^6 - 6*a^5*b^7*d^5*e + 15*a^6*b^6*d^4*e^2 - 20*a^7*b^5*d^3*e^3 + 15*a^8*b^4*d^2*e^4 - 6*a^9*b^3*d*e^5 + a^10*b^2*e^6)*x)]","B",0
1673,1,2314,0,0.504179," ","integrate(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(b^{5} e^{6} x^{6} + a^{5} d e^{5} + {\left(b^{5} d e^{5} + 5 \, a b^{4} e^{6}\right)} x^{5} + 5 \, {\left(a b^{4} d e^{5} + 2 \, a^{2} b^{3} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} x^{3} + 5 \, {\left(2 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} x^{2} + {\left(5 \, a^{4} b d e^{5} + a^{5} e^{6}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(3465 \, b^{5} e^{5} x^{5} + 128 \, b^{5} d^{5} - 816 \, a b^{4} d^{4} e + 2248 \, a^{2} b^{3} d^{3} e^{2} - 3590 \, a^{3} b^{2} d^{2} e^{3} + 4215 \, a^{4} b d e^{4} + 1280 \, a^{5} e^{5} + 1155 \, {\left(b^{5} d e^{4} + 14 \, a b^{4} e^{5}\right)} x^{4} - 462 \, {\left(b^{5} d^{2} e^{3} - 12 \, a b^{4} d e^{4} - 64 \, a^{2} b^{3} e^{5}\right)} x^{3} + 66 \, {\left(4 \, b^{5} d^{3} e^{2} - 33 \, a b^{4} d^{2} e^{3} + 159 \, a^{2} b^{3} d e^{4} + 395 \, a^{3} b^{2} e^{5}\right)} x^{2} - 11 \, {\left(16 \, b^{5} d^{4} e - 112 \, a b^{4} d^{3} e^{2} + 366 \, a^{2} b^{3} d^{2} e^{3} - 880 \, a^{3} b^{2} d e^{4} - 965 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(a^{5} b^{6} d^{7} - 6 \, a^{6} b^{5} d^{6} e + 15 \, a^{7} b^{4} d^{5} e^{2} - 20 \, a^{8} b^{3} d^{4} e^{3} + 15 \, a^{9} b^{2} d^{3} e^{4} - 6 \, a^{10} b d^{2} e^{5} + a^{11} d e^{6} + {\left(b^{11} d^{6} e - 6 \, a b^{10} d^{5} e^{2} + 15 \, a^{2} b^{9} d^{4} e^{3} - 20 \, a^{3} b^{8} d^{3} e^{4} + 15 \, a^{4} b^{7} d^{2} e^{5} - 6 \, a^{5} b^{6} d e^{6} + a^{6} b^{5} e^{7}\right)} x^{6} + {\left(b^{11} d^{7} - a b^{10} d^{6} e - 15 \, a^{2} b^{9} d^{5} e^{2} + 55 \, a^{3} b^{8} d^{4} e^{3} - 85 \, a^{4} b^{7} d^{3} e^{4} + 69 \, a^{5} b^{6} d^{2} e^{5} - 29 \, a^{6} b^{5} d e^{6} + 5 \, a^{7} b^{4} e^{7}\right)} x^{5} + 5 \, {\left(a b^{10} d^{7} - 4 \, a^{2} b^{9} d^{6} e + 3 \, a^{3} b^{8} d^{5} e^{2} + 10 \, a^{4} b^{7} d^{4} e^{3} - 25 \, a^{5} b^{6} d^{3} e^{4} + 24 \, a^{6} b^{5} d^{2} e^{5} - 11 \, a^{7} b^{4} d e^{6} + 2 \, a^{8} b^{3} e^{7}\right)} x^{4} + 10 \, {\left(a^{2} b^{9} d^{7} - 5 \, a^{3} b^{8} d^{6} e + 9 \, a^{4} b^{7} d^{5} e^{2} - 5 \, a^{5} b^{6} d^{4} e^{3} - 5 \, a^{6} b^{5} d^{3} e^{4} + 9 \, a^{7} b^{4} d^{2} e^{5} - 5 \, a^{8} b^{3} d e^{6} + a^{9} b^{2} e^{7}\right)} x^{3} + 5 \, {\left(2 \, a^{3} b^{8} d^{7} - 11 \, a^{4} b^{7} d^{6} e + 24 \, a^{5} b^{6} d^{5} e^{2} - 25 \, a^{6} b^{5} d^{4} e^{3} + 10 \, a^{7} b^{4} d^{3} e^{4} + 3 \, a^{8} b^{3} d^{2} e^{5} - 4 \, a^{9} b^{2} d e^{6} + a^{10} b e^{7}\right)} x^{2} + {\left(5 \, a^{4} b^{7} d^{7} - 29 \, a^{5} b^{6} d^{6} e + 69 \, a^{6} b^{5} d^{5} e^{2} - 85 \, a^{7} b^{4} d^{4} e^{3} + 55 \, a^{8} b^{3} d^{3} e^{4} - 15 \, a^{9} b^{2} d^{2} e^{5} - a^{10} b d e^{6} + a^{11} e^{7}\right)} x\right)}}, \frac{3465 \, {\left(b^{5} e^{6} x^{6} + a^{5} d e^{5} + {\left(b^{5} d e^{5} + 5 \, a b^{4} e^{6}\right)} x^{5} + 5 \, {\left(a b^{4} d e^{5} + 2 \, a^{2} b^{3} e^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} x^{3} + 5 \, {\left(2 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} x^{2} + {\left(5 \, a^{4} b d e^{5} + a^{5} e^{6}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3465 \, b^{5} e^{5} x^{5} + 128 \, b^{5} d^{5} - 816 \, a b^{4} d^{4} e + 2248 \, a^{2} b^{3} d^{3} e^{2} - 3590 \, a^{3} b^{2} d^{2} e^{3} + 4215 \, a^{4} b d e^{4} + 1280 \, a^{5} e^{5} + 1155 \, {\left(b^{5} d e^{4} + 14 \, a b^{4} e^{5}\right)} x^{4} - 462 \, {\left(b^{5} d^{2} e^{3} - 12 \, a b^{4} d e^{4} - 64 \, a^{2} b^{3} e^{5}\right)} x^{3} + 66 \, {\left(4 \, b^{5} d^{3} e^{2} - 33 \, a b^{4} d^{2} e^{3} + 159 \, a^{2} b^{3} d e^{4} + 395 \, a^{3} b^{2} e^{5}\right)} x^{2} - 11 \, {\left(16 \, b^{5} d^{4} e - 112 \, a b^{4} d^{3} e^{2} + 366 \, a^{2} b^{3} d^{2} e^{3} - 880 \, a^{3} b^{2} d e^{4} - 965 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(a^{5} b^{6} d^{7} - 6 \, a^{6} b^{5} d^{6} e + 15 \, a^{7} b^{4} d^{5} e^{2} - 20 \, a^{8} b^{3} d^{4} e^{3} + 15 \, a^{9} b^{2} d^{3} e^{4} - 6 \, a^{10} b d^{2} e^{5} + a^{11} d e^{6} + {\left(b^{11} d^{6} e - 6 \, a b^{10} d^{5} e^{2} + 15 \, a^{2} b^{9} d^{4} e^{3} - 20 \, a^{3} b^{8} d^{3} e^{4} + 15 \, a^{4} b^{7} d^{2} e^{5} - 6 \, a^{5} b^{6} d e^{6} + a^{6} b^{5} e^{7}\right)} x^{6} + {\left(b^{11} d^{7} - a b^{10} d^{6} e - 15 \, a^{2} b^{9} d^{5} e^{2} + 55 \, a^{3} b^{8} d^{4} e^{3} - 85 \, a^{4} b^{7} d^{3} e^{4} + 69 \, a^{5} b^{6} d^{2} e^{5} - 29 \, a^{6} b^{5} d e^{6} + 5 \, a^{7} b^{4} e^{7}\right)} x^{5} + 5 \, {\left(a b^{10} d^{7} - 4 \, a^{2} b^{9} d^{6} e + 3 \, a^{3} b^{8} d^{5} e^{2} + 10 \, a^{4} b^{7} d^{4} e^{3} - 25 \, a^{5} b^{6} d^{3} e^{4} + 24 \, a^{6} b^{5} d^{2} e^{5} - 11 \, a^{7} b^{4} d e^{6} + 2 \, a^{8} b^{3} e^{7}\right)} x^{4} + 10 \, {\left(a^{2} b^{9} d^{7} - 5 \, a^{3} b^{8} d^{6} e + 9 \, a^{4} b^{7} d^{5} e^{2} - 5 \, a^{5} b^{6} d^{4} e^{3} - 5 \, a^{6} b^{5} d^{3} e^{4} + 9 \, a^{7} b^{4} d^{2} e^{5} - 5 \, a^{8} b^{3} d e^{6} + a^{9} b^{2} e^{7}\right)} x^{3} + 5 \, {\left(2 \, a^{3} b^{8} d^{7} - 11 \, a^{4} b^{7} d^{6} e + 24 \, a^{5} b^{6} d^{5} e^{2} - 25 \, a^{6} b^{5} d^{4} e^{3} + 10 \, a^{7} b^{4} d^{3} e^{4} + 3 \, a^{8} b^{3} d^{2} e^{5} - 4 \, a^{9} b^{2} d e^{6} + a^{10} b e^{7}\right)} x^{2} + {\left(5 \, a^{4} b^{7} d^{7} - 29 \, a^{5} b^{6} d^{6} e + 69 \, a^{6} b^{5} d^{5} e^{2} - 85 \, a^{7} b^{4} d^{4} e^{3} + 55 \, a^{8} b^{3} d^{3} e^{4} - 15 \, a^{9} b^{2} d^{2} e^{5} - a^{10} b d e^{6} + a^{11} e^{7}\right)} x\right)}}\right]"," ",0,"[1/1280*(3465*(b^5*e^6*x^6 + a^5*d*e^5 + (b^5*d*e^5 + 5*a*b^4*e^6)*x^5 + 5*(a*b^4*d*e^5 + 2*a^2*b^3*e^6)*x^4 + 10*(a^2*b^3*d*e^5 + a^3*b^2*e^6)*x^3 + 5*(2*a^3*b^2*d*e^5 + a^4*b*e^6)*x^2 + (5*a^4*b*d*e^5 + a^5*e^6)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(3465*b^5*e^5*x^5 + 128*b^5*d^5 - 816*a*b^4*d^4*e + 2248*a^2*b^3*d^3*e^2 - 3590*a^3*b^2*d^2*e^3 + 4215*a^4*b*d*e^4 + 1280*a^5*e^5 + 1155*(b^5*d*e^4 + 14*a*b^4*e^5)*x^4 - 462*(b^5*d^2*e^3 - 12*a*b^4*d*e^4 - 64*a^2*b^3*e^5)*x^3 + 66*(4*b^5*d^3*e^2 - 33*a*b^4*d^2*e^3 + 159*a^2*b^3*d*e^4 + 395*a^3*b^2*e^5)*x^2 - 11*(16*b^5*d^4*e - 112*a*b^4*d^3*e^2 + 366*a^2*b^3*d^2*e^3 - 880*a^3*b^2*d*e^4 - 965*a^4*b*e^5)*x)*sqrt(e*x + d))/(a^5*b^6*d^7 - 6*a^6*b^5*d^6*e + 15*a^7*b^4*d^5*e^2 - 20*a^8*b^3*d^4*e^3 + 15*a^9*b^2*d^3*e^4 - 6*a^10*b*d^2*e^5 + a^11*d*e^6 + (b^11*d^6*e - 6*a*b^10*d^5*e^2 + 15*a^2*b^9*d^4*e^3 - 20*a^3*b^8*d^3*e^4 + 15*a^4*b^7*d^2*e^5 - 6*a^5*b^6*d*e^6 + a^6*b^5*e^7)*x^6 + (b^11*d^7 - a*b^10*d^6*e - 15*a^2*b^9*d^5*e^2 + 55*a^3*b^8*d^4*e^3 - 85*a^4*b^7*d^3*e^4 + 69*a^5*b^6*d^2*e^5 - 29*a^6*b^5*d*e^6 + 5*a^7*b^4*e^7)*x^5 + 5*(a*b^10*d^7 - 4*a^2*b^9*d^6*e + 3*a^3*b^8*d^5*e^2 + 10*a^4*b^7*d^4*e^3 - 25*a^5*b^6*d^3*e^4 + 24*a^6*b^5*d^2*e^5 - 11*a^7*b^4*d*e^6 + 2*a^8*b^3*e^7)*x^4 + 10*(a^2*b^9*d^7 - 5*a^3*b^8*d^6*e + 9*a^4*b^7*d^5*e^2 - 5*a^5*b^6*d^4*e^3 - 5*a^6*b^5*d^3*e^4 + 9*a^7*b^4*d^2*e^5 - 5*a^8*b^3*d*e^6 + a^9*b^2*e^7)*x^3 + 5*(2*a^3*b^8*d^7 - 11*a^4*b^7*d^6*e + 24*a^5*b^6*d^5*e^2 - 25*a^6*b^5*d^4*e^3 + 10*a^7*b^4*d^3*e^4 + 3*a^8*b^3*d^2*e^5 - 4*a^9*b^2*d*e^6 + a^10*b*e^7)*x^2 + (5*a^4*b^7*d^7 - 29*a^5*b^6*d^6*e + 69*a^6*b^5*d^5*e^2 - 85*a^7*b^4*d^4*e^3 + 55*a^8*b^3*d^3*e^4 - 15*a^9*b^2*d^2*e^5 - a^10*b*d*e^6 + a^11*e^7)*x), 1/640*(3465*(b^5*e^6*x^6 + a^5*d*e^5 + (b^5*d*e^5 + 5*a*b^4*e^6)*x^5 + 5*(a*b^4*d*e^5 + 2*a^2*b^3*e^6)*x^4 + 10*(a^2*b^3*d*e^5 + a^3*b^2*e^6)*x^3 + 5*(2*a^3*b^2*d*e^5 + a^4*b*e^6)*x^2 + (5*a^4*b*d*e^5 + a^5*e^6)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3465*b^5*e^5*x^5 + 128*b^5*d^5 - 816*a*b^4*d^4*e + 2248*a^2*b^3*d^3*e^2 - 3590*a^3*b^2*d^2*e^3 + 4215*a^4*b*d*e^4 + 1280*a^5*e^5 + 1155*(b^5*d*e^4 + 14*a*b^4*e^5)*x^4 - 462*(b^5*d^2*e^3 - 12*a*b^4*d*e^4 - 64*a^2*b^3*e^5)*x^3 + 66*(4*b^5*d^3*e^2 - 33*a*b^4*d^2*e^3 + 159*a^2*b^3*d*e^4 + 395*a^3*b^2*e^5)*x^2 - 11*(16*b^5*d^4*e - 112*a*b^4*d^3*e^2 + 366*a^2*b^3*d^2*e^3 - 880*a^3*b^2*d*e^4 - 965*a^4*b*e^5)*x)*sqrt(e*x + d))/(a^5*b^6*d^7 - 6*a^6*b^5*d^6*e + 15*a^7*b^4*d^5*e^2 - 20*a^8*b^3*d^4*e^3 + 15*a^9*b^2*d^3*e^4 - 6*a^10*b*d^2*e^5 + a^11*d*e^6 + (b^11*d^6*e - 6*a*b^10*d^5*e^2 + 15*a^2*b^9*d^4*e^3 - 20*a^3*b^8*d^3*e^4 + 15*a^4*b^7*d^2*e^5 - 6*a^5*b^6*d*e^6 + a^6*b^5*e^7)*x^6 + (b^11*d^7 - a*b^10*d^6*e - 15*a^2*b^9*d^5*e^2 + 55*a^3*b^8*d^4*e^3 - 85*a^4*b^7*d^3*e^4 + 69*a^5*b^6*d^2*e^5 - 29*a^6*b^5*d*e^6 + 5*a^7*b^4*e^7)*x^5 + 5*(a*b^10*d^7 - 4*a^2*b^9*d^6*e + 3*a^3*b^8*d^5*e^2 + 10*a^4*b^7*d^4*e^3 - 25*a^5*b^6*d^3*e^4 + 24*a^6*b^5*d^2*e^5 - 11*a^7*b^4*d*e^6 + 2*a^8*b^3*e^7)*x^4 + 10*(a^2*b^9*d^7 - 5*a^3*b^8*d^6*e + 9*a^4*b^7*d^5*e^2 - 5*a^5*b^6*d^4*e^3 - 5*a^6*b^5*d^3*e^4 + 9*a^7*b^4*d^2*e^5 - 5*a^8*b^3*d*e^6 + a^9*b^2*e^7)*x^3 + 5*(2*a^3*b^8*d^7 - 11*a^4*b^7*d^6*e + 24*a^5*b^6*d^5*e^2 - 25*a^6*b^5*d^4*e^3 + 10*a^7*b^4*d^3*e^4 + 3*a^8*b^3*d^2*e^5 - 4*a^9*b^2*d*e^6 + a^10*b*e^7)*x^2 + (5*a^4*b^7*d^7 - 29*a^5*b^6*d^6*e + 69*a^6*b^5*d^5*e^2 - 85*a^7*b^4*d^4*e^3 + 55*a^8*b^3*d^3*e^4 - 15*a^9*b^2*d^2*e^5 - a^10*b*d*e^6 + a^11*e^7)*x)]","B",0
1674,1,3244,0,0.525194," ","integrate(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[-\frac{45045 \, {\left(b^{6} e^{7} x^{7} + a^{5} b d^{2} e^{5} + {\left(2 \, b^{6} d e^{6} + 5 \, a b^{5} e^{7}\right)} x^{6} + {\left(b^{6} d^{2} e^{5} + 10 \, a b^{5} d e^{6} + 10 \, a^{2} b^{4} e^{7}\right)} x^{5} + 5 \, {\left(a b^{5} d^{2} e^{5} + 4 \, a^{2} b^{4} d e^{6} + 2 \, a^{3} b^{3} e^{7}\right)} x^{4} + 5 \, {\left(2 \, a^{2} b^{4} d^{2} e^{5} + 4 \, a^{3} b^{3} d e^{6} + a^{4} b^{2} e^{7}\right)} x^{3} + {\left(10 \, a^{3} b^{3} d^{2} e^{5} + 10 \, a^{4} b^{2} d e^{6} + a^{5} b e^{7}\right)} x^{2} + {\left(5 \, a^{4} b^{2} d^{2} e^{5} + 2 \, a^{5} b d e^{6}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(45045 \, b^{6} e^{6} x^{6} + 384 \, b^{6} d^{6} - 2928 \, a b^{5} d^{5} e + 10024 \, a^{2} b^{4} d^{4} e^{2} - 21070 \, a^{3} b^{3} d^{3} e^{3} + 35595 \, a^{4} b^{2} d^{2} e^{4} + 24320 \, a^{5} b d e^{5} - 1280 \, a^{6} e^{6} + 30030 \, {\left(2 \, b^{6} d e^{5} + 7 \, a b^{5} e^{6}\right)} x^{5} + 3003 \, {\left(3 \, b^{6} d^{2} e^{4} + 94 \, a b^{5} d e^{5} + 128 \, a^{2} b^{4} e^{6}\right)} x^{4} - 858 \, {\left(3 \, b^{6} d^{3} e^{3} - 51 \, a b^{5} d^{2} e^{4} - 607 \, a^{2} b^{4} d e^{5} - 395 \, a^{3} b^{3} e^{6}\right)} x^{3} + 143 \, {\left(8 \, b^{6} d^{4} e^{2} - 86 \, a b^{5} d^{3} e^{3} + 588 \, a^{2} b^{4} d^{2} e^{4} + 3250 \, a^{3} b^{3} d e^{5} + 965 \, a^{4} b^{2} e^{6}\right)} x^{2} - 26 \, {\left(24 \, b^{6} d^{5} e - 208 \, a b^{5} d^{4} e^{2} + 889 \, a^{2} b^{4} d^{3} e^{3} - 3045 \, a^{3} b^{3} d^{2} e^{4} - 7415 \, a^{4} b^{2} d e^{5} - 640 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{3840 \, {\left(a^{5} b^{7} d^{9} - 7 \, a^{6} b^{6} d^{8} e + 21 \, a^{7} b^{5} d^{7} e^{2} - 35 \, a^{8} b^{4} d^{6} e^{3} + 35 \, a^{9} b^{3} d^{5} e^{4} - 21 \, a^{10} b^{2} d^{4} e^{5} + 7 \, a^{11} b d^{3} e^{6} - a^{12} d^{2} e^{7} + {\left(b^{12} d^{7} e^{2} - 7 \, a b^{11} d^{6} e^{3} + 21 \, a^{2} b^{10} d^{5} e^{4} - 35 \, a^{3} b^{9} d^{4} e^{5} + 35 \, a^{4} b^{8} d^{3} e^{6} - 21 \, a^{5} b^{7} d^{2} e^{7} + 7 \, a^{6} b^{6} d e^{8} - a^{7} b^{5} e^{9}\right)} x^{7} + {\left(2 \, b^{12} d^{8} e - 9 \, a b^{11} d^{7} e^{2} + 7 \, a^{2} b^{10} d^{6} e^{3} + 35 \, a^{3} b^{9} d^{5} e^{4} - 105 \, a^{4} b^{8} d^{4} e^{5} + 133 \, a^{5} b^{7} d^{3} e^{6} - 91 \, a^{6} b^{6} d^{2} e^{7} + 33 \, a^{7} b^{5} d e^{8} - 5 \, a^{8} b^{4} e^{9}\right)} x^{6} + {\left(b^{12} d^{9} + 3 \, a b^{11} d^{8} e - 39 \, a^{2} b^{10} d^{7} e^{2} + 105 \, a^{3} b^{9} d^{6} e^{3} - 105 \, a^{4} b^{8} d^{5} e^{4} - 21 \, a^{5} b^{7} d^{4} e^{5} + 147 \, a^{6} b^{6} d^{3} e^{6} - 141 \, a^{7} b^{5} d^{2} e^{7} + 60 \, a^{8} b^{4} d e^{8} - 10 \, a^{9} b^{3} e^{9}\right)} x^{5} + 5 \, {\left(a b^{11} d^{9} - 3 \, a^{2} b^{10} d^{8} e - 5 \, a^{3} b^{9} d^{7} e^{2} + 35 \, a^{4} b^{8} d^{6} e^{3} - 63 \, a^{5} b^{7} d^{5} e^{4} + 49 \, a^{6} b^{6} d^{4} e^{5} - 7 \, a^{7} b^{5} d^{3} e^{6} - 15 \, a^{8} b^{4} d^{2} e^{7} + 10 \, a^{9} b^{3} d e^{8} - 2 \, a^{10} b^{2} e^{9}\right)} x^{4} + 5 \, {\left(2 \, a^{2} b^{10} d^{9} - 10 \, a^{3} b^{9} d^{8} e + 15 \, a^{4} b^{8} d^{7} e^{2} + 7 \, a^{5} b^{7} d^{6} e^{3} - 49 \, a^{6} b^{6} d^{5} e^{4} + 63 \, a^{7} b^{5} d^{4} e^{5} - 35 \, a^{8} b^{4} d^{3} e^{6} + 5 \, a^{9} b^{3} d^{2} e^{7} + 3 \, a^{10} b^{2} d e^{8} - a^{11} b e^{9}\right)} x^{3} + {\left(10 \, a^{3} b^{9} d^{9} - 60 \, a^{4} b^{8} d^{8} e + 141 \, a^{5} b^{7} d^{7} e^{2} - 147 \, a^{6} b^{6} d^{6} e^{3} + 21 \, a^{7} b^{5} d^{5} e^{4} + 105 \, a^{8} b^{4} d^{4} e^{5} - 105 \, a^{9} b^{3} d^{3} e^{6} + 39 \, a^{10} b^{2} d^{2} e^{7} - 3 \, a^{11} b d e^{8} - a^{12} e^{9}\right)} x^{2} + {\left(5 \, a^{4} b^{8} d^{9} - 33 \, a^{5} b^{7} d^{8} e + 91 \, a^{6} b^{6} d^{7} e^{2} - 133 \, a^{7} b^{5} d^{6} e^{3} + 105 \, a^{8} b^{4} d^{5} e^{4} - 35 \, a^{9} b^{3} d^{4} e^{5} - 7 \, a^{10} b^{2} d^{3} e^{6} + 9 \, a^{11} b d^{2} e^{7} - 2 \, a^{12} d e^{8}\right)} x\right)}}, \frac{45045 \, {\left(b^{6} e^{7} x^{7} + a^{5} b d^{2} e^{5} + {\left(2 \, b^{6} d e^{6} + 5 \, a b^{5} e^{7}\right)} x^{6} + {\left(b^{6} d^{2} e^{5} + 10 \, a b^{5} d e^{6} + 10 \, a^{2} b^{4} e^{7}\right)} x^{5} + 5 \, {\left(a b^{5} d^{2} e^{5} + 4 \, a^{2} b^{4} d e^{6} + 2 \, a^{3} b^{3} e^{7}\right)} x^{4} + 5 \, {\left(2 \, a^{2} b^{4} d^{2} e^{5} + 4 \, a^{3} b^{3} d e^{6} + a^{4} b^{2} e^{7}\right)} x^{3} + {\left(10 \, a^{3} b^{3} d^{2} e^{5} + 10 \, a^{4} b^{2} d e^{6} + a^{5} b e^{7}\right)} x^{2} + {\left(5 \, a^{4} b^{2} d^{2} e^{5} + 2 \, a^{5} b d e^{6}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(45045 \, b^{6} e^{6} x^{6} + 384 \, b^{6} d^{6} - 2928 \, a b^{5} d^{5} e + 10024 \, a^{2} b^{4} d^{4} e^{2} - 21070 \, a^{3} b^{3} d^{3} e^{3} + 35595 \, a^{4} b^{2} d^{2} e^{4} + 24320 \, a^{5} b d e^{5} - 1280 \, a^{6} e^{6} + 30030 \, {\left(2 \, b^{6} d e^{5} + 7 \, a b^{5} e^{6}\right)} x^{5} + 3003 \, {\left(3 \, b^{6} d^{2} e^{4} + 94 \, a b^{5} d e^{5} + 128 \, a^{2} b^{4} e^{6}\right)} x^{4} - 858 \, {\left(3 \, b^{6} d^{3} e^{3} - 51 \, a b^{5} d^{2} e^{4} - 607 \, a^{2} b^{4} d e^{5} - 395 \, a^{3} b^{3} e^{6}\right)} x^{3} + 143 \, {\left(8 \, b^{6} d^{4} e^{2} - 86 \, a b^{5} d^{3} e^{3} + 588 \, a^{2} b^{4} d^{2} e^{4} + 3250 \, a^{3} b^{3} d e^{5} + 965 \, a^{4} b^{2} e^{6}\right)} x^{2} - 26 \, {\left(24 \, b^{6} d^{5} e - 208 \, a b^{5} d^{4} e^{2} + 889 \, a^{2} b^{4} d^{3} e^{3} - 3045 \, a^{3} b^{3} d^{2} e^{4} - 7415 \, a^{4} b^{2} d e^{5} - 640 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{5} b^{7} d^{9} - 7 \, a^{6} b^{6} d^{8} e + 21 \, a^{7} b^{5} d^{7} e^{2} - 35 \, a^{8} b^{4} d^{6} e^{3} + 35 \, a^{9} b^{3} d^{5} e^{4} - 21 \, a^{10} b^{2} d^{4} e^{5} + 7 \, a^{11} b d^{3} e^{6} - a^{12} d^{2} e^{7} + {\left(b^{12} d^{7} e^{2} - 7 \, a b^{11} d^{6} e^{3} + 21 \, a^{2} b^{10} d^{5} e^{4} - 35 \, a^{3} b^{9} d^{4} e^{5} + 35 \, a^{4} b^{8} d^{3} e^{6} - 21 \, a^{5} b^{7} d^{2} e^{7} + 7 \, a^{6} b^{6} d e^{8} - a^{7} b^{5} e^{9}\right)} x^{7} + {\left(2 \, b^{12} d^{8} e - 9 \, a b^{11} d^{7} e^{2} + 7 \, a^{2} b^{10} d^{6} e^{3} + 35 \, a^{3} b^{9} d^{5} e^{4} - 105 \, a^{4} b^{8} d^{4} e^{5} + 133 \, a^{5} b^{7} d^{3} e^{6} - 91 \, a^{6} b^{6} d^{2} e^{7} + 33 \, a^{7} b^{5} d e^{8} - 5 \, a^{8} b^{4} e^{9}\right)} x^{6} + {\left(b^{12} d^{9} + 3 \, a b^{11} d^{8} e - 39 \, a^{2} b^{10} d^{7} e^{2} + 105 \, a^{3} b^{9} d^{6} e^{3} - 105 \, a^{4} b^{8} d^{5} e^{4} - 21 \, a^{5} b^{7} d^{4} e^{5} + 147 \, a^{6} b^{6} d^{3} e^{6} - 141 \, a^{7} b^{5} d^{2} e^{7} + 60 \, a^{8} b^{4} d e^{8} - 10 \, a^{9} b^{3} e^{9}\right)} x^{5} + 5 \, {\left(a b^{11} d^{9} - 3 \, a^{2} b^{10} d^{8} e - 5 \, a^{3} b^{9} d^{7} e^{2} + 35 \, a^{4} b^{8} d^{6} e^{3} - 63 \, a^{5} b^{7} d^{5} e^{4} + 49 \, a^{6} b^{6} d^{4} e^{5} - 7 \, a^{7} b^{5} d^{3} e^{6} - 15 \, a^{8} b^{4} d^{2} e^{7} + 10 \, a^{9} b^{3} d e^{8} - 2 \, a^{10} b^{2} e^{9}\right)} x^{4} + 5 \, {\left(2 \, a^{2} b^{10} d^{9} - 10 \, a^{3} b^{9} d^{8} e + 15 \, a^{4} b^{8} d^{7} e^{2} + 7 \, a^{5} b^{7} d^{6} e^{3} - 49 \, a^{6} b^{6} d^{5} e^{4} + 63 \, a^{7} b^{5} d^{4} e^{5} - 35 \, a^{8} b^{4} d^{3} e^{6} + 5 \, a^{9} b^{3} d^{2} e^{7} + 3 \, a^{10} b^{2} d e^{8} - a^{11} b e^{9}\right)} x^{3} + {\left(10 \, a^{3} b^{9} d^{9} - 60 \, a^{4} b^{8} d^{8} e + 141 \, a^{5} b^{7} d^{7} e^{2} - 147 \, a^{6} b^{6} d^{6} e^{3} + 21 \, a^{7} b^{5} d^{5} e^{4} + 105 \, a^{8} b^{4} d^{4} e^{5} - 105 \, a^{9} b^{3} d^{3} e^{6} + 39 \, a^{10} b^{2} d^{2} e^{7} - 3 \, a^{11} b d e^{8} - a^{12} e^{9}\right)} x^{2} + {\left(5 \, a^{4} b^{8} d^{9} - 33 \, a^{5} b^{7} d^{8} e + 91 \, a^{6} b^{6} d^{7} e^{2} - 133 \, a^{7} b^{5} d^{6} e^{3} + 105 \, a^{8} b^{4} d^{5} e^{4} - 35 \, a^{9} b^{3} d^{4} e^{5} - 7 \, a^{10} b^{2} d^{3} e^{6} + 9 \, a^{11} b d^{2} e^{7} - 2 \, a^{12} d e^{8}\right)} x\right)}}\right]"," ",0,"[-1/3840*(45045*(b^6*e^7*x^7 + a^5*b*d^2*e^5 + (2*b^6*d*e^6 + 5*a*b^5*e^7)*x^6 + (b^6*d^2*e^5 + 10*a*b^5*d*e^6 + 10*a^2*b^4*e^7)*x^5 + 5*(a*b^5*d^2*e^5 + 4*a^2*b^4*d*e^6 + 2*a^3*b^3*e^7)*x^4 + 5*(2*a^2*b^4*d^2*e^5 + 4*a^3*b^3*d*e^6 + a^4*b^2*e^7)*x^3 + (10*a^3*b^3*d^2*e^5 + 10*a^4*b^2*d*e^6 + a^5*b*e^7)*x^2 + (5*a^4*b^2*d^2*e^5 + 2*a^5*b*d*e^6)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(45045*b^6*e^6*x^6 + 384*b^6*d^6 - 2928*a*b^5*d^5*e + 10024*a^2*b^4*d^4*e^2 - 21070*a^3*b^3*d^3*e^3 + 35595*a^4*b^2*d^2*e^4 + 24320*a^5*b*d*e^5 - 1280*a^6*e^6 + 30030*(2*b^6*d*e^5 + 7*a*b^5*e^6)*x^5 + 3003*(3*b^6*d^2*e^4 + 94*a*b^5*d*e^5 + 128*a^2*b^4*e^6)*x^4 - 858*(3*b^6*d^3*e^3 - 51*a*b^5*d^2*e^4 - 607*a^2*b^4*d*e^5 - 395*a^3*b^3*e^6)*x^3 + 143*(8*b^6*d^4*e^2 - 86*a*b^5*d^3*e^3 + 588*a^2*b^4*d^2*e^4 + 3250*a^3*b^3*d*e^5 + 965*a^4*b^2*e^6)*x^2 - 26*(24*b^6*d^5*e - 208*a*b^5*d^4*e^2 + 889*a^2*b^4*d^3*e^3 - 3045*a^3*b^3*d^2*e^4 - 7415*a^4*b^2*d*e^5 - 640*a^5*b*e^6)*x)*sqrt(e*x + d))/(a^5*b^7*d^9 - 7*a^6*b^6*d^8*e + 21*a^7*b^5*d^7*e^2 - 35*a^8*b^4*d^6*e^3 + 35*a^9*b^3*d^5*e^4 - 21*a^10*b^2*d^4*e^5 + 7*a^11*b*d^3*e^6 - a^12*d^2*e^7 + (b^12*d^7*e^2 - 7*a*b^11*d^6*e^3 + 21*a^2*b^10*d^5*e^4 - 35*a^3*b^9*d^4*e^5 + 35*a^4*b^8*d^3*e^6 - 21*a^5*b^7*d^2*e^7 + 7*a^6*b^6*d*e^8 - a^7*b^5*e^9)*x^7 + (2*b^12*d^8*e - 9*a*b^11*d^7*e^2 + 7*a^2*b^10*d^6*e^3 + 35*a^3*b^9*d^5*e^4 - 105*a^4*b^8*d^4*e^5 + 133*a^5*b^7*d^3*e^6 - 91*a^6*b^6*d^2*e^7 + 33*a^7*b^5*d*e^8 - 5*a^8*b^4*e^9)*x^6 + (b^12*d^9 + 3*a*b^11*d^8*e - 39*a^2*b^10*d^7*e^2 + 105*a^3*b^9*d^6*e^3 - 105*a^4*b^8*d^5*e^4 - 21*a^5*b^7*d^4*e^5 + 147*a^6*b^6*d^3*e^6 - 141*a^7*b^5*d^2*e^7 + 60*a^8*b^4*d*e^8 - 10*a^9*b^3*e^9)*x^5 + 5*(a*b^11*d^9 - 3*a^2*b^10*d^8*e - 5*a^3*b^9*d^7*e^2 + 35*a^4*b^8*d^6*e^3 - 63*a^5*b^7*d^5*e^4 + 49*a^6*b^6*d^4*e^5 - 7*a^7*b^5*d^3*e^6 - 15*a^8*b^4*d^2*e^7 + 10*a^9*b^3*d*e^8 - 2*a^10*b^2*e^9)*x^4 + 5*(2*a^2*b^10*d^9 - 10*a^3*b^9*d^8*e + 15*a^4*b^8*d^7*e^2 + 7*a^5*b^7*d^6*e^3 - 49*a^6*b^6*d^5*e^4 + 63*a^7*b^5*d^4*e^5 - 35*a^8*b^4*d^3*e^6 + 5*a^9*b^3*d^2*e^7 + 3*a^10*b^2*d*e^8 - a^11*b*e^9)*x^3 + (10*a^3*b^9*d^9 - 60*a^4*b^8*d^8*e + 141*a^5*b^7*d^7*e^2 - 147*a^6*b^6*d^6*e^3 + 21*a^7*b^5*d^5*e^4 + 105*a^8*b^4*d^4*e^5 - 105*a^9*b^3*d^3*e^6 + 39*a^10*b^2*d^2*e^7 - 3*a^11*b*d*e^8 - a^12*e^9)*x^2 + (5*a^4*b^8*d^9 - 33*a^5*b^7*d^8*e + 91*a^6*b^6*d^7*e^2 - 133*a^7*b^5*d^6*e^3 + 105*a^8*b^4*d^5*e^4 - 35*a^9*b^3*d^4*e^5 - 7*a^10*b^2*d^3*e^6 + 9*a^11*b*d^2*e^7 - 2*a^12*d*e^8)*x), 1/1920*(45045*(b^6*e^7*x^7 + a^5*b*d^2*e^5 + (2*b^6*d*e^6 + 5*a*b^5*e^7)*x^6 + (b^6*d^2*e^5 + 10*a*b^5*d*e^6 + 10*a^2*b^4*e^7)*x^5 + 5*(a*b^5*d^2*e^5 + 4*a^2*b^4*d*e^6 + 2*a^3*b^3*e^7)*x^4 + 5*(2*a^2*b^4*d^2*e^5 + 4*a^3*b^3*d*e^6 + a^4*b^2*e^7)*x^3 + (10*a^3*b^3*d^2*e^5 + 10*a^4*b^2*d*e^6 + a^5*b*e^7)*x^2 + (5*a^4*b^2*d^2*e^5 + 2*a^5*b*d*e^6)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (45045*b^6*e^6*x^6 + 384*b^6*d^6 - 2928*a*b^5*d^5*e + 10024*a^2*b^4*d^4*e^2 - 21070*a^3*b^3*d^3*e^3 + 35595*a^4*b^2*d^2*e^4 + 24320*a^5*b*d*e^5 - 1280*a^6*e^6 + 30030*(2*b^6*d*e^5 + 7*a*b^5*e^6)*x^5 + 3003*(3*b^6*d^2*e^4 + 94*a*b^5*d*e^5 + 128*a^2*b^4*e^6)*x^4 - 858*(3*b^6*d^3*e^3 - 51*a*b^5*d^2*e^4 - 607*a^2*b^4*d*e^5 - 395*a^3*b^3*e^6)*x^3 + 143*(8*b^6*d^4*e^2 - 86*a*b^5*d^3*e^3 + 588*a^2*b^4*d^2*e^4 + 3250*a^3*b^3*d*e^5 + 965*a^4*b^2*e^6)*x^2 - 26*(24*b^6*d^5*e - 208*a*b^5*d^4*e^2 + 889*a^2*b^4*d^3*e^3 - 3045*a^3*b^3*d^2*e^4 - 7415*a^4*b^2*d*e^5 - 640*a^5*b*e^6)*x)*sqrt(e*x + d))/(a^5*b^7*d^9 - 7*a^6*b^6*d^8*e + 21*a^7*b^5*d^7*e^2 - 35*a^8*b^4*d^6*e^3 + 35*a^9*b^3*d^5*e^4 - 21*a^10*b^2*d^4*e^5 + 7*a^11*b*d^3*e^6 - a^12*d^2*e^7 + (b^12*d^7*e^2 - 7*a*b^11*d^6*e^3 + 21*a^2*b^10*d^5*e^4 - 35*a^3*b^9*d^4*e^5 + 35*a^4*b^8*d^3*e^6 - 21*a^5*b^7*d^2*e^7 + 7*a^6*b^6*d*e^8 - a^7*b^5*e^9)*x^7 + (2*b^12*d^8*e - 9*a*b^11*d^7*e^2 + 7*a^2*b^10*d^6*e^3 + 35*a^3*b^9*d^5*e^4 - 105*a^4*b^8*d^4*e^5 + 133*a^5*b^7*d^3*e^6 - 91*a^6*b^6*d^2*e^7 + 33*a^7*b^5*d*e^8 - 5*a^8*b^4*e^9)*x^6 + (b^12*d^9 + 3*a*b^11*d^8*e - 39*a^2*b^10*d^7*e^2 + 105*a^3*b^9*d^6*e^3 - 105*a^4*b^8*d^5*e^4 - 21*a^5*b^7*d^4*e^5 + 147*a^6*b^6*d^3*e^6 - 141*a^7*b^5*d^2*e^7 + 60*a^8*b^4*d*e^8 - 10*a^9*b^3*e^9)*x^5 + 5*(a*b^11*d^9 - 3*a^2*b^10*d^8*e - 5*a^3*b^9*d^7*e^2 + 35*a^4*b^8*d^6*e^3 - 63*a^5*b^7*d^5*e^4 + 49*a^6*b^6*d^4*e^5 - 7*a^7*b^5*d^3*e^6 - 15*a^8*b^4*d^2*e^7 + 10*a^9*b^3*d*e^8 - 2*a^10*b^2*e^9)*x^4 + 5*(2*a^2*b^10*d^9 - 10*a^3*b^9*d^8*e + 15*a^4*b^8*d^7*e^2 + 7*a^5*b^7*d^6*e^3 - 49*a^6*b^6*d^5*e^4 + 63*a^7*b^5*d^4*e^5 - 35*a^8*b^4*d^3*e^6 + 5*a^9*b^3*d^2*e^7 + 3*a^10*b^2*d*e^8 - a^11*b*e^9)*x^3 + (10*a^3*b^9*d^9 - 60*a^4*b^8*d^8*e + 141*a^5*b^7*d^7*e^2 - 147*a^6*b^6*d^6*e^3 + 21*a^7*b^5*d^5*e^4 + 105*a^8*b^4*d^4*e^5 - 105*a^9*b^3*d^3*e^6 + 39*a^10*b^2*d^2*e^7 - 3*a^11*b*d*e^8 - a^12*e^9)*x^2 + (5*a^4*b^8*d^9 - 33*a^5*b^7*d^8*e + 91*a^6*b^6*d^7*e^2 - 133*a^7*b^5*d^6*e^3 + 105*a^8*b^4*d^5*e^4 - 35*a^9*b^3*d^4*e^5 - 7*a^10*b^2*d^3*e^6 + 9*a^11*b*d^2*e^7 - 2*a^12*d*e^8)*x)]","B",0
1675,1,4232,0,0.544487," ","integrate(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\left[\frac{45045 \, {\left(b^{7} e^{8} x^{8} + a^{5} b^{2} d^{3} e^{5} + {\left(3 \, b^{7} d e^{7} + 5 \, a b^{6} e^{8}\right)} x^{7} + {\left(3 \, b^{7} d^{2} e^{6} + 15 \, a b^{6} d e^{7} + 10 \, a^{2} b^{5} e^{8}\right)} x^{6} + {\left(b^{7} d^{3} e^{5} + 15 \, a b^{6} d^{2} e^{6} + 30 \, a^{2} b^{5} d e^{7} + 10 \, a^{3} b^{4} e^{8}\right)} x^{5} + 5 \, {\left(a b^{6} d^{3} e^{5} + 6 \, a^{2} b^{5} d^{2} e^{6} + 6 \, a^{3} b^{4} d e^{7} + a^{4} b^{3} e^{8}\right)} x^{4} + {\left(10 \, a^{2} b^{5} d^{3} e^{5} + 30 \, a^{3} b^{4} d^{2} e^{6} + 15 \, a^{4} b^{3} d e^{7} + a^{5} b^{2} e^{8}\right)} x^{3} + {\left(10 \, a^{3} b^{4} d^{3} e^{5} + 15 \, a^{4} b^{3} d^{2} e^{6} + 3 \, a^{5} b^{2} d e^{7}\right)} x^{2} + {\left(5 \, a^{4} b^{3} d^{3} e^{5} + 3 \, a^{5} b^{2} d^{2} e^{6}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(45045 \, b^{7} e^{7} x^{7} + 128 \, b^{7} d^{7} - 1136 \, a b^{6} d^{6} e + 4648 \, a^{2} b^{5} d^{5} e^{2} - 12110 \, a^{3} b^{4} d^{4} e^{3} + 26635 \, a^{4} b^{3} d^{3} e^{4} + 29696 \, a^{5} b^{2} d^{2} e^{5} - 3072 \, a^{6} b d e^{6} + 256 \, a^{7} e^{7} + 105105 \, {\left(b^{7} d e^{6} + 2 \, a b^{6} e^{7}\right)} x^{6} + 3003 \, {\left(23 \, b^{7} d^{2} e^{5} + 164 \, a b^{6} d e^{6} + 128 \, a^{2} b^{5} e^{7}\right)} x^{5} + 2145 \, {\left(3 \, b^{7} d^{3} e^{4} + 152 \, a b^{6} d^{2} e^{5} + 422 \, a^{2} b^{5} d e^{6} + 158 \, a^{3} b^{4} e^{7}\right)} x^{4} - 715 \, {\left(2 \, b^{7} d^{4} e^{3} - 44 \, a b^{6} d^{3} e^{4} - 846 \, a^{2} b^{5} d^{2} e^{5} - 1124 \, a^{3} b^{4} d e^{6} - 193 \, a^{4} b^{3} e^{7}\right)} x^{3} + 65 \, {\left(8 \, b^{7} d^{5} e^{2} - 106 \, a b^{6} d^{4} e^{3} + 938 \, a^{2} b^{5} d^{3} e^{4} + 8368 \, a^{3} b^{4} d^{2} e^{5} + 5089 \, a^{4} b^{3} d e^{6} + 256 \, a^{5} b^{2} e^{7}\right)} x^{2} - 5 \, {\left(48 \, b^{7} d^{6} e - 496 \, a b^{6} d^{5} e^{2} + 2618 \, a^{2} b^{5} d^{4} e^{3} - 11620 \, a^{3} b^{4} d^{3} e^{4} - 45677 \, a^{4} b^{3} d^{2} e^{5} - 8192 \, a^{5} b^{2} d e^{6} + 256 \, a^{6} b e^{7}\right)} x\right)} \sqrt{e x + d}}{1280 \, {\left(a^{5} b^{8} d^{11} - 8 \, a^{6} b^{7} d^{10} e + 28 \, a^{7} b^{6} d^{9} e^{2} - 56 \, a^{8} b^{5} d^{8} e^{3} + 70 \, a^{9} b^{4} d^{7} e^{4} - 56 \, a^{10} b^{3} d^{6} e^{5} + 28 \, a^{11} b^{2} d^{5} e^{6} - 8 \, a^{12} b d^{4} e^{7} + a^{13} d^{3} e^{8} + {\left(b^{13} d^{8} e^{3} - 8 \, a b^{12} d^{7} e^{4} + 28 \, a^{2} b^{11} d^{6} e^{5} - 56 \, a^{3} b^{10} d^{5} e^{6} + 70 \, a^{4} b^{9} d^{4} e^{7} - 56 \, a^{5} b^{8} d^{3} e^{8} + 28 \, a^{6} b^{7} d^{2} e^{9} - 8 \, a^{7} b^{6} d e^{10} + a^{8} b^{5} e^{11}\right)} x^{8} + {\left(3 \, b^{13} d^{9} e^{2} - 19 \, a b^{12} d^{8} e^{3} + 44 \, a^{2} b^{11} d^{7} e^{4} - 28 \, a^{3} b^{10} d^{6} e^{5} - 70 \, a^{4} b^{9} d^{5} e^{6} + 182 \, a^{5} b^{8} d^{4} e^{7} - 196 \, a^{6} b^{7} d^{3} e^{8} + 116 \, a^{7} b^{6} d^{2} e^{9} - 37 \, a^{8} b^{5} d e^{10} + 5 \, a^{9} b^{4} e^{11}\right)} x^{7} + {\left(3 \, b^{13} d^{10} e - 9 \, a b^{12} d^{9} e^{2} - 26 \, a^{2} b^{11} d^{8} e^{3} + 172 \, a^{3} b^{10} d^{7} e^{4} - 350 \, a^{4} b^{9} d^{6} e^{5} + 322 \, a^{5} b^{8} d^{5} e^{6} - 56 \, a^{6} b^{7} d^{4} e^{7} - 164 \, a^{7} b^{6} d^{3} e^{8} + 163 \, a^{8} b^{5} d^{2} e^{9} - 65 \, a^{9} b^{4} d e^{10} + 10 \, a^{10} b^{3} e^{11}\right)} x^{6} + {\left(b^{13} d^{11} + 7 \, a b^{12} d^{10} e - 62 \, a^{2} b^{11} d^{9} e^{2} + 134 \, a^{3} b^{10} d^{8} e^{3} - 10 \, a^{4} b^{9} d^{7} e^{4} - 406 \, a^{5} b^{8} d^{6} e^{5} + 728 \, a^{6} b^{7} d^{5} e^{6} - 568 \, a^{7} b^{6} d^{4} e^{7} + 161 \, a^{8} b^{5} d^{3} e^{8} + 55 \, a^{9} b^{4} d^{2} e^{9} - 50 \, a^{10} b^{3} d e^{10} + 10 \, a^{11} b^{2} e^{11}\right)} x^{5} + 5 \, {\left(a b^{12} d^{11} - 2 \, a^{2} b^{11} d^{10} e - 14 \, a^{3} b^{10} d^{9} e^{2} + 65 \, a^{4} b^{9} d^{8} e^{3} - 106 \, a^{5} b^{8} d^{7} e^{4} + 56 \, a^{6} b^{7} d^{6} e^{5} + 56 \, a^{7} b^{6} d^{5} e^{6} - 106 \, a^{8} b^{5} d^{4} e^{7} + 65 \, a^{9} b^{4} d^{3} e^{8} - 14 \, a^{10} b^{3} d^{2} e^{9} - 2 \, a^{11} b^{2} d e^{10} + a^{12} b e^{11}\right)} x^{4} + {\left(10 \, a^{2} b^{11} d^{11} - 50 \, a^{3} b^{10} d^{10} e + 55 \, a^{4} b^{9} d^{9} e^{2} + 161 \, a^{5} b^{8} d^{8} e^{3} - 568 \, a^{6} b^{7} d^{7} e^{4} + 728 \, a^{7} b^{6} d^{6} e^{5} - 406 \, a^{8} b^{5} d^{5} e^{6} - 10 \, a^{9} b^{4} d^{4} e^{7} + 134 \, a^{10} b^{3} d^{3} e^{8} - 62 \, a^{11} b^{2} d^{2} e^{9} + 7 \, a^{12} b d e^{10} + a^{13} e^{11}\right)} x^{3} + {\left(10 \, a^{3} b^{10} d^{11} - 65 \, a^{4} b^{9} d^{10} e + 163 \, a^{5} b^{8} d^{9} e^{2} - 164 \, a^{6} b^{7} d^{8} e^{3} - 56 \, a^{7} b^{6} d^{7} e^{4} + 322 \, a^{8} b^{5} d^{6} e^{5} - 350 \, a^{9} b^{4} d^{5} e^{6} + 172 \, a^{10} b^{3} d^{4} e^{7} - 26 \, a^{11} b^{2} d^{3} e^{8} - 9 \, a^{12} b d^{2} e^{9} + 3 \, a^{13} d e^{10}\right)} x^{2} + {\left(5 \, a^{4} b^{9} d^{11} - 37 \, a^{5} b^{8} d^{10} e + 116 \, a^{6} b^{7} d^{9} e^{2} - 196 \, a^{7} b^{6} d^{8} e^{3} + 182 \, a^{8} b^{5} d^{7} e^{4} - 70 \, a^{9} b^{4} d^{6} e^{5} - 28 \, a^{10} b^{3} d^{5} e^{6} + 44 \, a^{11} b^{2} d^{4} e^{7} - 19 \, a^{12} b d^{3} e^{8} + 3 \, a^{13} d^{2} e^{9}\right)} x\right)}}, \frac{45045 \, {\left(b^{7} e^{8} x^{8} + a^{5} b^{2} d^{3} e^{5} + {\left(3 \, b^{7} d e^{7} + 5 \, a b^{6} e^{8}\right)} x^{7} + {\left(3 \, b^{7} d^{2} e^{6} + 15 \, a b^{6} d e^{7} + 10 \, a^{2} b^{5} e^{8}\right)} x^{6} + {\left(b^{7} d^{3} e^{5} + 15 \, a b^{6} d^{2} e^{6} + 30 \, a^{2} b^{5} d e^{7} + 10 \, a^{3} b^{4} e^{8}\right)} x^{5} + 5 \, {\left(a b^{6} d^{3} e^{5} + 6 \, a^{2} b^{5} d^{2} e^{6} + 6 \, a^{3} b^{4} d e^{7} + a^{4} b^{3} e^{8}\right)} x^{4} + {\left(10 \, a^{2} b^{5} d^{3} e^{5} + 30 \, a^{3} b^{4} d^{2} e^{6} + 15 \, a^{4} b^{3} d e^{7} + a^{5} b^{2} e^{8}\right)} x^{3} + {\left(10 \, a^{3} b^{4} d^{3} e^{5} + 15 \, a^{4} b^{3} d^{2} e^{6} + 3 \, a^{5} b^{2} d e^{7}\right)} x^{2} + {\left(5 \, a^{4} b^{3} d^{3} e^{5} + 3 \, a^{5} b^{2} d^{2} e^{6}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(45045 \, b^{7} e^{7} x^{7} + 128 \, b^{7} d^{7} - 1136 \, a b^{6} d^{6} e + 4648 \, a^{2} b^{5} d^{5} e^{2} - 12110 \, a^{3} b^{4} d^{4} e^{3} + 26635 \, a^{4} b^{3} d^{3} e^{4} + 29696 \, a^{5} b^{2} d^{2} e^{5} - 3072 \, a^{6} b d e^{6} + 256 \, a^{7} e^{7} + 105105 \, {\left(b^{7} d e^{6} + 2 \, a b^{6} e^{7}\right)} x^{6} + 3003 \, {\left(23 \, b^{7} d^{2} e^{5} + 164 \, a b^{6} d e^{6} + 128 \, a^{2} b^{5} e^{7}\right)} x^{5} + 2145 \, {\left(3 \, b^{7} d^{3} e^{4} + 152 \, a b^{6} d^{2} e^{5} + 422 \, a^{2} b^{5} d e^{6} + 158 \, a^{3} b^{4} e^{7}\right)} x^{4} - 715 \, {\left(2 \, b^{7} d^{4} e^{3} - 44 \, a b^{6} d^{3} e^{4} - 846 \, a^{2} b^{5} d^{2} e^{5} - 1124 \, a^{3} b^{4} d e^{6} - 193 \, a^{4} b^{3} e^{7}\right)} x^{3} + 65 \, {\left(8 \, b^{7} d^{5} e^{2} - 106 \, a b^{6} d^{4} e^{3} + 938 \, a^{2} b^{5} d^{3} e^{4} + 8368 \, a^{3} b^{4} d^{2} e^{5} + 5089 \, a^{4} b^{3} d e^{6} + 256 \, a^{5} b^{2} e^{7}\right)} x^{2} - 5 \, {\left(48 \, b^{7} d^{6} e - 496 \, a b^{6} d^{5} e^{2} + 2618 \, a^{2} b^{5} d^{4} e^{3} - 11620 \, a^{3} b^{4} d^{3} e^{4} - 45677 \, a^{4} b^{3} d^{2} e^{5} - 8192 \, a^{5} b^{2} d e^{6} + 256 \, a^{6} b e^{7}\right)} x\right)} \sqrt{e x + d}}{640 \, {\left(a^{5} b^{8} d^{11} - 8 \, a^{6} b^{7} d^{10} e + 28 \, a^{7} b^{6} d^{9} e^{2} - 56 \, a^{8} b^{5} d^{8} e^{3} + 70 \, a^{9} b^{4} d^{7} e^{4} - 56 \, a^{10} b^{3} d^{6} e^{5} + 28 \, a^{11} b^{2} d^{5} e^{6} - 8 \, a^{12} b d^{4} e^{7} + a^{13} d^{3} e^{8} + {\left(b^{13} d^{8} e^{3} - 8 \, a b^{12} d^{7} e^{4} + 28 \, a^{2} b^{11} d^{6} e^{5} - 56 \, a^{3} b^{10} d^{5} e^{6} + 70 \, a^{4} b^{9} d^{4} e^{7} - 56 \, a^{5} b^{8} d^{3} e^{8} + 28 \, a^{6} b^{7} d^{2} e^{9} - 8 \, a^{7} b^{6} d e^{10} + a^{8} b^{5} e^{11}\right)} x^{8} + {\left(3 \, b^{13} d^{9} e^{2} - 19 \, a b^{12} d^{8} e^{3} + 44 \, a^{2} b^{11} d^{7} e^{4} - 28 \, a^{3} b^{10} d^{6} e^{5} - 70 \, a^{4} b^{9} d^{5} e^{6} + 182 \, a^{5} b^{8} d^{4} e^{7} - 196 \, a^{6} b^{7} d^{3} e^{8} + 116 \, a^{7} b^{6} d^{2} e^{9} - 37 \, a^{8} b^{5} d e^{10} + 5 \, a^{9} b^{4} e^{11}\right)} x^{7} + {\left(3 \, b^{13} d^{10} e - 9 \, a b^{12} d^{9} e^{2} - 26 \, a^{2} b^{11} d^{8} e^{3} + 172 \, a^{3} b^{10} d^{7} e^{4} - 350 \, a^{4} b^{9} d^{6} e^{5} + 322 \, a^{5} b^{8} d^{5} e^{6} - 56 \, a^{6} b^{7} d^{4} e^{7} - 164 \, a^{7} b^{6} d^{3} e^{8} + 163 \, a^{8} b^{5} d^{2} e^{9} - 65 \, a^{9} b^{4} d e^{10} + 10 \, a^{10} b^{3} e^{11}\right)} x^{6} + {\left(b^{13} d^{11} + 7 \, a b^{12} d^{10} e - 62 \, a^{2} b^{11} d^{9} e^{2} + 134 \, a^{3} b^{10} d^{8} e^{3} - 10 \, a^{4} b^{9} d^{7} e^{4} - 406 \, a^{5} b^{8} d^{6} e^{5} + 728 \, a^{6} b^{7} d^{5} e^{6} - 568 \, a^{7} b^{6} d^{4} e^{7} + 161 \, a^{8} b^{5} d^{3} e^{8} + 55 \, a^{9} b^{4} d^{2} e^{9} - 50 \, a^{10} b^{3} d e^{10} + 10 \, a^{11} b^{2} e^{11}\right)} x^{5} + 5 \, {\left(a b^{12} d^{11} - 2 \, a^{2} b^{11} d^{10} e - 14 \, a^{3} b^{10} d^{9} e^{2} + 65 \, a^{4} b^{9} d^{8} e^{3} - 106 \, a^{5} b^{8} d^{7} e^{4} + 56 \, a^{6} b^{7} d^{6} e^{5} + 56 \, a^{7} b^{6} d^{5} e^{6} - 106 \, a^{8} b^{5} d^{4} e^{7} + 65 \, a^{9} b^{4} d^{3} e^{8} - 14 \, a^{10} b^{3} d^{2} e^{9} - 2 \, a^{11} b^{2} d e^{10} + a^{12} b e^{11}\right)} x^{4} + {\left(10 \, a^{2} b^{11} d^{11} - 50 \, a^{3} b^{10} d^{10} e + 55 \, a^{4} b^{9} d^{9} e^{2} + 161 \, a^{5} b^{8} d^{8} e^{3} - 568 \, a^{6} b^{7} d^{7} e^{4} + 728 \, a^{7} b^{6} d^{6} e^{5} - 406 \, a^{8} b^{5} d^{5} e^{6} - 10 \, a^{9} b^{4} d^{4} e^{7} + 134 \, a^{10} b^{3} d^{3} e^{8} - 62 \, a^{11} b^{2} d^{2} e^{9} + 7 \, a^{12} b d e^{10} + a^{13} e^{11}\right)} x^{3} + {\left(10 \, a^{3} b^{10} d^{11} - 65 \, a^{4} b^{9} d^{10} e + 163 \, a^{5} b^{8} d^{9} e^{2} - 164 \, a^{6} b^{7} d^{8} e^{3} - 56 \, a^{7} b^{6} d^{7} e^{4} + 322 \, a^{8} b^{5} d^{6} e^{5} - 350 \, a^{9} b^{4} d^{5} e^{6} + 172 \, a^{10} b^{3} d^{4} e^{7} - 26 \, a^{11} b^{2} d^{3} e^{8} - 9 \, a^{12} b d^{2} e^{9} + 3 \, a^{13} d e^{10}\right)} x^{2} + {\left(5 \, a^{4} b^{9} d^{11} - 37 \, a^{5} b^{8} d^{10} e + 116 \, a^{6} b^{7} d^{9} e^{2} - 196 \, a^{7} b^{6} d^{8} e^{3} + 182 \, a^{8} b^{5} d^{7} e^{4} - 70 \, a^{9} b^{4} d^{6} e^{5} - 28 \, a^{10} b^{3} d^{5} e^{6} + 44 \, a^{11} b^{2} d^{4} e^{7} - 19 \, a^{12} b d^{3} e^{8} + 3 \, a^{13} d^{2} e^{9}\right)} x\right)}}\right]"," ",0,"[1/1280*(45045*(b^7*e^8*x^8 + a^5*b^2*d^3*e^5 + (3*b^7*d*e^7 + 5*a*b^6*e^8)*x^7 + (3*b^7*d^2*e^6 + 15*a*b^6*d*e^7 + 10*a^2*b^5*e^8)*x^6 + (b^7*d^3*e^5 + 15*a*b^6*d^2*e^6 + 30*a^2*b^5*d*e^7 + 10*a^3*b^4*e^8)*x^5 + 5*(a*b^6*d^3*e^5 + 6*a^2*b^5*d^2*e^6 + 6*a^3*b^4*d*e^7 + a^4*b^3*e^8)*x^4 + (10*a^2*b^5*d^3*e^5 + 30*a^3*b^4*d^2*e^6 + 15*a^4*b^3*d*e^7 + a^5*b^2*e^8)*x^3 + (10*a^3*b^4*d^3*e^5 + 15*a^4*b^3*d^2*e^6 + 3*a^5*b^2*d*e^7)*x^2 + (5*a^4*b^3*d^3*e^5 + 3*a^5*b^2*d^2*e^6)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(45045*b^7*e^7*x^7 + 128*b^7*d^7 - 1136*a*b^6*d^6*e + 4648*a^2*b^5*d^5*e^2 - 12110*a^3*b^4*d^4*e^3 + 26635*a^4*b^3*d^3*e^4 + 29696*a^5*b^2*d^2*e^5 - 3072*a^6*b*d*e^6 + 256*a^7*e^7 + 105105*(b^7*d*e^6 + 2*a*b^6*e^7)*x^6 + 3003*(23*b^7*d^2*e^5 + 164*a*b^6*d*e^6 + 128*a^2*b^5*e^7)*x^5 + 2145*(3*b^7*d^3*e^4 + 152*a*b^6*d^2*e^5 + 422*a^2*b^5*d*e^6 + 158*a^3*b^4*e^7)*x^4 - 715*(2*b^7*d^4*e^3 - 44*a*b^6*d^3*e^4 - 846*a^2*b^5*d^2*e^5 - 1124*a^3*b^4*d*e^6 - 193*a^4*b^3*e^7)*x^3 + 65*(8*b^7*d^5*e^2 - 106*a*b^6*d^4*e^3 + 938*a^2*b^5*d^3*e^4 + 8368*a^3*b^4*d^2*e^5 + 5089*a^4*b^3*d*e^6 + 256*a^5*b^2*e^7)*x^2 - 5*(48*b^7*d^6*e - 496*a*b^6*d^5*e^2 + 2618*a^2*b^5*d^4*e^3 - 11620*a^3*b^4*d^3*e^4 - 45677*a^4*b^3*d^2*e^5 - 8192*a^5*b^2*d*e^6 + 256*a^6*b*e^7)*x)*sqrt(e*x + d))/(a^5*b^8*d^11 - 8*a^6*b^7*d^10*e + 28*a^7*b^6*d^9*e^2 - 56*a^8*b^5*d^8*e^3 + 70*a^9*b^4*d^7*e^4 - 56*a^10*b^3*d^6*e^5 + 28*a^11*b^2*d^5*e^6 - 8*a^12*b*d^4*e^7 + a^13*d^3*e^8 + (b^13*d^8*e^3 - 8*a*b^12*d^7*e^4 + 28*a^2*b^11*d^6*e^5 - 56*a^3*b^10*d^5*e^6 + 70*a^4*b^9*d^4*e^7 - 56*a^5*b^8*d^3*e^8 + 28*a^6*b^7*d^2*e^9 - 8*a^7*b^6*d*e^10 + a^8*b^5*e^11)*x^8 + (3*b^13*d^9*e^2 - 19*a*b^12*d^8*e^3 + 44*a^2*b^11*d^7*e^4 - 28*a^3*b^10*d^6*e^5 - 70*a^4*b^9*d^5*e^6 + 182*a^5*b^8*d^4*e^7 - 196*a^6*b^7*d^3*e^8 + 116*a^7*b^6*d^2*e^9 - 37*a^8*b^5*d*e^10 + 5*a^9*b^4*e^11)*x^7 + (3*b^13*d^10*e - 9*a*b^12*d^9*e^2 - 26*a^2*b^11*d^8*e^3 + 172*a^3*b^10*d^7*e^4 - 350*a^4*b^9*d^6*e^5 + 322*a^5*b^8*d^5*e^6 - 56*a^6*b^7*d^4*e^7 - 164*a^7*b^6*d^3*e^8 + 163*a^8*b^5*d^2*e^9 - 65*a^9*b^4*d*e^10 + 10*a^10*b^3*e^11)*x^6 + (b^13*d^11 + 7*a*b^12*d^10*e - 62*a^2*b^11*d^9*e^2 + 134*a^3*b^10*d^8*e^3 - 10*a^4*b^9*d^7*e^4 - 406*a^5*b^8*d^6*e^5 + 728*a^6*b^7*d^5*e^6 - 568*a^7*b^6*d^4*e^7 + 161*a^8*b^5*d^3*e^8 + 55*a^9*b^4*d^2*e^9 - 50*a^10*b^3*d*e^10 + 10*a^11*b^2*e^11)*x^5 + 5*(a*b^12*d^11 - 2*a^2*b^11*d^10*e - 14*a^3*b^10*d^9*e^2 + 65*a^4*b^9*d^8*e^3 - 106*a^5*b^8*d^7*e^4 + 56*a^6*b^7*d^6*e^5 + 56*a^7*b^6*d^5*e^6 - 106*a^8*b^5*d^4*e^7 + 65*a^9*b^4*d^3*e^8 - 14*a^10*b^3*d^2*e^9 - 2*a^11*b^2*d*e^10 + a^12*b*e^11)*x^4 + (10*a^2*b^11*d^11 - 50*a^3*b^10*d^10*e + 55*a^4*b^9*d^9*e^2 + 161*a^5*b^8*d^8*e^3 - 568*a^6*b^7*d^7*e^4 + 728*a^7*b^6*d^6*e^5 - 406*a^8*b^5*d^5*e^6 - 10*a^9*b^4*d^4*e^7 + 134*a^10*b^3*d^3*e^8 - 62*a^11*b^2*d^2*e^9 + 7*a^12*b*d*e^10 + a^13*e^11)*x^3 + (10*a^3*b^10*d^11 - 65*a^4*b^9*d^10*e + 163*a^5*b^8*d^9*e^2 - 164*a^6*b^7*d^8*e^3 - 56*a^7*b^6*d^7*e^4 + 322*a^8*b^5*d^6*e^5 - 350*a^9*b^4*d^5*e^6 + 172*a^10*b^3*d^4*e^7 - 26*a^11*b^2*d^3*e^8 - 9*a^12*b*d^2*e^9 + 3*a^13*d*e^10)*x^2 + (5*a^4*b^9*d^11 - 37*a^5*b^8*d^10*e + 116*a^6*b^7*d^9*e^2 - 196*a^7*b^6*d^8*e^3 + 182*a^8*b^5*d^7*e^4 - 70*a^9*b^4*d^6*e^5 - 28*a^10*b^3*d^5*e^6 + 44*a^11*b^2*d^4*e^7 - 19*a^12*b*d^3*e^8 + 3*a^13*d^2*e^9)*x), 1/640*(45045*(b^7*e^8*x^8 + a^5*b^2*d^3*e^5 + (3*b^7*d*e^7 + 5*a*b^6*e^8)*x^7 + (3*b^7*d^2*e^6 + 15*a*b^6*d*e^7 + 10*a^2*b^5*e^8)*x^6 + (b^7*d^3*e^5 + 15*a*b^6*d^2*e^6 + 30*a^2*b^5*d*e^7 + 10*a^3*b^4*e^8)*x^5 + 5*(a*b^6*d^3*e^5 + 6*a^2*b^5*d^2*e^6 + 6*a^3*b^4*d*e^7 + a^4*b^3*e^8)*x^4 + (10*a^2*b^5*d^3*e^5 + 30*a^3*b^4*d^2*e^6 + 15*a^4*b^3*d*e^7 + a^5*b^2*e^8)*x^3 + (10*a^3*b^4*d^3*e^5 + 15*a^4*b^3*d^2*e^6 + 3*a^5*b^2*d*e^7)*x^2 + (5*a^4*b^3*d^3*e^5 + 3*a^5*b^2*d^2*e^6)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (45045*b^7*e^7*x^7 + 128*b^7*d^7 - 1136*a*b^6*d^6*e + 4648*a^2*b^5*d^5*e^2 - 12110*a^3*b^4*d^4*e^3 + 26635*a^4*b^3*d^3*e^4 + 29696*a^5*b^2*d^2*e^5 - 3072*a^6*b*d*e^6 + 256*a^7*e^7 + 105105*(b^7*d*e^6 + 2*a*b^6*e^7)*x^6 + 3003*(23*b^7*d^2*e^5 + 164*a*b^6*d*e^6 + 128*a^2*b^5*e^7)*x^5 + 2145*(3*b^7*d^3*e^4 + 152*a*b^6*d^2*e^5 + 422*a^2*b^5*d*e^6 + 158*a^3*b^4*e^7)*x^4 - 715*(2*b^7*d^4*e^3 - 44*a*b^6*d^3*e^4 - 846*a^2*b^5*d^2*e^5 - 1124*a^3*b^4*d*e^6 - 193*a^4*b^3*e^7)*x^3 + 65*(8*b^7*d^5*e^2 - 106*a*b^6*d^4*e^3 + 938*a^2*b^5*d^3*e^4 + 8368*a^3*b^4*d^2*e^5 + 5089*a^4*b^3*d*e^6 + 256*a^5*b^2*e^7)*x^2 - 5*(48*b^7*d^6*e - 496*a*b^6*d^5*e^2 + 2618*a^2*b^5*d^4*e^3 - 11620*a^3*b^4*d^3*e^4 - 45677*a^4*b^3*d^2*e^5 - 8192*a^5*b^2*d*e^6 + 256*a^6*b*e^7)*x)*sqrt(e*x + d))/(a^5*b^8*d^11 - 8*a^6*b^7*d^10*e + 28*a^7*b^6*d^9*e^2 - 56*a^8*b^5*d^8*e^3 + 70*a^9*b^4*d^7*e^4 - 56*a^10*b^3*d^6*e^5 + 28*a^11*b^2*d^5*e^6 - 8*a^12*b*d^4*e^7 + a^13*d^3*e^8 + (b^13*d^8*e^3 - 8*a*b^12*d^7*e^4 + 28*a^2*b^11*d^6*e^5 - 56*a^3*b^10*d^5*e^6 + 70*a^4*b^9*d^4*e^7 - 56*a^5*b^8*d^3*e^8 + 28*a^6*b^7*d^2*e^9 - 8*a^7*b^6*d*e^10 + a^8*b^5*e^11)*x^8 + (3*b^13*d^9*e^2 - 19*a*b^12*d^8*e^3 + 44*a^2*b^11*d^7*e^4 - 28*a^3*b^10*d^6*e^5 - 70*a^4*b^9*d^5*e^6 + 182*a^5*b^8*d^4*e^7 - 196*a^6*b^7*d^3*e^8 + 116*a^7*b^6*d^2*e^9 - 37*a^8*b^5*d*e^10 + 5*a^9*b^4*e^11)*x^7 + (3*b^13*d^10*e - 9*a*b^12*d^9*e^2 - 26*a^2*b^11*d^8*e^3 + 172*a^3*b^10*d^7*e^4 - 350*a^4*b^9*d^6*e^5 + 322*a^5*b^8*d^5*e^6 - 56*a^6*b^7*d^4*e^7 - 164*a^7*b^6*d^3*e^8 + 163*a^8*b^5*d^2*e^9 - 65*a^9*b^4*d*e^10 + 10*a^10*b^3*e^11)*x^6 + (b^13*d^11 + 7*a*b^12*d^10*e - 62*a^2*b^11*d^9*e^2 + 134*a^3*b^10*d^8*e^3 - 10*a^4*b^9*d^7*e^4 - 406*a^5*b^8*d^6*e^5 + 728*a^6*b^7*d^5*e^6 - 568*a^7*b^6*d^4*e^7 + 161*a^8*b^5*d^3*e^8 + 55*a^9*b^4*d^2*e^9 - 50*a^10*b^3*d*e^10 + 10*a^11*b^2*e^11)*x^5 + 5*(a*b^12*d^11 - 2*a^2*b^11*d^10*e - 14*a^3*b^10*d^9*e^2 + 65*a^4*b^9*d^8*e^3 - 106*a^5*b^8*d^7*e^4 + 56*a^6*b^7*d^6*e^5 + 56*a^7*b^6*d^5*e^6 - 106*a^8*b^5*d^4*e^7 + 65*a^9*b^4*d^3*e^8 - 14*a^10*b^3*d^2*e^9 - 2*a^11*b^2*d*e^10 + a^12*b*e^11)*x^4 + (10*a^2*b^11*d^11 - 50*a^3*b^10*d^10*e + 55*a^4*b^9*d^9*e^2 + 161*a^5*b^8*d^8*e^3 - 568*a^6*b^7*d^7*e^4 + 728*a^7*b^6*d^6*e^5 - 406*a^8*b^5*d^5*e^6 - 10*a^9*b^4*d^4*e^7 + 134*a^10*b^3*d^3*e^8 - 62*a^11*b^2*d^2*e^9 + 7*a^12*b*d*e^10 + a^13*e^11)*x^3 + (10*a^3*b^10*d^11 - 65*a^4*b^9*d^10*e + 163*a^5*b^8*d^9*e^2 - 164*a^6*b^7*d^8*e^3 - 56*a^7*b^6*d^7*e^4 + 322*a^8*b^5*d^6*e^5 - 350*a^9*b^4*d^5*e^6 + 172*a^10*b^3*d^4*e^7 - 26*a^11*b^2*d^3*e^8 - 9*a^12*b*d^2*e^9 + 3*a^13*d*e^10)*x^2 + (5*a^4*b^9*d^11 - 37*a^5*b^8*d^10*e + 116*a^6*b^7*d^9*e^2 - 196*a^7*b^6*d^8*e^3 + 182*a^8*b^5*d^7*e^4 - 70*a^9*b^4*d^6*e^5 - 28*a^10*b^3*d^5*e^6 + 44*a^11*b^2*d^4*e^7 - 19*a^12*b*d^3*e^8 + 3*a^13*d^2*e^9)*x)]","B",0
1676,1,93,0,0.396713," ","integrate((e*x+d)^(5/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b e^{4} x^{4} - 2 \, b d^{4} + 9 \, a d^{3} e + {\left(19 \, b d e^{3} + 9 \, a e^{4}\right)} x^{3} + 3 \, {\left(5 \, b d^{2} e^{2} + 9 \, a d e^{3}\right)} x^{2} + {\left(b d^{3} e + 27 \, a d^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{63 \, e^{2}}"," ",0,"2/63*(7*b*e^4*x^4 - 2*b*d^4 + 9*a*d^3*e + (19*b*d*e^3 + 9*a*e^4)*x^3 + 3*(5*b*d^2*e^2 + 9*a*d*e^3)*x^2 + (b*d^3*e + 27*a*d^2*e^2)*x)*sqrt(e*x + d)/e^2","A",0
1677,1,69,0,0.396481," ","integrate((e*x+d)^(3/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b e^{3} x^{3} - 2 \, b d^{3} + 7 \, a d^{2} e + {\left(8 \, b d e^{2} + 7 \, a e^{3}\right)} x^{2} + {\left(b d^{2} e + 14 \, a d e^{2}\right)} x\right)} \sqrt{e x + d}}{35 \, e^{2}}"," ",0,"2/35*(5*b*e^3*x^3 - 2*b*d^3 + 7*a*d^2*e + (8*b*d*e^2 + 7*a*e^3)*x^2 + (b*d^2*e + 14*a*d*e^2)*x)*sqrt(e*x + d)/e^2","A",0
1678,1,46,0,0.394873," ","integrate((e*x+d)^(1/2)*((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b e^{2} x^{2} - 2 \, b d^{2} + 5 \, a d e + {\left(b d e + 5 \, a e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, e^{2}}"," ",0,"2/15*(3*b*e^2*x^2 - 2*b*d^2 + 5*a*d*e + (b*d*e + 5*a*e^2)*x)*sqrt(e*x + d)/e^2","A",0
1679,1,25,0,0.397079," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b e x - 2 \, b d + 3 \, a e\right)} \sqrt{e x + d}}{3 \, e^{2}}"," ",0,"2/3*(b*e*x - 2*b*d + 3*a*e)*sqrt(e*x + d)/e^2","A",0
1680,1,35,0,0.397234," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b e x + 2 \, b d - a e\right)} \sqrt{e x + d}}{e^{3} x + d e^{2}}"," ",0,"2*(b*e*x + 2*b*d - a*e)*sqrt(e*x + d)/(e^3*x + d*e^2)","A",0
1681,1,46,0,0.388787," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b e x + 2 \, b d + a e\right)} \sqrt{e x + d}}{3 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}"," ",0,"-2/3*(3*b*e*x + 2*b*d + a*e)*sqrt(e*x + d)/(e^4*x^2 + 2*d*e^3*x + d^2*e^2)","A",0
1682,1,58,0,0.387192," ","integrate(((b*x+a)^2)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, b e x + 2 \, b d + 3 \, a e\right)} \sqrt{e x + d}}{15 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}}"," ",0,"-2/15*(5*b*e*x + 2*b*d + 3*a*e)*sqrt(e*x + d)/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2)","A",0
1683,1,268,0,0.395052," ","integrate((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, b^{3} e^{6} x^{6} - 16 \, b^{3} d^{6} + 104 \, a b^{2} d^{5} e - 286 \, a^{2} b d^{4} e^{2} + 429 \, a^{3} d^{3} e^{3} + 63 \, {\left(9 \, b^{3} d e^{5} + 13 \, a b^{2} e^{6}\right)} x^{5} + 7 \, {\left(53 \, b^{3} d^{2} e^{4} + 299 \, a b^{2} d e^{5} + 143 \, a^{2} b e^{6}\right)} x^{4} + {\left(5 \, b^{3} d^{3} e^{3} + 1469 \, a b^{2} d^{2} e^{4} + 2717 \, a^{2} b d e^{5} + 429 \, a^{3} e^{6}\right)} x^{3} - 3 \, {\left(2 \, b^{3} d^{4} e^{2} - 13 \, a b^{2} d^{3} e^{3} - 715 \, a^{2} b d^{2} e^{4} - 429 \, a^{3} d e^{5}\right)} x^{2} + {\left(8 \, b^{3} d^{5} e - 52 \, a b^{2} d^{4} e^{2} + 143 \, a^{2} b d^{3} e^{3} + 1287 \, a^{3} d^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{3003 \, e^{4}}"," ",0,"2/3003*(231*b^3*e^6*x^6 - 16*b^3*d^6 + 104*a*b^2*d^5*e - 286*a^2*b*d^4*e^2 + 429*a^3*d^3*e^3 + 63*(9*b^3*d*e^5 + 13*a*b^2*e^6)*x^5 + 7*(53*b^3*d^2*e^4 + 299*a*b^2*d*e^5 + 143*a^2*b*e^6)*x^4 + (5*b^3*d^3*e^3 + 1469*a*b^2*d^2*e^4 + 2717*a^2*b*d*e^5 + 429*a^3*e^6)*x^3 - 3*(2*b^3*d^4*e^2 - 13*a*b^2*d^3*e^3 - 715*a^2*b*d^2*e^4 - 429*a^3*d*e^5)*x^2 + (8*b^3*d^5*e - 52*a*b^2*d^4*e^2 + 143*a^2*b*d^3*e^3 + 1287*a^3*d^2*e^4)*x)*sqrt(e*x + d)/e^4","A",0
1684,1,216,0,0.406812," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, b^{3} e^{5} x^{5} - 16 \, b^{3} d^{5} + 88 \, a b^{2} d^{4} e - 198 \, a^{2} b d^{3} e^{2} + 231 \, a^{3} d^{2} e^{3} + 35 \, {\left(4 \, b^{3} d e^{4} + 11 \, a b^{2} e^{5}\right)} x^{4} + 5 \, {\left(b^{3} d^{2} e^{3} + 110 \, a b^{2} d e^{4} + 99 \, a^{2} b e^{5}\right)} x^{3} - 3 \, {\left(2 \, b^{3} d^{3} e^{2} - 11 \, a b^{2} d^{2} e^{3} - 264 \, a^{2} b d e^{4} - 77 \, a^{3} e^{5}\right)} x^{2} + {\left(8 \, b^{3} d^{4} e - 44 \, a b^{2} d^{3} e^{2} + 99 \, a^{2} b d^{2} e^{3} + 462 \, a^{3} d e^{4}\right)} x\right)} \sqrt{e x + d}}{1155 \, e^{4}}"," ",0,"2/1155*(105*b^3*e^5*x^5 - 16*b^3*d^5 + 88*a*b^2*d^4*e - 198*a^2*b*d^3*e^2 + 231*a^3*d^2*e^3 + 35*(4*b^3*d*e^4 + 11*a*b^2*e^5)*x^4 + 5*(b^3*d^2*e^3 + 110*a*b^2*d*e^4 + 99*a^2*b*e^5)*x^3 - 3*(2*b^3*d^3*e^2 - 11*a*b^2*d^2*e^3 - 264*a^2*b*d*e^4 - 77*a^3*e^5)*x^2 + (8*b^3*d^4*e - 44*a*b^2*d^3*e^2 + 99*a^2*b*d^2*e^3 + 462*a^3*d*e^4)*x)*sqrt(e*x + d)/e^4","A",0
1685,1,164,0,0.401685," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{3} e^{4} x^{4} - 16 \, b^{3} d^{4} + 72 \, a b^{2} d^{3} e - 126 \, a^{2} b d^{2} e^{2} + 105 \, a^{3} d e^{3} + 5 \, {\left(b^{3} d e^{3} + 27 \, a b^{2} e^{4}\right)} x^{3} - 3 \, {\left(2 \, b^{3} d^{2} e^{2} - 9 \, a b^{2} d e^{3} - 63 \, a^{2} b e^{4}\right)} x^{2} + {\left(8 \, b^{3} d^{3} e - 36 \, a b^{2} d^{2} e^{2} + 63 \, a^{2} b d e^{3} + 105 \, a^{3} e^{4}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{4}}"," ",0,"2/315*(35*b^3*e^4*x^4 - 16*b^3*d^4 + 72*a*b^2*d^3*e - 126*a^2*b*d^2*e^2 + 105*a^3*d*e^3 + 5*(b^3*d*e^3 + 27*a*b^2*e^4)*x^3 - 3*(2*b^3*d^2*e^2 - 9*a*b^2*d*e^3 - 63*a^2*b*e^4)*x^2 + (8*b^3*d^3*e - 36*a*b^2*d^2*e^2 + 63*a^2*b*d*e^3 + 105*a^3*e^4)*x)*sqrt(e*x + d)/e^4","A",0
1686,1,115,0,0.401524," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} e^{3} x^{3} - 16 \, b^{3} d^{3} + 56 \, a b^{2} d^{2} e - 70 \, a^{2} b d e^{2} + 35 \, a^{3} e^{3} - 3 \, {\left(2 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} + {\left(8 \, b^{3} d^{2} e - 28 \, a b^{2} d e^{2} + 35 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{35 \, e^{4}}"," ",0,"2/35*(5*b^3*e^3*x^3 - 16*b^3*d^3 + 56*a*b^2*d^2*e - 70*a^2*b*d*e^2 + 35*a^3*e^3 - 3*(2*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 + (8*b^3*d^2*e - 28*a*b^2*d*e^2 + 35*a^2*b*e^3)*x)*sqrt(e*x + d)/e^4","A",0
1687,1,124,0,0.400334," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} e^{3} x^{3} + 16 \, b^{3} d^{3} - 40 \, a b^{2} d^{2} e + 30 \, a^{2} b d e^{2} - 5 \, a^{3} e^{3} - {\left(2 \, b^{3} d e^{2} - 5 \, a b^{2} e^{3}\right)} x^{2} + {\left(8 \, b^{3} d^{2} e - 20 \, a b^{2} d e^{2} + 15 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{5 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"2/5*(b^3*e^3*x^3 + 16*b^3*d^3 - 40*a*b^2*d^2*e + 30*a^2*b*d*e^2 - 5*a^3*e^3 - (2*b^3*d*e^2 - 5*a*b^2*e^3)*x^2 + (8*b^3*d^2*e - 20*a*b^2*d*e^2 + 15*a^2*b*e^3)*x)*sqrt(e*x + d)/(e^5*x + d*e^4)","A",0
1688,1,136,0,0.405905," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} e^{3} x^{3} - 16 \, b^{3} d^{3} + 24 \, a b^{2} d^{2} e - 6 \, a^{2} b d e^{2} - a^{3} e^{3} - 3 \, {\left(2 \, b^{3} d e^{2} - 3 \, a b^{2} e^{3}\right)} x^{2} - 3 \, {\left(8 \, b^{3} d^{2} e - 12 \, a b^{2} d e^{2} + 3 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"2/3*(b^3*e^3*x^3 - 16*b^3*d^3 + 24*a*b^2*d^2*e - 6*a^2*b*d*e^2 - a^3*e^3 - 3*(2*b^3*d*e^2 - 3*a*b^2*e^3)*x^2 - 3*(8*b^3*d^2*e - 12*a*b^2*d*e^2 + 3*a^2*b*e^3)*x)*sqrt(e*x + d)/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1689,1,148,0,0.404089," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} e^{3} x^{3} + 16 \, b^{3} d^{3} - 8 \, a b^{2} d^{2} e - 2 \, a^{2} b d e^{2} - a^{3} e^{3} + 15 \, {\left(2 \, b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 5 \, {\left(8 \, b^{3} d^{2} e - 4 \, a b^{2} d e^{2} - a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{5 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"2/5*(5*b^3*e^3*x^3 + 16*b^3*d^3 - 8*a*b^2*d^2*e - 2*a^2*b*d*e^2 - a^3*e^3 + 15*(2*b^3*d*e^2 - a*b^2*e^3)*x^2 + 5*(8*b^3*d^2*e - 4*a*b^2*d*e^2 - a^2*b*e^3)*x)*sqrt(e*x + d)/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
1690,1,158,0,0.404741," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, b^{3} e^{3} x^{3} + 16 \, b^{3} d^{3} + 8 \, a b^{2} d^{2} e + 6 \, a^{2} b d e^{2} + 5 \, a^{3} e^{3} + 35 \, {\left(2 \, b^{3} d e^{2} + a b^{2} e^{3}\right)} x^{2} + 7 \, {\left(8 \, b^{3} d^{2} e + 4 \, a b^{2} d e^{2} + 3 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{8} x^{4} + 4 \, d e^{7} x^{3} + 6 \, d^{2} e^{6} x^{2} + 4 \, d^{3} e^{5} x + d^{4} e^{4}\right)}}"," ",0,"-2/35*(35*b^3*e^3*x^3 + 16*b^3*d^3 + 8*a*b^2*d^2*e + 6*a^2*b*d*e^2 + 5*a^3*e^3 + 35*(2*b^3*d*e^2 + a*b^2*e^3)*x^2 + 7*(8*b^3*d^2*e + 4*a*b^2*d*e^2 + 3*a^2*b*e^3)*x)*sqrt(e*x + d)/(e^8*x^4 + 4*d*e^7*x^3 + 6*d^2*e^6*x^2 + 4*d^3*e^5*x + d^4*e^4)","A",0
1691,1,170,0,0.407874," ","integrate((b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(105 \, b^{3} e^{3} x^{3} + 16 \, b^{3} d^{3} + 24 \, a b^{2} d^{2} e + 30 \, a^{2} b d e^{2} + 35 \, a^{3} e^{3} + 63 \, {\left(2 \, b^{3} d e^{2} + 3 \, a b^{2} e^{3}\right)} x^{2} + 9 \, {\left(8 \, b^{3} d^{2} e + 12 \, a b^{2} d e^{2} + 15 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{9} x^{5} + 5 \, d e^{8} x^{4} + 10 \, d^{2} e^{7} x^{3} + 10 \, d^{3} e^{6} x^{2} + 5 \, d^{4} e^{5} x + d^{5} e^{4}\right)}}"," ",0,"-2/315*(105*b^3*e^3*x^3 + 16*b^3*d^3 + 24*a*b^2*d^2*e + 30*a^2*b*d*e^2 + 35*a^3*e^3 + 63*(2*b^3*d*e^2 + 3*a*b^2*e^3)*x^2 + 9*(8*b^3*d^2*e + 12*a*b^2*d*e^2 + 15*a^2*b*e^3)*x)*sqrt(e*x + d)/(e^9*x^5 + 5*d*e^8*x^4 + 10*d^2*e^7*x^3 + 10*d^3*e^6*x^2 + 5*d^4*e^5*x + d^5*e^4)","A",0
1692,1,497,0,0.412505," ","integrate((e*x+d)^(5/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(9009 \, b^{5} e^{8} x^{8} - 256 \, b^{5} d^{8} + 2176 \, a b^{4} d^{7} e - 8160 \, a^{2} b^{3} d^{6} e^{2} + 17680 \, a^{3} b^{2} d^{5} e^{3} - 24310 \, a^{4} b d^{4} e^{4} + 21879 \, a^{5} d^{3} e^{5} + 3003 \, {\left(7 \, b^{5} d e^{7} + 17 \, a b^{4} e^{8}\right)} x^{7} + 231 \, {\left(55 \, b^{5} d^{2} e^{6} + 527 \, a b^{4} d e^{7} + 510 \, a^{2} b^{3} e^{8}\right)} x^{6} + 63 \, {\left(b^{5} d^{3} e^{5} + 1207 \, a b^{4} d^{2} e^{6} + 4590 \, a^{2} b^{3} d e^{7} + 2210 \, a^{3} b^{2} e^{8}\right)} x^{5} - 35 \, {\left(2 \, b^{5} d^{4} e^{4} - 17 \, a b^{4} d^{3} e^{5} - 5406 \, a^{2} b^{3} d^{2} e^{6} - 10166 \, a^{3} b^{2} d e^{7} - 2431 \, a^{4} b e^{8}\right)} x^{4} + {\left(80 \, b^{5} d^{5} e^{3} - 680 \, a b^{4} d^{4} e^{4} + 2550 \, a^{2} b^{3} d^{3} e^{5} + 249730 \, a^{3} b^{2} d^{2} e^{6} + 230945 \, a^{4} b d e^{7} + 21879 \, a^{5} e^{8}\right)} x^{3} - 3 \, {\left(32 \, b^{5} d^{6} e^{2} - 272 \, a b^{4} d^{5} e^{3} + 1020 \, a^{2} b^{3} d^{4} e^{4} - 2210 \, a^{3} b^{2} d^{3} e^{5} - 60775 \, a^{4} b d^{2} e^{6} - 21879 \, a^{5} d e^{7}\right)} x^{2} + {\left(128 \, b^{5} d^{7} e - 1088 \, a b^{4} d^{6} e^{2} + 4080 \, a^{2} b^{3} d^{5} e^{3} - 8840 \, a^{3} b^{2} d^{4} e^{4} + 12155 \, a^{4} b d^{3} e^{5} + 65637 \, a^{5} d^{2} e^{6}\right)} x\right)} \sqrt{e x + d}}{153153 \, e^{6}}"," ",0,"2/153153*(9009*b^5*e^8*x^8 - 256*b^5*d^8 + 2176*a*b^4*d^7*e - 8160*a^2*b^3*d^6*e^2 + 17680*a^3*b^2*d^5*e^3 - 24310*a^4*b*d^4*e^4 + 21879*a^5*d^3*e^5 + 3003*(7*b^5*d*e^7 + 17*a*b^4*e^8)*x^7 + 231*(55*b^5*d^2*e^6 + 527*a*b^4*d*e^7 + 510*a^2*b^3*e^8)*x^6 + 63*(b^5*d^3*e^5 + 1207*a*b^4*d^2*e^6 + 4590*a^2*b^3*d*e^7 + 2210*a^3*b^2*e^8)*x^5 - 35*(2*b^5*d^4*e^4 - 17*a*b^4*d^3*e^5 - 5406*a^2*b^3*d^2*e^6 - 10166*a^3*b^2*d*e^7 - 2431*a^4*b*e^8)*x^4 + (80*b^5*d^5*e^3 - 680*a*b^4*d^4*e^4 + 2550*a^2*b^3*d^3*e^5 + 249730*a^3*b^2*d^2*e^6 + 230945*a^4*b*d*e^7 + 21879*a^5*e^8)*x^3 - 3*(32*b^5*d^6*e^2 - 272*a*b^4*d^5*e^3 + 1020*a^2*b^3*d^4*e^4 - 2210*a^3*b^2*d^3*e^5 - 60775*a^4*b*d^2*e^6 - 21879*a^5*d*e^7)*x^2 + (128*b^5*d^7*e - 1088*a*b^4*d^6*e^2 + 4080*a^2*b^3*d^5*e^3 - 8840*a^3*b^2*d^4*e^4 + 12155*a^4*b*d^3*e^5 + 65637*a^5*d^2*e^6)*x)*sqrt(e*x + d)/e^6","B",0
1693,1,418,0,0.409569," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, b^{5} e^{7} x^{7} - 256 \, b^{5} d^{7} + 1920 \, a b^{4} d^{6} e - 6240 \, a^{2} b^{3} d^{5} e^{2} + 11440 \, a^{3} b^{2} d^{4} e^{3} - 12870 \, a^{4} b d^{3} e^{4} + 9009 \, a^{5} d^{2} e^{5} + 231 \, {\left(16 \, b^{5} d e^{6} + 75 \, a b^{4} e^{7}\right)} x^{6} + 63 \, {\left(b^{5} d^{2} e^{5} + 350 \, a b^{4} d e^{6} + 650 \, a^{2} b^{3} e^{7}\right)} x^{5} - 35 \, {\left(2 \, b^{5} d^{3} e^{4} - 15 \, a b^{4} d^{2} e^{5} - 1560 \, a^{2} b^{3} d e^{6} - 1430 \, a^{3} b^{2} e^{7}\right)} x^{4} + 5 \, {\left(16 \, b^{5} d^{4} e^{3} - 120 \, a b^{4} d^{3} e^{4} + 390 \, a^{2} b^{3} d^{2} e^{5} + 14300 \, a^{3} b^{2} d e^{6} + 6435 \, a^{4} b e^{7}\right)} x^{3} - 3 \, {\left(32 \, b^{5} d^{5} e^{2} - 240 \, a b^{4} d^{4} e^{3} + 780 \, a^{2} b^{3} d^{3} e^{4} - 1430 \, a^{3} b^{2} d^{2} e^{5} - 17160 \, a^{4} b d e^{6} - 3003 \, a^{5} e^{7}\right)} x^{2} + {\left(128 \, b^{5} d^{6} e - 960 \, a b^{4} d^{5} e^{2} + 3120 \, a^{2} b^{3} d^{4} e^{3} - 5720 \, a^{3} b^{2} d^{3} e^{4} + 6435 \, a^{4} b d^{2} e^{5} + 18018 \, a^{5} d e^{6}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{6}}"," ",0,"2/45045*(3003*b^5*e^7*x^7 - 256*b^5*d^7 + 1920*a*b^4*d^6*e - 6240*a^2*b^3*d^5*e^2 + 11440*a^3*b^2*d^4*e^3 - 12870*a^4*b*d^3*e^4 + 9009*a^5*d^2*e^5 + 231*(16*b^5*d*e^6 + 75*a*b^4*e^7)*x^6 + 63*(b^5*d^2*e^5 + 350*a*b^4*d*e^6 + 650*a^2*b^3*e^7)*x^5 - 35*(2*b^5*d^3*e^4 - 15*a*b^4*d^2*e^5 - 1560*a^2*b^3*d*e^6 - 1430*a^3*b^2*e^7)*x^4 + 5*(16*b^5*d^4*e^3 - 120*a*b^4*d^3*e^4 + 390*a^2*b^3*d^2*e^5 + 14300*a^3*b^2*d*e^6 + 6435*a^4*b*e^7)*x^3 - 3*(32*b^5*d^5*e^2 - 240*a*b^4*d^4*e^3 + 780*a^2*b^3*d^3*e^4 - 1430*a^3*b^2*d^2*e^5 - 17160*a^4*b*d*e^6 - 3003*a^5*e^7)*x^2 + (128*b^5*d^6*e - 960*a*b^4*d^5*e^2 + 3120*a^2*b^3*d^4*e^3 - 5720*a^3*b^2*d^3*e^4 + 6435*a^4*b*d^2*e^5 + 18018*a^5*d*e^6)*x)*sqrt(e*x + d)/e^6","A",0
1694,1,338,0,0.412001," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(693 \, b^{5} e^{6} x^{6} - 256 \, b^{5} d^{6} + 1664 \, a b^{4} d^{5} e - 4576 \, a^{2} b^{3} d^{4} e^{2} + 6864 \, a^{3} b^{2} d^{3} e^{3} - 6006 \, a^{4} b d^{2} e^{4} + 3003 \, a^{5} d e^{5} + 63 \, {\left(b^{5} d e^{5} + 65 \, a b^{4} e^{6}\right)} x^{5} - 35 \, {\left(2 \, b^{5} d^{2} e^{4} - 13 \, a b^{4} d e^{5} - 286 \, a^{2} b^{3} e^{6}\right)} x^{4} + 10 \, {\left(8 \, b^{5} d^{3} e^{3} - 52 \, a b^{4} d^{2} e^{4} + 143 \, a^{2} b^{3} d e^{5} + 1287 \, a^{3} b^{2} e^{6}\right)} x^{3} - 3 \, {\left(32 \, b^{5} d^{4} e^{2} - 208 \, a b^{4} d^{3} e^{3} + 572 \, a^{2} b^{3} d^{2} e^{4} - 858 \, a^{3} b^{2} d e^{5} - 3003 \, a^{4} b e^{6}\right)} x^{2} + {\left(128 \, b^{5} d^{5} e - 832 \, a b^{4} d^{4} e^{2} + 2288 \, a^{2} b^{3} d^{3} e^{3} - 3432 \, a^{3} b^{2} d^{2} e^{4} + 3003 \, a^{4} b d e^{5} + 3003 \, a^{5} e^{6}\right)} x\right)} \sqrt{e x + d}}{9009 \, e^{6}}"," ",0,"2/9009*(693*b^5*e^6*x^6 - 256*b^5*d^6 + 1664*a*b^4*d^5*e - 4576*a^2*b^3*d^4*e^2 + 6864*a^3*b^2*d^3*e^3 - 6006*a^4*b*d^2*e^4 + 3003*a^5*d*e^5 + 63*(b^5*d*e^5 + 65*a*b^4*e^6)*x^5 - 35*(2*b^5*d^2*e^4 - 13*a*b^4*d*e^5 - 286*a^2*b^3*e^6)*x^4 + 10*(8*b^5*d^3*e^3 - 52*a*b^4*d^2*e^4 + 143*a^2*b^3*d*e^5 + 1287*a^3*b^2*e^6)*x^3 - 3*(32*b^5*d^4*e^2 - 208*a*b^4*d^3*e^3 + 572*a^2*b^3*d^2*e^4 - 858*a^3*b^2*d*e^5 - 3003*a^4*b*e^6)*x^2 + (128*b^5*d^5*e - 832*a*b^4*d^4*e^2 + 2288*a^2*b^3*d^3*e^3 - 3432*a^3*b^2*d^2*e^4 + 3003*a^4*b*d*e^5 + 3003*a^5*e^6)*x)*sqrt(e*x + d)/e^6","A",0
1695,1,261,0,0.412516," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, b^{5} e^{5} x^{5} - 256 \, b^{5} d^{5} + 1408 \, a b^{4} d^{4} e - 3168 \, a^{2} b^{3} d^{3} e^{2} + 3696 \, a^{3} b^{2} d^{2} e^{3} - 2310 \, a^{4} b d e^{4} + 693 \, a^{5} e^{5} - 35 \, {\left(2 \, b^{5} d e^{4} - 11 \, a b^{4} e^{5}\right)} x^{4} + 10 \, {\left(8 \, b^{5} d^{2} e^{3} - 44 \, a b^{4} d e^{4} + 99 \, a^{2} b^{3} e^{5}\right)} x^{3} - 6 \, {\left(16 \, b^{5} d^{3} e^{2} - 88 \, a b^{4} d^{2} e^{3} + 198 \, a^{2} b^{3} d e^{4} - 231 \, a^{3} b^{2} e^{5}\right)} x^{2} + {\left(128 \, b^{5} d^{4} e - 704 \, a b^{4} d^{3} e^{2} + 1584 \, a^{2} b^{3} d^{2} e^{3} - 1848 \, a^{3} b^{2} d e^{4} + 1155 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{693 \, e^{6}}"," ",0,"2/693*(63*b^5*e^5*x^5 - 256*b^5*d^5 + 1408*a*b^4*d^4*e - 3168*a^2*b^3*d^3*e^2 + 3696*a^3*b^2*d^2*e^3 - 2310*a^4*b*d*e^4 + 693*a^5*e^5 - 35*(2*b^5*d*e^4 - 11*a*b^4*e^5)*x^4 + 10*(8*b^5*d^2*e^3 - 44*a*b^4*d*e^4 + 99*a^2*b^3*e^5)*x^3 - 6*(16*b^5*d^3*e^2 - 88*a*b^4*d^2*e^3 + 198*a^2*b^3*d*e^4 - 231*a^3*b^2*e^5)*x^2 + (128*b^5*d^4*e - 704*a*b^4*d^3*e^2 + 1584*a^2*b^3*d^2*e^3 - 1848*a^3*b^2*d*e^4 + 1155*a^4*b*e^5)*x)*sqrt(e*x + d)/e^6","A",0
1696,1,271,0,0.397592," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b^{5} e^{5} x^{5} + 256 \, b^{5} d^{5} - 1152 \, a b^{4} d^{4} e + 2016 \, a^{2} b^{3} d^{3} e^{2} - 1680 \, a^{3} b^{2} d^{2} e^{3} + 630 \, a^{4} b d e^{4} - 63 \, a^{5} e^{5} - 5 \, {\left(2 \, b^{5} d e^{4} - 9 \, a b^{4} e^{5}\right)} x^{4} + 2 \, {\left(8 \, b^{5} d^{2} e^{3} - 36 \, a b^{4} d e^{4} + 63 \, a^{2} b^{3} e^{5}\right)} x^{3} - 2 \, {\left(16 \, b^{5} d^{3} e^{2} - 72 \, a b^{4} d^{2} e^{3} + 126 \, a^{2} b^{3} d e^{4} - 105 \, a^{3} b^{2} e^{5}\right)} x^{2} + {\left(128 \, b^{5} d^{4} e - 576 \, a b^{4} d^{3} e^{2} + 1008 \, a^{2} b^{3} d^{2} e^{3} - 840 \, a^{3} b^{2} d e^{4} + 315 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{63 \, {\left(e^{7} x + d e^{6}\right)}}"," ",0,"2/63*(7*b^5*e^5*x^5 + 256*b^5*d^5 - 1152*a*b^4*d^4*e + 2016*a^2*b^3*d^3*e^2 - 1680*a^3*b^2*d^2*e^3 + 630*a^4*b*d*e^4 - 63*a^5*e^5 - 5*(2*b^5*d*e^4 - 9*a*b^4*e^5)*x^4 + 2*(8*b^5*d^2*e^3 - 36*a*b^4*d*e^4 + 63*a^2*b^3*e^5)*x^3 - 2*(16*b^5*d^3*e^2 - 72*a*b^4*d^2*e^3 + 126*a^2*b^3*d*e^4 - 105*a^3*b^2*e^5)*x^2 + (128*b^5*d^4*e - 576*a*b^4*d^3*e^2 + 1008*a^2*b^3*d^2*e^3 - 840*a^3*b^2*d*e^4 + 315*a^4*b*e^5)*x)*sqrt(e*x + d)/(e^7*x + d*e^6)","A",0
1697,1,283,0,0.388235," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{5} e^{5} x^{5} - 256 \, b^{5} d^{5} + 896 \, a b^{4} d^{4} e - 1120 \, a^{2} b^{3} d^{3} e^{2} + 560 \, a^{3} b^{2} d^{2} e^{3} - 70 \, a^{4} b d e^{4} - 7 \, a^{5} e^{5} - 3 \, {\left(2 \, b^{5} d e^{4} - 7 \, a b^{4} e^{5}\right)} x^{4} + 2 \, {\left(8 \, b^{5} d^{2} e^{3} - 28 \, a b^{4} d e^{4} + 35 \, a^{2} b^{3} e^{5}\right)} x^{3} - 6 \, {\left(16 \, b^{5} d^{3} e^{2} - 56 \, a b^{4} d^{2} e^{3} + 70 \, a^{2} b^{3} d e^{4} - 35 \, a^{3} b^{2} e^{5}\right)} x^{2} - 3 \, {\left(128 \, b^{5} d^{4} e - 448 \, a b^{4} d^{3} e^{2} + 560 \, a^{2} b^{3} d^{2} e^{3} - 280 \, a^{3} b^{2} d e^{4} + 35 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{21 \, {\left(e^{8} x^{2} + 2 \, d e^{7} x + d^{2} e^{6}\right)}}"," ",0,"2/21*(3*b^5*e^5*x^5 - 256*b^5*d^5 + 896*a*b^4*d^4*e - 1120*a^2*b^3*d^3*e^2 + 560*a^3*b^2*d^2*e^3 - 70*a^4*b*d*e^4 - 7*a^5*e^5 - 3*(2*b^5*d*e^4 - 7*a*b^4*e^5)*x^4 + 2*(8*b^5*d^2*e^3 - 28*a*b^4*d*e^4 + 35*a^2*b^3*e^5)*x^3 - 6*(16*b^5*d^3*e^2 - 56*a*b^4*d^2*e^3 + 70*a^2*b^3*d*e^4 - 35*a^3*b^2*e^5)*x^2 - 3*(128*b^5*d^4*e - 448*a*b^4*d^3*e^2 + 560*a^2*b^3*d^2*e^3 - 280*a^3*b^2*d*e^4 + 35*a^4*b*e^5)*x)*sqrt(e*x + d)/(e^8*x^2 + 2*d*e^7*x + d^2*e^6)","A",0
1698,1,294,0,0.403153," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{5} e^{5} x^{5} + 256 \, b^{5} d^{5} - 640 \, a b^{4} d^{4} e + 480 \, a^{2} b^{3} d^{3} e^{2} - 80 \, a^{3} b^{2} d^{2} e^{3} - 10 \, a^{4} b d e^{4} - 3 \, a^{5} e^{5} - 5 \, {\left(2 \, b^{5} d e^{4} - 5 \, a b^{4} e^{5}\right)} x^{4} + 10 \, {\left(8 \, b^{5} d^{2} e^{3} - 20 \, a b^{4} d e^{4} + 15 \, a^{2} b^{3} e^{5}\right)} x^{3} + 30 \, {\left(16 \, b^{5} d^{3} e^{2} - 40 \, a b^{4} d^{2} e^{3} + 30 \, a^{2} b^{3} d e^{4} - 5 \, a^{3} b^{2} e^{5}\right)} x^{2} + 5 \, {\left(128 \, b^{5} d^{4} e - 320 \, a b^{4} d^{3} e^{2} + 240 \, a^{2} b^{3} d^{2} e^{3} - 40 \, a^{3} b^{2} d e^{4} - 5 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{9} x^{3} + 3 \, d e^{8} x^{2} + 3 \, d^{2} e^{7} x + d^{3} e^{6}\right)}}"," ",0,"2/15*(3*b^5*e^5*x^5 + 256*b^5*d^5 - 640*a*b^4*d^4*e + 480*a^2*b^3*d^3*e^2 - 80*a^3*b^2*d^2*e^3 - 10*a^4*b*d*e^4 - 3*a^5*e^5 - 5*(2*b^5*d*e^4 - 5*a*b^4*e^5)*x^4 + 10*(8*b^5*d^2*e^3 - 20*a*b^4*d*e^4 + 15*a^2*b^3*e^5)*x^3 + 30*(16*b^5*d^3*e^2 - 40*a*b^4*d^2*e^3 + 30*a^2*b^3*d*e^4 - 5*a^3*b^2*e^5)*x^2 + 5*(128*b^5*d^4*e - 320*a*b^4*d^3*e^2 + 240*a^2*b^3*d^2*e^3 - 40*a^3*b^2*d*e^4 - 5*a^4*b*e^5)*x)*sqrt(e*x + d)/(e^9*x^3 + 3*d*e^8*x^2 + 3*d^2*e^7*x + d^3*e^6)","A",0
1699,1,304,0,0.397585," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b^{5} e^{5} x^{5} - 256 \, b^{5} d^{5} + 384 \, a b^{4} d^{4} e - 96 \, a^{2} b^{3} d^{3} e^{2} - 16 \, a^{3} b^{2} d^{2} e^{3} - 6 \, a^{4} b d e^{4} - 3 \, a^{5} e^{5} - 35 \, {\left(2 \, b^{5} d e^{4} - 3 \, a b^{4} e^{5}\right)} x^{4} - 70 \, {\left(8 \, b^{5} d^{2} e^{3} - 12 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} - 70 \, {\left(16 \, b^{5} d^{3} e^{2} - 24 \, a b^{4} d^{2} e^{3} + 6 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} x^{2} - 7 \, {\left(128 \, b^{5} d^{4} e - 192 \, a b^{4} d^{3} e^{2} + 48 \, a^{2} b^{3} d^{2} e^{3} + 8 \, a^{3} b^{2} d e^{4} + 3 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{21 \, {\left(e^{10} x^{4} + 4 \, d e^{9} x^{3} + 6 \, d^{2} e^{8} x^{2} + 4 \, d^{3} e^{7} x + d^{4} e^{6}\right)}}"," ",0,"2/21*(7*b^5*e^5*x^5 - 256*b^5*d^5 + 384*a*b^4*d^4*e - 96*a^2*b^3*d^3*e^2 - 16*a^3*b^2*d^2*e^3 - 6*a^4*b*d*e^4 - 3*a^5*e^5 - 35*(2*b^5*d*e^4 - 3*a*b^4*e^5)*x^4 - 70*(8*b^5*d^2*e^3 - 12*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 - 70*(16*b^5*d^3*e^2 - 24*a*b^4*d^2*e^3 + 6*a^2*b^3*d*e^4 + a^3*b^2*e^5)*x^2 - 7*(128*b^5*d^4*e - 192*a*b^4*d^3*e^2 + 48*a^2*b^3*d^2*e^3 + 8*a^3*b^2*d*e^4 + 3*a^4*b*e^5)*x)*sqrt(e*x + d)/(e^10*x^4 + 4*d*e^9*x^3 + 6*d^2*e^8*x^2 + 4*d^3*e^7*x + d^4*e^6)","A",0
1700,1,316,0,0.402103," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, b^{5} e^{5} x^{5} + 256 \, b^{5} d^{5} - 128 \, a b^{4} d^{4} e - 32 \, a^{2} b^{3} d^{3} e^{2} - 16 \, a^{3} b^{2} d^{2} e^{3} - 10 \, a^{4} b d e^{4} - 7 \, a^{5} e^{5} + 315 \, {\left(2 \, b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 210 \, {\left(8 \, b^{5} d^{2} e^{3} - 4 \, a b^{4} d e^{4} - a^{2} b^{3} e^{5}\right)} x^{3} + 126 \, {\left(16 \, b^{5} d^{3} e^{2} - 8 \, a b^{4} d^{2} e^{3} - 2 \, a^{2} b^{3} d e^{4} - a^{3} b^{2} e^{5}\right)} x^{2} + 9 \, {\left(128 \, b^{5} d^{4} e - 64 \, a b^{4} d^{3} e^{2} - 16 \, a^{2} b^{3} d^{2} e^{3} - 8 \, a^{3} b^{2} d e^{4} - 5 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{63 \, {\left(e^{11} x^{5} + 5 \, d e^{10} x^{4} + 10 \, d^{2} e^{9} x^{3} + 10 \, d^{3} e^{8} x^{2} + 5 \, d^{4} e^{7} x + d^{5} e^{6}\right)}}"," ",0,"2/63*(63*b^5*e^5*x^5 + 256*b^5*d^5 - 128*a*b^4*d^4*e - 32*a^2*b^3*d^3*e^2 - 16*a^3*b^2*d^2*e^3 - 10*a^4*b*d*e^4 - 7*a^5*e^5 + 315*(2*b^5*d*e^4 - a*b^4*e^5)*x^4 + 210*(8*b^5*d^2*e^3 - 4*a*b^4*d*e^4 - a^2*b^3*e^5)*x^3 + 126*(16*b^5*d^3*e^2 - 8*a*b^4*d^2*e^3 - 2*a^2*b^3*d*e^4 - a^3*b^2*e^5)*x^2 + 9*(128*b^5*d^4*e - 64*a*b^4*d^3*e^2 - 16*a^2*b^3*d^2*e^3 - 8*a^3*b^2*d*e^4 - 5*a^4*b*e^5)*x)*sqrt(e*x + d)/(e^11*x^5 + 5*d*e^10*x^4 + 10*d^2*e^9*x^3 + 10*d^3*e^8*x^2 + 5*d^4*e^7*x + d^5*e^6)","A",0
1701,1,326,0,0.405334," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(13/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(693 \, b^{5} e^{5} x^{5} + 256 \, b^{5} d^{5} + 128 \, a b^{4} d^{4} e + 96 \, a^{2} b^{3} d^{3} e^{2} + 80 \, a^{3} b^{2} d^{2} e^{3} + 70 \, a^{4} b d e^{4} + 63 \, a^{5} e^{5} + 1155 \, {\left(2 \, b^{5} d e^{4} + a b^{4} e^{5}\right)} x^{4} + 462 \, {\left(8 \, b^{5} d^{2} e^{3} + 4 \, a b^{4} d e^{4} + 3 \, a^{2} b^{3} e^{5}\right)} x^{3} + 198 \, {\left(16 \, b^{5} d^{3} e^{2} + 8 \, a b^{4} d^{2} e^{3} + 6 \, a^{2} b^{3} d e^{4} + 5 \, a^{3} b^{2} e^{5}\right)} x^{2} + 11 \, {\left(128 \, b^{5} d^{4} e + 64 \, a b^{4} d^{3} e^{2} + 48 \, a^{2} b^{3} d^{2} e^{3} + 40 \, a^{3} b^{2} d e^{4} + 35 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{693 \, {\left(e^{12} x^{6} + 6 \, d e^{11} x^{5} + 15 \, d^{2} e^{10} x^{4} + 20 \, d^{3} e^{9} x^{3} + 15 \, d^{4} e^{8} x^{2} + 6 \, d^{5} e^{7} x + d^{6} e^{6}\right)}}"," ",0,"-2/693*(693*b^5*e^5*x^5 + 256*b^5*d^5 + 128*a*b^4*d^4*e + 96*a^2*b^3*d^3*e^2 + 80*a^3*b^2*d^2*e^3 + 70*a^4*b*d*e^4 + 63*a^5*e^5 + 1155*(2*b^5*d*e^4 + a*b^4*e^5)*x^4 + 462*(8*b^5*d^2*e^3 + 4*a*b^4*d*e^4 + 3*a^2*b^3*e^5)*x^3 + 198*(16*b^5*d^3*e^2 + 8*a*b^4*d^2*e^3 + 6*a^2*b^3*d*e^4 + 5*a^3*b^2*e^5)*x^2 + 11*(128*b^5*d^4*e + 64*a*b^4*d^3*e^2 + 48*a^2*b^3*d^2*e^3 + 40*a^3*b^2*d*e^4 + 35*a^4*b*e^5)*x)*sqrt(e*x + d)/(e^12*x^6 + 6*d*e^11*x^5 + 15*d^2*e^10*x^4 + 20*d^3*e^9*x^3 + 15*d^4*e^8*x^2 + 6*d^5*e^7*x + d^6*e^6)","A",0
1702,1,338,0,0.404703," ","integrate((b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(15/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3003 \, b^{5} e^{5} x^{5} + 256 \, b^{5} d^{5} + 384 \, a b^{4} d^{4} e + 480 \, a^{2} b^{3} d^{3} e^{2} + 560 \, a^{3} b^{2} d^{2} e^{3} + 630 \, a^{4} b d e^{4} + 693 \, a^{5} e^{5} + 3003 \, {\left(2 \, b^{5} d e^{4} + 3 \, a b^{4} e^{5}\right)} x^{4} + 858 \, {\left(8 \, b^{5} d^{2} e^{3} + 12 \, a b^{4} d e^{4} + 15 \, a^{2} b^{3} e^{5}\right)} x^{3} + 286 \, {\left(16 \, b^{5} d^{3} e^{2} + 24 \, a b^{4} d^{2} e^{3} + 30 \, a^{2} b^{3} d e^{4} + 35 \, a^{3} b^{2} e^{5}\right)} x^{2} + 13 \, {\left(128 \, b^{5} d^{4} e + 192 \, a b^{4} d^{3} e^{2} + 240 \, a^{2} b^{3} d^{2} e^{3} + 280 \, a^{3} b^{2} d e^{4} + 315 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{9009 \, {\left(e^{13} x^{7} + 7 \, d e^{12} x^{6} + 21 \, d^{2} e^{11} x^{5} + 35 \, d^{3} e^{10} x^{4} + 35 \, d^{4} e^{9} x^{3} + 21 \, d^{5} e^{8} x^{2} + 7 \, d^{6} e^{7} x + d^{7} e^{6}\right)}}"," ",0,"-2/9009*(3003*b^5*e^5*x^5 + 256*b^5*d^5 + 384*a*b^4*d^4*e + 480*a^2*b^3*d^3*e^2 + 560*a^3*b^2*d^2*e^3 + 630*a^4*b*d*e^4 + 693*a^5*e^5 + 3003*(2*b^5*d*e^4 + 3*a*b^4*e^5)*x^4 + 858*(8*b^5*d^2*e^3 + 12*a*b^4*d*e^4 + 15*a^2*b^3*e^5)*x^3 + 286*(16*b^5*d^3*e^2 + 24*a*b^4*d^2*e^3 + 30*a^2*b^3*d*e^4 + 35*a^3*b^2*e^5)*x^2 + 13*(128*b^5*d^4*e + 192*a*b^4*d^3*e^2 + 240*a^2*b^3*d^2*e^3 + 280*a^3*b^2*d*e^4 + 315*a^4*b*e^5)*x)*sqrt(e*x + d)/(e^13*x^7 + 7*d*e^12*x^6 + 21*d^2*e^11*x^5 + 35*d^3*e^10*x^4 + 35*d^4*e^9*x^3 + 21*d^5*e^8*x^2 + 7*d^6*e^7*x + d^7*e^6)","A",0
1703,1,424,0,0.426233," ","integrate((e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\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{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(15 \, b^{3} e^{3} x^{3} + 176 \, b^{3} d^{3} - 406 \, a b^{2} d^{2} e + 350 \, a^{2} b d e^{2} - 105 \, a^{3} e^{3} + 3 \, {\left(22 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} + {\left(122 \, b^{3} d^{2} e - 112 \, a b^{2} d e^{2} + 35 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, b^{4}}, -\frac{2 \, {\left(105 \, {\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{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(15 \, b^{3} e^{3} x^{3} + 176 \, b^{3} d^{3} - 406 \, a b^{2} d^{2} e + 350 \, a^{2} b d e^{2} - 105 \, a^{3} e^{3} + 3 \, {\left(22 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} + {\left(122 \, b^{3} d^{2} e - 112 \, a b^{2} d e^{2} + 35 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{105 \, b^{4}}\right]"," ",0,"[-1/105*(105*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(15*b^3*e^3*x^3 + 176*b^3*d^3 - 406*a*b^2*d^2*e + 350*a^2*b*d*e^2 - 105*a^3*e^3 + 3*(22*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 + (122*b^3*d^2*e - 112*a*b^2*d*e^2 + 35*a^2*b*e^3)*x)*sqrt(e*x + d))/b^4, -2/105*(105*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (15*b^3*e^3*x^3 + 176*b^3*d^3 - 406*a*b^2*d^2*e + 350*a^2*b*d*e^2 - 105*a^3*e^3 + 3*(22*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 + (122*b^3*d^2*e - 112*a*b^2*d*e^2 + 35*a^2*b*e^3)*x)*sqrt(e*x + d))/b^4]","A",0
1704,1,290,0,0.419499," ","integrate((e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(3 \, b^{2} e^{2} x^{2} + 23 \, b^{2} d^{2} - 35 \, a b d e + 15 \, a^{2} e^{2} + {\left(11 \, b^{2} d e - 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, b^{3}}, -\frac{2 \, {\left(15 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(3 \, b^{2} e^{2} x^{2} + 23 \, b^{2} d^{2} - 35 \, a b d e + 15 \, a^{2} e^{2} + {\left(11 \, b^{2} d e - 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, b^{3}}\right]"," ",0,"[1/15*(15*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(3*b^2*e^2*x^2 + 23*b^2*d^2 - 35*a*b*d*e + 15*a^2*e^2 + (11*b^2*d*e - 5*a*b*e^2)*x)*sqrt(e*x + d))/b^3, -2/15*(15*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (3*b^2*e^2*x^2 + 23*b^2*d^2 - 35*a*b*d*e + 15*a^2*e^2 + (11*b^2*d*e - 5*a*b*e^2)*x)*sqrt(e*x + d))/b^3]","A",0
1705,1,188,0,0.422637," ","integrate((e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b d - a e\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(b e x + 4 \, b d - 3 \, a e\right)} \sqrt{e x + d}}{3 \, b^{2}}, -\frac{2 \, {\left(3 \, {\left(b d - a e\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(b e x + 4 \, b d - 3 \, a e\right)} \sqrt{e x + d}\right)}}{3 \, b^{2}}\right]"," ",0,"[-1/3*(3*(b*d - a*e)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(b*e*x + 4*b*d - 3*a*e)*sqrt(e*x + d))/b^2, -2/3*(3*(b*d - a*e)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (b*e*x + 4*b*d - 3*a*e)*sqrt(e*x + d))/b^2]","A",0
1706,1,143,0,0.420689," ","integrate((e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, \sqrt{e x + d}}{b}, -\frac{2 \, {\left(\sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - \sqrt{e x + d}\right)}}{b}\right]"," ",0,"[(sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*sqrt(e*x + d))/b, -2*(sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - sqrt(e*x + d))/b]","A",0
1707,1,119,0,0.423329," ","integrate(1/(e*x+d)^(1/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right)}{\sqrt{b^{2} d - a b e}}, \frac{2 \, \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right)}{b^{2} d - a b e}\right]"," ",0,"[log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a))/sqrt(b^2*d - a*b*e), 2*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d))/(b^2*d - a*b*e)]","A",0
1708,1,214,0,0.425496," ","integrate(1/(e*x+d)^(3/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(e x + d\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, \sqrt{e x + d}}{b d^{2} - a d e + {\left(b d e - a e^{2}\right)} x}, -\frac{2 \, {\left({\left(e x + d\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - \sqrt{e x + d}\right)}}{b d^{2} - a d e + {\left(b d e - a e^{2}\right)} x}\right]"," ",0,"[-((e*x + d)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*sqrt(e*x + d))/(b*d^2 - a*d*e + (b*d*e - a*e^2)*x), -2*((e*x + d)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - sqrt(e*x + d))/(b*d^2 - a*d*e + (b*d*e - a*e^2)*x)]","A",0
1709,1,398,0,0.433686," ","integrate(1/(e*x+d)^(5/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b e^{2} x^{2} + 2 \, b d e x + b d^{2}\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(3 \, b e x + 4 \, b d - a e\right)} \sqrt{e x + d}}{3 \, {\left(b^{2} d^{4} - 2 \, a b d^{3} e + a^{2} d^{2} e^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e - 2 \, a b d^{2} e^{2} + a^{2} d e^{3}\right)} x\right)}}, -\frac{2 \, {\left(3 \, {\left(b e^{2} x^{2} + 2 \, b d e x + b d^{2}\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3 \, b e x + 4 \, b d - a e\right)} \sqrt{e x + d}\right)}}{3 \, {\left(b^{2} d^{4} - 2 \, a b d^{3} e + a^{2} d^{2} e^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e - 2 \, a b d^{2} e^{2} + a^{2} d e^{3}\right)} x\right)}}\right]"," ",0,"[1/3*(3*(b*e^2*x^2 + 2*b*d*e*x + b*d^2)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(3*b*e*x + 4*b*d - a*e)*sqrt(e*x + d))/(b^2*d^4 - 2*a*b*d^3*e + a^2*d^2*e^2 + (b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*x^2 + 2*(b^2*d^3*e - 2*a*b*d^2*e^2 + a^2*d*e^3)*x), -2/3*(3*(b*e^2*x^2 + 2*b*d*e*x + b*d^2)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3*b*e*x + 4*b*d - a*e)*sqrt(e*x + d))/(b^2*d^4 - 2*a*b*d^3*e + a^2*d^2*e^2 + (b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*x^2 + 2*(b^2*d^3*e - 2*a*b*d^2*e^2 + a^2*d*e^3)*x)]","A",0
1710,1,706,0,0.419421," ","integrate(1/(e*x+d)^(7/2)/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{2} e^{3} x^{3} + 3 \, b^{2} d e^{2} x^{2} + 3 \, b^{2} d^{2} e x + b^{2} d^{3}\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(15 \, b^{2} e^{2} x^{2} + 23 \, b^{2} d^{2} - 11 \, a b d e + 3 \, a^{2} e^{2} + 5 \, {\left(7 \, b^{2} d e - a b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(b^{3} d^{6} - 3 \, a b^{2} d^{5} e + 3 \, a^{2} b d^{4} e^{2} - a^{3} d^{3} e^{3} + {\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)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{2} - 3 \, a b^{2} d^{3} e^{3} + 3 \, a^{2} b d^{2} e^{4} - a^{3} d e^{5}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e - 3 \, a b^{2} d^{4} e^{2} + 3 \, a^{2} b d^{3} e^{3} - a^{3} d^{2} e^{4}\right)} x\right)}}, -\frac{2 \, {\left(15 \, {\left(b^{2} e^{3} x^{3} + 3 \, b^{2} d e^{2} x^{2} + 3 \, b^{2} d^{2} e x + b^{2} d^{3}\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(15 \, b^{2} e^{2} x^{2} + 23 \, b^{2} d^{2} - 11 \, a b d e + 3 \, a^{2} e^{2} + 5 \, {\left(7 \, b^{2} d e - a b e^{2}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, {\left(b^{3} d^{6} - 3 \, a b^{2} d^{5} e + 3 \, a^{2} b d^{4} e^{2} - a^{3} d^{3} e^{3} + {\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)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{2} - 3 \, a b^{2} d^{3} e^{3} + 3 \, a^{2} b d^{2} e^{4} - a^{3} d e^{5}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e - 3 \, a b^{2} d^{4} e^{2} + 3 \, a^{2} b d^{3} e^{3} - a^{3} d^{2} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/15*(15*(b^2*e^3*x^3 + 3*b^2*d*e^2*x^2 + 3*b^2*d^2*e*x + b^2*d^3)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(15*b^2*e^2*x^2 + 23*b^2*d^2 - 11*a*b*d*e + 3*a^2*e^2 + 5*(7*b^2*d*e - a*b*e^2)*x)*sqrt(e*x + d))/(b^3*d^6 - 3*a*b^2*d^5*e + 3*a^2*b*d^4*e^2 - a^3*d^3*e^3 + (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)*x^3 + 3*(b^3*d^4*e^2 - 3*a*b^2*d^3*e^3 + 3*a^2*b*d^2*e^4 - a^3*d*e^5)*x^2 + 3*(b^3*d^5*e - 3*a*b^2*d^4*e^2 + 3*a^2*b*d^3*e^3 - a^3*d^2*e^4)*x), -2/15*(15*(b^2*e^3*x^3 + 3*b^2*d*e^2*x^2 + 3*b^2*d^2*e*x + b^2*d^3)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (15*b^2*e^2*x^2 + 23*b^2*d^2 - 11*a*b*d*e + 3*a^2*e^2 + 5*(7*b^2*d*e - a*b*e^2)*x)*sqrt(e*x + d))/(b^3*d^6 - 3*a*b^2*d^5*e + 3*a^2*b*d^4*e^2 - a^3*d^3*e^3 + (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)*x^3 + 3*(b^3*d^4*e^2 - 3*a*b^2*d^3*e^3 + 3*a^2*b*d^2*e^4 - a^3*d*e^5)*x^2 + 3*(b^3*d^5*e - 3*a*b^2*d^4*e^2 + 3*a^2*b*d^3*e^3 - a^3*d^2*e^4)*x)]","B",0
1711,1,730,0,0.428830," ","integrate((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{2} b^{2} d^{2} e^{2} - 2 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} e^{2} - 2 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(8 \, b^{4} e^{4} x^{4} - 10 \, b^{4} d^{4} - 45 \, a b^{3} d^{3} e + 483 \, a^{2} b^{2} d^{2} e^{2} - 735 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} + 8 \, {\left(7 \, b^{4} d e^{3} - 3 \, a b^{3} e^{4}\right)} x^{3} + 24 \, {\left(12 \, b^{4} d^{2} e^{2} - 17 \, a b^{3} d e^{3} + 7 \, a^{2} b^{2} e^{4}\right)} x^{2} - {\left(85 \, b^{4} d^{3} e - 831 \, a b^{3} d^{2} e^{2} + 1239 \, a^{2} b^{2} d e^{3} - 525 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{40 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}, -\frac{315 \, {\left(a^{2} b^{2} d^{2} e^{2} - 2 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} d^{2} e^{2} - 2 \, a b^{3} d e^{3} + a^{2} b^{2} e^{4}\right)} x^{2} + 2 \, {\left(a b^{3} d^{2} e^{2} - 2 \, a^{2} b^{2} d e^{3} + a^{3} b e^{4}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(8 \, b^{4} e^{4} x^{4} - 10 \, b^{4} d^{4} - 45 \, a b^{3} d^{3} e + 483 \, a^{2} b^{2} d^{2} e^{2} - 735 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} + 8 \, {\left(7 \, b^{4} d e^{3} - 3 \, a b^{3} e^{4}\right)} x^{3} + 24 \, {\left(12 \, b^{4} d^{2} e^{2} - 17 \, a b^{3} d e^{3} + 7 \, a^{2} b^{2} e^{4}\right)} x^{2} - {\left(85 \, b^{4} d^{3} e - 831 \, a b^{3} d^{2} e^{2} + 1239 \, a^{2} b^{2} d e^{3} - 525 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{20 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}\right]"," ",0,"[1/40*(315*(a^2*b^2*d^2*e^2 - 2*a^3*b*d*e^3 + a^4*e^4 + (b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(a*b^3*d^2*e^2 - 2*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(8*b^4*e^4*x^4 - 10*b^4*d^4 - 45*a*b^3*d^3*e + 483*a^2*b^2*d^2*e^2 - 735*a^3*b*d*e^3 + 315*a^4*e^4 + 8*(7*b^4*d*e^3 - 3*a*b^3*e^4)*x^3 + 24*(12*b^4*d^2*e^2 - 17*a*b^3*d*e^3 + 7*a^2*b^2*e^4)*x^2 - (85*b^4*d^3*e - 831*a*b^3*d^2*e^2 + 1239*a^2*b^2*d*e^3 - 525*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5), -1/20*(315*(a^2*b^2*d^2*e^2 - 2*a^3*b*d*e^3 + a^4*e^4 + (b^4*d^2*e^2 - 2*a*b^3*d*e^3 + a^2*b^2*e^4)*x^2 + 2*(a*b^3*d^2*e^2 - 2*a^2*b^2*d*e^3 + a^3*b*e^4)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (8*b^4*e^4*x^4 - 10*b^4*d^4 - 45*a*b^3*d^3*e + 483*a^2*b^2*d^2*e^2 - 735*a^3*b*d*e^3 + 315*a^4*e^4 + 8*(7*b^4*d*e^3 - 3*a*b^3*e^4)*x^3 + 24*(12*b^4*d^2*e^2 - 17*a*b^3*d*e^3 + 7*a^2*b^2*e^4)*x^2 - (85*b^4*d^3*e - 831*a*b^3*d^2*e^2 + 1239*a^2*b^2*d*e^3 - 525*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)]","A",0
1712,1,520,0,0.418711," ","integrate((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{105 \, {\left(a^{2} b d e^{2} - a^{3} e^{3} + {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(a b^{2} d e^{2} - a^{2} b e^{3}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(8 \, b^{3} e^{3} x^{3} - 6 \, b^{3} d^{3} - 21 \, a b^{2} d^{2} e + 140 \, a^{2} b d e^{2} - 105 \, a^{3} e^{3} + 8 \, {\left(10 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} - {\left(39 \, b^{3} d^{2} e - 238 \, a b^{2} d e^{2} + 175 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, -\frac{105 \, {\left(a^{2} b d e^{2} - a^{3} e^{3} + {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{2} + 2 \, {\left(a b^{2} d e^{2} - a^{2} b e^{3}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(8 \, b^{3} e^{3} x^{3} - 6 \, b^{3} d^{3} - 21 \, a b^{2} d^{2} e + 140 \, a^{2} b d e^{2} - 105 \, a^{3} e^{3} + 8 \, {\left(10 \, b^{3} d e^{2} - 7 \, a b^{2} e^{3}\right)} x^{2} - {\left(39 \, b^{3} d^{2} e - 238 \, a b^{2} d e^{2} + 175 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[-1/24*(105*(a^2*b*d*e^2 - a^3*e^3 + (b^3*d*e^2 - a*b^2*e^3)*x^2 + 2*(a*b^2*d*e^2 - a^2*b*e^3)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(8*b^3*e^3*x^3 - 6*b^3*d^3 - 21*a*b^2*d^2*e + 140*a^2*b*d*e^2 - 105*a^3*e^3 + 8*(10*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 - (39*b^3*d^2*e - 238*a*b^2*d*e^2 + 175*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), -1/12*(105*(a^2*b*d*e^2 - a^3*e^3 + (b^3*d*e^2 - a*b^2*e^3)*x^2 + 2*(a*b^2*d*e^2 - a^2*b*e^3)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (8*b^3*e^3*x^3 - 6*b^3*d^3 - 21*a*b^2*d^2*e + 140*a^2*b*d*e^2 - 105*a^3*e^3 + 8*(10*b^3*d*e^2 - 7*a*b^2*e^3)*x^2 - (39*b^3*d^2*e - 238*a*b^2*d*e^2 + 175*a^2*b*e^3)*x)*sqrt(e*x + d))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
1713,1,344,0,0.432679," ","integrate((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(8 \, b^{2} e^{2} x^{2} - 2 \, b^{2} d^{2} - 5 \, a b d e + 15 \, a^{2} e^{2} - {\left(9 \, b^{2} d e - 25 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}, -\frac{15 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(8 \, b^{2} e^{2} x^{2} - 2 \, b^{2} d^{2} - 5 \, a b d e + 15 \, a^{2} e^{2} - {\left(9 \, b^{2} d e - 25 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}\right]"," ",0,"[1/8*(15*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(8*b^2*e^2*x^2 - 2*b^2*d^2 - 5*a*b*d*e + 15*a^2*e^2 - (9*b^2*d*e - 25*a*b*e^2)*x)*sqrt(e*x + d))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3), -1/4*(15*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (8*b^2*e^2*x^2 - 2*b^2*d^2 - 5*a*b*d*e + 15*a^2*e^2 - (9*b^2*d*e - 25*a*b*e^2)*x)*sqrt(e*x + d))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)]","A",0
1714,1,383,0,0.432714," ","integrate((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(2 \, b^{3} d^{2} + a b^{2} d e - 3 \, a^{2} b e^{2} + 5 \, {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{4} d - a^{3} b^{3} e + {\left(b^{6} d - a b^{5} e\right)} x^{2} + 2 \, {\left(a b^{5} d - a^{2} b^{4} e\right)} x\right)}}, \frac{3 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(2 \, b^{3} d^{2} + a b^{2} d e - 3 \, a^{2} b e^{2} + 5 \, {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{4} d - a^{3} b^{3} e + {\left(b^{6} d - a b^{5} e\right)} x^{2} + 2 \, {\left(a b^{5} d - a^{2} b^{4} e\right)} x\right)}}\right]"," ",0,"[1/8*(3*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(2*b^3*d^2 + a*b^2*d*e - 3*a^2*b*e^2 + 5*(b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d - a^3*b^3*e + (b^6*d - a*b^5*e)*x^2 + 2*(a*b^5*d - a^2*b^4*e)*x), 1/4*(3*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (2*b^3*d^2 + a*b^2*d*e - 3*a^2*b*e^2 + 5*(b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d - a^3*b^3*e + (b^6*d - a*b^5*e)*x^2 + 2*(a*b^5*d - a^2*b^4*e)*x)]","A",0
1715,1,456,0,0.428592," ","integrate((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(2 \, b^{3} d^{2} - 3 \, a b^{2} d e + a^{2} b e^{2} + {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{4} d^{2} - 2 \, a^{3} b^{3} d e + a^{4} b^{2} e^{2} + {\left(b^{6} d^{2} - 2 \, a b^{5} d e + a^{2} b^{4} e^{2}\right)} x^{2} + 2 \, {\left(a b^{5} d^{2} - 2 \, a^{2} b^{4} d e + a^{3} b^{3} e^{2}\right)} x\right)}}, -\frac{{\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(2 \, b^{3} d^{2} - 3 \, a b^{2} d e + a^{2} b e^{2} + {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{4} d^{2} - 2 \, a^{3} b^{3} d e + a^{4} b^{2} e^{2} + {\left(b^{6} d^{2} - 2 \, a b^{5} d e + a^{2} b^{4} e^{2}\right)} x^{2} + 2 \, {\left(a b^{5} d^{2} - 2 \, a^{2} b^{4} d e + a^{3} b^{3} e^{2}\right)} x\right)}}\right]"," ",0,"[-1/8*((b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(2*b^3*d^2 - 3*a*b^2*d*e + a^2*b*e^2 + (b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d^2 - 2*a^3*b^3*d*e + a^4*b^2*e^2 + (b^6*d^2 - 2*a*b^5*d*e + a^2*b^4*e^2)*x^2 + 2*(a*b^5*d^2 - 2*a^2*b^4*d*e + a^3*b^3*e^2)*x), -1/4*((b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (2*b^3*d^2 - 3*a*b^2*d*e + a^2*b*e^2 + (b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d^2 - 2*a^3*b^3*d*e + a^4*b^2*e^2 + (b^6*d^2 - 2*a*b^5*d*e + a^2*b^4*e^2)*x^2 + 2*(a*b^5*d^2 - 2*a^2*b^4*d*e + a^3*b^3*e^2)*x)]","A",0
1716,1,549,0,0.424520," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(2 \, b^{3} d^{2} - 7 \, a b^{2} d e + 5 \, a^{2} b e^{2} - 3 \, {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{4} d^{3} - 3 \, a^{3} b^{3} d^{2} e + 3 \, a^{4} b^{2} d e^{2} - a^{5} b e^{3} + {\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)} x^{2} + 2 \, {\left(a b^{5} d^{3} - 3 \, a^{2} b^{4} d^{2} e + 3 \, a^{3} b^{3} d e^{2} - a^{4} b^{2} e^{3}\right)} x\right)}}, \frac{3 \, {\left(b^{2} e^{2} x^{2} + 2 \, a b e^{2} x + a^{2} e^{2}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(2 \, b^{3} d^{2} - 7 \, a b^{2} d e + 5 \, a^{2} b e^{2} - 3 \, {\left(b^{3} d e - a b^{2} e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{4} d^{3} - 3 \, a^{3} b^{3} d^{2} e + 3 \, a^{4} b^{2} d e^{2} - a^{5} b e^{3} + {\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)} x^{2} + 2 \, {\left(a b^{5} d^{3} - 3 \, a^{2} b^{4} d^{2} e + 3 \, a^{3} b^{3} d e^{2} - a^{4} b^{2} e^{3}\right)} x\right)}}\right]"," ",0,"[1/8*(3*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(2*b^3*d^2 - 7*a*b^2*d*e + 5*a^2*b*e^2 - 3*(b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d^3 - 3*a^3*b^3*d^2*e + 3*a^4*b^2*d*e^2 - a^5*b*e^3 + (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)*x^2 + 2*(a*b^5*d^3 - 3*a^2*b^4*d^2*e + 3*a^3*b^3*d*e^2 - a^4*b^2*e^3)*x), 1/4*(3*(b^2*e^2*x^2 + 2*a*b*e^2*x + a^2*e^2)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (2*b^3*d^2 - 7*a*b^2*d*e + 5*a^2*b*e^2 - 3*(b^3*d*e - a*b^2*e^2)*x)*sqrt(e*x + d))/(a^2*b^4*d^3 - 3*a^3*b^3*d^2*e + 3*a^4*b^2*d*e^2 - a^5*b*e^3 + (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)*x^2 + 2*(a*b^5*d^3 - 3*a^2*b^4*d^2*e + 3*a^3*b^3*d*e^2 - a^4*b^2*e^3)*x)]","B",0
1717,1,782,0,0.441900," ","integrate(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{2} e^{3} x^{3} + a^{2} d e^{2} + {\left(b^{2} d e^{2} + 2 \, a b e^{3}\right)} x^{2} + {\left(2 \, a b d e^{2} + a^{2} e^{3}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(15 \, b^{2} e^{2} x^{2} - 2 \, b^{2} d^{2} + 9 \, a b d e + 8 \, a^{2} e^{2} + 5 \, {\left(b^{2} d e + 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{3} d^{4} - 3 \, a^{3} b^{2} d^{3} e + 3 \, a^{4} b d^{2} e^{2} - a^{5} d e^{3} + {\left(b^{5} d^{3} e - 3 \, a b^{4} d^{2} e^{2} + 3 \, a^{2} b^{3} d e^{3} - a^{3} b^{2} e^{4}\right)} x^{3} + {\left(b^{5} d^{4} - a b^{4} d^{3} e - 3 \, a^{2} b^{3} d^{2} e^{2} + 5 \, a^{3} b^{2} d e^{3} - 2 \, a^{4} b e^{4}\right)} x^{2} + {\left(2 \, a b^{4} d^{4} - 5 \, a^{2} b^{3} d^{3} e + 3 \, a^{3} b^{2} d^{2} e^{2} + a^{4} b d e^{3} - a^{5} e^{4}\right)} x\right)}}, -\frac{15 \, {\left(b^{2} e^{3} x^{3} + a^{2} d e^{2} + {\left(b^{2} d e^{2} + 2 \, a b e^{3}\right)} x^{2} + {\left(2 \, a b d e^{2} + a^{2} e^{3}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(15 \, b^{2} e^{2} x^{2} - 2 \, b^{2} d^{2} + 9 \, a b d e + 8 \, a^{2} e^{2} + 5 \, {\left(b^{2} d e + 5 \, a b e^{2}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} b^{3} d^{4} - 3 \, a^{3} b^{2} d^{3} e + 3 \, a^{4} b d^{2} e^{2} - a^{5} d e^{3} + {\left(b^{5} d^{3} e - 3 \, a b^{4} d^{2} e^{2} + 3 \, a^{2} b^{3} d e^{3} - a^{3} b^{2} e^{4}\right)} x^{3} + {\left(b^{5} d^{4} - a b^{4} d^{3} e - 3 \, a^{2} b^{3} d^{2} e^{2} + 5 \, a^{3} b^{2} d e^{3} - 2 \, a^{4} b e^{4}\right)} x^{2} + {\left(2 \, a b^{4} d^{4} - 5 \, a^{2} b^{3} d^{3} e + 3 \, a^{3} b^{2} d^{2} e^{2} + a^{4} b d e^{3} - a^{5} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/8*(15*(b^2*e^3*x^3 + a^2*d*e^2 + (b^2*d*e^2 + 2*a*b*e^3)*x^2 + (2*a*b*d*e^2 + a^2*e^3)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(15*b^2*e^2*x^2 - 2*b^2*d^2 + 9*a*b*d*e + 8*a^2*e^2 + 5*(b^2*d*e + 5*a*b*e^2)*x)*sqrt(e*x + d))/(a^2*b^3*d^4 - 3*a^3*b^2*d^3*e + 3*a^4*b*d^2*e^2 - a^5*d*e^3 + (b^5*d^3*e - 3*a*b^4*d^2*e^2 + 3*a^2*b^3*d*e^3 - a^3*b^2*e^4)*x^3 + (b^5*d^4 - a*b^4*d^3*e - 3*a^2*b^3*d^2*e^2 + 5*a^3*b^2*d*e^3 - 2*a^4*b*e^4)*x^2 + (2*a*b^4*d^4 - 5*a^2*b^3*d^3*e + 3*a^3*b^2*d^2*e^2 + a^4*b*d*e^3 - a^5*e^4)*x), -1/4*(15*(b^2*e^3*x^3 + a^2*d*e^2 + (b^2*d*e^2 + 2*a*b*e^3)*x^2 + (2*a*b*d*e^2 + a^2*e^3)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (15*b^2*e^2*x^2 - 2*b^2*d^2 + 9*a*b*d*e + 8*a^2*e^2 + 5*(b^2*d*e + 5*a*b*e^2)*x)*sqrt(e*x + d))/(a^2*b^3*d^4 - 3*a^3*b^2*d^3*e + 3*a^4*b*d^2*e^2 - a^5*d*e^3 + (b^5*d^3*e - 3*a*b^4*d^2*e^2 + 3*a^2*b^3*d*e^3 - a^3*b^2*e^4)*x^3 + (b^5*d^4 - a*b^4*d^3*e - 3*a^2*b^3*d^2*e^2 + 5*a^3*b^2*d*e^3 - 2*a^4*b*e^4)*x^2 + (2*a*b^4*d^4 - 5*a^2*b^3*d^3*e + 3*a^3*b^2*d^2*e^2 + a^4*b*d*e^3 - a^5*e^4)*x)]","B",0
1718,1,1226,0,0.448603," ","integrate(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} e^{4} x^{4} + a^{2} b d^{2} e^{2} + 2 \, {\left(b^{3} d e^{3} + a b^{2} e^{4}\right)} x^{3} + {\left(b^{3} d^{2} e^{2} + 4 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)} x^{2} + 2 \, {\left(a b^{2} d^{2} e^{2} + a^{2} b d e^{3}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(105 \, b^{3} e^{3} x^{3} - 6 \, b^{3} d^{3} + 39 \, a b^{2} d^{2} e + 80 \, a^{2} b d e^{2} - 8 \, a^{3} e^{3} + 35 \, {\left(4 \, b^{3} d e^{2} + 5 \, a b^{2} e^{3}\right)} x^{2} + 7 \, {\left(3 \, b^{3} d^{2} e + 34 \, a b^{2} d e^{2} + 8 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{2} b^{4} d^{6} - 4 \, a^{3} b^{3} d^{5} e + 6 \, a^{4} b^{2} d^{4} e^{2} - 4 \, a^{5} b d^{3} e^{3} + a^{6} d^{2} e^{4} + {\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^{4} + 2 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 2 \, a^{2} b^{4} d^{3} e^{3} + 2 \, a^{3} b^{3} d^{2} e^{4} - 3 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x^{3} + {\left(b^{6} d^{6} - 9 \, a^{2} b^{4} d^{4} e^{2} + 16 \, a^{3} b^{3} d^{3} e^{3} - 9 \, a^{4} b^{2} d^{2} e^{4} + a^{6} e^{6}\right)} x^{2} + 2 \, {\left(a b^{5} d^{6} - 3 \, a^{2} b^{4} d^{5} e + 2 \, a^{3} b^{3} d^{4} e^{2} + 2 \, a^{4} b^{2} d^{3} e^{3} - 3 \, a^{5} b d^{2} e^{4} + a^{6} d e^{5}\right)} x\right)}}, -\frac{105 \, {\left(b^{3} e^{4} x^{4} + a^{2} b d^{2} e^{2} + 2 \, {\left(b^{3} d e^{3} + a b^{2} e^{4}\right)} x^{3} + {\left(b^{3} d^{2} e^{2} + 4 \, a b^{2} d e^{3} + a^{2} b e^{4}\right)} x^{2} + 2 \, {\left(a b^{2} d^{2} e^{2} + a^{2} b d e^{3}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(105 \, b^{3} e^{3} x^{3} - 6 \, b^{3} d^{3} + 39 \, a b^{2} d^{2} e + 80 \, a^{2} b d e^{2} - 8 \, a^{3} e^{3} + 35 \, {\left(4 \, b^{3} d e^{2} + 5 \, a b^{2} e^{3}\right)} x^{2} + 7 \, {\left(3 \, b^{3} d^{2} e + 34 \, a b^{2} d e^{2} + 8 \, a^{2} b e^{3}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(a^{2} b^{4} d^{6} - 4 \, a^{3} b^{3} d^{5} e + 6 \, a^{4} b^{2} d^{4} e^{2} - 4 \, a^{5} b d^{3} e^{3} + a^{6} d^{2} e^{4} + {\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^{4} + 2 \, {\left(b^{6} d^{5} e - 3 \, a b^{5} d^{4} e^{2} + 2 \, a^{2} b^{4} d^{3} e^{3} + 2 \, a^{3} b^{3} d^{2} e^{4} - 3 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x^{3} + {\left(b^{6} d^{6} - 9 \, a^{2} b^{4} d^{4} e^{2} + 16 \, a^{3} b^{3} d^{3} e^{3} - 9 \, a^{4} b^{2} d^{2} e^{4} + a^{6} e^{6}\right)} x^{2} + 2 \, {\left(a b^{5} d^{6} - 3 \, a^{2} b^{4} d^{5} e + 2 \, a^{3} b^{3} d^{4} e^{2} + 2 \, a^{4} b^{2} d^{3} e^{3} - 3 \, a^{5} b d^{2} e^{4} + a^{6} d e^{5}\right)} x\right)}}\right]"," ",0,"[1/24*(105*(b^3*e^4*x^4 + a^2*b*d^2*e^2 + 2*(b^3*d*e^3 + a*b^2*e^4)*x^3 + (b^3*d^2*e^2 + 4*a*b^2*d*e^3 + a^2*b*e^4)*x^2 + 2*(a*b^2*d^2*e^2 + a^2*b*d*e^3)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(105*b^3*e^3*x^3 - 6*b^3*d^3 + 39*a*b^2*d^2*e + 80*a^2*b*d*e^2 - 8*a^3*e^3 + 35*(4*b^3*d*e^2 + 5*a*b^2*e^3)*x^2 + 7*(3*b^3*d^2*e + 34*a*b^2*d*e^2 + 8*a^2*b*e^3)*x)*sqrt(e*x + d))/(a^2*b^4*d^6 - 4*a^3*b^3*d^5*e + 6*a^4*b^2*d^4*e^2 - 4*a^5*b*d^3*e^3 + a^6*d^2*e^4 + (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^4 + 2*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 2*a^2*b^4*d^3*e^3 + 2*a^3*b^3*d^2*e^4 - 3*a^4*b^2*d*e^5 + a^5*b*e^6)*x^3 + (b^6*d^6 - 9*a^2*b^4*d^4*e^2 + 16*a^3*b^3*d^3*e^3 - 9*a^4*b^2*d^2*e^4 + a^6*e^6)*x^2 + 2*(a*b^5*d^6 - 3*a^2*b^4*d^5*e + 2*a^3*b^3*d^4*e^2 + 2*a^4*b^2*d^3*e^3 - 3*a^5*b*d^2*e^4 + a^6*d*e^5)*x), -1/12*(105*(b^3*e^4*x^4 + a^2*b*d^2*e^2 + 2*(b^3*d*e^3 + a*b^2*e^4)*x^3 + (b^3*d^2*e^2 + 4*a*b^2*d*e^3 + a^2*b*e^4)*x^2 + 2*(a*b^2*d^2*e^2 + a^2*b*d*e^3)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (105*b^3*e^3*x^3 - 6*b^3*d^3 + 39*a*b^2*d^2*e + 80*a^2*b*d*e^2 - 8*a^3*e^3 + 35*(4*b^3*d*e^2 + 5*a*b^2*e^3)*x^2 + 7*(3*b^3*d^2*e + 34*a*b^2*d*e^2 + 8*a^2*b*e^3)*x)*sqrt(e*x + d))/(a^2*b^4*d^6 - 4*a^3*b^3*d^5*e + 6*a^4*b^2*d^4*e^2 - 4*a^5*b*d^3*e^3 + a^6*d^2*e^4 + (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^4 + 2*(b^6*d^5*e - 3*a*b^5*d^4*e^2 + 2*a^2*b^4*d^3*e^3 + 2*a^3*b^3*d^2*e^4 - 3*a^4*b^2*d*e^5 + a^5*b*e^6)*x^3 + (b^6*d^6 - 9*a^2*b^4*d^4*e^2 + 16*a^3*b^3*d^3*e^3 - 9*a^4*b^2*d^2*e^4 + a^6*e^6)*x^2 + 2*(a*b^5*d^6 - 3*a^2*b^4*d^5*e + 2*a^3*b^3*d^4*e^2 + 2*a^4*b^2*d^3*e^3 - 3*a^5*b*d^2*e^4 + a^6*d*e^5)*x)]","B",0
1719,1,1858,0,0.456665," ","integrate(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{2} b^{2} d^{3} e^{2} + {\left(3 \, b^{4} d e^{4} + 2 \, a b^{3} e^{5}\right)} x^{4} + {\left(3 \, b^{4} d^{2} e^{3} + 6 \, a b^{3} d e^{4} + a^{2} b^{2} e^{5}\right)} x^{3} + {\left(b^{4} d^{3} e^{2} + 6 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4}\right)} x^{2} + {\left(2 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(315 \, b^{4} e^{4} x^{4} - 10 \, b^{4} d^{4} + 85 \, a b^{3} d^{3} e + 288 \, a^{2} b^{2} d^{2} e^{2} - 56 \, a^{3} b d e^{3} + 8 \, a^{4} e^{4} + 105 \, {\left(7 \, b^{4} d e^{3} + 5 \, a b^{3} e^{4}\right)} x^{3} + 21 \, {\left(23 \, b^{4} d^{2} e^{2} + 59 \, a b^{3} d e^{3} + 8 \, a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(15 \, b^{4} d^{3} e + 277 \, a b^{3} d^{2} e^{2} + 136 \, a^{2} b^{2} d e^{3} - 8 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{40 \, {\left(a^{2} b^{5} d^{8} - 5 \, a^{3} b^{4} d^{7} e + 10 \, a^{4} b^{3} d^{6} e^{2} - 10 \, a^{5} b^{2} d^{5} e^{3} + 5 \, a^{6} b d^{4} e^{4} - a^{7} d^{3} e^{5} + {\left(b^{7} d^{5} e^{3} - 5 \, a b^{6} d^{4} e^{4} + 10 \, a^{2} b^{5} d^{3} e^{5} - 10 \, a^{3} b^{4} d^{2} e^{6} + 5 \, a^{4} b^{3} d e^{7} - a^{5} b^{2} e^{8}\right)} x^{5} + {\left(3 \, b^{7} d^{6} e^{2} - 13 \, a b^{6} d^{5} e^{3} + 20 \, a^{2} b^{5} d^{4} e^{4} - 10 \, a^{3} b^{4} d^{3} e^{5} - 5 \, a^{4} b^{3} d^{2} e^{6} + 7 \, a^{5} b^{2} d e^{7} - 2 \, a^{6} b e^{8}\right)} x^{4} + {\left(3 \, b^{7} d^{7} e - 9 \, a b^{6} d^{6} e^{2} + a^{2} b^{5} d^{5} e^{3} + 25 \, a^{3} b^{4} d^{4} e^{4} - 35 \, a^{4} b^{3} d^{3} e^{5} + 17 \, a^{5} b^{2} d^{2} e^{6} - a^{6} b d e^{7} - a^{7} e^{8}\right)} x^{3} + {\left(b^{7} d^{8} + a b^{6} d^{7} e - 17 \, a^{2} b^{5} d^{6} e^{2} + 35 \, a^{3} b^{4} d^{5} e^{3} - 25 \, a^{4} b^{3} d^{4} e^{4} - a^{5} b^{2} d^{3} e^{5} + 9 \, a^{6} b d^{2} e^{6} - 3 \, a^{7} d e^{7}\right)} x^{2} + {\left(2 \, a b^{6} d^{8} - 7 \, a^{2} b^{5} d^{7} e + 5 \, a^{3} b^{4} d^{6} e^{2} + 10 \, a^{4} b^{3} d^{5} e^{3} - 20 \, a^{5} b^{2} d^{4} e^{4} + 13 \, a^{6} b d^{3} e^{5} - 3 \, a^{7} d^{2} e^{6}\right)} x\right)}}, -\frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{2} b^{2} d^{3} e^{2} + {\left(3 \, b^{4} d e^{4} + 2 \, a b^{3} e^{5}\right)} x^{4} + {\left(3 \, b^{4} d^{2} e^{3} + 6 \, a b^{3} d e^{4} + a^{2} b^{2} e^{5}\right)} x^{3} + {\left(b^{4} d^{3} e^{2} + 6 \, a b^{3} d^{2} e^{3} + 3 \, a^{2} b^{2} d e^{4}\right)} x^{2} + {\left(2 \, a b^{3} d^{3} e^{2} + 3 \, a^{2} b^{2} d^{2} e^{3}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(315 \, b^{4} e^{4} x^{4} - 10 \, b^{4} d^{4} + 85 \, a b^{3} d^{3} e + 288 \, a^{2} b^{2} d^{2} e^{2} - 56 \, a^{3} b d e^{3} + 8 \, a^{4} e^{4} + 105 \, {\left(7 \, b^{4} d e^{3} + 5 \, a b^{3} e^{4}\right)} x^{3} + 21 \, {\left(23 \, b^{4} d^{2} e^{2} + 59 \, a b^{3} d e^{3} + 8 \, a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(15 \, b^{4} d^{3} e + 277 \, a b^{3} d^{2} e^{2} + 136 \, a^{2} b^{2} d e^{3} - 8 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{20 \, {\left(a^{2} b^{5} d^{8} - 5 \, a^{3} b^{4} d^{7} e + 10 \, a^{4} b^{3} d^{6} e^{2} - 10 \, a^{5} b^{2} d^{5} e^{3} + 5 \, a^{6} b d^{4} e^{4} - a^{7} d^{3} e^{5} + {\left(b^{7} d^{5} e^{3} - 5 \, a b^{6} d^{4} e^{4} + 10 \, a^{2} b^{5} d^{3} e^{5} - 10 \, a^{3} b^{4} d^{2} e^{6} + 5 \, a^{4} b^{3} d e^{7} - a^{5} b^{2} e^{8}\right)} x^{5} + {\left(3 \, b^{7} d^{6} e^{2} - 13 \, a b^{6} d^{5} e^{3} + 20 \, a^{2} b^{5} d^{4} e^{4} - 10 \, a^{3} b^{4} d^{3} e^{5} - 5 \, a^{4} b^{3} d^{2} e^{6} + 7 \, a^{5} b^{2} d e^{7} - 2 \, a^{6} b e^{8}\right)} x^{4} + {\left(3 \, b^{7} d^{7} e - 9 \, a b^{6} d^{6} e^{2} + a^{2} b^{5} d^{5} e^{3} + 25 \, a^{3} b^{4} d^{4} e^{4} - 35 \, a^{4} b^{3} d^{3} e^{5} + 17 \, a^{5} b^{2} d^{2} e^{6} - a^{6} b d e^{7} - a^{7} e^{8}\right)} x^{3} + {\left(b^{7} d^{8} + a b^{6} d^{7} e - 17 \, a^{2} b^{5} d^{6} e^{2} + 35 \, a^{3} b^{4} d^{5} e^{3} - 25 \, a^{4} b^{3} d^{4} e^{4} - a^{5} b^{2} d^{3} e^{5} + 9 \, a^{6} b d^{2} e^{6} - 3 \, a^{7} d e^{7}\right)} x^{2} + {\left(2 \, a b^{6} d^{8} - 7 \, a^{2} b^{5} d^{7} e + 5 \, a^{3} b^{4} d^{6} e^{2} + 10 \, a^{4} b^{3} d^{5} e^{3} - 20 \, a^{5} b^{2} d^{4} e^{4} + 13 \, a^{6} b d^{3} e^{5} - 3 \, a^{7} d^{2} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/40*(315*(b^4*e^5*x^5 + a^2*b^2*d^3*e^2 + (3*b^4*d*e^4 + 2*a*b^3*e^5)*x^4 + (3*b^4*d^2*e^3 + 6*a*b^3*d*e^4 + a^2*b^2*e^5)*x^3 + (b^4*d^3*e^2 + 6*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4)*x^2 + (2*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(315*b^4*e^4*x^4 - 10*b^4*d^4 + 85*a*b^3*d^3*e + 288*a^2*b^2*d^2*e^2 - 56*a^3*b*d*e^3 + 8*a^4*e^4 + 105*(7*b^4*d*e^3 + 5*a*b^3*e^4)*x^3 + 21*(23*b^4*d^2*e^2 + 59*a*b^3*d*e^3 + 8*a^2*b^2*e^4)*x^2 + 3*(15*b^4*d^3*e + 277*a*b^3*d^2*e^2 + 136*a^2*b^2*d*e^3 - 8*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^2*b^5*d^8 - 5*a^3*b^4*d^7*e + 10*a^4*b^3*d^6*e^2 - 10*a^5*b^2*d^5*e^3 + 5*a^6*b*d^4*e^4 - a^7*d^3*e^5 + (b^7*d^5*e^3 - 5*a*b^6*d^4*e^4 + 10*a^2*b^5*d^3*e^5 - 10*a^3*b^4*d^2*e^6 + 5*a^4*b^3*d*e^7 - a^5*b^2*e^8)*x^5 + (3*b^7*d^6*e^2 - 13*a*b^6*d^5*e^3 + 20*a^2*b^5*d^4*e^4 - 10*a^3*b^4*d^3*e^5 - 5*a^4*b^3*d^2*e^6 + 7*a^5*b^2*d*e^7 - 2*a^6*b*e^8)*x^4 + (3*b^7*d^7*e - 9*a*b^6*d^6*e^2 + a^2*b^5*d^5*e^3 + 25*a^3*b^4*d^4*e^4 - 35*a^4*b^3*d^3*e^5 + 17*a^5*b^2*d^2*e^6 - a^6*b*d*e^7 - a^7*e^8)*x^3 + (b^7*d^8 + a*b^6*d^7*e - 17*a^2*b^5*d^6*e^2 + 35*a^3*b^4*d^5*e^3 - 25*a^4*b^3*d^4*e^4 - a^5*b^2*d^3*e^5 + 9*a^6*b*d^2*e^6 - 3*a^7*d*e^7)*x^2 + (2*a*b^6*d^8 - 7*a^2*b^5*d^7*e + 5*a^3*b^4*d^6*e^2 + 10*a^4*b^3*d^5*e^3 - 20*a^5*b^2*d^4*e^4 + 13*a^6*b*d^3*e^5 - 3*a^7*d^2*e^6)*x), -1/20*(315*(b^4*e^5*x^5 + a^2*b^2*d^3*e^2 + (3*b^4*d*e^4 + 2*a*b^3*e^5)*x^4 + (3*b^4*d^2*e^3 + 6*a*b^3*d*e^4 + a^2*b^2*e^5)*x^3 + (b^4*d^3*e^2 + 6*a*b^3*d^2*e^3 + 3*a^2*b^2*d*e^4)*x^2 + (2*a*b^3*d^3*e^2 + 3*a^2*b^2*d^2*e^3)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (315*b^4*e^4*x^4 - 10*b^4*d^4 + 85*a*b^3*d^3*e + 288*a^2*b^2*d^2*e^2 - 56*a^3*b*d*e^3 + 8*a^4*e^4 + 105*(7*b^4*d*e^3 + 5*a*b^3*e^4)*x^3 + 21*(23*b^4*d^2*e^2 + 59*a*b^3*d*e^3 + 8*a^2*b^2*e^4)*x^2 + 3*(15*b^4*d^3*e + 277*a*b^3*d^2*e^2 + 136*a^2*b^2*d*e^3 - 8*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^2*b^5*d^8 - 5*a^3*b^4*d^7*e + 10*a^4*b^3*d^6*e^2 - 10*a^5*b^2*d^5*e^3 + 5*a^6*b*d^4*e^4 - a^7*d^3*e^5 + (b^7*d^5*e^3 - 5*a*b^6*d^4*e^4 + 10*a^2*b^5*d^3*e^5 - 10*a^3*b^4*d^2*e^6 + 5*a^4*b^3*d*e^7 - a^5*b^2*e^8)*x^5 + (3*b^7*d^6*e^2 - 13*a*b^6*d^5*e^3 + 20*a^2*b^5*d^4*e^4 - 10*a^3*b^4*d^3*e^5 - 5*a^4*b^3*d^2*e^6 + 7*a^5*b^2*d*e^7 - 2*a^6*b*e^8)*x^4 + (3*b^7*d^7*e - 9*a*b^6*d^6*e^2 + a^2*b^5*d^5*e^3 + 25*a^3*b^4*d^4*e^4 - 35*a^4*b^3*d^3*e^5 + 17*a^5*b^2*d^2*e^6 - a^6*b*d*e^7 - a^7*e^8)*x^3 + (b^7*d^8 + a*b^6*d^7*e - 17*a^2*b^5*d^6*e^2 + 35*a^3*b^4*d^5*e^3 - 25*a^4*b^3*d^4*e^4 - a^5*b^2*d^3*e^5 + 9*a^6*b*d^2*e^6 - 3*a^7*d*e^7)*x^2 + (2*a*b^6*d^8 - 7*a^2*b^5*d^7*e + 5*a^3*b^4*d^6*e^2 + 10*a^4*b^3*d^5*e^3 - 20*a^5*b^2*d^4*e^4 + 13*a^6*b*d^3*e^5 - 3*a^7*d^2*e^6)*x)]","B",0
1720,1,1286,0,0.440100," ","integrate((e*x+d)^(13/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{45045 \, {\left(a^{4} b^{2} d^{2} e^{4} - 2 \, a^{5} b d e^{5} + a^{6} e^{6} + {\left(b^{6} d^{2} e^{4} - 2 \, a b^{5} d e^{5} + a^{2} b^{4} e^{6}\right)} x^{4} + 4 \, {\left(a b^{5} d^{2} e^{4} - 2 \, a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + 6 \, {\left(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} + 4 \, {\left(a^{3} b^{3} d^{2} e^{4} - 2 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(384 \, b^{6} e^{6} x^{6} - 240 \, b^{6} d^{6} - 520 \, a b^{5} d^{5} e - 1430 \, a^{2} b^{4} d^{4} e^{2} - 6435 \, a^{3} b^{3} d^{3} e^{3} + 69069 \, a^{4} b^{2} d^{2} e^{4} - 105105 \, a^{5} b d e^{5} + 45045 \, a^{6} e^{6} + 128 \, {\left(31 \, b^{6} d e^{5} - 13 \, a b^{5} e^{6}\right)} x^{5} + 128 \, {\left(253 \, b^{6} d^{2} e^{4} - 351 \, a b^{5} d e^{5} + 143 \, a^{2} b^{4} e^{6}\right)} x^{4} - {\left(22155 \, b^{6} d^{3} e^{3} - 196001 \, a b^{5} d^{2} e^{4} + 285857 \, a^{2} b^{4} d e^{5} - 119691 \, a^{3} b^{3} e^{6}\right)} x^{3} - {\left(7630 \, b^{6} d^{4} e^{2} + 35945 \, a b^{5} d^{3} e^{3} - 347919 \, a^{2} b^{4} d^{2} e^{4} + 517803 \, a^{3} b^{3} d e^{5} - 219219 \, a^{4} b^{2} e^{6}\right)} x^{2} - {\left(1960 \, b^{6} d^{5} e + 5460 \, a b^{5} d^{4} e^{2} + 25025 \, a^{2} b^{4} d^{3} e^{3} - 256971 \, a^{3} b^{3} d^{2} e^{4} + 387387 \, a^{4} b^{2} d e^{5} - 165165 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(b^{11} x^{4} + 4 \, a b^{10} x^{3} + 6 \, a^{2} b^{9} x^{2} + 4 \, a^{3} b^{8} x + a^{4} b^{7}\right)}}, -\frac{45045 \, {\left(a^{4} b^{2} d^{2} e^{4} - 2 \, a^{5} b d e^{5} + a^{6} e^{6} + {\left(b^{6} d^{2} e^{4} - 2 \, a b^{5} d e^{5} + a^{2} b^{4} e^{6}\right)} x^{4} + 4 \, {\left(a b^{5} d^{2} e^{4} - 2 \, a^{2} b^{4} d e^{5} + a^{3} b^{3} e^{6}\right)} x^{3} + 6 \, {\left(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} + 4 \, {\left(a^{3} b^{3} d^{2} e^{4} - 2 \, a^{4} b^{2} d e^{5} + a^{5} b e^{6}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(384 \, b^{6} e^{6} x^{6} - 240 \, b^{6} d^{6} - 520 \, a b^{5} d^{5} e - 1430 \, a^{2} b^{4} d^{4} e^{2} - 6435 \, a^{3} b^{3} d^{3} e^{3} + 69069 \, a^{4} b^{2} d^{2} e^{4} - 105105 \, a^{5} b d e^{5} + 45045 \, a^{6} e^{6} + 128 \, {\left(31 \, b^{6} d e^{5} - 13 \, a b^{5} e^{6}\right)} x^{5} + 128 \, {\left(253 \, b^{6} d^{2} e^{4} - 351 \, a b^{5} d e^{5} + 143 \, a^{2} b^{4} e^{6}\right)} x^{4} - {\left(22155 \, b^{6} d^{3} e^{3} - 196001 \, a b^{5} d^{2} e^{4} + 285857 \, a^{2} b^{4} d e^{5} - 119691 \, a^{3} b^{3} e^{6}\right)} x^{3} - {\left(7630 \, b^{6} d^{4} e^{2} + 35945 \, a b^{5} d^{3} e^{3} - 347919 \, a^{2} b^{4} d^{2} e^{4} + 517803 \, a^{3} b^{3} d e^{5} - 219219 \, a^{4} b^{2} e^{6}\right)} x^{2} - {\left(1960 \, b^{6} d^{5} e + 5460 \, a b^{5} d^{4} e^{2} + 25025 \, a^{2} b^{4} d^{3} e^{3} - 256971 \, a^{3} b^{3} d^{2} e^{4} + 387387 \, a^{4} b^{2} d e^{5} - 165165 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{960 \, {\left(b^{11} x^{4} + 4 \, a b^{10} x^{3} + 6 \, a^{2} b^{9} x^{2} + 4 \, a^{3} b^{8} x + a^{4} b^{7}\right)}}\right]"," ",0,"[1/1920*(45045*(a^4*b^2*d^2*e^4 - 2*a^5*b*d*e^5 + a^6*e^6 + (b^6*d^2*e^4 - 2*a*b^5*d*e^5 + a^2*b^4*e^6)*x^4 + 4*(a*b^5*d^2*e^4 - 2*a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^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 + 4*(a^3*b^3*d^2*e^4 - 2*a^4*b^2*d*e^5 + a^5*b*e^6)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(384*b^6*e^6*x^6 - 240*b^6*d^6 - 520*a*b^5*d^5*e - 1430*a^2*b^4*d^4*e^2 - 6435*a^3*b^3*d^3*e^3 + 69069*a^4*b^2*d^2*e^4 - 105105*a^5*b*d*e^5 + 45045*a^6*e^6 + 128*(31*b^6*d*e^5 - 13*a*b^5*e^6)*x^5 + 128*(253*b^6*d^2*e^4 - 351*a*b^5*d*e^5 + 143*a^2*b^4*e^6)*x^4 - (22155*b^6*d^3*e^3 - 196001*a*b^5*d^2*e^4 + 285857*a^2*b^4*d*e^5 - 119691*a^3*b^3*e^6)*x^3 - (7630*b^6*d^4*e^2 + 35945*a*b^5*d^3*e^3 - 347919*a^2*b^4*d^2*e^4 + 517803*a^3*b^3*d*e^5 - 219219*a^4*b^2*e^6)*x^2 - (1960*b^6*d^5*e + 5460*a*b^5*d^4*e^2 + 25025*a^2*b^4*d^3*e^3 - 256971*a^3*b^3*d^2*e^4 + 387387*a^4*b^2*d*e^5 - 165165*a^5*b*e^6)*x)*sqrt(e*x + d))/(b^11*x^4 + 4*a*b^10*x^3 + 6*a^2*b^9*x^2 + 4*a^3*b^8*x + a^4*b^7), -1/960*(45045*(a^4*b^2*d^2*e^4 - 2*a^5*b*d*e^5 + a^6*e^6 + (b^6*d^2*e^4 - 2*a*b^5*d*e^5 + a^2*b^4*e^6)*x^4 + 4*(a*b^5*d^2*e^4 - 2*a^2*b^4*d*e^5 + a^3*b^3*e^6)*x^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 + 4*(a^3*b^3*d^2*e^4 - 2*a^4*b^2*d*e^5 + a^5*b*e^6)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (384*b^6*e^6*x^6 - 240*b^6*d^6 - 520*a*b^5*d^5*e - 1430*a^2*b^4*d^4*e^2 - 6435*a^3*b^3*d^3*e^3 + 69069*a^4*b^2*d^2*e^4 - 105105*a^5*b*d*e^5 + 45045*a^6*e^6 + 128*(31*b^6*d*e^5 - 13*a*b^5*e^6)*x^5 + 128*(253*b^6*d^2*e^4 - 351*a*b^5*d*e^5 + 143*a^2*b^4*e^6)*x^4 - (22155*b^6*d^3*e^3 - 196001*a*b^5*d^2*e^4 + 285857*a^2*b^4*d*e^5 - 119691*a^3*b^3*e^6)*x^3 - (7630*b^6*d^4*e^2 + 35945*a*b^5*d^3*e^3 - 347919*a^2*b^4*d^2*e^4 + 517803*a^3*b^3*d*e^5 - 219219*a^4*b^2*e^6)*x^2 - (1960*b^6*d^5*e + 5460*a*b^5*d^4*e^2 + 25025*a^2*b^4*d^3*e^3 - 256971*a^3*b^3*d^2*e^4 + 387387*a^4*b^2*d*e^5 - 165165*a^5*b*e^6)*x)*sqrt(e*x + d))/(b^11*x^4 + 4*a*b^10*x^3 + 6*a^2*b^9*x^2 + 4*a^3*b^8*x + a^4*b^7)]","B",0
1721,1,968,0,0.441587," ","integrate((e*x+d)^(11/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3465 \, {\left(a^{4} b d e^{4} - a^{5} e^{5} + {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 4 \, {\left(a b^{4} d e^{4} - a^{2} b^{3} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{3} d e^{4} - a^{3} b^{2} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{2} d e^{4} - a^{4} b e^{5}\right)} x\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) - 2 \, {\left(128 \, b^{5} e^{5} x^{5} - 48 \, b^{5} d^{5} - 88 \, a b^{4} d^{4} e - 198 \, a^{2} b^{3} d^{3} e^{2} - 693 \, a^{3} b^{2} d^{2} e^{3} + 4620 \, a^{4} b d e^{4} - 3465 \, a^{5} e^{5} + 128 \, {\left(16 \, b^{5} d e^{4} - 11 \, a b^{4} e^{5}\right)} x^{4} - {\left(2295 \, b^{5} d^{2} e^{3} - 12782 \, a b^{4} d e^{4} + 9207 \, a^{2} b^{3} e^{5}\right)} x^{3} - {\left(1030 \, b^{5} d^{3} e^{2} + 3795 \, a b^{4} d^{2} e^{3} - 22968 \, a^{2} b^{3} d e^{4} + 16863 \, a^{3} b^{2} e^{5}\right)} x^{2} - {\left(328 \, b^{5} d^{4} e + 748 \, a b^{4} d^{3} e^{2} + 2673 \, a^{2} b^{3} d^{2} e^{3} - 17094 \, a^{3} b^{2} d e^{4} + 12705 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}, -\frac{3465 \, {\left(a^{4} b d e^{4} - a^{5} e^{5} + {\left(b^{5} d e^{4} - a b^{4} e^{5}\right)} x^{4} + 4 \, {\left(a b^{4} d e^{4} - a^{2} b^{3} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{3} d e^{4} - a^{3} b^{2} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{2} d e^{4} - a^{4} b e^{5}\right)} x\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(128 \, b^{5} e^{5} x^{5} - 48 \, b^{5} d^{5} - 88 \, a b^{4} d^{4} e - 198 \, a^{2} b^{3} d^{3} e^{2} - 693 \, a^{3} b^{2} d^{2} e^{3} + 4620 \, a^{4} b d e^{4} - 3465 \, a^{5} e^{5} + 128 \, {\left(16 \, b^{5} d e^{4} - 11 \, a b^{4} e^{5}\right)} x^{4} - {\left(2295 \, b^{5} d^{2} e^{3} - 12782 \, a b^{4} d e^{4} + 9207 \, a^{2} b^{3} e^{5}\right)} x^{3} - {\left(1030 \, b^{5} d^{3} e^{2} + 3795 \, a b^{4} d^{2} e^{3} - 22968 \, a^{2} b^{3} d e^{4} + 16863 \, a^{3} b^{2} e^{5}\right)} x^{2} - {\left(328 \, b^{5} d^{4} e + 748 \, a b^{4} d^{3} e^{2} + 2673 \, a^{2} b^{3} d^{2} e^{3} - 17094 \, a^{3} b^{2} d e^{4} + 12705 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(b^{10} x^{4} + 4 \, a b^{9} x^{3} + 6 \, a^{2} b^{8} x^{2} + 4 \, a^{3} b^{7} x + a^{4} b^{6}\right)}}\right]"," ",0,"[-1/384*(3465*(a^4*b*d*e^4 - a^5*e^5 + (b^5*d*e^4 - a*b^4*e^5)*x^4 + 4*(a*b^4*d*e^4 - a^2*b^3*e^5)*x^3 + 6*(a^2*b^3*d*e^4 - a^3*b^2*e^5)*x^2 + 4*(a^3*b^2*d*e^4 - a^4*b*e^5)*x)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e + 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) - 2*(128*b^5*e^5*x^5 - 48*b^5*d^5 - 88*a*b^4*d^4*e - 198*a^2*b^3*d^3*e^2 - 693*a^3*b^2*d^2*e^3 + 4620*a^4*b*d*e^4 - 3465*a^5*e^5 + 128*(16*b^5*d*e^4 - 11*a*b^4*e^5)*x^4 - (2295*b^5*d^2*e^3 - 12782*a*b^4*d*e^4 + 9207*a^2*b^3*e^5)*x^3 - (1030*b^5*d^3*e^2 + 3795*a*b^4*d^2*e^3 - 22968*a^2*b^3*d*e^4 + 16863*a^3*b^2*e^5)*x^2 - (328*b^5*d^4*e + 748*a*b^4*d^3*e^2 + 2673*a^2*b^3*d^2*e^3 - 17094*a^3*b^2*d*e^4 + 12705*a^4*b*e^5)*x)*sqrt(e*x + d))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6), -1/192*(3465*(a^4*b*d*e^4 - a^5*e^5 + (b^5*d*e^4 - a*b^4*e^5)*x^4 + 4*(a*b^4*d*e^4 - a^2*b^3*e^5)*x^3 + 6*(a^2*b^3*d*e^4 - a^3*b^2*e^5)*x^2 + 4*(a^3*b^2*d*e^4 - a^4*b*e^5)*x)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (128*b^5*e^5*x^5 - 48*b^5*d^5 - 88*a*b^4*d^4*e - 198*a^2*b^3*d^3*e^2 - 693*a^3*b^2*d^2*e^3 + 4620*a^4*b*d*e^4 - 3465*a^5*e^5 + 128*(16*b^5*d*e^4 - 11*a*b^4*e^5)*x^4 - (2295*b^5*d^2*e^3 - 12782*a*b^4*d*e^4 + 9207*a^2*b^3*e^5)*x^3 - (1030*b^5*d^3*e^2 + 3795*a*b^4*d^2*e^3 - 22968*a^2*b^3*d*e^4 + 16863*a^3*b^2*e^5)*x^2 - (328*b^5*d^4*e + 748*a*b^4*d^3*e^2 + 2673*a^2*b^3*d^2*e^3 - 17094*a^3*b^2*d*e^4 + 12705*a^4*b*e^5)*x)*sqrt(e*x + d))/(b^10*x^4 + 4*a*b^9*x^3 + 6*a^2*b^8*x^2 + 4*a^3*b^7*x + a^4*b^6)]","B",0
1722,1,680,0,0.429294," ","integrate((e*x+d)^(9/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{\frac{b d - a e}{b}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{e x + d} b \sqrt{\frac{b d - a e}{b}}}{b x + a}\right) + 2 \, {\left(128 \, b^{4} e^{4} x^{4} - 16 \, b^{4} d^{4} - 24 \, a b^{3} d^{3} e - 42 \, a^{2} b^{2} d^{2} e^{2} - 105 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} - {\left(325 \, b^{4} d e^{3} - 837 \, a b^{3} e^{4}\right)} x^{3} - 3 \, {\left(70 \, b^{4} d^{2} e^{2} + 185 \, a b^{3} d e^{3} - 511 \, a^{2} b^{2} e^{4}\right)} x^{2} - {\left(88 \, b^{4} d^{3} e + 156 \, a b^{3} d^{2} e^{2} + 399 \, a^{2} b^{2} d e^{3} - 1155 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{128 \, {\left(b^{9} x^{4} + 4 \, a b^{8} x^{3} + 6 \, a^{2} b^{7} x^{2} + 4 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}, -\frac{315 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-\frac{b d - a e}{b}} \arctan\left(-\frac{\sqrt{e x + d} b \sqrt{-\frac{b d - a e}{b}}}{b d - a e}\right) - {\left(128 \, b^{4} e^{4} x^{4} - 16 \, b^{4} d^{4} - 24 \, a b^{3} d^{3} e - 42 \, a^{2} b^{2} d^{2} e^{2} - 105 \, a^{3} b d e^{3} + 315 \, a^{4} e^{4} - {\left(325 \, b^{4} d e^{3} - 837 \, a b^{3} e^{4}\right)} x^{3} - 3 \, {\left(70 \, b^{4} d^{2} e^{2} + 185 \, a b^{3} d e^{3} - 511 \, a^{2} b^{2} e^{4}\right)} x^{2} - {\left(88 \, b^{4} d^{3} e + 156 \, a b^{3} d^{2} e^{2} + 399 \, a^{2} b^{2} d e^{3} - 1155 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(b^{9} x^{4} + 4 \, a b^{8} x^{3} + 6 \, a^{2} b^{7} x^{2} + 4 \, a^{3} b^{6} x + a^{4} b^{5}\right)}}\right]"," ",0,"[1/128*(315*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt((b*d - a*e)/b)*log((b*e*x + 2*b*d - a*e - 2*sqrt(e*x + d)*b*sqrt((b*d - a*e)/b))/(b*x + a)) + 2*(128*b^4*e^4*x^4 - 16*b^4*d^4 - 24*a*b^3*d^3*e - 42*a^2*b^2*d^2*e^2 - 105*a^3*b*d*e^3 + 315*a^4*e^4 - (325*b^4*d*e^3 - 837*a*b^3*e^4)*x^3 - 3*(70*b^4*d^2*e^2 + 185*a*b^3*d*e^3 - 511*a^2*b^2*e^4)*x^2 - (88*b^4*d^3*e + 156*a*b^3*d^2*e^2 + 399*a^2*b^2*d*e^3 - 1155*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^9*x^4 + 4*a*b^8*x^3 + 6*a^2*b^7*x^2 + 4*a^3*b^6*x + a^4*b^5), -1/64*(315*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-(b*d - a*e)/b)*arctan(-sqrt(e*x + d)*b*sqrt(-(b*d - a*e)/b)/(b*d - a*e)) - (128*b^4*e^4*x^4 - 16*b^4*d^4 - 24*a*b^3*d^3*e - 42*a^2*b^2*d^2*e^2 - 105*a^3*b*d*e^3 + 315*a^4*e^4 - (325*b^4*d*e^3 - 837*a*b^3*e^4)*x^3 - 3*(70*b^4*d^2*e^2 + 185*a*b^3*d*e^3 - 511*a^2*b^2*e^4)*x^2 - (88*b^4*d^3*e + 156*a*b^3*d^2*e^2 + 399*a^2*b^2*d*e^3 - 1155*a^3*b*e^4)*x)*sqrt(e*x + d))/(b^9*x^4 + 4*a*b^8*x^3 + 6*a^2*b^7*x^2 + 4*a^3*b^6*x + a^4*b^5)]","A",0
1723,1,765,0,0.443023," ","integrate((e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(48 \, b^{5} d^{4} + 8 \, a b^{4} d^{3} e + 14 \, a^{2} b^{3} d^{2} e^{2} + 35 \, a^{3} b^{2} d e^{3} - 105 \, a^{4} b e^{4} + 279 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(326 \, b^{5} d^{2} e^{2} + 185 \, a b^{4} d e^{3} - 511 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(200 \, b^{5} d^{3} e + 52 \, a b^{4} d^{2} e^{2} + 133 \, a^{2} b^{3} d e^{3} - 385 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d - a^{5} b^{5} e + {\left(b^{10} d - a b^{9} e\right)} x^{4} + 4 \, {\left(a b^{9} d - a^{2} b^{8} e\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d - a^{3} b^{7} e\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d - a^{4} b^{6} e\right)} x\right)}}, \frac{105 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(48 \, b^{5} d^{4} + 8 \, a b^{4} d^{3} e + 14 \, a^{2} b^{3} d^{2} e^{2} + 35 \, a^{3} b^{2} d e^{3} - 105 \, a^{4} b e^{4} + 279 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(326 \, b^{5} d^{2} e^{2} + 185 \, a b^{4} d e^{3} - 511 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(200 \, b^{5} d^{3} e + 52 \, a b^{4} d^{2} e^{2} + 133 \, a^{2} b^{3} d e^{3} - 385 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d - a^{5} b^{5} e + {\left(b^{10} d - a b^{9} e\right)} x^{4} + 4 \, {\left(a b^{9} d - a^{2} b^{8} e\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d - a^{3} b^{7} e\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d - a^{4} b^{6} e\right)} x\right)}}\right]"," ",0,"[1/384*(105*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(48*b^5*d^4 + 8*a*b^4*d^3*e + 14*a^2*b^3*d^2*e^2 + 35*a^3*b^2*d*e^3 - 105*a^4*b*e^4 + 279*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (326*b^5*d^2*e^2 + 185*a*b^4*d*e^3 - 511*a^2*b^3*e^4)*x^2 + (200*b^5*d^3*e + 52*a*b^4*d^2*e^2 + 133*a^2*b^3*d*e^3 - 385*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d - a^5*b^5*e + (b^10*d - a*b^9*e)*x^4 + 4*(a*b^9*d - a^2*b^8*e)*x^3 + 6*(a^2*b^8*d - a^3*b^7*e)*x^2 + 4*(a^3*b^7*d - a^4*b^6*e)*x), 1/192*(105*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (48*b^5*d^4 + 8*a*b^4*d^3*e + 14*a^2*b^3*d^2*e^2 + 35*a^3*b^2*d*e^3 - 105*a^4*b*e^4 + 279*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (326*b^5*d^2*e^2 + 185*a*b^4*d*e^3 - 511*a^2*b^3*e^4)*x^2 + (200*b^5*d^3*e + 52*a*b^4*d^2*e^2 + 133*a^2*b^3*d*e^3 - 385*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d - a^5*b^5*e + (b^10*d - a*b^9*e)*x^4 + 4*(a*b^9*d - a^2*b^8*e)*x^3 + 6*(a^2*b^8*d - a^3*b^7*e)*x^2 + 4*(a^3*b^7*d - a^4*b^6*e)*x)]","B",0
1724,1,894,0,0.443738," ","integrate((e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(48 \, b^{5} d^{4} - 56 \, a b^{4} d^{3} e - 2 \, a^{2} b^{3} d^{2} e^{2} - 5 \, a^{3} b^{2} d e^{3} + 15 \, a^{4} b e^{4} + 15 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(118 \, b^{5} d^{2} e^{2} - 191 \, a b^{4} d e^{3} + 73 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(136 \, b^{5} d^{3} e - 172 \, a b^{4} d^{2} e^{2} - 19 \, a^{2} b^{3} d e^{3} + 55 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d^{2} - 2 \, a^{5} b^{5} d e + a^{6} b^{4} e^{2} + {\left(b^{10} d^{2} - 2 \, a b^{9} d e + a^{2} b^{8} e^{2}\right)} x^{4} + 4 \, {\left(a b^{9} d^{2} - 2 \, a^{2} b^{8} d e + a^{3} b^{7} e^{2}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{2} - 2 \, a^{3} b^{7} d e + a^{4} b^{6} e^{2}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{2} - 2 \, a^{4} b^{6} d e + a^{5} b^{5} e^{2}\right)} x\right)}}, -\frac{15 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(48 \, b^{5} d^{4} - 56 \, a b^{4} d^{3} e - 2 \, a^{2} b^{3} d^{2} e^{2} - 5 \, a^{3} b^{2} d e^{3} + 15 \, a^{4} b e^{4} + 15 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(118 \, b^{5} d^{2} e^{2} - 191 \, a b^{4} d e^{3} + 73 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(136 \, b^{5} d^{3} e - 172 \, a b^{4} d^{2} e^{2} - 19 \, a^{2} b^{3} d e^{3} + 55 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d^{2} - 2 \, a^{5} b^{5} d e + a^{6} b^{4} e^{2} + {\left(b^{10} d^{2} - 2 \, a b^{9} d e + a^{2} b^{8} e^{2}\right)} x^{4} + 4 \, {\left(a b^{9} d^{2} - 2 \, a^{2} b^{8} d e + a^{3} b^{7} e^{2}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{2} - 2 \, a^{3} b^{7} d e + a^{4} b^{6} e^{2}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{2} - 2 \, a^{4} b^{6} d e + a^{5} b^{5} e^{2}\right)} x\right)}}\right]"," ",0,"[-1/384*(15*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(48*b^5*d^4 - 56*a*b^4*d^3*e - 2*a^2*b^3*d^2*e^2 - 5*a^3*b^2*d*e^3 + 15*a^4*b*e^4 + 15*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (118*b^5*d^2*e^2 - 191*a*b^4*d*e^3 + 73*a^2*b^3*e^4)*x^2 + (136*b^5*d^3*e - 172*a*b^4*d^2*e^2 - 19*a^2*b^3*d*e^3 + 55*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^2 - 2*a^5*b^5*d*e + a^6*b^4*e^2 + (b^10*d^2 - 2*a*b^9*d*e + a^2*b^8*e^2)*x^4 + 4*(a*b^9*d^2 - 2*a^2*b^8*d*e + a^3*b^7*e^2)*x^3 + 6*(a^2*b^8*d^2 - 2*a^3*b^7*d*e + a^4*b^6*e^2)*x^2 + 4*(a^3*b^7*d^2 - 2*a^4*b^6*d*e + a^5*b^5*e^2)*x), -1/192*(15*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (48*b^5*d^4 - 56*a*b^4*d^3*e - 2*a^2*b^3*d^2*e^2 - 5*a^3*b^2*d*e^3 + 15*a^4*b*e^4 + 15*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (118*b^5*d^2*e^2 - 191*a*b^4*d*e^3 + 73*a^2*b^3*e^4)*x^2 + (136*b^5*d^3*e - 172*a*b^4*d^2*e^2 - 19*a^2*b^3*d*e^3 + 55*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^2 - 2*a^5*b^5*d*e + a^6*b^4*e^2 + (b^10*d^2 - 2*a*b^9*d*e + a^2*b^8*e^2)*x^4 + 4*(a*b^9*d^2 - 2*a^2*b^8*d*e + a^3*b^7*e^2)*x^3 + 6*(a^2*b^8*d^2 - 2*a^3*b^7*d*e + a^4*b^6*e^2)*x^2 + 4*(a^3*b^7*d^2 - 2*a^4*b^6*d*e + a^5*b^5*e^2)*x)]","B",0
1725,1,1043,0,0.433633," ","integrate((e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(16 \, b^{5} d^{4} - 40 \, a b^{4} d^{3} e + 26 \, a^{2} b^{3} d^{2} e^{2} + a^{3} b^{2} d e^{3} - 3 \, a^{4} b e^{4} - 3 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(24 \, b^{5} d^{3} e - 68 \, a b^{4} d^{2} e^{2} + 55 \, a^{2} b^{3} d e^{3} - 11 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{128 \, {\left(a^{4} b^{6} d^{3} - 3 \, a^{5} b^{5} d^{2} e + 3 \, a^{6} b^{4} d e^{2} - a^{7} b^{3} e^{3} + {\left(b^{10} d^{3} - 3 \, a b^{9} d^{2} e + 3 \, a^{2} b^{8} d e^{2} - a^{3} b^{7} e^{3}\right)} x^{4} + 4 \, {\left(a b^{9} d^{3} - 3 \, a^{2} b^{8} d^{2} e + 3 \, a^{3} b^{7} d e^{2} - a^{4} b^{6} e^{3}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{3} - 3 \, a^{3} b^{7} d^{2} e + 3 \, a^{4} b^{6} d e^{2} - a^{5} b^{5} e^{3}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{3} - 3 \, a^{4} b^{6} d^{2} e + 3 \, a^{5} b^{5} d e^{2} - a^{6} b^{4} e^{3}\right)} x\right)}}, \frac{3 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(16 \, b^{5} d^{4} - 40 \, a b^{4} d^{3} e + 26 \, a^{2} b^{3} d^{2} e^{2} + a^{3} b^{2} d e^{3} - 3 \, a^{4} b e^{4} - 3 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(24 \, b^{5} d^{3} e - 68 \, a b^{4} d^{2} e^{2} + 55 \, a^{2} b^{3} d e^{3} - 11 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{4} b^{6} d^{3} - 3 \, a^{5} b^{5} d^{2} e + 3 \, a^{6} b^{4} d e^{2} - a^{7} b^{3} e^{3} + {\left(b^{10} d^{3} - 3 \, a b^{9} d^{2} e + 3 \, a^{2} b^{8} d e^{2} - a^{3} b^{7} e^{3}\right)} x^{4} + 4 \, {\left(a b^{9} d^{3} - 3 \, a^{2} b^{8} d^{2} e + 3 \, a^{3} b^{7} d e^{2} - a^{4} b^{6} e^{3}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{3} - 3 \, a^{3} b^{7} d^{2} e + 3 \, a^{4} b^{6} d e^{2} - a^{5} b^{5} e^{3}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{3} - 3 \, a^{4} b^{6} d^{2} e + 3 \, a^{5} b^{5} d e^{2} - a^{6} b^{4} e^{3}\right)} x\right)}}\right]"," ",0,"[1/128*(3*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(16*b^5*d^4 - 40*a*b^4*d^3*e + 26*a^2*b^3*d^2*e^2 + a^3*b^2*d*e^3 - 3*a^4*b*e^4 - 3*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 + (24*b^5*d^3*e - 68*a*b^4*d^2*e^2 + 55*a^2*b^3*d*e^3 - 11*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^3 - 3*a^5*b^5*d^2*e + 3*a^6*b^4*d*e^2 - a^7*b^3*e^3 + (b^10*d^3 - 3*a*b^9*d^2*e + 3*a^2*b^8*d*e^2 - a^3*b^7*e^3)*x^4 + 4*(a*b^9*d^3 - 3*a^2*b^8*d^2*e + 3*a^3*b^7*d*e^2 - a^4*b^6*e^3)*x^3 + 6*(a^2*b^8*d^3 - 3*a^3*b^7*d^2*e + 3*a^4*b^6*d*e^2 - a^5*b^5*e^3)*x^2 + 4*(a^3*b^7*d^3 - 3*a^4*b^6*d^2*e + 3*a^5*b^5*d*e^2 - a^6*b^4*e^3)*x), 1/64*(3*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (16*b^5*d^4 - 40*a*b^4*d^3*e + 26*a^2*b^3*d^2*e^2 + a^3*b^2*d*e^3 - 3*a^4*b*e^4 - 3*(b^5*d*e^3 - a*b^4*e^4)*x^3 + (2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 + (24*b^5*d^3*e - 68*a*b^4*d^2*e^2 + 55*a^2*b^3*d*e^3 - 11*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^3 - 3*a^5*b^5*d^2*e + 3*a^6*b^4*d*e^2 - a^7*b^3*e^3 + (b^10*d^3 - 3*a*b^9*d^2*e + 3*a^2*b^8*d*e^2 - a^3*b^7*e^3)*x^4 + 4*(a*b^9*d^3 - 3*a^2*b^8*d^2*e + 3*a^3*b^7*d*e^2 - a^4*b^6*e^3)*x^3 + 6*(a^2*b^8*d^3 - 3*a^3*b^7*d^2*e + 3*a^4*b^6*d*e^2 - a^5*b^5*e^3)*x^2 + 4*(a^3*b^7*d^3 - 3*a^4*b^6*d^2*e + 3*a^5*b^5*d*e^2 - a^6*b^4*e^3)*x)]","B",0
1726,1,1176,0,0.440219," ","integrate((e*x+d)^(1/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) + 2 \, {\left(48 \, b^{5} d^{4} - 184 \, a b^{4} d^{3} e + 254 \, a^{2} b^{3} d^{2} e^{2} - 133 \, a^{3} b^{2} d e^{3} + 15 \, a^{4} b e^{4} + 15 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} - 5 \, {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(8 \, b^{5} d^{3} e - 44 \, a b^{4} d^{2} e^{2} + 109 \, a^{2} b^{3} d e^{3} - 73 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d^{4} - 4 \, a^{5} b^{5} d^{3} e + 6 \, a^{6} b^{4} d^{2} e^{2} - 4 \, a^{7} b^{3} d e^{3} + a^{8} b^{2} e^{4} + {\left(b^{10} d^{4} - 4 \, a b^{9} d^{3} e + 6 \, a^{2} b^{8} d^{2} e^{2} - 4 \, a^{3} b^{7} d e^{3} + a^{4} b^{6} e^{4}\right)} x^{4} + 4 \, {\left(a b^{9} d^{4} - 4 \, a^{2} b^{8} d^{3} e + 6 \, a^{3} b^{7} d^{2} e^{2} - 4 \, a^{4} b^{6} d e^{3} + a^{5} b^{5} e^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{4} - 4 \, a^{3} b^{7} d^{3} e + 6 \, a^{4} b^{6} d^{2} e^{2} - 4 \, a^{5} b^{5} d e^{3} + a^{6} b^{4} e^{4}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{4} - 4 \, a^{4} b^{6} d^{3} e + 6 \, a^{5} b^{5} d^{2} e^{2} - 4 \, a^{6} b^{4} d e^{3} + a^{7} b^{3} e^{4}\right)} x\right)}}, -\frac{15 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) + {\left(48 \, b^{5} d^{4} - 184 \, a b^{4} d^{3} e + 254 \, a^{2} b^{3} d^{2} e^{2} - 133 \, a^{3} b^{2} d e^{3} + 15 \, a^{4} b e^{4} + 15 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} - 5 \, {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} + {\left(8 \, b^{5} d^{3} e - 44 \, a b^{4} d^{2} e^{2} + 109 \, a^{2} b^{3} d e^{3} - 73 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d^{4} - 4 \, a^{5} b^{5} d^{3} e + 6 \, a^{6} b^{4} d^{2} e^{2} - 4 \, a^{7} b^{3} d e^{3} + a^{8} b^{2} e^{4} + {\left(b^{10} d^{4} - 4 \, a b^{9} d^{3} e + 6 \, a^{2} b^{8} d^{2} e^{2} - 4 \, a^{3} b^{7} d e^{3} + a^{4} b^{6} e^{4}\right)} x^{4} + 4 \, {\left(a b^{9} d^{4} - 4 \, a^{2} b^{8} d^{3} e + 6 \, a^{3} b^{7} d^{2} e^{2} - 4 \, a^{4} b^{6} d e^{3} + a^{5} b^{5} e^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{4} - 4 \, a^{3} b^{7} d^{3} e + 6 \, a^{4} b^{6} d^{2} e^{2} - 4 \, a^{5} b^{5} d e^{3} + a^{6} b^{4} e^{4}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{4} - 4 \, a^{4} b^{6} d^{3} e + 6 \, a^{5} b^{5} d^{2} e^{2} - 4 \, a^{6} b^{4} d e^{3} + a^{7} b^{3} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/384*(15*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) + 2*(48*b^5*d^4 - 184*a*b^4*d^3*e + 254*a^2*b^3*d^2*e^2 - 133*a^3*b^2*d*e^3 + 15*a^4*b*e^4 + 15*(b^5*d*e^3 - a*b^4*e^4)*x^3 - 5*(2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 + (8*b^5*d^3*e - 44*a*b^4*d^2*e^2 + 109*a^2*b^3*d*e^3 - 73*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^4 - 4*a^5*b^5*d^3*e + 6*a^6*b^4*d^2*e^2 - 4*a^7*b^3*d*e^3 + a^8*b^2*e^4 + (b^10*d^4 - 4*a*b^9*d^3*e + 6*a^2*b^8*d^2*e^2 - 4*a^3*b^7*d*e^3 + a^4*b^6*e^4)*x^4 + 4*(a*b^9*d^4 - 4*a^2*b^8*d^3*e + 6*a^3*b^7*d^2*e^2 - 4*a^4*b^6*d*e^3 + a^5*b^5*e^4)*x^3 + 6*(a^2*b^8*d^4 - 4*a^3*b^7*d^3*e + 6*a^4*b^6*d^2*e^2 - 4*a^5*b^5*d*e^3 + a^6*b^4*e^4)*x^2 + 4*(a^3*b^7*d^4 - 4*a^4*b^6*d^3*e + 6*a^5*b^5*d^2*e^2 - 4*a^6*b^4*d*e^3 + a^7*b^3*e^4)*x), -1/192*(15*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) + (48*b^5*d^4 - 184*a*b^4*d^3*e + 254*a^2*b^3*d^2*e^2 - 133*a^3*b^2*d*e^3 + 15*a^4*b*e^4 + 15*(b^5*d*e^3 - a*b^4*e^4)*x^3 - 5*(2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 + (8*b^5*d^3*e - 44*a*b^4*d^2*e^2 + 109*a^2*b^3*d*e^3 - 73*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^4 - 4*a^5*b^5*d^3*e + 6*a^6*b^4*d^2*e^2 - 4*a^7*b^3*d*e^3 + a^8*b^2*e^4 + (b^10*d^4 - 4*a*b^9*d^3*e + 6*a^2*b^8*d^2*e^2 - 4*a^3*b^7*d*e^3 + a^4*b^6*e^4)*x^4 + 4*(a*b^9*d^4 - 4*a^2*b^8*d^3*e + 6*a^3*b^7*d^2*e^2 - 4*a^4*b^6*d*e^3 + a^5*b^5*e^4)*x^3 + 6*(a^2*b^8*d^4 - 4*a^3*b^7*d^3*e + 6*a^4*b^6*d^2*e^2 - 4*a^5*b^5*d*e^3 + a^6*b^4*e^4)*x^2 + 4*(a^3*b^7*d^4 - 4*a^4*b^6*d^3*e + 6*a^5*b^5*d^2*e^2 - 4*a^6*b^4*d*e^3 + a^7*b^3*e^4)*x)]","B",0
1727,1,1325,0,0.449774," ","integrate(1/(b^2*x^2+2*a*b*x+a^2)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{b^{2} d - a b e} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, \sqrt{b^{2} d - a b e} \sqrt{e x + d}}{b x + a}\right) - 2 \, {\left(48 \, b^{5} d^{4} - 248 \, a b^{4} d^{3} e + 526 \, a^{2} b^{3} d^{2} e^{2} - 605 \, a^{3} b^{2} d e^{3} + 279 \, a^{4} b e^{4} - 105 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + 35 \, {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} - 7 \, {\left(8 \, b^{5} d^{3} e - 44 \, a b^{4} d^{2} e^{2} + 109 \, a^{2} b^{3} d e^{3} - 73 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d^{5} - 5 \, a^{5} b^{5} d^{4} e + 10 \, a^{6} b^{4} d^{3} e^{2} - 10 \, a^{7} b^{3} d^{2} e^{3} + 5 \, a^{8} b^{2} d e^{4} - a^{9} b e^{5} + {\left(b^{10} d^{5} - 5 \, a b^{9} d^{4} e + 10 \, a^{2} b^{8} d^{3} e^{2} - 10 \, a^{3} b^{7} d^{2} e^{3} + 5 \, a^{4} b^{6} d e^{4} - a^{5} b^{5} e^{5}\right)} x^{4} + 4 \, {\left(a b^{9} d^{5} - 5 \, a^{2} b^{8} d^{4} e + 10 \, a^{3} b^{7} d^{3} e^{2} - 10 \, a^{4} b^{6} d^{2} e^{3} + 5 \, a^{5} b^{5} d e^{4} - a^{6} b^{4} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{5} - 5 \, a^{3} b^{7} d^{4} e + 10 \, a^{4} b^{6} d^{3} e^{2} - 10 \, a^{5} b^{5} d^{2} e^{3} + 5 \, a^{6} b^{4} d e^{4} - a^{7} b^{3} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{5} - 5 \, a^{4} b^{6} d^{4} e + 10 \, a^{5} b^{5} d^{3} e^{2} - 10 \, a^{6} b^{4} d^{2} e^{3} + 5 \, a^{7} b^{3} d e^{4} - a^{8} b^{2} e^{5}\right)} x\right)}}, \frac{105 \, {\left(b^{4} e^{4} x^{4} + 4 \, a b^{3} e^{4} x^{3} + 6 \, a^{2} b^{2} e^{4} x^{2} + 4 \, a^{3} b e^{4} x + a^{4} e^{4}\right)} \sqrt{-b^{2} d + a b e} \arctan\left(\frac{\sqrt{-b^{2} d + a b e} \sqrt{e x + d}}{b e x + b d}\right) - {\left(48 \, b^{5} d^{4} - 248 \, a b^{4} d^{3} e + 526 \, a^{2} b^{3} d^{2} e^{2} - 605 \, a^{3} b^{2} d e^{3} + 279 \, a^{4} b e^{4} - 105 \, {\left(b^{5} d e^{3} - a b^{4} e^{4}\right)} x^{3} + 35 \, {\left(2 \, b^{5} d^{2} e^{2} - 13 \, a b^{4} d e^{3} + 11 \, a^{2} b^{3} e^{4}\right)} x^{2} - 7 \, {\left(8 \, b^{5} d^{3} e - 44 \, a b^{4} d^{2} e^{2} + 109 \, a^{2} b^{3} d e^{3} - 73 \, a^{3} b^{2} e^{4}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d^{5} - 5 \, a^{5} b^{5} d^{4} e + 10 \, a^{6} b^{4} d^{3} e^{2} - 10 \, a^{7} b^{3} d^{2} e^{3} + 5 \, a^{8} b^{2} d e^{4} - a^{9} b e^{5} + {\left(b^{10} d^{5} - 5 \, a b^{9} d^{4} e + 10 \, a^{2} b^{8} d^{3} e^{2} - 10 \, a^{3} b^{7} d^{2} e^{3} + 5 \, a^{4} b^{6} d e^{4} - a^{5} b^{5} e^{5}\right)} x^{4} + 4 \, {\left(a b^{9} d^{5} - 5 \, a^{2} b^{8} d^{4} e + 10 \, a^{3} b^{7} d^{3} e^{2} - 10 \, a^{4} b^{6} d^{2} e^{3} + 5 \, a^{5} b^{5} d e^{4} - a^{6} b^{4} e^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} d^{5} - 5 \, a^{3} b^{7} d^{4} e + 10 \, a^{4} b^{6} d^{3} e^{2} - 10 \, a^{5} b^{5} d^{2} e^{3} + 5 \, a^{6} b^{4} d e^{4} - a^{7} b^{3} e^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} d^{5} - 5 \, a^{4} b^{6} d^{4} e + 10 \, a^{5} b^{5} d^{3} e^{2} - 10 \, a^{6} b^{4} d^{2} e^{3} + 5 \, a^{7} b^{3} d e^{4} - a^{8} b^{2} e^{5}\right)} x\right)}}\right]"," ",0,"[1/384*(105*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(b^2*d - a*b*e)*log((b*e*x + 2*b*d - a*e - 2*sqrt(b^2*d - a*b*e)*sqrt(e*x + d))/(b*x + a)) - 2*(48*b^5*d^4 - 248*a*b^4*d^3*e + 526*a^2*b^3*d^2*e^2 - 605*a^3*b^2*d*e^3 + 279*a^4*b*e^4 - 105*(b^5*d*e^3 - a*b^4*e^4)*x^3 + 35*(2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 - 7*(8*b^5*d^3*e - 44*a*b^4*d^2*e^2 + 109*a^2*b^3*d*e^3 - 73*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^5 - 5*a^5*b^5*d^4*e + 10*a^6*b^4*d^3*e^2 - 10*a^7*b^3*d^2*e^3 + 5*a^8*b^2*d*e^4 - a^9*b*e^5 + (b^10*d^5 - 5*a*b^9*d^4*e + 10*a^2*b^8*d^3*e^2 - 10*a^3*b^7*d^2*e^3 + 5*a^4*b^6*d*e^4 - a^5*b^5*e^5)*x^4 + 4*(a*b^9*d^5 - 5*a^2*b^8*d^4*e + 10*a^3*b^7*d^3*e^2 - 10*a^4*b^6*d^2*e^3 + 5*a^5*b^5*d*e^4 - a^6*b^4*e^5)*x^3 + 6*(a^2*b^8*d^5 - 5*a^3*b^7*d^4*e + 10*a^4*b^6*d^3*e^2 - 10*a^5*b^5*d^2*e^3 + 5*a^6*b^4*d*e^4 - a^7*b^3*e^5)*x^2 + 4*(a^3*b^7*d^5 - 5*a^4*b^6*d^4*e + 10*a^5*b^5*d^3*e^2 - 10*a^6*b^4*d^2*e^3 + 5*a^7*b^3*d*e^4 - a^8*b^2*e^5)*x), 1/192*(105*(b^4*e^4*x^4 + 4*a*b^3*e^4*x^3 + 6*a^2*b^2*e^4*x^2 + 4*a^3*b*e^4*x + a^4*e^4)*sqrt(-b^2*d + a*b*e)*arctan(sqrt(-b^2*d + a*b*e)*sqrt(e*x + d)/(b*e*x + b*d)) - (48*b^5*d^4 - 248*a*b^4*d^3*e + 526*a^2*b^3*d^2*e^2 - 605*a^3*b^2*d*e^3 + 279*a^4*b*e^4 - 105*(b^5*d*e^3 - a*b^4*e^4)*x^3 + 35*(2*b^5*d^2*e^2 - 13*a*b^4*d*e^3 + 11*a^2*b^3*e^4)*x^2 - 7*(8*b^5*d^3*e - 44*a*b^4*d^2*e^2 + 109*a^2*b^3*d*e^3 - 73*a^3*b^2*e^4)*x)*sqrt(e*x + d))/(a^4*b^6*d^5 - 5*a^5*b^5*d^4*e + 10*a^6*b^4*d^3*e^2 - 10*a^7*b^3*d^2*e^3 + 5*a^8*b^2*d*e^4 - a^9*b*e^5 + (b^10*d^5 - 5*a*b^9*d^4*e + 10*a^2*b^8*d^3*e^2 - 10*a^3*b^7*d^2*e^3 + 5*a^4*b^6*d*e^4 - a^5*b^5*e^5)*x^4 + 4*(a*b^9*d^5 - 5*a^2*b^8*d^4*e + 10*a^3*b^7*d^3*e^2 - 10*a^4*b^6*d^2*e^3 + 5*a^5*b^5*d*e^4 - a^6*b^4*e^5)*x^3 + 6*(a^2*b^8*d^5 - 5*a^3*b^7*d^4*e + 10*a^4*b^6*d^3*e^2 - 10*a^5*b^5*d^2*e^3 + 5*a^6*b^4*d*e^4 - a^7*b^3*e^5)*x^2 + 4*(a^3*b^7*d^5 - 5*a^4*b^6*d^4*e + 10*a^5*b^5*d^3*e^2 - 10*a^6*b^4*d^2*e^3 + 5*a^7*b^3*d*e^4 - a^8*b^2*e^5)*x)]","B",0
1728,1,1734,0,0.459536," ","integrate(1/(e*x+d)^(3/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{4} d e^{4} + {\left(b^{4} d e^{4} + 4 \, a b^{3} e^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} d e^{4} + 2 \, a^{3} b e^{5}\right)} x^{2} + {\left(4 \, a^{3} b d e^{4} + a^{4} e^{5}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(315 \, b^{4} e^{4} x^{4} - 16 \, b^{4} d^{4} + 88 \, a b^{3} d^{3} e - 210 \, a^{2} b^{2} d^{2} e^{2} + 325 \, a^{3} b d e^{3} + 128 \, a^{4} e^{4} + 105 \, {\left(b^{4} d e^{3} + 11 \, a b^{3} e^{4}\right)} x^{3} - 21 \, {\left(2 \, b^{4} d^{2} e^{2} - 19 \, a b^{3} d e^{3} - 73 \, a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(8 \, b^{4} d^{3} e - 52 \, a b^{3} d^{2} e^{2} + 185 \, a^{2} b^{2} d e^{3} + 279 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{128 \, {\left(a^{4} b^{5} d^{6} - 5 \, a^{5} b^{4} d^{5} e + 10 \, a^{6} b^{3} d^{4} e^{2} - 10 \, a^{7} b^{2} d^{3} e^{3} + 5 \, a^{8} b d^{2} e^{4} - a^{9} d e^{5} + {\left(b^{9} d^{5} e - 5 \, a b^{8} d^{4} e^{2} + 10 \, a^{2} b^{7} d^{3} e^{3} - 10 \, a^{3} b^{6} d^{2} e^{4} + 5 \, a^{4} b^{5} d e^{5} - a^{5} b^{4} e^{6}\right)} x^{5} + {\left(b^{9} d^{6} - a b^{8} d^{5} e - 10 \, a^{2} b^{7} d^{4} e^{2} + 30 \, a^{3} b^{6} d^{3} e^{3} - 35 \, a^{4} b^{5} d^{2} e^{4} + 19 \, a^{5} b^{4} d e^{5} - 4 \, a^{6} b^{3} e^{6}\right)} x^{4} + 2 \, {\left(2 \, a b^{8} d^{6} - 7 \, a^{2} b^{7} d^{5} e + 5 \, a^{3} b^{6} d^{4} e^{2} + 10 \, a^{4} b^{5} d^{3} e^{3} - 20 \, a^{5} b^{4} d^{2} e^{4} + 13 \, a^{6} b^{3} d e^{5} - 3 \, a^{7} b^{2} e^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{7} d^{6} - 13 \, a^{3} b^{6} d^{5} e + 20 \, a^{4} b^{5} d^{4} e^{2} - 10 \, a^{5} b^{4} d^{3} e^{3} - 5 \, a^{6} b^{3} d^{2} e^{4} + 7 \, a^{7} b^{2} d e^{5} - 2 \, a^{8} b e^{6}\right)} x^{2} + {\left(4 \, a^{3} b^{6} d^{6} - 19 \, a^{4} b^{5} d^{5} e + 35 \, a^{5} b^{4} d^{4} e^{2} - 30 \, a^{6} b^{3} d^{3} e^{3} + 10 \, a^{7} b^{2} d^{2} e^{4} + a^{8} b d e^{5} - a^{9} e^{6}\right)} x\right)}}, -\frac{315 \, {\left(b^{4} e^{5} x^{5} + a^{4} d e^{4} + {\left(b^{4} d e^{4} + 4 \, a b^{3} e^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} d e^{4} + 2 \, a^{3} b e^{5}\right)} x^{2} + {\left(4 \, a^{3} b d e^{4} + a^{4} e^{5}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(315 \, b^{4} e^{4} x^{4} - 16 \, b^{4} d^{4} + 88 \, a b^{3} d^{3} e - 210 \, a^{2} b^{2} d^{2} e^{2} + 325 \, a^{3} b d e^{3} + 128 \, a^{4} e^{4} + 105 \, {\left(b^{4} d e^{3} + 11 \, a b^{3} e^{4}\right)} x^{3} - 21 \, {\left(2 \, b^{4} d^{2} e^{2} - 19 \, a b^{3} d e^{3} - 73 \, a^{2} b^{2} e^{4}\right)} x^{2} + 3 \, {\left(8 \, b^{4} d^{3} e - 52 \, a b^{3} d^{2} e^{2} + 185 \, a^{2} b^{2} d e^{3} + 279 \, a^{3} b e^{4}\right)} x\right)} \sqrt{e x + d}}{64 \, {\left(a^{4} b^{5} d^{6} - 5 \, a^{5} b^{4} d^{5} e + 10 \, a^{6} b^{3} d^{4} e^{2} - 10 \, a^{7} b^{2} d^{3} e^{3} + 5 \, a^{8} b d^{2} e^{4} - a^{9} d e^{5} + {\left(b^{9} d^{5} e - 5 \, a b^{8} d^{4} e^{2} + 10 \, a^{2} b^{7} d^{3} e^{3} - 10 \, a^{3} b^{6} d^{2} e^{4} + 5 \, a^{4} b^{5} d e^{5} - a^{5} b^{4} e^{6}\right)} x^{5} + {\left(b^{9} d^{6} - a b^{8} d^{5} e - 10 \, a^{2} b^{7} d^{4} e^{2} + 30 \, a^{3} b^{6} d^{3} e^{3} - 35 \, a^{4} b^{5} d^{2} e^{4} + 19 \, a^{5} b^{4} d e^{5} - 4 \, a^{6} b^{3} e^{6}\right)} x^{4} + 2 \, {\left(2 \, a b^{8} d^{6} - 7 \, a^{2} b^{7} d^{5} e + 5 \, a^{3} b^{6} d^{4} e^{2} + 10 \, a^{4} b^{5} d^{3} e^{3} - 20 \, a^{5} b^{4} d^{2} e^{4} + 13 \, a^{6} b^{3} d e^{5} - 3 \, a^{7} b^{2} e^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{7} d^{6} - 13 \, a^{3} b^{6} d^{5} e + 20 \, a^{4} b^{5} d^{4} e^{2} - 10 \, a^{5} b^{4} d^{3} e^{3} - 5 \, a^{6} b^{3} d^{2} e^{4} + 7 \, a^{7} b^{2} d e^{5} - 2 \, a^{8} b e^{6}\right)} x^{2} + {\left(4 \, a^{3} b^{6} d^{6} - 19 \, a^{4} b^{5} d^{5} e + 35 \, a^{5} b^{4} d^{4} e^{2} - 30 \, a^{6} b^{3} d^{3} e^{3} + 10 \, a^{7} b^{2} d^{2} e^{4} + a^{8} b d e^{5} - a^{9} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/128*(315*(b^4*e^5*x^5 + a^4*d*e^4 + (b^4*d*e^4 + 4*a*b^3*e^5)*x^4 + 2*(2*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*x^3 + 2*(3*a^2*b^2*d*e^4 + 2*a^3*b*e^5)*x^2 + (4*a^3*b*d*e^4 + a^4*e^5)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(315*b^4*e^4*x^4 - 16*b^4*d^4 + 88*a*b^3*d^3*e - 210*a^2*b^2*d^2*e^2 + 325*a^3*b*d*e^3 + 128*a^4*e^4 + 105*(b^4*d*e^3 + 11*a*b^3*e^4)*x^3 - 21*(2*b^4*d^2*e^2 - 19*a*b^3*d*e^3 - 73*a^2*b^2*e^4)*x^2 + 3*(8*b^4*d^3*e - 52*a*b^3*d^2*e^2 + 185*a^2*b^2*d*e^3 + 279*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^4*b^5*d^6 - 5*a^5*b^4*d^5*e + 10*a^6*b^3*d^4*e^2 - 10*a^7*b^2*d^3*e^3 + 5*a^8*b*d^2*e^4 - a^9*d*e^5 + (b^9*d^5*e - 5*a*b^8*d^4*e^2 + 10*a^2*b^7*d^3*e^3 - 10*a^3*b^6*d^2*e^4 + 5*a^4*b^5*d*e^5 - a^5*b^4*e^6)*x^5 + (b^9*d^6 - a*b^8*d^5*e - 10*a^2*b^7*d^4*e^2 + 30*a^3*b^6*d^3*e^3 - 35*a^4*b^5*d^2*e^4 + 19*a^5*b^4*d*e^5 - 4*a^6*b^3*e^6)*x^4 + 2*(2*a*b^8*d^6 - 7*a^2*b^7*d^5*e + 5*a^3*b^6*d^4*e^2 + 10*a^4*b^5*d^3*e^3 - 20*a^5*b^4*d^2*e^4 + 13*a^6*b^3*d*e^5 - 3*a^7*b^2*e^6)*x^3 + 2*(3*a^2*b^7*d^6 - 13*a^3*b^6*d^5*e + 20*a^4*b^5*d^4*e^2 - 10*a^5*b^4*d^3*e^3 - 5*a^6*b^3*d^2*e^4 + 7*a^7*b^2*d*e^5 - 2*a^8*b*e^6)*x^2 + (4*a^3*b^6*d^6 - 19*a^4*b^5*d^5*e + 35*a^5*b^4*d^4*e^2 - 30*a^6*b^3*d^3*e^3 + 10*a^7*b^2*d^2*e^4 + a^8*b*d*e^5 - a^9*e^6)*x), -1/64*(315*(b^4*e^5*x^5 + a^4*d*e^4 + (b^4*d*e^4 + 4*a*b^3*e^5)*x^4 + 2*(2*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*x^3 + 2*(3*a^2*b^2*d*e^4 + 2*a^3*b*e^5)*x^2 + (4*a^3*b*d*e^4 + a^4*e^5)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (315*b^4*e^4*x^4 - 16*b^4*d^4 + 88*a*b^3*d^3*e - 210*a^2*b^2*d^2*e^2 + 325*a^3*b*d*e^3 + 128*a^4*e^4 + 105*(b^4*d*e^3 + 11*a*b^3*e^4)*x^3 - 21*(2*b^4*d^2*e^2 - 19*a*b^3*d*e^3 - 73*a^2*b^2*e^4)*x^2 + 3*(8*b^4*d^3*e - 52*a*b^3*d^2*e^2 + 185*a^2*b^2*d*e^3 + 279*a^3*b*e^4)*x)*sqrt(e*x + d))/(a^4*b^5*d^6 - 5*a^5*b^4*d^5*e + 10*a^6*b^3*d^4*e^2 - 10*a^7*b^2*d^3*e^3 + 5*a^8*b*d^2*e^4 - a^9*d*e^5 + (b^9*d^5*e - 5*a*b^8*d^4*e^2 + 10*a^2*b^7*d^3*e^3 - 10*a^3*b^6*d^2*e^4 + 5*a^4*b^5*d*e^5 - a^5*b^4*e^6)*x^5 + (b^9*d^6 - a*b^8*d^5*e - 10*a^2*b^7*d^4*e^2 + 30*a^3*b^6*d^3*e^3 - 35*a^4*b^5*d^2*e^4 + 19*a^5*b^4*d*e^5 - 4*a^6*b^3*e^6)*x^4 + 2*(2*a*b^8*d^6 - 7*a^2*b^7*d^5*e + 5*a^3*b^6*d^4*e^2 + 10*a^4*b^5*d^3*e^3 - 20*a^5*b^4*d^2*e^4 + 13*a^6*b^3*d*e^5 - 3*a^7*b^2*e^6)*x^3 + 2*(3*a^2*b^7*d^6 - 13*a^3*b^6*d^5*e + 20*a^4*b^5*d^4*e^2 - 10*a^5*b^4*d^3*e^3 - 5*a^6*b^3*d^2*e^4 + 7*a^7*b^2*d*e^5 - 2*a^8*b*e^6)*x^2 + (4*a^3*b^6*d^6 - 19*a^4*b^5*d^5*e + 35*a^5*b^4*d^4*e^2 - 30*a^6*b^3*d^3*e^3 + 10*a^7*b^2*d^2*e^4 + a^8*b*d*e^5 - a^9*e^6)*x)]","B",0
1729,1,2494,0,0.486131," ","integrate(1/(e*x+d)^(5/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3465 \, {\left(b^{5} e^{6} x^{6} + a^{4} b d^{2} e^{4} + 2 \, {\left(b^{5} d e^{5} + 2 \, a b^{4} e^{6}\right)} x^{5} + {\left(b^{5} d^{2} e^{4} + 8 \, a b^{4} d e^{5} + 6 \, a^{2} b^{3} e^{6}\right)} x^{4} + 4 \, {\left(a b^{4} d^{2} e^{4} + 3 \, a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} x^{3} + {\left(6 \, a^{2} b^{3} d^{2} e^{4} + 8 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} d^{2} e^{4} + a^{4} b d e^{5}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e - 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) + 2 \, {\left(3465 \, b^{5} e^{5} x^{5} - 48 \, b^{5} d^{5} + 328 \, a b^{4} d^{4} e - 1030 \, a^{2} b^{3} d^{3} e^{2} + 2295 \, a^{3} b^{2} d^{2} e^{3} + 2048 \, a^{4} b d e^{4} - 128 \, a^{5} e^{5} + 1155 \, {\left(4 \, b^{5} d e^{4} + 11 \, a b^{4} e^{5}\right)} x^{4} + 231 \, {\left(3 \, b^{5} d^{2} e^{3} + 74 \, a b^{4} d e^{4} + 73 \, a^{2} b^{3} e^{5}\right)} x^{3} - 99 \, {\left(2 \, b^{5} d^{3} e^{2} - 27 \, a b^{4} d^{2} e^{3} - 232 \, a^{2} b^{3} d e^{4} - 93 \, a^{3} b^{2} e^{5}\right)} x^{2} + 11 \, {\left(8 \, b^{5} d^{4} e - 68 \, a b^{4} d^{3} e^{2} + 345 \, a^{2} b^{3} d^{2} e^{3} + 1162 \, a^{3} b^{2} d e^{4} + 128 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{384 \, {\left(a^{4} b^{6} d^{8} - 6 \, a^{5} b^{5} d^{7} e + 15 \, a^{6} b^{4} d^{6} e^{2} - 20 \, a^{7} b^{3} d^{5} e^{3} + 15 \, a^{8} b^{2} d^{4} e^{4} - 6 \, a^{9} b d^{3} e^{5} + a^{10} d^{2} e^{6} + {\left(b^{10} d^{6} e^{2} - 6 \, a b^{9} d^{5} e^{3} + 15 \, a^{2} b^{8} d^{4} e^{4} - 20 \, a^{3} b^{7} d^{3} e^{5} + 15 \, a^{4} b^{6} d^{2} e^{6} - 6 \, a^{5} b^{5} d e^{7} + a^{6} b^{4} e^{8}\right)} x^{6} + 2 \, {\left(b^{10} d^{7} e - 4 \, a b^{9} d^{6} e^{2} + 3 \, a^{2} b^{8} d^{5} e^{3} + 10 \, a^{3} b^{7} d^{4} e^{4} - 25 \, a^{4} b^{6} d^{3} e^{5} + 24 \, a^{5} b^{5} d^{2} e^{6} - 11 \, a^{6} b^{4} d e^{7} + 2 \, a^{7} b^{3} e^{8}\right)} x^{5} + {\left(b^{10} d^{8} + 2 \, a b^{9} d^{7} e - 27 \, a^{2} b^{8} d^{6} e^{2} + 64 \, a^{3} b^{7} d^{5} e^{3} - 55 \, a^{4} b^{6} d^{4} e^{4} - 6 \, a^{5} b^{5} d^{3} e^{5} + 43 \, a^{6} b^{4} d^{2} e^{6} - 28 \, a^{7} b^{3} d e^{7} + 6 \, a^{8} b^{2} e^{8}\right)} x^{4} + 4 \, {\left(a b^{9} d^{8} - 3 \, a^{2} b^{8} d^{7} e - 2 \, a^{3} b^{7} d^{6} e^{2} + 19 \, a^{4} b^{6} d^{5} e^{3} - 30 \, a^{5} b^{5} d^{4} e^{4} + 19 \, a^{6} b^{4} d^{3} e^{5} - 2 \, a^{7} b^{3} d^{2} e^{6} - 3 \, a^{8} b^{2} d e^{7} + a^{9} b e^{8}\right)} x^{3} + {\left(6 \, a^{2} b^{8} d^{8} - 28 \, a^{3} b^{7} d^{7} e + 43 \, a^{4} b^{6} d^{6} e^{2} - 6 \, a^{5} b^{5} d^{5} e^{3} - 55 \, a^{6} b^{4} d^{4} e^{4} + 64 \, a^{7} b^{3} d^{3} e^{5} - 27 \, a^{8} b^{2} d^{2} e^{6} + 2 \, a^{9} b d e^{7} + a^{10} e^{8}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{7} d^{8} - 11 \, a^{4} b^{6} d^{7} e + 24 \, a^{5} b^{5} d^{6} e^{2} - 25 \, a^{6} b^{4} d^{5} e^{3} + 10 \, a^{7} b^{3} d^{4} e^{4} + 3 \, a^{8} b^{2} d^{3} e^{5} - 4 \, a^{9} b d^{2} e^{6} + a^{10} d e^{7}\right)} x\right)}}, -\frac{3465 \, {\left(b^{5} e^{6} x^{6} + a^{4} b d^{2} e^{4} + 2 \, {\left(b^{5} d e^{5} + 2 \, a b^{4} e^{6}\right)} x^{5} + {\left(b^{5} d^{2} e^{4} + 8 \, a b^{4} d e^{5} + 6 \, a^{2} b^{3} e^{6}\right)} x^{4} + 4 \, {\left(a b^{4} d^{2} e^{4} + 3 \, a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} x^{3} + {\left(6 \, a^{2} b^{3} d^{2} e^{4} + 8 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} d^{2} e^{4} + a^{4} b d e^{5}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(3465 \, b^{5} e^{5} x^{5} - 48 \, b^{5} d^{5} + 328 \, a b^{4} d^{4} e - 1030 \, a^{2} b^{3} d^{3} e^{2} + 2295 \, a^{3} b^{2} d^{2} e^{3} + 2048 \, a^{4} b d e^{4} - 128 \, a^{5} e^{5} + 1155 \, {\left(4 \, b^{5} d e^{4} + 11 \, a b^{4} e^{5}\right)} x^{4} + 231 \, {\left(3 \, b^{5} d^{2} e^{3} + 74 \, a b^{4} d e^{4} + 73 \, a^{2} b^{3} e^{5}\right)} x^{3} - 99 \, {\left(2 \, b^{5} d^{3} e^{2} - 27 \, a b^{4} d^{2} e^{3} - 232 \, a^{2} b^{3} d e^{4} - 93 \, a^{3} b^{2} e^{5}\right)} x^{2} + 11 \, {\left(8 \, b^{5} d^{4} e - 68 \, a b^{4} d^{3} e^{2} + 345 \, a^{2} b^{3} d^{2} e^{3} + 1162 \, a^{3} b^{2} d e^{4} + 128 \, a^{4} b e^{5}\right)} x\right)} \sqrt{e x + d}}{192 \, {\left(a^{4} b^{6} d^{8} - 6 \, a^{5} b^{5} d^{7} e + 15 \, a^{6} b^{4} d^{6} e^{2} - 20 \, a^{7} b^{3} d^{5} e^{3} + 15 \, a^{8} b^{2} d^{4} e^{4} - 6 \, a^{9} b d^{3} e^{5} + a^{10} d^{2} e^{6} + {\left(b^{10} d^{6} e^{2} - 6 \, a b^{9} d^{5} e^{3} + 15 \, a^{2} b^{8} d^{4} e^{4} - 20 \, a^{3} b^{7} d^{3} e^{5} + 15 \, a^{4} b^{6} d^{2} e^{6} - 6 \, a^{5} b^{5} d e^{7} + a^{6} b^{4} e^{8}\right)} x^{6} + 2 \, {\left(b^{10} d^{7} e - 4 \, a b^{9} d^{6} e^{2} + 3 \, a^{2} b^{8} d^{5} e^{3} + 10 \, a^{3} b^{7} d^{4} e^{4} - 25 \, a^{4} b^{6} d^{3} e^{5} + 24 \, a^{5} b^{5} d^{2} e^{6} - 11 \, a^{6} b^{4} d e^{7} + 2 \, a^{7} b^{3} e^{8}\right)} x^{5} + {\left(b^{10} d^{8} + 2 \, a b^{9} d^{7} e - 27 \, a^{2} b^{8} d^{6} e^{2} + 64 \, a^{3} b^{7} d^{5} e^{3} - 55 \, a^{4} b^{6} d^{4} e^{4} - 6 \, a^{5} b^{5} d^{3} e^{5} + 43 \, a^{6} b^{4} d^{2} e^{6} - 28 \, a^{7} b^{3} d e^{7} + 6 \, a^{8} b^{2} e^{8}\right)} x^{4} + 4 \, {\left(a b^{9} d^{8} - 3 \, a^{2} b^{8} d^{7} e - 2 \, a^{3} b^{7} d^{6} e^{2} + 19 \, a^{4} b^{6} d^{5} e^{3} - 30 \, a^{5} b^{5} d^{4} e^{4} + 19 \, a^{6} b^{4} d^{3} e^{5} - 2 \, a^{7} b^{3} d^{2} e^{6} - 3 \, a^{8} b^{2} d e^{7} + a^{9} b e^{8}\right)} x^{3} + {\left(6 \, a^{2} b^{8} d^{8} - 28 \, a^{3} b^{7} d^{7} e + 43 \, a^{4} b^{6} d^{6} e^{2} - 6 \, a^{5} b^{5} d^{5} e^{3} - 55 \, a^{6} b^{4} d^{4} e^{4} + 64 \, a^{7} b^{3} d^{3} e^{5} - 27 \, a^{8} b^{2} d^{2} e^{6} + 2 \, a^{9} b d e^{7} + a^{10} e^{8}\right)} x^{2} + 2 \, {\left(2 \, a^{3} b^{7} d^{8} - 11 \, a^{4} b^{6} d^{7} e + 24 \, a^{5} b^{5} d^{6} e^{2} - 25 \, a^{6} b^{4} d^{5} e^{3} + 10 \, a^{7} b^{3} d^{4} e^{4} + 3 \, a^{8} b^{2} d^{3} e^{5} - 4 \, a^{9} b d^{2} e^{6} + a^{10} d e^{7}\right)} x\right)}}\right]"," ",0,"[1/384*(3465*(b^5*e^6*x^6 + a^4*b*d^2*e^4 + 2*(b^5*d*e^5 + 2*a*b^4*e^6)*x^5 + (b^5*d^2*e^4 + 8*a*b^4*d*e^5 + 6*a^2*b^3*e^6)*x^4 + 4*(a*b^4*d^2*e^4 + 3*a^2*b^3*d*e^5 + a^3*b^2*e^6)*x^3 + (6*a^2*b^3*d^2*e^4 + 8*a^3*b^2*d*e^5 + a^4*b*e^6)*x^2 + 2*(2*a^3*b^2*d^2*e^4 + a^4*b*d*e^5)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e - 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) + 2*(3465*b^5*e^5*x^5 - 48*b^5*d^5 + 328*a*b^4*d^4*e - 1030*a^2*b^3*d^3*e^2 + 2295*a^3*b^2*d^2*e^3 + 2048*a^4*b*d*e^4 - 128*a^5*e^5 + 1155*(4*b^5*d*e^4 + 11*a*b^4*e^5)*x^4 + 231*(3*b^5*d^2*e^3 + 74*a*b^4*d*e^4 + 73*a^2*b^3*e^5)*x^3 - 99*(2*b^5*d^3*e^2 - 27*a*b^4*d^2*e^3 - 232*a^2*b^3*d*e^4 - 93*a^3*b^2*e^5)*x^2 + 11*(8*b^5*d^4*e - 68*a*b^4*d^3*e^2 + 345*a^2*b^3*d^2*e^3 + 1162*a^3*b^2*d*e^4 + 128*a^4*b*e^5)*x)*sqrt(e*x + d))/(a^4*b^6*d^8 - 6*a^5*b^5*d^7*e + 15*a^6*b^4*d^6*e^2 - 20*a^7*b^3*d^5*e^3 + 15*a^8*b^2*d^4*e^4 - 6*a^9*b*d^3*e^5 + a^10*d^2*e^6 + (b^10*d^6*e^2 - 6*a*b^9*d^5*e^3 + 15*a^2*b^8*d^4*e^4 - 20*a^3*b^7*d^3*e^5 + 15*a^4*b^6*d^2*e^6 - 6*a^5*b^5*d*e^7 + a^6*b^4*e^8)*x^6 + 2*(b^10*d^7*e - 4*a*b^9*d^6*e^2 + 3*a^2*b^8*d^5*e^3 + 10*a^3*b^7*d^4*e^4 - 25*a^4*b^6*d^3*e^5 + 24*a^5*b^5*d^2*e^6 - 11*a^6*b^4*d*e^7 + 2*a^7*b^3*e^8)*x^5 + (b^10*d^8 + 2*a*b^9*d^7*e - 27*a^2*b^8*d^6*e^2 + 64*a^3*b^7*d^5*e^3 - 55*a^4*b^6*d^4*e^4 - 6*a^5*b^5*d^3*e^5 + 43*a^6*b^4*d^2*e^6 - 28*a^7*b^3*d*e^7 + 6*a^8*b^2*e^8)*x^4 + 4*(a*b^9*d^8 - 3*a^2*b^8*d^7*e - 2*a^3*b^7*d^6*e^2 + 19*a^4*b^6*d^5*e^3 - 30*a^5*b^5*d^4*e^4 + 19*a^6*b^4*d^3*e^5 - 2*a^7*b^3*d^2*e^6 - 3*a^8*b^2*d*e^7 + a^9*b*e^8)*x^3 + (6*a^2*b^8*d^8 - 28*a^3*b^7*d^7*e + 43*a^4*b^6*d^6*e^2 - 6*a^5*b^5*d^5*e^3 - 55*a^6*b^4*d^4*e^4 + 64*a^7*b^3*d^3*e^5 - 27*a^8*b^2*d^2*e^6 + 2*a^9*b*d*e^7 + a^10*e^8)*x^2 + 2*(2*a^3*b^7*d^8 - 11*a^4*b^6*d^7*e + 24*a^5*b^5*d^6*e^2 - 25*a^6*b^4*d^5*e^3 + 10*a^7*b^3*d^4*e^4 + 3*a^8*b^2*d^3*e^5 - 4*a^9*b*d^2*e^6 + a^10*d*e^7)*x), -1/192*(3465*(b^5*e^6*x^6 + a^4*b*d^2*e^4 + 2*(b^5*d*e^5 + 2*a*b^4*e^6)*x^5 + (b^5*d^2*e^4 + 8*a*b^4*d*e^5 + 6*a^2*b^3*e^6)*x^4 + 4*(a*b^4*d^2*e^4 + 3*a^2*b^3*d*e^5 + a^3*b^2*e^6)*x^3 + (6*a^2*b^3*d^2*e^4 + 8*a^3*b^2*d*e^5 + a^4*b*e^6)*x^2 + 2*(2*a^3*b^2*d^2*e^4 + a^4*b*d*e^5)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (3465*b^5*e^5*x^5 - 48*b^5*d^5 + 328*a*b^4*d^4*e - 1030*a^2*b^3*d^3*e^2 + 2295*a^3*b^2*d^2*e^3 + 2048*a^4*b*d*e^4 - 128*a^5*e^5 + 1155*(4*b^5*d*e^4 + 11*a*b^4*e^5)*x^4 + 231*(3*b^5*d^2*e^3 + 74*a*b^4*d*e^4 + 73*a^2*b^3*e^5)*x^3 - 99*(2*b^5*d^3*e^2 - 27*a*b^4*d^2*e^3 - 232*a^2*b^3*d*e^4 - 93*a^3*b^2*e^5)*x^2 + 11*(8*b^5*d^4*e - 68*a*b^4*d^3*e^2 + 345*a^2*b^3*d^2*e^3 + 1162*a^3*b^2*d*e^4 + 128*a^4*b*e^5)*x)*sqrt(e*x + d))/(a^4*b^6*d^8 - 6*a^5*b^5*d^7*e + 15*a^6*b^4*d^6*e^2 - 20*a^7*b^3*d^5*e^3 + 15*a^8*b^2*d^4*e^4 - 6*a^9*b*d^3*e^5 + a^10*d^2*e^6 + (b^10*d^6*e^2 - 6*a*b^9*d^5*e^3 + 15*a^2*b^8*d^4*e^4 - 20*a^3*b^7*d^3*e^5 + 15*a^4*b^6*d^2*e^6 - 6*a^5*b^5*d*e^7 + a^6*b^4*e^8)*x^6 + 2*(b^10*d^7*e - 4*a*b^9*d^6*e^2 + 3*a^2*b^8*d^5*e^3 + 10*a^3*b^7*d^4*e^4 - 25*a^4*b^6*d^3*e^5 + 24*a^5*b^5*d^2*e^6 - 11*a^6*b^4*d*e^7 + 2*a^7*b^3*e^8)*x^5 + (b^10*d^8 + 2*a*b^9*d^7*e - 27*a^2*b^8*d^6*e^2 + 64*a^3*b^7*d^5*e^3 - 55*a^4*b^6*d^4*e^4 - 6*a^5*b^5*d^3*e^5 + 43*a^6*b^4*d^2*e^6 - 28*a^7*b^3*d*e^7 + 6*a^8*b^2*e^8)*x^4 + 4*(a*b^9*d^8 - 3*a^2*b^8*d^7*e - 2*a^3*b^7*d^6*e^2 + 19*a^4*b^6*d^5*e^3 - 30*a^5*b^5*d^4*e^4 + 19*a^6*b^4*d^3*e^5 - 2*a^7*b^3*d^2*e^6 - 3*a^8*b^2*d*e^7 + a^9*b*e^8)*x^3 + (6*a^2*b^8*d^8 - 28*a^3*b^7*d^7*e + 43*a^4*b^6*d^6*e^2 - 6*a^5*b^5*d^5*e^3 - 55*a^6*b^4*d^4*e^4 + 64*a^7*b^3*d^3*e^5 - 27*a^8*b^2*d^2*e^6 + 2*a^9*b*d*e^7 + a^10*e^8)*x^2 + 2*(2*a^3*b^7*d^8 - 11*a^4*b^6*d^7*e + 24*a^5*b^5*d^6*e^2 - 25*a^6*b^4*d^5*e^3 + 10*a^7*b^3*d^4*e^4 + 3*a^8*b^2*d^3*e^5 - 4*a^9*b*d^2*e^6 + a^10*d*e^7)*x)]","B",0
1730,1,3368,0,0.509937," ","integrate(1/(e*x+d)^(7/2)/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{45045 \, {\left(b^{6} e^{7} x^{7} + a^{4} b^{2} d^{3} e^{4} + {\left(3 \, b^{6} d e^{6} + 4 \, a b^{5} e^{7}\right)} x^{6} + 3 \, {\left(b^{6} d^{2} e^{5} + 4 \, a b^{5} d e^{6} + 2 \, a^{2} b^{4} e^{7}\right)} x^{5} + {\left(b^{6} d^{3} e^{4} + 12 \, a b^{5} d^{2} e^{5} + 18 \, a^{2} b^{4} d e^{6} + 4 \, a^{3} b^{3} e^{7}\right)} x^{4} + {\left(4 \, a b^{5} d^{3} e^{4} + 18 \, a^{2} b^{4} d^{2} e^{5} + 12 \, a^{3} b^{3} d e^{6} + a^{4} b^{2} e^{7}\right)} x^{3} + 3 \, {\left(2 \, a^{2} b^{4} d^{3} e^{4} + 4 \, a^{3} b^{3} d^{2} e^{5} + a^{4} b^{2} d e^{6}\right)} x^{2} + {\left(4 \, a^{3} b^{3} d^{3} e^{4} + 3 \, a^{4} b^{2} d^{2} e^{5}\right)} x\right)} \sqrt{\frac{b}{b d - a e}} \log\left(\frac{b e x + 2 \, b d - a e + 2 \, {\left(b d - a e\right)} \sqrt{e x + d} \sqrt{\frac{b}{b d - a e}}}{b x + a}\right) - 2 \, {\left(45045 \, b^{6} e^{6} x^{6} - 240 \, b^{6} d^{6} + 1960 \, a b^{5} d^{5} e - 7630 \, a^{2} b^{4} d^{4} e^{2} + 22155 \, a^{3} b^{3} d^{3} e^{3} + 32384 \, a^{4} b^{2} d^{2} e^{4} - 3968 \, a^{5} b d e^{5} + 384 \, a^{6} e^{6} + 15015 \, {\left(7 \, b^{6} d e^{5} + 11 \, a b^{5} e^{6}\right)} x^{5} + 3003 \, {\left(23 \, b^{6} d^{2} e^{4} + 129 \, a b^{5} d e^{5} + 73 \, a^{2} b^{4} e^{6}\right)} x^{4} + 429 \, {\left(15 \, b^{6} d^{3} e^{3} + 599 \, a b^{5} d^{2} e^{4} + 1207 \, a^{2} b^{4} d e^{5} + 279 \, a^{3} b^{3} e^{6}\right)} x^{3} - 143 \, {\left(10 \, b^{6} d^{4} e^{2} - 175 \, a b^{5} d^{3} e^{3} - 2433 \, a^{2} b^{4} d^{2} e^{4} - 1999 \, a^{3} b^{3} d e^{5} - 128 \, a^{4} b^{2} e^{6}\right)} x^{2} + 13 \, {\left(40 \, b^{6} d^{5} e - 420 \, a b^{5} d^{4} e^{2} + 2765 \, a^{2} b^{4} d^{3} e^{3} + 15077 \, a^{3} b^{3} d^{2} e^{4} + 3456 \, a^{4} b^{2} d e^{5} - 128 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{1920 \, {\left(a^{4} b^{7} d^{10} - 7 \, a^{5} b^{6} d^{9} e + 21 \, a^{6} b^{5} d^{8} e^{2} - 35 \, a^{7} b^{4} d^{7} e^{3} + 35 \, a^{8} b^{3} d^{6} e^{4} - 21 \, a^{9} b^{2} d^{5} e^{5} + 7 \, a^{10} b d^{4} e^{6} - a^{11} d^{3} e^{7} + {\left(b^{11} d^{7} e^{3} - 7 \, a b^{10} d^{6} e^{4} + 21 \, a^{2} b^{9} d^{5} e^{5} - 35 \, a^{3} b^{8} d^{4} e^{6} + 35 \, a^{4} b^{7} d^{3} e^{7} - 21 \, a^{5} b^{6} d^{2} e^{8} + 7 \, a^{6} b^{5} d e^{9} - a^{7} b^{4} e^{10}\right)} x^{7} + {\left(3 \, b^{11} d^{8} e^{2} - 17 \, a b^{10} d^{7} e^{3} + 35 \, a^{2} b^{9} d^{6} e^{4} - 21 \, a^{3} b^{8} d^{5} e^{5} - 35 \, a^{4} b^{7} d^{4} e^{6} + 77 \, a^{5} b^{6} d^{3} e^{7} - 63 \, a^{6} b^{5} d^{2} e^{8} + 25 \, a^{7} b^{4} d e^{9} - 4 \, a^{8} b^{3} e^{10}\right)} x^{6} + 3 \, {\left(b^{11} d^{9} e - 3 \, a b^{10} d^{8} e^{2} - 5 \, a^{2} b^{9} d^{7} e^{3} + 35 \, a^{3} b^{8} d^{6} e^{4} - 63 \, a^{4} b^{7} d^{5} e^{5} + 49 \, a^{5} b^{6} d^{4} e^{6} - 7 \, a^{6} b^{5} d^{3} e^{7} - 15 \, a^{7} b^{4} d^{2} e^{8} + 10 \, a^{8} b^{3} d e^{9} - 2 \, a^{9} b^{2} e^{10}\right)} x^{5} + {\left(b^{11} d^{10} + 5 \, a b^{10} d^{9} e - 45 \, a^{2} b^{9} d^{8} e^{2} + 95 \, a^{3} b^{8} d^{7} e^{3} - 35 \, a^{4} b^{7} d^{6} e^{4} - 147 \, a^{5} b^{6} d^{5} e^{5} + 245 \, a^{6} b^{5} d^{4} e^{6} - 155 \, a^{7} b^{4} d^{3} e^{7} + 30 \, a^{8} b^{3} d^{2} e^{8} + 10 \, a^{9} b^{2} d e^{9} - 4 \, a^{10} b e^{10}\right)} x^{4} + {\left(4 \, a b^{10} d^{10} - 10 \, a^{2} b^{9} d^{9} e - 30 \, a^{3} b^{8} d^{8} e^{2} + 155 \, a^{4} b^{7} d^{7} e^{3} - 245 \, a^{5} b^{6} d^{6} e^{4} + 147 \, a^{6} b^{5} d^{5} e^{5} + 35 \, a^{7} b^{4} d^{4} e^{6} - 95 \, a^{8} b^{3} d^{3} e^{7} + 45 \, a^{9} b^{2} d^{2} e^{8} - 5 \, a^{10} b d e^{9} - a^{11} e^{10}\right)} x^{3} + 3 \, {\left(2 \, a^{2} b^{9} d^{10} - 10 \, a^{3} b^{8} d^{9} e + 15 \, a^{4} b^{7} d^{8} e^{2} + 7 \, a^{5} b^{6} d^{7} e^{3} - 49 \, a^{6} b^{5} d^{6} e^{4} + 63 \, a^{7} b^{4} d^{5} e^{5} - 35 \, a^{8} b^{3} d^{4} e^{6} + 5 \, a^{9} b^{2} d^{3} e^{7} + 3 \, a^{10} b d^{2} e^{8} - a^{11} d e^{9}\right)} x^{2} + {\left(4 \, a^{3} b^{8} d^{10} - 25 \, a^{4} b^{7} d^{9} e + 63 \, a^{5} b^{6} d^{8} e^{2} - 77 \, a^{6} b^{5} d^{7} e^{3} + 35 \, a^{7} b^{4} d^{6} e^{4} + 21 \, a^{8} b^{3} d^{5} e^{5} - 35 \, a^{9} b^{2} d^{4} e^{6} + 17 \, a^{10} b d^{3} e^{7} - 3 \, a^{11} d^{2} e^{8}\right)} x\right)}}, -\frac{45045 \, {\left(b^{6} e^{7} x^{7} + a^{4} b^{2} d^{3} e^{4} + {\left(3 \, b^{6} d e^{6} + 4 \, a b^{5} e^{7}\right)} x^{6} + 3 \, {\left(b^{6} d^{2} e^{5} + 4 \, a b^{5} d e^{6} + 2 \, a^{2} b^{4} e^{7}\right)} x^{5} + {\left(b^{6} d^{3} e^{4} + 12 \, a b^{5} d^{2} e^{5} + 18 \, a^{2} b^{4} d e^{6} + 4 \, a^{3} b^{3} e^{7}\right)} x^{4} + {\left(4 \, a b^{5} d^{3} e^{4} + 18 \, a^{2} b^{4} d^{2} e^{5} + 12 \, a^{3} b^{3} d e^{6} + a^{4} b^{2} e^{7}\right)} x^{3} + 3 \, {\left(2 \, a^{2} b^{4} d^{3} e^{4} + 4 \, a^{3} b^{3} d^{2} e^{5} + a^{4} b^{2} d e^{6}\right)} x^{2} + {\left(4 \, a^{3} b^{3} d^{3} e^{4} + 3 \, a^{4} b^{2} d^{2} e^{5}\right)} x\right)} \sqrt{-\frac{b}{b d - a e}} \arctan\left(-\frac{{\left(b d - a e\right)} \sqrt{e x + d} \sqrt{-\frac{b}{b d - a e}}}{b e x + b d}\right) - {\left(45045 \, b^{6} e^{6} x^{6} - 240 \, b^{6} d^{6} + 1960 \, a b^{5} d^{5} e - 7630 \, a^{2} b^{4} d^{4} e^{2} + 22155 \, a^{3} b^{3} d^{3} e^{3} + 32384 \, a^{4} b^{2} d^{2} e^{4} - 3968 \, a^{5} b d e^{5} + 384 \, a^{6} e^{6} + 15015 \, {\left(7 \, b^{6} d e^{5} + 11 \, a b^{5} e^{6}\right)} x^{5} + 3003 \, {\left(23 \, b^{6} d^{2} e^{4} + 129 \, a b^{5} d e^{5} + 73 \, a^{2} b^{4} e^{6}\right)} x^{4} + 429 \, {\left(15 \, b^{6} d^{3} e^{3} + 599 \, a b^{5} d^{2} e^{4} + 1207 \, a^{2} b^{4} d e^{5} + 279 \, a^{3} b^{3} e^{6}\right)} x^{3} - 143 \, {\left(10 \, b^{6} d^{4} e^{2} - 175 \, a b^{5} d^{3} e^{3} - 2433 \, a^{2} b^{4} d^{2} e^{4} - 1999 \, a^{3} b^{3} d e^{5} - 128 \, a^{4} b^{2} e^{6}\right)} x^{2} + 13 \, {\left(40 \, b^{6} d^{5} e - 420 \, a b^{5} d^{4} e^{2} + 2765 \, a^{2} b^{4} d^{3} e^{3} + 15077 \, a^{3} b^{3} d^{2} e^{4} + 3456 \, a^{4} b^{2} d e^{5} - 128 \, a^{5} b e^{6}\right)} x\right)} \sqrt{e x + d}}{960 \, {\left(a^{4} b^{7} d^{10} - 7 \, a^{5} b^{6} d^{9} e + 21 \, a^{6} b^{5} d^{8} e^{2} - 35 \, a^{7} b^{4} d^{7} e^{3} + 35 \, a^{8} b^{3} d^{6} e^{4} - 21 \, a^{9} b^{2} d^{5} e^{5} + 7 \, a^{10} b d^{4} e^{6} - a^{11} d^{3} e^{7} + {\left(b^{11} d^{7} e^{3} - 7 \, a b^{10} d^{6} e^{4} + 21 \, a^{2} b^{9} d^{5} e^{5} - 35 \, a^{3} b^{8} d^{4} e^{6} + 35 \, a^{4} b^{7} d^{3} e^{7} - 21 \, a^{5} b^{6} d^{2} e^{8} + 7 \, a^{6} b^{5} d e^{9} - a^{7} b^{4} e^{10}\right)} x^{7} + {\left(3 \, b^{11} d^{8} e^{2} - 17 \, a b^{10} d^{7} e^{3} + 35 \, a^{2} b^{9} d^{6} e^{4} - 21 \, a^{3} b^{8} d^{5} e^{5} - 35 \, a^{4} b^{7} d^{4} e^{6} + 77 \, a^{5} b^{6} d^{3} e^{7} - 63 \, a^{6} b^{5} d^{2} e^{8} + 25 \, a^{7} b^{4} d e^{9} - 4 \, a^{8} b^{3} e^{10}\right)} x^{6} + 3 \, {\left(b^{11} d^{9} e - 3 \, a b^{10} d^{8} e^{2} - 5 \, a^{2} b^{9} d^{7} e^{3} + 35 \, a^{3} b^{8} d^{6} e^{4} - 63 \, a^{4} b^{7} d^{5} e^{5} + 49 \, a^{5} b^{6} d^{4} e^{6} - 7 \, a^{6} b^{5} d^{3} e^{7} - 15 \, a^{7} b^{4} d^{2} e^{8} + 10 \, a^{8} b^{3} d e^{9} - 2 \, a^{9} b^{2} e^{10}\right)} x^{5} + {\left(b^{11} d^{10} + 5 \, a b^{10} d^{9} e - 45 \, a^{2} b^{9} d^{8} e^{2} + 95 \, a^{3} b^{8} d^{7} e^{3} - 35 \, a^{4} b^{7} d^{6} e^{4} - 147 \, a^{5} b^{6} d^{5} e^{5} + 245 \, a^{6} b^{5} d^{4} e^{6} - 155 \, a^{7} b^{4} d^{3} e^{7} + 30 \, a^{8} b^{3} d^{2} e^{8} + 10 \, a^{9} b^{2} d e^{9} - 4 \, a^{10} b e^{10}\right)} x^{4} + {\left(4 \, a b^{10} d^{10} - 10 \, a^{2} b^{9} d^{9} e - 30 \, a^{3} b^{8} d^{8} e^{2} + 155 \, a^{4} b^{7} d^{7} e^{3} - 245 \, a^{5} b^{6} d^{6} e^{4} + 147 \, a^{6} b^{5} d^{5} e^{5} + 35 \, a^{7} b^{4} d^{4} e^{6} - 95 \, a^{8} b^{3} d^{3} e^{7} + 45 \, a^{9} b^{2} d^{2} e^{8} - 5 \, a^{10} b d e^{9} - a^{11} e^{10}\right)} x^{3} + 3 \, {\left(2 \, a^{2} b^{9} d^{10} - 10 \, a^{3} b^{8} d^{9} e + 15 \, a^{4} b^{7} d^{8} e^{2} + 7 \, a^{5} b^{6} d^{7} e^{3} - 49 \, a^{6} b^{5} d^{6} e^{4} + 63 \, a^{7} b^{4} d^{5} e^{5} - 35 \, a^{8} b^{3} d^{4} e^{6} + 5 \, a^{9} b^{2} d^{3} e^{7} + 3 \, a^{10} b d^{2} e^{8} - a^{11} d e^{9}\right)} x^{2} + {\left(4 \, a^{3} b^{8} d^{10} - 25 \, a^{4} b^{7} d^{9} e + 63 \, a^{5} b^{6} d^{8} e^{2} - 77 \, a^{6} b^{5} d^{7} e^{3} + 35 \, a^{7} b^{4} d^{6} e^{4} + 21 \, a^{8} b^{3} d^{5} e^{5} - 35 \, a^{9} b^{2} d^{4} e^{6} + 17 \, a^{10} b d^{3} e^{7} - 3 \, a^{11} d^{2} e^{8}\right)} x\right)}}\right]"," ",0,"[-1/1920*(45045*(b^6*e^7*x^7 + a^4*b^2*d^3*e^4 + (3*b^6*d*e^6 + 4*a*b^5*e^7)*x^6 + 3*(b^6*d^2*e^5 + 4*a*b^5*d*e^6 + 2*a^2*b^4*e^7)*x^5 + (b^6*d^3*e^4 + 12*a*b^5*d^2*e^5 + 18*a^2*b^4*d*e^6 + 4*a^3*b^3*e^7)*x^4 + (4*a*b^5*d^3*e^4 + 18*a^2*b^4*d^2*e^5 + 12*a^3*b^3*d*e^6 + a^4*b^2*e^7)*x^3 + 3*(2*a^2*b^4*d^3*e^4 + 4*a^3*b^3*d^2*e^5 + a^4*b^2*d*e^6)*x^2 + (4*a^3*b^3*d^3*e^4 + 3*a^4*b^2*d^2*e^5)*x)*sqrt(b/(b*d - a*e))*log((b*e*x + 2*b*d - a*e + 2*(b*d - a*e)*sqrt(e*x + d)*sqrt(b/(b*d - a*e)))/(b*x + a)) - 2*(45045*b^6*e^6*x^6 - 240*b^6*d^6 + 1960*a*b^5*d^5*e - 7630*a^2*b^4*d^4*e^2 + 22155*a^3*b^3*d^3*e^3 + 32384*a^4*b^2*d^2*e^4 - 3968*a^5*b*d*e^5 + 384*a^6*e^6 + 15015*(7*b^6*d*e^5 + 11*a*b^5*e^6)*x^5 + 3003*(23*b^6*d^2*e^4 + 129*a*b^5*d*e^5 + 73*a^2*b^4*e^6)*x^4 + 429*(15*b^6*d^3*e^3 + 599*a*b^5*d^2*e^4 + 1207*a^2*b^4*d*e^5 + 279*a^3*b^3*e^6)*x^3 - 143*(10*b^6*d^4*e^2 - 175*a*b^5*d^3*e^3 - 2433*a^2*b^4*d^2*e^4 - 1999*a^3*b^3*d*e^5 - 128*a^4*b^2*e^6)*x^2 + 13*(40*b^6*d^5*e - 420*a*b^5*d^4*e^2 + 2765*a^2*b^4*d^3*e^3 + 15077*a^3*b^3*d^2*e^4 + 3456*a^4*b^2*d*e^5 - 128*a^5*b*e^6)*x)*sqrt(e*x + d))/(a^4*b^7*d^10 - 7*a^5*b^6*d^9*e + 21*a^6*b^5*d^8*e^2 - 35*a^7*b^4*d^7*e^3 + 35*a^8*b^3*d^6*e^4 - 21*a^9*b^2*d^5*e^5 + 7*a^10*b*d^4*e^6 - a^11*d^3*e^7 + (b^11*d^7*e^3 - 7*a*b^10*d^6*e^4 + 21*a^2*b^9*d^5*e^5 - 35*a^3*b^8*d^4*e^6 + 35*a^4*b^7*d^3*e^7 - 21*a^5*b^6*d^2*e^8 + 7*a^6*b^5*d*e^9 - a^7*b^4*e^10)*x^7 + (3*b^11*d^8*e^2 - 17*a*b^10*d^7*e^3 + 35*a^2*b^9*d^6*e^4 - 21*a^3*b^8*d^5*e^5 - 35*a^4*b^7*d^4*e^6 + 77*a^5*b^6*d^3*e^7 - 63*a^6*b^5*d^2*e^8 + 25*a^7*b^4*d*e^9 - 4*a^8*b^3*e^10)*x^6 + 3*(b^11*d^9*e - 3*a*b^10*d^8*e^2 - 5*a^2*b^9*d^7*e^3 + 35*a^3*b^8*d^6*e^4 - 63*a^4*b^7*d^5*e^5 + 49*a^5*b^6*d^4*e^6 - 7*a^6*b^5*d^3*e^7 - 15*a^7*b^4*d^2*e^8 + 10*a^8*b^3*d*e^9 - 2*a^9*b^2*e^10)*x^5 + (b^11*d^10 + 5*a*b^10*d^9*e - 45*a^2*b^9*d^8*e^2 + 95*a^3*b^8*d^7*e^3 - 35*a^4*b^7*d^6*e^4 - 147*a^5*b^6*d^5*e^5 + 245*a^6*b^5*d^4*e^6 - 155*a^7*b^4*d^3*e^7 + 30*a^8*b^3*d^2*e^8 + 10*a^9*b^2*d*e^9 - 4*a^10*b*e^10)*x^4 + (4*a*b^10*d^10 - 10*a^2*b^9*d^9*e - 30*a^3*b^8*d^8*e^2 + 155*a^4*b^7*d^7*e^3 - 245*a^5*b^6*d^6*e^4 + 147*a^6*b^5*d^5*e^5 + 35*a^7*b^4*d^4*e^6 - 95*a^8*b^3*d^3*e^7 + 45*a^9*b^2*d^2*e^8 - 5*a^10*b*d*e^9 - a^11*e^10)*x^3 + 3*(2*a^2*b^9*d^10 - 10*a^3*b^8*d^9*e + 15*a^4*b^7*d^8*e^2 + 7*a^5*b^6*d^7*e^3 - 49*a^6*b^5*d^6*e^4 + 63*a^7*b^4*d^5*e^5 - 35*a^8*b^3*d^4*e^6 + 5*a^9*b^2*d^3*e^7 + 3*a^10*b*d^2*e^8 - a^11*d*e^9)*x^2 + (4*a^3*b^8*d^10 - 25*a^4*b^7*d^9*e + 63*a^5*b^6*d^8*e^2 - 77*a^6*b^5*d^7*e^3 + 35*a^7*b^4*d^6*e^4 + 21*a^8*b^3*d^5*e^5 - 35*a^9*b^2*d^4*e^6 + 17*a^10*b*d^3*e^7 - 3*a^11*d^2*e^8)*x), -1/960*(45045*(b^6*e^7*x^7 + a^4*b^2*d^3*e^4 + (3*b^6*d*e^6 + 4*a*b^5*e^7)*x^6 + 3*(b^6*d^2*e^5 + 4*a*b^5*d*e^6 + 2*a^2*b^4*e^7)*x^5 + (b^6*d^3*e^4 + 12*a*b^5*d^2*e^5 + 18*a^2*b^4*d*e^6 + 4*a^3*b^3*e^7)*x^4 + (4*a*b^5*d^3*e^4 + 18*a^2*b^4*d^2*e^5 + 12*a^3*b^3*d*e^6 + a^4*b^2*e^7)*x^3 + 3*(2*a^2*b^4*d^3*e^4 + 4*a^3*b^3*d^2*e^5 + a^4*b^2*d*e^6)*x^2 + (4*a^3*b^3*d^3*e^4 + 3*a^4*b^2*d^2*e^5)*x)*sqrt(-b/(b*d - a*e))*arctan(-(b*d - a*e)*sqrt(e*x + d)*sqrt(-b/(b*d - a*e))/(b*e*x + b*d)) - (45045*b^6*e^6*x^6 - 240*b^6*d^6 + 1960*a*b^5*d^5*e - 7630*a^2*b^4*d^4*e^2 + 22155*a^3*b^3*d^3*e^3 + 32384*a^4*b^2*d^2*e^4 - 3968*a^5*b*d*e^5 + 384*a^6*e^6 + 15015*(7*b^6*d*e^5 + 11*a*b^5*e^6)*x^5 + 3003*(23*b^6*d^2*e^4 + 129*a*b^5*d*e^5 + 73*a^2*b^4*e^6)*x^4 + 429*(15*b^6*d^3*e^3 + 599*a*b^5*d^2*e^4 + 1207*a^2*b^4*d*e^5 + 279*a^3*b^3*e^6)*x^3 - 143*(10*b^6*d^4*e^2 - 175*a*b^5*d^3*e^3 - 2433*a^2*b^4*d^2*e^4 - 1999*a^3*b^3*d*e^5 - 128*a^4*b^2*e^6)*x^2 + 13*(40*b^6*d^5*e - 420*a*b^5*d^4*e^2 + 2765*a^2*b^4*d^3*e^3 + 15077*a^3*b^3*d^2*e^4 + 3456*a^4*b^2*d*e^5 - 128*a^5*b*e^6)*x)*sqrt(e*x + d))/(a^4*b^7*d^10 - 7*a^5*b^6*d^9*e + 21*a^6*b^5*d^8*e^2 - 35*a^7*b^4*d^7*e^3 + 35*a^8*b^3*d^6*e^4 - 21*a^9*b^2*d^5*e^5 + 7*a^10*b*d^4*e^6 - a^11*d^3*e^7 + (b^11*d^7*e^3 - 7*a*b^10*d^6*e^4 + 21*a^2*b^9*d^5*e^5 - 35*a^3*b^8*d^4*e^6 + 35*a^4*b^7*d^3*e^7 - 21*a^5*b^6*d^2*e^8 + 7*a^6*b^5*d*e^9 - a^7*b^4*e^10)*x^7 + (3*b^11*d^8*e^2 - 17*a*b^10*d^7*e^3 + 35*a^2*b^9*d^6*e^4 - 21*a^3*b^8*d^5*e^5 - 35*a^4*b^7*d^4*e^6 + 77*a^5*b^6*d^3*e^7 - 63*a^6*b^5*d^2*e^8 + 25*a^7*b^4*d*e^9 - 4*a^8*b^3*e^10)*x^6 + 3*(b^11*d^9*e - 3*a*b^10*d^8*e^2 - 5*a^2*b^9*d^7*e^3 + 35*a^3*b^8*d^6*e^4 - 63*a^4*b^7*d^5*e^5 + 49*a^5*b^6*d^4*e^6 - 7*a^6*b^5*d^3*e^7 - 15*a^7*b^4*d^2*e^8 + 10*a^8*b^3*d*e^9 - 2*a^9*b^2*e^10)*x^5 + (b^11*d^10 + 5*a*b^10*d^9*e - 45*a^2*b^9*d^8*e^2 + 95*a^3*b^8*d^7*e^3 - 35*a^4*b^7*d^6*e^4 - 147*a^5*b^6*d^5*e^5 + 245*a^6*b^5*d^4*e^6 - 155*a^7*b^4*d^3*e^7 + 30*a^8*b^3*d^2*e^8 + 10*a^9*b^2*d*e^9 - 4*a^10*b*e^10)*x^4 + (4*a*b^10*d^10 - 10*a^2*b^9*d^9*e - 30*a^3*b^8*d^8*e^2 + 155*a^4*b^7*d^7*e^3 - 245*a^5*b^6*d^6*e^4 + 147*a^6*b^5*d^5*e^5 + 35*a^7*b^4*d^4*e^6 - 95*a^8*b^3*d^3*e^7 + 45*a^9*b^2*d^2*e^8 - 5*a^10*b*d*e^9 - a^11*e^10)*x^3 + 3*(2*a^2*b^9*d^10 - 10*a^3*b^8*d^9*e + 15*a^4*b^7*d^8*e^2 + 7*a^5*b^6*d^7*e^3 - 49*a^6*b^5*d^6*e^4 + 63*a^7*b^4*d^5*e^5 - 35*a^8*b^3*d^4*e^6 + 5*a^9*b^2*d^3*e^7 + 3*a^10*b*d^2*e^8 - a^11*d*e^9)*x^2 + (4*a^3*b^8*d^10 - 25*a^4*b^7*d^9*e + 63*a^5*b^6*d^8*e^2 - 77*a^6*b^5*d^7*e^3 + 35*a^7*b^4*d^6*e^4 + 21*a^8*b^3*d^5*e^5 - 35*a^9*b^2*d^4*e^6 + 17*a^10*b*d^3*e^7 - 3*a^11*d^2*e^8)*x)]","B",0
1731,1,2230,0,0.451313," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","\frac{{\left(a^{6} d e^{6} m^{6} + 720 \, b^{6} d^{7} - 5040 \, a b^{5} d^{6} e + 15120 \, a^{2} b^{4} d^{5} e^{2} - 25200 \, a^{3} b^{3} d^{4} e^{3} + 25200 \, a^{4} b^{2} d^{3} e^{4} - 15120 \, a^{5} b d^{2} e^{5} + 5040 \, a^{6} d e^{6} + {\left(b^{6} e^{7} m^{6} + 21 \, b^{6} e^{7} m^{5} + 175 \, b^{6} e^{7} m^{4} + 735 \, b^{6} e^{7} m^{3} + 1624 \, b^{6} e^{7} m^{2} + 1764 \, b^{6} e^{7} m + 720 \, b^{6} e^{7}\right)} x^{7} + {\left(5040 \, a b^{5} e^{7} + {\left(b^{6} d e^{6} + 6 \, a b^{5} e^{7}\right)} m^{6} + 3 \, {\left(5 \, b^{6} d e^{6} + 44 \, a b^{5} e^{7}\right)} m^{5} + 5 \, {\left(17 \, b^{6} d e^{6} + 228 \, a b^{5} e^{7}\right)} m^{4} + 15 \, {\left(15 \, b^{6} d e^{6} + 328 \, a b^{5} e^{7}\right)} m^{3} + 2 \, {\left(137 \, b^{6} d e^{6} + 5547 \, a b^{5} e^{7}\right)} m^{2} + 12 \, {\left(10 \, b^{6} d e^{6} + 1019 \, a b^{5} e^{7}\right)} m\right)} x^{6} - 3 \, {\left(2 \, a^{5} b d^{2} e^{5} - 9 \, a^{6} d e^{6}\right)} m^{5} + 3 \, {\left(5040 \, a^{2} b^{4} e^{7} + {\left(2 \, a b^{5} d e^{6} + 5 \, a^{2} b^{4} e^{7}\right)} m^{6} - {\left(2 \, b^{6} d^{2} e^{5} - 34 \, a b^{5} d e^{6} - 115 \, a^{2} b^{4} e^{7}\right)} m^{5} - 5 \, {\left(4 \, b^{6} d^{2} e^{5} - 42 \, a b^{5} d e^{6} - 207 \, a^{2} b^{4} e^{7}\right)} m^{4} - 5 \, {\left(14 \, b^{6} d^{2} e^{5} - 118 \, a b^{5} d e^{6} - 925 \, a^{2} b^{4} e^{7}\right)} m^{3} - 4 \, {\left(25 \, b^{6} d^{2} e^{5} - 187 \, a b^{5} d e^{6} - 2680 \, a^{2} b^{4} e^{7}\right)} m^{2} - 12 \, {\left(4 \, b^{6} d^{2} e^{5} - 28 \, a b^{5} d e^{6} - 1005 \, a^{2} b^{4} e^{7}\right)} m\right)} x^{5} + 5 \, {\left(6 \, a^{4} b^{2} d^{3} e^{4} - 30 \, a^{5} b d^{2} e^{5} + 59 \, a^{6} d e^{6}\right)} m^{4} + 5 \, {\left(5040 \, a^{3} b^{3} e^{7} + {\left(3 \, a^{2} b^{4} d e^{6} + 4 \, a^{3} b^{3} e^{7}\right)} m^{6} - 3 \, {\left(2 \, a b^{5} d^{2} e^{5} - 19 \, a^{2} b^{4} d e^{6} - 32 \, a^{3} b^{3} e^{7}\right)} m^{5} + {\left(6 \, b^{6} d^{3} e^{4} - 78 \, a b^{5} d^{2} e^{5} + 393 \, a^{2} b^{4} d e^{6} + 904 \, a^{3} b^{3} e^{7}\right)} m^{4} + 3 \, {\left(12 \, b^{6} d^{3} e^{4} - 106 \, a b^{5} d^{2} e^{5} + 401 \, a^{2} b^{4} d e^{6} + 1408 \, a^{3} b^{3} e^{7}\right)} m^{3} + 2 \, {\left(33 \, b^{6} d^{3} e^{4} - 249 \, a b^{5} d^{2} e^{5} + 810 \, a^{2} b^{4} d e^{6} + 5090 \, a^{3} b^{3} e^{7}\right)} m^{2} + 36 \, {\left(b^{6} d^{3} e^{4} - 7 \, a b^{5} d^{2} e^{5} + 21 \, a^{2} b^{4} d e^{6} + 328 \, a^{3} b^{3} e^{7}\right)} m\right)} x^{4} - 15 \, {\left(8 \, a^{3} b^{3} d^{4} e^{3} - 44 \, a^{4} b^{2} d^{3} e^{4} + 98 \, a^{5} b d^{2} e^{5} - 111 \, a^{6} d e^{6}\right)} m^{3} + 5 \, {\left(5040 \, a^{4} b^{2} e^{7} + {\left(4 \, a^{3} b^{3} d e^{6} + 3 \, a^{4} b^{2} e^{7}\right)} m^{6} - 3 \, {\left(4 \, a^{2} b^{4} d^{2} e^{5} - 28 \, a^{3} b^{3} d e^{6} - 25 \, a^{4} b^{2} e^{7}\right)} m^{5} + {\left(24 \, a b^{5} d^{3} e^{4} - 192 \, a^{2} b^{4} d^{2} e^{5} + 652 \, a^{3} b^{3} d e^{6} + 741 \, a^{4} b^{2} e^{7}\right)} m^{4} - 3 \, {\left(8 \, b^{6} d^{4} e^{3} - 80 \, a b^{5} d^{3} e^{4} + 332 \, a^{2} b^{4} d^{2} e^{5} - 756 \, a^{3} b^{3} d e^{6} - 1219 \, a^{4} b^{2} e^{7}\right)} m^{3} - 8 \, {\left(9 \, b^{6} d^{4} e^{3} - 69 \, a b^{5} d^{3} e^{4} + 228 \, a^{2} b^{4} d^{2} e^{5} - 422 \, a^{3} b^{3} d e^{6} - 1167 \, a^{4} b^{2} e^{7}\right)} m^{2} - 12 \, {\left(4 \, b^{6} d^{4} e^{3} - 28 \, a b^{5} d^{3} e^{4} + 84 \, a^{2} b^{4} d^{2} e^{5} - 140 \, a^{3} b^{3} d e^{6} - 949 \, a^{4} b^{2} e^{7}\right)} m\right)} x^{3} + 2 \, {\left(180 \, a^{2} b^{4} d^{5} e^{2} - 1080 \, a^{3} b^{3} d^{4} e^{3} + 2685 \, a^{4} b^{2} d^{3} e^{4} - 3525 \, a^{5} b d^{2} e^{5} + 2552 \, a^{6} d e^{6}\right)} m^{2} + 3 \, {\left(5040 \, a^{5} b e^{7} + {\left(5 \, a^{4} b^{2} d e^{6} + 2 \, a^{5} b e^{7}\right)} m^{6} - {\left(20 \, a^{3} b^{3} d^{2} e^{5} - 115 \, a^{4} b^{2} d e^{6} - 52 \, a^{5} b e^{7}\right)} m^{5} + 5 \, {\left(12 \, a^{2} b^{4} d^{3} e^{4} - 76 \, a^{3} b^{3} d^{2} e^{5} + 201 \, a^{4} b^{2} d e^{6} + 108 \, a^{5} b e^{7}\right)} m^{4} - 5 \, {\left(24 \, a b^{5} d^{4} e^{3} - 168 \, a^{2} b^{4} d^{3} e^{4} + 500 \, a^{3} b^{3} d^{2} e^{5} - 817 \, a^{4} b^{2} d e^{6} - 568 \, a^{5} b e^{7}\right)} m^{3} + 2 \, {\left(60 \, b^{6} d^{5} e^{2} - 480 \, a b^{5} d^{4} e^{3} + 1650 \, a^{2} b^{4} d^{3} e^{4} - 3170 \, a^{3} b^{3} d^{2} e^{5} + 3695 \, a^{4} b^{2} d e^{6} + 3929 \, a^{5} b e^{7}\right)} m^{2} + 12 \, {\left(10 \, b^{6} d^{5} e^{2} - 70 \, a b^{5} d^{4} e^{3} + 210 \, a^{2} b^{4} d^{3} e^{4} - 350 \, a^{3} b^{3} d^{2} e^{5} + 350 \, a^{4} b^{2} d e^{6} + 879 \, a^{5} b e^{7}\right)} m\right)} x^{2} - 12 \, {\left(60 \, a b^{5} d^{6} e - 390 \, a^{2} b^{4} d^{5} e^{2} + 1070 \, a^{3} b^{3} d^{4} e^{3} - 1595 \, a^{4} b^{2} d^{3} e^{4} + 1377 \, a^{5} b d^{2} e^{5} - 669 \, a^{6} d e^{6}\right)} m + {\left(5040 \, a^{6} e^{7} + {\left(6 \, a^{5} b d e^{6} + a^{6} e^{7}\right)} m^{6} - 3 \, {\left(10 \, a^{4} b^{2} d^{2} e^{5} - 50 \, a^{5} b d e^{6} - 9 \, a^{6} e^{7}\right)} m^{5} + 5 \, {\left(24 \, a^{3} b^{3} d^{3} e^{4} - 132 \, a^{4} b^{2} d^{2} e^{5} + 294 \, a^{5} b d e^{6} + 59 \, a^{6} e^{7}\right)} m^{4} - 15 \, {\left(24 \, a^{2} b^{4} d^{4} e^{3} - 144 \, a^{3} b^{3} d^{3} e^{4} + 358 \, a^{4} b^{2} d^{2} e^{5} - 470 \, a^{5} b d e^{6} - 111 \, a^{6} e^{7}\right)} m^{3} + 4 \, {\left(180 \, a b^{5} d^{5} e^{2} - 1170 \, a^{2} b^{4} d^{4} e^{3} + 3210 \, a^{3} b^{3} d^{3} e^{4} - 4785 \, a^{4} b^{2} d^{2} e^{5} + 4131 \, a^{5} b d e^{6} + 1276 \, a^{6} e^{7}\right)} m^{2} - 36 \, {\left(20 \, b^{6} d^{6} e - 140 \, a b^{5} d^{5} e^{2} + 420 \, a^{2} b^{4} d^{4} e^{3} - 700 \, a^{3} b^{3} d^{3} e^{4} + 700 \, a^{4} b^{2} d^{2} e^{5} - 420 \, a^{5} b d e^{6} - 223 \, a^{6} e^{7}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{7} m^{7} + 28 \, e^{7} m^{6} + 322 \, e^{7} m^{5} + 1960 \, e^{7} m^{4} + 6769 \, e^{7} m^{3} + 13132 \, e^{7} m^{2} + 13068 \, e^{7} m + 5040 \, e^{7}}"," ",0,"(a^6*d*e^6*m^6 + 720*b^6*d^7 - 5040*a*b^5*d^6*e + 15120*a^2*b^4*d^5*e^2 - 25200*a^3*b^3*d^4*e^3 + 25200*a^4*b^2*d^3*e^4 - 15120*a^5*b*d^2*e^5 + 5040*a^6*d*e^6 + (b^6*e^7*m^6 + 21*b^6*e^7*m^5 + 175*b^6*e^7*m^4 + 735*b^6*e^7*m^3 + 1624*b^6*e^7*m^2 + 1764*b^6*e^7*m + 720*b^6*e^7)*x^7 + (5040*a*b^5*e^7 + (b^6*d*e^6 + 6*a*b^5*e^7)*m^6 + 3*(5*b^6*d*e^6 + 44*a*b^5*e^7)*m^5 + 5*(17*b^6*d*e^6 + 228*a*b^5*e^7)*m^4 + 15*(15*b^6*d*e^6 + 328*a*b^5*e^7)*m^3 + 2*(137*b^6*d*e^6 + 5547*a*b^5*e^7)*m^2 + 12*(10*b^6*d*e^6 + 1019*a*b^5*e^7)*m)*x^6 - 3*(2*a^5*b*d^2*e^5 - 9*a^6*d*e^6)*m^5 + 3*(5040*a^2*b^4*e^7 + (2*a*b^5*d*e^6 + 5*a^2*b^4*e^7)*m^6 - (2*b^6*d^2*e^5 - 34*a*b^5*d*e^6 - 115*a^2*b^4*e^7)*m^5 - 5*(4*b^6*d^2*e^5 - 42*a*b^5*d*e^6 - 207*a^2*b^4*e^7)*m^4 - 5*(14*b^6*d^2*e^5 - 118*a*b^5*d*e^6 - 925*a^2*b^4*e^7)*m^3 - 4*(25*b^6*d^2*e^5 - 187*a*b^5*d*e^6 - 2680*a^2*b^4*e^7)*m^2 - 12*(4*b^6*d^2*e^5 - 28*a*b^5*d*e^6 - 1005*a^2*b^4*e^7)*m)*x^5 + 5*(6*a^4*b^2*d^3*e^4 - 30*a^5*b*d^2*e^5 + 59*a^6*d*e^6)*m^4 + 5*(5040*a^3*b^3*e^7 + (3*a^2*b^4*d*e^6 + 4*a^3*b^3*e^7)*m^6 - 3*(2*a*b^5*d^2*e^5 - 19*a^2*b^4*d*e^6 - 32*a^3*b^3*e^7)*m^5 + (6*b^6*d^3*e^4 - 78*a*b^5*d^2*e^5 + 393*a^2*b^4*d*e^6 + 904*a^3*b^3*e^7)*m^4 + 3*(12*b^6*d^3*e^4 - 106*a*b^5*d^2*e^5 + 401*a^2*b^4*d*e^6 + 1408*a^3*b^3*e^7)*m^3 + 2*(33*b^6*d^3*e^4 - 249*a*b^5*d^2*e^5 + 810*a^2*b^4*d*e^6 + 5090*a^3*b^3*e^7)*m^2 + 36*(b^6*d^3*e^4 - 7*a*b^5*d^2*e^5 + 21*a^2*b^4*d*e^6 + 328*a^3*b^3*e^7)*m)*x^4 - 15*(8*a^3*b^3*d^4*e^3 - 44*a^4*b^2*d^3*e^4 + 98*a^5*b*d^2*e^5 - 111*a^6*d*e^6)*m^3 + 5*(5040*a^4*b^2*e^7 + (4*a^3*b^3*d*e^6 + 3*a^4*b^2*e^7)*m^6 - 3*(4*a^2*b^4*d^2*e^5 - 28*a^3*b^3*d*e^6 - 25*a^4*b^2*e^7)*m^5 + (24*a*b^5*d^3*e^4 - 192*a^2*b^4*d^2*e^5 + 652*a^3*b^3*d*e^6 + 741*a^4*b^2*e^7)*m^4 - 3*(8*b^6*d^4*e^3 - 80*a*b^5*d^3*e^4 + 332*a^2*b^4*d^2*e^5 - 756*a^3*b^3*d*e^6 - 1219*a^4*b^2*e^7)*m^3 - 8*(9*b^6*d^4*e^3 - 69*a*b^5*d^3*e^4 + 228*a^2*b^4*d^2*e^5 - 422*a^3*b^3*d*e^6 - 1167*a^4*b^2*e^7)*m^2 - 12*(4*b^6*d^4*e^3 - 28*a*b^5*d^3*e^4 + 84*a^2*b^4*d^2*e^5 - 140*a^3*b^3*d*e^6 - 949*a^4*b^2*e^7)*m)*x^3 + 2*(180*a^2*b^4*d^5*e^2 - 1080*a^3*b^3*d^4*e^3 + 2685*a^4*b^2*d^3*e^4 - 3525*a^5*b*d^2*e^5 + 2552*a^6*d*e^6)*m^2 + 3*(5040*a^5*b*e^7 + (5*a^4*b^2*d*e^6 + 2*a^5*b*e^7)*m^6 - (20*a^3*b^3*d^2*e^5 - 115*a^4*b^2*d*e^6 - 52*a^5*b*e^7)*m^5 + 5*(12*a^2*b^4*d^3*e^4 - 76*a^3*b^3*d^2*e^5 + 201*a^4*b^2*d*e^6 + 108*a^5*b*e^7)*m^4 - 5*(24*a*b^5*d^4*e^3 - 168*a^2*b^4*d^3*e^4 + 500*a^3*b^3*d^2*e^5 - 817*a^4*b^2*d*e^6 - 568*a^5*b*e^7)*m^3 + 2*(60*b^6*d^5*e^2 - 480*a*b^5*d^4*e^3 + 1650*a^2*b^4*d^3*e^4 - 3170*a^3*b^3*d^2*e^5 + 3695*a^4*b^2*d*e^6 + 3929*a^5*b*e^7)*m^2 + 12*(10*b^6*d^5*e^2 - 70*a*b^5*d^4*e^3 + 210*a^2*b^4*d^3*e^4 - 350*a^3*b^3*d^2*e^5 + 350*a^4*b^2*d*e^6 + 879*a^5*b*e^7)*m)*x^2 - 12*(60*a*b^5*d^6*e - 390*a^2*b^4*d^5*e^2 + 1070*a^3*b^3*d^4*e^3 - 1595*a^4*b^2*d^3*e^4 + 1377*a^5*b*d^2*e^5 - 669*a^6*d*e^6)*m + (5040*a^6*e^7 + (6*a^5*b*d*e^6 + a^6*e^7)*m^6 - 3*(10*a^4*b^2*d^2*e^5 - 50*a^5*b*d*e^6 - 9*a^6*e^7)*m^5 + 5*(24*a^3*b^3*d^3*e^4 - 132*a^4*b^2*d^2*e^5 + 294*a^5*b*d*e^6 + 59*a^6*e^7)*m^4 - 15*(24*a^2*b^4*d^4*e^3 - 144*a^3*b^3*d^3*e^4 + 358*a^4*b^2*d^2*e^5 - 470*a^5*b*d*e^6 - 111*a^6*e^7)*m^3 + 4*(180*a*b^5*d^5*e^2 - 1170*a^2*b^4*d^4*e^3 + 3210*a^3*b^3*d^3*e^4 - 4785*a^4*b^2*d^2*e^5 + 4131*a^5*b*d*e^6 + 1276*a^6*e^7)*m^2 - 36*(20*b^6*d^6*e - 140*a*b^5*d^5*e^2 + 420*a^2*b^4*d^4*e^3 - 700*a^3*b^3*d^3*e^4 + 700*a^4*b^2*d^2*e^5 - 420*a^5*b*d*e^6 - 223*a^6*e^7)*m)*x)*(e*x + d)^m/(e^7*m^7 + 28*e^7*m^6 + 322*e^7*m^5 + 1960*e^7*m^4 + 6769*e^7*m^3 + 13132*e^7*m^2 + 13068*e^7*m + 5040*e^7)","B",0
1732,1,901,0,0.417919," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","\frac{{\left(a^{4} d e^{4} m^{4} + 24 \, b^{4} d^{5} - 120 \, a b^{3} d^{4} e + 240 \, a^{2} b^{2} d^{3} e^{2} - 240 \, a^{3} b d^{2} e^{3} + 120 \, a^{4} d e^{4} + {\left(b^{4} e^{5} m^{4} + 10 \, b^{4} e^{5} m^{3} + 35 \, b^{4} e^{5} m^{2} + 50 \, b^{4} e^{5} m + 24 \, b^{4} e^{5}\right)} x^{5} + {\left(120 \, a b^{3} e^{5} + {\left(b^{4} d e^{4} + 4 \, a b^{3} e^{5}\right)} m^{4} + 2 \, {\left(3 \, b^{4} d e^{4} + 22 \, a b^{3} e^{5}\right)} m^{3} + {\left(11 \, b^{4} d e^{4} + 164 \, a b^{3} e^{5}\right)} m^{2} + 2 \, {\left(3 \, b^{4} d e^{4} + 122 \, a b^{3} e^{5}\right)} m\right)} x^{4} - 2 \, {\left(2 \, a^{3} b d^{2} e^{3} - 7 \, a^{4} d e^{4}\right)} m^{3} + 2 \, {\left(120 \, a^{2} b^{2} e^{5} + {\left(2 \, a b^{3} d e^{4} + 3 \, a^{2} b^{2} e^{5}\right)} m^{4} - 2 \, {\left(b^{4} d^{2} e^{3} - 8 \, a b^{3} d e^{4} - 18 \, a^{2} b^{2} e^{5}\right)} m^{3} - {\left(6 \, b^{4} d^{2} e^{3} - 34 \, a b^{3} d e^{4} - 147 \, a^{2} b^{2} e^{5}\right)} m^{2} - 2 \, {\left(2 \, b^{4} d^{2} e^{3} - 10 \, a b^{3} d e^{4} - 117 \, a^{2} b^{2} e^{5}\right)} m\right)} x^{3} + {\left(12 \, a^{2} b^{2} d^{3} e^{2} - 48 \, a^{3} b d^{2} e^{3} + 71 \, a^{4} d e^{4}\right)} m^{2} + 2 \, {\left(120 \, a^{3} b e^{5} + {\left(3 \, a^{2} b^{2} d e^{4} + 2 \, a^{3} b e^{5}\right)} m^{4} - 2 \, {\left(3 \, a b^{3} d^{2} e^{3} - 15 \, a^{2} b^{2} d e^{4} - 13 \, a^{3} b e^{5}\right)} m^{3} + {\left(6 \, b^{4} d^{3} e^{2} - 36 \, a b^{3} d^{2} e^{3} + 87 \, a^{2} b^{2} d e^{4} + 118 \, a^{3} b e^{5}\right)} m^{2} + 2 \, {\left(3 \, b^{4} d^{3} e^{2} - 15 \, a b^{3} d^{2} e^{3} + 30 \, a^{2} b^{2} d e^{4} + 107 \, a^{3} b e^{5}\right)} m\right)} x^{2} - 2 \, {\left(12 \, a b^{3} d^{4} e - 54 \, a^{2} b^{2} d^{3} e^{2} + 94 \, a^{3} b d^{2} e^{3} - 77 \, a^{4} d e^{4}\right)} m + {\left(120 \, a^{4} e^{5} + {\left(4 \, a^{3} b d e^{4} + a^{4} e^{5}\right)} m^{4} - 2 \, {\left(6 \, a^{2} b^{2} d^{2} e^{3} - 24 \, a^{3} b d e^{4} - 7 \, a^{4} e^{5}\right)} m^{3} + {\left(24 \, a b^{3} d^{3} e^{2} - 108 \, a^{2} b^{2} d^{2} e^{3} + 188 \, a^{3} b d e^{4} + 71 \, a^{4} e^{5}\right)} m^{2} - 2 \, {\left(12 \, b^{4} d^{4} e - 60 \, a b^{3} d^{3} e^{2} + 120 \, a^{2} b^{2} d^{2} e^{3} - 120 \, a^{3} b d e^{4} - 77 \, a^{4} e^{5}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{5} m^{5} + 15 \, e^{5} m^{4} + 85 \, e^{5} m^{3} + 225 \, e^{5} m^{2} + 274 \, e^{5} m + 120 \, e^{5}}"," ",0,"(a^4*d*e^4*m^4 + 24*b^4*d^5 - 120*a*b^3*d^4*e + 240*a^2*b^2*d^3*e^2 - 240*a^3*b*d^2*e^3 + 120*a^4*d*e^4 + (b^4*e^5*m^4 + 10*b^4*e^5*m^3 + 35*b^4*e^5*m^2 + 50*b^4*e^5*m + 24*b^4*e^5)*x^5 + (120*a*b^3*e^5 + (b^4*d*e^4 + 4*a*b^3*e^5)*m^4 + 2*(3*b^4*d*e^4 + 22*a*b^3*e^5)*m^3 + (11*b^4*d*e^4 + 164*a*b^3*e^5)*m^2 + 2*(3*b^4*d*e^4 + 122*a*b^3*e^5)*m)*x^4 - 2*(2*a^3*b*d^2*e^3 - 7*a^4*d*e^4)*m^3 + 2*(120*a^2*b^2*e^5 + (2*a*b^3*d*e^4 + 3*a^2*b^2*e^5)*m^4 - 2*(b^4*d^2*e^3 - 8*a*b^3*d*e^4 - 18*a^2*b^2*e^5)*m^3 - (6*b^4*d^2*e^3 - 34*a*b^3*d*e^4 - 147*a^2*b^2*e^5)*m^2 - 2*(2*b^4*d^2*e^3 - 10*a*b^3*d*e^4 - 117*a^2*b^2*e^5)*m)*x^3 + (12*a^2*b^2*d^3*e^2 - 48*a^3*b*d^2*e^3 + 71*a^4*d*e^4)*m^2 + 2*(120*a^3*b*e^5 + (3*a^2*b^2*d*e^4 + 2*a^3*b*e^5)*m^4 - 2*(3*a*b^3*d^2*e^3 - 15*a^2*b^2*d*e^4 - 13*a^3*b*e^5)*m^3 + (6*b^4*d^3*e^2 - 36*a*b^3*d^2*e^3 + 87*a^2*b^2*d*e^4 + 118*a^3*b*e^5)*m^2 + 2*(3*b^4*d^3*e^2 - 15*a*b^3*d^2*e^3 + 30*a^2*b^2*d*e^4 + 107*a^3*b*e^5)*m)*x^2 - 2*(12*a*b^3*d^4*e - 54*a^2*b^2*d^3*e^2 + 94*a^3*b*d^2*e^3 - 77*a^4*d*e^4)*m + (120*a^4*e^5 + (4*a^3*b*d*e^4 + a^4*e^5)*m^4 - 2*(6*a^2*b^2*d^2*e^3 - 24*a^3*b*d*e^4 - 7*a^4*e^5)*m^3 + (24*a*b^3*d^3*e^2 - 108*a^2*b^2*d^2*e^3 + 188*a^3*b*d*e^4 + 71*a^4*e^5)*m^2 - 2*(12*b^4*d^4*e - 60*a*b^3*d^3*e^2 + 120*a^2*b^2*d^2*e^3 - 120*a^3*b*d*e^4 - 77*a^4*e^5)*m)*x)*(e*x + d)^m/(e^5*m^5 + 15*e^5*m^4 + 85*e^5*m^3 + 225*e^5*m^2 + 274*e^5*m + 120*e^5)","B",0
1733,1,237,0,0.414673," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","\frac{{\left(a^{2} d e^{2} m^{2} + 2 \, b^{2} d^{3} - 6 \, a b d^{2} e + 6 \, a^{2} d e^{2} + {\left(b^{2} e^{3} m^{2} + 3 \, b^{2} e^{3} m + 2 \, b^{2} e^{3}\right)} x^{3} + {\left(6 \, a b e^{3} + {\left(b^{2} d e^{2} + 2 \, a b e^{3}\right)} m^{2} + {\left(b^{2} d e^{2} + 8 \, a b e^{3}\right)} m\right)} x^{2} - {\left(2 \, a b d^{2} e - 5 \, a^{2} d e^{2}\right)} m + {\left(6 \, a^{2} e^{3} + {\left(2 \, a b d e^{2} + a^{2} e^{3}\right)} m^{2} - {\left(2 \, b^{2} d^{2} e - 6 \, a b d e^{2} - 5 \, a^{2} e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{3} m^{3} + 6 \, e^{3} m^{2} + 11 \, e^{3} m + 6 \, e^{3}}"," ",0,"(a^2*d*e^2*m^2 + 2*b^2*d^3 - 6*a*b*d^2*e + 6*a^2*d*e^2 + (b^2*e^3*m^2 + 3*b^2*e^3*m + 2*b^2*e^3)*x^3 + (6*a*b*e^3 + (b^2*d*e^2 + 2*a*b*e^3)*m^2 + (b^2*d*e^2 + 8*a*b*e^3)*m)*x^2 - (2*a*b*d^2*e - 5*a^2*d*e^2)*m + (6*a^2*e^3 + (2*a*b*d*e^2 + a^2*e^3)*m^2 - (2*b^2*d^2*e - 6*a*b*d*e^2 - 5*a^2*e^3)*m)*x)*(e*x + d)^m/(e^3*m^3 + 6*e^3*m^2 + 11*e^3*m + 6*e^3)","B",0
1734,0,0,0,0.413379," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right)"," ",0,"integral((e*x + d)^m/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
1735,0,0,0,0.416992," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}}, x\right)"," ",0,"integral((e*x + d)^m/(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4), x)","F",0
1736,0,0,0,0.447716," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{b^{6} x^{6} + 6 \, a b^{5} x^{5} + 15 \, a^{2} b^{4} x^{4} + 20 \, a^{3} b^{3} x^{3} + 15 \, a^{4} b^{2} x^{2} + 6 \, a^{5} b x + a^{6}}, x\right)"," ",0,"integral((e*x + d)^m/(b^6*x^6 + 6*a*b^5*x^5 + 15*a^2*b^4*x^4 + 20*a^3*b^3*x^3 + 15*a^4*b^2*x^2 + 6*a^5*b*x + a^6), x)","F",0
1737,1,1460,0,0.444477," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","\frac{{\left(a^{5} d e^{5} m^{5} - 120 \, b^{5} d^{6} + 720 \, a b^{4} d^{5} e - 1800 \, a^{2} b^{3} d^{4} e^{2} + 2400 \, a^{3} b^{2} d^{3} e^{3} - 1800 \, a^{4} b d^{2} e^{4} + 720 \, a^{5} d e^{5} + {\left(b^{5} e^{6} m^{5} + 15 \, b^{5} e^{6} m^{4} + 85 \, b^{5} e^{6} m^{3} + 225 \, b^{5} e^{6} m^{2} + 274 \, b^{5} e^{6} m + 120 \, b^{5} e^{6}\right)} x^{6} + {\left(720 \, a b^{4} e^{6} + {\left(b^{5} d e^{5} + 5 \, a b^{4} e^{6}\right)} m^{5} + 10 \, {\left(b^{5} d e^{5} + 8 \, a b^{4} e^{6}\right)} m^{4} + 5 \, {\left(7 \, b^{5} d e^{5} + 95 \, a b^{4} e^{6}\right)} m^{3} + 50 \, {\left(b^{5} d e^{5} + 26 \, a b^{4} e^{6}\right)} m^{2} + 12 \, {\left(2 \, b^{5} d e^{5} + 135 \, a b^{4} e^{6}\right)} m\right)} x^{5} - 5 \, {\left(a^{4} b d^{2} e^{4} - 4 \, a^{5} d e^{5}\right)} m^{4} + 5 \, {\left(360 \, a^{2} b^{3} e^{6} + {\left(a b^{4} d e^{5} + 2 \, a^{2} b^{3} e^{6}\right)} m^{5} - {\left(b^{5} d^{2} e^{4} - 12 \, a b^{4} d e^{5} - 34 \, a^{2} b^{3} e^{6}\right)} m^{4} - {\left(6 \, b^{5} d^{2} e^{4} - 47 \, a b^{4} d e^{5} - 214 \, a^{2} b^{3} e^{6}\right)} m^{3} - {\left(11 \, b^{5} d^{2} e^{4} - 72 \, a b^{4} d e^{5} - 614 \, a^{2} b^{3} e^{6}\right)} m^{2} - 6 \, {\left(b^{5} d^{2} e^{4} - 6 \, a b^{4} d e^{5} - 132 \, a^{2} b^{3} e^{6}\right)} m\right)} x^{4} + 5 \, {\left(4 \, a^{3} b^{2} d^{3} e^{3} - 18 \, a^{4} b d^{2} e^{4} + 31 \, a^{5} d e^{5}\right)} m^{3} + 10 \, {\left(240 \, a^{3} b^{2} e^{6} + {\left(a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} m^{5} - 2 \, {\left(a b^{4} d^{2} e^{4} - 7 \, a^{2} b^{3} d e^{5} - 9 \, a^{3} b^{2} e^{6}\right)} m^{4} + {\left(2 \, b^{5} d^{3} e^{3} - 18 \, a b^{4} d^{2} e^{4} + 65 \, a^{2} b^{3} d e^{5} + 121 \, a^{3} b^{2} e^{6}\right)} m^{3} + 2 \, {\left(3 \, b^{5} d^{3} e^{3} - 20 \, a b^{4} d^{2} e^{4} + 56 \, a^{2} b^{3} d e^{5} + 186 \, a^{3} b^{2} e^{6}\right)} m^{2} + 4 \, {\left(b^{5} d^{3} e^{3} - 6 \, a b^{4} d^{2} e^{4} + 15 \, a^{2} b^{3} d e^{5} + 127 \, a^{3} b^{2} e^{6}\right)} m\right)} x^{3} - 5 \, {\left(12 \, a^{2} b^{3} d^{4} e^{2} - 60 \, a^{3} b^{2} d^{3} e^{3} + 119 \, a^{4} b d^{2} e^{4} - 116 \, a^{5} d e^{5}\right)} m^{2} + 5 \, {\left(360 \, a^{4} b e^{6} + {\left(2 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} m^{5} - {\left(6 \, a^{2} b^{3} d^{2} e^{4} - 32 \, a^{3} b^{2} d e^{5} - 19 \, a^{4} b e^{6}\right)} m^{4} + {\left(12 \, a b^{4} d^{3} e^{3} - 72 \, a^{2} b^{3} d^{2} e^{4} + 178 \, a^{3} b^{2} d e^{5} + 137 \, a^{4} b e^{6}\right)} m^{3} - {\left(12 \, b^{5} d^{4} e^{2} - 84 \, a b^{4} d^{3} e^{3} + 246 \, a^{2} b^{3} d^{2} e^{4} - 388 \, a^{3} b^{2} d e^{5} - 461 \, a^{4} b e^{6}\right)} m^{2} - 6 \, {\left(2 \, b^{5} d^{4} e^{2} - 12 \, a b^{4} d^{3} e^{3} + 30 \, a^{2} b^{3} d^{2} e^{4} - 40 \, a^{3} b^{2} d e^{5} - 117 \, a^{4} b e^{6}\right)} m\right)} x^{2} + 2 \, {\left(60 \, a b^{4} d^{5} e - 330 \, a^{2} b^{3} d^{4} e^{2} + 740 \, a^{3} b^{2} d^{3} e^{3} - 855 \, a^{4} b d^{2} e^{4} + 522 \, a^{5} d e^{5}\right)} m + {\left(720 \, a^{5} e^{6} + {\left(5 \, a^{4} b d e^{5} + a^{5} e^{6}\right)} m^{5} - 10 \, {\left(2 \, a^{3} b^{2} d^{2} e^{4} - 9 \, a^{4} b d e^{5} - 2 \, a^{5} e^{6}\right)} m^{4} + 5 \, {\left(12 \, a^{2} b^{3} d^{3} e^{3} - 60 \, a^{3} b^{2} d^{2} e^{4} + 119 \, a^{4} b d e^{5} + 31 \, a^{5} e^{6}\right)} m^{3} - 10 \, {\left(12 \, a b^{4} d^{4} e^{2} - 66 \, a^{2} b^{3} d^{3} e^{3} + 148 \, a^{3} b^{2} d^{2} e^{4} - 171 \, a^{4} b d e^{5} - 58 \, a^{5} e^{6}\right)} m^{2} + 12 \, {\left(10 \, b^{5} d^{5} e - 60 \, a b^{4} d^{4} e^{2} + 150 \, a^{2} b^{3} d^{3} e^{3} - 200 \, a^{3} b^{2} d^{2} e^{4} + 150 \, a^{4} b d e^{5} + 87 \, a^{5} e^{6}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{6} m^{6} + 21 \, e^{6} m^{5} + 175 \, e^{6} m^{4} + 735 \, e^{6} m^{3} + 1624 \, e^{6} m^{2} + 1764 \, e^{6} m + 720 \, e^{6}}"," ",0,"(a^5*d*e^5*m^5 - 120*b^5*d^6 + 720*a*b^4*d^5*e - 1800*a^2*b^3*d^4*e^2 + 2400*a^3*b^2*d^3*e^3 - 1800*a^4*b*d^2*e^4 + 720*a^5*d*e^5 + (b^5*e^6*m^5 + 15*b^5*e^6*m^4 + 85*b^5*e^6*m^3 + 225*b^5*e^6*m^2 + 274*b^5*e^6*m + 120*b^5*e^6)*x^6 + (720*a*b^4*e^6 + (b^5*d*e^5 + 5*a*b^4*e^6)*m^5 + 10*(b^5*d*e^5 + 8*a*b^4*e^6)*m^4 + 5*(7*b^5*d*e^5 + 95*a*b^4*e^6)*m^3 + 50*(b^5*d*e^5 + 26*a*b^4*e^6)*m^2 + 12*(2*b^5*d*e^5 + 135*a*b^4*e^6)*m)*x^5 - 5*(a^4*b*d^2*e^4 - 4*a^5*d*e^5)*m^4 + 5*(360*a^2*b^3*e^6 + (a*b^4*d*e^5 + 2*a^2*b^3*e^6)*m^5 - (b^5*d^2*e^4 - 12*a*b^4*d*e^5 - 34*a^2*b^3*e^6)*m^4 - (6*b^5*d^2*e^4 - 47*a*b^4*d*e^5 - 214*a^2*b^3*e^6)*m^3 - (11*b^5*d^2*e^4 - 72*a*b^4*d*e^5 - 614*a^2*b^3*e^6)*m^2 - 6*(b^5*d^2*e^4 - 6*a*b^4*d*e^5 - 132*a^2*b^3*e^6)*m)*x^4 + 5*(4*a^3*b^2*d^3*e^3 - 18*a^4*b*d^2*e^4 + 31*a^5*d*e^5)*m^3 + 10*(240*a^3*b^2*e^6 + (a^2*b^3*d*e^5 + a^3*b^2*e^6)*m^5 - 2*(a*b^4*d^2*e^4 - 7*a^2*b^3*d*e^5 - 9*a^3*b^2*e^6)*m^4 + (2*b^5*d^3*e^3 - 18*a*b^4*d^2*e^4 + 65*a^2*b^3*d*e^5 + 121*a^3*b^2*e^6)*m^3 + 2*(3*b^5*d^3*e^3 - 20*a*b^4*d^2*e^4 + 56*a^2*b^3*d*e^5 + 186*a^3*b^2*e^6)*m^2 + 4*(b^5*d^3*e^3 - 6*a*b^4*d^2*e^4 + 15*a^2*b^3*d*e^5 + 127*a^3*b^2*e^6)*m)*x^3 - 5*(12*a^2*b^3*d^4*e^2 - 60*a^3*b^2*d^3*e^3 + 119*a^4*b*d^2*e^4 - 116*a^5*d*e^5)*m^2 + 5*(360*a^4*b*e^6 + (2*a^3*b^2*d*e^5 + a^4*b*e^6)*m^5 - (6*a^2*b^3*d^2*e^4 - 32*a^3*b^2*d*e^5 - 19*a^4*b*e^6)*m^4 + (12*a*b^4*d^3*e^3 - 72*a^2*b^3*d^2*e^4 + 178*a^3*b^2*d*e^5 + 137*a^4*b*e^6)*m^3 - (12*b^5*d^4*e^2 - 84*a*b^4*d^3*e^3 + 246*a^2*b^3*d^2*e^4 - 388*a^3*b^2*d*e^5 - 461*a^4*b*e^6)*m^2 - 6*(2*b^5*d^4*e^2 - 12*a*b^4*d^3*e^3 + 30*a^2*b^3*d^2*e^4 - 40*a^3*b^2*d*e^5 - 117*a^4*b*e^6)*m)*x^2 + 2*(60*a*b^4*d^5*e - 330*a^2*b^3*d^4*e^2 + 740*a^3*b^2*d^3*e^3 - 855*a^4*b*d^2*e^4 + 522*a^5*d*e^5)*m + (720*a^5*e^6 + (5*a^4*b*d*e^5 + a^5*e^6)*m^5 - 10*(2*a^3*b^2*d^2*e^4 - 9*a^4*b*d*e^5 - 2*a^5*e^6)*m^4 + 5*(12*a^2*b^3*d^3*e^3 - 60*a^3*b^2*d^2*e^4 + 119*a^4*b*d*e^5 + 31*a^5*e^6)*m^3 - 10*(12*a*b^4*d^4*e^2 - 66*a^2*b^3*d^3*e^3 + 148*a^3*b^2*d^2*e^4 - 171*a^4*b*d*e^5 - 58*a^5*e^6)*m^2 + 12*(10*b^5*d^5*e - 60*a*b^4*d^4*e^2 + 150*a^2*b^3*d^3*e^3 - 200*a^3*b^2*d^2*e^4 + 150*a^4*b*d*e^5 + 87*a^5*e^6)*m)*x)*(e*x + d)^m/(e^6*m^6 + 21*e^6*m^5 + 175*e^6*m^4 + 735*e^6*m^3 + 1624*e^6*m^2 + 1764*e^6*m + 720*e^6)","B",0
1738,1,496,0,0.418952," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{3} d e^{3} m^{3} - 6 \, b^{3} d^{4} + 24 \, a b^{2} d^{3} e - 36 \, a^{2} b d^{2} e^{2} + 24 \, a^{3} d e^{3} + {\left(b^{3} e^{4} m^{3} + 6 \, b^{3} e^{4} m^{2} + 11 \, b^{3} e^{4} m + 6 \, b^{3} e^{4}\right)} x^{4} + {\left(24 \, a b^{2} e^{4} + {\left(b^{3} d e^{3} + 3 \, a b^{2} e^{4}\right)} m^{3} + 3 \, {\left(b^{3} d e^{3} + 7 \, a b^{2} e^{4}\right)} m^{2} + 2 \, {\left(b^{3} d e^{3} + 21 \, a b^{2} e^{4}\right)} m\right)} x^{3} - 3 \, {\left(a^{2} b d^{2} e^{2} - 3 \, a^{3} d e^{3}\right)} m^{2} + 3 \, {\left(12 \, a^{2} b e^{4} + {\left(a b^{2} d e^{3} + a^{2} b e^{4}\right)} m^{3} - {\left(b^{3} d^{2} e^{2} - 5 \, a b^{2} d e^{3} - 8 \, a^{2} b e^{4}\right)} m^{2} - {\left(b^{3} d^{2} e^{2} - 4 \, a b^{2} d e^{3} - 19 \, a^{2} b e^{4}\right)} m\right)} x^{2} + {\left(6 \, a b^{2} d^{3} e - 21 \, a^{2} b d^{2} e^{2} + 26 \, a^{3} d e^{3}\right)} m + {\left(24 \, a^{3} e^{4} + {\left(3 \, a^{2} b d e^{3} + a^{3} e^{4}\right)} m^{3} - 3 \, {\left(2 \, a b^{2} d^{2} e^{2} - 7 \, a^{2} b d e^{3} - 3 \, a^{3} e^{4}\right)} m^{2} + 2 \, {\left(3 \, b^{3} d^{3} e - 12 \, a b^{2} d^{2} e^{2} + 18 \, a^{2} b d e^{3} + 13 \, a^{3} e^{4}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 10 \, e^{4} m^{3} + 35 \, e^{4} m^{2} + 50 \, e^{4} m + 24 \, e^{4}}"," ",0,"(a^3*d*e^3*m^3 - 6*b^3*d^4 + 24*a*b^2*d^3*e - 36*a^2*b*d^2*e^2 + 24*a^3*d*e^3 + (b^3*e^4*m^3 + 6*b^3*e^4*m^2 + 11*b^3*e^4*m + 6*b^3*e^4)*x^4 + (24*a*b^2*e^4 + (b^3*d*e^3 + 3*a*b^2*e^4)*m^3 + 3*(b^3*d*e^3 + 7*a*b^2*e^4)*m^2 + 2*(b^3*d*e^3 + 21*a*b^2*e^4)*m)*x^3 - 3*(a^2*b*d^2*e^2 - 3*a^3*d*e^3)*m^2 + 3*(12*a^2*b*e^4 + (a*b^2*d*e^3 + a^2*b*e^4)*m^3 - (b^3*d^2*e^2 - 5*a*b^2*d*e^3 - 8*a^2*b*e^4)*m^2 - (b^3*d^2*e^2 - 4*a*b^2*d*e^3 - 19*a^2*b*e^4)*m)*x^2 + (6*a*b^2*d^3*e - 21*a^2*b*d^2*e^2 + 26*a^3*d*e^3)*m + (24*a^3*e^4 + (3*a^2*b*d*e^3 + a^3*e^4)*m^3 - 3*(2*a*b^2*d^2*e^2 - 7*a^2*b*d*e^3 - 3*a^3*e^4)*m^2 + 2*(3*b^3*d^3*e - 12*a*b^2*d^2*e^2 + 18*a^2*b*d*e^3 + 13*a^3*e^4)*m)*x)*(e*x + d)^m/(e^4*m^4 + 10*e^4*m^3 + 35*e^4*m^2 + 50*e^4*m + 24*e^4)","B",0
1739,1,83,0,0.417973," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d e m - b d^{2} + 2 \, a d e + {\left(b e^{2} m + b e^{2}\right)} x^{2} + {\left(2 \, a e^{2} + {\left(b d e + a e^{2}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{2} m^{2} + 3 \, e^{2} m + 2 \, e^{2}}"," ",0,"(a*d*e*m - b*d^2 + 2*a*d*e + (b*e^2*m + b*e^2)*x^2 + (2*a*e^2 + (b*d*e + a*e^2)*m)*x)*(e*x + d)^m/(e^2*m^2 + 3*e^2*m + 2*e^2)","A",0
1740,0,0,0,0.417722," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}}}, x\right)"," ",0,"integral((e*x + d)^m/sqrt(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
1741,0,0,0,0.432980," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}} {\left(e x + d\right)}^{m}}{b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}}, x\right)"," ",0,"integral(sqrt(b^2*x^2 + 2*a*b*x + a^2)*(e*x + d)^m/(b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4), x)","F",0
1742,0,0,0,0.431598," ","integrate((e*x+d)^m/(b^2*x^2+2*a*b*x+a^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2}} {\left(e x + d\right)}^{m}}{b^{6} x^{6} + 6 \, a b^{5} x^{5} + 15 \, a^{2} b^{4} x^{4} + 20 \, a^{3} b^{3} x^{3} + 15 \, a^{4} b^{2} x^{2} + 6 \, a^{5} b x + a^{6}}, x\right)"," ",0,"integral(sqrt(b^2*x^2 + 2*a*b*x + a^2)*(e*x + d)^m/(b^6*x^6 + 6*a*b^5*x^5 + 15*a^2*b^4*x^4 + 20*a^3*b^3*x^3 + 15*a^4*b^2*x^2 + 6*a^5*b*x + a^6), x)","F",0
1743,0,0,0,0.436285," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)^p*(e*x + d)^m, x)","F",0
1744,1,516,0,0.428459," ","integrate((e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(4 \, a b^{3} d^{3} p^{3} + 12 \, a b^{3} d^{3} - 18 \, a^{2} b^{2} d^{2} e + 12 \, a^{3} b d e^{2} - 3 \, a^{4} e^{3} + {\left(4 \, b^{4} e^{3} p^{3} + 12 \, b^{4} e^{3} p^{2} + 11 \, b^{4} e^{3} p + 3 \, b^{4} e^{3}\right)} x^{4} + 2 \, {\left(6 \, b^{4} d e^{2} + 2 \, {\left(3 \, b^{4} d e^{2} + a b^{3} e^{3}\right)} p^{3} + 3 \, {\left(7 \, b^{4} d e^{2} + a b^{3} e^{3}\right)} p^{2} + {\left(21 \, b^{4} d e^{2} + a b^{3} e^{3}\right)} p\right)} x^{3} + 6 \, {\left(3 \, a b^{3} d^{3} - a^{2} b^{2} d^{2} e\right)} p^{2} + 3 \, {\left(6 \, b^{4} d^{2} e + 4 \, {\left(b^{4} d^{2} e + a b^{3} d e^{2}\right)} p^{3} + 2 \, {\left(8 \, b^{4} d^{2} e + 5 \, a b^{3} d e^{2} - a^{2} b^{2} e^{3}\right)} p^{2} + {\left(19 \, b^{4} d^{2} e + 4 \, a b^{3} d e^{2} - a^{2} b^{2} e^{3}\right)} p\right)} x^{2} + {\left(26 \, a b^{3} d^{3} - 21 \, a^{2} b^{2} d^{2} e + 6 \, a^{3} b d e^{2}\right)} p + 2 \, {\left(6 \, b^{4} d^{3} + 2 \, {\left(b^{4} d^{3} + 3 \, a b^{3} d^{2} e\right)} p^{3} + 3 \, {\left(3 \, b^{4} d^{3} + 7 \, a b^{3} d^{2} e - 2 \, a^{2} b^{2} d e^{2}\right)} p^{2} + {\left(13 \, b^{4} d^{3} + 18 \, a b^{3} d^{2} e - 12 \, a^{2} b^{2} d e^{2} + 3 \, a^{3} b e^{3}\right)} p\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{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*a*b^3*d^3*p^3 + 12*a*b^3*d^3 - 18*a^2*b^2*d^2*e + 12*a^3*b*d*e^2 - 3*a^4*e^3 + (4*b^4*e^3*p^3 + 12*b^4*e^3*p^2 + 11*b^4*e^3*p + 3*b^4*e^3)*x^4 + 2*(6*b^4*d*e^2 + 2*(3*b^4*d*e^2 + a*b^3*e^3)*p^3 + 3*(7*b^4*d*e^2 + a*b^3*e^3)*p^2 + (21*b^4*d*e^2 + a*b^3*e^3)*p)*x^3 + 6*(3*a*b^3*d^3 - a^2*b^2*d^2*e)*p^2 + 3*(6*b^4*d^2*e + 4*(b^4*d^2*e + a*b^3*d*e^2)*p^3 + 2*(8*b^4*d^2*e + 5*a*b^3*d*e^2 - a^2*b^2*e^3)*p^2 + (19*b^4*d^2*e + 4*a*b^3*d*e^2 - a^2*b^2*e^3)*p)*x^2 + (26*a*b^3*d^3 - 21*a^2*b^2*d^2*e + 6*a^3*b*d*e^2)*p + 2*(6*b^4*d^3 + 2*(b^4*d^3 + 3*a*b^3*d^2*e)*p^3 + 3*(3*b^4*d^3 + 7*a*b^3*d^2*e - 2*a^2*b^2*d*e^2)*p^2 + (13*b^4*d^3 + 18*a*b^3*d^2*e - 12*a^2*b^2*d*e^2 + 3*a^3*b*e^3)*p)*x)*(b^2*x^2 + 2*a*b*x + a^2)^p/(4*b^4*p^4 + 20*b^4*p^3 + 35*b^4*p^2 + 25*b^4*p + 6*b^4)","B",0
1745,1,249,0,0.405588," ","integrate((e*x+d)^2*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(2 \, a b^{2} d^{2} p^{2} + 3 \, a b^{2} d^{2} - 3 \, a^{2} b d e + a^{3} e^{2} + {\left(2 \, b^{3} e^{2} p^{2} + 3 \, b^{3} e^{2} p + b^{3} e^{2}\right)} x^{3} + {\left(3 \, b^{3} d e + 2 \, {\left(2 \, b^{3} d e + a b^{2} e^{2}\right)} p^{2} + {\left(8 \, b^{3} d e + a b^{2} e^{2}\right)} p\right)} x^{2} + {\left(5 \, a b^{2} d^{2} - 2 \, a^{2} b d e\right)} p + {\left(3 \, b^{3} d^{2} + 2 \, {\left(b^{3} d^{2} + 2 \, a b^{2} d e\right)} p^{2} + {\left(5 \, b^{3} d^{2} + 6 \, a b^{2} d e - 2 \, a^{2} b e^{2}\right)} p\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{4 \, b^{3} p^{3} + 12 \, b^{3} p^{2} + 11 \, b^{3} p + 3 \, b^{3}}"," ",0,"(2*a*b^2*d^2*p^2 + 3*a*b^2*d^2 - 3*a^2*b*d*e + a^3*e^2 + (2*b^3*e^2*p^2 + 3*b^3*e^2*p + b^3*e^2)*x^3 + (3*b^3*d*e + 2*(2*b^3*d*e + a*b^2*e^2)*p^2 + (8*b^3*d*e + a*b^2*e^2)*p)*x^2 + (5*a*b^2*d^2 - 2*a^2*b*d*e)*p + (3*b^3*d^2 + 2*(b^3*d^2 + 2*a*b^2*d*e)*p^2 + (5*b^3*d^2 + 6*a*b^2*d*e - 2*a^2*b*e^2)*p)*x)*(b^2*x^2 + 2*a*b*x + a^2)^p/(4*b^3*p^3 + 12*b^3*p^2 + 11*b^3*p + 3*b^3)","A",0
1746,1,96,0,0.409892," ","integrate((e*x+d)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(2 \, a b d p + 2 \, a b d - a^{2} e + {\left(2 \, b^{2} e p + b^{2} e\right)} x^{2} + 2 \, {\left(b^{2} d + {\left(b^{2} d + a b e\right)} p\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{2 \, {\left(2 \, b^{2} p^{2} + 3 \, b^{2} p + b^{2}\right)}}"," ",0,"1/2*(2*a*b*d*p + 2*a*b*d - a^2*e + (2*b^2*e*p + b^2*e)*x^2 + 2*(b^2*d + (b^2*d + a*b*e)*p)*x)*(b^2*x^2 + 2*a*b*x + a^2)^p/(2*b^2*p^2 + 3*b^2*p + b^2)","A",0
1747,1,32,0,0.417293," ","integrate((b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(b x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{2 \, b p + b}"," ",0,"(b*x + a)*(b^2*x^2 + 2*a*b*x + a^2)^p/(2*b*p + b)","A",0
1748,0,0,0,0.423812," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{e x + d}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)^p/(e*x + d), x)","F",0
1749,0,0,0,0.436473," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)^p/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
1750,0,0,0,0.430245," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)^p/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
1751,0,0,0,0.431828," ","integrate((e*x+d)^(3/2)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)}^{\frac{3}{2}} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}, x\right)"," ",0,"integral((e*x + d)^(3/2)*(b^2*x^2 + 2*a*b*x + a^2)^p, x)","F",0
1752,0,0,0,0.425687," ","integrate((e*x+d)^(1/2)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x + d} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}, x\right)"," ",0,"integral(sqrt(e*x + d)*(b^2*x^2 + 2*a*b*x + a^2)^p, x)","F",0
1753,0,0,0,0.414049," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)^p/sqrt(e*x + d), x)","F",0
1754,0,0,0,0.427610," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x + d} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral(sqrt(e*x + d)*(b^2*x^2 + 2*a*b*x + a^2)^p/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
1755,0,0,0,0.421078," ","integrate((b^2*x^2+2*a*b*x+a^2)^p/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x + d} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral(sqrt(e*x + d)*(b^2*x^2 + 2*a*b*x + a^2)^p/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
1756,0,0,0,0.422467," ","integrate((e*x+d)^m*(b^2*x^2+2*a*b*x+a^2)^(5+p),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p + 5} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)^(p + 5)*(e*x + d)^m, x)","F",0
1757,1,219,0,0.429436," ","integrate((e*x+d)^(-3-2*p)*(b^2*x^2+2*a*b*x+a^2)^p,x, algorithm=""fricas"")","\frac{{\left(b^{2} e^{2} x^{3} + 2 \, a b d^{2} - a^{2} d e + {\left(3 \, b^{2} d e + 2 \, {\left(b^{2} d e - a b e^{2}\right)} p\right)} x^{2} + 2 \, {\left(a b d^{2} - a^{2} d e\right)} p + {\left(2 \, b^{2} d^{2} + 2 \, a b d e - a^{2} e^{2} + 2 \, {\left(b^{2} d^{2} - a^{2} e^{2}\right)} p\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}}{2 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2} + 2 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} p^{2} + 3 \, {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} p\right)}}"," ",0,"1/2*(b^2*e^2*x^3 + 2*a*b*d^2 - a^2*d*e + (3*b^2*d*e + 2*(b^2*d*e - a*b*e^2)*p)*x^2 + 2*(a*b*d^2 - a^2*d*e)*p + (2*b^2*d^2 + 2*a*b*d*e - a^2*e^2 + 2*(b^2*d^2 - a^2*e^2)*p)*x)*(b^2*x^2 + 2*a*b*x + a^2)^p*(e*x + d)^(-2*p - 3)/(b^2*d^2 - 2*a*b*d*e + a^2*e^2 + 2*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*p^2 + 3*(b^2*d^2 - 2*a*b*d*e + a^2*e^2)*p)","A",0
1758,1,64,0,0.404415," ","integrate((e*x+d)*(4*x^2+12*x+9)^p,x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(2 \, e p + e\right)} x^{2} + 12 \, d p + 4 \, {\left({\left(2 \, d + 3 \, e\right)} p + 2 \, d\right)} x + 12 \, d - 9 \, e\right)} {\left(4 \, x^{2} + 12 \, x + 9\right)}^{p}}{8 \, {\left(2 \, p^{2} + 3 \, p + 1\right)}}"," ",0,"1/8*(4*(2*e*p + e)*x^2 + 12*d*p + 4*((2*d + 3*e)*p + 2*d)*x + 12*d - 9*e)*(4*x^2 + 12*x + 9)^p/(2*p^2 + 3*p + 1)","A",0
1759,1,97,0,0.356102," ","integrate((b*x+a)^3*(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{1}{6} x^{6} d b^{4} + \frac{1}{5} x^{5} c b^{4} + \frac{4}{5} x^{5} d b^{3} a + x^{4} c b^{3} a + \frac{3}{2} x^{4} d b^{2} a^{2} + 2 x^{3} c b^{2} a^{2} + \frac{4}{3} x^{3} d b a^{3} + 2 x^{2} c b a^{3} + \frac{1}{2} x^{2} d a^{4} + x c a^{4}"," ",0,"1/6*x^6*d*b^4 + 1/5*x^5*c*b^4 + 4/5*x^5*d*b^3*a + x^4*c*b^3*a + 3/2*x^4*d*b^2*a^2 + 2*x^3*c*b^2*a^2 + 4/3*x^3*d*b*a^3 + 2*x^2*c*b*a^3 + 1/2*x^2*d*a^4 + x*c*a^4","B",0
1760,1,72,0,0.341949," ","integrate((b*x+a)^2*(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{1}{5} x^{5} d b^{3} + \frac{1}{4} x^{4} c b^{3} + \frac{3}{4} x^{4} d b^{2} a + x^{3} c b^{2} a + x^{3} d b a^{2} + \frac{3}{2} x^{2} c b a^{2} + \frac{1}{2} x^{2} d a^{3} + x c a^{3}"," ",0,"1/5*x^5*d*b^3 + 1/4*x^4*c*b^3 + 3/4*x^4*d*b^2*a + x^3*c*b^2*a + x^3*d*b*a^2 + 3/2*x^2*c*b*a^2 + 1/2*x^2*d*a^3 + x*c*a^3","B",0
1761,1,49,0,0.336723," ","integrate((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{1}{4} x^{4} d b^{2} + \frac{1}{3} x^{3} c b^{2} + \frac{2}{3} x^{3} d b a + x^{2} c b a + \frac{1}{2} x^{2} d a^{2} + x c a^{2}"," ",0,"1/4*x^4*d*b^2 + 1/3*x^3*c*b^2 + 2/3*x^3*d*b*a + x^2*c*b*a + 1/2*x^2*d*a^2 + x*c*a^2","A",0
1762,1,26,0,0.340231," ","integrate(a*c+(a*d+b*c)*x+b*d*x^2,x, algorithm=""fricas"")","\frac{1}{3} x^{3} d b + \frac{1}{2} x^{2} c b + \frac{1}{2} x^{2} d a + x c a"," ",0,"1/3*x^3*d*b + 1/2*x^2*c*b + 1/2*x^2*d*a + x*c*a","A",0
1763,1,10,0,0.390917," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a),x, algorithm=""fricas"")","\frac{1}{2} \, d x^{2} + c x"," ",0,"1/2*d*x^2 + c*x","A",0
1764,1,24,0,0.400968," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{b d x + {\left(b c - a d\right)} \log\left(b x + a\right)}{b^{2}}"," ",0,"(b*d*x + (b*c - a*d)*log(b*x + a))/b^2","A",0
1765,1,39,0,0.398528," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{b c - a d - {\left(b d x + a d\right)} \log\left(b x + a\right)}{b^{3} x + a b^{2}}"," ",0,"-(b*c - a*d - (b*d*x + a*d)*log(b*x + a))/(b^3*x + a*b^2)","A",0
1766,1,38,0,0.392384," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^4,x, algorithm=""fricas"")","-\frac{2 \, b d x + b c + a d}{2 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-1/2*(2*b*d*x + b*c + a*d)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
1767,1,50,0,0.393147," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^5,x, algorithm=""fricas"")","-\frac{3 \, b d x + 2 \, b c + a d}{6 \, {\left(b^{5} x^{3} + 3 \, a b^{4} x^{2} + 3 \, a^{2} b^{3} x + a^{3} b^{2}\right)}}"," ",0,"-1/6*(3*b*d*x + 2*b*c + a*d)/(b^5*x^3 + 3*a*b^4*x^2 + 3*a^2*b^3*x + a^3*b^2)","A",0
1768,1,61,0,0.389387," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)/(b*x+a)^6,x, algorithm=""fricas"")","-\frac{4 \, b d x + 3 \, b c + a d}{12 \, {\left(b^{6} x^{4} + 4 \, a b^{5} x^{3} + 6 \, a^{2} b^{4} x^{2} + 4 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}"," ",0,"-1/12*(4*b*d*x + 3*b*c + a*d)/(b^6*x^4 + 4*a*b^5*x^3 + 6*a^2*b^4*x^2 + 4*a^3*b^3*x + a^4*b^2)","A",0
1769,1,212,0,0.348209," ","integrate((b*x+a)^3*(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} d^{2} b^{5} + \frac{2}{7} x^{7} d c b^{5} + \frac{5}{7} x^{7} d^{2} b^{4} a + \frac{1}{6} x^{6} c^{2} b^{5} + \frac{5}{3} x^{6} d c b^{4} a + \frac{5}{3} x^{6} d^{2} b^{3} a^{2} + x^{5} c^{2} b^{4} a + 4 x^{5} d c b^{3} a^{2} + 2 x^{5} d^{2} b^{2} a^{3} + \frac{5}{2} x^{4} c^{2} b^{3} a^{2} + 5 x^{4} d c b^{2} a^{3} + \frac{5}{4} x^{4} d^{2} b a^{4} + \frac{10}{3} x^{3} c^{2} b^{2} a^{3} + \frac{10}{3} x^{3} d c b a^{4} + \frac{1}{3} x^{3} d^{2} a^{5} + \frac{5}{2} x^{2} c^{2} b a^{4} + x^{2} d c a^{5} + x c^{2} a^{5}"," ",0,"1/8*x^8*d^2*b^5 + 2/7*x^7*d*c*b^5 + 5/7*x^7*d^2*b^4*a + 1/6*x^6*c^2*b^5 + 5/3*x^6*d*c*b^4*a + 5/3*x^6*d^2*b^3*a^2 + x^5*c^2*b^4*a + 4*x^5*d*c*b^3*a^2 + 2*x^5*d^2*b^2*a^3 + 5/2*x^4*c^2*b^3*a^2 + 5*x^4*d*c*b^2*a^3 + 5/4*x^4*d^2*b*a^4 + 10/3*x^3*c^2*b^2*a^3 + 10/3*x^3*d*c*b*a^4 + 1/3*x^3*d^2*a^5 + 5/2*x^2*c^2*b*a^4 + x^2*d*c*a^5 + x*c^2*a^5","B",0
1770,1,170,0,0.344964," ","integrate((b*x+a)^2*(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} d^{2} b^{4} + \frac{1}{3} x^{6} d c b^{4} + \frac{2}{3} x^{6} d^{2} b^{3} a + \frac{1}{5} x^{5} c^{2} b^{4} + \frac{8}{5} x^{5} d c b^{3} a + \frac{6}{5} x^{5} d^{2} b^{2} a^{2} + x^{4} c^{2} b^{3} a + 3 x^{4} d c b^{2} a^{2} + x^{4} d^{2} b a^{3} + 2 x^{3} c^{2} b^{2} a^{2} + \frac{8}{3} x^{3} d c b a^{3} + \frac{1}{3} x^{3} d^{2} a^{4} + 2 x^{2} c^{2} b a^{3} + x^{2} d c a^{4} + x c^{2} a^{4}"," ",0,"1/7*x^7*d^2*b^4 + 1/3*x^6*d*c*b^4 + 2/3*x^6*d^2*b^3*a + 1/5*x^5*c^2*b^4 + 8/5*x^5*d*c*b^3*a + 6/5*x^5*d^2*b^2*a^2 + x^4*c^2*b^3*a + 3*x^4*d*c*b^2*a^2 + x^4*d^2*b*a^3 + 2*x^3*c^2*b^2*a^2 + 8/3*x^3*d*c*b*a^3 + 1/3*x^3*d^2*a^4 + 2*x^2*c^2*b*a^3 + x^2*d*c*a^4 + x*c^2*a^4","B",0
1771,1,130,0,0.352951," ","integrate((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} d^{2} b^{3} + \frac{2}{5} x^{5} d c b^{3} + \frac{3}{5} x^{5} d^{2} b^{2} a + \frac{1}{4} x^{4} c^{2} b^{3} + \frac{3}{2} x^{4} d c b^{2} a + \frac{3}{4} x^{4} d^{2} b a^{2} + x^{3} c^{2} b^{2} a + 2 x^{3} d c b a^{2} + \frac{1}{3} x^{3} d^{2} a^{3} + \frac{3}{2} x^{2} c^{2} b a^{2} + x^{2} d c a^{3} + x c^{2} a^{3}"," ",0,"1/6*x^6*d^2*b^3 + 2/5*x^5*d*c*b^3 + 3/5*x^5*d^2*b^2*a + 1/4*x^4*c^2*b^3 + 3/2*x^4*d*c*b^2*a + 3/4*x^4*d^2*b*a^2 + x^3*c^2*b^2*a + 2*x^3*d*c*b*a^2 + 1/3*x^3*d^2*a^3 + 3/2*x^2*c^2*b*a^2 + x^2*d*c*a^3 + x*c^2*a^3","B",0
1772,1,89,0,0.355496," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","\frac{1}{5} x^{5} d^{2} b^{2} + \frac{1}{2} x^{4} d c b^{2} + \frac{1}{2} x^{4} d^{2} b a + \frac{1}{3} x^{3} c^{2} b^{2} + \frac{4}{3} x^{3} d c b a + \frac{1}{3} x^{3} d^{2} a^{2} + x^{2} c^{2} b a + x^{2} d c a^{2} + x c^{2} a^{2}"," ",0,"1/5*x^5*d^2*b^2 + 1/2*x^4*d*c*b^2 + 1/2*x^4*d^2*b*a + 1/3*x^3*c^2*b^2 + 4/3*x^3*d*c*b*a + 1/3*x^3*d^2*a^2 + x^2*c^2*b*a + x^2*d*c*a^2 + x*c^2*a^2","A",0
1773,1,48,0,0.387457," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a),x, algorithm=""fricas"")","\frac{1}{4} \, b d^{2} x^{4} + a c^{2} x + \frac{1}{3} \, {\left(2 \, b c d + a d^{2}\right)} x^{3} + \frac{1}{2} \, {\left(b c^{2} + 2 \, a c d\right)} x^{2}"," ",0,"1/4*b*d^2*x^4 + a*c^2*x + 1/3*(2*b*c*d + a*d^2)*x^3 + 1/2*(b*c^2 + 2*a*c*d)*x^2","A",0
1774,1,20,0,0.386823," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{3} \, d^{2} x^{3} + c d x^{2} + c^{2} x"," ",0,"1/3*d^2*x^3 + c*d*x^2 + c^2*x","A",0
1775,1,63,0,0.393738," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^3,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + 2 \, {\left(2 \, b^{2} c d - a b d^{2}\right)} x + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(b^2*d^2*x^2 + 2*(2*b^2*c*d - a*b*d^2)*x + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(b*x + a))/b^3","A",0
1776,1,92,0,0.411742," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^4,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + a b d^{2} x - b^{2} c^{2} + 2 \, a b c d - a^{2} d^{2} + 2 \, {\left(a b c d - a^{2} d^{2} + {\left(b^{2} c d - a b d^{2}\right)} x\right)} \log\left(b x + a\right)}{b^{4} x + a b^{3}}"," ",0,"(b^2*d^2*x^2 + a*b*d^2*x - b^2*c^2 + 2*a*b*c*d - a^2*d^2 + 2*(a*b*c*d - a^2*d^2 + (b^2*c*d - a*b*d^2)*x)*log(b*x + a))/(b^4*x + a*b^3)","A",0
1777,1,99,0,0.388621," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^5,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2} + 4 \, {\left(b^{2} c d - a b d^{2}\right)} x - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"-1/2*(b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2 + 4*(b^2*c*d - a*b*d^2)*x - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
1778,1,84,0,0.400802," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^6,x, algorithm=""fricas"")","-\frac{3 \, b^{2} d^{2} x^{2} + b^{2} c^{2} + a b c d + a^{2} d^{2} + 3 \, {\left(b^{2} c d + a b d^{2}\right)} x}{3 \, {\left(b^{6} x^{3} + 3 \, a b^{5} x^{2} + 3 \, a^{2} b^{4} x + a^{3} b^{3}\right)}}"," ",0,"-1/3*(3*b^2*d^2*x^2 + b^2*c^2 + a*b*c*d + a^2*d^2 + 3*(b^2*c*d + a*b*d^2)*x)/(b^6*x^3 + 3*a*b^5*x^2 + 3*a^2*b^4*x + a^3*b^3)","B",0
1779,1,98,0,0.384986," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^7,x, algorithm=""fricas"")","-\frac{6 \, b^{2} d^{2} x^{2} + 3 \, b^{2} c^{2} + 2 \, a b c d + a^{2} d^{2} + 4 \, {\left(2 \, b^{2} c d + a b d^{2}\right)} x}{12 \, {\left(b^{7} x^{4} + 4 \, a b^{6} x^{3} + 6 \, a^{2} b^{5} x^{2} + 4 \, a^{3} b^{4} x + a^{4} b^{3}\right)}}"," ",0,"-1/12*(6*b^2*d^2*x^2 + 3*b^2*c^2 + 2*a*b*c*d + a^2*d^2 + 4*(2*b^2*c*d + a*b*d^2)*x)/(b^7*x^4 + 4*a*b^6*x^3 + 6*a^2*b^5*x^2 + 4*a^3*b^4*x + a^4*b^3)","A",0
1780,1,109,0,0.381939," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^8,x, algorithm=""fricas"")","-\frac{10 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c^{2} + 3 \, a b c d + a^{2} d^{2} + 5 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{30 \, {\left(b^{8} x^{5} + 5 \, a b^{7} x^{4} + 10 \, a^{2} b^{6} x^{3} + 10 \, a^{3} b^{5} x^{2} + 5 \, a^{4} b^{4} x + a^{5} b^{3}\right)}}"," ",0,"-1/30*(10*b^2*d^2*x^2 + 6*b^2*c^2 + 3*a*b*c*d + a^2*d^2 + 5*(3*b^2*c*d + a*b*d^2)*x)/(b^8*x^5 + 5*a*b^7*x^4 + 10*a^2*b^6*x^3 + 10*a^3*b^5*x^2 + 5*a^4*b^4*x + a^5*b^3)","A",0
1781,1,120,0,0.394731," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^9,x, algorithm=""fricas"")","-\frac{15 \, b^{2} d^{2} x^{2} + 10 \, b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2} + 6 \, {\left(4 \, b^{2} c d + a b d^{2}\right)} x}{60 \, {\left(b^{9} x^{6} + 6 \, a b^{8} x^{5} + 15 \, a^{2} b^{7} x^{4} + 20 \, a^{3} b^{6} x^{3} + 15 \, a^{4} b^{5} x^{2} + 6 \, a^{5} b^{4} x + a^{6} b^{3}\right)}}"," ",0,"-1/60*(15*b^2*d^2*x^2 + 10*b^2*c^2 + 4*a*b*c*d + a^2*d^2 + 6*(4*b^2*c*d + a*b*d^2)*x)/(b^9*x^6 + 6*a*b^8*x^5 + 15*a^2*b^7*x^4 + 20*a^3*b^6*x^3 + 15*a^4*b^5*x^2 + 6*a^5*b^4*x + a^6*b^3)","B",0
1782,1,131,0,0.390697," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^2/(b*x+a)^10,x, algorithm=""fricas"")","-\frac{21 \, b^{2} d^{2} x^{2} + 15 \, b^{2} c^{2} + 5 \, a b c d + a^{2} d^{2} + 7 \, {\left(5 \, b^{2} c d + a b d^{2}\right)} x}{105 \, {\left(b^{10} x^{7} + 7 \, a b^{9} x^{6} + 21 \, a^{2} b^{8} x^{5} + 35 \, a^{3} b^{7} x^{4} + 35 \, a^{4} b^{6} x^{3} + 21 \, a^{5} b^{5} x^{2} + 7 \, a^{6} b^{4} x + a^{7} b^{3}\right)}}"," ",0,"-1/105*(21*b^2*d^2*x^2 + 15*b^2*c^2 + 5*a*b*c*d + a^2*d^2 + 7*(5*b^2*c*d + a*b*d^2)*x)/(b^10*x^7 + 7*a*b^9*x^6 + 21*a^2*b^8*x^5 + 35*a^3*b^7*x^4 + 35*a^4*b^6*x^3 + 21*a^5*b^5*x^2 + 7*a^6*b^4*x + a^7*b^3)","B",0
1783,1,362,0,0.355820," ","integrate((b*x+a)^3*(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} d^{3} b^{6} + \frac{1}{3} x^{9} d^{2} c b^{6} + \frac{2}{3} x^{9} d^{3} b^{5} a + \frac{3}{8} x^{8} d c^{2} b^{6} + \frac{9}{4} x^{8} d^{2} c b^{5} a + \frac{15}{8} x^{8} d^{3} b^{4} a^{2} + \frac{1}{7} x^{7} c^{3} b^{6} + \frac{18}{7} x^{7} d c^{2} b^{5} a + \frac{45}{7} x^{7} d^{2} c b^{4} a^{2} + \frac{20}{7} x^{7} d^{3} b^{3} a^{3} + x^{6} c^{3} b^{5} a + \frac{15}{2} x^{6} d c^{2} b^{4} a^{2} + 10 x^{6} d^{2} c b^{3} a^{3} + \frac{5}{2} x^{6} d^{3} b^{2} a^{4} + 3 x^{5} c^{3} b^{4} a^{2} + 12 x^{5} d c^{2} b^{3} a^{3} + 9 x^{5} d^{2} c b^{2} a^{4} + \frac{6}{5} x^{5} d^{3} b a^{5} + 5 x^{4} c^{3} b^{3} a^{3} + \frac{45}{4} x^{4} d c^{2} b^{2} a^{4} + \frac{9}{2} x^{4} d^{2} c b a^{5} + \frac{1}{4} x^{4} d^{3} a^{6} + 5 x^{3} c^{3} b^{2} a^{4} + 6 x^{3} d c^{2} b a^{5} + x^{3} d^{2} c a^{6} + 3 x^{2} c^{3} b a^{5} + \frac{3}{2} x^{2} d c^{2} a^{6} + x c^{3} a^{6}"," ",0,"1/10*x^10*d^3*b^6 + 1/3*x^9*d^2*c*b^6 + 2/3*x^9*d^3*b^5*a + 3/8*x^8*d*c^2*b^6 + 9/4*x^8*d^2*c*b^5*a + 15/8*x^8*d^3*b^4*a^2 + 1/7*x^7*c^3*b^6 + 18/7*x^7*d*c^2*b^5*a + 45/7*x^7*d^2*c*b^4*a^2 + 20/7*x^7*d^3*b^3*a^3 + x^6*c^3*b^5*a + 15/2*x^6*d*c^2*b^4*a^2 + 10*x^6*d^2*c*b^3*a^3 + 5/2*x^6*d^3*b^2*a^4 + 3*x^5*c^3*b^4*a^2 + 12*x^5*d*c^2*b^3*a^3 + 9*x^5*d^2*c*b^2*a^4 + 6/5*x^5*d^3*b*a^5 + 5*x^4*c^3*b^3*a^3 + 45/4*x^4*d*c^2*b^2*a^4 + 9/2*x^4*d^2*c*b*a^5 + 1/4*x^4*d^3*a^6 + 5*x^3*c^3*b^2*a^4 + 6*x^3*d*c^2*b*a^5 + x^3*d^2*c*a^6 + 3*x^2*c^3*b*a^5 + 3/2*x^2*d*c^2*a^6 + x*c^3*a^6","B",0
1784,1,303,0,0.350022," ","integrate((b*x+a)^2*(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} d^{3} b^{5} + \frac{3}{8} x^{8} d^{2} c b^{5} + \frac{5}{8} x^{8} d^{3} b^{4} a + \frac{3}{7} x^{7} d c^{2} b^{5} + \frac{15}{7} x^{7} d^{2} c b^{4} a + \frac{10}{7} x^{7} d^{3} b^{3} a^{2} + \frac{1}{6} x^{6} c^{3} b^{5} + \frac{5}{2} x^{6} d c^{2} b^{4} a + 5 x^{6} d^{2} c b^{3} a^{2} + \frac{5}{3} x^{6} d^{3} b^{2} a^{3} + x^{5} c^{3} b^{4} a + 6 x^{5} d c^{2} b^{3} a^{2} + 6 x^{5} d^{2} c b^{2} a^{3} + x^{5} d^{3} b a^{4} + \frac{5}{2} x^{4} c^{3} b^{3} a^{2} + \frac{15}{2} x^{4} d c^{2} b^{2} a^{3} + \frac{15}{4} x^{4} d^{2} c b a^{4} + \frac{1}{4} x^{4} d^{3} a^{5} + \frac{10}{3} x^{3} c^{3} b^{2} a^{3} + 5 x^{3} d c^{2} b a^{4} + x^{3} d^{2} c a^{5} + \frac{5}{2} x^{2} c^{3} b a^{4} + \frac{3}{2} x^{2} d c^{2} a^{5} + x c^{3} a^{5}"," ",0,"1/9*x^9*d^3*b^5 + 3/8*x^8*d^2*c*b^5 + 5/8*x^8*d^3*b^4*a + 3/7*x^7*d*c^2*b^5 + 15/7*x^7*d^2*c*b^4*a + 10/7*x^7*d^3*b^3*a^2 + 1/6*x^6*c^3*b^5 + 5/2*x^6*d*c^2*b^4*a + 5*x^6*d^2*c*b^3*a^2 + 5/3*x^6*d^3*b^2*a^3 + x^5*c^3*b^4*a + 6*x^5*d*c^2*b^3*a^2 + 6*x^5*d^2*c*b^2*a^3 + x^5*d^3*b*a^4 + 5/2*x^4*c^3*b^3*a^2 + 15/2*x^4*d*c^2*b^2*a^3 + 15/4*x^4*d^2*c*b*a^4 + 1/4*x^4*d^3*a^5 + 10/3*x^3*c^3*b^2*a^3 + 5*x^3*d*c^2*b*a^4 + x^3*d^2*c*a^5 + 5/2*x^2*c^3*b*a^4 + 3/2*x^2*d*c^2*a^5 + x*c^3*a^5","B",0
1785,1,245,0,0.348644," ","integrate((b*x+a)*(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} d^{3} b^{4} + \frac{3}{7} x^{7} d^{2} c b^{4} + \frac{4}{7} x^{7} d^{3} b^{3} a + \frac{1}{2} x^{6} d c^{2} b^{4} + 2 x^{6} d^{2} c b^{3} a + x^{6} d^{3} b^{2} a^{2} + \frac{1}{5} x^{5} c^{3} b^{4} + \frac{12}{5} x^{5} d c^{2} b^{3} a + \frac{18}{5} x^{5} d^{2} c b^{2} a^{2} + \frac{4}{5} x^{5} d^{3} b a^{3} + x^{4} c^{3} b^{3} a + \frac{9}{2} x^{4} d c^{2} b^{2} a^{2} + 3 x^{4} d^{2} c b a^{3} + \frac{1}{4} x^{4} d^{3} a^{4} + 2 x^{3} c^{3} b^{2} a^{2} + 4 x^{3} d c^{2} b a^{3} + x^{3} d^{2} c a^{4} + 2 x^{2} c^{3} b a^{3} + \frac{3}{2} x^{2} d c^{2} a^{4} + x c^{3} a^{4}"," ",0,"1/8*x^8*d^3*b^4 + 3/7*x^7*d^2*c*b^4 + 4/7*x^7*d^3*b^3*a + 1/2*x^6*d*c^2*b^4 + 2*x^6*d^2*c*b^3*a + x^6*d^3*b^2*a^2 + 1/5*x^5*c^3*b^4 + 12/5*x^5*d*c^2*b^3*a + 18/5*x^5*d^2*c*b^2*a^2 + 4/5*x^5*d^3*b*a^3 + x^4*c^3*b^3*a + 9/2*x^4*d*c^2*b^2*a^2 + 3*x^4*d^2*c*b*a^3 + 1/4*x^4*d^3*a^4 + 2*x^3*c^3*b^2*a^2 + 4*x^3*d*c^2*b*a^3 + x^3*d^2*c*a^4 + 2*x^2*c^3*b*a^3 + 3/2*x^2*d*c^2*a^4 + x*c^3*a^4","B",0
1786,1,188,0,0.349256," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","\frac{1}{7} x^{7} d^{3} b^{3} + \frac{1}{2} x^{6} d^{2} c b^{3} + \frac{1}{2} x^{6} d^{3} b^{2} a + \frac{3}{5} x^{5} d c^{2} b^{3} + \frac{9}{5} x^{5} d^{2} c b^{2} a + \frac{3}{5} x^{5} d^{3} b a^{2} + \frac{1}{4} x^{4} c^{3} b^{3} + \frac{9}{4} x^{4} d c^{2} b^{2} a + \frac{9}{4} x^{4} d^{2} c b a^{2} + \frac{1}{4} x^{4} d^{3} a^{3} + x^{3} c^{3} b^{2} a + 3 x^{3} d c^{2} b a^{2} + x^{3} d^{2} c a^{3} + \frac{3}{2} x^{2} c^{3} b a^{2} + \frac{3}{2} x^{2} d c^{2} a^{3} + x c^{3} a^{3}"," ",0,"1/7*x^7*d^3*b^3 + 1/2*x^6*d^2*c*b^3 + 1/2*x^6*d^3*b^2*a + 3/5*x^5*d*c^2*b^3 + 9/5*x^5*d^2*c*b^2*a + 3/5*x^5*d^3*b*a^2 + 1/4*x^4*c^3*b^3 + 9/4*x^4*d*c^2*b^2*a + 9/4*x^4*d^2*c*b*a^2 + 1/4*x^4*d^3*a^3 + x^3*c^3*b^2*a + 3*x^3*d*c^2*b*a^2 + x^3*d^2*c*a^3 + 3/2*x^2*c^3*b*a^2 + 3/2*x^2*d*c^2*a^3 + x*c^3*a^3","B",0
1787,1,124,0,0.395604," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a),x, algorithm=""fricas"")","\frac{1}{6} \, b^{2} d^{3} x^{6} + a^{2} c^{3} x + \frac{1}{5} \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} x^{5} + \frac{1}{4} \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + a^{2} d^{3}\right)} x^{4} + \frac{1}{3} \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 3 \, a^{2} c d^{2}\right)} x^{3} + \frac{1}{2} \, {\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d\right)} x^{2}"," ",0,"1/6*b^2*d^3*x^6 + a^2*c^3*x + 1/5*(3*b^2*c*d^2 + 2*a*b*d^3)*x^5 + 1/4*(3*b^2*c^2*d + 6*a*b*c*d^2 + a^2*d^3)*x^4 + 1/3*(b^2*c^3 + 6*a*b*c^2*d + 3*a^2*c*d^2)*x^3 + 1/2*(2*a*b*c^3 + 3*a^2*c^2*d)*x^2","B",0
1788,1,69,0,0.378265," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{5} \, b d^{3} x^{5} + a c^{3} x + \frac{1}{4} \, {\left(3 \, b c d^{2} + a d^{3}\right)} x^{4} + {\left(b c^{2} d + a c d^{2}\right)} x^{3} + \frac{1}{2} \, {\left(b c^{3} + 3 \, a c^{2} d\right)} x^{2}"," ",0,"1/5*b*d^3*x^5 + a*c^3*x + 1/4*(3*b*c*d^2 + a*d^3)*x^4 + (b*c^2*d + a*c*d^2)*x^3 + 1/2*(b*c^3 + 3*a*c^2*d)*x^2","B",0
1789,1,31,0,0.382557," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^3,x, algorithm=""fricas"")","\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
1790,1,116,0,0.402391," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^4,x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 3 \, {\left(3 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(3 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x + 6 \, {\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(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*b^3*d^3*x^3 + 3*(3*b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(3*b^3*c^2*d - 3*a*b^2*c*d^2 + a^2*b*d^3)*x + 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(b*x + a))/b^4","A",0
1791,1,173,0,0.399237," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^5,x, algorithm=""fricas"")","\frac{b^{3} d^{3} x^{3} - 2 \, b^{3} c^{3} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + 2 \, a^{3} d^{3} + 3 \, {\left(2 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} c d^{2} - 2 \, a^{2} b d^{3}\right)} x + 6 \, {\left(a b^{2} c^{2} d - 2 \, a^{2} b c d^{2} + a^{3} d^{3} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"1/2*(b^3*d^3*x^3 - 2*b^3*c^3 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + 2*a^3*d^3 + 3*(2*b^3*c*d^2 - a*b^2*d^3)*x^2 + 2*(3*a*b^2*c*d^2 - 2*a^2*b*d^3)*x + 6*(a*b^2*c^2*d - 2*a^2*b*c*d^2 + a^3*d^3 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))/(b^5*x + a*b^4)","B",0
1792,1,188,0,0.407902," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^6,x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 4 \, a b^{2} d^{3} x^{2} - b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3} - 2 \, {\left(3 \, b^{3} c^{2} d - 6 \, a b^{2} c d^{2} + 2 \, a^{2} b d^{3}\right)} x + 6 \, {\left(a^{2} b c d^{2} - a^{3} d^{3} + {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(a b^{2} c d^{2} - a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/2*(2*b^3*d^3*x^3 + 4*a*b^2*d^3*x^2 - b^3*c^3 - 3*a*b^2*c^2*d + 9*a^2*b*c*d^2 - 5*a^3*d^3 - 2*(3*b^3*c^2*d - 6*a*b^2*c*d^2 + 2*a^2*b*d^3)*x + 6*(a^2*b*c*d^2 - a^3*d^3 + (b^3*c*d^2 - a*b^2*d^3)*x^2 + 2*(a*b^2*c*d^2 - a^2*b*d^3)*x)*log(b*x + a))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","B",0
1793,1,176,0,0.395478," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^7,x, algorithm=""fricas"")","-\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} + 18 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 9 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)}{6 \, {\left(b^{7} x^{3} + 3 \, a b^{6} x^{2} + 3 \, a^{2} b^{5} x + a^{3} b^{4}\right)}}"," ",0,"-1/6*(2*b^3*c^3 + 3*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 11*a^3*d^3 + 18*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 9*(b^3*c^2*d + 2*a*b^2*c*d^2 - 3*a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))/(b^7*x^3 + 3*a*b^6*x^2 + 3*a^2*b^5*x + a^3*b^4)","B",0
1794,1,143,0,0.401521," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^8,x, algorithm=""fricas"")","-\frac{4 \, b^{3} d^{3} x^{3} + b^{3} c^{3} + a b^{2} c^{2} d + 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} + 4 \, {\left(b^{3} c^{2} d + a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{4 \, {\left(b^{8} x^{4} + 4 \, a b^{7} x^{3} + 6 \, a^{2} b^{6} x^{2} + 4 \, a^{3} b^{5} x + a^{4} b^{4}\right)}}"," ",0,"-1/4*(4*b^3*d^3*x^3 + b^3*c^3 + a*b^2*c^2*d + a^2*b*c*d^2 + a^3*d^3 + 6*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + a*b^2*c*d^2 + a^2*b*d^3)*x)/(b^8*x^4 + 4*a*b^7*x^3 + 6*a^2*b^6*x^2 + 4*a^3*b^5*x + a^4*b^4)","B",0
1795,1,160,0,0.394080," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^9,x, algorithm=""fricas"")","-\frac{10 \, b^{3} d^{3} x^{3} + 4 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d + 2 \, a^{2} b c d^{2} + a^{3} d^{3} + 10 \, {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 5 \, {\left(3 \, b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{20 \, {\left(b^{9} x^{5} + 5 \, a b^{8} x^{4} + 10 \, a^{2} b^{7} x^{3} + 10 \, a^{3} b^{6} x^{2} + 5 \, a^{4} b^{5} x + a^{5} b^{4}\right)}}"," ",0,"-1/20*(10*b^3*d^3*x^3 + 4*b^3*c^3 + 3*a*b^2*c^2*d + 2*a^2*b*c*d^2 + a^3*d^3 + 10*(2*b^3*c*d^2 + a*b^2*d^3)*x^2 + 5*(3*b^3*c^2*d + 2*a*b^2*c*d^2 + a^2*b*d^3)*x)/(b^9*x^5 + 5*a*b^8*x^4 + 10*a^2*b^7*x^3 + 10*a^3*b^6*x^2 + 5*a^4*b^5*x + a^5*b^4)","B",0
1796,1,171,0,0.400886," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^10,x, algorithm=""fricas"")","-\frac{20 \, b^{3} d^{3} x^{3} + 10 \, b^{3} c^{3} + 6 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3} + 15 \, {\left(3 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(6 \, b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{60 \, {\left(b^{10} x^{6} + 6 \, a b^{9} x^{5} + 15 \, a^{2} b^{8} x^{4} + 20 \, a^{3} b^{7} x^{3} + 15 \, a^{4} b^{6} x^{2} + 6 \, a^{5} b^{5} x + a^{6} b^{4}\right)}}"," ",0,"-1/60*(20*b^3*d^3*x^3 + 10*b^3*c^3 + 6*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3 + 15*(3*b^3*c*d^2 + a*b^2*d^3)*x^2 + 6*(6*b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*x)/(b^10*x^6 + 6*a*b^9*x^5 + 15*a^2*b^8*x^4 + 20*a^3*b^7*x^3 + 15*a^4*b^6*x^2 + 6*a^5*b^5*x + a^6*b^4)","B",0
1797,1,182,0,0.391537," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^11,x, algorithm=""fricas"")","-\frac{35 \, b^{3} d^{3} x^{3} + 20 \, b^{3} c^{3} + 10 \, a b^{2} c^{2} d + 4 \, a^{2} b c d^{2} + a^{3} d^{3} + 21 \, {\left(4 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 7 \, {\left(10 \, b^{3} c^{2} d + 4 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{140 \, {\left(b^{11} x^{7} + 7 \, a b^{10} x^{6} + 21 \, a^{2} b^{9} x^{5} + 35 \, a^{3} b^{8} x^{4} + 35 \, a^{4} b^{7} x^{3} + 21 \, a^{5} b^{6} x^{2} + 7 \, a^{6} b^{5} x + a^{7} b^{4}\right)}}"," ",0,"-1/140*(35*b^3*d^3*x^3 + 20*b^3*c^3 + 10*a*b^2*c^2*d + 4*a^2*b*c*d^2 + a^3*d^3 + 21*(4*b^3*c*d^2 + a*b^2*d^3)*x^2 + 7*(10*b^3*c^2*d + 4*a*b^2*c*d^2 + a^2*b*d^3)*x)/(b^11*x^7 + 7*a*b^10*x^6 + 21*a^2*b^9*x^5 + 35*a^3*b^8*x^4 + 35*a^4*b^7*x^3 + 21*a^5*b^6*x^2 + 7*a^6*b^5*x + a^7*b^4)","B",0
1798,1,193,0,0.395003," ","integrate((a*c+(a*d+b*c)*x+b*d*x^2)^3/(b*x+a)^12,x, algorithm=""fricas"")","-\frac{56 \, b^{3} d^{3} x^{3} + 35 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d + 5 \, a^{2} b c d^{2} + a^{3} d^{3} + 28 \, {\left(5 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 8 \, {\left(15 \, b^{3} c^{2} d + 5 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{280 \, {\left(b^{12} x^{8} + 8 \, a b^{11} x^{7} + 28 \, a^{2} b^{10} x^{6} + 56 \, a^{3} b^{9} x^{5} + 70 \, a^{4} b^{8} x^{4} + 56 \, a^{5} b^{7} x^{3} + 28 \, a^{6} b^{6} x^{2} + 8 \, a^{7} b^{5} x + a^{8} b^{4}\right)}}"," ",0,"-1/280*(56*b^3*d^3*x^3 + 35*b^3*c^3 + 15*a*b^2*c^2*d + 5*a^2*b*c*d^2 + a^3*d^3 + 28*(5*b^3*c*d^2 + a*b^2*d^3)*x^2 + 8*(15*b^3*c^2*d + 5*a*b^2*c*d^2 + a^2*b*d^3)*x)/(b^12*x^8 + 8*a*b^11*x^7 + 28*a^2*b^10*x^6 + 56*a^3*b^9*x^5 + 70*a^4*b^8*x^4 + 56*a^5*b^7*x^3 + 28*a^6*b^6*x^2 + 8*a^7*b^5*x + a^8*b^4)","B",0
1799,1,259,0,0.395446," ","integrate((b*x+a)^6/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{12 \, b^{5} d^{5} x^{5} - 15 \, {\left(b^{5} c d^{4} - 5 \, a b^{4} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{2} d^{3} - 5 \, a b^{4} c d^{4} + 10 \, a^{2} b^{3} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{3} d^{2} - 5 \, a b^{4} c^{2} d^{3} + 10 \, a^{2} b^{3} c d^{4} - 10 \, a^{3} b^{2} d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{4} d - 5 \, a b^{4} c^{3} d^{2} + 10 \, a^{2} b^{3} c^{2} d^{3} - 10 \, a^{3} b^{2} c d^{4} + 5 \, a^{4} b d^{5}\right)} x - 60 \, {\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(d x + c\right)}{60 \, d^{6}}"," ",0,"1/60*(12*b^5*d^5*x^5 - 15*(b^5*c*d^4 - 5*a*b^4*d^5)*x^4 + 20*(b^5*c^2*d^3 - 5*a*b^4*c*d^4 + 10*a^2*b^3*d^5)*x^3 - 30*(b^5*c^3*d^2 - 5*a*b^4*c^2*d^3 + 10*a^2*b^3*c*d^4 - 10*a^3*b^2*d^5)*x^2 + 60*(b^5*c^4*d - 5*a*b^4*c^3*d^2 + 10*a^2*b^3*c^2*d^3 - 10*a^3*b^2*c*d^4 + 5*a^4*b*d^5)*x - 60*(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(d*x + c))/d^6","B",0
1800,1,179,0,0.396813," ","integrate((b*x+a)^5/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{3 \, b^{4} d^{4} x^{4} - 4 \, {\left(b^{4} c d^{3} - 4 \, a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{2} d^{2} - 4 \, a b^{3} c d^{3} + 6 \, a^{2} b^{2} d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} - 4 \, a^{3} b d^{4}\right)} x + 12 \, {\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(d x + c\right)}{12 \, d^{5}}"," ",0,"1/12*(3*b^4*d^4*x^4 - 4*(b^4*c*d^3 - 4*a*b^3*d^4)*x^3 + 6*(b^4*c^2*d^2 - 4*a*b^3*c*d^3 + 6*a^2*b^2*d^4)*x^2 - 12*(b^4*c^3*d - 4*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 - 4*a^3*b*d^4)*x + 12*(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(d*x + c))/d^5","A",0
1801,1,115,0,0.391236," ","integrate((b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} - 3 \, {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} x - 6 \, {\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(d x + c\right)}{6 \, d^{4}}"," ",0,"1/6*(2*b^3*d^3*x^3 - 3*(b^3*c*d^2 - 3*a*b^2*d^3)*x^2 + 6*(b^3*c^2*d - 3*a*b^2*c*d^2 + 3*a^2*b*d^3)*x - 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(d*x + c))/d^4","A",0
1802,1,62,0,0.393073," ","integrate((b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} - 2 \, {\left(b^{2} c d - 2 \, a b d^{2}\right)} x + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(d x + c\right)}{2 \, d^{3}}"," ",0,"1/2*(b^2*d^2*x^2 - 2*(b^2*c*d - 2*a*b*d^2)*x + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(d*x + c))/d^3","A",0
1803,1,25,0,0.395525," ","integrate((b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{b d x - {\left(b c - a d\right)} \log\left(d x + c\right)}{d^{2}}"," ",0,"(b*d*x - (b*c - a*d)*log(d*x + c))/d^2","A",0
1804,1,10,0,0.379689," ","integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{\log\left(d x + c\right)}{d}"," ",0,"log(d*x + c)/d","A",0
1805,1,26,0,0.388129," ","integrate(1/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{\log\left(b x + a\right) - \log\left(d x + c\right)}{b c - a d}"," ",0,"(log(b*x + a) - log(d*x + c))/(b*c - a*d)","A",0
1806,1,93,0,0.385439," ","integrate(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","-\frac{b c - a d + {\left(b d x + a d\right)} \log\left(b x + a\right) - {\left(b d x + a d\right)} \log\left(d x + c\right)}{a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2} + {\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} x}"," ",0,"-(b*c - a*d + (b*d*x + a*d)*log(b*x + a) - (b*d*x + a*d)*log(d*x + c))/(a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2 + (b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*x)","A",0
1807,1,242,0,0.397068," ","integrate(1/(b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","-\frac{b^{2} c^{2} - 4 \, a b c d + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} c d - a b d^{2}\right)} x - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3} + {\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)} x^{2} + 2 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} x\right)}}"," ",0,"-1/2*(b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2 - 2*(b^2*c*d - a*b*d^2)*x - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c))/(a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3 + (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)*x^2 + 2*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*x)","B",0
1808,1,425,0,0.406295," ","integrate(1/(b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","-\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^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)}{6 \, {\left(a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4} + {\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{6} c^{4} - 4 \, a^{2} b^{5} c^{3} d + 6 \, a^{3} b^{4} c^{2} d^{2} - 4 \, a^{4} b^{3} c d^{3} + a^{5} b^{2} d^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 6 \, a^{4} b^{3} c^{2} d^{2} - 4 \, a^{5} b^{2} c d^{3} + a^{6} b d^{4}\right)} x\right)}}"," ",0,"-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 + 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c))/(a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4 + (b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*x^3 + 3*(a*b^6*c^4 - 4*a^2*b^5*c^3*d + 6*a^3*b^4*c^2*d^2 - 4*a^4*b^3*c*d^3 + a^5*b^2*d^4)*x^2 + 3*(a^2*b^5*c^4 - 4*a^3*b^4*c^3*d + 6*a^4*b^3*c^2*d^2 - 4*a^5*b^2*c*d^3 + a^6*b*d^4)*x)","B",0
1809,1,657,0,0.407855," ","integrate(1/(b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","-\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^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right) + 12 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(d x + c\right)}{12 \, {\left(a^{4} b^{5} c^{5} - 5 \, a^{5} b^{4} c^{4} d + 10 \, a^{6} b^{3} c^{3} d^{2} - 10 \, a^{7} b^{2} c^{2} d^{3} + 5 \, a^{8} b c d^{4} - a^{9} d^{5} + {\left(b^{9} c^{5} - 5 \, a b^{8} c^{4} d + 10 \, a^{2} b^{7} c^{3} d^{2} - 10 \, a^{3} b^{6} c^{2} d^{3} + 5 \, a^{4} b^{5} c d^{4} - a^{5} b^{4} d^{5}\right)} x^{4} + 4 \, {\left(a b^{8} c^{5} - 5 \, a^{2} b^{7} c^{4} d + 10 \, a^{3} b^{6} c^{3} d^{2} - 10 \, a^{4} b^{5} c^{2} d^{3} + 5 \, a^{5} b^{4} c d^{4} - a^{6} b^{3} d^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} c^{5} - 5 \, a^{3} b^{6} c^{4} d + 10 \, a^{4} b^{5} c^{3} d^{2} - 10 \, a^{5} b^{4} c^{2} d^{3} + 5 \, a^{6} b^{3} c d^{4} - a^{7} b^{2} d^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} c^{5} - 5 \, a^{4} b^{5} c^{4} d + 10 \, a^{5} b^{4} c^{3} d^{2} - 10 \, a^{6} b^{3} c^{2} d^{3} + 5 \, a^{7} b^{2} c d^{4} - a^{8} b d^{5}\right)} x\right)}}"," ",0,"-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 - 12*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a) + 12*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(d*x + c))/(a^4*b^5*c^5 - 5*a^5*b^4*c^4*d + 10*a^6*b^3*c^3*d^2 - 10*a^7*b^2*c^2*d^3 + 5*a^8*b*c*d^4 - a^9*d^5 + (b^9*c^5 - 5*a*b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 10*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*x^4 + 4*(a*b^8*c^5 - 5*a^2*b^7*c^4*d + 10*a^3*b^6*c^3*d^2 - 10*a^4*b^5*c^2*d^3 + 5*a^5*b^4*c*d^4 - a^6*b^3*d^5)*x^3 + 6*(a^2*b^7*c^5 - 5*a^3*b^6*c^4*d + 10*a^4*b^5*c^3*d^2 - 10*a^5*b^4*c^2*d^3 + 5*a^6*b^3*c*d^4 - a^7*b^2*d^5)*x^2 + 4*(a^3*b^6*c^5 - 5*a^4*b^5*c^4*d + 10*a^5*b^4*c^3*d^2 - 10*a^6*b^3*c^2*d^3 + 5*a^7*b^2*c*d^4 - a^8*b*d^5)*x)","B",0
1810,1,267,0,0.406193," ","integrate((b*x+a)^6/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","\frac{b^{4} d^{4} x^{4} - 3 \, b^{4} c^{4} + 12 \, a b^{3} c^{3} d - 18 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} - 2 \, {\left(b^{4} c d^{3} - 3 \, a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{2} d^{2} - 3 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} x^{2} + 3 \, {\left(3 \, b^{4} c^{3} d - 8 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3}\right)} x - 12 \, {\left(b^{4} c^{4} - 3 \, a b^{3} c^{3} d + 3 \, a^{2} b^{2} c^{2} d^{2} - a^{3} b c d^{3} + {\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\right)} \log\left(d x + c\right)}{3 \, {\left(d^{6} x + c d^{5}\right)}}"," ",0,"1/3*(b^4*d^4*x^4 - 3*b^4*c^4 + 12*a*b^3*c^3*d - 18*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 - 3*a^4*d^4 - 2*(b^4*c*d^3 - 3*a*b^3*d^4)*x^3 + 6*(b^4*c^2*d^2 - 3*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*x^2 + 3*(3*b^4*c^3*d - 8*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3)*x - 12*(b^4*c^4 - 3*a*b^3*c^3*d + 3*a^2*b^2*c^2*d^2 - a^3*b*c*d^3 + (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)*log(d*x + c))/(d^6*x + c*d^5)","B",0
1811,1,172,0,0.401924," ","integrate((b*x+a)^5/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","\frac{b^{3} d^{3} x^{3} + 2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3} - 3 \, {\left(b^{3} c d^{2} - 2 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(2 \, b^{3} c^{2} d - 3 \, a b^{2} c d^{2}\right)} x + 6 \, {\left(b^{3} c^{3} - 2 \, a b^{2} c^{2} d + a^{2} b c d^{2} + {\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(d^{5} x + c d^{4}\right)}}"," ",0,"1/2*(b^3*d^3*x^3 + 2*b^3*c^3 - 6*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 2*a^3*d^3 - 3*(b^3*c*d^2 - 2*a*b^2*d^3)*x^2 - 2*(2*b^3*c^2*d - 3*a*b^2*c*d^2)*x + 6*(b^3*c^3 - 2*a*b^2*c^2*d + a^2*b*c*d^2 + (b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(d*x + c))/(d^5*x + c*d^4)","B",0
1812,1,92,0,0.396805," ","integrate((b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + b^{2} c d x - b^{2} c^{2} + 2 \, a b c d - a^{2} d^{2} - 2 \, {\left(b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x\right)} \log\left(d x + c\right)}{d^{4} x + c d^{3}}"," ",0,"(b^2*d^2*x^2 + b^2*c*d*x - b^2*c^2 + 2*a*b*c*d - a^2*d^2 - 2*(b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x)*log(d*x + c))/(d^4*x + c*d^3)","A",0
1813,1,37,0,0.395764," ","integrate((b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","\frac{b c - a d + {\left(b d x + b c\right)} \log\left(d x + c\right)}{d^{3} x + c d^{2}}"," ",0,"(b*c - a*d + (b*d*x + b*c)*log(d*x + c))/(d^3*x + c*d^2)","A",0
1814,1,13,0,0.387060," ","integrate((b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","-\frac{1}{d^{2} x + c d}"," ",0,"-1/(d^2*x + c*d)","A",0
1815,1,92,0,0.413843," ","integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","\frac{b c - a d + {\left(b d x + b c\right)} \log\left(b x + a\right) - {\left(b d x + b c\right)} \log\left(d x + c\right)}{b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} x}"," ",0,"(b*c - a*d + (b*d*x + b*c)*log(b*x + a) - (b*d*x + b*c)*log(d*x + c))/(b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*x)","A",0
1816,1,241,0,0.403004," ","integrate(1/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} - a^{2} d^{2} + 2 \, {\left(b^{2} c d - a b d^{2}\right)} x + 2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)}{a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3} + {\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(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} x}"," ",0,"-(b^2*c^2 - a^2*d^2 + 2*(b^2*c*d - a*b*d^2)*x + 2*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a) - 2*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(d*x + c))/(a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3 + (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^2 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*x)","B",0
1817,1,494,0,0.406394," ","integrate(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^2,x, algorithm=""fricas"")","-\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 - 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{4} c^{5} - 4 \, a^{3} b^{3} c^{4} d + 6 \, a^{4} b^{2} c^{3} d^{2} - 4 \, a^{5} b c^{2} d^{3} + a^{6} c d^{4} + {\left(b^{6} c^{4} d - 4 \, a b^{5} c^{3} d^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} - 4 \, a^{3} b^{3} c d^{4} + a^{4} b^{2} d^{5}\right)} x^{3} + {\left(b^{6} c^{5} - 2 \, a b^{5} c^{4} d - 2 \, a^{2} b^{4} c^{3} d^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} - 7 \, a^{4} b^{2} c d^{4} + 2 \, a^{5} b d^{5}\right)} x^{2} + {\left(2 \, a b^{5} c^{5} - 7 \, a^{2} b^{4} c^{4} d + 8 \, a^{3} b^{3} c^{3} d^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} - 2 \, a^{5} b c d^{4} + a^{6} d^{5}\right)} x\right)}}"," ",0,"-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 - 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(d*x + c))/(a^2*b^4*c^5 - 4*a^3*b^3*c^4*d + 6*a^4*b^2*c^3*d^2 - 4*a^5*b*c^2*d^3 + a^6*c*d^4 + (b^6*c^4*d - 4*a*b^5*c^3*d^2 + 6*a^2*b^4*c^2*d^3 - 4*a^3*b^3*c*d^4 + a^4*b^2*d^5)*x^3 + (b^6*c^5 - 2*a*b^5*c^4*d - 2*a^2*b^4*c^3*d^2 + 8*a^3*b^3*c^2*d^3 - 7*a^4*b^2*c*d^4 + 2*a^5*b*d^5)*x^2 + (2*a*b^5*c^5 - 7*a^2*b^4*c^4*d + 8*a^3*b^3*c^3*d^2 - 2*a^4*b^2*c^2*d^3 - 2*a^5*b*c*d^4 + a^6*d^5)*x)","B",0
1818,1,416,0,0.409860," ","integrate((b*x+a)^8/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","\frac{2 \, b^{5} d^{5} x^{5} - 27 \, b^{5} c^{5} + 105 \, a b^{4} c^{4} d - 150 \, a^{2} b^{3} c^{3} d^{2} + 90 \, a^{3} b^{2} c^{2} d^{3} - 15 \, a^{4} b c d^{4} - 3 \, a^{5} d^{5} - 5 \, {\left(b^{5} c d^{4} - 3 \, a b^{4} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{2} d^{3} - 3 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + 3 \, {\left(21 \, b^{5} c^{3} d^{2} - 55 \, a b^{4} c^{2} d^{3} + 40 \, a^{2} b^{3} c d^{4}\right)} x^{2} + 6 \, {\left(b^{5} c^{4} d + 5 \, a b^{4} c^{3} d^{2} - 20 \, a^{2} b^{3} c^{2} d^{3} + 20 \, a^{3} b^{2} c d^{4} - 5 \, a^{4} b d^{5}\right)} x - 60 \, {\left(b^{5} c^{5} - 3 \, a b^{4} c^{4} d + 3 \, a^{2} b^{3} c^{3} d^{2} - a^{3} b^{2} c^{2} d^{3} + {\left(b^{5} c^{3} d^{2} - 3 \, a b^{4} c^{2} d^{3} + 3 \, a^{2} b^{3} c d^{4} - a^{3} b^{2} d^{5}\right)} x^{2} + 2 \, {\left(b^{5} c^{4} d - 3 \, a b^{4} c^{3} d^{2} + 3 \, a^{2} b^{3} c^{2} d^{3} - a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)}{6 \, {\left(d^{8} x^{2} + 2 \, c d^{7} x + c^{2} d^{6}\right)}}"," ",0,"1/6*(2*b^5*d^5*x^5 - 27*b^5*c^5 + 105*a*b^4*c^4*d - 150*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 - 15*a^4*b*c*d^4 - 3*a^5*d^5 - 5*(b^5*c*d^4 - 3*a*b^4*d^5)*x^4 + 20*(b^5*c^2*d^3 - 3*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + 3*(21*b^5*c^3*d^2 - 55*a*b^4*c^2*d^3 + 40*a^2*b^3*c*d^4)*x^2 + 6*(b^5*c^4*d + 5*a*b^4*c^3*d^2 - 20*a^2*b^3*c^2*d^3 + 20*a^3*b^2*c*d^4 - 5*a^4*b*d^5)*x - 60*(b^5*c^5 - 3*a*b^4*c^4*d + 3*a^2*b^3*c^3*d^2 - a^3*b^2*c^2*d^3 + (b^5*c^3*d^2 - 3*a*b^4*c^2*d^3 + 3*a^2*b^3*c*d^4 - a^3*b^2*d^5)*x^2 + 2*(b^5*c^4*d - 3*a*b^4*c^3*d^2 + 3*a^2*b^3*c^2*d^3 - a^3*b^2*c*d^4)*x)*log(d*x + c))/(d^8*x^2 + 2*c*d^7*x + c^2*d^6)","B",0
1819,1,291,0,0.393159," ","integrate((b*x+a)^7/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","\frac{b^{4} d^{4} x^{4} + 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} - 4 \, {\left(b^{4} c d^{3} - 2 \, a b^{3} d^{4}\right)} x^{3} - {\left(11 \, b^{4} c^{2} d^{2} - 16 \, a b^{3} c d^{3}\right)} x^{2} + 2 \, {\left(b^{4} c^{3} d - 8 \, a b^{3} c^{2} d^{2} + 12 \, a^{2} b^{2} c d^{3} - 4 \, a^{3} b d^{4}\right)} x + 12 \, {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + a^{2} b^{2} c^{2} d^{2} + {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(b^{4} c^{3} d - 2 \, a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(d^{7} x^{2} + 2 \, c d^{6} x + c^{2} d^{5}\right)}}"," ",0,"1/2*(b^4*d^4*x^4 + 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 - 4*(b^4*c*d^3 - 2*a*b^3*d^4)*x^3 - (11*b^4*c^2*d^2 - 16*a*b^3*c*d^3)*x^2 + 2*(b^4*c^3*d - 8*a*b^3*c^2*d^2 + 12*a^2*b^2*c*d^3 - 4*a^3*b*d^4)*x + 12*(b^4*c^4 - 2*a*b^3*c^3*d + a^2*b^2*c^2*d^2 + (b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(b^4*c^3*d - 2*a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c))/(d^7*x^2 + 2*c*d^6*x + c^2*d^5)","B",0
1820,1,188,0,0.399845," ","integrate((b*x+a)^6/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 4 \, b^{3} c d^{2} x^{2} - 5 \, b^{3} c^{3} + 9 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - a^{3} d^{3} - 2 \, {\left(2 \, b^{3} c^{2} d - 6 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d + {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{2} d - a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(d^{6} x^{2} + 2 \, c d^{5} x + c^{2} d^{4}\right)}}"," ",0,"1/2*(2*b^3*d^3*x^3 + 4*b^3*c*d^2*x^2 - 5*b^3*c^3 + 9*a*b^2*c^2*d - 3*a^2*b*c*d^2 - a^3*d^3 - 2*(2*b^3*c^2*d - 6*a*b^2*c*d^2 + 3*a^2*b*d^3)*x - 6*(b^3*c^3 - a*b^2*c^2*d + (b^3*c*d^2 - a*b^2*d^3)*x^2 + 2*(b^3*c^2*d - a*b^2*c*d^2)*x)*log(d*x + c))/(d^6*x^2 + 2*c*d^5*x + c^2*d^4)","B",0
1821,1,100,0,0.396104," ","integrate((b*x+a)^5/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","\frac{3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2} + 4 \, {\left(b^{2} c d - a b d^{2}\right)} x + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)}{2 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/2*(3*b^2*c^2 - 2*a*b*c*d - a^2*d^2 + 4*(b^2*c*d - a*b*d^2)*x + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
1822,1,38,0,0.398786," ","integrate((b*x+a)^4/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","-\frac{2 \, b d x + b c + a d}{2 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)}}"," ",0,"-1/2*(2*b*d*x + b*c + a*d)/(d^4*x^2 + 2*c*d^3*x + c^2*d^2)","A",0
1823,1,24,0,0.393244," ","integrate((b*x+a)^3/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(d^{3} x^{2} + 2 \, c d^{2} x + c^{2} d\right)}}"," ",0,"-1/2/(d^3*x^2 + 2*c*d^2*x + c^2*d)","A",0
1824,1,242,0,0.415293," ","integrate((b*x+a)^2/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","\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^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)}{2 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3} + {\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} x\right)}}"," ",0,"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 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c))/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3 + (b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*x^2 + 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*x)","B",0
1825,1,495,0,0.409604," ","integrate((b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","-\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 + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4} + {\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} x^{2} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} x\right)}}"," ",0,"-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 + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a) - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(d*x + c))/(a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4 + (b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*x^3 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*x^2 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*x)","B",0
1826,1,760,0,0.416554," ","integrate(1/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","-\frac{b^{4} c^{4} - 8 \, a b^{3} c^{3} d + 8 \, a^{3} b c d^{3} - a^{4} d^{4} - 12 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} - 18 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{2} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} - 6 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} x - 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)}{2 \, {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} - 10 \, a^{5} b^{2} c^{4} d^{3} + 5 \, a^{6} b c^{3} d^{4} - a^{7} c^{2} d^{5} + {\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} - 10 \, a^{3} b^{4} c^{2} d^{5} + 5 \, a^{4} b^{3} c d^{6} - a^{5} b^{2} d^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} + 4 \, a^{5} b^{2} c d^{6} - a^{6} b d^{7}\right)} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 25 \, a^{3} b^{4} c^{4} d^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} - a^{7} d^{7}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} - 5 \, a^{5} b^{2} c^{3} d^{4} + 4 \, a^{6} b c^{2} d^{5} - a^{7} c d^{6}\right)} x\right)}}"," ",0,"-1/2*(b^4*c^4 - 8*a*b^3*c^3*d + 8*a^3*b*c*d^3 - a^4*d^4 - 12*(b^4*c*d^3 - a*b^3*d^4)*x^3 - 18*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 - 6*a^2*b^2*c*d^3 - a^3*b*d^4)*x - 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a) + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c))/(a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 - 10*a^5*b^2*c^4*d^3 + 5*a^6*b*c^3*d^4 - a^7*c^2*d^5 + (b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4 - 10*a^3*b^4*c^2*d^5 + 5*a^4*b^3*c*d^6 - a^5*b^2*d^7)*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 - 5*a^4*b^3*c^2*d^5 + 4*a^5*b^2*c*d^6 - a^6*b*d^7)*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 25*a^3*b^4*c^4*d^3 - 25*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 - a^7*d^7)*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 - 5*a^5*b^2*c^3*d^4 + 4*a^6*b*c^2*d^5 - a^7*c*d^6)*x)","B",0
1827,1,1151,0,0.417279," ","integrate(1/(b*x+a)/(a*c+(a*d+b*c)*x+b*d*x^2)^3,x, algorithm=""fricas"")","-\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 + 60 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right) - 60 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)}{6 \, {\left(a^{3} b^{6} c^{8} - 6 \, a^{4} b^{5} c^{7} d + 15 \, a^{5} b^{4} c^{6} d^{2} - 20 \, a^{6} b^{3} c^{5} d^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} - 6 \, a^{8} b c^{3} d^{5} + a^{9} c^{2} d^{6} + {\left(b^{9} c^{6} d^{2} - 6 \, a b^{8} c^{5} d^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} - 20 \, a^{3} b^{6} c^{3} d^{5} + 15 \, a^{4} b^{5} c^{2} d^{6} - 6 \, a^{5} b^{4} c d^{7} + a^{6} b^{3} d^{8}\right)} x^{5} + {\left(2 \, b^{9} c^{7} d - 9 \, a b^{8} c^{6} d^{2} + 12 \, a^{2} b^{7} c^{5} d^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} - 30 \, a^{4} b^{5} c^{3} d^{5} + 33 \, a^{5} b^{4} c^{2} d^{6} - 16 \, a^{6} b^{3} c d^{7} + 3 \, a^{7} b^{2} d^{8}\right)} x^{4} + {\left(b^{9} c^{8} - 18 \, a^{2} b^{7} c^{6} d^{2} + 52 \, a^{3} b^{6} c^{5} d^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} + 24 \, a^{5} b^{4} c^{3} d^{5} + 10 \, a^{6} b^{3} c^{2} d^{6} - 12 \, a^{7} b^{2} c d^{7} + 3 \, a^{8} b d^{8}\right)} x^{3} + {\left(3 \, a b^{8} c^{8} - 12 \, a^{2} b^{7} c^{7} d + 10 \, a^{3} b^{6} c^{6} d^{2} + 24 \, a^{4} b^{5} c^{5} d^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} + 52 \, a^{6} b^{3} c^{3} d^{5} - 18 \, a^{7} b^{2} c^{2} d^{6} + a^{9} d^{8}\right)} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} - 16 \, a^{3} b^{6} c^{7} d + 33 \, a^{4} b^{5} c^{6} d^{2} - 30 \, a^{5} b^{4} c^{5} d^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} + 12 \, a^{7} b^{2} c^{3} d^{5} - 9 \, a^{8} b c^{2} d^{6} + 2 \, a^{9} c d^{7}\right)} x\right)}}"," ",0,"-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 + 60*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a) - 60*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(d*x + c))/(a^3*b^6*c^8 - 6*a^4*b^5*c^7*d + 15*a^5*b^4*c^6*d^2 - 20*a^6*b^3*c^5*d^3 + 15*a^7*b^2*c^4*d^4 - 6*a^8*b*c^3*d^5 + a^9*c^2*d^6 + (b^9*c^6*d^2 - 6*a*b^8*c^5*d^3 + 15*a^2*b^7*c^4*d^4 - 20*a^3*b^6*c^3*d^5 + 15*a^4*b^5*c^2*d^6 - 6*a^5*b^4*c*d^7 + a^6*b^3*d^8)*x^5 + (2*b^9*c^7*d - 9*a*b^8*c^6*d^2 + 12*a^2*b^7*c^5*d^3 + 5*a^3*b^6*c^4*d^4 - 30*a^4*b^5*c^3*d^5 + 33*a^5*b^4*c^2*d^6 - 16*a^6*b^3*c*d^7 + 3*a^7*b^2*d^8)*x^4 + (b^9*c^8 - 18*a^2*b^7*c^6*d^2 + 52*a^3*b^6*c^5*d^3 - 60*a^4*b^5*c^4*d^4 + 24*a^5*b^4*c^3*d^5 + 10*a^6*b^3*c^2*d^6 - 12*a^7*b^2*c*d^7 + 3*a^8*b*d^8)*x^3 + (3*a*b^8*c^8 - 12*a^2*b^7*c^7*d + 10*a^3*b^6*c^6*d^2 + 24*a^4*b^5*c^5*d^3 - 60*a^5*b^4*c^4*d^4 + 52*a^6*b^3*c^3*d^5 - 18*a^7*b^2*c^2*d^6 + a^9*d^8)*x^2 + (3*a^2*b^7*c^8 - 16*a^3*b^6*c^7*d + 33*a^4*b^5*c^6*d^2 - 30*a^5*b^4*c^5*d^3 + 5*a^6*b^3*c^4*d^4 + 12*a^7*b^2*c^3*d^5 - 9*a^8*b*c^2*d^6 + 2*a^9*c*d^7)*x)","B",0
1828,1,127,0,0.347111," ","integrate((e*x+d)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{5} d c + \frac{5}{6} x^{6} e^{4} d^{2} c + \frac{1}{6} x^{6} e^{6} a + 2 x^{5} e^{3} d^{3} c + x^{5} e^{5} d a + \frac{5}{2} x^{4} e^{2} d^{4} c + \frac{5}{2} x^{4} e^{4} d^{2} a + \frac{5}{3} x^{3} e d^{5} c + \frac{10}{3} x^{3} e^{3} d^{3} a + \frac{1}{2} x^{2} d^{6} c + \frac{5}{2} x^{2} e^{2} d^{4} a + x e d^{5} a"," ",0,"1/7*x^7*e^5*d*c + 5/6*x^6*e^4*d^2*c + 1/6*x^6*e^6*a + 2*x^5*e^3*d^3*c + x^5*e^5*d*a + 5/2*x^4*e^2*d^4*c + 5/2*x^4*e^4*d^2*a + 5/3*x^3*e*d^5*c + 10/3*x^3*e^3*d^3*a + 1/2*x^2*d^6*c + 5/2*x^2*e^2*d^4*a + x*e*d^5*a","B",0
1829,1,103,0,0.349111," ","integrate((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{4} d c + \frac{4}{5} x^{5} e^{3} d^{2} c + \frac{1}{5} x^{5} e^{5} a + \frac{3}{2} x^{4} e^{2} d^{3} c + x^{4} e^{4} d a + \frac{4}{3} x^{3} e d^{4} c + 2 x^{3} e^{3} d^{2} a + \frac{1}{2} x^{2} d^{5} c + 2 x^{2} e^{2} d^{3} a + x e d^{4} a"," ",0,"1/6*x^6*e^4*d*c + 4/5*x^5*e^3*d^2*c + 1/5*x^5*e^5*a + 3/2*x^4*e^2*d^3*c + x^4*e^4*d*a + 4/3*x^3*e*d^4*c + 2*x^3*e^3*d^2*a + 1/2*x^2*d^5*c + 2*x^2*e^2*d^3*a + x*e*d^4*a","B",0
1830,1,78,0,0.341014," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e^{3} d c + \frac{3}{4} x^{4} e^{2} d^{2} c + \frac{1}{4} x^{4} e^{4} a + x^{3} e d^{3} c + x^{3} e^{3} d a + \frac{1}{2} x^{2} d^{4} c + \frac{3}{2} x^{2} e^{2} d^{2} a + x e d^{3} a"," ",0,"1/5*x^5*e^3*d*c + 3/4*x^4*e^2*d^2*c + 1/4*x^4*e^4*a + x^3*e*d^3*c + x^3*e^3*d*a + 1/2*x^2*d^4*c + 3/2*x^2*e^2*d^2*a + x*e*d^3*a","B",0
1831,1,55,0,0.351678," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{1}{4} x^{4} e^{2} d c + \frac{2}{3} x^{3} e d^{2} c + \frac{1}{3} x^{3} e^{3} a + \frac{1}{2} x^{2} d^{3} c + x^{2} e^{2} d a + x e d^{2} a"," ",0,"1/4*x^4*e^2*d*c + 2/3*x^3*e*d^2*c + 1/3*x^3*e^3*a + 1/2*x^2*d^3*c + x^2*e^2*d*a + x*e*d^2*a","A",0
1832,1,32,0,0.350884," ","integrate(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2,x, algorithm=""fricas"")","\frac{1}{3} x^{3} e d c + \frac{1}{2} x^{2} d^{2} c + \frac{1}{2} x^{2} e^{2} a + x e d a"," ",0,"1/3*x^3*e*d*c + 1/2*x^2*d^2*c + 1/2*x^2*e^2*a + x*e*d*a","A",0
1833,1,12,0,0.386045," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d),x, algorithm=""fricas"")","\frac{1}{2} \, c d x^{2} + a e x"," ",0,"1/2*c*d*x^2 + a*e*x","A",0
1834,1,30,0,0.389832," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{c d e x - {\left(c d^{2} - a e^{2}\right)} \log\left(e x + d\right)}{e^{2}}"," ",0,"(c*d*e*x - (c*d^2 - a*e^2)*log(e*x + d))/e^2","A",0
1835,1,44,0,0.390762," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{c d^{2} - a e^{2} + {\left(c d e x + c d^{2}\right)} \log\left(e x + d\right)}{e^{3} x + d e^{2}}"," ",0,"(c*d^2 - a*e^2 + (c*d*e*x + c*d^2)*log(e*x + d))/(e^3*x + d*e^2)","A",0
1836,1,43,0,0.397548," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{2 \, c d e x + c d^{2} + a e^{2}}{2 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}"," ",0,"-1/2*(2*c*d*e*x + c*d^2 + a*e^2)/(e^4*x^2 + 2*d*e^3*x + d^2*e^2)","A",0
1837,1,55,0,0.387268," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{3 \, c d e x + c d^{2} + 2 \, a e^{2}}{6 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}}"," ",0,"-1/6*(3*c*d*e*x + c*d^2 + 2*a*e^2)/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2)","A",0
1838,1,66,0,0.389571," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{4 \, c d e x + c d^{2} + 3 \, a e^{2}}{12 \, {\left(e^{6} x^{4} + 4 \, d e^{5} x^{3} + 6 \, d^{2} e^{4} x^{2} + 4 \, d^{3} e^{3} x + d^{4} e^{2}\right)}}"," ",0,"-1/12*(4*c*d*e*x + c*d^2 + 3*a*e^2)/(e^6*x^4 + 4*d*e^5*x^3 + 6*d^2*e^4*x^2 + 4*d^3*e^3*x + d^4*e^2)","A",0
1839,1,186,0,0.340919," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{4} d^{2} c^{2} + \frac{2}{3} x^{6} e^{3} d^{3} c^{2} + \frac{1}{3} x^{6} e^{5} d c a + \frac{6}{5} x^{5} e^{2} d^{4} c^{2} + \frac{8}{5} x^{5} e^{4} d^{2} c a + \frac{1}{5} x^{5} e^{6} a^{2} + x^{4} e d^{5} c^{2} + 3 x^{4} e^{3} d^{3} c a + x^{4} e^{5} d a^{2} + \frac{1}{3} x^{3} d^{6} c^{2} + \frac{8}{3} x^{3} e^{2} d^{4} c a + 2 x^{3} e^{4} d^{2} a^{2} + x^{2} e d^{5} c a + 2 x^{2} e^{3} d^{3} a^{2} + x e^{2} d^{4} a^{2}"," ",0,"1/7*x^7*e^4*d^2*c^2 + 2/3*x^6*e^3*d^3*c^2 + 1/3*x^6*e^5*d*c*a + 6/5*x^5*e^2*d^4*c^2 + 8/5*x^5*e^4*d^2*c*a + 1/5*x^5*e^6*a^2 + x^4*e*d^5*c^2 + 3*x^4*e^3*d^3*c*a + x^4*e^5*d*a^2 + 1/3*x^3*d^6*c^2 + 8/3*x^3*e^2*d^4*c*a + 2*x^3*e^4*d^2*a^2 + x^2*e*d^5*c*a + 2*x^2*e^3*d^3*a^2 + x*e^2*d^4*a^2","B",0
1840,1,146,0,0.350033," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{3} d^{2} c^{2} + \frac{3}{5} x^{5} e^{2} d^{3} c^{2} + \frac{2}{5} x^{5} e^{4} d c a + \frac{3}{4} x^{4} e d^{4} c^{2} + \frac{3}{2} x^{4} e^{3} d^{2} c a + \frac{1}{4} x^{4} e^{5} a^{2} + \frac{1}{3} x^{3} d^{5} c^{2} + 2 x^{3} e^{2} d^{3} c a + x^{3} e^{4} d a^{2} + x^{2} e d^{4} c a + \frac{3}{2} x^{2} e^{3} d^{2} a^{2} + x e^{2} d^{3} a^{2}"," ",0,"1/6*x^6*e^3*d^2*c^2 + 3/5*x^5*e^2*d^3*c^2 + 2/5*x^5*e^4*d*c*a + 3/4*x^4*e*d^4*c^2 + 3/2*x^4*e^3*d^2*c*a + 1/4*x^4*e^5*a^2 + 1/3*x^3*d^5*c^2 + 2*x^3*e^2*d^3*c*a + x^3*e^4*d*a^2 + x^2*e*d^4*c*a + 3/2*x^2*e^3*d^2*a^2 + x*e^2*d^3*a^2","B",0
1841,1,105,0,0.348884," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\frac{1}{5} x^{5} e^{2} d^{2} c^{2} + \frac{1}{2} x^{4} e d^{3} c^{2} + \frac{1}{2} x^{4} e^{3} d c a + \frac{1}{3} x^{3} d^{4} c^{2} + \frac{4}{3} x^{3} e^{2} d^{2} c a + \frac{1}{3} x^{3} e^{4} a^{2} + x^{2} e d^{3} c a + x^{2} e^{3} d a^{2} + x e^{2} d^{2} a^{2}"," ",0,"1/5*x^5*e^2*d^2*c^2 + 1/2*x^4*e*d^3*c^2 + 1/2*x^4*e^3*d*c*a + 1/3*x^3*d^4*c^2 + 4/3*x^3*e^2*d^2*c*a + 1/3*x^3*e^4*a^2 + x^2*e*d^3*c*a + x^2*e^3*d*a^2 + x*e^2*d^2*a^2","A",0
1842,1,64,0,0.379004," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d),x, algorithm=""fricas"")","\frac{1}{4} \, c^{2} d^{2} e x^{4} + a^{2} d e^{2} x + \frac{1}{3} \, {\left(c^{2} d^{3} + 2 \, a c d e^{2}\right)} x^{3} + \frac{1}{2} \, {\left(2 \, a c d^{2} e + a^{2} e^{3}\right)} x^{2}"," ",0,"1/4*c^2*d^2*e*x^4 + a^2*d*e^2*x + 1/3*(c^2*d^3 + 2*a*c*d*e^2)*x^3 + 1/2*(2*a*c*d^2*e + a^2*e^3)*x^2","A",0
1843,1,28,0,0.372079," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{1}{3} \, c^{2} d^{2} x^{3} + a c d e x^{2} + a^{2} e^{2} x"," ",0,"1/3*c^2*d^2*x^3 + a*c*d*e*x^2 + a^2*e^2*x","A",0
1844,1,72,0,0.396997," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{c^{2} d^{2} e^{2} x^{2} - 2 \, {\left(c^{2} d^{3} e - 2 \, a c d e^{3}\right)} x + 2 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \log\left(e x + d\right)}{2 \, e^{3}}"," ",0,"1/2*(c^2*d^2*e^2*x^2 - 2*(c^2*d^3*e - 2*a*c*d*e^3)*x + 2*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*log(e*x + d))/e^3","A",0
1845,1,108,0,0.400065," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{c^{2} d^{2} e^{2} x^{2} + c^{2} d^{3} e x - c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4} - 2 \, {\left(c^{2} d^{4} - a c d^{2} e^{2} + {\left(c^{2} d^{3} e - a c d e^{3}\right)} x\right)} \log\left(e x + d\right)}{e^{4} x + d e^{3}}"," ",0,"(c^2*d^2*e^2*x^2 + c^2*d^3*e*x - c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4 - 2*(c^2*d^4 - a*c*d^2*e^2 + (c^2*d^3*e - a*c*d*e^3)*x)*log(e*x + d))/(e^4*x + d*e^3)","A",0
1846,1,112,0,0.398658," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{3 \, c^{2} d^{4} - 2 \, a c d^{2} e^{2} - a^{2} e^{4} + 4 \, {\left(c^{2} d^{3} e - a c d e^{3}\right)} x + 2 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, c^{2} d^{3} e x + c^{2} d^{4}\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"1/2*(3*c^2*d^4 - 2*a*c*d^2*e^2 - a^2*e^4 + 4*(c^2*d^3*e - a*c*d*e^3)*x + 2*(c^2*d^2*e^2*x^2 + 2*c^2*d^3*e*x + c^2*d^4)*log(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
1847,1,94,0,0.397348," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{3 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + a c d^{2} e^{2} + a^{2} e^{4} + 3 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x}{3 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/3*(3*c^2*d^2*e^2*x^2 + c^2*d^4 + a*c*d^2*e^2 + a^2*e^4 + 3*(c^2*d^3*e + a*c*d*e^3)*x)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","B",0
1848,1,108,0,0.392632," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{6 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 2 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} + 4 \, {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x}{12 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/12*(6*c^2*d^2*e^2*x^2 + c^2*d^4 + 2*a*c*d^2*e^2 + 3*a^2*e^4 + 4*(c^2*d^3*e + 2*a*c*d*e^3)*x)/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)","A",0
1849,1,119,0,0.386253," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{10 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 3 \, a c d^{2} e^{2} + 6 \, a^{2} e^{4} + 5 \, {\left(c^{2} d^{3} e + 3 \, a c d e^{3}\right)} x}{30 \, {\left(e^{8} x^{5} + 5 \, d e^{7} x^{4} + 10 \, d^{2} e^{6} x^{3} + 10 \, d^{3} e^{5} x^{2} + 5 \, d^{4} e^{4} x + d^{5} e^{3}\right)}}"," ",0,"-1/30*(10*c^2*d^2*e^2*x^2 + c^2*d^4 + 3*a*c*d^2*e^2 + 6*a^2*e^4 + 5*(c^2*d^3*e + 3*a*c*d*e^3)*x)/(e^8*x^5 + 5*d*e^7*x^4 + 10*d^2*e^6*x^3 + 10*d^3*e^5*x^2 + 5*d^4*e^4*x + d^5*e^3)","A",0
1850,1,130,0,0.394587," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{15 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 4 \, a c d^{2} e^{2} + 10 \, a^{2} e^{4} + 6 \, {\left(c^{2} d^{3} e + 4 \, a c d e^{3}\right)} x}{60 \, {\left(e^{9} x^{6} + 6 \, d e^{8} x^{5} + 15 \, d^{2} e^{7} x^{4} + 20 \, d^{3} e^{6} x^{3} + 15 \, d^{4} e^{5} x^{2} + 6 \, d^{5} e^{4} x + d^{6} e^{3}\right)}}"," ",0,"-1/60*(15*c^2*d^2*e^2*x^2 + c^2*d^4 + 4*a*c*d^2*e^2 + 10*a^2*e^4 + 6*(c^2*d^3*e + 4*a*c*d*e^3)*x)/(e^9*x^6 + 6*d*e^8*x^5 + 15*d^2*e^7*x^4 + 20*d^3*e^6*x^3 + 15*d^4*e^5*x^2 + 6*d^5*e^4*x + d^6*e^3)","A",0
1851,1,329,0,0.357740," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{5} d^{3} c^{3} + \frac{5}{8} x^{8} e^{4} d^{4} c^{3} + \frac{3}{8} x^{8} e^{6} d^{2} c^{2} a + \frac{10}{7} x^{7} e^{3} d^{5} c^{3} + \frac{15}{7} x^{7} e^{5} d^{3} c^{2} a + \frac{3}{7} x^{7} e^{7} d c a^{2} + \frac{5}{3} x^{6} e^{2} d^{6} c^{3} + 5 x^{6} e^{4} d^{4} c^{2} a + \frac{5}{2} x^{6} e^{6} d^{2} c a^{2} + \frac{1}{6} x^{6} e^{8} a^{3} + x^{5} e d^{7} c^{3} + 6 x^{5} e^{3} d^{5} c^{2} a + 6 x^{5} e^{5} d^{3} c a^{2} + x^{5} e^{7} d a^{3} + \frac{1}{4} x^{4} d^{8} c^{3} + \frac{15}{4} x^{4} e^{2} d^{6} c^{2} a + \frac{15}{2} x^{4} e^{4} d^{4} c a^{2} + \frac{5}{2} x^{4} e^{6} d^{2} a^{3} + x^{3} e d^{7} c^{2} a + 5 x^{3} e^{3} d^{5} c a^{2} + \frac{10}{3} x^{3} e^{5} d^{3} a^{3} + \frac{3}{2} x^{2} e^{2} d^{6} c a^{2} + \frac{5}{2} x^{2} e^{4} d^{4} a^{3} + x e^{3} d^{5} a^{3}"," ",0,"1/9*x^9*e^5*d^3*c^3 + 5/8*x^8*e^4*d^4*c^3 + 3/8*x^8*e^6*d^2*c^2*a + 10/7*x^7*e^3*d^5*c^3 + 15/7*x^7*e^5*d^3*c^2*a + 3/7*x^7*e^7*d*c*a^2 + 5/3*x^6*e^2*d^6*c^3 + 5*x^6*e^4*d^4*c^2*a + 5/2*x^6*e^6*d^2*c*a^2 + 1/6*x^6*e^8*a^3 + x^5*e*d^7*c^3 + 6*x^5*e^3*d^5*c^2*a + 6*x^5*e^5*d^3*c*a^2 + x^5*e^7*d*a^3 + 1/4*x^4*d^8*c^3 + 15/4*x^4*e^2*d^6*c^2*a + 15/2*x^4*e^4*d^4*c*a^2 + 5/2*x^4*e^6*d^2*a^3 + x^3*e*d^7*c^2*a + 5*x^3*e^3*d^5*c*a^2 + 10/3*x^3*e^5*d^3*a^3 + 3/2*x^2*e^2*d^6*c*a^2 + 5/2*x^2*e^4*d^4*a^3 + x*e^3*d^5*a^3","B",0
1852,1,271,0,0.350032," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{4} d^{3} c^{3} + \frac{4}{7} x^{7} e^{3} d^{4} c^{3} + \frac{3}{7} x^{7} e^{5} d^{2} c^{2} a + x^{6} e^{2} d^{5} c^{3} + 2 x^{6} e^{4} d^{3} c^{2} a + \frac{1}{2} x^{6} e^{6} d c a^{2} + \frac{4}{5} x^{5} e d^{6} c^{3} + \frac{18}{5} x^{5} e^{3} d^{4} c^{2} a + \frac{12}{5} x^{5} e^{5} d^{2} c a^{2} + \frac{1}{5} x^{5} e^{7} a^{3} + \frac{1}{4} x^{4} d^{7} c^{3} + 3 x^{4} e^{2} d^{5} c^{2} a + \frac{9}{2} x^{4} e^{4} d^{3} c a^{2} + x^{4} e^{6} d a^{3} + x^{3} e d^{6} c^{2} a + 4 x^{3} e^{3} d^{4} c a^{2} + 2 x^{3} e^{5} d^{2} a^{3} + \frac{3}{2} x^{2} e^{2} d^{5} c a^{2} + 2 x^{2} e^{4} d^{3} a^{3} + x e^{3} d^{4} a^{3}"," ",0,"1/8*x^8*e^4*d^3*c^3 + 4/7*x^7*e^3*d^4*c^3 + 3/7*x^7*e^5*d^2*c^2*a + x^6*e^2*d^5*c^3 + 2*x^6*e^4*d^3*c^2*a + 1/2*x^6*e^6*d*c*a^2 + 4/5*x^5*e*d^6*c^3 + 18/5*x^5*e^3*d^4*c^2*a + 12/5*x^5*e^5*d^2*c*a^2 + 1/5*x^5*e^7*a^3 + 1/4*x^4*d^7*c^3 + 3*x^4*e^2*d^5*c^2*a + 9/2*x^4*e^4*d^3*c*a^2 + x^4*e^6*d*a^3 + x^3*e*d^6*c^2*a + 4*x^3*e^3*d^4*c*a^2 + 2*x^3*e^5*d^2*a^3 + 3/2*x^2*e^2*d^5*c*a^2 + 2*x^2*e^4*d^3*a^3 + x*e^3*d^4*a^3","B",0
1853,1,214,0,0.350864," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{3} d^{3} c^{3} + \frac{1}{2} x^{6} e^{2} d^{4} c^{3} + \frac{1}{2} x^{6} e^{4} d^{2} c^{2} a + \frac{3}{5} x^{5} e d^{5} c^{3} + \frac{9}{5} x^{5} e^{3} d^{3} c^{2} a + \frac{3}{5} x^{5} e^{5} d c a^{2} + \frac{1}{4} x^{4} d^{6} c^{3} + \frac{9}{4} x^{4} e^{2} d^{4} c^{2} a + \frac{9}{4} x^{4} e^{4} d^{2} c a^{2} + \frac{1}{4} x^{4} e^{6} a^{3} + x^{3} e d^{5} c^{2} a + 3 x^{3} e^{3} d^{3} c a^{2} + x^{3} e^{5} d a^{3} + \frac{3}{2} x^{2} e^{2} d^{4} c a^{2} + \frac{3}{2} x^{2} e^{4} d^{2} a^{3} + x e^{3} d^{3} a^{3}"," ",0,"1/7*x^7*e^3*d^3*c^3 + 1/2*x^6*e^2*d^4*c^3 + 1/2*x^6*e^4*d^2*c^2*a + 3/5*x^5*e*d^5*c^3 + 9/5*x^5*e^3*d^3*c^2*a + 3/5*x^5*e^5*d*c*a^2 + 1/4*x^4*d^6*c^3 + 9/4*x^4*e^2*d^4*c^2*a + 9/4*x^4*e^4*d^2*c*a^2 + 1/4*x^4*e^6*a^3 + x^3*e*d^5*c^2*a + 3*x^3*e^3*d^3*c*a^2 + x^3*e^5*d*a^3 + 3/2*x^2*e^2*d^4*c*a^2 + 3/2*x^2*e^4*d^2*a^3 + x*e^3*d^3*a^3","B",0
1854,1,150,0,0.373294," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d),x, algorithm=""fricas"")","\frac{1}{6} \, c^{3} d^{3} e^{2} x^{6} + a^{3} d^{2} e^{3} x + \frac{1}{5} \, {\left(2 \, c^{3} d^{4} e + 3 \, a c^{2} d^{2} e^{3}\right)} x^{5} + \frac{1}{4} \, {\left(c^{3} d^{5} + 6 \, a c^{2} d^{3} e^{2} + 3 \, a^{2} c d e^{4}\right)} x^{4} + \frac{1}{3} \, {\left(3 \, a c^{2} d^{4} e + 6 \, a^{2} c d^{2} e^{3} + a^{3} e^{5}\right)} x^{3} + \frac{1}{2} \, {\left(3 \, a^{2} c d^{3} e^{2} + 2 \, a^{3} d e^{4}\right)} x^{2}"," ",0,"1/6*c^3*d^3*e^2*x^6 + a^3*d^2*e^3*x + 1/5*(2*c^3*d^4*e + 3*a*c^2*d^2*e^3)*x^5 + 1/4*(c^3*d^5 + 6*a*c^2*d^3*e^2 + 3*a^2*c*d*e^4)*x^4 + 1/3*(3*a*c^2*d^4*e + 6*a^2*c*d^2*e^3 + a^3*e^5)*x^3 + 1/2*(3*a^2*c*d^3*e^2 + 2*a^3*d*e^4)*x^2","A",0
1855,1,95,0,0.386528," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^2,x, algorithm=""fricas"")","\frac{1}{5} \, c^{3} d^{3} e x^{5} + a^{3} d e^{3} x + \frac{1}{4} \, {\left(c^{3} d^{4} + 3 \, a c^{2} d^{2} e^{2}\right)} x^{4} + {\left(a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x^{3} + \frac{1}{2} \, {\left(3 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} x^{2}"," ",0,"1/5*c^3*d^3*e*x^5 + a^3*d*e^3*x + 1/4*(c^3*d^4 + 3*a*c^2*d^2*e^2)*x^4 + (a*c^2*d^3*e + a^2*c*d*e^3)*x^3 + 1/2*(3*a^2*c*d^2*e^2 + a^3*e^4)*x^2","A",0
1856,1,45,0,0.375542," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{1}{4} \, c^{3} d^{3} x^{4} + a c^{2} d^{2} e x^{3} + \frac{3}{2} \, a^{2} c d e^{2} x^{2} + a^{3} e^{3} x"," ",0,"1/4*c^3*d^3*x^4 + a*c^2*d^2*e*x^3 + 3/2*a^2*c*d*e^2*x^2 + a^3*e^3*x","B",0
1857,1,130,0,0.391156," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{2 \, c^{3} d^{3} e^{3} x^{3} - 3 \, {\left(c^{3} d^{4} e^{2} - 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 6 \, {\left(c^{3} d^{5} e - 3 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x - 6 \, {\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(e x + d\right)}{6 \, e^{4}}"," ",0,"1/6*(2*c^3*d^3*e^3*x^3 - 3*(c^3*d^4*e^2 - 3*a*c^2*d^2*e^4)*x^2 + 6*(c^3*d^5*e - 3*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x - 6*(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(e*x + d))/e^4","A",0
1858,1,193,0,0.396268," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^5,x, algorithm=""fricas"")","\frac{c^{3} d^{3} e^{3} x^{3} + 2 \, c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 6 \, a^{2} c d^{2} e^{4} - 2 \, a^{3} e^{6} - 3 \, {\left(c^{3} d^{4} e^{2} - 2 \, a c^{2} d^{2} e^{4}\right)} x^{2} - 2 \, {\left(2 \, c^{3} d^{5} e - 3 \, a c^{2} d^{3} e^{3}\right)} x + 6 \, {\left(c^{3} d^{6} - 2 \, a c^{2} d^{4} e^{2} + a^{2} c d^{2} e^{4} + {\left(c^{3} d^{5} e - 2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"1/2*(c^3*d^3*e^3*x^3 + 2*c^3*d^6 - 6*a*c^2*d^4*e^2 + 6*a^2*c*d^2*e^4 - 2*a^3*e^6 - 3*(c^3*d^4*e^2 - 2*a*c^2*d^2*e^4)*x^2 - 2*(2*c^3*d^5*e - 3*a*c^2*d^3*e^3)*x + 6*(c^3*d^6 - 2*a*c^2*d^4*e^2 + a^2*c*d^2*e^4 + (c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*log(e*x + d))/(e^5*x + d*e^4)","B",0
1859,1,209,0,0.395028," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^6,x, algorithm=""fricas"")","\frac{2 \, c^{3} d^{3} e^{3} x^{3} + 4 \, c^{3} d^{4} e^{2} x^{2} - 5 \, c^{3} d^{6} + 9 \, a c^{2} d^{4} e^{2} - 3 \, a^{2} c d^{2} e^{4} - a^{3} e^{6} - 2 \, {\left(2 \, c^{3} d^{5} e - 6 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x - 6 \, {\left(c^{3} d^{6} - a c^{2} d^{4} e^{2} + {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(c^{3} d^{5} e - a c^{2} d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"1/2*(2*c^3*d^3*e^3*x^3 + 4*c^3*d^4*e^2*x^2 - 5*c^3*d^6 + 9*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4 - a^3*e^6 - 2*(2*c^3*d^5*e - 6*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x - 6*(c^3*d^6 - a*c^2*d^4*e^2 + (c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 2*(c^3*d^5*e - a*c^2*d^3*e^3)*x)*log(e*x + d))/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","B",0
1860,1,194,0,0.403458," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^7,x, algorithm=""fricas"")","\frac{11 \, c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} - 3 \, a^{2} c d^{2} e^{4} - 2 \, a^{3} e^{6} + 18 \, {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 9 \, {\left(3 \, c^{3} d^{5} e - 2 \, a c^{2} d^{3} e^{3} - a^{2} c d e^{5}\right)} x + 6 \, {\left(c^{3} d^{3} e^{3} x^{3} + 3 \, c^{3} d^{4} e^{2} x^{2} + 3 \, c^{3} d^{5} e x + c^{3} d^{6}\right)} \log\left(e x + d\right)}{6 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"1/6*(11*c^3*d^6 - 6*a*c^2*d^4*e^2 - 3*a^2*c*d^2*e^4 - 2*a^3*e^6 + 18*(c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 9*(3*c^3*d^5*e - 2*a*c^2*d^3*e^3 - a^2*c*d*e^5)*x + 6*(c^3*d^3*e^3*x^3 + 3*c^3*d^4*e^2*x^2 + 3*c^3*d^5*e*x + c^3*d^6)*log(e*x + d))/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
1861,1,158,0,0.393334," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{4 \, c^{3} d^{3} e^{3} x^{3} + c^{3} d^{6} + a c^{2} d^{4} e^{2} + a^{2} c d^{2} e^{4} + a^{3} e^{6} + 6 \, {\left(c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(c^{3} d^{5} e + a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x}{4 \, {\left(e^{8} x^{4} + 4 \, d e^{7} x^{3} + 6 \, d^{2} e^{6} x^{2} + 4 \, d^{3} e^{5} x + d^{4} e^{4}\right)}}"," ",0,"-1/4*(4*c^3*d^3*e^3*x^3 + c^3*d^6 + a*c^2*d^4*e^2 + a^2*c*d^2*e^4 + a^3*e^6 + 6*(c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^2 + 4*(c^3*d^5*e + a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)/(e^8*x^4 + 4*d*e^7*x^3 + 6*d^2*e^6*x^2 + 4*d^3*e^5*x + d^4*e^4)","B",0
1862,1,175,0,0.390448," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{10 \, c^{3} d^{3} e^{3} x^{3} + c^{3} d^{6} + 2 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + 4 \, a^{3} e^{6} + 10 \, {\left(c^{3} d^{4} e^{2} + 2 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 5 \, {\left(c^{3} d^{5} e + 2 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x}{20 \, {\left(e^{9} x^{5} + 5 \, d e^{8} x^{4} + 10 \, d^{2} e^{7} x^{3} + 10 \, d^{3} e^{6} x^{2} + 5 \, d^{4} e^{5} x + d^{5} e^{4}\right)}}"," ",0,"-1/20*(10*c^3*d^3*e^3*x^3 + c^3*d^6 + 2*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + 4*a^3*e^6 + 10*(c^3*d^4*e^2 + 2*a*c^2*d^2*e^4)*x^2 + 5*(c^3*d^5*e + 2*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x)/(e^9*x^5 + 5*d*e^8*x^4 + 10*d^2*e^7*x^3 + 10*d^3*e^6*x^2 + 5*d^4*e^5*x + d^5*e^4)","B",0
1863,1,186,0,0.390202," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{20 \, c^{3} d^{3} e^{3} x^{3} + c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 6 \, a^{2} c d^{2} e^{4} + 10 \, a^{3} e^{6} + 15 \, {\left(c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 6 \, {\left(c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3} + 6 \, a^{2} c d e^{5}\right)} x}{60 \, {\left(e^{10} x^{6} + 6 \, d e^{9} x^{5} + 15 \, d^{2} e^{8} x^{4} + 20 \, d^{3} e^{7} x^{3} + 15 \, d^{4} e^{6} x^{2} + 6 \, d^{5} e^{5} x + d^{6} e^{4}\right)}}"," ",0,"-1/60*(20*c^3*d^3*e^3*x^3 + c^3*d^6 + 3*a*c^2*d^4*e^2 + 6*a^2*c*d^2*e^4 + 10*a^3*e^6 + 15*(c^3*d^4*e^2 + 3*a*c^2*d^2*e^4)*x^2 + 6*(c^3*d^5*e + 3*a*c^2*d^3*e^3 + 6*a^2*c*d*e^5)*x)/(e^10*x^6 + 6*d*e^9*x^5 + 15*d^2*e^8*x^4 + 20*d^3*e^7*x^3 + 15*d^4*e^6*x^2 + 6*d^5*e^5*x + d^6*e^4)","A",0
1864,1,197,0,0.396237," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{35 \, c^{3} d^{3} e^{3} x^{3} + c^{3} d^{6} + 4 \, a c^{2} d^{4} e^{2} + 10 \, a^{2} c d^{2} e^{4} + 20 \, a^{3} e^{6} + 21 \, {\left(c^{3} d^{4} e^{2} + 4 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(c^{3} d^{5} e + 4 \, a c^{2} d^{3} e^{3} + 10 \, a^{2} c d e^{5}\right)} x}{140 \, {\left(e^{11} x^{7} + 7 \, d e^{10} x^{6} + 21 \, d^{2} e^{9} x^{5} + 35 \, d^{3} e^{8} x^{4} + 35 \, d^{4} e^{7} x^{3} + 21 \, d^{5} e^{6} x^{2} + 7 \, d^{6} e^{5} x + d^{7} e^{4}\right)}}"," ",0,"-1/140*(35*c^3*d^3*e^3*x^3 + c^3*d^6 + 4*a*c^2*d^4*e^2 + 10*a^2*c*d^2*e^4 + 20*a^3*e^6 + 21*(c^3*d^4*e^2 + 4*a*c^2*d^2*e^4)*x^2 + 7*(c^3*d^5*e + 4*a*c^2*d^3*e^3 + 10*a^2*c*d*e^5)*x)/(e^11*x^7 + 7*d*e^10*x^6 + 21*d^2*e^9*x^5 + 35*d^3*e^8*x^4 + 35*d^4*e^7*x^3 + 21*d^5*e^6*x^2 + 7*d^6*e^5*x + d^7*e^4)","A",0
1865,1,207,0,0.400263," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{3 \, c^{4} d^{4} e^{4} x^{4} + 4 \, {\left(4 \, c^{4} d^{5} e^{3} - a c^{3} d^{3} e^{5}\right)} x^{3} + 6 \, {\left(6 \, c^{4} d^{6} e^{2} - 4 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 12 \, {\left(4 \, c^{4} d^{7} e - 6 \, a c^{3} d^{5} e^{3} + 4 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x + 12 \, {\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 + a e\right)}{12 \, c^{5} d^{5}}"," ",0,"1/12*(3*c^4*d^4*e^4*x^4 + 4*(4*c^4*d^5*e^3 - a*c^3*d^3*e^5)*x^3 + 6*(6*c^4*d^6*e^2 - 4*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + 12*(4*c^4*d^7*e - 6*a*c^3*d^5*e^3 + 4*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x + 12*(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 + a*e))/(c^5*d^5)","A",0
1866,1,137,0,0.391174," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{2 \, c^{3} d^{3} e^{3} x^{3} + 3 \, {\left(3 \, c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 6 \, {\left(3 \, c^{3} d^{5} e - 3 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x + 6 \, {\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 + a e\right)}{6 \, c^{4} d^{4}}"," ",0,"1/6*(2*c^3*d^3*e^3*x^3 + 3*(3*c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 6*(3*c^3*d^5*e - 3*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x + 6*(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 + a*e))/(c^4*d^4)","A",0
1867,1,79,0,0.391319," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{c^{2} d^{2} e^{2} x^{2} + 2 \, {\left(2 \, c^{2} d^{3} e - a c d e^{3}\right)} x + 2 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \log\left(c d x + a e\right)}{2 \, c^{3} d^{3}}"," ",0,"1/2*(c^2*d^2*e^2*x^2 + 2*(2*c^2*d^3*e - a*c*d*e^3)*x + 2*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*log(c*d*x + a*e))/(c^3*d^3)","A",0
1868,1,35,0,0.397576," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{c d e x + {\left(c d^{2} - a e^{2}\right)} \log\left(c d x + a e\right)}{c^{2} d^{2}}"," ",0,"(c*d*e*x + (c*d^2 - a*e^2)*log(c*d*x + a*e))/(c^2*d^2)","A",0
1869,1,16,0,0.378419," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{\log\left(c d x + a e\right)}{c d}"," ",0,"log(c*d*x + a*e)/(c*d)","A",0
1870,1,33,0,0.394754," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{\log\left(c d x + a e\right) - \log\left(e x + d\right)}{c d^{2} - a e^{2}}"," ",0,"(log(c*d*x + a*e) - log(e*x + d))/(c*d^2 - a*e^2)","A",0
1871,1,109,0,0.391717," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{c d^{2} - a e^{2} + {\left(c d e x + c d^{2}\right)} \log\left(c d x + a e\right) - {\left(c d e x + c d^{2}\right)} \log\left(e x + d\right)}{c^{2} d^{5} - 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e - 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x}"," ",0,"(c*d^2 - a*e^2 + (c*d*e*x + c*d^2)*log(c*d*x + a*e) - (c*d*e*x + c*d^2)*log(e*x + d))/(c^2*d^5 - 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e - 2*a*c*d^2*e^3 + a^2*e^5)*x)","A",0
1872,1,266,0,0.406314," ","integrate(1/(e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{3 \, c^{2} d^{4} - 4 \, a c d^{2} e^{2} + a^{2} e^{4} + 2 \, {\left(c^{2} d^{3} e - a c d e^{3}\right)} x + 2 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, c^{2} d^{3} e x + c^{2} d^{4}\right)} \log\left(c d x + a e\right) - 2 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, c^{2} d^{3} e x + c^{2} d^{4}\right)} \log\left(e x + d\right)}{2 \, {\left(c^{3} d^{8} - 3 \, a c^{2} d^{6} e^{2} + 3 \, a^{2} c d^{4} e^{4} - a^{3} d^{2} e^{6} + {\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)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, a c^{2} d^{5} e^{3} + 3 \, a^{2} c d^{3} e^{5} - a^{3} d e^{7}\right)} x\right)}}"," ",0,"1/2*(3*c^2*d^4 - 4*a*c*d^2*e^2 + a^2*e^4 + 2*(c^2*d^3*e - a*c*d*e^3)*x + 2*(c^2*d^2*e^2*x^2 + 2*c^2*d^3*e*x + c^2*d^4)*log(c*d*x + a*e) - 2*(c^2*d^2*e^2*x^2 + 2*c^2*d^3*e*x + c^2*d^4)*log(e*x + d))/(c^3*d^8 - 3*a*c^2*d^6*e^2 + 3*a^2*c*d^4*e^4 - a^3*d^2*e^6 + (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)*x^2 + 2*(c^3*d^7*e - 3*a*c^2*d^5*e^3 + 3*a^2*c*d^3*e^5 - a^3*d*e^7)*x)","B",0
1873,1,454,0,0.419467," ","integrate(1/(e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{11 \, c^{3} d^{6} - 18 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4} - 2 \, a^{3} e^{6} + 6 \, {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(5 \, c^{3} d^{5} e - 6 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x + 6 \, {\left(c^{3} d^{3} e^{3} x^{3} + 3 \, c^{3} d^{4} e^{2} x^{2} + 3 \, c^{3} d^{5} e x + c^{3} d^{6}\right)} \log\left(c d x + a e\right) - 6 \, {\left(c^{3} d^{3} e^{3} x^{3} + 3 \, c^{3} d^{4} e^{2} x^{2} + 3 \, c^{3} d^{5} e x + c^{3} d^{6}\right)} \log\left(e x + d\right)}{6 \, {\left(c^{4} d^{11} - 4 \, a c^{3} d^{9} e^{2} + 6 \, a^{2} c^{2} d^{7} e^{4} - 4 \, a^{3} c d^{5} e^{6} + a^{4} d^{3} e^{8} + {\left(c^{4} d^{8} e^{3} - 4 \, a c^{3} d^{6} e^{5} + 6 \, a^{2} c^{2} d^{4} e^{7} - 4 \, a^{3} c d^{2} e^{9} + a^{4} e^{11}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} - 4 \, a c^{3} d^{7} e^{4} + 6 \, a^{2} c^{2} d^{5} e^{6} - 4 \, a^{3} c d^{3} e^{8} + a^{4} d e^{10}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e - 4 \, a c^{3} d^{8} e^{3} + 6 \, a^{2} c^{2} d^{6} e^{5} - 4 \, a^{3} c d^{4} e^{7} + a^{4} d^{2} e^{9}\right)} x\right)}}"," ",0,"1/6*(11*c^3*d^6 - 18*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4 - 2*a^3*e^6 + 6*(c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 3*(5*c^3*d^5*e - 6*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x + 6*(c^3*d^3*e^3*x^3 + 3*c^3*d^4*e^2*x^2 + 3*c^3*d^5*e*x + c^3*d^6)*log(c*d*x + a*e) - 6*(c^3*d^3*e^3*x^3 + 3*c^3*d^4*e^2*x^2 + 3*c^3*d^5*e*x + c^3*d^6)*log(e*x + d))/(c^4*d^11 - 4*a*c^3*d^9*e^2 + 6*a^2*c^2*d^7*e^4 - 4*a^3*c*d^5*e^6 + a^4*d^3*e^8 + (c^4*d^8*e^3 - 4*a*c^3*d^6*e^5 + 6*a^2*c^2*d^4*e^7 - 4*a^3*c*d^2*e^9 + a^4*e^11)*x^3 + 3*(c^4*d^9*e^2 - 4*a*c^3*d^7*e^4 + 6*a^2*c^2*d^5*e^6 - 4*a^3*c*d^3*e^8 + a^4*d*e^10)*x^2 + 3*(c^4*d^10*e - 4*a*c^3*d^8*e^3 + 6*a^2*c^2*d^6*e^5 - 4*a^3*c*d^4*e^7 + a^4*d^2*e^9)*x)","B",0
1874,1,545,0,0.398800," ","integrate((e*x+d)^8/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\frac{2 \, c^{6} d^{6} e^{6} x^{6} - 10 \, c^{6} d^{12} + 60 \, a c^{5} d^{10} e^{2} - 150 \, a^{2} c^{4} d^{8} e^{4} + 200 \, a^{3} c^{3} d^{6} e^{6} - 150 \, a^{4} c^{2} d^{4} e^{8} + 60 \, a^{5} c d^{2} e^{10} - 10 \, a^{6} e^{12} + 3 \, {\left(5 \, c^{6} d^{7} e^{5} - a c^{5} d^{5} e^{7}\right)} x^{5} + 5 \, {\left(10 \, c^{6} d^{8} e^{4} - 5 \, a c^{5} d^{6} e^{6} + a^{2} c^{4} d^{4} e^{8}\right)} x^{4} + 10 \, {\left(10 \, c^{6} d^{9} e^{3} - 10 \, a c^{5} d^{7} e^{5} + 5 \, a^{2} c^{4} d^{5} e^{7} - a^{3} c^{3} d^{3} e^{9}\right)} x^{3} + 30 \, {\left(5 \, c^{6} d^{10} e^{2} - 10 \, a c^{5} d^{8} e^{4} + 10 \, a^{2} c^{4} d^{6} e^{6} - 5 \, a^{3} c^{3} d^{4} e^{8} + a^{4} c^{2} d^{2} e^{10}\right)} x^{2} + 10 \, {\left(15 \, a c^{5} d^{9} e^{3} - 40 \, a^{2} c^{4} d^{7} e^{5} + 45 \, a^{3} c^{3} d^{5} e^{7} - 24 \, a^{4} c^{2} d^{3} e^{9} + 5 \, a^{5} c d e^{11}\right)} x + 60 \, {\left(a c^{5} d^{10} e^{2} - 5 \, a^{2} c^{4} d^{8} e^{4} + 10 \, a^{3} c^{3} d^{6} e^{6} - 10 \, a^{4} c^{2} d^{4} e^{8} + 5 \, a^{5} c d^{2} e^{10} - a^{6} e^{12} + {\left(c^{6} d^{11} e - 5 \, a c^{5} d^{9} e^{3} + 10 \, a^{2} c^{4} d^{7} e^{5} - 10 \, a^{3} c^{3} d^{5} e^{7} + 5 \, a^{4} c^{2} d^{3} e^{9} - a^{5} c d e^{11}\right)} x\right)} \log\left(c d x + a e\right)}{10 \, {\left(c^{8} d^{8} x + a c^{7} d^{7} e\right)}}"," ",0,"1/10*(2*c^6*d^6*e^6*x^6 - 10*c^6*d^12 + 60*a*c^5*d^10*e^2 - 150*a^2*c^4*d^8*e^4 + 200*a^3*c^3*d^6*e^6 - 150*a^4*c^2*d^4*e^8 + 60*a^5*c*d^2*e^10 - 10*a^6*e^12 + 3*(5*c^6*d^7*e^5 - a*c^5*d^5*e^7)*x^5 + 5*(10*c^6*d^8*e^4 - 5*a*c^5*d^6*e^6 + a^2*c^4*d^4*e^8)*x^4 + 10*(10*c^6*d^9*e^3 - 10*a*c^5*d^7*e^5 + 5*a^2*c^4*d^5*e^7 - a^3*c^3*d^3*e^9)*x^3 + 30*(5*c^6*d^10*e^2 - 10*a*c^5*d^8*e^4 + 10*a^2*c^4*d^6*e^6 - 5*a^3*c^3*d^4*e^8 + a^4*c^2*d^2*e^10)*x^2 + 10*(15*a*c^5*d^9*e^3 - 40*a^2*c^4*d^7*e^5 + 45*a^3*c^3*d^5*e^7 - 24*a^4*c^2*d^3*e^9 + 5*a^5*c*d*e^11)*x + 60*(a*c^5*d^10*e^2 - 5*a^2*c^4*d^8*e^4 + 10*a^3*c^3*d^6*e^6 - 10*a^4*c^2*d^4*e^8 + 5*a^5*c*d^2*e^10 - a^6*e^12 + (c^6*d^11*e - 5*a*c^5*d^9*e^3 + 10*a^2*c^4*d^7*e^5 - 10*a^3*c^3*d^5*e^7 + 5*a^4*c^2*d^3*e^9 - a^5*c*d*e^11)*x)*log(c*d*x + a*e))/(c^8*d^8*x + a*c^7*d^7*e)","B",0
1875,1,417,0,0.388377," ","integrate((e*x+d)^7/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\frac{3 \, c^{5} d^{5} e^{5} x^{5} - 12 \, c^{5} d^{10} + 60 \, a c^{4} d^{8} e^{2} - 120 \, a^{2} c^{3} d^{6} e^{4} + 120 \, a^{3} c^{2} d^{4} e^{6} - 60 \, a^{4} c d^{2} e^{8} + 12 \, a^{5} e^{10} + 5 \, {\left(4 \, c^{5} d^{6} e^{4} - a c^{4} d^{4} e^{6}\right)} x^{4} + 10 \, {\left(6 \, c^{5} d^{7} e^{3} - 4 \, a c^{4} d^{5} e^{5} + a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 30 \, {\left(4 \, c^{5} d^{8} e^{2} - 6 \, a c^{4} d^{6} e^{4} + 4 \, a^{2} c^{3} d^{4} e^{6} - a^{3} c^{2} d^{2} e^{8}\right)} x^{2} + 12 \, {\left(10 \, a c^{4} d^{7} e^{3} - 20 \, a^{2} c^{3} d^{5} e^{5} + 15 \, a^{3} c^{2} d^{3} e^{7} - 4 \, a^{4} c d e^{9}\right)} x + 60 \, {\left(a c^{4} d^{8} e^{2} - 4 \, a^{2} c^{3} d^{6} e^{4} + 6 \, a^{3} c^{2} d^{4} e^{6} - 4 \, a^{4} c d^{2} e^{8} + a^{5} e^{10} + {\left(c^{5} d^{9} e - 4 \, a c^{4} d^{7} e^{3} + 6 \, a^{2} c^{3} d^{5} e^{5} - 4 \, a^{3} c^{2} d^{3} e^{7} + a^{4} c d e^{9}\right)} x\right)} \log\left(c d x + a e\right)}{12 \, {\left(c^{7} d^{7} x + a c^{6} d^{6} e\right)}}"," ",0,"1/12*(3*c^5*d^5*e^5*x^5 - 12*c^5*d^10 + 60*a*c^4*d^8*e^2 - 120*a^2*c^3*d^6*e^4 + 120*a^3*c^2*d^4*e^6 - 60*a^4*c*d^2*e^8 + 12*a^5*e^10 + 5*(4*c^5*d^6*e^4 - a*c^4*d^4*e^6)*x^4 + 10*(6*c^5*d^7*e^3 - 4*a*c^4*d^5*e^5 + a^2*c^3*d^3*e^7)*x^3 + 30*(4*c^5*d^8*e^2 - 6*a*c^4*d^6*e^4 + 4*a^2*c^3*d^4*e^6 - a^3*c^2*d^2*e^8)*x^2 + 12*(10*a*c^4*d^7*e^3 - 20*a^2*c^3*d^5*e^5 + 15*a^3*c^2*d^3*e^7 - 4*a^4*c*d*e^9)*x + 60*(a*c^4*d^8*e^2 - 4*a^2*c^3*d^6*e^4 + 6*a^3*c^2*d^4*e^6 - 4*a^4*c*d^2*e^8 + a^5*e^10 + (c^5*d^9*e - 4*a*c^4*d^7*e^3 + 6*a^2*c^3*d^5*e^5 - 4*a^3*c^2*d^3*e^7 + a^4*c*d*e^9)*x)*log(c*d*x + a*e))/(c^7*d^7*x + a*c^6*d^6*e)","B",0
1876,1,305,0,0.403671," ","integrate((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\frac{c^{4} d^{4} e^{4} x^{4} - 3 \, c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} - 18 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} - 3 \, a^{4} e^{8} + 2 \, {\left(3 \, c^{4} d^{5} e^{3} - a c^{3} d^{3} e^{5}\right)} x^{3} + 6 \, {\left(3 \, c^{4} d^{6} e^{2} - 3 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(6 \, a c^{3} d^{5} e^{3} - 8 \, a^{2} c^{2} d^{3} e^{5} + 3 \, a^{3} c d e^{7}\right)} x + 12 \, {\left(a c^{3} d^{6} e^{2} - 3 \, a^{2} c^{2} d^{4} e^{4} + 3 \, a^{3} c d^{2} e^{6} - a^{4} e^{8} + {\left(c^{4} d^{7} e - 3 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x\right)} \log\left(c d x + a e\right)}{3 \, {\left(c^{6} d^{6} x + a c^{5} d^{5} e\right)}}"," ",0,"1/3*(c^4*d^4*e^4*x^4 - 3*c^4*d^8 + 12*a*c^3*d^6*e^2 - 18*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 - 3*a^4*e^8 + 2*(3*c^4*d^5*e^3 - a*c^3*d^3*e^5)*x^3 + 6*(3*c^4*d^6*e^2 - 3*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + 3*(6*a*c^3*d^5*e^3 - 8*a^2*c^2*d^3*e^5 + 3*a^3*c*d*e^7)*x + 12*(a*c^3*d^6*e^2 - 3*a^2*c^2*d^4*e^4 + 3*a^3*c*d^2*e^6 - a^4*e^8 + (c^4*d^7*e - 3*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x)*log(c*d*x + a*e))/(c^6*d^6*x + a*c^5*d^5*e)","B",0
1877,1,205,0,0.388173," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\frac{c^{3} d^{3} e^{3} x^{3} - 2 \, c^{3} d^{6} + 6 \, a c^{2} d^{4} e^{2} - 6 \, a^{2} c d^{2} e^{4} + 2 \, a^{3} e^{6} + 3 \, {\left(2 \, c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(3 \, a c^{2} d^{3} e^{3} - 2 \, a^{2} c d e^{5}\right)} x + 6 \, {\left(a c^{2} d^{4} e^{2} - 2 \, a^{2} c d^{2} e^{4} + a^{3} e^{6} + {\left(c^{3} d^{5} e - 2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} \log\left(c d x + a e\right)}{2 \, {\left(c^{5} d^{5} x + a c^{4} d^{4} e\right)}}"," ",0,"1/2*(c^3*d^3*e^3*x^3 - 2*c^3*d^6 + 6*a*c^2*d^4*e^2 - 6*a^2*c*d^2*e^4 + 2*a^3*e^6 + 3*(2*c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 2*(3*a*c^2*d^3*e^3 - 2*a^2*c*d*e^5)*x + 6*(a*c^2*d^4*e^2 - 2*a^2*c*d^2*e^4 + a^3*e^6 + (c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*log(c*d*x + a*e))/(c^5*d^5*x + a*c^4*d^4*e)","A",0
1878,1,117,0,0.402600," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\frac{c^{2} d^{2} e^{2} x^{2} + a c d e^{3} x - c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4} + 2 \, {\left(a c d^{2} e^{2} - a^{2} e^{4} + {\left(c^{2} d^{3} e - a c d e^{3}\right)} x\right)} \log\left(c d x + a e\right)}{c^{4} d^{4} x + a c^{3} d^{3} e}"," ",0,"(c^2*d^2*e^2*x^2 + a*c*d*e^3*x - c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4 + 2*(a*c*d^2*e^2 - a^2*e^4 + (c^2*d^3*e - a*c*d*e^3)*x)*log(c*d*x + a*e))/(c^4*d^4*x + a*c^3*d^3*e)","A",0
1879,1,56,0,0.400217," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","-\frac{c d^{2} - a e^{2} - {\left(c d e x + a e^{2}\right)} \log\left(c d x + a e\right)}{c^{3} d^{3} x + a c^{2} d^{2} e}"," ",0,"-(c*d^2 - a*e^2 - (c*d*e*x + a*e^2)*log(c*d*x + a*e))/(c^3*d^3*x + a*c^2*d^2*e)","A",0
1880,1,18,0,0.388311," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","-\frac{1}{c^{2} d^{2} x + a c d e}"," ",0,"-1/(c^2*d^2*x + a*c*d*e)","A",0
1881,1,116,0,0.407305," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","-\frac{c d^{2} - a e^{2} + {\left(c d e x + a e^{2}\right)} \log\left(c d x + a e\right) - {\left(c d e x + a e^{2}\right)} \log\left(e x + d\right)}{a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} + {\left(c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x}"," ",0,"-(c*d^2 - a*e^2 + (c*d*e*x + a*e^2)*log(c*d*x + a*e) - (c*d*e*x + a*e^2)*log(e*x + d))/(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5 + (c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x)","A",0
1882,1,277,0,0.403834," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","-\frac{c^{2} d^{4} - a^{2} e^{4} + 2 \, {\left(c^{2} d^{3} e - a c d e^{3}\right)} x + 2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \log\left(c d x + a e\right) - 2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \log\left(e x + d\right)}{a c^{3} d^{7} e - 3 \, a^{2} c^{2} d^{5} e^{3} + 3 \, a^{3} c d^{3} e^{5} - a^{4} d e^{7} + {\left(c^{4} d^{7} e - 3 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x^{2} + {\left(c^{4} d^{8} - 2 \, a c^{3} d^{6} e^{2} + 2 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} x}"," ",0,"-(c^2*d^4 - a^2*e^4 + 2*(c^2*d^3*e - a*c*d*e^3)*x + 2*(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)*log(c*d*x + a*e) - 2*(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)*log(e*x + d))/(a*c^3*d^7*e - 3*a^2*c^2*d^5*e^3 + 3*a^3*c*d^3*e^5 - a^4*d*e^7 + (c^4*d^7*e - 3*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x^2 + (c^4*d^8 - 2*a*c^3*d^6*e^2 + 2*a^3*c*d^2*e^6 - a^4*e^8)*x)","B",0
1883,1,544,0,0.417696," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","-\frac{2 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} - 6 \, a^{2} c d^{2} e^{4} + a^{3} e^{6} + 6 \, {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 3 \, {\left(3 \, c^{3} d^{5} e - 2 \, a c^{2} d^{3} e^{3} - a^{2} c d e^{5}\right)} x + 6 \, {\left(c^{3} d^{3} e^{3} x^{3} + a c^{2} d^{4} e^{2} + {\left(2 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(c^{3} d^{5} e + 2 \, a c^{2} d^{3} e^{3}\right)} x\right)} \log\left(c d x + a e\right) - 6 \, {\left(c^{3} d^{3} e^{3} x^{3} + a c^{2} d^{4} e^{2} + {\left(2 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(c^{3} d^{5} e + 2 \, a c^{2} d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a c^{4} d^{10} e - 4 \, a^{2} c^{3} d^{8} e^{3} + 6 \, a^{3} c^{2} d^{6} e^{5} - 4 \, a^{4} c d^{4} e^{7} + a^{5} d^{2} e^{9} + {\left(c^{5} d^{9} e^{2} - 4 \, a c^{4} d^{7} e^{4} + 6 \, a^{2} c^{3} d^{5} e^{6} - 4 \, a^{3} c^{2} d^{3} e^{8} + a^{4} c d e^{10}\right)} x^{3} + {\left(2 \, c^{5} d^{10} e - 7 \, a c^{4} d^{8} e^{3} + 8 \, a^{2} c^{3} d^{6} e^{5} - 2 \, a^{3} c^{2} d^{4} e^{7} - 2 \, a^{4} c d^{2} e^{9} + a^{5} e^{11}\right)} x^{2} + {\left(c^{5} d^{11} - 2 \, a c^{4} d^{9} e^{2} - 2 \, a^{2} c^{3} d^{7} e^{4} + 8 \, a^{3} c^{2} d^{5} e^{6} - 7 \, a^{4} c d^{3} e^{8} + 2 \, a^{5} d e^{10}\right)} x\right)}}"," ",0,"-1/2*(2*c^3*d^6 + 3*a*c^2*d^4*e^2 - 6*a^2*c*d^2*e^4 + a^3*e^6 + 6*(c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 3*(3*c^3*d^5*e - 2*a*c^2*d^3*e^3 - a^2*c*d*e^5)*x + 6*(c^3*d^3*e^3*x^3 + a*c^2*d^4*e^2 + (2*c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^2 + (c^3*d^5*e + 2*a*c^2*d^3*e^3)*x)*log(c*d*x + a*e) - 6*(c^3*d^3*e^3*x^3 + a*c^2*d^4*e^2 + (2*c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^2 + (c^3*d^5*e + 2*a*c^2*d^3*e^3)*x)*log(e*x + d))/(a*c^4*d^10*e - 4*a^2*c^3*d^8*e^3 + 6*a^3*c^2*d^6*e^5 - 4*a^4*c*d^4*e^7 + a^5*d^2*e^9 + (c^5*d^9*e^2 - 4*a*c^4*d^7*e^4 + 6*a^2*c^3*d^5*e^6 - 4*a^3*c^2*d^3*e^8 + a^4*c*d*e^10)*x^3 + (2*c^5*d^10*e - 7*a*c^4*d^8*e^3 + 8*a^2*c^3*d^6*e^5 - 2*a^3*c^2*d^4*e^7 - 2*a^4*c*d^2*e^9 + a^5*e^11)*x^2 + (c^5*d^11 - 2*a*c^4*d^9*e^2 - 2*a^2*c^3*d^7*e^4 + 8*a^3*c^2*d^5*e^6 - 7*a^4*c*d^3*e^8 + 2*a^5*d*e^10)*x)","B",0
1884,1,807,0,0.419263," ","integrate(1/(e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","-\frac{3 \, c^{4} d^{8} + 10 \, a c^{3} d^{6} e^{2} - 18 \, a^{2} c^{2} d^{4} e^{4} + 6 \, a^{3} c d^{2} e^{6} - a^{4} e^{8} + 12 \, {\left(c^{4} d^{5} e^{3} - a c^{3} d^{3} e^{5}\right)} x^{3} + 6 \, {\left(5 \, c^{4} d^{6} e^{2} - 4 \, a c^{3} d^{4} e^{4} - a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(11 \, c^{4} d^{7} e - 3 \, a c^{3} d^{5} e^{3} - 9 \, a^{2} c^{2} d^{3} e^{5} + a^{3} c d e^{7}\right)} x + 12 \, {\left(c^{4} d^{4} e^{4} x^{4} + a c^{3} d^{6} e^{2} + {\left(3 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{3} + 3 \, {\left(c^{4} d^{6} e^{2} + a c^{3} d^{4} e^{4}\right)} x^{2} + {\left(c^{4} d^{7} e + 3 \, a c^{3} d^{5} e^{3}\right)} x\right)} \log\left(c d x + a e\right) - 12 \, {\left(c^{4} d^{4} e^{4} x^{4} + a c^{3} d^{6} e^{2} + {\left(3 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{3} + 3 \, {\left(c^{4} d^{6} e^{2} + a c^{3} d^{4} e^{4}\right)} x^{2} + {\left(c^{4} d^{7} e + 3 \, a c^{3} d^{5} e^{3}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(a c^{5} d^{13} e - 5 \, a^{2} c^{4} d^{11} e^{3} + 10 \, a^{3} c^{3} d^{9} e^{5} - 10 \, a^{4} c^{2} d^{7} e^{7} + 5 \, a^{5} c d^{5} e^{9} - a^{6} d^{3} e^{11} + {\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^{4} + {\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^{3} + 3 \, {\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^{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}\right)} x\right)}}"," ",0,"-1/3*(3*c^4*d^8 + 10*a*c^3*d^6*e^2 - 18*a^2*c^2*d^4*e^4 + 6*a^3*c*d^2*e^6 - a^4*e^8 + 12*(c^4*d^5*e^3 - a*c^3*d^3*e^5)*x^3 + 6*(5*c^4*d^6*e^2 - 4*a*c^3*d^4*e^4 - a^2*c^2*d^2*e^6)*x^2 + 2*(11*c^4*d^7*e - 3*a*c^3*d^5*e^3 - 9*a^2*c^2*d^3*e^5 + a^3*c*d*e^7)*x + 12*(c^4*d^4*e^4*x^4 + a*c^3*d^6*e^2 + (3*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^3 + 3*(c^4*d^6*e^2 + a*c^3*d^4*e^4)*x^2 + (c^4*d^7*e + 3*a*c^3*d^5*e^3)*x)*log(c*d*x + a*e) - 12*(c^4*d^4*e^4*x^4 + a*c^3*d^6*e^2 + (3*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^3 + 3*(c^4*d^6*e^2 + a*c^3*d^4*e^4)*x^2 + (c^4*d^7*e + 3*a*c^3*d^5*e^3)*x)*log(e*x + d))/(a*c^5*d^13*e - 5*a^2*c^4*d^11*e^3 + 10*a^3*c^3*d^9*e^5 - 10*a^4*c^2*d^7*e^7 + 5*a^5*c*d^5*e^9 - a^6*d^3*e^11 + (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^4 + (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^3 + 3*(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^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)*x)","B",0
1885,1,606,0,0.404690," ","integrate((e*x+d)^9/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\frac{c^{6} d^{6} e^{6} x^{6} - 2 \, c^{6} d^{12} - 12 \, a c^{5} d^{10} e^{2} + 90 \, a^{2} c^{4} d^{8} e^{4} - 200 \, a^{3} c^{3} d^{6} e^{6} + 210 \, a^{4} c^{2} d^{4} e^{8} - 108 \, a^{5} c d^{2} e^{10} + 22 \, a^{6} e^{12} + 2 \, {\left(4 \, c^{6} d^{7} e^{5} - a c^{5} d^{5} e^{7}\right)} x^{5} + 5 \, {\left(6 \, c^{6} d^{8} e^{4} - 4 \, a c^{5} d^{6} e^{6} + a^{2} c^{4} d^{4} e^{8}\right)} x^{4} + 20 \, {\left(4 \, c^{6} d^{9} e^{3} - 6 \, a c^{5} d^{7} e^{5} + 4 \, a^{2} c^{4} d^{5} e^{7} - a^{3} c^{3} d^{3} e^{9}\right)} x^{3} + 2 \, {\left(80 \, a c^{5} d^{8} e^{4} - 165 \, a^{2} c^{4} d^{6} e^{6} + 126 \, a^{3} c^{3} d^{4} e^{8} - 34 \, a^{4} c^{2} d^{2} e^{10}\right)} x^{2} - 4 \, {\left(6 \, c^{6} d^{11} e - 30 \, a c^{5} d^{9} e^{3} + 40 \, a^{2} c^{4} d^{7} e^{5} - 15 \, a^{3} c^{3} d^{5} e^{7} - 6 \, a^{4} c^{2} d^{3} e^{9} + 4 \, a^{5} c d e^{11}\right)} x + 60 \, {\left(a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} + 6 \, a^{4} c^{2} d^{4} e^{8} - 4 \, a^{5} c d^{2} e^{10} + a^{6} e^{12} + {\left(c^{6} d^{10} e^{2} - 4 \, a c^{5} d^{8} e^{4} + 6 \, a^{2} c^{4} d^{6} e^{6} - 4 \, a^{3} c^{3} d^{4} e^{8} + a^{4} c^{2} d^{2} e^{10}\right)} x^{2} + 2 \, {\left(a c^{5} d^{9} e^{3} - 4 \, a^{2} c^{4} d^{7} e^{5} + 6 \, a^{3} c^{3} d^{5} e^{7} - 4 \, a^{4} c^{2} d^{3} e^{9} + a^{5} c d e^{11}\right)} x\right)} \log\left(c d x + a e\right)}{4 \, {\left(c^{9} d^{9} x^{2} + 2 \, a c^{8} d^{8} e x + a^{2} c^{7} d^{7} e^{2}\right)}}"," ",0,"1/4*(c^6*d^6*e^6*x^6 - 2*c^6*d^12 - 12*a*c^5*d^10*e^2 + 90*a^2*c^4*d^8*e^4 - 200*a^3*c^3*d^6*e^6 + 210*a^4*c^2*d^4*e^8 - 108*a^5*c*d^2*e^10 + 22*a^6*e^12 + 2*(4*c^6*d^7*e^5 - a*c^5*d^5*e^7)*x^5 + 5*(6*c^6*d^8*e^4 - 4*a*c^5*d^6*e^6 + a^2*c^4*d^4*e^8)*x^4 + 20*(4*c^6*d^9*e^3 - 6*a*c^5*d^7*e^5 + 4*a^2*c^4*d^5*e^7 - a^3*c^3*d^3*e^9)*x^3 + 2*(80*a*c^5*d^8*e^4 - 165*a^2*c^4*d^6*e^6 + 126*a^3*c^3*d^4*e^8 - 34*a^4*c^2*d^2*e^10)*x^2 - 4*(6*c^6*d^11*e - 30*a*c^5*d^9*e^3 + 40*a^2*c^4*d^7*e^5 - 15*a^3*c^3*d^5*e^7 - 6*a^4*c^2*d^3*e^9 + 4*a^5*c*d*e^11)*x + 60*(a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 + 6*a^4*c^2*d^4*e^8 - 4*a^5*c*d^2*e^10 + a^6*e^12 + (c^6*d^10*e^2 - 4*a*c^5*d^8*e^4 + 6*a^2*c^4*d^6*e^6 - 4*a^3*c^3*d^4*e^8 + a^4*c^2*d^2*e^10)*x^2 + 2*(a*c^5*d^9*e^3 - 4*a^2*c^4*d^7*e^5 + 6*a^3*c^3*d^5*e^7 - 4*a^4*c^2*d^3*e^9 + a^5*c*d*e^11)*x)*log(c*d*x + a*e))/(c^9*d^9*x^2 + 2*a*c^8*d^8*e*x + a^2*c^7*d^7*e^2)","B",0
1886,1,469,0,0.401979," ","integrate((e*x+d)^8/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\frac{2 \, c^{5} d^{5} e^{5} x^{5} - 3 \, c^{5} d^{10} - 15 \, a c^{4} d^{8} e^{2} + 90 \, a^{2} c^{3} d^{6} e^{4} - 150 \, a^{3} c^{2} d^{4} e^{6} + 105 \, a^{4} c d^{2} e^{8} - 27 \, a^{5} e^{10} + 5 \, {\left(3 \, c^{5} d^{6} e^{4} - a c^{4} d^{4} e^{6}\right)} x^{4} + 20 \, {\left(3 \, c^{5} d^{7} e^{3} - 3 \, a c^{4} d^{5} e^{5} + a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 3 \, {\left(40 \, a c^{4} d^{6} e^{4} - 55 \, a^{2} c^{3} d^{4} e^{6} + 21 \, a^{3} c^{2} d^{2} e^{8}\right)} x^{2} - 6 \, {\left(5 \, c^{5} d^{9} e - 20 \, a c^{4} d^{7} e^{3} + 20 \, a^{2} c^{3} d^{5} e^{5} - 5 \, a^{3} c^{2} d^{3} e^{7} - a^{4} c d e^{9}\right)} x + 60 \, {\left(a^{2} c^{3} d^{6} e^{4} - 3 \, a^{3} c^{2} d^{4} e^{6} + 3 \, a^{4} c d^{2} e^{8} - a^{5} e^{10} + {\left(c^{5} d^{8} e^{2} - 3 \, a c^{4} d^{6} e^{4} + 3 \, a^{2} c^{3} d^{4} e^{6} - a^{3} c^{2} d^{2} e^{8}\right)} x^{2} + 2 \, {\left(a c^{4} d^{7} e^{3} - 3 \, a^{2} c^{3} d^{5} e^{5} + 3 \, a^{3} c^{2} d^{3} e^{7} - a^{4} c d e^{9}\right)} x\right)} \log\left(c d x + a e\right)}{6 \, {\left(c^{8} d^{8} x^{2} + 2 \, a c^{7} d^{7} e x + a^{2} c^{6} d^{6} e^{2}\right)}}"," ",0,"1/6*(2*c^5*d^5*e^5*x^5 - 3*c^5*d^10 - 15*a*c^4*d^8*e^2 + 90*a^2*c^3*d^6*e^4 - 150*a^3*c^2*d^4*e^6 + 105*a^4*c*d^2*e^8 - 27*a^5*e^10 + 5*(3*c^5*d^6*e^4 - a*c^4*d^4*e^6)*x^4 + 20*(3*c^5*d^7*e^3 - 3*a*c^4*d^5*e^5 + a^2*c^3*d^3*e^7)*x^3 + 3*(40*a*c^4*d^6*e^4 - 55*a^2*c^3*d^4*e^6 + 21*a^3*c^2*d^2*e^8)*x^2 - 6*(5*c^5*d^9*e - 20*a*c^4*d^7*e^3 + 20*a^2*c^3*d^5*e^5 - 5*a^3*c^2*d^3*e^7 - a^4*c*d*e^9)*x + 60*(a^2*c^3*d^6*e^4 - 3*a^3*c^2*d^4*e^6 + 3*a^4*c*d^2*e^8 - a^5*e^10 + (c^5*d^8*e^2 - 3*a*c^4*d^6*e^4 + 3*a^2*c^3*d^4*e^6 - a^3*c^2*d^2*e^8)*x^2 + 2*(a*c^4*d^7*e^3 - 3*a^2*c^3*d^5*e^5 + 3*a^3*c^2*d^3*e^7 - a^4*c*d*e^9)*x)*log(c*d*x + a*e))/(c^8*d^8*x^2 + 2*a*c^7*d^7*e*x + a^2*c^6*d^6*e^2)","B",0
1887,1,338,0,0.404063," ","integrate((e*x+d)^7/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\frac{c^{4} d^{4} e^{4} x^{4} - c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} + 18 \, a^{2} c^{2} d^{4} e^{4} - 20 \, a^{3} c d^{2} e^{6} + 7 \, a^{4} e^{8} + 4 \, {\left(2 \, c^{4} d^{5} e^{3} - a c^{3} d^{3} e^{5}\right)} x^{3} + {\left(16 \, a c^{3} d^{4} e^{4} - 11 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} - 2 \, {\left(4 \, c^{4} d^{7} e - 12 \, a c^{3} d^{5} e^{3} + 8 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x + 12 \, {\left(a^{2} c^{2} d^{4} e^{4} - 2 \, a^{3} c d^{2} e^{6} + a^{4} e^{8} + {\left(c^{4} d^{6} e^{2} - 2 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(a c^{3} d^{5} e^{3} - 2 \, a^{2} c^{2} d^{3} e^{5} + a^{3} c d e^{7}\right)} x\right)} \log\left(c d x + a e\right)}{2 \, {\left(c^{7} d^{7} x^{2} + 2 \, a c^{6} d^{6} e x + a^{2} c^{5} d^{5} e^{2}\right)}}"," ",0,"1/2*(c^4*d^4*e^4*x^4 - c^4*d^8 - 4*a*c^3*d^6*e^2 + 18*a^2*c^2*d^4*e^4 - 20*a^3*c*d^2*e^6 + 7*a^4*e^8 + 4*(2*c^4*d^5*e^3 - a*c^3*d^3*e^5)*x^3 + (16*a*c^3*d^4*e^4 - 11*a^2*c^2*d^2*e^6)*x^2 - 2*(4*c^4*d^7*e - 12*a*c^3*d^5*e^3 + 8*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x + 12*(a^2*c^2*d^4*e^4 - 2*a^3*c*d^2*e^6 + a^4*e^8 + (c^4*d^6*e^2 - 2*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + 2*(a*c^3*d^5*e^3 - 2*a^2*c^2*d^3*e^5 + a^3*c*d*e^7)*x)*log(c*d*x + a*e))/(c^7*d^7*x^2 + 2*a*c^6*d^6*e*x + a^2*c^5*d^5*e^2)","B",0
1888,1,227,0,0.405922," ","integrate((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\frac{2 \, c^{3} d^{3} e^{3} x^{3} + 4 \, a c^{2} d^{2} e^{4} x^{2} - c^{3} d^{6} - 3 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4} - 5 \, a^{3} e^{6} - 2 \, {\left(3 \, c^{3} d^{5} e - 6 \, a c^{2} d^{3} e^{3} + 2 \, a^{2} c d e^{5}\right)} x + 6 \, {\left(a^{2} c d^{2} e^{4} - a^{3} e^{6} + {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(a c^{2} d^{3} e^{3} - a^{2} c d e^{5}\right)} x\right)} \log\left(c d x + a e\right)}{2 \, {\left(c^{6} d^{6} x^{2} + 2 \, a c^{5} d^{5} e x + a^{2} c^{4} d^{4} e^{2}\right)}}"," ",0,"1/2*(2*c^3*d^3*e^3*x^3 + 4*a*c^2*d^2*e^4*x^2 - c^3*d^6 - 3*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4 - 5*a^3*e^6 - 2*(3*c^3*d^5*e - 6*a*c^2*d^3*e^3 + 2*a^2*c*d*e^5)*x + 6*(a^2*c*d^2*e^4 - a^3*e^6 + (c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 2*(a*c^2*d^3*e^3 - a^2*c*d*e^5)*x)*log(c*d*x + a*e))/(c^6*d^6*x^2 + 2*a*c^5*d^5*e*x + a^2*c^4*d^4*e^2)","B",0
1889,1,126,0,0.403893," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","-\frac{c^{2} d^{4} + 2 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4} + 4 \, {\left(c^{2} d^{3} e - a c d e^{3}\right)} x - 2 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \log\left(c d x + a e\right)}{2 \, {\left(c^{5} d^{5} x^{2} + 2 \, a c^{4} d^{4} e x + a^{2} c^{3} d^{3} e^{2}\right)}}"," ",0,"-1/2*(c^2*d^4 + 2*a*c*d^2*e^2 - 3*a^2*e^4 + 4*(c^2*d^3*e - a*c*d*e^3)*x - 2*(c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*log(c*d*x + a*e))/(c^5*d^5*x^2 + 2*a*c^4*d^4*e*x + a^2*c^3*d^3*e^2)","A",0
1890,1,56,0,0.382681," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","-\frac{2 \, c d e x + c d^{2} + a e^{2}}{2 \, {\left(c^{4} d^{4} x^{2} + 2 \, a c^{3} d^{3} e x + a^{2} c^{2} d^{2} e^{2}\right)}}"," ",0,"-1/2*(2*c*d*e*x + c*d^2 + a*e^2)/(c^4*d^4*x^2 + 2*a*c^3*d^3*e*x + a^2*c^2*d^2*e^2)","A",0
1891,1,35,0,0.388257," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(c^{3} d^{3} x^{2} + 2 \, a c^{2} d^{2} e x + a^{2} c d e^{2}\right)}}"," ",0,"-1/2/(c^3*d^3*x^2 + 2*a*c^2*d^2*e*x + a^2*c*d*e^2)","A",0
1892,1,280,0,0.410787," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","-\frac{c^{2} d^{4} - 4 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} - 2 \, {\left(c^{2} d^{3} e - a c d e^{3}\right)} x - 2 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \log\left(c d x + a e\right) + 2 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} c^{3} d^{6} e^{2} - 3 \, a^{3} c^{2} d^{4} e^{4} + 3 \, a^{4} c d^{2} e^{6} - a^{5} e^{8} + {\left(c^{5} d^{8} - 3 \, a c^{4} d^{6} e^{2} + 3 \, a^{2} c^{3} d^{4} e^{4} - a^{3} c^{2} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(a c^{4} d^{7} e - 3 \, a^{2} c^{3} d^{5} e^{3} + 3 \, a^{3} c^{2} d^{3} e^{5} - a^{4} c d e^{7}\right)} x\right)}}"," ",0,"-1/2*(c^2*d^4 - 4*a*c*d^2*e^2 + 3*a^2*e^4 - 2*(c^2*d^3*e - a*c*d*e^3)*x - 2*(c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*log(c*d*x + a*e) + 2*(c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*log(e*x + d))/(a^2*c^3*d^6*e^2 - 3*a^3*c^2*d^4*e^4 + 3*a^4*c*d^2*e^6 - a^5*e^8 + (c^5*d^8 - 3*a*c^4*d^6*e^2 + 3*a^2*c^3*d^4*e^4 - a^3*c^2*d^2*e^6)*x^2 + 2*(a*c^4*d^7*e - 3*a^2*c^3*d^5*e^3 + 3*a^3*c^2*d^3*e^5 - a^4*c*d*e^7)*x)","B",0
1893,1,555,0,0.415070," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","-\frac{c^{3} d^{6} - 6 \, a c^{2} d^{4} e^{2} + 3 \, a^{2} c d^{2} e^{4} + 2 \, a^{3} e^{6} - 6 \, {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} - 3 \, {\left(c^{3} d^{5} e + 2 \, a c^{2} d^{3} e^{3} - 3 \, a^{2} c d e^{5}\right)} x - 6 \, {\left(c^{3} d^{3} e^{3} x^{3} + a^{2} c d^{2} e^{4} + {\left(c^{3} d^{4} e^{2} + 2 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} \log\left(c d x + a e\right) + 6 \, {\left(c^{3} d^{3} e^{3} x^{3} + a^{2} c d^{2} e^{4} + {\left(c^{3} d^{4} e^{2} + 2 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} c^{4} d^{9} e^{2} - 4 \, a^{3} c^{3} d^{7} e^{4} + 6 \, a^{4} c^{2} d^{5} e^{6} - 4 \, a^{5} c d^{3} e^{8} + a^{6} d e^{10} + {\left(c^{6} d^{10} e - 4 \, a c^{5} d^{8} e^{3} + 6 \, a^{2} c^{4} d^{6} e^{5} - 4 \, a^{3} c^{3} d^{4} e^{7} + a^{4} c^{2} d^{2} e^{9}\right)} x^{3} + {\left(c^{6} d^{11} - 2 \, a c^{5} d^{9} e^{2} - 2 \, a^{2} c^{4} d^{7} e^{4} + 8 \, a^{3} c^{3} d^{5} e^{6} - 7 \, a^{4} c^{2} d^{3} e^{8} + 2 \, a^{5} c d e^{10}\right)} x^{2} + {\left(2 \, a c^{5} d^{10} e - 7 \, a^{2} c^{4} d^{8} e^{3} + 8 \, a^{3} c^{3} d^{6} e^{5} - 2 \, a^{4} c^{2} d^{4} e^{7} - 2 \, a^{5} c d^{2} e^{9} + a^{6} e^{11}\right)} x\right)}}"," ",0,"-1/2*(c^3*d^6 - 6*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + 2*a^3*e^6 - 6*(c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 - 3*(c^3*d^5*e + 2*a*c^2*d^3*e^3 - 3*a^2*c*d*e^5)*x - 6*(c^3*d^3*e^3*x^3 + a^2*c*d^2*e^4 + (c^3*d^4*e^2 + 2*a*c^2*d^2*e^4)*x^2 + (2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*log(c*d*x + a*e) + 6*(c^3*d^3*e^3*x^3 + a^2*c*d^2*e^4 + (c^3*d^4*e^2 + 2*a*c^2*d^2*e^4)*x^2 + (2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*log(e*x + d))/(a^2*c^4*d^9*e^2 - 4*a^3*c^3*d^7*e^4 + 6*a^4*c^2*d^5*e^6 - 4*a^5*c*d^3*e^8 + a^6*d*e^10 + (c^6*d^10*e - 4*a*c^5*d^8*e^3 + 6*a^2*c^4*d^6*e^5 - 4*a^3*c^3*d^4*e^7 + a^4*c^2*d^2*e^9)*x^3 + (c^6*d^11 - 2*a*c^5*d^9*e^2 - 2*a^2*c^4*d^7*e^4 + 8*a^3*c^3*d^5*e^6 - 7*a^4*c^2*d^3*e^8 + 2*a^5*c*d*e^10)*x^2 + (2*a*c^5*d^10*e - 7*a^2*c^4*d^8*e^3 + 8*a^3*c^3*d^6*e^5 - 2*a^4*c^2*d^4*e^7 - 2*a^5*c*d^2*e^9 + a^6*e^11)*x)","B",0
1894,1,828,0,0.424517," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","-\frac{c^{4} d^{8} - 8 \, a c^{3} d^{6} e^{2} + 8 \, a^{3} c d^{2} e^{6} - a^{4} e^{8} - 12 \, {\left(c^{4} d^{5} e^{3} - a c^{3} d^{3} e^{5}\right)} x^{3} - 18 \, {\left(c^{4} d^{6} e^{2} - a^{2} c^{2} d^{2} e^{6}\right)} x^{2} - 4 \, {\left(c^{4} d^{7} e + 6 \, a c^{3} d^{5} e^{3} - 6 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x - 12 \, {\left(c^{4} d^{4} e^{4} x^{4} + a^{2} c^{2} d^{4} e^{4} + 2 \, {\left(c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{3} + {\left(c^{4} d^{6} e^{2} + 4 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(a c^{3} d^{5} e^{3} + a^{2} c^{2} d^{3} e^{5}\right)} x\right)} \log\left(c d x + a e\right) + 12 \, {\left(c^{4} d^{4} e^{4} x^{4} + a^{2} c^{2} d^{4} e^{4} + 2 \, {\left(c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{3} + {\left(c^{4} d^{6} e^{2} + 4 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(a c^{3} d^{5} e^{3} + a^{2} c^{2} d^{3} e^{5}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(a^{2} c^{5} d^{12} e^{2} - 5 \, a^{3} c^{4} d^{10} e^{4} + 10 \, a^{4} c^{3} d^{8} e^{6} - 10 \, a^{5} c^{2} d^{6} e^{8} + 5 \, a^{6} c d^{4} e^{10} - a^{7} d^{2} e^{12} + {\left(c^{7} d^{12} e^{2} - 5 \, a c^{6} d^{10} e^{4} + 10 \, a^{2} c^{5} d^{8} e^{6} - 10 \, a^{3} c^{4} d^{6} e^{8} + 5 \, a^{4} c^{3} d^{4} e^{10} - a^{5} c^{2} d^{2} e^{12}\right)} x^{4} + 2 \, {\left(c^{7} d^{13} e - 4 \, a c^{6} d^{11} e^{3} + 5 \, a^{2} c^{5} d^{9} e^{5} - 5 \, a^{4} c^{3} d^{5} e^{9} + 4 \, a^{5} c^{2} d^{3} e^{11} - a^{6} c d e^{13}\right)} x^{3} + {\left(c^{7} d^{14} - a c^{6} d^{12} e^{2} - 9 \, a^{2} c^{5} d^{10} e^{4} + 25 \, a^{3} c^{4} d^{8} e^{6} - 25 \, a^{4} c^{3} d^{6} e^{8} + 9 \, a^{5} c^{2} d^{4} e^{10} + a^{6} c d^{2} e^{12} - a^{7} e^{14}\right)} x^{2} + 2 \, {\left(a c^{6} d^{13} e - 4 \, a^{2} c^{5} d^{11} e^{3} + 5 \, a^{3} c^{4} d^{9} e^{5} - 5 \, a^{5} c^{2} d^{5} e^{9} + 4 \, a^{6} c d^{3} e^{11} - a^{7} d e^{13}\right)} x\right)}}"," ",0,"-1/2*(c^4*d^8 - 8*a*c^3*d^6*e^2 + 8*a^3*c*d^2*e^6 - a^4*e^8 - 12*(c^4*d^5*e^3 - a*c^3*d^3*e^5)*x^3 - 18*(c^4*d^6*e^2 - a^2*c^2*d^2*e^6)*x^2 - 4*(c^4*d^7*e + 6*a*c^3*d^5*e^3 - 6*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x - 12*(c^4*d^4*e^4*x^4 + a^2*c^2*d^4*e^4 + 2*(c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^3 + (c^4*d^6*e^2 + 4*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + 2*(a*c^3*d^5*e^3 + a^2*c^2*d^3*e^5)*x)*log(c*d*x + a*e) + 12*(c^4*d^4*e^4*x^4 + a^2*c^2*d^4*e^4 + 2*(c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^3 + (c^4*d^6*e^2 + 4*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + 2*(a*c^3*d^5*e^3 + a^2*c^2*d^3*e^5)*x)*log(e*x + d))/(a^2*c^5*d^12*e^2 - 5*a^3*c^4*d^10*e^4 + 10*a^4*c^3*d^8*e^6 - 10*a^5*c^2*d^6*e^8 + 5*a^6*c*d^4*e^10 - a^7*d^2*e^12 + (c^7*d^12*e^2 - 5*a*c^6*d^10*e^4 + 10*a^2*c^5*d^8*e^6 - 10*a^3*c^4*d^6*e^8 + 5*a^4*c^3*d^4*e^10 - a^5*c^2*d^2*e^12)*x^4 + 2*(c^7*d^13*e - 4*a*c^6*d^11*e^3 + 5*a^2*c^5*d^9*e^5 - 5*a^4*c^3*d^5*e^9 + 4*a^5*c^2*d^3*e^11 - a^6*c*d*e^13)*x^3 + (c^7*d^14 - a*c^6*d^12*e^2 - 9*a^2*c^5*d^10*e^4 + 25*a^3*c^4*d^8*e^6 - 25*a^4*c^3*d^6*e^8 + 9*a^5*c^2*d^4*e^10 + a^6*c*d^2*e^12 - a^7*e^14)*x^2 + 2*(a*c^6*d^13*e - 4*a^2*c^5*d^11*e^3 + 5*a^3*c^4*d^9*e^5 - 5*a^5*c^2*d^5*e^9 + 4*a^6*c*d^3*e^11 - a^7*d*e^13)*x)","B",0
1895,1,1222,0,0.437336," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","-\frac{3 \, c^{5} d^{10} - 30 \, a c^{4} d^{8} e^{2} - 20 \, a^{2} c^{3} d^{6} e^{4} + 60 \, a^{3} c^{2} d^{4} e^{6} - 15 \, a^{4} c d^{2} e^{8} + 2 \, a^{5} e^{10} - 60 \, {\left(c^{5} d^{6} e^{4} - a c^{4} d^{4} e^{6}\right)} x^{4} - 30 \, {\left(5 \, c^{5} d^{7} e^{3} - 2 \, a c^{4} d^{5} e^{5} - 3 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} - 10 \, {\left(11 \, c^{5} d^{8} e^{2} + 12 \, a c^{4} d^{6} e^{4} - 21 \, a^{2} c^{3} d^{4} e^{6} - 2 \, a^{3} c^{2} d^{2} e^{8}\right)} x^{2} - 5 \, {\left(3 \, c^{5} d^{9} e + 32 \, a c^{4} d^{7} e^{3} - 24 \, a^{2} c^{3} d^{5} e^{5} - 12 \, a^{3} c^{2} d^{3} e^{7} + a^{4} c d e^{9}\right)} x - 60 \, {\left(c^{5} d^{5} e^{5} x^{5} + a^{2} c^{3} d^{6} e^{4} + {\left(3 \, c^{5} d^{6} e^{4} + 2 \, a c^{4} d^{4} e^{6}\right)} x^{4} + {\left(3 \, c^{5} d^{7} e^{3} + 6 \, a c^{4} d^{5} e^{5} + a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + {\left(c^{5} d^{8} e^{2} + 6 \, a c^{4} d^{6} e^{4} + 3 \, a^{2} c^{3} d^{4} e^{6}\right)} x^{2} + {\left(2 \, a c^{4} d^{7} e^{3} + 3 \, a^{2} c^{3} d^{5} e^{5}\right)} x\right)} \log\left(c d x + a e\right) + 60 \, {\left(c^{5} d^{5} e^{5} x^{5} + a^{2} c^{3} d^{6} e^{4} + {\left(3 \, c^{5} d^{6} e^{4} + 2 \, a c^{4} d^{4} e^{6}\right)} x^{4} + {\left(3 \, c^{5} d^{7} e^{3} + 6 \, a c^{4} d^{5} e^{5} + a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + {\left(c^{5} d^{8} e^{2} + 6 \, a c^{4} d^{6} e^{4} + 3 \, a^{2} c^{3} d^{4} e^{6}\right)} x^{2} + {\left(2 \, a c^{4} d^{7} e^{3} + 3 \, a^{2} c^{3} d^{5} e^{5}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(a^{2} c^{6} d^{15} e^{2} - 6 \, a^{3} c^{5} d^{13} e^{4} + 15 \, a^{4} c^{4} d^{11} e^{6} - 20 \, a^{5} c^{3} d^{9} e^{8} + 15 \, a^{6} c^{2} d^{7} e^{10} - 6 \, a^{7} c d^{5} e^{12} + a^{8} d^{3} e^{14} + {\left(c^{8} d^{14} e^{3} - 6 \, a c^{7} d^{12} e^{5} + 15 \, a^{2} c^{6} d^{10} e^{7} - 20 \, a^{3} c^{5} d^{8} e^{9} + 15 \, a^{4} c^{4} d^{6} e^{11} - 6 \, a^{5} c^{3} d^{4} e^{13} + a^{6} c^{2} d^{2} e^{15}\right)} x^{5} + {\left(3 \, c^{8} d^{15} e^{2} - 16 \, a c^{7} d^{13} e^{4} + 33 \, a^{2} c^{6} d^{11} e^{6} - 30 \, a^{3} c^{5} d^{9} e^{8} + 5 \, a^{4} c^{4} d^{7} e^{10} + 12 \, a^{5} c^{3} d^{5} e^{12} - 9 \, a^{6} c^{2} d^{3} e^{14} + 2 \, a^{7} c d e^{16}\right)} x^{4} + {\left(3 \, c^{8} d^{16} e - 12 \, a c^{7} d^{14} e^{3} + 10 \, a^{2} c^{6} d^{12} e^{5} + 24 \, a^{3} c^{5} d^{10} e^{7} - 60 \, a^{4} c^{4} d^{8} e^{9} + 52 \, a^{5} c^{3} d^{6} e^{11} - 18 \, a^{6} c^{2} d^{4} e^{13} + a^{8} e^{17}\right)} x^{3} + {\left(c^{8} d^{17} - 18 \, a^{2} c^{6} d^{13} e^{4} + 52 \, a^{3} c^{5} d^{11} e^{6} - 60 \, a^{4} c^{4} d^{9} e^{8} + 24 \, a^{5} c^{3} d^{7} e^{10} + 10 \, a^{6} c^{2} d^{5} e^{12} - 12 \, a^{7} c d^{3} e^{14} + 3 \, a^{8} d e^{16}\right)} x^{2} + {\left(2 \, a c^{7} d^{16} e - 9 \, a^{2} c^{6} d^{14} e^{3} + 12 \, a^{3} c^{5} d^{12} e^{5} + 5 \, a^{4} c^{4} d^{10} e^{7} - 30 \, a^{5} c^{3} d^{8} e^{9} + 33 \, a^{6} c^{2} d^{6} e^{11} - 16 \, a^{7} c d^{4} e^{13} + 3 \, a^{8} d^{2} e^{15}\right)} x\right)}}"," ",0,"-1/6*(3*c^5*d^10 - 30*a*c^4*d^8*e^2 - 20*a^2*c^3*d^6*e^4 + 60*a^3*c^2*d^4*e^6 - 15*a^4*c*d^2*e^8 + 2*a^5*e^10 - 60*(c^5*d^6*e^4 - a*c^4*d^4*e^6)*x^4 - 30*(5*c^5*d^7*e^3 - 2*a*c^4*d^5*e^5 - 3*a^2*c^3*d^3*e^7)*x^3 - 10*(11*c^5*d^8*e^2 + 12*a*c^4*d^6*e^4 - 21*a^2*c^3*d^4*e^6 - 2*a^3*c^2*d^2*e^8)*x^2 - 5*(3*c^5*d^9*e + 32*a*c^4*d^7*e^3 - 24*a^2*c^3*d^5*e^5 - 12*a^3*c^2*d^3*e^7 + a^4*c*d*e^9)*x - 60*(c^5*d^5*e^5*x^5 + a^2*c^3*d^6*e^4 + (3*c^5*d^6*e^4 + 2*a*c^4*d^4*e^6)*x^4 + (3*c^5*d^7*e^3 + 6*a*c^4*d^5*e^5 + a^2*c^3*d^3*e^7)*x^3 + (c^5*d^8*e^2 + 6*a*c^4*d^6*e^4 + 3*a^2*c^3*d^4*e^6)*x^2 + (2*a*c^4*d^7*e^3 + 3*a^2*c^3*d^5*e^5)*x)*log(c*d*x + a*e) + 60*(c^5*d^5*e^5*x^5 + a^2*c^3*d^6*e^4 + (3*c^5*d^6*e^4 + 2*a*c^4*d^4*e^6)*x^4 + (3*c^5*d^7*e^3 + 6*a*c^4*d^5*e^5 + a^2*c^3*d^3*e^7)*x^3 + (c^5*d^8*e^2 + 6*a*c^4*d^6*e^4 + 3*a^2*c^3*d^4*e^6)*x^2 + (2*a*c^4*d^7*e^3 + 3*a^2*c^3*d^5*e^5)*x)*log(e*x + d))/(a^2*c^6*d^15*e^2 - 6*a^3*c^5*d^13*e^4 + 15*a^4*c^4*d^11*e^6 - 20*a^5*c^3*d^9*e^8 + 15*a^6*c^2*d^7*e^10 - 6*a^7*c*d^5*e^12 + a^8*d^3*e^14 + (c^8*d^14*e^3 - 6*a*c^7*d^12*e^5 + 15*a^2*c^6*d^10*e^7 - 20*a^3*c^5*d^8*e^9 + 15*a^4*c^4*d^6*e^11 - 6*a^5*c^3*d^4*e^13 + a^6*c^2*d^2*e^15)*x^5 + (3*c^8*d^15*e^2 - 16*a*c^7*d^13*e^4 + 33*a^2*c^6*d^11*e^6 - 30*a^3*c^5*d^9*e^8 + 5*a^4*c^4*d^7*e^10 + 12*a^5*c^3*d^5*e^12 - 9*a^6*c^2*d^3*e^14 + 2*a^7*c*d*e^16)*x^4 + (3*c^8*d^16*e - 12*a*c^7*d^14*e^3 + 10*a^2*c^6*d^12*e^5 + 24*a^3*c^5*d^10*e^7 - 60*a^4*c^4*d^8*e^9 + 52*a^5*c^3*d^6*e^11 - 18*a^6*c^2*d^4*e^13 + a^8*e^17)*x^3 + (c^8*d^17 - 18*a^2*c^6*d^13*e^4 + 52*a^3*c^5*d^11*e^6 - 60*a^4*c^4*d^9*e^8 + 24*a^5*c^3*d^7*e^10 + 10*a^6*c^2*d^5*e^12 - 12*a^7*c*d^3*e^14 + 3*a^8*d*e^16)*x^2 + (2*a*c^7*d^16*e - 9*a^2*c^6*d^14*e^3 + 12*a^3*c^5*d^12*e^5 + 5*a^4*c^4*d^10*e^7 - 30*a^5*c^3*d^8*e^9 + 33*a^6*c^2*d^6*e^11 - 16*a^7*c*d^4*e^13 + 3*a^8*d^2*e^15)*x)","B",0
1896,1,644,0,0.408625," ","integrate((e*x+d)^10/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","\frac{c^{6} d^{6} e^{6} x^{6} - c^{6} d^{12} - 3 \, a c^{5} d^{10} e^{2} - 15 \, a^{2} c^{4} d^{8} e^{4} + 110 \, a^{3} c^{3} d^{6} e^{6} - 195 \, a^{4} c^{2} d^{4} e^{8} + 141 \, a^{5} c d^{2} e^{10} - 37 \, a^{6} e^{12} + 3 \, {\left(3 \, c^{6} d^{7} e^{5} - a c^{5} d^{5} e^{7}\right)} x^{5} + 15 \, {\left(3 \, c^{6} d^{8} e^{4} - 3 \, a c^{5} d^{6} e^{6} + a^{2} c^{4} d^{4} e^{8}\right)} x^{4} + {\left(135 \, a c^{5} d^{7} e^{5} - 189 \, a^{2} c^{4} d^{5} e^{7} + 73 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{3} - 3 \, {\left(15 \, c^{6} d^{10} e^{2} - 60 \, a c^{5} d^{8} e^{4} + 45 \, a^{2} c^{4} d^{6} e^{6} + 9 \, a^{3} c^{3} d^{4} e^{8} - 13 \, a^{4} c^{2} d^{2} e^{10}\right)} x^{2} - 3 \, {\left(3 \, c^{6} d^{11} e + 15 \, a c^{5} d^{9} e^{3} - 90 \, a^{2} c^{4} d^{7} e^{5} + 135 \, a^{3} c^{3} d^{5} e^{7} - 81 \, a^{4} c^{2} d^{3} e^{9} + 17 \, a^{5} c d e^{11}\right)} x + 60 \, {\left(a^{3} c^{3} d^{6} e^{6} - 3 \, a^{4} c^{2} d^{4} e^{8} + 3 \, a^{5} c d^{2} e^{10} - a^{6} e^{12} + {\left(c^{6} d^{9} e^{3} - 3 \, a c^{5} d^{7} e^{5} + 3 \, a^{2} c^{4} d^{5} e^{7} - a^{3} c^{3} d^{3} e^{9}\right)} x^{3} + 3 \, {\left(a c^{5} d^{8} e^{4} - 3 \, a^{2} c^{4} d^{6} e^{6} + 3 \, a^{3} c^{3} d^{4} e^{8} - a^{4} c^{2} d^{2} e^{10}\right)} x^{2} + 3 \, {\left(a^{2} c^{4} d^{7} e^{5} - 3 \, a^{3} c^{3} d^{5} e^{7} + 3 \, a^{4} c^{2} d^{3} e^{9} - a^{5} c d e^{11}\right)} x\right)} \log\left(c d x + a e\right)}{3 \, {\left(c^{10} d^{10} x^{3} + 3 \, a c^{9} d^{9} e x^{2} + 3 \, a^{2} c^{8} d^{8} e^{2} x + a^{3} c^{7} d^{7} e^{3}\right)}}"," ",0,"1/3*(c^6*d^6*e^6*x^6 - c^6*d^12 - 3*a*c^5*d^10*e^2 - 15*a^2*c^4*d^8*e^4 + 110*a^3*c^3*d^6*e^6 - 195*a^4*c^2*d^4*e^8 + 141*a^5*c*d^2*e^10 - 37*a^6*e^12 + 3*(3*c^6*d^7*e^5 - a*c^5*d^5*e^7)*x^5 + 15*(3*c^6*d^8*e^4 - 3*a*c^5*d^6*e^6 + a^2*c^4*d^4*e^8)*x^4 + (135*a*c^5*d^7*e^5 - 189*a^2*c^4*d^5*e^7 + 73*a^3*c^3*d^3*e^9)*x^3 - 3*(15*c^6*d^10*e^2 - 60*a*c^5*d^8*e^4 + 45*a^2*c^4*d^6*e^6 + 9*a^3*c^3*d^4*e^8 - 13*a^4*c^2*d^2*e^10)*x^2 - 3*(3*c^6*d^11*e + 15*a*c^5*d^9*e^3 - 90*a^2*c^4*d^7*e^5 + 135*a^3*c^3*d^5*e^7 - 81*a^4*c^2*d^3*e^9 + 17*a^5*c*d*e^11)*x + 60*(a^3*c^3*d^6*e^6 - 3*a^4*c^2*d^4*e^8 + 3*a^5*c*d^2*e^10 - a^6*e^12 + (c^6*d^9*e^3 - 3*a*c^5*d^7*e^5 + 3*a^2*c^4*d^5*e^7 - a^3*c^3*d^3*e^9)*x^3 + 3*(a*c^5*d^8*e^4 - 3*a^2*c^4*d^6*e^6 + 3*a^3*c^3*d^4*e^8 - a^4*c^2*d^2*e^10)*x^2 + 3*(a^2*c^4*d^7*e^5 - 3*a^3*c^3*d^5*e^7 + 3*a^4*c^2*d^3*e^9 - a^5*c*d*e^11)*x)*log(c*d*x + a*e))/(c^10*d^10*x^3 + 3*a*c^9*d^9*e*x^2 + 3*a^2*c^8*d^8*e^2*x + a^3*c^7*d^7*e^3)","B",0
1897,1,488,0,0.403223," ","integrate((e*x+d)^9/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","\frac{3 \, c^{5} d^{5} e^{5} x^{5} - 2 \, c^{5} d^{10} - 5 \, a c^{4} d^{8} e^{2} - 20 \, a^{2} c^{3} d^{6} e^{4} + 110 \, a^{3} c^{2} d^{4} e^{6} - 130 \, a^{4} c d^{2} e^{8} + 47 \, a^{5} e^{10} + 15 \, {\left(2 \, c^{5} d^{6} e^{4} - a c^{4} d^{4} e^{6}\right)} x^{4} + 9 \, {\left(10 \, a c^{4} d^{5} e^{5} - 7 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} - 3 \, {\left(20 \, c^{5} d^{8} e^{2} - 60 \, a c^{4} d^{6} e^{4} + 30 \, a^{2} c^{3} d^{4} e^{6} + 3 \, a^{3} c^{2} d^{2} e^{8}\right)} x^{2} - 3 \, {\left(5 \, c^{5} d^{9} e + 20 \, a c^{4} d^{7} e^{3} - 90 \, a^{2} c^{3} d^{5} e^{5} + 90 \, a^{3} c^{2} d^{3} e^{7} - 27 \, a^{4} c d e^{9}\right)} x + 60 \, {\left(a^{3} c^{2} d^{4} e^{6} - 2 \, a^{4} c d^{2} e^{8} + a^{5} e^{10} + {\left(c^{5} d^{7} e^{3} - 2 \, a c^{4} d^{5} e^{5} + a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 3 \, {\left(a c^{4} d^{6} e^{4} - 2 \, a^{2} c^{3} d^{4} e^{6} + a^{3} c^{2} d^{2} e^{8}\right)} x^{2} + 3 \, {\left(a^{2} c^{3} d^{5} e^{5} - 2 \, a^{3} c^{2} d^{3} e^{7} + a^{4} c d e^{9}\right)} x\right)} \log\left(c d x + a e\right)}{6 \, {\left(c^{9} d^{9} x^{3} + 3 \, a c^{8} d^{8} e x^{2} + 3 \, a^{2} c^{7} d^{7} e^{2} x + a^{3} c^{6} d^{6} e^{3}\right)}}"," ",0,"1/6*(3*c^5*d^5*e^5*x^5 - 2*c^5*d^10 - 5*a*c^4*d^8*e^2 - 20*a^2*c^3*d^6*e^4 + 110*a^3*c^2*d^4*e^6 - 130*a^4*c*d^2*e^8 + 47*a^5*e^10 + 15*(2*c^5*d^6*e^4 - a*c^4*d^4*e^6)*x^4 + 9*(10*a*c^4*d^5*e^5 - 7*a^2*c^3*d^3*e^7)*x^3 - 3*(20*c^5*d^8*e^2 - 60*a*c^4*d^6*e^4 + 30*a^2*c^3*d^4*e^6 + 3*a^3*c^2*d^2*e^8)*x^2 - 3*(5*c^5*d^9*e + 20*a*c^4*d^7*e^3 - 90*a^2*c^3*d^5*e^5 + 90*a^3*c^2*d^3*e^7 - 27*a^4*c*d*e^9)*x + 60*(a^3*c^2*d^4*e^6 - 2*a^4*c*d^2*e^8 + a^5*e^10 + (c^5*d^7*e^3 - 2*a*c^4*d^5*e^5 + a^2*c^3*d^3*e^7)*x^3 + 3*(a*c^4*d^6*e^4 - 2*a^2*c^3*d^4*e^6 + a^3*c^2*d^2*e^8)*x^2 + 3*(a^2*c^3*d^5*e^5 - 2*a^3*c^2*d^3*e^7 + a^4*c*d*e^9)*x)*log(c*d*x + a*e))/(c^9*d^9*x^3 + 3*a*c^8*d^8*e*x^2 + 3*a^2*c^7*d^7*e^2*x + a^3*c^6*d^6*e^3)","B",0
1898,1,347,0,0.401537," ","integrate((e*x+d)^8/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","\frac{3 \, c^{4} d^{4} e^{4} x^{4} + 9 \, a c^{3} d^{3} e^{5} x^{3} - c^{4} d^{8} - 2 \, a c^{3} d^{6} e^{2} - 6 \, a^{2} c^{2} d^{4} e^{4} + 22 \, a^{3} c d^{2} e^{6} - 13 \, a^{4} e^{8} - 9 \, {\left(2 \, c^{4} d^{6} e^{2} - 4 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} - 3 \, {\left(2 \, c^{4} d^{7} e + 6 \, a c^{3} d^{5} e^{3} - 18 \, a^{2} c^{2} d^{3} e^{5} + 9 \, a^{3} c d e^{7}\right)} x + 12 \, {\left(a^{3} c d^{2} e^{6} - a^{4} e^{8} + {\left(c^{4} d^{5} e^{3} - a c^{3} d^{3} e^{5}\right)} x^{3} + 3 \, {\left(a c^{3} d^{4} e^{4} - a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x\right)} \log\left(c d x + a e\right)}{3 \, {\left(c^{8} d^{8} x^{3} + 3 \, a c^{7} d^{7} e x^{2} + 3 \, a^{2} c^{6} d^{6} e^{2} x + a^{3} c^{5} d^{5} e^{3}\right)}}"," ",0,"1/3*(3*c^4*d^4*e^4*x^4 + 9*a*c^3*d^3*e^5*x^3 - c^4*d^8 - 2*a*c^3*d^6*e^2 - 6*a^2*c^2*d^4*e^4 + 22*a^3*c*d^2*e^6 - 13*a^4*e^8 - 9*(2*c^4*d^6*e^2 - 4*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 - 3*(2*c^4*d^7*e + 6*a*c^3*d^5*e^3 - 18*a^2*c^2*d^3*e^5 + 9*a^3*c*d*e^7)*x + 12*(a^3*c*d^2*e^6 - a^4*e^8 + (c^4*d^5*e^3 - a*c^3*d^3*e^5)*x^3 + 3*(a*c^3*d^4*e^4 - a^2*c^2*d^2*e^6)*x^2 + 3*(a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x)*log(c*d*x + a*e))/(c^8*d^8*x^3 + 3*a*c^7*d^7*e*x^2 + 3*a^2*c^6*d^6*e^2*x + a^3*c^5*d^5*e^3)","B",0
1899,1,217,0,0.397838," ","integrate((e*x+d)^7/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","-\frac{2 \, c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2} + 6 \, a^{2} c d^{2} e^{4} - 11 \, a^{3} e^{6} + 18 \, {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 9 \, {\left(c^{3} d^{5} e + 2 \, a c^{2} d^{3} e^{3} - 3 \, a^{2} c d e^{5}\right)} x - 6 \, {\left(c^{3} d^{3} e^{3} x^{3} + 3 \, a c^{2} d^{2} e^{4} x^{2} + 3 \, a^{2} c d e^{5} x + a^{3} e^{6}\right)} \log\left(c d x + a e\right)}{6 \, {\left(c^{7} d^{7} x^{3} + 3 \, a c^{6} d^{6} e x^{2} + 3 \, a^{2} c^{5} d^{5} e^{2} x + a^{3} c^{4} d^{4} e^{3}\right)}}"," ",0,"-1/6*(2*c^3*d^6 + 3*a*c^2*d^4*e^2 + 6*a^2*c*d^2*e^4 - 11*a^3*e^6 + 18*(c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 9*(c^3*d^5*e + 2*a*c^2*d^3*e^3 - 3*a^2*c*d*e^5)*x - 6*(c^3*d^3*e^3*x^3 + 3*a*c^2*d^2*e^4*x^2 + 3*a^2*c*d*e^5*x + a^3*e^6)*log(c*d*x + a*e))/(c^7*d^7*x^3 + 3*a*c^6*d^6*e*x^2 + 3*a^2*c^5*d^5*e^2*x + a^3*c^4*d^4*e^3)","A",0
1900,1,113,0,0.395655," ","integrate((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","-\frac{3 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + a c d^{2} e^{2} + a^{2} e^{4} + 3 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x}{3 \, {\left(c^{6} d^{6} x^{3} + 3 \, a c^{5} d^{5} e x^{2} + 3 \, a^{2} c^{4} d^{4} e^{2} x + a^{3} c^{3} d^{3} e^{3}\right)}}"," ",0,"-1/3*(3*c^2*d^2*e^2*x^2 + c^2*d^4 + a*c*d^2*e^2 + a^2*e^4 + 3*(c^2*d^3*e + a*c*d*e^3)*x)/(c^6*d^6*x^3 + 3*a*c^5*d^5*e*x^2 + 3*a^2*c^4*d^4*e^2*x + a^3*c^3*d^3*e^3)","B",0
1901,1,74,0,0.393483," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","-\frac{3 \, c d e x + 2 \, c d^{2} + a e^{2}}{6 \, {\left(c^{5} d^{5} x^{3} + 3 \, a c^{4} d^{4} e x^{2} + 3 \, a^{2} c^{3} d^{3} e^{2} x + a^{3} c^{2} d^{2} e^{3}\right)}}"," ",0,"-1/6*(3*c*d*e*x + 2*c*d^2 + a*e^2)/(c^5*d^5*x^3 + 3*a*c^4*d^4*e*x^2 + 3*a^2*c^3*d^3*e^2*x + a^3*c^2*d^2*e^3)","A",0
1902,1,52,0,0.372425," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","-\frac{1}{3 \, {\left(c^{4} d^{4} x^{3} + 3 \, a c^{3} d^{3} e x^{2} + 3 \, a^{2} c^{2} d^{2} e^{2} x + a^{3} c d e^{3}\right)}}"," ",0,"-1/3/(c^4*d^4*x^3 + 3*a*c^3*d^3*e*x^2 + 3*a^2*c^2*d^2*e^2*x + a^3*c*d*e^3)","B",0
1903,1,484,0,0.411167," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","-\frac{2 \, c^{3} d^{6} - 9 \, a c^{2} d^{4} e^{2} + 18 \, a^{2} c d^{2} e^{4} - 11 \, a^{3} e^{6} + 6 \, {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} - 3 \, {\left(c^{3} d^{5} e - 6 \, a c^{2} d^{3} e^{3} + 5 \, a^{2} c d e^{5}\right)} x + 6 \, {\left(c^{3} d^{3} e^{3} x^{3} + 3 \, a c^{2} d^{2} e^{4} x^{2} + 3 \, a^{2} c d e^{5} x + a^{3} e^{6}\right)} \log\left(c d x + a e\right) - 6 \, {\left(c^{3} d^{3} e^{3} x^{3} + 3 \, a c^{2} d^{2} e^{4} x^{2} + 3 \, a^{2} c d e^{5} x + a^{3} e^{6}\right)} \log\left(e x + d\right)}{6 \, {\left(a^{3} c^{4} d^{8} e^{3} - 4 \, a^{4} c^{3} d^{6} e^{5} + 6 \, a^{5} c^{2} d^{4} e^{7} - 4 \, a^{6} c d^{2} e^{9} + a^{7} e^{11} + {\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)} x^{3} + 3 \, {\left(a c^{6} d^{10} e - 4 \, a^{2} c^{5} d^{8} e^{3} + 6 \, a^{3} c^{4} d^{6} e^{5} - 4 \, a^{4} c^{3} d^{4} e^{7} + a^{5} c^{2} d^{2} e^{9}\right)} x^{2} + 3 \, {\left(a^{2} c^{5} d^{9} e^{2} - 4 \, a^{3} c^{4} d^{7} e^{4} + 6 \, a^{4} c^{3} d^{5} e^{6} - 4 \, a^{5} c^{2} d^{3} e^{8} + a^{6} c d e^{10}\right)} x\right)}}"," ",0,"-1/6*(2*c^3*d^6 - 9*a*c^2*d^4*e^2 + 18*a^2*c*d^2*e^4 - 11*a^3*e^6 + 6*(c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 - 3*(c^3*d^5*e - 6*a*c^2*d^3*e^3 + 5*a^2*c*d*e^5)*x + 6*(c^3*d^3*e^3*x^3 + 3*a*c^2*d^2*e^4*x^2 + 3*a^2*c*d*e^5*x + a^3*e^6)*log(c*d*x + a*e) - 6*(c^3*d^3*e^3*x^3 + 3*a*c^2*d^2*e^4*x^2 + 3*a^2*c*d*e^5*x + a^3*e^6)*log(e*x + d))/(a^3*c^4*d^8*e^3 - 4*a^4*c^3*d^6*e^5 + 6*a^5*c^2*d^4*e^7 - 4*a^6*c*d^2*e^9 + a^7*e^11 + (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)*x^3 + 3*(a*c^6*d^10*e - 4*a^2*c^5*d^8*e^3 + 6*a^3*c^4*d^6*e^5 - 4*a^4*c^3*d^4*e^7 + a^5*c^2*d^2*e^9)*x^2 + 3*(a^2*c^5*d^9*e^2 - 4*a^3*c^4*d^7*e^4 + 6*a^4*c^3*d^5*e^6 - 4*a^5*c^2*d^3*e^8 + a^6*c*d*e^10)*x)","B",0
1904,1,837,0,0.423949," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","-\frac{c^{4} d^{8} - 6 \, a c^{3} d^{6} e^{2} + 18 \, a^{2} c^{2} d^{4} e^{4} - 10 \, a^{3} c d^{2} e^{6} - 3 \, a^{4} e^{8} + 12 \, {\left(c^{4} d^{5} e^{3} - a c^{3} d^{3} e^{5}\right)} x^{3} + 6 \, {\left(c^{4} d^{6} e^{2} + 4 \, a c^{3} d^{4} e^{4} - 5 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} - 2 \, {\left(c^{4} d^{7} e - 9 \, a c^{3} d^{5} e^{3} - 3 \, a^{2} c^{2} d^{3} e^{5} + 11 \, a^{3} c d e^{7}\right)} x + 12 \, {\left(c^{4} d^{4} e^{4} x^{4} + a^{3} c d^{2} e^{6} + {\left(c^{4} d^{5} e^{3} + 3 \, a c^{3} d^{3} e^{5}\right)} x^{3} + 3 \, {\left(a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + {\left(3 \, a^{2} c^{2} d^{3} e^{5} + a^{3} c d e^{7}\right)} x\right)} \log\left(c d x + a e\right) - 12 \, {\left(c^{4} d^{4} e^{4} x^{4} + a^{3} c d^{2} e^{6} + {\left(c^{4} d^{5} e^{3} + 3 \, a c^{3} d^{3} e^{5}\right)} x^{3} + 3 \, {\left(a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + {\left(3 \, a^{2} c^{2} d^{3} e^{5} + a^{3} c d e^{7}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(a^{3} c^{5} d^{11} e^{3} - 5 \, a^{4} c^{4} d^{9} e^{5} + 10 \, a^{5} c^{3} d^{7} e^{7} - 10 \, a^{6} c^{2} d^{5} e^{9} + 5 \, a^{7} c d^{3} e^{11} - a^{8} d e^{13} + {\left(c^{8} d^{13} e - 5 \, a c^{7} d^{11} e^{3} + 10 \, a^{2} c^{6} d^{9} e^{5} - 10 \, a^{3} c^{5} d^{7} e^{7} + 5 \, a^{4} c^{4} d^{5} e^{9} - a^{5} c^{3} d^{3} e^{11}\right)} x^{4} + {\left(c^{8} d^{14} - 2 \, a c^{7} d^{12} e^{2} - 5 \, a^{2} c^{6} d^{10} e^{4} + 20 \, a^{3} c^{5} d^{8} e^{6} - 25 \, a^{4} c^{4} d^{6} e^{8} + 14 \, a^{5} c^{3} d^{4} e^{10} - 3 \, a^{6} c^{2} d^{2} e^{12}\right)} x^{3} + 3 \, {\left(a c^{7} d^{13} e - 4 \, a^{2} c^{6} d^{11} e^{3} + 5 \, a^{3} c^{5} d^{9} e^{5} - 5 \, a^{5} c^{3} d^{5} e^{9} + 4 \, a^{6} c^{2} d^{3} e^{11} - a^{7} c d e^{13}\right)} x^{2} + {\left(3 \, a^{2} c^{6} d^{12} e^{2} - 14 \, a^{3} c^{5} d^{10} e^{4} + 25 \, a^{4} c^{4} d^{8} e^{6} - 20 \, a^{5} c^{3} d^{6} e^{8} + 5 \, a^{6} c^{2} d^{4} e^{10} + 2 \, a^{7} c d^{2} e^{12} - a^{8} e^{14}\right)} x\right)}}"," ",0,"-1/3*(c^4*d^8 - 6*a*c^3*d^6*e^2 + 18*a^2*c^2*d^4*e^4 - 10*a^3*c*d^2*e^6 - 3*a^4*e^8 + 12*(c^4*d^5*e^3 - a*c^3*d^3*e^5)*x^3 + 6*(c^4*d^6*e^2 + 4*a*c^3*d^4*e^4 - 5*a^2*c^2*d^2*e^6)*x^2 - 2*(c^4*d^7*e - 9*a*c^3*d^5*e^3 - 3*a^2*c^2*d^3*e^5 + 11*a^3*c*d*e^7)*x + 12*(c^4*d^4*e^4*x^4 + a^3*c*d^2*e^6 + (c^4*d^5*e^3 + 3*a*c^3*d^3*e^5)*x^3 + 3*(a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + (3*a^2*c^2*d^3*e^5 + a^3*c*d*e^7)*x)*log(c*d*x + a*e) - 12*(c^4*d^4*e^4*x^4 + a^3*c*d^2*e^6 + (c^4*d^5*e^3 + 3*a*c^3*d^3*e^5)*x^3 + 3*(a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + (3*a^2*c^2*d^3*e^5 + a^3*c*d*e^7)*x)*log(e*x + d))/(a^3*c^5*d^11*e^3 - 5*a^4*c^4*d^9*e^5 + 10*a^5*c^3*d^7*e^7 - 10*a^6*c^2*d^5*e^9 + 5*a^7*c*d^3*e^11 - a^8*d*e^13 + (c^8*d^13*e - 5*a*c^7*d^11*e^3 + 10*a^2*c^6*d^9*e^5 - 10*a^3*c^5*d^7*e^7 + 5*a^4*c^4*d^5*e^9 - a^5*c^3*d^3*e^11)*x^4 + (c^8*d^14 - 2*a*c^7*d^12*e^2 - 5*a^2*c^6*d^10*e^4 + 20*a^3*c^5*d^8*e^6 - 25*a^4*c^4*d^6*e^8 + 14*a^5*c^3*d^4*e^10 - 3*a^6*c^2*d^2*e^12)*x^3 + 3*(a*c^7*d^13*e - 4*a^2*c^6*d^11*e^3 + 5*a^3*c^5*d^9*e^5 - 5*a^5*c^3*d^5*e^9 + 4*a^6*c^2*d^3*e^11 - a^7*c*d*e^13)*x^2 + (3*a^2*c^6*d^12*e^2 - 14*a^3*c^5*d^10*e^4 + 25*a^4*c^4*d^8*e^6 - 20*a^5*c^3*d^6*e^8 + 5*a^6*c^2*d^4*e^10 + 2*a^7*c*d^2*e^12 - a^8*e^14)*x)","B",0
1905,1,1242,0,0.441714," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","-\frac{2 \, c^{5} d^{10} - 15 \, a c^{4} d^{8} e^{2} + 60 \, a^{2} c^{3} d^{6} e^{4} - 20 \, a^{3} c^{2} d^{4} e^{6} - 30 \, a^{4} c d^{2} e^{8} + 3 \, a^{5} e^{10} + 60 \, {\left(c^{5} d^{6} e^{4} - a c^{4} d^{4} e^{6}\right)} x^{4} + 30 \, {\left(3 \, c^{5} d^{7} e^{3} + 2 \, a c^{4} d^{5} e^{5} - 5 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 10 \, {\left(2 \, c^{5} d^{8} e^{2} + 21 \, a c^{4} d^{6} e^{4} - 12 \, a^{2} c^{3} d^{4} e^{6} - 11 \, a^{3} c^{2} d^{2} e^{8}\right)} x^{2} - 5 \, {\left(c^{5} d^{9} e - 12 \, a c^{4} d^{7} e^{3} - 24 \, a^{2} c^{3} d^{5} e^{5} + 32 \, a^{3} c^{2} d^{3} e^{7} + 3 \, a^{4} c d e^{9}\right)} x + 60 \, {\left(c^{5} d^{5} e^{5} x^{5} + a^{3} c^{2} d^{4} e^{6} + {\left(2 \, c^{5} d^{6} e^{4} + 3 \, a c^{4} d^{4} e^{6}\right)} x^{4} + {\left(c^{5} d^{7} e^{3} + 6 \, a c^{4} d^{5} e^{5} + 3 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + {\left(3 \, a c^{4} d^{6} e^{4} + 6 \, a^{2} c^{3} d^{4} e^{6} + a^{3} c^{2} d^{2} e^{8}\right)} x^{2} + {\left(3 \, a^{2} c^{3} d^{5} e^{5} + 2 \, a^{3} c^{2} d^{3} e^{7}\right)} x\right)} \log\left(c d x + a e\right) - 60 \, {\left(c^{5} d^{5} e^{5} x^{5} + a^{3} c^{2} d^{4} e^{6} + {\left(2 \, c^{5} d^{6} e^{4} + 3 \, a c^{4} d^{4} e^{6}\right)} x^{4} + {\left(c^{5} d^{7} e^{3} + 6 \, a c^{4} d^{5} e^{5} + 3 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + {\left(3 \, a c^{4} d^{6} e^{4} + 6 \, a^{2} c^{3} d^{4} e^{6} + a^{3} c^{2} d^{2} e^{8}\right)} x^{2} + {\left(3 \, a^{2} c^{3} d^{5} e^{5} + 2 \, a^{3} c^{2} d^{3} e^{7}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(a^{3} c^{6} d^{14} e^{3} - 6 \, a^{4} c^{5} d^{12} e^{5} + 15 \, a^{5} c^{4} d^{10} e^{7} - 20 \, a^{6} c^{3} d^{8} e^{9} + 15 \, a^{7} c^{2} d^{6} e^{11} - 6 \, a^{8} c d^{4} e^{13} + a^{9} d^{2} e^{15} + {\left(c^{9} d^{15} e^{2} - 6 \, a c^{8} d^{13} e^{4} + 15 \, a^{2} c^{7} d^{11} e^{6} - 20 \, a^{3} c^{6} d^{9} e^{8} + 15 \, a^{4} c^{5} d^{7} e^{10} - 6 \, a^{5} c^{4} d^{5} e^{12} + a^{6} c^{3} d^{3} e^{14}\right)} x^{5} + {\left(2 \, c^{9} d^{16} e - 9 \, a c^{8} d^{14} e^{3} + 12 \, a^{2} c^{7} d^{12} e^{5} + 5 \, a^{3} c^{6} d^{10} e^{7} - 30 \, a^{4} c^{5} d^{8} e^{9} + 33 \, a^{5} c^{4} d^{6} e^{11} - 16 \, a^{6} c^{3} d^{4} e^{13} + 3 \, a^{7} c^{2} d^{2} e^{15}\right)} x^{4} + {\left(c^{9} d^{17} - 18 \, a^{2} c^{7} d^{13} e^{4} + 52 \, a^{3} c^{6} d^{11} e^{6} - 60 \, a^{4} c^{5} d^{9} e^{8} + 24 \, a^{5} c^{4} d^{7} e^{10} + 10 \, a^{6} c^{3} d^{5} e^{12} - 12 \, a^{7} c^{2} d^{3} e^{14} + 3 \, a^{8} c d e^{16}\right)} x^{3} + {\left(3 \, a c^{8} d^{16} e - 12 \, a^{2} c^{7} d^{14} e^{3} + 10 \, a^{3} c^{6} d^{12} e^{5} + 24 \, a^{4} c^{5} d^{10} e^{7} - 60 \, a^{5} c^{4} d^{8} e^{9} + 52 \, a^{6} c^{3} d^{6} e^{11} - 18 \, a^{7} c^{2} d^{4} e^{13} + a^{9} e^{17}\right)} x^{2} + {\left(3 \, a^{2} c^{7} d^{15} e^{2} - 16 \, a^{3} c^{6} d^{13} e^{4} + 33 \, a^{4} c^{5} d^{11} e^{6} - 30 \, a^{5} c^{4} d^{9} e^{8} + 5 \, a^{6} c^{3} d^{7} e^{10} + 12 \, a^{7} c^{2} d^{5} e^{12} - 9 \, a^{8} c d^{3} e^{14} + 2 \, a^{9} d e^{16}\right)} x\right)}}"," ",0,"-1/6*(2*c^5*d^10 - 15*a*c^4*d^8*e^2 + 60*a^2*c^3*d^6*e^4 - 20*a^3*c^2*d^4*e^6 - 30*a^4*c*d^2*e^8 + 3*a^5*e^10 + 60*(c^5*d^6*e^4 - a*c^4*d^4*e^6)*x^4 + 30*(3*c^5*d^7*e^3 + 2*a*c^4*d^5*e^5 - 5*a^2*c^3*d^3*e^7)*x^3 + 10*(2*c^5*d^8*e^2 + 21*a*c^4*d^6*e^4 - 12*a^2*c^3*d^4*e^6 - 11*a^3*c^2*d^2*e^8)*x^2 - 5*(c^5*d^9*e - 12*a*c^4*d^7*e^3 - 24*a^2*c^3*d^5*e^5 + 32*a^3*c^2*d^3*e^7 + 3*a^4*c*d*e^9)*x + 60*(c^5*d^5*e^5*x^5 + a^3*c^2*d^4*e^6 + (2*c^5*d^6*e^4 + 3*a*c^4*d^4*e^6)*x^4 + (c^5*d^7*e^3 + 6*a*c^4*d^5*e^5 + 3*a^2*c^3*d^3*e^7)*x^3 + (3*a*c^4*d^6*e^4 + 6*a^2*c^3*d^4*e^6 + a^3*c^2*d^2*e^8)*x^2 + (3*a^2*c^3*d^5*e^5 + 2*a^3*c^2*d^3*e^7)*x)*log(c*d*x + a*e) - 60*(c^5*d^5*e^5*x^5 + a^3*c^2*d^4*e^6 + (2*c^5*d^6*e^4 + 3*a*c^4*d^4*e^6)*x^4 + (c^5*d^7*e^3 + 6*a*c^4*d^5*e^5 + 3*a^2*c^3*d^3*e^7)*x^3 + (3*a*c^4*d^6*e^4 + 6*a^2*c^3*d^4*e^6 + a^3*c^2*d^2*e^8)*x^2 + (3*a^2*c^3*d^5*e^5 + 2*a^3*c^2*d^3*e^7)*x)*log(e*x + d))/(a^3*c^6*d^14*e^3 - 6*a^4*c^5*d^12*e^5 + 15*a^5*c^4*d^10*e^7 - 20*a^6*c^3*d^8*e^9 + 15*a^7*c^2*d^6*e^11 - 6*a^8*c*d^4*e^13 + a^9*d^2*e^15 + (c^9*d^15*e^2 - 6*a*c^8*d^13*e^4 + 15*a^2*c^7*d^11*e^6 - 20*a^3*c^6*d^9*e^8 + 15*a^4*c^5*d^7*e^10 - 6*a^5*c^4*d^5*e^12 + a^6*c^3*d^3*e^14)*x^5 + (2*c^9*d^16*e - 9*a*c^8*d^14*e^3 + 12*a^2*c^7*d^12*e^5 + 5*a^3*c^6*d^10*e^7 - 30*a^4*c^5*d^8*e^9 + 33*a^5*c^4*d^6*e^11 - 16*a^6*c^3*d^4*e^13 + 3*a^7*c^2*d^2*e^15)*x^4 + (c^9*d^17 - 18*a^2*c^7*d^13*e^4 + 52*a^3*c^6*d^11*e^6 - 60*a^4*c^5*d^9*e^8 + 24*a^5*c^4*d^7*e^10 + 10*a^6*c^3*d^5*e^12 - 12*a^7*c^2*d^3*e^14 + 3*a^8*c*d*e^16)*x^3 + (3*a*c^8*d^16*e - 12*a^2*c^7*d^14*e^3 + 10*a^3*c^6*d^12*e^5 + 24*a^4*c^5*d^10*e^7 - 60*a^5*c^4*d^8*e^9 + 52*a^6*c^3*d^6*e^11 - 18*a^7*c^2*d^4*e^13 + a^9*e^17)*x^2 + (3*a^2*c^7*d^15*e^2 - 16*a^3*c^6*d^13*e^4 + 33*a^4*c^5*d^11*e^6 - 30*a^5*c^4*d^9*e^8 + 5*a^6*c^3*d^7*e^10 + 12*a^7*c^2*d^5*e^12 - 9*a^8*c*d^3*e^14 + 2*a^9*d*e^16)*x)","B",0
1906,1,1618,0,0.463557," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","-\frac{c^{6} d^{12} - 9 \, a c^{5} d^{10} e^{2} + 45 \, a^{2} c^{4} d^{8} e^{4} - 45 \, a^{4} c^{2} d^{4} e^{8} + 9 \, a^{5} c d^{2} e^{10} - a^{6} e^{12} + 60 \, {\left(c^{6} d^{7} e^{5} - a c^{5} d^{5} e^{7}\right)} x^{5} + 150 \, {\left(c^{6} d^{8} e^{4} - a^{2} c^{4} d^{4} e^{8}\right)} x^{4} + 10 \, {\left(11 \, c^{6} d^{9} e^{3} + 27 \, a c^{5} d^{7} e^{5} - 27 \, a^{2} c^{4} d^{5} e^{7} - 11 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{3} + 15 \, {\left(c^{6} d^{10} e^{2} + 18 \, a c^{5} d^{8} e^{4} - 18 \, a^{3} c^{3} d^{4} e^{8} - a^{4} c^{2} d^{2} e^{10}\right)} x^{2} - 3 \, {\left(c^{6} d^{11} e - 15 \, a c^{5} d^{9} e^{3} - 60 \, a^{2} c^{4} d^{7} e^{5} + 60 \, a^{3} c^{3} d^{5} e^{7} + 15 \, a^{4} c^{2} d^{3} e^{9} - a^{5} c d e^{11}\right)} x + 60 \, {\left(c^{6} d^{6} e^{6} x^{6} + a^{3} c^{3} d^{6} e^{6} + 3 \, {\left(c^{6} d^{7} e^{5} + a c^{5} d^{5} e^{7}\right)} x^{5} + 3 \, {\left(c^{6} d^{8} e^{4} + 3 \, a c^{5} d^{6} e^{6} + a^{2} c^{4} d^{4} e^{8}\right)} x^{4} + {\left(c^{6} d^{9} e^{3} + 9 \, a c^{5} d^{7} e^{5} + 9 \, a^{2} c^{4} d^{5} e^{7} + a^{3} c^{3} d^{3} e^{9}\right)} x^{3} + 3 \, {\left(a c^{5} d^{8} e^{4} + 3 \, a^{2} c^{4} d^{6} e^{6} + a^{3} c^{3} d^{4} e^{8}\right)} x^{2} + 3 \, {\left(a^{2} c^{4} d^{7} e^{5} + a^{3} c^{3} d^{5} e^{7}\right)} x\right)} \log\left(c d x + a e\right) - 60 \, {\left(c^{6} d^{6} e^{6} x^{6} + a^{3} c^{3} d^{6} e^{6} + 3 \, {\left(c^{6} d^{7} e^{5} + a c^{5} d^{5} e^{7}\right)} x^{5} + 3 \, {\left(c^{6} d^{8} e^{4} + 3 \, a c^{5} d^{6} e^{6} + a^{2} c^{4} d^{4} e^{8}\right)} x^{4} + {\left(c^{6} d^{9} e^{3} + 9 \, a c^{5} d^{7} e^{5} + 9 \, a^{2} c^{4} d^{5} e^{7} + a^{3} c^{3} d^{3} e^{9}\right)} x^{3} + 3 \, {\left(a c^{5} d^{8} e^{4} + 3 \, a^{2} c^{4} d^{6} e^{6} + a^{3} c^{3} d^{4} e^{8}\right)} x^{2} + 3 \, {\left(a^{2} c^{4} d^{7} e^{5} + a^{3} c^{3} d^{5} e^{7}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(a^{3} c^{7} d^{17} e^{3} - 7 \, a^{4} c^{6} d^{15} e^{5} + 21 \, a^{5} c^{5} d^{13} e^{7} - 35 \, a^{6} c^{4} d^{11} e^{9} + 35 \, a^{7} c^{3} d^{9} e^{11} - 21 \, a^{8} c^{2} d^{7} e^{13} + 7 \, a^{9} c d^{5} e^{15} - a^{10} d^{3} e^{17} + {\left(c^{10} d^{17} e^{3} - 7 \, a c^{9} d^{15} e^{5} + 21 \, a^{2} c^{8} d^{13} e^{7} - 35 \, a^{3} c^{7} d^{11} e^{9} + 35 \, a^{4} c^{6} d^{9} e^{11} - 21 \, a^{5} c^{5} d^{7} e^{13} + 7 \, a^{6} c^{4} d^{5} e^{15} - a^{7} c^{3} d^{3} e^{17}\right)} x^{6} + 3 \, {\left(c^{10} d^{18} e^{2} - 6 \, a c^{9} d^{16} e^{4} + 14 \, a^{2} c^{8} d^{14} e^{6} - 14 \, a^{3} c^{7} d^{12} e^{8} + 14 \, a^{5} c^{5} d^{8} e^{12} - 14 \, a^{6} c^{4} d^{6} e^{14} + 6 \, a^{7} c^{3} d^{4} e^{16} - a^{8} c^{2} d^{2} e^{18}\right)} x^{5} + 3 \, {\left(c^{10} d^{19} e - 4 \, a c^{9} d^{17} e^{3} + a^{2} c^{8} d^{15} e^{5} + 21 \, a^{3} c^{7} d^{13} e^{7} - 49 \, a^{4} c^{6} d^{11} e^{9} + 49 \, a^{5} c^{5} d^{9} e^{11} - 21 \, a^{6} c^{4} d^{7} e^{13} - a^{7} c^{3} d^{5} e^{15} + 4 \, a^{8} c^{2} d^{3} e^{17} - a^{9} c d e^{19}\right)} x^{4} + {\left(c^{10} d^{20} + 2 \, a c^{9} d^{18} e^{2} - 33 \, a^{2} c^{8} d^{16} e^{4} + 92 \, a^{3} c^{7} d^{14} e^{6} - 98 \, a^{4} c^{6} d^{12} e^{8} + 98 \, a^{6} c^{4} d^{8} e^{12} - 92 \, a^{7} c^{3} d^{6} e^{14} + 33 \, a^{8} c^{2} d^{4} e^{16} - 2 \, a^{9} c d^{2} e^{18} - a^{10} e^{20}\right)} x^{3} + 3 \, {\left(a c^{9} d^{19} e - 4 \, a^{2} c^{8} d^{17} e^{3} + a^{3} c^{7} d^{15} e^{5} + 21 \, a^{4} c^{6} d^{13} e^{7} - 49 \, a^{5} c^{5} d^{11} e^{9} + 49 \, a^{6} c^{4} d^{9} e^{11} - 21 \, a^{7} c^{3} d^{7} e^{13} - a^{8} c^{2} d^{5} e^{15} + 4 \, a^{9} c d^{3} e^{17} - a^{10} d e^{19}\right)} x^{2} + 3 \, {\left(a^{2} c^{8} d^{18} e^{2} - 6 \, a^{3} c^{7} d^{16} e^{4} + 14 \, a^{4} c^{6} d^{14} e^{6} - 14 \, a^{5} c^{5} d^{12} e^{8} + 14 \, a^{7} c^{3} d^{8} e^{12} - 14 \, a^{8} c^{2} d^{6} e^{14} + 6 \, a^{9} c d^{4} e^{16} - a^{10} d^{2} e^{18}\right)} x\right)}}"," ",0,"-1/3*(c^6*d^12 - 9*a*c^5*d^10*e^2 + 45*a^2*c^4*d^8*e^4 - 45*a^4*c^2*d^4*e^8 + 9*a^5*c*d^2*e^10 - a^6*e^12 + 60*(c^6*d^7*e^5 - a*c^5*d^5*e^7)*x^5 + 150*(c^6*d^8*e^4 - a^2*c^4*d^4*e^8)*x^4 + 10*(11*c^6*d^9*e^3 + 27*a*c^5*d^7*e^5 - 27*a^2*c^4*d^5*e^7 - 11*a^3*c^3*d^3*e^9)*x^3 + 15*(c^6*d^10*e^2 + 18*a*c^5*d^8*e^4 - 18*a^3*c^3*d^4*e^8 - a^4*c^2*d^2*e^10)*x^2 - 3*(c^6*d^11*e - 15*a*c^5*d^9*e^3 - 60*a^2*c^4*d^7*e^5 + 60*a^3*c^3*d^5*e^7 + 15*a^4*c^2*d^3*e^9 - a^5*c*d*e^11)*x + 60*(c^6*d^6*e^6*x^6 + a^3*c^3*d^6*e^6 + 3*(c^6*d^7*e^5 + a*c^5*d^5*e^7)*x^5 + 3*(c^6*d^8*e^4 + 3*a*c^5*d^6*e^6 + a^2*c^4*d^4*e^8)*x^4 + (c^6*d^9*e^3 + 9*a*c^5*d^7*e^5 + 9*a^2*c^4*d^5*e^7 + a^3*c^3*d^3*e^9)*x^3 + 3*(a*c^5*d^8*e^4 + 3*a^2*c^4*d^6*e^6 + a^3*c^3*d^4*e^8)*x^2 + 3*(a^2*c^4*d^7*e^5 + a^3*c^3*d^5*e^7)*x)*log(c*d*x + a*e) - 60*(c^6*d^6*e^6*x^6 + a^3*c^3*d^6*e^6 + 3*(c^6*d^7*e^5 + a*c^5*d^5*e^7)*x^5 + 3*(c^6*d^8*e^4 + 3*a*c^5*d^6*e^6 + a^2*c^4*d^4*e^8)*x^4 + (c^6*d^9*e^3 + 9*a*c^5*d^7*e^5 + 9*a^2*c^4*d^5*e^7 + a^3*c^3*d^3*e^9)*x^3 + 3*(a*c^5*d^8*e^4 + 3*a^2*c^4*d^6*e^6 + a^3*c^3*d^4*e^8)*x^2 + 3*(a^2*c^4*d^7*e^5 + a^3*c^3*d^5*e^7)*x)*log(e*x + d))/(a^3*c^7*d^17*e^3 - 7*a^4*c^6*d^15*e^5 + 21*a^5*c^5*d^13*e^7 - 35*a^6*c^4*d^11*e^9 + 35*a^7*c^3*d^9*e^11 - 21*a^8*c^2*d^7*e^13 + 7*a^9*c*d^5*e^15 - a^10*d^3*e^17 + (c^10*d^17*e^3 - 7*a*c^9*d^15*e^5 + 21*a^2*c^8*d^13*e^7 - 35*a^3*c^7*d^11*e^9 + 35*a^4*c^6*d^9*e^11 - 21*a^5*c^5*d^7*e^13 + 7*a^6*c^4*d^5*e^15 - a^7*c^3*d^3*e^17)*x^6 + 3*(c^10*d^18*e^2 - 6*a*c^9*d^16*e^4 + 14*a^2*c^8*d^14*e^6 - 14*a^3*c^7*d^12*e^8 + 14*a^5*c^5*d^8*e^12 - 14*a^6*c^4*d^6*e^14 + 6*a^7*c^3*d^4*e^16 - a^8*c^2*d^2*e^18)*x^5 + 3*(c^10*d^19*e - 4*a*c^9*d^17*e^3 + a^2*c^8*d^15*e^5 + 21*a^3*c^7*d^13*e^7 - 49*a^4*c^6*d^11*e^9 + 49*a^5*c^5*d^9*e^11 - 21*a^6*c^4*d^7*e^13 - a^7*c^3*d^5*e^15 + 4*a^8*c^2*d^3*e^17 - a^9*c*d*e^19)*x^4 + (c^10*d^20 + 2*a*c^9*d^18*e^2 - 33*a^2*c^8*d^16*e^4 + 92*a^3*c^7*d^14*e^6 - 98*a^4*c^6*d^12*e^8 + 98*a^6*c^4*d^8*e^12 - 92*a^7*c^3*d^6*e^14 + 33*a^8*c^2*d^4*e^16 - 2*a^9*c*d^2*e^18 - a^10*e^20)*x^3 + 3*(a*c^9*d^19*e - 4*a^2*c^8*d^17*e^3 + a^3*c^7*d^15*e^5 + 21*a^4*c^6*d^13*e^7 - 49*a^5*c^5*d^11*e^9 + 49*a^6*c^4*d^9*e^11 - 21*a^7*c^3*d^7*e^13 - a^8*c^2*d^5*e^15 + 4*a^9*c*d^3*e^17 - a^10*d*e^19)*x^2 + 3*(a^2*c^8*d^18*e^2 - 6*a^3*c^7*d^16*e^4 + 14*a^4*c^6*d^14*e^6 - 14*a^5*c^5*d^12*e^8 + 14*a^7*c^3*d^8*e^12 - 14*a^8*c^2*d^6*e^14 + 6*a^9*c*d^4*e^16 - a^10*d^2*e^18)*x)","B",0
1907,1,1040,0,0.496552," ","integrate((e*x+d)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\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 d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(1280 \, c^{6} d^{6} e^{6} x^{5} + 315 \, c^{6} d^{11} e + 3335 \, a c^{5} d^{9} e^{3} - 5058 \, a^{2} c^{4} d^{7} e^{5} + 4158 \, a^{3} c^{3} d^{5} e^{7} - 1785 \, a^{4} c^{2} d^{3} e^{9} + 315 \, a^{5} c d e^{11} + 128 \, {\left(49 \, c^{6} d^{7} e^{5} + a c^{5} d^{5} e^{7}\right)} x^{4} + 16 \, {\left(759 \, c^{6} d^{8} e^{4} + 50 \, a c^{5} d^{6} e^{6} - 9 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{3} + 8 \, {\left(1429 \, c^{6} d^{9} e^{3} + 267 \, a c^{5} d^{7} e^{5} - 117 \, a^{2} c^{4} d^{5} e^{7} + 21 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{2} + 2 \, {\left(2455 \, c^{6} d^{10} e^{2} + 1612 \, a c^{5} d^{8} e^{4} - 1350 \, a^{2} c^{4} d^{6} e^{6} + 588 \, a^{3} c^{3} d^{4} e^{8} - 105 \, a^{4} c^{2} d^{2} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{30720 \, c^{6} d^{6} e^{2}}, \frac{315 \, {\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 d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(1280 \, c^{6} d^{6} e^{6} x^{5} + 315 \, c^{6} d^{11} e + 3335 \, a c^{5} d^{9} e^{3} - 5058 \, a^{2} c^{4} d^{7} e^{5} + 4158 \, a^{3} c^{3} d^{5} e^{7} - 1785 \, a^{4} c^{2} d^{3} e^{9} + 315 \, a^{5} c d e^{11} + 128 \, {\left(49 \, c^{6} d^{7} e^{5} + a c^{5} d^{5} e^{7}\right)} x^{4} + 16 \, {\left(759 \, c^{6} d^{8} e^{4} + 50 \, a c^{5} d^{6} e^{6} - 9 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{3} + 8 \, {\left(1429 \, c^{6} d^{9} e^{3} + 267 \, a c^{5} d^{7} e^{5} - 117 \, a^{2} c^{4} d^{5} e^{7} + 21 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{2} + 2 \, {\left(2455 \, c^{6} d^{10} e^{2} + 1612 \, a c^{5} d^{8} e^{4} - 1350 \, a^{2} c^{4} d^{6} e^{6} + 588 \, a^{3} c^{3} d^{4} e^{8} - 105 \, a^{4} c^{2} d^{2} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15360 \, c^{6} d^{6} e^{2}}\right]"," ",0,"[1/30720*(315*(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*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(1280*c^6*d^6*e^6*x^5 + 315*c^6*d^11*e + 3335*a*c^5*d^9*e^3 - 5058*a^2*c^4*d^7*e^5 + 4158*a^3*c^3*d^5*e^7 - 1785*a^4*c^2*d^3*e^9 + 315*a^5*c*d*e^11 + 128*(49*c^6*d^7*e^5 + a*c^5*d^5*e^7)*x^4 + 16*(759*c^6*d^8*e^4 + 50*a*c^5*d^6*e^6 - 9*a^2*c^4*d^4*e^8)*x^3 + 8*(1429*c^6*d^9*e^3 + 267*a*c^5*d^7*e^5 - 117*a^2*c^4*d^5*e^7 + 21*a^3*c^3*d^3*e^9)*x^2 + 2*(2455*c^6*d^10*e^2 + 1612*a*c^5*d^8*e^4 - 1350*a^2*c^4*d^6*e^6 + 588*a^3*c^3*d^4*e^8 - 105*a^4*c^2*d^2*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^6*d^6*e^2), 1/15360*(315*(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*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(1280*c^6*d^6*e^6*x^5 + 315*c^6*d^11*e + 3335*a*c^5*d^9*e^3 - 5058*a^2*c^4*d^7*e^5 + 4158*a^3*c^3*d^5*e^7 - 1785*a^4*c^2*d^3*e^9 + 315*a^5*c*d*e^11 + 128*(49*c^6*d^7*e^5 + a*c^5*d^5*e^7)*x^4 + 16*(759*c^6*d^8*e^4 + 50*a*c^5*d^6*e^6 - 9*a^2*c^4*d^4*e^8)*x^3 + 8*(1429*c^6*d^9*e^3 + 267*a*c^5*d^7*e^5 - 117*a^2*c^4*d^5*e^7 + 21*a^3*c^3*d^3*e^9)*x^2 + 2*(2455*c^6*d^10*e^2 + 1612*a*c^5*d^8*e^4 - 1350*a^2*c^4*d^6*e^6 + 588*a^3*c^3*d^4*e^8 - 105*a^4*c^2*d^2*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^6*d^6*e^2)]","A",0
1908,1,844,0,0.469807," ","integrate((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\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 e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(384 \, c^{5} d^{5} e^{5} x^{4} + 105 \, c^{5} d^{9} e + 790 \, a c^{4} d^{7} e^{3} - 896 \, a^{2} c^{3} d^{5} e^{5} + 490 \, a^{3} c^{2} d^{3} e^{7} - 105 \, a^{4} c d e^{9} + 48 \, {\left(31 \, c^{5} d^{6} e^{4} + a c^{4} d^{4} e^{6}\right)} x^{3} + 8 \, {\left(263 \, c^{5} d^{7} e^{3} + 32 \, a c^{4} d^{5} e^{5} - 7 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{2} + 2 \, {\left(605 \, c^{5} d^{8} e^{2} + 289 \, a c^{4} d^{6} e^{4} - 161 \, a^{2} c^{3} d^{4} e^{6} + 35 \, a^{3} c^{2} d^{2} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{7680 \, c^{5} d^{5} e^{2}}, \frac{105 \, {\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 e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(384 \, c^{5} d^{5} e^{5} x^{4} + 105 \, c^{5} d^{9} e + 790 \, a c^{4} d^{7} e^{3} - 896 \, a^{2} c^{3} d^{5} e^{5} + 490 \, a^{3} c^{2} d^{3} e^{7} - 105 \, a^{4} c d e^{9} + 48 \, {\left(31 \, c^{5} d^{6} e^{4} + a c^{4} d^{4} e^{6}\right)} x^{3} + 8 \, {\left(263 \, c^{5} d^{7} e^{3} + 32 \, a c^{4} d^{5} e^{5} - 7 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{2} + 2 \, {\left(605 \, c^{5} d^{8} e^{2} + 289 \, a c^{4} d^{6} e^{4} - 161 \, a^{2} c^{3} d^{4} e^{6} + 35 \, a^{3} c^{2} d^{2} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3840 \, c^{5} d^{5} e^{2}}\right]"," ",0,"[1/7680*(105*(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*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(384*c^5*d^5*e^5*x^4 + 105*c^5*d^9*e + 790*a*c^4*d^7*e^3 - 896*a^2*c^3*d^5*e^5 + 490*a^3*c^2*d^3*e^7 - 105*a^4*c*d*e^9 + 48*(31*c^5*d^6*e^4 + a*c^4*d^4*e^6)*x^3 + 8*(263*c^5*d^7*e^3 + 32*a*c^4*d^5*e^5 - 7*a^2*c^3*d^3*e^7)*x^2 + 2*(605*c^5*d^8*e^2 + 289*a*c^4*d^6*e^4 - 161*a^2*c^3*d^4*e^6 + 35*a^3*c^2*d^2*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*e^2), 1/3840*(105*(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*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(384*c^5*d^5*e^5*x^4 + 105*c^5*d^9*e + 790*a*c^4*d^7*e^3 - 896*a^2*c^3*d^5*e^5 + 490*a^3*c^2*d^3*e^7 - 105*a^4*c*d*e^9 + 48*(31*c^5*d^6*e^4 + a*c^4*d^4*e^6)*x^3 + 8*(263*c^5*d^7*e^3 + 32*a*c^4*d^5*e^5 - 7*a^2*c^3*d^3*e^7)*x^2 + 2*(605*c^5*d^8*e^2 + 289*a*c^4*d^6*e^4 - 161*a^2*c^3*d^4*e^6 + 35*a^3*c^2*d^2*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*e^2)]","A",0
1909,1,672,0,0.459436," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\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 e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} + 15 \, c^{4} d^{7} e + 73 \, a c^{3} d^{5} e^{3} - 55 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7} + 8 \, {\left(17 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(59 \, c^{4} d^{6} e^{2} + 18 \, a c^{3} d^{4} e^{4} - 5 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{768 \, c^{4} d^{4} e^{2}}, \frac{15 \, {\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 e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} + 15 \, c^{4} d^{7} e + 73 \, a c^{3} d^{5} e^{3} - 55 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7} + 8 \, {\left(17 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(59 \, c^{4} d^{6} e^{2} + 18 \, a c^{3} d^{4} e^{4} - 5 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{384 \, c^{4} d^{4} e^{2}}\right]"," ",0,"[1/768*(15*(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*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(48*c^4*d^4*e^4*x^3 + 15*c^4*d^7*e + 73*a*c^3*d^5*e^3 - 55*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7 + 8*(17*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^2 + 2*(59*c^4*d^6*e^2 + 18*a*c^3*d^4*e^4 - 5*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^2), 1/384*(15*(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*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(48*c^4*d^4*e^4*x^3 + 15*c^4*d^7*e + 73*a*c^3*d^5*e^3 - 55*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7 + 8*(17*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^2 + 2*(59*c^4*d^6*e^2 + 18*a*c^3*d^4*e^4 - 5*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^2)]","A",0
1910,1,532,0,0.440324," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{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)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} + 3 \, c^{3} d^{5} e + 8 \, a c^{2} d^{3} e^{3} - 3 \, a^{2} c d e^{5} + 2 \, {\left(7 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, c^{3} d^{3} e^{2}}, \frac{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)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} + 3 \, c^{3} d^{5} e + 8 \, a c^{2} d^{3} e^{3} - 3 \, a^{2} c d e^{5} + 2 \, {\left(7 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, c^{3} d^{3} e^{2}}\right]"," ",0,"[-1/96*(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)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(8*c^3*d^3*e^3*x^2 + 3*c^3*d^5*e + 8*a*c^2*d^3*e^3 - 3*a^2*c*d*e^5 + 2*(7*c^3*d^4*e^2 + a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^2), 1/48*(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)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(8*c^3*d^3*e^3*x^2 + 3*c^3*d^5*e + 8*a*c^2*d^3*e^3 - 3*a^2*c*d*e^5 + 2*(7*c^3*d^4*e^2 + a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^2)]","A",0
1911,1,412,0,0.446205," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(2 \, c^{2} d^{2} e^{2} x + c^{2} d^{3} e + a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, c^{2} d^{2} e^{2}}, \frac{{\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(2 \, c^{2} d^{2} e^{2} x + c^{2} d^{3} e + a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, c^{2} d^{2} e^{2}}\right]"," ",0,"[1/16*((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(2*c^2*d^2*e^2*x + c^2*d^3*e + a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^2), 1/8*((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(2*c^2*d^2*e^2*x + c^2*d^3*e + a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^2)]","A",0
1912,1,337,0,0.436935," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} c d e - {\left(c d^{2} - a e^{2}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}{4 \, c d e^{2}}, \frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} c d e + {\left(c d^{2} - a e^{2}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right)}{2 \, c d e^{2}}\right]"," ",0,"[1/4*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*c*d*e - (c*d^2 - a*e^2)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x))/(c*d*e^2), 1/2*(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*c*d*e + (c*d^2 - a*e^2)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)))/(c*d*e^2)]","A",0
1913,1,326,0,0.494935," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{{\left(e x + d\right)} \sqrt{\frac{c d}{e}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{2 \, {\left(e^{2} x + d e\right)}}, -\frac{{\left(e x + d\right)} \sqrt{-\frac{c d}{e}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{e^{2} x + d e}\right]"," ",0,"[1/2*((e*x + d)*sqrt(c*d/e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(e^2*x + d*e), -((e*x + d)*sqrt(-c*d/e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(e^2*x + d*e)]","A",0
1914,1,90,0,0.532748," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d x + a e\right)}}{3 \, {\left(c d^{4} - a d^{2} e^{2} + {\left(c d^{2} e^{2} - a e^{4}\right)} x^{2} + 2 \, {\left(c d^{3} e - a d e^{3}\right)} x\right)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*x + a*e)/(c*d^4 - a*d^2*e^2 + (c*d^2*e^2 - a*e^4)*x^2 + 2*(c*d^3*e - a*d*e^3)*x)","A",0
1915,1,205,0,0.961853," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, c^{2} d^{2} e x^{2} + 5 \, a c d^{2} e - 3 \, a^{2} e^{3} + {\left(5 \, c^{2} d^{3} - a c d e^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15 \, {\left(c^{2} d^{7} - 2 \, a c d^{5} e^{2} + a^{2} d^{3} e^{4} + {\left(c^{2} d^{4} e^{3} - 2 \, a c d^{2} e^{5} + a^{2} e^{7}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{2} - 2 \, a c d^{3} e^{4} + a^{2} d e^{6}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e - 2 \, a c d^{4} e^{3} + a^{2} d^{2} e^{5}\right)} x\right)}}"," ",0,"2/15*(2*c^2*d^2*e*x^2 + 5*a*c*d^2*e - 3*a^2*e^3 + (5*c^2*d^3 - a*c*d*e^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^2*d^7 - 2*a*c*d^5*e^2 + a^2*d^3*e^4 + (c^2*d^4*e^3 - 2*a*c*d^2*e^5 + a^2*e^7)*x^3 + 3*(c^2*d^5*e^2 - 2*a*c*d^3*e^4 + a^2*d*e^6)*x^2 + 3*(c^2*d^6*e - 2*a*c*d^4*e^3 + a^2*d^2*e^5)*x)","A",0
1916,1,373,0,2.465098," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{3} d^{3} e^{2} x^{3} + 35 \, a c^{2} d^{4} e - 42 \, a^{2} c d^{2} e^{3} + 15 \, a^{3} e^{5} + 4 \, {\left(7 \, c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} x^{2} + {\left(35 \, c^{3} d^{5} - 14 \, a c^{2} d^{3} e^{2} + 3 \, a^{2} c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{105 \, {\left(c^{3} d^{10} - 3 \, a c^{2} d^{8} e^{2} + 3 \, a^{2} c d^{6} e^{4} - a^{3} d^{4} e^{6} + {\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)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{3} - 3 \, a c^{2} d^{5} e^{5} + 3 \, a^{2} c d^{3} e^{7} - a^{3} d e^{9}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{2} - 3 \, a c^{2} d^{6} e^{4} + 3 \, a^{2} c d^{4} e^{6} - a^{3} d^{2} e^{8}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e - 3 \, a c^{2} d^{7} e^{3} + 3 \, a^{2} c d^{5} e^{5} - a^{3} d^{3} e^{7}\right)} x\right)}}"," ",0,"2/105*(8*c^3*d^3*e^2*x^3 + 35*a*c^2*d^4*e - 42*a^2*c*d^2*e^3 + 15*a^3*e^5 + 4*(7*c^3*d^4*e - a*c^2*d^2*e^3)*x^2 + (35*c^3*d^5 - 14*a*c^2*d^3*e^2 + 3*a^2*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^3*d^10 - 3*a*c^2*d^8*e^2 + 3*a^2*c*d^6*e^4 - a^3*d^4*e^6 + (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)*x^4 + 4*(c^3*d^7*e^3 - 3*a*c^2*d^5*e^5 + 3*a^2*c*d^3*e^7 - a^3*d*e^9)*x^3 + 6*(c^3*d^8*e^2 - 3*a*c^2*d^6*e^4 + 3*a^2*c*d^4*e^6 - a^3*d^2*e^8)*x^2 + 4*(c^3*d^9*e - 3*a*c^2*d^7*e^3 + 3*a^2*c*d^5*e^5 - a^3*d^3*e^7)*x)","B",0
1917,1,572,0,8.796680," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{4} d^{4} e^{3} x^{4} + 105 \, a c^{3} d^{6} e - 189 \, a^{2} c^{2} d^{4} e^{3} + 135 \, a^{3} c d^{2} e^{5} - 35 \, a^{4} e^{7} + 8 \, {\left(9 \, c^{4} d^{5} e^{2} - a c^{3} d^{3} e^{4}\right)} x^{3} + 6 \, {\left(21 \, c^{4} d^{6} e - 6 \, a c^{3} d^{4} e^{3} + a^{2} c^{2} d^{2} e^{5}\right)} x^{2} + {\left(105 \, c^{4} d^{7} - 63 \, a c^{3} d^{5} e^{2} + 27 \, a^{2} c^{2} d^{3} e^{4} - 5 \, a^{3} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{315 \, {\left(c^{4} d^{13} - 4 \, a c^{3} d^{11} e^{2} + 6 \, a^{2} c^{2} d^{9} e^{4} - 4 \, a^{3} c d^{7} e^{6} + a^{4} d^{5} e^{8} + {\left(c^{4} d^{8} e^{5} - 4 \, a c^{3} d^{6} e^{7} + 6 \, a^{2} c^{2} d^{4} e^{9} - 4 \, a^{3} c d^{2} e^{11} + a^{4} e^{13}\right)} x^{5} + 5 \, {\left(c^{4} d^{9} e^{4} - 4 \, a c^{3} d^{7} e^{6} + 6 \, a^{2} c^{2} d^{5} e^{8} - 4 \, a^{3} c d^{3} e^{10} + a^{4} d e^{12}\right)} x^{4} + 10 \, {\left(c^{4} d^{10} e^{3} - 4 \, a c^{3} d^{8} e^{5} + 6 \, a^{2} c^{2} d^{6} e^{7} - 4 \, a^{3} c d^{4} e^{9} + a^{4} d^{2} e^{11}\right)} x^{3} + 10 \, {\left(c^{4} d^{11} e^{2} - 4 \, a c^{3} d^{9} e^{4} + 6 \, a^{2} c^{2} d^{7} e^{6} - 4 \, a^{3} c d^{5} e^{8} + a^{4} d^{3} e^{10}\right)} x^{2} + 5 \, {\left(c^{4} d^{12} e - 4 \, a c^{3} d^{10} e^{3} + 6 \, a^{2} c^{2} d^{8} e^{5} - 4 \, a^{3} c d^{6} e^{7} + a^{4} d^{4} e^{9}\right)} x\right)}}"," ",0,"2/315*(16*c^4*d^4*e^3*x^4 + 105*a*c^3*d^6*e - 189*a^2*c^2*d^4*e^3 + 135*a^3*c*d^2*e^5 - 35*a^4*e^7 + 8*(9*c^4*d^5*e^2 - a*c^3*d^3*e^4)*x^3 + 6*(21*c^4*d^6*e - 6*a*c^3*d^4*e^3 + a^2*c^2*d^2*e^5)*x^2 + (105*c^4*d^7 - 63*a*c^3*d^5*e^2 + 27*a^2*c^2*d^3*e^4 - 5*a^3*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^4*d^13 - 4*a*c^3*d^11*e^2 + 6*a^2*c^2*d^9*e^4 - 4*a^3*c*d^7*e^6 + a^4*d^5*e^8 + (c^4*d^8*e^5 - 4*a*c^3*d^6*e^7 + 6*a^2*c^2*d^4*e^9 - 4*a^3*c*d^2*e^11 + a^4*e^13)*x^5 + 5*(c^4*d^9*e^4 - 4*a*c^3*d^7*e^6 + 6*a^2*c^2*d^5*e^8 - 4*a^3*c*d^3*e^10 + a^4*d*e^12)*x^4 + 10*(c^4*d^10*e^3 - 4*a*c^3*d^8*e^5 + 6*a^2*c^2*d^6*e^7 - 4*a^3*c*d^4*e^9 + a^4*d^2*e^11)*x^3 + 10*(c^4*d^11*e^2 - 4*a*c^3*d^9*e^4 + 6*a^2*c^2*d^7*e^6 - 4*a^3*c*d^5*e^8 + a^4*d^3*e^10)*x^2 + 5*(c^4*d^12*e - 4*a*c^3*d^10*e^3 + 6*a^2*c^2*d^8*e^5 - 4*a^3*c*d^6*e^7 + a^4*d^4*e^9)*x)","B",0
1918,1,1520,0,0.549003," ","integrate((e*x+d)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3465 \, {\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)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(71680 \, c^{8} d^{8} e^{8} x^{7} - 3465 \, c^{8} d^{15} e + 26565 \, a c^{7} d^{13} e^{3} + 140903 \, a^{2} c^{6} d^{11} e^{5} - 193699 \, a^{3} c^{5} d^{9} e^{7} + 166749 \, a^{4} c^{4} d^{7} e^{9} - 88473 \, a^{5} c^{3} d^{5} e^{11} + 26565 \, a^{6} c^{2} d^{3} e^{13} - 3465 \, a^{7} c d e^{15} + 5120 \, {\left(81 \, c^{8} d^{9} e^{7} + 17 \, a c^{7} d^{7} e^{9}\right)} x^{6} + 1280 \, {\left(769 \, c^{8} d^{10} e^{6} + 406 \, a c^{7} d^{8} e^{8} + a^{2} c^{6} d^{6} e^{10}\right)} x^{5} + 128 \, {\left(9461 \, c^{8} d^{11} e^{5} + 10067 \, a c^{7} d^{9} e^{7} + 83 \, a^{2} c^{6} d^{7} e^{9} - 11 \, a^{3} c^{5} d^{5} e^{11}\right)} x^{4} + 16 \, {\left(49251 \, c^{8} d^{12} e^{4} + 105748 \, a c^{7} d^{10} e^{6} + 2450 \, a^{2} c^{6} d^{8} e^{8} - 748 \, a^{3} c^{5} d^{6} e^{10} + 99 \, a^{4} c^{4} d^{4} e^{12}\right)} x^{3} + 8 \, {\left(28441 \, c^{8} d^{13} e^{3} + 153301 \, a c^{7} d^{11} e^{5} + 10642 \, a^{2} c^{6} d^{9} e^{7} - 5742 \, a^{3} c^{5} d^{7} e^{9} + 1749 \, a^{4} c^{4} d^{5} e^{11} - 231 \, a^{5} c^{3} d^{3} e^{13}\right)} x^{2} + 2 \, {\left(1155 \, c^{8} d^{14} e^{2} + 220598 \, a c^{7} d^{12} e^{4} + 61709 \, a^{2} c^{6} d^{10} e^{6} - 53900 \, a^{3} c^{5} d^{8} e^{8} + 28941 \, a^{4} c^{4} d^{6} e^{10} - 8778 \, a^{5} c^{3} d^{4} e^{12} + 1155 \, a^{6} c^{2} d^{2} e^{14}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{2293760 \, c^{7} d^{7} e^{3}}, -\frac{3465 \, {\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)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(71680 \, c^{8} d^{8} e^{8} x^{7} - 3465 \, c^{8} d^{15} e + 26565 \, a c^{7} d^{13} e^{3} + 140903 \, a^{2} c^{6} d^{11} e^{5} - 193699 \, a^{3} c^{5} d^{9} e^{7} + 166749 \, a^{4} c^{4} d^{7} e^{9} - 88473 \, a^{5} c^{3} d^{5} e^{11} + 26565 \, a^{6} c^{2} d^{3} e^{13} - 3465 \, a^{7} c d e^{15} + 5120 \, {\left(81 \, c^{8} d^{9} e^{7} + 17 \, a c^{7} d^{7} e^{9}\right)} x^{6} + 1280 \, {\left(769 \, c^{8} d^{10} e^{6} + 406 \, a c^{7} d^{8} e^{8} + a^{2} c^{6} d^{6} e^{10}\right)} x^{5} + 128 \, {\left(9461 \, c^{8} d^{11} e^{5} + 10067 \, a c^{7} d^{9} e^{7} + 83 \, a^{2} c^{6} d^{7} e^{9} - 11 \, a^{3} c^{5} d^{5} e^{11}\right)} x^{4} + 16 \, {\left(49251 \, c^{8} d^{12} e^{4} + 105748 \, a c^{7} d^{10} e^{6} + 2450 \, a^{2} c^{6} d^{8} e^{8} - 748 \, a^{3} c^{5} d^{6} e^{10} + 99 \, a^{4} c^{4} d^{4} e^{12}\right)} x^{3} + 8 \, {\left(28441 \, c^{8} d^{13} e^{3} + 153301 \, a c^{7} d^{11} e^{5} + 10642 \, a^{2} c^{6} d^{9} e^{7} - 5742 \, a^{3} c^{5} d^{7} e^{9} + 1749 \, a^{4} c^{4} d^{5} e^{11} - 231 \, a^{5} c^{3} d^{3} e^{13}\right)} x^{2} + 2 \, {\left(1155 \, c^{8} d^{14} e^{2} + 220598 \, a c^{7} d^{12} e^{4} + 61709 \, a^{2} c^{6} d^{10} e^{6} - 53900 \, a^{3} c^{5} d^{8} e^{8} + 28941 \, a^{4} c^{4} d^{6} e^{10} - 8778 \, a^{5} c^{3} d^{4} e^{12} + 1155 \, a^{6} c^{2} d^{2} e^{14}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{1146880 \, c^{7} d^{7} e^{3}}\right]"," ",0,"[1/2293760*(3465*(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)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(71680*c^8*d^8*e^8*x^7 - 3465*c^8*d^15*e + 26565*a*c^7*d^13*e^3 + 140903*a^2*c^6*d^11*e^5 - 193699*a^3*c^5*d^9*e^7 + 166749*a^4*c^4*d^7*e^9 - 88473*a^5*c^3*d^5*e^11 + 26565*a^6*c^2*d^3*e^13 - 3465*a^7*c*d*e^15 + 5120*(81*c^8*d^9*e^7 + 17*a*c^7*d^7*e^9)*x^6 + 1280*(769*c^8*d^10*e^6 + 406*a*c^7*d^8*e^8 + a^2*c^6*d^6*e^10)*x^5 + 128*(9461*c^8*d^11*e^5 + 10067*a*c^7*d^9*e^7 + 83*a^2*c^6*d^7*e^9 - 11*a^3*c^5*d^5*e^11)*x^4 + 16*(49251*c^8*d^12*e^4 + 105748*a*c^7*d^10*e^6 + 2450*a^2*c^6*d^8*e^8 - 748*a^3*c^5*d^6*e^10 + 99*a^4*c^4*d^4*e^12)*x^3 + 8*(28441*c^8*d^13*e^3 + 153301*a*c^7*d^11*e^5 + 10642*a^2*c^6*d^9*e^7 - 5742*a^3*c^5*d^7*e^9 + 1749*a^4*c^4*d^5*e^11 - 231*a^5*c^3*d^3*e^13)*x^2 + 2*(1155*c^8*d^14*e^2 + 220598*a*c^7*d^12*e^4 + 61709*a^2*c^6*d^10*e^6 - 53900*a^3*c^5*d^8*e^8 + 28941*a^4*c^4*d^6*e^10 - 8778*a^5*c^3*d^4*e^12 + 1155*a^6*c^2*d^2*e^14)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^7*d^7*e^3), -1/1146880*(3465*(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)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(71680*c^8*d^8*e^8*x^7 - 3465*c^8*d^15*e + 26565*a*c^7*d^13*e^3 + 140903*a^2*c^6*d^11*e^5 - 193699*a^3*c^5*d^9*e^7 + 166749*a^4*c^4*d^7*e^9 - 88473*a^5*c^3*d^5*e^11 + 26565*a^6*c^2*d^3*e^13 - 3465*a^7*c*d*e^15 + 5120*(81*c^8*d^9*e^7 + 17*a*c^7*d^7*e^9)*x^6 + 1280*(769*c^8*d^10*e^6 + 406*a*c^7*d^8*e^8 + a^2*c^6*d^6*e^10)*x^5 + 128*(9461*c^8*d^11*e^5 + 10067*a*c^7*d^9*e^7 + 83*a^2*c^6*d^7*e^9 - 11*a^3*c^5*d^5*e^11)*x^4 + 16*(49251*c^8*d^12*e^4 + 105748*a*c^7*d^10*e^6 + 2450*a^2*c^6*d^8*e^8 - 748*a^3*c^5*d^6*e^10 + 99*a^4*c^4*d^4*e^12)*x^3 + 8*(28441*c^8*d^13*e^3 + 153301*a*c^7*d^11*e^5 + 10642*a^2*c^6*d^9*e^7 - 5742*a^3*c^5*d^7*e^9 + 1749*a^4*c^4*d^5*e^11 - 231*a^5*c^3*d^3*e^13)*x^2 + 2*(1155*c^8*d^14*e^2 + 220598*a*c^7*d^12*e^4 + 61709*a^2*c^6*d^10*e^6 - 53900*a^3*c^5*d^8*e^8 + 28941*a^4*c^4*d^6*e^10 - 8778*a^5*c^3*d^4*e^12 + 1155*a^6*c^2*d^2*e^14)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^7*d^7*e^3)]","A",0
1919,1,1268,0,0.524754," ","integrate((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\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)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(5120 \, c^{7} d^{7} e^{7} x^{6} - 315 \, c^{7} d^{13} e + 2100 \, a c^{6} d^{11} e^{3} + 8393 \, a^{2} c^{5} d^{9} e^{5} - 9216 \, a^{3} c^{4} d^{7} e^{7} + 5943 \, a^{4} c^{3} d^{5} e^{9} - 2100 \, a^{5} c^{2} d^{3} e^{11} + 315 \, a^{6} c d e^{13} + 1280 \, {\left(19 \, c^{7} d^{8} e^{6} + 5 \, a c^{6} d^{6} e^{8}\right)} x^{5} + 128 \, {\left(351 \, c^{7} d^{9} e^{5} + 248 \, a c^{6} d^{7} e^{7} + a^{2} c^{5} d^{5} e^{9}\right)} x^{4} + 16 \, {\left(2441 \, c^{7} d^{10} e^{4} + 3909 \, a c^{6} d^{8} e^{6} + 59 \, a^{2} c^{5} d^{6} e^{8} - 9 \, a^{3} c^{4} d^{4} e^{10}\right)} x^{3} + 8 \, {\left(1771 \, c^{7} d^{11} e^{3} + 7562 \, a c^{6} d^{9} e^{5} + 384 \, a^{2} c^{5} d^{7} e^{7} - 138 \, a^{3} c^{4} d^{5} e^{9} + 21 \, a^{4} c^{3} d^{3} e^{11}\right)} x^{2} + 2 \, {\left(105 \, c^{7} d^{12} e^{2} + 13643 \, a c^{6} d^{10} e^{4} + 2962 \, a^{2} c^{5} d^{8} e^{6} - 1938 \, a^{3} c^{4} d^{6} e^{8} + 693 \, a^{4} c^{3} d^{4} e^{10} - 105 \, a^{5} c^{2} d^{2} e^{12}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{143360 \, c^{6} d^{6} e^{3}}, -\frac{315 \, {\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)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(5120 \, c^{7} d^{7} e^{7} x^{6} - 315 \, c^{7} d^{13} e + 2100 \, a c^{6} d^{11} e^{3} + 8393 \, a^{2} c^{5} d^{9} e^{5} - 9216 \, a^{3} c^{4} d^{7} e^{7} + 5943 \, a^{4} c^{3} d^{5} e^{9} - 2100 \, a^{5} c^{2} d^{3} e^{11} + 315 \, a^{6} c d e^{13} + 1280 \, {\left(19 \, c^{7} d^{8} e^{6} + 5 \, a c^{6} d^{6} e^{8}\right)} x^{5} + 128 \, {\left(351 \, c^{7} d^{9} e^{5} + 248 \, a c^{6} d^{7} e^{7} + a^{2} c^{5} d^{5} e^{9}\right)} x^{4} + 16 \, {\left(2441 \, c^{7} d^{10} e^{4} + 3909 \, a c^{6} d^{8} e^{6} + 59 \, a^{2} c^{5} d^{6} e^{8} - 9 \, a^{3} c^{4} d^{4} e^{10}\right)} x^{3} + 8 \, {\left(1771 \, c^{7} d^{11} e^{3} + 7562 \, a c^{6} d^{9} e^{5} + 384 \, a^{2} c^{5} d^{7} e^{7} - 138 \, a^{3} c^{4} d^{5} e^{9} + 21 \, a^{4} c^{3} d^{3} e^{11}\right)} x^{2} + 2 \, {\left(105 \, c^{7} d^{12} e^{2} + 13643 \, a c^{6} d^{10} e^{4} + 2962 \, a^{2} c^{5} d^{8} e^{6} - 1938 \, a^{3} c^{4} d^{6} e^{8} + 693 \, a^{4} c^{3} d^{4} e^{10} - 105 \, a^{5} c^{2} d^{2} e^{12}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{71680 \, c^{6} d^{6} e^{3}}\right]"," ",0,"[1/143360*(315*(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)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(5120*c^7*d^7*e^7*x^6 - 315*c^7*d^13*e + 2100*a*c^6*d^11*e^3 + 8393*a^2*c^5*d^9*e^5 - 9216*a^3*c^4*d^7*e^7 + 5943*a^4*c^3*d^5*e^9 - 2100*a^5*c^2*d^3*e^11 + 315*a^6*c*d*e^13 + 1280*(19*c^7*d^8*e^6 + 5*a*c^6*d^6*e^8)*x^5 + 128*(351*c^7*d^9*e^5 + 248*a*c^6*d^7*e^7 + a^2*c^5*d^5*e^9)*x^4 + 16*(2441*c^7*d^10*e^4 + 3909*a*c^6*d^8*e^6 + 59*a^2*c^5*d^6*e^8 - 9*a^3*c^4*d^4*e^10)*x^3 + 8*(1771*c^7*d^11*e^3 + 7562*a*c^6*d^9*e^5 + 384*a^2*c^5*d^7*e^7 - 138*a^3*c^4*d^5*e^9 + 21*a^4*c^3*d^3*e^11)*x^2 + 2*(105*c^7*d^12*e^2 + 13643*a*c^6*d^10*e^4 + 2962*a^2*c^5*d^8*e^6 - 1938*a^3*c^4*d^6*e^8 + 693*a^4*c^3*d^4*e^10 - 105*a^5*c^2*d^2*e^12)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^6*d^6*e^3), -1/71680*(315*(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)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(5120*c^7*d^7*e^7*x^6 - 315*c^7*d^13*e + 2100*a*c^6*d^11*e^3 + 8393*a^2*c^5*d^9*e^5 - 9216*a^3*c^4*d^7*e^7 + 5943*a^4*c^3*d^5*e^9 - 2100*a^5*c^2*d^3*e^11 + 315*a^6*c*d*e^13 + 1280*(19*c^7*d^8*e^6 + 5*a*c^6*d^6*e^8)*x^5 + 128*(351*c^7*d^9*e^5 + 248*a*c^6*d^7*e^7 + a^2*c^5*d^5*e^9)*x^4 + 16*(2441*c^7*d^10*e^4 + 3909*a*c^6*d^8*e^6 + 59*a^2*c^5*d^6*e^8 - 9*a^3*c^4*d^4*e^10)*x^3 + 8*(1771*c^7*d^11*e^3 + 7562*a*c^6*d^9*e^5 + 384*a^2*c^5*d^7*e^7 - 138*a^3*c^4*d^5*e^9 + 21*a^4*c^3*d^3*e^11)*x^2 + 2*(105*c^7*d^12*e^2 + 13643*a*c^6*d^10*e^4 + 2962*a^2*c^5*d^8*e^6 - 1938*a^3*c^4*d^6*e^8 + 693*a^4*c^3*d^4*e^10 - 105*a^5*c^2*d^2*e^12)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^6*d^6*e^3)]","A",0
1920,1,1042,0,0.518974," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\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 d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(1280 \, c^{6} d^{6} e^{6} x^{5} - 105 \, c^{6} d^{11} e + 595 \, a c^{5} d^{9} e^{3} + 1686 \, a^{2} c^{4} d^{7} e^{5} - 1386 \, a^{3} c^{3} d^{5} e^{7} + 595 \, a^{4} c^{2} d^{3} e^{9} - 105 \, a^{5} c d e^{11} + 128 \, {\left(37 \, c^{6} d^{7} e^{5} + 13 \, a c^{5} d^{5} e^{7}\right)} x^{4} + 16 \, {\left(387 \, c^{6} d^{8} e^{4} + 410 \, a c^{5} d^{6} e^{6} + 3 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{3} + 8 \, {\left(377 \, c^{6} d^{9} e^{3} + 1191 \, a c^{5} d^{7} e^{5} + 39 \, a^{2} c^{4} d^{5} e^{7} - 7 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{2} + 2 \, {\left(35 \, c^{6} d^{10} e^{2} + 2876 \, a c^{5} d^{8} e^{4} + 450 \, a^{2} c^{4} d^{6} e^{6} - 196 \, a^{3} c^{3} d^{4} e^{8} + 35 \, a^{4} c^{2} d^{2} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{30720 \, c^{5} d^{5} e^{3}}, -\frac{105 \, {\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 d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(1280 \, c^{6} d^{6} e^{6} x^{5} - 105 \, c^{6} d^{11} e + 595 \, a c^{5} d^{9} e^{3} + 1686 \, a^{2} c^{4} d^{7} e^{5} - 1386 \, a^{3} c^{3} d^{5} e^{7} + 595 \, a^{4} c^{2} d^{3} e^{9} - 105 \, a^{5} c d e^{11} + 128 \, {\left(37 \, c^{6} d^{7} e^{5} + 13 \, a c^{5} d^{5} e^{7}\right)} x^{4} + 16 \, {\left(387 \, c^{6} d^{8} e^{4} + 410 \, a c^{5} d^{6} e^{6} + 3 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{3} + 8 \, {\left(377 \, c^{6} d^{9} e^{3} + 1191 \, a c^{5} d^{7} e^{5} + 39 \, a^{2} c^{4} d^{5} e^{7} - 7 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{2} + 2 \, {\left(35 \, c^{6} d^{10} e^{2} + 2876 \, a c^{5} d^{8} e^{4} + 450 \, a^{2} c^{4} d^{6} e^{6} - 196 \, a^{3} c^{3} d^{4} e^{8} + 35 \, a^{4} c^{2} d^{2} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15360 \, c^{5} d^{5} e^{3}}\right]"," ",0,"[1/30720*(105*(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*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(1280*c^6*d^6*e^6*x^5 - 105*c^6*d^11*e + 595*a*c^5*d^9*e^3 + 1686*a^2*c^4*d^7*e^5 - 1386*a^3*c^3*d^5*e^7 + 595*a^4*c^2*d^3*e^9 - 105*a^5*c*d*e^11 + 128*(37*c^6*d^7*e^5 + 13*a*c^5*d^5*e^7)*x^4 + 16*(387*c^6*d^8*e^4 + 410*a*c^5*d^6*e^6 + 3*a^2*c^4*d^4*e^8)*x^3 + 8*(377*c^6*d^9*e^3 + 1191*a*c^5*d^7*e^5 + 39*a^2*c^4*d^5*e^7 - 7*a^3*c^3*d^3*e^9)*x^2 + 2*(35*c^6*d^10*e^2 + 2876*a*c^5*d^8*e^4 + 450*a^2*c^4*d^6*e^6 - 196*a^3*c^3*d^4*e^8 + 35*a^4*c^2*d^2*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*e^3), -1/15360*(105*(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*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(1280*c^6*d^6*e^6*x^5 - 105*c^6*d^11*e + 595*a*c^5*d^9*e^3 + 1686*a^2*c^4*d^7*e^5 - 1386*a^3*c^3*d^5*e^7 + 595*a^4*c^2*d^3*e^9 - 105*a^5*c*d*e^11 + 128*(37*c^6*d^7*e^5 + 13*a*c^5*d^5*e^7)*x^4 + 16*(387*c^6*d^8*e^4 + 410*a*c^5*d^6*e^6 + 3*a^2*c^4*d^4*e^8)*x^3 + 8*(377*c^6*d^9*e^3 + 1191*a*c^5*d^7*e^5 + 39*a^2*c^4*d^5*e^7 - 7*a^3*c^3*d^3*e^9)*x^2 + 2*(35*c^6*d^10*e^2 + 2876*a*c^5*d^8*e^4 + 450*a^2*c^4*d^6*e^6 - 196*a^3*c^3*d^4*e^8 + 35*a^4*c^2*d^2*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*e^3)]","A",0
1921,1,844,0,0.469903," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\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 e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(128 \, c^{5} d^{5} e^{5} x^{4} - 15 \, c^{5} d^{9} e + 70 \, a c^{4} d^{7} e^{3} + 128 \, a^{2} c^{3} d^{5} e^{5} - 70 \, a^{3} c^{2} d^{3} e^{7} + 15 \, a^{4} c d e^{9} + 16 \, {\left(21 \, c^{5} d^{6} e^{4} + 11 \, a c^{4} d^{4} e^{6}\right)} x^{3} + 8 \, {\left(31 \, c^{5} d^{7} e^{3} + 64 \, a c^{4} d^{5} e^{5} + a^{2} c^{3} d^{3} e^{7}\right)} x^{2} + 2 \, {\left(5 \, c^{5} d^{8} e^{2} + 233 \, a c^{4} d^{6} e^{4} + 23 \, a^{2} c^{3} d^{4} e^{6} - 5 \, a^{3} c^{2} d^{2} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{2560 \, c^{4} d^{4} e^{3}}, -\frac{15 \, {\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 e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(128 \, c^{5} d^{5} e^{5} x^{4} - 15 \, c^{5} d^{9} e + 70 \, a c^{4} d^{7} e^{3} + 128 \, a^{2} c^{3} d^{5} e^{5} - 70 \, a^{3} c^{2} d^{3} e^{7} + 15 \, a^{4} c d e^{9} + 16 \, {\left(21 \, c^{5} d^{6} e^{4} + 11 \, a c^{4} d^{4} e^{6}\right)} x^{3} + 8 \, {\left(31 \, c^{5} d^{7} e^{3} + 64 \, a c^{4} d^{5} e^{5} + a^{2} c^{3} d^{3} e^{7}\right)} x^{2} + 2 \, {\left(5 \, c^{5} d^{8} e^{2} + 233 \, a c^{4} d^{6} e^{4} + 23 \, a^{2} c^{3} d^{4} e^{6} - 5 \, a^{3} c^{2} d^{2} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{1280 \, c^{4} d^{4} e^{3}}\right]"," ",0,"[1/2560*(15*(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*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(128*c^5*d^5*e^5*x^4 - 15*c^5*d^9*e + 70*a*c^4*d^7*e^3 + 128*a^2*c^3*d^5*e^5 - 70*a^3*c^2*d^3*e^7 + 15*a^4*c*d*e^9 + 16*(21*c^5*d^6*e^4 + 11*a*c^4*d^4*e^6)*x^3 + 8*(31*c^5*d^7*e^3 + 64*a*c^4*d^5*e^5 + a^2*c^3*d^3*e^7)*x^2 + 2*(5*c^5*d^8*e^2 + 233*a*c^4*d^6*e^4 + 23*a^2*c^3*d^4*e^6 - 5*a^3*c^2*d^2*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^3), -1/1280*(15*(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*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(128*c^5*d^5*e^5*x^4 - 15*c^5*d^9*e + 70*a*c^4*d^7*e^3 + 128*a^2*c^3*d^5*e^5 - 70*a^3*c^2*d^3*e^7 + 15*a^4*c*d*e^9 + 16*(21*c^5*d^6*e^4 + 11*a*c^4*d^4*e^6)*x^3 + 8*(31*c^5*d^7*e^3 + 64*a*c^4*d^5*e^5 + a^2*c^3*d^3*e^7)*x^2 + 2*(5*c^5*d^8*e^2 + 233*a*c^4*d^6*e^4 + 23*a^2*c^3*d^4*e^6 - 5*a^3*c^2*d^2*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^3)]","A",0
1922,1,666,0,0.463202," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\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)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(16 \, c^{4} d^{4} e^{4} x^{3} - 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} + 24 \, {\left(c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(c^{4} d^{6} e^{2} + 22 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{256 \, c^{3} d^{3} e^{3}}, -\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)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(16 \, c^{4} d^{4} e^{4} x^{3} - 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} + 24 \, {\left(c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{2} + 2 \, {\left(c^{4} d^{6} e^{2} + 22 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{128 \, c^{3} d^{3} e^{3}}\right]"," ",0,"[1/256*(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)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(16*c^4*d^4*e^4*x^3 - 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 + 24*(c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^2 + 2*(c^4*d^6*e^2 + 22*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^3), -1/128*(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)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(16*c^4*d^4*e^4*x^3 - 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 + 24*(c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^2 + 2*(c^4*d^6*e^2 + 22*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^3)]","A",0
1923,1,532,0,0.450738," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{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)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} - 3 \, c^{3} d^{5} e + 8 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5} + 2 \, {\left(c^{3} d^{4} e^{2} + 7 \, a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, c^{2} d^{2} e^{3}}, -\frac{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)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} - 3 \, c^{3} d^{5} e + 8 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5} + 2 \, {\left(c^{3} d^{4} e^{2} + 7 \, a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, c^{2} d^{2} e^{3}}\right]"," ",0,"[-1/96*(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)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(8*c^3*d^3*e^3*x^2 - 3*c^3*d^5*e + 8*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5 + 2*(c^3*d^4*e^2 + 7*a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^3), -1/48*(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)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(8*c^3*d^3*e^3*x^2 - 3*c^3*d^5*e + 8*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5 + 2*(c^3*d^4*e^2 + 7*a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^3)]","A",0
1924,1,418,0,0.445747," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(2 \, c^{2} d^{2} e^{2} x - 3 \, c^{2} d^{3} e + 5 \, a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, c d e^{3}}, -\frac{3 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(2 \, c^{2} d^{2} e^{2} x - 3 \, c^{2} d^{3} e + 5 \, a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, c d e^{3}}\right]"," ",0,"[1/16*(3*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(2*c^2*d^2*e^2*x - 3*c^2*d^3*e + 5*a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^3), -1/8*(3*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(2*c^2*d^2*e^2*x - 3*c^2*d^3*e + 5*a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^3)]","A",0
1925,1,414,0,0.499622," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{\frac{c d}{e}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d e x + 3 \, c d^{2} - 2 \, a e^{2}\right)}}{4 \, {\left(e^{3} x + d e^{2}\right)}}, \frac{3 \, {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{-\frac{c d}{e}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d e x + 3 \, c d^{2} - 2 \, a e^{2}\right)}}{2 \, {\left(e^{3} x + d e^{2}\right)}}\right]"," ",0,"[1/4*(3*(c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(c*d/e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*e*x + 3*c*d^2 - 2*a*e^2))/(e^3*x + d*e^2), 1/2*(3*(c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(-c*d/e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*e*x + 3*c*d^2 - 2*a*e^2))/(e^3*x + d*e^2)]","A",0
1926,1,426,0,0.731038," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d e^{2} x^{2} + 2 \, c d^{2} e x + c d^{3}\right)} \sqrt{\frac{c d}{e}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(4 \, c d e x + 3 \, c d^{2} + a e^{2}\right)}}{6 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}, -\frac{3 \, {\left(c d e^{2} x^{2} + 2 \, c d^{2} e x + c d^{3}\right)} \sqrt{-\frac{c d}{e}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(4 \, c d e x + 3 \, c d^{2} + a e^{2}\right)}}{3 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}\right]"," ",0,"[1/6*(3*(c*d*e^2*x^2 + 2*c*d^2*e*x + c*d^3)*sqrt(c*d/e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(4*c*d*e*x + 3*c*d^2 + a*e^2))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2), -1/3*(3*(c*d*e^2*x^2 + 2*c*d^2*e*x + c*d^3)*sqrt(-c*d/e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(4*c*d*e*x + 3*c*d^2 + a*e^2))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2)]","A",0
1927,1,130,0,1.215732," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^5,x, algorithm=""fricas"")","\frac{2 \, {\left(c^{2} d^{2} x^{2} + 2 \, a c d e x + a^{2} e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{5 \, {\left(c d^{5} - a d^{3} e^{2} + {\left(c d^{2} e^{3} - a e^{5}\right)} x^{3} + 3 \, {\left(c d^{3} e^{2} - a d e^{4}\right)} x^{2} + 3 \, {\left(c d^{4} e - a d^{2} e^{3}\right)} x\right)}}"," ",0,"2/5*(c^2*d^2*x^2 + 2*a*c*d*e*x + a^2*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c*d^5 - a*d^3*e^2 + (c*d^2*e^3 - a*e^5)*x^3 + 3*(c*d^3*e^2 - a*d*e^4)*x^2 + 3*(c*d^4*e - a*d^2*e^3)*x)","B",0
1928,1,275,0,3.329846," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^6,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, c^{3} d^{3} e x^{3} + 7 \, a^{2} c d^{2} e^{2} - 5 \, a^{3} e^{4} + {\left(7 \, c^{3} d^{4} - a c^{2} d^{2} e^{2}\right)} x^{2} + 2 \, {\left(7 \, a c^{2} d^{3} e - 4 \, a^{2} c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{35 \, {\left(c^{2} d^{8} - 2 \, a c d^{6} e^{2} + a^{2} d^{4} e^{4} + {\left(c^{2} d^{4} e^{4} - 2 \, a c d^{2} e^{6} + a^{2} e^{8}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{3} - 2 \, a c d^{3} e^{5} + a^{2} d e^{7}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{2} - 2 \, a c d^{4} e^{4} + a^{2} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e - 2 \, a c d^{5} e^{3} + a^{2} d^{3} e^{5}\right)} x\right)}}"," ",0,"2/35*(2*c^3*d^3*e*x^3 + 7*a^2*c*d^2*e^2 - 5*a^3*e^4 + (7*c^3*d^4 - a*c^2*d^2*e^2)*x^2 + 2*(7*a*c^2*d^3*e - 4*a^2*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^2*d^8 - 2*a*c*d^6*e^2 + a^2*d^4*e^4 + (c^2*d^4*e^4 - 2*a*c*d^2*e^6 + a^2*e^8)*x^4 + 4*(c^2*d^5*e^3 - 2*a*c*d^3*e^5 + a^2*d*e^7)*x^3 + 6*(c^2*d^6*e^2 - 2*a*c*d^4*e^4 + a^2*d^2*e^6)*x^2 + 4*(c^2*d^7*e - 2*a*c*d^5*e^3 + a^2*d^3*e^5)*x)","B",0
1929,1,472,0,11.320324," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^7,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{4} d^{4} e^{2} x^{4} + 63 \, a^{2} c^{2} d^{4} e^{2} - 90 \, a^{3} c d^{2} e^{4} + 35 \, a^{4} e^{6} + 4 \, {\left(9 \, c^{4} d^{5} e - a c^{3} d^{3} e^{3}\right)} x^{3} + 3 \, {\left(21 \, c^{4} d^{6} - 6 \, a c^{3} d^{4} e^{2} + a^{2} c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(63 \, a c^{3} d^{5} e - 72 \, a^{2} c^{2} d^{3} e^{3} + 25 \, a^{3} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{315 \, {\left(c^{3} d^{11} - 3 \, a c^{2} d^{9} e^{2} + 3 \, a^{2} c d^{7} e^{4} - a^{3} d^{5} e^{6} + {\left(c^{3} d^{6} e^{5} - 3 \, a c^{2} d^{4} e^{7} + 3 \, a^{2} c d^{2} e^{9} - a^{3} e^{11}\right)} x^{5} + 5 \, {\left(c^{3} d^{7} e^{4} - 3 \, a c^{2} d^{5} e^{6} + 3 \, a^{2} c d^{3} e^{8} - a^{3} d e^{10}\right)} x^{4} + 10 \, {\left(c^{3} d^{8} e^{3} - 3 \, a c^{2} d^{6} e^{5} + 3 \, a^{2} c d^{4} e^{7} - a^{3} d^{2} e^{9}\right)} x^{3} + 10 \, {\left(c^{3} d^{9} e^{2} - 3 \, a c^{2} d^{7} e^{4} + 3 \, a^{2} c d^{5} e^{6} - a^{3} d^{3} e^{8}\right)} x^{2} + 5 \, {\left(c^{3} d^{10} e - 3 \, a c^{2} d^{8} e^{3} + 3 \, a^{2} c d^{6} e^{5} - a^{3} d^{4} e^{7}\right)} x\right)}}"," ",0,"2/315*(8*c^4*d^4*e^2*x^4 + 63*a^2*c^2*d^4*e^2 - 90*a^3*c*d^2*e^4 + 35*a^4*e^6 + 4*(9*c^4*d^5*e - a*c^3*d^3*e^3)*x^3 + 3*(21*c^4*d^6 - 6*a*c^3*d^4*e^2 + a^2*c^2*d^2*e^4)*x^2 + 2*(63*a*c^3*d^5*e - 72*a^2*c^2*d^3*e^3 + 25*a^3*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^3*d^11 - 3*a*c^2*d^9*e^2 + 3*a^2*c*d^7*e^4 - a^3*d^5*e^6 + (c^3*d^6*e^5 - 3*a*c^2*d^4*e^7 + 3*a^2*c*d^2*e^9 - a^3*e^11)*x^5 + 5*(c^3*d^7*e^4 - 3*a*c^2*d^5*e^6 + 3*a^2*c*d^3*e^8 - a^3*d*e^10)*x^4 + 10*(c^3*d^8*e^3 - 3*a*c^2*d^6*e^5 + 3*a^2*c*d^4*e^7 - a^3*d^2*e^9)*x^3 + 10*(c^3*d^9*e^2 - 3*a*c^2*d^7*e^4 + 3*a^2*c*d^5*e^6 - a^3*d^3*e^8)*x^2 + 5*(c^3*d^10*e - 3*a*c^2*d^8*e^3 + 3*a^2*c*d^6*e^5 - a^3*d^4*e^7)*x)","B",0
1930,1,699,0,27.325448," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/(e*x+d)^8,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{5} d^{5} e^{3} x^{5} + 231 \, a^{2} c^{3} d^{6} e^{2} - 495 \, a^{3} c^{2} d^{4} e^{4} + 385 \, a^{4} c d^{2} e^{6} - 105 \, a^{5} e^{8} + 8 \, {\left(11 \, c^{5} d^{6} e^{2} - a c^{4} d^{4} e^{4}\right)} x^{4} + 2 \, {\left(99 \, c^{5} d^{7} e - 22 \, a c^{4} d^{5} e^{3} + 3 \, a^{2} c^{3} d^{3} e^{5}\right)} x^{3} + {\left(231 \, c^{5} d^{8} - 99 \, a c^{4} d^{6} e^{2} + 33 \, a^{2} c^{3} d^{4} e^{4} - 5 \, a^{3} c^{2} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(231 \, a c^{4} d^{7} e - 396 \, a^{2} c^{3} d^{5} e^{3} + 275 \, a^{3} c^{2} d^{3} e^{5} - 70 \, a^{4} c d e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{1155 \, {\left(c^{4} d^{14} - 4 \, a c^{3} d^{12} e^{2} + 6 \, a^{2} c^{2} d^{10} e^{4} - 4 \, a^{3} c d^{8} e^{6} + a^{4} d^{6} e^{8} + {\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)} x^{6} + 6 \, {\left(c^{4} d^{9} e^{5} - 4 \, a c^{3} d^{7} e^{7} + 6 \, a^{2} c^{2} d^{5} e^{9} - 4 \, a^{3} c d^{3} e^{11} + a^{4} d e^{13}\right)} x^{5} + 15 \, {\left(c^{4} d^{10} e^{4} - 4 \, a c^{3} d^{8} e^{6} + 6 \, a^{2} c^{2} d^{6} e^{8} - 4 \, a^{3} c d^{4} e^{10} + a^{4} d^{2} e^{12}\right)} x^{4} + 20 \, {\left(c^{4} d^{11} e^{3} - 4 \, a c^{3} d^{9} e^{5} + 6 \, a^{2} c^{2} d^{7} e^{7} - 4 \, a^{3} c d^{5} e^{9} + a^{4} d^{3} e^{11}\right)} x^{3} + 15 \, {\left(c^{4} d^{12} e^{2} - 4 \, a c^{3} d^{10} e^{4} + 6 \, a^{2} c^{2} d^{8} e^{6} - 4 \, a^{3} c d^{6} e^{8} + a^{4} d^{4} e^{10}\right)} x^{2} + 6 \, {\left(c^{4} d^{13} e - 4 \, a c^{3} d^{11} e^{3} + 6 \, a^{2} c^{2} d^{9} e^{5} - 4 \, a^{3} c d^{7} e^{7} + a^{4} d^{5} e^{9}\right)} x\right)}}"," ",0,"2/1155*(16*c^5*d^5*e^3*x^5 + 231*a^2*c^3*d^6*e^2 - 495*a^3*c^2*d^4*e^4 + 385*a^4*c*d^2*e^6 - 105*a^5*e^8 + 8*(11*c^5*d^6*e^2 - a*c^4*d^4*e^4)*x^4 + 2*(99*c^5*d^7*e - 22*a*c^4*d^5*e^3 + 3*a^2*c^3*d^3*e^5)*x^3 + (231*c^5*d^8 - 99*a*c^4*d^6*e^2 + 33*a^2*c^3*d^4*e^4 - 5*a^3*c^2*d^2*e^6)*x^2 + 2*(231*a*c^4*d^7*e - 396*a^2*c^3*d^5*e^3 + 275*a^3*c^2*d^3*e^5 - 70*a^4*c*d*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^4*d^14 - 4*a*c^3*d^12*e^2 + 6*a^2*c^2*d^10*e^4 - 4*a^3*c*d^8*e^6 + a^4*d^6*e^8 + (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)*x^6 + 6*(c^4*d^9*e^5 - 4*a*c^3*d^7*e^7 + 6*a^2*c^2*d^5*e^9 - 4*a^3*c*d^3*e^11 + a^4*d*e^13)*x^5 + 15*(c^4*d^10*e^4 - 4*a*c^3*d^8*e^6 + 6*a^2*c^2*d^6*e^8 - 4*a^3*c*d^4*e^10 + a^4*d^2*e^12)*x^4 + 20*(c^4*d^11*e^3 - 4*a*c^3*d^9*e^5 + 6*a^2*c^2*d^7*e^7 - 4*a^3*c*d^5*e^9 + a^4*d^3*e^11)*x^3 + 15*(c^4*d^12*e^2 - 4*a*c^3*d^10*e^4 + 6*a^2*c^2*d^8*e^6 - 4*a^3*c*d^6*e^8 + a^4*d^4*e^10)*x^2 + 6*(c^4*d^13*e - 4*a*c^3*d^11*e^3 + 6*a^2*c^2*d^9*e^5 - 4*a^3*c*d^7*e^7 + a^4*d^5*e^9)*x)","B",0
1931,1,2114,0,0.662958," ","integrate((e*x+d)^4*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{45045 \, {\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)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(4128768 \, c^{10} d^{10} e^{10} x^{9} + 45045 \, c^{10} d^{19} e - 435435 \, a c^{9} d^{17} e^{3} + 1885884 \, a^{2} c^{8} d^{15} e^{5} + 6983100 \, a^{3} c^{7} d^{13} e^{7} - 9035650 \, a^{4} c^{6} d^{11} e^{9} + 8003710 \, a^{5} c^{5} d^{9} e^{11} - 4813380 \, a^{6} c^{4} d^{7} e^{13} + 1885884 \, a^{7} c^{3} d^{5} e^{15} - 435435 \, a^{8} c^{2} d^{3} e^{17} + 45045 \, a^{9} c d e^{19} + 229376 \, {\left(121 \, c^{10} d^{11} e^{9} + 41 \, a c^{9} d^{9} e^{11}\right)} x^{8} + 14336 \, {\left(5503 \, c^{10} d^{12} e^{8} + 4482 \, a c^{9} d^{10} e^{10} + 383 \, a^{2} c^{8} d^{8} e^{12}\right)} x^{7} + 1024 \, {\left(119055 \, c^{10} d^{13} e^{7} + 182129 \, a c^{9} d^{11} e^{9} + 37489 \, a^{2} c^{8} d^{9} e^{11} + 15 \, a^{3} c^{7} d^{7} e^{13}\right)} x^{6} + 256 \, {\left(424895 \, c^{10} d^{14} e^{6} + 1157740 \, a c^{9} d^{12} e^{8} + 448938 \, a^{2} c^{8} d^{10} e^{10} + 620 \, a^{3} c^{7} d^{8} e^{12} - 65 \, a^{4} c^{6} d^{6} e^{14}\right)} x^{5} + 128 \, {\left(419983 \, c^{10} d^{15} e^{5} + 2149035 \, a c^{9} d^{13} e^{7} + 1490630 \, a^{2} c^{8} d^{11} e^{9} + 5830 \, a^{3} c^{7} d^{9} e^{11} - 1365 \, a^{4} c^{6} d^{7} e^{13} + 143 \, a^{5} c^{5} d^{5} e^{15}\right)} x^{4} + 16 \, {\left(735993 \, c^{10} d^{16} e^{4} + 9023498 \, a c^{9} d^{14} e^{6} + 11825815 \, a^{2} c^{8} d^{12} e^{8} + 132300 \, a^{3} c^{7} d^{10} e^{10} - 52585 \, a^{4} c^{6} d^{8} e^{12} + 12298 \, a^{5} c^{5} d^{6} e^{14} - 1287 \, a^{6} c^{4} d^{4} e^{16}\right)} x^{3} + 8 \, {\left(3003 \, c^{10} d^{17} e^{3} + 4394937 \, a c^{9} d^{15} e^{5} + 13885683 \, a^{2} c^{8} d^{13} e^{7} + 508825 \, a^{3} c^{7} d^{11} e^{9} - 310375 \, a^{4} c^{6} d^{9} e^{11} + 123123 \, a^{5} c^{5} d^{7} e^{13} - 28743 \, a^{6} c^{4} d^{5} e^{15} + 3003 \, a^{7} c^{3} d^{3} e^{17}\right)} x^{2} - 2 \, {\left(15015 \, c^{10} d^{18} e^{2} - 144144 \, a c^{9} d^{16} e^{4} - 17075244 \, a^{2} c^{8} d^{14} e^{6} - 2878000 \, a^{3} c^{7} d^{12} e^{8} + 2579850 \, a^{4} c^{6} d^{10} e^{10} - 1567280 \, a^{5} c^{5} d^{8} e^{12} + 619476 \, a^{6} c^{4} d^{6} e^{14} - 144144 \, a^{7} c^{3} d^{4} e^{16} + 15015 \, a^{8} c^{2} d^{2} e^{18}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{165150720 \, c^{8} d^{8} e^{4}}, \frac{45045 \, {\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)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(4128768 \, c^{10} d^{10} e^{10} x^{9} + 45045 \, c^{10} d^{19} e - 435435 \, a c^{9} d^{17} e^{3} + 1885884 \, a^{2} c^{8} d^{15} e^{5} + 6983100 \, a^{3} c^{7} d^{13} e^{7} - 9035650 \, a^{4} c^{6} d^{11} e^{9} + 8003710 \, a^{5} c^{5} d^{9} e^{11} - 4813380 \, a^{6} c^{4} d^{7} e^{13} + 1885884 \, a^{7} c^{3} d^{5} e^{15} - 435435 \, a^{8} c^{2} d^{3} e^{17} + 45045 \, a^{9} c d e^{19} + 229376 \, {\left(121 \, c^{10} d^{11} e^{9} + 41 \, a c^{9} d^{9} e^{11}\right)} x^{8} + 14336 \, {\left(5503 \, c^{10} d^{12} e^{8} + 4482 \, a c^{9} d^{10} e^{10} + 383 \, a^{2} c^{8} d^{8} e^{12}\right)} x^{7} + 1024 \, {\left(119055 \, c^{10} d^{13} e^{7} + 182129 \, a c^{9} d^{11} e^{9} + 37489 \, a^{2} c^{8} d^{9} e^{11} + 15 \, a^{3} c^{7} d^{7} e^{13}\right)} x^{6} + 256 \, {\left(424895 \, c^{10} d^{14} e^{6} + 1157740 \, a c^{9} d^{12} e^{8} + 448938 \, a^{2} c^{8} d^{10} e^{10} + 620 \, a^{3} c^{7} d^{8} e^{12} - 65 \, a^{4} c^{6} d^{6} e^{14}\right)} x^{5} + 128 \, {\left(419983 \, c^{10} d^{15} e^{5} + 2149035 \, a c^{9} d^{13} e^{7} + 1490630 \, a^{2} c^{8} d^{11} e^{9} + 5830 \, a^{3} c^{7} d^{9} e^{11} - 1365 \, a^{4} c^{6} d^{7} e^{13} + 143 \, a^{5} c^{5} d^{5} e^{15}\right)} x^{4} + 16 \, {\left(735993 \, c^{10} d^{16} e^{4} + 9023498 \, a c^{9} d^{14} e^{6} + 11825815 \, a^{2} c^{8} d^{12} e^{8} + 132300 \, a^{3} c^{7} d^{10} e^{10} - 52585 \, a^{4} c^{6} d^{8} e^{12} + 12298 \, a^{5} c^{5} d^{6} e^{14} - 1287 \, a^{6} c^{4} d^{4} e^{16}\right)} x^{3} + 8 \, {\left(3003 \, c^{10} d^{17} e^{3} + 4394937 \, a c^{9} d^{15} e^{5} + 13885683 \, a^{2} c^{8} d^{13} e^{7} + 508825 \, a^{3} c^{7} d^{11} e^{9} - 310375 \, a^{4} c^{6} d^{9} e^{11} + 123123 \, a^{5} c^{5} d^{7} e^{13} - 28743 \, a^{6} c^{4} d^{5} e^{15} + 3003 \, a^{7} c^{3} d^{3} e^{17}\right)} x^{2} - 2 \, {\left(15015 \, c^{10} d^{18} e^{2} - 144144 \, a c^{9} d^{16} e^{4} - 17075244 \, a^{2} c^{8} d^{14} e^{6} - 2878000 \, a^{3} c^{7} d^{12} e^{8} + 2579850 \, a^{4} c^{6} d^{10} e^{10} - 1567280 \, a^{5} c^{5} d^{8} e^{12} + 619476 \, a^{6} c^{4} d^{6} e^{14} - 144144 \, a^{7} c^{3} d^{4} e^{16} + 15015 \, a^{8} c^{2} d^{2} e^{18}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{82575360 \, c^{8} d^{8} e^{4}}\right]"," ",0,"[1/165150720*(45045*(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)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(4128768*c^10*d^10*e^10*x^9 + 45045*c^10*d^19*e - 435435*a*c^9*d^17*e^3 + 1885884*a^2*c^8*d^15*e^5 + 6983100*a^3*c^7*d^13*e^7 - 9035650*a^4*c^6*d^11*e^9 + 8003710*a^5*c^5*d^9*e^11 - 4813380*a^6*c^4*d^7*e^13 + 1885884*a^7*c^3*d^5*e^15 - 435435*a^8*c^2*d^3*e^17 + 45045*a^9*c*d*e^19 + 229376*(121*c^10*d^11*e^9 + 41*a*c^9*d^9*e^11)*x^8 + 14336*(5503*c^10*d^12*e^8 + 4482*a*c^9*d^10*e^10 + 383*a^2*c^8*d^8*e^12)*x^7 + 1024*(119055*c^10*d^13*e^7 + 182129*a*c^9*d^11*e^9 + 37489*a^2*c^8*d^9*e^11 + 15*a^3*c^7*d^7*e^13)*x^6 + 256*(424895*c^10*d^14*e^6 + 1157740*a*c^9*d^12*e^8 + 448938*a^2*c^8*d^10*e^10 + 620*a^3*c^7*d^8*e^12 - 65*a^4*c^6*d^6*e^14)*x^5 + 128*(419983*c^10*d^15*e^5 + 2149035*a*c^9*d^13*e^7 + 1490630*a^2*c^8*d^11*e^9 + 5830*a^3*c^7*d^9*e^11 - 1365*a^4*c^6*d^7*e^13 + 143*a^5*c^5*d^5*e^15)*x^4 + 16*(735993*c^10*d^16*e^4 + 9023498*a*c^9*d^14*e^6 + 11825815*a^2*c^8*d^12*e^8 + 132300*a^3*c^7*d^10*e^10 - 52585*a^4*c^6*d^8*e^12 + 12298*a^5*c^5*d^6*e^14 - 1287*a^6*c^4*d^4*e^16)*x^3 + 8*(3003*c^10*d^17*e^3 + 4394937*a*c^9*d^15*e^5 + 13885683*a^2*c^8*d^13*e^7 + 508825*a^3*c^7*d^11*e^9 - 310375*a^4*c^6*d^9*e^11 + 123123*a^5*c^5*d^7*e^13 - 28743*a^6*c^4*d^5*e^15 + 3003*a^7*c^3*d^3*e^17)*x^2 - 2*(15015*c^10*d^18*e^2 - 144144*a*c^9*d^16*e^4 - 17075244*a^2*c^8*d^14*e^6 - 2878000*a^3*c^7*d^12*e^8 + 2579850*a^4*c^6*d^10*e^10 - 1567280*a^5*c^5*d^8*e^12 + 619476*a^6*c^4*d^6*e^14 - 144144*a^7*c^3*d^4*e^16 + 15015*a^8*c^2*d^2*e^18)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^8*d^8*e^4), 1/82575360*(45045*(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)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(4128768*c^10*d^10*e^10*x^9 + 45045*c^10*d^19*e - 435435*a*c^9*d^17*e^3 + 1885884*a^2*c^8*d^15*e^5 + 6983100*a^3*c^7*d^13*e^7 - 9035650*a^4*c^6*d^11*e^9 + 8003710*a^5*c^5*d^9*e^11 - 4813380*a^6*c^4*d^7*e^13 + 1885884*a^7*c^3*d^5*e^15 - 435435*a^8*c^2*d^3*e^17 + 45045*a^9*c*d*e^19 + 229376*(121*c^10*d^11*e^9 + 41*a*c^9*d^9*e^11)*x^8 + 14336*(5503*c^10*d^12*e^8 + 4482*a*c^9*d^10*e^10 + 383*a^2*c^8*d^8*e^12)*x^7 + 1024*(119055*c^10*d^13*e^7 + 182129*a*c^9*d^11*e^9 + 37489*a^2*c^8*d^9*e^11 + 15*a^3*c^7*d^7*e^13)*x^6 + 256*(424895*c^10*d^14*e^6 + 1157740*a*c^9*d^12*e^8 + 448938*a^2*c^8*d^10*e^10 + 620*a^3*c^7*d^8*e^12 - 65*a^4*c^6*d^6*e^14)*x^5 + 128*(419983*c^10*d^15*e^5 + 2149035*a*c^9*d^13*e^7 + 1490630*a^2*c^8*d^11*e^9 + 5830*a^3*c^7*d^9*e^11 - 1365*a^4*c^6*d^7*e^13 + 143*a^5*c^5*d^5*e^15)*x^4 + 16*(735993*c^10*d^16*e^4 + 9023498*a*c^9*d^14*e^6 + 11825815*a^2*c^8*d^12*e^8 + 132300*a^3*c^7*d^10*e^10 - 52585*a^4*c^6*d^8*e^12 + 12298*a^5*c^5*d^6*e^14 - 1287*a^6*c^4*d^4*e^16)*x^3 + 8*(3003*c^10*d^17*e^3 + 4394937*a*c^9*d^15*e^5 + 13885683*a^2*c^8*d^13*e^7 + 508825*a^3*c^7*d^11*e^9 - 310375*a^4*c^6*d^9*e^11 + 123123*a^5*c^5*d^7*e^13 - 28743*a^6*c^4*d^5*e^15 + 3003*a^7*c^3*d^3*e^17)*x^2 - 2*(15015*c^10*d^18*e^2 - 144144*a*c^9*d^16*e^4 - 17075244*a^2*c^8*d^14*e^6 - 2878000*a^3*c^7*d^12*e^8 + 2579850*a^4*c^6*d^10*e^10 - 1567280*a^5*c^5*d^8*e^12 + 619476*a^6*c^4*d^6*e^14 - 144144*a^7*c^3*d^4*e^16 + 15015*a^8*c^2*d^2*e^18)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^8*d^8*e^4)]","B",0
1932,1,1806,0,0.593139," ","integrate((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3465 \, {\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)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(229376 \, c^{9} d^{9} e^{9} x^{8} + 3465 \, c^{9} d^{17} e - 30030 \, a c^{8} d^{15} e^{3} + 115038 \, a^{2} c^{7} d^{13} e^{5} + 334602 \, a^{3} c^{6} d^{11} e^{7} - 360448 \, a^{4} c^{5} d^{9} e^{9} + 255222 \, a^{5} c^{4} d^{7} e^{11} - 115038 \, a^{6} c^{3} d^{5} e^{13} + 30030 \, a^{7} c^{2} d^{3} e^{15} - 3465 \, a^{8} c d e^{17} + 14336 \, {\left(91 \, c^{9} d^{10} e^{8} + 37 \, a c^{8} d^{8} e^{10}\right)} x^{7} + 1024 \, {\left(2955 \, c^{9} d^{11} e^{7} + 3008 \, a c^{8} d^{9} e^{9} + 309 \, a^{2} c^{7} d^{7} e^{11}\right)} x^{6} + 256 \, {\left(14075 \, c^{9} d^{12} e^{6} + 28695 \, a c^{8} d^{10} e^{8} + 7401 \, a^{2} c^{7} d^{8} e^{10} + 5 \, a^{3} c^{6} d^{6} e^{12}\right)} x^{5} + 128 \, {\left(17419 \, c^{9} d^{13} e^{5} + 71074 \, a c^{8} d^{11} e^{7} + 36864 \, a^{2} c^{7} d^{9} e^{9} + 94 \, a^{3} c^{6} d^{7} e^{11} - 11 \, a^{4} c^{5} d^{5} e^{13}\right)} x^{4} + 16 \, {\left(36765 \, c^{9} d^{14} e^{4} + 373583 \, a c^{8} d^{12} e^{6} + 390018 \, a^{2} c^{7} d^{10} e^{8} + 3198 \, a^{3} c^{6} d^{8} e^{10} - 847 \, a^{4} c^{5} d^{6} e^{12} + 99 \, a^{5} c^{4} d^{4} e^{14}\right)} x^{3} + 8 \, {\left(231 \, c^{9} d^{15} e^{3} + 219204 \, a c^{8} d^{13} e^{5} + 572739 \, a^{2} c^{7} d^{11} e^{7} + 16384 \, a^{3} c^{6} d^{9} e^{9} - 7491 \, a^{4} c^{5} d^{7} e^{11} + 1980 \, a^{5} c^{4} d^{5} e^{13} - 231 \, a^{6} c^{3} d^{3} e^{15}\right)} x^{2} - 2 \, {\left(1155 \, c^{9} d^{16} e^{2} - 9933 \, a c^{8} d^{14} e^{4} - 847017 \, a^{2} c^{7} d^{12} e^{6} - 115609 \, a^{3} c^{6} d^{10} e^{8} + 82841 \, a^{4} c^{5} d^{8} e^{10} - 37719 \, a^{5} c^{4} d^{6} e^{12} + 9933 \, a^{6} c^{3} d^{4} e^{14} - 1155 \, a^{7} c^{2} d^{2} e^{16}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8257536 \, c^{7} d^{7} e^{4}}, \frac{3465 \, {\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)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(229376 \, c^{9} d^{9} e^{9} x^{8} + 3465 \, c^{9} d^{17} e - 30030 \, a c^{8} d^{15} e^{3} + 115038 \, a^{2} c^{7} d^{13} e^{5} + 334602 \, a^{3} c^{6} d^{11} e^{7} - 360448 \, a^{4} c^{5} d^{9} e^{9} + 255222 \, a^{5} c^{4} d^{7} e^{11} - 115038 \, a^{6} c^{3} d^{5} e^{13} + 30030 \, a^{7} c^{2} d^{3} e^{15} - 3465 \, a^{8} c d e^{17} + 14336 \, {\left(91 \, c^{9} d^{10} e^{8} + 37 \, a c^{8} d^{8} e^{10}\right)} x^{7} + 1024 \, {\left(2955 \, c^{9} d^{11} e^{7} + 3008 \, a c^{8} d^{9} e^{9} + 309 \, a^{2} c^{7} d^{7} e^{11}\right)} x^{6} + 256 \, {\left(14075 \, c^{9} d^{12} e^{6} + 28695 \, a c^{8} d^{10} e^{8} + 7401 \, a^{2} c^{7} d^{8} e^{10} + 5 \, a^{3} c^{6} d^{6} e^{12}\right)} x^{5} + 128 \, {\left(17419 \, c^{9} d^{13} e^{5} + 71074 \, a c^{8} d^{11} e^{7} + 36864 \, a^{2} c^{7} d^{9} e^{9} + 94 \, a^{3} c^{6} d^{7} e^{11} - 11 \, a^{4} c^{5} d^{5} e^{13}\right)} x^{4} + 16 \, {\left(36765 \, c^{9} d^{14} e^{4} + 373583 \, a c^{8} d^{12} e^{6} + 390018 \, a^{2} c^{7} d^{10} e^{8} + 3198 \, a^{3} c^{6} d^{8} e^{10} - 847 \, a^{4} c^{5} d^{6} e^{12} + 99 \, a^{5} c^{4} d^{4} e^{14}\right)} x^{3} + 8 \, {\left(231 \, c^{9} d^{15} e^{3} + 219204 \, a c^{8} d^{13} e^{5} + 572739 \, a^{2} c^{7} d^{11} e^{7} + 16384 \, a^{3} c^{6} d^{9} e^{9} - 7491 \, a^{4} c^{5} d^{7} e^{11} + 1980 \, a^{5} c^{4} d^{5} e^{13} - 231 \, a^{6} c^{3} d^{3} e^{15}\right)} x^{2} - 2 \, {\left(1155 \, c^{9} d^{16} e^{2} - 9933 \, a c^{8} d^{14} e^{4} - 847017 \, a^{2} c^{7} d^{12} e^{6} - 115609 \, a^{3} c^{6} d^{10} e^{8} + 82841 \, a^{4} c^{5} d^{8} e^{10} - 37719 \, a^{5} c^{4} d^{6} e^{12} + 9933 \, a^{6} c^{3} d^{4} e^{14} - 1155 \, a^{7} c^{2} d^{2} e^{16}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{4128768 \, c^{7} d^{7} e^{4}}\right]"," ",0,"[1/8257536*(3465*(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)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(229376*c^9*d^9*e^9*x^8 + 3465*c^9*d^17*e - 30030*a*c^8*d^15*e^3 + 115038*a^2*c^7*d^13*e^5 + 334602*a^3*c^6*d^11*e^7 - 360448*a^4*c^5*d^9*e^9 + 255222*a^5*c^4*d^7*e^11 - 115038*a^6*c^3*d^5*e^13 + 30030*a^7*c^2*d^3*e^15 - 3465*a^8*c*d*e^17 + 14336*(91*c^9*d^10*e^8 + 37*a*c^8*d^8*e^10)*x^7 + 1024*(2955*c^9*d^11*e^7 + 3008*a*c^8*d^9*e^9 + 309*a^2*c^7*d^7*e^11)*x^6 + 256*(14075*c^9*d^12*e^6 + 28695*a*c^8*d^10*e^8 + 7401*a^2*c^7*d^8*e^10 + 5*a^3*c^6*d^6*e^12)*x^5 + 128*(17419*c^9*d^13*e^5 + 71074*a*c^8*d^11*e^7 + 36864*a^2*c^7*d^9*e^9 + 94*a^3*c^6*d^7*e^11 - 11*a^4*c^5*d^5*e^13)*x^4 + 16*(36765*c^9*d^14*e^4 + 373583*a*c^8*d^12*e^6 + 390018*a^2*c^7*d^10*e^8 + 3198*a^3*c^6*d^8*e^10 - 847*a^4*c^5*d^6*e^12 + 99*a^5*c^4*d^4*e^14)*x^3 + 8*(231*c^9*d^15*e^3 + 219204*a*c^8*d^13*e^5 + 572739*a^2*c^7*d^11*e^7 + 16384*a^3*c^6*d^9*e^9 - 7491*a^4*c^5*d^7*e^11 + 1980*a^5*c^4*d^5*e^13 - 231*a^6*c^3*d^3*e^15)*x^2 - 2*(1155*c^9*d^16*e^2 - 9933*a*c^8*d^14*e^4 - 847017*a^2*c^7*d^12*e^6 - 115609*a^3*c^6*d^10*e^8 + 82841*a^4*c^5*d^8*e^10 - 37719*a^5*c^4*d^6*e^12 + 9933*a^6*c^3*d^4*e^14 - 1155*a^7*c^2*d^2*e^16)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^7*d^7*e^4), 1/4128768*(3465*(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)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(229376*c^9*d^9*e^9*x^8 + 3465*c^9*d^17*e - 30030*a*c^8*d^15*e^3 + 115038*a^2*c^7*d^13*e^5 + 334602*a^3*c^6*d^11*e^7 - 360448*a^4*c^5*d^9*e^9 + 255222*a^5*c^4*d^7*e^11 - 115038*a^6*c^3*d^5*e^13 + 30030*a^7*c^2*d^3*e^15 - 3465*a^8*c*d*e^17 + 14336*(91*c^9*d^10*e^8 + 37*a*c^8*d^8*e^10)*x^7 + 1024*(2955*c^9*d^11*e^7 + 3008*a*c^8*d^9*e^9 + 309*a^2*c^7*d^7*e^11)*x^6 + 256*(14075*c^9*d^12*e^6 + 28695*a*c^8*d^10*e^8 + 7401*a^2*c^7*d^8*e^10 + 5*a^3*c^6*d^6*e^12)*x^5 + 128*(17419*c^9*d^13*e^5 + 71074*a*c^8*d^11*e^7 + 36864*a^2*c^7*d^9*e^9 + 94*a^3*c^6*d^7*e^11 - 11*a^4*c^5*d^5*e^13)*x^4 + 16*(36765*c^9*d^14*e^4 + 373583*a*c^8*d^12*e^6 + 390018*a^2*c^7*d^10*e^8 + 3198*a^3*c^6*d^8*e^10 - 847*a^4*c^5*d^6*e^12 + 99*a^5*c^4*d^4*e^14)*x^3 + 8*(231*c^9*d^15*e^3 + 219204*a*c^8*d^13*e^5 + 572739*a^2*c^7*d^11*e^7 + 16384*a^3*c^6*d^9*e^9 - 7491*a^4*c^5*d^7*e^11 + 1980*a^5*c^4*d^5*e^13 - 231*a^6*c^3*d^3*e^15)*x^2 - 2*(1155*c^9*d^16*e^2 - 9933*a*c^8*d^14*e^4 - 847017*a^2*c^7*d^12*e^6 - 115609*a^3*c^6*d^10*e^8 + 82841*a^4*c^5*d^8*e^10 - 37719*a^5*c^4*d^6*e^12 + 9933*a^6*c^3*d^4*e^14 - 1155*a^7*c^2*d^2*e^16)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^7*d^7*e^4)]","B",0
1933,1,1520,0,0.574447," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\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)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(14336 \, c^{8} d^{8} e^{8} x^{7} + 315 \, c^{8} d^{15} e - 2415 \, a c^{7} d^{13} e^{3} + 8043 \, a^{2} c^{6} d^{11} e^{5} + 17609 \, a^{3} c^{5} d^{9} e^{7} - 15159 \, a^{4} c^{4} d^{7} e^{9} + 8043 \, a^{5} c^{3} d^{5} e^{11} - 2415 \, a^{6} c^{2} d^{3} e^{13} + 315 \, a^{7} c d e^{15} + 1024 \, {\left(65 \, c^{8} d^{9} e^{7} + 33 \, a c^{7} d^{7} e^{9}\right)} x^{6} + 768 \, {\left(155 \, c^{8} d^{10} e^{6} + 210 \, a c^{7} d^{8} e^{8} + 27 \, a^{2} c^{6} d^{6} e^{10}\right)} x^{5} + 128 \, {\left(769 \, c^{8} d^{11} e^{5} + 2343 \, a c^{7} d^{9} e^{7} + 807 \, a^{2} c^{6} d^{7} e^{9} + a^{3} c^{5} d^{5} e^{11}\right)} x^{4} + 16 \, {\left(2039 \, c^{8} d^{12} e^{4} + 16452 \, a c^{7} d^{10} e^{6} + 12810 \, a^{2} c^{6} d^{8} e^{8} + 68 \, a^{3} c^{5} d^{6} e^{10} - 9 \, a^{4} c^{4} d^{4} e^{12}\right)} x^{3} + 24 \, {\left(7 \, c^{8} d^{13} e^{3} + 4043 \, a c^{7} d^{11} e^{5} + 8366 \, a^{2} c^{6} d^{9} e^{7} + 174 \, a^{3} c^{5} d^{7} e^{9} - 53 \, a^{4} c^{4} d^{5} e^{11} + 7 \, a^{5} c^{3} d^{3} e^{13}\right)} x^{2} - 2 \, {\left(105 \, c^{8} d^{14} e^{2} - 798 \, a c^{7} d^{12} e^{4} - 46521 \, a^{2} c^{6} d^{10} e^{6} - 4900 \, a^{3} c^{5} d^{8} e^{8} + 2631 \, a^{4} c^{4} d^{6} e^{10} - 798 \, a^{5} c^{3} d^{4} e^{12} + 105 \, a^{6} c^{2} d^{2} e^{14}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{458752 \, c^{6} d^{6} e^{4}}, \frac{315 \, {\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)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(14336 \, c^{8} d^{8} e^{8} x^{7} + 315 \, c^{8} d^{15} e - 2415 \, a c^{7} d^{13} e^{3} + 8043 \, a^{2} c^{6} d^{11} e^{5} + 17609 \, a^{3} c^{5} d^{9} e^{7} - 15159 \, a^{4} c^{4} d^{7} e^{9} + 8043 \, a^{5} c^{3} d^{5} e^{11} - 2415 \, a^{6} c^{2} d^{3} e^{13} + 315 \, a^{7} c d e^{15} + 1024 \, {\left(65 \, c^{8} d^{9} e^{7} + 33 \, a c^{7} d^{7} e^{9}\right)} x^{6} + 768 \, {\left(155 \, c^{8} d^{10} e^{6} + 210 \, a c^{7} d^{8} e^{8} + 27 \, a^{2} c^{6} d^{6} e^{10}\right)} x^{5} + 128 \, {\left(769 \, c^{8} d^{11} e^{5} + 2343 \, a c^{7} d^{9} e^{7} + 807 \, a^{2} c^{6} d^{7} e^{9} + a^{3} c^{5} d^{5} e^{11}\right)} x^{4} + 16 \, {\left(2039 \, c^{8} d^{12} e^{4} + 16452 \, a c^{7} d^{10} e^{6} + 12810 \, a^{2} c^{6} d^{8} e^{8} + 68 \, a^{3} c^{5} d^{6} e^{10} - 9 \, a^{4} c^{4} d^{4} e^{12}\right)} x^{3} + 24 \, {\left(7 \, c^{8} d^{13} e^{3} + 4043 \, a c^{7} d^{11} e^{5} + 8366 \, a^{2} c^{6} d^{9} e^{7} + 174 \, a^{3} c^{5} d^{7} e^{9} - 53 \, a^{4} c^{4} d^{5} e^{11} + 7 \, a^{5} c^{3} d^{3} e^{13}\right)} x^{2} - 2 \, {\left(105 \, c^{8} d^{14} e^{2} - 798 \, a c^{7} d^{12} e^{4} - 46521 \, a^{2} c^{6} d^{10} e^{6} - 4900 \, a^{3} c^{5} d^{8} e^{8} + 2631 \, a^{4} c^{4} d^{6} e^{10} - 798 \, a^{5} c^{3} d^{4} e^{12} + 105 \, a^{6} c^{2} d^{2} e^{14}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{229376 \, c^{6} d^{6} e^{4}}\right]"," ",0,"[1/458752*(315*(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)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(14336*c^8*d^8*e^8*x^7 + 315*c^8*d^15*e - 2415*a*c^7*d^13*e^3 + 8043*a^2*c^6*d^11*e^5 + 17609*a^3*c^5*d^9*e^7 - 15159*a^4*c^4*d^7*e^9 + 8043*a^5*c^3*d^5*e^11 - 2415*a^6*c^2*d^3*e^13 + 315*a^7*c*d*e^15 + 1024*(65*c^8*d^9*e^7 + 33*a*c^7*d^7*e^9)*x^6 + 768*(155*c^8*d^10*e^6 + 210*a*c^7*d^8*e^8 + 27*a^2*c^6*d^6*e^10)*x^5 + 128*(769*c^8*d^11*e^5 + 2343*a*c^7*d^9*e^7 + 807*a^2*c^6*d^7*e^9 + a^3*c^5*d^5*e^11)*x^4 + 16*(2039*c^8*d^12*e^4 + 16452*a*c^7*d^10*e^6 + 12810*a^2*c^6*d^8*e^8 + 68*a^3*c^5*d^6*e^10 - 9*a^4*c^4*d^4*e^12)*x^3 + 24*(7*c^8*d^13*e^3 + 4043*a*c^7*d^11*e^5 + 8366*a^2*c^6*d^9*e^7 + 174*a^3*c^5*d^7*e^9 - 53*a^4*c^4*d^5*e^11 + 7*a^5*c^3*d^3*e^13)*x^2 - 2*(105*c^8*d^14*e^2 - 798*a*c^7*d^12*e^4 - 46521*a^2*c^6*d^10*e^6 - 4900*a^3*c^5*d^8*e^8 + 2631*a^4*c^4*d^6*e^10 - 798*a^5*c^3*d^4*e^12 + 105*a^6*c^2*d^2*e^14)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^6*d^6*e^4), 1/229376*(315*(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)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(14336*c^8*d^8*e^8*x^7 + 315*c^8*d^15*e - 2415*a*c^7*d^13*e^3 + 8043*a^2*c^6*d^11*e^5 + 17609*a^3*c^5*d^9*e^7 - 15159*a^4*c^4*d^7*e^9 + 8043*a^5*c^3*d^5*e^11 - 2415*a^6*c^2*d^3*e^13 + 315*a^7*c*d*e^15 + 1024*(65*c^8*d^9*e^7 + 33*a*c^7*d^7*e^9)*x^6 + 768*(155*c^8*d^10*e^6 + 210*a*c^7*d^8*e^8 + 27*a^2*c^6*d^6*e^10)*x^5 + 128*(769*c^8*d^11*e^5 + 2343*a*c^7*d^9*e^7 + 807*a^2*c^6*d^7*e^9 + a^3*c^5*d^5*e^11)*x^4 + 16*(2039*c^8*d^12*e^4 + 16452*a*c^7*d^10*e^6 + 12810*a^2*c^6*d^8*e^8 + 68*a^3*c^5*d^6*e^10 - 9*a^4*c^4*d^4*e^12)*x^3 + 24*(7*c^8*d^13*e^3 + 4043*a*c^7*d^11*e^5 + 8366*a^2*c^6*d^9*e^7 + 174*a^3*c^5*d^7*e^9 - 53*a^4*c^4*d^5*e^11 + 7*a^5*c^3*d^3*e^13)*x^2 - 2*(105*c^8*d^14*e^2 - 798*a*c^7*d^12*e^4 - 46521*a^2*c^6*d^10*e^6 - 4900*a^3*c^5*d^8*e^8 + 2631*a^4*c^4*d^6*e^10 - 798*a^5*c^3*d^4*e^12 + 105*a^6*c^2*d^2*e^14)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^6*d^6*e^4)]","B",0
1934,1,1270,0,0.534117," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\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)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(3072 \, c^{7} d^{7} e^{7} x^{6} + 105 \, c^{7} d^{13} e - 700 \, a c^{6} d^{11} e^{3} + 1981 \, a^{2} c^{5} d^{9} e^{5} + 3072 \, a^{3} c^{4} d^{7} e^{7} - 1981 \, a^{4} c^{3} d^{5} e^{9} + 700 \, a^{5} c^{2} d^{3} e^{11} - 105 \, a^{6} c d e^{13} + 256 \, {\left(43 \, c^{7} d^{8} e^{6} + 29 \, a c^{6} d^{6} e^{8}\right)} x^{5} + 128 \, {\left(107 \, c^{7} d^{9} e^{5} + 216 \, a c^{6} d^{7} e^{7} + 37 \, a^{2} c^{5} d^{5} e^{9}\right)} x^{4} + 16 \, {\left(381 \, c^{7} d^{10} e^{4} + 2281 \, a c^{6} d^{8} e^{6} + 1175 \, a^{2} c^{5} d^{6} e^{8} + 3 \, a^{3} c^{4} d^{4} e^{10}\right)} x^{3} + 8 \, {\left(7 \, c^{7} d^{11} e^{3} + 2258 \, a c^{6} d^{9} e^{5} + 3456 \, a^{2} c^{5} d^{7} e^{7} + 46 \, a^{3} c^{4} d^{5} e^{9} - 7 \, a^{4} c^{3} d^{3} e^{11}\right)} x^{2} - 2 \, {\left(35 \, c^{7} d^{12} e^{2} - 231 \, a c^{6} d^{10} e^{4} - 8570 \, a^{2} c^{5} d^{8} e^{6} - 646 \, a^{3} c^{4} d^{6} e^{8} + 231 \, a^{4} c^{3} d^{4} e^{10} - 35 \, a^{5} c^{2} d^{2} e^{12}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{86016 \, c^{5} d^{5} e^{4}}, \frac{105 \, {\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)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(3072 \, c^{7} d^{7} e^{7} x^{6} + 105 \, c^{7} d^{13} e - 700 \, a c^{6} d^{11} e^{3} + 1981 \, a^{2} c^{5} d^{9} e^{5} + 3072 \, a^{3} c^{4} d^{7} e^{7} - 1981 \, a^{4} c^{3} d^{5} e^{9} + 700 \, a^{5} c^{2} d^{3} e^{11} - 105 \, a^{6} c d e^{13} + 256 \, {\left(43 \, c^{7} d^{8} e^{6} + 29 \, a c^{6} d^{6} e^{8}\right)} x^{5} + 128 \, {\left(107 \, c^{7} d^{9} e^{5} + 216 \, a c^{6} d^{7} e^{7} + 37 \, a^{2} c^{5} d^{5} e^{9}\right)} x^{4} + 16 \, {\left(381 \, c^{7} d^{10} e^{4} + 2281 \, a c^{6} d^{8} e^{6} + 1175 \, a^{2} c^{5} d^{6} e^{8} + 3 \, a^{3} c^{4} d^{4} e^{10}\right)} x^{3} + 8 \, {\left(7 \, c^{7} d^{11} e^{3} + 2258 \, a c^{6} d^{9} e^{5} + 3456 \, a^{2} c^{5} d^{7} e^{7} + 46 \, a^{3} c^{4} d^{5} e^{9} - 7 \, a^{4} c^{3} d^{3} e^{11}\right)} x^{2} - 2 \, {\left(35 \, c^{7} d^{12} e^{2} - 231 \, a c^{6} d^{10} e^{4} - 8570 \, a^{2} c^{5} d^{8} e^{6} - 646 \, a^{3} c^{4} d^{6} e^{8} + 231 \, a^{4} c^{3} d^{4} e^{10} - 35 \, a^{5} c^{2} d^{2} e^{12}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{43008 \, c^{5} d^{5} e^{4}}\right]"," ",0,"[1/86016*(105*(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)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(3072*c^7*d^7*e^7*x^6 + 105*c^7*d^13*e - 700*a*c^6*d^11*e^3 + 1981*a^2*c^5*d^9*e^5 + 3072*a^3*c^4*d^7*e^7 - 1981*a^4*c^3*d^5*e^9 + 700*a^5*c^2*d^3*e^11 - 105*a^6*c*d*e^13 + 256*(43*c^7*d^8*e^6 + 29*a*c^6*d^6*e^8)*x^5 + 128*(107*c^7*d^9*e^5 + 216*a*c^6*d^7*e^7 + 37*a^2*c^5*d^5*e^9)*x^4 + 16*(381*c^7*d^10*e^4 + 2281*a*c^6*d^8*e^6 + 1175*a^2*c^5*d^6*e^8 + 3*a^3*c^4*d^4*e^10)*x^3 + 8*(7*c^7*d^11*e^3 + 2258*a*c^6*d^9*e^5 + 3456*a^2*c^5*d^7*e^7 + 46*a^3*c^4*d^5*e^9 - 7*a^4*c^3*d^3*e^11)*x^2 - 2*(35*c^7*d^12*e^2 - 231*a*c^6*d^10*e^4 - 8570*a^2*c^5*d^8*e^6 - 646*a^3*c^4*d^6*e^8 + 231*a^4*c^3*d^4*e^10 - 35*a^5*c^2*d^2*e^12)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*e^4), 1/43008*(105*(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)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(3072*c^7*d^7*e^7*x^6 + 105*c^7*d^13*e - 700*a*c^6*d^11*e^3 + 1981*a^2*c^5*d^9*e^5 + 3072*a^3*c^4*d^7*e^7 - 1981*a^4*c^3*d^5*e^9 + 700*a^5*c^2*d^3*e^11 - 105*a^6*c*d*e^13 + 256*(43*c^7*d^8*e^6 + 29*a*c^6*d^6*e^8)*x^5 + 128*(107*c^7*d^9*e^5 + 216*a*c^6*d^7*e^7 + 37*a^2*c^5*d^5*e^9)*x^4 + 16*(381*c^7*d^10*e^4 + 2281*a*c^6*d^8*e^6 + 1175*a^2*c^5*d^6*e^8 + 3*a^3*c^4*d^4*e^10)*x^3 + 8*(7*c^7*d^11*e^3 + 2258*a*c^6*d^9*e^5 + 3456*a^2*c^5*d^7*e^7 + 46*a^3*c^4*d^5*e^9 - 7*a^4*c^3*d^3*e^11)*x^2 - 2*(35*c^7*d^12*e^2 - 231*a*c^6*d^10*e^4 - 8570*a^2*c^5*d^8*e^6 - 646*a^3*c^4*d^6*e^8 + 231*a^4*c^3*d^4*e^10 - 35*a^5*c^2*d^2*e^12)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*e^4)]","A",0
1935,1,1034,0,0.513432," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\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 d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(256 \, c^{6} d^{6} e^{6} x^{5} + 15 \, c^{6} d^{11} e - 85 \, a c^{5} d^{9} e^{3} + 198 \, a^{2} c^{4} d^{7} e^{5} + 198 \, a^{3} c^{3} d^{5} e^{7} - 85 \, a^{4} c^{2} d^{3} e^{9} + 15 \, a^{5} c d e^{11} + 640 \, {\left(c^{6} d^{7} e^{5} + a c^{5} d^{5} e^{7}\right)} x^{4} + 16 \, {\left(27 \, c^{6} d^{8} e^{4} + 106 \, a c^{5} d^{6} e^{6} + 27 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{3} + 8 \, {\left(c^{6} d^{9} e^{3} + 159 \, a c^{5} d^{7} e^{5} + 159 \, a^{2} c^{4} d^{5} e^{7} + a^{3} c^{3} d^{3} e^{9}\right)} x^{2} - 2 \, {\left(5 \, c^{6} d^{10} e^{2} - 28 \, a c^{5} d^{8} e^{4} - 594 \, a^{2} c^{4} d^{6} e^{6} - 28 \, a^{3} c^{3} d^{4} e^{8} + 5 \, a^{4} c^{2} d^{2} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{6144 \, c^{4} d^{4} e^{4}}, \frac{15 \, {\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 d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(256 \, c^{6} d^{6} e^{6} x^{5} + 15 \, c^{6} d^{11} e - 85 \, a c^{5} d^{9} e^{3} + 198 \, a^{2} c^{4} d^{7} e^{5} + 198 \, a^{3} c^{3} d^{5} e^{7} - 85 \, a^{4} c^{2} d^{3} e^{9} + 15 \, a^{5} c d e^{11} + 640 \, {\left(c^{6} d^{7} e^{5} + a c^{5} d^{5} e^{7}\right)} x^{4} + 16 \, {\left(27 \, c^{6} d^{8} e^{4} + 106 \, a c^{5} d^{6} e^{6} + 27 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{3} + 8 \, {\left(c^{6} d^{9} e^{3} + 159 \, a c^{5} d^{7} e^{5} + 159 \, a^{2} c^{4} d^{5} e^{7} + a^{3} c^{3} d^{3} e^{9}\right)} x^{2} - 2 \, {\left(5 \, c^{6} d^{10} e^{2} - 28 \, a c^{5} d^{8} e^{4} - 594 \, a^{2} c^{4} d^{6} e^{6} - 28 \, a^{3} c^{3} d^{4} e^{8} + 5 \, a^{4} c^{2} d^{2} e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3072 \, c^{4} d^{4} e^{4}}\right]"," ",0,"[1/6144*(15*(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*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(256*c^6*d^6*e^6*x^5 + 15*c^6*d^11*e - 85*a*c^5*d^9*e^3 + 198*a^2*c^4*d^7*e^5 + 198*a^3*c^3*d^5*e^7 - 85*a^4*c^2*d^3*e^9 + 15*a^5*c*d*e^11 + 640*(c^6*d^7*e^5 + a*c^5*d^5*e^7)*x^4 + 16*(27*c^6*d^8*e^4 + 106*a*c^5*d^6*e^6 + 27*a^2*c^4*d^4*e^8)*x^3 + 8*(c^6*d^9*e^3 + 159*a*c^5*d^7*e^5 + 159*a^2*c^4*d^5*e^7 + a^3*c^3*d^3*e^9)*x^2 - 2*(5*c^6*d^10*e^2 - 28*a*c^5*d^8*e^4 - 594*a^2*c^4*d^6*e^6 - 28*a^3*c^3*d^4*e^8 + 5*a^4*c^2*d^2*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^4), 1/3072*(15*(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*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(256*c^6*d^6*e^6*x^5 + 15*c^6*d^11*e - 85*a*c^5*d^9*e^3 + 198*a^2*c^4*d^7*e^5 + 198*a^3*c^3*d^5*e^7 - 85*a^4*c^2*d^3*e^9 + 15*a^5*c*d*e^11 + 640*(c^6*d^7*e^5 + a*c^5*d^5*e^7)*x^4 + 16*(27*c^6*d^8*e^4 + 106*a*c^5*d^6*e^6 + 27*a^2*c^4*d^4*e^8)*x^3 + 8*(c^6*d^9*e^3 + 159*a*c^5*d^7*e^5 + 159*a^2*c^4*d^5*e^7 + a^3*c^3*d^3*e^9)*x^2 - 2*(5*c^6*d^10*e^2 - 28*a*c^5*d^8*e^4 - 594*a^2*c^4*d^6*e^6 - 28*a^3*c^3*d^4*e^8 + 5*a^4*c^2*d^2*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e^4)]","A",0
1936,1,844,0,0.472035," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{15 \, {\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 e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(128 \, c^{5} d^{5} e^{5} x^{4} + 15 \, c^{5} d^{9} e - 70 \, a c^{4} d^{7} e^{3} + 128 \, a^{2} c^{3} d^{5} e^{5} + 70 \, a^{3} c^{2} d^{3} e^{7} - 15 \, a^{4} c d e^{9} + 16 \, {\left(11 \, c^{5} d^{6} e^{4} + 21 \, a c^{4} d^{4} e^{6}\right)} x^{3} + 8 \, {\left(c^{5} d^{7} e^{3} + 64 \, a c^{4} d^{5} e^{5} + 31 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{2} - 2 \, {\left(5 \, c^{5} d^{8} e^{2} - 23 \, a c^{4} d^{6} e^{4} - 233 \, a^{2} c^{3} d^{4} e^{6} - 5 \, a^{3} c^{2} d^{2} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{2560 \, c^{3} d^{3} e^{4}}, \frac{15 \, {\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 e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(128 \, c^{5} d^{5} e^{5} x^{4} + 15 \, c^{5} d^{9} e - 70 \, a c^{4} d^{7} e^{3} + 128 \, a^{2} c^{3} d^{5} e^{5} + 70 \, a^{3} c^{2} d^{3} e^{7} - 15 \, a^{4} c d e^{9} + 16 \, {\left(11 \, c^{5} d^{6} e^{4} + 21 \, a c^{4} d^{4} e^{6}\right)} x^{3} + 8 \, {\left(c^{5} d^{7} e^{3} + 64 \, a c^{4} d^{5} e^{5} + 31 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{2} - 2 \, {\left(5 \, c^{5} d^{8} e^{2} - 23 \, a c^{4} d^{6} e^{4} - 233 \, a^{2} c^{3} d^{4} e^{6} - 5 \, a^{3} c^{2} d^{2} e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{1280 \, c^{3} d^{3} e^{4}}\right]"," ",0,"[1/2560*(15*(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*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(128*c^5*d^5*e^5*x^4 + 15*c^5*d^9*e - 70*a*c^4*d^7*e^3 + 128*a^2*c^3*d^5*e^5 + 70*a^3*c^2*d^3*e^7 - 15*a^4*c*d*e^9 + 16*(11*c^5*d^6*e^4 + 21*a*c^4*d^4*e^6)*x^3 + 8*(c^5*d^7*e^3 + 64*a*c^4*d^5*e^5 + 31*a^2*c^3*d^3*e^7)*x^2 - 2*(5*c^5*d^8*e^2 - 23*a*c^4*d^6*e^4 - 233*a^2*c^3*d^4*e^6 - 5*a^3*c^2*d^2*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^4), 1/1280*(15*(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*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(128*c^5*d^5*e^5*x^4 + 15*c^5*d^9*e - 70*a*c^4*d^7*e^3 + 128*a^2*c^3*d^5*e^5 + 70*a^3*c^2*d^3*e^7 - 15*a^4*c*d*e^9 + 16*(11*c^5*d^6*e^4 + 21*a*c^4*d^4*e^6)*x^3 + 8*(c^5*d^7*e^3 + 64*a*c^4*d^5*e^5 + 31*a^2*c^3*d^3*e^7)*x^2 - 2*(5*c^5*d^8*e^2 - 23*a*c^4*d^6*e^4 - 233*a^2*c^3*d^4*e^6 - 5*a^3*c^2*d^2*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e^4)]","A",0
1937,1,672,0,0.454260," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\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 e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} + 15 \, c^{4} d^{7} e - 55 \, a c^{3} d^{5} e^{3} + 73 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7} + 8 \, {\left(c^{4} d^{5} e^{3} + 17 \, a c^{3} d^{3} e^{5}\right)} x^{2} - 2 \, {\left(5 \, c^{4} d^{6} e^{2} - 18 \, a c^{3} d^{4} e^{4} - 59 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{768 \, c^{2} d^{2} e^{4}}, \frac{15 \, {\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 e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(48 \, c^{4} d^{4} e^{4} x^{3} + 15 \, c^{4} d^{7} e - 55 \, a c^{3} d^{5} e^{3} + 73 \, a^{2} c^{2} d^{3} e^{5} + 15 \, a^{3} c d e^{7} + 8 \, {\left(c^{4} d^{5} e^{3} + 17 \, a c^{3} d^{3} e^{5}\right)} x^{2} - 2 \, {\left(5 \, c^{4} d^{6} e^{2} - 18 \, a c^{3} d^{4} e^{4} - 59 \, a^{2} c^{2} d^{2} e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{384 \, c^{2} d^{2} e^{4}}\right]"," ",0,"[1/768*(15*(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*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(48*c^4*d^4*e^4*x^3 + 15*c^4*d^7*e - 55*a*c^3*d^5*e^3 + 73*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7 + 8*(c^4*d^5*e^3 + 17*a*c^3*d^3*e^5)*x^2 - 2*(5*c^4*d^6*e^2 - 18*a*c^3*d^4*e^4 - 59*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^4), 1/384*(15*(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*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(48*c^4*d^4*e^4*x^3 + 15*c^4*d^7*e - 55*a*c^3*d^5*e^3 + 73*a^2*c^2*d^3*e^5 + 15*a^3*c*d*e^7 + 8*(c^4*d^5*e^3 + 17*a*c^3*d^3*e^5)*x^2 - 2*(5*c^4*d^6*e^2 - 18*a*c^3*d^4*e^4 - 59*a^2*c^2*d^2*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*e^4)]","A",0
1938,1,534,0,0.472288," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\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} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} + 15 \, c^{3} d^{5} e - 40 \, a c^{2} d^{3} e^{3} + 33 \, a^{2} c d e^{5} - 2 \, {\left(5 \, c^{3} d^{4} e^{2} - 13 \, a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, c d e^{4}}, \frac{15 \, {\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} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) + 2 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} + 15 \, c^{3} d^{5} e - 40 \, a c^{2} d^{3} e^{3} + 33 \, a^{2} c d e^{5} - 2 \, {\left(5 \, c^{3} d^{4} e^{2} - 13 \, a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, c d e^{4}}\right]"," ",0,"[1/96*(15*(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)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(8*c^3*d^3*e^3*x^2 + 15*c^3*d^5*e - 40*a*c^2*d^3*e^3 + 33*a^2*c*d*e^5 - 2*(5*c^3*d^4*e^2 - 13*a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^4), 1/48*(15*(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)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) + 2*(8*c^3*d^3*e^3*x^2 + 15*c^3*d^5*e - 40*a*c^2*d^3*e^3 + 33*a^2*c*d*e^5 - 2*(5*c^3*d^4*e^2 - 13*a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c*d*e^4)]","A",0
1939,1,554,0,0.646595," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{5} - 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e - 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{\frac{c d}{e}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(2 \, c^{2} d^{2} e^{2} x^{2} - 15 \, c^{2} d^{4} + 25 \, a c d^{2} e^{2} - 8 \, a^{2} e^{4} - {\left(5 \, c^{2} d^{3} e - 9 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, {\left(e^{4} x + d e^{3}\right)}}, -\frac{15 \, {\left(c^{2} d^{5} - 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e - 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{-\frac{c d}{e}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, c^{2} d^{2} e^{2} x^{2} - 15 \, c^{2} d^{4} + 25 \, a c d^{2} e^{2} - 8 \, a^{2} e^{4} - {\left(5 \, c^{2} d^{3} e - 9 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, {\left(e^{4} x + d e^{3}\right)}}\right]"," ",0,"[1/16*(15*(c^2*d^5 - 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e - 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(c*d/e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(2*c^2*d^2*e^2*x^2 - 15*c^2*d^4 + 25*a*c*d^2*e^2 - 8*a^2*e^4 - (5*c^2*d^3*e - 9*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(e^4*x + d*e^3), -1/8*(15*(c^2*d^5 - 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e - 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(-c*d/e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) - 2*(2*c^2*d^2*e^2*x^2 - 15*c^2*d^4 + 25*a*c*d^2*e^2 - 8*a^2*e^4 - (5*c^2*d^3*e - 9*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(e^4*x + d*e^3)]","A",0
1940,1,594,0,0.846063," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{5} - a c d^{3} e^{2} + {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{4} e - a c d^{2} e^{3}\right)} x\right)} \sqrt{\frac{c d}{e}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(3 \, c^{2} d^{2} e^{2} x^{2} + 15 \, c^{2} d^{4} - 10 \, a c d^{2} e^{2} - 2 \, a^{2} e^{4} + 2 \, {\left(10 \, c^{2} d^{3} e - 7 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{12 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}, \frac{15 \, {\left(c^{2} d^{5} - a c d^{3} e^{2} + {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{4} e - a c d^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c d}{e}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) + 2 \, {\left(3 \, c^{2} d^{2} e^{2} x^{2} + 15 \, c^{2} d^{4} - 10 \, a c d^{2} e^{2} - 2 \, a^{2} e^{4} + 2 \, {\left(10 \, c^{2} d^{3} e - 7 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{6 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}\right]"," ",0,"[1/12*(15*(c^2*d^5 - a*c*d^3*e^2 + (c^2*d^3*e^2 - a*c*d*e^4)*x^2 + 2*(c^2*d^4*e - a*c*d^2*e^3)*x)*sqrt(c*d/e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(3*c^2*d^2*e^2*x^2 + 15*c^2*d^4 - 10*a*c*d^2*e^2 - 2*a^2*e^4 + 2*(10*c^2*d^3*e - 7*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3), 1/6*(15*(c^2*d^5 - a*c*d^3*e^2 + (c^2*d^3*e^2 - a*c*d*e^4)*x^2 + 2*(c^2*d^4*e - a*c*d^2*e^3)*x)*sqrt(-c*d/e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) + 2*(3*c^2*d^2*e^2*x^2 + 15*c^2*d^4 - 10*a*c*d^2*e^2 - 2*a^2*e^4 + 2*(10*c^2*d^3*e - 7*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)]","A",0
1941,1,578,0,1.834355," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^6,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{\frac{c d}{e}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, {\left(2 \, c d e^{2} x + c d^{2} e + a e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{c d}{e}} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) - 4 \, {\left(23 \, c^{2} d^{2} e^{2} x^{2} + 15 \, c^{2} d^{4} + 5 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} + {\left(35 \, c^{2} d^{3} e + 11 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{30 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}, -\frac{15 \, {\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{-\frac{c d}{e}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{c d}{e}}}{2 \, {\left(c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x\right)}}\right) + 2 \, {\left(23 \, c^{2} d^{2} e^{2} x^{2} + 15 \, c^{2} d^{4} + 5 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} + {\left(35 \, c^{2} d^{3} e + 11 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}\right]"," ",0,"[1/30*(15*(c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(c*d/e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*(2*c*d*e^2*x + c*d^2*e + a*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d/e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) - 4*(23*c^2*d^2*e^2*x^2 + 15*c^2*d^4 + 5*a*c*d^2*e^2 + 3*a^2*e^4 + (35*c^2*d^3*e + 11*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3), -1/15*(15*(c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(-c*d/e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d/e)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)) + 2*(23*c^2*d^2*e^2*x^2 + 15*c^2*d^4 + 5*a*c*d^2*e^2 + 3*a^2*e^4 + (35*c^2*d^3*e + 11*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)]","A",0
1942,1,170,0,3.881028," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^7,x, algorithm=""fricas"")","\frac{2 \, {\left(c^{3} d^{3} x^{3} + 3 \, a c^{2} d^{2} e x^{2} + 3 \, a^{2} c d e^{2} x + a^{3} e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{7 \, {\left(c d^{6} - a d^{4} e^{2} + {\left(c d^{2} e^{4} - a e^{6}\right)} x^{4} + 4 \, {\left(c d^{3} e^{3} - a d e^{5}\right)} x^{3} + 6 \, {\left(c d^{4} e^{2} - a d^{2} e^{4}\right)} x^{2} + 4 \, {\left(c d^{5} e - a d^{3} e^{3}\right)} x\right)}}"," ",0,"2/7*(c^3*d^3*x^3 + 3*a*c^2*d^2*e*x^2 + 3*a^2*c*d*e^2*x + a^3*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c*d^6 - a*d^4*e^2 + (c*d^2*e^4 - a*e^6)*x^4 + 4*(c*d^3*e^3 - a*d*e^5)*x^3 + 6*(c*d^4*e^2 - a*d^2*e^4)*x^2 + 4*(c*d^5*e - a*d^3*e^3)*x)","B",0
1943,1,344,0,14.151795," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^8,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, c^{4} d^{4} e x^{4} + 9 \, a^{3} c d^{2} e^{3} - 7 \, a^{4} e^{5} + {\left(9 \, c^{4} d^{5} - a c^{3} d^{3} e^{2}\right)} x^{3} + 3 \, {\left(9 \, a c^{3} d^{4} e - 5 \, a^{2} c^{2} d^{2} e^{3}\right)} x^{2} + {\left(27 \, a^{2} c^{2} d^{3} e^{2} - 19 \, a^{3} c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{63 \, {\left(c^{2} d^{9} - 2 \, a c d^{7} e^{2} + a^{2} d^{5} e^{4} + {\left(c^{2} d^{4} e^{5} - 2 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} x^{5} + 5 \, {\left(c^{2} d^{5} e^{4} - 2 \, a c d^{3} e^{6} + a^{2} d e^{8}\right)} x^{4} + 10 \, {\left(c^{2} d^{6} e^{3} - 2 \, a c d^{4} e^{5} + a^{2} d^{2} e^{7}\right)} x^{3} + 10 \, {\left(c^{2} d^{7} e^{2} - 2 \, a c d^{5} e^{4} + a^{2} d^{3} e^{6}\right)} x^{2} + 5 \, {\left(c^{2} d^{8} e - 2 \, a c d^{6} e^{3} + a^{2} d^{4} e^{5}\right)} x\right)}}"," ",0,"2/63*(2*c^4*d^4*e*x^4 + 9*a^3*c*d^2*e^3 - 7*a^4*e^5 + (9*c^4*d^5 - a*c^3*d^3*e^2)*x^3 + 3*(9*a*c^3*d^4*e - 5*a^2*c^2*d^2*e^3)*x^2 + (27*a^2*c^2*d^3*e^2 - 19*a^3*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^2*d^9 - 2*a*c*d^7*e^2 + a^2*d^5*e^4 + (c^2*d^4*e^5 - 2*a*c*d^2*e^7 + a^2*e^9)*x^5 + 5*(c^2*d^5*e^4 - 2*a*c*d^3*e^6 + a^2*d*e^8)*x^4 + 10*(c^2*d^6*e^3 - 2*a*c*d^4*e^5 + a^2*d^2*e^7)*x^3 + 10*(c^2*d^7*e^2 - 2*a*c*d^5*e^4 + a^2*d^3*e^6)*x^2 + 5*(c^2*d^8*e - 2*a*c*d^6*e^3 + a^2*d^4*e^5)*x)","B",0
1944,1,569,0,32.841343," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^9,x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{5} d^{5} e^{2} x^{5} + 99 \, a^{3} c^{2} d^{4} e^{3} - 154 \, a^{4} c d^{2} e^{5} + 63 \, a^{5} e^{7} + 4 \, {\left(11 \, c^{5} d^{6} e - a c^{4} d^{4} e^{3}\right)} x^{4} + {\left(99 \, c^{5} d^{7} - 22 \, a c^{4} d^{5} e^{2} + 3 \, a^{2} c^{3} d^{3} e^{4}\right)} x^{3} + {\left(297 \, a c^{4} d^{6} e - 330 \, a^{2} c^{3} d^{4} e^{3} + 113 \, a^{3} c^{2} d^{2} e^{5}\right)} x^{2} + {\left(297 \, a^{2} c^{3} d^{5} e^{2} - 418 \, a^{3} c^{2} d^{3} e^{4} + 161 \, a^{4} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{693 \, {\left(c^{3} d^{12} - 3 \, a c^{2} d^{10} e^{2} + 3 \, a^{2} c d^{8} e^{4} - a^{3} d^{6} e^{6} + {\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)} x^{6} + 6 \, {\left(c^{3} d^{7} e^{5} - 3 \, a c^{2} d^{5} e^{7} + 3 \, a^{2} c d^{3} e^{9} - a^{3} d e^{11}\right)} x^{5} + 15 \, {\left(c^{3} d^{8} e^{4} - 3 \, a c^{2} d^{6} e^{6} + 3 \, a^{2} c d^{4} e^{8} - a^{3} d^{2} e^{10}\right)} x^{4} + 20 \, {\left(c^{3} d^{9} e^{3} - 3 \, a c^{2} d^{7} e^{5} + 3 \, a^{2} c d^{5} e^{7} - a^{3} d^{3} e^{9}\right)} x^{3} + 15 \, {\left(c^{3} d^{10} e^{2} - 3 \, a c^{2} d^{8} e^{4} + 3 \, a^{2} c d^{6} e^{6} - a^{3} d^{4} e^{8}\right)} x^{2} + 6 \, {\left(c^{3} d^{11} e - 3 \, a c^{2} d^{9} e^{3} + 3 \, a^{2} c d^{7} e^{5} - a^{3} d^{5} e^{7}\right)} x\right)}}"," ",0,"2/693*(8*c^5*d^5*e^2*x^5 + 99*a^3*c^2*d^4*e^3 - 154*a^4*c*d^2*e^5 + 63*a^5*e^7 + 4*(11*c^5*d^6*e - a*c^4*d^4*e^3)*x^4 + (99*c^5*d^7 - 22*a*c^4*d^5*e^2 + 3*a^2*c^3*d^3*e^4)*x^3 + (297*a*c^4*d^6*e - 330*a^2*c^3*d^4*e^3 + 113*a^3*c^2*d^2*e^5)*x^2 + (297*a^2*c^3*d^5*e^2 - 418*a^3*c^2*d^3*e^4 + 161*a^4*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^3*d^12 - 3*a*c^2*d^10*e^2 + 3*a^2*c*d^8*e^4 - a^3*d^6*e^6 + (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^6 + 6*(c^3*d^7*e^5 - 3*a*c^2*d^5*e^7 + 3*a^2*c*d^3*e^9 - a^3*d*e^11)*x^5 + 15*(c^3*d^8*e^4 - 3*a*c^2*d^6*e^6 + 3*a^2*c*d^4*e^8 - a^3*d^2*e^10)*x^4 + 20*(c^3*d^9*e^3 - 3*a*c^2*d^7*e^5 + 3*a^2*c*d^5*e^7 - a^3*d^3*e^9)*x^3 + 15*(c^3*d^10*e^2 - 3*a*c^2*d^8*e^4 + 3*a^2*c*d^6*e^6 - a^3*d^4*e^8)*x^2 + 6*(c^3*d^11*e - 3*a*c^2*d^9*e^3 + 3*a^2*c*d^7*e^5 - a^3*d^5*e^7)*x)","B",0
1945,1,823,0,71.502105," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2)/(e*x+d)^10,x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{6} d^{6} e^{3} x^{6} + 429 \, a^{3} c^{3} d^{6} e^{3} - 1001 \, a^{4} c^{2} d^{4} e^{5} + 819 \, a^{5} c d^{2} e^{7} - 231 \, a^{6} e^{9} + 8 \, {\left(13 \, c^{6} d^{7} e^{2} - a c^{5} d^{5} e^{4}\right)} x^{5} + 2 \, {\left(143 \, c^{6} d^{8} e - 26 \, a c^{5} d^{6} e^{3} + 3 \, a^{2} c^{4} d^{4} e^{5}\right)} x^{4} + {\left(429 \, c^{6} d^{9} - 143 \, a c^{5} d^{7} e^{2} + 39 \, a^{2} c^{4} d^{5} e^{4} - 5 \, a^{3} c^{3} d^{3} e^{6}\right)} x^{3} + {\left(1287 \, a c^{5} d^{8} e - 2145 \, a^{2} c^{4} d^{6} e^{3} + 1469 \, a^{3} c^{3} d^{4} e^{5} - 371 \, a^{4} c^{2} d^{2} e^{7}\right)} x^{2} + {\left(1287 \, a^{2} c^{4} d^{7} e^{2} - 2717 \, a^{3} c^{3} d^{5} e^{4} + 2093 \, a^{4} c^{2} d^{3} e^{6} - 567 \, a^{5} c d e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3003 \, {\left(c^{4} d^{15} - 4 \, a c^{3} d^{13} e^{2} + 6 \, a^{2} c^{2} d^{11} e^{4} - 4 \, a^{3} c d^{9} e^{6} + a^{4} d^{7} e^{8} + {\left(c^{4} d^{8} e^{7} - 4 \, a c^{3} d^{6} e^{9} + 6 \, a^{2} c^{2} d^{4} e^{11} - 4 \, a^{3} c d^{2} e^{13} + a^{4} e^{15}\right)} x^{7} + 7 \, {\left(c^{4} d^{9} e^{6} - 4 \, a c^{3} d^{7} e^{8} + 6 \, a^{2} c^{2} d^{5} e^{10} - 4 \, a^{3} c d^{3} e^{12} + a^{4} d e^{14}\right)} x^{6} + 21 \, {\left(c^{4} d^{10} e^{5} - 4 \, a c^{3} d^{8} e^{7} + 6 \, a^{2} c^{2} d^{6} e^{9} - 4 \, a^{3} c d^{4} e^{11} + a^{4} d^{2} e^{13}\right)} x^{5} + 35 \, {\left(c^{4} d^{11} e^{4} - 4 \, a c^{3} d^{9} e^{6} + 6 \, a^{2} c^{2} d^{7} e^{8} - 4 \, a^{3} c d^{5} e^{10} + a^{4} d^{3} e^{12}\right)} x^{4} + 35 \, {\left(c^{4} d^{12} e^{3} - 4 \, a c^{3} d^{10} e^{5} + 6 \, a^{2} c^{2} d^{8} e^{7} - 4 \, a^{3} c d^{6} e^{9} + a^{4} d^{4} e^{11}\right)} x^{3} + 21 \, {\left(c^{4} d^{13} e^{2} - 4 \, a c^{3} d^{11} e^{4} + 6 \, a^{2} c^{2} d^{9} e^{6} - 4 \, a^{3} c d^{7} e^{8} + a^{4} d^{5} e^{10}\right)} x^{2} + 7 \, {\left(c^{4} d^{14} e - 4 \, a c^{3} d^{12} e^{3} + 6 \, a^{2} c^{2} d^{10} e^{5} - 4 \, a^{3} c d^{8} e^{7} + a^{4} d^{6} e^{9}\right)} x\right)}}"," ",0,"2/3003*(16*c^6*d^6*e^3*x^6 + 429*a^3*c^3*d^6*e^3 - 1001*a^4*c^2*d^4*e^5 + 819*a^5*c*d^2*e^7 - 231*a^6*e^9 + 8*(13*c^6*d^7*e^2 - a*c^5*d^5*e^4)*x^5 + 2*(143*c^6*d^8*e - 26*a*c^5*d^6*e^3 + 3*a^2*c^4*d^4*e^5)*x^4 + (429*c^6*d^9 - 143*a*c^5*d^7*e^2 + 39*a^2*c^4*d^5*e^4 - 5*a^3*c^3*d^3*e^6)*x^3 + (1287*a*c^5*d^8*e - 2145*a^2*c^4*d^6*e^3 + 1469*a^3*c^3*d^4*e^5 - 371*a^4*c^2*d^2*e^7)*x^2 + (1287*a^2*c^4*d^7*e^2 - 2717*a^3*c^3*d^5*e^4 + 2093*a^4*c^2*d^3*e^6 - 567*a^5*c*d*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^4*d^15 - 4*a*c^3*d^13*e^2 + 6*a^2*c^2*d^11*e^4 - 4*a^3*c*d^9*e^6 + a^4*d^7*e^8 + (c^4*d^8*e^7 - 4*a*c^3*d^6*e^9 + 6*a^2*c^2*d^4*e^11 - 4*a^3*c*d^2*e^13 + a^4*e^15)*x^7 + 7*(c^4*d^9*e^6 - 4*a*c^3*d^7*e^8 + 6*a^2*c^2*d^5*e^10 - 4*a^3*c*d^3*e^12 + a^4*d*e^14)*x^6 + 21*(c^4*d^10*e^5 - 4*a*c^3*d^8*e^7 + 6*a^2*c^2*d^6*e^9 - 4*a^3*c*d^4*e^11 + a^4*d^2*e^13)*x^5 + 35*(c^4*d^11*e^4 - 4*a*c^3*d^9*e^6 + 6*a^2*c^2*d^7*e^8 - 4*a^3*c*d^5*e^10 + a^4*d^3*e^12)*x^4 + 35*(c^4*d^12*e^3 - 4*a*c^3*d^10*e^5 + 6*a^2*c^2*d^8*e^7 - 4*a^3*c*d^6*e^9 + a^4*d^4*e^11)*x^3 + 21*(c^4*d^13*e^2 - 4*a*c^3*d^11*e^4 + 6*a^2*c^2*d^9*e^6 - 4*a^3*c*d^7*e^8 + a^4*d^5*e^10)*x^2 + 7*(c^4*d^14*e - 4*a*c^3*d^12*e^3 + 6*a^2*c^2*d^10*e^5 - 4*a^3*c*d^8*e^7 + a^4*d^6*e^9)*x)","B",0
1946,1,534,0,0.520480," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\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} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} + 33 \, c^{3} d^{5} e - 40 \, a c^{2} d^{3} e^{3} + 15 \, a^{2} c d e^{5} + 2 \, {\left(13 \, c^{3} d^{4} e^{2} - 5 \, a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, c^{4} d^{4} e}, -\frac{15 \, {\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} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(8 \, c^{3} d^{3} e^{3} x^{2} + 33 \, c^{3} d^{5} e - 40 \, a c^{2} d^{3} e^{3} + 15 \, a^{2} c d e^{5} + 2 \, {\left(13 \, c^{3} d^{4} e^{2} - 5 \, a c^{2} d^{2} e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, c^{4} d^{4} e}\right]"," ",0,"[1/96*(15*(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)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(8*c^3*d^3*e^3*x^2 + 33*c^3*d^5*e - 40*a*c^2*d^3*e^3 + 15*a^2*c*d*e^5 + 2*(13*c^3*d^4*e^2 - 5*a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e), -1/48*(15*(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)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(8*c^3*d^3*e^3*x^2 + 33*c^3*d^5*e - 40*a*c^2*d^3*e^3 + 15*a^2*c*d*e^5 + 2*(13*c^3*d^4*e^2 - 5*a*c^2*d^2*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*e)]","A",0
1947,1,418,0,0.449905," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right) + 4 \, {\left(2 \, c^{2} d^{2} e^{2} x + 5 \, c^{2} d^{3} e - 3 \, a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, c^{3} d^{3} e}, -\frac{3 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right) - 2 \, {\left(2 \, c^{2} d^{2} e^{2} x + 5 \, c^{2} d^{3} e - 3 \, a c d e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, c^{3} d^{3} e}\right]"," ",0,"[1/16*(3*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x) + 4*(2*c^2*d^2*e^2*x + 5*c^2*d^3*e - 3*a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e), -1/8*(3*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)) - 2*(2*c^2*d^2*e^2*x + 5*c^2*d^3*e - 3*a*c*d*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^3*d^3*e)]","A",0
1948,1,338,0,0.434789," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} c d e - {\left(c d^{2} - a e^{2}\right)} \sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}{4 \, c^{2} d^{2} e}, \frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} c d e - {\left(c d^{2} - a e^{2}\right)} \sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right)}{2 \, c^{2} d^{2} e}\right]"," ",0,"[1/4*(4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*c*d*e - (c*d^2 - a*e^2)*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x))/(c^2*d^2*e), 1/2*(2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*c*d*e - (c*d^2 - a*e^2)*sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x)))/(c^2*d^2*e)]","A",0
1949,1,244,0,0.447034," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{c d e} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + c^{2} d^{4} + 6 \, a c d^{2} e^{2} + a^{2} e^{4} + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{c d e} + 8 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}{2 \, c d e}, -\frac{\sqrt{-c d e} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-c d e}}{2 \, {\left(c^{2} d^{2} e^{2} x^{2} + a c d^{2} e^{2} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x\right)}}\right)}{c d e}\right]"," ",0,"[1/2*sqrt(c*d*e)*log(8*c^2*d^2*e^2*x^2 + c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4 + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(c*d*e) + 8*(c^2*d^3*e + a*c*d*e^3)*x)/(c*d*e), -sqrt(-c*d*e)*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-c*d*e)/(c^2*d^2*e^2*x^2 + a*c*d^2*e^2 + (c^2*d^3*e + a*c*d*e^3)*x))/(c*d*e)]","A",0
1950,1,59,0,0.509179," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x}"," ",0,"2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)","A",0
1951,1,140,0,0.753168," ","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=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + 3 \, c d^{2} - a e^{2}\right)}}{3 \, {\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)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + 3*c*d^2 - a*e^2)/(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)","A",0
1952,1,279,0,1.798458," ","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=""fricas"")","\frac{2 \, {\left(8 \, c^{2} d^{2} e^{2} x^{2} + 15 \, c^{2} d^{4} - 10 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} + 4 \, {\left(5 \, c^{2} d^{3} e - a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15 \, {\left(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} + {\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^{3} + 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)} x^{2} + 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)} x\right)}}"," ",0,"2/15*(8*c^2*d^2*e^2*x^2 + 15*c^2*d^4 - 10*a*c*d^2*e^2 + 3*a^2*e^4 + 4*(5*c^2*d^3*e - a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*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^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^3 + 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)*x^2 + 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)*x)","A",0
1953,1,452,0,5.427228," ","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=""fricas"")","\frac{2 \, {\left(16 \, c^{3} d^{3} e^{3} x^{3} + 35 \, c^{3} d^{6} - 35 \, a c^{2} d^{4} e^{2} + 21 \, a^{2} c d^{2} e^{4} - 5 \, a^{3} e^{6} + 8 \, {\left(7 \, c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(35 \, c^{3} d^{5} e - 14 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{35 \, {\left(c^{4} d^{12} - 4 \, a c^{3} d^{10} e^{2} + 6 \, a^{2} c^{2} d^{8} e^{4} - 4 \, a^{3} c d^{6} e^{6} + a^{4} d^{4} e^{8} + {\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)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, a c^{3} d^{7} e^{5} + 6 \, a^{2} c^{2} d^{5} e^{7} - 4 \, a^{3} c d^{3} e^{9} + a^{4} d e^{11}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, a c^{3} d^{8} e^{4} + 6 \, a^{2} c^{2} d^{6} e^{6} - 4 \, a^{3} c d^{4} e^{8} + a^{4} d^{2} e^{10}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, a c^{3} d^{9} e^{3} + 6 \, a^{2} c^{2} d^{7} e^{5} - 4 \, a^{3} c d^{5} e^{7} + a^{4} d^{3} e^{9}\right)} x\right)}}"," ",0,"2/35*(16*c^3*d^3*e^3*x^3 + 35*c^3*d^6 - 35*a*c^2*d^4*e^2 + 21*a^2*c*d^2*e^4 - 5*a^3*e^6 + 8*(7*c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 2*(35*c^3*d^5*e - 14*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(c^4*d^12 - 4*a*c^3*d^10*e^2 + 6*a^2*c^2*d^8*e^4 - 4*a^3*c*d^6*e^6 + a^4*d^4*e^8 + (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)*x^4 + 4*(c^4*d^9*e^3 - 4*a*c^3*d^7*e^5 + 6*a^2*c^2*d^5*e^7 - 4*a^3*c*d^3*e^9 + a^4*d*e^11)*x^3 + 6*(c^4*d^10*e^2 - 4*a*c^3*d^8*e^4 + 6*a^2*c^2*d^6*e^6 - 4*a^3*c*d^4*e^8 + a^4*d^2*e^10)*x^2 + 4*(c^4*d^11*e - 4*a*c^3*d^9*e^3 + 6*a^2*c^2*d^7*e^5 - 4*a^3*c*d^5*e^7 + a^4*d^3*e^9)*x)","B",0
1954,1,759,0,1.310143," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\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} + {\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)} x\right)} \sqrt{\frac{e}{c d}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + 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 + 4 \, {\left(2 \, c^{2} d^{2} e x + c^{2} d^{3} + a c d e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{e}{c d}}\right) + 4 \, {\left(8 \, c^{3} d^{3} e^{3} x^{3} - 48 \, c^{3} d^{6} + 231 \, a c^{2} d^{4} e^{2} - 280 \, a^{2} c d^{2} e^{4} + 105 \, a^{3} e^{6} + 2 \, {\left(19 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(87 \, c^{3} d^{5} e - 98 \, a c^{2} d^{3} e^{3} + 35 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{96 \, {\left(c^{5} d^{5} x + a c^{4} d^{4} e\right)}}, -\frac{105 \, {\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} + {\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)} x\right)} \sqrt{-\frac{e}{c d}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{e}{c d}}}{2 \, {\left(c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)}}\right) - 2 \, {\left(8 \, c^{3} d^{3} e^{3} x^{3} - 48 \, c^{3} d^{6} + 231 \, a c^{2} d^{4} e^{2} - 280 \, a^{2} c d^{2} e^{4} + 105 \, a^{3} e^{6} + 2 \, {\left(19 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(87 \, c^{3} d^{5} e - 98 \, a c^{2} d^{3} e^{3} + 35 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, {\left(c^{5} d^{5} x + a c^{4} d^{4} e\right)}}\right]"," ",0,"[1/96*(105*(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 + (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)*x)*sqrt(e/(c*d))*log(8*c^2*d^2*e^2*x^2 + 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 + 4*(2*c^2*d^2*e*x + c^2*d^3 + a*c*d*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e/(c*d))) + 4*(8*c^3*d^3*e^3*x^3 - 48*c^3*d^6 + 231*a*c^2*d^4*e^2 - 280*a^2*c*d^2*e^4 + 105*a^3*e^6 + 2*(19*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 + (87*c^3*d^5*e - 98*a*c^2*d^3*e^3 + 35*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*x + a*c^4*d^4*e), -1/48*(105*(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 + (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)*x)*sqrt(-e/(c*d))*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-e/(c*d))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) - 2*(8*c^3*d^3*e^3*x^3 - 48*c^3*d^6 + 231*a*c^2*d^4*e^2 - 280*a^2*c*d^2*e^4 + 105*a^3*e^6 + 2*(19*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 + (87*c^3*d^5*e - 98*a*c^2*d^3*e^3 + 35*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*x + a*c^4*d^4*e)]","A",0
1955,1,585,0,0.757738," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} + {\left(c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x\right)} \sqrt{\frac{e}{c d}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + 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 + 4 \, {\left(2 \, c^{2} d^{2} e x + c^{2} d^{3} + a c d e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{e}{c d}}\right) + 4 \, {\left(2 \, c^{2} d^{2} e^{2} x^{2} - 8 \, c^{2} d^{4} + 25 \, a c d^{2} e^{2} - 15 \, a^{2} e^{4} + {\left(9 \, c^{2} d^{3} e - 5 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{16 \, {\left(c^{4} d^{4} x + a c^{3} d^{3} e\right)}}, -\frac{15 \, {\left(a c^{2} d^{4} e - 2 \, a^{2} c d^{2} e^{3} + a^{3} e^{5} + {\left(c^{3} d^{5} - 2 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4}\right)} x\right)} \sqrt{-\frac{e}{c d}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{e}{c d}}}{2 \, {\left(c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)}}\right) - 2 \, {\left(2 \, c^{2} d^{2} e^{2} x^{2} - 8 \, c^{2} d^{4} + 25 \, a c d^{2} e^{2} - 15 \, a^{2} e^{4} + {\left(9 \, c^{2} d^{3} e - 5 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{8 \, {\left(c^{4} d^{4} x + a c^{3} d^{3} e\right)}}\right]"," ",0,"[1/16*(15*(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5 + (c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x)*sqrt(e/(c*d))*log(8*c^2*d^2*e^2*x^2 + 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 + 4*(2*c^2*d^2*e*x + c^2*d^3 + a*c*d*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e/(c*d))) + 4*(2*c^2*d^2*e^2*x^2 - 8*c^2*d^4 + 25*a*c*d^2*e^2 - 15*a^2*e^4 + (9*c^2*d^3*e - 5*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*x + a*c^3*d^3*e), -1/8*(15*(a*c^2*d^4*e - 2*a^2*c*d^2*e^3 + a^3*e^5 + (c^3*d^5 - 2*a*c^2*d^3*e^2 + a^2*c*d*e^4)*x)*sqrt(-e/(c*d))*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-e/(c*d))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) - 2*(2*c^2*d^2*e^2*x^2 - 8*c^2*d^4 + 25*a*c*d^2*e^2 - 15*a^2*e^4 + (9*c^2*d^3*e - 5*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^4*d^4*x + a*c^3*d^3*e)]","A",0
1956,1,447,0,0.558919," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a c d^{2} e - a^{2} e^{3} + {\left(c^{2} d^{3} - a c d e^{2}\right)} x\right)} \sqrt{\frac{e}{c d}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + 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 + 4 \, {\left(2 \, c^{2} d^{2} e x + c^{2} d^{3} + a c d e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{e}{c d}}\right) + 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d e x - 2 \, c d^{2} + 3 \, a e^{2}\right)}}{4 \, {\left(c^{3} d^{3} x + a c^{2} d^{2} e\right)}}, -\frac{3 \, {\left(a c d^{2} e - a^{2} e^{3} + {\left(c^{2} d^{3} - a c d e^{2}\right)} x\right)} \sqrt{-\frac{e}{c d}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{e}{c d}}}{2 \, {\left(c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)}}\right) - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d e x - 2 \, c d^{2} + 3 \, a e^{2}\right)}}{2 \, {\left(c^{3} d^{3} x + a c^{2} d^{2} e\right)}}\right]"," ",0,"[1/4*(3*(a*c*d^2*e - a^2*e^3 + (c^2*d^3 - a*c*d*e^2)*x)*sqrt(e/(c*d))*log(8*c^2*d^2*e^2*x^2 + 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 + 4*(2*c^2*d^2*e*x + c^2*d^3 + a*c*d*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e/(c*d))) + 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*e*x - 2*c*d^2 + 3*a*e^2))/(c^3*d^3*x + a*c^2*d^2*e), -1/2*(3*(a*c*d^2*e - a^2*e^3 + (c^2*d^3 - a*c*d*e^2)*x)*sqrt(-e/(c*d))*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-e/(c*d))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*e*x - 2*c*d^2 + 3*a*e^2))/(c^3*d^3*x + a*c^2*d^2*e)]","A",0
1957,1,349,0,0.522645," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(c d x + a e\right)} \sqrt{\frac{e}{c d}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + 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 + 4 \, {\left(2 \, c^{2} d^{2} e x + c^{2} d^{3} + a c d e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{e}{c d}}\right) - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{2 \, {\left(c^{2} d^{2} x + a c d e\right)}}, -\frac{{\left(c d x + a e\right)} \sqrt{-\frac{e}{c d}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{e}{c d}}}{2 \, {\left(c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{c^{2} d^{2} x + a c d e}\right]"," ",0,"[1/2*((c*d*x + a*e)*sqrt(e/(c*d))*log(8*c^2*d^2*e^2*x^2 + 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 + 4*(2*c^2*d^2*e*x + c^2*d^3 + a*c*d*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e/(c*d))) - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*x + a*c*d*e), -((c*d*x + a*e)*sqrt(-e/(c*d))*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-e/(c*d))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^2*d^2*x + a*c*d*e)]","A",0
1958,1,65,0,0.525232," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{a c d^{2} e - a^{2} e^{3} + {\left(c^{2} d^{3} - a c d e^{2}\right)} x}"," ",0,"-2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a*c*d^2*e - a^2*e^3 + (c^2*d^3 - a*c*d*e^2)*x)","A",0
1959,1,153,0,1.035901," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)}}{a c^{2} d^{5} e - 2 \, a^{2} c d^{3} e^{3} + a^{3} d e^{5} + {\left(c^{3} d^{5} e - 2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x^{2} + {\left(c^{3} d^{6} - a c^{2} d^{4} e^{2} - a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} x}"," ",0,"-2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)/(a*c^2*d^5*e - 2*a^2*c*d^3*e^3 + a^3*d*e^5 + (c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x^2 + (c^3*d^6 - a*c^2*d^4*e^2 - a^2*c*d^2*e^4 + a^3*e^6)*x)","B",0
1960,1,306,0,2.360617," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, c^{2} d^{2} e^{2} x^{2} + 3 \, c^{2} d^{4} + 6 \, a c d^{2} e^{2} - a^{2} e^{4} + 4 \, {\left(3 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3 \, {\left(a c^{3} d^{8} e - 3 \, a^{2} c^{2} d^{6} e^{3} + 3 \, a^{3} c d^{4} e^{5} - a^{4} d^{2} e^{7} + {\left(c^{4} d^{7} e^{2} - 3 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6} - a^{3} c d e^{8}\right)} x^{3} + {\left(2 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5} + a^{3} c d^{2} e^{7} - a^{4} e^{9}\right)} x^{2} + {\left(c^{4} d^{9} - a c^{3} d^{7} e^{2} - 3 \, a^{2} c^{2} d^{5} e^{4} + 5 \, a^{3} c d^{3} e^{6} - 2 \, a^{4} d e^{8}\right)} x\right)}}"," ",0,"-2/3*(8*c^2*d^2*e^2*x^2 + 3*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4 + 4*(3*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a*c^3*d^8*e - 3*a^2*c^2*d^6*e^3 + 3*a^3*c*d^4*e^5 - a^4*d^2*e^7 + (c^4*d^7*e^2 - 3*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6 - a^3*c*d*e^8)*x^3 + (2*c^4*d^8*e - 5*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5 + a^3*c*d^2*e^7 - a^4*e^9)*x^2 + (c^4*d^9 - a*c^3*d^7*e^2 - 3*a^2*c^2*d^5*e^4 + 5*a^3*c*d^3*e^6 - 2*a^4*d*e^8)*x)","B",0
1961,1,494,0,6.419441," ","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=""fricas"")","-\frac{2 \, {\left(16 \, c^{3} d^{3} e^{3} x^{3} + 5 \, c^{3} d^{6} + 15 \, a c^{2} d^{4} e^{2} - 5 \, a^{2} c d^{2} e^{4} + a^{3} e^{6} + 8 \, {\left(5 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(15 \, c^{3} d^{5} e + 10 \, a c^{2} d^{3} e^{3} - a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{5 \, {\left(a c^{4} d^{11} e - 4 \, a^{2} c^{3} d^{9} e^{3} + 6 \, a^{3} c^{2} d^{7} e^{5} - 4 \, a^{4} c d^{5} e^{7} + a^{5} d^{3} e^{9} + {\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^{4} + {\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)} x^{3} + 3 \, {\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)} x^{2} + {\left(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}\right)} x\right)}}"," ",0,"-2/5*(16*c^3*d^3*e^3*x^3 + 5*c^3*d^6 + 15*a*c^2*d^4*e^2 - 5*a^2*c*d^2*e^4 + a^3*e^6 + 8*(5*c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^2 + 2*(15*c^3*d^5*e + 10*a*c^2*d^3*e^3 - a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a*c^4*d^11*e - 4*a^2*c^3*d^9*e^3 + 6*a^3*c^2*d^7*e^5 - 4*a^4*c*d^5*e^7 + a^5*d^3*e^9 + (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^4 + (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)*x^3 + 3*(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)*x^2 + (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)*x)","B",0
1962,1,733,0,16.402521," ","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=""fricas"")","-\frac{2 \, {\left(128 \, c^{4} d^{4} e^{4} x^{4} + 35 \, c^{4} d^{8} + 140 \, a c^{3} d^{6} e^{2} - 70 \, a^{2} c^{2} d^{4} e^{4} + 28 \, a^{3} c d^{2} e^{6} - 5 \, a^{4} e^{8} + 64 \, {\left(7 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{3} + 16 \, {\left(35 \, c^{4} d^{6} e^{2} + 14 \, a c^{3} d^{4} e^{4} - a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 8 \, {\left(35 \, c^{4} d^{7} e + 35 \, a c^{3} d^{5} e^{3} - 7 \, a^{2} c^{2} d^{3} e^{5} + a^{3} c d e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{35 \, {\left(a c^{5} d^{14} e - 5 \, a^{2} c^{4} d^{12} e^{3} + 10 \, a^{3} c^{3} d^{10} e^{5} - 10 \, a^{4} c^{2} d^{8} e^{7} + 5 \, a^{5} c d^{6} e^{9} - a^{6} d^{4} e^{11} + {\left(c^{6} d^{11} e^{4} - 5 \, a c^{5} d^{9} e^{6} + 10 \, a^{2} c^{4} d^{7} e^{8} - 10 \, a^{3} c^{3} d^{5} e^{10} + 5 \, a^{4} c^{2} d^{3} e^{12} - a^{5} c d e^{14}\right)} x^{5} + {\left(4 \, c^{6} d^{12} e^{3} - 19 \, a c^{5} d^{10} e^{5} + 35 \, a^{2} c^{4} d^{8} e^{7} - 30 \, a^{3} c^{3} d^{6} e^{9} + 10 \, a^{4} c^{2} d^{4} e^{11} + a^{5} c d^{2} e^{13} - a^{6} e^{15}\right)} x^{4} + 2 \, {\left(3 \, c^{6} d^{13} e^{2} - 13 \, a c^{5} d^{11} e^{4} + 20 \, a^{2} c^{4} d^{9} e^{6} - 10 \, a^{3} c^{3} d^{7} e^{8} - 5 \, a^{4} c^{2} d^{5} e^{10} + 7 \, a^{5} c d^{3} e^{12} - 2 \, a^{6} d e^{14}\right)} x^{3} + 2 \, {\left(2 \, c^{6} d^{14} e - 7 \, a c^{5} d^{12} e^{3} + 5 \, a^{2} c^{4} d^{10} e^{5} + 10 \, a^{3} c^{3} d^{8} e^{7} - 20 \, a^{4} c^{2} d^{6} e^{9} + 13 \, a^{5} c d^{4} e^{11} - 3 \, a^{6} d^{2} e^{13}\right)} x^{2} + {\left(c^{6} d^{15} - a c^{5} d^{13} e^{2} - 10 \, a^{2} c^{4} d^{11} e^{4} + 30 \, a^{3} c^{3} d^{9} e^{6} - 35 \, a^{4} c^{2} d^{7} e^{8} + 19 \, a^{5} c d^{5} e^{10} - 4 \, a^{6} d^{3} e^{12}\right)} x\right)}}"," ",0,"-2/35*(128*c^4*d^4*e^4*x^4 + 35*c^4*d^8 + 140*a*c^3*d^6*e^2 - 70*a^2*c^2*d^4*e^4 + 28*a^3*c*d^2*e^6 - 5*a^4*e^8 + 64*(7*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^3 + 16*(35*c^4*d^6*e^2 + 14*a*c^3*d^4*e^4 - a^2*c^2*d^2*e^6)*x^2 + 8*(35*c^4*d^7*e + 35*a*c^3*d^5*e^3 - 7*a^2*c^2*d^3*e^5 + a^3*c*d*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a*c^5*d^14*e - 5*a^2*c^4*d^12*e^3 + 10*a^3*c^3*d^10*e^5 - 10*a^4*c^2*d^8*e^7 + 5*a^5*c*d^6*e^9 - a^6*d^4*e^11 + (c^6*d^11*e^4 - 5*a*c^5*d^9*e^6 + 10*a^2*c^4*d^7*e^8 - 10*a^3*c^3*d^5*e^10 + 5*a^4*c^2*d^3*e^12 - a^5*c*d*e^14)*x^5 + (4*c^6*d^12*e^3 - 19*a*c^5*d^10*e^5 + 35*a^2*c^4*d^8*e^7 - 30*a^3*c^3*d^6*e^9 + 10*a^4*c^2*d^4*e^11 + a^5*c*d^2*e^13 - a^6*e^15)*x^4 + 2*(3*c^6*d^13*e^2 - 13*a*c^5*d^11*e^4 + 20*a^2*c^4*d^9*e^6 - 10*a^3*c^3*d^7*e^8 - 5*a^4*c^2*d^5*e^10 + 7*a^5*c*d^3*e^12 - 2*a^6*d*e^14)*x^3 + 2*(2*c^6*d^14*e - 7*a*c^5*d^12*e^3 + 5*a^2*c^4*d^10*e^5 + 10*a^3*c^3*d^8*e^7 - 20*a^4*c^2*d^6*e^9 + 13*a^5*c*d^4*e^11 - 3*a^6*d^2*e^13)*x^2 + (c^6*d^15 - a*c^5*d^13*e^2 - 10*a^2*c^4*d^11*e^4 + 30*a^3*c^3*d^9*e^6 - 35*a^4*c^2*d^7*e^8 + 19*a^5*c*d^5*e^10 - 4*a^6*d^3*e^12)*x)","B",0
1963,1,1004,0,40.314075," ","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=""fricas"")","-\frac{2 \, {\left(256 \, c^{5} d^{5} e^{5} x^{5} + 63 \, c^{5} d^{10} + 315 \, a c^{4} d^{8} e^{2} - 210 \, a^{2} c^{3} d^{6} e^{4} + 126 \, a^{3} c^{2} d^{4} e^{6} - 45 \, a^{4} c d^{2} e^{8} + 7 \, a^{5} e^{10} + 128 \, {\left(9 \, c^{5} d^{6} e^{4} + a c^{4} d^{4} e^{6}\right)} x^{4} + 32 \, {\left(63 \, c^{5} d^{7} e^{3} + 18 \, a c^{4} d^{5} e^{5} - a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 16 \, {\left(105 \, c^{5} d^{8} e^{2} + 63 \, a c^{4} d^{6} e^{4} - 9 \, a^{2} c^{3} d^{4} e^{6} + a^{3} c^{2} d^{2} e^{8}\right)} x^{2} + 2 \, {\left(315 \, c^{5} d^{9} e + 420 \, a c^{4} d^{7} e^{3} - 126 \, a^{2} c^{3} d^{5} e^{5} + 36 \, a^{3} c^{2} d^{3} e^{7} - 5 \, a^{4} c d e^{9}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{63 \, {\left(a c^{6} d^{17} e - 6 \, a^{2} c^{5} d^{15} e^{3} + 15 \, a^{3} c^{4} d^{13} e^{5} - 20 \, a^{4} c^{3} d^{11} e^{7} + 15 \, a^{5} c^{2} d^{9} e^{9} - 6 \, a^{6} c d^{7} e^{11} + a^{7} d^{5} e^{13} + {\left(c^{7} d^{13} e^{5} - 6 \, a c^{6} d^{11} e^{7} + 15 \, a^{2} c^{5} d^{9} e^{9} - 20 \, a^{3} c^{4} d^{7} e^{11} + 15 \, a^{4} c^{3} d^{5} e^{13} - 6 \, a^{5} c^{2} d^{3} e^{15} + a^{6} c d e^{17}\right)} x^{6} + {\left(5 \, c^{7} d^{14} e^{4} - 29 \, a c^{6} d^{12} e^{6} + 69 \, a^{2} c^{5} d^{10} e^{8} - 85 \, a^{3} c^{4} d^{8} e^{10} + 55 \, a^{4} c^{3} d^{6} e^{12} - 15 \, a^{5} c^{2} d^{4} e^{14} - a^{6} c d^{2} e^{16} + a^{7} e^{18}\right)} x^{5} + 5 \, {\left(2 \, c^{7} d^{15} e^{3} - 11 \, a c^{6} d^{13} e^{5} + 24 \, a^{2} c^{5} d^{11} e^{7} - 25 \, a^{3} c^{4} d^{9} e^{9} + 10 \, a^{4} c^{3} d^{7} e^{11} + 3 \, a^{5} c^{2} d^{5} e^{13} - 4 \, a^{6} c d^{3} e^{15} + a^{7} d e^{17}\right)} x^{4} + 10 \, {\left(c^{7} d^{16} e^{2} - 5 \, a c^{6} d^{14} e^{4} + 9 \, a^{2} c^{5} d^{12} e^{6} - 5 \, a^{3} c^{4} d^{10} e^{8} - 5 \, a^{4} c^{3} d^{8} e^{10} + 9 \, a^{5} c^{2} d^{6} e^{12} - 5 \, a^{6} c d^{4} e^{14} + a^{7} d^{2} e^{16}\right)} x^{3} + 5 \, {\left(c^{7} d^{17} e - 4 \, a c^{6} d^{15} e^{3} + 3 \, a^{2} c^{5} d^{13} e^{5} + 10 \, a^{3} c^{4} d^{11} e^{7} - 25 \, a^{4} c^{3} d^{9} e^{9} + 24 \, a^{5} c^{2} d^{7} e^{11} - 11 \, a^{6} c d^{5} e^{13} + 2 \, a^{7} d^{3} e^{15}\right)} x^{2} + {\left(c^{7} d^{18} - a c^{6} d^{16} e^{2} - 15 \, a^{2} c^{5} d^{14} e^{4} + 55 \, a^{3} c^{4} d^{12} e^{6} - 85 \, a^{4} c^{3} d^{10} e^{8} + 69 \, a^{5} c^{2} d^{8} e^{10} - 29 \, a^{6} c d^{6} e^{12} + 5 \, a^{7} d^{4} e^{14}\right)} x\right)}}"," ",0,"-2/63*(256*c^5*d^5*e^5*x^5 + 63*c^5*d^10 + 315*a*c^4*d^8*e^2 - 210*a^2*c^3*d^6*e^4 + 126*a^3*c^2*d^4*e^6 - 45*a^4*c*d^2*e^8 + 7*a^5*e^10 + 128*(9*c^5*d^6*e^4 + a*c^4*d^4*e^6)*x^4 + 32*(63*c^5*d^7*e^3 + 18*a*c^4*d^5*e^5 - a^2*c^3*d^3*e^7)*x^3 + 16*(105*c^5*d^8*e^2 + 63*a*c^4*d^6*e^4 - 9*a^2*c^3*d^4*e^6 + a^3*c^2*d^2*e^8)*x^2 + 2*(315*c^5*d^9*e + 420*a*c^4*d^7*e^3 - 126*a^2*c^3*d^5*e^5 + 36*a^3*c^2*d^3*e^7 - 5*a^4*c*d*e^9)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a*c^6*d^17*e - 6*a^2*c^5*d^15*e^3 + 15*a^3*c^4*d^13*e^5 - 20*a^4*c^3*d^11*e^7 + 15*a^5*c^2*d^9*e^9 - 6*a^6*c*d^7*e^11 + a^7*d^5*e^13 + (c^7*d^13*e^5 - 6*a*c^6*d^11*e^7 + 15*a^2*c^5*d^9*e^9 - 20*a^3*c^4*d^7*e^11 + 15*a^4*c^3*d^5*e^13 - 6*a^5*c^2*d^3*e^15 + a^6*c*d*e^17)*x^6 + (5*c^7*d^14*e^4 - 29*a*c^6*d^12*e^6 + 69*a^2*c^5*d^10*e^8 - 85*a^3*c^4*d^8*e^10 + 55*a^4*c^3*d^6*e^12 - 15*a^5*c^2*d^4*e^14 - a^6*c*d^2*e^16 + a^7*e^18)*x^5 + 5*(2*c^7*d^15*e^3 - 11*a*c^6*d^13*e^5 + 24*a^2*c^5*d^11*e^7 - 25*a^3*c^4*d^9*e^9 + 10*a^4*c^3*d^7*e^11 + 3*a^5*c^2*d^5*e^13 - 4*a^6*c*d^3*e^15 + a^7*d*e^17)*x^4 + 10*(c^7*d^16*e^2 - 5*a*c^6*d^14*e^4 + 9*a^2*c^5*d^12*e^6 - 5*a^3*c^4*d^10*e^8 - 5*a^4*c^3*d^8*e^10 + 9*a^5*c^2*d^6*e^12 - 5*a^6*c*d^4*e^14 + a^7*d^2*e^16)*x^3 + 5*(c^7*d^17*e - 4*a*c^6*d^15*e^3 + 3*a^2*c^5*d^13*e^5 + 10*a^3*c^4*d^11*e^7 - 25*a^4*c^3*d^9*e^9 + 24*a^5*c^2*d^7*e^11 - 11*a^6*c*d^5*e^13 + 2*a^7*d^3*e^15)*x^2 + (c^7*d^18 - a*c^6*d^16*e^2 - 15*a^2*c^5*d^14*e^4 + 55*a^3*c^4*d^12*e^6 - 85*a^4*c^3*d^10*e^8 + 69*a^5*c^2*d^8*e^10 - 29*a^6*c*d^6*e^12 + 5*a^7*d^4*e^14)*x)","B",0
1964,1,833,0,2.784341," ","integrate((e*x+d)^6/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{2} c^{2} d^{4} e^{3} - 2 \, a^{3} c d^{2} e^{5} + a^{4} e^{7} + {\left(c^{4} d^{6} e - 2 \, a c^{3} d^{4} e^{3} + a^{2} c^{2} d^{2} e^{5}\right)} x^{2} + 2 \, {\left(a c^{3} d^{5} e^{2} - 2 \, a^{2} c^{2} d^{3} e^{4} + a^{3} c d e^{6}\right)} x\right)} \sqrt{\frac{e}{c d}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + 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 + 4 \, {\left(2 \, c^{2} d^{2} e x + c^{2} d^{3} + a c d e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{e}{c d}}\right) + 4 \, {\left(6 \, c^{3} d^{3} e^{3} x^{3} - 8 \, c^{3} d^{6} - 56 \, a c^{2} d^{4} e^{2} + 175 \, a^{2} c d^{2} e^{4} - 105 \, a^{3} e^{6} + 3 \, {\left(13 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} - 2 \, {\left(40 \, c^{3} d^{5} e - 119 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{48 \, {\left(c^{6} d^{6} x^{2} + 2 \, a c^{5} d^{5} e x + a^{2} c^{4} d^{4} e^{2}\right)}}, -\frac{105 \, {\left(a^{2} c^{2} d^{4} e^{3} - 2 \, a^{3} c d^{2} e^{5} + a^{4} e^{7} + {\left(c^{4} d^{6} e - 2 \, a c^{3} d^{4} e^{3} + a^{2} c^{2} d^{2} e^{5}\right)} x^{2} + 2 \, {\left(a c^{3} d^{5} e^{2} - 2 \, a^{2} c^{2} d^{3} e^{4} + a^{3} c d e^{6}\right)} x\right)} \sqrt{-\frac{e}{c d}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{e}{c d}}}{2 \, {\left(c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)}}\right) - 2 \, {\left(6 \, c^{3} d^{3} e^{3} x^{3} - 8 \, c^{3} d^{6} - 56 \, a c^{2} d^{4} e^{2} + 175 \, a^{2} c d^{2} e^{4} - 105 \, a^{3} e^{6} + 3 \, {\left(13 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} - 2 \, {\left(40 \, c^{3} d^{5} e - 119 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{24 \, {\left(c^{6} d^{6} x^{2} + 2 \, a c^{5} d^{5} e x + a^{2} c^{4} d^{4} e^{2}\right)}}\right]"," ",0,"[1/48*(105*(a^2*c^2*d^4*e^3 - 2*a^3*c*d^2*e^5 + a^4*e^7 + (c^4*d^6*e - 2*a*c^3*d^4*e^3 + a^2*c^2*d^2*e^5)*x^2 + 2*(a*c^3*d^5*e^2 - 2*a^2*c^2*d^3*e^4 + a^3*c*d*e^6)*x)*sqrt(e/(c*d))*log(8*c^2*d^2*e^2*x^2 + 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 + 4*(2*c^2*d^2*e*x + c^2*d^3 + a*c*d*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e/(c*d))) + 4*(6*c^3*d^3*e^3*x^3 - 8*c^3*d^6 - 56*a*c^2*d^4*e^2 + 175*a^2*c*d^2*e^4 - 105*a^3*e^6 + 3*(13*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 - 2*(40*c^3*d^5*e - 119*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^6*d^6*x^2 + 2*a*c^5*d^5*e*x + a^2*c^4*d^4*e^2), -1/24*(105*(a^2*c^2*d^4*e^3 - 2*a^3*c*d^2*e^5 + a^4*e^7 + (c^4*d^6*e - 2*a*c^3*d^4*e^3 + a^2*c^2*d^2*e^5)*x^2 + 2*(a*c^3*d^5*e^2 - 2*a^2*c^2*d^3*e^4 + a^3*c*d*e^6)*x)*sqrt(-e/(c*d))*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-e/(c*d))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) - 2*(6*c^3*d^3*e^3*x^3 - 8*c^3*d^6 - 56*a*c^2*d^4*e^2 + 175*a^2*c*d^2*e^4 - 105*a^3*e^6 + 3*(13*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 - 2*(40*c^3*d^5*e - 119*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^6*d^6*x^2 + 2*a*c^5*d^5*e*x + a^2*c^4*d^4*e^2)]","A",0
1965,1,641,0,1.403702," ","integrate((e*x+d)^5/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} c d^{2} e^{3} - a^{3} e^{5} + {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} x^{2} + 2 \, {\left(a c^{2} d^{3} e^{2} - a^{2} c d e^{4}\right)} x\right)} \sqrt{\frac{e}{c d}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + 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 + 4 \, {\left(2 \, c^{2} d^{2} e x + c^{2} d^{3} + a c d e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{e}{c d}}\right) + 4 \, {\left(3 \, c^{2} d^{2} e^{2} x^{2} - 2 \, c^{2} d^{4} - 10 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} - 2 \, {\left(7 \, c^{2} d^{3} e - 10 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{12 \, {\left(c^{5} d^{5} x^{2} + 2 \, a c^{4} d^{4} e x + a^{2} c^{3} d^{3} e^{2}\right)}}, -\frac{15 \, {\left(a^{2} c d^{2} e^{3} - a^{3} e^{5} + {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} x^{2} + 2 \, {\left(a c^{2} d^{3} e^{2} - a^{2} c d e^{4}\right)} x\right)} \sqrt{-\frac{e}{c d}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{e}{c d}}}{2 \, {\left(c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)}}\right) - 2 \, {\left(3 \, c^{2} d^{2} e^{2} x^{2} - 2 \, c^{2} d^{4} - 10 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} - 2 \, {\left(7 \, c^{2} d^{3} e - 10 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{6 \, {\left(c^{5} d^{5} x^{2} + 2 \, a c^{4} d^{4} e x + a^{2} c^{3} d^{3} e^{2}\right)}}\right]"," ",0,"[1/12*(15*(a^2*c*d^2*e^3 - a^3*e^5 + (c^3*d^4*e - a*c^2*d^2*e^3)*x^2 + 2*(a*c^2*d^3*e^2 - a^2*c*d*e^4)*x)*sqrt(e/(c*d))*log(8*c^2*d^2*e^2*x^2 + 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 + 4*(2*c^2*d^2*e*x + c^2*d^3 + a*c*d*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e/(c*d))) + 4*(3*c^2*d^2*e^2*x^2 - 2*c^2*d^4 - 10*a*c*d^2*e^2 + 15*a^2*e^4 - 2*(7*c^2*d^3*e - 10*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*x^2 + 2*a*c^4*d^4*e*x + a^2*c^3*d^3*e^2), -1/6*(15*(a^2*c*d^2*e^3 - a^3*e^5 + (c^3*d^4*e - a*c^2*d^2*e^3)*x^2 + 2*(a*c^2*d^3*e^2 - a^2*c*d*e^4)*x)*sqrt(-e/(c*d))*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-e/(c*d))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) - 2*(3*c^2*d^2*e^2*x^2 - 2*c^2*d^4 - 10*a*c*d^2*e^2 + 15*a^2*e^4 - 2*(7*c^2*d^3*e - 10*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x))/(c^5*d^5*x^2 + 2*a*c^4*d^4*e*x + a^2*c^3*d^3*e^2)]","A",0
1966,1,469,0,1.012282," ","integrate((e*x+d)^4/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{2} e x^{2} + 2 \, a c d e^{2} x + a^{2} e^{3}\right)} \sqrt{\frac{e}{c d}} \log\left(8 \, c^{2} d^{2} e^{2} x^{2} + 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 + 4 \, {\left(2 \, c^{2} d^{2} e x + c^{2} d^{3} + a c d e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{\frac{e}{c d}}\right) - 4 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(4 \, c d e x + c d^{2} + 3 \, a e^{2}\right)}}{6 \, {\left(c^{4} d^{4} x^{2} + 2 \, a c^{3} d^{3} e x + a^{2} c^{2} d^{2} e^{2}\right)}}, -\frac{3 \, {\left(c^{2} d^{2} e x^{2} + 2 \, a c d e^{2} x + a^{2} e^{3}\right)} \sqrt{-\frac{e}{c d}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + c d^{2} + a e^{2}\right)} \sqrt{-\frac{e}{c d}}}{2 \, {\left(c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(4 \, c d e x + c d^{2} + 3 \, a e^{2}\right)}}{3 \, {\left(c^{4} d^{4} x^{2} + 2 \, a c^{3} d^{3} e x + a^{2} c^{2} d^{2} e^{2}\right)}}\right]"," ",0,"[1/6*(3*(c^2*d^2*e*x^2 + 2*a*c*d*e^2*x + a^2*e^3)*sqrt(e/(c*d))*log(8*c^2*d^2*e^2*x^2 + 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 + 4*(2*c^2*d^2*e*x + c^2*d^3 + a*c*d*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e/(c*d))) - 4*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(4*c*d*e*x + c*d^2 + 3*a*e^2))/(c^4*d^4*x^2 + 2*a*c^3*d^3*e*x + a^2*c^2*d^2*e^2), -1/3*(3*(c^2*d^2*e*x^2 + 2*a*c*d*e^2*x + a^2*e^3)*sqrt(-e/(c*d))*arctan(1/2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + c*d^2 + a*e^2)*sqrt(-e/(c*d))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(4*c*d*e*x + c*d^2 + 3*a*e^2))/(c^4*d^4*x^2 + 2*a*c^3*d^3*e*x + a^2*c^2*d^2*e^2)]","A",0
1967,1,103,0,0.828117," ","integrate((e*x+d)^3/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(e x + d\right)}}{3 \, {\left(a^{2} c d^{2} e^{2} - a^{3} e^{4} + {\left(c^{3} d^{4} - a c^{2} d^{2} e^{2}\right)} x^{2} + 2 \, {\left(a c^{2} d^{3} e - a^{2} c d e^{3}\right)} x\right)}}"," ",0,"-2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(e*x + d)/(a^2*c*d^2*e^2 - a^3*e^4 + (c^3*d^4 - a*c^2*d^2*e^2)*x^2 + 2*(a*c^2*d^3*e - a^2*c*d*e^3)*x)","B",0
1968,1,156,0,1.101841," ","integrate((e*x+d)^2/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x - c d^{2} + 3 \, a e^{2}\right)}}{3 \, {\left(a^{2} c^{2} d^{4} e^{2} - 2 \, a^{3} c d^{2} e^{4} + a^{4} e^{6} + {\left(c^{4} d^{6} - 2 \, a c^{3} d^{4} e^{2} + a^{2} c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(a c^{3} d^{5} e - 2 \, a^{2} c^{2} d^{3} e^{3} + a^{3} c d e^{5}\right)} x\right)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x - c*d^2 + 3*a*e^2)/(a^2*c^2*d^4*e^2 - 2*a^3*c*d^2*e^4 + a^4*e^6 + (c^4*d^6 - 2*a*c^3*d^4*e^2 + a^2*c^2*d^2*e^4)*x^2 + 2*(a*c^3*d^5*e - 2*a^2*c^2*d^3*e^3 + a^3*c*d*e^5)*x)","A",0
1969,1,316,0,2.913571," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, c^{2} d^{2} e^{2} x^{2} - c^{2} d^{4} + 6 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} + 4 \, {\left(c^{2} d^{3} e + 3 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3 \, {\left(a^{2} c^{3} d^{7} e^{2} - 3 \, a^{3} c^{2} d^{5} e^{4} + 3 \, a^{4} c d^{3} e^{6} - a^{5} d e^{8} + {\left(c^{5} d^{8} e - 3 \, a c^{4} d^{6} e^{3} + 3 \, a^{2} c^{3} d^{4} e^{5} - a^{3} c^{2} d^{2} e^{7}\right)} x^{3} + {\left(c^{5} d^{9} - a c^{4} d^{7} e^{2} - 3 \, a^{2} c^{3} d^{5} e^{4} + 5 \, a^{3} c^{2} d^{3} e^{6} - 2 \, a^{4} c d e^{8}\right)} x^{2} + {\left(2 \, a c^{4} d^{8} e - 5 \, a^{2} c^{3} d^{6} e^{3} + 3 \, a^{3} c^{2} d^{4} e^{5} + a^{4} c d^{2} e^{7} - a^{5} e^{9}\right)} x\right)}}"," ",0,"2/3*(8*c^2*d^2*e^2*x^2 - c^2*d^4 + 6*a*c*d^2*e^2 + 3*a^2*e^4 + 4*(c^2*d^3*e + 3*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a^2*c^3*d^7*e^2 - 3*a^3*c^2*d^5*e^4 + 3*a^4*c*d^3*e^6 - a^5*d*e^8 + (c^5*d^8*e - 3*a*c^4*d^6*e^3 + 3*a^2*c^3*d^4*e^5 - a^3*c^2*d^2*e^7)*x^3 + (c^5*d^9 - a*c^4*d^7*e^2 - 3*a^2*c^3*d^5*e^4 + 5*a^3*c^2*d^3*e^6 - 2*a^4*c*d*e^8)*x^2 + (2*a*c^4*d^8*e - 5*a^2*c^3*d^6*e^3 + 3*a^3*c^2*d^4*e^5 + a^4*c*d^2*e^7 - a^5*e^9)*x)","B",0
1970,1,491,0,8.504143," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{3} d^{3} e^{3} x^{3} - c^{3} d^{6} + 9 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4} - a^{3} e^{6} + 24 \, {\left(c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{2} + 6 \, {\left(c^{3} d^{5} e + 6 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{3 \, {\left(a^{2} c^{4} d^{10} e^{2} - 4 \, a^{3} c^{3} d^{8} e^{4} + 6 \, a^{4} c^{2} d^{6} e^{6} - 4 \, a^{5} c d^{4} e^{8} + a^{6} d^{2} e^{10} + {\left(c^{6} d^{10} e^{2} - 4 \, a c^{5} d^{8} e^{4} + 6 \, a^{2} c^{4} d^{6} e^{6} - 4 \, a^{3} c^{3} d^{4} e^{8} + a^{4} c^{2} d^{2} e^{10}\right)} x^{4} + 2 \, {\left(c^{6} d^{11} e - 3 \, a c^{5} d^{9} e^{3} + 2 \, a^{2} c^{4} d^{7} e^{5} + 2 \, a^{3} c^{3} d^{5} e^{7} - 3 \, a^{4} c^{2} d^{3} e^{9} + a^{5} c d e^{11}\right)} x^{3} + {\left(c^{6} d^{12} - 9 \, a^{2} c^{4} d^{8} e^{4} + 16 \, a^{3} c^{3} d^{6} e^{6} - 9 \, a^{4} c^{2} d^{4} e^{8} + a^{6} e^{12}\right)} x^{2} + 2 \, {\left(a c^{5} d^{11} e - 3 \, a^{2} c^{4} d^{9} e^{3} + 2 \, a^{3} c^{3} d^{7} e^{5} + 2 \, a^{4} c^{2} d^{5} e^{7} - 3 \, a^{5} c d^{3} e^{9} + a^{6} d e^{11}\right)} x\right)}}"," ",0,"2/3*(16*c^3*d^3*e^3*x^3 - c^3*d^6 + 9*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4 - a^3*e^6 + 24*(c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^2 + 6*(c^3*d^5*e + 6*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a^2*c^4*d^10*e^2 - 4*a^3*c^3*d^8*e^4 + 6*a^4*c^2*d^6*e^6 - 4*a^5*c*d^4*e^8 + a^6*d^2*e^10 + (c^6*d^10*e^2 - 4*a*c^5*d^8*e^4 + 6*a^2*c^4*d^6*e^6 - 4*a^3*c^3*d^4*e^8 + a^4*c^2*d^2*e^10)*x^4 + 2*(c^6*d^11*e - 3*a*c^5*d^9*e^3 + 2*a^2*c^4*d^7*e^5 + 2*a^3*c^3*d^5*e^7 - 3*a^4*c^2*d^3*e^9 + a^5*c*d*e^11)*x^3 + (c^6*d^12 - 9*a^2*c^4*d^8*e^4 + 16*a^3*c^3*d^6*e^6 - 9*a^4*c^2*d^4*e^8 + a^6*e^12)*x^2 + 2*(a*c^5*d^11*e - 3*a^2*c^4*d^9*e^3 + 2*a^3*c^3*d^7*e^5 + 2*a^4*c^2*d^5*e^7 - 3*a^5*c*d^3*e^9 + a^6*d*e^11)*x)","B",0
1971,1,769,0,24.468298," ","integrate(1/(e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(128 \, c^{4} d^{4} e^{4} x^{4} - 5 \, c^{4} d^{8} + 60 \, a c^{3} d^{6} e^{2} + 90 \, a^{2} c^{2} d^{4} e^{4} - 20 \, a^{3} c d^{2} e^{6} + 3 \, a^{4} e^{8} + 64 \, {\left(5 \, c^{4} d^{5} e^{3} + 3 \, a c^{3} d^{3} e^{5}\right)} x^{3} + 48 \, {\left(5 \, c^{4} d^{6} e^{2} + 10 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 8 \, {\left(5 \, c^{4} d^{7} e + 45 \, a c^{3} d^{5} e^{3} + 15 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{15 \, {\left(a^{2} c^{5} d^{13} e^{2} - 5 \, a^{3} c^{4} d^{11} e^{4} + 10 \, a^{4} c^{3} d^{9} e^{6} - 10 \, a^{5} c^{2} d^{7} e^{8} + 5 \, a^{6} c d^{5} e^{10} - a^{7} d^{3} e^{12} + {\left(c^{7} d^{12} e^{3} - 5 \, a c^{6} d^{10} e^{5} + 10 \, a^{2} c^{5} d^{8} e^{7} - 10 \, a^{3} c^{4} d^{6} e^{9} + 5 \, a^{4} c^{3} d^{4} e^{11} - a^{5} c^{2} d^{2} e^{13}\right)} x^{5} + {\left(3 \, c^{7} d^{13} e^{2} - 13 \, a c^{6} d^{11} e^{4} + 20 \, a^{2} c^{5} d^{9} e^{6} - 10 \, a^{3} c^{4} d^{7} e^{8} - 5 \, a^{4} c^{3} d^{5} e^{10} + 7 \, a^{5} c^{2} d^{3} e^{12} - 2 \, a^{6} c d e^{14}\right)} x^{4} + {\left(3 \, c^{7} d^{14} e - 9 \, a c^{6} d^{12} e^{3} + a^{2} c^{5} d^{10} e^{5} + 25 \, a^{3} c^{4} d^{8} e^{7} - 35 \, a^{4} c^{3} d^{6} e^{9} + 17 \, a^{5} c^{2} d^{4} e^{11} - a^{6} c d^{2} e^{13} - a^{7} e^{15}\right)} x^{3} + {\left(c^{7} d^{15} + a c^{6} d^{13} e^{2} - 17 \, a^{2} c^{5} d^{11} e^{4} + 35 \, a^{3} c^{4} d^{9} e^{6} - 25 \, a^{4} c^{3} d^{7} e^{8} - a^{5} c^{2} d^{5} e^{10} + 9 \, a^{6} c d^{3} e^{12} - 3 \, a^{7} d e^{14}\right)} x^{2} + {\left(2 \, a c^{6} d^{14} e - 7 \, a^{2} c^{5} d^{12} e^{3} + 5 \, a^{3} c^{4} d^{10} e^{5} + 10 \, a^{4} c^{3} d^{8} e^{7} - 20 \, a^{5} c^{2} d^{6} e^{9} + 13 \, a^{6} c d^{4} e^{11} - 3 \, a^{7} d^{2} e^{13}\right)} x\right)}}"," ",0,"2/15*(128*c^4*d^4*e^4*x^4 - 5*c^4*d^8 + 60*a*c^3*d^6*e^2 + 90*a^2*c^2*d^4*e^4 - 20*a^3*c*d^2*e^6 + 3*a^4*e^8 + 64*(5*c^4*d^5*e^3 + 3*a*c^3*d^3*e^5)*x^3 + 48*(5*c^4*d^6*e^2 + 10*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + 8*(5*c^4*d^7*e + 45*a*c^3*d^5*e^3 + 15*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a^2*c^5*d^13*e^2 - 5*a^3*c^4*d^11*e^4 + 10*a^4*c^3*d^9*e^6 - 10*a^5*c^2*d^7*e^8 + 5*a^6*c*d^5*e^10 - a^7*d^3*e^12 + (c^7*d^12*e^3 - 5*a*c^6*d^10*e^5 + 10*a^2*c^5*d^8*e^7 - 10*a^3*c^4*d^6*e^9 + 5*a^4*c^3*d^4*e^11 - a^5*c^2*d^2*e^13)*x^5 + (3*c^7*d^13*e^2 - 13*a*c^6*d^11*e^4 + 20*a^2*c^5*d^9*e^6 - 10*a^3*c^4*d^7*e^8 - 5*a^4*c^3*d^5*e^10 + 7*a^5*c^2*d^3*e^12 - 2*a^6*c*d*e^14)*x^4 + (3*c^7*d^14*e - 9*a*c^6*d^12*e^3 + a^2*c^5*d^10*e^5 + 25*a^3*c^4*d^8*e^7 - 35*a^4*c^3*d^6*e^9 + 17*a^5*c^2*d^4*e^11 - a^6*c*d^2*e^13 - a^7*e^15)*x^3 + (c^7*d^15 + a*c^6*d^13*e^2 - 17*a^2*c^5*d^11*e^4 + 35*a^3*c^4*d^9*e^6 - 25*a^4*c^3*d^7*e^8 - a^5*c^2*d^5*e^10 + 9*a^6*c*d^3*e^12 - 3*a^7*d*e^14)*x^2 + (2*a*c^6*d^14*e - 7*a^2*c^5*d^12*e^3 + 5*a^3*c^4*d^10*e^5 + 10*a^4*c^3*d^8*e^7 - 20*a^5*c^2*d^6*e^9 + 13*a^6*c*d^4*e^11 - 3*a^7*d^2*e^13)*x)","B",0
1972,1,1058,0,57.722887," ","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=""fricas"")","\frac{2 \, {\left(256 \, c^{5} d^{5} e^{5} x^{5} - 7 \, c^{5} d^{10} + 105 \, a c^{4} d^{8} e^{2} + 210 \, a^{2} c^{3} d^{6} e^{4} - 70 \, a^{3} c^{2} d^{4} e^{6} + 21 \, a^{4} c d^{2} e^{8} - 3 \, a^{5} e^{10} + 128 \, {\left(7 \, c^{5} d^{6} e^{4} + 3 \, a c^{4} d^{4} e^{6}\right)} x^{4} + 32 \, {\left(35 \, c^{5} d^{7} e^{3} + 42 \, a c^{4} d^{5} e^{5} + 3 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 16 \, {\left(35 \, c^{5} d^{8} e^{2} + 105 \, a c^{4} d^{6} e^{4} + 21 \, a^{2} c^{3} d^{4} e^{6} - a^{3} c^{2} d^{2} e^{8}\right)} x^{2} + 2 \, {\left(35 \, c^{5} d^{9} e + 420 \, a c^{4} d^{7} e^{3} + 210 \, a^{2} c^{3} d^{5} e^{5} - 28 \, a^{3} c^{2} d^{3} e^{7} + 3 \, a^{4} c d e^{9}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{21 \, {\left(a^{2} c^{6} d^{16} e^{2} - 6 \, a^{3} c^{5} d^{14} e^{4} + 15 \, a^{4} c^{4} d^{12} e^{6} - 20 \, a^{5} c^{3} d^{10} e^{8} + 15 \, a^{6} c^{2} d^{8} e^{10} - 6 \, a^{7} c d^{6} e^{12} + a^{8} d^{4} e^{14} + {\left(c^{8} d^{14} e^{4} - 6 \, a c^{7} d^{12} e^{6} + 15 \, a^{2} c^{6} d^{10} e^{8} - 20 \, a^{3} c^{5} d^{8} e^{10} + 15 \, a^{4} c^{4} d^{6} e^{12} - 6 \, a^{5} c^{3} d^{4} e^{14} + a^{6} c^{2} d^{2} e^{16}\right)} x^{6} + 2 \, {\left(2 \, c^{8} d^{15} e^{3} - 11 \, a c^{7} d^{13} e^{5} + 24 \, a^{2} c^{6} d^{11} e^{7} - 25 \, a^{3} c^{5} d^{9} e^{9} + 10 \, a^{4} c^{4} d^{7} e^{11} + 3 \, a^{5} c^{3} d^{5} e^{13} - 4 \, a^{6} c^{2} d^{3} e^{15} + a^{7} c d e^{17}\right)} x^{5} + {\left(6 \, c^{8} d^{16} e^{2} - 28 \, a c^{7} d^{14} e^{4} + 43 \, a^{2} c^{6} d^{12} e^{6} - 6 \, a^{3} c^{5} d^{10} e^{8} - 55 \, a^{4} c^{4} d^{8} e^{10} + 64 \, a^{5} c^{3} d^{6} e^{12} - 27 \, a^{6} c^{2} d^{4} e^{14} + 2 \, a^{7} c d^{2} e^{16} + a^{8} e^{18}\right)} x^{4} + 4 \, {\left(c^{8} d^{17} e - 3 \, a c^{7} d^{15} e^{3} - 2 \, a^{2} c^{6} d^{13} e^{5} + 19 \, a^{3} c^{5} d^{11} e^{7} - 30 \, a^{4} c^{4} d^{9} e^{9} + 19 \, a^{5} c^{3} d^{7} e^{11} - 2 \, a^{6} c^{2} d^{5} e^{13} - 3 \, a^{7} c d^{3} e^{15} + a^{8} d e^{17}\right)} x^{3} + {\left(c^{8} d^{18} + 2 \, a c^{7} d^{16} e^{2} - 27 \, a^{2} c^{6} d^{14} e^{4} + 64 \, a^{3} c^{5} d^{12} e^{6} - 55 \, a^{4} c^{4} d^{10} e^{8} - 6 \, a^{5} c^{3} d^{8} e^{10} + 43 \, a^{6} c^{2} d^{6} e^{12} - 28 \, a^{7} c d^{4} e^{14} + 6 \, a^{8} d^{2} e^{16}\right)} x^{2} + 2 \, {\left(a c^{7} d^{17} e - 4 \, a^{2} c^{6} d^{15} e^{3} + 3 \, a^{3} c^{5} d^{13} e^{5} + 10 \, a^{4} c^{4} d^{11} e^{7} - 25 \, a^{5} c^{3} d^{9} e^{9} + 24 \, a^{6} c^{2} d^{7} e^{11} - 11 \, a^{7} c d^{5} e^{13} + 2 \, a^{8} d^{3} e^{15}\right)} x\right)}}"," ",0,"2/21*(256*c^5*d^5*e^5*x^5 - 7*c^5*d^10 + 105*a*c^4*d^8*e^2 + 210*a^2*c^3*d^6*e^4 - 70*a^3*c^2*d^4*e^6 + 21*a^4*c*d^2*e^8 - 3*a^5*e^10 + 128*(7*c^5*d^6*e^4 + 3*a*c^4*d^4*e^6)*x^4 + 32*(35*c^5*d^7*e^3 + 42*a*c^4*d^5*e^5 + 3*a^2*c^3*d^3*e^7)*x^3 + 16*(35*c^5*d^8*e^2 + 105*a*c^4*d^6*e^4 + 21*a^2*c^3*d^4*e^6 - a^3*c^2*d^2*e^8)*x^2 + 2*(35*c^5*d^9*e + 420*a*c^4*d^7*e^3 + 210*a^2*c^3*d^5*e^5 - 28*a^3*c^2*d^3*e^7 + 3*a^4*c*d*e^9)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a^2*c^6*d^16*e^2 - 6*a^3*c^5*d^14*e^4 + 15*a^4*c^4*d^12*e^6 - 20*a^5*c^3*d^10*e^8 + 15*a^6*c^2*d^8*e^10 - 6*a^7*c*d^6*e^12 + a^8*d^4*e^14 + (c^8*d^14*e^4 - 6*a*c^7*d^12*e^6 + 15*a^2*c^6*d^10*e^8 - 20*a^3*c^5*d^8*e^10 + 15*a^4*c^4*d^6*e^12 - 6*a^5*c^3*d^4*e^14 + a^6*c^2*d^2*e^16)*x^6 + 2*(2*c^8*d^15*e^3 - 11*a*c^7*d^13*e^5 + 24*a^2*c^6*d^11*e^7 - 25*a^3*c^5*d^9*e^9 + 10*a^4*c^4*d^7*e^11 + 3*a^5*c^3*d^5*e^13 - 4*a^6*c^2*d^3*e^15 + a^7*c*d*e^17)*x^5 + (6*c^8*d^16*e^2 - 28*a*c^7*d^14*e^4 + 43*a^2*c^6*d^12*e^6 - 6*a^3*c^5*d^10*e^8 - 55*a^4*c^4*d^8*e^10 + 64*a^5*c^3*d^6*e^12 - 27*a^6*c^2*d^4*e^14 + 2*a^7*c*d^2*e^16 + a^8*e^18)*x^4 + 4*(c^8*d^17*e - 3*a*c^7*d^15*e^3 - 2*a^2*c^6*d^13*e^5 + 19*a^3*c^5*d^11*e^7 - 30*a^4*c^4*d^9*e^9 + 19*a^5*c^3*d^7*e^11 - 2*a^6*c^2*d^5*e^13 - 3*a^7*c*d^3*e^15 + a^8*d*e^17)*x^3 + (c^8*d^18 + 2*a*c^7*d^16*e^2 - 27*a^2*c^6*d^14*e^4 + 64*a^3*c^5*d^12*e^6 - 55*a^4*c^4*d^10*e^8 - 6*a^5*c^3*d^8*e^10 + 43*a^6*c^2*d^6*e^12 - 28*a^7*c*d^4*e^14 + 6*a^8*d^2*e^16)*x^2 + 2*(a*c^7*d^17*e - 4*a^2*c^6*d^15*e^3 + 3*a^3*c^5*d^13*e^5 + 10*a^4*c^4*d^11*e^7 - 25*a^5*c^3*d^9*e^9 + 24*a^6*c^2*d^7*e^11 - 11*a^7*c*d^5*e^13 + 2*a^8*d^3*e^15)*x)","B",0
1973,1,1392,0,110.048622," ","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=""fricas"")","\frac{2 \, {\left(1024 \, c^{6} d^{6} e^{6} x^{6} - 21 \, c^{6} d^{12} + 378 \, a c^{5} d^{10} e^{2} + 945 \, a^{2} c^{4} d^{8} e^{4} - 420 \, a^{3} c^{3} d^{6} e^{6} + 189 \, a^{4} c^{2} d^{4} e^{8} - 54 \, a^{5} c d^{2} e^{10} + 7 \, a^{6} e^{12} + 1536 \, {\left(3 \, c^{6} d^{7} e^{5} + a c^{5} d^{5} e^{7}\right)} x^{5} + 384 \, {\left(21 \, c^{6} d^{8} e^{4} + 18 \, a c^{5} d^{6} e^{6} + a^{2} c^{4} d^{4} e^{8}\right)} x^{4} + 64 \, {\left(105 \, c^{6} d^{9} e^{3} + 189 \, a c^{5} d^{7} e^{5} + 27 \, a^{2} c^{4} d^{5} e^{7} - a^{3} c^{3} d^{3} e^{9}\right)} x^{3} + 24 \, {\left(105 \, c^{6} d^{10} e^{2} + 420 \, a c^{5} d^{8} e^{4} + 126 \, a^{2} c^{4} d^{6} e^{6} - 12 \, a^{3} c^{3} d^{4} e^{8} + a^{4} c^{2} d^{2} e^{10}\right)} x^{2} + 12 \, {\left(21 \, c^{6} d^{11} e + 315 \, a c^{5} d^{9} e^{3} + 210 \, a^{2} c^{4} d^{7} e^{5} - 42 \, a^{3} c^{3} d^{5} e^{7} + 9 \, a^{4} c^{2} d^{3} e^{9} - a^{5} c d e^{11}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}{63 \, {\left(a^{2} c^{7} d^{19} e^{2} - 7 \, a^{3} c^{6} d^{17} e^{4} + 21 \, a^{4} c^{5} d^{15} e^{6} - 35 \, a^{5} c^{4} d^{13} e^{8} + 35 \, a^{6} c^{3} d^{11} e^{10} - 21 \, a^{7} c^{2} d^{9} e^{12} + 7 \, a^{8} c d^{7} e^{14} - a^{9} d^{5} e^{16} + {\left(c^{9} d^{16} e^{5} - 7 \, a c^{8} d^{14} e^{7} + 21 \, a^{2} c^{7} d^{12} e^{9} - 35 \, a^{3} c^{6} d^{10} e^{11} + 35 \, a^{4} c^{5} d^{8} e^{13} - 21 \, a^{5} c^{4} d^{6} e^{15} + 7 \, a^{6} c^{3} d^{4} e^{17} - a^{7} c^{2} d^{2} e^{19}\right)} x^{7} + {\left(5 \, c^{9} d^{17} e^{4} - 33 \, a c^{8} d^{15} e^{6} + 91 \, a^{2} c^{7} d^{13} e^{8} - 133 \, a^{3} c^{6} d^{11} e^{10} + 105 \, a^{4} c^{5} d^{9} e^{12} - 35 \, a^{5} c^{4} d^{7} e^{14} - 7 \, a^{6} c^{3} d^{5} e^{16} + 9 \, a^{7} c^{2} d^{3} e^{18} - 2 \, a^{8} c d e^{20}\right)} x^{6} + {\left(10 \, c^{9} d^{18} e^{3} - 60 \, a c^{8} d^{16} e^{5} + 141 \, a^{2} c^{7} d^{14} e^{7} - 147 \, a^{3} c^{6} d^{12} e^{9} + 21 \, a^{4} c^{5} d^{10} e^{11} + 105 \, a^{5} c^{4} d^{8} e^{13} - 105 \, a^{6} c^{3} d^{6} e^{15} + 39 \, a^{7} c^{2} d^{4} e^{17} - 3 \, a^{8} c d^{2} e^{19} - a^{9} e^{21}\right)} x^{5} + 5 \, {\left(2 \, c^{9} d^{19} e^{2} - 10 \, a c^{8} d^{17} e^{4} + 15 \, a^{2} c^{7} d^{15} e^{6} + 7 \, a^{3} c^{6} d^{13} e^{8} - 49 \, a^{4} c^{5} d^{11} e^{10} + 63 \, a^{5} c^{4} d^{9} e^{12} - 35 \, a^{6} c^{3} d^{7} e^{14} + 5 \, a^{7} c^{2} d^{5} e^{16} + 3 \, a^{8} c d^{3} e^{18} - a^{9} d e^{20}\right)} x^{4} + 5 \, {\left(c^{9} d^{20} e - 3 \, a c^{8} d^{18} e^{3} - 5 \, a^{2} c^{7} d^{16} e^{5} + 35 \, a^{3} c^{6} d^{14} e^{7} - 63 \, a^{4} c^{5} d^{12} e^{9} + 49 \, a^{5} c^{4} d^{10} e^{11} - 7 \, a^{6} c^{3} d^{8} e^{13} - 15 \, a^{7} c^{2} d^{6} e^{15} + 10 \, a^{8} c d^{4} e^{17} - 2 \, a^{9} d^{2} e^{19}\right)} x^{3} + {\left(c^{9} d^{21} + 3 \, a c^{8} d^{19} e^{2} - 39 \, a^{2} c^{7} d^{17} e^{4} + 105 \, a^{3} c^{6} d^{15} e^{6} - 105 \, a^{4} c^{5} d^{13} e^{8} - 21 \, a^{5} c^{4} d^{11} e^{10} + 147 \, a^{6} c^{3} d^{9} e^{12} - 141 \, a^{7} c^{2} d^{7} e^{14} + 60 \, a^{8} c d^{5} e^{16} - 10 \, a^{9} d^{3} e^{18}\right)} x^{2} + {\left(2 \, a c^{8} d^{20} e - 9 \, a^{2} c^{7} d^{18} e^{3} + 7 \, a^{3} c^{6} d^{16} e^{5} + 35 \, a^{4} c^{5} d^{14} e^{7} - 105 \, a^{5} c^{4} d^{12} e^{9} + 133 \, a^{6} c^{3} d^{10} e^{11} - 91 \, a^{7} c^{2} d^{8} e^{13} + 33 \, a^{8} c d^{6} e^{15} - 5 \, a^{9} d^{4} e^{17}\right)} x\right)}}"," ",0,"2/63*(1024*c^6*d^6*e^6*x^6 - 21*c^6*d^12 + 378*a*c^5*d^10*e^2 + 945*a^2*c^4*d^8*e^4 - 420*a^3*c^3*d^6*e^6 + 189*a^4*c^2*d^4*e^8 - 54*a^5*c*d^2*e^10 + 7*a^6*e^12 + 1536*(3*c^6*d^7*e^5 + a*c^5*d^5*e^7)*x^5 + 384*(21*c^6*d^8*e^4 + 18*a*c^5*d^6*e^6 + a^2*c^4*d^4*e^8)*x^4 + 64*(105*c^6*d^9*e^3 + 189*a*c^5*d^7*e^5 + 27*a^2*c^4*d^5*e^7 - a^3*c^3*d^3*e^9)*x^3 + 24*(105*c^6*d^10*e^2 + 420*a*c^5*d^8*e^4 + 126*a^2*c^4*d^6*e^6 - 12*a^3*c^3*d^4*e^8 + a^4*c^2*d^2*e^10)*x^2 + 12*(21*c^6*d^11*e + 315*a*c^5*d^9*e^3 + 210*a^2*c^4*d^7*e^5 - 42*a^3*c^3*d^5*e^7 + 9*a^4*c^2*d^3*e^9 - a^5*c*d*e^11)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)/(a^2*c^7*d^19*e^2 - 7*a^3*c^6*d^17*e^4 + 21*a^4*c^5*d^15*e^6 - 35*a^5*c^4*d^13*e^8 + 35*a^6*c^3*d^11*e^10 - 21*a^7*c^2*d^9*e^12 + 7*a^8*c*d^7*e^14 - a^9*d^5*e^16 + (c^9*d^16*e^5 - 7*a*c^8*d^14*e^7 + 21*a^2*c^7*d^12*e^9 - 35*a^3*c^6*d^10*e^11 + 35*a^4*c^5*d^8*e^13 - 21*a^5*c^4*d^6*e^15 + 7*a^6*c^3*d^4*e^17 - a^7*c^2*d^2*e^19)*x^7 + (5*c^9*d^17*e^4 - 33*a*c^8*d^15*e^6 + 91*a^2*c^7*d^13*e^8 - 133*a^3*c^6*d^11*e^10 + 105*a^4*c^5*d^9*e^12 - 35*a^5*c^4*d^7*e^14 - 7*a^6*c^3*d^5*e^16 + 9*a^7*c^2*d^3*e^18 - 2*a^8*c*d*e^20)*x^6 + (10*c^9*d^18*e^3 - 60*a*c^8*d^16*e^5 + 141*a^2*c^7*d^14*e^7 - 147*a^3*c^6*d^12*e^9 + 21*a^4*c^5*d^10*e^11 + 105*a^5*c^4*d^8*e^13 - 105*a^6*c^3*d^6*e^15 + 39*a^7*c^2*d^4*e^17 - 3*a^8*c*d^2*e^19 - a^9*e^21)*x^5 + 5*(2*c^9*d^19*e^2 - 10*a*c^8*d^17*e^4 + 15*a^2*c^7*d^15*e^6 + 7*a^3*c^6*d^13*e^8 - 49*a^4*c^5*d^11*e^10 + 63*a^5*c^4*d^9*e^12 - 35*a^6*c^3*d^7*e^14 + 5*a^7*c^2*d^5*e^16 + 3*a^8*c*d^3*e^18 - a^9*d*e^20)*x^4 + 5*(c^9*d^20*e - 3*a*c^8*d^18*e^3 - 5*a^2*c^7*d^16*e^5 + 35*a^3*c^6*d^14*e^7 - 63*a^4*c^5*d^12*e^9 + 49*a^5*c^4*d^10*e^11 - 7*a^6*c^3*d^8*e^13 - 15*a^7*c^2*d^6*e^15 + 10*a^8*c*d^4*e^17 - 2*a^9*d^2*e^19)*x^3 + (c^9*d^21 + 3*a*c^8*d^19*e^2 - 39*a^2*c^7*d^17*e^4 + 105*a^3*c^6*d^15*e^6 - 105*a^4*c^5*d^13*e^8 - 21*a^5*c^4*d^11*e^10 + 147*a^6*c^3*d^9*e^12 - 141*a^7*c^2*d^7*e^14 + 60*a^8*c*d^5*e^16 - 10*a^9*d^3*e^18)*x^2 + (2*a*c^8*d^20*e - 9*a^2*c^7*d^18*e^3 + 7*a^3*c^6*d^16*e^5 + 35*a^4*c^5*d^14*e^7 - 105*a^5*c^4*d^12*e^9 + 133*a^6*c^3*d^10*e^11 - 91*a^7*c^2*d^8*e^13 + 33*a^8*c*d^6*e^15 - 5*a^9*d^4*e^17)*x)","B",0
1974,0,0,0,0.432922," ","integrate((e*x+d)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{2}{3}}}{c d x + a e}, x\right)"," ",0,"integral((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(2/3)/(c*d*x + a*e), x)","F",0
1975,0,0,0,0.400942," ","integrate(1/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^(-1/3), x)","F",0
1976,1,98,0,0.390985," ","integrate((e*x+d)^(3/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, c d e^{4} x^{4} - 2 \, c d^{5} + 9 \, a d^{3} e^{2} + {\left(19 \, c d^{2} e^{3} + 9 \, a e^{5}\right)} x^{3} + 3 \, {\left(5 \, c d^{3} e^{2} + 9 \, a d e^{4}\right)} x^{2} + {\left(c d^{4} e + 27 \, a d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{63 \, e^{2}}"," ",0,"2/63*(7*c*d*e^4*x^4 - 2*c*d^5 + 9*a*d^3*e^2 + (19*c*d^2*e^3 + 9*a*e^5)*x^3 + 3*(5*c*d^3*e^2 + 9*a*d*e^4)*x^2 + (c*d^4*e + 27*a*d^2*e^3)*x)*sqrt(e*x + d)/e^2","B",0
1977,1,74,0,0.386835," ","integrate((e*x+d)^(1/2)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c d e^{3} x^{3} - 2 \, c d^{4} + 7 \, a d^{2} e^{2} + {\left(8 \, c d^{2} e^{2} + 7 \, a e^{4}\right)} x^{2} + {\left(c d^{3} e + 14 \, a d e^{3}\right)} x\right)} \sqrt{e x + d}}{35 \, e^{2}}"," ",0,"2/35*(5*c*d*e^3*x^3 - 2*c*d^4 + 7*a*d^2*e^2 + (8*c*d^2*e^2 + 7*a*e^4)*x^2 + (c*d^3*e + 14*a*d*e^3)*x)*sqrt(e*x + d)/e^2","B",0
1978,1,51,0,0.403538," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c d e^{2} x^{2} - 2 \, c d^{3} + 5 \, a d e^{2} + {\left(c d^{2} e + 5 \, a e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, e^{2}}"," ",0,"2/15*(3*c*d*e^2*x^2 - 2*c*d^3 + 5*a*d*e^2 + (c*d^2*e + 5*a*e^3)*x)*sqrt(e*x + d)/e^2","A",0
1979,1,30,0,0.393797," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c d e x - 2 \, c d^{2} + 3 \, a e^{2}\right)} \sqrt{e x + d}}{3 \, e^{2}}"," ",0,"2/3*(c*d*e*x - 2*c*d^2 + 3*a*e^2)*sqrt(e*x + d)/e^2","A",0
1980,1,40,0,0.421930," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c d e x + 2 \, c d^{2} - a e^{2}\right)} \sqrt{e x + d}}{e^{3} x + d e^{2}}"," ",0,"2*(c*d*e*x + 2*c*d^2 - a*e^2)*sqrt(e*x + d)/(e^3*x + d*e^2)","A",0
1981,1,51,0,0.390431," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, c d e x + 2 \, c d^{2} + a e^{2}\right)} \sqrt{e x + d}}{3 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}"," ",0,"-2/3*(3*c*d*e*x + 2*c*d^2 + a*e^2)*sqrt(e*x + d)/(e^4*x^2 + 2*d*e^3*x + d^2*e^2)","A",0
1982,1,63,0,0.410345," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, c d e x + 2 \, c d^{2} + 3 \, a e^{2}\right)} \sqrt{e x + d}}{15 \, {\left(e^{5} x^{3} + 3 \, d e^{4} x^{2} + 3 \, d^{2} e^{3} x + d^{3} e^{2}\right)}}"," ",0,"-2/15*(5*c*d*e*x + 2*c*d^2 + 3*a*e^2)*sqrt(e*x + d)/(e^5*x^3 + 3*d*e^4*x^2 + 3*d^2*e^3*x + d^3*e^2)","A",0
1983,1,74,0,0.411685," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(7 \, c d e x + 2 \, c d^{2} + 5 \, a e^{2}\right)} \sqrt{e x + d}}{35 \, {\left(e^{6} x^{4} + 4 \, d e^{5} x^{3} + 6 \, d^{2} e^{4} x^{2} + 4 \, d^{3} e^{3} x + d^{4} e^{2}\right)}}"," ",0,"-2/35*(7*c*d*e*x + 2*c*d^2 + 5*a*e^2)*sqrt(e*x + d)/(e^6*x^4 + 4*d*e^5*x^3 + 6*d^2*e^4*x^2 + 4*d^3*e^3*x + d^4*e^2)","B",0
1984,1,184,0,0.396940," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, c^{2} d^{2} e^{5} x^{5} + 8 \, c^{2} d^{7} - 44 \, a c d^{5} e^{2} + 99 \, a^{2} d^{3} e^{4} + 7 \, {\left(23 \, c^{2} d^{3} e^{4} + 22 \, a c d e^{6}\right)} x^{4} + {\left(113 \, c^{2} d^{4} e^{3} + 418 \, a c d^{2} e^{5} + 99 \, a^{2} e^{7}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{2} + 110 \, a c d^{3} e^{4} + 99 \, a^{2} d e^{6}\right)} x^{2} - {\left(4 \, c^{2} d^{6} e - 22 \, a c d^{4} e^{3} - 297 \, a^{2} d^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{693 \, e^{3}}"," ",0,"2/693*(63*c^2*d^2*e^5*x^5 + 8*c^2*d^7 - 44*a*c*d^5*e^2 + 99*a^2*d^3*e^4 + 7*(23*c^2*d^3*e^4 + 22*a*c*d*e^6)*x^4 + (113*c^2*d^4*e^3 + 418*a*c*d^2*e^5 + 99*a^2*e^7)*x^3 + 3*(c^2*d^5*e^2 + 110*a*c*d^3*e^4 + 99*a^2*d*e^6)*x^2 - (4*c^2*d^6*e - 22*a*c*d^4*e^3 - 297*a^2*d^2*e^5)*x)*sqrt(e*x + d)/e^3","B",0
1985,1,147,0,0.387472," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{2} d^{2} e^{4} x^{4} + 8 \, c^{2} d^{6} - 36 \, a c d^{4} e^{2} + 63 \, a^{2} d^{2} e^{4} + 10 \, {\left(5 \, c^{2} d^{3} e^{3} + 9 \, a c d e^{5}\right)} x^{3} + 3 \, {\left(c^{2} d^{4} e^{2} + 48 \, a c d^{2} e^{4} + 21 \, a^{2} e^{6}\right)} x^{2} - 2 \, {\left(2 \, c^{2} d^{5} e - 9 \, a c d^{3} e^{3} - 63 \, a^{2} d e^{5}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{3}}"," ",0,"2/315*(35*c^2*d^2*e^4*x^4 + 8*c^2*d^6 - 36*a*c*d^4*e^2 + 63*a^2*d^2*e^4 + 10*(5*c^2*d^3*e^3 + 9*a*c*d*e^5)*x^3 + 3*(c^2*d^4*e^2 + 48*a*c*d^2*e^4 + 21*a^2*e^6)*x^2 - 2*(2*c^2*d^5*e - 9*a*c*d^3*e^3 - 63*a^2*d*e^5)*x)*sqrt(e*x + d)/e^3","B",0
1986,1,109,0,0.403921," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c^{2} d^{2} e^{3} x^{3} + 8 \, c^{2} d^{5} - 28 \, a c d^{3} e^{2} + 35 \, a^{2} d e^{4} + 3 \, {\left(c^{2} d^{3} e^{2} + 14 \, a c d e^{4}\right)} x^{2} - {\left(4 \, c^{2} d^{4} e - 14 \, a c d^{2} e^{3} - 35 \, a^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{3}}"," ",0,"2/105*(15*c^2*d^2*e^3*x^3 + 8*c^2*d^5 - 28*a*c*d^3*e^2 + 35*a^2*d*e^4 + 3*(c^2*d^3*e^2 + 14*a*c*d*e^4)*x^2 - (4*c^2*d^4*e - 14*a*c*d^2*e^3 - 35*a^2*e^5)*x)*sqrt(e*x + d)/e^3","A",0
1987,1,74,0,0.406156," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} d^{2} e^{2} x^{2} + 8 \, c^{2} d^{4} - 20 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} - 2 \, {\left(2 \, c^{2} d^{3} e - 5 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, e^{3}}"," ",0,"2/15*(3*c^2*d^2*e^2*x^2 + 8*c^2*d^4 - 20*a*c*d^2*e^2 + 15*a^2*e^4 - 2*(2*c^2*d^3*e - 5*a*c*d*e^3)*x)*sqrt(e*x + d)/e^3","A",0
1988,1,83,0,0.408013," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{2} d^{2} e^{2} x^{2} - 8 \, c^{2} d^{4} + 12 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4} - 2 \, {\left(2 \, c^{2} d^{3} e - 3 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{4} x + d e^{3}\right)}}"," ",0,"2/3*(c^2*d^2*e^2*x^2 - 8*c^2*d^4 + 12*a*c*d^2*e^2 - 3*a^2*e^4 - 2*(2*c^2*d^3*e - 3*a*c*d*e^3)*x)*sqrt(e*x + d)/(e^4*x + d*e^3)","A",0
1989,1,95,0,0.395436," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} d^{2} e^{2} x^{2} + 8 \, c^{2} d^{4} - 4 \, a c d^{2} e^{2} - a^{2} e^{4} + 6 \, {\left(2 \, c^{2} d^{3} e - a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"2/3*(3*c^2*d^2*e^2*x^2 + 8*c^2*d^4 - 4*a*c*d^2*e^2 - a^2*e^4 + 6*(2*c^2*d^3*e - a*c*d*e^3)*x)*sqrt(e*x + d)/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
1990,1,105,0,0.399389," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, c^{2} d^{2} e^{2} x^{2} + 8 \, c^{2} d^{4} + 4 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} + 10 \, {\left(2 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-2/15*(15*c^2*d^2*e^2*x^2 + 8*c^2*d^4 + 4*a*c*d^2*e^2 + 3*a^2*e^4 + 10*(2*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(e*x + d)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
1991,1,117,0,0.400141," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2/(e*x+d)^(13/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, c^{2} d^{2} e^{2} x^{2} + 8 \, c^{2} d^{4} + 12 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} + 14 \, {\left(2 \, c^{2} d^{3} e + 3 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-2/105*(35*c^2*d^2*e^2*x^2 + 8*c^2*d^4 + 12*a*c*d^2*e^2 + 15*a^2*e^4 + 14*(2*c^2*d^3*e + 3*a*c*d*e^3)*x)*sqrt(e*x + d)/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)","A",0
1992,1,335,0,0.400173," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(429 \, c^{3} d^{3} e^{7} x^{7} - 16 \, c^{3} d^{10} + 120 \, a c^{2} d^{8} e^{2} - 390 \, a^{2} c d^{6} e^{4} + 715 \, a^{3} d^{4} e^{6} + 33 \, {\left(46 \, c^{3} d^{4} e^{6} + 45 \, a c^{2} d^{2} e^{8}\right)} x^{6} + 9 \, {\left(206 \, c^{3} d^{5} e^{5} + 600 \, a c^{2} d^{3} e^{7} + 195 \, a^{2} c d e^{9}\right)} x^{5} + 5 \, {\left(160 \, c^{3} d^{6} e^{4} + 1374 \, a c^{2} d^{4} e^{6} + 1326 \, a^{2} c d^{2} e^{8} + 143 \, a^{3} e^{10}\right)} x^{4} + 5 \, {\left(c^{3} d^{7} e^{3} + 636 \, a c^{2} d^{5} e^{5} + 1794 \, a^{2} c d^{3} e^{7} + 572 \, a^{3} d e^{9}\right)} x^{3} - 3 \, {\left(2 \, c^{3} d^{8} e^{2} - 15 \, a c^{2} d^{6} e^{4} - 1560 \, a^{2} c d^{4} e^{6} - 1430 \, a^{3} d^{2} e^{8}\right)} x^{2} + {\left(8 \, c^{3} d^{9} e - 60 \, a c^{2} d^{7} e^{3} + 195 \, a^{2} c d^{5} e^{5} + 2860 \, a^{3} d^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{6435 \, e^{4}}"," ",0,"2/6435*(429*c^3*d^3*e^7*x^7 - 16*c^3*d^10 + 120*a*c^2*d^8*e^2 - 390*a^2*c*d^6*e^4 + 715*a^3*d^4*e^6 + 33*(46*c^3*d^4*e^6 + 45*a*c^2*d^2*e^8)*x^6 + 9*(206*c^3*d^5*e^5 + 600*a*c^2*d^3*e^7 + 195*a^2*c*d*e^9)*x^5 + 5*(160*c^3*d^6*e^4 + 1374*a*c^2*d^4*e^6 + 1326*a^2*c*d^2*e^8 + 143*a^3*e^10)*x^4 + 5*(c^3*d^7*e^3 + 636*a*c^2*d^5*e^5 + 1794*a^2*c*d^3*e^7 + 572*a^3*d*e^9)*x^3 - 3*(2*c^3*d^8*e^2 - 15*a*c^2*d^6*e^4 - 1560*a^2*c*d^4*e^6 - 1430*a^3*d^2*e^8)*x^2 + (8*c^3*d^9*e - 60*a*c^2*d^7*e^3 + 195*a^2*c*d^5*e^5 + 2860*a^3*d^3*e^7)*x)*sqrt(e*x + d)/e^4","B",0
1993,1,283,0,0.400585," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, c^{3} d^{3} e^{6} x^{6} - 16 \, c^{3} d^{9} + 104 \, a c^{2} d^{7} e^{2} - 286 \, a^{2} c d^{5} e^{4} + 429 \, a^{3} d^{3} e^{6} + 63 \, {\left(9 \, c^{3} d^{4} e^{5} + 13 \, a c^{2} d^{2} e^{7}\right)} x^{5} + 7 \, {\left(53 \, c^{3} d^{5} e^{4} + 299 \, a c^{2} d^{3} e^{6} + 143 \, a^{2} c d e^{8}\right)} x^{4} + {\left(5 \, c^{3} d^{6} e^{3} + 1469 \, a c^{2} d^{4} e^{5} + 2717 \, a^{2} c d^{2} e^{7} + 429 \, a^{3} e^{9}\right)} x^{3} - 3 \, {\left(2 \, c^{3} d^{7} e^{2} - 13 \, a c^{2} d^{5} e^{4} - 715 \, a^{2} c d^{3} e^{6} - 429 \, a^{3} d e^{8}\right)} x^{2} + {\left(8 \, c^{3} d^{8} e - 52 \, a c^{2} d^{6} e^{3} + 143 \, a^{2} c d^{4} e^{5} + 1287 \, a^{3} d^{2} e^{7}\right)} x\right)} \sqrt{e x + d}}{3003 \, e^{4}}"," ",0,"2/3003*(231*c^3*d^3*e^6*x^6 - 16*c^3*d^9 + 104*a*c^2*d^7*e^2 - 286*a^2*c*d^5*e^4 + 429*a^3*d^3*e^6 + 63*(9*c^3*d^4*e^5 + 13*a*c^2*d^2*e^7)*x^5 + 7*(53*c^3*d^5*e^4 + 299*a*c^2*d^3*e^6 + 143*a^2*c*d*e^8)*x^4 + (5*c^3*d^6*e^3 + 1469*a*c^2*d^4*e^5 + 2717*a^2*c*d^2*e^7 + 429*a^3*e^9)*x^3 - 3*(2*c^3*d^7*e^2 - 13*a*c^2*d^5*e^4 - 715*a^2*c*d^3*e^6 - 429*a^3*d*e^8)*x^2 + (8*c^3*d^8*e - 52*a*c^2*d^6*e^3 + 143*a^2*c*d^4*e^5 + 1287*a^3*d^2*e^7)*x)*sqrt(e*x + d)/e^4","B",0
1994,1,231,0,0.395300," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, c^{3} d^{3} e^{5} x^{5} - 16 \, c^{3} d^{8} + 88 \, a c^{2} d^{6} e^{2} - 198 \, a^{2} c d^{4} e^{4} + 231 \, a^{3} d^{2} e^{6} + 35 \, {\left(4 \, c^{3} d^{4} e^{4} + 11 \, a c^{2} d^{2} e^{6}\right)} x^{4} + 5 \, {\left(c^{3} d^{5} e^{3} + 110 \, a c^{2} d^{3} e^{5} + 99 \, a^{2} c d e^{7}\right)} x^{3} - 3 \, {\left(2 \, c^{3} d^{6} e^{2} - 11 \, a c^{2} d^{4} e^{4} - 264 \, a^{2} c d^{2} e^{6} - 77 \, a^{3} e^{8}\right)} x^{2} + {\left(8 \, c^{3} d^{7} e - 44 \, a c^{2} d^{5} e^{3} + 99 \, a^{2} c d^{3} e^{5} + 462 \, a^{3} d e^{7}\right)} x\right)} \sqrt{e x + d}}{1155 \, e^{4}}"," ",0,"2/1155*(105*c^3*d^3*e^5*x^5 - 16*c^3*d^8 + 88*a*c^2*d^6*e^2 - 198*a^2*c*d^4*e^4 + 231*a^3*d^2*e^6 + 35*(4*c^3*d^4*e^4 + 11*a*c^2*d^2*e^6)*x^4 + 5*(c^3*d^5*e^3 + 110*a*c^2*d^3*e^5 + 99*a^2*c*d*e^7)*x^3 - 3*(2*c^3*d^6*e^2 - 11*a*c^2*d^4*e^4 - 264*a^2*c*d^2*e^6 - 77*a^3*e^8)*x^2 + (8*c^3*d^7*e - 44*a*c^2*d^5*e^3 + 99*a^2*c*d^3*e^5 + 462*a^3*d*e^7)*x)*sqrt(e*x + d)/e^4","B",0
1995,1,179,0,0.440048," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{3} d^{3} e^{4} x^{4} - 16 \, c^{3} d^{7} + 72 \, a c^{2} d^{5} e^{2} - 126 \, a^{2} c d^{3} e^{4} + 105 \, a^{3} d e^{6} + 5 \, {\left(c^{3} d^{4} e^{3} + 27 \, a c^{2} d^{2} e^{5}\right)} x^{3} - 3 \, {\left(2 \, c^{3} d^{5} e^{2} - 9 \, a c^{2} d^{3} e^{4} - 63 \, a^{2} c d e^{6}\right)} x^{2} + {\left(8 \, c^{3} d^{6} e - 36 \, a c^{2} d^{4} e^{3} + 63 \, a^{2} c d^{2} e^{5} + 105 \, a^{3} e^{7}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{4}}"," ",0,"2/315*(35*c^3*d^3*e^4*x^4 - 16*c^3*d^7 + 72*a*c^2*d^5*e^2 - 126*a^2*c*d^3*e^4 + 105*a^3*d*e^6 + 5*(c^3*d^4*e^3 + 27*a*c^2*d^2*e^5)*x^3 - 3*(2*c^3*d^5*e^2 - 9*a*c^2*d^3*e^4 - 63*a^2*c*d*e^6)*x^2 + (8*c^3*d^6*e - 36*a*c^2*d^4*e^3 + 63*a^2*c*d^2*e^5 + 105*a^3*e^7)*x)*sqrt(e*x + d)/e^4","A",0
1996,1,130,0,0.413042," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{3} d^{3} e^{3} x^{3} - 16 \, c^{3} d^{6} + 56 \, a c^{2} d^{4} e^{2} - 70 \, a^{2} c d^{2} e^{4} + 35 \, a^{3} e^{6} - 3 \, {\left(2 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(8 \, c^{3} d^{5} e - 28 \, a c^{2} d^{3} e^{3} + 35 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{35 \, e^{4}}"," ",0,"2/35*(5*c^3*d^3*e^3*x^3 - 16*c^3*d^6 + 56*a*c^2*d^4*e^2 - 70*a^2*c*d^2*e^4 + 35*a^3*e^6 - 3*(2*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 + (8*c^3*d^5*e - 28*a*c^2*d^3*e^3 + 35*a^2*c*d*e^5)*x)*sqrt(e*x + d)/e^4","A",0
1997,1,139,0,0.409230," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{3} d^{3} e^{3} x^{3} + 16 \, c^{3} d^{6} - 40 \, a c^{2} d^{4} e^{2} + 30 \, a^{2} c d^{2} e^{4} - 5 \, a^{3} e^{6} - {\left(2 \, c^{3} d^{4} e^{2} - 5 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(8 \, c^{3} d^{5} e - 20 \, a c^{2} d^{3} e^{3} + 15 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{5 \, {\left(e^{5} x + d e^{4}\right)}}"," ",0,"2/5*(c^3*d^3*e^3*x^3 + 16*c^3*d^6 - 40*a*c^2*d^4*e^2 + 30*a^2*c*d^2*e^4 - 5*a^3*e^6 - (2*c^3*d^4*e^2 - 5*a*c^2*d^2*e^4)*x^2 + (8*c^3*d^5*e - 20*a*c^2*d^3*e^3 + 15*a^2*c*d*e^5)*x)*sqrt(e*x + d)/(e^5*x + d*e^4)","A",0
1998,1,151,0,0.418496," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c^{3} d^{3} e^{3} x^{3} - 16 \, c^{3} d^{6} + 24 \, a c^{2} d^{4} e^{2} - 6 \, a^{2} c d^{2} e^{4} - a^{3} e^{6} - 3 \, {\left(2 \, c^{3} d^{4} e^{2} - 3 \, a c^{2} d^{2} e^{4}\right)} x^{2} - 3 \, {\left(8 \, c^{3} d^{5} e - 12 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{6} x^{2} + 2 \, d e^{5} x + d^{2} e^{4}\right)}}"," ",0,"2/3*(c^3*d^3*e^3*x^3 - 16*c^3*d^6 + 24*a*c^2*d^4*e^2 - 6*a^2*c*d^2*e^4 - a^3*e^6 - 3*(2*c^3*d^4*e^2 - 3*a*c^2*d^2*e^4)*x^2 - 3*(8*c^3*d^5*e - 12*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x)*sqrt(e*x + d)/(e^6*x^2 + 2*d*e^5*x + d^2*e^4)","A",0
1999,1,163,0,0.408328," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3/(e*x+d)^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{3} d^{3} e^{3} x^{3} + 16 \, c^{3} d^{6} - 8 \, a c^{2} d^{4} e^{2} - 2 \, a^{2} c d^{2} e^{4} - a^{3} e^{6} + 15 \, {\left(2 \, c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 5 \, {\left(8 \, c^{3} d^{5} e - 4 \, a c^{2} d^{3} e^{3} - a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{5 \, {\left(e^{7} x^{3} + 3 \, d e^{6} x^{2} + 3 \, d^{2} e^{5} x + d^{3} e^{4}\right)}}"," ",0,"2/5*(5*c^3*d^3*e^3*x^3 + 16*c^3*d^6 - 8*a*c^2*d^4*e^2 - 2*a^2*c*d^2*e^4 - a^3*e^6 + 15*(2*c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 5*(8*c^3*d^5*e - 4*a*c^2*d^3*e^3 - a^2*c*d*e^5)*x)*sqrt(e*x + d)/(e^7*x^3 + 3*d*e^6*x^2 + 3*d^2*e^5*x + d^3*e^4)","A",0
2000,1,510,0,0.431344," ","integrate((e*x+d)^(9/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\left[\frac{105 \, {\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{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, {\left(15 \, c^{3} d^{3} e^{3} x^{3} + 176 \, c^{3} d^{6} - 406 \, a c^{2} d^{4} e^{2} + 350 \, a^{2} c d^{2} e^{4} - 105 \, a^{3} e^{6} + 3 \, {\left(22 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(122 \, c^{3} d^{5} e - 112 \, a c^{2} d^{3} e^{3} + 35 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{105 \, c^{4} d^{4}}, -\frac{2 \, {\left(105 \, {\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{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - {\left(15 \, c^{3} d^{3} e^{3} x^{3} + 176 \, c^{3} d^{6} - 406 \, a c^{2} d^{4} e^{2} + 350 \, a^{2} c d^{2} e^{4} - 105 \, a^{3} e^{6} + 3 \, {\left(22 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(122 \, c^{3} d^{5} e - 112 \, a c^{2} d^{3} e^{3} + 35 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}\right)}}{105 \, c^{4} d^{4}}\right]"," ",0,"[1/105*(105*(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)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(15*c^3*d^3*e^3*x^3 + 176*c^3*d^6 - 406*a*c^2*d^4*e^2 + 350*a^2*c*d^2*e^4 - 105*a^3*e^6 + 3*(22*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 + (122*c^3*d^5*e - 112*a*c^2*d^3*e^3 + 35*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(c^4*d^4), -2/105*(105*(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)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - (15*c^3*d^3*e^3*x^3 + 176*c^3*d^6 - 406*a*c^2*d^4*e^2 + 350*a^2*c*d^2*e^4 - 105*a^3*e^6 + 3*(22*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 + (122*c^3*d^5*e - 112*a*c^2*d^3*e^3 + 35*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(c^4*d^4)]","A",0
2001,1,366,0,0.441814," ","integrate((e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, {\left(3 \, c^{2} d^{2} e^{2} x^{2} + 23 \, c^{2} d^{4} - 35 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} + {\left(11 \, c^{2} d^{3} e - 5 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, c^{3} d^{3}}, -\frac{2 \, {\left(15 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - {\left(3 \, c^{2} d^{2} e^{2} x^{2} + 23 \, c^{2} d^{4} - 35 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} + {\left(11 \, c^{2} d^{3} e - 5 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, c^{3} d^{3}}\right]"," ",0,"[1/15*(15*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(3*c^2*d^2*e^2*x^2 + 23*c^2*d^4 - 35*a*c*d^2*e^2 + 15*a^2*e^4 + (11*c^2*d^3*e - 5*a*c*d*e^3)*x)*sqrt(e*x + d))/(c^3*d^3), -2/15*(15*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - (3*c^2*d^2*e^2*x^2 + 23*c^2*d^4 - 35*a*c*d^2*e^2 + 15*a^2*e^4 + (11*c^2*d^3*e - 5*a*c*d*e^3)*x)*sqrt(e*x + d))/(c^3*d^3)]","A",0
2002,1,254,0,0.411240," ","integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, {\left(c d e x + 4 \, c d^{2} - 3 \, a e^{2}\right)} \sqrt{e x + d}}{3 \, c^{2} d^{2}}, -\frac{2 \, {\left(3 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - {\left(c d e x + 4 \, c d^{2} - 3 \, a e^{2}\right)} \sqrt{e x + d}\right)}}{3 \, c^{2} d^{2}}\right]"," ",0,"[1/3*(3*(c*d^2 - a*e^2)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(c*d*e*x + 4*c*d^2 - 3*a*e^2)*sqrt(e*x + d))/(c^2*d^2), -2/3*(3*(c*d^2 - a*e^2)*sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - (c*d*e*x + 4*c*d^2 - 3*a*e^2)*sqrt(e*x + d))/(c^2*d^2)]","A",0
2003,1,191,0,0.410666," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, \sqrt{e x + d}}{c d}, -\frac{2 \, {\left(\sqrt{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - \sqrt{e x + d}\right)}}{c d}\right]"," ",0,"[(sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*sqrt(e*x + d))/(c*d), -2*(sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - sqrt(e*x + d))/(c*d)]","A",0
2004,1,155,0,0.420579," ","integrate((e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{c^{2} d^{3} - a c d e^{2}} \sqrt{e x + d}}{c d x + a e}\right)}{\sqrt{c^{2} d^{3} - a c d e^{2}}}, \frac{2 \, \sqrt{-c^{2} d^{3} + a c d e^{2}} \arctan\left(\frac{\sqrt{-c^{2} d^{3} + a c d e^{2}} \sqrt{e x + d}}{c d e x + c d^{2}}\right)}{c^{2} d^{3} - a c d e^{2}}\right]"," ",0,"[log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(c^2*d^3 - a*c*d*e^2)*sqrt(e*x + d))/(c*d*x + a*e))/sqrt(c^2*d^3 - a*c*d*e^2), 2*sqrt(-c^2*d^3 + a*c*d*e^2)*arctan(sqrt(-c^2*d^3 + a*c*d*e^2)*sqrt(e*x + d)/(c*d*e*x + c*d^2))/(c^2*d^3 - a*c*d*e^2)]","A",0
2005,1,261,0,0.424288," ","integrate(1/(e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\left[-\frac{{\left(e x + d\right)} \sqrt{\frac{c d}{c d^{2} - a e^{2}}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} + 2 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{c d}{c d^{2} - a e^{2}}}}{c d x + a e}\right) - 2 \, \sqrt{e x + d}}{c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x}, -\frac{2 \, {\left({\left(e x + d\right)} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}} \arctan\left(-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}}}{c d e x + c d^{2}}\right) - \sqrt{e x + d}\right)}}{c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x}\right]"," ",0,"[-((e*x + d)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 + 2*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) - 2*sqrt(e*x + d))/(c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x), -2*((e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - sqrt(e*x + d))/(c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)]","A",0
2006,1,461,0,0.428036," ","integrate(1/(e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d e^{2} x^{2} + 2 \, c d^{2} e x + c d^{3}\right)} \sqrt{\frac{c d}{c d^{2} - a e^{2}}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{c d}{c d^{2} - a e^{2}}}}{c d x + a e}\right) + 2 \, {\left(3 \, c d e x + 4 \, c d^{2} - a e^{2}\right)} \sqrt{e x + d}}{3 \, {\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)}}, -\frac{2 \, {\left(3 \, {\left(c d e^{2} x^{2} + 2 \, c d^{2} e x + c d^{3}\right)} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}} \arctan\left(-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}}}{c d e x + c d^{2}}\right) - {\left(3 \, c d e x + 4 \, c d^{2} - a e^{2}\right)} \sqrt{e x + d}\right)}}{3 \, {\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)}}\right]"," ",0,"[1/3*(3*(c*d*e^2*x^2 + 2*c*d^2*e*x + c*d^3)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) + 2*(3*c*d*e*x + 4*c*d^2 - a*e^2)*sqrt(e*x + 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), -2/3*(3*(c*d*e^2*x^2 + 2*c*d^2*e*x + c*d^3)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - (3*c*d*e*x + 4*c*d^2 - a*e^2)*sqrt(e*x + 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)]","B",0
2007,1,783,0,0.441531," ","integrate(1/(e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{\frac{c d}{c d^{2} - a e^{2}}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} + 2 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{c d}{c d^{2} - a e^{2}}}}{c d x + a e}\right) - 2 \, {\left(15 \, c^{2} d^{2} e^{2} x^{2} + 23 \, c^{2} d^{4} - 11 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} + 5 \, {\left(7 \, c^{2} d^{3} e - a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(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} + {\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^{3} + 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)} x^{2} + 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)} x\right)}}, -\frac{2 \, {\left(15 \, {\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}} \arctan\left(-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}}}{c d e x + c d^{2}}\right) - {\left(15 \, c^{2} d^{2} e^{2} x^{2} + 23 \, c^{2} d^{4} - 11 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} + 5 \, {\left(7 \, c^{2} d^{3} e - a c d e^{3}\right)} x\right)} \sqrt{e x + d}\right)}}{15 \, {\left(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} + {\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^{3} + 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)} x^{2} + 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)} x\right)}}\right]"," ",0,"[-1/15*(15*(c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 + 2*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) - 2*(15*c^2*d^2*e^2*x^2 + 23*c^2*d^4 - 11*a*c*d^2*e^2 + 3*a^2*e^4 + 5*(7*c^2*d^3*e - a*c*d*e^3)*x)*sqrt(e*x + d))/(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^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^3 + 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)*x^2 + 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)*x), -2/15*(15*(c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - (15*c^2*d^2*e^2*x^2 + 23*c^2*d^4 - 11*a*c*d^2*e^2 + 3*a^2*e^4 + 5*(7*c^2*d^3*e - a*c*d*e^3)*x)*sqrt(e*x + d))/(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^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^3 + 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)*x^2 + 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)*x)]","B",0
2008,1,1157,0,0.433048," ","integrate(1/(e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(c^{3} d^{3} e^{4} x^{4} + 4 \, c^{3} d^{4} e^{3} x^{3} + 6 \, c^{3} d^{5} e^{2} x^{2} + 4 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{\frac{c d}{c d^{2} - a e^{2}}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{c d}{c d^{2} - a e^{2}}}}{c d x + a e}\right) + 2 \, {\left(105 \, c^{3} d^{3} e^{3} x^{3} + 176 \, c^{3} d^{6} - 122 \, a c^{2} d^{4} e^{2} + 66 \, a^{2} c d^{2} e^{4} - 15 \, a^{3} e^{6} + 35 \, {\left(10 \, c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(58 \, c^{3} d^{5} e - 16 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(c^{4} d^{12} - 4 \, a c^{3} d^{10} e^{2} + 6 \, a^{2} c^{2} d^{8} e^{4} - 4 \, a^{3} c d^{6} e^{6} + a^{4} d^{4} e^{8} + {\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)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, a c^{3} d^{7} e^{5} + 6 \, a^{2} c^{2} d^{5} e^{7} - 4 \, a^{3} c d^{3} e^{9} + a^{4} d e^{11}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, a c^{3} d^{8} e^{4} + 6 \, a^{2} c^{2} d^{6} e^{6} - 4 \, a^{3} c d^{4} e^{8} + a^{4} d^{2} e^{10}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, a c^{3} d^{9} e^{3} + 6 \, a^{2} c^{2} d^{7} e^{5} - 4 \, a^{3} c d^{5} e^{7} + a^{4} d^{3} e^{9}\right)} x\right)}}, -\frac{2 \, {\left(105 \, {\left(c^{3} d^{3} e^{4} x^{4} + 4 \, c^{3} d^{4} e^{3} x^{3} + 6 \, c^{3} d^{5} e^{2} x^{2} + 4 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}} \arctan\left(-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}}}{c d e x + c d^{2}}\right) - {\left(105 \, c^{3} d^{3} e^{3} x^{3} + 176 \, c^{3} d^{6} - 122 \, a c^{2} d^{4} e^{2} + 66 \, a^{2} c d^{2} e^{4} - 15 \, a^{3} e^{6} + 35 \, {\left(10 \, c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(58 \, c^{3} d^{5} e - 16 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}\right)}}{105 \, {\left(c^{4} d^{12} - 4 \, a c^{3} d^{10} e^{2} + 6 \, a^{2} c^{2} d^{8} e^{4} - 4 \, a^{3} c d^{6} e^{6} + a^{4} d^{4} e^{8} + {\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)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, a c^{3} d^{7} e^{5} + 6 \, a^{2} c^{2} d^{5} e^{7} - 4 \, a^{3} c d^{3} e^{9} + a^{4} d e^{11}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, a c^{3} d^{8} e^{4} + 6 \, a^{2} c^{2} d^{6} e^{6} - 4 \, a^{3} c d^{4} e^{8} + a^{4} d^{2} e^{10}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, a c^{3} d^{9} e^{3} + 6 \, a^{2} c^{2} d^{7} e^{5} - 4 \, a^{3} c d^{5} e^{7} + a^{4} d^{3} e^{9}\right)} x\right)}}\right]"," ",0,"[1/105*(105*(c^3*d^3*e^4*x^4 + 4*c^3*d^4*e^3*x^3 + 6*c^3*d^5*e^2*x^2 + 4*c^3*d^6*e*x + c^3*d^7)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) + 2*(105*c^3*d^3*e^3*x^3 + 176*c^3*d^6 - 122*a*c^2*d^4*e^2 + 66*a^2*c*d^2*e^4 - 15*a^3*e^6 + 35*(10*c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 7*(58*c^3*d^5*e - 16*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(c^4*d^12 - 4*a*c^3*d^10*e^2 + 6*a^2*c^2*d^8*e^4 - 4*a^3*c*d^6*e^6 + a^4*d^4*e^8 + (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)*x^4 + 4*(c^4*d^9*e^3 - 4*a*c^3*d^7*e^5 + 6*a^2*c^2*d^5*e^7 - 4*a^3*c*d^3*e^9 + a^4*d*e^11)*x^3 + 6*(c^4*d^10*e^2 - 4*a*c^3*d^8*e^4 + 6*a^2*c^2*d^6*e^6 - 4*a^3*c*d^4*e^8 + a^4*d^2*e^10)*x^2 + 4*(c^4*d^11*e - 4*a*c^3*d^9*e^3 + 6*a^2*c^2*d^7*e^5 - 4*a^3*c*d^5*e^7 + a^4*d^3*e^9)*x), -2/105*(105*(c^3*d^3*e^4*x^4 + 4*c^3*d^4*e^3*x^3 + 6*c^3*d^5*e^2*x^2 + 4*c^3*d^6*e*x + c^3*d^7)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - (105*c^3*d^3*e^3*x^3 + 176*c^3*d^6 - 122*a*c^2*d^4*e^2 + 66*a^2*c*d^2*e^4 - 15*a^3*e^6 + 35*(10*c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 7*(58*c^3*d^5*e - 16*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(c^4*d^12 - 4*a*c^3*d^10*e^2 + 6*a^2*c^2*d^8*e^4 - 4*a^3*c*d^6*e^6 + a^4*d^4*e^8 + (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)*x^4 + 4*(c^4*d^9*e^3 - 4*a*c^3*d^7*e^5 + 6*a^2*c^2*d^5*e^7 - 4*a^3*c*d^3*e^9 + a^4*d*e^11)*x^3 + 6*(c^4*d^10*e^2 - 4*a*c^3*d^8*e^4 + 6*a^2*c^2*d^6*e^6 - 4*a^3*c*d^4*e^8 + a^4*d^2*e^10)*x^2 + 4*(c^4*d^11*e - 4*a*c^3*d^9*e^3 + 6*a^2*c^2*d^7*e^5 - 4*a^3*c*d^5*e^7 + a^4*d^3*e^9)*x)]","B",0
2009,1,788,0,0.428158," ","integrate((e*x+d)^(13/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a c^{3} d^{6} e^{2} - 3 \, a^{2} c^{2} d^{4} e^{4} + 3 \, a^{3} c d^{2} e^{6} - a^{4} e^{8} + {\left(c^{4} d^{7} e - 3 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x\right)} \sqrt{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, {\left(10 \, c^{4} d^{4} e^{4} x^{4} - 35 \, c^{4} d^{8} + 528 \, a c^{3} d^{6} e^{2} - 1218 \, a^{2} c^{2} d^{4} e^{4} + 1050 \, a^{3} c d^{2} e^{6} - 315 \, a^{4} e^{8} + 2 \, {\left(29 \, c^{4} d^{5} e^{3} - 9 \, a c^{3} d^{3} e^{5}\right)} x^{3} + 6 \, {\left(26 \, c^{4} d^{6} e^{2} - 23 \, a c^{3} d^{4} e^{4} + 7 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(194 \, c^{4} d^{7} e - 426 \, a c^{3} d^{5} e^{3} + 357 \, a^{2} c^{2} d^{3} e^{5} - 105 \, a^{3} c d e^{7}\right)} x\right)} \sqrt{e x + d}}{70 \, {\left(c^{6} d^{6} x + a c^{5} d^{5} e\right)}}, -\frac{315 \, {\left(a c^{3} d^{6} e^{2} - 3 \, a^{2} c^{2} d^{4} e^{4} + 3 \, a^{3} c d^{2} e^{6} - a^{4} e^{8} + {\left(c^{4} d^{7} e - 3 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - {\left(10 \, c^{4} d^{4} e^{4} x^{4} - 35 \, c^{4} d^{8} + 528 \, a c^{3} d^{6} e^{2} - 1218 \, a^{2} c^{2} d^{4} e^{4} + 1050 \, a^{3} c d^{2} e^{6} - 315 \, a^{4} e^{8} + 2 \, {\left(29 \, c^{4} d^{5} e^{3} - 9 \, a c^{3} d^{3} e^{5}\right)} x^{3} + 6 \, {\left(26 \, c^{4} d^{6} e^{2} - 23 \, a c^{3} d^{4} e^{4} + 7 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(194 \, c^{4} d^{7} e - 426 \, a c^{3} d^{5} e^{3} + 357 \, a^{2} c^{2} d^{3} e^{5} - 105 \, a^{3} c d e^{7}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(c^{6} d^{6} x + a c^{5} d^{5} e\right)}}\right]"," ",0,"[1/70*(315*(a*c^3*d^6*e^2 - 3*a^2*c^2*d^4*e^4 + 3*a^3*c*d^2*e^6 - a^4*e^8 + (c^4*d^7*e - 3*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(10*c^4*d^4*e^4*x^4 - 35*c^4*d^8 + 528*a*c^3*d^6*e^2 - 1218*a^2*c^2*d^4*e^4 + 1050*a^3*c*d^2*e^6 - 315*a^4*e^8 + 2*(29*c^4*d^5*e^3 - 9*a*c^3*d^3*e^5)*x^3 + 6*(26*c^4*d^6*e^2 - 23*a*c^3*d^4*e^4 + 7*a^2*c^2*d^2*e^6)*x^2 + 2*(194*c^4*d^7*e - 426*a*c^3*d^5*e^3 + 357*a^2*c^2*d^3*e^5 - 105*a^3*c*d*e^7)*x)*sqrt(e*x + d))/(c^6*d^6*x + a*c^5*d^5*e), -1/35*(315*(a*c^3*d^6*e^2 - 3*a^2*c^2*d^4*e^4 + 3*a^3*c*d^2*e^6 - a^4*e^8 + (c^4*d^7*e - 3*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x)*sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - (10*c^4*d^4*e^4*x^4 - 35*c^4*d^8 + 528*a*c^3*d^6*e^2 - 1218*a^2*c^2*d^4*e^4 + 1050*a^3*c*d^2*e^6 - 315*a^4*e^8 + 2*(29*c^4*d^5*e^3 - 9*a*c^3*d^3*e^5)*x^3 + 6*(26*c^4*d^6*e^2 - 23*a*c^3*d^4*e^4 + 7*a^2*c^2*d^2*e^6)*x^2 + 2*(194*c^4*d^7*e - 426*a*c^3*d^5*e^3 + 357*a^2*c^2*d^3*e^5 - 105*a^3*c*d*e^7)*x)*sqrt(e*x + d))/(c^6*d^6*x + a*c^5*d^5*e)]","B",0
2010,1,586,0,0.435250," ","integrate((e*x+d)^(11/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a c^{2} d^{4} e^{2} - 2 \, a^{2} c d^{2} e^{4} + a^{3} e^{6} + {\left(c^{3} d^{5} e - 2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} \sqrt{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, {\left(6 \, c^{3} d^{3} e^{3} x^{3} - 15 \, c^{3} d^{6} + 161 \, a c^{2} d^{4} e^{2} - 245 \, a^{2} c d^{2} e^{4} + 105 \, a^{3} e^{6} + 2 \, {\left(16 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(58 \, c^{3} d^{5} e - 84 \, a c^{2} d^{3} e^{3} + 35 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left(c^{5} d^{5} x + a c^{4} d^{4} e\right)}}, -\frac{105 \, {\left(a c^{2} d^{4} e^{2} - 2 \, a^{2} c d^{2} e^{4} + a^{3} e^{6} + {\left(c^{3} d^{5} e - 2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - {\left(6 \, c^{3} d^{3} e^{3} x^{3} - 15 \, c^{3} d^{6} + 161 \, a c^{2} d^{4} e^{2} - 245 \, a^{2} c d^{2} e^{4} + 105 \, a^{3} e^{6} + 2 \, {\left(16 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(58 \, c^{3} d^{5} e - 84 \, a c^{2} d^{3} e^{3} + 35 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(c^{5} d^{5} x + a c^{4} d^{4} e\right)}}\right]"," ",0,"[1/30*(105*(a*c^2*d^4*e^2 - 2*a^2*c*d^2*e^4 + a^3*e^6 + (c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(6*c^3*d^3*e^3*x^3 - 15*c^3*d^6 + 161*a*c^2*d^4*e^2 - 245*a^2*c*d^2*e^4 + 105*a^3*e^6 + 2*(16*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 + 2*(58*c^3*d^5*e - 84*a*c^2*d^3*e^3 + 35*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(c^5*d^5*x + a*c^4*d^4*e), -1/15*(105*(a*c^2*d^4*e^2 - 2*a^2*c*d^2*e^4 + a^3*e^6 + (c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x)*sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - (6*c^3*d^3*e^3*x^3 - 15*c^3*d^6 + 161*a*c^2*d^4*e^2 - 245*a^2*c*d^2*e^4 + 105*a^3*e^6 + 2*(16*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 + 2*(58*c^3*d^5*e - 84*a*c^2*d^3*e^3 + 35*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(c^5*d^5*x + a*c^4*d^4*e)]","A",0
2011,1,420,0,0.436454," ","integrate((e*x+d)^(9/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a c d^{2} e^{2} - a^{2} e^{4} + {\left(c^{2} d^{3} e - a c d e^{3}\right)} x\right)} \sqrt{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, {\left(2 \, c^{2} d^{2} e^{2} x^{2} - 3 \, c^{2} d^{4} + 20 \, a c d^{2} e^{2} - 15 \, a^{2} e^{4} + 2 \, {\left(7 \, c^{2} d^{3} e - 5 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(c^{4} d^{4} x + a c^{3} d^{3} e\right)}}, -\frac{15 \, {\left(a c d^{2} e^{2} - a^{2} e^{4} + {\left(c^{2} d^{3} e - a c d e^{3}\right)} x\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - {\left(2 \, c^{2} d^{2} e^{2} x^{2} - 3 \, c^{2} d^{4} + 20 \, a c d^{2} e^{2} - 15 \, a^{2} e^{4} + 2 \, {\left(7 \, c^{2} d^{3} e - 5 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(c^{4} d^{4} x + a c^{3} d^{3} e\right)}}\right]"," ",0,"[1/6*(15*(a*c*d^2*e^2 - a^2*e^4 + (c^2*d^3*e - a*c*d*e^3)*x)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(2*c^2*d^2*e^2*x^2 - 3*c^2*d^4 + 20*a*c*d^2*e^2 - 15*a^2*e^4 + 2*(7*c^2*d^3*e - 5*a*c*d*e^3)*x)*sqrt(e*x + d))/(c^4*d^4*x + a*c^3*d^3*e), -1/3*(15*(a*c*d^2*e^2 - a^2*e^4 + (c^2*d^3*e - a*c*d*e^3)*x)*sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - (2*c^2*d^2*e^2*x^2 - 3*c^2*d^4 + 20*a*c*d^2*e^2 - 15*a^2*e^4 + 2*(7*c^2*d^3*e - 5*a*c*d*e^3)*x)*sqrt(e*x + d))/(c^4*d^4*x + a*c^3*d^3*e)]","A",0
2012,1,282,0,0.427134," ","integrate((e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d e x + a e^{2}\right)} \sqrt{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, {\left(2 \, c d e x - c d^{2} + 3 \, a e^{2}\right)} \sqrt{e x + d}}{2 \, {\left(c^{3} d^{3} x + a c^{2} d^{2} e\right)}}, -\frac{3 \, {\left(c d e x + a e^{2}\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - {\left(2 \, c d e x - c d^{2} + 3 \, a e^{2}\right)} \sqrt{e x + d}}{c^{3} d^{3} x + a c^{2} d^{2} e}\right]"," ",0,"[1/2*(3*(c*d*e*x + a*e^2)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(2*c*d*e*x - c*d^2 + 3*a*e^2)*sqrt(e*x + d))/(c^3*d^3*x + a*c^2*d^2*e), -(3*(c*d*e*x + a*e^2)*sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - (2*c*d*e*x - c*d^2 + 3*a*e^2)*sqrt(e*x + d))/(c^3*d^3*x + a*c^2*d^2*e)]","A",0
2013,1,309,0,0.407928," ","integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\left[\frac{\sqrt{c^{2} d^{3} - a c d e^{2}} {\left(c d e x + a e^{2}\right)} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{c^{2} d^{3} - a c d e^{2}} \sqrt{e x + d}}{c d x + a e}\right) - 2 \, {\left(c^{2} d^{3} - a c d e^{2}\right)} \sqrt{e x + d}}{2 \, {\left(a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3} + {\left(c^{4} d^{5} - a c^{3} d^{3} e^{2}\right)} x\right)}}, \frac{\sqrt{-c^{2} d^{3} + a c d e^{2}} {\left(c d e x + a e^{2}\right)} \arctan\left(\frac{\sqrt{-c^{2} d^{3} + a c d e^{2}} \sqrt{e x + d}}{c d e x + c d^{2}}\right) - {\left(c^{2} d^{3} - a c d e^{2}\right)} \sqrt{e x + d}}{a c^{3} d^{4} e - a^{2} c^{2} d^{2} e^{3} + {\left(c^{4} d^{5} - a c^{3} d^{3} e^{2}\right)} x}\right]"," ",0,"[1/2*(sqrt(c^2*d^3 - a*c*d*e^2)*(c*d*e*x + a*e^2)*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(c^2*d^3 - a*c*d*e^2)*sqrt(e*x + d))/(c*d*x + a*e)) - 2*(c^2*d^3 - a*c*d*e^2)*sqrt(e*x + d))/(a*c^3*d^4*e - a^2*c^2*d^2*e^3 + (c^4*d^5 - a*c^3*d^3*e^2)*x), (sqrt(-c^2*d^3 + a*c*d*e^2)*(c*d*e*x + a*e^2)*arctan(sqrt(-c^2*d^3 + a*c*d*e^2)*sqrt(e*x + d)/(c*d*e*x + c*d^2)) - (c^2*d^3 - a*c*d*e^2)*sqrt(e*x + d))/(a*c^3*d^4*e - a^2*c^2*d^2*e^3 + (c^4*d^5 - a*c^3*d^3*e^2)*x)]","A",0
2014,1,353,0,0.428848," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{c^{2} d^{3} - a c d e^{2}} {\left(c d e x + a e^{2}\right)} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{c^{2} d^{3} - a c d e^{2}} \sqrt{e x + d}}{c d x + a e}\right) + 2 \, {\left(c^{2} d^{3} - a c d e^{2}\right)} \sqrt{e x + d}}{2 \, {\left(a c^{3} d^{5} e - 2 \, a^{2} c^{2} d^{3} e^{3} + a^{3} c d e^{5} + {\left(c^{4} d^{6} - 2 \, a c^{3} d^{4} e^{2} + a^{2} c^{2} d^{2} e^{4}\right)} x\right)}}, -\frac{\sqrt{-c^{2} d^{3} + a c d e^{2}} {\left(c d e x + a e^{2}\right)} \arctan\left(\frac{\sqrt{-c^{2} d^{3} + a c d e^{2}} \sqrt{e x + d}}{c d e x + c d^{2}}\right) + {\left(c^{2} d^{3} - a c d e^{2}\right)} \sqrt{e x + d}}{a c^{3} d^{5} e - 2 \, a^{2} c^{2} d^{3} e^{3} + a^{3} c d e^{5} + {\left(c^{4} d^{6} - 2 \, a c^{3} d^{4} e^{2} + a^{2} c^{2} d^{2} e^{4}\right)} x}\right]"," ",0,"[-1/2*(sqrt(c^2*d^3 - a*c*d*e^2)*(c*d*e*x + a*e^2)*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(c^2*d^3 - a*c*d*e^2)*sqrt(e*x + d))/(c*d*x + a*e)) + 2*(c^2*d^3 - a*c*d*e^2)*sqrt(e*x + d))/(a*c^3*d^5*e - 2*a^2*c^2*d^3*e^3 + a^3*c*d*e^5 + (c^4*d^6 - 2*a*c^3*d^4*e^2 + a^2*c^2*d^2*e^4)*x), -(sqrt(-c^2*d^3 + a*c*d*e^2)*(c*d*e*x + a*e^2)*arctan(sqrt(-c^2*d^3 + a*c*d*e^2)*sqrt(e*x + d)/(c*d*e*x + c*d^2)) + (c^2*d^3 - a*c*d*e^2)*sqrt(e*x + d))/(a*c^3*d^5*e - 2*a^2*c^2*d^3*e^3 + a^3*c*d*e^5 + (c^4*d^6 - 2*a*c^3*d^4*e^2 + a^2*c^2*d^2*e^4)*x)]","A",0
2015,1,502,0,0.422441," ","integrate((e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{\frac{c d}{c d^{2} - a e^{2}}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} + 2 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{c d}{c d^{2} - a e^{2}}}}{c d x + a e}\right) - 2 \, {\left(3 \, c d e x + c d^{2} + 2 \, a e^{2}\right)} \sqrt{e x + d}}{2 \, {\left(a c^{2} d^{5} e - 2 \, a^{2} c d^{3} e^{3} + a^{3} d e^{5} + {\left(c^{3} d^{5} e - 2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x^{2} + {\left(c^{3} d^{6} - a c^{2} d^{4} e^{2} - a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} x\right)}}, \frac{3 \, {\left(c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x\right)} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}} \arctan\left(-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}}}{c d e x + c d^{2}}\right) - {\left(3 \, c d e x + c d^{2} + 2 \, a e^{2}\right)} \sqrt{e x + d}}{a c^{2} d^{5} e - 2 \, a^{2} c d^{3} e^{3} + a^{3} d e^{5} + {\left(c^{3} d^{5} e - 2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x^{2} + {\left(c^{3} d^{6} - a c^{2} d^{4} e^{2} - a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} x}\right]"," ",0,"[1/2*(3*(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 + 2*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) - 2*(3*c*d*e*x + c*d^2 + 2*a*e^2)*sqrt(e*x + d))/(a*c^2*d^5*e - 2*a^2*c*d^3*e^3 + a^3*d*e^5 + (c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x^2 + (c^3*d^6 - a*c^2*d^4*e^2 - a^2*c*d^2*e^4 + a^3*e^6)*x), (3*(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - (3*c*d*e*x + c*d^2 + 2*a*e^2)*sqrt(e*x + d))/(a*c^2*d^5*e - 2*a^2*c*d^3*e^3 + a^3*d*e^5 + (c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x^2 + (c^3*d^6 - a*c^2*d^4*e^2 - a^2*c*d^2*e^4 + a^3*e^6)*x)]","B",0
2016,1,881,0,0.444832," ","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=""fricas"")","\left[-\frac{15 \, {\left(c^{2} d^{2} e^{3} x^{3} + a c d^{3} e^{2} + {\left(2 \, c^{2} d^{3} e^{2} + a c d e^{4}\right)} x^{2} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{\frac{c d}{c d^{2} - a e^{2}}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{c d}{c d^{2} - a e^{2}}}}{c d x + a e}\right) + 2 \, {\left(15 \, c^{2} d^{2} e^{2} x^{2} + 3 \, c^{2} d^{4} + 14 \, a c d^{2} e^{2} - 2 \, a^{2} e^{4} + 10 \, {\left(2 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{6 \, {\left(a c^{3} d^{8} e - 3 \, a^{2} c^{2} d^{6} e^{3} + 3 \, a^{3} c d^{4} e^{5} - a^{4} d^{2} e^{7} + {\left(c^{4} d^{7} e^{2} - 3 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6} - a^{3} c d e^{8}\right)} x^{3} + {\left(2 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5} + a^{3} c d^{2} e^{7} - a^{4} e^{9}\right)} x^{2} + {\left(c^{4} d^{9} - a c^{3} d^{7} e^{2} - 3 \, a^{2} c^{2} d^{5} e^{4} + 5 \, a^{3} c d^{3} e^{6} - 2 \, a^{4} d e^{8}\right)} x\right)}}, \frac{15 \, {\left(c^{2} d^{2} e^{3} x^{3} + a c d^{3} e^{2} + {\left(2 \, c^{2} d^{3} e^{2} + a c d e^{4}\right)} x^{2} + {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}} \arctan\left(-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}}}{c d e x + c d^{2}}\right) - {\left(15 \, c^{2} d^{2} e^{2} x^{2} + 3 \, c^{2} d^{4} + 14 \, a c d^{2} e^{2} - 2 \, a^{2} e^{4} + 10 \, {\left(2 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(a c^{3} d^{8} e - 3 \, a^{2} c^{2} d^{6} e^{3} + 3 \, a^{3} c d^{4} e^{5} - a^{4} d^{2} e^{7} + {\left(c^{4} d^{7} e^{2} - 3 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6} - a^{3} c d e^{8}\right)} x^{3} + {\left(2 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5} + a^{3} c d^{2} e^{7} - a^{4} e^{9}\right)} x^{2} + {\left(c^{4} d^{9} - a c^{3} d^{7} e^{2} - 3 \, a^{2} c^{2} d^{5} e^{4} + 5 \, a^{3} c d^{3} e^{6} - 2 \, a^{4} d e^{8}\right)} x\right)}}\right]"," ",0,"[-1/6*(15*(c^2*d^2*e^3*x^3 + a*c*d^3*e^2 + (2*c^2*d^3*e^2 + a*c*d*e^4)*x^2 + (c^2*d^4*e + 2*a*c*d^2*e^3)*x)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) + 2*(15*c^2*d^2*e^2*x^2 + 3*c^2*d^4 + 14*a*c*d^2*e^2 - 2*a^2*e^4 + 10*(2*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(e*x + d))/(a*c^3*d^8*e - 3*a^2*c^2*d^6*e^3 + 3*a^3*c*d^4*e^5 - a^4*d^2*e^7 + (c^4*d^7*e^2 - 3*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6 - a^3*c*d*e^8)*x^3 + (2*c^4*d^8*e - 5*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5 + a^3*c*d^2*e^7 - a^4*e^9)*x^2 + (c^4*d^9 - a*c^3*d^7*e^2 - 3*a^2*c^2*d^5*e^4 + 5*a^3*c*d^3*e^6 - 2*a^4*d*e^8)*x), 1/3*(15*(c^2*d^2*e^3*x^3 + a*c*d^3*e^2 + (2*c^2*d^3*e^2 + a*c*d*e^4)*x^2 + (c^2*d^4*e + 2*a*c*d^2*e^3)*x)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - (15*c^2*d^2*e^2*x^2 + 3*c^2*d^4 + 14*a*c*d^2*e^2 - 2*a^2*e^4 + 10*(2*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(e*x + d))/(a*c^3*d^8*e - 3*a^2*c^2*d^6*e^3 + 3*a^3*c*d^4*e^5 - a^4*d^2*e^7 + (c^4*d^7*e^2 - 3*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6 - a^3*c*d*e^8)*x^3 + (2*c^4*d^8*e - 5*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5 + a^3*c*d^2*e^7 - a^4*e^9)*x^2 + (c^4*d^9 - a*c^3*d^7*e^2 - 3*a^2*c^2*d^5*e^4 + 5*a^3*c*d^3*e^6 - 2*a^4*d*e^8)*x)]","B",0
2017,1,1331,0,0.451194," ","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=""fricas"")","\left[\frac{105 \, {\left(c^{3} d^{3} e^{4} x^{4} + a c^{2} d^{5} e^{2} + {\left(3 \, c^{3} d^{4} e^{3} + a c^{2} d^{2} e^{5}\right)} x^{3} + 3 \, {\left(c^{3} d^{5} e^{2} + a c^{2} d^{3} e^{4}\right)} x^{2} + {\left(c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3}\right)} x\right)} \sqrt{\frac{c d}{c d^{2} - a e^{2}}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} + 2 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{c d}{c d^{2} - a e^{2}}}}{c d x + a e}\right) - 2 \, {\left(105 \, c^{3} d^{3} e^{3} x^{3} + 15 \, c^{3} d^{6} + 116 \, a c^{2} d^{4} e^{2} - 32 \, a^{2} c d^{2} e^{4} + 6 \, a^{3} e^{6} + 35 \, {\left(7 \, c^{3} d^{4} e^{2} + 2 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(23 \, c^{3} d^{5} e + 24 \, a c^{2} d^{3} e^{3} - 2 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{30 \, {\left(a c^{4} d^{11} e - 4 \, a^{2} c^{3} d^{9} e^{3} + 6 \, a^{3} c^{2} d^{7} e^{5} - 4 \, a^{4} c d^{5} e^{7} + a^{5} d^{3} e^{9} + {\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^{4} + {\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)} x^{3} + 3 \, {\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)} x^{2} + {\left(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}\right)} x\right)}}, \frac{105 \, {\left(c^{3} d^{3} e^{4} x^{4} + a c^{2} d^{5} e^{2} + {\left(3 \, c^{3} d^{4} e^{3} + a c^{2} d^{2} e^{5}\right)} x^{3} + 3 \, {\left(c^{3} d^{5} e^{2} + a c^{2} d^{3} e^{4}\right)} x^{2} + {\left(c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3}\right)} x\right)} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}} \arctan\left(-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}}}{c d e x + c d^{2}}\right) - {\left(105 \, c^{3} d^{3} e^{3} x^{3} + 15 \, c^{3} d^{6} + 116 \, a c^{2} d^{4} e^{2} - 32 \, a^{2} c d^{2} e^{4} + 6 \, a^{3} e^{6} + 35 \, {\left(7 \, c^{3} d^{4} e^{2} + 2 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(23 \, c^{3} d^{5} e + 24 \, a c^{2} d^{3} e^{3} - 2 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(a c^{4} d^{11} e - 4 \, a^{2} c^{3} d^{9} e^{3} + 6 \, a^{3} c^{2} d^{7} e^{5} - 4 \, a^{4} c d^{5} e^{7} + a^{5} d^{3} e^{9} + {\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^{4} + {\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)} x^{3} + 3 \, {\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)} x^{2} + {\left(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}\right)} x\right)}}\right]"," ",0,"[1/30*(105*(c^3*d^3*e^4*x^4 + a*c^2*d^5*e^2 + (3*c^3*d^4*e^3 + a*c^2*d^2*e^5)*x^3 + 3*(c^3*d^5*e^2 + a*c^2*d^3*e^4)*x^2 + (c^3*d^6*e + 3*a*c^2*d^4*e^3)*x)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 + 2*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) - 2*(105*c^3*d^3*e^3*x^3 + 15*c^3*d^6 + 116*a*c^2*d^4*e^2 - 32*a^2*c*d^2*e^4 + 6*a^3*e^6 + 35*(7*c^3*d^4*e^2 + 2*a*c^2*d^2*e^4)*x^2 + 7*(23*c^3*d^5*e + 24*a*c^2*d^3*e^3 - 2*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(a*c^4*d^11*e - 4*a^2*c^3*d^9*e^3 + 6*a^3*c^2*d^7*e^5 - 4*a^4*c*d^5*e^7 + a^5*d^3*e^9 + (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^4 + (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)*x^3 + 3*(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)*x^2 + (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)*x), 1/15*(105*(c^3*d^3*e^4*x^4 + a*c^2*d^5*e^2 + (3*c^3*d^4*e^3 + a*c^2*d^2*e^5)*x^3 + 3*(c^3*d^5*e^2 + a*c^2*d^3*e^4)*x^2 + (c^3*d^6*e + 3*a*c^2*d^4*e^3)*x)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - (105*c^3*d^3*e^3*x^3 + 15*c^3*d^6 + 116*a*c^2*d^4*e^2 - 32*a^2*c*d^2*e^4 + 6*a^3*e^6 + 35*(7*c^3*d^4*e^2 + 2*a*c^2*d^2*e^4)*x^2 + 7*(23*c^3*d^5*e + 24*a*c^2*d^3*e^3 - 2*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(a*c^4*d^11*e - 4*a^2*c^3*d^9*e^3 + 6*a^3*c^2*d^7*e^5 - 4*a^4*c*d^5*e^7 + a^5*d^3*e^9 + (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^4 + (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)*x^3 + 3*(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)*x^2 + (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)*x)]","B",0
2018,1,858,0,0.435980," ","integrate((e*x+d)^(15/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{2} c^{2} d^{4} e^{4} - 2 \, a^{3} c d^{2} e^{6} + a^{4} e^{8} + {\left(c^{4} d^{6} e^{2} - 2 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(a c^{3} d^{5} e^{3} - 2 \, a^{2} c^{2} d^{3} e^{5} + a^{3} c d e^{7}\right)} x\right)} \sqrt{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, {\left(8 \, c^{4} d^{4} e^{4} x^{4} - 10 \, c^{4} d^{8} - 45 \, a c^{3} d^{6} e^{2} + 483 \, a^{2} c^{2} d^{4} e^{4} - 735 \, a^{3} c d^{2} e^{6} + 315 \, a^{4} e^{8} + 8 \, {\left(7 \, c^{4} d^{5} e^{3} - 3 \, a c^{3} d^{3} e^{5}\right)} x^{3} + 24 \, {\left(12 \, c^{4} d^{6} e^{2} - 17 \, a c^{3} d^{4} e^{4} + 7 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} - {\left(85 \, c^{4} d^{7} e - 831 \, a c^{3} d^{5} e^{3} + 1239 \, a^{2} c^{2} d^{3} e^{5} - 525 \, a^{3} c d e^{7}\right)} x\right)} \sqrt{e x + d}}{40 \, {\left(c^{7} d^{7} x^{2} + 2 \, a c^{6} d^{6} e x + a^{2} c^{5} d^{5} e^{2}\right)}}, -\frac{315 \, {\left(a^{2} c^{2} d^{4} e^{4} - 2 \, a^{3} c d^{2} e^{6} + a^{4} e^{8} + {\left(c^{4} d^{6} e^{2} - 2 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(a c^{3} d^{5} e^{3} - 2 \, a^{2} c^{2} d^{3} e^{5} + a^{3} c d e^{7}\right)} x\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - {\left(8 \, c^{4} d^{4} e^{4} x^{4} - 10 \, c^{4} d^{8} - 45 \, a c^{3} d^{6} e^{2} + 483 \, a^{2} c^{2} d^{4} e^{4} - 735 \, a^{3} c d^{2} e^{6} + 315 \, a^{4} e^{8} + 8 \, {\left(7 \, c^{4} d^{5} e^{3} - 3 \, a c^{3} d^{3} e^{5}\right)} x^{3} + 24 \, {\left(12 \, c^{4} d^{6} e^{2} - 17 \, a c^{3} d^{4} e^{4} + 7 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} - {\left(85 \, c^{4} d^{7} e - 831 \, a c^{3} d^{5} e^{3} + 1239 \, a^{2} c^{2} d^{3} e^{5} - 525 \, a^{3} c d e^{7}\right)} x\right)} \sqrt{e x + d}}{20 \, {\left(c^{7} d^{7} x^{2} + 2 \, a c^{6} d^{6} e x + a^{2} c^{5} d^{5} e^{2}\right)}}\right]"," ",0,"[1/40*(315*(a^2*c^2*d^4*e^4 - 2*a^3*c*d^2*e^6 + a^4*e^8 + (c^4*d^6*e^2 - 2*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + 2*(a*c^3*d^5*e^3 - 2*a^2*c^2*d^3*e^5 + a^3*c*d*e^7)*x)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(8*c^4*d^4*e^4*x^4 - 10*c^4*d^8 - 45*a*c^3*d^6*e^2 + 483*a^2*c^2*d^4*e^4 - 735*a^3*c*d^2*e^6 + 315*a^4*e^8 + 8*(7*c^4*d^5*e^3 - 3*a*c^3*d^3*e^5)*x^3 + 24*(12*c^4*d^6*e^2 - 17*a*c^3*d^4*e^4 + 7*a^2*c^2*d^2*e^6)*x^2 - (85*c^4*d^7*e - 831*a*c^3*d^5*e^3 + 1239*a^2*c^2*d^3*e^5 - 525*a^3*c*d*e^7)*x)*sqrt(e*x + d))/(c^7*d^7*x^2 + 2*a*c^6*d^6*e*x + a^2*c^5*d^5*e^2), -1/20*(315*(a^2*c^2*d^4*e^4 - 2*a^3*c*d^2*e^6 + a^4*e^8 + (c^4*d^6*e^2 - 2*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + 2*(a*c^3*d^5*e^3 - 2*a^2*c^2*d^3*e^5 + a^3*c*d*e^7)*x)*sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - (8*c^4*d^4*e^4*x^4 - 10*c^4*d^8 - 45*a*c^3*d^6*e^2 + 483*a^2*c^2*d^4*e^4 - 735*a^3*c*d^2*e^6 + 315*a^4*e^8 + 8*(7*c^4*d^5*e^3 - 3*a*c^3*d^3*e^5)*x^3 + 24*(12*c^4*d^6*e^2 - 17*a*c^3*d^4*e^4 + 7*a^2*c^2*d^2*e^6)*x^2 - (85*c^4*d^7*e - 831*a*c^3*d^5*e^3 + 1239*a^2*c^2*d^3*e^5 - 525*a^3*c*d*e^7)*x)*sqrt(e*x + d))/(c^7*d^7*x^2 + 2*a*c^6*d^6*e*x + a^2*c^5*d^5*e^2)]","B",0
2019,1,638,0,0.428080," ","integrate((e*x+d)^(13/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{2} c d^{2} e^{4} - a^{3} e^{6} + {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(a c^{2} d^{3} e^{3} - a^{2} c d e^{5}\right)} x\right)} \sqrt{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, {\left(8 \, c^{3} d^{3} e^{3} x^{3} - 6 \, c^{3} d^{6} - 21 \, a c^{2} d^{4} e^{2} + 140 \, a^{2} c d^{2} e^{4} - 105 \, a^{3} e^{6} + 8 \, {\left(10 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} - {\left(39 \, c^{3} d^{5} e - 238 \, a c^{2} d^{3} e^{3} + 175 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(c^{6} d^{6} x^{2} + 2 \, a c^{5} d^{5} e x + a^{2} c^{4} d^{4} e^{2}\right)}}, -\frac{105 \, {\left(a^{2} c d^{2} e^{4} - a^{3} e^{6} + {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(a c^{2} d^{3} e^{3} - a^{2} c d e^{5}\right)} x\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - {\left(8 \, c^{3} d^{3} e^{3} x^{3} - 6 \, c^{3} d^{6} - 21 \, a c^{2} d^{4} e^{2} + 140 \, a^{2} c d^{2} e^{4} - 105 \, a^{3} e^{6} + 8 \, {\left(10 \, c^{3} d^{4} e^{2} - 7 \, a c^{2} d^{2} e^{4}\right)} x^{2} - {\left(39 \, c^{3} d^{5} e - 238 \, a c^{2} d^{3} e^{3} + 175 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(c^{6} d^{6} x^{2} + 2 \, a c^{5} d^{5} e x + a^{2} c^{4} d^{4} e^{2}\right)}}\right]"," ",0,"[1/24*(105*(a^2*c*d^2*e^4 - a^3*e^6 + (c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 2*(a*c^2*d^3*e^3 - a^2*c*d*e^5)*x)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(8*c^3*d^3*e^3*x^3 - 6*c^3*d^6 - 21*a*c^2*d^4*e^2 + 140*a^2*c*d^2*e^4 - 105*a^3*e^6 + 8*(10*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 - (39*c^3*d^5*e - 238*a*c^2*d^3*e^3 + 175*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(c^6*d^6*x^2 + 2*a*c^5*d^5*e*x + a^2*c^4*d^4*e^2), -1/12*(105*(a^2*c*d^2*e^4 - a^3*e^6 + (c^3*d^4*e^2 - a*c^2*d^2*e^4)*x^2 + 2*(a*c^2*d^3*e^3 - a^2*c*d*e^5)*x)*sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - (8*c^3*d^3*e^3*x^3 - 6*c^3*d^6 - 21*a*c^2*d^4*e^2 + 140*a^2*c*d^2*e^4 - 105*a^3*e^6 + 8*(10*c^3*d^4*e^2 - 7*a*c^2*d^2*e^4)*x^2 - (39*c^3*d^5*e - 238*a*c^2*d^3*e^3 + 175*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(c^6*d^6*x^2 + 2*a*c^5*d^5*e*x + a^2*c^4*d^4*e^2)]","B",0
2020,1,440,0,0.425446," ","integrate((e*x+d)^(11/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \sqrt{\frac{c d^{2} - a e^{2}}{c d}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{e x + d} c d \sqrt{\frac{c d^{2} - a e^{2}}{c d}}}{c d x + a e}\right) + 2 \, {\left(8 \, c^{2} d^{2} e^{2} x^{2} - 2 \, c^{2} d^{4} - 5 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} - {\left(9 \, c^{2} d^{3} e - 25 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(c^{5} d^{5} x^{2} + 2 \, a c^{4} d^{4} e x + a^{2} c^{3} d^{3} e^{2}\right)}}, -\frac{15 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{c d}} \arctan\left(-\frac{\sqrt{e x + d} c d \sqrt{-\frac{c d^{2} - a e^{2}}{c d}}}{c d^{2} - a e^{2}}\right) - {\left(8 \, c^{2} d^{2} e^{2} x^{2} - 2 \, c^{2} d^{4} - 5 \, a c d^{2} e^{2} + 15 \, a^{2} e^{4} - {\left(9 \, c^{2} d^{3} e - 25 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(c^{5} d^{5} x^{2} + 2 \, a c^{4} d^{4} e x + a^{2} c^{3} d^{3} e^{2}\right)}}\right]"," ",0,"[1/8*(15*(c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*sqrt((c*d^2 - a*e^2)/(c*d))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(e*x + d)*c*d*sqrt((c*d^2 - a*e^2)/(c*d)))/(c*d*x + a*e)) + 2*(8*c^2*d^2*e^2*x^2 - 2*c^2*d^4 - 5*a*c*d^2*e^2 + 15*a^2*e^4 - (9*c^2*d^3*e - 25*a*c*d*e^3)*x)*sqrt(e*x + d))/(c^5*d^5*x^2 + 2*a*c^4*d^4*e*x + a^2*c^3*d^3*e^2), -1/4*(15*(c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*sqrt(-(c*d^2 - a*e^2)/(c*d))*arctan(-sqrt(e*x + d)*c*d*sqrt(-(c*d^2 - a*e^2)/(c*d))/(c*d^2 - a*e^2)) - (8*c^2*d^2*e^2*x^2 - 2*c^2*d^4 - 5*a*c*d^2*e^2 + 15*a^2*e^4 - (9*c^2*d^3*e - 25*a*c*d*e^3)*x)*sqrt(e*x + d))/(c^5*d^5*x^2 + 2*a*c^4*d^4*e*x + a^2*c^3*d^3*e^2)]","A",0
2021,1,492,0,0.432710," ","integrate((e*x+d)^(9/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \sqrt{c^{2} d^{3} - a c d e^{2}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{c^{2} d^{3} - a c d e^{2}} \sqrt{e x + d}}{c d x + a e}\right) - 2 \, {\left(2 \, c^{3} d^{5} + a c^{2} d^{3} e^{2} - 3 \, a^{2} c d e^{4} + 5 \, {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} c^{4} d^{5} e^{2} - a^{3} c^{3} d^{3} e^{4} + {\left(c^{6} d^{7} - a c^{5} d^{5} e^{2}\right)} x^{2} + 2 \, {\left(a c^{5} d^{6} e - a^{2} c^{4} d^{4} e^{3}\right)} x\right)}}, \frac{3 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \sqrt{-c^{2} d^{3} + a c d e^{2}} \arctan\left(\frac{\sqrt{-c^{2} d^{3} + a c d e^{2}} \sqrt{e x + d}}{c d e x + c d^{2}}\right) - {\left(2 \, c^{3} d^{5} + a c^{2} d^{3} e^{2} - 3 \, a^{2} c d e^{4} + 5 \, {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} c^{4} d^{5} e^{2} - a^{3} c^{3} d^{3} e^{4} + {\left(c^{6} d^{7} - a c^{5} d^{5} e^{2}\right)} x^{2} + 2 \, {\left(a c^{5} d^{6} e - a^{2} c^{4} d^{4} e^{3}\right)} x\right)}}\right]"," ",0,"[1/8*(3*(c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*sqrt(c^2*d^3 - a*c*d*e^2)*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(c^2*d^3 - a*c*d*e^2)*sqrt(e*x + d))/(c*d*x + a*e)) - 2*(2*c^3*d^5 + a*c^2*d^3*e^2 - 3*a^2*c*d*e^4 + 5*(c^3*d^4*e - a*c^2*d^2*e^3)*x)*sqrt(e*x + d))/(a^2*c^4*d^5*e^2 - a^3*c^3*d^3*e^4 + (c^6*d^7 - a*c^5*d^5*e^2)*x^2 + 2*(a*c^5*d^6*e - a^2*c^4*d^4*e^3)*x), 1/4*(3*(c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2)*arctan(sqrt(-c^2*d^3 + a*c*d*e^2)*sqrt(e*x + d)/(c*d*e*x + c*d^2)) - (2*c^3*d^5 + a*c^2*d^3*e^2 - 3*a^2*c*d*e^4 + 5*(c^3*d^4*e - a*c^2*d^2*e^3)*x)*sqrt(e*x + d))/(a^2*c^4*d^5*e^2 - a^3*c^3*d^3*e^4 + (c^6*d^7 - a*c^5*d^5*e^2)*x^2 + 2*(a*c^5*d^6*e - a^2*c^4*d^4*e^3)*x)]","B",0
2022,1,565,0,0.437157," ","integrate((e*x+d)^(7/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\left[\frac{{\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \sqrt{c^{2} d^{3} - a c d e^{2}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} + 2 \, \sqrt{c^{2} d^{3} - a c d e^{2}} \sqrt{e x + d}}{c d x + a e}\right) - 2 \, {\left(2 \, c^{3} d^{5} - 3 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4} + {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} c^{4} d^{6} e^{2} - 2 \, a^{3} c^{3} d^{4} e^{4} + a^{4} c^{2} d^{2} e^{6} + {\left(c^{6} d^{8} - 2 \, a c^{5} d^{6} e^{2} + a^{2} c^{4} d^{4} e^{4}\right)} x^{2} + 2 \, {\left(a c^{5} d^{7} e - 2 \, a^{2} c^{4} d^{5} e^{3} + a^{3} c^{3} d^{3} e^{5}\right)} x\right)}}, -\frac{{\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \sqrt{-c^{2} d^{3} + a c d e^{2}} \arctan\left(\frac{\sqrt{-c^{2} d^{3} + a c d e^{2}} \sqrt{e x + d}}{c d e x + c d^{2}}\right) + {\left(2 \, c^{3} d^{5} - 3 \, a c^{2} d^{3} e^{2} + a^{2} c d e^{4} + {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} c^{4} d^{6} e^{2} - 2 \, a^{3} c^{3} d^{4} e^{4} + a^{4} c^{2} d^{2} e^{6} + {\left(c^{6} d^{8} - 2 \, a c^{5} d^{6} e^{2} + a^{2} c^{4} d^{4} e^{4}\right)} x^{2} + 2 \, {\left(a c^{5} d^{7} e - 2 \, a^{2} c^{4} d^{5} e^{3} + a^{3} c^{3} d^{3} e^{5}\right)} x\right)}}\right]"," ",0,"[1/8*((c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*sqrt(c^2*d^3 - a*c*d*e^2)*log((c*d*e*x + 2*c*d^2 - a*e^2 + 2*sqrt(c^2*d^3 - a*c*d*e^2)*sqrt(e*x + d))/(c*d*x + a*e)) - 2*(2*c^3*d^5 - 3*a*c^2*d^3*e^2 + a^2*c*d*e^4 + (c^3*d^4*e - a*c^2*d^2*e^3)*x)*sqrt(e*x + d))/(a^2*c^4*d^6*e^2 - 2*a^3*c^3*d^4*e^4 + a^4*c^2*d^2*e^6 + (c^6*d^8 - 2*a*c^5*d^6*e^2 + a^2*c^4*d^4*e^4)*x^2 + 2*(a*c^5*d^7*e - 2*a^2*c^4*d^5*e^3 + a^3*c^3*d^3*e^5)*x), -1/4*((c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2)*arctan(sqrt(-c^2*d^3 + a*c*d*e^2)*sqrt(e*x + d)/(c*d*e*x + c*d^2)) + (2*c^3*d^5 - 3*a*c^2*d^3*e^2 + a^2*c*d*e^4 + (c^3*d^4*e - a*c^2*d^2*e^3)*x)*sqrt(e*x + d))/(a^2*c^4*d^6*e^2 - 2*a^3*c^3*d^4*e^4 + a^4*c^2*d^2*e^6 + (c^6*d^8 - 2*a*c^5*d^6*e^2 + a^2*c^4*d^4*e^4)*x^2 + 2*(a*c^5*d^7*e - 2*a^2*c^4*d^5*e^3 + a^3*c^3*d^3*e^5)*x)]","B",0
2023,1,654,0,0.439016," ","integrate((e*x+d)^(5/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \sqrt{c^{2} d^{3} - a c d e^{2}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, \sqrt{c^{2} d^{3} - a c d e^{2}} \sqrt{e x + d}}{c d x + a e}\right) - 2 \, {\left(2 \, c^{3} d^{5} - 7 \, a c^{2} d^{3} e^{2} + 5 \, a^{2} c d e^{4} - 3 \, {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} c^{4} d^{7} e^{2} - 3 \, a^{3} c^{3} d^{5} e^{4} + 3 \, a^{4} c^{2} d^{3} e^{6} - a^{5} c d e^{8} + {\left(c^{6} d^{9} - 3 \, a c^{5} d^{7} e^{2} + 3 \, a^{2} c^{4} d^{5} e^{4} - a^{3} c^{3} d^{3} e^{6}\right)} x^{2} + 2 \, {\left(a c^{5} d^{8} e - 3 \, a^{2} c^{4} d^{6} e^{3} + 3 \, a^{3} c^{3} d^{4} e^{5} - a^{4} c^{2} d^{2} e^{7}\right)} x\right)}}, \frac{3 \, {\left(c^{2} d^{2} e^{2} x^{2} + 2 \, a c d e^{3} x + a^{2} e^{4}\right)} \sqrt{-c^{2} d^{3} + a c d e^{2}} \arctan\left(\frac{\sqrt{-c^{2} d^{3} + a c d e^{2}} \sqrt{e x + d}}{c d e x + c d^{2}}\right) - {\left(2 \, c^{3} d^{5} - 7 \, a c^{2} d^{3} e^{2} + 5 \, a^{2} c d e^{4} - 3 \, {\left(c^{3} d^{4} e - a c^{2} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} c^{4} d^{7} e^{2} - 3 \, a^{3} c^{3} d^{5} e^{4} + 3 \, a^{4} c^{2} d^{3} e^{6} - a^{5} c d e^{8} + {\left(c^{6} d^{9} - 3 \, a c^{5} d^{7} e^{2} + 3 \, a^{2} c^{4} d^{5} e^{4} - a^{3} c^{3} d^{3} e^{6}\right)} x^{2} + 2 \, {\left(a c^{5} d^{8} e - 3 \, a^{2} c^{4} d^{6} e^{3} + 3 \, a^{3} c^{3} d^{4} e^{5} - a^{4} c^{2} d^{2} e^{7}\right)} x\right)}}\right]"," ",0,"[1/8*(3*(c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*sqrt(c^2*d^3 - a*c*d*e^2)*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*sqrt(c^2*d^3 - a*c*d*e^2)*sqrt(e*x + d))/(c*d*x + a*e)) - 2*(2*c^3*d^5 - 7*a*c^2*d^3*e^2 + 5*a^2*c*d*e^4 - 3*(c^3*d^4*e - a*c^2*d^2*e^3)*x)*sqrt(e*x + d))/(a^2*c^4*d^7*e^2 - 3*a^3*c^3*d^5*e^4 + 3*a^4*c^2*d^3*e^6 - a^5*c*d*e^8 + (c^6*d^9 - 3*a*c^5*d^7*e^2 + 3*a^2*c^4*d^5*e^4 - a^3*c^3*d^3*e^6)*x^2 + 2*(a*c^5*d^8*e - 3*a^2*c^4*d^6*e^3 + 3*a^3*c^3*d^4*e^5 - a^4*c^2*d^2*e^7)*x), 1/4*(3*(c^2*d^2*e^2*x^2 + 2*a*c*d*e^3*x + a^2*e^4)*sqrt(-c^2*d^3 + a*c*d*e^2)*arctan(sqrt(-c^2*d^3 + a*c*d*e^2)*sqrt(e*x + d)/(c*d*e*x + c*d^2)) - (2*c^3*d^5 - 7*a*c^2*d^3*e^2 + 5*a^2*c*d*e^4 - 3*(c^3*d^4*e - a*c^2*d^2*e^3)*x)*sqrt(e*x + d))/(a^2*c^4*d^7*e^2 - 3*a^3*c^3*d^5*e^4 + 3*a^4*c^2*d^3*e^6 - a^5*c*d*e^8 + (c^6*d^9 - 3*a*c^5*d^7*e^2 + 3*a^2*c^4*d^5*e^4 - a^3*c^3*d^3*e^6)*x^2 + 2*(a*c^5*d^8*e - 3*a^2*c^4*d^6*e^3 + 3*a^3*c^3*d^4*e^5 - a^4*c^2*d^2*e^7)*x)]","B",0
2024,1,897,0,0.443751," ","integrate((e*x+d)^(3/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{2} e^{3} x^{3} + a^{2} d e^{4} + {\left(c^{2} d^{3} e^{2} + 2 \, a c d e^{4}\right)} x^{2} + {\left(2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{\frac{c d}{c d^{2} - a e^{2}}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{c d}{c d^{2} - a e^{2}}}}{c d x + a e}\right) + 2 \, {\left(15 \, c^{2} d^{2} e^{2} x^{2} - 2 \, c^{2} d^{4} + 9 \, a c d^{2} e^{2} + 8 \, a^{2} e^{4} + 5 \, {\left(c^{2} d^{3} e + 5 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} c^{3} d^{7} e^{2} - 3 \, a^{3} c^{2} d^{5} e^{4} + 3 \, a^{4} c d^{3} e^{6} - a^{5} d e^{8} + {\left(c^{5} d^{8} e - 3 \, a c^{4} d^{6} e^{3} + 3 \, a^{2} c^{3} d^{4} e^{5} - a^{3} c^{2} d^{2} e^{7}\right)} x^{3} + {\left(c^{5} d^{9} - a c^{4} d^{7} e^{2} - 3 \, a^{2} c^{3} d^{5} e^{4} + 5 \, a^{3} c^{2} d^{3} e^{6} - 2 \, a^{4} c d e^{8}\right)} x^{2} + {\left(2 \, a c^{4} d^{8} e - 5 \, a^{2} c^{3} d^{6} e^{3} + 3 \, a^{3} c^{2} d^{4} e^{5} + a^{4} c d^{2} e^{7} - a^{5} e^{9}\right)} x\right)}}, -\frac{15 \, {\left(c^{2} d^{2} e^{3} x^{3} + a^{2} d e^{4} + {\left(c^{2} d^{3} e^{2} + 2 \, a c d e^{4}\right)} x^{2} + {\left(2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}} \arctan\left(-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}}}{c d e x + c d^{2}}\right) - {\left(15 \, c^{2} d^{2} e^{2} x^{2} - 2 \, c^{2} d^{4} + 9 \, a c d^{2} e^{2} + 8 \, a^{2} e^{4} + 5 \, {\left(c^{2} d^{3} e + 5 \, a c d e^{3}\right)} x\right)} \sqrt{e x + d}}{4 \, {\left(a^{2} c^{3} d^{7} e^{2} - 3 \, a^{3} c^{2} d^{5} e^{4} + 3 \, a^{4} c d^{3} e^{6} - a^{5} d e^{8} + {\left(c^{5} d^{8} e - 3 \, a c^{4} d^{6} e^{3} + 3 \, a^{2} c^{3} d^{4} e^{5} - a^{3} c^{2} d^{2} e^{7}\right)} x^{3} + {\left(c^{5} d^{9} - a c^{4} d^{7} e^{2} - 3 \, a^{2} c^{3} d^{5} e^{4} + 5 \, a^{3} c^{2} d^{3} e^{6} - 2 \, a^{4} c d e^{8}\right)} x^{2} + {\left(2 \, a c^{4} d^{8} e - 5 \, a^{2} c^{3} d^{6} e^{3} + 3 \, a^{3} c^{2} d^{4} e^{5} + a^{4} c d^{2} e^{7} - a^{5} e^{9}\right)} x\right)}}\right]"," ",0,"[1/8*(15*(c^2*d^2*e^3*x^3 + a^2*d*e^4 + (c^2*d^3*e^2 + 2*a*c*d*e^4)*x^2 + (2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) + 2*(15*c^2*d^2*e^2*x^2 - 2*c^2*d^4 + 9*a*c*d^2*e^2 + 8*a^2*e^4 + 5*(c^2*d^3*e + 5*a*c*d*e^3)*x)*sqrt(e*x + d))/(a^2*c^3*d^7*e^2 - 3*a^3*c^2*d^5*e^4 + 3*a^4*c*d^3*e^6 - a^5*d*e^8 + (c^5*d^8*e - 3*a*c^4*d^6*e^3 + 3*a^2*c^3*d^4*e^5 - a^3*c^2*d^2*e^7)*x^3 + (c^5*d^9 - a*c^4*d^7*e^2 - 3*a^2*c^3*d^5*e^4 + 5*a^3*c^2*d^3*e^6 - 2*a^4*c*d*e^8)*x^2 + (2*a*c^4*d^8*e - 5*a^2*c^3*d^6*e^3 + 3*a^3*c^2*d^4*e^5 + a^4*c*d^2*e^7 - a^5*e^9)*x), -1/4*(15*(c^2*d^2*e^3*x^3 + a^2*d*e^4 + (c^2*d^3*e^2 + 2*a*c*d*e^4)*x^2 + (2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - (15*c^2*d^2*e^2*x^2 - 2*c^2*d^4 + 9*a*c*d^2*e^2 + 8*a^2*e^4 + 5*(c^2*d^3*e + 5*a*c*d*e^3)*x)*sqrt(e*x + d))/(a^2*c^3*d^7*e^2 - 3*a^3*c^2*d^5*e^4 + 3*a^4*c*d^3*e^6 - a^5*d*e^8 + (c^5*d^8*e - 3*a*c^4*d^6*e^3 + 3*a^2*c^3*d^4*e^5 - a^3*c^2*d^2*e^7)*x^3 + (c^5*d^9 - a*c^4*d^7*e^2 - 3*a^2*c^3*d^5*e^4 + 5*a^3*c^2*d^3*e^6 - 2*a^4*c*d*e^8)*x^2 + (2*a*c^4*d^8*e - 5*a^2*c^3*d^6*e^3 + 3*a^3*c^2*d^4*e^5 + a^4*c*d^2*e^7 - a^5*e^9)*x)]","B",0
2025,1,1353,0,0.451755," ","integrate((e*x+d)^(1/2)/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(c^{3} d^{3} e^{4} x^{4} + a^{2} c d^{3} e^{4} + 2 \, {\left(c^{3} d^{4} e^{3} + a c^{2} d^{2} e^{5}\right)} x^{3} + {\left(c^{3} d^{5} e^{2} + 4 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{2} + 2 \, {\left(a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} x\right)} \sqrt{\frac{c d}{c d^{2} - a e^{2}}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{c d}{c d^{2} - a e^{2}}}}{c d x + a e}\right) + 2 \, {\left(105 \, c^{3} d^{3} e^{3} x^{3} - 6 \, c^{3} d^{6} + 39 \, a c^{2} d^{4} e^{2} + 80 \, a^{2} c d^{2} e^{4} - 8 \, a^{3} e^{6} + 35 \, {\left(4 \, c^{3} d^{4} e^{2} + 5 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(3 \, c^{3} d^{5} e + 34 \, a c^{2} d^{3} e^{3} + 8 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{24 \, {\left(a^{2} c^{4} d^{10} e^{2} - 4 \, a^{3} c^{3} d^{8} e^{4} + 6 \, a^{4} c^{2} d^{6} e^{6} - 4 \, a^{5} c d^{4} e^{8} + a^{6} d^{2} e^{10} + {\left(c^{6} d^{10} e^{2} - 4 \, a c^{5} d^{8} e^{4} + 6 \, a^{2} c^{4} d^{6} e^{6} - 4 \, a^{3} c^{3} d^{4} e^{8} + a^{4} c^{2} d^{2} e^{10}\right)} x^{4} + 2 \, {\left(c^{6} d^{11} e - 3 \, a c^{5} d^{9} e^{3} + 2 \, a^{2} c^{4} d^{7} e^{5} + 2 \, a^{3} c^{3} d^{5} e^{7} - 3 \, a^{4} c^{2} d^{3} e^{9} + a^{5} c d e^{11}\right)} x^{3} + {\left(c^{6} d^{12} - 9 \, a^{2} c^{4} d^{8} e^{4} + 16 \, a^{3} c^{3} d^{6} e^{6} - 9 \, a^{4} c^{2} d^{4} e^{8} + a^{6} e^{12}\right)} x^{2} + 2 \, {\left(a c^{5} d^{11} e - 3 \, a^{2} c^{4} d^{9} e^{3} + 2 \, a^{3} c^{3} d^{7} e^{5} + 2 \, a^{4} c^{2} d^{5} e^{7} - 3 \, a^{5} c d^{3} e^{9} + a^{6} d e^{11}\right)} x\right)}}, -\frac{105 \, {\left(c^{3} d^{3} e^{4} x^{4} + a^{2} c d^{3} e^{4} + 2 \, {\left(c^{3} d^{4} e^{3} + a c^{2} d^{2} e^{5}\right)} x^{3} + {\left(c^{3} d^{5} e^{2} + 4 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{2} + 2 \, {\left(a c^{2} d^{4} e^{3} + a^{2} c d^{2} e^{5}\right)} x\right)} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}} \arctan\left(-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}}}{c d e x + c d^{2}}\right) - {\left(105 \, c^{3} d^{3} e^{3} x^{3} - 6 \, c^{3} d^{6} + 39 \, a c^{2} d^{4} e^{2} + 80 \, a^{2} c d^{2} e^{4} - 8 \, a^{3} e^{6} + 35 \, {\left(4 \, c^{3} d^{4} e^{2} + 5 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(3 \, c^{3} d^{5} e + 34 \, a c^{2} d^{3} e^{3} + 8 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{e x + d}}{12 \, {\left(a^{2} c^{4} d^{10} e^{2} - 4 \, a^{3} c^{3} d^{8} e^{4} + 6 \, a^{4} c^{2} d^{6} e^{6} - 4 \, a^{5} c d^{4} e^{8} + a^{6} d^{2} e^{10} + {\left(c^{6} d^{10} e^{2} - 4 \, a c^{5} d^{8} e^{4} + 6 \, a^{2} c^{4} d^{6} e^{6} - 4 \, a^{3} c^{3} d^{4} e^{8} + a^{4} c^{2} d^{2} e^{10}\right)} x^{4} + 2 \, {\left(c^{6} d^{11} e - 3 \, a c^{5} d^{9} e^{3} + 2 \, a^{2} c^{4} d^{7} e^{5} + 2 \, a^{3} c^{3} d^{5} e^{7} - 3 \, a^{4} c^{2} d^{3} e^{9} + a^{5} c d e^{11}\right)} x^{3} + {\left(c^{6} d^{12} - 9 \, a^{2} c^{4} d^{8} e^{4} + 16 \, a^{3} c^{3} d^{6} e^{6} - 9 \, a^{4} c^{2} d^{4} e^{8} + a^{6} e^{12}\right)} x^{2} + 2 \, {\left(a c^{5} d^{11} e - 3 \, a^{2} c^{4} d^{9} e^{3} + 2 \, a^{3} c^{3} d^{7} e^{5} + 2 \, a^{4} c^{2} d^{5} e^{7} - 3 \, a^{5} c d^{3} e^{9} + a^{6} d e^{11}\right)} x\right)}}\right]"," ",0,"[1/24*(105*(c^3*d^3*e^4*x^4 + a^2*c*d^3*e^4 + 2*(c^3*d^4*e^3 + a*c^2*d^2*e^5)*x^3 + (c^3*d^5*e^2 + 4*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^2 + 2*(a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*x)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) + 2*(105*c^3*d^3*e^3*x^3 - 6*c^3*d^6 + 39*a*c^2*d^4*e^2 + 80*a^2*c*d^2*e^4 - 8*a^3*e^6 + 35*(4*c^3*d^4*e^2 + 5*a*c^2*d^2*e^4)*x^2 + 7*(3*c^3*d^5*e + 34*a*c^2*d^3*e^3 + 8*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(a^2*c^4*d^10*e^2 - 4*a^3*c^3*d^8*e^4 + 6*a^4*c^2*d^6*e^6 - 4*a^5*c*d^4*e^8 + a^6*d^2*e^10 + (c^6*d^10*e^2 - 4*a*c^5*d^8*e^4 + 6*a^2*c^4*d^6*e^6 - 4*a^3*c^3*d^4*e^8 + a^4*c^2*d^2*e^10)*x^4 + 2*(c^6*d^11*e - 3*a*c^5*d^9*e^3 + 2*a^2*c^4*d^7*e^5 + 2*a^3*c^3*d^5*e^7 - 3*a^4*c^2*d^3*e^9 + a^5*c*d*e^11)*x^3 + (c^6*d^12 - 9*a^2*c^4*d^8*e^4 + 16*a^3*c^3*d^6*e^6 - 9*a^4*c^2*d^4*e^8 + a^6*e^12)*x^2 + 2*(a*c^5*d^11*e - 3*a^2*c^4*d^9*e^3 + 2*a^3*c^3*d^7*e^5 + 2*a^4*c^2*d^5*e^7 - 3*a^5*c*d^3*e^9 + a^6*d*e^11)*x), -1/12*(105*(c^3*d^3*e^4*x^4 + a^2*c*d^3*e^4 + 2*(c^3*d^4*e^3 + a*c^2*d^2*e^5)*x^3 + (c^3*d^5*e^2 + 4*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^2 + 2*(a*c^2*d^4*e^3 + a^2*c*d^2*e^5)*x)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - (105*c^3*d^3*e^3*x^3 - 6*c^3*d^6 + 39*a*c^2*d^4*e^2 + 80*a^2*c*d^2*e^4 - 8*a^3*e^6 + 35*(4*c^3*d^4*e^2 + 5*a*c^2*d^2*e^4)*x^2 + 7*(3*c^3*d^5*e + 34*a*c^2*d^3*e^3 + 8*a^2*c*d*e^5)*x)*sqrt(e*x + d))/(a^2*c^4*d^10*e^2 - 4*a^3*c^3*d^8*e^4 + 6*a^4*c^2*d^6*e^6 - 4*a^5*c*d^4*e^8 + a^6*d^2*e^10 + (c^6*d^10*e^2 - 4*a*c^5*d^8*e^4 + 6*a^2*c^4*d^6*e^6 - 4*a^3*c^3*d^4*e^8 + a^4*c^2*d^2*e^10)*x^4 + 2*(c^6*d^11*e - 3*a*c^5*d^9*e^3 + 2*a^2*c^4*d^7*e^5 + 2*a^3*c^3*d^5*e^7 - 3*a^4*c^2*d^3*e^9 + a^5*c*d*e^11)*x^3 + (c^6*d^12 - 9*a^2*c^4*d^8*e^4 + 16*a^3*c^3*d^6*e^6 - 9*a^4*c^2*d^4*e^8 + a^6*e^12)*x^2 + 2*(a*c^5*d^11*e - 3*a^2*c^4*d^9*e^3 + 2*a^3*c^3*d^7*e^5 + 2*a^4*c^2*d^5*e^7 - 3*a^5*c*d^3*e^9 + a^6*d*e^11)*x)]","B",0
2026,1,2007,0,0.455277," ","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=""fricas"")","\left[\frac{315 \, {\left(c^{4} d^{4} e^{5} x^{5} + a^{2} c^{2} d^{5} e^{4} + {\left(3 \, c^{4} d^{5} e^{4} + 2 \, a c^{3} d^{3} e^{6}\right)} x^{4} + {\left(3 \, c^{4} d^{6} e^{3} + 6 \, a c^{3} d^{4} e^{5} + a^{2} c^{2} d^{2} e^{7}\right)} x^{3} + {\left(c^{4} d^{7} e^{2} + 6 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6}\right)} x^{2} + {\left(2 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5}\right)} x\right)} \sqrt{\frac{c d}{c d^{2} - a e^{2}}} \log\left(\frac{c d e x + 2 \, c d^{2} - a e^{2} - 2 \, {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{c d}{c d^{2} - a e^{2}}}}{c d x + a e}\right) + 2 \, {\left(315 \, c^{4} d^{4} e^{4} x^{4} - 10 \, c^{4} d^{8} + 85 \, a c^{3} d^{6} e^{2} + 288 \, a^{2} c^{2} d^{4} e^{4} - 56 \, a^{3} c d^{2} e^{6} + 8 \, a^{4} e^{8} + 105 \, {\left(7 \, c^{4} d^{5} e^{3} + 5 \, a c^{3} d^{3} e^{5}\right)} x^{3} + 21 \, {\left(23 \, c^{4} d^{6} e^{2} + 59 \, a c^{3} d^{4} e^{4} + 8 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(15 \, c^{4} d^{7} e + 277 \, a c^{3} d^{5} e^{3} + 136 \, a^{2} c^{2} d^{3} e^{5} - 8 \, a^{3} c d e^{7}\right)} x\right)} \sqrt{e x + d}}{40 \, {\left(a^{2} c^{5} d^{13} e^{2} - 5 \, a^{3} c^{4} d^{11} e^{4} + 10 \, a^{4} c^{3} d^{9} e^{6} - 10 \, a^{5} c^{2} d^{7} e^{8} + 5 \, a^{6} c d^{5} e^{10} - a^{7} d^{3} e^{12} + {\left(c^{7} d^{12} e^{3} - 5 \, a c^{6} d^{10} e^{5} + 10 \, a^{2} c^{5} d^{8} e^{7} - 10 \, a^{3} c^{4} d^{6} e^{9} + 5 \, a^{4} c^{3} d^{4} e^{11} - a^{5} c^{2} d^{2} e^{13}\right)} x^{5} + {\left(3 \, c^{7} d^{13} e^{2} - 13 \, a c^{6} d^{11} e^{4} + 20 \, a^{2} c^{5} d^{9} e^{6} - 10 \, a^{3} c^{4} d^{7} e^{8} - 5 \, a^{4} c^{3} d^{5} e^{10} + 7 \, a^{5} c^{2} d^{3} e^{12} - 2 \, a^{6} c d e^{14}\right)} x^{4} + {\left(3 \, c^{7} d^{14} e - 9 \, a c^{6} d^{12} e^{3} + a^{2} c^{5} d^{10} e^{5} + 25 \, a^{3} c^{4} d^{8} e^{7} - 35 \, a^{4} c^{3} d^{6} e^{9} + 17 \, a^{5} c^{2} d^{4} e^{11} - a^{6} c d^{2} e^{13} - a^{7} e^{15}\right)} x^{3} + {\left(c^{7} d^{15} + a c^{6} d^{13} e^{2} - 17 \, a^{2} c^{5} d^{11} e^{4} + 35 \, a^{3} c^{4} d^{9} e^{6} - 25 \, a^{4} c^{3} d^{7} e^{8} - a^{5} c^{2} d^{5} e^{10} + 9 \, a^{6} c d^{3} e^{12} - 3 \, a^{7} d e^{14}\right)} x^{2} + {\left(2 \, a c^{6} d^{14} e - 7 \, a^{2} c^{5} d^{12} e^{3} + 5 \, a^{3} c^{4} d^{10} e^{5} + 10 \, a^{4} c^{3} d^{8} e^{7} - 20 \, a^{5} c^{2} d^{6} e^{9} + 13 \, a^{6} c d^{4} e^{11} - 3 \, a^{7} d^{2} e^{13}\right)} x\right)}}, -\frac{315 \, {\left(c^{4} d^{4} e^{5} x^{5} + a^{2} c^{2} d^{5} e^{4} + {\left(3 \, c^{4} d^{5} e^{4} + 2 \, a c^{3} d^{3} e^{6}\right)} x^{4} + {\left(3 \, c^{4} d^{6} e^{3} + 6 \, a c^{3} d^{4} e^{5} + a^{2} c^{2} d^{2} e^{7}\right)} x^{3} + {\left(c^{4} d^{7} e^{2} + 6 \, a c^{3} d^{5} e^{4} + 3 \, a^{2} c^{2} d^{3} e^{6}\right)} x^{2} + {\left(2 \, a c^{3} d^{6} e^{3} + 3 \, a^{2} c^{2} d^{4} e^{5}\right)} x\right)} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}} \arctan\left(-\frac{{\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{c d}{c d^{2} - a e^{2}}}}{c d e x + c d^{2}}\right) - {\left(315 \, c^{4} d^{4} e^{4} x^{4} - 10 \, c^{4} d^{8} + 85 \, a c^{3} d^{6} e^{2} + 288 \, a^{2} c^{2} d^{4} e^{4} - 56 \, a^{3} c d^{2} e^{6} + 8 \, a^{4} e^{8} + 105 \, {\left(7 \, c^{4} d^{5} e^{3} + 5 \, a c^{3} d^{3} e^{5}\right)} x^{3} + 21 \, {\left(23 \, c^{4} d^{6} e^{2} + 59 \, a c^{3} d^{4} e^{4} + 8 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(15 \, c^{4} d^{7} e + 277 \, a c^{3} d^{5} e^{3} + 136 \, a^{2} c^{2} d^{3} e^{5} - 8 \, a^{3} c d e^{7}\right)} x\right)} \sqrt{e x + d}}{20 \, {\left(a^{2} c^{5} d^{13} e^{2} - 5 \, a^{3} c^{4} d^{11} e^{4} + 10 \, a^{4} c^{3} d^{9} e^{6} - 10 \, a^{5} c^{2} d^{7} e^{8} + 5 \, a^{6} c d^{5} e^{10} - a^{7} d^{3} e^{12} + {\left(c^{7} d^{12} e^{3} - 5 \, a c^{6} d^{10} e^{5} + 10 \, a^{2} c^{5} d^{8} e^{7} - 10 \, a^{3} c^{4} d^{6} e^{9} + 5 \, a^{4} c^{3} d^{4} e^{11} - a^{5} c^{2} d^{2} e^{13}\right)} x^{5} + {\left(3 \, c^{7} d^{13} e^{2} - 13 \, a c^{6} d^{11} e^{4} + 20 \, a^{2} c^{5} d^{9} e^{6} - 10 \, a^{3} c^{4} d^{7} e^{8} - 5 \, a^{4} c^{3} d^{5} e^{10} + 7 \, a^{5} c^{2} d^{3} e^{12} - 2 \, a^{6} c d e^{14}\right)} x^{4} + {\left(3 \, c^{7} d^{14} e - 9 \, a c^{6} d^{12} e^{3} + a^{2} c^{5} d^{10} e^{5} + 25 \, a^{3} c^{4} d^{8} e^{7} - 35 \, a^{4} c^{3} d^{6} e^{9} + 17 \, a^{5} c^{2} d^{4} e^{11} - a^{6} c d^{2} e^{13} - a^{7} e^{15}\right)} x^{3} + {\left(c^{7} d^{15} + a c^{6} d^{13} e^{2} - 17 \, a^{2} c^{5} d^{11} e^{4} + 35 \, a^{3} c^{4} d^{9} e^{6} - 25 \, a^{4} c^{3} d^{7} e^{8} - a^{5} c^{2} d^{5} e^{10} + 9 \, a^{6} c d^{3} e^{12} - 3 \, a^{7} d e^{14}\right)} x^{2} + {\left(2 \, a c^{6} d^{14} e - 7 \, a^{2} c^{5} d^{12} e^{3} + 5 \, a^{3} c^{4} d^{10} e^{5} + 10 \, a^{4} c^{3} d^{8} e^{7} - 20 \, a^{5} c^{2} d^{6} e^{9} + 13 \, a^{6} c d^{4} e^{11} - 3 \, a^{7} d^{2} e^{13}\right)} x\right)}}\right]"," ",0,"[1/40*(315*(c^4*d^4*e^5*x^5 + a^2*c^2*d^5*e^4 + (3*c^4*d^5*e^4 + 2*a*c^3*d^3*e^6)*x^4 + (3*c^4*d^6*e^3 + 6*a*c^3*d^4*e^5 + a^2*c^2*d^2*e^7)*x^3 + (c^4*d^7*e^2 + 6*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6)*x^2 + (2*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5)*x)*sqrt(c*d/(c*d^2 - a*e^2))*log((c*d*e*x + 2*c*d^2 - a*e^2 - 2*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(c*d/(c*d^2 - a*e^2)))/(c*d*x + a*e)) + 2*(315*c^4*d^4*e^4*x^4 - 10*c^4*d^8 + 85*a*c^3*d^6*e^2 + 288*a^2*c^2*d^4*e^4 - 56*a^3*c*d^2*e^6 + 8*a^4*e^8 + 105*(7*c^4*d^5*e^3 + 5*a*c^3*d^3*e^5)*x^3 + 21*(23*c^4*d^6*e^2 + 59*a*c^3*d^4*e^4 + 8*a^2*c^2*d^2*e^6)*x^2 + 3*(15*c^4*d^7*e + 277*a*c^3*d^5*e^3 + 136*a^2*c^2*d^3*e^5 - 8*a^3*c*d*e^7)*x)*sqrt(e*x + d))/(a^2*c^5*d^13*e^2 - 5*a^3*c^4*d^11*e^4 + 10*a^4*c^3*d^9*e^6 - 10*a^5*c^2*d^7*e^8 + 5*a^6*c*d^5*e^10 - a^7*d^3*e^12 + (c^7*d^12*e^3 - 5*a*c^6*d^10*e^5 + 10*a^2*c^5*d^8*e^7 - 10*a^3*c^4*d^6*e^9 + 5*a^4*c^3*d^4*e^11 - a^5*c^2*d^2*e^13)*x^5 + (3*c^7*d^13*e^2 - 13*a*c^6*d^11*e^4 + 20*a^2*c^5*d^9*e^6 - 10*a^3*c^4*d^7*e^8 - 5*a^4*c^3*d^5*e^10 + 7*a^5*c^2*d^3*e^12 - 2*a^6*c*d*e^14)*x^4 + (3*c^7*d^14*e - 9*a*c^6*d^12*e^3 + a^2*c^5*d^10*e^5 + 25*a^3*c^4*d^8*e^7 - 35*a^4*c^3*d^6*e^9 + 17*a^5*c^2*d^4*e^11 - a^6*c*d^2*e^13 - a^7*e^15)*x^3 + (c^7*d^15 + a*c^6*d^13*e^2 - 17*a^2*c^5*d^11*e^4 + 35*a^3*c^4*d^9*e^6 - 25*a^4*c^3*d^7*e^8 - a^5*c^2*d^5*e^10 + 9*a^6*c*d^3*e^12 - 3*a^7*d*e^14)*x^2 + (2*a*c^6*d^14*e - 7*a^2*c^5*d^12*e^3 + 5*a^3*c^4*d^10*e^5 + 10*a^4*c^3*d^8*e^7 - 20*a^5*c^2*d^6*e^9 + 13*a^6*c*d^4*e^11 - 3*a^7*d^2*e^13)*x), -1/20*(315*(c^4*d^4*e^5*x^5 + a^2*c^2*d^5*e^4 + (3*c^4*d^5*e^4 + 2*a*c^3*d^3*e^6)*x^4 + (3*c^4*d^6*e^3 + 6*a*c^3*d^4*e^5 + a^2*c^2*d^2*e^7)*x^3 + (c^4*d^7*e^2 + 6*a*c^3*d^5*e^4 + 3*a^2*c^2*d^3*e^6)*x^2 + (2*a*c^3*d^6*e^3 + 3*a^2*c^2*d^4*e^5)*x)*sqrt(-c*d/(c*d^2 - a*e^2))*arctan(-(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-c*d/(c*d^2 - a*e^2))/(c*d*e*x + c*d^2)) - (315*c^4*d^4*e^4*x^4 - 10*c^4*d^8 + 85*a*c^3*d^6*e^2 + 288*a^2*c^2*d^4*e^4 - 56*a^3*c*d^2*e^6 + 8*a^4*e^8 + 105*(7*c^4*d^5*e^3 + 5*a*c^3*d^3*e^5)*x^3 + 21*(23*c^4*d^6*e^2 + 59*a*c^3*d^4*e^4 + 8*a^2*c^2*d^2*e^6)*x^2 + 3*(15*c^4*d^7*e + 277*a*c^3*d^5*e^3 + 136*a^2*c^2*d^3*e^5 - 8*a^3*c*d*e^7)*x)*sqrt(e*x + d))/(a^2*c^5*d^13*e^2 - 5*a^3*c^4*d^11*e^4 + 10*a^4*c^3*d^9*e^6 - 10*a^5*c^2*d^7*e^8 + 5*a^6*c*d^5*e^10 - a^7*d^3*e^12 + (c^7*d^12*e^3 - 5*a*c^6*d^10*e^5 + 10*a^2*c^5*d^8*e^7 - 10*a^3*c^4*d^6*e^9 + 5*a^4*c^3*d^4*e^11 - a^5*c^2*d^2*e^13)*x^5 + (3*c^7*d^13*e^2 - 13*a*c^6*d^11*e^4 + 20*a^2*c^5*d^9*e^6 - 10*a^3*c^4*d^7*e^8 - 5*a^4*c^3*d^5*e^10 + 7*a^5*c^2*d^3*e^12 - 2*a^6*c*d*e^14)*x^4 + (3*c^7*d^14*e - 9*a*c^6*d^12*e^3 + a^2*c^5*d^10*e^5 + 25*a^3*c^4*d^8*e^7 - 35*a^4*c^3*d^6*e^9 + 17*a^5*c^2*d^4*e^11 - a^6*c*d^2*e^13 - a^7*e^15)*x^3 + (c^7*d^15 + a*c^6*d^13*e^2 - 17*a^2*c^5*d^11*e^4 + 35*a^3*c^4*d^9*e^6 - 25*a^4*c^3*d^7*e^8 - a^5*c^2*d^5*e^10 + 9*a^6*c*d^3*e^12 - 3*a^7*d*e^14)*x^2 + (2*a*c^6*d^14*e - 7*a^2*c^5*d^12*e^3 + 5*a^3*c^4*d^10*e^5 + 10*a^4*c^3*d^8*e^7 - 20*a^5*c^2*d^6*e^9 + 13*a^6*c*d^4*e^11 - 3*a^7*d^2*e^13)*x)]","B",0
2027,1,315,0,0.415842," ","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=""fricas"")","\frac{2 \, {\left(315 \, c^{5} d^{5} e^{4} x^{5} + 1155 \, a c^{4} d^{8} e - 1848 \, a^{2} c^{3} d^{6} e^{3} + 1584 \, a^{3} c^{2} d^{4} e^{5} - 704 \, a^{4} c d^{2} e^{7} + 128 \, a^{5} e^{9} + 35 \, {\left(44 \, c^{5} d^{6} e^{3} + a c^{4} d^{4} e^{5}\right)} x^{4} + 10 \, {\left(297 \, c^{5} d^{7} e^{2} + 22 \, a c^{4} d^{5} e^{4} - 4 \, a^{2} c^{3} d^{3} e^{6}\right)} x^{3} + 6 \, {\left(462 \, c^{5} d^{8} e + 99 \, a c^{4} d^{6} e^{3} - 44 \, a^{2} c^{3} d^{4} e^{5} + 8 \, a^{3} c^{2} d^{2} e^{7}\right)} x^{2} + {\left(1155 \, c^{5} d^{9} + 924 \, a c^{4} d^{7} e^{2} - 792 \, a^{2} c^{3} d^{5} e^{4} + 352 \, a^{3} c^{2} d^{3} e^{6} - 64 \, a^{4} c d e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3465 \, {\left(c^{5} d^{5} e x + c^{5} d^{6}\right)}}"," ",0,"2/3465*(315*c^5*d^5*e^4*x^5 + 1155*a*c^4*d^8*e - 1848*a^2*c^3*d^6*e^3 + 1584*a^3*c^2*d^4*e^5 - 704*a^4*c*d^2*e^7 + 128*a^5*e^9 + 35*(44*c^5*d^6*e^3 + a*c^4*d^4*e^5)*x^4 + 10*(297*c^5*d^7*e^2 + 22*a*c^4*d^5*e^4 - 4*a^2*c^3*d^3*e^6)*x^3 + 6*(462*c^5*d^8*e + 99*a*c^4*d^6*e^3 - 44*a^2*c^3*d^4*e^5 + 8*a^3*c^2*d^2*e^7)*x^2 + (1155*c^5*d^9 + 924*a*c^4*d^7*e^2 - 792*a^2*c^3*d^5*e^4 + 352*a^3*c^2*d^3*e^6 - 64*a^4*c*d*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^5*d^5*e*x + c^5*d^6)","A",0
2028,1,230,0,0.404247," ","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=""fricas"")","\frac{2 \, {\left(35 \, c^{4} d^{4} e^{3} x^{4} + 105 \, a c^{3} d^{6} e - 126 \, a^{2} c^{2} d^{4} e^{3} + 72 \, a^{3} c d^{2} e^{5} - 16 \, a^{4} e^{7} + 5 \, {\left(27 \, c^{4} d^{5} e^{2} + a c^{3} d^{3} e^{4}\right)} x^{3} + 3 \, {\left(63 \, c^{4} d^{6} e + 9 \, a c^{3} d^{4} e^{3} - 2 \, a^{2} c^{2} d^{2} e^{5}\right)} x^{2} + {\left(105 \, c^{4} d^{7} + 63 \, a c^{3} d^{5} e^{2} - 36 \, a^{2} c^{2} d^{3} e^{4} + 8 \, a^{3} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{315 \, {\left(c^{4} d^{4} e x + c^{4} d^{5}\right)}}"," ",0,"2/315*(35*c^4*d^4*e^3*x^4 + 105*a*c^3*d^6*e - 126*a^2*c^2*d^4*e^3 + 72*a^3*c*d^2*e^5 - 16*a^4*e^7 + 5*(27*c^4*d^5*e^2 + a*c^3*d^3*e^4)*x^3 + 3*(63*c^4*d^6*e + 9*a*c^3*d^4*e^3 - 2*a^2*c^2*d^2*e^5)*x^2 + (105*c^4*d^7 + 63*a*c^3*d^5*e^2 - 36*a^2*c^2*d^3*e^4 + 8*a^3*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x + c^4*d^5)","A",0
2029,1,159,0,0.400392," ","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=""fricas"")","\frac{2 \, {\left(15 \, c^{3} d^{3} e^{2} x^{3} + 35 \, a c^{2} d^{4} e - 28 \, a^{2} c d^{2} e^{3} + 8 \, a^{3} e^{5} + 3 \, {\left(14 \, c^{3} d^{4} e + a c^{2} d^{2} e^{3}\right)} x^{2} + {\left(35 \, c^{3} d^{5} + 14 \, a c^{2} d^{3} e^{2} - 4 \, a^{2} c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{105 \, {\left(c^{3} d^{3} e x + c^{3} d^{4}\right)}}"," ",0,"2/105*(15*c^3*d^3*e^2*x^3 + 35*a*c^2*d^4*e - 28*a^2*c*d^2*e^3 + 8*a^3*e^5 + 3*(14*c^3*d^4*e + a*c^2*d^2*e^3)*x^2 + (35*c^3*d^5 + 14*a*c^2*d^3*e^2 - 4*a^2*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x + c^3*d^4)","A",0
2030,1,102,0,0.404930," ","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=""fricas"")","\frac{2 \, {\left(3 \, c^{2} d^{2} e x^{2} + 5 \, a c d^{2} e - 2 \, a^{2} e^{3} + {\left(5 \, c^{2} d^{3} + a c d e^{2}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{15 \, {\left(c^{2} d^{2} e x + c^{2} d^{3}\right)}}"," ",0,"2/15*(3*c^2*d^2*e*x^2 + 5*a*c*d^2*e - 2*a^2*e^3 + (5*c^2*d^3 + a*c*d*e^2)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^2*d^2*e*x + c^2*d^3)","A",0
2031,1,57,0,0.394168," ","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=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d x + a e\right)} \sqrt{e x + d}}{3 \, {\left(c d e x + c d^{2}\right)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*x + a*e)*sqrt(e*x + d)/(c*d*e*x + c*d^2)","A",0
2032,1,309,0,0.434243," ","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=""fricas"")","\left[\frac{{\left(e x + d\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{e}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} e \sqrt{-\frac{c d^{2} - a e^{2}}{e}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{e^{2} x + d e}, \frac{2 \, {\left({\left(e x + d\right)} \sqrt{\frac{c d^{2} - a e^{2}}{e}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d^{2} - a e^{2}}{e}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}\right)}}{e^{2} x + d e}\right]"," ",0,"[((e*x + d)*sqrt(-(c*d^2 - a*e^2)/e)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*e*sqrt(-(c*d^2 - a*e^2)/e))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e^2*x + d*e), 2*((e*x + d)*sqrt((c*d^2 - a*e^2)/e)*arctan(sqrt(e*x + d)*sqrt((c*d^2 - a*e^2)/e)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e^2*x + d*e)]","A",0
2033,1,483,0,0.426147," ","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=""fricas"")","\left[-\frac{{\left(c d e^{2} x^{2} + 2 \, c d^{2} e x + c d^{3}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} e - a e^{3}\right)} \sqrt{e x + d}}{2 \, {\left(c d^{4} e^{2} - a d^{2} e^{4} + {\left(c d^{2} e^{4} - a e^{6}\right)} x^{2} + 2 \, {\left(c d^{3} e^{3} - a d e^{5}\right)} x\right)}}, -\frac{{\left(c d e^{2} x^{2} + 2 \, c d^{2} e x + c d^{3}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} e - a e^{3}\right)} \sqrt{e x + d}}{c d^{4} e^{2} - a d^{2} e^{4} + {\left(c d^{2} e^{4} - a e^{6}\right)} x^{2} + 2 \, {\left(c d^{3} e^{3} - a d e^{5}\right)} x}\right]"," ",0,"[-1/2*((c*d*e^2*x^2 + 2*c*d^2*e*x + c*d^3)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2*e - a*e^3)*sqrt(e*x + d))/(c*d^4*e^2 - a*d^2*e^4 + (c*d^2*e^4 - a*e^6)*x^2 + 2*(c*d^3*e^3 - a*d*e^5)*x), -((c*d*e^2*x^2 + 2*c*d^2*e*x + c*d^3)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2*e - a*e^3)*sqrt(e*x + d))/(c*d^4*e^2 - a*d^2*e^4 + (c*d^2*e^4 - a*e^6)*x^2 + 2*(c*d^3*e^3 - a*d*e^5)*x)]","B",0
2034,1,749,0,0.422699," ","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=""fricas"")","\left[-\frac{{\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(c^{2} d^{4} e - 3 \, a c d^{2} e^{3} + 2 \, a^{2} e^{5} - {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(c^{2} d^{7} e^{2} - 2 \, a c d^{5} e^{4} + a^{2} d^{3} e^{6} + {\left(c^{2} d^{4} e^{5} - 2 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{4} - 2 \, a c d^{3} e^{6} + a^{2} d e^{8}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e^{3} - 2 \, a c d^{4} e^{5} + a^{2} d^{2} e^{7}\right)} x\right)}}, -\frac{{\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(c^{2} d^{4} e - 3 \, a c d^{2} e^{3} + 2 \, a^{2} e^{5} - {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(c^{2} d^{7} e^{2} - 2 \, a c d^{5} e^{4} + a^{2} d^{3} e^{6} + {\left(c^{2} d^{4} e^{5} - 2 \, a c d^{2} e^{7} + a^{2} e^{9}\right)} x^{3} + 3 \, {\left(c^{2} d^{5} e^{4} - 2 \, a c d^{3} e^{6} + a^{2} d e^{8}\right)} x^{2} + 3 \, {\left(c^{2} d^{6} e^{3} - 2 \, a c d^{4} e^{5} + a^{2} d^{2} e^{7}\right)} x\right)}}\right]"," ",0,"[-1/8*((c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(c^2*d^4*e - 3*a*c*d^2*e^3 + 2*a^2*e^5 - (c^2*d^3*e^2 - a*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^7*e^2 - 2*a*c*d^5*e^4 + a^2*d^3*e^6 + (c^2*d^4*e^5 - 2*a*c*d^2*e^7 + a^2*e^9)*x^3 + 3*(c^2*d^5*e^4 - 2*a*c*d^3*e^6 + a^2*d*e^8)*x^2 + 3*(c^2*d^6*e^3 - 2*a*c*d^4*e^5 + a^2*d^2*e^7)*x), -1/4*((c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (c^2*d^4*e - 3*a*c*d^2*e^3 + 2*a^2*e^5 - (c^2*d^3*e^2 - a*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^7*e^2 - 2*a*c*d^5*e^4 + a^2*d^3*e^6 + (c^2*d^4*e^5 - 2*a*c*d^2*e^7 + a^2*e^9)*x^3 + 3*(c^2*d^5*e^4 - 2*a*c*d^3*e^6 + a^2*d*e^8)*x^2 + 3*(c^2*d^6*e^3 - 2*a*c*d^4*e^5 + a^2*d^2*e^7)*x)]","B",0
2035,1,1115,0,0.450013," ","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=""fricas"")","\left[-\frac{3 \, {\left(c^{3} d^{3} e^{4} x^{4} + 4 \, c^{3} d^{4} e^{3} x^{3} + 6 \, c^{3} d^{5} e^{2} x^{2} + 4 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(3 \, c^{3} d^{6} e - 17 \, a c^{2} d^{4} e^{3} + 22 \, a^{2} c d^{2} e^{5} - 8 \, a^{3} e^{7} - 3 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x^{2} - 2 \, {\left(4 \, c^{3} d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(c^{3} d^{10} e^{2} - 3 \, a c^{2} d^{8} e^{4} + 3 \, a^{2} c d^{6} e^{6} - a^{3} d^{4} e^{8} + {\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)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{5} - 3 \, a c^{2} d^{5} e^{7} + 3 \, a^{2} c d^{3} e^{9} - a^{3} d e^{11}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{4} - 3 \, a c^{2} d^{6} e^{6} + 3 \, a^{2} c d^{4} e^{8} - a^{3} d^{2} e^{10}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e^{3} - 3 \, a c^{2} d^{7} e^{5} + 3 \, a^{2} c d^{5} e^{7} - a^{3} d^{3} e^{9}\right)} x\right)}}, -\frac{3 \, {\left(c^{3} d^{3} e^{4} x^{4} + 4 \, c^{3} d^{4} e^{3} x^{3} + 6 \, c^{3} d^{5} e^{2} x^{2} + 4 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(3 \, c^{3} d^{6} e - 17 \, a c^{2} d^{4} e^{3} + 22 \, a^{2} c d^{2} e^{5} - 8 \, a^{3} e^{7} - 3 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x^{2} - 2 \, {\left(4 \, c^{3} d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(c^{3} d^{10} e^{2} - 3 \, a c^{2} d^{8} e^{4} + 3 \, a^{2} c d^{6} e^{6} - a^{3} d^{4} e^{8} + {\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)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{5} - 3 \, a c^{2} d^{5} e^{7} + 3 \, a^{2} c d^{3} e^{9} - a^{3} d e^{11}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{4} - 3 \, a c^{2} d^{6} e^{6} + 3 \, a^{2} c d^{4} e^{8} - a^{3} d^{2} e^{10}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e^{3} - 3 \, a c^{2} d^{7} e^{5} + 3 \, a^{2} c d^{5} e^{7} - a^{3} d^{3} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(c^3*d^3*e^4*x^4 + 4*c^3*d^4*e^3*x^3 + 6*c^3*d^5*e^2*x^2 + 4*c^3*d^6*e*x + c^3*d^7)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(3*c^3*d^6*e - 17*a*c^2*d^4*e^3 + 22*a^2*c*d^2*e^5 - 8*a^3*e^7 - 3*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x^2 - 2*(4*c^3*d^5*e^2 - 5*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^10*e^2 - 3*a*c^2*d^8*e^4 + 3*a^2*c*d^6*e^6 - a^3*d^4*e^8 + (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^4 + 4*(c^3*d^7*e^5 - 3*a*c^2*d^5*e^7 + 3*a^2*c*d^3*e^9 - a^3*d*e^11)*x^3 + 6*(c^3*d^8*e^4 - 3*a*c^2*d^6*e^6 + 3*a^2*c*d^4*e^8 - a^3*d^2*e^10)*x^2 + 4*(c^3*d^9*e^3 - 3*a*c^2*d^7*e^5 + 3*a^2*c*d^5*e^7 - a^3*d^3*e^9)*x), -1/24*(3*(c^3*d^3*e^4*x^4 + 4*c^3*d^4*e^3*x^3 + 6*c^3*d^5*e^2*x^2 + 4*c^3*d^6*e*x + c^3*d^7)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (3*c^3*d^6*e - 17*a*c^2*d^4*e^3 + 22*a^2*c*d^2*e^5 - 8*a^3*e^7 - 3*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x^2 - 2*(4*c^3*d^5*e^2 - 5*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^10*e^2 - 3*a*c^2*d^8*e^4 + 3*a^2*c*d^6*e^6 - a^3*d^4*e^8 + (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^4 + 4*(c^3*d^7*e^5 - 3*a*c^2*d^5*e^7 + 3*a^2*c*d^3*e^9 - a^3*d*e^11)*x^3 + 6*(c^3*d^8*e^4 - 3*a*c^2*d^6*e^6 + 3*a^2*c*d^4*e^8 - a^3*d^2*e^10)*x^2 + 4*(c^3*d^9*e^3 - 3*a*c^2*d^7*e^5 + 3*a^2*c*d^5*e^7 - a^3*d^3*e^9)*x)]","B",0
2036,1,392,0,0.413052," ","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=""fricas"")","\frac{2 \, {\left(1155 \, c^{6} d^{6} e^{4} x^{6} + 3003 \, a^{2} c^{4} d^{8} e^{2} - 3432 \, a^{3} c^{3} d^{6} e^{4} + 2288 \, a^{4} c^{2} d^{4} e^{6} - 832 \, a^{5} c d^{2} e^{8} + 128 \, a^{6} e^{10} + 210 \, {\left(26 \, c^{6} d^{7} e^{3} + 7 \, a c^{5} d^{5} e^{5}\right)} x^{5} + 35 \, {\left(286 \, c^{6} d^{8} e^{2} + 208 \, a c^{5} d^{6} e^{4} + a^{2} c^{4} d^{4} e^{6}\right)} x^{4} + 20 \, {\left(429 \, c^{6} d^{9} e + 715 \, a c^{5} d^{7} e^{3} + 13 \, a^{2} c^{4} d^{5} e^{5} - 2 \, a^{3} c^{3} d^{3} e^{7}\right)} x^{3} + 3 \, {\left(1001 \, c^{6} d^{10} + 4576 \, a c^{5} d^{8} e^{2} + 286 \, a^{2} c^{4} d^{6} e^{4} - 104 \, a^{3} c^{3} d^{4} e^{6} + 16 \, a^{4} c^{2} d^{2} e^{8}\right)} x^{2} + 2 \, {\left(3003 \, a c^{5} d^{9} e + 858 \, a^{2} c^{4} d^{7} e^{3} - 572 \, a^{3} c^{3} d^{5} e^{5} + 208 \, a^{4} c^{2} d^{3} e^{7} - 32 \, a^{5} c d e^{9}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{15015 \, {\left(c^{5} d^{5} e x + c^{5} d^{6}\right)}}"," ",0,"2/15015*(1155*c^6*d^6*e^4*x^6 + 3003*a^2*c^4*d^8*e^2 - 3432*a^3*c^3*d^6*e^4 + 2288*a^4*c^2*d^4*e^6 - 832*a^5*c*d^2*e^8 + 128*a^6*e^10 + 210*(26*c^6*d^7*e^3 + 7*a*c^5*d^5*e^5)*x^5 + 35*(286*c^6*d^8*e^2 + 208*a*c^5*d^6*e^4 + a^2*c^4*d^4*e^6)*x^4 + 20*(429*c^6*d^9*e + 715*a*c^5*d^7*e^3 + 13*a^2*c^4*d^5*e^5 - 2*a^3*c^3*d^3*e^7)*x^3 + 3*(1001*c^6*d^10 + 4576*a*c^5*d^8*e^2 + 286*a^2*c^4*d^6*e^4 - 104*a^3*c^3*d^4*e^6 + 16*a^4*c^2*d^2*e^8)*x^2 + 2*(3003*a*c^5*d^9*e + 858*a^2*c^4*d^7*e^3 - 572*a^3*c^3*d^5*e^5 + 208*a^4*c^2*d^3*e^7 - 32*a^5*c*d*e^9)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^5*d^5*e*x + c^5*d^6)","A",0
2037,1,292,0,0.410341," ","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=""fricas"")","\frac{2 \, {\left(105 \, c^{5} d^{5} e^{3} x^{5} + 231 \, a^{2} c^{3} d^{6} e^{2} - 198 \, a^{3} c^{2} d^{4} e^{4} + 88 \, a^{4} c d^{2} e^{6} - 16 \, a^{5} e^{8} + 35 \, {\left(11 \, c^{5} d^{6} e^{2} + 4 \, a c^{4} d^{4} e^{4}\right)} x^{4} + 5 \, {\left(99 \, c^{5} d^{7} e + 110 \, a c^{4} d^{5} e^{3} + a^{2} c^{3} d^{3} e^{5}\right)} x^{3} + 3 \, {\left(77 \, c^{5} d^{8} + 264 \, a c^{4} d^{6} e^{2} + 11 \, a^{2} c^{3} d^{4} e^{4} - 2 \, a^{3} c^{2} d^{2} e^{6}\right)} x^{2} + {\left(462 \, a c^{4} d^{7} e + 99 \, a^{2} c^{3} d^{5} e^{3} - 44 \, a^{3} c^{2} d^{3} e^{5} + 8 \, a^{4} c d e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{1155 \, {\left(c^{4} d^{4} e x + c^{4} d^{5}\right)}}"," ",0,"2/1155*(105*c^5*d^5*e^3*x^5 + 231*a^2*c^3*d^6*e^2 - 198*a^3*c^2*d^4*e^4 + 88*a^4*c*d^2*e^6 - 16*a^5*e^8 + 35*(11*c^5*d^6*e^2 + 4*a*c^4*d^4*e^4)*x^4 + 5*(99*c^5*d^7*e + 110*a*c^4*d^5*e^3 + a^2*c^3*d^3*e^5)*x^3 + 3*(77*c^5*d^8 + 264*a*c^4*d^6*e^2 + 11*a^2*c^3*d^4*e^4 - 2*a^3*c^2*d^2*e^6)*x^2 + (462*a*c^4*d^7*e + 99*a^2*c^3*d^5*e^3 - 44*a^3*c^2*d^3*e^5 + 8*a^4*c*d*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x + c^4*d^5)","A",0
2038,1,208,0,0.405565," ","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=""fricas"")","\frac{2 \, {\left(35 \, c^{4} d^{4} e^{2} x^{4} + 63 \, a^{2} c^{2} d^{4} e^{2} - 36 \, a^{3} c d^{2} e^{4} + 8 \, a^{4} e^{6} + 10 \, {\left(9 \, c^{4} d^{5} e + 5 \, a c^{3} d^{3} e^{3}\right)} x^{3} + 3 \, {\left(21 \, c^{4} d^{6} + 48 \, a c^{3} d^{4} e^{2} + a^{2} c^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(63 \, a c^{3} d^{5} e + 9 \, a^{2} c^{2} d^{3} e^{3} - 2 \, a^{3} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{315 \, {\left(c^{3} d^{3} e x + c^{3} d^{4}\right)}}"," ",0,"2/315*(35*c^4*d^4*e^2*x^4 + 63*a^2*c^2*d^4*e^2 - 36*a^3*c*d^2*e^4 + 8*a^4*e^6 + 10*(9*c^4*d^5*e + 5*a*c^3*d^3*e^3)*x^3 + 3*(21*c^4*d^6 + 48*a*c^3*d^4*e^2 + a^2*c^2*d^2*e^4)*x^2 + 2*(63*a*c^3*d^5*e + 9*a^2*c^2*d^3*e^3 - 2*a^3*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x + c^3*d^4)","A",0
2039,1,135,0,0.407250," ","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=""fricas"")","\frac{2 \, {\left(5 \, c^{3} d^{3} e x^{3} + 7 \, a^{2} c d^{2} e^{2} - 2 \, a^{3} e^{4} + {\left(7 \, c^{3} d^{4} + 8 \, a c^{2} d^{2} e^{2}\right)} x^{2} + {\left(14 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{35 \, {\left(c^{2} d^{2} e x + c^{2} d^{3}\right)}}"," ",0,"2/35*(5*c^3*d^3*e*x^3 + 7*a^2*c*d^2*e^2 - 2*a^3*e^4 + (7*c^3*d^4 + 8*a*c^2*d^2*e^2)*x^2 + (14*a*c^2*d^3*e + a^2*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^2*d^2*e*x + c^2*d^3)","A",0
2040,1,74,0,0.406285," ","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=""fricas"")","\frac{2 \, {\left(c^{2} d^{2} x^{2} + 2 \, a c d e x + a^{2} e^{2}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{5 \, {\left(c d e x + c d^{2}\right)}}"," ",0,"2/5*(c^2*d^2*x^2 + 2*a*c*d*e*x + a^2*e^2)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c*d*e*x + c*d^2)","A",0
2041,1,399,0,0.439914," ","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=""fricas"")","\left[\frac{3 \, {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{e}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} e \sqrt{-\frac{c d^{2} - a e^{2}}{e}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d e x - 3 \, c d^{2} + 4 \, a e^{2}\right)} \sqrt{e x + d}}{3 \, {\left(e^{3} x + d e^{2}\right)}}, -\frac{2 \, {\left(3 \, {\left(c d^{3} - a d e^{2} + {\left(c d^{2} e - a e^{3}\right)} x\right)} \sqrt{\frac{c d^{2} - a e^{2}}{e}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d^{2} - a e^{2}}{e}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) - \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d e x - 3 \, c d^{2} + 4 \, a e^{2}\right)} \sqrt{e x + d}\right)}}{3 \, {\left(e^{3} x + d e^{2}\right)}}\right]"," ",0,"[1/3*(3*(c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt(-(c*d^2 - a*e^2)/e)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*e*sqrt(-(c*d^2 - a*e^2)/e))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*e*x - 3*c*d^2 + 4*a*e^2)*sqrt(e*x + d))/(e^3*x + d*e^2), -2/3*(3*(c*d^3 - a*d*e^2 + (c*d^2*e - a*e^3)*x)*sqrt((c*d^2 - a*e^2)/e)*arctan(sqrt(e*x + d)*sqrt((c*d^2 - a*e^2)/e)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) - sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*e*x - 3*c*d^2 + 4*a*e^2)*sqrt(e*x + d))/(e^3*x + d*e^2)]","A",0
2042,1,411,0,0.440868," ","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=""fricas"")","\left[\frac{3 \, {\left(c d e^{2} x^{2} + 2 \, c d^{2} e x + c d^{3}\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{e}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} e \sqrt{-\frac{c d^{2} - a e^{2}}{e}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + 3 \, c d^{2} - a e^{2}\right)} \sqrt{e x + d}}{2 \, {\left(e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}\right)}}, \frac{3 \, {\left(c d e^{2} x^{2} + 2 \, c d^{2} e x + c d^{3}\right)} \sqrt{\frac{c d^{2} - a e^{2}}{e}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d^{2} - a e^{2}}{e}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(2 \, c d e x + 3 \, c d^{2} - a e^{2}\right)} \sqrt{e x + d}}{e^{4} x^{2} + 2 \, d e^{3} x + d^{2} e^{2}}\right]"," ",0,"[1/2*(3*(c*d*e^2*x^2 + 2*c*d^2*e*x + c*d^3)*sqrt(-(c*d^2 - a*e^2)/e)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*e*sqrt(-(c*d^2 - a*e^2)/e))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + 3*c*d^2 - a*e^2)*sqrt(e*x + d))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2), (3*(c*d*e^2*x^2 + 2*c*d^2*e*x + c*d^3)*sqrt((c*d^2 - a*e^2)/e)*arctan(sqrt(e*x + d)*sqrt((c*d^2 - a*e^2)/e)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(2*c*d*e*x + 3*c*d^2 - a*e^2)*sqrt(e*x + d))/(e^4*x^2 + 2*d*e^3*x + d^2*e^2)]","A",0
2043,1,649,0,0.440949," ","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=""fricas"")","\left[-\frac{3 \, {\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(3 \, c^{2} d^{4} e - a c d^{2} e^{3} - 2 \, a^{2} e^{5} + 5 \, {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(c d^{5} e^{3} - a d^{3} e^{5} + {\left(c d^{2} e^{6} - a e^{8}\right)} x^{3} + 3 \, {\left(c d^{3} e^{5} - a d e^{7}\right)} x^{2} + 3 \, {\left(c d^{4} e^{4} - a d^{2} e^{6}\right)} x\right)}}, -\frac{3 \, {\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(3 \, c^{2} d^{4} e - a c d^{2} e^{3} - 2 \, a^{2} e^{5} + 5 \, {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(c d^{5} e^{3} - a d^{3} e^{5} + {\left(c d^{2} e^{6} - a e^{8}\right)} x^{3} + 3 \, {\left(c d^{3} e^{5} - a d e^{7}\right)} x^{2} + 3 \, {\left(c d^{4} e^{4} - a d^{2} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/8*(3*(c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(3*c^2*d^4*e - a*c*d^2*e^3 - 2*a^2*e^5 + 5*(c^2*d^3*e^2 - a*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c*d^5*e^3 - a*d^3*e^5 + (c*d^2*e^6 - a*e^8)*x^3 + 3*(c*d^3*e^5 - a*d*e^7)*x^2 + 3*(c*d^4*e^4 - a*d^2*e^6)*x), -1/4*(3*(c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (3*c^2*d^4*e - a*c*d^2*e^3 - 2*a^2*e^5 + 5*(c^2*d^3*e^2 - a*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c*d^5*e^3 - a*d^3*e^5 + (c*d^2*e^6 - a*e^8)*x^3 + 3*(c*d^3*e^5 - a*d*e^7)*x^2 + 3*(c*d^4*e^4 - a*d^2*e^6)*x)]","A",0
2044,1,967,0,0.435993," ","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=""fricas"")","\left[-\frac{3 \, {\left(c^{3} d^{3} e^{4} x^{4} + 4 \, c^{3} d^{4} e^{3} x^{3} + 6 \, c^{3} d^{5} e^{2} x^{2} + 4 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(3 \, c^{3} d^{6} e - a c^{2} d^{4} e^{3} - 10 \, a^{2} c d^{2} e^{5} + 8 \, a^{3} e^{7} - 3 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x^{2} + 2 \, {\left(4 \, c^{3} d^{5} e^{2} - 11 \, a c^{2} d^{3} e^{4} + 7 \, a^{2} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(c^{2} d^{8} e^{3} - 2 \, a c d^{6} e^{5} + a^{2} d^{4} e^{7} + {\left(c^{2} d^{4} e^{7} - 2 \, a c d^{2} e^{9} + a^{2} e^{11}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{6} - 2 \, a c d^{3} e^{8} + a^{2} d e^{10}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{5} - 2 \, a c d^{4} e^{7} + a^{2} d^{2} e^{9}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e^{4} - 2 \, a c d^{5} e^{6} + a^{2} d^{3} e^{8}\right)} x\right)}}, -\frac{3 \, {\left(c^{3} d^{3} e^{4} x^{4} + 4 \, c^{3} d^{4} e^{3} x^{3} + 6 \, c^{3} d^{5} e^{2} x^{2} + 4 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(3 \, c^{3} d^{6} e - a c^{2} d^{4} e^{3} - 10 \, a^{2} c d^{2} e^{5} + 8 \, a^{3} e^{7} - 3 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x^{2} + 2 \, {\left(4 \, c^{3} d^{5} e^{2} - 11 \, a c^{2} d^{3} e^{4} + 7 \, a^{2} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(c^{2} d^{8} e^{3} - 2 \, a c d^{6} e^{5} + a^{2} d^{4} e^{7} + {\left(c^{2} d^{4} e^{7} - 2 \, a c d^{2} e^{9} + a^{2} e^{11}\right)} x^{4} + 4 \, {\left(c^{2} d^{5} e^{6} - 2 \, a c d^{3} e^{8} + a^{2} d e^{10}\right)} x^{3} + 6 \, {\left(c^{2} d^{6} e^{5} - 2 \, a c d^{4} e^{7} + a^{2} d^{2} e^{9}\right)} x^{2} + 4 \, {\left(c^{2} d^{7} e^{4} - 2 \, a c d^{5} e^{6} + a^{2} d^{3} e^{8}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*(c^3*d^3*e^4*x^4 + 4*c^3*d^4*e^3*x^3 + 6*c^3*d^5*e^2*x^2 + 4*c^3*d^6*e*x + c^3*d^7)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(3*c^3*d^6*e - a*c^2*d^4*e^3 - 10*a^2*c*d^2*e^5 + 8*a^3*e^7 - 3*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x^2 + 2*(4*c^3*d^5*e^2 - 11*a*c^2*d^3*e^4 + 7*a^2*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^8*e^3 - 2*a*c*d^6*e^5 + a^2*d^4*e^7 + (c^2*d^4*e^7 - 2*a*c*d^2*e^9 + a^2*e^11)*x^4 + 4*(c^2*d^5*e^6 - 2*a*c*d^3*e^8 + a^2*d*e^10)*x^3 + 6*(c^2*d^6*e^5 - 2*a*c*d^4*e^7 + a^2*d^2*e^9)*x^2 + 4*(c^2*d^7*e^4 - 2*a*c*d^5*e^6 + a^2*d^3*e^8)*x), -1/24*(3*(c^3*d^3*e^4*x^4 + 4*c^3*d^4*e^3*x^3 + 6*c^3*d^5*e^2*x^2 + 4*c^3*d^6*e*x + c^3*d^7)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (3*c^3*d^6*e - a*c^2*d^4*e^3 - 10*a^2*c*d^2*e^5 + 8*a^3*e^7 - 3*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x^2 + 2*(4*c^3*d^5*e^2 - 11*a*c^2*d^3*e^4 + 7*a^2*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^8*e^3 - 2*a*c*d^6*e^5 + a^2*d^4*e^7 + (c^2*d^4*e^7 - 2*a*c*d^2*e^9 + a^2*e^11)*x^4 + 4*(c^2*d^5*e^6 - 2*a*c*d^3*e^8 + a^2*d*e^10)*x^3 + 6*(c^2*d^6*e^5 - 2*a*c*d^4*e^7 + a^2*d^2*e^9)*x^2 + 4*(c^2*d^7*e^4 - 2*a*c*d^5*e^6 + a^2*d^3*e^8)*x)]","B",0
2045,1,1387,0,0.453532," ","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=""fricas"")","\left[-\frac{3 \, {\left(c^{4} d^{4} e^{5} x^{5} + 5 \, c^{4} d^{5} e^{4} x^{4} + 10 \, c^{4} d^{6} e^{3} x^{3} + 10 \, c^{4} d^{7} e^{2} x^{2} + 5 \, c^{4} d^{8} e x + c^{4} d^{9}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(3 \, c^{4} d^{8} e - a c^{3} d^{6} e^{3} - 26 \, a^{2} c^{2} d^{4} e^{5} + 40 \, a^{3} c d^{2} e^{7} - 16 \, a^{4} e^{9} - 3 \, {\left(c^{4} d^{5} e^{4} - a c^{3} d^{3} e^{6}\right)} x^{3} - {\left(11 \, c^{4} d^{6} e^{3} - 13 \, a c^{3} d^{4} e^{5} + 2 \, a^{2} c^{2} d^{2} e^{7}\right)} x^{2} + {\left(11 \, c^{4} d^{7} e^{2} - 55 \, a c^{3} d^{5} e^{4} + 68 \, a^{2} c^{2} d^{3} e^{6} - 24 \, a^{3} c d e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{128 \, {\left(c^{3} d^{11} e^{3} - 3 \, a c^{2} d^{9} e^{5} + 3 \, a^{2} c d^{7} e^{7} - a^{3} d^{5} e^{9} + {\left(c^{3} d^{6} e^{8} - 3 \, a c^{2} d^{4} e^{10} + 3 \, a^{2} c d^{2} e^{12} - a^{3} e^{14}\right)} x^{5} + 5 \, {\left(c^{3} d^{7} e^{7} - 3 \, a c^{2} d^{5} e^{9} + 3 \, a^{2} c d^{3} e^{11} - a^{3} d e^{13}\right)} x^{4} + 10 \, {\left(c^{3} d^{8} e^{6} - 3 \, a c^{2} d^{6} e^{8} + 3 \, a^{2} c d^{4} e^{10} - a^{3} d^{2} e^{12}\right)} x^{3} + 10 \, {\left(c^{3} d^{9} e^{5} - 3 \, a c^{2} d^{7} e^{7} + 3 \, a^{2} c d^{5} e^{9} - a^{3} d^{3} e^{11}\right)} x^{2} + 5 \, {\left(c^{3} d^{10} e^{4} - 3 \, a c^{2} d^{8} e^{6} + 3 \, a^{2} c d^{6} e^{8} - a^{3} d^{4} e^{10}\right)} x\right)}}, -\frac{3 \, {\left(c^{4} d^{4} e^{5} x^{5} + 5 \, c^{4} d^{5} e^{4} x^{4} + 10 \, c^{4} d^{6} e^{3} x^{3} + 10 \, c^{4} d^{7} e^{2} x^{2} + 5 \, c^{4} d^{8} e x + c^{4} d^{9}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(3 \, c^{4} d^{8} e - a c^{3} d^{6} e^{3} - 26 \, a^{2} c^{2} d^{4} e^{5} + 40 \, a^{3} c d^{2} e^{7} - 16 \, a^{4} e^{9} - 3 \, {\left(c^{4} d^{5} e^{4} - a c^{3} d^{3} e^{6}\right)} x^{3} - {\left(11 \, c^{4} d^{6} e^{3} - 13 \, a c^{3} d^{4} e^{5} + 2 \, a^{2} c^{2} d^{2} e^{7}\right)} x^{2} + {\left(11 \, c^{4} d^{7} e^{2} - 55 \, a c^{3} d^{5} e^{4} + 68 \, a^{2} c^{2} d^{3} e^{6} - 24 \, a^{3} c d e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{64 \, {\left(c^{3} d^{11} e^{3} - 3 \, a c^{2} d^{9} e^{5} + 3 \, a^{2} c d^{7} e^{7} - a^{3} d^{5} e^{9} + {\left(c^{3} d^{6} e^{8} - 3 \, a c^{2} d^{4} e^{10} + 3 \, a^{2} c d^{2} e^{12} - a^{3} e^{14}\right)} x^{5} + 5 \, {\left(c^{3} d^{7} e^{7} - 3 \, a c^{2} d^{5} e^{9} + 3 \, a^{2} c d^{3} e^{11} - a^{3} d e^{13}\right)} x^{4} + 10 \, {\left(c^{3} d^{8} e^{6} - 3 \, a c^{2} d^{6} e^{8} + 3 \, a^{2} c d^{4} e^{10} - a^{3} d^{2} e^{12}\right)} x^{3} + 10 \, {\left(c^{3} d^{9} e^{5} - 3 \, a c^{2} d^{7} e^{7} + 3 \, a^{2} c d^{5} e^{9} - a^{3} d^{3} e^{11}\right)} x^{2} + 5 \, {\left(c^{3} d^{10} e^{4} - 3 \, a c^{2} d^{8} e^{6} + 3 \, a^{2} c d^{6} e^{8} - a^{3} d^{4} e^{10}\right)} x\right)}}\right]"," ",0,"[-1/128*(3*(c^4*d^4*e^5*x^5 + 5*c^4*d^5*e^4*x^4 + 10*c^4*d^6*e^3*x^3 + 10*c^4*d^7*e^2*x^2 + 5*c^4*d^8*e*x + c^4*d^9)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(3*c^4*d^8*e - a*c^3*d^6*e^3 - 26*a^2*c^2*d^4*e^5 + 40*a^3*c*d^2*e^7 - 16*a^4*e^9 - 3*(c^4*d^5*e^4 - a*c^3*d^3*e^6)*x^3 - (11*c^4*d^6*e^3 - 13*a*c^3*d^4*e^5 + 2*a^2*c^2*d^2*e^7)*x^2 + (11*c^4*d^7*e^2 - 55*a*c^3*d^5*e^4 + 68*a^2*c^2*d^3*e^6 - 24*a^3*c*d*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^11*e^3 - 3*a*c^2*d^9*e^5 + 3*a^2*c*d^7*e^7 - a^3*d^5*e^9 + (c^3*d^6*e^8 - 3*a*c^2*d^4*e^10 + 3*a^2*c*d^2*e^12 - a^3*e^14)*x^5 + 5*(c^3*d^7*e^7 - 3*a*c^2*d^5*e^9 + 3*a^2*c*d^3*e^11 - a^3*d*e^13)*x^4 + 10*(c^3*d^8*e^6 - 3*a*c^2*d^6*e^8 + 3*a^2*c*d^4*e^10 - a^3*d^2*e^12)*x^3 + 10*(c^3*d^9*e^5 - 3*a*c^2*d^7*e^7 + 3*a^2*c*d^5*e^9 - a^3*d^3*e^11)*x^2 + 5*(c^3*d^10*e^4 - 3*a*c^2*d^8*e^6 + 3*a^2*c*d^6*e^8 - a^3*d^4*e^10)*x), -1/64*(3*(c^4*d^4*e^5*x^5 + 5*c^4*d^5*e^4*x^4 + 10*c^4*d^6*e^3*x^3 + 10*c^4*d^7*e^2*x^2 + 5*c^4*d^8*e*x + c^4*d^9)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (3*c^4*d^8*e - a*c^3*d^6*e^3 - 26*a^2*c^2*d^4*e^5 + 40*a^3*c*d^2*e^7 - 16*a^4*e^9 - 3*(c^4*d^5*e^4 - a*c^3*d^3*e^6)*x^3 - (11*c^4*d^6*e^3 - 13*a*c^3*d^4*e^5 + 2*a^2*c^2*d^2*e^7)*x^2 + (11*c^4*d^7*e^2 - 55*a*c^3*d^5*e^4 + 68*a^2*c^2*d^3*e^6 - 24*a^3*c*d*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^11*e^3 - 3*a*c^2*d^9*e^5 + 3*a^2*c*d^7*e^7 - a^3*d^5*e^9 + (c^3*d^6*e^8 - 3*a*c^2*d^4*e^10 + 3*a^2*c*d^2*e^12 - a^3*e^14)*x^5 + 5*(c^3*d^7*e^7 - 3*a*c^2*d^5*e^9 + 3*a^2*c*d^3*e^11 - a^3*d*e^13)*x^4 + 10*(c^3*d^8*e^6 - 3*a*c^2*d^6*e^8 + 3*a^2*c*d^4*e^10 - a^3*d^2*e^12)*x^3 + 10*(c^3*d^9*e^5 - 3*a*c^2*d^7*e^7 + 3*a^2*c*d^5*e^9 - a^3*d^3*e^11)*x^2 + 5*(c^3*d^10*e^4 - 3*a*c^2*d^8*e^6 + 3*a^2*c*d^6*e^8 - a^3*d^4*e^10)*x)]","B",0
2046,1,467,0,0.423973," ","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=""fricas"")","\frac{2 \, {\left(3003 \, c^{7} d^{7} e^{4} x^{7} + 6435 \, a^{3} c^{4} d^{8} e^{3} - 5720 \, a^{4} c^{3} d^{6} e^{5} + 3120 \, a^{5} c^{2} d^{4} e^{7} - 960 \, a^{6} c d^{2} e^{9} + 128 \, a^{7} e^{11} + 231 \, {\left(60 \, c^{7} d^{8} e^{3} + 31 \, a c^{6} d^{6} e^{5}\right)} x^{6} + 63 \, {\left(390 \, c^{7} d^{9} e^{2} + 540 \, a c^{6} d^{7} e^{4} + 71 \, a^{2} c^{5} d^{5} e^{6}\right)} x^{5} + 35 \, {\left(572 \, c^{7} d^{10} e + 1794 \, a c^{6} d^{8} e^{3} + 636 \, a^{2} c^{5} d^{6} e^{5} + a^{3} c^{4} d^{4} e^{7}\right)} x^{4} + 5 \, {\left(1287 \, c^{7} d^{11} + 10868 \, a c^{6} d^{9} e^{2} + 8814 \, a^{2} c^{5} d^{7} e^{4} + 60 \, a^{3} c^{4} d^{5} e^{6} - 8 \, a^{4} c^{3} d^{3} e^{8}\right)} x^{3} + 3 \, {\left(6435 \, a c^{6} d^{10} e + 14300 \, a^{2} c^{5} d^{8} e^{3} + 390 \, a^{3} c^{4} d^{6} e^{5} - 120 \, a^{4} c^{3} d^{4} e^{7} + 16 \, a^{5} c^{2} d^{2} e^{9}\right)} x^{2} + {\left(19305 \, a^{2} c^{5} d^{9} e^{2} + 2860 \, a^{3} c^{4} d^{7} e^{4} - 1560 \, a^{4} c^{3} d^{5} e^{6} + 480 \, a^{5} c^{2} d^{3} e^{8} - 64 \, a^{6} c d e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{45045 \, {\left(c^{5} d^{5} e x + c^{5} d^{6}\right)}}"," ",0,"2/45045*(3003*c^7*d^7*e^4*x^7 + 6435*a^3*c^4*d^8*e^3 - 5720*a^4*c^3*d^6*e^5 + 3120*a^5*c^2*d^4*e^7 - 960*a^6*c*d^2*e^9 + 128*a^7*e^11 + 231*(60*c^7*d^8*e^3 + 31*a*c^6*d^6*e^5)*x^6 + 63*(390*c^7*d^9*e^2 + 540*a*c^6*d^7*e^4 + 71*a^2*c^5*d^5*e^6)*x^5 + 35*(572*c^7*d^10*e + 1794*a*c^6*d^8*e^3 + 636*a^2*c^5*d^6*e^5 + a^3*c^4*d^4*e^7)*x^4 + 5*(1287*c^7*d^11 + 10868*a*c^6*d^9*e^2 + 8814*a^2*c^5*d^7*e^4 + 60*a^3*c^4*d^5*e^6 - 8*a^4*c^3*d^3*e^8)*x^3 + 3*(6435*a*c^6*d^10*e + 14300*a^2*c^5*d^8*e^3 + 390*a^3*c^4*d^6*e^5 - 120*a^4*c^3*d^4*e^7 + 16*a^5*c^2*d^2*e^9)*x^2 + (19305*a^2*c^5*d^9*e^2 + 2860*a^3*c^4*d^7*e^4 - 1560*a^4*c^3*d^5*e^6 + 480*a^5*c^2*d^3*e^8 - 64*a^6*c*d*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^5*d^5*e*x + c^5*d^6)","A",0
2047,1,354,0,0.416965," ","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=""fricas"")","\frac{2 \, {\left(231 \, c^{6} d^{6} e^{3} x^{6} + 429 \, a^{3} c^{3} d^{6} e^{3} - 286 \, a^{4} c^{2} d^{4} e^{5} + 104 \, a^{5} c d^{2} e^{7} - 16 \, a^{6} e^{9} + 63 \, {\left(13 \, c^{6} d^{7} e^{2} + 9 \, a c^{5} d^{5} e^{4}\right)} x^{5} + 7 \, {\left(143 \, c^{6} d^{8} e + 299 \, a c^{5} d^{6} e^{3} + 53 \, a^{2} c^{4} d^{4} e^{5}\right)} x^{4} + {\left(429 \, c^{6} d^{9} + 2717 \, a c^{5} d^{7} e^{2} + 1469 \, a^{2} c^{4} d^{5} e^{4} + 5 \, a^{3} c^{3} d^{3} e^{6}\right)} x^{3} + 3 \, {\left(429 \, a c^{5} d^{8} e + 715 \, a^{2} c^{4} d^{6} e^{3} + 13 \, a^{3} c^{3} d^{4} e^{5} - 2 \, a^{4} c^{2} d^{2} e^{7}\right)} x^{2} + {\left(1287 \, a^{2} c^{4} d^{7} e^{2} + 143 \, a^{3} c^{3} d^{5} e^{4} - 52 \, a^{4} c^{2} d^{3} e^{6} + 8 \, a^{5} c d e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3003 \, {\left(c^{4} d^{4} e x + c^{4} d^{5}\right)}}"," ",0,"2/3003*(231*c^6*d^6*e^3*x^6 + 429*a^3*c^3*d^6*e^3 - 286*a^4*c^2*d^4*e^5 + 104*a^5*c*d^2*e^7 - 16*a^6*e^9 + 63*(13*c^6*d^7*e^2 + 9*a*c^5*d^5*e^4)*x^5 + 7*(143*c^6*d^8*e + 299*a*c^5*d^6*e^3 + 53*a^2*c^4*d^4*e^5)*x^4 + (429*c^6*d^9 + 2717*a*c^5*d^7*e^2 + 1469*a^2*c^4*d^5*e^4 + 5*a^3*c^3*d^3*e^6)*x^3 + 3*(429*a*c^5*d^8*e + 715*a^2*c^4*d^6*e^3 + 13*a^3*c^3*d^4*e^5 - 2*a^4*c^2*d^2*e^7)*x^2 + (1287*a^2*c^4*d^7*e^2 + 143*a^3*c^3*d^5*e^4 - 52*a^4*c^2*d^3*e^6 + 8*a^5*c*d*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x + c^4*d^5)","A",0
2048,1,254,0,0.395445," ","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=""fricas"")","\frac{2 \, {\left(63 \, c^{5} d^{5} e^{2} x^{5} + 99 \, a^{3} c^{2} d^{4} e^{3} - 44 \, a^{4} c d^{2} e^{5} + 8 \, a^{5} e^{7} + 7 \, {\left(22 \, c^{5} d^{6} e + 23 \, a c^{4} d^{4} e^{3}\right)} x^{4} + {\left(99 \, c^{5} d^{7} + 418 \, a c^{4} d^{5} e^{2} + 113 \, a^{2} c^{3} d^{3} e^{4}\right)} x^{3} + 3 \, {\left(99 \, a c^{4} d^{6} e + 110 \, a^{2} c^{3} d^{4} e^{3} + a^{3} c^{2} d^{2} e^{5}\right)} x^{2} + {\left(297 \, a^{2} c^{3} d^{5} e^{2} + 22 \, a^{3} c^{2} d^{3} e^{4} - 4 \, a^{4} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{693 \, {\left(c^{3} d^{3} e x + c^{3} d^{4}\right)}}"," ",0,"2/693*(63*c^5*d^5*e^2*x^5 + 99*a^3*c^2*d^4*e^3 - 44*a^4*c*d^2*e^5 + 8*a^5*e^7 + 7*(22*c^5*d^6*e + 23*a*c^4*d^4*e^3)*x^4 + (99*c^5*d^7 + 418*a*c^4*d^5*e^2 + 113*a^2*c^3*d^3*e^4)*x^3 + 3*(99*a*c^4*d^6*e + 110*a^2*c^3*d^4*e^3 + a^3*c^2*d^2*e^5)*x^2 + (297*a^2*c^3*d^5*e^2 + 22*a^3*c^2*d^3*e^4 - 4*a^4*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x + c^3*d^4)","A",0
2049,1,169,0,0.408202," ","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=""fricas"")","\frac{2 \, {\left(7 \, c^{4} d^{4} e x^{4} + 9 \, a^{3} c d^{2} e^{3} - 2 \, a^{4} e^{5} + {\left(9 \, c^{4} d^{5} + 19 \, a c^{3} d^{3} e^{2}\right)} x^{3} + 3 \, {\left(9 \, a c^{3} d^{4} e + 5 \, a^{2} c^{2} d^{2} e^{3}\right)} x^{2} + {\left(27 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{63 \, {\left(c^{2} d^{2} e x + c^{2} d^{3}\right)}}"," ",0,"2/63*(7*c^4*d^4*e*x^4 + 9*a^3*c*d^2*e^3 - 2*a^4*e^5 + (9*c^4*d^5 + 19*a*c^3*d^3*e^2)*x^3 + 3*(9*a*c^3*d^4*e + 5*a^2*c^2*d^2*e^3)*x^2 + (27*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^2*d^2*e*x + c^2*d^3)","A",0
2050,1,91,0,0.405974," ","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=""fricas"")","\frac{2 \, {\left(c^{3} d^{3} x^{3} + 3 \, a c^{2} d^{2} e x^{2} + 3 \, a^{2} c d e^{2} x + a^{3} e^{3}\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{7 \, {\left(c d e x + c d^{2}\right)}}"," ",0,"2/7*(c^3*d^3*x^3 + 3*a*c^2*d^2*e*x^2 + 3*a^2*c*d*e^2*x + a^3*e^3)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c*d*e*x + c*d^2)","B",0
2051,1,538,0,0.442870," ","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=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{5} - 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e - 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{e}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} e \sqrt{-\frac{c d^{2} - a e^{2}}{e}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(3 \, c^{2} d^{2} e^{2} x^{2} + 15 \, c^{2} d^{4} - 35 \, a c d^{2} e^{2} + 23 \, a^{2} e^{4} - {\left(5 \, c^{2} d^{3} e - 11 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{15 \, {\left(e^{4} x + d e^{3}\right)}}, \frac{2 \, {\left(15 \, {\left(c^{2} d^{5} - 2 \, a c d^{3} e^{2} + a^{2} d e^{4} + {\left(c^{2} d^{4} e - 2 \, a c d^{2} e^{3} + a^{2} e^{5}\right)} x\right)} \sqrt{\frac{c d^{2} - a e^{2}}{e}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d^{2} - a e^{2}}{e}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) + {\left(3 \, c^{2} d^{2} e^{2} x^{2} + 15 \, c^{2} d^{4} - 35 \, a c d^{2} e^{2} + 23 \, a^{2} e^{4} - {\left(5 \, c^{2} d^{3} e - 11 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}\right)}}{15 \, {\left(e^{4} x + d e^{3}\right)}}\right]"," ",0,"[1/15*(15*(c^2*d^5 - 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e - 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt(-(c*d^2 - a*e^2)/e)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*e*sqrt(-(c*d^2 - a*e^2)/e))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(3*c^2*d^2*e^2*x^2 + 15*c^2*d^4 - 35*a*c*d^2*e^2 + 23*a^2*e^4 - (5*c^2*d^3*e - 11*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e^4*x + d*e^3), 2/15*(15*(c^2*d^5 - 2*a*c*d^3*e^2 + a^2*d*e^4 + (c^2*d^4*e - 2*a*c*d^2*e^3 + a^2*e^5)*x)*sqrt((c*d^2 - a*e^2)/e)*arctan(sqrt(e*x + d)*sqrt((c*d^2 - a*e^2)/e)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) + (3*c^2*d^2*e^2*x^2 + 15*c^2*d^4 - 35*a*c*d^2*e^2 + 23*a^2*e^4 - (5*c^2*d^3*e - 11*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e^4*x + d*e^3)]","A",0
2052,1,579,0,0.450210," ","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=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{5} - a c d^{3} e^{2} + {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{4} e - a c d^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{e}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} e \sqrt{-\frac{c d^{2} - a e^{2}}{e}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(2 \, c^{2} d^{2} e^{2} x^{2} - 15 \, c^{2} d^{4} + 20 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4} - 2 \, {\left(5 \, c^{2} d^{3} e - 7 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{6 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}, -\frac{15 \, {\left(c^{2} d^{5} - a c d^{3} e^{2} + {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{4} e - a c d^{2} e^{3}\right)} x\right)} \sqrt{\frac{c d^{2} - a e^{2}}{e}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d^{2} - a e^{2}}{e}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) - {\left(2 \, c^{2} d^{2} e^{2} x^{2} - 15 \, c^{2} d^{4} + 20 \, a c d^{2} e^{2} - 3 \, a^{2} e^{4} - 2 \, {\left(5 \, c^{2} d^{3} e - 7 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}\right]"," ",0,"[1/6*(15*(c^2*d^5 - a*c*d^3*e^2 + (c^2*d^3*e^2 - a*c*d*e^4)*x^2 + 2*(c^2*d^4*e - a*c*d^2*e^3)*x)*sqrt(-(c*d^2 - a*e^2)/e)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*e*sqrt(-(c*d^2 - a*e^2)/e))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(2*c^2*d^2*e^2*x^2 - 15*c^2*d^4 + 20*a*c*d^2*e^2 - 3*a^2*e^4 - 2*(5*c^2*d^3*e - 7*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3), -1/3*(15*(c^2*d^5 - a*c*d^3*e^2 + (c^2*d^3*e^2 - a*c*d*e^4)*x^2 + 2*(c^2*d^4*e - a*c*d^2*e^3)*x)*sqrt((c*d^2 - a*e^2)/e)*arctan(sqrt(e*x + d)*sqrt((c*d^2 - a*e^2)/e)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) - (2*c^2*d^2*e^2*x^2 - 15*c^2*d^4 + 20*a*c*d^2*e^2 - 3*a^2*e^4 - 2*(5*c^2*d^3*e - 7*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)]","A",0
2053,1,562,0,0.470983," ","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=""fricas"")","\left[\frac{15 \, {\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{-\frac{c d^{2} - a e^{2}}{e}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d} e \sqrt{-\frac{c d^{2} - a e^{2}}{e}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(8 \, c^{2} d^{2} e^{2} x^{2} + 15 \, c^{2} d^{4} - 5 \, a c d^{2} e^{2} - 2 \, a^{2} e^{4} + {\left(25 \, c^{2} d^{3} e - 9 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}, \frac{15 \, {\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{\frac{c d^{2} - a e^{2}}{e}} \arctan\left(\frac{\sqrt{e x + d} \sqrt{\frac{c d^{2} - a e^{2}}{e}}}{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}}\right) + {\left(8 \, c^{2} d^{2} e^{2} x^{2} + 15 \, c^{2} d^{4} - 5 \, a c d^{2} e^{2} - 2 \, a^{2} e^{4} + {\left(25 \, c^{2} d^{3} e - 9 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}\right]"," ",0,"[1/8*(15*(c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(-(c*d^2 - a*e^2)/e)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)*e*sqrt(-(c*d^2 - a*e^2)/e))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(8*c^2*d^2*e^2*x^2 + 15*c^2*d^4 - 5*a*c*d^2*e^2 - 2*a^2*e^4 + (25*c^2*d^3*e - 9*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3), 1/4*(15*(c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt((c*d^2 - a*e^2)/e)*arctan(sqrt(e*x + d)*sqrt((c*d^2 - a*e^2)/e)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)) + (8*c^2*d^2*e^2*x^2 + 15*c^2*d^4 - 5*a*c*d^2*e^2 - 2*a^2*e^4 + (25*c^2*d^3*e - 9*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)]","A",0
2054,1,837,0,0.441903," ","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=""fricas"")","\left[-\frac{15 \, {\left(c^{3} d^{3} e^{4} x^{4} + 4 \, c^{3} d^{4} e^{3} x^{3} + 6 \, c^{3} d^{5} e^{2} x^{2} + 4 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(15 \, c^{3} d^{6} e - 5 \, a c^{2} d^{4} e^{3} - 2 \, a^{2} c d^{2} e^{5} - 8 \, a^{3} e^{7} + 33 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x^{2} + 2 \, {\left(20 \, c^{3} d^{5} e^{2} - 7 \, a c^{2} d^{3} e^{4} - 13 \, a^{2} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(c d^{6} e^{4} - a d^{4} e^{6} + {\left(c d^{2} e^{8} - a e^{10}\right)} x^{4} + 4 \, {\left(c d^{3} e^{7} - a d e^{9}\right)} x^{3} + 6 \, {\left(c d^{4} e^{6} - a d^{2} e^{8}\right)} x^{2} + 4 \, {\left(c d^{5} e^{5} - a d^{3} e^{7}\right)} x\right)}}, -\frac{15 \, {\left(c^{3} d^{3} e^{4} x^{4} + 4 \, c^{3} d^{4} e^{3} x^{3} + 6 \, c^{3} d^{5} e^{2} x^{2} + 4 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(15 \, c^{3} d^{6} e - 5 \, a c^{2} d^{4} e^{3} - 2 \, a^{2} c d^{2} e^{5} - 8 \, a^{3} e^{7} + 33 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x^{2} + 2 \, {\left(20 \, c^{3} d^{5} e^{2} - 7 \, a c^{2} d^{3} e^{4} - 13 \, a^{2} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(c d^{6} e^{4} - a d^{4} e^{6} + {\left(c d^{2} e^{8} - a e^{10}\right)} x^{4} + 4 \, {\left(c d^{3} e^{7} - a d e^{9}\right)} x^{3} + 6 \, {\left(c d^{4} e^{6} - a d^{2} e^{8}\right)} x^{2} + 4 \, {\left(c d^{5} e^{5} - a d^{3} e^{7}\right)} x\right)}}\right]"," ",0,"[-1/48*(15*(c^3*d^3*e^4*x^4 + 4*c^3*d^4*e^3*x^3 + 6*c^3*d^5*e^2*x^2 + 4*c^3*d^6*e*x + c^3*d^7)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(15*c^3*d^6*e - 5*a*c^2*d^4*e^3 - 2*a^2*c*d^2*e^5 - 8*a^3*e^7 + 33*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x^2 + 2*(20*c^3*d^5*e^2 - 7*a*c^2*d^3*e^4 - 13*a^2*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c*d^6*e^4 - a*d^4*e^6 + (c*d^2*e^8 - a*e^10)*x^4 + 4*(c*d^3*e^7 - a*d*e^9)*x^3 + 6*(c*d^4*e^6 - a*d^2*e^8)*x^2 + 4*(c*d^5*e^5 - a*d^3*e^7)*x), -1/24*(15*(c^3*d^3*e^4*x^4 + 4*c^3*d^4*e^3*x^3 + 6*c^3*d^5*e^2*x^2 + 4*c^3*d^6*e*x + c^3*d^7)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (15*c^3*d^6*e - 5*a*c^2*d^4*e^3 - 2*a^2*c*d^2*e^5 - 8*a^3*e^7 + 33*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x^2 + 2*(20*c^3*d^5*e^2 - 7*a*c^2*d^3*e^4 - 13*a^2*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c*d^6*e^4 - a*d^4*e^6 + (c*d^2*e^8 - a*e^10)*x^4 + 4*(c*d^3*e^7 - a*d*e^9)*x^3 + 6*(c*d^4*e^6 - a*d^2*e^8)*x^2 + 4*(c*d^5*e^5 - a*d^3*e^7)*x)]","A",0
2055,1,1205,0,0.457056," ","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=""fricas"")","\left[-\frac{15 \, {\left(c^{4} d^{4} e^{5} x^{5} + 5 \, c^{4} d^{5} e^{4} x^{4} + 10 \, c^{4} d^{6} e^{3} x^{3} + 10 \, c^{4} d^{7} e^{2} x^{2} + 5 \, c^{4} d^{8} e x + c^{4} d^{9}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(15 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} - 2 \, a^{2} c^{2} d^{4} e^{5} - 56 \, a^{3} c d^{2} e^{7} + 48 \, a^{4} e^{9} - 15 \, {\left(c^{4} d^{5} e^{4} - a c^{3} d^{3} e^{6}\right)} x^{3} + {\left(73 \, c^{4} d^{6} e^{3} - 191 \, a c^{3} d^{4} e^{5} + 118 \, a^{2} c^{2} d^{2} e^{7}\right)} x^{2} + {\left(55 \, c^{4} d^{7} e^{2} - 19 \, a c^{3} d^{5} e^{4} - 172 \, a^{2} c^{2} d^{3} e^{6} + 136 \, a^{3} c d e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{384 \, {\left(c^{2} d^{9} e^{4} - 2 \, a c d^{7} e^{6} + a^{2} d^{5} e^{8} + {\left(c^{2} d^{4} e^{9} - 2 \, a c d^{2} e^{11} + a^{2} e^{13}\right)} x^{5} + 5 \, {\left(c^{2} d^{5} e^{8} - 2 \, a c d^{3} e^{10} + a^{2} d e^{12}\right)} x^{4} + 10 \, {\left(c^{2} d^{6} e^{7} - 2 \, a c d^{4} e^{9} + a^{2} d^{2} e^{11}\right)} x^{3} + 10 \, {\left(c^{2} d^{7} e^{6} - 2 \, a c d^{5} e^{8} + a^{2} d^{3} e^{10}\right)} x^{2} + 5 \, {\left(c^{2} d^{8} e^{5} - 2 \, a c d^{6} e^{7} + a^{2} d^{4} e^{9}\right)} x\right)}}, -\frac{15 \, {\left(c^{4} d^{4} e^{5} x^{5} + 5 \, c^{4} d^{5} e^{4} x^{4} + 10 \, c^{4} d^{6} e^{3} x^{3} + 10 \, c^{4} d^{7} e^{2} x^{2} + 5 \, c^{4} d^{8} e x + c^{4} d^{9}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(15 \, c^{4} d^{8} e - 5 \, a c^{3} d^{6} e^{3} - 2 \, a^{2} c^{2} d^{4} e^{5} - 56 \, a^{3} c d^{2} e^{7} + 48 \, a^{4} e^{9} - 15 \, {\left(c^{4} d^{5} e^{4} - a c^{3} d^{3} e^{6}\right)} x^{3} + {\left(73 \, c^{4} d^{6} e^{3} - 191 \, a c^{3} d^{4} e^{5} + 118 \, a^{2} c^{2} d^{2} e^{7}\right)} x^{2} + {\left(55 \, c^{4} d^{7} e^{2} - 19 \, a c^{3} d^{5} e^{4} - 172 \, a^{2} c^{2} d^{3} e^{6} + 136 \, a^{3} c d e^{8}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{192 \, {\left(c^{2} d^{9} e^{4} - 2 \, a c d^{7} e^{6} + a^{2} d^{5} e^{8} + {\left(c^{2} d^{4} e^{9} - 2 \, a c d^{2} e^{11} + a^{2} e^{13}\right)} x^{5} + 5 \, {\left(c^{2} d^{5} e^{8} - 2 \, a c d^{3} e^{10} + a^{2} d e^{12}\right)} x^{4} + 10 \, {\left(c^{2} d^{6} e^{7} - 2 \, a c d^{4} e^{9} + a^{2} d^{2} e^{11}\right)} x^{3} + 10 \, {\left(c^{2} d^{7} e^{6} - 2 \, a c d^{5} e^{8} + a^{2} d^{3} e^{10}\right)} x^{2} + 5 \, {\left(c^{2} d^{8} e^{5} - 2 \, a c d^{6} e^{7} + a^{2} d^{4} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/384*(15*(c^4*d^4*e^5*x^5 + 5*c^4*d^5*e^4*x^4 + 10*c^4*d^6*e^3*x^3 + 10*c^4*d^7*e^2*x^2 + 5*c^4*d^8*e*x + c^4*d^9)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(15*c^4*d^8*e - 5*a*c^3*d^6*e^3 - 2*a^2*c^2*d^4*e^5 - 56*a^3*c*d^2*e^7 + 48*a^4*e^9 - 15*(c^4*d^5*e^4 - a*c^3*d^3*e^6)*x^3 + (73*c^4*d^6*e^3 - 191*a*c^3*d^4*e^5 + 118*a^2*c^2*d^2*e^7)*x^2 + (55*c^4*d^7*e^2 - 19*a*c^3*d^5*e^4 - 172*a^2*c^2*d^3*e^6 + 136*a^3*c*d*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^9*e^4 - 2*a*c*d^7*e^6 + a^2*d^5*e^8 + (c^2*d^4*e^9 - 2*a*c*d^2*e^11 + a^2*e^13)*x^5 + 5*(c^2*d^5*e^8 - 2*a*c*d^3*e^10 + a^2*d*e^12)*x^4 + 10*(c^2*d^6*e^7 - 2*a*c*d^4*e^9 + a^2*d^2*e^11)*x^3 + 10*(c^2*d^7*e^6 - 2*a*c*d^5*e^8 + a^2*d^3*e^10)*x^2 + 5*(c^2*d^8*e^5 - 2*a*c*d^6*e^7 + a^2*d^4*e^9)*x), -1/192*(15*(c^4*d^4*e^5*x^5 + 5*c^4*d^5*e^4*x^4 + 10*c^4*d^6*e^3*x^3 + 10*c^4*d^7*e^2*x^2 + 5*c^4*d^8*e*x + c^4*d^9)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (15*c^4*d^8*e - 5*a*c^3*d^6*e^3 - 2*a^2*c^2*d^4*e^5 - 56*a^3*c*d^2*e^7 + 48*a^4*e^9 - 15*(c^4*d^5*e^4 - a*c^3*d^3*e^6)*x^3 + (73*c^4*d^6*e^3 - 191*a*c^3*d^4*e^5 + 118*a^2*c^2*d^2*e^7)*x^2 + (55*c^4*d^7*e^2 - 19*a*c^3*d^5*e^4 - 172*a^2*c^2*d^3*e^6 + 136*a^3*c*d*e^8)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^2*d^9*e^4 - 2*a*c*d^7*e^6 + a^2*d^5*e^8 + (c^2*d^4*e^9 - 2*a*c*d^2*e^11 + a^2*e^13)*x^5 + 5*(c^2*d^5*e^8 - 2*a*c*d^3*e^10 + a^2*d*e^12)*x^4 + 10*(c^2*d^6*e^7 - 2*a*c*d^4*e^9 + a^2*d^2*e^11)*x^3 + 10*(c^2*d^7*e^6 - 2*a*c*d^5*e^8 + a^2*d^3*e^10)*x^2 + 5*(c^2*d^8*e^5 - 2*a*c*d^6*e^7 + a^2*d^4*e^9)*x)]","B",0
2056,1,1687,0,0.459776," ","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=""fricas"")","\left[-\frac{15 \, {\left(c^{5} d^{5} e^{6} x^{6} + 6 \, c^{5} d^{6} e^{5} x^{5} + 15 \, c^{5} d^{7} e^{4} x^{4} + 20 \, c^{5} d^{8} e^{3} x^{3} + 15 \, c^{5} d^{9} e^{2} x^{2} + 6 \, c^{5} d^{10} e x + c^{5} d^{11}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(15 \, c^{5} d^{10} e - 5 \, a c^{4} d^{8} e^{3} - 2 \, a^{2} c^{3} d^{6} e^{5} - 184 \, a^{3} c^{2} d^{4} e^{7} + 304 \, a^{4} c d^{2} e^{9} - 128 \, a^{5} e^{11} - 15 \, {\left(c^{5} d^{6} e^{5} - a c^{4} d^{4} e^{7}\right)} x^{4} - 10 \, {\left(7 \, c^{5} d^{7} e^{4} - 8 \, a c^{4} d^{5} e^{6} + a^{2} c^{3} d^{3} e^{8}\right)} x^{3} + 2 \, {\left(64 \, c^{5} d^{8} e^{3} - 297 \, a c^{4} d^{6} e^{5} + 357 \, a^{2} c^{3} d^{4} e^{7} - 124 \, a^{3} c^{2} d^{2} e^{9}\right)} x^{2} + 2 \, {\left(35 \, c^{5} d^{9} e^{2} - 12 \, a c^{4} d^{7} e^{4} - 279 \, a^{2} c^{3} d^{5} e^{6} + 424 \, a^{3} c^{2} d^{3} e^{8} - 168 \, a^{4} c d e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{1280 \, {\left(c^{3} d^{12} e^{4} - 3 \, a c^{2} d^{10} e^{6} + 3 \, a^{2} c d^{8} e^{8} - a^{3} d^{6} e^{10} + {\left(c^{3} d^{6} e^{10} - 3 \, a c^{2} d^{4} e^{12} + 3 \, a^{2} c d^{2} e^{14} - a^{3} e^{16}\right)} x^{6} + 6 \, {\left(c^{3} d^{7} e^{9} - 3 \, a c^{2} d^{5} e^{11} + 3 \, a^{2} c d^{3} e^{13} - a^{3} d e^{15}\right)} x^{5} + 15 \, {\left(c^{3} d^{8} e^{8} - 3 \, a c^{2} d^{6} e^{10} + 3 \, a^{2} c d^{4} e^{12} - a^{3} d^{2} e^{14}\right)} x^{4} + 20 \, {\left(c^{3} d^{9} e^{7} - 3 \, a c^{2} d^{7} e^{9} + 3 \, a^{2} c d^{5} e^{11} - a^{3} d^{3} e^{13}\right)} x^{3} + 15 \, {\left(c^{3} d^{10} e^{6} - 3 \, a c^{2} d^{8} e^{8} + 3 \, a^{2} c d^{6} e^{10} - a^{3} d^{4} e^{12}\right)} x^{2} + 6 \, {\left(c^{3} d^{11} e^{5} - 3 \, a c^{2} d^{9} e^{7} + 3 \, a^{2} c d^{7} e^{9} - a^{3} d^{5} e^{11}\right)} x\right)}}, -\frac{15 \, {\left(c^{5} d^{5} e^{6} x^{6} + 6 \, c^{5} d^{6} e^{5} x^{5} + 15 \, c^{5} d^{7} e^{4} x^{4} + 20 \, c^{5} d^{8} e^{3} x^{3} + 15 \, c^{5} d^{9} e^{2} x^{2} + 6 \, c^{5} d^{10} e x + c^{5} d^{11}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(15 \, c^{5} d^{10} e - 5 \, a c^{4} d^{8} e^{3} - 2 \, a^{2} c^{3} d^{6} e^{5} - 184 \, a^{3} c^{2} d^{4} e^{7} + 304 \, a^{4} c d^{2} e^{9} - 128 \, a^{5} e^{11} - 15 \, {\left(c^{5} d^{6} e^{5} - a c^{4} d^{4} e^{7}\right)} x^{4} - 10 \, {\left(7 \, c^{5} d^{7} e^{4} - 8 \, a c^{4} d^{5} e^{6} + a^{2} c^{3} d^{3} e^{8}\right)} x^{3} + 2 \, {\left(64 \, c^{5} d^{8} e^{3} - 297 \, a c^{4} d^{6} e^{5} + 357 \, a^{2} c^{3} d^{4} e^{7} - 124 \, a^{3} c^{2} d^{2} e^{9}\right)} x^{2} + 2 \, {\left(35 \, c^{5} d^{9} e^{2} - 12 \, a c^{4} d^{7} e^{4} - 279 \, a^{2} c^{3} d^{5} e^{6} + 424 \, a^{3} c^{2} d^{3} e^{8} - 168 \, a^{4} c d e^{10}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{640 \, {\left(c^{3} d^{12} e^{4} - 3 \, a c^{2} d^{10} e^{6} + 3 \, a^{2} c d^{8} e^{8} - a^{3} d^{6} e^{10} + {\left(c^{3} d^{6} e^{10} - 3 \, a c^{2} d^{4} e^{12} + 3 \, a^{2} c d^{2} e^{14} - a^{3} e^{16}\right)} x^{6} + 6 \, {\left(c^{3} d^{7} e^{9} - 3 \, a c^{2} d^{5} e^{11} + 3 \, a^{2} c d^{3} e^{13} - a^{3} d e^{15}\right)} x^{5} + 15 \, {\left(c^{3} d^{8} e^{8} - 3 \, a c^{2} d^{6} e^{10} + 3 \, a^{2} c d^{4} e^{12} - a^{3} d^{2} e^{14}\right)} x^{4} + 20 \, {\left(c^{3} d^{9} e^{7} - 3 \, a c^{2} d^{7} e^{9} + 3 \, a^{2} c d^{5} e^{11} - a^{3} d^{3} e^{13}\right)} x^{3} + 15 \, {\left(c^{3} d^{10} e^{6} - 3 \, a c^{2} d^{8} e^{8} + 3 \, a^{2} c d^{6} e^{10} - a^{3} d^{4} e^{12}\right)} x^{2} + 6 \, {\left(c^{3} d^{11} e^{5} - 3 \, a c^{2} d^{9} e^{7} + 3 \, a^{2} c d^{7} e^{9} - a^{3} d^{5} e^{11}\right)} x\right)}}\right]"," ",0,"[-1/1280*(15*(c^5*d^5*e^6*x^6 + 6*c^5*d^6*e^5*x^5 + 15*c^5*d^7*e^4*x^4 + 20*c^5*d^8*e^3*x^3 + 15*c^5*d^9*e^2*x^2 + 6*c^5*d^10*e*x + c^5*d^11)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(15*c^5*d^10*e - 5*a*c^4*d^8*e^3 - 2*a^2*c^3*d^6*e^5 - 184*a^3*c^2*d^4*e^7 + 304*a^4*c*d^2*e^9 - 128*a^5*e^11 - 15*(c^5*d^6*e^5 - a*c^4*d^4*e^7)*x^4 - 10*(7*c^5*d^7*e^4 - 8*a*c^4*d^5*e^6 + a^2*c^3*d^3*e^8)*x^3 + 2*(64*c^5*d^8*e^3 - 297*a*c^4*d^6*e^5 + 357*a^2*c^3*d^4*e^7 - 124*a^3*c^2*d^2*e^9)*x^2 + 2*(35*c^5*d^9*e^2 - 12*a*c^4*d^7*e^4 - 279*a^2*c^3*d^5*e^6 + 424*a^3*c^2*d^3*e^8 - 168*a^4*c*d*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^12*e^4 - 3*a*c^2*d^10*e^6 + 3*a^2*c*d^8*e^8 - a^3*d^6*e^10 + (c^3*d^6*e^10 - 3*a*c^2*d^4*e^12 + 3*a^2*c*d^2*e^14 - a^3*e^16)*x^6 + 6*(c^3*d^7*e^9 - 3*a*c^2*d^5*e^11 + 3*a^2*c*d^3*e^13 - a^3*d*e^15)*x^5 + 15*(c^3*d^8*e^8 - 3*a*c^2*d^6*e^10 + 3*a^2*c*d^4*e^12 - a^3*d^2*e^14)*x^4 + 20*(c^3*d^9*e^7 - 3*a*c^2*d^7*e^9 + 3*a^2*c*d^5*e^11 - a^3*d^3*e^13)*x^3 + 15*(c^3*d^10*e^6 - 3*a*c^2*d^8*e^8 + 3*a^2*c*d^6*e^10 - a^3*d^4*e^12)*x^2 + 6*(c^3*d^11*e^5 - 3*a*c^2*d^9*e^7 + 3*a^2*c*d^7*e^9 - a^3*d^5*e^11)*x), -1/640*(15*(c^5*d^5*e^6*x^6 + 6*c^5*d^6*e^5*x^5 + 15*c^5*d^7*e^4*x^4 + 20*c^5*d^8*e^3*x^3 + 15*c^5*d^9*e^2*x^2 + 6*c^5*d^10*e*x + c^5*d^11)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (15*c^5*d^10*e - 5*a*c^4*d^8*e^3 - 2*a^2*c^3*d^6*e^5 - 184*a^3*c^2*d^4*e^7 + 304*a^4*c*d^2*e^9 - 128*a^5*e^11 - 15*(c^5*d^6*e^5 - a*c^4*d^4*e^7)*x^4 - 10*(7*c^5*d^7*e^4 - 8*a*c^4*d^5*e^6 + a^2*c^3*d^3*e^8)*x^3 + 2*(64*c^5*d^8*e^3 - 297*a*c^4*d^6*e^5 + 357*a^2*c^3*d^4*e^7 - 124*a^3*c^2*d^2*e^9)*x^2 + 2*(35*c^5*d^9*e^2 - 12*a*c^4*d^7*e^4 - 279*a^2*c^3*d^5*e^6 + 424*a^3*c^2*d^3*e^8 - 168*a^4*c*d*e^10)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^12*e^4 - 3*a*c^2*d^10*e^6 + 3*a^2*c*d^8*e^8 - a^3*d^6*e^10 + (c^3*d^6*e^10 - 3*a*c^2*d^4*e^12 + 3*a^2*c*d^2*e^14 - a^3*e^16)*x^6 + 6*(c^3*d^7*e^9 - 3*a*c^2*d^5*e^11 + 3*a^2*c*d^3*e^13 - a^3*d*e^15)*x^5 + 15*(c^3*d^8*e^8 - 3*a*c^2*d^6*e^10 + 3*a^2*c*d^4*e^12 - a^3*d^2*e^14)*x^4 + 20*(c^3*d^9*e^7 - 3*a*c^2*d^7*e^9 + 3*a^2*c*d^5*e^11 - a^3*d^3*e^13)*x^3 + 15*(c^3*d^10*e^6 - 3*a*c^2*d^8*e^8 + 3*a^2*c*d^6*e^10 - a^3*d^4*e^12)*x^2 + 6*(c^3*d^11*e^5 - 3*a*c^2*d^9*e^7 + 3*a^2*c*d^7*e^9 - a^3*d^5*e^11)*x)]","B",0
2057,1,173,0,0.403951," ","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=""fricas"")","\frac{2 \, {\left(5 \, c^{3} d^{3} e^{3} x^{3} + 35 \, c^{3} d^{6} - 70 \, a c^{2} d^{4} e^{2} + 56 \, a^{2} c d^{2} e^{4} - 16 \, a^{3} e^{6} + 3 \, {\left(7 \, c^{3} d^{4} e^{2} - 2 \, a c^{2} d^{2} e^{4}\right)} x^{2} + {\left(35 \, c^{3} d^{5} e - 28 \, a c^{2} d^{3} e^{3} + 8 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{35 \, {\left(c^{4} d^{4} e x + c^{4} d^{5}\right)}}"," ",0,"2/35*(5*c^3*d^3*e^3*x^3 + 35*c^3*d^6 - 70*a*c^2*d^4*e^2 + 56*a^2*c*d^2*e^4 - 16*a^3*e^6 + 3*(7*c^3*d^4*e^2 - 2*a*c^2*d^2*e^4)*x^2 + (35*c^3*d^5*e - 28*a*c^2*d^3*e^3 + 8*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x + c^4*d^5)","A",0
2058,1,117,0,0.419910," ","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=""fricas"")","\frac{2 \, {\left(3 \, c^{2} d^{2} e^{2} x^{2} + 15 \, c^{2} d^{4} - 20 \, a c d^{2} e^{2} + 8 \, a^{2} e^{4} + 2 \, {\left(5 \, c^{2} d^{3} e - 2 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{15 \, {\left(c^{3} d^{3} e x + c^{3} d^{4}\right)}}"," ",0,"2/15*(3*c^2*d^2*e^2*x^2 + 15*c^2*d^4 - 20*a*c*d^2*e^2 + 8*a^2*e^4 + 2*(5*c^2*d^3*e - 2*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x + c^3*d^4)","A",0
2059,1,73,0,0.407778," ","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=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d e x + 3 \, c d^{2} - 2 \, a e^{2}\right)} \sqrt{e x + d}}{3 \, {\left(c^{2} d^{2} e x + c^{2} d^{3}\right)}}"," ",0,"2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*e*x + 3*c*d^2 - 2*a*e^2)*sqrt(e*x + d)/(c^2*d^2*e*x + c^2*d^3)","A",0
2060,1,49,0,0.407530," ","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=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{c d e x + c d^{2}}"," ",0,"2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c*d*e*x + c*d^2)","A",0
2061,1,235,0,0.429296," ","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=""fricas"")","\left[-\frac{\sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{c d^{2} e - a e^{3}}, -\frac{2 \, \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right)}{\sqrt{c d^{2} e - a e^{3}}}\right]"," ",0,"[-sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2))/(c*d^2*e - a*e^3), -2*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x))/sqrt(c*d^2*e - a*e^3)]","A",0
2062,1,558,0,0.436669," ","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=""fricas"")","\left[\frac{{\left(c d e^{2} x^{2} + 2 \, c d^{2} e x + c d^{3}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} e - a e^{3}\right)} \sqrt{e x + d}}{2 \, {\left(c^{2} d^{6} e - 2 \, a c d^{4} e^{3} + a^{2} d^{2} e^{5} + {\left(c^{2} d^{4} e^{3} - 2 \, a c d^{2} e^{5} + a^{2} e^{7}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e^{2} - 2 \, a c d^{3} e^{4} + a^{2} d e^{6}\right)} x\right)}}, -\frac{{\left(c d e^{2} x^{2} + 2 \, c d^{2} e x + c d^{3}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) - \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} e - a e^{3}\right)} \sqrt{e x + d}}{c^{2} d^{6} e - 2 \, a c d^{4} e^{3} + a^{2} d^{2} e^{5} + {\left(c^{2} d^{4} e^{3} - 2 \, a c d^{2} e^{5} + a^{2} e^{7}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e^{2} - 2 \, a c d^{3} e^{4} + a^{2} d e^{6}\right)} x}\right]"," ",0,"[1/2*((c*d*e^2*x^2 + 2*c*d^2*e*x + c*d^3)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2*e - a*e^3)*sqrt(e*x + d))/(c^2*d^6*e - 2*a*c*d^4*e^3 + a^2*d^2*e^5 + (c^2*d^4*e^3 - 2*a*c*d^2*e^5 + a^2*e^7)*x^2 + 2*(c^2*d^5*e^2 - 2*a*c*d^3*e^4 + a^2*d*e^6)*x), -((c*d*e^2*x^2 + 2*c*d^2*e*x + c*d^3)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) - sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2*e - a*e^3)*sqrt(e*x + d))/(c^2*d^6*e - 2*a*c*d^4*e^3 + a^2*d^2*e^5 + (c^2*d^4*e^3 - 2*a*c*d^2*e^5 + a^2*e^7)*x^2 + 2*(c^2*d^5*e^2 - 2*a*c*d^3*e^4 + a^2*d*e^6)*x)]","B",0
2063,1,870,0,0.436944," ","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=""fricas"")","\left[-\frac{3 \, {\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(5 \, c^{2} d^{4} e - 7 \, a c d^{2} e^{3} + 2 \, a^{2} e^{5} + 3 \, {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(c^{3} d^{9} e - 3 \, a c^{2} d^{7} e^{3} + 3 \, a^{2} c d^{5} e^{5} - a^{3} d^{3} e^{7} + {\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)} x^{3} + 3 \, {\left(c^{3} d^{7} e^{3} - 3 \, a c^{2} d^{5} e^{5} + 3 \, a^{2} c d^{3} e^{7} - a^{3} d e^{9}\right)} x^{2} + 3 \, {\left(c^{3} d^{8} e^{2} - 3 \, a c^{2} d^{6} e^{4} + 3 \, a^{2} c d^{4} e^{6} - a^{3} d^{2} e^{8}\right)} x\right)}}, -\frac{3 \, {\left(c^{2} d^{2} e^{3} x^{3} + 3 \, c^{2} d^{3} e^{2} x^{2} + 3 \, c^{2} d^{4} e x + c^{2} d^{5}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) - {\left(5 \, c^{2} d^{4} e - 7 \, a c d^{2} e^{3} + 2 \, a^{2} e^{5} + 3 \, {\left(c^{2} d^{3} e^{2} - a c d e^{4}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(c^{3} d^{9} e - 3 \, a c^{2} d^{7} e^{3} + 3 \, a^{2} c d^{5} e^{5} - a^{3} d^{3} e^{7} + {\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)} x^{3} + 3 \, {\left(c^{3} d^{7} e^{3} - 3 \, a c^{2} d^{5} e^{5} + 3 \, a^{2} c d^{3} e^{7} - a^{3} d e^{9}\right)} x^{2} + 3 \, {\left(c^{3} d^{8} e^{2} - 3 \, a c^{2} d^{6} e^{4} + 3 \, a^{2} c d^{4} e^{6} - a^{3} d^{2} e^{8}\right)} x\right)}}\right]"," ",0,"[-1/8*(3*(c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(5*c^2*d^4*e - 7*a*c*d^2*e^3 + 2*a^2*e^5 + 3*(c^2*d^3*e^2 - a*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^9*e - 3*a*c^2*d^7*e^3 + 3*a^2*c*d^5*e^5 - a^3*d^3*e^7 + (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)*x^3 + 3*(c^3*d^7*e^3 - 3*a*c^2*d^5*e^5 + 3*a^2*c*d^3*e^7 - a^3*d*e^9)*x^2 + 3*(c^3*d^8*e^2 - 3*a*c^2*d^6*e^4 + 3*a^2*c*d^4*e^6 - a^3*d^2*e^8)*x), -1/4*(3*(c^2*d^2*e^3*x^3 + 3*c^2*d^3*e^2*x^2 + 3*c^2*d^4*e*x + c^2*d^5)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) - (5*c^2*d^4*e - 7*a*c*d^2*e^3 + 2*a^2*e^5 + 3*(c^2*d^3*e^2 - a*c*d*e^4)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^3*d^9*e - 3*a*c^2*d^7*e^3 + 3*a^2*c*d^5*e^5 - a^3*d^3*e^7 + (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)*x^3 + 3*(c^3*d^7*e^3 - 3*a*c^2*d^5*e^5 + 3*a^2*c*d^3*e^7 - a^3*d*e^9)*x^2 + 3*(c^3*d^8*e^2 - 3*a*c^2*d^6*e^4 + 3*a^2*c*d^4*e^6 - a^3*d^2*e^8)*x)]","B",0
2064,1,1242,0,0.449471," ","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=""fricas"")","\left[-\frac{15 \, {\left(c^{3} d^{3} e^{4} x^{4} + 4 \, c^{3} d^{4} e^{3} x^{3} + 6 \, c^{3} d^{5} e^{2} x^{2} + 4 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{-c d^{2} e + a e^{3}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{-c d^{2} e + a e^{3}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(33 \, c^{3} d^{6} e - 59 \, a c^{2} d^{4} e^{3} + 34 \, a^{2} c d^{2} e^{5} - 8 \, a^{3} e^{7} + 15 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x^{2} + 10 \, {\left(4 \, c^{3} d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(c^{4} d^{12} e - 4 \, a c^{3} d^{10} e^{3} + 6 \, a^{2} c^{2} d^{8} e^{5} - 4 \, a^{3} c d^{6} e^{7} + a^{4} d^{4} e^{9} + {\left(c^{4} d^{8} e^{5} - 4 \, a c^{3} d^{6} e^{7} + 6 \, a^{2} c^{2} d^{4} e^{9} - 4 \, a^{3} c d^{2} e^{11} + a^{4} e^{13}\right)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{4} - 4 \, a c^{3} d^{7} e^{6} + 6 \, a^{2} c^{2} d^{5} e^{8} - 4 \, a^{3} c d^{3} e^{10} + a^{4} d e^{12}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{3} - 4 \, a c^{3} d^{8} e^{5} + 6 \, a^{2} c^{2} d^{6} e^{7} - 4 \, a^{3} c d^{4} e^{9} + a^{4} d^{2} e^{11}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e^{2} - 4 \, a c^{3} d^{9} e^{4} + 6 \, a^{2} c^{2} d^{7} e^{6} - 4 \, a^{3} c d^{5} e^{8} + a^{4} d^{3} e^{10}\right)} x\right)}}, -\frac{15 \, {\left(c^{3} d^{3} e^{4} x^{4} + 4 \, c^{3} d^{4} e^{3} x^{3} + 6 \, c^{3} d^{5} e^{2} x^{2} + 4 \, c^{3} d^{6} e x + c^{3} d^{7}\right)} \sqrt{c d^{2} e - a e^{3}} \arctan\left(\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{c d^{2} e - a e^{3}} \sqrt{e x + d}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) - {\left(33 \, c^{3} d^{6} e - 59 \, a c^{2} d^{4} e^{3} + 34 \, a^{2} c d^{2} e^{5} - 8 \, a^{3} e^{7} + 15 \, {\left(c^{3} d^{4} e^{3} - a c^{2} d^{2} e^{5}\right)} x^{2} + 10 \, {\left(4 \, c^{3} d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(c^{4} d^{12} e - 4 \, a c^{3} d^{10} e^{3} + 6 \, a^{2} c^{2} d^{8} e^{5} - 4 \, a^{3} c d^{6} e^{7} + a^{4} d^{4} e^{9} + {\left(c^{4} d^{8} e^{5} - 4 \, a c^{3} d^{6} e^{7} + 6 \, a^{2} c^{2} d^{4} e^{9} - 4 \, a^{3} c d^{2} e^{11} + a^{4} e^{13}\right)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{4} - 4 \, a c^{3} d^{7} e^{6} + 6 \, a^{2} c^{2} d^{5} e^{8} - 4 \, a^{3} c d^{3} e^{10} + a^{4} d e^{12}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{3} - 4 \, a c^{3} d^{8} e^{5} + 6 \, a^{2} c^{2} d^{6} e^{7} - 4 \, a^{3} c d^{4} e^{9} + a^{4} d^{2} e^{11}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e^{2} - 4 \, a c^{3} d^{9} e^{4} + 6 \, a^{2} c^{2} d^{7} e^{6} - 4 \, a^{3} c d^{5} e^{8} + a^{4} d^{3} e^{10}\right)} x\right)}}\right]"," ",0,"[-1/48*(15*(c^3*d^3*e^4*x^4 + 4*c^3*d^4*e^3*x^3 + 6*c^3*d^5*e^2*x^2 + 4*c^3*d^6*e*x + c^3*d^7)*sqrt(-c*d^2*e + a*e^3)*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-c*d^2*e + a*e^3)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(33*c^3*d^6*e - 59*a*c^2*d^4*e^3 + 34*a^2*c*d^2*e^5 - 8*a^3*e^7 + 15*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x^2 + 10*(4*c^3*d^5*e^2 - 5*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^12*e - 4*a*c^3*d^10*e^3 + 6*a^2*c^2*d^8*e^5 - 4*a^3*c*d^6*e^7 + a^4*d^4*e^9 + (c^4*d^8*e^5 - 4*a*c^3*d^6*e^7 + 6*a^2*c^2*d^4*e^9 - 4*a^3*c*d^2*e^11 + a^4*e^13)*x^4 + 4*(c^4*d^9*e^4 - 4*a*c^3*d^7*e^6 + 6*a^2*c^2*d^5*e^8 - 4*a^3*c*d^3*e^10 + a^4*d*e^12)*x^3 + 6*(c^4*d^10*e^3 - 4*a*c^3*d^8*e^5 + 6*a^2*c^2*d^6*e^7 - 4*a^3*c*d^4*e^9 + a^4*d^2*e^11)*x^2 + 4*(c^4*d^11*e^2 - 4*a*c^3*d^9*e^4 + 6*a^2*c^2*d^7*e^6 - 4*a^3*c*d^5*e^8 + a^4*d^3*e^10)*x), -1/24*(15*(c^3*d^3*e^4*x^4 + 4*c^3*d^4*e^3*x^3 + 6*c^3*d^5*e^2*x^2 + 4*c^3*d^6*e*x + c^3*d^7)*sqrt(c*d^2*e - a*e^3)*arctan(sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(c*d^2*e - a*e^3)*sqrt(e*x + d)/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) - (33*c^3*d^6*e - 59*a*c^2*d^4*e^3 + 34*a^2*c*d^2*e^5 - 8*a^3*e^7 + 15*(c^3*d^4*e^3 - a*c^2*d^2*e^5)*x^2 + 10*(4*c^3*d^5*e^2 - 5*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(c^4*d^12*e - 4*a*c^3*d^10*e^3 + 6*a^2*c^2*d^8*e^5 - 4*a^3*c*d^6*e^7 + a^4*d^4*e^9 + (c^4*d^8*e^5 - 4*a*c^3*d^6*e^7 + 6*a^2*c^2*d^4*e^9 - 4*a^3*c*d^2*e^11 + a^4*e^13)*x^4 + 4*(c^4*d^9*e^4 - 4*a*c^3*d^7*e^6 + 6*a^2*c^2*d^5*e^8 - 4*a^3*c*d^3*e^10 + a^4*d*e^12)*x^3 + 6*(c^4*d^10*e^3 - 4*a*c^3*d^8*e^5 + 6*a^2*c^2*d^6*e^7 - 4*a^3*c*d^4*e^9 + a^4*d^2*e^11)*x^2 + 4*(c^4*d^11*e^2 - 4*a*c^3*d^9*e^4 + 6*a^2*c^2*d^7*e^6 - 4*a^3*c*d^5*e^8 + a^4*d^3*e^10)*x)]","B",0
2065,1,141,0,0.403183," ","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=""fricas"")","\frac{2 \, {\left(c^{2} d^{2} e^{2} x^{2} - 3 \, c^{2} d^{4} + 12 \, a c d^{2} e^{2} - 8 \, a^{2} e^{4} + 2 \, {\left(3 \, c^{2} d^{3} e - 2 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3 \, {\left(c^{4} d^{4} e x^{2} + a c^{3} d^{4} e + {\left(c^{4} d^{5} + a c^{3} d^{3} e^{2}\right)} x\right)}}"," ",0,"2/3*(c^2*d^2*e^2*x^2 - 3*c^2*d^4 + 12*a*c*d^2*e^2 - 8*a^2*e^4 + 2*(3*c^2*d^3*e - 2*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^4*d^4*e*x^2 + a*c^3*d^4*e + (c^4*d^5 + a*c^3*d^3*e^2)*x)","A",0
2066,1,98,0,0.407181," ","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=""fricas"")","\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d e x - c d^{2} + 2 \, a e^{2}\right)} \sqrt{e x + d}}{c^{3} d^{3} e x^{2} + a c^{2} d^{3} e + {\left(c^{3} d^{4} + a c^{2} d^{2} e^{2}\right)} x}"," ",0,"2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*e*x - c*d^2 + 2*a*e^2)*sqrt(e*x + d)/(c^3*d^3*e*x^2 + a*c^2*d^3*e + (c^3*d^4 + a*c^2*d^2*e^2)*x)","A",0
2067,1,74,0,0.401951," ","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=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{c^{2} d^{2} e x^{2} + a c d^{2} e + {\left(c^{2} d^{3} + a c d e^{2}\right)} x}"," ",0,"-2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^2*d^2*e*x^2 + a*c*d^2*e + (c^2*d^3 + a*c*d*e^2)*x)","A",0
2068,1,500,0,0.431091," ","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=""fricas"")","\left[-\frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{a c d^{3} e - a^{2} d e^{3} + {\left(c^{2} d^{3} e - a c d e^{3}\right)} x^{2} + {\left(c^{2} d^{4} - a^{2} e^{4}\right)} x}, -\frac{2 \, {\left({\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}\right)}}{a c d^{3} e - a^{2} d e^{3} + {\left(c^{2} d^{3} e - a c d e^{3}\right)} x^{2} + {\left(c^{2} d^{4} - a^{2} e^{4}\right)} x}\right]"," ",0,"[-((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c*d^3*e - a^2*d*e^3 + (c^2*d^3*e - a*c*d*e^3)*x^2 + (c^2*d^4 - a^2*e^4)*x), -2*((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c*d^3*e - a^2*d*e^3 + (c^2*d^3*e - a*c*d*e^3)*x^2 + (c^2*d^4 - a^2*e^4)*x)]","A",0
2069,1,764,0,0.436474," ","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=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{2} e^{2} x^{3} + a c d^{3} e + {\left(2 \, c^{2} d^{3} e + a c d e^{3}\right)} x^{2} + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(3 \, c d e x + 2 \, c d^{2} + a e^{2}\right)} \sqrt{e x + d}}{2 \, {\left(a c^{2} d^{6} e - 2 \, a^{2} c d^{4} e^{3} + a^{3} d^{2} e^{5} + {\left(c^{3} d^{5} e^{2} - 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{3} + {\left(2 \, c^{3} d^{6} e - 3 \, a c^{2} d^{4} e^{3} + a^{3} e^{7}\right)} x^{2} + {\left(c^{3} d^{7} - 3 \, a^{2} c d^{3} e^{4} + 2 \, a^{3} d e^{6}\right)} x\right)}}, -\frac{3 \, {\left(c^{2} d^{2} e^{2} x^{3} + a c d^{3} e + {\left(2 \, c^{2} d^{3} e + a c d e^{3}\right)} x^{2} + {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(3 \, c d e x + 2 \, c d^{2} + a e^{2}\right)} \sqrt{e x + d}}{a c^{2} d^{6} e - 2 \, a^{2} c d^{4} e^{3} + a^{3} d^{2} e^{5} + {\left(c^{3} d^{5} e^{2} - 2 \, a c^{2} d^{3} e^{4} + a^{2} c d e^{6}\right)} x^{3} + {\left(2 \, c^{3} d^{6} e - 3 \, a c^{2} d^{4} e^{3} + a^{3} e^{7}\right)} x^{2} + {\left(c^{3} d^{7} - 3 \, a^{2} c d^{3} e^{4} + 2 \, a^{3} d e^{6}\right)} x}\right]"," ",0,"[1/2*(3*(c^2*d^2*e^2*x^3 + a*c*d^3*e + (2*c^2*d^3*e + a*c*d*e^3)*x^2 + (c^2*d^4 + 2*a*c*d^2*e^2)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(3*c*d*e*x + 2*c*d^2 + a*e^2)*sqrt(e*x + d))/(a*c^2*d^6*e - 2*a^2*c*d^4*e^3 + a^3*d^2*e^5 + (c^3*d^5*e^2 - 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^3 + (2*c^3*d^6*e - 3*a*c^2*d^4*e^3 + a^3*e^7)*x^2 + (c^3*d^7 - 3*a^2*c*d^3*e^4 + 2*a^3*d*e^6)*x), -(3*(c^2*d^2*e^2*x^3 + a*c*d^3*e + (2*c^2*d^3*e + a*c*d*e^3)*x^2 + (c^2*d^4 + 2*a*c*d^2*e^2)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(3*c*d*e*x + 2*c*d^2 + a*e^2)*sqrt(e*x + d))/(a*c^2*d^6*e - 2*a^2*c*d^4*e^3 + a^3*d^2*e^5 + (c^3*d^5*e^2 - 2*a*c^2*d^3*e^4 + a^2*c*d*e^6)*x^3 + (2*c^3*d^6*e - 3*a*c^2*d^4*e^3 + a^3*e^7)*x^2 + (c^3*d^7 - 3*a^2*c*d^3*e^4 + 2*a^3*d*e^6)*x)]","B",0
2070,1,1140,0,0.441733," ","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=""fricas"")","\left[\frac{15 \, {\left(c^{3} d^{3} e^{3} x^{4} + a c^{2} d^{5} e + {\left(3 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{3} + 3 \, {\left(c^{3} d^{5} e + a c^{2} d^{3} e^{3}\right)} x^{2} + {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(15 \, c^{2} d^{2} e^{2} x^{2} + 8 \, c^{2} d^{4} + 9 \, a c d^{2} e^{2} - 2 \, a^{2} e^{4} + 5 \, {\left(5 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{8 \, {\left(a c^{3} d^{9} e - 3 \, a^{2} c^{2} d^{7} e^{3} + 3 \, a^{3} c d^{5} e^{5} - a^{4} d^{3} e^{7} + {\left(c^{4} d^{7} e^{3} - 3 \, a c^{3} d^{5} e^{5} + 3 \, a^{2} c^{2} d^{3} e^{7} - a^{3} c d e^{9}\right)} x^{4} + {\left(3 \, c^{4} d^{8} e^{2} - 8 \, a c^{3} d^{6} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{6} - a^{4} e^{10}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e - 2 \, a c^{3} d^{7} e^{3} + 2 \, a^{3} c d^{3} e^{7} - a^{4} d e^{9}\right)} x^{2} + {\left(c^{4} d^{10} - 6 \, a^{2} c^{2} d^{6} e^{4} + 8 \, a^{3} c d^{4} e^{6} - 3 \, a^{4} d^{2} e^{8}\right)} x\right)}}, -\frac{15 \, {\left(c^{3} d^{3} e^{3} x^{4} + a c^{2} d^{5} e + {\left(3 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{3} + 3 \, {\left(c^{3} d^{5} e + a c^{2} d^{3} e^{3}\right)} x^{2} + {\left(c^{3} d^{6} + 3 \, a c^{2} d^{4} e^{2}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(15 \, c^{2} d^{2} e^{2} x^{2} + 8 \, c^{2} d^{4} + 9 \, a c d^{2} e^{2} - 2 \, a^{2} e^{4} + 5 \, {\left(5 \, c^{2} d^{3} e + a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{4 \, {\left(a c^{3} d^{9} e - 3 \, a^{2} c^{2} d^{7} e^{3} + 3 \, a^{3} c d^{5} e^{5} - a^{4} d^{3} e^{7} + {\left(c^{4} d^{7} e^{3} - 3 \, a c^{3} d^{5} e^{5} + 3 \, a^{2} c^{2} d^{3} e^{7} - a^{3} c d e^{9}\right)} x^{4} + {\left(3 \, c^{4} d^{8} e^{2} - 8 \, a c^{3} d^{6} e^{4} + 6 \, a^{2} c^{2} d^{4} e^{6} - a^{4} e^{10}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e - 2 \, a c^{3} d^{7} e^{3} + 2 \, a^{3} c d^{3} e^{7} - a^{4} d e^{9}\right)} x^{2} + {\left(c^{4} d^{10} - 6 \, a^{2} c^{2} d^{6} e^{4} + 8 \, a^{3} c d^{4} e^{6} - 3 \, a^{4} d^{2} e^{8}\right)} x\right)}}\right]"," ",0,"[1/8*(15*(c^3*d^3*e^3*x^4 + a*c^2*d^5*e + (3*c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^3 + 3*(c^3*d^5*e + a*c^2*d^3*e^3)*x^2 + (c^3*d^6 + 3*a*c^2*d^4*e^2)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(15*c^2*d^2*e^2*x^2 + 8*c^2*d^4 + 9*a*c*d^2*e^2 - 2*a^2*e^4 + 5*(5*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c^3*d^9*e - 3*a^2*c^2*d^7*e^3 + 3*a^3*c*d^5*e^5 - a^4*d^3*e^7 + (c^4*d^7*e^3 - 3*a*c^3*d^5*e^5 + 3*a^2*c^2*d^3*e^7 - a^3*c*d*e^9)*x^4 + (3*c^4*d^8*e^2 - 8*a*c^3*d^6*e^4 + 6*a^2*c^2*d^4*e^6 - a^4*e^10)*x^3 + 3*(c^4*d^9*e - 2*a*c^3*d^7*e^3 + 2*a^3*c*d^3*e^7 - a^4*d*e^9)*x^2 + (c^4*d^10 - 6*a^2*c^2*d^6*e^4 + 8*a^3*c*d^4*e^6 - 3*a^4*d^2*e^8)*x), -1/4*(15*(c^3*d^3*e^3*x^4 + a*c^2*d^5*e + (3*c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^3 + 3*(c^3*d^5*e + a*c^2*d^3*e^3)*x^2 + (c^3*d^6 + 3*a*c^2*d^4*e^2)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (15*c^2*d^2*e^2*x^2 + 8*c^2*d^4 + 9*a*c*d^2*e^2 - 2*a^2*e^4 + 5*(5*c^2*d^3*e + a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c^3*d^9*e - 3*a^2*c^2*d^7*e^3 + 3*a^3*c*d^5*e^5 - a^4*d^3*e^7 + (c^4*d^7*e^3 - 3*a*c^3*d^5*e^5 + 3*a^2*c^2*d^3*e^7 - a^3*c*d*e^9)*x^4 + (3*c^4*d^8*e^2 - 8*a*c^3*d^6*e^4 + 6*a^2*c^2*d^4*e^6 - a^4*e^10)*x^3 + 3*(c^4*d^9*e - 2*a*c^3*d^7*e^3 + 2*a^3*c*d^3*e^7 - a^4*d*e^9)*x^2 + (c^4*d^10 - 6*a^2*c^2*d^6*e^4 + 8*a^3*c*d^4*e^6 - 3*a^4*d^2*e^8)*x)]","B",0
2071,1,1584,0,0.470458," ","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=""fricas"")","\left[\frac{105 \, {\left(c^{4} d^{4} e^{4} x^{5} + a c^{3} d^{7} e + {\left(4 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{6} e^{2} + 2 \, a c^{3} d^{4} e^{4}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{7} e + 3 \, a c^{3} d^{5} e^{3}\right)} x^{2} + {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(105 \, c^{3} d^{3} e^{3} x^{3} + 48 \, c^{3} d^{6} + 87 \, a c^{2} d^{4} e^{2} - 38 \, a^{2} c d^{2} e^{4} + 8 \, a^{3} e^{6} + 35 \, {\left(8 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(33 \, c^{3} d^{5} e + 14 \, a c^{2} d^{3} e^{3} - 2 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(a c^{4} d^{12} e - 4 \, a^{2} c^{3} d^{10} e^{3} + 6 \, a^{3} c^{2} d^{8} e^{5} - 4 \, a^{4} c d^{6} e^{7} + a^{5} d^{4} e^{9} + {\left(c^{5} d^{9} e^{4} - 4 \, a c^{4} d^{7} e^{6} + 6 \, a^{2} c^{3} d^{5} e^{8} - 4 \, a^{3} c^{2} d^{3} e^{10} + a^{4} c d e^{12}\right)} x^{5} + {\left(4 \, c^{5} d^{10} e^{3} - 15 \, a c^{4} d^{8} e^{5} + 20 \, a^{2} c^{3} d^{6} e^{7} - 10 \, a^{3} c^{2} d^{4} e^{9} + a^{5} e^{13}\right)} x^{4} + 2 \, {\left(3 \, c^{5} d^{11} e^{2} - 10 \, a c^{4} d^{9} e^{4} + 10 \, a^{2} c^{3} d^{7} e^{6} - 5 \, a^{4} c d^{3} e^{10} + 2 \, a^{5} d e^{12}\right)} x^{3} + 2 \, {\left(2 \, c^{5} d^{12} e - 5 \, a c^{4} d^{10} e^{3} + 10 \, a^{3} c^{2} d^{6} e^{7} - 10 \, a^{4} c d^{4} e^{9} + 3 \, a^{5} d^{2} e^{11}\right)} x^{2} + {\left(c^{5} d^{13} - 10 \, a^{2} c^{3} d^{9} e^{4} + 20 \, a^{3} c^{2} d^{7} e^{6} - 15 \, a^{4} c d^{5} e^{8} + 4 \, a^{5} d^{3} e^{10}\right)} x\right)}}, -\frac{105 \, {\left(c^{4} d^{4} e^{4} x^{5} + a c^{3} d^{7} e + {\left(4 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{4} + 2 \, {\left(3 \, c^{4} d^{6} e^{2} + 2 \, a c^{3} d^{4} e^{4}\right)} x^{3} + 2 \, {\left(2 \, c^{4} d^{7} e + 3 \, a c^{3} d^{5} e^{3}\right)} x^{2} + {\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(105 \, c^{3} d^{3} e^{3} x^{3} + 48 \, c^{3} d^{6} + 87 \, a c^{2} d^{4} e^{2} - 38 \, a^{2} c d^{2} e^{4} + 8 \, a^{3} e^{6} + 35 \, {\left(8 \, c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(33 \, c^{3} d^{5} e + 14 \, a c^{2} d^{3} e^{3} - 2 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(a c^{4} d^{12} e - 4 \, a^{2} c^{3} d^{10} e^{3} + 6 \, a^{3} c^{2} d^{8} e^{5} - 4 \, a^{4} c d^{6} e^{7} + a^{5} d^{4} e^{9} + {\left(c^{5} d^{9} e^{4} - 4 \, a c^{4} d^{7} e^{6} + 6 \, a^{2} c^{3} d^{5} e^{8} - 4 \, a^{3} c^{2} d^{3} e^{10} + a^{4} c d e^{12}\right)} x^{5} + {\left(4 \, c^{5} d^{10} e^{3} - 15 \, a c^{4} d^{8} e^{5} + 20 \, a^{2} c^{3} d^{6} e^{7} - 10 \, a^{3} c^{2} d^{4} e^{9} + a^{5} e^{13}\right)} x^{4} + 2 \, {\left(3 \, c^{5} d^{11} e^{2} - 10 \, a c^{4} d^{9} e^{4} + 10 \, a^{2} c^{3} d^{7} e^{6} - 5 \, a^{4} c d^{3} e^{10} + 2 \, a^{5} d e^{12}\right)} x^{3} + 2 \, {\left(2 \, c^{5} d^{12} e - 5 \, a c^{4} d^{10} e^{3} + 10 \, a^{3} c^{2} d^{6} e^{7} - 10 \, a^{4} c d^{4} e^{9} + 3 \, a^{5} d^{2} e^{11}\right)} x^{2} + {\left(c^{5} d^{13} - 10 \, a^{2} c^{3} d^{9} e^{4} + 20 \, a^{3} c^{2} d^{7} e^{6} - 15 \, a^{4} c d^{5} e^{8} + 4 \, a^{5} d^{3} e^{10}\right)} x\right)}}\right]"," ",0,"[1/48*(105*(c^4*d^4*e^4*x^5 + a*c^3*d^7*e + (4*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^4 + 2*(3*c^4*d^6*e^2 + 2*a*c^3*d^4*e^4)*x^3 + 2*(2*c^4*d^7*e + 3*a*c^3*d^5*e^3)*x^2 + (c^4*d^8 + 4*a*c^3*d^6*e^2)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(105*c^3*d^3*e^3*x^3 + 48*c^3*d^6 + 87*a*c^2*d^4*e^2 - 38*a^2*c*d^2*e^4 + 8*a^3*e^6 + 35*(8*c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^2 + 7*(33*c^3*d^5*e + 14*a*c^2*d^3*e^3 - 2*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c^4*d^12*e - 4*a^2*c^3*d^10*e^3 + 6*a^3*c^2*d^8*e^5 - 4*a^4*c*d^6*e^7 + a^5*d^4*e^9 + (c^5*d^9*e^4 - 4*a*c^4*d^7*e^6 + 6*a^2*c^3*d^5*e^8 - 4*a^3*c^2*d^3*e^10 + a^4*c*d*e^12)*x^5 + (4*c^5*d^10*e^3 - 15*a*c^4*d^8*e^5 + 20*a^2*c^3*d^6*e^7 - 10*a^3*c^2*d^4*e^9 + a^5*e^13)*x^4 + 2*(3*c^5*d^11*e^2 - 10*a*c^4*d^9*e^4 + 10*a^2*c^3*d^7*e^6 - 5*a^4*c*d^3*e^10 + 2*a^5*d*e^12)*x^3 + 2*(2*c^5*d^12*e - 5*a*c^4*d^10*e^3 + 10*a^3*c^2*d^6*e^7 - 10*a^4*c*d^4*e^9 + 3*a^5*d^2*e^11)*x^2 + (c^5*d^13 - 10*a^2*c^3*d^9*e^4 + 20*a^3*c^2*d^7*e^6 - 15*a^4*c*d^5*e^8 + 4*a^5*d^3*e^10)*x), -1/24*(105*(c^4*d^4*e^4*x^5 + a*c^3*d^7*e + (4*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^4 + 2*(3*c^4*d^6*e^2 + 2*a*c^3*d^4*e^4)*x^3 + 2*(2*c^4*d^7*e + 3*a*c^3*d^5*e^3)*x^2 + (c^4*d^8 + 4*a*c^3*d^6*e^2)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (105*c^3*d^3*e^3*x^3 + 48*c^3*d^6 + 87*a*c^2*d^4*e^2 - 38*a^2*c*d^2*e^4 + 8*a^3*e^6 + 35*(8*c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^2 + 7*(33*c^3*d^5*e + 14*a*c^2*d^3*e^3 - 2*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c^4*d^12*e - 4*a^2*c^3*d^10*e^3 + 6*a^3*c^2*d^8*e^5 - 4*a^4*c*d^6*e^7 + a^5*d^4*e^9 + (c^5*d^9*e^4 - 4*a*c^4*d^7*e^6 + 6*a^2*c^3*d^5*e^8 - 4*a^3*c^2*d^3*e^10 + a^4*c*d*e^12)*x^5 + (4*c^5*d^10*e^3 - 15*a*c^4*d^8*e^5 + 20*a^2*c^3*d^6*e^7 - 10*a^3*c^2*d^4*e^9 + a^5*e^13)*x^4 + 2*(3*c^5*d^11*e^2 - 10*a*c^4*d^9*e^4 + 10*a^2*c^3*d^7*e^6 - 5*a^4*c*d^3*e^10 + 2*a^5*d*e^12)*x^3 + 2*(2*c^5*d^12*e - 5*a*c^4*d^10*e^3 + 10*a^3*c^2*d^6*e^7 - 10*a^4*c*d^4*e^9 + 3*a^5*d^2*e^11)*x^2 + (c^5*d^13 - 10*a^2*c^3*d^9*e^4 + 20*a^3*c^2*d^7*e^6 - 15*a^4*c*d^5*e^8 + 4*a^5*d^3*e^10)*x)]","B",0
2072,1,2106,0,0.481529," ","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=""fricas"")","\left[\frac{315 \, {\left(c^{5} d^{5} e^{5} x^{6} + a c^{4} d^{9} e + {\left(5 \, c^{5} d^{6} e^{4} + a c^{4} d^{4} e^{6}\right)} x^{5} + 5 \, {\left(2 \, c^{5} d^{7} e^{3} + a c^{4} d^{5} e^{5}\right)} x^{4} + 10 \, {\left(c^{5} d^{8} e^{2} + a c^{4} d^{6} e^{4}\right)} x^{3} + 5 \, {\left(c^{5} d^{9} e + 2 \, a c^{4} d^{7} e^{3}\right)} x^{2} + {\left(c^{5} d^{10} + 5 \, a c^{4} d^{8} e^{2}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(315 \, c^{4} d^{4} e^{4} x^{4} + 128 \, c^{4} d^{8} + 325 \, a c^{3} d^{6} e^{2} - 210 \, a^{2} c^{2} d^{4} e^{4} + 88 \, a^{3} c d^{2} e^{6} - 16 \, a^{4} e^{8} + 105 \, {\left(11 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{3} + 21 \, {\left(73 \, c^{4} d^{6} e^{2} + 19 \, a c^{3} d^{4} e^{4} - 2 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(279 \, c^{4} d^{7} e + 185 \, a c^{3} d^{5} e^{3} - 52 \, a^{2} c^{2} d^{3} e^{5} + 8 \, a^{3} c d e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{128 \, {\left(a c^{5} d^{15} e - 5 \, a^{2} c^{4} d^{13} e^{3} + 10 \, a^{3} c^{3} d^{11} e^{5} - 10 \, a^{4} c^{2} d^{9} e^{7} + 5 \, a^{5} c d^{7} e^{9} - a^{6} d^{5} e^{11} + {\left(c^{6} d^{11} e^{5} - 5 \, a c^{5} d^{9} e^{7} + 10 \, a^{2} c^{4} d^{7} e^{9} - 10 \, a^{3} c^{3} d^{5} e^{11} + 5 \, a^{4} c^{2} d^{3} e^{13} - a^{5} c d e^{15}\right)} x^{6} + {\left(5 \, c^{6} d^{12} e^{4} - 24 \, a c^{5} d^{10} e^{6} + 45 \, a^{2} c^{4} d^{8} e^{8} - 40 \, a^{3} c^{3} d^{6} e^{10} + 15 \, a^{4} c^{2} d^{4} e^{12} - a^{6} e^{16}\right)} x^{5} + 5 \, {\left(2 \, c^{6} d^{13} e^{3} - 9 \, a c^{5} d^{11} e^{5} + 15 \, a^{2} c^{4} d^{9} e^{7} - 10 \, a^{3} c^{3} d^{7} e^{9} + 3 \, a^{5} c d^{3} e^{13} - a^{6} d e^{15}\right)} x^{4} + 10 \, {\left(c^{6} d^{14} e^{2} - 4 \, a c^{5} d^{12} e^{4} + 5 \, a^{2} c^{4} d^{10} e^{6} - 5 \, a^{4} c^{2} d^{6} e^{10} + 4 \, a^{5} c d^{4} e^{12} - a^{6} d^{2} e^{14}\right)} x^{3} + 5 \, {\left(c^{6} d^{15} e - 3 \, a c^{5} d^{13} e^{3} + 10 \, a^{3} c^{3} d^{9} e^{7} - 15 \, a^{4} c^{2} d^{7} e^{9} + 9 \, a^{5} c d^{5} e^{11} - 2 \, a^{6} d^{3} e^{13}\right)} x^{2} + {\left(c^{6} d^{16} - 15 \, a^{2} c^{4} d^{12} e^{4} + 40 \, a^{3} c^{3} d^{10} e^{6} - 45 \, a^{4} c^{2} d^{8} e^{8} + 24 \, a^{5} c d^{6} e^{10} - 5 \, a^{6} d^{4} e^{12}\right)} x\right)}}, -\frac{315 \, {\left(c^{5} d^{5} e^{5} x^{6} + a c^{4} d^{9} e + {\left(5 \, c^{5} d^{6} e^{4} + a c^{4} d^{4} e^{6}\right)} x^{5} + 5 \, {\left(2 \, c^{5} d^{7} e^{3} + a c^{4} d^{5} e^{5}\right)} x^{4} + 10 \, {\left(c^{5} d^{8} e^{2} + a c^{4} d^{6} e^{4}\right)} x^{3} + 5 \, {\left(c^{5} d^{9} e + 2 \, a c^{4} d^{7} e^{3}\right)} x^{2} + {\left(c^{5} d^{10} + 5 \, a c^{4} d^{8} e^{2}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(315 \, c^{4} d^{4} e^{4} x^{4} + 128 \, c^{4} d^{8} + 325 \, a c^{3} d^{6} e^{2} - 210 \, a^{2} c^{2} d^{4} e^{4} + 88 \, a^{3} c d^{2} e^{6} - 16 \, a^{4} e^{8} + 105 \, {\left(11 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{3} + 21 \, {\left(73 \, c^{4} d^{6} e^{2} + 19 \, a c^{3} d^{4} e^{4} - 2 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 3 \, {\left(279 \, c^{4} d^{7} e + 185 \, a c^{3} d^{5} e^{3} - 52 \, a^{2} c^{2} d^{3} e^{5} + 8 \, a^{3} c d e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{64 \, {\left(a c^{5} d^{15} e - 5 \, a^{2} c^{4} d^{13} e^{3} + 10 \, a^{3} c^{3} d^{11} e^{5} - 10 \, a^{4} c^{2} d^{9} e^{7} + 5 \, a^{5} c d^{7} e^{9} - a^{6} d^{5} e^{11} + {\left(c^{6} d^{11} e^{5} - 5 \, a c^{5} d^{9} e^{7} + 10 \, a^{2} c^{4} d^{7} e^{9} - 10 \, a^{3} c^{3} d^{5} e^{11} + 5 \, a^{4} c^{2} d^{3} e^{13} - a^{5} c d e^{15}\right)} x^{6} + {\left(5 \, c^{6} d^{12} e^{4} - 24 \, a c^{5} d^{10} e^{6} + 45 \, a^{2} c^{4} d^{8} e^{8} - 40 \, a^{3} c^{3} d^{6} e^{10} + 15 \, a^{4} c^{2} d^{4} e^{12} - a^{6} e^{16}\right)} x^{5} + 5 \, {\left(2 \, c^{6} d^{13} e^{3} - 9 \, a c^{5} d^{11} e^{5} + 15 \, a^{2} c^{4} d^{9} e^{7} - 10 \, a^{3} c^{3} d^{7} e^{9} + 3 \, a^{5} c d^{3} e^{13} - a^{6} d e^{15}\right)} x^{4} + 10 \, {\left(c^{6} d^{14} e^{2} - 4 \, a c^{5} d^{12} e^{4} + 5 \, a^{2} c^{4} d^{10} e^{6} - 5 \, a^{4} c^{2} d^{6} e^{10} + 4 \, a^{5} c d^{4} e^{12} - a^{6} d^{2} e^{14}\right)} x^{3} + 5 \, {\left(c^{6} d^{15} e - 3 \, a c^{5} d^{13} e^{3} + 10 \, a^{3} c^{3} d^{9} e^{7} - 15 \, a^{4} c^{2} d^{7} e^{9} + 9 \, a^{5} c d^{5} e^{11} - 2 \, a^{6} d^{3} e^{13}\right)} x^{2} + {\left(c^{6} d^{16} - 15 \, a^{2} c^{4} d^{12} e^{4} + 40 \, a^{3} c^{3} d^{10} e^{6} - 45 \, a^{4} c^{2} d^{8} e^{8} + 24 \, a^{5} c d^{6} e^{10} - 5 \, a^{6} d^{4} e^{12}\right)} x\right)}}\right]"," ",0,"[1/128*(315*(c^5*d^5*e^5*x^6 + a*c^4*d^9*e + (5*c^5*d^6*e^4 + a*c^4*d^4*e^6)*x^5 + 5*(2*c^5*d^7*e^3 + a*c^4*d^5*e^5)*x^4 + 10*(c^5*d^8*e^2 + a*c^4*d^6*e^4)*x^3 + 5*(c^5*d^9*e + 2*a*c^4*d^7*e^3)*x^2 + (c^5*d^10 + 5*a*c^4*d^8*e^2)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(315*c^4*d^4*e^4*x^4 + 128*c^4*d^8 + 325*a*c^3*d^6*e^2 - 210*a^2*c^2*d^4*e^4 + 88*a^3*c*d^2*e^6 - 16*a^4*e^8 + 105*(11*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^3 + 21*(73*c^4*d^6*e^2 + 19*a*c^3*d^4*e^4 - 2*a^2*c^2*d^2*e^6)*x^2 + 3*(279*c^4*d^7*e + 185*a*c^3*d^5*e^3 - 52*a^2*c^2*d^3*e^5 + 8*a^3*c*d*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c^5*d^15*e - 5*a^2*c^4*d^13*e^3 + 10*a^3*c^3*d^11*e^5 - 10*a^4*c^2*d^9*e^7 + 5*a^5*c*d^7*e^9 - a^6*d^5*e^11 + (c^6*d^11*e^5 - 5*a*c^5*d^9*e^7 + 10*a^2*c^4*d^7*e^9 - 10*a^3*c^3*d^5*e^11 + 5*a^4*c^2*d^3*e^13 - a^5*c*d*e^15)*x^6 + (5*c^6*d^12*e^4 - 24*a*c^5*d^10*e^6 + 45*a^2*c^4*d^8*e^8 - 40*a^3*c^3*d^6*e^10 + 15*a^4*c^2*d^4*e^12 - a^6*e^16)*x^5 + 5*(2*c^6*d^13*e^3 - 9*a*c^5*d^11*e^5 + 15*a^2*c^4*d^9*e^7 - 10*a^3*c^3*d^7*e^9 + 3*a^5*c*d^3*e^13 - a^6*d*e^15)*x^4 + 10*(c^6*d^14*e^2 - 4*a*c^5*d^12*e^4 + 5*a^2*c^4*d^10*e^6 - 5*a^4*c^2*d^6*e^10 + 4*a^5*c*d^4*e^12 - a^6*d^2*e^14)*x^3 + 5*(c^6*d^15*e - 3*a*c^5*d^13*e^3 + 10*a^3*c^3*d^9*e^7 - 15*a^4*c^2*d^7*e^9 + 9*a^5*c*d^5*e^11 - 2*a^6*d^3*e^13)*x^2 + (c^6*d^16 - 15*a^2*c^4*d^12*e^4 + 40*a^3*c^3*d^10*e^6 - 45*a^4*c^2*d^8*e^8 + 24*a^5*c*d^6*e^10 - 5*a^6*d^4*e^12)*x), -1/64*(315*(c^5*d^5*e^5*x^6 + a*c^4*d^9*e + (5*c^5*d^6*e^4 + a*c^4*d^4*e^6)*x^5 + 5*(2*c^5*d^7*e^3 + a*c^4*d^5*e^5)*x^4 + 10*(c^5*d^8*e^2 + a*c^4*d^6*e^4)*x^3 + 5*(c^5*d^9*e + 2*a*c^4*d^7*e^3)*x^2 + (c^5*d^10 + 5*a*c^4*d^8*e^2)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (315*c^4*d^4*e^4*x^4 + 128*c^4*d^8 + 325*a*c^3*d^6*e^2 - 210*a^2*c^2*d^4*e^4 + 88*a^3*c*d^2*e^6 - 16*a^4*e^8 + 105*(11*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^3 + 21*(73*c^4*d^6*e^2 + 19*a*c^3*d^4*e^4 - 2*a^2*c^2*d^2*e^6)*x^2 + 3*(279*c^4*d^7*e + 185*a*c^3*d^5*e^3 - 52*a^2*c^2*d^3*e^5 + 8*a^3*c*d*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a*c^5*d^15*e - 5*a^2*c^4*d^13*e^3 + 10*a^3*c^3*d^11*e^5 - 10*a^4*c^2*d^9*e^7 + 5*a^5*c*d^7*e^9 - a^6*d^5*e^11 + (c^6*d^11*e^5 - 5*a*c^5*d^9*e^7 + 10*a^2*c^4*d^7*e^9 - 10*a^3*c^3*d^5*e^11 + 5*a^4*c^2*d^3*e^13 - a^5*c*d*e^15)*x^6 + (5*c^6*d^12*e^4 - 24*a*c^5*d^10*e^6 + 45*a^2*c^4*d^8*e^8 - 40*a^3*c^3*d^6*e^10 + 15*a^4*c^2*d^4*e^12 - a^6*e^16)*x^5 + 5*(2*c^6*d^13*e^3 - 9*a*c^5*d^11*e^5 + 15*a^2*c^4*d^9*e^7 - 10*a^3*c^3*d^7*e^9 + 3*a^5*c*d^3*e^13 - a^6*d*e^15)*x^4 + 10*(c^6*d^14*e^2 - 4*a*c^5*d^12*e^4 + 5*a^2*c^4*d^10*e^6 - 5*a^4*c^2*d^6*e^10 + 4*a^5*c*d^4*e^12 - a^6*d^2*e^14)*x^3 + 5*(c^6*d^15*e - 3*a*c^5*d^13*e^3 + 10*a^3*c^3*d^9*e^7 - 15*a^4*c^2*d^7*e^9 + 9*a^5*c*d^5*e^11 - 2*a^6*d^3*e^13)*x^2 + (c^6*d^16 - 15*a^2*c^4*d^12*e^4 + 40*a^3*c^3*d^10*e^6 - 45*a^4*c^2*d^8*e^8 + 24*a^5*c*d^6*e^10 - 5*a^6*d^4*e^12)*x)]","B",0
2073,1,131,0,0.407177," ","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=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(3 \, c d e x + c d^{2} + 2 \, a e^{2}\right)} \sqrt{e x + d}}{3 \, {\left(c^{4} d^{4} e x^{3} + a^{2} c^{2} d^{3} e^{2} + {\left(c^{4} d^{5} + 2 \, a c^{3} d^{3} e^{2}\right)} x^{2} + {\left(2 \, a c^{3} d^{4} e + a^{2} c^{2} d^{2} e^{3}\right)} x\right)}}"," ",0,"-2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(3*c*d*e*x + c*d^2 + 2*a*e^2)*sqrt(e*x + d)/(c^4*d^4*e*x^3 + a^2*c^2*d^3*e^2 + (c^4*d^5 + 2*a*c^3*d^3*e^2)*x^2 + (2*a*c^3*d^4*e + a^2*c^2*d^2*e^3)*x)","A",0
2074,1,107,0,0.409031," ","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=""fricas"")","-\frac{2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3 \, {\left(c^{3} d^{3} e x^{3} + a^{2} c d^{2} e^{2} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2}\right)} x^{2} + {\left(2 \, a c^{2} d^{3} e + a^{2} c d e^{3}\right)} x\right)}}"," ",0,"-2/3*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d)/(c^3*d^3*e*x^3 + a^2*c*d^2*e^2 + (c^3*d^4 + 2*a*c^2*d^2*e^2)*x^2 + (2*a*c^2*d^3*e + a^2*c*d*e^3)*x)","B",0
2075,1,788,0,0.442258," ","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=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{2} e^{2} x^{3} + a^{2} d e^{3} + {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x^{2} + {\left(2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(3 \, c d e x - c d^{2} + 4 \, a e^{2}\right)} \sqrt{e x + d}}{3 \, {\left(a^{2} c^{2} d^{5} e^{2} - 2 \, a^{3} c d^{3} e^{4} + a^{4} d e^{6} + {\left(c^{4} d^{6} e - 2 \, a c^{3} d^{4} e^{3} + a^{2} c^{2} d^{2} e^{5}\right)} x^{3} + {\left(c^{4} d^{7} - 3 \, a^{2} c^{2} d^{3} e^{4} + 2 \, a^{3} c d e^{6}\right)} x^{2} + {\left(2 \, a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} + a^{4} e^{7}\right)} x\right)}}, \frac{2 \, {\left(3 \, {\left(c^{2} d^{2} e^{2} x^{3} + a^{2} d e^{3} + {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x^{2} + {\left(2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(3 \, c d e x - c d^{2} + 4 \, a e^{2}\right)} \sqrt{e x + d}\right)}}{3 \, {\left(a^{2} c^{2} d^{5} e^{2} - 2 \, a^{3} c d^{3} e^{4} + a^{4} d e^{6} + {\left(c^{4} d^{6} e - 2 \, a c^{3} d^{4} e^{3} + a^{2} c^{2} d^{2} e^{5}\right)} x^{3} + {\left(c^{4} d^{7} - 3 \, a^{2} c^{2} d^{3} e^{4} + 2 \, a^{3} c d e^{6}\right)} x^{2} + {\left(2 \, a c^{3} d^{6} e - 3 \, a^{2} c^{2} d^{4} e^{3} + a^{4} e^{7}\right)} x\right)}}\right]"," ",0,"[1/3*(3*(c^2*d^2*e^2*x^3 + a^2*d*e^3 + (c^2*d^3*e + 2*a*c*d*e^3)*x^2 + (2*a*c*d^2*e^2 + a^2*e^4)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(3*c*d*e*x - c*d^2 + 4*a*e^2)*sqrt(e*x + d))/(a^2*c^2*d^5*e^2 - 2*a^3*c*d^3*e^4 + a^4*d*e^6 + (c^4*d^6*e - 2*a*c^3*d^4*e^3 + a^2*c^2*d^2*e^5)*x^3 + (c^4*d^7 - 3*a^2*c^2*d^3*e^4 + 2*a^3*c*d*e^6)*x^2 + (2*a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 + a^4*e^7)*x), 2/3*(3*(c^2*d^2*e^2*x^3 + a^2*d*e^3 + (c^2*d^3*e + 2*a*c*d*e^3)*x^2 + (2*a*c*d^2*e^2 + a^2*e^4)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(3*c*d*e*x - c*d^2 + 4*a*e^2)*sqrt(e*x + d))/(a^2*c^2*d^5*e^2 - 2*a^3*c*d^3*e^4 + a^4*d*e^6 + (c^4*d^6*e - 2*a*c^3*d^4*e^3 + a^2*c^2*d^2*e^5)*x^3 + (c^4*d^7 - 3*a^2*c^2*d^3*e^4 + 2*a^3*c*d*e^6)*x^2 + (2*a*c^3*d^6*e - 3*a^2*c^2*d^4*e^3 + a^4*e^7)*x)]","A",0
2076,1,1236,0,0.433795," ","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=""fricas"")","\left[-\frac{15 \, {\left(c^{3} d^{3} e^{3} x^{4} + a^{2} c d^{3} e^{3} + 2 \, {\left(c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{3} + {\left(c^{3} d^{5} e + 4 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x^{2} + 2 \, {\left(a c^{2} d^{4} e^{2} + a^{2} c d^{2} e^{4}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} - 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(15 \, c^{2} d^{2} e^{2} x^{2} - 2 \, c^{2} d^{4} + 14 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} + 10 \, {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{6 \, {\left(a^{2} c^{3} d^{8} e^{2} - 3 \, a^{3} c^{2} d^{6} e^{4} + 3 \, a^{4} c d^{4} e^{6} - a^{5} d^{2} e^{8} + {\left(c^{5} d^{8} e^{2} - 3 \, a c^{4} d^{6} e^{4} + 3 \, a^{2} c^{3} d^{4} e^{6} - a^{3} c^{2} d^{2} e^{8}\right)} x^{4} + 2 \, {\left(c^{5} d^{9} e - 2 \, a c^{4} d^{7} e^{3} + 2 \, a^{3} c^{2} d^{3} e^{7} - a^{4} c d e^{9}\right)} x^{3} + {\left(c^{5} d^{10} + a c^{4} d^{8} e^{2} - 8 \, a^{2} c^{3} d^{6} e^{4} + 8 \, a^{3} c^{2} d^{4} e^{6} - a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} x^{2} + 2 \, {\left(a c^{4} d^{9} e - 2 \, a^{2} c^{3} d^{7} e^{3} + 2 \, a^{4} c d^{3} e^{7} - a^{5} d e^{9}\right)} x\right)}}, \frac{15 \, {\left(c^{3} d^{3} e^{3} x^{4} + a^{2} c d^{3} e^{3} + 2 \, {\left(c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{3} + {\left(c^{3} d^{5} e + 4 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x^{2} + 2 \, {\left(a c^{2} d^{4} e^{2} + a^{2} c d^{2} e^{4}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(15 \, c^{2} d^{2} e^{2} x^{2} - 2 \, c^{2} d^{4} + 14 \, a c d^{2} e^{2} + 3 \, a^{2} e^{4} + 10 \, {\left(c^{2} d^{3} e + 2 \, a c d e^{3}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3 \, {\left(a^{2} c^{3} d^{8} e^{2} - 3 \, a^{3} c^{2} d^{6} e^{4} + 3 \, a^{4} c d^{4} e^{6} - a^{5} d^{2} e^{8} + {\left(c^{5} d^{8} e^{2} - 3 \, a c^{4} d^{6} e^{4} + 3 \, a^{2} c^{3} d^{4} e^{6} - a^{3} c^{2} d^{2} e^{8}\right)} x^{4} + 2 \, {\left(c^{5} d^{9} e - 2 \, a c^{4} d^{7} e^{3} + 2 \, a^{3} c^{2} d^{3} e^{7} - a^{4} c d e^{9}\right)} x^{3} + {\left(c^{5} d^{10} + a c^{4} d^{8} e^{2} - 8 \, a^{2} c^{3} d^{6} e^{4} + 8 \, a^{3} c^{2} d^{4} e^{6} - a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} x^{2} + 2 \, {\left(a c^{4} d^{9} e - 2 \, a^{2} c^{3} d^{7} e^{3} + 2 \, a^{4} c d^{3} e^{7} - a^{5} d e^{9}\right)} x\right)}}\right]"," ",0,"[-1/6*(15*(c^3*d^3*e^3*x^4 + a^2*c*d^3*e^3 + 2*(c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^3 + (c^3*d^5*e + 4*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x^2 + 2*(a*c^2*d^4*e^2 + a^2*c*d^2*e^4)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 - 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(15*c^2*d^2*e^2*x^2 - 2*c^2*d^4 + 14*a*c*d^2*e^2 + 3*a^2*e^4 + 10*(c^2*d^3*e + 2*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^3*d^8*e^2 - 3*a^3*c^2*d^6*e^4 + 3*a^4*c*d^4*e^6 - a^5*d^2*e^8 + (c^5*d^8*e^2 - 3*a*c^4*d^6*e^4 + 3*a^2*c^3*d^4*e^6 - a^3*c^2*d^2*e^8)*x^4 + 2*(c^5*d^9*e - 2*a*c^4*d^7*e^3 + 2*a^3*c^2*d^3*e^7 - a^4*c*d*e^9)*x^3 + (c^5*d^10 + a*c^4*d^8*e^2 - 8*a^2*c^3*d^6*e^4 + 8*a^3*c^2*d^4*e^6 - a^4*c*d^2*e^8 - a^5*e^10)*x^2 + 2*(a*c^4*d^9*e - 2*a^2*c^3*d^7*e^3 + 2*a^4*c*d^3*e^7 - a^5*d*e^9)*x), 1/3*(15*(c^3*d^3*e^3*x^4 + a^2*c*d^3*e^3 + 2*(c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^3 + (c^3*d^5*e + 4*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x^2 + 2*(a*c^2*d^4*e^2 + a^2*c*d^2*e^4)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (15*c^2*d^2*e^2*x^2 - 2*c^2*d^4 + 14*a*c*d^2*e^2 + 3*a^2*e^4 + 10*(c^2*d^3*e + 2*a*c*d*e^3)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^3*d^8*e^2 - 3*a^3*c^2*d^6*e^4 + 3*a^4*c*d^4*e^6 - a^5*d^2*e^8 + (c^5*d^8*e^2 - 3*a*c^4*d^6*e^4 + 3*a^2*c^3*d^4*e^6 - a^3*c^2*d^2*e^8)*x^4 + 2*(c^5*d^9*e - 2*a*c^4*d^7*e^3 + 2*a^3*c^2*d^3*e^7 - a^4*c*d*e^9)*x^3 + (c^5*d^10 + a*c^4*d^8*e^2 - 8*a^2*c^3*d^6*e^4 + 8*a^3*c^2*d^4*e^6 - a^4*c*d^2*e^8 - a^5*e^10)*x^2 + 2*(a*c^4*d^9*e - 2*a^2*c^3*d^7*e^3 + 2*a^4*c*d^3*e^7 - a^5*d*e^9)*x)]","B",0
2077,1,1778,0,0.466908," ","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=""fricas"")","\left[\frac{105 \, {\left(c^{4} d^{4} e^{4} x^{5} + a^{2} c^{2} d^{5} e^{3} + {\left(3 \, c^{4} d^{5} e^{3} + 2 \, a c^{3} d^{3} e^{5}\right)} x^{4} + {\left(3 \, c^{4} d^{6} e^{2} + 6 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{3} + {\left(c^{4} d^{7} e + 6 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5}\right)} x^{2} + {\left(2 \, a c^{3} d^{6} e^{2} + 3 \, a^{2} c^{2} d^{4} e^{4}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(105 \, c^{3} d^{3} e^{3} x^{3} - 8 \, c^{3} d^{6} + 80 \, a c^{2} d^{4} e^{2} + 39 \, a^{2} c d^{2} e^{4} - 6 \, a^{3} e^{6} + 35 \, {\left(5 \, c^{3} d^{4} e^{2} + 4 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(8 \, c^{3} d^{5} e + 34 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(a^{2} c^{4} d^{11} e^{2} - 4 \, a^{3} c^{3} d^{9} e^{4} + 6 \, a^{4} c^{2} d^{7} e^{6} - 4 \, a^{5} c d^{5} e^{8} + a^{6} d^{3} e^{10} + {\left(c^{6} d^{10} e^{3} - 4 \, a c^{5} d^{8} e^{5} + 6 \, a^{2} c^{4} d^{6} e^{7} - 4 \, a^{3} c^{3} d^{4} e^{9} + a^{4} c^{2} d^{2} e^{11}\right)} x^{5} + {\left(3 \, c^{6} d^{11} e^{2} - 10 \, a c^{5} d^{9} e^{4} + 10 \, a^{2} c^{4} d^{7} e^{6} - 5 \, a^{4} c^{2} d^{3} e^{10} + 2 \, a^{5} c d e^{12}\right)} x^{4} + {\left(3 \, c^{6} d^{12} e - 6 \, a c^{5} d^{10} e^{3} - 5 \, 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} + 2 \, a^{5} c d^{2} e^{11} + a^{6} e^{13}\right)} x^{3} + {\left(c^{6} d^{13} + 2 \, 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} - 5 \, a^{4} c^{2} d^{5} e^{8} - 6 \, a^{5} c d^{3} e^{10} + 3 \, a^{6} d e^{12}\right)} x^{2} + {\left(2 \, a c^{5} d^{12} e - 5 \, a^{2} c^{4} d^{10} e^{3} + 10 \, a^{4} c^{2} d^{6} e^{7} - 10 \, a^{5} c d^{4} e^{9} + 3 \, a^{6} d^{2} e^{11}\right)} x\right)}}, \frac{105 \, {\left(c^{4} d^{4} e^{4} x^{5} + a^{2} c^{2} d^{5} e^{3} + {\left(3 \, c^{4} d^{5} e^{3} + 2 \, a c^{3} d^{3} e^{5}\right)} x^{4} + {\left(3 \, c^{4} d^{6} e^{2} + 6 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{3} + {\left(c^{4} d^{7} e + 6 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5}\right)} x^{2} + {\left(2 \, a c^{3} d^{6} e^{2} + 3 \, a^{2} c^{2} d^{4} e^{4}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(105 \, c^{3} d^{3} e^{3} x^{3} - 8 \, c^{3} d^{6} + 80 \, a c^{2} d^{4} e^{2} + 39 \, a^{2} c d^{2} e^{4} - 6 \, a^{3} e^{6} + 35 \, {\left(5 \, c^{3} d^{4} e^{2} + 4 \, a c^{2} d^{2} e^{4}\right)} x^{2} + 7 \, {\left(8 \, c^{3} d^{5} e + 34 \, a c^{2} d^{3} e^{3} + 3 \, a^{2} c d e^{5}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{12 \, {\left(a^{2} c^{4} d^{11} e^{2} - 4 \, a^{3} c^{3} d^{9} e^{4} + 6 \, a^{4} c^{2} d^{7} e^{6} - 4 \, a^{5} c d^{5} e^{8} + a^{6} d^{3} e^{10} + {\left(c^{6} d^{10} e^{3} - 4 \, a c^{5} d^{8} e^{5} + 6 \, a^{2} c^{4} d^{6} e^{7} - 4 \, a^{3} c^{3} d^{4} e^{9} + a^{4} c^{2} d^{2} e^{11}\right)} x^{5} + {\left(3 \, c^{6} d^{11} e^{2} - 10 \, a c^{5} d^{9} e^{4} + 10 \, a^{2} c^{4} d^{7} e^{6} - 5 \, a^{4} c^{2} d^{3} e^{10} + 2 \, a^{5} c d e^{12}\right)} x^{4} + {\left(3 \, c^{6} d^{12} e - 6 \, a c^{5} d^{10} e^{3} - 5 \, 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} + 2 \, a^{5} c d^{2} e^{11} + a^{6} e^{13}\right)} x^{3} + {\left(c^{6} d^{13} + 2 \, 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} - 5 \, a^{4} c^{2} d^{5} e^{8} - 6 \, a^{5} c d^{3} e^{10} + 3 \, a^{6} d e^{12}\right)} x^{2} + {\left(2 \, a c^{5} d^{12} e - 5 \, a^{2} c^{4} d^{10} e^{3} + 10 \, a^{4} c^{2} d^{6} e^{7} - 10 \, a^{5} c d^{4} e^{9} + 3 \, a^{6} d^{2} e^{11}\right)} x\right)}}\right]"," ",0,"[1/24*(105*(c^4*d^4*e^4*x^5 + a^2*c^2*d^5*e^3 + (3*c^4*d^5*e^3 + 2*a*c^3*d^3*e^5)*x^4 + (3*c^4*d^6*e^2 + 6*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^3 + (c^4*d^7*e + 6*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5)*x^2 + (2*a*c^3*d^6*e^2 + 3*a^2*c^2*d^4*e^4)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(105*c^3*d^3*e^3*x^3 - 8*c^3*d^6 + 80*a*c^2*d^4*e^2 + 39*a^2*c*d^2*e^4 - 6*a^3*e^6 + 35*(5*c^3*d^4*e^2 + 4*a*c^2*d^2*e^4)*x^2 + 7*(8*c^3*d^5*e + 34*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^4*d^11*e^2 - 4*a^3*c^3*d^9*e^4 + 6*a^4*c^2*d^7*e^6 - 4*a^5*c*d^5*e^8 + a^6*d^3*e^10 + (c^6*d^10*e^3 - 4*a*c^5*d^8*e^5 + 6*a^2*c^4*d^6*e^7 - 4*a^3*c^3*d^4*e^9 + a^4*c^2*d^2*e^11)*x^5 + (3*c^6*d^11*e^2 - 10*a*c^5*d^9*e^4 + 10*a^2*c^4*d^7*e^6 - 5*a^4*c^2*d^3*e^10 + 2*a^5*c*d*e^12)*x^4 + (3*c^6*d^12*e - 6*a*c^5*d^10*e^3 - 5*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 + 2*a^5*c*d^2*e^11 + a^6*e^13)*x^3 + (c^6*d^13 + 2*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 - 5*a^4*c^2*d^5*e^8 - 6*a^5*c*d^3*e^10 + 3*a^6*d*e^12)*x^2 + (2*a*c^5*d^12*e - 5*a^2*c^4*d^10*e^3 + 10*a^4*c^2*d^6*e^7 - 10*a^5*c*d^4*e^9 + 3*a^6*d^2*e^11)*x), 1/12*(105*(c^4*d^4*e^4*x^5 + a^2*c^2*d^5*e^3 + (3*c^4*d^5*e^3 + 2*a*c^3*d^3*e^5)*x^4 + (3*c^4*d^6*e^2 + 6*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^3 + (c^4*d^7*e + 6*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5)*x^2 + (2*a*c^3*d^6*e^2 + 3*a^2*c^2*d^4*e^4)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (105*c^3*d^3*e^3*x^3 - 8*c^3*d^6 + 80*a*c^2*d^4*e^2 + 39*a^2*c*d^2*e^4 - 6*a^3*e^6 + 35*(5*c^3*d^4*e^2 + 4*a*c^2*d^2*e^4)*x^2 + 7*(8*c^3*d^5*e + 34*a*c^2*d^3*e^3 + 3*a^2*c*d*e^5)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^4*d^11*e^2 - 4*a^3*c^3*d^9*e^4 + 6*a^4*c^2*d^7*e^6 - 4*a^5*c*d^5*e^8 + a^6*d^3*e^10 + (c^6*d^10*e^3 - 4*a*c^5*d^8*e^5 + 6*a^2*c^4*d^6*e^7 - 4*a^3*c^3*d^4*e^9 + a^4*c^2*d^2*e^11)*x^5 + (3*c^6*d^11*e^2 - 10*a*c^5*d^9*e^4 + 10*a^2*c^4*d^7*e^6 - 5*a^4*c^2*d^3*e^10 + 2*a^5*c*d*e^12)*x^4 + (3*c^6*d^12*e - 6*a*c^5*d^10*e^3 - 5*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 + 2*a^5*c*d^2*e^11 + a^6*e^13)*x^3 + (c^6*d^13 + 2*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 - 5*a^4*c^2*d^5*e^8 - 6*a^5*c*d^3*e^10 + 3*a^6*d*e^12)*x^2 + (2*a*c^5*d^12*e - 5*a^2*c^4*d^10*e^3 + 10*a^4*c^2*d^6*e^7 - 10*a^5*c*d^4*e^9 + 3*a^6*d^2*e^11)*x)]","B",0
2078,1,2388,0,0.479015," ","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=""fricas"")","\left[\frac{315 \, {\left(c^{5} d^{5} e^{5} x^{6} + a^{2} c^{3} d^{7} e^{3} + 2 \, {\left(2 \, c^{5} d^{6} e^{4} + a c^{4} d^{4} e^{6}\right)} x^{5} + {\left(6 \, c^{5} d^{7} e^{3} + 8 \, a c^{4} d^{5} e^{5} + a^{2} c^{3} d^{3} e^{7}\right)} x^{4} + 4 \, {\left(c^{5} d^{8} e^{2} + 3 \, a c^{4} d^{6} e^{4} + a^{2} c^{3} d^{4} e^{6}\right)} x^{3} + {\left(c^{5} d^{9} e + 8 \, a c^{4} d^{7} e^{3} + 6 \, a^{2} c^{3} d^{5} e^{5}\right)} x^{2} + 2 \, {\left(a c^{4} d^{8} e^{2} + 2 \, a^{2} c^{3} d^{6} e^{4}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(315 \, c^{4} d^{4} e^{4} x^{4} - 16 \, c^{4} d^{8} + 208 \, a c^{3} d^{6} e^{2} + 165 \, a^{2} c^{2} d^{4} e^{4} - 50 \, a^{3} c d^{2} e^{6} + 8 \, a^{4} e^{8} + 420 \, {\left(2 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{3} + 63 \, {\left(11 \, c^{4} d^{6} e^{2} + 18 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 18 \, {\left(8 \, c^{4} d^{7} e + 53 \, a c^{3} d^{5} e^{3} + 10 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{48 \, {\left(a^{2} c^{5} d^{14} e^{2} - 5 \, a^{3} c^{4} d^{12} e^{4} + 10 \, a^{4} c^{3} d^{10} e^{6} - 10 \, a^{5} c^{2} d^{8} e^{8} + 5 \, a^{6} c d^{6} e^{10} - a^{7} d^{4} e^{12} + {\left(c^{7} d^{12} e^{4} - 5 \, a c^{6} d^{10} e^{6} + 10 \, a^{2} c^{5} d^{8} e^{8} - 10 \, a^{3} c^{4} d^{6} e^{10} + 5 \, a^{4} c^{3} d^{4} e^{12} - a^{5} c^{2} d^{2} e^{14}\right)} x^{6} + 2 \, {\left(2 \, c^{7} d^{13} e^{3} - 9 \, a c^{6} d^{11} e^{5} + 15 \, a^{2} c^{5} d^{9} e^{7} - 10 \, a^{3} c^{4} d^{7} e^{9} + 3 \, a^{5} c^{2} d^{3} e^{13} - a^{6} c d e^{15}\right)} x^{5} + {\left(6 \, c^{7} d^{14} e^{2} - 22 \, a c^{6} d^{12} e^{4} + 21 \, a^{2} c^{5} d^{10} e^{6} + 15 \, a^{3} c^{4} d^{8} e^{8} - 40 \, a^{4} c^{3} d^{6} e^{10} + 24 \, a^{5} c^{2} d^{4} e^{12} - 3 \, a^{6} c d^{2} e^{14} - a^{7} e^{16}\right)} x^{4} + 4 \, {\left(c^{7} d^{15} e - 2 \, a c^{6} d^{13} e^{3} - 4 \, a^{2} c^{5} d^{11} e^{5} + 15 \, a^{3} c^{4} d^{9} e^{7} - 15 \, a^{4} c^{3} d^{7} e^{9} + 4 \, a^{5} c^{2} d^{5} e^{11} + 2 \, a^{6} c d^{3} e^{13} - a^{7} d e^{15}\right)} x^{3} + {\left(c^{7} d^{16} + 3 \, a c^{6} d^{14} e^{2} - 24 \, a^{2} c^{5} d^{12} e^{4} + 40 \, a^{3} c^{4} d^{10} e^{6} - 15 \, a^{4} c^{3} d^{8} e^{8} - 21 \, a^{5} c^{2} d^{6} e^{10} + 22 \, a^{6} c d^{4} e^{12} - 6 \, a^{7} d^{2} e^{14}\right)} x^{2} + 2 \, {\left(a c^{6} d^{15} e - 3 \, a^{2} c^{5} d^{13} e^{3} + 10 \, a^{4} c^{3} d^{9} e^{7} - 15 \, a^{5} c^{2} d^{7} e^{9} + 9 \, a^{6} c d^{5} e^{11} - 2 \, a^{7} d^{3} e^{13}\right)} x\right)}}, \frac{315 \, {\left(c^{5} d^{5} e^{5} x^{6} + a^{2} c^{3} d^{7} e^{3} + 2 \, {\left(2 \, c^{5} d^{6} e^{4} + a c^{4} d^{4} e^{6}\right)} x^{5} + {\left(6 \, c^{5} d^{7} e^{3} + 8 \, a c^{4} d^{5} e^{5} + a^{2} c^{3} d^{3} e^{7}\right)} x^{4} + 4 \, {\left(c^{5} d^{8} e^{2} + 3 \, a c^{4} d^{6} e^{4} + a^{2} c^{3} d^{4} e^{6}\right)} x^{3} + {\left(c^{5} d^{9} e + 8 \, a c^{4} d^{7} e^{3} + 6 \, a^{2} c^{3} d^{5} e^{5}\right)} x^{2} + 2 \, {\left(a c^{4} d^{8} e^{2} + 2 \, a^{2} c^{3} d^{6} e^{4}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(315 \, c^{4} d^{4} e^{4} x^{4} - 16 \, c^{4} d^{8} + 208 \, a c^{3} d^{6} e^{2} + 165 \, a^{2} c^{2} d^{4} e^{4} - 50 \, a^{3} c d^{2} e^{6} + 8 \, a^{4} e^{8} + 420 \, {\left(2 \, c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{3} + 63 \, {\left(11 \, c^{4} d^{6} e^{2} + 18 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} x^{2} + 18 \, {\left(8 \, c^{4} d^{7} e + 53 \, a c^{3} d^{5} e^{3} + 10 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{24 \, {\left(a^{2} c^{5} d^{14} e^{2} - 5 \, a^{3} c^{4} d^{12} e^{4} + 10 \, a^{4} c^{3} d^{10} e^{6} - 10 \, a^{5} c^{2} d^{8} e^{8} + 5 \, a^{6} c d^{6} e^{10} - a^{7} d^{4} e^{12} + {\left(c^{7} d^{12} e^{4} - 5 \, a c^{6} d^{10} e^{6} + 10 \, a^{2} c^{5} d^{8} e^{8} - 10 \, a^{3} c^{4} d^{6} e^{10} + 5 \, a^{4} c^{3} d^{4} e^{12} - a^{5} c^{2} d^{2} e^{14}\right)} x^{6} + 2 \, {\left(2 \, c^{7} d^{13} e^{3} - 9 \, a c^{6} d^{11} e^{5} + 15 \, a^{2} c^{5} d^{9} e^{7} - 10 \, a^{3} c^{4} d^{7} e^{9} + 3 \, a^{5} c^{2} d^{3} e^{13} - a^{6} c d e^{15}\right)} x^{5} + {\left(6 \, c^{7} d^{14} e^{2} - 22 \, a c^{6} d^{12} e^{4} + 21 \, a^{2} c^{5} d^{10} e^{6} + 15 \, a^{3} c^{4} d^{8} e^{8} - 40 \, a^{4} c^{3} d^{6} e^{10} + 24 \, a^{5} c^{2} d^{4} e^{12} - 3 \, a^{6} c d^{2} e^{14} - a^{7} e^{16}\right)} x^{4} + 4 \, {\left(c^{7} d^{15} e - 2 \, a c^{6} d^{13} e^{3} - 4 \, a^{2} c^{5} d^{11} e^{5} + 15 \, a^{3} c^{4} d^{9} e^{7} - 15 \, a^{4} c^{3} d^{7} e^{9} + 4 \, a^{5} c^{2} d^{5} e^{11} + 2 \, a^{6} c d^{3} e^{13} - a^{7} d e^{15}\right)} x^{3} + {\left(c^{7} d^{16} + 3 \, a c^{6} d^{14} e^{2} - 24 \, a^{2} c^{5} d^{12} e^{4} + 40 \, a^{3} c^{4} d^{10} e^{6} - 15 \, a^{4} c^{3} d^{8} e^{8} - 21 \, a^{5} c^{2} d^{6} e^{10} + 22 \, a^{6} c d^{4} e^{12} - 6 \, a^{7} d^{2} e^{14}\right)} x^{2} + 2 \, {\left(a c^{6} d^{15} e - 3 \, a^{2} c^{5} d^{13} e^{3} + 10 \, a^{4} c^{3} d^{9} e^{7} - 15 \, a^{5} c^{2} d^{7} e^{9} + 9 \, a^{6} c d^{5} e^{11} - 2 \, a^{7} d^{3} e^{13}\right)} x\right)}}\right]"," ",0,"[1/48*(315*(c^5*d^5*e^5*x^6 + a^2*c^3*d^7*e^3 + 2*(2*c^5*d^6*e^4 + a*c^4*d^4*e^6)*x^5 + (6*c^5*d^7*e^3 + 8*a*c^4*d^5*e^5 + a^2*c^3*d^3*e^7)*x^4 + 4*(c^5*d^8*e^2 + 3*a*c^4*d^6*e^4 + a^2*c^3*d^4*e^6)*x^3 + (c^5*d^9*e + 8*a*c^4*d^7*e^3 + 6*a^2*c^3*d^5*e^5)*x^2 + 2*(a*c^4*d^8*e^2 + 2*a^2*c^3*d^6*e^4)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(315*c^4*d^4*e^4*x^4 - 16*c^4*d^8 + 208*a*c^3*d^6*e^2 + 165*a^2*c^2*d^4*e^4 - 50*a^3*c*d^2*e^6 + 8*a^4*e^8 + 420*(2*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^3 + 63*(11*c^4*d^6*e^2 + 18*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + 18*(8*c^4*d^7*e + 53*a*c^3*d^5*e^3 + 10*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^5*d^14*e^2 - 5*a^3*c^4*d^12*e^4 + 10*a^4*c^3*d^10*e^6 - 10*a^5*c^2*d^8*e^8 + 5*a^6*c*d^6*e^10 - a^7*d^4*e^12 + (c^7*d^12*e^4 - 5*a*c^6*d^10*e^6 + 10*a^2*c^5*d^8*e^8 - 10*a^3*c^4*d^6*e^10 + 5*a^4*c^3*d^4*e^12 - a^5*c^2*d^2*e^14)*x^6 + 2*(2*c^7*d^13*e^3 - 9*a*c^6*d^11*e^5 + 15*a^2*c^5*d^9*e^7 - 10*a^3*c^4*d^7*e^9 + 3*a^5*c^2*d^3*e^13 - a^6*c*d*e^15)*x^5 + (6*c^7*d^14*e^2 - 22*a*c^6*d^12*e^4 + 21*a^2*c^5*d^10*e^6 + 15*a^3*c^4*d^8*e^8 - 40*a^4*c^3*d^6*e^10 + 24*a^5*c^2*d^4*e^12 - 3*a^6*c*d^2*e^14 - a^7*e^16)*x^4 + 4*(c^7*d^15*e - 2*a*c^6*d^13*e^3 - 4*a^2*c^5*d^11*e^5 + 15*a^3*c^4*d^9*e^7 - 15*a^4*c^3*d^7*e^9 + 4*a^5*c^2*d^5*e^11 + 2*a^6*c*d^3*e^13 - a^7*d*e^15)*x^3 + (c^7*d^16 + 3*a*c^6*d^14*e^2 - 24*a^2*c^5*d^12*e^4 + 40*a^3*c^4*d^10*e^6 - 15*a^4*c^3*d^8*e^8 - 21*a^5*c^2*d^6*e^10 + 22*a^6*c*d^4*e^12 - 6*a^7*d^2*e^14)*x^2 + 2*(a*c^6*d^15*e - 3*a^2*c^5*d^13*e^3 + 10*a^4*c^3*d^9*e^7 - 15*a^5*c^2*d^7*e^9 + 9*a^6*c*d^5*e^11 - 2*a^7*d^3*e^13)*x), 1/24*(315*(c^5*d^5*e^5*x^6 + a^2*c^3*d^7*e^3 + 2*(2*c^5*d^6*e^4 + a*c^4*d^4*e^6)*x^5 + (6*c^5*d^7*e^3 + 8*a*c^4*d^5*e^5 + a^2*c^3*d^3*e^7)*x^4 + 4*(c^5*d^8*e^2 + 3*a*c^4*d^6*e^4 + a^2*c^3*d^4*e^6)*x^3 + (c^5*d^9*e + 8*a*c^4*d^7*e^3 + 6*a^2*c^3*d^5*e^5)*x^2 + 2*(a*c^4*d^8*e^2 + 2*a^2*c^3*d^6*e^4)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (315*c^4*d^4*e^4*x^4 - 16*c^4*d^8 + 208*a*c^3*d^6*e^2 + 165*a^2*c^2*d^4*e^4 - 50*a^3*c*d^2*e^6 + 8*a^4*e^8 + 420*(2*c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^3 + 63*(11*c^4*d^6*e^2 + 18*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*x^2 + 18*(8*c^4*d^7*e + 53*a*c^3*d^5*e^3 + 10*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^5*d^14*e^2 - 5*a^3*c^4*d^12*e^4 + 10*a^4*c^3*d^10*e^6 - 10*a^5*c^2*d^8*e^8 + 5*a^6*c*d^6*e^10 - a^7*d^4*e^12 + (c^7*d^12*e^4 - 5*a*c^6*d^10*e^6 + 10*a^2*c^5*d^8*e^8 - 10*a^3*c^4*d^6*e^10 + 5*a^4*c^3*d^4*e^12 - a^5*c^2*d^2*e^14)*x^6 + 2*(2*c^7*d^13*e^3 - 9*a*c^6*d^11*e^5 + 15*a^2*c^5*d^9*e^7 - 10*a^3*c^4*d^7*e^9 + 3*a^5*c^2*d^3*e^13 - a^6*c*d*e^15)*x^5 + (6*c^7*d^14*e^2 - 22*a*c^6*d^12*e^4 + 21*a^2*c^5*d^10*e^6 + 15*a^3*c^4*d^8*e^8 - 40*a^4*c^3*d^6*e^10 + 24*a^5*c^2*d^4*e^12 - 3*a^6*c*d^2*e^14 - a^7*e^16)*x^4 + 4*(c^7*d^15*e - 2*a*c^6*d^13*e^3 - 4*a^2*c^5*d^11*e^5 + 15*a^3*c^4*d^9*e^7 - 15*a^4*c^3*d^7*e^9 + 4*a^5*c^2*d^5*e^11 + 2*a^6*c*d^3*e^13 - a^7*d*e^15)*x^3 + (c^7*d^16 + 3*a*c^6*d^14*e^2 - 24*a^2*c^5*d^12*e^4 + 40*a^3*c^4*d^10*e^6 - 15*a^4*c^3*d^8*e^8 - 21*a^5*c^2*d^6*e^10 + 22*a^6*c*d^4*e^12 - 6*a^7*d^2*e^14)*x^2 + 2*(a*c^6*d^15*e - 3*a^2*c^5*d^13*e^3 + 10*a^4*c^3*d^9*e^7 - 15*a^5*c^2*d^7*e^9 + 9*a^6*c*d^5*e^11 - 2*a^7*d^3*e^13)*x)]","B",0
2079,1,3078,0,0.491171," ","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=""fricas"")","\left[\frac{3465 \, {\left(c^{6} d^{6} e^{6} x^{7} + a^{2} c^{4} d^{9} e^{3} + {\left(5 \, c^{6} d^{7} e^{5} + 2 \, a c^{5} d^{5} e^{7}\right)} x^{6} + {\left(10 \, c^{6} d^{8} e^{4} + 10 \, a c^{5} d^{6} e^{6} + a^{2} c^{4} d^{4} e^{8}\right)} x^{5} + 5 \, {\left(2 \, c^{6} d^{9} e^{3} + 4 \, a c^{5} d^{7} e^{5} + a^{2} c^{4} d^{5} e^{7}\right)} x^{4} + 5 \, {\left(c^{6} d^{10} e^{2} + 4 \, a c^{5} d^{8} e^{4} + 2 \, a^{2} c^{4} d^{6} e^{6}\right)} x^{3} + {\left(c^{6} d^{11} e + 10 \, a c^{5} d^{9} e^{3} + 10 \, a^{2} c^{4} d^{7} e^{5}\right)} x^{2} + {\left(2 \, a c^{5} d^{10} e^{2} + 5 \, a^{2} c^{4} d^{8} e^{4}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(3465 \, c^{5} d^{5} e^{5} x^{5} - 128 \, c^{5} d^{10} + 2048 \, a c^{4} d^{8} e^{2} + 2295 \, a^{2} c^{3} d^{6} e^{4} - 1030 \, a^{3} c^{2} d^{4} e^{6} + 328 \, a^{4} c d^{2} e^{8} - 48 \, a^{5} e^{10} + 1155 \, {\left(11 \, c^{5} d^{6} e^{4} + 4 \, a c^{4} d^{4} e^{6}\right)} x^{4} + 231 \, {\left(73 \, c^{5} d^{7} e^{3} + 74 \, a c^{4} d^{5} e^{5} + 3 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 99 \, {\left(93 \, c^{5} d^{8} e^{2} + 232 \, a c^{4} d^{6} e^{4} + 27 \, a^{2} c^{3} d^{4} e^{6} - 2 \, a^{3} c^{2} d^{2} e^{8}\right)} x^{2} + 11 \, {\left(128 \, c^{5} d^{9} e + 1162 \, a c^{4} d^{7} e^{3} + 345 \, a^{2} c^{3} d^{5} e^{5} - 68 \, a^{3} c^{2} d^{3} e^{7} + 8 \, a^{4} c d e^{9}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{384 \, {\left(a^{2} c^{6} d^{17} e^{2} - 6 \, a^{3} c^{5} d^{15} e^{4} + 15 \, a^{4} c^{4} d^{13} e^{6} - 20 \, a^{5} c^{3} d^{11} e^{8} + 15 \, a^{6} c^{2} d^{9} e^{10} - 6 \, a^{7} c d^{7} e^{12} + a^{8} d^{5} e^{14} + {\left(c^{8} d^{14} e^{5} - 6 \, a c^{7} d^{12} e^{7} + 15 \, a^{2} c^{6} d^{10} e^{9} - 20 \, a^{3} c^{5} d^{8} e^{11} + 15 \, a^{4} c^{4} d^{6} e^{13} - 6 \, a^{5} c^{3} d^{4} e^{15} + a^{6} c^{2} d^{2} e^{17}\right)} x^{7} + {\left(5 \, c^{8} d^{15} e^{4} - 28 \, a c^{7} d^{13} e^{6} + 63 \, a^{2} c^{6} d^{11} e^{8} - 70 \, a^{3} c^{5} d^{9} e^{10} + 35 \, a^{4} c^{4} d^{7} e^{12} - 7 \, a^{6} c^{2} d^{3} e^{16} + 2 \, a^{7} c d e^{18}\right)} x^{6} + {\left(10 \, c^{8} d^{16} e^{3} - 50 \, a c^{7} d^{14} e^{5} + 91 \, a^{2} c^{6} d^{12} e^{7} - 56 \, a^{3} c^{5} d^{10} e^{9} - 35 \, a^{4} c^{4} d^{8} e^{11} + 70 \, a^{5} c^{3} d^{6} e^{13} - 35 \, a^{6} c^{2} d^{4} e^{15} + 4 \, a^{7} c d^{2} e^{17} + a^{8} e^{19}\right)} x^{5} + 5 \, {\left(2 \, c^{8} d^{17} e^{2} - 8 \, a c^{7} d^{15} e^{4} + 7 \, a^{2} c^{6} d^{13} e^{6} + 14 \, a^{3} c^{5} d^{11} e^{8} - 35 \, a^{4} c^{4} d^{9} e^{10} + 28 \, a^{5} c^{3} d^{7} e^{12} - 7 \, a^{6} c^{2} d^{5} e^{14} - 2 \, a^{7} c d^{3} e^{16} + a^{8} d e^{18}\right)} x^{4} + 5 \, {\left(c^{8} d^{18} e - 2 \, a c^{7} d^{16} e^{3} - 7 \, a^{2} c^{6} d^{14} e^{5} + 28 \, a^{3} c^{5} d^{12} e^{7} - 35 \, a^{4} c^{4} d^{10} e^{9} + 14 \, a^{5} c^{3} d^{8} e^{11} + 7 \, a^{6} c^{2} d^{6} e^{13} - 8 \, a^{7} c d^{4} e^{15} + 2 \, a^{8} d^{2} e^{17}\right)} x^{3} + {\left(c^{8} d^{19} + 4 \, a c^{7} d^{17} e^{2} - 35 \, a^{2} c^{6} d^{15} e^{4} + 70 \, a^{3} c^{5} d^{13} e^{6} - 35 \, a^{4} c^{4} d^{11} e^{8} - 56 \, a^{5} c^{3} d^{9} e^{10} + 91 \, a^{6} c^{2} d^{7} e^{12} - 50 \, a^{7} c d^{5} e^{14} + 10 \, a^{8} d^{3} e^{16}\right)} x^{2} + {\left(2 \, a c^{7} d^{18} e - 7 \, a^{2} c^{6} d^{16} e^{3} + 35 \, a^{4} c^{4} d^{12} e^{7} - 70 \, a^{5} c^{3} d^{10} e^{9} + 63 \, a^{6} c^{2} d^{8} e^{11} - 28 \, a^{7} c d^{6} e^{13} + 5 \, a^{8} d^{4} e^{15}\right)} x\right)}}, \frac{3465 \, {\left(c^{6} d^{6} e^{6} x^{7} + a^{2} c^{4} d^{9} e^{3} + {\left(5 \, c^{6} d^{7} e^{5} + 2 \, a c^{5} d^{5} e^{7}\right)} x^{6} + {\left(10 \, c^{6} d^{8} e^{4} + 10 \, a c^{5} d^{6} e^{6} + a^{2} c^{4} d^{4} e^{8}\right)} x^{5} + 5 \, {\left(2 \, c^{6} d^{9} e^{3} + 4 \, a c^{5} d^{7} e^{5} + a^{2} c^{4} d^{5} e^{7}\right)} x^{4} + 5 \, {\left(c^{6} d^{10} e^{2} + 4 \, a c^{5} d^{8} e^{4} + 2 \, a^{2} c^{4} d^{6} e^{6}\right)} x^{3} + {\left(c^{6} d^{11} e + 10 \, a c^{5} d^{9} e^{3} + 10 \, a^{2} c^{4} d^{7} e^{5}\right)} x^{2} + {\left(2 \, a c^{5} d^{10} e^{2} + 5 \, a^{2} c^{4} d^{8} e^{4}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(3465 \, c^{5} d^{5} e^{5} x^{5} - 128 \, c^{5} d^{10} + 2048 \, a c^{4} d^{8} e^{2} + 2295 \, a^{2} c^{3} d^{6} e^{4} - 1030 \, a^{3} c^{2} d^{4} e^{6} + 328 \, a^{4} c d^{2} e^{8} - 48 \, a^{5} e^{10} + 1155 \, {\left(11 \, c^{5} d^{6} e^{4} + 4 \, a c^{4} d^{4} e^{6}\right)} x^{4} + 231 \, {\left(73 \, c^{5} d^{7} e^{3} + 74 \, a c^{4} d^{5} e^{5} + 3 \, a^{2} c^{3} d^{3} e^{7}\right)} x^{3} + 99 \, {\left(93 \, c^{5} d^{8} e^{2} + 232 \, a c^{4} d^{6} e^{4} + 27 \, a^{2} c^{3} d^{4} e^{6} - 2 \, a^{3} c^{2} d^{2} e^{8}\right)} x^{2} + 11 \, {\left(128 \, c^{5} d^{9} e + 1162 \, a c^{4} d^{7} e^{3} + 345 \, a^{2} c^{3} d^{5} e^{5} - 68 \, a^{3} c^{2} d^{3} e^{7} + 8 \, a^{4} c d e^{9}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{192 \, {\left(a^{2} c^{6} d^{17} e^{2} - 6 \, a^{3} c^{5} d^{15} e^{4} + 15 \, a^{4} c^{4} d^{13} e^{6} - 20 \, a^{5} c^{3} d^{11} e^{8} + 15 \, a^{6} c^{2} d^{9} e^{10} - 6 \, a^{7} c d^{7} e^{12} + a^{8} d^{5} e^{14} + {\left(c^{8} d^{14} e^{5} - 6 \, a c^{7} d^{12} e^{7} + 15 \, a^{2} c^{6} d^{10} e^{9} - 20 \, a^{3} c^{5} d^{8} e^{11} + 15 \, a^{4} c^{4} d^{6} e^{13} - 6 \, a^{5} c^{3} d^{4} e^{15} + a^{6} c^{2} d^{2} e^{17}\right)} x^{7} + {\left(5 \, c^{8} d^{15} e^{4} - 28 \, a c^{7} d^{13} e^{6} + 63 \, a^{2} c^{6} d^{11} e^{8} - 70 \, a^{3} c^{5} d^{9} e^{10} + 35 \, a^{4} c^{4} d^{7} e^{12} - 7 \, a^{6} c^{2} d^{3} e^{16} + 2 \, a^{7} c d e^{18}\right)} x^{6} + {\left(10 \, c^{8} d^{16} e^{3} - 50 \, a c^{7} d^{14} e^{5} + 91 \, a^{2} c^{6} d^{12} e^{7} - 56 \, a^{3} c^{5} d^{10} e^{9} - 35 \, a^{4} c^{4} d^{8} e^{11} + 70 \, a^{5} c^{3} d^{6} e^{13} - 35 \, a^{6} c^{2} d^{4} e^{15} + 4 \, a^{7} c d^{2} e^{17} + a^{8} e^{19}\right)} x^{5} + 5 \, {\left(2 \, c^{8} d^{17} e^{2} - 8 \, a c^{7} d^{15} e^{4} + 7 \, a^{2} c^{6} d^{13} e^{6} + 14 \, a^{3} c^{5} d^{11} e^{8} - 35 \, a^{4} c^{4} d^{9} e^{10} + 28 \, a^{5} c^{3} d^{7} e^{12} - 7 \, a^{6} c^{2} d^{5} e^{14} - 2 \, a^{7} c d^{3} e^{16} + a^{8} d e^{18}\right)} x^{4} + 5 \, {\left(c^{8} d^{18} e - 2 \, a c^{7} d^{16} e^{3} - 7 \, a^{2} c^{6} d^{14} e^{5} + 28 \, a^{3} c^{5} d^{12} e^{7} - 35 \, a^{4} c^{4} d^{10} e^{9} + 14 \, a^{5} c^{3} d^{8} e^{11} + 7 \, a^{6} c^{2} d^{6} e^{13} - 8 \, a^{7} c d^{4} e^{15} + 2 \, a^{8} d^{2} e^{17}\right)} x^{3} + {\left(c^{8} d^{19} + 4 \, a c^{7} d^{17} e^{2} - 35 \, a^{2} c^{6} d^{15} e^{4} + 70 \, a^{3} c^{5} d^{13} e^{6} - 35 \, a^{4} c^{4} d^{11} e^{8} - 56 \, a^{5} c^{3} d^{9} e^{10} + 91 \, a^{6} c^{2} d^{7} e^{12} - 50 \, a^{7} c d^{5} e^{14} + 10 \, a^{8} d^{3} e^{16}\right)} x^{2} + {\left(2 \, a c^{7} d^{18} e - 7 \, a^{2} c^{6} d^{16} e^{3} + 35 \, a^{4} c^{4} d^{12} e^{7} - 70 \, a^{5} c^{3} d^{10} e^{9} + 63 \, a^{6} c^{2} d^{8} e^{11} - 28 \, a^{7} c d^{6} e^{13} + 5 \, a^{8} d^{4} e^{15}\right)} x\right)}}\right]"," ",0,"[1/384*(3465*(c^6*d^6*e^6*x^7 + a^2*c^4*d^9*e^3 + (5*c^6*d^7*e^5 + 2*a*c^5*d^5*e^7)*x^6 + (10*c^6*d^8*e^4 + 10*a*c^5*d^6*e^6 + a^2*c^4*d^4*e^8)*x^5 + 5*(2*c^6*d^9*e^3 + 4*a*c^5*d^7*e^5 + a^2*c^4*d^5*e^7)*x^4 + 5*(c^6*d^10*e^2 + 4*a*c^5*d^8*e^4 + 2*a^2*c^4*d^6*e^6)*x^3 + (c^6*d^11*e + 10*a*c^5*d^9*e^3 + 10*a^2*c^4*d^7*e^5)*x^2 + (2*a*c^5*d^10*e^2 + 5*a^2*c^4*d^8*e^4)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(3465*c^5*d^5*e^5*x^5 - 128*c^5*d^10 + 2048*a*c^4*d^8*e^2 + 2295*a^2*c^3*d^6*e^4 - 1030*a^3*c^2*d^4*e^6 + 328*a^4*c*d^2*e^8 - 48*a^5*e^10 + 1155*(11*c^5*d^6*e^4 + 4*a*c^4*d^4*e^6)*x^4 + 231*(73*c^5*d^7*e^3 + 74*a*c^4*d^5*e^5 + 3*a^2*c^3*d^3*e^7)*x^3 + 99*(93*c^5*d^8*e^2 + 232*a*c^4*d^6*e^4 + 27*a^2*c^3*d^4*e^6 - 2*a^3*c^2*d^2*e^8)*x^2 + 11*(128*c^5*d^9*e + 1162*a*c^4*d^7*e^3 + 345*a^2*c^3*d^5*e^5 - 68*a^3*c^2*d^3*e^7 + 8*a^4*c*d*e^9)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^6*d^17*e^2 - 6*a^3*c^5*d^15*e^4 + 15*a^4*c^4*d^13*e^6 - 20*a^5*c^3*d^11*e^8 + 15*a^6*c^2*d^9*e^10 - 6*a^7*c*d^7*e^12 + a^8*d^5*e^14 + (c^8*d^14*e^5 - 6*a*c^7*d^12*e^7 + 15*a^2*c^6*d^10*e^9 - 20*a^3*c^5*d^8*e^11 + 15*a^4*c^4*d^6*e^13 - 6*a^5*c^3*d^4*e^15 + a^6*c^2*d^2*e^17)*x^7 + (5*c^8*d^15*e^4 - 28*a*c^7*d^13*e^6 + 63*a^2*c^6*d^11*e^8 - 70*a^3*c^5*d^9*e^10 + 35*a^4*c^4*d^7*e^12 - 7*a^6*c^2*d^3*e^16 + 2*a^7*c*d*e^18)*x^6 + (10*c^8*d^16*e^3 - 50*a*c^7*d^14*e^5 + 91*a^2*c^6*d^12*e^7 - 56*a^3*c^5*d^10*e^9 - 35*a^4*c^4*d^8*e^11 + 70*a^5*c^3*d^6*e^13 - 35*a^6*c^2*d^4*e^15 + 4*a^7*c*d^2*e^17 + a^8*e^19)*x^5 + 5*(2*c^8*d^17*e^2 - 8*a*c^7*d^15*e^4 + 7*a^2*c^6*d^13*e^6 + 14*a^3*c^5*d^11*e^8 - 35*a^4*c^4*d^9*e^10 + 28*a^5*c^3*d^7*e^12 - 7*a^6*c^2*d^5*e^14 - 2*a^7*c*d^3*e^16 + a^8*d*e^18)*x^4 + 5*(c^8*d^18*e - 2*a*c^7*d^16*e^3 - 7*a^2*c^6*d^14*e^5 + 28*a^3*c^5*d^12*e^7 - 35*a^4*c^4*d^10*e^9 + 14*a^5*c^3*d^8*e^11 + 7*a^6*c^2*d^6*e^13 - 8*a^7*c*d^4*e^15 + 2*a^8*d^2*e^17)*x^3 + (c^8*d^19 + 4*a*c^7*d^17*e^2 - 35*a^2*c^6*d^15*e^4 + 70*a^3*c^5*d^13*e^6 - 35*a^4*c^4*d^11*e^8 - 56*a^5*c^3*d^9*e^10 + 91*a^6*c^2*d^7*e^12 - 50*a^7*c*d^5*e^14 + 10*a^8*d^3*e^16)*x^2 + (2*a*c^7*d^18*e - 7*a^2*c^6*d^16*e^3 + 35*a^4*c^4*d^12*e^7 - 70*a^5*c^3*d^10*e^9 + 63*a^6*c^2*d^8*e^11 - 28*a^7*c*d^6*e^13 + 5*a^8*d^4*e^15)*x), 1/192*(3465*(c^6*d^6*e^6*x^7 + a^2*c^4*d^9*e^3 + (5*c^6*d^7*e^5 + 2*a*c^5*d^5*e^7)*x^6 + (10*c^6*d^8*e^4 + 10*a*c^5*d^6*e^6 + a^2*c^4*d^4*e^8)*x^5 + 5*(2*c^6*d^9*e^3 + 4*a*c^5*d^7*e^5 + a^2*c^4*d^5*e^7)*x^4 + 5*(c^6*d^10*e^2 + 4*a*c^5*d^8*e^4 + 2*a^2*c^4*d^6*e^6)*x^3 + (c^6*d^11*e + 10*a*c^5*d^9*e^3 + 10*a^2*c^4*d^7*e^5)*x^2 + (2*a*c^5*d^10*e^2 + 5*a^2*c^4*d^8*e^4)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (3465*c^5*d^5*e^5*x^5 - 128*c^5*d^10 + 2048*a*c^4*d^8*e^2 + 2295*a^2*c^3*d^6*e^4 - 1030*a^3*c^2*d^4*e^6 + 328*a^4*c*d^2*e^8 - 48*a^5*e^10 + 1155*(11*c^5*d^6*e^4 + 4*a*c^4*d^4*e^6)*x^4 + 231*(73*c^5*d^7*e^3 + 74*a*c^4*d^5*e^5 + 3*a^2*c^3*d^3*e^7)*x^3 + 99*(93*c^5*d^8*e^2 + 232*a*c^4*d^6*e^4 + 27*a^2*c^3*d^4*e^6 - 2*a^3*c^2*d^2*e^8)*x^2 + 11*(128*c^5*d^9*e + 1162*a*c^4*d^7*e^3 + 345*a^2*c^3*d^5*e^5 - 68*a^3*c^2*d^3*e^7 + 8*a^4*c*d*e^9)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^6*d^17*e^2 - 6*a^3*c^5*d^15*e^4 + 15*a^4*c^4*d^13*e^6 - 20*a^5*c^3*d^11*e^8 + 15*a^6*c^2*d^9*e^10 - 6*a^7*c*d^7*e^12 + a^8*d^5*e^14 + (c^8*d^14*e^5 - 6*a*c^7*d^12*e^7 + 15*a^2*c^6*d^10*e^9 - 20*a^3*c^5*d^8*e^11 + 15*a^4*c^4*d^6*e^13 - 6*a^5*c^3*d^4*e^15 + a^6*c^2*d^2*e^17)*x^7 + (5*c^8*d^15*e^4 - 28*a*c^7*d^13*e^6 + 63*a^2*c^6*d^11*e^8 - 70*a^3*c^5*d^9*e^10 + 35*a^4*c^4*d^7*e^12 - 7*a^6*c^2*d^3*e^16 + 2*a^7*c*d*e^18)*x^6 + (10*c^8*d^16*e^3 - 50*a*c^7*d^14*e^5 + 91*a^2*c^6*d^12*e^7 - 56*a^3*c^5*d^10*e^9 - 35*a^4*c^4*d^8*e^11 + 70*a^5*c^3*d^6*e^13 - 35*a^6*c^2*d^4*e^15 + 4*a^7*c*d^2*e^17 + a^8*e^19)*x^5 + 5*(2*c^8*d^17*e^2 - 8*a*c^7*d^15*e^4 + 7*a^2*c^6*d^13*e^6 + 14*a^3*c^5*d^11*e^8 - 35*a^4*c^4*d^9*e^10 + 28*a^5*c^3*d^7*e^12 - 7*a^6*c^2*d^5*e^14 - 2*a^7*c*d^3*e^16 + a^8*d*e^18)*x^4 + 5*(c^8*d^18*e - 2*a*c^7*d^16*e^3 - 7*a^2*c^6*d^14*e^5 + 28*a^3*c^5*d^12*e^7 - 35*a^4*c^4*d^10*e^9 + 14*a^5*c^3*d^8*e^11 + 7*a^6*c^2*d^6*e^13 - 8*a^7*c*d^4*e^15 + 2*a^8*d^2*e^17)*x^3 + (c^8*d^19 + 4*a*c^7*d^17*e^2 - 35*a^2*c^6*d^15*e^4 + 70*a^3*c^5*d^13*e^6 - 35*a^4*c^4*d^11*e^8 - 56*a^5*c^3*d^9*e^10 + 91*a^6*c^2*d^7*e^12 - 50*a^7*c*d^5*e^14 + 10*a^8*d^3*e^16)*x^2 + (2*a*c^7*d^18*e - 7*a^2*c^6*d^16*e^3 + 35*a^4*c^4*d^12*e^7 - 70*a^5*c^3*d^10*e^9 + 63*a^6*c^2*d^8*e^11 - 28*a^7*c*d^6*e^13 + 5*a^8*d^4*e^15)*x)]","B",0
2080,1,3874,0,0.540149," ","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=""fricas"")","\left[\frac{45045 \, {\left(c^{7} d^{7} e^{7} x^{8} + a^{2} c^{5} d^{11} e^{3} + 2 \, {\left(3 \, c^{7} d^{8} e^{6} + a c^{6} d^{6} e^{8}\right)} x^{7} + {\left(15 \, c^{7} d^{9} e^{5} + 12 \, a c^{6} d^{7} e^{7} + a^{2} c^{5} d^{5} e^{9}\right)} x^{6} + 2 \, {\left(10 \, c^{7} d^{10} e^{4} + 15 \, a c^{6} d^{8} e^{6} + 3 \, a^{2} c^{5} d^{6} e^{8}\right)} x^{5} + 5 \, {\left(3 \, c^{7} d^{11} e^{3} + 8 \, a c^{6} d^{9} e^{5} + 3 \, a^{2} c^{5} d^{7} e^{7}\right)} x^{4} + 2 \, {\left(3 \, c^{7} d^{12} e^{2} + 15 \, a c^{6} d^{10} e^{4} + 10 \, a^{2} c^{5} d^{8} e^{6}\right)} x^{3} + {\left(c^{7} d^{13} e + 12 \, a c^{6} d^{11} e^{3} + 15 \, a^{2} c^{5} d^{9} e^{5}\right)} x^{2} + 2 \, {\left(a c^{6} d^{12} e^{2} + 3 \, a^{2} c^{5} d^{10} e^{4}\right)} x\right)} \sqrt{-\frac{e}{c d^{2} - a e^{2}}} \log\left(-\frac{c d e^{2} x^{2} + 2 \, a e^{3} x - c d^{3} + 2 \, a d e^{2} + 2 \, \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{-\frac{e}{c d^{2} - a e^{2}}}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(45045 \, c^{6} d^{6} e^{6} x^{6} - 1280 \, c^{6} d^{12} + 24320 \, a c^{5} d^{10} e^{2} + 35595 \, a^{2} c^{4} d^{8} e^{4} - 21070 \, a^{3} c^{3} d^{6} e^{6} + 10024 \, a^{4} c^{2} d^{4} e^{8} - 2928 \, a^{5} c d^{2} e^{10} + 384 \, a^{6} e^{12} + 30030 \, {\left(7 \, c^{6} d^{7} e^{5} + 2 \, a c^{5} d^{5} e^{7}\right)} x^{5} + 3003 \, {\left(128 \, c^{6} d^{8} e^{4} + 94 \, a c^{5} d^{6} e^{6} + 3 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{4} + 858 \, {\left(395 \, c^{6} d^{9} e^{3} + 607 \, a c^{5} d^{7} e^{5} + 51 \, a^{2} c^{4} d^{5} e^{7} - 3 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{3} + 143 \, {\left(965 \, c^{6} d^{10} e^{2} + 3250 \, a c^{5} d^{8} e^{4} + 588 \, a^{2} c^{4} d^{6} e^{6} - 86 \, a^{3} c^{3} d^{4} e^{8} + 8 \, a^{4} c^{2} d^{2} e^{10}\right)} x^{2} + 26 \, {\left(640 \, c^{6} d^{11} e + 7415 \, a c^{5} d^{9} e^{3} + 3045 \, a^{2} c^{4} d^{7} e^{5} - 889 \, a^{3} c^{3} d^{5} e^{7} + 208 \, a^{4} c^{2} d^{3} e^{9} - 24 \, a^{5} c d e^{11}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{3840 \, {\left(a^{2} c^{7} d^{20} e^{2} - 7 \, a^{3} c^{6} d^{18} e^{4} + 21 \, a^{4} c^{5} d^{16} e^{6} - 35 \, a^{5} c^{4} d^{14} e^{8} + 35 \, a^{6} c^{3} d^{12} e^{10} - 21 \, a^{7} c^{2} d^{10} e^{12} + 7 \, a^{8} c d^{8} e^{14} - a^{9} d^{6} e^{16} + {\left(c^{9} d^{16} e^{6} - 7 \, a c^{8} d^{14} e^{8} + 21 \, a^{2} c^{7} d^{12} e^{10} - 35 \, a^{3} c^{6} d^{10} e^{12} + 35 \, a^{4} c^{5} d^{8} e^{14} - 21 \, a^{5} c^{4} d^{6} e^{16} + 7 \, a^{6} c^{3} d^{4} e^{18} - a^{7} c^{2} d^{2} e^{20}\right)} x^{8} + 2 \, {\left(3 \, c^{9} d^{17} e^{5} - 20 \, a c^{8} d^{15} e^{7} + 56 \, a^{2} c^{7} d^{13} e^{9} - 84 \, a^{3} c^{6} d^{11} e^{11} + 70 \, a^{4} c^{5} d^{9} e^{13} - 28 \, a^{5} c^{4} d^{7} e^{15} + 4 \, a^{7} c^{2} d^{3} e^{19} - a^{8} c d e^{21}\right)} x^{7} + {\left(15 \, c^{9} d^{18} e^{4} - 93 \, a c^{8} d^{16} e^{6} + 232 \, a^{2} c^{7} d^{14} e^{8} - 280 \, a^{3} c^{6} d^{12} e^{10} + 126 \, a^{4} c^{5} d^{10} e^{12} + 70 \, a^{5} c^{4} d^{8} e^{14} - 112 \, a^{6} c^{3} d^{6} e^{16} + 48 \, a^{7} c^{2} d^{4} e^{18} - 5 \, a^{8} c d^{2} e^{20} - a^{9} e^{22}\right)} x^{6} + 2 \, {\left(10 \, c^{9} d^{19} e^{3} - 55 \, a c^{8} d^{17} e^{5} + 108 \, a^{2} c^{7} d^{15} e^{7} - 56 \, a^{3} c^{6} d^{13} e^{9} - 112 \, a^{4} c^{5} d^{11} e^{11} + 210 \, a^{5} c^{4} d^{9} e^{13} - 140 \, a^{6} c^{3} d^{7} e^{15} + 32 \, a^{7} c^{2} d^{5} e^{17} + 6 \, a^{8} c d^{3} e^{19} - 3 \, a^{9} d e^{21}\right)} x^{5} + 5 \, {\left(3 \, c^{9} d^{20} e^{2} - 13 \, a c^{8} d^{18} e^{4} + 10 \, a^{2} c^{7} d^{16} e^{6} + 42 \, a^{3} c^{6} d^{14} e^{8} - 112 \, a^{4} c^{5} d^{12} e^{10} + 112 \, a^{5} c^{4} d^{10} e^{12} - 42 \, a^{6} c^{3} d^{8} e^{14} - 10 \, a^{7} c^{2} d^{6} e^{16} + 13 \, a^{8} c d^{4} e^{18} - 3 \, a^{9} d^{2} e^{20}\right)} x^{4} + 2 \, {\left(3 \, c^{9} d^{21} e - 6 \, a c^{8} d^{19} e^{3} - 32 \, a^{2} c^{7} d^{17} e^{5} + 140 \, a^{3} c^{6} d^{15} e^{7} - 210 \, a^{4} c^{5} d^{13} e^{9} + 112 \, a^{5} c^{4} d^{11} e^{11} + 56 \, a^{6} c^{3} d^{9} e^{13} - 108 \, a^{7} c^{2} d^{7} e^{15} + 55 \, a^{8} c d^{5} e^{17} - 10 \, a^{9} d^{3} e^{19}\right)} x^{3} + {\left(c^{9} d^{22} + 5 \, a c^{8} d^{20} e^{2} - 48 \, a^{2} c^{7} d^{18} e^{4} + 112 \, a^{3} c^{6} d^{16} e^{6} - 70 \, a^{4} c^{5} d^{14} e^{8} - 126 \, a^{5} c^{4} d^{12} e^{10} + 280 \, a^{6} c^{3} d^{10} e^{12} - 232 \, a^{7} c^{2} d^{8} e^{14} + 93 \, a^{8} c d^{6} e^{16} - 15 \, a^{9} d^{4} e^{18}\right)} x^{2} + 2 \, {\left(a c^{8} d^{21} e - 4 \, a^{2} c^{7} d^{19} e^{3} + 28 \, a^{4} c^{5} d^{15} e^{7} - 70 \, a^{5} c^{4} d^{13} e^{9} + 84 \, a^{6} c^{3} d^{11} e^{11} - 56 \, a^{7} c^{2} d^{9} e^{13} + 20 \, a^{8} c d^{7} e^{15} - 3 \, a^{9} d^{5} e^{17}\right)} x\right)}}, \frac{45045 \, {\left(c^{7} d^{7} e^{7} x^{8} + a^{2} c^{5} d^{11} e^{3} + 2 \, {\left(3 \, c^{7} d^{8} e^{6} + a c^{6} d^{6} e^{8}\right)} x^{7} + {\left(15 \, c^{7} d^{9} e^{5} + 12 \, a c^{6} d^{7} e^{7} + a^{2} c^{5} d^{5} e^{9}\right)} x^{6} + 2 \, {\left(10 \, c^{7} d^{10} e^{4} + 15 \, a c^{6} d^{8} e^{6} + 3 \, a^{2} c^{5} d^{6} e^{8}\right)} x^{5} + 5 \, {\left(3 \, c^{7} d^{11} e^{3} + 8 \, a c^{6} d^{9} e^{5} + 3 \, a^{2} c^{5} d^{7} e^{7}\right)} x^{4} + 2 \, {\left(3 \, c^{7} d^{12} e^{2} + 15 \, a c^{6} d^{10} e^{4} + 10 \, a^{2} c^{5} d^{8} e^{6}\right)} x^{3} + {\left(c^{7} d^{13} e + 12 \, a c^{6} d^{11} e^{3} + 15 \, a^{2} c^{5} d^{9} e^{5}\right)} x^{2} + 2 \, {\left(a c^{6} d^{12} e^{2} + 3 \, a^{2} c^{5} d^{10} e^{4}\right)} x\right)} \sqrt{\frac{e}{c d^{2} - a e^{2}}} \arctan\left(-\frac{\sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} {\left(c d^{2} - a e^{2}\right)} \sqrt{e x + d} \sqrt{\frac{e}{c d^{2} - a e^{2}}}}{c d e^{2} x^{2} + a d e^{2} + {\left(c d^{2} e + a e^{3}\right)} x}\right) + {\left(45045 \, c^{6} d^{6} e^{6} x^{6} - 1280 \, c^{6} d^{12} + 24320 \, a c^{5} d^{10} e^{2} + 35595 \, a^{2} c^{4} d^{8} e^{4} - 21070 \, a^{3} c^{3} d^{6} e^{6} + 10024 \, a^{4} c^{2} d^{4} e^{8} - 2928 \, a^{5} c d^{2} e^{10} + 384 \, a^{6} e^{12} + 30030 \, {\left(7 \, c^{6} d^{7} e^{5} + 2 \, a c^{5} d^{5} e^{7}\right)} x^{5} + 3003 \, {\left(128 \, c^{6} d^{8} e^{4} + 94 \, a c^{5} d^{6} e^{6} + 3 \, a^{2} c^{4} d^{4} e^{8}\right)} x^{4} + 858 \, {\left(395 \, c^{6} d^{9} e^{3} + 607 \, a c^{5} d^{7} e^{5} + 51 \, a^{2} c^{4} d^{5} e^{7} - 3 \, a^{3} c^{3} d^{3} e^{9}\right)} x^{3} + 143 \, {\left(965 \, c^{6} d^{10} e^{2} + 3250 \, a c^{5} d^{8} e^{4} + 588 \, a^{2} c^{4} d^{6} e^{6} - 86 \, a^{3} c^{3} d^{4} e^{8} + 8 \, a^{4} c^{2} d^{2} e^{10}\right)} x^{2} + 26 \, {\left(640 \, c^{6} d^{11} e + 7415 \, a c^{5} d^{9} e^{3} + 3045 \, a^{2} c^{4} d^{7} e^{5} - 889 \, a^{3} c^{3} d^{5} e^{7} + 208 \, a^{4} c^{2} d^{3} e^{9} - 24 \, a^{5} c d e^{11}\right)} x\right)} \sqrt{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x} \sqrt{e x + d}}{1920 \, {\left(a^{2} c^{7} d^{20} e^{2} - 7 \, a^{3} c^{6} d^{18} e^{4} + 21 \, a^{4} c^{5} d^{16} e^{6} - 35 \, a^{5} c^{4} d^{14} e^{8} + 35 \, a^{6} c^{3} d^{12} e^{10} - 21 \, a^{7} c^{2} d^{10} e^{12} + 7 \, a^{8} c d^{8} e^{14} - a^{9} d^{6} e^{16} + {\left(c^{9} d^{16} e^{6} - 7 \, a c^{8} d^{14} e^{8} + 21 \, a^{2} c^{7} d^{12} e^{10} - 35 \, a^{3} c^{6} d^{10} e^{12} + 35 \, a^{4} c^{5} d^{8} e^{14} - 21 \, a^{5} c^{4} d^{6} e^{16} + 7 \, a^{6} c^{3} d^{4} e^{18} - a^{7} c^{2} d^{2} e^{20}\right)} x^{8} + 2 \, {\left(3 \, c^{9} d^{17} e^{5} - 20 \, a c^{8} d^{15} e^{7} + 56 \, a^{2} c^{7} d^{13} e^{9} - 84 \, a^{3} c^{6} d^{11} e^{11} + 70 \, a^{4} c^{5} d^{9} e^{13} - 28 \, a^{5} c^{4} d^{7} e^{15} + 4 \, a^{7} c^{2} d^{3} e^{19} - a^{8} c d e^{21}\right)} x^{7} + {\left(15 \, c^{9} d^{18} e^{4} - 93 \, a c^{8} d^{16} e^{6} + 232 \, a^{2} c^{7} d^{14} e^{8} - 280 \, a^{3} c^{6} d^{12} e^{10} + 126 \, a^{4} c^{5} d^{10} e^{12} + 70 \, a^{5} c^{4} d^{8} e^{14} - 112 \, a^{6} c^{3} d^{6} e^{16} + 48 \, a^{7} c^{2} d^{4} e^{18} - 5 \, a^{8} c d^{2} e^{20} - a^{9} e^{22}\right)} x^{6} + 2 \, {\left(10 \, c^{9} d^{19} e^{3} - 55 \, a c^{8} d^{17} e^{5} + 108 \, a^{2} c^{7} d^{15} e^{7} - 56 \, a^{3} c^{6} d^{13} e^{9} - 112 \, a^{4} c^{5} d^{11} e^{11} + 210 \, a^{5} c^{4} d^{9} e^{13} - 140 \, a^{6} c^{3} d^{7} e^{15} + 32 \, a^{7} c^{2} d^{5} e^{17} + 6 \, a^{8} c d^{3} e^{19} - 3 \, a^{9} d e^{21}\right)} x^{5} + 5 \, {\left(3 \, c^{9} d^{20} e^{2} - 13 \, a c^{8} d^{18} e^{4} + 10 \, a^{2} c^{7} d^{16} e^{6} + 42 \, a^{3} c^{6} d^{14} e^{8} - 112 \, a^{4} c^{5} d^{12} e^{10} + 112 \, a^{5} c^{4} d^{10} e^{12} - 42 \, a^{6} c^{3} d^{8} e^{14} - 10 \, a^{7} c^{2} d^{6} e^{16} + 13 \, a^{8} c d^{4} e^{18} - 3 \, a^{9} d^{2} e^{20}\right)} x^{4} + 2 \, {\left(3 \, c^{9} d^{21} e - 6 \, a c^{8} d^{19} e^{3} - 32 \, a^{2} c^{7} d^{17} e^{5} + 140 \, a^{3} c^{6} d^{15} e^{7} - 210 \, a^{4} c^{5} d^{13} e^{9} + 112 \, a^{5} c^{4} d^{11} e^{11} + 56 \, a^{6} c^{3} d^{9} e^{13} - 108 \, a^{7} c^{2} d^{7} e^{15} + 55 \, a^{8} c d^{5} e^{17} - 10 \, a^{9} d^{3} e^{19}\right)} x^{3} + {\left(c^{9} d^{22} + 5 \, a c^{8} d^{20} e^{2} - 48 \, a^{2} c^{7} d^{18} e^{4} + 112 \, a^{3} c^{6} d^{16} e^{6} - 70 \, a^{4} c^{5} d^{14} e^{8} - 126 \, a^{5} c^{4} d^{12} e^{10} + 280 \, a^{6} c^{3} d^{10} e^{12} - 232 \, a^{7} c^{2} d^{8} e^{14} + 93 \, a^{8} c d^{6} e^{16} - 15 \, a^{9} d^{4} e^{18}\right)} x^{2} + 2 \, {\left(a c^{8} d^{21} e - 4 \, a^{2} c^{7} d^{19} e^{3} + 28 \, a^{4} c^{5} d^{15} e^{7} - 70 \, a^{5} c^{4} d^{13} e^{9} + 84 \, a^{6} c^{3} d^{11} e^{11} - 56 \, a^{7} c^{2} d^{9} e^{13} + 20 \, a^{8} c d^{7} e^{15} - 3 \, a^{9} d^{5} e^{17}\right)} x\right)}}\right]"," ",0,"[1/3840*(45045*(c^7*d^7*e^7*x^8 + a^2*c^5*d^11*e^3 + 2*(3*c^7*d^8*e^6 + a*c^6*d^6*e^8)*x^7 + (15*c^7*d^9*e^5 + 12*a*c^6*d^7*e^7 + a^2*c^5*d^5*e^9)*x^6 + 2*(10*c^7*d^10*e^4 + 15*a*c^6*d^8*e^6 + 3*a^2*c^5*d^6*e^8)*x^5 + 5*(3*c^7*d^11*e^3 + 8*a*c^6*d^9*e^5 + 3*a^2*c^5*d^7*e^7)*x^4 + 2*(3*c^7*d^12*e^2 + 15*a*c^6*d^10*e^4 + 10*a^2*c^5*d^8*e^6)*x^3 + (c^7*d^13*e + 12*a*c^6*d^11*e^3 + 15*a^2*c^5*d^9*e^5)*x^2 + 2*(a*c^6*d^12*e^2 + 3*a^2*c^5*d^10*e^4)*x)*sqrt(-e/(c*d^2 - a*e^2))*log(-(c*d*e^2*x^2 + 2*a*e^3*x - c*d^3 + 2*a*d*e^2 + 2*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(-e/(c*d^2 - a*e^2)))/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(45045*c^6*d^6*e^6*x^6 - 1280*c^6*d^12 + 24320*a*c^5*d^10*e^2 + 35595*a^2*c^4*d^8*e^4 - 21070*a^3*c^3*d^6*e^6 + 10024*a^4*c^2*d^4*e^8 - 2928*a^5*c*d^2*e^10 + 384*a^6*e^12 + 30030*(7*c^6*d^7*e^5 + 2*a*c^5*d^5*e^7)*x^5 + 3003*(128*c^6*d^8*e^4 + 94*a*c^5*d^6*e^6 + 3*a^2*c^4*d^4*e^8)*x^4 + 858*(395*c^6*d^9*e^3 + 607*a*c^5*d^7*e^5 + 51*a^2*c^4*d^5*e^7 - 3*a^3*c^3*d^3*e^9)*x^3 + 143*(965*c^6*d^10*e^2 + 3250*a*c^5*d^8*e^4 + 588*a^2*c^4*d^6*e^6 - 86*a^3*c^3*d^4*e^8 + 8*a^4*c^2*d^2*e^10)*x^2 + 26*(640*c^6*d^11*e + 7415*a*c^5*d^9*e^3 + 3045*a^2*c^4*d^7*e^5 - 889*a^3*c^3*d^5*e^7 + 208*a^4*c^2*d^3*e^9 - 24*a^5*c*d*e^11)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^7*d^20*e^2 - 7*a^3*c^6*d^18*e^4 + 21*a^4*c^5*d^16*e^6 - 35*a^5*c^4*d^14*e^8 + 35*a^6*c^3*d^12*e^10 - 21*a^7*c^2*d^10*e^12 + 7*a^8*c*d^8*e^14 - a^9*d^6*e^16 + (c^9*d^16*e^6 - 7*a*c^8*d^14*e^8 + 21*a^2*c^7*d^12*e^10 - 35*a^3*c^6*d^10*e^12 + 35*a^4*c^5*d^8*e^14 - 21*a^5*c^4*d^6*e^16 + 7*a^6*c^3*d^4*e^18 - a^7*c^2*d^2*e^20)*x^8 + 2*(3*c^9*d^17*e^5 - 20*a*c^8*d^15*e^7 + 56*a^2*c^7*d^13*e^9 - 84*a^3*c^6*d^11*e^11 + 70*a^4*c^5*d^9*e^13 - 28*a^5*c^4*d^7*e^15 + 4*a^7*c^2*d^3*e^19 - a^8*c*d*e^21)*x^7 + (15*c^9*d^18*e^4 - 93*a*c^8*d^16*e^6 + 232*a^2*c^7*d^14*e^8 - 280*a^3*c^6*d^12*e^10 + 126*a^4*c^5*d^10*e^12 + 70*a^5*c^4*d^8*e^14 - 112*a^6*c^3*d^6*e^16 + 48*a^7*c^2*d^4*e^18 - 5*a^8*c*d^2*e^20 - a^9*e^22)*x^6 + 2*(10*c^9*d^19*e^3 - 55*a*c^8*d^17*e^5 + 108*a^2*c^7*d^15*e^7 - 56*a^3*c^6*d^13*e^9 - 112*a^4*c^5*d^11*e^11 + 210*a^5*c^4*d^9*e^13 - 140*a^6*c^3*d^7*e^15 + 32*a^7*c^2*d^5*e^17 + 6*a^8*c*d^3*e^19 - 3*a^9*d*e^21)*x^5 + 5*(3*c^9*d^20*e^2 - 13*a*c^8*d^18*e^4 + 10*a^2*c^7*d^16*e^6 + 42*a^3*c^6*d^14*e^8 - 112*a^4*c^5*d^12*e^10 + 112*a^5*c^4*d^10*e^12 - 42*a^6*c^3*d^8*e^14 - 10*a^7*c^2*d^6*e^16 + 13*a^8*c*d^4*e^18 - 3*a^9*d^2*e^20)*x^4 + 2*(3*c^9*d^21*e - 6*a*c^8*d^19*e^3 - 32*a^2*c^7*d^17*e^5 + 140*a^3*c^6*d^15*e^7 - 210*a^4*c^5*d^13*e^9 + 112*a^5*c^4*d^11*e^11 + 56*a^6*c^3*d^9*e^13 - 108*a^7*c^2*d^7*e^15 + 55*a^8*c*d^5*e^17 - 10*a^9*d^3*e^19)*x^3 + (c^9*d^22 + 5*a*c^8*d^20*e^2 - 48*a^2*c^7*d^18*e^4 + 112*a^3*c^6*d^16*e^6 - 70*a^4*c^5*d^14*e^8 - 126*a^5*c^4*d^12*e^10 + 280*a^6*c^3*d^10*e^12 - 232*a^7*c^2*d^8*e^14 + 93*a^8*c*d^6*e^16 - 15*a^9*d^4*e^18)*x^2 + 2*(a*c^8*d^21*e - 4*a^2*c^7*d^19*e^3 + 28*a^4*c^5*d^15*e^7 - 70*a^5*c^4*d^13*e^9 + 84*a^6*c^3*d^11*e^11 - 56*a^7*c^2*d^9*e^13 + 20*a^8*c*d^7*e^15 - 3*a^9*d^5*e^17)*x), 1/1920*(45045*(c^7*d^7*e^7*x^8 + a^2*c^5*d^11*e^3 + 2*(3*c^7*d^8*e^6 + a*c^6*d^6*e^8)*x^7 + (15*c^7*d^9*e^5 + 12*a*c^6*d^7*e^7 + a^2*c^5*d^5*e^9)*x^6 + 2*(10*c^7*d^10*e^4 + 15*a*c^6*d^8*e^6 + 3*a^2*c^5*d^6*e^8)*x^5 + 5*(3*c^7*d^11*e^3 + 8*a*c^6*d^9*e^5 + 3*a^2*c^5*d^7*e^7)*x^4 + 2*(3*c^7*d^12*e^2 + 15*a*c^6*d^10*e^4 + 10*a^2*c^5*d^8*e^6)*x^3 + (c^7*d^13*e + 12*a*c^6*d^11*e^3 + 15*a^2*c^5*d^9*e^5)*x^2 + 2*(a*c^6*d^12*e^2 + 3*a^2*c^5*d^10*e^4)*x)*sqrt(e/(c*d^2 - a*e^2))*arctan(-sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d^2 - a*e^2)*sqrt(e*x + d)*sqrt(e/(c*d^2 - a*e^2))/(c*d*e^2*x^2 + a*d*e^2 + (c*d^2*e + a*e^3)*x)) + (45045*c^6*d^6*e^6*x^6 - 1280*c^6*d^12 + 24320*a*c^5*d^10*e^2 + 35595*a^2*c^4*d^8*e^4 - 21070*a^3*c^3*d^6*e^6 + 10024*a^4*c^2*d^4*e^8 - 2928*a^5*c*d^2*e^10 + 384*a^6*e^12 + 30030*(7*c^6*d^7*e^5 + 2*a*c^5*d^5*e^7)*x^5 + 3003*(128*c^6*d^8*e^4 + 94*a*c^5*d^6*e^6 + 3*a^2*c^4*d^4*e^8)*x^4 + 858*(395*c^6*d^9*e^3 + 607*a*c^5*d^7*e^5 + 51*a^2*c^4*d^5*e^7 - 3*a^3*c^3*d^3*e^9)*x^3 + 143*(965*c^6*d^10*e^2 + 3250*a*c^5*d^8*e^4 + 588*a^2*c^4*d^6*e^6 - 86*a^3*c^3*d^4*e^8 + 8*a^4*c^2*d^2*e^10)*x^2 + 26*(640*c^6*d^11*e + 7415*a*c^5*d^9*e^3 + 3045*a^2*c^4*d^7*e^5 - 889*a^3*c^3*d^5*e^7 + 208*a^4*c^2*d^3*e^9 - 24*a^5*c*d*e^11)*x)*sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*sqrt(e*x + d))/(a^2*c^7*d^20*e^2 - 7*a^3*c^6*d^18*e^4 + 21*a^4*c^5*d^16*e^6 - 35*a^5*c^4*d^14*e^8 + 35*a^6*c^3*d^12*e^10 - 21*a^7*c^2*d^10*e^12 + 7*a^8*c*d^8*e^14 - a^9*d^6*e^16 + (c^9*d^16*e^6 - 7*a*c^8*d^14*e^8 + 21*a^2*c^7*d^12*e^10 - 35*a^3*c^6*d^10*e^12 + 35*a^4*c^5*d^8*e^14 - 21*a^5*c^4*d^6*e^16 + 7*a^6*c^3*d^4*e^18 - a^7*c^2*d^2*e^20)*x^8 + 2*(3*c^9*d^17*e^5 - 20*a*c^8*d^15*e^7 + 56*a^2*c^7*d^13*e^9 - 84*a^3*c^6*d^11*e^11 + 70*a^4*c^5*d^9*e^13 - 28*a^5*c^4*d^7*e^15 + 4*a^7*c^2*d^3*e^19 - a^8*c*d*e^21)*x^7 + (15*c^9*d^18*e^4 - 93*a*c^8*d^16*e^6 + 232*a^2*c^7*d^14*e^8 - 280*a^3*c^6*d^12*e^10 + 126*a^4*c^5*d^10*e^12 + 70*a^5*c^4*d^8*e^14 - 112*a^6*c^3*d^6*e^16 + 48*a^7*c^2*d^4*e^18 - 5*a^8*c*d^2*e^20 - a^9*e^22)*x^6 + 2*(10*c^9*d^19*e^3 - 55*a*c^8*d^17*e^5 + 108*a^2*c^7*d^15*e^7 - 56*a^3*c^6*d^13*e^9 - 112*a^4*c^5*d^11*e^11 + 210*a^5*c^4*d^9*e^13 - 140*a^6*c^3*d^7*e^15 + 32*a^7*c^2*d^5*e^17 + 6*a^8*c*d^3*e^19 - 3*a^9*d*e^21)*x^5 + 5*(3*c^9*d^20*e^2 - 13*a*c^8*d^18*e^4 + 10*a^2*c^7*d^16*e^6 + 42*a^3*c^6*d^14*e^8 - 112*a^4*c^5*d^12*e^10 + 112*a^5*c^4*d^10*e^12 - 42*a^6*c^3*d^8*e^14 - 10*a^7*c^2*d^6*e^16 + 13*a^8*c*d^4*e^18 - 3*a^9*d^2*e^20)*x^4 + 2*(3*c^9*d^21*e - 6*a*c^8*d^19*e^3 - 32*a^2*c^7*d^17*e^5 + 140*a^3*c^6*d^15*e^7 - 210*a^4*c^5*d^13*e^9 + 112*a^5*c^4*d^11*e^11 + 56*a^6*c^3*d^9*e^13 - 108*a^7*c^2*d^7*e^15 + 55*a^8*c*d^5*e^17 - 10*a^9*d^3*e^19)*x^3 + (c^9*d^22 + 5*a*c^8*d^20*e^2 - 48*a^2*c^7*d^18*e^4 + 112*a^3*c^6*d^16*e^6 - 70*a^4*c^5*d^14*e^8 - 126*a^5*c^4*d^12*e^10 + 280*a^6*c^3*d^10*e^12 - 232*a^7*c^2*d^8*e^14 + 93*a^8*c*d^6*e^16 - 15*a^9*d^4*e^18)*x^2 + 2*(a*c^8*d^21*e - 4*a^2*c^7*d^19*e^3 + 28*a^4*c^5*d^15*e^7 - 70*a^5*c^4*d^13*e^9 + 84*a^6*c^3*d^11*e^11 - 56*a^7*c^2*d^9*e^13 + 20*a^8*c*d^7*e^15 - 3*a^9*d^5*e^17)*x)]","B",0
2081,1,144,0,0.423913," ","integrate(1/(e*x+d)^(1/2)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(-\frac{e^{2} x^{2} - 2 \, d e x + 2 \, \sqrt{2} \sqrt{-e^{2} x^{2} + d^{2}} \sqrt{e x + d} \sqrt{d} - 3 \, d^{2}}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, \sqrt{d} e}, -\frac{\sqrt{2} \sqrt{-\frac{1}{d}} \arctan\left(\frac{\sqrt{2} \sqrt{-e^{2} x^{2} + d^{2}} \sqrt{e x + d} d \sqrt{-\frac{1}{d}}}{e^{2} x^{2} - d^{2}}\right)}{e}\right]"," ",0,"[1/2*sqrt(2)*log(-(e^2*x^2 - 2*d*e*x + 2*sqrt(2)*sqrt(-e^2*x^2 + d^2)*sqrt(e*x + d)*sqrt(d) - 3*d^2)/(e^2*x^2 + 2*d*e*x + d^2))/(sqrt(d)*e), -sqrt(2)*sqrt(-1/d)*arctan(sqrt(2)*sqrt(-e^2*x^2 + d^2)*sqrt(e*x + d)*d*sqrt(-1/d)/(e^2*x^2 - d^2))/e]","A",0
2082,1,147,0,0.422547," ","integrate(1/(e*x-d)^(1/2)/(-e^2*x^2+d^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-\frac{1}{d}} \log\left(-\frac{e^{2} x^{2} + 2 \, d e x - 2 \, \sqrt{2} \sqrt{-e^{2} x^{2} + d^{2}} \sqrt{e x - d} d \sqrt{-\frac{1}{d}} - 3 \, d^{2}}{e^{2} x^{2} - 2 \, d e x + d^{2}}\right)}{2 \, e}, \frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-e^{2} x^{2} + d^{2}} \sqrt{e x - d} \sqrt{d}}{e^{2} x^{2} - d^{2}}\right)}{\sqrt{d} e}\right]"," ",0,"[1/2*sqrt(2)*sqrt(-1/d)*log(-(e^2*x^2 + 2*d*e*x - 2*sqrt(2)*sqrt(-e^2*x^2 + d^2)*sqrt(e*x - d)*d*sqrt(-1/d) - 3*d^2)/(e^2*x^2 - 2*d*e*x + d^2))/e, sqrt(2)*arctan(sqrt(2)*sqrt(-e^2*x^2 + d^2)*sqrt(e*x - d)*sqrt(d)/(e^2*x^2 - d^2))/(sqrt(d)*e)]","A",0
2083,0,0,0,0.587062," ","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=""fricas"")","{\rm integral}\left(\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}}, x\right)"," ",0,"integral((e*x + d)^(2/3)/sqrt(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x), x)","F",0
2084,1,1156,0,0.427788," ","integrate((e*x+d)^m*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} d^{4} e^{6} m^{3} - 6 \, c^{3} d^{10} + 42 \, a c^{2} d^{8} e^{2} - 126 \, a^{2} c d^{6} e^{4} + 210 \, a^{3} d^{4} e^{6} + {\left(c^{3} d^{3} e^{7} m^{3} + 15 \, c^{3} d^{3} e^{7} m^{2} + 74 \, c^{3} d^{3} e^{7} m + 120 \, c^{3} d^{3} e^{7}\right)} x^{7} + {\left(420 \, c^{3} d^{4} e^{6} + 420 \, a c^{2} d^{2} e^{8} + {\left(4 \, c^{3} d^{4} e^{6} + 3 \, a c^{2} d^{2} e^{8}\right)} m^{3} + 3 \, {\left(19 \, c^{3} d^{4} e^{6} + 16 \, a c^{2} d^{2} e^{8}\right)} m^{2} + {\left(269 \, c^{3} d^{4} e^{6} + 249 \, a c^{2} d^{2} e^{8}\right)} m\right)} x^{6} + 3 \, {\left(168 \, c^{3} d^{5} e^{5} + 504 \, a c^{2} d^{3} e^{7} + 168 \, a^{2} c d e^{9} + {\left(2 \, c^{3} d^{5} e^{5} + 4 \, a c^{2} d^{3} e^{7} + a^{2} c d e^{9}\right)} m^{3} + {\left(26 \, c^{3} d^{5} e^{5} + 62 \, a c^{2} d^{3} e^{7} + 17 \, a^{2} c d e^{9}\right)} m^{2} + 2 \, {\left(57 \, c^{3} d^{5} e^{5} + 155 \, a c^{2} d^{3} e^{7} + 47 \, a^{2} c d e^{9}\right)} m\right)} x^{5} + {\left(210 \, c^{3} d^{6} e^{4} + 1890 \, a c^{2} d^{4} e^{6} + 1890 \, a^{2} c d^{2} e^{8} + 210 \, a^{3} e^{10} + {\left(4 \, c^{3} d^{6} e^{4} + 18 \, a c^{2} d^{4} e^{6} + 12 \, a^{2} c d^{2} e^{8} + a^{3} e^{10}\right)} m^{3} + 3 \, {\left(14 \, c^{3} d^{6} e^{4} + 88 \, a c^{2} d^{4} e^{6} + 67 \, a^{2} c d^{2} e^{8} + 6 \, a^{3} e^{10}\right)} m^{2} + {\left(158 \, c^{3} d^{6} e^{4} + 1236 \, a c^{2} d^{4} e^{6} + 1089 \, a^{2} c d^{2} e^{8} + 107 \, a^{3} e^{10}\right)} m\right)} x^{4} + {\left(840 \, a c^{2} d^{5} e^{5} + 2520 \, a^{2} c d^{3} e^{7} + 840 \, a^{3} d e^{9} + {\left(c^{3} d^{7} e^{3} + 12 \, a c^{2} d^{5} e^{5} + 18 \, a^{2} c d^{3} e^{7} + 4 \, a^{3} d e^{9}\right)} m^{3} + 3 \, {\left(c^{3} d^{7} e^{3} + 52 \, a c^{2} d^{5} e^{5} + 98 \, a^{2} c d^{3} e^{7} + 24 \, a^{3} d e^{9}\right)} m^{2} + 2 \, {\left(c^{3} d^{7} e^{3} + 312 \, a c^{2} d^{5} e^{5} + 768 \, a^{2} c d^{3} e^{7} + 214 \, a^{3} d e^{9}\right)} m\right)} x^{3} - 3 \, {\left(a^{2} c d^{6} e^{4} - 6 \, a^{3} d^{4} e^{6}\right)} m^{2} + 3 \, {\left(420 \, a^{2} c d^{4} e^{6} + 420 \, a^{3} d^{2} e^{8} + {\left(a c^{2} d^{6} e^{4} + 4 \, a^{2} c d^{4} e^{6} + 2 \, a^{3} d^{2} e^{8}\right)} m^{3} - {\left(c^{3} d^{8} e^{2} - 8 \, a c^{2} d^{6} e^{4} - 62 \, a^{2} c d^{4} e^{6} - 36 \, a^{3} d^{2} e^{8}\right)} m^{2} - {\left(c^{3} d^{8} e^{2} - 7 \, a c^{2} d^{6} e^{4} - 298 \, a^{2} c d^{4} e^{6} - 214 \, a^{3} d^{2} e^{8}\right)} m\right)} x^{2} + {\left(6 \, a c^{2} d^{8} e^{2} - 39 \, a^{2} c d^{6} e^{4} + 107 \, a^{3} d^{4} e^{6}\right)} m + {\left(840 \, a^{3} d^{3} e^{7} + {\left(3 \, a^{2} c d^{5} e^{5} + 4 \, a^{3} d^{3} e^{7}\right)} m^{3} - 3 \, {\left(2 \, a c^{2} d^{7} e^{3} - 13 \, a^{2} c d^{5} e^{5} - 24 \, a^{3} d^{3} e^{7}\right)} m^{2} + 2 \, {\left(3 \, c^{3} d^{9} e - 21 \, a c^{2} d^{7} e^{3} + 63 \, a^{2} c d^{5} e^{5} + 214 \, a^{3} d^{3} e^{7}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{4} m^{4} + 22 \, e^{4} m^{3} + 179 \, e^{4} m^{2} + 638 \, e^{4} m + 840 \, e^{4}}"," ",0,"(a^3*d^4*e^6*m^3 - 6*c^3*d^10 + 42*a*c^2*d^8*e^2 - 126*a^2*c*d^6*e^4 + 210*a^3*d^4*e^6 + (c^3*d^3*e^7*m^3 + 15*c^3*d^3*e^7*m^2 + 74*c^3*d^3*e^7*m + 120*c^3*d^3*e^7)*x^7 + (420*c^3*d^4*e^6 + 420*a*c^2*d^2*e^8 + (4*c^3*d^4*e^6 + 3*a*c^2*d^2*e^8)*m^3 + 3*(19*c^3*d^4*e^6 + 16*a*c^2*d^2*e^8)*m^2 + (269*c^3*d^4*e^6 + 249*a*c^2*d^2*e^8)*m)*x^6 + 3*(168*c^3*d^5*e^5 + 504*a*c^2*d^3*e^7 + 168*a^2*c*d*e^9 + (2*c^3*d^5*e^5 + 4*a*c^2*d^3*e^7 + a^2*c*d*e^9)*m^3 + (26*c^3*d^5*e^5 + 62*a*c^2*d^3*e^7 + 17*a^2*c*d*e^9)*m^2 + 2*(57*c^3*d^5*e^5 + 155*a*c^2*d^3*e^7 + 47*a^2*c*d*e^9)*m)*x^5 + (210*c^3*d^6*e^4 + 1890*a*c^2*d^4*e^6 + 1890*a^2*c*d^2*e^8 + 210*a^3*e^10 + (4*c^3*d^6*e^4 + 18*a*c^2*d^4*e^6 + 12*a^2*c*d^2*e^8 + a^3*e^10)*m^3 + 3*(14*c^3*d^6*e^4 + 88*a*c^2*d^4*e^6 + 67*a^2*c*d^2*e^8 + 6*a^3*e^10)*m^2 + (158*c^3*d^6*e^4 + 1236*a*c^2*d^4*e^6 + 1089*a^2*c*d^2*e^8 + 107*a^3*e^10)*m)*x^4 + (840*a*c^2*d^5*e^5 + 2520*a^2*c*d^3*e^7 + 840*a^3*d*e^9 + (c^3*d^7*e^3 + 12*a*c^2*d^5*e^5 + 18*a^2*c*d^3*e^7 + 4*a^3*d*e^9)*m^3 + 3*(c^3*d^7*e^3 + 52*a*c^2*d^5*e^5 + 98*a^2*c*d^3*e^7 + 24*a^3*d*e^9)*m^2 + 2*(c^3*d^7*e^3 + 312*a*c^2*d^5*e^5 + 768*a^2*c*d^3*e^7 + 214*a^3*d*e^9)*m)*x^3 - 3*(a^2*c*d^6*e^4 - 6*a^3*d^4*e^6)*m^2 + 3*(420*a^2*c*d^4*e^6 + 420*a^3*d^2*e^8 + (a*c^2*d^6*e^4 + 4*a^2*c*d^4*e^6 + 2*a^3*d^2*e^8)*m^3 - (c^3*d^8*e^2 - 8*a*c^2*d^6*e^4 - 62*a^2*c*d^4*e^6 - 36*a^3*d^2*e^8)*m^2 - (c^3*d^8*e^2 - 7*a*c^2*d^6*e^4 - 298*a^2*c*d^4*e^6 - 214*a^3*d^2*e^8)*m)*x^2 + (6*a*c^2*d^8*e^2 - 39*a^2*c*d^6*e^4 + 107*a^3*d^4*e^6)*m + (840*a^3*d^3*e^7 + (3*a^2*c*d^5*e^5 + 4*a^3*d^3*e^7)*m^3 - 3*(2*a*c^2*d^7*e^3 - 13*a^2*c*d^5*e^5 - 24*a^3*d^3*e^7)*m^2 + 2*(3*c^3*d^9*e - 21*a*c^2*d^7*e^3 + 63*a^2*c*d^5*e^5 + 214*a^3*d^3*e^7)*m)*x)*(e*x + d)^m/(e^4*m^4 + 22*e^4*m^3 + 179*e^4*m^2 + 638*e^4*m + 840*e^4)","B",0
2085,1,479,0,0.421927," ","integrate((e*x+d)^m*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} d^{3} e^{4} m^{2} + 2 \, c^{2} d^{7} - 10 \, a c d^{5} e^{2} + 20 \, a^{2} d^{3} e^{4} + {\left(c^{2} d^{2} e^{5} m^{2} + 7 \, c^{2} d^{2} e^{5} m + 12 \, c^{2} d^{2} e^{5}\right)} x^{5} + {\left(30 \, c^{2} d^{3} e^{4} + 30 \, a c d e^{6} + {\left(3 \, c^{2} d^{3} e^{4} + 2 \, a c d e^{6}\right)} m^{2} + {\left(19 \, c^{2} d^{3} e^{4} + 16 \, a c d e^{6}\right)} m\right)} x^{4} + {\left(20 \, c^{2} d^{4} e^{3} + 80 \, a c d^{2} e^{5} + 20 \, a^{2} e^{7} + {\left(3 \, c^{2} d^{4} e^{3} + 6 \, a c d^{2} e^{5} + a^{2} e^{7}\right)} m^{2} + {\left(15 \, c^{2} d^{4} e^{3} + 46 \, a c d^{2} e^{5} + 9 \, a^{2} e^{7}\right)} m\right)} x^{3} + {\left(60 \, a c d^{3} e^{4} + 60 \, a^{2} d e^{6} + {\left(c^{2} d^{5} e^{2} + 6 \, a c d^{3} e^{4} + 3 \, a^{2} d e^{6}\right)} m^{2} + {\left(c^{2} d^{5} e^{2} + 42 \, a c d^{3} e^{4} + 27 \, a^{2} d e^{6}\right)} m\right)} x^{2} - {\left(2 \, a c d^{5} e^{2} - 9 \, a^{2} d^{3} e^{4}\right)} m + {\left(60 \, a^{2} d^{2} e^{5} + {\left(2 \, a c d^{4} e^{3} + 3 \, a^{2} d^{2} e^{5}\right)} m^{2} - {\left(2 \, c^{2} d^{6} e - 10 \, a c d^{4} e^{3} - 27 \, a^{2} d^{2} e^{5}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{3} m^{3} + 12 \, e^{3} m^{2} + 47 \, e^{3} m + 60 \, e^{3}}"," ",0,"(a^2*d^3*e^4*m^2 + 2*c^2*d^7 - 10*a*c*d^5*e^2 + 20*a^2*d^3*e^4 + (c^2*d^2*e^5*m^2 + 7*c^2*d^2*e^5*m + 12*c^2*d^2*e^5)*x^5 + (30*c^2*d^3*e^4 + 30*a*c*d*e^6 + (3*c^2*d^3*e^4 + 2*a*c*d*e^6)*m^2 + (19*c^2*d^3*e^4 + 16*a*c*d*e^6)*m)*x^4 + (20*c^2*d^4*e^3 + 80*a*c*d^2*e^5 + 20*a^2*e^7 + (3*c^2*d^4*e^3 + 6*a*c*d^2*e^5 + a^2*e^7)*m^2 + (15*c^2*d^4*e^3 + 46*a*c*d^2*e^5 + 9*a^2*e^7)*m)*x^3 + (60*a*c*d^3*e^4 + 60*a^2*d*e^6 + (c^2*d^5*e^2 + 6*a*c*d^3*e^4 + 3*a^2*d*e^6)*m^2 + (c^2*d^5*e^2 + 42*a*c*d^3*e^4 + 27*a^2*d*e^6)*m)*x^2 - (2*a*c*d^5*e^2 - 9*a^2*d^3*e^4)*m + (60*a^2*d^2*e^5 + (2*a*c*d^4*e^3 + 3*a^2*d^2*e^5)*m^2 - (2*c^2*d^6*e - 10*a*c*d^4*e^3 - 27*a^2*d^2*e^5)*m)*x)*(e*x + d)^m/(e^3*m^3 + 12*e^3*m^2 + 47*e^3*m + 60*e^3)","B",0
2086,1,136,0,0.434052," ","integrate((e*x+d)^m*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","\frac{{\left(a d^{2} e^{2} m - c d^{4} + 3 \, a d^{2} e^{2} + {\left(c d e^{3} m + 2 \, c d e^{3}\right)} x^{3} + {\left(3 \, c d^{2} e^{2} + 3 \, a e^{4} + {\left(2 \, c d^{2} e^{2} + a e^{4}\right)} m\right)} x^{2} + {\left(6 \, a d e^{3} + {\left(c d^{3} e + 2 \, a d e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{2} m^{2} + 5 \, e^{2} m + 6 \, e^{2}}"," ",0,"(a*d^2*e^2*m - c*d^4 + 3*a*d^2*e^2 + (c*d*e^3*m + 2*c*d*e^3)*x^3 + (3*c*d^2*e^2 + 3*a*e^4 + (2*c*d^2*e^2 + a*e^4)*m)*x^2 + (6*a*d*e^3 + (c*d^3*e + 2*a*d*e^3)*m)*x)*(e*x + d)^m/(e^2*m^2 + 5*e^2*m + 6*e^2)","B",0
2087,0,0,0,0.422532," ","integrate((e*x+d)^m/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x}, x\right)"," ",0,"integral((e*x + d)^m/(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x), x)","F",0
2088,0,0,0,0.434578," ","integrate((e*x+d)^m/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c^{2} d^{2} e^{2} x^{4} + a^{2} d^{2} e^{2} + 2 \, {\left(c^{2} d^{3} e + a c d e^{3}\right)} x^{3} + {\left(c^{2} d^{4} + 4 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} x^{2} + 2 \, {\left(a c d^{3} e + a^{2} d e^{3}\right)} x}, x\right)"," ",0,"integral((e*x + d)^m/(c^2*d^2*e^2*x^4 + a^2*d^2*e^2 + 2*(c^2*d^3*e + a*c*d*e^3)*x^3 + (c^2*d^4 + 4*a*c*d^2*e^2 + a^2*e^4)*x^2 + 2*(a*c*d^3*e + a^2*d*e^3)*x), x)","F",0
2089,0,0,0,0.444713," ","integrate((e*x+d)^m/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c^{3} d^{3} e^{3} x^{6} + a^{3} d^{3} e^{3} + 3 \, {\left(c^{3} d^{4} e^{2} + a c^{2} d^{2} e^{4}\right)} x^{5} + 3 \, {\left(c^{3} d^{5} e + 3 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} x^{4} + {\left(c^{3} d^{6} + 9 \, a c^{2} d^{4} e^{2} + 9 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} x^{3} + 3 \, {\left(a c^{2} d^{5} e + 3 \, a^{2} c d^{3} e^{3} + a^{3} d e^{5}\right)} x^{2} + 3 \, {\left(a^{2} c d^{4} e^{2} + a^{3} d^{2} e^{4}\right)} x}, x\right)"," ",0,"integral((e*x + d)^m/(c^3*d^3*e^3*x^6 + a^3*d^3*e^3 + 3*(c^3*d^4*e^2 + a*c^2*d^2*e^4)*x^5 + 3*(c^3*d^5*e + 3*a*c^2*d^3*e^3 + a^2*c*d*e^5)*x^4 + (c^3*d^6 + 9*a*c^2*d^4*e^2 + 9*a^2*c*d^2*e^4 + a^3*e^6)*x^3 + 3*(a*c^2*d^5*e + 3*a^2*c*d^3*e^3 + a^3*d*e^5)*x^2 + 3*(a^2*c*d^4*e^2 + a^3*d^2*e^4)*x), x)","F",0
2090,0,0,0,0.493161," ","integrate((e*x+d)^m/(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c^{4} d^{4} e^{4} x^{8} + a^{4} d^{4} e^{4} + 4 \, {\left(c^{4} d^{5} e^{3} + a c^{3} d^{3} e^{5}\right)} x^{7} + 2 \, {\left(3 \, c^{4} d^{6} e^{2} + 8 \, a c^{3} d^{4} e^{4} + 3 \, a^{2} c^{2} d^{2} e^{6}\right)} x^{6} + 4 \, {\left(c^{4} d^{7} e + 6 \, a c^{3} d^{5} e^{3} + 6 \, a^{2} c^{2} d^{3} e^{5} + a^{3} c d e^{7}\right)} x^{5} + {\left(c^{4} d^{8} + 16 \, a c^{3} d^{6} e^{2} + 36 \, a^{2} c^{2} d^{4} e^{4} + 16 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} x^{4} + 4 \, {\left(a c^{3} d^{7} e + 6 \, a^{2} c^{2} d^{5} e^{3} + 6 \, a^{3} c d^{3} e^{5} + a^{4} d e^{7}\right)} x^{3} + 2 \, {\left(3 \, a^{2} c^{2} d^{6} e^{2} + 8 \, a^{3} c d^{4} e^{4} + 3 \, a^{4} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(a^{3} c d^{5} e^{3} + a^{4} d^{3} e^{5}\right)} x}, x\right)"," ",0,"integral((e*x + d)^m/(c^4*d^4*e^4*x^8 + a^4*d^4*e^4 + 4*(c^4*d^5*e^3 + a*c^3*d^3*e^5)*x^7 + 2*(3*c^4*d^6*e^2 + 8*a*c^3*d^4*e^4 + 3*a^2*c^2*d^2*e^6)*x^6 + 4*(c^4*d^7*e + 6*a*c^3*d^5*e^3 + 6*a^2*c^2*d^3*e^5 + a^3*c*d*e^7)*x^5 + (c^4*d^8 + 16*a*c^3*d^6*e^2 + 36*a^2*c^2*d^4*e^4 + 16*a^3*c*d^2*e^6 + a^4*e^8)*x^4 + 4*(a*c^3*d^7*e + 6*a^2*c^2*d^5*e^3 + 6*a^3*c*d^3*e^5 + a^4*d*e^7)*x^3 + 2*(3*a^2*c^2*d^6*e^2 + 8*a^3*c*d^4*e^4 + 3*a^4*d^2*e^6)*x^2 + 4*(a^3*c*d^5*e^3 + a^4*d^3*e^5)*x), x)","F",0
2091,0,0,0,0.432392," ","integrate((e*x+d)^m*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\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}, x\right)"," ",0,"integral((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^m, x)","F",0
2092,0,0,0,0.431497," ","integrate((e*x+d)^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p, x)","F",0
2093,0,0,0,0.420134," ","integrate((e*x+d)^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p, x)","F",0
2094,0,0,0,0.423527," ","integrate((e*x+d)*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\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}, x\right)"," ",0,"integral((e*x + d)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p, x)","F",0
2095,0,0,0,0.421175," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}, x\right)"," ",0,"integral((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p, x)","F",0
2096,0,0,0,0.421880," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}}{e x + d}, x\right)"," ",0,"integral((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p/(e*x + d), x)","F",0
2097,0,0,0,0.431639," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
2098,0,0,0,0.419090," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
2099,0,0,0,0.441143," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p/((e*x+d)^(2*p)),x, algorithm=""fricas"")","{\rm integral}\left(\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}}, x\right)"," ",0,"integral((c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p/(e*x + d)^(2*p), x)","F",0
2100,0,0,0,0.435384," ","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=""fricas"")","{\rm integral}\left({\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}, x\right)"," ",0,"integral((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
2101,1,92,0,0.449012," ","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=""fricas"")","\frac{{\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)} {\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}}{c d^{2} - a e^{2} + {\left(c d^{2} - a e^{2}\right)} p}"," ",0,"(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^(-2*p - 2)/(c*d^2 - a*e^2 + (c*d^2 - a*e^2)*p)","A",0
2102,1,255,0,0.439982," ","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=""fricas"")","\frac{{\left(c^{2} d^{2} e^{2} x^{3} + 2 \, a c d^{3} e - a^{2} d e^{3} + {\left(3 \, c^{2} d^{3} e + {\left(c^{2} d^{3} e - a c d e^{3}\right)} p\right)} x^{2} + {\left(a c d^{3} e - a^{2} d e^{3}\right)} p + {\left(2 \, c^{2} d^{4} + 2 \, a c d^{2} e^{2} - a^{2} e^{4} + {\left(c^{2} d^{4} - a^{2} e^{4}\right)} p\right)} x\right)} {\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}}{2 \, c^{2} d^{4} - 4 \, a c d^{2} e^{2} + 2 \, a^{2} e^{4} + {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} p^{2} + 3 \, {\left(c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} p}"," ",0,"(c^2*d^2*e^2*x^3 + 2*a*c*d^3*e - a^2*d*e^3 + (3*c^2*d^3*e + (c^2*d^3*e - a*c*d*e^3)*p)*x^2 + (a*c*d^3*e - a^2*d*e^3)*p + (2*c^2*d^4 + 2*a*c*d^2*e^2 - a^2*e^4 + (c^2*d^4 - a^2*e^4)*p)*x)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^(-2*p - 3)/(2*c^2*d^4 - 4*a*c*d^2*e^2 + 2*a^2*e^4 + (c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*p^2 + 3*(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)*p)","A",0
2103,1,580,0,0.450314," ","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=""fricas"")","\frac{{\left(2 \, c^{3} d^{3} e^{3} x^{4} + 6 \, a c^{2} d^{5} e - 6 \, a^{2} c d^{3} e^{3} + 2 \, a^{3} d e^{5} + 2 \, {\left(4 \, c^{3} d^{4} e^{2} + {\left(c^{3} d^{4} e^{2} - a c^{2} d^{2} e^{4}\right)} p\right)} x^{3} + {\left(a c^{2} d^{5} e - 2 \, a^{2} c d^{3} e^{3} + a^{3} d e^{5}\right)} p^{2} + {\left(12 \, c^{3} d^{5} e + {\left(c^{3} d^{5} e - 2 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} p^{2} + {\left(7 \, c^{3} d^{5} e - 8 \, a c^{2} d^{3} e^{3} + a^{2} c d e^{5}\right)} p\right)} x^{2} + {\left(5 \, a c^{2} d^{5} e - 8 \, a^{2} c d^{3} e^{3} + 3 \, a^{3} d e^{5}\right)} p + {\left(6 \, c^{3} d^{6} + 6 \, a c^{2} d^{4} e^{2} - 6 \, a^{2} c d^{2} e^{4} + 2 \, a^{3} e^{6} + {\left(c^{3} d^{6} - a c^{2} d^{4} e^{2} - a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} p^{2} + {\left(5 \, c^{3} d^{6} - a c^{2} d^{4} e^{2} - 7 \, a^{2} c d^{2} e^{4} + 3 \, a^{3} e^{6}\right)} p\right)} x\right)} {\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}}{6 \, c^{3} d^{6} - 18 \, a c^{2} d^{4} e^{2} + 18 \, a^{2} c d^{2} e^{4} - 6 \, a^{3} e^{6} + {\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)} p^{3} + 6 \, {\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)} p^{2} + 11 \, {\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)} p}"," ",0,"(2*c^3*d^3*e^3*x^4 + 6*a*c^2*d^5*e - 6*a^2*c*d^3*e^3 + 2*a^3*d*e^5 + 2*(4*c^3*d^4*e^2 + (c^3*d^4*e^2 - a*c^2*d^2*e^4)*p)*x^3 + (a*c^2*d^5*e - 2*a^2*c*d^3*e^3 + a^3*d*e^5)*p^2 + (12*c^3*d^5*e + (c^3*d^5*e - 2*a*c^2*d^3*e^3 + a^2*c*d*e^5)*p^2 + (7*c^3*d^5*e - 8*a*c^2*d^3*e^3 + a^2*c*d*e^5)*p)*x^2 + (5*a*c^2*d^5*e - 8*a^2*c*d^3*e^3 + 3*a^3*d*e^5)*p + (6*c^3*d^6 + 6*a*c^2*d^4*e^2 - 6*a^2*c*d^2*e^4 + 2*a^3*e^6 + (c^3*d^6 - a*c^2*d^4*e^2 - a^2*c*d^2*e^4 + a^3*e^6)*p^2 + (5*c^3*d^6 - a*c^2*d^4*e^2 - 7*a^2*c*d^2*e^4 + 3*a^3*e^6)*p)*x)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^(-2*p - 4)/(6*c^3*d^6 - 18*a*c^2*d^4*e^2 + 18*a^2*c*d^2*e^4 - 6*a^3*e^6 + (c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*p^3 + 6*(c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*p^2 + 11*(c^3*d^6 - 3*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 - a^3*e^6)*p)","B",0
2104,1,1051,0,0.460001," ","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=""fricas"")","\frac{{\left(6 \, c^{4} d^{4} e^{4} x^{5} + 24 \, a c^{3} d^{7} e - 36 \, a^{2} c^{2} d^{5} e^{3} + 24 \, a^{3} c d^{3} e^{5} - 6 \, a^{4} d e^{7} + 6 \, {\left(5 \, c^{4} d^{5} e^{3} + {\left(c^{4} d^{5} e^{3} - a c^{3} d^{3} e^{5}\right)} p\right)} x^{4} + {\left(a c^{3} d^{7} e - 3 \, a^{2} c^{2} d^{5} e^{3} + 3 \, a^{3} c d^{3} e^{5} - a^{4} d e^{7}\right)} p^{3} + 3 \, {\left(20 \, c^{4} d^{6} e^{2} + {\left(c^{4} d^{6} e^{2} - 2 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} p^{2} + {\left(9 \, c^{4} d^{6} e^{2} - 10 \, a c^{3} d^{4} e^{4} + a^{2} c^{2} d^{2} e^{6}\right)} p\right)} x^{3} + 3 \, {\left(3 \, a c^{3} d^{7} e - 8 \, a^{2} c^{2} d^{5} e^{3} + 7 \, a^{3} c d^{3} e^{5} - 2 \, a^{4} d e^{7}\right)} p^{2} + {\left(60 \, c^{4} d^{7} e + {\left(c^{4} d^{7} e - 3 \, a c^{3} d^{5} e^{3} + 3 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} p^{3} + 3 \, {\left(4 \, c^{4} d^{7} e - 9 \, a c^{3} d^{5} e^{3} + 6 \, a^{2} c^{2} d^{3} e^{5} - a^{3} c d e^{7}\right)} p^{2} + {\left(47 \, c^{4} d^{7} e - 60 \, a c^{3} d^{5} e^{3} + 15 \, a^{2} c^{2} d^{3} e^{5} - 2 \, a^{3} c d e^{7}\right)} p\right)} x^{2} + {\left(26 \, a c^{3} d^{7} e - 57 \, a^{2} c^{2} d^{5} e^{3} + 42 \, a^{3} c d^{3} e^{5} - 11 \, a^{4} d e^{7}\right)} p + {\left(24 \, c^{4} d^{8} + 24 \, a c^{3} d^{6} e^{2} - 36 \, a^{2} c^{2} d^{4} e^{4} + 24 \, a^{3} c d^{2} e^{6} - 6 \, a^{4} e^{8} + {\left(c^{4} d^{8} - 2 \, a c^{3} d^{6} e^{2} + 2 \, a^{3} c d^{2} e^{6} - a^{4} e^{8}\right)} p^{3} + 3 \, {\left(3 \, c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} - 3 \, a^{2} c^{2} d^{4} e^{4} + 6 \, a^{3} c d^{2} e^{6} - 2 \, a^{4} e^{8}\right)} p^{2} + {\left(26 \, c^{4} d^{8} - 10 \, a c^{3} d^{6} e^{2} - 45 \, a^{2} c^{2} d^{4} e^{4} + 40 \, a^{3} c d^{2} e^{6} - 11 \, a^{4} e^{8}\right)} p\right)} x\right)} {\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}}{24 \, c^{4} d^{8} - 96 \, a c^{3} d^{6} e^{2} + 144 \, a^{2} c^{2} d^{4} e^{4} - 96 \, a^{3} c d^{2} e^{6} + 24 \, a^{4} e^{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)} p^{4} + 10 \, {\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)} p^{3} + 35 \, {\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)} p^{2} + 50 \, {\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)} p}"," ",0,"(6*c^4*d^4*e^4*x^5 + 24*a*c^3*d^7*e - 36*a^2*c^2*d^5*e^3 + 24*a^3*c*d^3*e^5 - 6*a^4*d*e^7 + 6*(5*c^4*d^5*e^3 + (c^4*d^5*e^3 - a*c^3*d^3*e^5)*p)*x^4 + (a*c^3*d^7*e - 3*a^2*c^2*d^5*e^3 + 3*a^3*c*d^3*e^5 - a^4*d*e^7)*p^3 + 3*(20*c^4*d^6*e^2 + (c^4*d^6*e^2 - 2*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*p^2 + (9*c^4*d^6*e^2 - 10*a*c^3*d^4*e^4 + a^2*c^2*d^2*e^6)*p)*x^3 + 3*(3*a*c^3*d^7*e - 8*a^2*c^2*d^5*e^3 + 7*a^3*c*d^3*e^5 - 2*a^4*d*e^7)*p^2 + (60*c^4*d^7*e + (c^4*d^7*e - 3*a*c^3*d^5*e^3 + 3*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*p^3 + 3*(4*c^4*d^7*e - 9*a*c^3*d^5*e^3 + 6*a^2*c^2*d^3*e^5 - a^3*c*d*e^7)*p^2 + (47*c^4*d^7*e - 60*a*c^3*d^5*e^3 + 15*a^2*c^2*d^3*e^5 - 2*a^3*c*d*e^7)*p)*x^2 + (26*a*c^3*d^7*e - 57*a^2*c^2*d^5*e^3 + 42*a^3*c*d^3*e^5 - 11*a^4*d*e^7)*p + (24*c^4*d^8 + 24*a*c^3*d^6*e^2 - 36*a^2*c^2*d^4*e^4 + 24*a^3*c*d^2*e^6 - 6*a^4*e^8 + (c^4*d^8 - 2*a*c^3*d^6*e^2 + 2*a^3*c*d^2*e^6 - a^4*e^8)*p^3 + 3*(3*c^4*d^8 - 4*a*c^3*d^6*e^2 - 3*a^2*c^2*d^4*e^4 + 6*a^3*c*d^2*e^6 - 2*a^4*e^8)*p^2 + (26*c^4*d^8 - 10*a*c^3*d^6*e^2 - 45*a^2*c^2*d^4*e^4 + 40*a^3*c*d^2*e^6 - 11*a^4*e^8)*p)*x)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p*(e*x + d)^(-2*p - 5)/(24*c^4*d^8 - 96*a*c^3*d^6*e^2 + 144*a^2*c^2*d^4*e^4 - 96*a^3*c*d^2*e^6 + 24*a^4*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)*p^4 + 10*(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)*p^3 + 35*(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)*p^2 + 50*(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)*p)","B",0
2105,1,57,0,0.425957," ","integrate((e*x+d)^m/((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^m),x, algorithm=""fricas"")","-\frac{{\left(c d x + a e\right)} {\left(e x + d\right)}^{m}}{{\left(c d m - c d\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{m}}"," ",0,"-(c*d*x + a*e)*(e*x + d)^m/((c*d*m - c*d)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^m)","A",0
2106,1,55,0,0.415976," ","integrate((a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^p/((e*x+d)^p),x, algorithm=""fricas"")","\frac{{\left(c d x + a e\right)} {\left(c d e x^{2} + a d e + {\left(c d^{2} + a e^{2}\right)} x\right)}^{p}}{{\left(c d p + c d\right)} {\left(e x + d\right)}^{p}}"," ",0,"(c*d*x + a*e)*(c*d*e*x^2 + a*d*e + (c*d^2 + a*e^2)*x)^p/((c*d*p + c*d)*(e*x + d)^p)","A",0
2107,1,146,0,0.343234," ","integrate((e*x+d)^4*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{4} c + \frac{2}{3} x^{6} e^{3} d c + \frac{1}{6} x^{6} e^{4} b + \frac{6}{5} x^{5} e^{2} d^{2} c + \frac{4}{5} x^{5} e^{3} d b + \frac{1}{5} x^{5} e^{4} a + x^{4} e d^{3} c + \frac{3}{2} x^{4} e^{2} d^{2} b + x^{4} e^{3} d a + \frac{1}{3} x^{3} d^{4} c + \frac{4}{3} x^{3} e d^{3} b + 2 x^{3} e^{2} d^{2} a + \frac{1}{2} x^{2} d^{4} b + 2 x^{2} e d^{3} a + x d^{4} a"," ",0,"1/7*x^7*e^4*c + 2/3*x^6*e^3*d*c + 1/6*x^6*e^4*b + 6/5*x^5*e^2*d^2*c + 4/5*x^5*e^3*d*b + 1/5*x^5*e^4*a + x^4*e*d^3*c + 3/2*x^4*e^2*d^2*b + x^4*e^3*d*a + 1/3*x^3*d^4*c + 4/3*x^3*e*d^3*b + 2*x^3*e^2*d^2*a + 1/2*x^2*d^4*b + 2*x^2*e*d^3*a + x*d^4*a","B",0
2108,1,110,0,0.337514," ","integrate((e*x+d)^3*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{6} x^{6} e^{3} c + \frac{3}{5} x^{5} e^{2} d c + \frac{1}{5} x^{5} e^{3} b + \frac{3}{4} x^{4} e d^{2} c + \frac{3}{4} x^{4} e^{2} d b + \frac{1}{4} x^{4} e^{3} a + \frac{1}{3} x^{3} d^{3} c + x^{3} e d^{2} b + x^{3} e^{2} d a + \frac{1}{2} x^{2} d^{3} b + \frac{3}{2} x^{2} e d^{2} a + x d^{3} a"," ",0,"1/6*x^6*e^3*c + 3/5*x^5*e^2*d*c + 1/5*x^5*e^3*b + 3/4*x^4*e*d^2*c + 3/4*x^4*e^2*d*b + 1/4*x^4*e^3*a + 1/3*x^3*d^3*c + x^3*e*d^2*b + x^3*e^2*d*a + 1/2*x^2*d^3*b + 3/2*x^2*e*d^2*a + x*d^3*a","A",0
2109,1,75,0,0.334072," ","integrate((e*x+d)^2*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{5} x^{5} e^{2} c + \frac{1}{2} x^{4} e d c + \frac{1}{4} x^{4} e^{2} b + \frac{1}{3} x^{3} d^{2} c + \frac{2}{3} x^{3} e d b + \frac{1}{3} x^{3} e^{2} a + \frac{1}{2} x^{2} d^{2} b + x^{2} e d a + x d^{2} a"," ",0,"1/5*x^5*e^2*c + 1/2*x^4*e*d*c + 1/4*x^4*e^2*b + 1/3*x^3*d^2*c + 2/3*x^3*e*d*b + 1/3*x^3*e^2*a + 1/2*x^2*d^2*b + x^2*e*d*a + x*d^2*a","A",0
2110,1,40,0,0.340874," ","integrate((e*x+d)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{1}{4} x^{4} e c + \frac{1}{3} x^{3} d c + \frac{1}{3} x^{3} e b + \frac{1}{2} x^{2} d b + \frac{1}{2} x^{2} e a + x d a"," ",0,"1/4*x^4*e*c + 1/3*x^3*d*c + 1/3*x^3*e*b + 1/2*x^2*d*b + 1/2*x^2*e*a + x*d*a","A",0
2111,1,16,0,0.333203," ","integrate(c*x^2+b*x+a,x, algorithm=""fricas"")","\frac{1}{3} x^{3} c + \frac{1}{2} x^{2} b + x a"," ",0,"1/3*x^3*c + 1/2*x^2*b + x*a","A",0
2112,1,52,0,0.377052," ","integrate((c*x^2+b*x+a)/(e*x+d),x, algorithm=""fricas"")","\frac{c e^{2} x^{2} - 2 \, {\left(c d e - b e^{2}\right)} x + 2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \log\left(e x + d\right)}{2 \, e^{3}}"," ",0,"1/2*(c*e^2*x^2 - 2*(c*d*e - b*e^2)*x + 2*(c*d^2 - b*d*e + a*e^2)*log(e*x + d))/e^3","A",0
2113,1,78,0,0.391437," ","integrate((c*x^2+b*x+a)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{c e^{2} x^{2} + c d e x - c d^{2} + b d e - a e^{2} - {\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \log\left(e x + d\right)}{e^{4} x + d e^{3}}"," ",0,"(c*e^2*x^2 + c*d*e*x - c*d^2 + b*d*e - a*e^2 - (2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*log(e*x + d))/(e^4*x + d*e^3)","A",0
2114,1,87,0,0.408231," ","integrate((c*x^2+b*x+a)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{3 \, c d^{2} - b d e - a e^{2} + 2 \, {\left(2 \, c d e - b e^{2}\right)} x + 2 \, {\left(c e^{2} x^{2} + 2 \, c d e x + c d^{2}\right)} \log\left(e x + d\right)}{2 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"1/2*(3*c*d^2 - b*d*e - a*e^2 + 2*(2*c*d*e - b*e^2)*x + 2*(c*e^2*x^2 + 2*c*d*e*x + c*d^2)*log(e*x + d))/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
2115,1,77,0,0.372499," ","integrate((c*x^2+b*x+a)/(e*x+d)^4,x, algorithm=""fricas"")","-\frac{6 \, c e^{2} x^{2} + 2 \, c d^{2} + b d e + 2 \, a e^{2} + 3 \, {\left(2 \, c d e + b e^{2}\right)} x}{6 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-1/6*(6*c*e^2*x^2 + 2*c*d^2 + b*d*e + 2*a*e^2 + 3*(2*c*d*e + b*e^2)*x)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
2116,1,86,0,0.394515," ","integrate((c*x^2+b*x+a)/(e*x+d)^5,x, algorithm=""fricas"")","-\frac{6 \, c e^{2} x^{2} + c d^{2} + b d e + 3 \, a e^{2} + 4 \, {\left(c d e + b e^{2}\right)} x}{12 \, {\left(e^{7} x^{4} + 4 \, d e^{6} x^{3} + 6 \, d^{2} e^{5} x^{2} + 4 \, d^{3} e^{4} x + d^{4} e^{3}\right)}}"," ",0,"-1/12*(6*c*e^2*x^2 + c*d^2 + b*d*e + 3*a*e^2 + 4*(c*d*e + b*e^2)*x)/(e^7*x^4 + 4*d*e^6*x^3 + 6*d^2*e^5*x^2 + 4*d^3*e^4*x + d^4*e^3)","A",0
2117,1,101,0,0.373311," ","integrate((c*x^2+b*x+a)/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{20 \, c e^{2} x^{2} + 2 \, c d^{2} + 3 \, b d e + 12 \, a e^{2} + 5 \, {\left(2 \, c d e + 3 \, b e^{2}\right)} x}{60 \, {\left(e^{8} x^{5} + 5 \, d e^{7} x^{4} + 10 \, d^{2} e^{6} x^{3} + 10 \, d^{3} e^{5} x^{2} + 5 \, d^{4} e^{4} x + d^{5} e^{3}\right)}}"," ",0,"-1/60*(20*c*e^2*x^2 + 2*c*d^2 + 3*b*d*e + 12*a*e^2 + 5*(2*c*d*e + 3*b*e^2)*x)/(e^8*x^5 + 5*d*e^7*x^4 + 10*d^2*e^6*x^3 + 10*d^3*e^5*x^2 + 5*d^4*e^4*x + d^5*e^3)","A",0
2118,1,340,0,0.347323," ","integrate((e*x+d)^4*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{4} c^{2} + \frac{1}{2} x^{8} e^{3} d c^{2} + \frac{1}{4} x^{8} e^{4} c b + \frac{6}{7} x^{7} e^{2} d^{2} c^{2} + \frac{8}{7} x^{7} e^{3} d c b + \frac{1}{7} x^{7} e^{4} b^{2} + \frac{2}{7} x^{7} e^{4} c a + \frac{2}{3} x^{6} e d^{3} c^{2} + 2 x^{6} e^{2} d^{2} c b + \frac{2}{3} x^{6} e^{3} d b^{2} + \frac{4}{3} x^{6} e^{3} d c a + \frac{1}{3} x^{6} e^{4} b a + \frac{1}{5} x^{5} d^{4} c^{2} + \frac{8}{5} x^{5} e d^{3} c b + \frac{6}{5} x^{5} e^{2} d^{2} b^{2} + \frac{12}{5} x^{5} e^{2} d^{2} c a + \frac{8}{5} x^{5} e^{3} d b a + \frac{1}{5} x^{5} e^{4} a^{2} + \frac{1}{2} x^{4} d^{4} c b + x^{4} e d^{3} b^{2} + 2 x^{4} e d^{3} c a + 3 x^{4} e^{2} d^{2} b a + x^{4} e^{3} d a^{2} + \frac{1}{3} x^{3} d^{4} b^{2} + \frac{2}{3} x^{3} d^{4} c a + \frac{8}{3} x^{3} e d^{3} b a + 2 x^{3} e^{2} d^{2} a^{2} + x^{2} d^{4} b a + 2 x^{2} e d^{3} a^{2} + x d^{4} a^{2}"," ",0,"1/9*x^9*e^4*c^2 + 1/2*x^8*e^3*d*c^2 + 1/4*x^8*e^4*c*b + 6/7*x^7*e^2*d^2*c^2 + 8/7*x^7*e^3*d*c*b + 1/7*x^7*e^4*b^2 + 2/7*x^7*e^4*c*a + 2/3*x^6*e*d^3*c^2 + 2*x^6*e^2*d^2*c*b + 2/3*x^6*e^3*d*b^2 + 4/3*x^6*e^3*d*c*a + 1/3*x^6*e^4*b*a + 1/5*x^5*d^4*c^2 + 8/5*x^5*e*d^3*c*b + 6/5*x^5*e^2*d^2*b^2 + 12/5*x^5*e^2*d^2*c*a + 8/5*x^5*e^3*d*b*a + 1/5*x^5*e^4*a^2 + 1/2*x^4*d^4*c*b + x^4*e*d^3*b^2 + 2*x^4*e*d^3*c*a + 3*x^4*e^2*d^2*b*a + x^4*e^3*d*a^2 + 1/3*x^3*d^4*b^2 + 2/3*x^3*d^4*c*a + 8/3*x^3*e*d^3*b*a + 2*x^3*e^2*d^2*a^2 + x^2*d^4*b*a + 2*x^2*e*d^3*a^2 + x*d^4*a^2","B",0
2119,1,259,0,0.350015," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e^{3} c^{2} + \frac{3}{7} x^{7} e^{2} d c^{2} + \frac{2}{7} x^{7} e^{3} c b + \frac{1}{2} x^{6} e d^{2} c^{2} + x^{6} e^{2} d c b + \frac{1}{6} x^{6} e^{3} b^{2} + \frac{1}{3} x^{6} e^{3} c a + \frac{1}{5} x^{5} d^{3} c^{2} + \frac{6}{5} x^{5} e d^{2} c b + \frac{3}{5} x^{5} e^{2} d b^{2} + \frac{6}{5} x^{5} e^{2} d c a + \frac{2}{5} x^{5} e^{3} b a + \frac{1}{2} x^{4} d^{3} c b + \frac{3}{4} x^{4} e d^{2} b^{2} + \frac{3}{2} x^{4} e d^{2} c a + \frac{3}{2} x^{4} e^{2} d b a + \frac{1}{4} x^{4} e^{3} a^{2} + \frac{1}{3} x^{3} d^{3} b^{2} + \frac{2}{3} x^{3} d^{3} c a + 2 x^{3} e d^{2} b a + x^{3} e^{2} d a^{2} + x^{2} d^{3} b a + \frac{3}{2} x^{2} e d^{2} a^{2} + x d^{3} a^{2}"," ",0,"1/8*x^8*e^3*c^2 + 3/7*x^7*e^2*d*c^2 + 2/7*x^7*e^3*c*b + 1/2*x^6*e*d^2*c^2 + x^6*e^2*d*c*b + 1/6*x^6*e^3*b^2 + 1/3*x^6*e^3*c*a + 1/5*x^5*d^3*c^2 + 6/5*x^5*e*d^2*c*b + 3/5*x^5*e^2*d*b^2 + 6/5*x^5*e^2*d*c*a + 2/5*x^5*e^3*b*a + 1/2*x^4*d^3*c*b + 3/4*x^4*e*d^2*b^2 + 3/2*x^4*e*d^2*c*a + 3/2*x^4*e^2*d*b*a + 1/4*x^4*e^3*a^2 + 1/3*x^3*d^3*b^2 + 2/3*x^3*d^3*c*a + 2*x^3*e*d^2*b*a + x^3*e^2*d*a^2 + x^2*d^3*b*a + 3/2*x^2*e*d^2*a^2 + x*d^3*a^2","A",0
2120,1,178,0,0.368435," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{7} x^{7} e^{2} c^{2} + \frac{1}{3} x^{6} e d c^{2} + \frac{1}{3} x^{6} e^{2} c b + \frac{1}{5} x^{5} d^{2} c^{2} + \frac{4}{5} x^{5} e d c b + \frac{1}{5} x^{5} e^{2} b^{2} + \frac{2}{5} x^{5} e^{2} c a + \frac{1}{2} x^{4} d^{2} c b + \frac{1}{2} x^{4} e d b^{2} + x^{4} e d c a + \frac{1}{2} x^{4} e^{2} b a + \frac{1}{3} x^{3} d^{2} b^{2} + \frac{2}{3} x^{3} d^{2} c a + \frac{4}{3} x^{3} e d b a + \frac{1}{3} x^{3} e^{2} a^{2} + x^{2} d^{2} b a + x^{2} e d a^{2} + x d^{2} a^{2}"," ",0,"1/7*x^7*e^2*c^2 + 1/3*x^6*e*d*c^2 + 1/3*x^6*e^2*c*b + 1/5*x^5*d^2*c^2 + 4/5*x^5*e*d*c*b + 1/5*x^5*e^2*b^2 + 2/5*x^5*e^2*c*a + 1/2*x^4*d^2*c*b + 1/2*x^4*e*d*b^2 + x^4*e*d*c*a + 1/2*x^4*e^2*b*a + 1/3*x^3*d^2*b^2 + 2/3*x^3*d^2*c*a + 4/3*x^3*e*d*b*a + 1/3*x^3*e^2*a^2 + x^2*d^2*b*a + x^2*e*d*a^2 + x*d^2*a^2","A",0
2121,1,99,0,0.348077," ","integrate((e*x+d)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{6} x^{6} e c^{2} + \frac{1}{5} x^{5} d c^{2} + \frac{2}{5} x^{5} e c b + \frac{1}{2} x^{4} d c b + \frac{1}{4} x^{4} e b^{2} + \frac{1}{2} x^{4} e c a + \frac{1}{3} x^{3} d b^{2} + \frac{2}{3} x^{3} d c a + \frac{2}{3} x^{3} e b a + x^{2} d b a + \frac{1}{2} x^{2} e a^{2} + x d a^{2}"," ",0,"1/6*x^6*e*c^2 + 1/5*x^5*d*c^2 + 2/5*x^5*e*c*b + 1/2*x^4*d*c*b + 1/4*x^4*e*b^2 + 1/2*x^4*e*c*a + 1/3*x^3*d*b^2 + 2/3*x^3*d*c*a + 2/3*x^3*e*b*a + x^2*d*b*a + 1/2*x^2*e*a^2 + x*d*a^2","A",0
2122,1,42,0,0.342559," ","integrate((c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{1}{5} x^{5} c^{2} + \frac{1}{2} x^{4} c b + \frac{1}{3} x^{3} b^{2} + \frac{2}{3} x^{3} c a + x^{2} b a + x a^{2}"," ",0,"1/5*x^5*c^2 + 1/2*x^4*c*b + 1/3*x^3*b^2 + 2/3*x^3*c*a + x^2*b*a + x*a^2","A",0
2123,1,170,0,0.376936," ","integrate((c*x^2+b*x+a)^2/(e*x+d),x, algorithm=""fricas"")","\frac{3 \, c^{2} e^{4} x^{4} - 4 \, {\left(c^{2} d e^{3} - 2 \, b c e^{4}\right)} x^{3} + 6 \, {\left(c^{2} d^{2} e^{2} - 2 \, b c d e^{3} + {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} - 12 \, {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} - 2 \, a b e^{4} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x + 12 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}\right)} \log\left(e x + d\right)}{12 \, e^{5}}"," ",0,"1/12*(3*c^2*e^4*x^4 - 4*(c^2*d*e^3 - 2*b*c*e^4)*x^3 + 6*(c^2*d^2*e^2 - 2*b*c*d*e^3 + (b^2 + 2*a*c)*e^4)*x^2 - 12*(c^2*d^3*e - 2*b*c*d^2*e^2 - 2*a*b*e^4 + (b^2 + 2*a*c)*d*e^3)*x + 12*(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)*log(e*x + d))/e^5","A",0
2124,1,259,0,0.396194," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^2,x, algorithm=""fricas"")","\frac{c^{2} e^{4} x^{4} - 3 \, c^{2} d^{4} + 6 \, b c d^{3} e + 6 \, a b d e^{3} - 3 \, a^{2} e^{4} - 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} - {\left(2 \, c^{2} d e^{3} - 3 \, b c e^{4}\right)} x^{3} + 3 \, {\left(2 \, c^{2} d^{2} e^{2} - 3 \, b c d e^{3} + {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} + 3 \, {\left(3 \, c^{2} d^{3} e - 4 \, b c d^{2} e^{2} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x - 6 \, {\left(2 \, c^{2} d^{4} - 3 \, b c d^{3} e - a b d e^{3} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} - a b e^{4} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"1/3*(c^2*e^4*x^4 - 3*c^2*d^4 + 6*b*c*d^3*e + 6*a*b*d*e^3 - 3*a^2*e^4 - 3*(b^2 + 2*a*c)*d^2*e^2 - (2*c^2*d*e^3 - 3*b*c*e^4)*x^3 + 3*(2*c^2*d^2*e^2 - 3*b*c*d*e^3 + (b^2 + 2*a*c)*e^4)*x^2 + 3*(3*c^2*d^3*e - 4*b*c*d^2*e^2 + (b^2 + 2*a*c)*d*e^3)*x - 6*(2*c^2*d^4 - 3*b*c*d^3*e - a*b*d*e^3 + (b^2 + 2*a*c)*d^2*e^2 + (2*c^2*d^3*e - 3*b*c*d^2*e^2 - a*b*e^4 + (b^2 + 2*a*c)*d*e^3)*x)*log(e*x + d))/(e^6*x + d*e^5)","B",0
2125,1,286,0,0.411499," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^3,x, algorithm=""fricas"")","\frac{c^{2} e^{4} x^{4} + 7 \, c^{2} d^{4} - 10 \, b c d^{3} e - 2 \, a b d e^{3} - a^{2} e^{4} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} - 4 \, {\left(c^{2} d e^{3} - b c e^{4}\right)} x^{3} - {\left(11 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3}\right)} x^{2} + 2 \, {\left(c^{2} d^{3} e - 4 \, b c d^{2} e^{2} - 2 \, a b e^{4} + 2 \, {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x + 2 \, {\left(6 \, c^{2} d^{4} - 6 \, b c d^{3} e + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + {\left(6 \, c^{2} d^{2} e^{2} - 6 \, b c d e^{3} + {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} + 2 \, {\left(6 \, c^{2} d^{3} e - 6 \, b c d^{2} e^{2} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"1/2*(c^2*e^4*x^4 + 7*c^2*d^4 - 10*b*c*d^3*e - 2*a*b*d*e^3 - a^2*e^4 + 3*(b^2 + 2*a*c)*d^2*e^2 - 4*(c^2*d*e^3 - b*c*e^4)*x^3 - (11*c^2*d^2*e^2 - 8*b*c*d*e^3)*x^2 + 2*(c^2*d^3*e - 4*b*c*d^2*e^2 - 2*a*b*e^4 + 2*(b^2 + 2*a*c)*d*e^3)*x + 2*(6*c^2*d^4 - 6*b*c*d^3*e + (b^2 + 2*a*c)*d^2*e^2 + (6*c^2*d^2*e^2 - 6*b*c*d*e^3 + (b^2 + 2*a*c)*e^4)*x^2 + 2*(6*c^2*d^3*e - 6*b*c*d^2*e^2 + (b^2 + 2*a*c)*d*e^3)*x)*log(e*x + d))/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","B",0
2126,1,282,0,0.379009," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, c^{2} e^{4} x^{4} + 9 \, c^{2} d e^{3} x^{3} - 13 \, c^{2} d^{4} + 11 \, b c d^{3} e - a b d e^{3} - a^{2} e^{4} - {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} - 3 \, {\left(3 \, c^{2} d^{2} e^{2} - 6 \, b c d e^{3} + {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} - 3 \, {\left(9 \, c^{2} d^{3} e - 9 \, b c d^{2} e^{2} + a b e^{4} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x - 6 \, {\left(2 \, c^{2} d^{4} - b c d^{3} e + {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} x^{3} + 3 \, {\left(2 \, c^{2} d^{2} e^{2} - b c d e^{3}\right)} x^{2} + 3 \, {\left(2 \, c^{2} d^{3} e - b c d^{2} e^{2}\right)} x\right)} \log\left(e x + d\right)}{3 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"1/3*(3*c^2*e^4*x^4 + 9*c^2*d*e^3*x^3 - 13*c^2*d^4 + 11*b*c*d^3*e - a*b*d*e^3 - a^2*e^4 - (b^2 + 2*a*c)*d^2*e^2 - 3*(3*c^2*d^2*e^2 - 6*b*c*d*e^3 + (b^2 + 2*a*c)*e^4)*x^2 - 3*(9*c^2*d^3*e - 9*b*c*d^2*e^2 + a*b*e^4 + (b^2 + 2*a*c)*d*e^3)*x - 6*(2*c^2*d^4 - b*c*d^3*e + (2*c^2*d*e^3 - b*c*e^4)*x^3 + 3*(2*c^2*d^2*e^2 - b*c*d*e^3)*x^2 + 3*(2*c^2*d^3*e - b*c*d^2*e^2)*x)*log(e*x + d))/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","B",0
2127,1,263,0,0.399384," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^5,x, algorithm=""fricas"")","\frac{25 \, c^{2} d^{4} - 6 \, b c d^{3} e - 2 \, a b d e^{3} - 3 \, a^{2} e^{4} - {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + 24 \, {\left(2 \, c^{2} d e^{3} - b c e^{4}\right)} x^{3} + 6 \, {\left(18 \, c^{2} d^{2} e^{2} - 6 \, b c d e^{3} - {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} + 4 \, {\left(22 \, c^{2} d^{3} e - 6 \, b c d^{2} e^{2} - 2 \, a b e^{4} - {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x + 12 \, {\left(c^{2} e^{4} x^{4} + 4 \, c^{2} d e^{3} x^{3} + 6 \, c^{2} d^{2} e^{2} x^{2} + 4 \, c^{2} d^{3} e x + c^{2} d^{4}\right)} \log\left(e x + d\right)}{12 \, {\left(e^{9} x^{4} + 4 \, d e^{8} x^{3} + 6 \, d^{2} e^{7} x^{2} + 4 \, d^{3} e^{6} x + d^{4} e^{5}\right)}}"," ",0,"1/12*(25*c^2*d^4 - 6*b*c*d^3*e - 2*a*b*d*e^3 - 3*a^2*e^4 - (b^2 + 2*a*c)*d^2*e^2 + 24*(2*c^2*d*e^3 - b*c*e^4)*x^3 + 6*(18*c^2*d^2*e^2 - 6*b*c*d*e^3 - (b^2 + 2*a*c)*e^4)*x^2 + 4*(22*c^2*d^3*e - 6*b*c*d^2*e^2 - 2*a*b*e^4 - (b^2 + 2*a*c)*d*e^3)*x + 12*(c^2*e^4*x^4 + 4*c^2*d*e^3*x^3 + 6*c^2*d^2*e^2*x^2 + 4*c^2*d^3*e*x + c^2*d^4)*log(e*x + d))/(e^9*x^4 + 4*d*e^8*x^3 + 6*d^2*e^7*x^2 + 4*d^3*e^6*x + d^4*e^5)","A",0
2128,1,219,0,0.400230," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^6,x, algorithm=""fricas"")","-\frac{30 \, c^{2} e^{4} x^{4} + 6 \, c^{2} d^{4} + 3 \, b c d^{3} e + 3 \, a b d e^{3} + 6 \, a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + 30 \, {\left(2 \, c^{2} d e^{3} + b c e^{4}\right)} x^{3} + 10 \, {\left(6 \, c^{2} d^{2} e^{2} + 3 \, b c d e^{3} + {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} + 5 \, {\left(6 \, c^{2} d^{3} e + 3 \, b c d^{2} e^{2} + 3 \, a b e^{4} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x}{30 \, {\left(e^{10} x^{5} + 5 \, d e^{9} x^{4} + 10 \, d^{2} e^{8} x^{3} + 10 \, d^{3} e^{7} x^{2} + 5 \, d^{4} e^{6} x + d^{5} e^{5}\right)}}"," ",0,"-1/30*(30*c^2*e^4*x^4 + 6*c^2*d^4 + 3*b*c*d^3*e + 3*a*b*d*e^3 + 6*a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2 + 30*(2*c^2*d*e^3 + b*c*e^4)*x^3 + 10*(6*c^2*d^2*e^2 + 3*b*c*d*e^3 + (b^2 + 2*a*c)*e^4)*x^2 + 5*(6*c^2*d^3*e + 3*b*c*d^2*e^2 + 3*a*b*e^4 + (b^2 + 2*a*c)*d*e^3)*x)/(e^10*x^5 + 5*d*e^9*x^4 + 10*d^2*e^8*x^3 + 10*d^3*e^7*x^2 + 5*d^4*e^6*x + d^5*e^5)","A",0
2129,1,229,0,0.384471," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^7,x, algorithm=""fricas"")","-\frac{30 \, c^{2} e^{4} x^{4} + 2 \, c^{2} d^{4} + 2 \, b c d^{3} e + 4 \, a b d e^{3} + 10 \, a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + 40 \, {\left(c^{2} d e^{3} + b c e^{4}\right)} x^{3} + 15 \, {\left(2 \, c^{2} d^{2} e^{2} + 2 \, b c d e^{3} + {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} + 6 \, {\left(2 \, c^{2} d^{3} e + 2 \, b c d^{2} e^{2} + 4 \, a b e^{4} + {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x}{60 \, {\left(e^{11} x^{6} + 6 \, d e^{10} x^{5} + 15 \, d^{2} e^{9} x^{4} + 20 \, d^{3} e^{8} x^{3} + 15 \, d^{4} e^{7} x^{2} + 6 \, d^{5} e^{6} x + d^{6} e^{5}\right)}}"," ",0,"-1/60*(30*c^2*e^4*x^4 + 2*c^2*d^4 + 2*b*c*d^3*e + 4*a*b*d*e^3 + 10*a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2 + 40*(c^2*d*e^3 + b*c*e^4)*x^3 + 15*(2*c^2*d^2*e^2 + 2*b*c*d*e^3 + (b^2 + 2*a*c)*e^4)*x^2 + 6*(2*c^2*d^3*e + 2*b*c*d^2*e^2 + 4*a*b*e^4 + (b^2 + 2*a*c)*d*e^3)*x)/(e^11*x^6 + 6*d*e^10*x^5 + 15*d^2*e^9*x^4 + 20*d^3*e^8*x^3 + 15*d^4*e^7*x^2 + 6*d^5*e^6*x + d^6*e^5)","A",0
2130,1,245,0,0.388579," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{70 \, c^{2} e^{4} x^{4} + 2 \, c^{2} d^{4} + 3 \, b c d^{3} e + 10 \, a b d e^{3} + 30 \, a^{2} e^{4} + 2 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} + 35 \, {\left(2 \, c^{2} d e^{3} + 3 \, b c e^{4}\right)} x^{3} + 21 \, {\left(2 \, c^{2} d^{2} e^{2} + 3 \, b c d e^{3} + 2 \, {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} + 7 \, {\left(2 \, c^{2} d^{3} e + 3 \, b c d^{2} e^{2} + 10 \, a b e^{4} + 2 \, {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x}{210 \, {\left(e^{12} x^{7} + 7 \, d e^{11} x^{6} + 21 \, d^{2} e^{10} x^{5} + 35 \, d^{3} e^{9} x^{4} + 35 \, d^{4} e^{8} x^{3} + 21 \, d^{5} e^{7} x^{2} + 7 \, d^{6} e^{6} x + d^{7} e^{5}\right)}}"," ",0,"-1/210*(70*c^2*e^4*x^4 + 2*c^2*d^4 + 3*b*c*d^3*e + 10*a*b*d*e^3 + 30*a^2*e^4 + 2*(b^2 + 2*a*c)*d^2*e^2 + 35*(2*c^2*d*e^3 + 3*b*c*e^4)*x^3 + 21*(2*c^2*d^2*e^2 + 3*b*c*d*e^3 + 2*(b^2 + 2*a*c)*e^4)*x^2 + 7*(2*c^2*d^3*e + 3*b*c*d^2*e^2 + 10*a*b*e^4 + 2*(b^2 + 2*a*c)*d*e^3)*x)/(e^12*x^7 + 7*d*e^11*x^6 + 21*d^2*e^10*x^5 + 35*d^3*e^9*x^4 + 35*d^4*e^8*x^3 + 21*d^5*e^7*x^2 + 7*d^6*e^6*x + d^7*e^5)","A",0
2131,1,624,0,0.349952," ","integrate((e*x+d)^4*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{4} c^{3} + \frac{2}{5} x^{10} e^{3} d c^{3} + \frac{3}{10} x^{10} e^{4} c^{2} b + \frac{2}{3} x^{9} e^{2} d^{2} c^{3} + \frac{4}{3} x^{9} e^{3} d c^{2} b + \frac{1}{3} x^{9} e^{4} c b^{2} + \frac{1}{3} x^{9} e^{4} c^{2} a + \frac{1}{2} x^{8} e d^{3} c^{3} + \frac{9}{4} x^{8} e^{2} d^{2} c^{2} b + \frac{3}{2} x^{8} e^{3} d c b^{2} + \frac{1}{8} x^{8} e^{4} b^{3} + \frac{3}{2} x^{8} e^{3} d c^{2} a + \frac{3}{4} x^{8} e^{4} c b a + \frac{1}{7} x^{7} d^{4} c^{3} + \frac{12}{7} x^{7} e d^{3} c^{2} b + \frac{18}{7} x^{7} e^{2} d^{2} c b^{2} + \frac{4}{7} x^{7} e^{3} d b^{3} + \frac{18}{7} x^{7} e^{2} d^{2} c^{2} a + \frac{24}{7} x^{7} e^{3} d c b a + \frac{3}{7} x^{7} e^{4} b^{2} a + \frac{3}{7} x^{7} e^{4} c a^{2} + \frac{1}{2} x^{6} d^{4} c^{2} b + 2 x^{6} e d^{3} c b^{2} + x^{6} e^{2} d^{2} b^{3} + 2 x^{6} e d^{3} c^{2} a + 6 x^{6} e^{2} d^{2} c b a + 2 x^{6} e^{3} d b^{2} a + 2 x^{6} e^{3} d c a^{2} + \frac{1}{2} x^{6} e^{4} b a^{2} + \frac{3}{5} x^{5} d^{4} c b^{2} + \frac{4}{5} x^{5} e d^{3} b^{3} + \frac{3}{5} x^{5} d^{4} c^{2} a + \frac{24}{5} x^{5} e d^{3} c b a + \frac{18}{5} x^{5} e^{2} d^{2} b^{2} a + \frac{18}{5} x^{5} e^{2} d^{2} c a^{2} + \frac{12}{5} x^{5} e^{3} d b a^{2} + \frac{1}{5} x^{5} e^{4} a^{3} + \frac{1}{4} x^{4} d^{4} b^{3} + \frac{3}{2} x^{4} d^{4} c b a + 3 x^{4} e d^{3} b^{2} a + 3 x^{4} e d^{3} c a^{2} + \frac{9}{2} x^{4} e^{2} d^{2} b a^{2} + x^{4} e^{3} d a^{3} + x^{3} d^{4} b^{2} a + x^{3} d^{4} c a^{2} + 4 x^{3} e d^{3} b a^{2} + 2 x^{3} e^{2} d^{2} a^{3} + \frac{3}{2} x^{2} d^{4} b a^{2} + 2 x^{2} e d^{3} a^{3} + x d^{4} a^{3}"," ",0,"1/11*x^11*e^4*c^3 + 2/5*x^10*e^3*d*c^3 + 3/10*x^10*e^4*c^2*b + 2/3*x^9*e^2*d^2*c^3 + 4/3*x^9*e^3*d*c^2*b + 1/3*x^9*e^4*c*b^2 + 1/3*x^9*e^4*c^2*a + 1/2*x^8*e*d^3*c^3 + 9/4*x^8*e^2*d^2*c^2*b + 3/2*x^8*e^3*d*c*b^2 + 1/8*x^8*e^4*b^3 + 3/2*x^8*e^3*d*c^2*a + 3/4*x^8*e^4*c*b*a + 1/7*x^7*d^4*c^3 + 12/7*x^7*e*d^3*c^2*b + 18/7*x^7*e^2*d^2*c*b^2 + 4/7*x^7*e^3*d*b^3 + 18/7*x^7*e^2*d^2*c^2*a + 24/7*x^7*e^3*d*c*b*a + 3/7*x^7*e^4*b^2*a + 3/7*x^7*e^4*c*a^2 + 1/2*x^6*d^4*c^2*b + 2*x^6*e*d^3*c*b^2 + x^6*e^2*d^2*b^3 + 2*x^6*e*d^3*c^2*a + 6*x^6*e^2*d^2*c*b*a + 2*x^6*e^3*d*b^2*a + 2*x^6*e^3*d*c*a^2 + 1/2*x^6*e^4*b*a^2 + 3/5*x^5*d^4*c*b^2 + 4/5*x^5*e*d^3*b^3 + 3/5*x^5*d^4*c^2*a + 24/5*x^5*e*d^3*c*b*a + 18/5*x^5*e^2*d^2*b^2*a + 18/5*x^5*e^2*d^2*c*a^2 + 12/5*x^5*e^3*d*b*a^2 + 1/5*x^5*e^4*a^3 + 1/4*x^4*d^4*b^3 + 3/2*x^4*d^4*c*b*a + 3*x^4*e*d^3*b^2*a + 3*x^4*e*d^3*c*a^2 + 9/2*x^4*e^2*d^2*b*a^2 + x^4*e^3*d*a^3 + x^3*d^4*b^2*a + x^3*d^4*c*a^2 + 4*x^3*e*d^3*b*a^2 + 2*x^3*e^2*d^2*a^3 + 3/2*x^2*d^4*b*a^2 + 2*x^2*e*d^3*a^3 + x*d^4*a^3","B",0
2132,1,479,0,0.349287," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e^{3} c^{3} + \frac{1}{3} x^{9} e^{2} d c^{3} + \frac{1}{3} x^{9} e^{3} c^{2} b + \frac{3}{8} x^{8} e d^{2} c^{3} + \frac{9}{8} x^{8} e^{2} d c^{2} b + \frac{3}{8} x^{8} e^{3} c b^{2} + \frac{3}{8} x^{8} e^{3} c^{2} a + \frac{1}{7} x^{7} d^{3} c^{3} + \frac{9}{7} x^{7} e d^{2} c^{2} b + \frac{9}{7} x^{7} e^{2} d c b^{2} + \frac{1}{7} x^{7} e^{3} b^{3} + \frac{9}{7} x^{7} e^{2} d c^{2} a + \frac{6}{7} x^{7} e^{3} c b a + \frac{1}{2} x^{6} d^{3} c^{2} b + \frac{3}{2} x^{6} e d^{2} c b^{2} + \frac{1}{2} x^{6} e^{2} d b^{3} + \frac{3}{2} x^{6} e d^{2} c^{2} a + 3 x^{6} e^{2} d c b a + \frac{1}{2} x^{6} e^{3} b^{2} a + \frac{1}{2} x^{6} e^{3} c a^{2} + \frac{3}{5} x^{5} d^{3} c b^{2} + \frac{3}{5} x^{5} e d^{2} b^{3} + \frac{3}{5} x^{5} d^{3} c^{2} a + \frac{18}{5} x^{5} e d^{2} c b a + \frac{9}{5} x^{5} e^{2} d b^{2} a + \frac{9}{5} x^{5} e^{2} d c a^{2} + \frac{3}{5} x^{5} e^{3} b a^{2} + \frac{1}{4} x^{4} d^{3} b^{3} + \frac{3}{2} x^{4} d^{3} c b a + \frac{9}{4} x^{4} e d^{2} b^{2} a + \frac{9}{4} x^{4} e d^{2} c a^{2} + \frac{9}{4} x^{4} e^{2} d b a^{2} + \frac{1}{4} x^{4} e^{3} a^{3} + x^{3} d^{3} b^{2} a + x^{3} d^{3} c a^{2} + 3 x^{3} e d^{2} b a^{2} + x^{3} e^{2} d a^{3} + \frac{3}{2} x^{2} d^{3} b a^{2} + \frac{3}{2} x^{2} e d^{2} a^{3} + x d^{3} a^{3}"," ",0,"1/10*x^10*e^3*c^3 + 1/3*x^9*e^2*d*c^3 + 1/3*x^9*e^3*c^2*b + 3/8*x^8*e*d^2*c^3 + 9/8*x^8*e^2*d*c^2*b + 3/8*x^8*e^3*c*b^2 + 3/8*x^8*e^3*c^2*a + 1/7*x^7*d^3*c^3 + 9/7*x^7*e*d^2*c^2*b + 9/7*x^7*e^2*d*c*b^2 + 1/7*x^7*e^3*b^3 + 9/7*x^7*e^2*d*c^2*a + 6/7*x^7*e^3*c*b*a + 1/2*x^6*d^3*c^2*b + 3/2*x^6*e*d^2*c*b^2 + 1/2*x^6*e^2*d*b^3 + 3/2*x^6*e*d^2*c^2*a + 3*x^6*e^2*d*c*b*a + 1/2*x^6*e^3*b^2*a + 1/2*x^6*e^3*c*a^2 + 3/5*x^5*d^3*c*b^2 + 3/5*x^5*e*d^2*b^3 + 3/5*x^5*d^3*c^2*a + 18/5*x^5*e*d^2*c*b*a + 9/5*x^5*e^2*d*b^2*a + 9/5*x^5*e^2*d*c*a^2 + 3/5*x^5*e^3*b*a^2 + 1/4*x^4*d^3*b^3 + 3/2*x^4*d^3*c*b*a + 9/4*x^4*e*d^2*b^2*a + 9/4*x^4*e*d^2*c*a^2 + 9/4*x^4*e^2*d*b*a^2 + 1/4*x^4*e^3*a^3 + x^3*d^3*b^2*a + x^3*d^3*c*a^2 + 3*x^3*e*d^2*b*a^2 + x^3*e^2*d*a^3 + 3/2*x^2*d^3*b*a^2 + 3/2*x^2*e*d^2*a^3 + x*d^3*a^3","A",0
2133,1,330,0,0.352817," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{2} c^{3} + \frac{1}{4} x^{8} e d c^{3} + \frac{3}{8} x^{8} e^{2} c^{2} b + \frac{1}{7} x^{7} d^{2} c^{3} + \frac{6}{7} x^{7} e d c^{2} b + \frac{3}{7} x^{7} e^{2} c b^{2} + \frac{3}{7} x^{7} e^{2} c^{2} a + \frac{1}{2} x^{6} d^{2} c^{2} b + x^{6} e d c b^{2} + \frac{1}{6} x^{6} e^{2} b^{3} + x^{6} e d c^{2} a + x^{6} e^{2} c b a + \frac{3}{5} x^{5} d^{2} c b^{2} + \frac{2}{5} x^{5} e d b^{3} + \frac{3}{5} x^{5} d^{2} c^{2} a + \frac{12}{5} x^{5} e d c b a + \frac{3}{5} x^{5} e^{2} b^{2} a + \frac{3}{5} x^{5} e^{2} c a^{2} + \frac{1}{4} x^{4} d^{2} b^{3} + \frac{3}{2} x^{4} d^{2} c b a + \frac{3}{2} x^{4} e d b^{2} a + \frac{3}{2} x^{4} e d c a^{2} + \frac{3}{4} x^{4} e^{2} b a^{2} + x^{3} d^{2} b^{2} a + x^{3} d^{2} c a^{2} + 2 x^{3} e d b a^{2} + \frac{1}{3} x^{3} e^{2} a^{3} + \frac{3}{2} x^{2} d^{2} b a^{2} + x^{2} e d a^{3} + x d^{2} a^{3}"," ",0,"1/9*x^9*e^2*c^3 + 1/4*x^8*e*d*c^3 + 3/8*x^8*e^2*c^2*b + 1/7*x^7*d^2*c^3 + 6/7*x^7*e*d*c^2*b + 3/7*x^7*e^2*c*b^2 + 3/7*x^7*e^2*c^2*a + 1/2*x^6*d^2*c^2*b + x^6*e*d*c*b^2 + 1/6*x^6*e^2*b^3 + x^6*e*d*c^2*a + x^6*e^2*c*b*a + 3/5*x^5*d^2*c*b^2 + 2/5*x^5*e*d*b^3 + 3/5*x^5*d^2*c^2*a + 12/5*x^5*e*d*c*b*a + 3/5*x^5*e^2*b^2*a + 3/5*x^5*e^2*c*a^2 + 1/4*x^4*d^2*b^3 + 3/2*x^4*d^2*c*b*a + 3/2*x^4*e*d*b^2*a + 3/2*x^4*e*d*c*a^2 + 3/4*x^4*e^2*b*a^2 + x^3*d^2*b^2*a + x^3*d^2*c*a^2 + 2*x^3*e*d*b*a^2 + 1/3*x^3*e^2*a^3 + 3/2*x^2*d^2*b*a^2 + x^2*e*d*a^3 + x*d^2*a^3","A",0
2134,1,187,0,0.350148," ","integrate((e*x+d)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{8} x^{8} e c^{3} + \frac{1}{7} x^{7} d c^{3} + \frac{3}{7} x^{7} e c^{2} b + \frac{1}{2} x^{6} d c^{2} b + \frac{1}{2} x^{6} e c b^{2} + \frac{1}{2} x^{6} e c^{2} a + \frac{3}{5} x^{5} d c b^{2} + \frac{1}{5} x^{5} e b^{3} + \frac{3}{5} x^{5} d c^{2} a + \frac{6}{5} x^{5} e c b a + \frac{1}{4} x^{4} d b^{3} + \frac{3}{2} x^{4} d c b a + \frac{3}{4} x^{4} e b^{2} a + \frac{3}{4} x^{4} e c a^{2} + x^{3} d b^{2} a + x^{3} d c a^{2} + x^{3} e b a^{2} + \frac{3}{2} x^{2} d b a^{2} + \frac{1}{2} x^{2} e a^{3} + x d a^{3}"," ",0,"1/8*x^8*e*c^3 + 1/7*x^7*d*c^3 + 3/7*x^7*e*c^2*b + 1/2*x^6*d*c^2*b + 1/2*x^6*e*c*b^2 + 1/2*x^6*e*c^2*a + 3/5*x^5*d*c*b^2 + 1/5*x^5*e*b^3 + 3/5*x^5*d*c^2*a + 6/5*x^5*e*c*b*a + 1/4*x^4*d*b^3 + 3/2*x^4*d*c*b*a + 3/4*x^4*e*b^2*a + 3/4*x^4*e*c*a^2 + x^3*d*b^2*a + x^3*d*c*a^2 + x^3*e*b*a^2 + 3/2*x^2*d*b*a^2 + 1/2*x^2*e*a^3 + x*d*a^3","A",0
2135,1,82,0,0.347168," ","integrate((c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{7} x^{7} c^{3} + \frac{1}{2} x^{6} c^{2} b + \frac{3}{5} x^{5} c b^{2} + \frac{3}{5} x^{5} c^{2} a + \frac{1}{4} x^{4} b^{3} + \frac{3}{2} x^{4} c b a + x^{3} b^{2} a + x^{3} c a^{2} + \frac{3}{2} x^{2} b a^{2} + x a^{3}"," ",0,"1/7*x^7*c^3 + 1/2*x^6*c^2*b + 3/5*x^5*c*b^2 + 3/5*x^5*c^2*a + 1/4*x^4*b^3 + 3/2*x^4*c*b*a + x^3*b^2*a + x^3*c*a^2 + 3/2*x^2*b*a^2 + x*a^3","A",0
2136,1,403,0,0.395771," ","integrate((c*x^2+b*x+a)^3/(e*x+d),x, algorithm=""fricas"")","\frac{10 \, c^{3} e^{6} x^{6} - 12 \, {\left(c^{3} d e^{5} - 3 \, b c^{2} e^{6}\right)} x^{5} + 15 \, {\left(c^{3} d^{2} e^{4} - 3 \, b c^{2} d e^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} - 20 \, {\left(c^{3} d^{3} e^{3} - 3 \, b c^{2} d^{2} e^{4} + 3 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} - {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + 30 \, {\left(c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} - 60 \, {\left(c^{3} d^{5} e - 3 \, b c^{2} d^{4} e^{2} - 3 \, a^{2} b e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x + 60 \, {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} + a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4}\right)} \log\left(e x + d\right)}{60 \, e^{7}}"," ",0,"1/60*(10*c^3*e^6*x^6 - 12*(c^3*d*e^5 - 3*b*c^2*e^6)*x^5 + 15*(c^3*d^2*e^4 - 3*b*c^2*d*e^5 + 3*(b^2*c + a*c^2)*e^6)*x^4 - 20*(c^3*d^3*e^3 - 3*b*c^2*d^2*e^4 + 3*(b^2*c + a*c^2)*d*e^5 - (b^3 + 6*a*b*c)*e^6)*x^3 + 30*(c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 + 3*(b^2*c + a*c^2)*d^2*e^4 - (b^3 + 6*a*b*c)*d*e^5 + 3*(a*b^2 + a^2*c)*e^6)*x^2 - 60*(c^3*d^5*e - 3*b*c^2*d^4*e^2 - 3*a^2*b*e^6 + 3*(b^2*c + a*c^2)*d^3*e^3 - (b^3 + 6*a*b*c)*d^2*e^4 + 3*(a*b^2 + a^2*c)*d*e^5)*x + 60*(c^3*d^6 - 3*b*c^2*d^5*e - 3*a^2*b*d*e^5 + a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 3*(a*b^2 + a^2*c)*d^2*e^4)*log(e*x + d))/e^7","A",0
2137,1,580,0,0.396774," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^2,x, algorithm=""fricas"")","\frac{4 \, c^{3} e^{6} x^{6} - 20 \, c^{3} d^{6} + 60 \, b c^{2} d^{5} e + 60 \, a^{2} b d e^{5} - 20 \, a^{3} e^{6} - 60 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + 20 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 60 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} - 3 \, {\left(2 \, c^{3} d e^{5} - 5 \, b c^{2} e^{6}\right)} x^{5} + 5 \, {\left(2 \, c^{3} d^{2} e^{4} - 5 \, b c^{2} d e^{5} + 4 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} - 10 \, {\left(2 \, c^{3} d^{3} e^{3} - 5 \, b c^{2} d^{2} e^{4} + 4 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} - {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + 30 \, {\left(2 \, c^{3} d^{4} e^{2} - 5 \, b c^{2} d^{3} e^{3} + 4 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 2 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} + 20 \, {\left(5 \, c^{3} d^{5} e - 12 \, b c^{2} d^{4} e^{2} + 9 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - 2 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x - 60 \, {\left(2 \, c^{3} d^{6} - 5 \, b c^{2} d^{5} e - a^{2} b d e^{5} + 4 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 2 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} + {\left(2 \, c^{3} d^{5} e - 5 \, b c^{2} d^{4} e^{2} - a^{2} b e^{6} + 4 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 2 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"1/20*(4*c^3*e^6*x^6 - 20*c^3*d^6 + 60*b*c^2*d^5*e + 60*a^2*b*d*e^5 - 20*a^3*e^6 - 60*(b^2*c + a*c^2)*d^4*e^2 + 20*(b^3 + 6*a*b*c)*d^3*e^3 - 60*(a*b^2 + a^2*c)*d^2*e^4 - 3*(2*c^3*d*e^5 - 5*b*c^2*e^6)*x^5 + 5*(2*c^3*d^2*e^4 - 5*b*c^2*d*e^5 + 4*(b^2*c + a*c^2)*e^6)*x^4 - 10*(2*c^3*d^3*e^3 - 5*b*c^2*d^2*e^4 + 4*(b^2*c + a*c^2)*d*e^5 - (b^3 + 6*a*b*c)*e^6)*x^3 + 30*(2*c^3*d^4*e^2 - 5*b*c^2*d^3*e^3 + 4*(b^2*c + a*c^2)*d^2*e^4 - (b^3 + 6*a*b*c)*d*e^5 + 2*(a*b^2 + a^2*c)*e^6)*x^2 + 20*(5*c^3*d^5*e - 12*b*c^2*d^4*e^2 + 9*(b^2*c + a*c^2)*d^3*e^3 - 2*(b^3 + 6*a*b*c)*d^2*e^4 + 3*(a*b^2 + a^2*c)*d*e^5)*x - 60*(2*c^3*d^6 - 5*b*c^2*d^5*e - a^2*b*d*e^5 + 4*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + 2*(a*b^2 + a^2*c)*d^2*e^4 + (2*c^3*d^5*e - 5*b*c^2*d^4*e^2 - a^2*b*e^6 + 4*(b^2*c + a*c^2)*d^3*e^3 - (b^3 + 6*a*b*c)*d^2*e^4 + 2*(a*b^2 + a^2*c)*d*e^5)*x)*log(e*x + d))/(e^8*x + d*e^7)","B",0
2138,1,638,0,0.402032," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^3,x, algorithm=""fricas"")","\frac{c^{3} e^{6} x^{6} + 22 \, c^{3} d^{6} - 54 \, b c^{2} d^{5} e - 6 \, a^{2} b d e^{5} - 2 \, a^{3} e^{6} + 42 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - 10 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 18 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} - 2 \, {\left(c^{3} d e^{5} - 2 \, b c^{2} e^{6}\right)} x^{5} + {\left(5 \, c^{3} d^{2} e^{4} - 10 \, b c^{2} d e^{5} + 6 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} - 4 \, {\left(5 \, c^{3} d^{3} e^{3} - 10 \, b c^{2} d^{2} e^{4} + 6 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} - {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} - 2 \, {\left(34 \, c^{3} d^{4} e^{2} - 63 \, b c^{2} d^{3} e^{3} + 33 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - 4 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5}\right)} x^{2} - 4 \, {\left(4 \, c^{3} d^{5} e - 3 \, b c^{2} d^{4} e^{2} + 3 \, a^{2} b e^{6} - 3 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} + 2 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} - 6 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x + 12 \, {\left(5 \, c^{3} d^{6} - 10 \, b c^{2} d^{5} e + 6 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} + {\left(5 \, c^{3} d^{4} e^{2} - 10 \, b c^{2} d^{3} e^{3} + 6 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d e^{5} + {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} + 2 \, {\left(5 \, c^{3} d^{5} e - 10 \, b c^{2} d^{4} e^{2} + 6 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"1/4*(c^3*e^6*x^6 + 22*c^3*d^6 - 54*b*c^2*d^5*e - 6*a^2*b*d*e^5 - 2*a^3*e^6 + 42*(b^2*c + a*c^2)*d^4*e^2 - 10*(b^3 + 6*a*b*c)*d^3*e^3 + 18*(a*b^2 + a^2*c)*d^2*e^4 - 2*(c^3*d*e^5 - 2*b*c^2*e^6)*x^5 + (5*c^3*d^2*e^4 - 10*b*c^2*d*e^5 + 6*(b^2*c + a*c^2)*e^6)*x^4 - 4*(5*c^3*d^3*e^3 - 10*b*c^2*d^2*e^4 + 6*(b^2*c + a*c^2)*d*e^5 - (b^3 + 6*a*b*c)*e^6)*x^3 - 2*(34*c^3*d^4*e^2 - 63*b*c^2*d^3*e^3 + 33*(b^2*c + a*c^2)*d^2*e^4 - 4*(b^3 + 6*a*b*c)*d*e^5)*x^2 - 4*(4*c^3*d^5*e - 3*b*c^2*d^4*e^2 + 3*a^2*b*e^6 - 3*(b^2*c + a*c^2)*d^3*e^3 + 2*(b^3 + 6*a*b*c)*d^2*e^4 - 6*(a*b^2 + a^2*c)*d*e^5)*x + 12*(5*c^3*d^6 - 10*b*c^2*d^5*e + 6*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + (a*b^2 + a^2*c)*d^2*e^4 + (5*c^3*d^4*e^2 - 10*b*c^2*d^3*e^3 + 6*(b^2*c + a*c^2)*d^2*e^4 - (b^3 + 6*a*b*c)*d*e^5 + (a*b^2 + a^2*c)*e^6)*x^2 + 2*(5*c^3*d^5*e - 10*b*c^2*d^4*e^2 + 6*(b^2*c + a*c^2)*d^3*e^3 - (b^3 + 6*a*b*c)*d^2*e^4 + (a*b^2 + a^2*c)*d*e^5)*x)*log(e*x + d))/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","B",0
2139,1,664,0,0.407270," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^4,x, algorithm=""fricas"")","\frac{2 \, c^{3} e^{6} x^{6} - 74 \, c^{3} d^{6} + 141 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} - 2 \, a^{3} e^{6} - 78 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + 11 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 6 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} - 3 \, {\left(2 \, c^{3} d e^{5} - 3 \, b c^{2} e^{6}\right)} x^{5} + 3 \, {\left(10 \, c^{3} d^{2} e^{4} - 15 \, b c^{2} d e^{5} + 6 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} + {\left(146 \, c^{3} d^{3} e^{3} - 189 \, b c^{2} d^{2} e^{4} + 54 \, {\left(b^{2} c + a c^{2}\right)} d e^{5}\right)} x^{3} + 3 \, {\left(26 \, c^{3} d^{4} e^{2} - 9 \, b c^{2} d^{3} e^{3} - 18 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} + 6 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} - 6 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} - 3 \, {\left(34 \, c^{3} d^{5} e - 81 \, b c^{2} d^{4} e^{2} + 3 \, a^{2} b e^{6} + 54 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - 9 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 6 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x - 6 \, {\left(20 \, c^{3} d^{6} - 30 \, b c^{2} d^{5} e + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + {\left(20 \, c^{3} d^{3} e^{3} - 30 \, b c^{2} d^{2} e^{4} + 12 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} - {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + 3 \, {\left(20 \, c^{3} d^{4} e^{2} - 30 \, b c^{2} d^{3} e^{3} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d e^{5}\right)} x^{2} + 3 \, {\left(20 \, c^{3} d^{5} e - 30 \, b c^{2} d^{4} e^{2} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4}\right)} x\right)} \log\left(e x + d\right)}{6 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"1/6*(2*c^3*e^6*x^6 - 74*c^3*d^6 + 141*b*c^2*d^5*e - 3*a^2*b*d*e^5 - 2*a^3*e^6 - 78*(b^2*c + a*c^2)*d^4*e^2 + 11*(b^3 + 6*a*b*c)*d^3*e^3 - 6*(a*b^2 + a^2*c)*d^2*e^4 - 3*(2*c^3*d*e^5 - 3*b*c^2*e^6)*x^5 + 3*(10*c^3*d^2*e^4 - 15*b*c^2*d*e^5 + 6*(b^2*c + a*c^2)*e^6)*x^4 + (146*c^3*d^3*e^3 - 189*b*c^2*d^2*e^4 + 54*(b^2*c + a*c^2)*d*e^5)*x^3 + 3*(26*c^3*d^4*e^2 - 9*b*c^2*d^3*e^3 - 18*(b^2*c + a*c^2)*d^2*e^4 + 6*(b^3 + 6*a*b*c)*d*e^5 - 6*(a*b^2 + a^2*c)*e^6)*x^2 - 3*(34*c^3*d^5*e - 81*b*c^2*d^4*e^2 + 3*a^2*b*e^6 + 54*(b^2*c + a*c^2)*d^3*e^3 - 9*(b^3 + 6*a*b*c)*d^2*e^4 + 6*(a*b^2 + a^2*c)*d*e^5)*x - 6*(20*c^3*d^6 - 30*b*c^2*d^5*e + 12*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 + (20*c^3*d^3*e^3 - 30*b*c^2*d^2*e^4 + 12*(b^2*c + a*c^2)*d*e^5 - (b^3 + 6*a*b*c)*e^6)*x^3 + 3*(20*c^3*d^4*e^2 - 30*b*c^2*d^3*e^3 + 12*(b^2*c + a*c^2)*d^2*e^4 - (b^3 + 6*a*b*c)*d*e^5)*x^2 + 3*(20*c^3*d^5*e - 30*b*c^2*d^4*e^2 + 12*(b^2*c + a*c^2)*d^3*e^3 - (b^3 + 6*a*b*c)*d^2*e^4)*x)*log(e*x + d))/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","B",0
2140,1,647,0,0.402626," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^5,x, algorithm=""fricas"")","\frac{2 \, c^{3} e^{6} x^{6} + 57 \, c^{3} d^{6} - 77 \, b c^{2} d^{5} e - a^{2} b d e^{5} - a^{3} e^{6} + 25 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} - 12 \, {\left(c^{3} d e^{5} - b c^{2} e^{6}\right)} x^{5} - 4 \, {\left(17 \, c^{3} d^{2} e^{4} - 12 \, b c^{2} d e^{5}\right)} x^{4} - 4 \, {\left(8 \, c^{3} d^{3} e^{3} + 12 \, b c^{2} d^{2} e^{4} - 12 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} + {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + 6 \, {\left(22 \, c^{3} d^{4} e^{2} - 42 \, b c^{2} d^{3} e^{3} + 18 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d e^{5} - {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} + 4 \, {\left(42 \, c^{3} d^{5} e - 62 \, b c^{2} d^{4} e^{2} - a^{2} b e^{6} + 22 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} - {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x + 12 \, {\left(5 \, c^{3} d^{6} - 5 \, b c^{2} d^{5} e + {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + {\left(5 \, c^{3} d^{2} e^{4} - 5 \, b c^{2} d e^{5} + {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} + 4 \, {\left(5 \, c^{3} d^{3} e^{3} - 5 \, b c^{2} d^{2} e^{4} + {\left(b^{2} c + a c^{2}\right)} d e^{5}\right)} x^{3} + 6 \, {\left(5 \, c^{3} d^{4} e^{2} - 5 \, b c^{2} d^{3} e^{3} + {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(5 \, c^{3} d^{5} e - 5 \, b c^{2} d^{4} e^{2} + {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{4 \, {\left(e^{11} x^{4} + 4 \, d e^{10} x^{3} + 6 \, d^{2} e^{9} x^{2} + 4 \, d^{3} e^{8} x + d^{4} e^{7}\right)}}"," ",0,"1/4*(2*c^3*e^6*x^6 + 57*c^3*d^6 - 77*b*c^2*d^5*e - a^2*b*d*e^5 - a^3*e^6 + 25*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 - (a*b^2 + a^2*c)*d^2*e^4 - 12*(c^3*d*e^5 - b*c^2*e^6)*x^5 - 4*(17*c^3*d^2*e^4 - 12*b*c^2*d*e^5)*x^4 - 4*(8*c^3*d^3*e^3 + 12*b*c^2*d^2*e^4 - 12*(b^2*c + a*c^2)*d*e^5 + (b^3 + 6*a*b*c)*e^6)*x^3 + 6*(22*c^3*d^4*e^2 - 42*b*c^2*d^3*e^3 + 18*(b^2*c + a*c^2)*d^2*e^4 - (b^3 + 6*a*b*c)*d*e^5 - (a*b^2 + a^2*c)*e^6)*x^2 + 4*(42*c^3*d^5*e - 62*b*c^2*d^4*e^2 - a^2*b*e^6 + 22*(b^2*c + a*c^2)*d^3*e^3 - (b^3 + 6*a*b*c)*d^2*e^4 - (a*b^2 + a^2*c)*d*e^5)*x + 12*(5*c^3*d^6 - 5*b*c^2*d^5*e + (b^2*c + a*c^2)*d^4*e^2 + (5*c^3*d^2*e^4 - 5*b*c^2*d*e^5 + (b^2*c + a*c^2)*e^6)*x^4 + 4*(5*c^3*d^3*e^3 - 5*b*c^2*d^2*e^4 + (b^2*c + a*c^2)*d*e^5)*x^3 + 6*(5*c^3*d^4*e^2 - 5*b*c^2*d^3*e^3 + (b^2*c + a*c^2)*d^2*e^4)*x^2 + 4*(5*c^3*d^5*e - 5*b*c^2*d^4*e^2 + (b^2*c + a*c^2)*d^3*e^3)*x)*log(e*x + d))/(e^11*x^4 + 4*d*e^10*x^3 + 6*d^2*e^9*x^2 + 4*d^3*e^8*x + d^4*e^7)","B",0
2141,1,600,0,0.399429," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^6,x, algorithm=""fricas"")","\frac{20 \, c^{3} e^{6} x^{6} + 100 \, c^{3} d e^{5} x^{5} - 174 \, c^{3} d^{6} + 137 \, b c^{2} d^{5} e - 3 \, a^{2} b d e^{5} - 4 \, a^{3} e^{6} - 12 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 2 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} - 20 \, {\left(5 \, c^{3} d^{2} e^{4} - 15 \, b c^{2} d e^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} - 10 \, {\left(80 \, c^{3} d^{3} e^{3} - 90 \, b c^{2} d^{2} e^{4} + 12 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} + {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} - 10 \, {\left(120 \, c^{3} d^{4} e^{2} - 110 \, b c^{2} d^{3} e^{3} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} + {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 2 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} - 5 \, {\left(150 \, c^{3} d^{5} e - 125 \, b c^{2} d^{4} e^{2} + 3 \, a^{2} b e^{6} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} + {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 2 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x - 60 \, {\left(2 \, c^{3} d^{6} - b c^{2} d^{5} e + {\left(2 \, c^{3} d e^{5} - b c^{2} e^{6}\right)} x^{5} + 5 \, {\left(2 \, c^{3} d^{2} e^{4} - b c^{2} d e^{5}\right)} x^{4} + 10 \, {\left(2 \, c^{3} d^{3} e^{3} - b c^{2} d^{2} e^{4}\right)} x^{3} + 10 \, {\left(2 \, c^{3} d^{4} e^{2} - b c^{2} d^{3} e^{3}\right)} x^{2} + 5 \, {\left(2 \, c^{3} d^{5} e - b c^{2} d^{4} e^{2}\right)} x\right)} \log\left(e x + d\right)}{20 \, {\left(e^{12} x^{5} + 5 \, d e^{11} x^{4} + 10 \, d^{2} e^{10} x^{3} + 10 \, d^{3} e^{9} x^{2} + 5 \, d^{4} e^{8} x + d^{5} e^{7}\right)}}"," ",0,"1/20*(20*c^3*e^6*x^6 + 100*c^3*d*e^5*x^5 - 174*c^3*d^6 + 137*b*c^2*d^5*e - 3*a^2*b*d*e^5 - 4*a^3*e^6 - 12*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 - 2*(a*b^2 + a^2*c)*d^2*e^4 - 20*(5*c^3*d^2*e^4 - 15*b*c^2*d*e^5 + 3*(b^2*c + a*c^2)*e^6)*x^4 - 10*(80*c^3*d^3*e^3 - 90*b*c^2*d^2*e^4 + 12*(b^2*c + a*c^2)*d*e^5 + (b^3 + 6*a*b*c)*e^6)*x^3 - 10*(120*c^3*d^4*e^2 - 110*b*c^2*d^3*e^3 + 12*(b^2*c + a*c^2)*d^2*e^4 + (b^3 + 6*a*b*c)*d*e^5 + 2*(a*b^2 + a^2*c)*e^6)*x^2 - 5*(150*c^3*d^5*e - 125*b*c^2*d^4*e^2 + 3*a^2*b*e^6 + 12*(b^2*c + a*c^2)*d^3*e^3 + (b^3 + 6*a*b*c)*d^2*e^4 + 2*(a*b^2 + a^2*c)*d*e^5)*x - 60*(2*c^3*d^6 - b*c^2*d^5*e + (2*c^3*d*e^5 - b*c^2*e^6)*x^5 + 5*(2*c^3*d^2*e^4 - b*c^2*d*e^5)*x^4 + 10*(2*c^3*d^3*e^3 - b*c^2*d^2*e^4)*x^3 + 10*(2*c^3*d^4*e^2 - b*c^2*d^3*e^3)*x^2 + 5*(2*c^3*d^5*e - b*c^2*d^4*e^2)*x)*log(e*x + d))/(e^12*x^5 + 5*d*e^11*x^4 + 10*d^2*e^10*x^3 + 10*d^3*e^9*x^2 + 5*d^4*e^8*x + d^5*e^7)","B",0
2142,1,545,0,0.388867," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^7,x, algorithm=""fricas"")","\frac{147 \, c^{3} d^{6} - 30 \, b c^{2} d^{5} e - 6 \, a^{2} b d e^{5} - 10 \, a^{3} e^{6} - 6 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} + 180 \, {\left(2 \, c^{3} d e^{5} - b c^{2} e^{6}\right)} x^{5} + 90 \, {\left(15 \, c^{3} d^{2} e^{4} - 5 \, b c^{2} d e^{5} - {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} + 20 \, {\left(110 \, c^{3} d^{3} e^{3} - 30 \, b c^{2} d^{2} e^{4} - 6 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} - {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + 15 \, {\left(125 \, c^{3} d^{4} e^{2} - 30 \, b c^{2} d^{3} e^{3} - 6 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d e^{5} - 3 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} + 6 \, {\left(137 \, c^{3} d^{5} e - 30 \, b c^{2} d^{4} e^{2} - 6 \, a^{2} b e^{6} - 6 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} - 3 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x + 60 \, {\left(c^{3} e^{6} x^{6} + 6 \, c^{3} d e^{5} x^{5} + 15 \, c^{3} d^{2} e^{4} x^{4} + 20 \, c^{3} d^{3} e^{3} x^{3} + 15 \, c^{3} d^{4} e^{2} x^{2} + 6 \, c^{3} d^{5} e x + c^{3} d^{6}\right)} \log\left(e x + d\right)}{60 \, {\left(e^{13} x^{6} + 6 \, d e^{12} x^{5} + 15 \, d^{2} e^{11} x^{4} + 20 \, d^{3} e^{10} x^{3} + 15 \, d^{4} e^{9} x^{2} + 6 \, d^{5} e^{8} x + d^{6} e^{7}\right)}}"," ",0,"1/60*(147*c^3*d^6 - 30*b*c^2*d^5*e - 6*a^2*b*d*e^5 - 10*a^3*e^6 - 6*(b^2*c + a*c^2)*d^4*e^2 - (b^3 + 6*a*b*c)*d^3*e^3 - 3*(a*b^2 + a^2*c)*d^2*e^4 + 180*(2*c^3*d*e^5 - b*c^2*e^6)*x^5 + 90*(15*c^3*d^2*e^4 - 5*b*c^2*d*e^5 - (b^2*c + a*c^2)*e^6)*x^4 + 20*(110*c^3*d^3*e^3 - 30*b*c^2*d^2*e^4 - 6*(b^2*c + a*c^2)*d*e^5 - (b^3 + 6*a*b*c)*e^6)*x^3 + 15*(125*c^3*d^4*e^2 - 30*b*c^2*d^3*e^3 - 6*(b^2*c + a*c^2)*d^2*e^4 - (b^3 + 6*a*b*c)*d*e^5 - 3*(a*b^2 + a^2*c)*e^6)*x^2 + 6*(137*c^3*d^5*e - 30*b*c^2*d^4*e^2 - 6*a^2*b*e^6 - 6*(b^2*c + a*c^2)*d^3*e^3 - (b^3 + 6*a*b*c)*d^2*e^4 - 3*(a*b^2 + a^2*c)*d*e^5)*x + 60*(c^3*e^6*x^6 + 6*c^3*d*e^5*x^5 + 15*c^3*d^2*e^4*x^4 + 20*c^3*d^3*e^3*x^3 + 15*c^3*d^4*e^2*x^2 + 6*c^3*d^5*e*x + c^3*d^6)*log(e*x + d))/(e^13*x^6 + 6*d*e^12*x^5 + 15*d^2*e^11*x^4 + 20*d^3*e^10*x^3 + 15*d^4*e^9*x^2 + 6*d^5*e^8*x + d^6*e^7)","B",0
2143,1,472,0,0.382315," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^8,x, algorithm=""fricas"")","-\frac{140 \, c^{3} e^{6} x^{6} + 20 \, c^{3} d^{6} + 10 \, b c^{2} d^{5} e + 10 \, a^{2} b d e^{5} + 20 \, a^{3} e^{6} + 4 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 4 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} + 210 \, {\left(2 \, c^{3} d e^{5} + b c^{2} e^{6}\right)} x^{5} + 70 \, {\left(10 \, c^{3} d^{2} e^{4} + 5 \, b c^{2} d e^{5} + 2 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} + 35 \, {\left(20 \, c^{3} d^{3} e^{3} + 10 \, b c^{2} d^{2} e^{4} + 4 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} + {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + 21 \, {\left(20 \, c^{3} d^{4} e^{2} + 10 \, b c^{2} d^{3} e^{3} + 4 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} + {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 4 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} + 7 \, {\left(20 \, c^{3} d^{5} e + 10 \, b c^{2} d^{4} e^{2} + 10 \, a^{2} b e^{6} + 4 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} + {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 4 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x}{140 \, {\left(e^{14} x^{7} + 7 \, d e^{13} x^{6} + 21 \, d^{2} e^{12} x^{5} + 35 \, d^{3} e^{11} x^{4} + 35 \, d^{4} e^{10} x^{3} + 21 \, d^{5} e^{9} x^{2} + 7 \, d^{6} e^{8} x + d^{7} e^{7}\right)}}"," ",0,"-1/140*(140*c^3*e^6*x^6 + 20*c^3*d^6 + 10*b*c^2*d^5*e + 10*a^2*b*d*e^5 + 20*a^3*e^6 + 4*(b^2*c + a*c^2)*d^4*e^2 + (b^3 + 6*a*b*c)*d^3*e^3 + 4*(a*b^2 + a^2*c)*d^2*e^4 + 210*(2*c^3*d*e^5 + b*c^2*e^6)*x^5 + 70*(10*c^3*d^2*e^4 + 5*b*c^2*d*e^5 + 2*(b^2*c + a*c^2)*e^6)*x^4 + 35*(20*c^3*d^3*e^3 + 10*b*c^2*d^2*e^4 + 4*(b^2*c + a*c^2)*d*e^5 + (b^3 + 6*a*b*c)*e^6)*x^3 + 21*(20*c^3*d^4*e^2 + 10*b*c^2*d^3*e^3 + 4*(b^2*c + a*c^2)*d^2*e^4 + (b^3 + 6*a*b*c)*d*e^5 + 4*(a*b^2 + a^2*c)*e^6)*x^2 + 7*(20*c^3*d^5*e + 10*b*c^2*d^4*e^2 + 10*a^2*b*e^6 + 4*(b^2*c + a*c^2)*d^3*e^3 + (b^3 + 6*a*b*c)*d^2*e^4 + 4*(a*b^2 + a^2*c)*d*e^5)*x)/(e^14*x^7 + 7*d*e^13*x^6 + 21*d^2*e^12*x^5 + 35*d^3*e^11*x^4 + 35*d^4*e^10*x^3 + 21*d^5*e^9*x^2 + 7*d^6*e^8*x + d^7*e^7)","A",0
2144,1,482,0,0.402011," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^9,x, algorithm=""fricas"")","-\frac{140 \, c^{3} e^{6} x^{6} + 5 \, c^{3} d^{6} + 5 \, b c^{2} d^{5} e + 15 \, a^{2} b d e^{5} + 35 \, a^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 5 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} + 280 \, {\left(c^{3} d e^{5} + b c^{2} e^{6}\right)} x^{5} + 70 \, {\left(5 \, c^{3} d^{2} e^{4} + 5 \, b c^{2} d e^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} + 56 \, {\left(5 \, c^{3} d^{3} e^{3} + 5 \, b c^{2} d^{2} e^{4} + 3 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} + {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + 28 \, {\left(5 \, c^{3} d^{4} e^{2} + 5 \, b c^{2} d^{3} e^{3} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} + {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 5 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} + 8 \, {\left(5 \, c^{3} d^{5} e + 5 \, b c^{2} d^{4} e^{2} + 15 \, a^{2} b e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} + {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 5 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x}{280 \, {\left(e^{15} x^{8} + 8 \, d e^{14} x^{7} + 28 \, d^{2} e^{13} x^{6} + 56 \, d^{3} e^{12} x^{5} + 70 \, d^{4} e^{11} x^{4} + 56 \, d^{5} e^{10} x^{3} + 28 \, d^{6} e^{9} x^{2} + 8 \, d^{7} e^{8} x + d^{8} e^{7}\right)}}"," ",0,"-1/280*(140*c^3*e^6*x^6 + 5*c^3*d^6 + 5*b*c^2*d^5*e + 15*a^2*b*d*e^5 + 35*a^3*e^6 + 3*(b^2*c + a*c^2)*d^4*e^2 + (b^3 + 6*a*b*c)*d^3*e^3 + 5*(a*b^2 + a^2*c)*d^2*e^4 + 280*(c^3*d*e^5 + b*c^2*e^6)*x^5 + 70*(5*c^3*d^2*e^4 + 5*b*c^2*d*e^5 + 3*(b^2*c + a*c^2)*e^6)*x^4 + 56*(5*c^3*d^3*e^3 + 5*b*c^2*d^2*e^4 + 3*(b^2*c + a*c^2)*d*e^5 + (b^3 + 6*a*b*c)*e^6)*x^3 + 28*(5*c^3*d^4*e^2 + 5*b*c^2*d^3*e^3 + 3*(b^2*c + a*c^2)*d^2*e^4 + (b^3 + 6*a*b*c)*d*e^5 + 5*(a*b^2 + a^2*c)*e^6)*x^2 + 8*(5*c^3*d^5*e + 5*b*c^2*d^4*e^2 + 15*a^2*b*e^6 + 3*(b^2*c + a*c^2)*d^3*e^3 + (b^3 + 6*a*b*c)*d^2*e^4 + 5*(a*b^2 + a^2*c)*d*e^5)*x)/(e^15*x^8 + 8*d*e^14*x^7 + 28*d^2*e^13*x^6 + 56*d^3*e^12*x^5 + 70*d^4*e^11*x^4 + 56*d^5*e^10*x^3 + 28*d^6*e^9*x^2 + 8*d^7*e^8*x + d^8*e^7)","A",0
2145,1,499,0,0.396497," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{840 \, c^{3} e^{6} x^{6} + 10 \, c^{3} d^{6} + 15 \, b c^{2} d^{5} e + 105 \, a^{2} b d e^{5} + 280 \, a^{3} e^{6} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + 5 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 30 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} + 630 \, {\left(2 \, c^{3} d e^{5} + 3 \, b c^{2} e^{6}\right)} x^{5} + 126 \, {\left(10 \, c^{3} d^{2} e^{4} + 15 \, b c^{2} d e^{5} + 12 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} + 84 \, {\left(10 \, c^{3} d^{3} e^{3} + 15 \, b c^{2} d^{2} e^{4} + 12 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} + 5 \, {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + 36 \, {\left(10 \, c^{3} d^{4} e^{2} + 15 \, b c^{2} d^{3} e^{3} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} + 5 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 30 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} + 9 \, {\left(10 \, c^{3} d^{5} e + 15 \, b c^{2} d^{4} e^{2} + 105 \, a^{2} b e^{6} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} + 5 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 30 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x}{2520 \, {\left(e^{16} x^{9} + 9 \, d e^{15} x^{8} + 36 \, d^{2} e^{14} x^{7} + 84 \, d^{3} e^{13} x^{6} + 126 \, d^{4} e^{12} x^{5} + 126 \, d^{5} e^{11} x^{4} + 84 \, d^{6} e^{10} x^{3} + 36 \, d^{7} e^{9} x^{2} + 9 \, d^{8} e^{8} x + d^{9} e^{7}\right)}}"," ",0,"-1/2520*(840*c^3*e^6*x^6 + 10*c^3*d^6 + 15*b*c^2*d^5*e + 105*a^2*b*d*e^5 + 280*a^3*e^6 + 12*(b^2*c + a*c^2)*d^4*e^2 + 5*(b^3 + 6*a*b*c)*d^3*e^3 + 30*(a*b^2 + a^2*c)*d^2*e^4 + 630*(2*c^3*d*e^5 + 3*b*c^2*e^6)*x^5 + 126*(10*c^3*d^2*e^4 + 15*b*c^2*d*e^5 + 12*(b^2*c + a*c^2)*e^6)*x^4 + 84*(10*c^3*d^3*e^3 + 15*b*c^2*d^2*e^4 + 12*(b^2*c + a*c^2)*d*e^5 + 5*(b^3 + 6*a*b*c)*e^6)*x^3 + 36*(10*c^3*d^4*e^2 + 15*b*c^2*d^3*e^3 + 12*(b^2*c + a*c^2)*d^2*e^4 + 5*(b^3 + 6*a*b*c)*d*e^5 + 30*(a*b^2 + a^2*c)*e^6)*x^2 + 9*(10*c^3*d^5*e + 15*b*c^2*d^4*e^2 + 105*a^2*b*e^6 + 12*(b^2*c + a*c^2)*d^3*e^3 + 5*(b^3 + 6*a*b*c)*d^2*e^4 + 30*(a*b^2 + a^2*c)*d*e^5)*x)/(e^16*x^9 + 9*d*e^15*x^8 + 36*d^2*e^14*x^7 + 84*d^3*e^13*x^6 + 126*d^4*e^12*x^5 + 126*d^5*e^11*x^4 + 84*d^6*e^10*x^3 + 36*d^7*e^9*x^2 + 9*d^8*e^8*x + d^9*e^7)","A",0
2146,1,1001,0,0.345498," ","integrate((e*x+d)^4*(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{4} c^{4} + \frac{1}{3} x^{12} e^{3} d c^{4} + \frac{1}{3} x^{12} e^{4} c^{3} b + \frac{6}{11} x^{11} e^{2} d^{2} c^{4} + \frac{16}{11} x^{11} e^{3} d c^{3} b + \frac{6}{11} x^{11} e^{4} c^{2} b^{2} + \frac{4}{11} x^{11} e^{4} c^{3} a + \frac{2}{5} x^{10} e d^{3} c^{4} + \frac{12}{5} x^{10} e^{2} d^{2} c^{3} b + \frac{12}{5} x^{10} e^{3} d c^{2} b^{2} + \frac{2}{5} x^{10} e^{4} c b^{3} + \frac{8}{5} x^{10} e^{3} d c^{3} a + \frac{6}{5} x^{10} e^{4} c^{2} b a + \frac{1}{9} x^{9} d^{4} c^{4} + \frac{16}{9} x^{9} e d^{3} c^{3} b + 4 x^{9} e^{2} d^{2} c^{2} b^{2} + \frac{16}{9} x^{9} e^{3} d c b^{3} + \frac{1}{9} x^{9} e^{4} b^{4} + \frac{8}{3} x^{9} e^{2} d^{2} c^{3} a + \frac{16}{3} x^{9} e^{3} d c^{2} b a + \frac{4}{3} x^{9} e^{4} c b^{2} a + \frac{2}{3} x^{9} e^{4} c^{2} a^{2} + \frac{1}{2} x^{8} d^{4} c^{3} b + 3 x^{8} e d^{3} c^{2} b^{2} + 3 x^{8} e^{2} d^{2} c b^{3} + \frac{1}{2} x^{8} e^{3} d b^{4} + 2 x^{8} e d^{3} c^{3} a + 9 x^{8} e^{2} d^{2} c^{2} b a + 6 x^{8} e^{3} d c b^{2} a + \frac{1}{2} x^{8} e^{4} b^{3} a + 3 x^{8} e^{3} d c^{2} a^{2} + \frac{3}{2} x^{8} e^{4} c b a^{2} + \frac{6}{7} x^{7} d^{4} c^{2} b^{2} + \frac{16}{7} x^{7} e d^{3} c b^{3} + \frac{6}{7} x^{7} e^{2} d^{2} b^{4} + \frac{4}{7} x^{7} d^{4} c^{3} a + \frac{48}{7} x^{7} e d^{3} c^{2} b a + \frac{72}{7} x^{7} e^{2} d^{2} c b^{2} a + \frac{16}{7} x^{7} e^{3} d b^{3} a + \frac{36}{7} x^{7} e^{2} d^{2} c^{2} a^{2} + \frac{48}{7} x^{7} e^{3} d c b a^{2} + \frac{6}{7} x^{7} e^{4} b^{2} a^{2} + \frac{4}{7} x^{7} e^{4} c a^{3} + \frac{2}{3} x^{6} d^{4} c b^{3} + \frac{2}{3} x^{6} e d^{3} b^{4} + 2 x^{6} d^{4} c^{2} b a + 8 x^{6} e d^{3} c b^{2} a + 4 x^{6} e^{2} d^{2} b^{3} a + 4 x^{6} e d^{3} c^{2} a^{2} + 12 x^{6} e^{2} d^{2} c b a^{2} + 4 x^{6} e^{3} d b^{2} a^{2} + \frac{8}{3} x^{6} e^{3} d c a^{3} + \frac{2}{3} x^{6} e^{4} b a^{3} + \frac{1}{5} x^{5} d^{4} b^{4} + \frac{12}{5} x^{5} d^{4} c b^{2} a + \frac{16}{5} x^{5} e d^{3} b^{3} a + \frac{6}{5} x^{5} d^{4} c^{2} a^{2} + \frac{48}{5} x^{5} e d^{3} c b a^{2} + \frac{36}{5} x^{5} e^{2} d^{2} b^{2} a^{2} + \frac{24}{5} x^{5} e^{2} d^{2} c a^{3} + \frac{16}{5} x^{5} e^{3} d b a^{3} + \frac{1}{5} x^{5} e^{4} a^{4} + x^{4} d^{4} b^{3} a + 3 x^{4} d^{4} c b a^{2} + 6 x^{4} e d^{3} b^{2} a^{2} + 4 x^{4} e d^{3} c a^{3} + 6 x^{4} e^{2} d^{2} b a^{3} + x^{4} e^{3} d a^{4} + 2 x^{3} d^{4} b^{2} a^{2} + \frac{4}{3} x^{3} d^{4} c a^{3} + \frac{16}{3} x^{3} e d^{3} b a^{3} + 2 x^{3} e^{2} d^{2} a^{4} + 2 x^{2} d^{4} b a^{3} + 2 x^{2} e d^{3} a^{4} + x d^{4} a^{4}"," ",0,"1/13*x^13*e^4*c^4 + 1/3*x^12*e^3*d*c^4 + 1/3*x^12*e^4*c^3*b + 6/11*x^11*e^2*d^2*c^4 + 16/11*x^11*e^3*d*c^3*b + 6/11*x^11*e^4*c^2*b^2 + 4/11*x^11*e^4*c^3*a + 2/5*x^10*e*d^3*c^4 + 12/5*x^10*e^2*d^2*c^3*b + 12/5*x^10*e^3*d*c^2*b^2 + 2/5*x^10*e^4*c*b^3 + 8/5*x^10*e^3*d*c^3*a + 6/5*x^10*e^4*c^2*b*a + 1/9*x^9*d^4*c^4 + 16/9*x^9*e*d^3*c^3*b + 4*x^9*e^2*d^2*c^2*b^2 + 16/9*x^9*e^3*d*c*b^3 + 1/9*x^9*e^4*b^4 + 8/3*x^9*e^2*d^2*c^3*a + 16/3*x^9*e^3*d*c^2*b*a + 4/3*x^9*e^4*c*b^2*a + 2/3*x^9*e^4*c^2*a^2 + 1/2*x^8*d^4*c^3*b + 3*x^8*e*d^3*c^2*b^2 + 3*x^8*e^2*d^2*c*b^3 + 1/2*x^8*e^3*d*b^4 + 2*x^8*e*d^3*c^3*a + 9*x^8*e^2*d^2*c^2*b*a + 6*x^8*e^3*d*c*b^2*a + 1/2*x^8*e^4*b^3*a + 3*x^8*e^3*d*c^2*a^2 + 3/2*x^8*e^4*c*b*a^2 + 6/7*x^7*d^4*c^2*b^2 + 16/7*x^7*e*d^3*c*b^3 + 6/7*x^7*e^2*d^2*b^4 + 4/7*x^7*d^4*c^3*a + 48/7*x^7*e*d^3*c^2*b*a + 72/7*x^7*e^2*d^2*c*b^2*a + 16/7*x^7*e^3*d*b^3*a + 36/7*x^7*e^2*d^2*c^2*a^2 + 48/7*x^7*e^3*d*c*b*a^2 + 6/7*x^7*e^4*b^2*a^2 + 4/7*x^7*e^4*c*a^3 + 2/3*x^6*d^4*c*b^3 + 2/3*x^6*e*d^3*b^4 + 2*x^6*d^4*c^2*b*a + 8*x^6*e*d^3*c*b^2*a + 4*x^6*e^2*d^2*b^3*a + 4*x^6*e*d^3*c^2*a^2 + 12*x^6*e^2*d^2*c*b*a^2 + 4*x^6*e^3*d*b^2*a^2 + 8/3*x^6*e^3*d*c*a^3 + 2/3*x^6*e^4*b*a^3 + 1/5*x^5*d^4*b^4 + 12/5*x^5*d^4*c*b^2*a + 16/5*x^5*e*d^3*b^3*a + 6/5*x^5*d^4*c^2*a^2 + 48/5*x^5*e*d^3*c*b*a^2 + 36/5*x^5*e^2*d^2*b^2*a^2 + 24/5*x^5*e^2*d^2*c*a^3 + 16/5*x^5*e^3*d*b*a^3 + 1/5*x^5*e^4*a^4 + x^4*d^4*b^3*a + 3*x^4*d^4*c*b*a^2 + 6*x^4*e*d^3*b^2*a^2 + 4*x^4*e*d^3*c*a^3 + 6*x^4*e^2*d^2*b*a^3 + x^4*e^3*d*a^4 + 2*x^3*d^4*b^2*a^2 + 4/3*x^3*d^4*c*a^3 + 16/3*x^3*e*d^3*b*a^3 + 2*x^3*e^2*d^2*a^4 + 2*x^2*d^4*b*a^3 + 2*x^2*e*d^3*a^4 + x*d^4*a^4","B",0
2147,1,769,0,0.354675," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\frac{1}{12} x^{12} e^{3} c^{4} + \frac{3}{11} x^{11} e^{2} d c^{4} + \frac{4}{11} x^{11} e^{3} c^{3} b + \frac{3}{10} x^{10} e d^{2} c^{4} + \frac{6}{5} x^{10} e^{2} d c^{3} b + \frac{3}{5} x^{10} e^{3} c^{2} b^{2} + \frac{2}{5} x^{10} e^{3} c^{3} a + \frac{1}{9} x^{9} d^{3} c^{4} + \frac{4}{3} x^{9} e d^{2} c^{3} b + 2 x^{9} e^{2} d c^{2} b^{2} + \frac{4}{9} x^{9} e^{3} c b^{3} + \frac{4}{3} x^{9} e^{2} d c^{3} a + \frac{4}{3} x^{9} e^{3} c^{2} b a + \frac{1}{2} x^{8} d^{3} c^{3} b + \frac{9}{4} x^{8} e d^{2} c^{2} b^{2} + \frac{3}{2} x^{8} e^{2} d c b^{3} + \frac{1}{8} x^{8} e^{3} b^{4} + \frac{3}{2} x^{8} e d^{2} c^{3} a + \frac{9}{2} x^{8} e^{2} d c^{2} b a + \frac{3}{2} x^{8} e^{3} c b^{2} a + \frac{3}{4} x^{8} e^{3} c^{2} a^{2} + \frac{6}{7} x^{7} d^{3} c^{2} b^{2} + \frac{12}{7} x^{7} e d^{2} c b^{3} + \frac{3}{7} x^{7} e^{2} d b^{4} + \frac{4}{7} x^{7} d^{3} c^{3} a + \frac{36}{7} x^{7} e d^{2} c^{2} b a + \frac{36}{7} x^{7} e^{2} d c b^{2} a + \frac{4}{7} x^{7} e^{3} b^{3} a + \frac{18}{7} x^{7} e^{2} d c^{2} a^{2} + \frac{12}{7} x^{7} e^{3} c b a^{2} + \frac{2}{3} x^{6} d^{3} c b^{3} + \frac{1}{2} x^{6} e d^{2} b^{4} + 2 x^{6} d^{3} c^{2} b a + 6 x^{6} e d^{2} c b^{2} a + 2 x^{6} e^{2} d b^{3} a + 3 x^{6} e d^{2} c^{2} a^{2} + 6 x^{6} e^{2} d c b a^{2} + x^{6} e^{3} b^{2} a^{2} + \frac{2}{3} x^{6} e^{3} c a^{3} + \frac{1}{5} x^{5} d^{3} b^{4} + \frac{12}{5} x^{5} d^{3} c b^{2} a + \frac{12}{5} x^{5} e d^{2} b^{3} a + \frac{6}{5} x^{5} d^{3} c^{2} a^{2} + \frac{36}{5} x^{5} e d^{2} c b a^{2} + \frac{18}{5} x^{5} e^{2} d b^{2} a^{2} + \frac{12}{5} x^{5} e^{2} d c a^{3} + \frac{4}{5} x^{5} e^{3} b a^{3} + x^{4} d^{3} b^{3} a + 3 x^{4} d^{3} c b a^{2} + \frac{9}{2} x^{4} e d^{2} b^{2} a^{2} + 3 x^{4} e d^{2} c a^{3} + 3 x^{4} e^{2} d b a^{3} + \frac{1}{4} x^{4} e^{3} a^{4} + 2 x^{3} d^{3} b^{2} a^{2} + \frac{4}{3} x^{3} d^{3} c a^{3} + 4 x^{3} e d^{2} b a^{3} + x^{3} e^{2} d a^{4} + 2 x^{2} d^{3} b a^{3} + \frac{3}{2} x^{2} e d^{2} a^{4} + x d^{3} a^{4}"," ",0,"1/12*x^12*e^3*c^4 + 3/11*x^11*e^2*d*c^4 + 4/11*x^11*e^3*c^3*b + 3/10*x^10*e*d^2*c^4 + 6/5*x^10*e^2*d*c^3*b + 3/5*x^10*e^3*c^2*b^2 + 2/5*x^10*e^3*c^3*a + 1/9*x^9*d^3*c^4 + 4/3*x^9*e*d^2*c^3*b + 2*x^9*e^2*d*c^2*b^2 + 4/9*x^9*e^3*c*b^3 + 4/3*x^9*e^2*d*c^3*a + 4/3*x^9*e^3*c^2*b*a + 1/2*x^8*d^3*c^3*b + 9/4*x^8*e*d^2*c^2*b^2 + 3/2*x^8*e^2*d*c*b^3 + 1/8*x^8*e^3*b^4 + 3/2*x^8*e*d^2*c^3*a + 9/2*x^8*e^2*d*c^2*b*a + 3/2*x^8*e^3*c*b^2*a + 3/4*x^8*e^3*c^2*a^2 + 6/7*x^7*d^3*c^2*b^2 + 12/7*x^7*e*d^2*c*b^3 + 3/7*x^7*e^2*d*b^4 + 4/7*x^7*d^3*c^3*a + 36/7*x^7*e*d^2*c^2*b*a + 36/7*x^7*e^2*d*c*b^2*a + 4/7*x^7*e^3*b^3*a + 18/7*x^7*e^2*d*c^2*a^2 + 12/7*x^7*e^3*c*b*a^2 + 2/3*x^6*d^3*c*b^3 + 1/2*x^6*e*d^2*b^4 + 2*x^6*d^3*c^2*b*a + 6*x^6*e*d^2*c*b^2*a + 2*x^6*e^2*d*b^3*a + 3*x^6*e*d^2*c^2*a^2 + 6*x^6*e^2*d*c*b*a^2 + x^6*e^3*b^2*a^2 + 2/3*x^6*e^3*c*a^3 + 1/5*x^5*d^3*b^4 + 12/5*x^5*d^3*c*b^2*a + 12/5*x^5*e*d^2*b^3*a + 6/5*x^5*d^3*c^2*a^2 + 36/5*x^5*e*d^2*c*b*a^2 + 18/5*x^5*e^2*d*b^2*a^2 + 12/5*x^5*e^2*d*c*a^3 + 4/5*x^5*e^3*b*a^3 + x^4*d^3*b^3*a + 3*x^4*d^3*c*b*a^2 + 9/2*x^4*e*d^2*b^2*a^2 + 3*x^4*e*d^2*c*a^3 + 3*x^4*e^2*d*b*a^3 + 1/4*x^4*e^3*a^4 + 2*x^3*d^3*b^2*a^2 + 4/3*x^3*d^3*c*a^3 + 4*x^3*e*d^2*b*a^3 + x^3*e^2*d*a^4 + 2*x^2*d^3*b*a^3 + 3/2*x^2*e*d^2*a^4 + x*d^3*a^4","A",0
2148,1,537,0,0.360631," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{2} c^{4} + \frac{1}{5} x^{10} e d c^{4} + \frac{2}{5} x^{10} e^{2} c^{3} b + \frac{1}{9} x^{9} d^{2} c^{4} + \frac{8}{9} x^{9} e d c^{3} b + \frac{2}{3} x^{9} e^{2} c^{2} b^{2} + \frac{4}{9} x^{9} e^{2} c^{3} a + \frac{1}{2} x^{8} d^{2} c^{3} b + \frac{3}{2} x^{8} e d c^{2} b^{2} + \frac{1}{2} x^{8} e^{2} c b^{3} + x^{8} e d c^{3} a + \frac{3}{2} x^{8} e^{2} c^{2} b a + \frac{6}{7} x^{7} d^{2} c^{2} b^{2} + \frac{8}{7} x^{7} e d c b^{3} + \frac{1}{7} x^{7} e^{2} b^{4} + \frac{4}{7} x^{7} d^{2} c^{3} a + \frac{24}{7} x^{7} e d c^{2} b a + \frac{12}{7} x^{7} e^{2} c b^{2} a + \frac{6}{7} x^{7} e^{2} c^{2} a^{2} + \frac{2}{3} x^{6} d^{2} c b^{3} + \frac{1}{3} x^{6} e d b^{4} + 2 x^{6} d^{2} c^{2} b a + 4 x^{6} e d c b^{2} a + \frac{2}{3} x^{6} e^{2} b^{3} a + 2 x^{6} e d c^{2} a^{2} + 2 x^{6} e^{2} c b a^{2} + \frac{1}{5} x^{5} d^{2} b^{4} + \frac{12}{5} x^{5} d^{2} c b^{2} a + \frac{8}{5} x^{5} e d b^{3} a + \frac{6}{5} x^{5} d^{2} c^{2} a^{2} + \frac{24}{5} x^{5} e d c b a^{2} + \frac{6}{5} x^{5} e^{2} b^{2} a^{2} + \frac{4}{5} x^{5} e^{2} c a^{3} + x^{4} d^{2} b^{3} a + 3 x^{4} d^{2} c b a^{2} + 3 x^{4} e d b^{2} a^{2} + 2 x^{4} e d c a^{3} + x^{4} e^{2} b a^{3} + 2 x^{3} d^{2} b^{2} a^{2} + \frac{4}{3} x^{3} d^{2} c a^{3} + \frac{8}{3} x^{3} e d b a^{3} + \frac{1}{3} x^{3} e^{2} a^{4} + 2 x^{2} d^{2} b a^{3} + x^{2} e d a^{4} + x d^{2} a^{4}"," ",0,"1/11*x^11*e^2*c^4 + 1/5*x^10*e*d*c^4 + 2/5*x^10*e^2*c^3*b + 1/9*x^9*d^2*c^4 + 8/9*x^9*e*d*c^3*b + 2/3*x^9*e^2*c^2*b^2 + 4/9*x^9*e^2*c^3*a + 1/2*x^8*d^2*c^3*b + 3/2*x^8*e*d*c^2*b^2 + 1/2*x^8*e^2*c*b^3 + x^8*e*d*c^3*a + 3/2*x^8*e^2*c^2*b*a + 6/7*x^7*d^2*c^2*b^2 + 8/7*x^7*e*d*c*b^3 + 1/7*x^7*e^2*b^4 + 4/7*x^7*d^2*c^3*a + 24/7*x^7*e*d*c^2*b*a + 12/7*x^7*e^2*c*b^2*a + 6/7*x^7*e^2*c^2*a^2 + 2/3*x^6*d^2*c*b^3 + 1/3*x^6*e*d*b^4 + 2*x^6*d^2*c^2*b*a + 4*x^6*e*d*c*b^2*a + 2/3*x^6*e^2*b^3*a + 2*x^6*e*d*c^2*a^2 + 2*x^6*e^2*c*b*a^2 + 1/5*x^5*d^2*b^4 + 12/5*x^5*d^2*c*b^2*a + 8/5*x^5*e*d*b^3*a + 6/5*x^5*d^2*c^2*a^2 + 24/5*x^5*e*d*c*b*a^2 + 6/5*x^5*e^2*b^2*a^2 + 4/5*x^5*e^2*c*a^3 + x^4*d^2*b^3*a + 3*x^4*d^2*c*b*a^2 + 3*x^4*e*d*b^2*a^2 + 2*x^4*e*d*c*a^3 + x^4*e^2*b*a^3 + 2*x^3*d^2*b^2*a^2 + 4/3*x^3*d^2*c*a^3 + 8/3*x^3*e*d*b*a^3 + 1/3*x^3*e^2*a^4 + 2*x^2*d^2*b*a^3 + x^2*e*d*a^4 + x*d^2*a^4","A",0
2149,1,307,0,0.354188," ","integrate((e*x+d)*(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\frac{1}{10} x^{10} e c^{4} + \frac{1}{9} x^{9} d c^{4} + \frac{4}{9} x^{9} e c^{3} b + \frac{1}{2} x^{8} d c^{3} b + \frac{3}{4} x^{8} e c^{2} b^{2} + \frac{1}{2} x^{8} e c^{3} a + \frac{6}{7} x^{7} d c^{2} b^{2} + \frac{4}{7} x^{7} e c b^{3} + \frac{4}{7} x^{7} d c^{3} a + \frac{12}{7} x^{7} e c^{2} b a + \frac{2}{3} x^{6} d c b^{3} + \frac{1}{6} x^{6} e b^{4} + 2 x^{6} d c^{2} b a + 2 x^{6} e c b^{2} a + x^{6} e c^{2} a^{2} + \frac{1}{5} x^{5} d b^{4} + \frac{12}{5} x^{5} d c b^{2} a + \frac{4}{5} x^{5} e b^{3} a + \frac{6}{5} x^{5} d c^{2} a^{2} + \frac{12}{5} x^{5} e c b a^{2} + x^{4} d b^{3} a + 3 x^{4} d c b a^{2} + \frac{3}{2} x^{4} e b^{2} a^{2} + x^{4} e c a^{3} + 2 x^{3} d b^{2} a^{2} + \frac{4}{3} x^{3} d c a^{3} + \frac{4}{3} x^{3} e b a^{3} + 2 x^{2} d b a^{3} + \frac{1}{2} x^{2} e a^{4} + x d a^{4}"," ",0,"1/10*x^10*e*c^4 + 1/9*x^9*d*c^4 + 4/9*x^9*e*c^3*b + 1/2*x^8*d*c^3*b + 3/4*x^8*e*c^2*b^2 + 1/2*x^8*e*c^3*a + 6/7*x^7*d*c^2*b^2 + 4/7*x^7*e*c*b^3 + 4/7*x^7*d*c^3*a + 12/7*x^7*e*c^2*b*a + 2/3*x^6*d*c*b^3 + 1/6*x^6*e*b^4 + 2*x^6*d*c^2*b*a + 2*x^6*e*c*b^2*a + x^6*e*c^2*a^2 + 1/5*x^5*d*b^4 + 12/5*x^5*d*c*b^2*a + 4/5*x^5*e*b^3*a + 6/5*x^5*d*c^2*a^2 + 12/5*x^5*e*c*b*a^2 + x^4*d*b^3*a + 3*x^4*d*c*b*a^2 + 3/2*x^4*e*b^2*a^2 + x^4*e*c*a^3 + 2*x^3*d*b^2*a^2 + 4/3*x^3*d*c*a^3 + 4/3*x^3*e*b*a^3 + 2*x^2*d*b*a^3 + 1/2*x^2*e*a^4 + x*d*a^4","A",0
2150,1,138,0,0.352596," ","integrate((c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{4} + \frac{1}{2} x^{8} c^{3} b + \frac{6}{7} x^{7} c^{2} b^{2} + \frac{4}{7} x^{7} c^{3} a + \frac{2}{3} x^{6} c b^{3} + 2 x^{6} c^{2} b a + \frac{1}{5} x^{5} b^{4} + \frac{12}{5} x^{5} c b^{2} a + \frac{6}{5} x^{5} c^{2} a^{2} + x^{4} b^{3} a + 3 x^{4} c b a^{2} + 2 x^{3} b^{2} a^{2} + \frac{4}{3} x^{3} c a^{3} + 2 x^{2} b a^{3} + x a^{4}"," ",0,"1/9*x^9*c^4 + 1/2*x^8*c^3*b + 6/7*x^7*c^2*b^2 + 4/7*x^7*c^3*a + 2/3*x^6*c*b^3 + 2*x^6*c^2*b*a + 1/5*x^5*b^4 + 12/5*x^5*c*b^2*a + 6/5*x^5*c^2*a^2 + x^4*b^3*a + 3*x^4*c*b*a^2 + 2*x^3*b^2*a^2 + 4/3*x^3*c*a^3 + 2*x^2*b*a^3 + x*a^4","A",0
2151,1,799,0,0.392362," ","integrate((c*x^2+b*x+a)^4/(e*x+d),x, algorithm=""fricas"")","\frac{105 \, c^{4} e^{8} x^{8} - 120 \, {\left(c^{4} d e^{7} - 4 \, b c^{3} e^{8}\right)} x^{7} + 140 \, {\left(c^{4} d^{2} e^{6} - 4 \, b c^{3} d e^{7} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} - 168 \, {\left(c^{4} d^{3} e^{5} - 4 \, b c^{3} d^{2} e^{6} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} + 210 \, {\left(c^{4} d^{4} e^{4} - 4 \, b c^{3} d^{3} e^{5} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} - 280 \, {\left(c^{4} d^{5} e^{3} - 4 \, b c^{3} d^{4} e^{4} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} + 420 \, {\left(c^{4} d^{6} e^{2} - 4 \, b c^{3} d^{5} e^{3} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} - 840 \, {\left(c^{4} d^{7} e - 4 \, b c^{3} d^{6} e^{2} - 4 \, a^{3} b e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x + 840 \, {\left(c^{4} d^{8} - 4 \, b c^{3} d^{7} e - 4 \, a^{3} b d e^{7} + a^{4} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6}\right)} \log\left(e x + d\right)}{840 \, e^{9}}"," ",0,"1/840*(105*c^4*e^8*x^8 - 120*(c^4*d*e^7 - 4*b*c^3*e^8)*x^7 + 140*(c^4*d^2*e^6 - 4*b*c^3*d*e^7 + 2*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 - 168*(c^4*d^3*e^5 - 4*b*c^3*d^2*e^6 + 2*(3*b^2*c^2 + 2*a*c^3)*d*e^7 - 4*(b^3*c + 3*a*b*c^2)*e^8)*x^5 + 210*(c^4*d^4*e^4 - 4*b*c^3*d^3*e^5 + 2*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 4*(b^3*c + 3*a*b*c^2)*d*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 - 280*(c^4*d^5*e^3 - 4*b*c^3*d^4*e^4 + 2*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^2*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 - 4*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 420*(c^4*d^6*e^2 - 4*b*c^3*d^5*e^3 + 2*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^3*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 - 840*(c^4*d^7*e - 4*b*c^3*d^6*e^2 - 4*a^3*b*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^4*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x + 840*(c^4*d^8 - 4*b*c^3*d^7*e - 4*a^3*b*d*e^7 + a^4*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6)*log(e*x + d))/e^9","A",0
2152,1,1095,0,0.412141," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^2,x, algorithm=""fricas"")","\frac{15 \, c^{4} e^{8} x^{8} - 105 \, c^{4} d^{8} + 420 \, b c^{3} d^{7} e + 420 \, a^{3} b d e^{7} - 105 \, a^{4} e^{8} - 210 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + 420 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - 105 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 420 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 210 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} - 10 \, {\left(2 \, c^{4} d e^{7} - 7 \, b c^{3} e^{8}\right)} x^{7} + 14 \, {\left(2 \, c^{4} d^{2} e^{6} - 7 \, b c^{3} d e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} - 21 \, {\left(2 \, c^{4} d^{3} e^{5} - 7 \, b c^{3} d^{2} e^{6} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} + 35 \, {\left(2 \, c^{4} d^{4} e^{4} - 7 \, b c^{3} d^{3} e^{5} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} - 70 \, {\left(2 \, c^{4} d^{5} e^{3} - 7 \, b c^{3} d^{4} e^{4} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} + 210 \, {\left(2 \, c^{4} d^{6} e^{2} - 7 \, b c^{3} d^{5} e^{3} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} + 105 \, {\left(7 \, c^{4} d^{7} e - 24 \, b c^{3} d^{6} e^{2} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 16 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 8 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x - 420 \, {\left(2 \, c^{4} d^{8} - 7 \, b c^{3} d^{7} e - a^{3} b d e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} + {\left(2 \, c^{4} d^{7} e - 7 \, b c^{3} d^{6} e^{2} - a^{3} b e^{8} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x\right)} \log\left(e x + d\right)}{105 \, {\left(e^{10} x + d e^{9}\right)}}"," ",0,"1/105*(15*c^4*e^8*x^8 - 105*c^4*d^8 + 420*b*c^3*d^7*e + 420*a^3*b*d*e^7 - 105*a^4*e^8 - 210*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + 420*(b^3*c + 3*a*b*c^2)*d^5*e^3 - 105*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 420*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 210*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 - 10*(2*c^4*d*e^7 - 7*b*c^3*e^8)*x^7 + 14*(2*c^4*d^2*e^6 - 7*b*c^3*d*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 - 21*(2*c^4*d^3*e^5 - 7*b*c^3*d^2*e^6 + 3*(3*b^2*c^2 + 2*a*c^3)*d*e^7 - 5*(b^3*c + 3*a*b*c^2)*e^8)*x^5 + 35*(2*c^4*d^4*e^4 - 7*b*c^3*d^3*e^5 + 3*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 5*(b^3*c + 3*a*b*c^2)*d*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 - 70*(2*c^4*d^5*e^3 - 7*b*c^3*d^4*e^4 + 3*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 5*(b^3*c + 3*a*b*c^2)*d^2*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 - 3*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 210*(2*c^4*d^6*e^2 - 7*b*c^3*d^5*e^3 + 3*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 5*(b^3*c + 3*a*b*c^2)*d^3*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 3*(a*b^3 + 3*a^2*b*c)*d*e^7 + (3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 + 105*(7*c^4*d^7*e - 24*b*c^3*d^6*e^2 + 10*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 16*(b^3*c + 3*a*b*c^2)*d^4*e^4 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 8*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x - 420*(2*c^4*d^8 - 7*b*c^3*d^7*e - a^3*b*d*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 5*(b^3*c + 3*a*b*c^2)*d^5*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - 3*(a*b^3 + 3*a^2*b*c)*d^3*e^5 + (3*a^2*b^2 + 2*a^3*c)*d^2*e^6 + (2*c^4*d^7*e - 7*b*c^3*d^6*e^2 - a^3*b*e^8 + 3*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 5*(b^3*c + 3*a*b*c^2)*d^4*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 3*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + (3*a^2*b^2 + 2*a^3*c)*d*e^7)*x)*log(e*x + d))/(e^10*x + d*e^9)","B",0
2153,1,1218,0,0.418263," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^3,x, algorithm=""fricas"")","\frac{5 \, c^{4} e^{8} x^{8} + 225 \, c^{4} d^{8} - 780 \, b c^{3} d^{7} e - 60 \, a^{3} b d e^{7} - 15 \, a^{4} e^{8} + 330 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - 540 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + 105 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} - 300 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} + 90 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} - 8 \, {\left(c^{4} d e^{7} - 3 \, b c^{3} e^{8}\right)} x^{7} + {\left(14 \, c^{4} d^{2} e^{6} - 42 \, b c^{3} d e^{7} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} - 2 \, {\left(14 \, c^{4} d^{3} e^{5} - 42 \, b c^{3} d^{2} e^{6} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} + 5 \, {\left(14 \, c^{4} d^{4} e^{4} - 42 \, b c^{3} d^{3} e^{5} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} - 20 \, {\left(14 \, c^{4} d^{5} e^{3} - 42 \, b c^{3} d^{4} e^{4} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} - 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} - 15 \, {\left(69 \, c^{4} d^{6} e^{2} - 200 \, b c^{3} d^{5} e^{3} + 68 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 84 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + 11 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 16 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7}\right)} x^{2} - 30 \, {\left(13 \, c^{4} d^{7} e - 32 \, b c^{3} d^{6} e^{2} + 4 \, a^{3} b e^{8} + 8 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} - {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} + 8 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} - 4 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x + 60 \, {\left(14 \, c^{4} d^{8} - 42 \, b c^{3} d^{7} e + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} - 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} + {\left(14 \, c^{4} d^{6} e^{2} - 42 \, b c^{3} d^{5} e^{3} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} + 2 \, {\left(14 \, c^{4} d^{7} e - 42 \, b c^{3} d^{6} e^{2} + 15 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x\right)} \log\left(e x + d\right)}{30 \, {\left(e^{11} x^{2} + 2 \, d e^{10} x + d^{2} e^{9}\right)}}"," ",0,"1/30*(5*c^4*e^8*x^8 + 225*c^4*d^8 - 780*b*c^3*d^7*e - 60*a^3*b*d*e^7 - 15*a^4*e^8 + 330*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 540*(b^3*c + 3*a*b*c^2)*d^5*e^3 + 105*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - 300*(a*b^3 + 3*a^2*b*c)*d^3*e^5 + 90*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 - 8*(c^4*d*e^7 - 3*b*c^3*e^8)*x^7 + (14*c^4*d^2*e^6 - 42*b*c^3*d*e^7 + 15*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 - 2*(14*c^4*d^3*e^5 - 42*b*c^3*d^2*e^6 + 15*(3*b^2*c^2 + 2*a*c^3)*d*e^7 - 20*(b^3*c + 3*a*b*c^2)*e^8)*x^5 + 5*(14*c^4*d^4*e^4 - 42*b*c^3*d^3*e^5 + 15*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 20*(b^3*c + 3*a*b*c^2)*d*e^7 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 - 20*(14*c^4*d^5*e^3 - 42*b*c^3*d^4*e^4 + 15*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 20*(b^3*c + 3*a*b*c^2)*d^2*e^6 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 - 6*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 - 15*(69*c^4*d^6*e^2 - 200*b*c^3*d^5*e^3 + 68*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 84*(b^3*c + 3*a*b*c^2)*d^3*e^5 + 11*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 16*(a*b^3 + 3*a^2*b*c)*d*e^7)*x^2 - 30*(13*c^4*d^7*e - 32*b*c^3*d^6*e^2 + 4*a^3*b*e^8 + 8*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^4*e^4 - (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 + 8*(a*b^3 + 3*a^2*b*c)*d^2*e^6 - 4*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x + 60*(14*c^4*d^8 - 42*b*c^3*d^7*e + 15*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 20*(b^3*c + 3*a*b*c^2)*d^5*e^3 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - 6*(a*b^3 + 3*a^2*b*c)*d^3*e^5 + (3*a^2*b^2 + 2*a^3*c)*d^2*e^6 + (14*c^4*d^6*e^2 - 42*b*c^3*d^5*e^3 + 15*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 20*(b^3*c + 3*a*b*c^2)*d^3*e^5 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 6*(a*b^3 + 3*a^2*b*c)*d*e^7 + (3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 + 2*(14*c^4*d^7*e - 42*b*c^3*d^6*e^2 + 15*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 20*(b^3*c + 3*a*b*c^2)*d^4*e^4 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 6*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + (3*a^2*b^2 + 2*a^3*c)*d*e^7)*x)*log(e*x + d))/(e^11*x^2 + 2*d*e^10*x + d^2*e^9)","B",0
2154,1,1282,0,0.404285," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^4,x, algorithm=""fricas"")","\frac{3 \, c^{4} e^{8} x^{8} - 365 \, c^{4} d^{8} + 1070 \, b c^{3} d^{7} e - 10 \, a^{3} b d e^{7} - 5 \, a^{4} e^{8} - 370 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + 470 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - 65 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 110 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 10 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} - 3 \, {\left(2 \, c^{4} d e^{7} - 5 \, b c^{3} e^{8}\right)} x^{7} + {\left(14 \, c^{4} d^{2} e^{6} - 35 \, b c^{3} d e^{7} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} - 3 \, {\left(14 \, c^{4} d^{3} e^{5} - 35 \, b c^{3} d^{2} e^{6} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} + 15 \, {\left(14 \, c^{4} d^{4} e^{4} - 35 \, b c^{3} d^{3} e^{5} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} + 5 \, {\left(235 \, c^{4} d^{5} e^{3} - 556 \, b c^{3} d^{4} e^{4} + 146 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 126 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + 9 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7}\right)} x^{3} + 15 \, {\left(67 \, c^{4} d^{6} e^{2} - 136 \, b c^{3} d^{5} e^{3} + 26 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 6 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} - 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} + 12 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} - 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} - 15 \, {\left(17 \, c^{4} d^{7} e - 74 \, b c^{3} d^{6} e^{2} + 2 \, a^{3} b e^{8} + 34 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 54 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + 9 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 18 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x - 60 \, {\left(14 \, c^{4} d^{8} - 35 \, b c^{3} d^{7} e + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} - {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} + {\left(14 \, c^{4} d^{5} e^{3} - 35 \, b c^{3} d^{4} e^{4} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} - {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} + 3 \, {\left(14 \, c^{4} d^{6} e^{2} - 35 \, b c^{3} d^{5} e^{3} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7}\right)} x^{2} + 3 \, {\left(14 \, c^{4} d^{7} e - 35 \, b c^{3} d^{6} e^{2} + 10 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6}\right)} x\right)} \log\left(e x + d\right)}{15 \, {\left(e^{12} x^{3} + 3 \, d e^{11} x^{2} + 3 \, d^{2} e^{10} x + d^{3} e^{9}\right)}}"," ",0,"1/15*(3*c^4*e^8*x^8 - 365*c^4*d^8 + 1070*b*c^3*d^7*e - 10*a^3*b*d*e^7 - 5*a^4*e^8 - 370*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + 470*(b^3*c + 3*a*b*c^2)*d^5*e^3 - 65*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 110*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 10*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 - 3*(2*c^4*d*e^7 - 5*b*c^3*e^8)*x^7 + (14*c^4*d^2*e^6 - 35*b*c^3*d*e^7 + 10*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 - 3*(14*c^4*d^3*e^5 - 35*b*c^3*d^2*e^6 + 10*(3*b^2*c^2 + 2*a*c^3)*d*e^7 - 10*(b^3*c + 3*a*b*c^2)*e^8)*x^5 + 15*(14*c^4*d^4*e^4 - 35*b*c^3*d^3*e^5 + 10*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 10*(b^3*c + 3*a*b*c^2)*d*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 + 5*(235*c^4*d^5*e^3 - 556*b*c^3*d^4*e^4 + 146*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 126*(b^3*c + 3*a*b*c^2)*d^2*e^6 + 9*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7)*x^3 + 15*(67*c^4*d^6*e^2 - 136*b*c^3*d^5*e^3 + 26*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 6*(b^3*c + 3*a*b*c^2)*d^3*e^5 - 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 + 12*(a*b^3 + 3*a^2*b*c)*d*e^7 - 2*(3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 - 15*(17*c^4*d^7*e - 74*b*c^3*d^6*e^2 + 2*a^3*b*e^8 + 34*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 54*(b^3*c + 3*a*b*c^2)*d^4*e^4 + 9*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 18*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x - 60*(14*c^4*d^8 - 35*b*c^3*d^7*e + 10*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 10*(b^3*c + 3*a*b*c^2)*d^5*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - (a*b^3 + 3*a^2*b*c)*d^3*e^5 + (14*c^4*d^5*e^3 - 35*b*c^3*d^4*e^4 + 10*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 10*(b^3*c + 3*a*b*c^2)*d^2*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 - (a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 3*(14*c^4*d^6*e^2 - 35*b*c^3*d^5*e^3 + 10*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 10*(b^3*c + 3*a*b*c^2)*d^3*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - (a*b^3 + 3*a^2*b*c)*d*e^7)*x^2 + 3*(14*c^4*d^7*e - 35*b*c^3*d^6*e^2 + 10*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 10*(b^3*c + 3*a*b*c^2)*d^4*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - (a*b^3 + 3*a^2*b*c)*d^2*e^6)*x)*log(e*x + d))/(e^12*x^3 + 3*d*e^11*x^2 + 3*d^2*e^10*x + d^3*e^9)","B",0
2155,1,1303,0,0.417253," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^5,x, algorithm=""fricas"")","\frac{3 \, c^{4} e^{8} x^{8} + 533 \, c^{4} d^{8} - 1276 \, b c^{3} d^{7} e - 4 \, a^{3} b d e^{7} - 3 \, a^{4} e^{8} + 342 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - 308 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + 25 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} - 12 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} - 8 \, {\left(c^{4} d e^{7} - 2 \, b c^{3} e^{8}\right)} x^{7} + 4 \, {\left(7 \, c^{4} d^{2} e^{6} - 14 \, b c^{3} d e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} - 24 \, {\left(7 \, c^{4} d^{3} e^{5} - 14 \, b c^{3} d^{2} e^{6} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} - 2 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} - {\left(1217 \, c^{4} d^{4} e^{4} - 2224 \, b c^{3} d^{3} e^{5} + 408 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 192 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7}\right)} x^{4} - 4 \, {\left(377 \, c^{4} d^{5} e^{3} - 544 \, b c^{3} d^{4} e^{4} + 48 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} + 48 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} - 12 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 12 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} + 6 \, {\left(43 \, c^{4} d^{6} e^{2} - 296 \, b c^{3} d^{5} e^{3} + 132 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 168 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + 18 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 12 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} - 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} + 4 \, {\left(323 \, c^{4} d^{7} e - 856 \, b c^{3} d^{6} e^{2} - 4 \, a^{3} b e^{8} + 252 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 248 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + 22 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 12 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} - 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x + 12 \, {\left(70 \, c^{4} d^{8} - 140 \, b c^{3} d^{7} e + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + {\left(70 \, c^{4} d^{4} e^{4} - 140 \, b c^{3} d^{3} e^{5} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} + 4 \, {\left(70 \, c^{4} d^{5} e^{3} - 140 \, b c^{3} d^{4} e^{4} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7}\right)} x^{3} + 6 \, {\left(70 \, c^{4} d^{6} e^{2} - 140 \, b c^{3} d^{5} e^{3} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6}\right)} x^{2} + 4 \, {\left(70 \, c^{4} d^{7} e - 140 \, b c^{3} d^{6} e^{2} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5}\right)} x\right)} \log\left(e x + d\right)}{12 \, {\left(e^{13} x^{4} + 4 \, d e^{12} x^{3} + 6 \, d^{2} e^{11} x^{2} + 4 \, d^{3} e^{10} x + d^{4} e^{9}\right)}}"," ",0,"1/12*(3*c^4*e^8*x^8 + 533*c^4*d^8 - 1276*b*c^3*d^7*e - 4*a^3*b*d*e^7 - 3*a^4*e^8 + 342*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 308*(b^3*c + 3*a*b*c^2)*d^5*e^3 + 25*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - 12*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 - 8*(c^4*d*e^7 - 2*b*c^3*e^8)*x^7 + 4*(7*c^4*d^2*e^6 - 14*b*c^3*d*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 - 24*(7*c^4*d^3*e^5 - 14*b*c^3*d^2*e^6 + 3*(3*b^2*c^2 + 2*a*c^3)*d*e^7 - 2*(b^3*c + 3*a*b*c^2)*e^8)*x^5 - (1217*c^4*d^4*e^4 - 2224*b*c^3*d^3*e^5 + 408*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 192*(b^3*c + 3*a*b*c^2)*d*e^7)*x^4 - 4*(377*c^4*d^5*e^3 - 544*b*c^3*d^4*e^4 + 48*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 + 48*(b^3*c + 3*a*b*c^2)*d^2*e^6 - 12*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 12*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 6*(43*c^4*d^6*e^2 - 296*b*c^3*d^5*e^3 + 132*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 168*(b^3*c + 3*a*b*c^2)*d^3*e^5 + 18*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 12*(a*b^3 + 3*a^2*b*c)*d*e^7 - 2*(3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 + 4*(323*c^4*d^7*e - 856*b*c^3*d^6*e^2 - 4*a^3*b*e^8 + 252*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 248*(b^3*c + 3*a*b*c^2)*d^4*e^4 + 22*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 12*(a*b^3 + 3*a^2*b*c)*d^2*e^6 - 2*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x + 12*(70*c^4*d^8 - 140*b*c^3*d^7*e + 30*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 20*(b^3*c + 3*a*b*c^2)*d^5*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + (70*c^4*d^4*e^4 - 140*b*c^3*d^3*e^5 + 30*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 20*(b^3*c + 3*a*b*c^2)*d*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 + 4*(70*c^4*d^5*e^3 - 140*b*c^3*d^4*e^4 + 30*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 20*(b^3*c + 3*a*b*c^2)*d^2*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7)*x^3 + 6*(70*c^4*d^6*e^2 - 140*b*c^3*d^5*e^3 + 30*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 20*(b^3*c + 3*a*b*c^2)*d^3*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6)*x^2 + 4*(70*c^4*d^7*e - 140*b*c^3*d^6*e^2 + 30*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 20*(b^3*c + 3*a*b*c^2)*d^4*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5)*x)*log(e*x + d))/(e^13*x^4 + 4*d*e^12*x^3 + 6*d^2*e^11*x^2 + 4*d^3*e^10*x + d^4*e^9)","B",0
2156,1,1262,0,0.413968," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^6,x, algorithm=""fricas"")","\frac{5 \, c^{4} e^{8} x^{8} - 743 \, c^{4} d^{8} + 1377 \, b c^{3} d^{7} e - 3 \, a^{3} b d e^{7} - 3 \, a^{4} e^{8} - 261 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + 137 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} - 10 \, {\left(2 \, c^{4} d e^{7} - 3 \, b c^{3} e^{8}\right)} x^{7} + 10 \, {\left(14 \, c^{4} d^{2} e^{6} - 21 \, b c^{3} d e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} + 25 \, {\left(47 \, c^{4} d^{3} e^{5} - 60 \, b c^{3} d^{2} e^{6} + 6 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7}\right)} x^{5} + 5 \, {\left(335 \, c^{4} d^{4} e^{4} - 240 \, b c^{3} d^{3} e^{5} - 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} + 60 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} - 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} - 10 \, {\left(85 \, c^{4} d^{5} e^{3} - 390 \, b c^{3} d^{4} e^{4} + 120 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 90 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} - 10 \, {\left(365 \, c^{4} d^{6} e^{2} - 810 \, b c^{3} d^{5} e^{3} + 180 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 110 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} + 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} - 5 \, {\left(575 \, c^{4} d^{7} e - 1125 \, b c^{3} d^{6} e^{2} + 3 \, a^{3} b e^{8} + 225 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 125 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} + 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x - 60 \, {\left(14 \, c^{4} d^{8} - 21 \, b c^{3} d^{7} e + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + {\left(14 \, c^{4} d^{3} e^{5} - 21 \, b c^{3} d^{2} e^{6} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} - {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} + 5 \, {\left(14 \, c^{4} d^{4} e^{4} - 21 \, b c^{3} d^{3} e^{5} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7}\right)} x^{4} + 10 \, {\left(14 \, c^{4} d^{5} e^{3} - 21 \, b c^{3} d^{4} e^{4} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6}\right)} x^{3} + 10 \, {\left(14 \, c^{4} d^{6} e^{2} - 21 \, b c^{3} d^{5} e^{3} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5}\right)} x^{2} + 5 \, {\left(14 \, c^{4} d^{7} e - 21 \, b c^{3} d^{6} e^{2} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4}\right)} x\right)} \log\left(e x + d\right)}{15 \, {\left(e^{14} x^{5} + 5 \, d e^{13} x^{4} + 10 \, d^{2} e^{12} x^{3} + 10 \, d^{3} e^{11} x^{2} + 5 \, d^{4} e^{10} x + d^{5} e^{9}\right)}}"," ",0,"1/15*(5*c^4*e^8*x^8 - 743*c^4*d^8 + 1377*b*c^3*d^7*e - 3*a^3*b*d*e^7 - 3*a^4*e^8 - 261*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + 137*(b^3*c + 3*a*b*c^2)*d^5*e^3 - 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - 3*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - (3*a^2*b^2 + 2*a^3*c)*d^2*e^6 - 10*(2*c^4*d*e^7 - 3*b*c^3*e^8)*x^7 + 10*(14*c^4*d^2*e^6 - 21*b*c^3*d*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 + 25*(47*c^4*d^3*e^5 - 60*b*c^3*d^2*e^6 + 6*(3*b^2*c^2 + 2*a*c^3)*d*e^7)*x^5 + 5*(335*c^4*d^4*e^4 - 240*b*c^3*d^3*e^5 - 30*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 + 60*(b^3*c + 3*a*b*c^2)*d*e^7 - 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 - 10*(85*c^4*d^5*e^3 - 390*b*c^3*d^4*e^4 + 120*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 90*(b^3*c + 3*a*b*c^2)*d^2*e^6 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 3*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 - 10*(365*c^4*d^6*e^2 - 810*b*c^3*d^5*e^3 + 180*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 110*(b^3*c + 3*a*b*c^2)*d^3*e^5 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 + 3*(a*b^3 + 3*a^2*b*c)*d*e^7 + (3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 - 5*(575*c^4*d^7*e - 1125*b*c^3*d^6*e^2 + 3*a^3*b*e^8 + 225*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 125*(b^3*c + 3*a*b*c^2)*d^4*e^4 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 + 3*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + (3*a^2*b^2 + 2*a^3*c)*d*e^7)*x - 60*(14*c^4*d^8 - 21*b*c^3*d^7*e + 3*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - (b^3*c + 3*a*b*c^2)*d^5*e^3 + (14*c^4*d^3*e^5 - 21*b*c^3*d^2*e^6 + 3*(3*b^2*c^2 + 2*a*c^3)*d*e^7 - (b^3*c + 3*a*b*c^2)*e^8)*x^5 + 5*(14*c^4*d^4*e^4 - 21*b*c^3*d^3*e^5 + 3*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - (b^3*c + 3*a*b*c^2)*d*e^7)*x^4 + 10*(14*c^4*d^5*e^3 - 21*b*c^3*d^4*e^4 + 3*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - (b^3*c + 3*a*b*c^2)*d^2*e^6)*x^3 + 10*(14*c^4*d^6*e^2 - 21*b*c^3*d^5*e^3 + 3*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - (b^3*c + 3*a*b*c^2)*d^3*e^5)*x^2 + 5*(14*c^4*d^7*e - 21*b*c^3*d^6*e^2 + 3*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - (b^3*c + 3*a*b*c^2)*d^4*e^4)*x)*log(e*x + d))/(e^14*x^5 + 5*d*e^13*x^4 + 10*d^2*e^12*x^3 + 10*d^3*e^11*x^2 + 5*d^4*e^10*x + d^5*e^9)","B",0
2157,1,1191,0,0.403692," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^7,x, algorithm=""fricas"")","\frac{15 \, c^{4} e^{8} x^{8} + 1023 \, c^{4} d^{8} - 1338 \, b c^{3} d^{7} e - 4 \, a^{3} b d e^{7} - 5 \, a^{4} e^{8} + 147 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} - 2 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} - 120 \, {\left(c^{4} d e^{7} - b c^{3} e^{8}\right)} x^{7} - 45 \, {\left(23 \, c^{4} d^{2} e^{6} - 16 \, b c^{3} d e^{7}\right)} x^{6} - 30 \, {\left(39 \, c^{4} d^{3} e^{5} + 24 \, b c^{3} d^{2} e^{6} - 12 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} + 15 \, {\left(225 \, c^{4} d^{4} e^{4} - 540 \, b c^{3} d^{3} e^{5} + 90 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} - {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} + 20 \, {\left(505 \, c^{4} d^{5} e^{3} - 820 \, b c^{3} d^{4} e^{4} + 110 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} - {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} - 2 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} + 15 \, {\left(715 \, c^{4} d^{6} e^{2} - 1030 \, b c^{3} d^{5} e^{3} + 125 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} - {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 2 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} - {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} + 6 \, {\left(883 \, c^{4} d^{7} e - 1198 \, b c^{3} d^{6} e^{2} - 4 \, a^{3} b e^{8} + 137 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} - {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 2 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} - {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x + 60 \, {\left(14 \, c^{4} d^{8} - 14 \, b c^{3} d^{7} e + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + {\left(14 \, c^{4} d^{2} e^{6} - 14 \, b c^{3} d e^{7} + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} + 6 \, {\left(14 \, c^{4} d^{3} e^{5} - 14 \, b c^{3} d^{2} e^{6} + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7}\right)} x^{5} + 15 \, {\left(14 \, c^{4} d^{4} e^{4} - 14 \, b c^{3} d^{3} e^{5} + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6}\right)} x^{4} + 20 \, {\left(14 \, c^{4} d^{5} e^{3} - 14 \, b c^{3} d^{4} e^{4} + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5}\right)} x^{3} + 15 \, {\left(14 \, c^{4} d^{6} e^{2} - 14 \, b c^{3} d^{5} e^{3} + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4}\right)} x^{2} + 6 \, {\left(14 \, c^{4} d^{7} e - 14 \, b c^{3} d^{6} e^{2} + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3}\right)} x\right)} \log\left(e x + d\right)}{30 \, {\left(e^{15} x^{6} + 6 \, d e^{14} x^{5} + 15 \, d^{2} e^{13} x^{4} + 20 \, d^{3} e^{12} x^{3} + 15 \, d^{4} e^{11} x^{2} + 6 \, d^{5} e^{10} x + d^{6} e^{9}\right)}}"," ",0,"1/30*(15*c^4*e^8*x^8 + 1023*c^4*d^8 - 1338*b*c^3*d^7*e - 4*a^3*b*d*e^7 - 5*a^4*e^8 + 147*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 20*(b^3*c + 3*a*b*c^2)*d^5*e^3 - (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - 2*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - (3*a^2*b^2 + 2*a^3*c)*d^2*e^6 - 120*(c^4*d*e^7 - b*c^3*e^8)*x^7 - 45*(23*c^4*d^2*e^6 - 16*b*c^3*d*e^7)*x^6 - 30*(39*c^4*d^3*e^5 + 24*b*c^3*d^2*e^6 - 12*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 4*(b^3*c + 3*a*b*c^2)*e^8)*x^5 + 15*(225*c^4*d^4*e^4 - 540*b*c^3*d^3*e^5 + 90*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 20*(b^3*c + 3*a*b*c^2)*d*e^7 - (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 + 20*(505*c^4*d^5*e^3 - 820*b*c^3*d^4*e^4 + 110*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 20*(b^3*c + 3*a*b*c^2)*d^2*e^6 - (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 - 2*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 15*(715*c^4*d^6*e^2 - 1030*b*c^3*d^5*e^3 + 125*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 20*(b^3*c + 3*a*b*c^2)*d^3*e^5 - (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 2*(a*b^3 + 3*a^2*b*c)*d*e^7 - (3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 + 6*(883*c^4*d^7*e - 1198*b*c^3*d^6*e^2 - 4*a^3*b*e^8 + 137*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 20*(b^3*c + 3*a*b*c^2)*d^4*e^4 - (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 2*(a*b^3 + 3*a^2*b*c)*d^2*e^6 - (3*a^2*b^2 + 2*a^3*c)*d*e^7)*x + 60*(14*c^4*d^8 - 14*b*c^3*d^7*e + (3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + (14*c^4*d^2*e^6 - 14*b*c^3*d*e^7 + (3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 + 6*(14*c^4*d^3*e^5 - 14*b*c^3*d^2*e^6 + (3*b^2*c^2 + 2*a*c^3)*d*e^7)*x^5 + 15*(14*c^4*d^4*e^4 - 14*b*c^3*d^3*e^5 + (3*b^2*c^2 + 2*a*c^3)*d^2*e^6)*x^4 + 20*(14*c^4*d^5*e^3 - 14*b*c^3*d^4*e^4 + (3*b^2*c^2 + 2*a*c^3)*d^3*e^5)*x^3 + 15*(14*c^4*d^6*e^2 - 14*b*c^3*d^5*e^3 + (3*b^2*c^2 + 2*a*c^3)*d^4*e^4)*x^2 + 6*(14*c^4*d^7*e - 14*b*c^3*d^6*e^2 + (3*b^2*c^2 + 2*a*c^3)*d^5*e^3)*x)*log(e*x + d))/(e^15*x^6 + 6*d*e^14*x^5 + 15*d^2*e^13*x^4 + 20*d^3*e^12*x^3 + 15*d^4*e^11*x^2 + 6*d^5*e^10*x + d^6*e^9)","B",0
2158,1,1082,0,0.400839," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^8,x, algorithm=""fricas"")","\frac{105 \, c^{4} e^{8} x^{8} + 735 \, c^{4} d e^{7} x^{7} - 1443 \, c^{4} d^{8} + 1089 \, b c^{3} d^{7} e - 10 \, a^{3} b d e^{7} - 15 \, a^{4} e^{8} - 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} - 105 \, {\left(7 \, c^{4} d^{2} e^{6} - 28 \, b c^{3} d e^{7} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} - 105 \, {\left(105 \, c^{4} d^{3} e^{5} - 126 \, b c^{3} d^{2} e^{6} + 6 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 2 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} - 35 \, {\left(805 \, c^{4} d^{4} e^{4} - 770 \, b c^{3} d^{3} e^{5} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} + 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} - 35 \, {\left(1015 \, c^{4} d^{5} e^{3} - 875 \, b c^{3} d^{4} e^{4} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} + 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} - 21 \, {\left(1183 \, c^{4} d^{6} e^{2} - 959 \, b c^{3} d^{5} e^{3} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} + 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} + 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} - 7 \, {\left(1323 \, c^{4} d^{7} e - 1029 \, b c^{3} d^{6} e^{2} + 10 \, a^{3} b e^{8} + 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} + 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} + 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x - 420 \, {\left(2 \, c^{4} d^{8} - b c^{3} d^{7} e + {\left(2 \, c^{4} d e^{7} - b c^{3} e^{8}\right)} x^{7} + 7 \, {\left(2 \, c^{4} d^{2} e^{6} - b c^{3} d e^{7}\right)} x^{6} + 21 \, {\left(2 \, c^{4} d^{3} e^{5} - b c^{3} d^{2} e^{6}\right)} x^{5} + 35 \, {\left(2 \, c^{4} d^{4} e^{4} - b c^{3} d^{3} e^{5}\right)} x^{4} + 35 \, {\left(2 \, c^{4} d^{5} e^{3} - b c^{3} d^{4} e^{4}\right)} x^{3} + 21 \, {\left(2 \, c^{4} d^{6} e^{2} - b c^{3} d^{5} e^{3}\right)} x^{2} + 7 \, {\left(2 \, c^{4} d^{7} e - b c^{3} d^{6} e^{2}\right)} x\right)} \log\left(e x + d\right)}{105 \, {\left(e^{16} x^{7} + 7 \, d e^{15} x^{6} + 21 \, d^{2} e^{14} x^{5} + 35 \, d^{3} e^{13} x^{4} + 35 \, d^{4} e^{12} x^{3} + 21 \, d^{5} e^{11} x^{2} + 7 \, d^{6} e^{10} x + d^{7} e^{9}\right)}}"," ",0,"1/105*(105*c^4*e^8*x^8 + 735*c^4*d*e^7*x^7 - 1443*c^4*d^8 + 1089*b*c^3*d^7*e - 10*a^3*b*d*e^7 - 15*a^4*e^8 - 30*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 10*(b^3*c + 3*a*b*c^2)*d^5*e^3 - (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - 3*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 - 105*(7*c^4*d^2*e^6 - 28*b*c^3*d*e^7 + 2*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 - 105*(105*c^4*d^3*e^5 - 126*b*c^3*d^2*e^6 + 6*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 2*(b^3*c + 3*a*b*c^2)*e^8)*x^5 - 35*(805*c^4*d^4*e^4 - 770*b*c^3*d^3*e^5 + 30*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 + 10*(b^3*c + 3*a*b*c^2)*d*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 - 35*(1015*c^4*d^5*e^3 - 875*b*c^3*d^4*e^4 + 30*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 + 10*(b^3*c + 3*a*b*c^2)*d^2*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 3*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 - 21*(1183*c^4*d^6*e^2 - 959*b*c^3*d^5*e^3 + 30*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 + 10*(b^3*c + 3*a*b*c^2)*d^3*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 + 3*(a*b^3 + 3*a^2*b*c)*d*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 - 7*(1323*c^4*d^7*e - 1029*b*c^3*d^6*e^2 + 10*a^3*b*e^8 + 30*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 + 10*(b^3*c + 3*a*b*c^2)*d^4*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 + 3*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x - 420*(2*c^4*d^8 - b*c^3*d^7*e + (2*c^4*d*e^7 - b*c^3*e^8)*x^7 + 7*(2*c^4*d^2*e^6 - b*c^3*d*e^7)*x^6 + 21*(2*c^4*d^3*e^5 - b*c^3*d^2*e^6)*x^5 + 35*(2*c^4*d^4*e^4 - b*c^3*d^3*e^5)*x^4 + 35*(2*c^4*d^5*e^3 - b*c^3*d^4*e^4)*x^3 + 21*(2*c^4*d^6*e^2 - b*c^3*d^5*e^3)*x^2 + 7*(2*c^4*d^7*e - b*c^3*d^6*e^2)*x)*log(e*x + d))/(e^16*x^7 + 7*d*e^15*x^6 + 21*d^2*e^14*x^5 + 35*d^3*e^13*x^4 + 35*d^4*e^12*x^3 + 21*d^5*e^11*x^2 + 7*d^6*e^10*x + d^7*e^9)","B",0
2159,1,998,0,0.396216," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^9,x, algorithm=""fricas"")","\frac{2283 \, c^{4} d^{8} - 420 \, b c^{3} d^{7} e - 60 \, a^{3} b d e^{7} - 105 \, a^{4} e^{8} - 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} - 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} - 12 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} - 10 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} + 3360 \, {\left(2 \, c^{4} d e^{7} - b c^{3} e^{8}\right)} x^{7} + 840 \, {\left(42 \, c^{4} d^{2} e^{6} - 14 \, b c^{3} d e^{7} - {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} + 560 \, {\left(154 \, c^{4} d^{3} e^{5} - 42 \, b c^{3} d^{2} e^{6} - 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} - 2 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} + 70 \, {\left(1750 \, c^{4} d^{4} e^{4} - 420 \, b c^{3} d^{3} e^{5} - 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} - 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} + 56 \, {\left(1918 \, c^{4} d^{5} e^{3} - 420 \, b c^{3} d^{4} e^{4} - 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} - 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} - 12 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} + 28 \, {\left(2058 \, c^{4} d^{6} e^{2} - 420 \, b c^{3} d^{5} e^{3} - 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} - 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} - 12 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} - 10 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} + 8 \, {\left(2178 \, c^{4} d^{7} e - 420 \, b c^{3} d^{6} e^{2} - 60 \, a^{3} b e^{8} - 30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} - 20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} - 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} - 12 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} - 10 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x + 840 \, {\left(c^{4} e^{8} x^{8} + 8 \, c^{4} d e^{7} x^{7} + 28 \, c^{4} d^{2} e^{6} x^{6} + 56 \, c^{4} d^{3} e^{5} x^{5} + 70 \, c^{4} d^{4} e^{4} x^{4} + 56 \, c^{4} d^{5} e^{3} x^{3} + 28 \, c^{4} d^{6} e^{2} x^{2} + 8 \, c^{4} d^{7} e x + c^{4} d^{8}\right)} \log\left(e x + d\right)}{840 \, {\left(e^{17} x^{8} + 8 \, d e^{16} x^{7} + 28 \, d^{2} e^{15} x^{6} + 56 \, d^{3} e^{14} x^{5} + 70 \, d^{4} e^{13} x^{4} + 56 \, d^{5} e^{12} x^{3} + 28 \, d^{6} e^{11} x^{2} + 8 \, d^{7} e^{10} x + d^{8} e^{9}\right)}}"," ",0,"1/840*(2283*c^4*d^8 - 420*b*c^3*d^7*e - 60*a^3*b*d*e^7 - 105*a^4*e^8 - 30*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 - 20*(b^3*c + 3*a*b*c^2)*d^5*e^3 - 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 - 12*(a*b^3 + 3*a^2*b*c)*d^3*e^5 - 10*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 + 3360*(2*c^4*d*e^7 - b*c^3*e^8)*x^7 + 840*(42*c^4*d^2*e^6 - 14*b*c^3*d*e^7 - (3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 + 560*(154*c^4*d^3*e^5 - 42*b*c^3*d^2*e^6 - 3*(3*b^2*c^2 + 2*a*c^3)*d*e^7 - 2*(b^3*c + 3*a*b*c^2)*e^8)*x^5 + 70*(1750*c^4*d^4*e^4 - 420*b*c^3*d^3*e^5 - 30*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 - 20*(b^3*c + 3*a*b*c^2)*d*e^7 - 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 + 56*(1918*c^4*d^5*e^3 - 420*b*c^3*d^4*e^4 - 30*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 - 20*(b^3*c + 3*a*b*c^2)*d^2*e^6 - 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 - 12*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 28*(2058*c^4*d^6*e^2 - 420*b*c^3*d^5*e^3 - 30*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 - 20*(b^3*c + 3*a*b*c^2)*d^3*e^5 - 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 - 12*(a*b^3 + 3*a^2*b*c)*d*e^7 - 10*(3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 + 8*(2178*c^4*d^7*e - 420*b*c^3*d^6*e^2 - 60*a^3*b*e^8 - 30*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 - 20*(b^3*c + 3*a*b*c^2)*d^4*e^4 - 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 - 12*(a*b^3 + 3*a^2*b*c)*d^2*e^6 - 10*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x + 840*(c^4*e^8*x^8 + 8*c^4*d*e^7*x^7 + 28*c^4*d^2*e^6*x^6 + 56*c^4*d^3*e^5*x^5 + 70*c^4*d^4*e^4*x^4 + 56*c^4*d^5*e^3*x^3 + 28*c^4*d^6*e^2*x^2 + 8*c^4*d^7*e*x + c^4*d^8)*log(e*x + d))/(e^17*x^8 + 8*d*e^16*x^7 + 28*d^2*e^15*x^6 + 56*d^3*e^14*x^5 + 70*d^4*e^13*x^4 + 56*d^5*e^12*x^3 + 28*d^6*e^11*x^2 + 8*d^7*e^10*x + d^8*e^9)","B",0
2160,1,893,0,0.388462," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^10,x, algorithm=""fricas"")","-\frac{630 \, c^{4} e^{8} x^{8} + 70 \, c^{4} d^{8} + 35 \, b c^{3} d^{7} e + 35 \, a^{3} b d e^{7} + 70 \, a^{4} e^{8} + 5 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 5 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} + 5 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} + 1260 \, {\left(2 \, c^{4} d e^{7} + b c^{3} e^{8}\right)} x^{7} + 420 \, {\left(14 \, c^{4} d^{2} e^{6} + 7 \, b c^{3} d e^{7} + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} + 630 \, {\left(14 \, c^{4} d^{3} e^{5} + 7 \, b c^{3} d^{2} e^{6} + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} + 126 \, {\left(70 \, c^{4} d^{4} e^{4} + 35 \, b c^{3} d^{3} e^{5} + 5 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} + 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} + 84 \, {\left(70 \, c^{4} d^{5} e^{3} + 35 \, b c^{3} d^{4} e^{4} + 5 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} + 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 5 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} + 36 \, {\left(70 \, c^{4} d^{6} e^{2} + 35 \, b c^{3} d^{5} e^{3} + 5 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} + 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} + 5 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + 5 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} + 9 \, {\left(70 \, c^{4} d^{7} e + 35 \, b c^{3} d^{6} e^{2} + 35 \, a^{3} b e^{8} + 5 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} + 5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} + 5 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 5 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x}{630 \, {\left(e^{18} x^{9} + 9 \, d e^{17} x^{8} + 36 \, d^{2} e^{16} x^{7} + 84 \, d^{3} e^{15} x^{6} + 126 \, d^{4} e^{14} x^{5} + 126 \, d^{5} e^{13} x^{4} + 84 \, d^{6} e^{12} x^{3} + 36 \, d^{7} e^{11} x^{2} + 9 \, d^{8} e^{10} x + d^{9} e^{9}\right)}}"," ",0,"-1/630*(630*c^4*e^8*x^8 + 70*c^4*d^8 + 35*b*c^3*d^7*e + 35*a^3*b*d*e^7 + 70*a^4*e^8 + 5*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + 5*(b^3*c + 3*a*b*c^2)*d^5*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 5*(a*b^3 + 3*a^2*b*c)*d^3*e^5 + 5*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 + 1260*(2*c^4*d*e^7 + b*c^3*e^8)*x^7 + 420*(14*c^4*d^2*e^6 + 7*b*c^3*d*e^7 + (3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 + 630*(14*c^4*d^3*e^5 + 7*b*c^3*d^2*e^6 + (3*b^2*c^2 + 2*a*c^3)*d*e^7 + (b^3*c + 3*a*b*c^2)*e^8)*x^5 + 126*(70*c^4*d^4*e^4 + 35*b*c^3*d^3*e^5 + 5*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 + 5*(b^3*c + 3*a*b*c^2)*d*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 + 84*(70*c^4*d^5*e^3 + 35*b*c^3*d^4*e^4 + 5*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 + 5*(b^3*c + 3*a*b*c^2)*d^2*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 5*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 36*(70*c^4*d^6*e^2 + 35*b*c^3*d^5*e^3 + 5*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 + 5*(b^3*c + 3*a*b*c^2)*d^3*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 + 5*(a*b^3 + 3*a^2*b*c)*d*e^7 + 5*(3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 + 9*(70*c^4*d^7*e + 35*b*c^3*d^6*e^2 + 35*a^3*b*e^8 + 5*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 + 5*(b^3*c + 3*a*b*c^2)*d^4*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 + 5*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 5*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x)/(e^18*x^9 + 9*d*e^17*x^8 + 36*d^2*e^16*x^7 + 84*d^3*e^15*x^6 + 126*d^4*e^14*x^5 + 126*d^5*e^13*x^4 + 84*d^6*e^12*x^3 + 36*d^7*e^11*x^2 + 9*d^8*e^10*x + d^9*e^9)","B",0
2161,1,906,0,0.401197," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^11,x, algorithm=""fricas"")","-\frac{630 \, c^{4} e^{8} x^{8} + 14 \, c^{4} d^{8} + 14 \, b c^{3} d^{7} e + 56 \, a^{3} b d e^{7} + 126 \, a^{4} e^{8} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} + 7 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} + 1680 \, {\left(c^{4} d e^{7} + b c^{3} e^{8}\right)} x^{7} + 210 \, {\left(14 \, c^{4} d^{2} e^{6} + 14 \, b c^{3} d e^{7} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} + 252 \, {\left(14 \, c^{4} d^{3} e^{5} + 14 \, b c^{3} d^{2} e^{6} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} + 210 \, {\left(14 \, c^{4} d^{4} e^{4} + 14 \, b c^{3} d^{3} e^{5} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} + 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} + 120 \, {\left(14 \, c^{4} d^{5} e^{3} + 14 \, b c^{3} d^{4} e^{4} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} + 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} + 45 \, {\left(14 \, c^{4} d^{6} e^{2} + 14 \, b c^{3} d^{5} e^{3} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} + 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} + 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + 7 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} + 10 \, {\left(14 \, c^{4} d^{7} e + 14 \, b c^{3} d^{6} e^{2} + 56 \, a^{3} b e^{8} + 3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} + 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} + 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 7 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x}{1260 \, {\left(e^{19} x^{10} + 10 \, d e^{18} x^{9} + 45 \, d^{2} e^{17} x^{8} + 120 \, d^{3} e^{16} x^{7} + 210 \, d^{4} e^{15} x^{6} + 252 \, d^{5} e^{14} x^{5} + 210 \, d^{6} e^{13} x^{4} + 120 \, d^{7} e^{12} x^{3} + 45 \, d^{8} e^{11} x^{2} + 10 \, d^{9} e^{10} x + d^{10} e^{9}\right)}}"," ",0,"-1/1260*(630*c^4*e^8*x^8 + 14*c^4*d^8 + 14*b*c^3*d^7*e + 56*a^3*b*d*e^7 + 126*a^4*e^8 + 3*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + 4*(b^3*c + 3*a*b*c^2)*d^5*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 6*(a*b^3 + 3*a^2*b*c)*d^3*e^5 + 7*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 + 1680*(c^4*d*e^7 + b*c^3*e^8)*x^7 + 210*(14*c^4*d^2*e^6 + 14*b*c^3*d*e^7 + 3*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 + 252*(14*c^4*d^3*e^5 + 14*b*c^3*d^2*e^6 + 3*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 4*(b^3*c + 3*a*b*c^2)*e^8)*x^5 + 210*(14*c^4*d^4*e^4 + 14*b*c^3*d^3*e^5 + 3*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 + 4*(b^3*c + 3*a*b*c^2)*d*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 + 120*(14*c^4*d^5*e^3 + 14*b*c^3*d^4*e^4 + 3*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 + 4*(b^3*c + 3*a*b*c^2)*d^2*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 6*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 45*(14*c^4*d^6*e^2 + 14*b*c^3*d^5*e^3 + 3*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 + 4*(b^3*c + 3*a*b*c^2)*d^3*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 + 6*(a*b^3 + 3*a^2*b*c)*d*e^7 + 7*(3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 + 10*(14*c^4*d^7*e + 14*b*c^3*d^6*e^2 + 56*a^3*b*e^8 + 3*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 + 4*(b^3*c + 3*a*b*c^2)*d^4*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 + 6*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 7*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x)/(e^19*x^10 + 10*d*e^18*x^9 + 45*d^2*e^17*x^8 + 120*d^3*e^16*x^7 + 210*d^4*e^15*x^6 + 252*d^5*e^14*x^5 + 210*d^6*e^13*x^4 + 120*d^7*e^12*x^3 + 45*d^8*e^11*x^2 + 10*d^9*e^10*x + d^10*e^9)","B",0
2162,1,924,0,0.384319," ","integrate((c*x^2+b*x+a)^4/(e*x+d)^12,x, algorithm=""fricas"")","-\frac{2310 \, c^{4} e^{8} x^{8} + 14 \, c^{4} d^{8} + 21 \, b c^{3} d^{7} e + 252 \, a^{3} b d e^{7} + 630 \, a^{4} e^{8} + 6 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{2} + 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{3} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{4} + 21 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{5} + 28 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{6} + 2310 \, {\left(2 \, c^{4} d e^{7} + 3 \, b c^{3} e^{8}\right)} x^{7} + 462 \, {\left(14 \, c^{4} d^{2} e^{6} + 21 \, b c^{3} d e^{7} + 6 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{8}\right)} x^{6} + 462 \, {\left(14 \, c^{4} d^{3} e^{5} + 21 \, b c^{3} d^{2} e^{6} + 6 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{7} + 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{8}\right)} x^{5} + 330 \, {\left(14 \, c^{4} d^{4} e^{4} + 21 \, b c^{3} d^{3} e^{5} + 6 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{6} + 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{7} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{8}\right)} x^{4} + 165 \, {\left(14 \, c^{4} d^{5} e^{3} + 21 \, b c^{3} d^{4} e^{4} + 6 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{5} + 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{6} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{7} + 21 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{8}\right)} x^{3} + 55 \, {\left(14 \, c^{4} d^{6} e^{2} + 21 \, b c^{3} d^{5} e^{3} + 6 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{4} + 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{5} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{6} + 21 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{7} + 28 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{8}\right)} x^{2} + 11 \, {\left(14 \, c^{4} d^{7} e + 21 \, b c^{3} d^{6} e^{2} + 252 \, a^{3} b e^{8} + 6 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{3} + 10 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{4} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{5} + 21 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{6} + 28 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{7}\right)} x}{6930 \, {\left(e^{20} x^{11} + 11 \, d e^{19} x^{10} + 55 \, d^{2} e^{18} x^{9} + 165 \, d^{3} e^{17} x^{8} + 330 \, d^{4} e^{16} x^{7} + 462 \, d^{5} e^{15} x^{6} + 462 \, d^{6} e^{14} x^{5} + 330 \, d^{7} e^{13} x^{4} + 165 \, d^{8} e^{12} x^{3} + 55 \, d^{9} e^{11} x^{2} + 11 \, d^{10} e^{10} x + d^{11} e^{9}\right)}}"," ",0,"-1/6930*(2310*c^4*e^8*x^8 + 14*c^4*d^8 + 21*b*c^3*d^7*e + 252*a^3*b*d*e^7 + 630*a^4*e^8 + 6*(3*b^2*c^2 + 2*a*c^3)*d^6*e^2 + 10*(b^3*c + 3*a*b*c^2)*d^5*e^3 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^4 + 21*(a*b^3 + 3*a^2*b*c)*d^3*e^5 + 28*(3*a^2*b^2 + 2*a^3*c)*d^2*e^6 + 2310*(2*c^4*d*e^7 + 3*b*c^3*e^8)*x^7 + 462*(14*c^4*d^2*e^6 + 21*b*c^3*d*e^7 + 6*(3*b^2*c^2 + 2*a*c^3)*e^8)*x^6 + 462*(14*c^4*d^3*e^5 + 21*b*c^3*d^2*e^6 + 6*(3*b^2*c^2 + 2*a*c^3)*d*e^7 + 10*(b^3*c + 3*a*b*c^2)*e^8)*x^5 + 330*(14*c^4*d^4*e^4 + 21*b*c^3*d^3*e^5 + 6*(3*b^2*c^2 + 2*a*c^3)*d^2*e^6 + 10*(b^3*c + 3*a*b*c^2)*d*e^7 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^8)*x^4 + 165*(14*c^4*d^5*e^3 + 21*b*c^3*d^4*e^4 + 6*(3*b^2*c^2 + 2*a*c^3)*d^3*e^5 + 10*(b^3*c + 3*a*b*c^2)*d^2*e^6 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^7 + 21*(a*b^3 + 3*a^2*b*c)*e^8)*x^3 + 55*(14*c^4*d^6*e^2 + 21*b*c^3*d^5*e^3 + 6*(3*b^2*c^2 + 2*a*c^3)*d^4*e^4 + 10*(b^3*c + 3*a*b*c^2)*d^3*e^5 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^6 + 21*(a*b^3 + 3*a^2*b*c)*d*e^7 + 28*(3*a^2*b^2 + 2*a^3*c)*e^8)*x^2 + 11*(14*c^4*d^7*e + 21*b*c^3*d^6*e^2 + 252*a^3*b*e^8 + 6*(3*b^2*c^2 + 2*a*c^3)*d^5*e^3 + 10*(b^3*c + 3*a*b*c^2)*d^4*e^4 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^5 + 21*(a*b^3 + 3*a^2*b*c)*d^2*e^6 + 28*(3*a^2*b^2 + 2*a^3*c)*d*e^7)*x)/(e^20*x^11 + 11*d*e^19*x^10 + 55*d^2*e^18*x^9 + 165*d^3*e^17*x^8 + 330*d^4*e^16*x^7 + 462*d^5*e^15*x^6 + 462*d^6*e^14*x^5 + 330*d^7*e^13*x^4 + 165*d^8*e^12*x^3 + 55*d^9*e^11*x^2 + 11*d^10*e^10*x + d^11*e^9)","B",0
2163,1,26,0,0.341736," ","integrate(x^4*(x^2-4*x+3)^2,x, algorithm=""fricas"")","\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
2164,1,26,0,0.355705," ","integrate(x^3*(x^2-4*x+3)^2,x, algorithm=""fricas"")","\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
2165,1,26,0,0.348785," ","integrate(x^2*(x^2-4*x+3)^2,x, algorithm=""fricas"")","\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
2166,1,26,0,0.331003," ","integrate(x*(x^2-4*x+3)^2,x, algorithm=""fricas"")","\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
2167,1,24,0,0.330848," ","integrate((x^2-4*x+3)^2,x, algorithm=""fricas"")","\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
2168,1,23,0,0.385851," ","integrate((x^2-4*x+3)^2/x,x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} - \frac{8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log\left(x\right)"," ",0,"1/4*x^4 - 8/3*x^3 + 11*x^2 - 24*x + 9*log(x)","A",0
2169,1,25,0,0.391363," ","integrate((x^2-4*x+3)^2/x^2,x, algorithm=""fricas"")","\frac{x^{4} - 12 \, x^{3} + 66 \, x^{2} - 72 \, x \log\left(x\right) - 27}{3 \, x}"," ",0,"1/3*(x^4 - 12*x^3 + 66*x^2 - 72*x*log(x) - 27)/x","A",0
2170,1,25,0,0.386564," ","integrate((x^2-4*x+3)^2/x^3,x, algorithm=""fricas"")","\frac{x^{4} - 16 \, x^{3} + 44 \, x^{2} \log\left(x\right) + 48 \, x - 9}{2 \, x^{2}}"," ",0,"1/2*(x^4 - 16*x^3 + 44*x^2*log(x) + 48*x - 9)/x^2","A",0
2171,1,24,0,0.382099," ","integrate((x^2-4*x+3)^2/x^4,x, algorithm=""fricas"")","\frac{x^{4} - 8 \, x^{3} \log\left(x\right) - 22 \, x^{2} + 12 \, x - 3}{x^{3}}"," ",0,"(x^4 - 8*x^3*log(x) - 22*x^2 + 12*x - 3)/x^3","A",0
2172,1,27,0,0.381760," ","integrate((x^2-4*x+3)^2/x^5,x, algorithm=""fricas"")","\frac{4 \, x^{4} \log\left(x\right) + 32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}}"," ",0,"1/4*(4*x^4*log(x) + 32*x^3 - 44*x^2 + 32*x - 9)/x^4","A",0
2173,1,25,0,0.369998," ","integrate((x^2-4*x+3)^2/x^6,x, algorithm=""fricas"")","-\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
2174,1,25,0,0.390912," ","integrate((x^2-4*x+3)^2/x^7,x, algorithm=""fricas"")","-\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
2175,1,12,0,0.392240," ","integrate((x^2+2*x+2)/(2+x),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + 2 \, \log\left(x + 2\right)"," ",0,"1/2*x^2 + 2*log(x + 2)","A",0
2176,1,15,0,0.377136," ","integrate((x^2+4*x+5)/(-2+x),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + 6 \, x + 17 \, \log\left(x - 2\right)"," ",0,"1/2*x^2 + 6*x + 17*log(x - 2)","A",0
2177,1,28,0,0.396000," ","integrate((x^2+2*x+2)/(1+x)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(x^{2} + 2 \, x + 1\right)} \log\left(x + 1\right) - 1}{2 \, {\left(x^{2} + 2 \, x + 1\right)}}"," ",0,"1/2*(2*(x^2 + 2*x + 1)*log(x + 1) - 1)/(x^2 + 2*x + 1)","B",0
2178,1,27,0,0.390860," ","integrate((2*x^2+3*x+3)/(1+x)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(x^{2} + 2 \, x + 1\right)} \log\left(x + 1\right) + x}{x^{2} + 2 \, x + 1}"," ",0,"(2*(x^2 + 2*x + 1)*log(x + 1) + x)/(x^2 + 2*x + 1)","A",0
2179,1,9,0,0.391884," ","integrate((x^2+x+1)/x,x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + x + \log\left(x\right)"," ",0,"1/2*x^2 + x + log(x)","A",0
2180,1,14,0,0.387657," ","integrate((x^2+6*x+9)/x^2,x, algorithm=""fricas"")","\frac{x^{2} + 6 \, x \log\left(x\right) - 9}{x}"," ",0,"(x^2 + 6*x*log(x) - 9)/x","A",0
2181,1,15,0,0.377630," ","integrate((x^2+2*x+1)/x^4,x, algorithm=""fricas"")","-\frac{3 \, x^{2} + 3 \, x + 1}{3 \, x^{3}}"," ",0,"-1/3*(3*x^2 + 3*x + 1)/x^3","A",0
2182,1,821,0,0.487054," ","integrate((e*x+d)^4/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{4} x^{3} + 3 \, {\left(4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{3} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{4}\right)} x^{2} + 3 \, {\left(2 \, c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{2} - 4 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{4}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 6 \, {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{2} - 4 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{4}\right)} x + 3 \, {\left(4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e - 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{2} + 4 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e^{3} - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} e^{4}\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}, \frac{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{4} x^{3} + 3 \, {\left(4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{3} - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{4}\right)} x^{2} - 6 \, {\left(2 \, c^{4} d^{4} - 4 \, b c^{3} d^{3} e + 6 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{2} - 4 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d e^{3} + {\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 6 \, {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{2} - 4 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} + {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{4}\right)} x + 3 \, {\left(4 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e - 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{2} + 4 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e^{3} - {\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} e^{4}\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)}}\right]"," ",0,"[1/6*(2*(b^2*c^3 - 4*a*c^4)*e^4*x^3 + 3*(4*(b^2*c^3 - 4*a*c^4)*d*e^3 - (b^3*c^2 - 4*a*b*c^3)*e^4)*x^2 + 3*(2*c^4*d^4 - 4*b*c^3*d^3*e + 6*(b^2*c^2 - 2*a*c^3)*d^2*e^2 - 4*(b^3*c - 3*a*b*c^2)*d*e^3 + (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e^4)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 6*(6*(b^2*c^3 - 4*a*c^4)*d^2*e^2 - 4*(b^3*c^2 - 4*a*b*c^3)*d*e^3 + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^4)*x + 3*(4*(b^2*c^3 - 4*a*c^4)*d^3*e - 6*(b^3*c^2 - 4*a*b*c^3)*d^2*e^2 + 4*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d*e^3 - (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*e^4)*log(c*x^2 + b*x + a))/(b^2*c^4 - 4*a*c^5), 1/6*(2*(b^2*c^3 - 4*a*c^4)*e^4*x^3 + 3*(4*(b^2*c^3 - 4*a*c^4)*d*e^3 - (b^3*c^2 - 4*a*b*c^3)*e^4)*x^2 - 6*(2*c^4*d^4 - 4*b*c^3*d^3*e + 6*(b^2*c^2 - 2*a*c^3)*d^2*e^2 - 4*(b^3*c - 3*a*b*c^2)*d*e^3 + (b^4 - 4*a*b^2*c + 2*a^2*c^2)*e^4)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 6*(6*(b^2*c^3 - 4*a*c^4)*d^2*e^2 - 4*(b^3*c^2 - 4*a*b*c^3)*d*e^3 + (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^4)*x + 3*(4*(b^2*c^3 - 4*a*c^4)*d^3*e - 6*(b^3*c^2 - 4*a*b*c^3)*d^2*e^2 + 4*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d*e^3 - (b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*e^4)*log(c*x^2 + b*x + a))/(b^2*c^4 - 4*a*c^5)]","A",0
2183,1,526,0,0.426667," ","integrate((e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{3} x^{2} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} x + {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}, \frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{3} x^{2} - 2 \, {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} x + {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{2} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}\right]"," ",0,"[1/2*((b^2*c^2 - 4*a*c^3)*e^3*x^2 + (2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(3*(b^2*c^2 - 4*a*c^3)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*x + (3*(b^2*c^2 - 4*a*c^3)*d^2*e - 3*(b^3*c - 4*a*b*c^2)*d*e^2 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^3)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4), 1/2*((b^2*c^2 - 4*a*c^3)*e^3*x^2 - 2*(2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(3*(b^2*c^2 - 4*a*c^3)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*x + (3*(b^2*c^2 - 4*a*c^3)*d^2*e - 3*(b^3*c - 4*a*b*c^2)*d*e^2 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^3)*log(c*x^2 + b*x + a))/(b^2*c^3 - 4*a*c^4)]","A",0
2184,1,324,0,0.424006," ","integrate((e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x - {\left(2 \, c^{2} d^{2} - 2 \, b c d e + {\left(b^{2} - 2 \, a c\right)} e^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e - {\left(b^{3} - 4 \, a b c\right)} e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x - 2 \, {\left(2 \, c^{2} d^{2} - 2 \, b c d e + {\left(b^{2} - 2 \, a c\right)} e^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e - {\left(b^{3} - 4 \, a b c\right)} e^{2}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/2*(2*(b^2*c - 4*a*c^2)*e^2*x - (2*c^2*d^2 - 2*b*c*d*e + (b^2 - 2*a*c)*e^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (2*(b^2*c - 4*a*c^2)*d*e - (b^3 - 4*a*b*c)*e^2)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3), 1/2*(2*(b^2*c - 4*a*c^2)*e^2*x - 2*(2*c^2*d^2 - 2*b*c*d*e + (b^2 - 2*a*c)*e^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (2*(b^2*c - 4*a*c^2)*d*e - (b^3 - 4*a*b*c)*e^2)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3)]","A",0
2185,1,204,0,0.420091," ","integrate((e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{2} + b x + a\right) - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c d - b e\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{2} + b x + a\right) - 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(2 \, c d - b e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[1/2*((b^2 - 4*a*c)*e*log(c*x^2 + b*x + a) - sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/(b^2*c - 4*a*c^2), 1/2*((b^2 - 4*a*c)*e*log(c*x^2 + b*x + a) - 2*sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/(b^2*c - 4*a*c^2)]","A",0
2186,1,120,0,0.413542," ","integrate(1/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{\sqrt{b^{2} - 4 \, a c}}, -\frac{2 \, \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{b^{2} - 4 \, a c}\right]"," ",0,"[log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a))/sqrt(b^2 - 4*a*c), -2*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c))/(b^2 - 4*a*c)]","A",0
2187,1,305,0,0.679906," ","integrate(1/(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{2} + b x + a\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} e \log\left(e x + d\right) + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c d - b e\right)} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right)}{2 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}, -\frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{2} + b x + a\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} e \log\left(e x + d\right) + 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(2 \, c d - b e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right)}{2 \, {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)}}\right]"," ",0,"[-1/2*((b^2 - 4*a*c)*e*log(c*x^2 + b*x + a) - 2*(b^2 - 4*a*c)*e*log(e*x + d) + sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2), -1/2*((b^2 - 4*a*c)*e*log(c*x^2 + b*x + a) - 2*(b^2 - 4*a*c)*e*log(e*x + d) + 2*sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)]","A",0
2188,1,1079,0,2.971599," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - 2 \, {\left(b^{3} - 4 \, a b c\right)} d e^{2} + 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{2} d^{3} - 2 \, b c d^{2} e + {\left(b^{2} - 2 \, a c\right)} d e^{2} + {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} + {\left(b^{2} - 2 \, a c\right)} e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(b^{3} - 4 \, a b c\right)} d e^{2} + {\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)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(b^{3} - 4 \, a b c\right)} d e^{2} + {\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)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{5} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{4} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{2} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{4} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{5}\right)} x\right)}}, -\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - 2 \, {\left(b^{3} - 4 \, a b c\right)} d e^{2} + 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} e^{3} + 2 \, {\left(2 \, c^{2} d^{3} - 2 \, b c d^{2} e + {\left(b^{2} - 2 \, a c\right)} d e^{2} + {\left(2 \, c^{2} d^{2} e - 2 \, b c d e^{2} + {\left(b^{2} - 2 \, a c\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(b^{3} - 4 \, a b c\right)} d e^{2} + {\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)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e - {\left(b^{3} - 4 \, a b c\right)} d e^{2} + {\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)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{5} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{2} e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d e^{4} + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{2} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{4} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*(b^2*c - 4*a*c^2)*d^2*e - 2*(b^3 - 4*a*b*c)*d*e^2 + 2*(a*b^2 - 4*a^2*c)*e^3 + (2*c^2*d^3 - 2*b*c*d^2*e + (b^2 - 2*a*c)*d*e^2 + (2*c^2*d^2*e - 2*b*c*d*e^2 + (b^2 - 2*a*c)*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (2*(b^2*c - 4*a*c^2)*d^2*e - (b^3 - 4*a*b*c)*d*e^2 + (2*(b^2*c - 4*a*c^2)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*x)*log(c*x^2 + b*x + a) - 2*(2*(b^2*c - 4*a*c^2)*d^2*e - (b^3 - 4*a*b*c)*d*e^2 + (2*(b^2*c - 4*a*c^2)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*x)*log(e*x + d))/((b^2*c^2 - 4*a*c^3)*d^5 - 2*(b^3*c - 4*a*b*c^2)*d^4*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^3*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e^3 + (a^2*b^2 - 4*a^3*c)*d*e^4 + ((b^2*c^2 - 4*a*c^3)*d^4*e - 2*(b^3*c - 4*a*b*c^2)*d^3*e^2 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^3 - 2*(a*b^3 - 4*a^2*b*c)*d*e^4 + (a^2*b^2 - 4*a^3*c)*e^5)*x), -1/2*(2*(b^2*c - 4*a*c^2)*d^2*e - 2*(b^3 - 4*a*b*c)*d*e^2 + 2*(a*b^2 - 4*a^2*c)*e^3 + 2*(2*c^2*d^3 - 2*b*c*d^2*e + (b^2 - 2*a*c)*d*e^2 + (2*c^2*d^2*e - 2*b*c*d*e^2 + (b^2 - 2*a*c)*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (2*(b^2*c - 4*a*c^2)*d^2*e - (b^3 - 4*a*b*c)*d*e^2 + (2*(b^2*c - 4*a*c^2)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*x)*log(c*x^2 + b*x + a) - 2*(2*(b^2*c - 4*a*c^2)*d^2*e - (b^3 - 4*a*b*c)*d*e^2 + (2*(b^2*c - 4*a*c^2)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*x)*log(e*x + d))/((b^2*c^2 - 4*a*c^3)*d^5 - 2*(b^3*c - 4*a*b*c^2)*d^4*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^3*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d^2*e^3 + (a^2*b^2 - 4*a^3*c)*d*e^4 + ((b^2*c^2 - 4*a*c^3)*d^4*e - 2*(b^3*c - 4*a*b*c^2)*d^3*e^2 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^3 - 2*(a*b^3 - 4*a^2*b*c)*d*e^4 + (a^2*b^2 - 4*a^3*c)*e^5)*x)]","B",0
2189,1,2793,0,44.437554," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a),x, algorithm=""fricas"")","\left[-\frac{5 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e - 8 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{2} + 3 \, {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{3} - 4 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{4} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{5} - {\left(2 \, c^{3} d^{5} - 3 \, b c^{2} d^{4} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} - 3 \, a b c\right)} d^{2} e^{3} + {\left(2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d^{4} e - 3 \, b c^{2} d^{3} e^{2} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} - 3 \, a b c\right)} d e^{4}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{4} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{5}\right)} x + {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{2} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} e^{3} + {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{5}\right)} x^{2} + 2 \, {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d e^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{2} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} e^{3} + {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{5}\right)} x^{2} + 2 \, {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{8} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{7} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{6} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{5} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{4} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{6} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e^{3} + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{4} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{5} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{6} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{7} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{8}\right)} x^{2} + 2 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{7} e - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} e^{2} + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{5} e^{3} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{4} e^{4} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} e^{5} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{2} e^{6} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d e^{7}\right)} x\right)}}, -\frac{5 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e - 8 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{2} + 3 \, {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{3} - 4 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{4} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{5} + 2 \, {\left(2 \, c^{3} d^{5} - 3 \, b c^{2} d^{4} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} - 3 \, a b c\right)} d^{2} e^{3} + {\left(2 \, c^{3} d^{3} e^{2} - 3 \, b c^{2} d^{2} e^{3} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4} - {\left(b^{3} - 3 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, c^{3} d^{4} e - 3 \, b c^{2} d^{3} e^{2} + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} - 3 \, a b c\right)} d e^{4}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{4} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{5}\right)} x + {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{2} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} e^{3} + {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{5}\right)} x^{2} + 2 \, {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d e^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{2} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} e^{3} + {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{5}\right)} x^{2} + 2 \, {\left(3 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} e^{2} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d e^{4}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{8} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{7} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{6} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{5} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{4} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{6} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e^{3} + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{4} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{5} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{6} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{7} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{8}\right)} x^{2} + 2 \, {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{7} e - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} e^{2} + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{5} e^{3} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{4} e^{4} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} e^{5} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{2} e^{6} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d e^{7}\right)} x\right)}}\right]"," ",0,"[-1/2*(5*(b^2*c^2 - 4*a*c^3)*d^4*e - 8*(b^3*c - 4*a*b*c^2)*d^3*e^2 + 3*(b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^3 - 4*(a*b^3 - 4*a^2*b*c)*d*e^4 + (a^2*b^2 - 4*a^3*c)*e^5 - (2*c^3*d^5 - 3*b*c^2*d^4*e + 3*(b^2*c - 2*a*c^2)*d^3*e^2 - (b^3 - 3*a*b*c)*d^2*e^3 + (2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5)*x^2 + 2*(2*c^3*d^4*e - 3*b*c^2*d^3*e^2 + 3*(b^2*c - 2*a*c^2)*d^2*e^3 - (b^3 - 3*a*b*c)*d*e^4)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(2*(b^2*c^2 - 4*a*c^3)*d^3*e^2 - 3*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d*e^4 - (a*b^3 - 4*a^2*b*c)*e^5)*x + (3*(b^2*c^2 - 4*a*c^3)*d^4*e - 3*(b^3*c - 4*a*b*c^2)*d^3*e^2 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^2*e^3 + (3*(b^2*c^2 - 4*a*c^3)*d^2*e^3 - 3*(b^3*c - 4*a*b*c^2)*d*e^4 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^5)*x^2 + 2*(3*(b^2*c^2 - 4*a*c^3)*d^3*e^2 - 3*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*d*e^4)*x)*log(c*x^2 + b*x + a) - 2*(3*(b^2*c^2 - 4*a*c^3)*d^4*e - 3*(b^3*c - 4*a*b*c^2)*d^3*e^2 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^2*e^3 + (3*(b^2*c^2 - 4*a*c^3)*d^2*e^3 - 3*(b^3*c - 4*a*b*c^2)*d*e^4 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^5)*x^2 + 2*(3*(b^2*c^2 - 4*a*c^3)*d^3*e^2 - 3*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*d*e^4)*x)*log(e*x + d))/((b^2*c^3 - 4*a*c^4)*d^8 - 3*(b^3*c^2 - 4*a*b*c^3)*d^7*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^6*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^5*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^4*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d^3*e^5 + (a^3*b^2 - 4*a^4*c)*d^2*e^6 + ((b^2*c^3 - 4*a*c^4)*d^6*e^2 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e^3 + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^4 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^5 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^6 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^7 + (a^3*b^2 - 4*a^4*c)*e^8)*x^2 + 2*((b^2*c^3 - 4*a*c^4)*d^7*e - 3*(b^3*c^2 - 4*a*b*c^3)*d^6*e^2 + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^5*e^3 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^4*e^4 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^3*e^5 - 3*(a^2*b^3 - 4*a^3*b*c)*d^2*e^6 + (a^3*b^2 - 4*a^4*c)*d*e^7)*x), -1/2*(5*(b^2*c^2 - 4*a*c^3)*d^4*e - 8*(b^3*c - 4*a*b*c^2)*d^3*e^2 + 3*(b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^3 - 4*(a*b^3 - 4*a^2*b*c)*d*e^4 + (a^2*b^2 - 4*a^3*c)*e^5 + 2*(2*c^3*d^5 - 3*b*c^2*d^4*e + 3*(b^2*c - 2*a*c^2)*d^3*e^2 - (b^3 - 3*a*b*c)*d^2*e^3 + (2*c^3*d^3*e^2 - 3*b*c^2*d^2*e^3 + 3*(b^2*c - 2*a*c^2)*d*e^4 - (b^3 - 3*a*b*c)*e^5)*x^2 + 2*(2*c^3*d^4*e - 3*b*c^2*d^3*e^2 + 3*(b^2*c - 2*a*c^2)*d^2*e^3 - (b^3 - 3*a*b*c)*d*e^4)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(2*(b^2*c^2 - 4*a*c^3)*d^3*e^2 - 3*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d*e^4 - (a*b^3 - 4*a^2*b*c)*e^5)*x + (3*(b^2*c^2 - 4*a*c^3)*d^4*e - 3*(b^3*c - 4*a*b*c^2)*d^3*e^2 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^2*e^3 + (3*(b^2*c^2 - 4*a*c^3)*d^2*e^3 - 3*(b^3*c - 4*a*b*c^2)*d*e^4 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^5)*x^2 + 2*(3*(b^2*c^2 - 4*a*c^3)*d^3*e^2 - 3*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*d*e^4)*x)*log(c*x^2 + b*x + a) - 2*(3*(b^2*c^2 - 4*a*c^3)*d^4*e - 3*(b^3*c - 4*a*b*c^2)*d^3*e^2 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^2*e^3 + (3*(b^2*c^2 - 4*a*c^3)*d^2*e^3 - 3*(b^3*c - 4*a*b*c^2)*d*e^4 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e^5)*x^2 + 2*(3*(b^2*c^2 - 4*a*c^3)*d^3*e^2 - 3*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^4 - 5*a*b^2*c + 4*a^2*c^2)*d*e^4)*x)*log(e*x + d))/((b^2*c^3 - 4*a*c^4)*d^8 - 3*(b^3*c^2 - 4*a*b*c^3)*d^7*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^6*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^5*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^4*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d^3*e^5 + (a^3*b^2 - 4*a^4*c)*d^2*e^6 + ((b^2*c^3 - 4*a*c^4)*d^6*e^2 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e^3 + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^4 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^5 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^6 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^7 + (a^3*b^2 - 4*a^4*c)*e^8)*x^2 + 2*((b^2*c^3 - 4*a*c^4)*d^7*e - 3*(b^3*c^2 - 4*a*b*c^3)*d^6*e^2 + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^5*e^3 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^4*e^4 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^3*e^5 - 3*(a^2*b^3 - 4*a^3*b*c)*d^2*e^6 + (a^3*b^2 - 4*a^4*c)*d*e^7)*x)]","B",0
2190,1,2763,0,0.549262," ","integrate((e*x+d)^5/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e^{5} x^{4} - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{5} + 20 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{4} e - 20 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{3} e^{2} + 20 \, {\left(a b^{4} c^{2} - 6 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{2} e^{3} - 10 \, {\left(a b^{5} c - 7 \, a^{2} b^{3} c^{2} + 12 \, a^{3} b c^{3}\right)} d e^{4} + 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} e^{5} + {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{4} - 3 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{3} + {\left(10 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} - {\left(4 \, b^{6} c - 33 \, a b^{4} c^{2} + 72 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} e^{5}\right)} x^{2} - {\left(4 \, a c^{5} d^{5} - 10 \, a b c^{4} d^{4} e + 40 \, a^{2} c^{4} d^{3} e^{2} + 10 \, {\left(a b^{3} c^{2} - 6 \, a^{2} b c^{3}\right)} d^{2} e^{3} - 10 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 6 \, a^{3} c^{3}\right)} d e^{4} + {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} e^{5} + {\left(4 \, c^{6} d^{5} - 10 \, b c^{5} d^{4} e + 40 \, a c^{5} d^{3} e^{2} + 10 \, {\left(b^{3} c^{3} - 6 \, a b c^{4}\right)} d^{2} e^{3} - 10 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d e^{4} + {\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{2} + {\left(4 \, b c^{5} d^{5} - 10 \, b^{2} c^{4} d^{4} e + 40 \, a b c^{4} d^{3} e^{2} + 10 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3}\right)} d^{2} e^{3} - 10 \, {\left(b^{5} c - 6 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} d e^{4} + {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{5} - 5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e + 10 \, {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} e^{2} - 10 \, {\left(b^{5} c^{2} - 7 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} d^{2} e^{3} + 5 \, {\left(b^{6} c - 9 \, a b^{4} c^{2} + 26 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 11 \, a b^{5} c + 41 \, a^{2} b^{3} c^{2} - 52 \, a^{3} b c^{3}\right)} e^{5}\right)} x + {\left(10 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2} e^{3} - 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{4} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} e^{5} + {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{2} e^{3} - 10 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} + {\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} e^{5}\right)} x^{2} + {\left(10 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{3} - 10 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d e^{4} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} e^{5}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{2} + {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x\right)}}, \frac{{\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e^{5} x^{4} - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{5} + 20 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{4} e - 20 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{3} e^{2} + 20 \, {\left(a b^{4} c^{2} - 6 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{2} e^{3} - 10 \, {\left(a b^{5} c - 7 \, a^{2} b^{3} c^{2} + 12 \, a^{3} b c^{3}\right)} d e^{4} + 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} e^{5} + {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{4} - 3 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{3} + {\left(10 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} - {\left(4 \, b^{6} c - 33 \, a b^{4} c^{2} + 72 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(4 \, a c^{5} d^{5} - 10 \, a b c^{4} d^{4} e + 40 \, a^{2} c^{4} d^{3} e^{2} + 10 \, {\left(a b^{3} c^{2} - 6 \, a^{2} b c^{3}\right)} d^{2} e^{3} - 10 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 6 \, a^{3} c^{3}\right)} d e^{4} + {\left(3 \, a b^{5} - 20 \, a^{2} b^{3} c + 30 \, a^{3} b c^{2}\right)} e^{5} + {\left(4 \, c^{6} d^{5} - 10 \, b c^{5} d^{4} e + 40 \, a c^{5} d^{3} e^{2} + 10 \, {\left(b^{3} c^{3} - 6 \, a b c^{4}\right)} d^{2} e^{3} - 10 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d e^{4} + {\left(3 \, b^{5} c - 20 \, a b^{3} c^{2} + 30 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{2} + {\left(4 \, b c^{5} d^{5} - 10 \, b^{2} c^{4} d^{4} e + 40 \, a b c^{4} d^{3} e^{2} + 10 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3}\right)} d^{2} e^{3} - 10 \, {\left(b^{5} c - 6 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} d e^{4} + {\left(3 \, b^{6} - 20 \, a b^{4} c + 30 \, a^{2} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{5} - 5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e + 10 \, {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} e^{2} - 10 \, {\left(b^{5} c^{2} - 7 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} d^{2} e^{3} + 5 \, {\left(b^{6} c - 9 \, a b^{4} c^{2} + 26 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 11 \, a b^{5} c + 41 \, a^{2} b^{3} c^{2} - 52 \, a^{3} b c^{3}\right)} e^{5}\right)} x + {\left(10 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{2} e^{3} - 10 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{4} + {\left(3 \, a b^{6} - 26 \, a^{2} b^{4} c + 64 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} e^{5} + {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{2} e^{3} - 10 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} + {\left(3 \, b^{6} c - 26 \, a b^{4} c^{2} + 64 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} e^{5}\right)} x^{2} + {\left(10 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{3} - 10 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d e^{4} + {\left(3 \, b^{7} - 26 \, a b^{5} c + 64 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} e^{5}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{2} + {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x\right)}}\right]"," ",0,"[1/2*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*e^5*x^4 - 2*(b^3*c^4 - 4*a*b*c^5)*d^5 + 20*(a*b^2*c^4 - 4*a^2*c^5)*d^4*e - 20*(a*b^3*c^3 - 4*a^2*b*c^4)*d^3*e^2 + 20*(a*b^4*c^2 - 6*a^2*b^2*c^3 + 8*a^3*c^4)*d^2*e^3 - 10*(a*b^5*c - 7*a^2*b^3*c^2 + 12*a^3*b*c^3)*d*e^4 + 2*(a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*e^5 + (10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^4 - 3*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5)*x^3 + (10*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 - (4*b^6*c - 33*a*b^4*c^2 + 72*a^2*b^2*c^3 - 16*a^3*c^4)*e^5)*x^2 - (4*a*c^5*d^5 - 10*a*b*c^4*d^4*e + 40*a^2*c^4*d^3*e^2 + 10*(a*b^3*c^2 - 6*a^2*b*c^3)*d^2*e^3 - 10*(a*b^4*c - 6*a^2*b^2*c^2 + 6*a^3*c^3)*d*e^4 + (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*e^5 + (4*c^6*d^5 - 10*b*c^5*d^4*e + 40*a*c^5*d^3*e^2 + 10*(b^3*c^3 - 6*a*b*c^4)*d^2*e^3 - 10*(b^4*c^2 - 6*a*b^2*c^3 + 6*a^2*c^4)*d*e^4 + (3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*e^5)*x^2 + (4*b*c^5*d^5 - 10*b^2*c^4*d^4*e + 40*a*b*c^4*d^3*e^2 + 10*(b^4*c^2 - 6*a*b^2*c^3)*d^2*e^3 - 10*(b^5*c - 6*a*b^3*c^2 + 6*a^2*b*c^3)*d*e^4 + (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*e^5)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(2*(b^2*c^5 - 4*a*c^6)*d^5 - 5*(b^3*c^4 - 4*a*b*c^5)*d^4*e + 10*(b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*d^3*e^2 - 10*(b^5*c^2 - 7*a*b^3*c^3 + 12*a^2*b*c^4)*d^2*e^3 + 5*(b^6*c - 9*a*b^4*c^2 + 26*a^2*b^2*c^3 - 24*a^3*c^4)*d*e^4 - (b^7 - 11*a*b^5*c + 41*a^2*b^3*c^2 - 52*a^3*b*c^3)*e^5)*x + (10*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2*e^3 - 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^4 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*e^5 + (10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^2*e^3 - 10*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 + (3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*e^5)*x^2 + (10*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^3 - 10*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d*e^4 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*e^5)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^2 + (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x), 1/2*((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*e^5*x^4 - 2*(b^3*c^4 - 4*a*b*c^5)*d^5 + 20*(a*b^2*c^4 - 4*a^2*c^5)*d^4*e - 20*(a*b^3*c^3 - 4*a^2*b*c^4)*d^3*e^2 + 20*(a*b^4*c^2 - 6*a^2*b^2*c^3 + 8*a^3*c^4)*d^2*e^3 - 10*(a*b^5*c - 7*a^2*b^3*c^2 + 12*a^3*b*c^3)*d*e^4 + 2*(a*b^6 - 8*a^2*b^4*c + 18*a^3*b^2*c^2 - 8*a^4*c^3)*e^5 + (10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^4 - 3*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5)*x^3 + (10*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 - (4*b^6*c - 33*a*b^4*c^2 + 72*a^2*b^2*c^3 - 16*a^3*c^4)*e^5)*x^2 + 2*(4*a*c^5*d^5 - 10*a*b*c^4*d^4*e + 40*a^2*c^4*d^3*e^2 + 10*(a*b^3*c^2 - 6*a^2*b*c^3)*d^2*e^3 - 10*(a*b^4*c - 6*a^2*b^2*c^2 + 6*a^3*c^3)*d*e^4 + (3*a*b^5 - 20*a^2*b^3*c + 30*a^3*b*c^2)*e^5 + (4*c^6*d^5 - 10*b*c^5*d^4*e + 40*a*c^5*d^3*e^2 + 10*(b^3*c^3 - 6*a*b*c^4)*d^2*e^3 - 10*(b^4*c^2 - 6*a*b^2*c^3 + 6*a^2*c^4)*d*e^4 + (3*b^5*c - 20*a*b^3*c^2 + 30*a^2*b*c^3)*e^5)*x^2 + (4*b*c^5*d^5 - 10*b^2*c^4*d^4*e + 40*a*b*c^4*d^3*e^2 + 10*(b^4*c^2 - 6*a*b^2*c^3)*d^2*e^3 - 10*(b^5*c - 6*a*b^3*c^2 + 6*a^2*b*c^3)*d*e^4 + (3*b^6 - 20*a*b^4*c + 30*a^2*b^2*c^2)*e^5)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(2*(b^2*c^5 - 4*a*c^6)*d^5 - 5*(b^3*c^4 - 4*a*b*c^5)*d^4*e + 10*(b^4*c^3 - 6*a*b^2*c^4 + 8*a^2*c^5)*d^3*e^2 - 10*(b^5*c^2 - 7*a*b^3*c^3 + 12*a^2*b*c^4)*d^2*e^3 + 5*(b^6*c - 9*a*b^4*c^2 + 26*a^2*b^2*c^3 - 24*a^3*c^4)*d*e^4 - (b^7 - 11*a*b^5*c + 41*a^2*b^3*c^2 - 52*a^3*b*c^3)*e^5)*x + (10*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^2*e^3 - 10*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^4 + (3*a*b^6 - 26*a^2*b^4*c + 64*a^3*b^2*c^2 - 32*a^4*c^3)*e^5 + (10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^2*e^3 - 10*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 + (3*b^6*c - 26*a*b^4*c^2 + 64*a^2*b^2*c^3 - 32*a^3*c^4)*e^5)*x^2 + (10*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^3 - 10*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d*e^4 + (3*b^7 - 26*a*b^5*c + 64*a^2*b^3*c^2 - 32*a^3*b*c^3)*e^5)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^2 + (b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x)]","B",0
2191,1,1857,0,0.490853," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{4} x^{3} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{4} x^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{4} + 8 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} e - 6 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e^{2} + 4 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d e^{3} - {\left(a b^{5} - 7 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} e^{4} + {\left(2 \, a c^{4} d^{4} - 4 \, a b c^{3} d^{3} e + 12 \, a^{2} c^{3} d^{2} e^{2} + 2 \, {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} e^{4} + {\left(2 \, c^{5} d^{4} - 4 \, b c^{4} d^{3} e + 12 \, a c^{4} d^{2} e^{2} + 2 \, {\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} d e^{3} - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e^{4}\right)} x^{2} + {\left(2 \, b c^{4} d^{4} - 4 \, b^{2} c^{3} d^{3} e + 12 \, a b c^{3} d^{2} e^{2} + 2 \, {\left(b^{4} c - 6 \, a b^{2} c^{2}\right)} d e^{3} - {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e + 6 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{2} - 4 \, {\left(b^{5} c - 7 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d e^{3} + {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} e^{4}\right)} x + {\left(2 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d e^{3} - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{4} + {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{3} - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{4}\right)} x^{2} + {\left(2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{3} - {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} e^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x}, \frac{{\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{4} x^{3} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{4} x^{2} - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{4} + 8 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} e - 6 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{2} e^{2} + 4 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d e^{3} - {\left(a b^{5} - 7 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} e^{4} + 2 \, {\left(2 \, a c^{4} d^{4} - 4 \, a b c^{3} d^{3} e + 12 \, a^{2} c^{3} d^{2} e^{2} + 2 \, {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} e^{4} + {\left(2 \, c^{5} d^{4} - 4 \, b c^{4} d^{3} e + 12 \, a c^{4} d^{2} e^{2} + 2 \, {\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} d e^{3} - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e^{4}\right)} x^{2} + {\left(2 \, b c^{4} d^{4} - 4 \, b^{2} c^{3} d^{3} e + 12 \, a b c^{3} d^{2} e^{2} + 2 \, {\left(b^{4} c - 6 \, a b^{2} c^{2}\right)} d e^{3} - {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} - 4 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e + 6 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{2} - 4 \, {\left(b^{5} c - 7 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d e^{3} + {\left(b^{6} - 9 \, a b^{4} c + 26 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} e^{4}\right)} x + {\left(2 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d e^{3} - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{4} + {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{3} - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{4}\right)} x^{2} + {\left(2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{3} - {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} e^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{2} + {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x}\right]"," ",0,"[((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^4*x^3 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^4*x^2 - (b^3*c^3 - 4*a*b*c^4)*d^4 + 8*(a*b^2*c^3 - 4*a^2*c^4)*d^3*e - 6*(a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e^2 + 4*(a*b^4*c - 6*a^2*b^2*c^2 + 8*a^3*c^3)*d*e^3 - (a*b^5 - 7*a^2*b^3*c + 12*a^3*b*c^2)*e^4 + (2*a*c^4*d^4 - 4*a*b*c^3*d^3*e + 12*a^2*c^3*d^2*e^2 + 2*(a*b^3*c - 6*a^2*b*c^2)*d*e^3 - (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*e^4 + (2*c^5*d^4 - 4*b*c^4*d^3*e + 12*a*c^4*d^2*e^2 + 2*(b^3*c^2 - 6*a*b*c^3)*d*e^3 - (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e^4)*x^2 + (2*b*c^4*d^4 - 4*b^2*c^3*d^3*e + 12*a*b*c^3*d^2*e^2 + 2*(b^4*c - 6*a*b^2*c^2)*d*e^3 - (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*e^4)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (2*(b^2*c^4 - 4*a*c^5)*d^4 - 4*(b^3*c^3 - 4*a*b*c^4)*d^3*e + 6*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^2 - 4*(b^5*c - 7*a*b^3*c^2 + 12*a^2*b*c^3)*d*e^3 + (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*e^4)*x + (2*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d*e^3 - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^4 + (2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^3 - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^4)*x^2 + (2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^3 - (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*e^4)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x), ((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^4*x^3 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^4*x^2 - (b^3*c^3 - 4*a*b*c^4)*d^4 + 8*(a*b^2*c^3 - 4*a^2*c^4)*d^3*e - 6*(a*b^3*c^2 - 4*a^2*b*c^3)*d^2*e^2 + 4*(a*b^4*c - 6*a^2*b^2*c^2 + 8*a^3*c^3)*d*e^3 - (a*b^5 - 7*a^2*b^3*c + 12*a^3*b*c^2)*e^4 + 2*(2*a*c^4*d^4 - 4*a*b*c^3*d^3*e + 12*a^2*c^3*d^2*e^2 + 2*(a*b^3*c - 6*a^2*b*c^2)*d*e^3 - (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*e^4 + (2*c^5*d^4 - 4*b*c^4*d^3*e + 12*a*c^4*d^2*e^2 + 2*(b^3*c^2 - 6*a*b*c^3)*d*e^3 - (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e^4)*x^2 + (2*b*c^4*d^4 - 4*b^2*c^3*d^3*e + 12*a*b*c^3*d^2*e^2 + 2*(b^4*c - 6*a*b^2*c^2)*d*e^3 - (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*e^4)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (2*(b^2*c^4 - 4*a*c^5)*d^4 - 4*(b^3*c^3 - 4*a*b*c^4)*d^3*e + 6*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^2 - 4*(b^5*c - 7*a*b^3*c^2 + 12*a^2*b*c^3)*d*e^3 + (b^6 - 9*a*b^4*c + 26*a^2*b^2*c^2 - 24*a^3*c^3)*e^4)*x + (2*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d*e^3 - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^4 + (2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^3 - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^4)*x^2 + (2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^3 - (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*e^4)*x)*log(c*x^2 + b*x + a))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^2 + (b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x)]","B",0
2192,1,1164,0,0.433299," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} - 12 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e + 6 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{2} - 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e^{3} - {\left(4 \, a c^{3} d^{3} - 6 \, a b c^{2} d^{2} e + 12 \, a^{2} c^{2} d e^{2} + {\left(a b^{3} - 6 \, a^{2} b c\right)} e^{3} + {\left(4 \, c^{4} d^{3} - 6 \, b c^{3} d^{2} e + 12 \, a c^{3} d e^{2} + {\left(b^{3} c - 6 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 6 \, b^{2} c^{2} d^{2} e + 12 \, a b c^{2} d e^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e + 3 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d e^{2} - {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} e^{3}\right)} x - {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{3} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{3} x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{2} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x\right)}}, -\frac{2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} - 12 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e + 6 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{2} - 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e^{3} - 2 \, {\left(4 \, a c^{3} d^{3} - 6 \, a b c^{2} d^{2} e + 12 \, a^{2} c^{2} d e^{2} + {\left(a b^{3} - 6 \, a^{2} b c\right)} e^{3} + {\left(4 \, c^{4} d^{3} - 6 \, b c^{3} d^{2} e + 12 \, a c^{3} d e^{2} + {\left(b^{3} c - 6 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 6 \, b^{2} c^{2} d^{2} e + 12 \, a b c^{2} d e^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e + 3 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d e^{2} - {\left(b^{5} - 7 \, a b^{3} c + 12 \, a^{2} b c^{2}\right)} e^{3}\right)} x - {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{3} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{3} x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{2} + {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*(b^3*c^2 - 4*a*b*c^3)*d^3 - 12*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e + 6*(a*b^3*c - 4*a^2*b*c^2)*d*e^2 - 2*(a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e^3 - (4*a*c^3*d^3 - 6*a*b*c^2*d^2*e + 12*a^2*c^2*d*e^2 + (a*b^3 - 6*a^2*b*c)*e^3 + (4*c^4*d^3 - 6*b*c^3*d^2*e + 12*a*c^3*d*e^2 + (b^3*c - 6*a*b*c^2)*e^3)*x^2 + (4*b*c^3*d^3 - 6*b^2*c^2*d^2*e + 12*a*b*c^2*d*e^2 + (b^4 - 6*a*b^2*c)*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(2*(b^2*c^3 - 4*a*c^4)*d^3 - 3*(b^3*c^2 - 4*a*b*c^3)*d^2*e + 3*(b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d*e^2 - (b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*e^3)*x - ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^3*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^3*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*e^3)*log(c*x^2 + b*x + a))/(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)*x^2 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x), -1/2*(2*(b^3*c^2 - 4*a*b*c^3)*d^3 - 12*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e + 6*(a*b^3*c - 4*a^2*b*c^2)*d*e^2 - 2*(a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e^3 - 2*(4*a*c^3*d^3 - 6*a*b*c^2*d^2*e + 12*a^2*c^2*d*e^2 + (a*b^3 - 6*a^2*b*c)*e^3 + (4*c^4*d^3 - 6*b*c^3*d^2*e + 12*a*c^3*d*e^2 + (b^3*c - 6*a*b*c^2)*e^3)*x^2 + (4*b*c^3*d^3 - 6*b^2*c^2*d^2*e + 12*a*b*c^2*d*e^2 + (b^4 - 6*a*b^2*c)*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(2*(b^2*c^3 - 4*a*c^4)*d^3 - 3*(b^3*c^2 - 4*a*b*c^3)*d^2*e + 3*(b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d*e^2 - (b^5 - 7*a*b^3*c + 12*a^2*b*c^2)*e^3)*x - ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^3*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^3*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*e^3)*log(c*x^2 + b*x + a))/(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)*x^2 + (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x)]","B",0
2193,1,669,0,0.414499," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e + {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{2} + 2 \, {\left(a c^{2} d^{2} - a b c d e + a^{2} c e^{2} + {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)} x^{2} + {\left(b c^{2} d^{2} - b^{2} c d e + a b c e^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} e^{2}\right)} x}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}, -\frac{{\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} - 4 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e + {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{2} - 4 \, {\left(a c^{2} d^{2} - a b c d e + a^{2} c e^{2} + {\left(c^{3} d^{2} - b c^{2} d e + a c^{2} e^{2}\right)} x^{2} + {\left(b c^{2} d^{2} - b^{2} c d e + a b c e^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} e^{2}\right)} x}{a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{2} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x}\right]"," ",0,"[-((b^3*c - 4*a*b*c^2)*d^2 - 4*(a*b^2*c - 4*a^2*c^2)*d*e + (a*b^3 - 4*a^2*b*c)*e^2 + 2*(a*c^2*d^2 - a*b*c*d*e + a^2*c*e^2 + (c^3*d^2 - b*c^2*d*e + a*c^2*e^2)*x^2 + (b*c^2*d^2 - b^2*c*d*e + a*b*c*e^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (2*(b^2*c^2 - 4*a*c^3)*d^2 - 2*(b^3*c - 4*a*b*c^2)*d*e + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*e^2)*x)/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x), -((b^3*c - 4*a*b*c^2)*d^2 - 4*(a*b^2*c - 4*a^2*c^2)*d*e + (a*b^3 - 4*a^2*b*c)*e^2 - 4*(a*c^2*d^2 - a*b*c*d*e + a^2*c*e^2 + (c^3*d^2 - b*c^2*d*e + a*c^2*e^2)*x^2 + (b*c^2*d^2 - b^2*c*d*e + a*b*c*e^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (2*(b^2*c^2 - 4*a*c^3)*d^2 - 2*(b^3*c - 4*a*b*c^2)*d*e + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*e^2)*x)/(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^2 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x)]","B",0
2194,1,459,0,0.411035," ","integrate((e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a c d - a b e + {\left(2 \, c^{2} d - b c e\right)} x^{2} + {\left(2 \, b c d - b^{2} e\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(b^{3} - 4 \, a b c\right)} d + 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} e - {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}, \frac{2 \, {\left(2 \, a c d - a b e + {\left(2 \, c^{2} d - b c e\right)} x^{2} + {\left(2 \, b c d - b^{2} e\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} - 4 \, a b c\right)} d + 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} e - {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} x}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}\right]"," ",0,"[((2*a*c*d - a*b*e + (2*c^2*d - b*c*e)*x^2 + (2*b*c*d - b^2*e)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (b^3 - 4*a*b*c)*d + 2*(a*b^2 - 4*a^2*c)*e - (2*(b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x), (2*(2*a*c*d - a*b*e + (2*c^2*d - b*c*e)*x^2 + (2*b*c*d - b^2*e)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (b^3 - 4*a*b*c)*d + 2*(a*b^2 - 4*a^2*c)*e - (2*(b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)]","B",0
2195,1,341,0,0.412516," ","integrate(1/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{b^{3} - 4 \, a b c + 2 \, {\left(c^{2} x^{2} + b c x + a c\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}, -\frac{b^{3} - 4 \, a b c - 4 \, {\left(c^{2} x^{2} + b c x + a c\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} x}{a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2} + {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} x}\right]"," ",0,"[-(b^3 - 4*a*b*c + 2*(c^2*x^2 + b*c*x + a*c)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(b^2*c - 4*a*c^2)*x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x), -(b^3 - 4*a*b*c - 4*(c^2*x^2 + b*c*x + a*c)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(b^2*c - 4*a*c^2)*x)/(a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2 + (b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*x)]","B",0
2196,1,2128,0,22.289013," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} - 4 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} e + 2 \, {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d e^{2} - 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e^{3} - {\left(4 \, a c^{3} d^{3} - 6 \, a b c^{2} d^{2} e + 12 \, a^{2} c^{2} d e^{2} + {\left(a b^{3} - 6 \, a^{2} b c\right)} e^{3} + {\left(4 \, c^{4} d^{3} - 6 \, b c^{3} d^{2} e + 12 \, a c^{3} d e^{2} + {\left(b^{3} c - 6 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 6 \, b^{2} c^{2} d^{2} e + 12 \, a b c^{2} d e^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d e^{2} - {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e^{3}\right)} x + {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{3} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{3} x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e^{3}\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{3} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{3} x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e^{3}\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} e + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{3} + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} e^{4} + {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} - 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{3} e + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{4} - 2 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d^{3} e + {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} d e^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{4}\right)} x\right)}}, -\frac{2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} - 4 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} e + 2 \, {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d e^{2} - 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e^{3} - 2 \, {\left(4 \, a c^{3} d^{3} - 6 \, a b c^{2} d^{2} e + 12 \, a^{2} c^{2} d e^{2} + {\left(a b^{3} - 6 \, a^{2} b c\right)} e^{3} + {\left(4 \, c^{4} d^{3} - 6 \, b c^{3} d^{2} e + 12 \, a c^{3} d e^{2} + {\left(b^{3} c - 6 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(4 \, b c^{3} d^{3} - 6 \, b^{2} c^{2} d^{2} e + 12 \, a b c^{2} d e^{2} + {\left(b^{4} - 6 \, a b^{2} c\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d e^{2} - {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e^{3}\right)} x + {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{3} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{3} x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e^{3}\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left({\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{3} x^{2} + {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{3} x + {\left(a b^{4} - 8 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e^{3}\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d^{4} - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{3} e + {\left(a b^{6} - 6 \, a^{2} b^{4} c + 32 \, a^{4} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{3} + {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} e^{4} + {\left({\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} - 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{3} e + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{4} - 2 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} d^{3} e + {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} d e^{3} + {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{4}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*(b^3*c^2 - 4*a*b*c^3)*d^3 - 4*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*e + 2*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d*e^2 - 2*(a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e^3 - (4*a*c^3*d^3 - 6*a*b*c^2*d^2*e + 12*a^2*c^2*d*e^2 + (a*b^3 - 6*a^2*b*c)*e^3 + (4*c^4*d^3 - 6*b*c^3*d^2*e + 12*a*c^3*d*e^2 + (b^3*c - 6*a*b*c^2)*e^3)*x^2 + (4*b*c^3*d^3 - 6*b^2*c^2*d^2*e + 12*a*b*c^2*d*e^2 + (b^4 - 6*a*b^2*c)*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(2*(b^2*c^3 - 4*a*c^4)*d^3 - 3*(b^3*c^2 - 4*a*b*c^3)*d^2*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d*e^2 - (a*b^3*c - 4*a^2*b*c^2)*e^3)*x + ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^3*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^3*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*e^3)*log(c*x^2 + b*x + a) - 2*((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^3*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^3*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*e^3)*log(e*x + d))/((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 - 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3*e + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2*e^2 - 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d*e^3 + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*e^4 + ((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^4 - 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^3*e + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d^2*e^2 - 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^3 + (a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*e^4)*x^2 + ((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^4 - 2*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d^3*e + (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*d^2*e^2 - 2*(a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*d*e^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^4)*x), -1/2*(2*(b^3*c^2 - 4*a*b*c^3)*d^3 - 4*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*e + 2*(b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d*e^2 - 2*(a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e^3 - 2*(4*a*c^3*d^3 - 6*a*b*c^2*d^2*e + 12*a^2*c^2*d*e^2 + (a*b^3 - 6*a^2*b*c)*e^3 + (4*c^4*d^3 - 6*b*c^3*d^2*e + 12*a*c^3*d*e^2 + (b^3*c - 6*a*b*c^2)*e^3)*x^2 + (4*b*c^3*d^3 - 6*b^2*c^2*d^2*e + 12*a*b*c^2*d*e^2 + (b^4 - 6*a*b^2*c)*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(2*(b^2*c^3 - 4*a*c^4)*d^3 - 3*(b^3*c^2 - 4*a*b*c^3)*d^2*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d*e^2 - (a*b^3*c - 4*a^2*b*c^2)*e^3)*x + ((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^3*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^3*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*e^3)*log(c*x^2 + b*x + a) - 2*((b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*e^3*x^2 + (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^3*x + (a*b^4 - 8*a^2*b^2*c + 16*a^3*c^2)*e^3)*log(e*x + d))/((a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d^4 - 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^3*e + (a*b^6 - 6*a^2*b^4*c + 32*a^4*c^3)*d^2*e^2 - 2*(a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d*e^3 + (a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*e^4 + ((b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^4 - 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^3*e + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d^2*e^2 - 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^3 + (a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*e^4)*x^2 + ((b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^4 - 2*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*d^3*e + (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*d^2*e^2 - 2*(a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*d*e^3 + (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^4)*x)]","B",0
2197,1,5498,0,79.617368," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - {\left(3 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} e + 3 \, {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} d^{3} e^{2} - {\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d^{2} e^{3} + {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e^{5} + 2 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e - 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{2} + 2 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{2} e^{3} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} d e^{4} + {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} e^{5}\right)} x^{2} - {\left(2 \, a c^{4} d^{5} - 4 \, a b c^{3} d^{4} e + 12 \, a^{2} c^{3} d^{3} e^{2} + 2 \, {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} d^{2} e^{3} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d e^{4} + {\left(2 \, c^{5} d^{4} e - 4 \, b c^{4} d^{3} e^{2} + 12 \, a c^{4} d^{2} e^{3} + 2 \, {\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} d e^{4} - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, c^{5} d^{5} - 2 \, b c^{4} d^{4} e + 2 \, b^{3} c^{2} d^{2} e^{3} - 4 \, {\left(b^{2} c^{3} - 3 \, a c^{4}\right)} d^{3} e^{2} + {\left(b^{4} c - 6 \, a b^{2} c^{2} - 6 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} e^{5}\right)} x^{2} + {\left(2 \, b c^{4} d^{5} + 8 \, a b c^{3} d^{3} e^{2} - 2 \, {\left(2 \, b^{2} c^{3} - a c^{4}\right)} d^{4} e + 2 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{2} e^{3} - {\left(b^{5} - 8 \, a b^{3} c + 18 \, a^{2} b c^{2}\right)} d e^{4} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{5} - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{4} e + 4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} e^{2} + {\left(3 \, b^{5} c - 22 \, a b^{3} c^{2} + 40 \, a^{2} b c^{3}\right)} d^{2} e^{3} - 2 \, {\left(b^{6} - 7 \, a b^{4} c + 11 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d e^{4} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} e^{5}\right)} x + {\left(2 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d^{2} e^{3} - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d e^{4} + {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{4} - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} e^{3} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{4} - {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} e^{5}\right)} x^{2} + {\left(2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} e^{3} - {\left(b^{6} - 10 \, a b^{4} c + 32 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d e^{4} - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{5}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(2 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d^{2} e^{3} - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d e^{4} + {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{4} - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} e^{3} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{4} - {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} e^{5}\right)} x^{2} + {\left(2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} e^{3} - {\left(b^{6} - 10 \, a b^{4} c + 32 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d e^{4} - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{5}\right)} x\right)} \log\left(e x + d\right)}{{\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d^{7} - 3 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} d^{6} e + 3 \, {\left(a b^{6} c - 7 \, a^{2} b^{4} c^{2} + 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{5} e^{2} - {\left(a b^{7} - 2 \, a^{2} b^{5} c - 32 \, a^{3} b^{3} c^{2} + 96 \, a^{4} b c^{3}\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{6} - 7 \, a^{3} b^{4} c + 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{3} e^{4} - 3 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2} e^{5} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} d e^{6} + {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{6} e - 3 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{5} e^{2} + 3 \, {\left(b^{6} c^{2} - 7 \, a b^{4} c^{3} + 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d^{4} e^{3} - {\left(b^{7} c - 2 \, a b^{5} c^{2} - 32 \, a^{2} b^{3} c^{3} + 96 \, a^{3} b c^{4}\right)} d^{3} e^{4} + 3 \, {\left(a b^{6} c - 7 \, a^{2} b^{4} c^{2} + 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{2} e^{5} - 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d e^{6} + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} e^{7}\right)} x^{3} + {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{7} - 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{6} e + 3 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d^{5} e^{2} + {\left(2 \, b^{7} c - 19 \, a b^{5} c^{2} + 56 \, a^{2} b^{3} c^{3} - 48 \, a^{3} b c^{4}\right)} d^{4} e^{3} - {\left(b^{8} - 5 \, a b^{6} c - 11 \, a^{2} b^{4} c^{2} + 72 \, a^{3} b^{2} c^{3} - 48 \, a^{4} c^{4}\right)} d^{3} e^{4} + 3 \, {\left(a b^{7} - 8 \, a^{2} b^{5} c + 16 \, a^{3} b^{3} c^{2}\right)} d^{2} e^{5} - {\left(3 \, a^{2} b^{6} - 25 \, a^{3} b^{4} c + 56 \, a^{4} b^{2} c^{2} - 16 \, a^{5} c^{3}\right)} d e^{6} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} e^{7}\right)} x^{2} + {\left({\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{7} - {\left(3 \, b^{6} c^{2} - 25 \, a b^{4} c^{3} + 56 \, a^{2} b^{2} c^{4} - 16 \, a^{3} c^{5}\right)} d^{6} e + 3 \, {\left(b^{7} c - 8 \, a b^{5} c^{2} + 16 \, a^{2} b^{3} c^{3}\right)} d^{5} e^{2} - {\left(b^{8} - 5 \, a b^{6} c - 11 \, a^{2} b^{4} c^{2} + 72 \, a^{3} b^{2} c^{3} - 48 \, a^{4} c^{4}\right)} d^{4} e^{3} + {\left(2 \, a b^{7} - 19 \, a^{2} b^{5} c + 56 \, a^{3} b^{3} c^{2} - 48 \, a^{4} b c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d e^{6} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} e^{7}\right)} x}, -\frac{{\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} - {\left(3 \, b^{4} c^{2} - 16 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{4} e + 3 \, {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} d^{3} e^{2} - {\left(b^{6} - 6 \, a b^{4} c + 8 \, a^{2} b^{2} c^{2}\right)} d^{2} e^{3} + {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{4} + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e^{5} + 2 \, {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e - 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{2} + 2 \, {\left(b^{4} c^{2} - 5 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{2} e^{3} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} d e^{4} + {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} e^{5}\right)} x^{2} - 2 \, {\left(2 \, a c^{4} d^{5} - 4 \, a b c^{3} d^{4} e + 12 \, a^{2} c^{3} d^{3} e^{2} + 2 \, {\left(a b^{3} c - 6 \, a^{2} b c^{2}\right)} d^{2} e^{3} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} d e^{4} + {\left(2 \, c^{5} d^{4} e - 4 \, b c^{4} d^{3} e^{2} + 12 \, a c^{4} d^{2} e^{3} + 2 \, {\left(b^{3} c^{2} - 6 \, a b c^{3}\right)} d e^{4} - {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, c^{5} d^{5} - 2 \, b c^{4} d^{4} e + 2 \, b^{3} c^{2} d^{2} e^{3} - 4 \, {\left(b^{2} c^{3} - 3 \, a c^{4}\right)} d^{3} e^{2} + {\left(b^{4} c - 6 \, a b^{2} c^{2} - 6 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 6 \, a b^{3} c + 6 \, a^{2} b c^{2}\right)} e^{5}\right)} x^{2} + {\left(2 \, b c^{4} d^{5} + 8 \, a b c^{3} d^{3} e^{2} - 2 \, {\left(2 \, b^{2} c^{3} - a c^{4}\right)} d^{4} e + 2 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 6 \, a^{2} c^{3}\right)} d^{2} e^{3} - {\left(b^{5} - 8 \, a b^{3} c + 18 \, a^{2} b c^{2}\right)} d e^{4} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 6 \, a^{3} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{5} - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{4} e + 4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{3} e^{2} + {\left(3 \, b^{5} c - 22 \, a b^{3} c^{2} + 40 \, a^{2} b c^{3}\right)} d^{2} e^{3} - 2 \, {\left(b^{6} - 7 \, a b^{4} c + 11 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} d e^{4} + {\left(2 \, a b^{5} - 15 \, a^{2} b^{3} c + 28 \, a^{3} b c^{2}\right)} e^{5}\right)} x + {\left(2 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d^{2} e^{3} - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d e^{4} + {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{4} - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} e^{3} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{4} - {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} e^{5}\right)} x^{2} + {\left(2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} e^{3} - {\left(b^{6} - 10 \, a b^{4} c + 32 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d e^{4} - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{5}\right)} x\right)} \log\left(c x^{2} + b x + a\right) - 2 \, {\left(2 \, {\left(a b^{4} c - 8 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d^{2} e^{3} - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d e^{4} + {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{4} - {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} e^{3} + {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e^{4} - {\left(b^{6} - 8 \, a b^{4} c + 16 \, a^{2} b^{2} c^{2}\right)} e^{5}\right)} x^{2} + {\left(2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{2} e^{3} - {\left(b^{6} - 10 \, a b^{4} c + 32 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d e^{4} - {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{5}\right)} x\right)} \log\left(e x + d\right)}{{\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d^{7} - 3 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} d^{6} e + 3 \, {\left(a b^{6} c - 7 \, a^{2} b^{4} c^{2} + 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{5} e^{2} - {\left(a b^{7} - 2 \, a^{2} b^{5} c - 32 \, a^{3} b^{3} c^{2} + 96 \, a^{4} b c^{3}\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{6} - 7 \, a^{3} b^{4} c + 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{3} e^{4} - 3 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d^{2} e^{5} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} d e^{6} + {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{6} e - 3 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{5} e^{2} + 3 \, {\left(b^{6} c^{2} - 7 \, a b^{4} c^{3} + 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d^{4} e^{3} - {\left(b^{7} c - 2 \, a b^{5} c^{2} - 32 \, a^{2} b^{3} c^{3} + 96 \, a^{3} b c^{4}\right)} d^{3} e^{4} + 3 \, {\left(a b^{6} c - 7 \, a^{2} b^{4} c^{2} + 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{2} e^{5} - 3 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d e^{6} + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} e^{7}\right)} x^{3} + {\left({\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{7} - 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{6} e + 3 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d^{5} e^{2} + {\left(2 \, b^{7} c - 19 \, a b^{5} c^{2} + 56 \, a^{2} b^{3} c^{3} - 48 \, a^{3} b c^{4}\right)} d^{4} e^{3} - {\left(b^{8} - 5 \, a b^{6} c - 11 \, a^{2} b^{4} c^{2} + 72 \, a^{3} b^{2} c^{3} - 48 \, a^{4} c^{4}\right)} d^{3} e^{4} + 3 \, {\left(a b^{7} - 8 \, a^{2} b^{5} c + 16 \, a^{3} b^{3} c^{2}\right)} d^{2} e^{5} - {\left(3 \, a^{2} b^{6} - 25 \, a^{3} b^{4} c + 56 \, a^{4} b^{2} c^{2} - 16 \, a^{5} c^{3}\right)} d e^{6} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} e^{7}\right)} x^{2} + {\left({\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{7} - {\left(3 \, b^{6} c^{2} - 25 \, a b^{4} c^{3} + 56 \, a^{2} b^{2} c^{4} - 16 \, a^{3} c^{5}\right)} d^{6} e + 3 \, {\left(b^{7} c - 8 \, a b^{5} c^{2} + 16 \, a^{2} b^{3} c^{3}\right)} d^{5} e^{2} - {\left(b^{8} - 5 \, a b^{6} c - 11 \, a^{2} b^{4} c^{2} + 72 \, a^{3} b^{2} c^{3} - 48 \, a^{4} c^{4}\right)} d^{4} e^{3} + {\left(2 \, a b^{7} - 19 \, a^{2} b^{5} c + 56 \, a^{3} b^{3} c^{2} - 48 \, a^{4} b c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d e^{6} + {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} e^{7}\right)} x}\right]"," ",0,"[-((b^3*c^3 - 4*a*b*c^4)*d^5 - (3*b^4*c^2 - 16*a*b^2*c^3 + 16*a^2*c^4)*d^4*e + 3*(b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*d^3*e^2 - (b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d^2*e^3 + (a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e^5 + 2*((b^2*c^4 - 4*a*c^5)*d^4*e - 2*(b^3*c^3 - 4*a*b*c^4)*d^3*e^2 + 2*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d^2*e^3 - (b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*d*e^4 + (a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*e^5)*x^2 - (2*a*c^4*d^5 - 4*a*b*c^3*d^4*e + 12*a^2*c^3*d^3*e^2 + 2*(a*b^3*c - 6*a^2*b*c^2)*d^2*e^3 - (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d*e^4 + (2*c^5*d^4*e - 4*b*c^4*d^3*e^2 + 12*a*c^4*d^2*e^3 + 2*(b^3*c^2 - 6*a*b*c^3)*d*e^4 - (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e^5)*x^3 + (2*c^5*d^5 - 2*b*c^4*d^4*e + 2*b^3*c^2*d^2*e^3 - 4*(b^2*c^3 - 3*a*c^4)*d^3*e^2 + (b^4*c - 6*a*b^2*c^2 - 6*a^2*c^3)*d*e^4 - (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*e^5)*x^2 + (2*b*c^4*d^5 + 8*a*b*c^3*d^3*e^2 - 2*(2*b^2*c^3 - a*c^4)*d^4*e + 2*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^2*e^3 - (b^5 - 8*a*b^3*c + 18*a^2*b*c^2)*d*e^4 - (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*e^5)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (2*(b^2*c^4 - 4*a*c^5)*d^5 - 3*(b^3*c^3 - 4*a*b*c^4)*d^4*e + 4*(a*b^2*c^3 - 4*a^2*c^4)*d^3*e^2 + (3*b^5*c - 22*a*b^3*c^2 + 40*a^2*b*c^3)*d^2*e^3 - 2*(b^6 - 7*a*b^4*c + 11*a^2*b^2*c^2 + 4*a^3*c^3)*d*e^4 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*e^5)*x + (2*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d^2*e^3 - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d*e^4 + (2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^4 - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^5)*x^3 + (2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*e^3 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^4 - (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*e^5)*x^2 + (2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*e^3 - (b^6 - 10*a*b^4*c + 32*a^2*b^2*c^2 - 32*a^3*c^3)*d*e^4 - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^5)*x)*log(c*x^2 + b*x + a) - 2*(2*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d^2*e^3 - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d*e^4 + (2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^4 - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^5)*x^3 + (2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*e^3 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^4 - (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*e^5)*x^2 + (2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*e^3 - (b^6 - 10*a*b^4*c + 32*a^2*b^2*c^2 - 32*a^3*c^3)*d*e^4 - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^5)*x)*log(e*x + d))/((a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*d^7 - 3*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*d^6*e + 3*(a*b^6*c - 7*a^2*b^4*c^2 + 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^5*e^2 - (a*b^7 - 2*a^2*b^5*c - 32*a^3*b^3*c^2 + 96*a^4*b*c^3)*d^4*e^3 + 3*(a^2*b^6 - 7*a^3*b^4*c + 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^3*e^4 - 3*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2*e^5 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*d*e^6 + ((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^6*e - 3*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^5*e^2 + 3*(b^6*c^2 - 7*a*b^4*c^3 + 8*a^2*b^2*c^4 + 16*a^3*c^5)*d^4*e^3 - (b^7*c - 2*a*b^5*c^2 - 32*a^2*b^3*c^3 + 96*a^3*b*c^4)*d^3*e^4 + 3*(a*b^6*c - 7*a^2*b^4*c^2 + 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^2*e^5 - 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d*e^6 + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*e^7)*x^3 + ((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^7 - 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^6*e + 3*(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*d^5*e^2 + (2*b^7*c - 19*a*b^5*c^2 + 56*a^2*b^3*c^3 - 48*a^3*b*c^4)*d^4*e^3 - (b^8 - 5*a*b^6*c - 11*a^2*b^4*c^2 + 72*a^3*b^2*c^3 - 48*a^4*c^4)*d^3*e^4 + 3*(a*b^7 - 8*a^2*b^5*c + 16*a^3*b^3*c^2)*d^2*e^5 - (3*a^2*b^6 - 25*a^3*b^4*c + 56*a^4*b^2*c^2 - 16*a^5*c^3)*d*e^6 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*e^7)*x^2 + ((b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^7 - (3*b^6*c^2 - 25*a*b^4*c^3 + 56*a^2*b^2*c^4 - 16*a^3*c^5)*d^6*e + 3*(b^7*c - 8*a*b^5*c^2 + 16*a^2*b^3*c^3)*d^5*e^2 - (b^8 - 5*a*b^6*c - 11*a^2*b^4*c^2 + 72*a^3*b^2*c^3 - 48*a^4*c^4)*d^4*e^3 + (2*a*b^7 - 19*a^2*b^5*c + 56*a^3*b^3*c^2 - 48*a^4*b*c^3)*d^3*e^4 + 3*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^2*e^5 - 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d*e^6 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*e^7)*x), -((b^3*c^3 - 4*a*b*c^4)*d^5 - (3*b^4*c^2 - 16*a*b^2*c^3 + 16*a^2*c^4)*d^4*e + 3*(b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*d^3*e^2 - (b^6 - 6*a*b^4*c + 8*a^2*b^2*c^2)*d^2*e^3 + (a^2*b^3*c - 4*a^3*b*c^2)*d*e^4 + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e^5 + 2*((b^2*c^4 - 4*a*c^5)*d^4*e - 2*(b^3*c^3 - 4*a*b*c^4)*d^3*e^2 + 2*(b^4*c^2 - 5*a*b^2*c^3 + 4*a^2*c^4)*d^2*e^3 - (b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*d*e^4 + (a*b^4*c - 7*a^2*b^2*c^2 + 12*a^3*c^3)*e^5)*x^2 - 2*(2*a*c^4*d^5 - 4*a*b*c^3*d^4*e + 12*a^2*c^3*d^3*e^2 + 2*(a*b^3*c - 6*a^2*b*c^2)*d^2*e^3 - (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*d*e^4 + (2*c^5*d^4*e - 4*b*c^4*d^3*e^2 + 12*a*c^4*d^2*e^3 + 2*(b^3*c^2 - 6*a*b*c^3)*d*e^4 - (b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*e^5)*x^3 + (2*c^5*d^5 - 2*b*c^4*d^4*e + 2*b^3*c^2*d^2*e^3 - 4*(b^2*c^3 - 3*a*c^4)*d^3*e^2 + (b^4*c - 6*a*b^2*c^2 - 6*a^2*c^3)*d*e^4 - (b^5 - 6*a*b^3*c + 6*a^2*b*c^2)*e^5)*x^2 + (2*b*c^4*d^5 + 8*a*b*c^3*d^3*e^2 - 2*(2*b^2*c^3 - a*c^4)*d^4*e + 2*(b^4*c - 6*a*b^2*c^2 + 6*a^2*c^3)*d^2*e^3 - (b^5 - 8*a*b^3*c + 18*a^2*b*c^2)*d*e^4 - (a*b^4 - 6*a^2*b^2*c + 6*a^3*c^2)*e^5)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (2*(b^2*c^4 - 4*a*c^5)*d^5 - 3*(b^3*c^3 - 4*a*b*c^4)*d^4*e + 4*(a*b^2*c^3 - 4*a^2*c^4)*d^3*e^2 + (3*b^5*c - 22*a*b^3*c^2 + 40*a^2*b*c^3)*d^2*e^3 - 2*(b^6 - 7*a*b^4*c + 11*a^2*b^2*c^2 + 4*a^3*c^3)*d*e^4 + (2*a*b^5 - 15*a^2*b^3*c + 28*a^3*b*c^2)*e^5)*x + (2*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d^2*e^3 - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d*e^4 + (2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^4 - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^5)*x^3 + (2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*e^3 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^4 - (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*e^5)*x^2 + (2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*e^3 - (b^6 - 10*a*b^4*c + 32*a^2*b^2*c^2 - 32*a^3*c^3)*d*e^4 - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^5)*x)*log(c*x^2 + b*x + a) - 2*(2*(a*b^4*c - 8*a^2*b^2*c^2 + 16*a^3*c^3)*d^2*e^3 - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*d*e^4 + (2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d*e^4 - (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^5)*x^3 + (2*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2*e^3 + (b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e^4 - (b^6 - 8*a*b^4*c + 16*a^2*b^2*c^2)*e^5)*x^2 + (2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d^2*e^3 - (b^6 - 10*a*b^4*c + 32*a^2*b^2*c^2 - 32*a^3*c^3)*d*e^4 - (a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^5)*x)*log(e*x + d))/((a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*d^7 - 3*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*d^6*e + 3*(a*b^6*c - 7*a^2*b^4*c^2 + 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^5*e^2 - (a*b^7 - 2*a^2*b^5*c - 32*a^3*b^3*c^2 + 96*a^4*b*c^3)*d^4*e^3 + 3*(a^2*b^6 - 7*a^3*b^4*c + 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^3*e^4 - 3*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d^2*e^5 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*d*e^6 + ((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^6*e - 3*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^5*e^2 + 3*(b^6*c^2 - 7*a*b^4*c^3 + 8*a^2*b^2*c^4 + 16*a^3*c^5)*d^4*e^3 - (b^7*c - 2*a*b^5*c^2 - 32*a^2*b^3*c^3 + 96*a^3*b*c^4)*d^3*e^4 + 3*(a*b^6*c - 7*a^2*b^4*c^2 + 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^2*e^5 - 3*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d*e^6 + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*e^7)*x^3 + ((b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^7 - 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^6*e + 3*(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*d^5*e^2 + (2*b^7*c - 19*a*b^5*c^2 + 56*a^2*b^3*c^3 - 48*a^3*b*c^4)*d^4*e^3 - (b^8 - 5*a*b^6*c - 11*a^2*b^4*c^2 + 72*a^3*b^2*c^3 - 48*a^4*c^4)*d^3*e^4 + 3*(a*b^7 - 8*a^2*b^5*c + 16*a^3*b^3*c^2)*d^2*e^5 - (3*a^2*b^6 - 25*a^3*b^4*c + 56*a^4*b^2*c^2 - 16*a^5*c^3)*d*e^6 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*e^7)*x^2 + ((b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^7 - (3*b^6*c^2 - 25*a*b^4*c^3 + 56*a^2*b^2*c^4 - 16*a^3*c^5)*d^6*e + 3*(b^7*c - 8*a*b^5*c^2 + 16*a^2*b^3*c^3)*d^5*e^2 - (b^8 - 5*a*b^6*c - 11*a^2*b^4*c^2 + 72*a^3*b^2*c^3 - 48*a^4*c^4)*d^4*e^3 + (2*a*b^7 - 19*a^2*b^5*c + 56*a^3*b^3*c^2 - 48*a^4*b*c^3)*d^3*e^4 + 3*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*d^2*e^5 - 2*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d*e^6 + (a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*e^7)*x)]","B",0
2198,-1,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2199,1,2207,0,0.489061," ","integrate(x^7/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{7 \, a^{2} b^{8} - 83 \, a^{3} b^{6} c + 335 \, a^{4} b^{4} c^{2} - 500 \, a^{5} b^{2} c^{3} + 160 \, a^{6} c^{4} + {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} x^{6} - 4 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} x^{5} - {\left(11 \, b^{8} c^{2} - 134 \, a b^{6} c^{3} + 552 \, a^{2} b^{4} c^{4} - 800 \, a^{3} b^{2} c^{5} + 128 \, a^{4} c^{6}\right)} x^{4} + 2 \, {\left(b^{9} c - 20 \, a b^{7} c^{2} + 147 \, a^{2} b^{5} c^{3} - 475 \, a^{3} b^{3} c^{4} + 572 \, a^{4} b c^{5}\right)} x^{3} + {\left(7 \, b^{10} - 93 \, a b^{8} c + 451 \, a^{2} b^{6} c^{2} - 937 \, a^{3} b^{4} c^{3} + 660 \, a^{4} b^{2} c^{4} + 128 \, a^{5} c^{5}\right)} x^{2} - 3 \, {\left(2 \, a^{2} b^{7} - 21 \, a^{3} b^{5} c + 70 \, a^{4} b^{3} c^{2} - 70 \, a^{5} b c^{3} + {\left(2 \, b^{7} c^{2} - 21 \, a b^{5} c^{3} + 70 \, a^{2} b^{3} c^{4} - 70 \, a^{3} b c^{5}\right)} x^{4} + 2 \, {\left(2 \, b^{8} c - 21 \, a b^{6} c^{2} + 70 \, a^{2} b^{4} c^{3} - 70 \, a^{3} b^{2} c^{4}\right)} x^{3} + {\left(2 \, b^{9} - 17 \, a b^{7} c + 28 \, a^{2} b^{5} c^{2} + 70 \, a^{3} b^{3} c^{3} - 140 \, a^{4} b c^{4}\right)} x^{2} + 2 \, {\left(2 \, a b^{8} - 21 \, a^{2} b^{6} c + 70 \, a^{3} b^{4} c^{2} - 70 \, a^{4} b^{2} c^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(7 \, a b^{9} - 89 \, a^{2} b^{7} c + 404 \, a^{3} b^{5} c^{2} - 761 \, a^{4} b^{3} c^{3} + 484 \, a^{5} b c^{4}\right)} x + 3 \, {\left(2 \, a^{2} b^{8} - 25 \, a^{3} b^{6} c + 108 \, a^{4} b^{4} c^{2} - 176 \, a^{5} b^{2} c^{3} + 64 \, a^{6} c^{4} + {\left(2 \, b^{8} c^{2} - 25 \, a b^{6} c^{3} + 108 \, a^{2} b^{4} c^{4} - 176 \, a^{3} b^{2} c^{5} + 64 \, a^{4} c^{6}\right)} x^{4} + 2 \, {\left(2 \, b^{9} c - 25 \, a b^{7} c^{2} + 108 \, a^{2} b^{5} c^{3} - 176 \, a^{3} b^{3} c^{4} + 64 \, a^{4} b c^{5}\right)} x^{3} + {\left(2 \, b^{10} - 21 \, a b^{8} c + 58 \, a^{2} b^{6} c^{2} + 40 \, a^{3} b^{4} c^{3} - 288 \, a^{4} b^{2} c^{4} + 128 \, a^{5} c^{5}\right)} x^{2} + 2 \, {\left(2 \, a b^{9} - 25 \, a^{2} b^{7} c + 108 \, a^{3} b^{5} c^{2} - 176 \, a^{4} b^{3} c^{3} + 64 \, a^{5} b c^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{6} c^{5} - 12 \, a^{3} b^{4} c^{6} + 48 \, a^{4} b^{2} c^{7} - 64 \, a^{5} c^{8} + {\left(b^{6} c^{7} - 12 \, a b^{4} c^{8} + 48 \, a^{2} b^{2} c^{9} - 64 \, a^{3} c^{10}\right)} x^{4} + 2 \, {\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)} x^{3} + {\left(b^{8} c^{5} - 10 \, a b^{6} c^{6} + 24 \, a^{2} b^{4} c^{7} + 32 \, a^{3} b^{2} c^{8} - 128 \, a^{4} c^{9}\right)} x^{2} + 2 \, {\left(a b^{7} c^{5} - 12 \, a^{2} b^{5} c^{6} + 48 \, a^{3} b^{3} c^{7} - 64 \, a^{4} b c^{8}\right)} x\right)}}, \frac{7 \, a^{2} b^{8} - 83 \, a^{3} b^{6} c + 335 \, a^{4} b^{4} c^{2} - 500 \, a^{5} b^{2} c^{3} + 160 \, a^{6} c^{4} + {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} x^{6} - 4 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} x^{5} - {\left(11 \, b^{8} c^{2} - 134 \, a b^{6} c^{3} + 552 \, a^{2} b^{4} c^{4} - 800 \, a^{3} b^{2} c^{5} + 128 \, a^{4} c^{6}\right)} x^{4} + 2 \, {\left(b^{9} c - 20 \, a b^{7} c^{2} + 147 \, a^{2} b^{5} c^{3} - 475 \, a^{3} b^{3} c^{4} + 572 \, a^{4} b c^{5}\right)} x^{3} + {\left(7 \, b^{10} - 93 \, a b^{8} c + 451 \, a^{2} b^{6} c^{2} - 937 \, a^{3} b^{4} c^{3} + 660 \, a^{4} b^{2} c^{4} + 128 \, a^{5} c^{5}\right)} x^{2} + 6 \, {\left(2 \, a^{2} b^{7} - 21 \, a^{3} b^{5} c + 70 \, a^{4} b^{3} c^{2} - 70 \, a^{5} b c^{3} + {\left(2 \, b^{7} c^{2} - 21 \, a b^{5} c^{3} + 70 \, a^{2} b^{3} c^{4} - 70 \, a^{3} b c^{5}\right)} x^{4} + 2 \, {\left(2 \, b^{8} c - 21 \, a b^{6} c^{2} + 70 \, a^{2} b^{4} c^{3} - 70 \, a^{3} b^{2} c^{4}\right)} x^{3} + {\left(2 \, b^{9} - 17 \, a b^{7} c + 28 \, a^{2} b^{5} c^{2} + 70 \, a^{3} b^{3} c^{3} - 140 \, a^{4} b c^{4}\right)} x^{2} + 2 \, {\left(2 \, a b^{8} - 21 \, a^{2} b^{6} c + 70 \, a^{3} b^{4} c^{2} - 70 \, a^{4} b^{2} c^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(7 \, a b^{9} - 89 \, a^{2} b^{7} c + 404 \, a^{3} b^{5} c^{2} - 761 \, a^{4} b^{3} c^{3} + 484 \, a^{5} b c^{4}\right)} x + 3 \, {\left(2 \, a^{2} b^{8} - 25 \, a^{3} b^{6} c + 108 \, a^{4} b^{4} c^{2} - 176 \, a^{5} b^{2} c^{3} + 64 \, a^{6} c^{4} + {\left(2 \, b^{8} c^{2} - 25 \, a b^{6} c^{3} + 108 \, a^{2} b^{4} c^{4} - 176 \, a^{3} b^{2} c^{5} + 64 \, a^{4} c^{6}\right)} x^{4} + 2 \, {\left(2 \, b^{9} c - 25 \, a b^{7} c^{2} + 108 \, a^{2} b^{5} c^{3} - 176 \, a^{3} b^{3} c^{4} + 64 \, a^{4} b c^{5}\right)} x^{3} + {\left(2 \, b^{10} - 21 \, a b^{8} c + 58 \, a^{2} b^{6} c^{2} + 40 \, a^{3} b^{4} c^{3} - 288 \, a^{4} b^{2} c^{4} + 128 \, a^{5} c^{5}\right)} x^{2} + 2 \, {\left(2 \, a b^{9} - 25 \, a^{2} b^{7} c + 108 \, a^{3} b^{5} c^{2} - 176 \, a^{4} b^{3} c^{3} + 64 \, a^{5} b c^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{6} c^{5} - 12 \, a^{3} b^{4} c^{6} + 48 \, a^{4} b^{2} c^{7} - 64 \, a^{5} c^{8} + {\left(b^{6} c^{7} - 12 \, a b^{4} c^{8} + 48 \, a^{2} b^{2} c^{9} - 64 \, a^{3} c^{10}\right)} x^{4} + 2 \, {\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)} x^{3} + {\left(b^{8} c^{5} - 10 \, a b^{6} c^{6} + 24 \, a^{2} b^{4} c^{7} + 32 \, a^{3} b^{2} c^{8} - 128 \, a^{4} c^{9}\right)} x^{2} + 2 \, {\left(a b^{7} c^{5} - 12 \, a^{2} b^{5} c^{6} + 48 \, a^{3} b^{3} c^{7} - 64 \, a^{4} b c^{8}\right)} x\right)}}\right]"," ",0,"[1/2*(7*a^2*b^8 - 83*a^3*b^6*c + 335*a^4*b^4*c^2 - 500*a^5*b^2*c^3 + 160*a^6*c^4 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*x^6 - 4*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*x^5 - (11*b^8*c^2 - 134*a*b^6*c^3 + 552*a^2*b^4*c^4 - 800*a^3*b^2*c^5 + 128*a^4*c^6)*x^4 + 2*(b^9*c - 20*a*b^7*c^2 + 147*a^2*b^5*c^3 - 475*a^3*b^3*c^4 + 572*a^4*b*c^5)*x^3 + (7*b^10 - 93*a*b^8*c + 451*a^2*b^6*c^2 - 937*a^3*b^4*c^3 + 660*a^4*b^2*c^4 + 128*a^5*c^5)*x^2 - 3*(2*a^2*b^7 - 21*a^3*b^5*c + 70*a^4*b^3*c^2 - 70*a^5*b*c^3 + (2*b^7*c^2 - 21*a*b^5*c^3 + 70*a^2*b^3*c^4 - 70*a^3*b*c^5)*x^4 + 2*(2*b^8*c - 21*a*b^6*c^2 + 70*a^2*b^4*c^3 - 70*a^3*b^2*c^4)*x^3 + (2*b^9 - 17*a*b^7*c + 28*a^2*b^5*c^2 + 70*a^3*b^3*c^3 - 140*a^4*b*c^4)*x^2 + 2*(2*a*b^8 - 21*a^2*b^6*c + 70*a^3*b^4*c^2 - 70*a^4*b^2*c^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(7*a*b^9 - 89*a^2*b^7*c + 404*a^3*b^5*c^2 - 761*a^4*b^3*c^3 + 484*a^5*b*c^4)*x + 3*(2*a^2*b^8 - 25*a^3*b^6*c + 108*a^4*b^4*c^2 - 176*a^5*b^2*c^3 + 64*a^6*c^4 + (2*b^8*c^2 - 25*a*b^6*c^3 + 108*a^2*b^4*c^4 - 176*a^3*b^2*c^5 + 64*a^4*c^6)*x^4 + 2*(2*b^9*c - 25*a*b^7*c^2 + 108*a^2*b^5*c^3 - 176*a^3*b^3*c^4 + 64*a^4*b*c^5)*x^3 + (2*b^10 - 21*a*b^8*c + 58*a^2*b^6*c^2 + 40*a^3*b^4*c^3 - 288*a^4*b^2*c^4 + 128*a^5*c^5)*x^2 + 2*(2*a*b^9 - 25*a^2*b^7*c + 108*a^3*b^5*c^2 - 176*a^4*b^3*c^3 + 64*a^5*b*c^4)*x)*log(c*x^2 + b*x + a))/(a^2*b^6*c^5 - 12*a^3*b^4*c^6 + 48*a^4*b^2*c^7 - 64*a^5*c^8 + (b^6*c^7 - 12*a*b^4*c^8 + 48*a^2*b^2*c^9 - 64*a^3*c^10)*x^4 + 2*(b^7*c^6 - 12*a*b^5*c^7 + 48*a^2*b^3*c^8 - 64*a^3*b*c^9)*x^3 + (b^8*c^5 - 10*a*b^6*c^6 + 24*a^2*b^4*c^7 + 32*a^3*b^2*c^8 - 128*a^4*c^9)*x^2 + 2*(a*b^7*c^5 - 12*a^2*b^5*c^6 + 48*a^3*b^3*c^7 - 64*a^4*b*c^8)*x), 1/2*(7*a^2*b^8 - 83*a^3*b^6*c + 335*a^4*b^4*c^2 - 500*a^5*b^2*c^3 + 160*a^6*c^4 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*x^6 - 4*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*x^5 - (11*b^8*c^2 - 134*a*b^6*c^3 + 552*a^2*b^4*c^4 - 800*a^3*b^2*c^5 + 128*a^4*c^6)*x^4 + 2*(b^9*c - 20*a*b^7*c^2 + 147*a^2*b^5*c^3 - 475*a^3*b^3*c^4 + 572*a^4*b*c^5)*x^3 + (7*b^10 - 93*a*b^8*c + 451*a^2*b^6*c^2 - 937*a^3*b^4*c^3 + 660*a^4*b^2*c^4 + 128*a^5*c^5)*x^2 + 6*(2*a^2*b^7 - 21*a^3*b^5*c + 70*a^4*b^3*c^2 - 70*a^5*b*c^3 + (2*b^7*c^2 - 21*a*b^5*c^3 + 70*a^2*b^3*c^4 - 70*a^3*b*c^5)*x^4 + 2*(2*b^8*c - 21*a*b^6*c^2 + 70*a^2*b^4*c^3 - 70*a^3*b^2*c^4)*x^3 + (2*b^9 - 17*a*b^7*c + 28*a^2*b^5*c^2 + 70*a^3*b^3*c^3 - 140*a^4*b*c^4)*x^2 + 2*(2*a*b^8 - 21*a^2*b^6*c + 70*a^3*b^4*c^2 - 70*a^4*b^2*c^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(7*a*b^9 - 89*a^2*b^7*c + 404*a^3*b^5*c^2 - 761*a^4*b^3*c^3 + 484*a^5*b*c^4)*x + 3*(2*a^2*b^8 - 25*a^3*b^6*c + 108*a^4*b^4*c^2 - 176*a^5*b^2*c^3 + 64*a^6*c^4 + (2*b^8*c^2 - 25*a*b^6*c^3 + 108*a^2*b^4*c^4 - 176*a^3*b^2*c^5 + 64*a^4*c^6)*x^4 + 2*(2*b^9*c - 25*a*b^7*c^2 + 108*a^2*b^5*c^3 - 176*a^3*b^3*c^4 + 64*a^4*b*c^5)*x^3 + (2*b^10 - 21*a*b^8*c + 58*a^2*b^6*c^2 + 40*a^3*b^4*c^3 - 288*a^4*b^2*c^4 + 128*a^5*c^5)*x^2 + 2*(2*a*b^9 - 25*a^2*b^7*c + 108*a^3*b^5*c^2 - 176*a^4*b^3*c^3 + 64*a^5*b*c^4)*x)*log(c*x^2 + b*x + a))/(a^2*b^6*c^5 - 12*a^3*b^4*c^6 + 48*a^4*b^2*c^7 - 64*a^5*c^8 + (b^6*c^7 - 12*a*b^4*c^8 + 48*a^2*b^2*c^9 - 64*a^3*c^10)*x^4 + 2*(b^7*c^6 - 12*a*b^5*c^7 + 48*a^2*b^3*c^8 - 64*a^3*b*c^9)*x^3 + (b^8*c^5 - 10*a*b^6*c^6 + 24*a^2*b^4*c^7 + 32*a^3*b^2*c^8 - 128*a^4*c^9)*x^2 + 2*(a*b^7*c^5 - 12*a^2*b^5*c^6 + 48*a^3*b^3*c^7 - 64*a^4*b*c^8)*x)]","B",0
2200,1,1926,0,0.479545," ","integrate(x^6/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{5 \, a^{2} b^{7} - 56 \, a^{3} b^{5} c + 202 \, a^{4} b^{3} c^{2} - 232 \, a^{5} b c^{3} - 2 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{5} - 4 \, {\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)} x^{4} + 2 \, {\left(2 \, b^{8} c - 26 \, a b^{6} c^{2} + 123 \, a^{2} b^{4} c^{3} - 254 \, a^{3} b^{2} c^{4} + 200 \, a^{4} c^{5}\right)} x^{3} + {\left(5 \, b^{9} - 58 \, a b^{7} c + 225 \, a^{2} b^{5} c^{2} - 314 \, a^{3} b^{3} c^{3} + 88 \, a^{4} b c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(5 \, a b^{8} - 59 \, a^{2} b^{6} c + 235 \, a^{3} b^{4} c^{2} - 346 \, a^{4} b^{2} c^{3} + 120 \, a^{5} c^{4}\right)} x + 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} + {\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)} x^{4} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{3} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{2} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7} + {\left(b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}\right)} x^{4} + 2 \, {\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)} x^{3} + {\left(b^{8} c^{4} - 10 \, a b^{6} c^{5} + 24 \, a^{2} b^{4} c^{6} + 32 \, a^{3} b^{2} c^{7} - 128 \, a^{4} c^{8}\right)} x^{2} + 2 \, {\left(a b^{7} c^{4} - 12 \, a^{2} b^{5} c^{5} + 48 \, a^{3} b^{3} c^{6} - 64 \, a^{4} b c^{7}\right)} x\right)}}, -\frac{5 \, a^{2} b^{7} - 56 \, a^{3} b^{5} c + 202 \, a^{4} b^{3} c^{2} - 232 \, a^{5} b c^{3} - 2 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{5} - 4 \, {\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)} x^{4} + 2 \, {\left(2 \, b^{8} c - 26 \, a b^{6} c^{2} + 123 \, a^{2} b^{4} c^{3} - 254 \, a^{3} b^{2} c^{4} + 200 \, a^{4} c^{5}\right)} x^{3} + {\left(5 \, b^{9} - 58 \, a b^{7} c + 225 \, a^{2} b^{5} c^{2} - 314 \, a^{3} b^{3} c^{3} + 88 \, a^{4} b c^{4}\right)} x^{2} + 6 \, {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(5 \, a b^{8} - 59 \, a^{2} b^{6} c + 235 \, a^{3} b^{4} c^{2} - 346 \, a^{4} b^{2} c^{3} + 120 \, a^{5} c^{4}\right)} x + 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} + {\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)} x^{4} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{3} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{2} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7} + {\left(b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}\right)} x^{4} + 2 \, {\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)} x^{3} + {\left(b^{8} c^{4} - 10 \, a b^{6} c^{5} + 24 \, a^{2} b^{4} c^{6} + 32 \, a^{3} b^{2} c^{7} - 128 \, a^{4} c^{8}\right)} x^{2} + 2 \, {\left(a b^{7} c^{4} - 12 \, a^{2} b^{5} c^{5} + 48 \, a^{3} b^{3} c^{6} - 64 \, a^{4} b c^{7}\right)} x\right)}}\right]"," ",0,"[-1/2*(5*a^2*b^7 - 56*a^3*b^5*c + 202*a^4*b^3*c^2 - 232*a^5*b*c^3 - 2*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^5 - 4*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^4 + 2*(2*b^8*c - 26*a*b^6*c^2 + 123*a^2*b^4*c^3 - 254*a^3*b^2*c^4 + 200*a^4*c^5)*x^3 + (5*b^9 - 58*a*b^7*c + 225*a^2*b^5*c^2 - 314*a^3*b^3*c^3 + 88*a^4*b*c^4)*x^2 + 3*(a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3 + (b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*x^4 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*x^3 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*x^2 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(5*a*b^8 - 59*a^2*b^6*c + 235*a^3*b^4*c^2 - 346*a^4*b^2*c^3 + 120*a^5*c^4)*x + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^4 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^3 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^2 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x)*log(c*x^2 + b*x + a))/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7 + (b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)*x^4 + 2*(b^7*c^5 - 12*a*b^5*c^6 + 48*a^2*b^3*c^7 - 64*a^3*b*c^8)*x^3 + (b^8*c^4 - 10*a*b^6*c^5 + 24*a^2*b^4*c^6 + 32*a^3*b^2*c^7 - 128*a^4*c^8)*x^2 + 2*(a*b^7*c^4 - 12*a^2*b^5*c^5 + 48*a^3*b^3*c^6 - 64*a^4*b*c^7)*x), -1/2*(5*a^2*b^7 - 56*a^3*b^5*c + 202*a^4*b^3*c^2 - 232*a^5*b*c^3 - 2*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^5 - 4*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^4 + 2*(2*b^8*c - 26*a*b^6*c^2 + 123*a^2*b^4*c^3 - 254*a^3*b^2*c^4 + 200*a^4*c^5)*x^3 + (5*b^9 - 58*a*b^7*c + 225*a^2*b^5*c^2 - 314*a^3*b^3*c^3 + 88*a^4*b*c^4)*x^2 + 6*(a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3 + (b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*x^4 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*x^3 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*x^2 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(5*a*b^8 - 59*a^2*b^6*c + 235*a^3*b^4*c^2 - 346*a^4*b^2*c^3 + 120*a^5*c^4)*x + 3*(a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3 + (b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^4 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^3 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^2 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x)*log(c*x^2 + b*x + a))/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7 + (b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)*x^4 + 2*(b^7*c^5 - 12*a*b^5*c^6 + 48*a^2*b^3*c^7 - 64*a^3*b*c^8)*x^3 + (b^8*c^4 - 10*a*b^6*c^5 + 24*a^2*b^4*c^6 + 32*a^3*b^2*c^7 - 128*a^4*c^8)*x^2 + 2*(a*b^7*c^4 - 12*a^2*b^5*c^5 + 48*a^3*b^3*c^6 - 64*a^4*b*c^7)*x)]","B",0
2201,1,3865,0,0.595030," ","integrate((e*x+d)^5/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{5} c^{3} - 14 \, a b^{3} c^{4} + 40 \, a^{2} b c^{5}\right)} d^{5} + 5 \, {\left(a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5}\right)} d^{4} e - 60 \, {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d^{3} e^{2} + 10 \, {\left(a^{2} b^{4} c^{2} + 4 \, a^{3} b^{2} c^{3} - 32 \, a^{4} c^{4}\right)} d^{2} e^{3} + 5 \, {\left(a^{2} b^{5} c - 14 \, a^{3} b^{3} c^{2} + 40 \, a^{4} b c^{3}\right)} d e^{4} - 3 \, {\left(a^{2} b^{6} - 11 \, a^{3} b^{4} c + 36 \, a^{4} b^{2} c^{2} - 32 \, a^{5} c^{3}\right)} e^{5} - 2 \, {\left(6 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{5} - 15 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{4} e + 10 \, {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{3} e^{2} - 30 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{2} e^{3} - 5 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} - 40 \, a^{3} c^{5}\right)} d e^{4} + {\left(2 \, b^{7} c - 23 \, a b^{5} c^{2} + 85 \, a^{2} b^{3} c^{3} - 100 \, a^{3} b c^{4}\right)} e^{5}\right)} x^{3} - {\left(18 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{5} - 45 \, {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5}\right)} d^{4} e + 30 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} d^{3} e^{2} - 10 \, {\left(b^{6} c^{2} - 3 \, a b^{4} c^{3} + 12 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e^{3} - 5 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} + 8 \, a^{3} b c^{4}\right)} d e^{4} + {\left(3 \, b^{8} - 31 \, a b^{6} c + 87 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} e^{5}\right)} x^{2} + {\left(12 \, a^{2} c^{5} d^{5} - 30 \, a^{2} b c^{4} d^{4} e - 60 \, a^{3} b c^{3} d^{2} e^{3} + 60 \, a^{4} c^{3} d e^{4} + 20 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} d^{3} e^{2} - {\left(a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2}\right)} e^{5} + {\left(12 \, c^{7} d^{5} - 30 \, b c^{6} d^{4} e - 60 \, a b c^{5} d^{2} e^{3} + 60 \, a^{2} c^{5} d e^{4} + 20 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{3} e^{2} - {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(12 \, b c^{6} d^{5} - 30 \, b^{2} c^{5} d^{4} e - 60 \, a b^{2} c^{4} d^{2} e^{3} + 60 \, a^{2} b c^{4} d e^{4} + 20 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{3} e^{2} - {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(12 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{5} - 30 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{4} e + 20 \, {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{3} e^{2} - 60 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d^{2} e^{3} + 60 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(12 \, a b c^{5} d^{5} - 30 \, a b^{2} c^{4} d^{4} e - 60 \, a^{2} b^{2} c^{3} d^{2} e^{3} + 60 \, a^{3} b c^{3} d e^{4} + 20 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d^{3} e^{2} - {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(2 \, {\left(b^{4} c^{4} + a b^{2} c^{5} - 20 \, a^{2} c^{6}\right)} d^{5} - 5 \, {\left(b^{5} c^{3} + a b^{3} c^{4} - 20 \, a^{2} b c^{5}\right)} d^{4} e + 10 \, {\left(5 \, a b^{4} c^{3} - 22 \, a^{2} b^{2} c^{4} + 8 \, a^{3} c^{5}\right)} d^{3} e^{2} - 10 \, {\left(a b^{5} c^{2} + a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{2} e^{3} - 5 \, {\left(a b^{6} c - 14 \, a^{2} b^{4} c^{2} + 46 \, a^{3} b^{2} c^{3} - 24 \, a^{4} c^{4}\right)} d e^{4} + {\left(3 \, a b^{7} - 34 \, a^{2} b^{5} c + 119 \, a^{3} b^{3} c^{2} - 124 \, a^{4} b c^{3}\right)} e^{5}\right)} x - {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{5} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e^{5} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} e^{5} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} e^{5} x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{5}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} x^{4} + 2 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} x^{3} + {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} + 32 \, a^{3} b^{2} c^{6} - 128 \, a^{4} c^{7}\right)} x^{2} + 2 \, {\left(a b^{7} c^{3} - 12 \, a^{2} b^{5} c^{4} + 48 \, a^{3} b^{3} c^{5} - 64 \, a^{4} b c^{6}\right)} x\right)}}, -\frac{{\left(b^{5} c^{3} - 14 \, a b^{3} c^{4} + 40 \, a^{2} b c^{5}\right)} d^{5} + 5 \, {\left(a b^{4} c^{3} + 4 \, a^{2} b^{2} c^{4} - 32 \, a^{3} c^{5}\right)} d^{4} e - 60 \, {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} d^{3} e^{2} + 10 \, {\left(a^{2} b^{4} c^{2} + 4 \, a^{3} b^{2} c^{3} - 32 \, a^{4} c^{4}\right)} d^{2} e^{3} + 5 \, {\left(a^{2} b^{5} c - 14 \, a^{3} b^{3} c^{2} + 40 \, a^{4} b c^{3}\right)} d e^{4} - 3 \, {\left(a^{2} b^{6} - 11 \, a^{3} b^{4} c + 36 \, a^{4} b^{2} c^{2} - 32 \, a^{5} c^{3}\right)} e^{5} - 2 \, {\left(6 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{5} - 15 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{4} e + 10 \, {\left(b^{4} c^{4} - 2 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{3} e^{2} - 30 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{2} e^{3} - 5 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} - 40 \, a^{3} c^{5}\right)} d e^{4} + {\left(2 \, b^{7} c - 23 \, a b^{5} c^{2} + 85 \, a^{2} b^{3} c^{3} - 100 \, a^{3} b c^{4}\right)} e^{5}\right)} x^{3} - {\left(18 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{5} - 45 \, {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5}\right)} d^{4} e + 30 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} d^{3} e^{2} - 10 \, {\left(b^{6} c^{2} - 3 \, a b^{4} c^{3} + 12 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e^{3} - 5 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} + 8 \, a^{3} b c^{4}\right)} d e^{4} + {\left(3 \, b^{8} - 31 \, a b^{6} c + 87 \, a^{2} b^{4} c^{2} - 12 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} e^{5}\right)} x^{2} + 2 \, {\left(12 \, a^{2} c^{5} d^{5} - 30 \, a^{2} b c^{4} d^{4} e - 60 \, a^{3} b c^{3} d^{2} e^{3} + 60 \, a^{4} c^{3} d e^{4} + 20 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} d^{3} e^{2} - {\left(a^{2} b^{5} - 10 \, a^{3} b^{3} c + 30 \, a^{4} b c^{2}\right)} e^{5} + {\left(12 \, c^{7} d^{5} - 30 \, b c^{6} d^{4} e - 60 \, a b c^{5} d^{2} e^{3} + 60 \, a^{2} c^{5} d e^{4} + 20 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{3} e^{2} - {\left(b^{5} c^{2} - 10 \, a b^{3} c^{3} + 30 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(12 \, b c^{6} d^{5} - 30 \, b^{2} c^{5} d^{4} e - 60 \, a b^{2} c^{4} d^{2} e^{3} + 60 \, a^{2} b c^{4} d e^{4} + 20 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{3} e^{2} - {\left(b^{6} c - 10 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(12 \, {\left(b^{2} c^{5} + 2 \, a c^{6}\right)} d^{5} - 30 \, {\left(b^{3} c^{4} + 2 \, a b c^{5}\right)} d^{4} e + 20 \, {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{3} e^{2} - 60 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d^{2} e^{3} + 60 \, {\left(a^{2} b^{2} c^{3} + 2 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 8 \, a b^{5} c + 10 \, a^{2} b^{3} c^{2} + 60 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(12 \, a b c^{5} d^{5} - 30 \, a b^{2} c^{4} d^{4} e - 60 \, a^{2} b^{2} c^{3} d^{2} e^{3} + 60 \, a^{3} b c^{3} d e^{4} + 20 \, {\left(a b^{3} c^{3} + 2 \, a^{2} b c^{4}\right)} d^{3} e^{2} - {\left(a b^{6} - 10 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(2 \, {\left(b^{4} c^{4} + a b^{2} c^{5} - 20 \, a^{2} c^{6}\right)} d^{5} - 5 \, {\left(b^{5} c^{3} + a b^{3} c^{4} - 20 \, a^{2} b c^{5}\right)} d^{4} e + 10 \, {\left(5 \, a b^{4} c^{3} - 22 \, a^{2} b^{2} c^{4} + 8 \, a^{3} c^{5}\right)} d^{3} e^{2} - 10 \, {\left(a b^{5} c^{2} + a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d^{2} e^{3} - 5 \, {\left(a b^{6} c - 14 \, a^{2} b^{4} c^{2} + 46 \, a^{3} b^{2} c^{3} - 24 \, a^{4} c^{4}\right)} d e^{4} + {\left(3 \, a b^{7} - 34 \, a^{2} b^{5} c + 119 \, a^{3} b^{3} c^{2} - 124 \, a^{4} b c^{3}\right)} e^{5}\right)} x - {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{5} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e^{5} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} e^{5} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} e^{5} x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{5}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6} + {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} x^{4} + 2 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} x^{3} + {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 24 \, a^{2} b^{4} c^{5} + 32 \, a^{3} b^{2} c^{6} - 128 \, a^{4} c^{7}\right)} x^{2} + 2 \, {\left(a b^{7} c^{3} - 12 \, a^{2} b^{5} c^{4} + 48 \, a^{3} b^{3} c^{5} - 64 \, a^{4} b c^{6}\right)} x\right)}}\right]"," ",0,"[-1/2*((b^5*c^3 - 14*a*b^3*c^4 + 40*a^2*b*c^5)*d^5 + 5*(a*b^4*c^3 + 4*a^2*b^2*c^4 - 32*a^3*c^5)*d^4*e - 60*(a^2*b^3*c^3 - 4*a^3*b*c^4)*d^3*e^2 + 10*(a^2*b^4*c^2 + 4*a^3*b^2*c^3 - 32*a^4*c^4)*d^2*e^3 + 5*(a^2*b^5*c - 14*a^3*b^3*c^2 + 40*a^4*b*c^3)*d*e^4 - 3*(a^2*b^6 - 11*a^3*b^4*c + 36*a^4*b^2*c^2 - 32*a^5*c^3)*e^5 - 2*(6*(b^2*c^6 - 4*a*c^7)*d^5 - 15*(b^3*c^5 - 4*a*b*c^6)*d^4*e + 10*(b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^3*e^2 - 30*(a*b^3*c^4 - 4*a^2*b*c^5)*d^2*e^3 - 5*(b^6*c^2 - 12*a*b^4*c^3 + 42*a^2*b^2*c^4 - 40*a^3*c^5)*d*e^4 + (2*b^7*c - 23*a*b^5*c^2 + 85*a^2*b^3*c^3 - 100*a^3*b*c^4)*e^5)*x^3 - (18*(b^3*c^5 - 4*a*b*c^6)*d^5 - 45*(b^4*c^4 - 4*a*b^2*c^5)*d^4*e + 30*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*d^3*e^2 - 10*(b^6*c^2 - 3*a*b^4*c^3 + 12*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e^3 - 5*(b^7*c - 12*a*b^5*c^2 + 30*a^2*b^3*c^3 + 8*a^3*b*c^4)*d*e^4 + (3*b^8 - 31*a*b^6*c + 87*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 128*a^4*c^4)*e^5)*x^2 + (12*a^2*c^5*d^5 - 30*a^2*b*c^4*d^4*e - 60*a^3*b*c^3*d^2*e^3 + 60*a^4*c^3*d*e^4 + 20*(a^2*b^2*c^3 + 2*a^3*c^4)*d^3*e^2 - (a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2)*e^5 + (12*c^7*d^5 - 30*b*c^6*d^4*e - 60*a*b*c^5*d^2*e^3 + 60*a^2*c^5*d*e^4 + 20*(b^2*c^5 + 2*a*c^6)*d^3*e^2 - (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*e^5)*x^4 + 2*(12*b*c^6*d^5 - 30*b^2*c^5*d^4*e - 60*a*b^2*c^4*d^2*e^3 + 60*a^2*b*c^4*d*e^4 + 20*(b^3*c^4 + 2*a*b*c^5)*d^3*e^2 - (b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*e^5)*x^3 + (12*(b^2*c^5 + 2*a*c^6)*d^5 - 30*(b^3*c^4 + 2*a*b*c^5)*d^4*e + 20*(b^4*c^3 + 4*a*b^2*c^4 + 4*a^2*c^5)*d^3*e^2 - 60*(a*b^3*c^3 + 2*a^2*b*c^4)*d^2*e^3 + 60*(a^2*b^2*c^3 + 2*a^3*c^4)*d*e^4 - (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*e^5)*x^2 + 2*(12*a*b*c^5*d^5 - 30*a*b^2*c^4*d^4*e - 60*a^2*b^2*c^3*d^2*e^3 + 60*a^3*b*c^3*d*e^4 + 20*(a*b^3*c^3 + 2*a^2*b*c^4)*d^3*e^2 - (a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*e^5)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(2*(b^4*c^4 + a*b^2*c^5 - 20*a^2*c^6)*d^5 - 5*(b^5*c^3 + a*b^3*c^4 - 20*a^2*b*c^5)*d^4*e + 10*(5*a*b^4*c^3 - 22*a^2*b^2*c^4 + 8*a^3*c^5)*d^3*e^2 - 10*(a*b^5*c^2 + a^2*b^3*c^3 - 20*a^3*b*c^4)*d^2*e^3 - 5*(a*b^6*c - 14*a^2*b^4*c^2 + 46*a^3*b^2*c^3 - 24*a^4*c^4)*d*e^4 + (3*a*b^7 - 34*a^2*b^5*c + 119*a^3*b^3*c^2 - 124*a^4*b*c^3)*e^5)*x - ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^5*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^5*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*e^5*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*e^5*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^5)*log(c*x^2 + b*x + a))/(a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*x^4 + 2*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*x^3 + (b^8*c^3 - 10*a*b^6*c^4 + 24*a^2*b^4*c^5 + 32*a^3*b^2*c^6 - 128*a^4*c^7)*x^2 + 2*(a*b^7*c^3 - 12*a^2*b^5*c^4 + 48*a^3*b^3*c^5 - 64*a^4*b*c^6)*x), -1/2*((b^5*c^3 - 14*a*b^3*c^4 + 40*a^2*b*c^5)*d^5 + 5*(a*b^4*c^3 + 4*a^2*b^2*c^4 - 32*a^3*c^5)*d^4*e - 60*(a^2*b^3*c^3 - 4*a^3*b*c^4)*d^3*e^2 + 10*(a^2*b^4*c^2 + 4*a^3*b^2*c^3 - 32*a^4*c^4)*d^2*e^3 + 5*(a^2*b^5*c - 14*a^3*b^3*c^2 + 40*a^4*b*c^3)*d*e^4 - 3*(a^2*b^6 - 11*a^3*b^4*c + 36*a^4*b^2*c^2 - 32*a^5*c^3)*e^5 - 2*(6*(b^2*c^6 - 4*a*c^7)*d^5 - 15*(b^3*c^5 - 4*a*b*c^6)*d^4*e + 10*(b^4*c^4 - 2*a*b^2*c^5 - 8*a^2*c^6)*d^3*e^2 - 30*(a*b^3*c^4 - 4*a^2*b*c^5)*d^2*e^3 - 5*(b^6*c^2 - 12*a*b^4*c^3 + 42*a^2*b^2*c^4 - 40*a^3*c^5)*d*e^4 + (2*b^7*c - 23*a*b^5*c^2 + 85*a^2*b^3*c^3 - 100*a^3*b*c^4)*e^5)*x^3 - (18*(b^3*c^5 - 4*a*b*c^6)*d^5 - 45*(b^4*c^4 - 4*a*b^2*c^5)*d^4*e + 30*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*d^3*e^2 - 10*(b^6*c^2 - 3*a*b^4*c^3 + 12*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e^3 - 5*(b^7*c - 12*a*b^5*c^2 + 30*a^2*b^3*c^3 + 8*a^3*b*c^4)*d*e^4 + (3*b^8 - 31*a*b^6*c + 87*a^2*b^4*c^2 - 12*a^3*b^2*c^3 - 128*a^4*c^4)*e^5)*x^2 + 2*(12*a^2*c^5*d^5 - 30*a^2*b*c^4*d^4*e - 60*a^3*b*c^3*d^2*e^3 + 60*a^4*c^3*d*e^4 + 20*(a^2*b^2*c^3 + 2*a^3*c^4)*d^3*e^2 - (a^2*b^5 - 10*a^3*b^3*c + 30*a^4*b*c^2)*e^5 + (12*c^7*d^5 - 30*b*c^6*d^4*e - 60*a*b*c^5*d^2*e^3 + 60*a^2*c^5*d*e^4 + 20*(b^2*c^5 + 2*a*c^6)*d^3*e^2 - (b^5*c^2 - 10*a*b^3*c^3 + 30*a^2*b*c^4)*e^5)*x^4 + 2*(12*b*c^6*d^5 - 30*b^2*c^5*d^4*e - 60*a*b^2*c^4*d^2*e^3 + 60*a^2*b*c^4*d*e^4 + 20*(b^3*c^4 + 2*a*b*c^5)*d^3*e^2 - (b^6*c - 10*a*b^4*c^2 + 30*a^2*b^2*c^3)*e^5)*x^3 + (12*(b^2*c^5 + 2*a*c^6)*d^5 - 30*(b^3*c^4 + 2*a*b*c^5)*d^4*e + 20*(b^4*c^3 + 4*a*b^2*c^4 + 4*a^2*c^5)*d^3*e^2 - 60*(a*b^3*c^3 + 2*a^2*b*c^4)*d^2*e^3 + 60*(a^2*b^2*c^3 + 2*a^3*c^4)*d*e^4 - (b^7 - 8*a*b^5*c + 10*a^2*b^3*c^2 + 60*a^3*b*c^3)*e^5)*x^2 + 2*(12*a*b*c^5*d^5 - 30*a*b^2*c^4*d^4*e - 60*a^2*b^2*c^3*d^2*e^3 + 60*a^3*b*c^3*d*e^4 + 20*(a*b^3*c^3 + 2*a^2*b*c^4)*d^3*e^2 - (a*b^6 - 10*a^2*b^4*c + 30*a^3*b^2*c^2)*e^5)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(2*(b^4*c^4 + a*b^2*c^5 - 20*a^2*c^6)*d^5 - 5*(b^5*c^3 + a*b^3*c^4 - 20*a^2*b*c^5)*d^4*e + 10*(5*a*b^4*c^3 - 22*a^2*b^2*c^4 + 8*a^3*c^5)*d^3*e^2 - 10*(a*b^5*c^2 + a^2*b^3*c^3 - 20*a^3*b*c^4)*d^2*e^3 - 5*(a*b^6*c - 14*a^2*b^4*c^2 + 46*a^3*b^2*c^3 - 24*a^4*c^4)*d*e^4 + (3*a*b^7 - 34*a^2*b^5*c + 119*a^3*b^3*c^2 - 124*a^4*b*c^3)*e^5)*x - ((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*e^5*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^5*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*e^5*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*e^5*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^5)*log(c*x^2 + b*x + a))/(a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*x^4 + 2*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*x^3 + (b^8*c^3 - 10*a*b^6*c^4 + 24*a^2*b^4*c^5 + 32*a^3*b^2*c^6 - 128*a^4*c^7)*x^2 + 2*(a*b^7*c^3 - 12*a^2*b^5*c^4 + 48*a^3*b^3*c^5 - 64*a^4*b*c^6)*x)]","B",0
2202,1,2631,0,0.448662," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{5} c^{2} - 14 \, a b^{3} c^{3} + 40 \, a^{2} b c^{4}\right)} d^{4} + 4 \, {\left(a b^{4} c^{2} + 4 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} d^{3} e - 36 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{2} e^{2} + 4 \, {\left(a^{2} b^{4} c + 4 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} d e^{3} + {\left(a^{2} b^{5} - 14 \, a^{3} b^{3} c + 40 \, a^{4} b c^{2}\right)} e^{4} - 2 \, {\left(6 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{4} - 12 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} e + 6 \, {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{2} e^{2} - 12 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e^{3} - {\left(b^{6} c - 12 \, a b^{4} c^{2} + 42 \, a^{2} b^{2} c^{3} - 40 \, a^{3} c^{4}\right)} e^{4}\right)} x^{3} - {\left(18 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} - 36 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{3} e + 18 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d^{2} e^{2} - 4 \, {\left(b^{6} c - 3 \, a b^{4} c^{2} + 12 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{3} - {\left(b^{7} - 12 \, a b^{5} c + 30 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} e^{4}\right)} x^{2} - 12 \, {\left(a^{2} c^{4} d^{4} - 2 \, a^{2} b c^{3} d^{3} e - 2 \, a^{3} b c^{2} d e^{3} + a^{4} c^{2} e^{4} + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{2} e^{2} + {\left(c^{6} d^{4} - 2 \, b c^{5} d^{3} e - 2 \, a b c^{4} d e^{3} + a^{2} c^{4} e^{4} + {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(b c^{5} d^{4} - 2 \, b^{2} c^{4} d^{3} e - 2 \, a b^{2} c^{3} d e^{3} + a^{2} b c^{3} e^{4} + {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{2} e^{2}\right)} x^{3} + {\left({\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{4} - 2 \, {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{3} e + {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} e^{4}\right)} x^{2} + 2 \, {\left(a b c^{4} d^{4} - 2 \, a b^{2} c^{3} d^{3} e - 2 \, a^{2} b^{2} c^{2} d e^{3} + a^{3} b c^{2} e^{4} + {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d^{2} e^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(2 \, {\left(b^{4} c^{3} + a b^{2} c^{4} - 20 \, a^{2} c^{5}\right)} d^{4} - 4 \, {\left(b^{5} c^{2} + a b^{3} c^{3} - 20 \, a^{2} b c^{4}\right)} d^{3} e + 6 \, {\left(5 \, a b^{4} c^{2} - 22 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{2} e^{2} - 4 \, {\left(a b^{5} c + a^{2} b^{3} c^{2} - 20 \, a^{3} b c^{3}\right)} d e^{3} - {\left(a b^{6} - 14 \, a^{2} b^{4} c + 46 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} e^{4}\right)} x}{2 \, {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5} + {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} x^{3} + {\left(b^{8} c^{2} - 10 \, a b^{6} c^{3} + 24 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} - 128 \, a^{4} c^{6}\right)} x^{2} + 2 \, {\left(a b^{7} c^{2} - 12 \, a^{2} b^{5} c^{3} + 48 \, a^{3} b^{3} c^{4} - 64 \, a^{4} b c^{5}\right)} x\right)}}, -\frac{{\left(b^{5} c^{2} - 14 \, a b^{3} c^{3} + 40 \, a^{2} b c^{4}\right)} d^{4} + 4 \, {\left(a b^{4} c^{2} + 4 \, a^{2} b^{2} c^{3} - 32 \, a^{3} c^{4}\right)} d^{3} e - 36 \, {\left(a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} d^{2} e^{2} + 4 \, {\left(a^{2} b^{4} c + 4 \, a^{3} b^{2} c^{2} - 32 \, a^{4} c^{3}\right)} d e^{3} + {\left(a^{2} b^{5} - 14 \, a^{3} b^{3} c + 40 \, a^{4} b c^{2}\right)} e^{4} - 2 \, {\left(6 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{4} - 12 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} e + 6 \, {\left(b^{4} c^{3} - 2 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{2} e^{2} - 12 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e^{3} - {\left(b^{6} c - 12 \, a b^{4} c^{2} + 42 \, a^{2} b^{2} c^{3} - 40 \, a^{3} c^{4}\right)} e^{4}\right)} x^{3} - {\left(18 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} - 36 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{3} e + 18 \, {\left(b^{5} c^{2} - 2 \, a b^{3} c^{3} - 8 \, a^{2} b c^{4}\right)} d^{2} e^{2} - 4 \, {\left(b^{6} c - 3 \, a b^{4} c^{2} + 12 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{3} - {\left(b^{7} - 12 \, a b^{5} c + 30 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} e^{4}\right)} x^{2} + 24 \, {\left(a^{2} c^{4} d^{4} - 2 \, a^{2} b c^{3} d^{3} e - 2 \, a^{3} b c^{2} d e^{3} + a^{4} c^{2} e^{4} + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{2} e^{2} + {\left(c^{6} d^{4} - 2 \, b c^{5} d^{3} e - 2 \, a b c^{4} d e^{3} + a^{2} c^{4} e^{4} + {\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{2} e^{2}\right)} x^{4} + 2 \, {\left(b c^{5} d^{4} - 2 \, b^{2} c^{4} d^{3} e - 2 \, a b^{2} c^{3} d e^{3} + a^{2} b c^{3} e^{4} + {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{2} e^{2}\right)} x^{3} + {\left({\left(b^{2} c^{4} + 2 \, a c^{5}\right)} d^{4} - 2 \, {\left(b^{3} c^{3} + 2 \, a b c^{4}\right)} d^{3} e + {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} e^{4}\right)} x^{2} + 2 \, {\left(a b c^{4} d^{4} - 2 \, a b^{2} c^{3} d^{3} e - 2 \, a^{2} b^{2} c^{2} d e^{3} + a^{3} b c^{2} e^{4} + {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(2 \, {\left(b^{4} c^{3} + a b^{2} c^{4} - 20 \, a^{2} c^{5}\right)} d^{4} - 4 \, {\left(b^{5} c^{2} + a b^{3} c^{3} - 20 \, a^{2} b c^{4}\right)} d^{3} e + 6 \, {\left(5 \, a b^{4} c^{2} - 22 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{2} e^{2} - 4 \, {\left(a b^{5} c + a^{2} b^{3} c^{2} - 20 \, a^{3} b c^{3}\right)} d e^{3} - {\left(a b^{6} - 14 \, a^{2} b^{4} c + 46 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} e^{4}\right)} x}{2 \, {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5} + {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} x^{4} + 2 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} x^{3} + {\left(b^{8} c^{2} - 10 \, a b^{6} c^{3} + 24 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} - 128 \, a^{4} c^{6}\right)} x^{2} + 2 \, {\left(a b^{7} c^{2} - 12 \, a^{2} b^{5} c^{3} + 48 \, a^{3} b^{3} c^{4} - 64 \, a^{4} b c^{5}\right)} x\right)}}\right]"," ",0,"[-1/2*((b^5*c^2 - 14*a*b^3*c^3 + 40*a^2*b*c^4)*d^4 + 4*(a*b^4*c^2 + 4*a^2*b^2*c^3 - 32*a^3*c^4)*d^3*e - 36*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^2*e^2 + 4*(a^2*b^4*c + 4*a^3*b^2*c^2 - 32*a^4*c^3)*d*e^3 + (a^2*b^5 - 14*a^3*b^3*c + 40*a^4*b*c^2)*e^4 - 2*(6*(b^2*c^5 - 4*a*c^6)*d^4 - 12*(b^3*c^4 - 4*a*b*c^5)*d^3*e + 6*(b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d^2*e^2 - 12*(a*b^3*c^3 - 4*a^2*b*c^4)*d*e^3 - (b^6*c - 12*a*b^4*c^2 + 42*a^2*b^2*c^3 - 40*a^3*c^4)*e^4)*x^3 - (18*(b^3*c^4 - 4*a*b*c^5)*d^4 - 36*(b^4*c^3 - 4*a*b^2*c^4)*d^3*e + 18*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d^2*e^2 - 4*(b^6*c - 3*a*b^4*c^2 + 12*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^3 - (b^7 - 12*a*b^5*c + 30*a^2*b^3*c^2 + 8*a^3*b*c^3)*e^4)*x^2 - 12*(a^2*c^4*d^4 - 2*a^2*b*c^3*d^3*e - 2*a^3*b*c^2*d*e^3 + a^4*c^2*e^4 + (a^2*b^2*c^2 + 2*a^3*c^3)*d^2*e^2 + (c^6*d^4 - 2*b*c^5*d^3*e - 2*a*b*c^4*d*e^3 + a^2*c^4*e^4 + (b^2*c^4 + 2*a*c^5)*d^2*e^2)*x^4 + 2*(b*c^5*d^4 - 2*b^2*c^4*d^3*e - 2*a*b^2*c^3*d*e^3 + a^2*b*c^3*e^4 + (b^3*c^3 + 2*a*b*c^4)*d^2*e^2)*x^3 + ((b^2*c^4 + 2*a*c^5)*d^4 - 2*(b^3*c^3 + 2*a*b*c^4)*d^3*e + (b^4*c^2 + 4*a*b^2*c^3 + 4*a^2*c^4)*d^2*e^2 - 2*(a*b^3*c^2 + 2*a^2*b*c^3)*d*e^3 + (a^2*b^2*c^2 + 2*a^3*c^3)*e^4)*x^2 + 2*(a*b*c^4*d^4 - 2*a*b^2*c^3*d^3*e - 2*a^2*b^2*c^2*d*e^3 + a^3*b*c^2*e^4 + (a*b^3*c^2 + 2*a^2*b*c^3)*d^2*e^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(2*(b^4*c^3 + a*b^2*c^4 - 20*a^2*c^5)*d^4 - 4*(b^5*c^2 + a*b^3*c^3 - 20*a^2*b*c^4)*d^3*e + 6*(5*a*b^4*c^2 - 22*a^2*b^2*c^3 + 8*a^3*c^4)*d^2*e^2 - 4*(a*b^5*c + a^2*b^3*c^2 - 20*a^3*b*c^3)*d*e^3 - (a*b^6 - 14*a^2*b^4*c + 46*a^3*b^2*c^2 - 24*a^4*c^3)*e^4)*x)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*x^4 + 2*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*x^3 + (b^8*c^2 - 10*a*b^6*c^3 + 24*a^2*b^4*c^4 + 32*a^3*b^2*c^5 - 128*a^4*c^6)*x^2 + 2*(a*b^7*c^2 - 12*a^2*b^5*c^3 + 48*a^3*b^3*c^4 - 64*a^4*b*c^5)*x), -1/2*((b^5*c^2 - 14*a*b^3*c^3 + 40*a^2*b*c^4)*d^4 + 4*(a*b^4*c^2 + 4*a^2*b^2*c^3 - 32*a^3*c^4)*d^3*e - 36*(a^2*b^3*c^2 - 4*a^3*b*c^3)*d^2*e^2 + 4*(a^2*b^4*c + 4*a^3*b^2*c^2 - 32*a^4*c^3)*d*e^3 + (a^2*b^5 - 14*a^3*b^3*c + 40*a^4*b*c^2)*e^4 - 2*(6*(b^2*c^5 - 4*a*c^6)*d^4 - 12*(b^3*c^4 - 4*a*b*c^5)*d^3*e + 6*(b^4*c^3 - 2*a*b^2*c^4 - 8*a^2*c^5)*d^2*e^2 - 12*(a*b^3*c^3 - 4*a^2*b*c^4)*d*e^3 - (b^6*c - 12*a*b^4*c^2 + 42*a^2*b^2*c^3 - 40*a^3*c^4)*e^4)*x^3 - (18*(b^3*c^4 - 4*a*b*c^5)*d^4 - 36*(b^4*c^3 - 4*a*b^2*c^4)*d^3*e + 18*(b^5*c^2 - 2*a*b^3*c^3 - 8*a^2*b*c^4)*d^2*e^2 - 4*(b^6*c - 3*a*b^4*c^2 + 12*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^3 - (b^7 - 12*a*b^5*c + 30*a^2*b^3*c^2 + 8*a^3*b*c^3)*e^4)*x^2 + 24*(a^2*c^4*d^4 - 2*a^2*b*c^3*d^3*e - 2*a^3*b*c^2*d*e^3 + a^4*c^2*e^4 + (a^2*b^2*c^2 + 2*a^3*c^3)*d^2*e^2 + (c^6*d^4 - 2*b*c^5*d^3*e - 2*a*b*c^4*d*e^3 + a^2*c^4*e^4 + (b^2*c^4 + 2*a*c^5)*d^2*e^2)*x^4 + 2*(b*c^5*d^4 - 2*b^2*c^4*d^3*e - 2*a*b^2*c^3*d*e^3 + a^2*b*c^3*e^4 + (b^3*c^3 + 2*a*b*c^4)*d^2*e^2)*x^3 + ((b^2*c^4 + 2*a*c^5)*d^4 - 2*(b^3*c^3 + 2*a*b*c^4)*d^3*e + (b^4*c^2 + 4*a*b^2*c^3 + 4*a^2*c^4)*d^2*e^2 - 2*(a*b^3*c^2 + 2*a^2*b*c^3)*d*e^3 + (a^2*b^2*c^2 + 2*a^3*c^3)*e^4)*x^2 + 2*(a*b*c^4*d^4 - 2*a*b^2*c^3*d^3*e - 2*a^2*b^2*c^2*d*e^3 + a^3*b*c^2*e^4 + (a*b^3*c^2 + 2*a^2*b*c^3)*d^2*e^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(2*(b^4*c^3 + a*b^2*c^4 - 20*a^2*c^5)*d^4 - 4*(b^5*c^2 + a*b^3*c^3 - 20*a^2*b*c^4)*d^3*e + 6*(5*a*b^4*c^2 - 22*a^2*b^2*c^3 + 8*a^3*c^4)*d^2*e^2 - 4*(a*b^5*c + a^2*b^3*c^2 - 20*a^3*b*c^3)*d*e^3 - (a*b^6 - 14*a^2*b^4*c + 46*a^3*b^2*c^2 - 24*a^4*c^3)*e^4)*x)/(a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5 + (b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*x^4 + 2*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*x^3 + (b^8*c^2 - 10*a*b^6*c^3 + 24*a^2*b^4*c^4 + 32*a^3*b^2*c^5 - 128*a^4*c^6)*x^2 + 2*(a*b^7*c^2 - 12*a^2*b^5*c^3 + 48*a^3*b^3*c^4 - 64*a^4*b*c^5)*x)]","B",0
2203,1,2084,0,0.443254," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{5} c - 14 \, a b^{3} c^{2} + 40 \, a^{2} b c^{3}\right)} d^{3} + 3 \, {\left(a b^{4} c + 4 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d^{2} e - 18 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{2} + {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c - 32 \, a^{4} c^{2}\right)} e^{3} - 6 \, {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e + {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d e^{2} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} e^{3}\right)} x^{3} - {\left(18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} - 27 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d^{2} e + 9 \, {\left(b^{5} c - 2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} d e^{2} - {\left(b^{6} - 3 \, a b^{4} c + 12 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} e^{3}\right)} x^{2} + 6 \, {\left(2 \, a^{2} c^{3} d^{3} - 3 \, a^{2} b c^{2} d^{2} e - a^{3} b c e^{3} + {\left(2 \, c^{5} d^{3} - 3 \, b c^{4} d^{2} e - a b c^{3} e^{3} + {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d e^{2}\right)} x^{4} + {\left(a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d e^{2} + 2 \, {\left(2 \, b c^{4} d^{3} - 3 \, b^{2} c^{3} d^{2} e - a b^{2} c^{2} e^{3} + {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d e^{2}\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{2} e + {\left(b^{4} c + 4 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e^{2} - {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} e^{3}\right)} x^{2} + 2 \, {\left(2 \, a b c^{3} d^{3} - 3 \, a b^{2} c^{2} d^{2} e - a^{2} b^{2} c e^{3} + {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} d e^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 2 \, {\left(2 \, {\left(b^{4} c^{2} + a b^{2} c^{3} - 20 \, a^{2} c^{4}\right)} d^{3} - 3 \, {\left(b^{5} c + a b^{3} c^{2} - 20 \, a^{2} b c^{3}\right)} d^{2} e + 3 \, {\left(5 \, a b^{4} c - 22 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d e^{2} - {\left(a b^{5} + a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} e^{3}\right)} x}{2 \, {\left(a^{2} b^{6} c - 12 \, a^{3} b^{4} c^{2} + 48 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{4} + 2 \, {\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)} x^{3} + {\left(b^{8} c - 10 \, a b^{6} c^{2} + 24 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} - 128 \, a^{4} c^{5}\right)} x^{2} + 2 \, {\left(a b^{7} c - 12 \, a^{2} b^{5} c^{2} + 48 \, a^{3} b^{3} c^{3} - 64 \, a^{4} b c^{4}\right)} x\right)}}, -\frac{{\left(b^{5} c - 14 \, a b^{3} c^{2} + 40 \, a^{2} b c^{3}\right)} d^{3} + 3 \, {\left(a b^{4} c + 4 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d^{2} e - 18 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{2} + {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c - 32 \, a^{4} c^{2}\right)} e^{3} - 6 \, {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e + {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} - 8 \, a^{2} c^{4}\right)} d e^{2} - {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} e^{3}\right)} x^{3} - {\left(18 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} - 27 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3}\right)} d^{2} e + 9 \, {\left(b^{5} c - 2 \, a b^{3} c^{2} - 8 \, a^{2} b c^{3}\right)} d e^{2} - {\left(b^{6} - 3 \, a b^{4} c + 12 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} e^{3}\right)} x^{2} + 12 \, {\left(2 \, a^{2} c^{3} d^{3} - 3 \, a^{2} b c^{2} d^{2} e - a^{3} b c e^{3} + {\left(2 \, c^{5} d^{3} - 3 \, b c^{4} d^{2} e - a b c^{3} e^{3} + {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d e^{2}\right)} x^{4} + {\left(a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d e^{2} + 2 \, {\left(2 \, b c^{4} d^{3} - 3 \, b^{2} c^{3} d^{2} e - a b^{2} c^{2} e^{3} + {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d e^{2}\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{3} + 2 \, a c^{4}\right)} d^{3} - 3 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{2} e + {\left(b^{4} c + 4 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e^{2} - {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} e^{3}\right)} x^{2} + 2 \, {\left(2 \, a b c^{3} d^{3} - 3 \, a b^{2} c^{2} d^{2} e - a^{2} b^{2} c e^{3} + {\left(a b^{3} c + 2 \, a^{2} b c^{2}\right)} d e^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left(2 \, {\left(b^{4} c^{2} + a b^{2} c^{3} - 20 \, a^{2} c^{4}\right)} d^{3} - 3 \, {\left(b^{5} c + a b^{3} c^{2} - 20 \, a^{2} b c^{3}\right)} d^{2} e + 3 \, {\left(5 \, a b^{4} c - 22 \, a^{2} b^{2} c^{2} + 8 \, a^{3} c^{3}\right)} d e^{2} - {\left(a b^{5} + a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} e^{3}\right)} x}{2 \, {\left(a^{2} b^{6} c - 12 \, a^{3} b^{4} c^{2} + 48 \, a^{4} b^{2} c^{3} - 64 \, a^{5} c^{4} + {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} x^{4} + 2 \, {\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)} x^{3} + {\left(b^{8} c - 10 \, a b^{6} c^{2} + 24 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} - 128 \, a^{4} c^{5}\right)} x^{2} + 2 \, {\left(a b^{7} c - 12 \, a^{2} b^{5} c^{2} + 48 \, a^{3} b^{3} c^{3} - 64 \, a^{4} b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/2*((b^5*c - 14*a*b^3*c^2 + 40*a^2*b*c^3)*d^3 + 3*(a*b^4*c + 4*a^2*b^2*c^2 - 32*a^3*c^3)*d^2*e - 18*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^2 + (a^2*b^4 + 4*a^3*b^2*c - 32*a^4*c^2)*e^3 - 6*(2*(b^2*c^4 - 4*a*c^5)*d^3 - 3*(b^3*c^3 - 4*a*b*c^4)*d^2*e + (b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*d*e^2 - (a*b^3*c^2 - 4*a^2*b*c^3)*e^3)*x^3 - (18*(b^3*c^3 - 4*a*b*c^4)*d^3 - 27*(b^4*c^2 - 4*a*b^2*c^3)*d^2*e + 9*(b^5*c - 2*a*b^3*c^2 - 8*a^2*b*c^3)*d*e^2 - (b^6 - 3*a*b^4*c + 12*a^2*b^2*c^2 - 64*a^3*c^3)*e^3)*x^2 + 6*(2*a^2*c^3*d^3 - 3*a^2*b*c^2*d^2*e - a^3*b*c*e^3 + (2*c^5*d^3 - 3*b*c^4*d^2*e - a*b*c^3*e^3 + (b^2*c^3 + 2*a*c^4)*d*e^2)*x^4 + (a^2*b^2*c + 2*a^3*c^2)*d*e^2 + 2*(2*b*c^4*d^3 - 3*b^2*c^3*d^2*e - a*b^2*c^2*e^3 + (b^3*c^2 + 2*a*b*c^3)*d*e^2)*x^3 + (2*(b^2*c^3 + 2*a*c^4)*d^3 - 3*(b^3*c^2 + 2*a*b*c^3)*d^2*e + (b^4*c + 4*a*b^2*c^2 + 4*a^2*c^3)*d*e^2 - (a*b^3*c + 2*a^2*b*c^2)*e^3)*x^2 + 2*(2*a*b*c^3*d^3 - 3*a*b^2*c^2*d^2*e - a^2*b^2*c*e^3 + (a*b^3*c + 2*a^2*b*c^2)*d*e^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 2*(2*(b^4*c^2 + a*b^2*c^3 - 20*a^2*c^4)*d^3 - 3*(b^5*c + a*b^3*c^2 - 20*a^2*b*c^3)*d^2*e + 3*(5*a*b^4*c - 22*a^2*b^2*c^2 + 8*a^3*c^3)*d*e^2 - (a*b^5 + a^2*b^3*c - 20*a^3*b*c^2)*e^3)*x)/(a^2*b^6*c - 12*a^3*b^4*c^2 + 48*a^4*b^2*c^3 - 64*a^5*c^4 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^4 + 2*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^3 + (b^8*c - 10*a*b^6*c^2 + 24*a^2*b^4*c^3 + 32*a^3*b^2*c^4 - 128*a^4*c^5)*x^2 + 2*(a*b^7*c - 12*a^2*b^5*c^2 + 48*a^3*b^3*c^3 - 64*a^4*b*c^4)*x), -1/2*((b^5*c - 14*a*b^3*c^2 + 40*a^2*b*c^3)*d^3 + 3*(a*b^4*c + 4*a^2*b^2*c^2 - 32*a^3*c^3)*d^2*e - 18*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^2 + (a^2*b^4 + 4*a^3*b^2*c - 32*a^4*c^2)*e^3 - 6*(2*(b^2*c^4 - 4*a*c^5)*d^3 - 3*(b^3*c^3 - 4*a*b*c^4)*d^2*e + (b^4*c^2 - 2*a*b^2*c^3 - 8*a^2*c^4)*d*e^2 - (a*b^3*c^2 - 4*a^2*b*c^3)*e^3)*x^3 - (18*(b^3*c^3 - 4*a*b*c^4)*d^3 - 27*(b^4*c^2 - 4*a*b^2*c^3)*d^2*e + 9*(b^5*c - 2*a*b^3*c^2 - 8*a^2*b*c^3)*d*e^2 - (b^6 - 3*a*b^4*c + 12*a^2*b^2*c^2 - 64*a^3*c^3)*e^3)*x^2 + 12*(2*a^2*c^3*d^3 - 3*a^2*b*c^2*d^2*e - a^3*b*c*e^3 + (2*c^5*d^3 - 3*b*c^4*d^2*e - a*b*c^3*e^3 + (b^2*c^3 + 2*a*c^4)*d*e^2)*x^4 + (a^2*b^2*c + 2*a^3*c^2)*d*e^2 + 2*(2*b*c^4*d^3 - 3*b^2*c^3*d^2*e - a*b^2*c^2*e^3 + (b^3*c^2 + 2*a*b*c^3)*d*e^2)*x^3 + (2*(b^2*c^3 + 2*a*c^4)*d^3 - 3*(b^3*c^2 + 2*a*b*c^3)*d^2*e + (b^4*c + 4*a*b^2*c^2 + 4*a^2*c^3)*d*e^2 - (a*b^3*c + 2*a^2*b*c^2)*e^3)*x^2 + 2*(2*a*b*c^3*d^3 - 3*a*b^2*c^2*d^2*e - a^2*b^2*c*e^3 + (a*b^3*c + 2*a^2*b*c^2)*d*e^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 2*(2*(b^4*c^2 + a*b^2*c^3 - 20*a^2*c^4)*d^3 - 3*(b^5*c + a*b^3*c^2 - 20*a^2*b*c^3)*d^2*e + 3*(5*a*b^4*c - 22*a^2*b^2*c^2 + 8*a^3*c^3)*d*e^2 - (a*b^5 + a^2*b^3*c - 20*a^3*b*c^2)*e^3)*x)/(a^2*b^6*c - 12*a^3*b^4*c^2 + 48*a^4*b^2*c^3 - 64*a^5*c^4 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*x^4 + 2*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^3 + (b^8*c - 10*a*b^6*c^2 + 24*a^2*b^4*c^3 + 32*a^3*b^2*c^4 - 128*a^4*c^5)*x^2 + 2*(a*b^7*c - 12*a^2*b^5*c^2 + 48*a^3*b^3*c^3 - 64*a^4*b*c^4)*x)]","B",0
2204,1,1555,0,0.466450," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} e^{2}\right)} x^{3} - {\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} d^{2} - 2 \, {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} d e + 6 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{2} + 3 \, {\left(6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} - 6 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} e^{2}\right)} x^{2} + 2 \, {\left(6 \, a^{2} c^{2} d^{2} - 6 \, a^{2} b c d e + {\left(6 \, c^{4} d^{2} - 6 \, b c^{3} d e + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} e^{2}\right)} x^{4} + 2 \, {\left(6 \, b c^{3} d^{2} - 6 \, b^{2} c^{2} d e + {\left(b^{3} c + 2 \, a b c^{2}\right)} e^{2}\right)} x^{3} + {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{2} + {\left(6 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} - 6 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} d e + {\left(b^{4} + 4 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{2}\right)} x^{2} + 2 \, {\left(6 \, a b c^{2} d^{2} - 6 \, a b^{2} c d e + {\left(a b^{3} + 2 \, a^{2} b c\right)} e^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d^{2} - 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d e + {\left(5 \, a b^{4} - 22 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e^{2}\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}, \frac{2 \, {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} - 6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} e^{2}\right)} x^{3} - {\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} d^{2} - 2 \, {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} d e + 6 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{2} + 3 \, {\left(6 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} - 6 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} e^{2}\right)} x^{2} - 4 \, {\left(6 \, a^{2} c^{2} d^{2} - 6 \, a^{2} b c d e + {\left(6 \, c^{4} d^{2} - 6 \, b c^{3} d e + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} e^{2}\right)} x^{4} + 2 \, {\left(6 \, b c^{3} d^{2} - 6 \, b^{2} c^{2} d e + {\left(b^{3} c + 2 \, a b c^{2}\right)} e^{2}\right)} x^{3} + {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{2} + {\left(6 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} - 6 \, {\left(b^{3} c + 2 \, a b c^{2}\right)} d e + {\left(b^{4} + 4 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e^{2}\right)} x^{2} + 2 \, {\left(6 \, a b c^{2} d^{2} - 6 \, a b^{2} c d e + {\left(a b^{3} + 2 \, a^{2} b c\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d^{2} - 2 \, {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} d e + {\left(5 \, a b^{4} - 22 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e^{2}\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}\right]"," ",0,"[1/2*(2*(6*(b^2*c^3 - 4*a*c^4)*d^2 - 6*(b^3*c^2 - 4*a*b*c^3)*d*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*e^2)*x^3 - (b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*d^2 - 2*(a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*d*e + 6*(a^2*b^3 - 4*a^3*b*c)*e^2 + 3*(6*(b^3*c^2 - 4*a*b*c^3)*d^2 - 6*(b^4*c - 4*a*b^2*c^2)*d*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*e^2)*x^2 + 2*(6*a^2*c^2*d^2 - 6*a^2*b*c*d*e + (6*c^4*d^2 - 6*b*c^3*d*e + (b^2*c^2 + 2*a*c^3)*e^2)*x^4 + 2*(6*b*c^3*d^2 - 6*b^2*c^2*d*e + (b^3*c + 2*a*b*c^2)*e^2)*x^3 + (a^2*b^2 + 2*a^3*c)*e^2 + (6*(b^2*c^2 + 2*a*c^3)*d^2 - 6*(b^3*c + 2*a*b*c^2)*d*e + (b^4 + 4*a*b^2*c + 4*a^2*c^2)*e^2)*x^2 + 2*(6*a*b*c^2*d^2 - 6*a*b^2*c*d*e + (a*b^3 + 2*a^2*b*c)*e^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d^2 - 2*(b^5 + a*b^3*c - 20*a^2*b*c^2)*d*e + (5*a*b^4 - 22*a^2*b^2*c + 8*a^3*c^2)*e^2)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x), 1/2*(2*(6*(b^2*c^3 - 4*a*c^4)*d^2 - 6*(b^3*c^2 - 4*a*b*c^3)*d*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*e^2)*x^3 - (b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*d^2 - 2*(a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*d*e + 6*(a^2*b^3 - 4*a^3*b*c)*e^2 + 3*(6*(b^3*c^2 - 4*a*b*c^3)*d^2 - 6*(b^4*c - 4*a*b^2*c^2)*d*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*e^2)*x^2 - 4*(6*a^2*c^2*d^2 - 6*a^2*b*c*d*e + (6*c^4*d^2 - 6*b*c^3*d*e + (b^2*c^2 + 2*a*c^3)*e^2)*x^4 + 2*(6*b*c^3*d^2 - 6*b^2*c^2*d*e + (b^3*c + 2*a*b*c^2)*e^2)*x^3 + (a^2*b^2 + 2*a^3*c)*e^2 + (6*(b^2*c^2 + 2*a*c^3)*d^2 - 6*(b^3*c + 2*a*b*c^2)*d*e + (b^4 + 4*a*b^2*c + 4*a^2*c^2)*e^2)*x^2 + 2*(6*a*b*c^2*d^2 - 6*a*b^2*c*d*e + (a*b^3 + 2*a^2*b*c)*e^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d^2 - 2*(b^5 + a*b^3*c - 20*a^2*b*c^2)*d*e + (5*a*b^4 - 22*a^2*b^2*c + 8*a^3*c^2)*e^2)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)]","B",0
2205,1,1116,0,0.452596," ","integrate((e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e\right)} x^{3} + 9 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e\right)} x^{2} - 6 \, {\left(2 \, a^{2} c^{2} d - a^{2} b c e + {\left(2 \, c^{4} d - b c^{3} e\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d - {\left(b^{3} c + 2 \, a b c^{2}\right)} e\right)} x^{2} + 2 \, {\left(2 \, a b c^{2} d - a b^{2} c e\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} e + 2 \, {\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d - {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} e\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}, \frac{6 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e\right)} x^{3} + 9 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e\right)} x^{2} - 12 \, {\left(2 \, a^{2} c^{2} d - a^{2} b c e + {\left(2 \, c^{4} d - b c^{3} e\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d - b^{2} c^{2} e\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d - {\left(b^{3} c + 2 \, a b c^{2}\right)} e\right)} x^{2} + 2 \, {\left(2 \, a b c^{2} d - a b^{2} c e\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} d - {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} e + 2 \, {\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} d - {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} e\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}\right]"," ",0,"[1/2*(6*(2*(b^2*c^3 - 4*a*c^4)*d - (b^3*c^2 - 4*a*b*c^3)*e)*x^3 + 9*(2*(b^3*c^2 - 4*a*b*c^3)*d - (b^4*c - 4*a*b^2*c^2)*e)*x^2 - 6*(2*a^2*c^2*d - a^2*b*c*e + (2*c^4*d - b*c^3*e)*x^4 + 2*(2*b*c^3*d - b^2*c^2*e)*x^3 + (2*(b^2*c^2 + 2*a*c^3)*d - (b^3*c + 2*a*b*c^2)*e)*x^2 + 2*(2*a*b*c^2*d - a*b^2*c*e)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*d - (a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*e + 2*(2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d - (b^5 + a*b^3*c - 20*a^2*b*c^2)*e)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x), 1/2*(6*(2*(b^2*c^3 - 4*a*c^4)*d - (b^3*c^2 - 4*a*b*c^3)*e)*x^3 + 9*(2*(b^3*c^2 - 4*a*b*c^3)*d - (b^4*c - 4*a*b^2*c^2)*e)*x^2 - 12*(2*a^2*c^2*d - a^2*b*c*e + (2*c^4*d - b*c^3*e)*x^4 + 2*(2*b*c^3*d - b^2*c^2*e)*x^3 + (2*(b^2*c^2 + 2*a*c^3)*d - (b^3*c + 2*a*b*c^2)*e)*x^2 + 2*(2*a*b*c^2*d - a*b^2*c*e)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*d - (a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*e + 2*(2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*d - (b^5 + a*b^3*c - 20*a^2*b*c^2)*e)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)]","B",0
2206,1,785,0,0.430458," ","integrate(1/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2} - 12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} - 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} - 12 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{3} + 2 \, a b c^{2} x + a^{2} c^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}, -\frac{b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2} - 12 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{3} - 18 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x^{2} + 24 \, {\left(c^{4} x^{4} + 2 \, b c^{3} x^{3} + 2 \, a b c^{2} x + a^{2} c^{2} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 4 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} x}{2 \, {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3} + {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} x\right)}}\right]"," ",0,"[-1/2*(b^5 - 14*a*b^3*c + 40*a^2*b*c^2 - 12*(b^2*c^3 - 4*a*c^4)*x^3 - 18*(b^3*c^2 - 4*a*b*c^3)*x^2 - 12*(c^4*x^4 + 2*b*c^3*x^3 + 2*a*b*c^2*x + a^2*c^2 + (b^2*c^2 + 2*a*c^3)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x), -1/2*(b^5 - 14*a*b^3*c + 40*a^2*b*c^2 - 12*(b^2*c^3 - 4*a*c^4)*x^3 - 18*(b^3*c^2 - 4*a*b*c^3)*x^2 + 24*(c^4*x^4 + 2*b*c^3*x^3 + 2*a*b*c^2*x + a^2*c^2 + (b^2*c^2 + 2*a*c^3)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 4*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*x)/(a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3 + (b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*x)]","B",0
2207,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2208,1,2280,0,1.077749," ","integrate(1/x^2/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{3} b^{6} - 24 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 128 \, a^{6} c^{3} + 6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} x^{4} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} x^{2} + 3 \, {\left({\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} x^{5} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} x^{4} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} x^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} x^{2} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} x - 3 \, {\left({\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)} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{2} + {\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)} x\right)} \log\left(c x^{2} + b x + a\right) + 6 \, {\left({\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)} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{2} + {\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)} x\right)} \log\left(x\right)}{2 \, {\left({\left(a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}\right)} x^{5} + 2 \, {\left(a^{4} b^{7} c - 12 \, a^{5} b^{5} c^{2} + 48 \, a^{6} b^{3} c^{3} - 64 \, a^{7} b c^{4}\right)} x^{4} + {\left(a^{4} b^{8} - 10 \, a^{5} b^{6} c + 24 \, a^{6} b^{4} c^{2} + 32 \, a^{7} b^{2} c^{3} - 128 \, a^{8} c^{4}\right)} x^{3} + 2 \, {\left(a^{5} b^{7} - 12 \, a^{6} b^{5} c + 48 \, a^{7} b^{3} c^{2} - 64 \, a^{8} b c^{3}\right)} x^{2} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} x\right)}}, -\frac{2 \, a^{3} b^{6} - 24 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 128 \, a^{6} c^{3} + 6 \, {\left(a b^{6} c^{2} - 11 \, a^{2} b^{4} c^{3} + 38 \, a^{3} b^{2} c^{4} - 40 \, a^{4} c^{5}\right)} x^{4} + 3 \, {\left(4 \, a b^{7} c - 45 \, a^{2} b^{5} c^{2} + 162 \, a^{3} b^{3} c^{3} - 184 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(3 \, a b^{8} - 30 \, a^{2} b^{6} c + 79 \, a^{3} b^{4} c^{2} + 22 \, a^{4} b^{2} c^{3} - 200 \, a^{5} c^{4}\right)} x^{2} + 6 \, {\left({\left(b^{6} c^{2} - 10 \, a b^{4} c^{3} + 30 \, a^{2} b^{2} c^{4} - 20 \, a^{3} c^{5}\right)} x^{5} + 2 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 30 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} x^{4} + {\left(b^{8} - 8 \, a b^{6} c + 10 \, a^{2} b^{4} c^{2} + 40 \, a^{3} b^{2} c^{3} - 40 \, a^{4} c^{4}\right)} x^{3} + 2 \, {\left(a b^{7} - 10 \, a^{2} b^{5} c + 30 \, a^{3} b^{3} c^{2} - 20 \, a^{4} b c^{3}\right)} x^{2} + {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 30 \, a^{4} b^{2} c^{2} - 20 \, a^{5} c^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(9 \, a^{2} b^{7} - 104 \, a^{3} b^{5} c + 394 \, a^{4} b^{3} c^{2} - 488 \, a^{5} b c^{3}\right)} x - 3 \, {\left({\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)} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{2} + {\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)} x\right)} \log\left(c x^{2} + b x + a\right) + 6 \, {\left({\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)} x^{5} + 2 \, {\left(b^{8} c - 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} - 64 \, a^{3} b^{2} c^{4}\right)} x^{4} + {\left(b^{9} - 10 \, a b^{7} c + 24 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} - 128 \, a^{4} b c^{4}\right)} x^{3} + 2 \, {\left(a b^{8} - 12 \, a^{2} b^{6} c + 48 \, a^{3} b^{4} c^{2} - 64 \, a^{4} b^{2} c^{3}\right)} x^{2} + {\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)} x\right)} \log\left(x\right)}{2 \, {\left({\left(a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}\right)} x^{5} + 2 \, {\left(a^{4} b^{7} c - 12 \, a^{5} b^{5} c^{2} + 48 \, a^{6} b^{3} c^{3} - 64 \, a^{7} b c^{4}\right)} x^{4} + {\left(a^{4} b^{8} - 10 \, a^{5} b^{6} c + 24 \, a^{6} b^{4} c^{2} + 32 \, a^{7} b^{2} c^{3} - 128 \, a^{8} c^{4}\right)} x^{3} + 2 \, {\left(a^{5} b^{7} - 12 \, a^{6} b^{5} c + 48 \, a^{7} b^{3} c^{2} - 64 \, a^{8} b c^{3}\right)} x^{2} + {\left(a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*a^3*b^6 - 24*a^4*b^4*c + 96*a^5*b^2*c^2 - 128*a^6*c^3 + 6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*x^4 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*x^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*x^2 + 3*((b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*x^5 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*x^4 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*x^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*x^2 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*x - 3*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)*log(c*x^2 + b*x + a) + 6*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)*log(x))/((a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)*x^5 + 2*(a^4*b^7*c - 12*a^5*b^5*c^2 + 48*a^6*b^3*c^3 - 64*a^7*b*c^4)*x^4 + (a^4*b^8 - 10*a^5*b^6*c + 24*a^6*b^4*c^2 + 32*a^7*b^2*c^3 - 128*a^8*c^4)*x^3 + 2*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*x^2 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*x), -1/2*(2*a^3*b^6 - 24*a^4*b^4*c + 96*a^5*b^2*c^2 - 128*a^6*c^3 + 6*(a*b^6*c^2 - 11*a^2*b^4*c^3 + 38*a^3*b^2*c^4 - 40*a^4*c^5)*x^4 + 3*(4*a*b^7*c - 45*a^2*b^5*c^2 + 162*a^3*b^3*c^3 - 184*a^4*b*c^4)*x^3 + 2*(3*a*b^8 - 30*a^2*b^6*c + 79*a^3*b^4*c^2 + 22*a^4*b^2*c^3 - 200*a^5*c^4)*x^2 + 6*((b^6*c^2 - 10*a*b^4*c^3 + 30*a^2*b^2*c^4 - 20*a^3*c^5)*x^5 + 2*(b^7*c - 10*a*b^5*c^2 + 30*a^2*b^3*c^3 - 20*a^3*b*c^4)*x^4 + (b^8 - 8*a*b^6*c + 10*a^2*b^4*c^2 + 40*a^3*b^2*c^3 - 40*a^4*c^4)*x^3 + 2*(a*b^7 - 10*a^2*b^5*c + 30*a^3*b^3*c^2 - 20*a^4*b*c^3)*x^2 + (a^2*b^6 - 10*a^3*b^4*c + 30*a^4*b^2*c^2 - 20*a^5*c^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (9*a^2*b^7 - 104*a^3*b^5*c + 394*a^4*b^3*c^2 - 488*a^5*b*c^3)*x - 3*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)*log(c*x^2 + b*x + a) + 6*((b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*x^5 + 2*(b^8*c - 12*a*b^6*c^2 + 48*a^2*b^4*c^3 - 64*a^3*b^2*c^4)*x^4 + (b^9 - 10*a*b^7*c + 24*a^2*b^5*c^2 + 32*a^3*b^3*c^3 - 128*a^4*b*c^4)*x^3 + 2*(a*b^8 - 12*a^2*b^6*c + 48*a^3*b^4*c^2 - 64*a^4*b^2*c^3)*x^2 + (a^2*b^7 - 12*a^3*b^5*c + 48*a^4*b^3*c^2 - 64*a^5*b*c^3)*x)*log(x))/((a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)*x^5 + 2*(a^4*b^7*c - 12*a^5*b^5*c^2 + 48*a^6*b^3*c^3 - 64*a^7*b*c^4)*x^4 + (a^4*b^8 - 10*a^5*b^6*c + 24*a^6*b^4*c^2 + 32*a^7*b^2*c^3 - 128*a^8*c^4)*x^3 + 2*(a^5*b^7 - 12*a^6*b^5*c + 48*a^7*b^3*c^2 - 64*a^8*b*c^3)*x^2 + (a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)*x)]","B",0
2209,1,2669,0,2.067445," ","integrate(1/x^3/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3} - 6 \, {\left(2 \, a b^{7} c^{2} - 23 \, a^{2} b^{5} c^{3} + 87 \, a^{3} b^{3} c^{4} - 108 \, a^{4} b c^{5}\right)} x^{5} - 3 \, {\left(8 \, a b^{8} c - 94 \, a^{2} b^{6} c^{2} + 369 \, a^{3} b^{4} c^{3} - 500 \, a^{4} b^{2} c^{4} + 64 \, a^{5} c^{5}\right)} x^{4} - 2 \, {\left(6 \, a b^{9} - 63 \, a^{2} b^{7} c + 188 \, a^{3} b^{5} c^{2} - 25 \, a^{4} b^{3} c^{3} - 412 \, a^{5} b c^{4}\right)} x^{3} - {\left(18 \, a^{2} b^{8} - 217 \, a^{3} b^{6} c + 887 \, a^{4} b^{4} c^{2} - 1300 \, a^{5} b^{2} c^{3} + 288 \, a^{6} c^{4}\right)} x^{2} + 3 \, {\left({\left(2 \, b^{7} c^{2} - 21 \, a b^{5} c^{3} + 70 \, a^{2} b^{3} c^{4} - 70 \, a^{3} b c^{5}\right)} x^{6} + 2 \, {\left(2 \, b^{8} c - 21 \, a b^{6} c^{2} + 70 \, a^{2} b^{4} c^{3} - 70 \, a^{3} b^{2} c^{4}\right)} x^{5} + {\left(2 \, b^{9} - 17 \, a b^{7} c + 28 \, a^{2} b^{5} c^{2} + 70 \, a^{3} b^{3} c^{3} - 140 \, a^{4} b c^{4}\right)} x^{4} + 2 \, {\left(2 \, a b^{8} - 21 \, a^{2} b^{6} c + 70 \, a^{3} b^{4} c^{2} - 70 \, a^{4} b^{2} c^{3}\right)} x^{3} + {\left(2 \, a^{2} b^{7} - 21 \, a^{3} b^{5} c + 70 \, a^{4} b^{3} c^{2} - 70 \, a^{5} b c^{3}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 4 \, {\left(a^{3} b^{7} - 12 \, a^{4} b^{5} c + 48 \, a^{5} b^{3} c^{2} - 64 \, a^{6} b c^{3}\right)} x + 3 \, {\left({\left(2 \, b^{8} c^{2} - 25 \, a b^{6} c^{3} + 108 \, a^{2} b^{4} c^{4} - 176 \, a^{3} b^{2} c^{5} + 64 \, a^{4} c^{6}\right)} x^{6} + 2 \, {\left(2 \, b^{9} c - 25 \, a b^{7} c^{2} + 108 \, a^{2} b^{5} c^{3} - 176 \, a^{3} b^{3} c^{4} + 64 \, a^{4} b c^{5}\right)} x^{5} + {\left(2 \, b^{10} - 21 \, a b^{8} c + 58 \, a^{2} b^{6} c^{2} + 40 \, a^{3} b^{4} c^{3} - 288 \, a^{4} b^{2} c^{4} + 128 \, a^{5} c^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{9} - 25 \, a^{2} b^{7} c + 108 \, a^{3} b^{5} c^{2} - 176 \, a^{4} b^{3} c^{3} + 64 \, a^{5} b c^{4}\right)} x^{3} + {\left(2 \, a^{2} b^{8} - 25 \, a^{3} b^{6} c + 108 \, a^{4} b^{4} c^{2} - 176 \, a^{5} b^{2} c^{3} + 64 \, a^{6} c^{4}\right)} x^{2}\right)} \log\left(c x^{2} + b x + a\right) - 6 \, {\left({\left(2 \, b^{8} c^{2} - 25 \, a b^{6} c^{3} + 108 \, a^{2} b^{4} c^{4} - 176 \, a^{3} b^{2} c^{5} + 64 \, a^{4} c^{6}\right)} x^{6} + 2 \, {\left(2 \, b^{9} c - 25 \, a b^{7} c^{2} + 108 \, a^{2} b^{5} c^{3} - 176 \, a^{3} b^{3} c^{4} + 64 \, a^{4} b c^{5}\right)} x^{5} + {\left(2 \, b^{10} - 21 \, a b^{8} c + 58 \, a^{2} b^{6} c^{2} + 40 \, a^{3} b^{4} c^{3} - 288 \, a^{4} b^{2} c^{4} + 128 \, a^{5} c^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{9} - 25 \, a^{2} b^{7} c + 108 \, a^{3} b^{5} c^{2} - 176 \, a^{4} b^{3} c^{3} + 64 \, a^{5} b c^{4}\right)} x^{3} + {\left(2 \, a^{2} b^{8} - 25 \, a^{3} b^{6} c + 108 \, a^{4} b^{4} c^{2} - 176 \, a^{5} b^{2} c^{3} + 64 \, a^{6} c^{4}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{5} b^{6} c^{2} - 12 \, a^{6} b^{4} c^{3} + 48 \, a^{7} b^{2} c^{4} - 64 \, a^{8} c^{5}\right)} x^{6} + 2 \, {\left(a^{5} b^{7} c - 12 \, a^{6} b^{5} c^{2} + 48 \, a^{7} b^{3} c^{3} - 64 \, a^{8} b c^{4}\right)} x^{5} + {\left(a^{5} b^{8} - 10 \, a^{6} b^{6} c + 24 \, a^{7} b^{4} c^{2} + 32 \, a^{8} b^{2} c^{3} - 128 \, a^{9} c^{4}\right)} x^{4} + 2 \, {\left(a^{6} b^{7} - 12 \, a^{7} b^{5} c + 48 \, a^{8} b^{3} c^{2} - 64 \, a^{9} b c^{3}\right)} x^{3} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} x^{2}\right)}}, -\frac{a^{4} b^{6} - 12 \, a^{5} b^{4} c + 48 \, a^{6} b^{2} c^{2} - 64 \, a^{7} c^{3} - 6 \, {\left(2 \, a b^{7} c^{2} - 23 \, a^{2} b^{5} c^{3} + 87 \, a^{3} b^{3} c^{4} - 108 \, a^{4} b c^{5}\right)} x^{5} - 3 \, {\left(8 \, a b^{8} c - 94 \, a^{2} b^{6} c^{2} + 369 \, a^{3} b^{4} c^{3} - 500 \, a^{4} b^{2} c^{4} + 64 \, a^{5} c^{5}\right)} x^{4} - 2 \, {\left(6 \, a b^{9} - 63 \, a^{2} b^{7} c + 188 \, a^{3} b^{5} c^{2} - 25 \, a^{4} b^{3} c^{3} - 412 \, a^{5} b c^{4}\right)} x^{3} - {\left(18 \, a^{2} b^{8} - 217 \, a^{3} b^{6} c + 887 \, a^{4} b^{4} c^{2} - 1300 \, a^{5} b^{2} c^{3} + 288 \, a^{6} c^{4}\right)} x^{2} - 6 \, {\left({\left(2 \, b^{7} c^{2} - 21 \, a b^{5} c^{3} + 70 \, a^{2} b^{3} c^{4} - 70 \, a^{3} b c^{5}\right)} x^{6} + 2 \, {\left(2 \, b^{8} c - 21 \, a b^{6} c^{2} + 70 \, a^{2} b^{4} c^{3} - 70 \, a^{3} b^{2} c^{4}\right)} x^{5} + {\left(2 \, b^{9} - 17 \, a b^{7} c + 28 \, a^{2} b^{5} c^{2} + 70 \, a^{3} b^{3} c^{3} - 140 \, a^{4} b c^{4}\right)} x^{4} + 2 \, {\left(2 \, a b^{8} - 21 \, a^{2} b^{6} c + 70 \, a^{3} b^{4} c^{2} - 70 \, a^{4} b^{2} c^{3}\right)} x^{3} + {\left(2 \, a^{2} b^{7} - 21 \, a^{3} b^{5} c + 70 \, a^{4} b^{3} c^{2} - 70 \, a^{5} b c^{3}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 4 \, {\left(a^{3} b^{7} - 12 \, a^{4} b^{5} c + 48 \, a^{5} b^{3} c^{2} - 64 \, a^{6} b c^{3}\right)} x + 3 \, {\left({\left(2 \, b^{8} c^{2} - 25 \, a b^{6} c^{3} + 108 \, a^{2} b^{4} c^{4} - 176 \, a^{3} b^{2} c^{5} + 64 \, a^{4} c^{6}\right)} x^{6} + 2 \, {\left(2 \, b^{9} c - 25 \, a b^{7} c^{2} + 108 \, a^{2} b^{5} c^{3} - 176 \, a^{3} b^{3} c^{4} + 64 \, a^{4} b c^{5}\right)} x^{5} + {\left(2 \, b^{10} - 21 \, a b^{8} c + 58 \, a^{2} b^{6} c^{2} + 40 \, a^{3} b^{4} c^{3} - 288 \, a^{4} b^{2} c^{4} + 128 \, a^{5} c^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{9} - 25 \, a^{2} b^{7} c + 108 \, a^{3} b^{5} c^{2} - 176 \, a^{4} b^{3} c^{3} + 64 \, a^{5} b c^{4}\right)} x^{3} + {\left(2 \, a^{2} b^{8} - 25 \, a^{3} b^{6} c + 108 \, a^{4} b^{4} c^{2} - 176 \, a^{5} b^{2} c^{3} + 64 \, a^{6} c^{4}\right)} x^{2}\right)} \log\left(c x^{2} + b x + a\right) - 6 \, {\left({\left(2 \, b^{8} c^{2} - 25 \, a b^{6} c^{3} + 108 \, a^{2} b^{4} c^{4} - 176 \, a^{3} b^{2} c^{5} + 64 \, a^{4} c^{6}\right)} x^{6} + 2 \, {\left(2 \, b^{9} c - 25 \, a b^{7} c^{2} + 108 \, a^{2} b^{5} c^{3} - 176 \, a^{3} b^{3} c^{4} + 64 \, a^{4} b c^{5}\right)} x^{5} + {\left(2 \, b^{10} - 21 \, a b^{8} c + 58 \, a^{2} b^{6} c^{2} + 40 \, a^{3} b^{4} c^{3} - 288 \, a^{4} b^{2} c^{4} + 128 \, a^{5} c^{5}\right)} x^{4} + 2 \, {\left(2 \, a b^{9} - 25 \, a^{2} b^{7} c + 108 \, a^{3} b^{5} c^{2} - 176 \, a^{4} b^{3} c^{3} + 64 \, a^{5} b c^{4}\right)} x^{3} + {\left(2 \, a^{2} b^{8} - 25 \, a^{3} b^{6} c + 108 \, a^{4} b^{4} c^{2} - 176 \, a^{5} b^{2} c^{3} + 64 \, a^{6} c^{4}\right)} x^{2}\right)} \log\left(x\right)}{2 \, {\left({\left(a^{5} b^{6} c^{2} - 12 \, a^{6} b^{4} c^{3} + 48 \, a^{7} b^{2} c^{4} - 64 \, a^{8} c^{5}\right)} x^{6} + 2 \, {\left(a^{5} b^{7} c - 12 \, a^{6} b^{5} c^{2} + 48 \, a^{7} b^{3} c^{3} - 64 \, a^{8} b c^{4}\right)} x^{5} + {\left(a^{5} b^{8} - 10 \, a^{6} b^{6} c + 24 \, a^{7} b^{4} c^{2} + 32 \, a^{8} b^{2} c^{3} - 128 \, a^{9} c^{4}\right)} x^{4} + 2 \, {\left(a^{6} b^{7} - 12 \, a^{7} b^{5} c + 48 \, a^{8} b^{3} c^{2} - 64 \, a^{9} b c^{3}\right)} x^{3} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/2*(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3 - 6*(2*a*b^7*c^2 - 23*a^2*b^5*c^3 + 87*a^3*b^3*c^4 - 108*a^4*b*c^5)*x^5 - 3*(8*a*b^8*c - 94*a^2*b^6*c^2 + 369*a^3*b^4*c^3 - 500*a^4*b^2*c^4 + 64*a^5*c^5)*x^4 - 2*(6*a*b^9 - 63*a^2*b^7*c + 188*a^3*b^5*c^2 - 25*a^4*b^3*c^3 - 412*a^5*b*c^4)*x^3 - (18*a^2*b^8 - 217*a^3*b^6*c + 887*a^4*b^4*c^2 - 1300*a^5*b^2*c^3 + 288*a^6*c^4)*x^2 + 3*((2*b^7*c^2 - 21*a*b^5*c^3 + 70*a^2*b^3*c^4 - 70*a^3*b*c^5)*x^6 + 2*(2*b^8*c - 21*a*b^6*c^2 + 70*a^2*b^4*c^3 - 70*a^3*b^2*c^4)*x^5 + (2*b^9 - 17*a*b^7*c + 28*a^2*b^5*c^2 + 70*a^3*b^3*c^3 - 140*a^4*b*c^4)*x^4 + 2*(2*a*b^8 - 21*a^2*b^6*c + 70*a^3*b^4*c^2 - 70*a^4*b^2*c^3)*x^3 + (2*a^2*b^7 - 21*a^3*b^5*c + 70*a^4*b^3*c^2 - 70*a^5*b*c^3)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 4*(a^3*b^7 - 12*a^4*b^5*c + 48*a^5*b^3*c^2 - 64*a^6*b*c^3)*x + 3*((2*b^8*c^2 - 25*a*b^6*c^3 + 108*a^2*b^4*c^4 - 176*a^3*b^2*c^5 + 64*a^4*c^6)*x^6 + 2*(2*b^9*c - 25*a*b^7*c^2 + 108*a^2*b^5*c^3 - 176*a^3*b^3*c^4 + 64*a^4*b*c^5)*x^5 + (2*b^10 - 21*a*b^8*c + 58*a^2*b^6*c^2 + 40*a^3*b^4*c^3 - 288*a^4*b^2*c^4 + 128*a^5*c^5)*x^4 + 2*(2*a*b^9 - 25*a^2*b^7*c + 108*a^3*b^5*c^2 - 176*a^4*b^3*c^3 + 64*a^5*b*c^4)*x^3 + (2*a^2*b^8 - 25*a^3*b^6*c + 108*a^4*b^4*c^2 - 176*a^5*b^2*c^3 + 64*a^6*c^4)*x^2)*log(c*x^2 + b*x + a) - 6*((2*b^8*c^2 - 25*a*b^6*c^3 + 108*a^2*b^4*c^4 - 176*a^3*b^2*c^5 + 64*a^4*c^6)*x^6 + 2*(2*b^9*c - 25*a*b^7*c^2 + 108*a^2*b^5*c^3 - 176*a^3*b^3*c^4 + 64*a^4*b*c^5)*x^5 + (2*b^10 - 21*a*b^8*c + 58*a^2*b^6*c^2 + 40*a^3*b^4*c^3 - 288*a^4*b^2*c^4 + 128*a^5*c^5)*x^4 + 2*(2*a*b^9 - 25*a^2*b^7*c + 108*a^3*b^5*c^2 - 176*a^4*b^3*c^3 + 64*a^5*b*c^4)*x^3 + (2*a^2*b^8 - 25*a^3*b^6*c + 108*a^4*b^4*c^2 - 176*a^5*b^2*c^3 + 64*a^6*c^4)*x^2)*log(x))/((a^5*b^6*c^2 - 12*a^6*b^4*c^3 + 48*a^7*b^2*c^4 - 64*a^8*c^5)*x^6 + 2*(a^5*b^7*c - 12*a^6*b^5*c^2 + 48*a^7*b^3*c^3 - 64*a^8*b*c^4)*x^5 + (a^5*b^8 - 10*a^6*b^6*c + 24*a^7*b^4*c^2 + 32*a^8*b^2*c^3 - 128*a^9*c^4)*x^4 + 2*(a^6*b^7 - 12*a^7*b^5*c + 48*a^8*b^3*c^2 - 64*a^9*b*c^3)*x^3 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*x^2), -1/2*(a^4*b^6 - 12*a^5*b^4*c + 48*a^6*b^2*c^2 - 64*a^7*c^3 - 6*(2*a*b^7*c^2 - 23*a^2*b^5*c^3 + 87*a^3*b^3*c^4 - 108*a^4*b*c^5)*x^5 - 3*(8*a*b^8*c - 94*a^2*b^6*c^2 + 369*a^3*b^4*c^3 - 500*a^4*b^2*c^4 + 64*a^5*c^5)*x^4 - 2*(6*a*b^9 - 63*a^2*b^7*c + 188*a^3*b^5*c^2 - 25*a^4*b^3*c^3 - 412*a^5*b*c^4)*x^3 - (18*a^2*b^8 - 217*a^3*b^6*c + 887*a^4*b^4*c^2 - 1300*a^5*b^2*c^3 + 288*a^6*c^4)*x^2 - 6*((2*b^7*c^2 - 21*a*b^5*c^3 + 70*a^2*b^3*c^4 - 70*a^3*b*c^5)*x^6 + 2*(2*b^8*c - 21*a*b^6*c^2 + 70*a^2*b^4*c^3 - 70*a^3*b^2*c^4)*x^5 + (2*b^9 - 17*a*b^7*c + 28*a^2*b^5*c^2 + 70*a^3*b^3*c^3 - 140*a^4*b*c^4)*x^4 + 2*(2*a*b^8 - 21*a^2*b^6*c + 70*a^3*b^4*c^2 - 70*a^4*b^2*c^3)*x^3 + (2*a^2*b^7 - 21*a^3*b^5*c + 70*a^4*b^3*c^2 - 70*a^5*b*c^3)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 4*(a^3*b^7 - 12*a^4*b^5*c + 48*a^5*b^3*c^2 - 64*a^6*b*c^3)*x + 3*((2*b^8*c^2 - 25*a*b^6*c^3 + 108*a^2*b^4*c^4 - 176*a^3*b^2*c^5 + 64*a^4*c^6)*x^6 + 2*(2*b^9*c - 25*a*b^7*c^2 + 108*a^2*b^5*c^3 - 176*a^3*b^3*c^4 + 64*a^4*b*c^5)*x^5 + (2*b^10 - 21*a*b^8*c + 58*a^2*b^6*c^2 + 40*a^3*b^4*c^3 - 288*a^4*b^2*c^4 + 128*a^5*c^5)*x^4 + 2*(2*a*b^9 - 25*a^2*b^7*c + 108*a^3*b^5*c^2 - 176*a^4*b^3*c^3 + 64*a^5*b*c^4)*x^3 + (2*a^2*b^8 - 25*a^3*b^6*c + 108*a^4*b^4*c^2 - 176*a^5*b^2*c^3 + 64*a^6*c^4)*x^2)*log(c*x^2 + b*x + a) - 6*((2*b^8*c^2 - 25*a*b^6*c^3 + 108*a^2*b^4*c^4 - 176*a^3*b^2*c^5 + 64*a^4*c^6)*x^6 + 2*(2*b^9*c - 25*a*b^7*c^2 + 108*a^2*b^5*c^3 - 176*a^3*b^3*c^4 + 64*a^4*b*c^5)*x^5 + (2*b^10 - 21*a*b^8*c + 58*a^2*b^6*c^2 + 40*a^3*b^4*c^3 - 288*a^4*b^2*c^4 + 128*a^5*c^5)*x^4 + 2*(2*a*b^9 - 25*a^2*b^7*c + 108*a^3*b^5*c^2 - 176*a^4*b^3*c^3 + 64*a^5*b*c^4)*x^3 + (2*a^2*b^8 - 25*a^3*b^6*c + 108*a^4*b^4*c^2 - 176*a^5*b^2*c^3 + 64*a^6*c^4)*x^2)*log(x))/((a^5*b^6*c^2 - 12*a^6*b^4*c^3 + 48*a^7*b^2*c^4 - 64*a^8*c^5)*x^6 + 2*(a^5*b^7*c - 12*a^6*b^5*c^2 + 48*a^7*b^3*c^3 - 64*a^8*b*c^4)*x^5 + (a^5*b^8 - 10*a^6*b^6*c + 24*a^7*b^4*c^2 + 32*a^8*b^2*c^3 - 128*a^9*c^4)*x^4 + 2*(a^6*b^7 - 12*a^7*b^5*c + 48*a^8*b^3*c^2 - 64*a^9*b*c^3)*x^3 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*x^2)]","B",0
2210,1,3314,0,0.494343," ","integrate(x^8/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[-\frac{13 \, a^{3} b^{9} - 199 \, a^{4} b^{7} c + 1123 \, a^{5} b^{5} c^{2} - 2730 \, a^{6} b^{3} c^{3} + 2360 \, a^{7} b c^{4} - 3 \, {\left(b^{8} c^{4} - 16 \, a b^{6} c^{5} + 96 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} + 256 \, a^{4} c^{8}\right)} x^{7} - 9 \, {\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{6} + 3 \, {\left(3 \, b^{10} c^{2} - 51 \, a b^{8} c^{3} + 340 \, a^{2} b^{6} c^{4} - 1112 \, a^{3} b^{4} c^{5} + 1812 \, a^{4} b^{2} c^{6} - 1232 \, a^{5} c^{7}\right)} x^{5} + 3 \, {\left(9 \, b^{11} c - 144 \, a b^{9} c^{2} + 874 \, a^{2} b^{7} c^{3} - 2444 \, a^{3} b^{5} c^{4} + 2994 \, a^{4} b^{3} c^{5} - 1160 \, a^{5} b c^{6}\right)} x^{4} + {\left(13 \, b^{12} - 157 \, a b^{10} c + 451 \, a^{2} b^{8} c^{2} + 1340 \, a^{3} b^{6} c^{3} - 8946 \, a^{4} b^{4} c^{4} + 13480 \, a^{5} b^{2} c^{5} - 4480 \, a^{6} c^{6}\right)} x^{3} + 3 \, {\left(13 \, a b^{11} - 198 \, a^{2} b^{9} c + 1106 \, a^{3} b^{7} c^{2} - 2619 \, a^{4} b^{5} c^{3} + 2012 \, a^{5} b^{3} c^{4} + 448 \, a^{6} b c^{5}\right)} x^{2} + 6 \, {\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 70 \, a^{5} b^{4} c^{2} - 140 \, a^{6} b^{2} c^{3} + 70 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 70 \, a^{2} b^{4} c^{5} - 140 \, a^{3} b^{2} c^{6} + 70 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 14 \, a b^{7} c^{3} + 70 \, a^{2} b^{5} c^{4} - 140 \, a^{3} b^{3} c^{5} + 70 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 13 \, a b^{8} c^{2} + 56 \, a^{2} b^{6} c^{3} - 70 \, a^{3} b^{4} c^{4} - 70 \, a^{4} b^{2} c^{5} + 70 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 8 \, a b^{9} c - 14 \, a^{2} b^{7} c^{2} + 280 \, a^{3} b^{5} c^{3} - 770 \, a^{4} b^{3} c^{4} + 420 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 13 \, a^{2} b^{8} c + 56 \, a^{3} b^{6} c^{2} - 70 \, a^{4} b^{4} c^{3} - 70 \, a^{5} b^{2} c^{4} + 70 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 14 \, a^{3} b^{7} c + 70 \, a^{4} b^{5} c^{2} - 140 \, a^{5} b^{3} c^{3} + 70 \, a^{6} b c^{4}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 3 \, {\left(13 \, a^{2} b^{10} - 203 \, a^{3} b^{8} c + 1183 \, a^{4} b^{6} c^{2} - 3058 \, a^{5} b^{4} c^{3} + 3108 \, a^{6} b^{2} c^{4} - 560 \, a^{7} c^{5}\right)} x + 6 \, {\left(a^{3} b^{9} - 16 \, a^{4} b^{7} c + 96 \, a^{5} b^{5} c^{2} - 256 \, a^{6} b^{3} c^{3} + 256 \, a^{7} b c^{4} + {\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{6} + 3 \, {\left(b^{10} c^{2} - 16 \, a b^{8} c^{3} + 96 \, a^{2} b^{6} c^{4} - 256 \, a^{3} b^{4} c^{5} + 256 \, a^{4} b^{2} c^{6}\right)} x^{5} + 3 \, {\left(b^{11} c - 15 \, a b^{9} c^{2} + 80 \, a^{2} b^{7} c^{3} - 160 \, a^{3} b^{5} c^{4} + 256 \, a^{5} b c^{6}\right)} x^{4} + {\left(b^{12} - 10 \, a b^{10} c + 320 \, a^{3} b^{6} c^{3} - 1280 \, a^{4} b^{4} c^{4} + 1536 \, a^{5} b^{2} c^{5}\right)} x^{3} + 3 \, {\left(a b^{11} - 15 \, a^{2} b^{9} c + 80 \, a^{3} b^{7} c^{2} - 160 \, a^{4} b^{5} c^{3} + 256 \, a^{6} b c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{10} - 16 \, a^{3} b^{8} c + 96 \, a^{4} b^{6} c^{2} - 256 \, a^{5} b^{4} c^{3} + 256 \, a^{6} b^{2} c^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{3 \, {\left(a^{3} b^{8} c^{5} - 16 \, a^{4} b^{6} c^{6} + 96 \, a^{5} b^{4} c^{7} - 256 \, a^{6} b^{2} c^{8} + 256 \, a^{7} c^{9} + {\left(b^{8} c^{8} - 16 \, a b^{6} c^{9} + 96 \, a^{2} b^{4} c^{10} - 256 \, a^{3} b^{2} c^{11} + 256 \, a^{4} c^{12}\right)} x^{6} + 3 \, {\left(b^{9} c^{7} - 16 \, a b^{7} c^{8} + 96 \, a^{2} b^{5} c^{9} - 256 \, a^{3} b^{3} c^{10} + 256 \, a^{4} b c^{11}\right)} x^{5} + 3 \, {\left(b^{10} c^{6} - 15 \, a b^{8} c^{7} + 80 \, a^{2} b^{6} c^{8} - 160 \, a^{3} b^{4} c^{9} + 256 \, a^{5} c^{11}\right)} x^{4} + {\left(b^{11} c^{5} - 10 \, a b^{9} c^{6} + 320 \, a^{3} b^{5} c^{8} - 1280 \, a^{4} b^{3} c^{9} + 1536 \, a^{5} b c^{10}\right)} x^{3} + 3 \, {\left(a b^{10} c^{5} - 15 \, a^{2} b^{8} c^{6} + 80 \, a^{3} b^{6} c^{7} - 160 \, a^{4} b^{4} c^{8} + 256 \, a^{6} c^{10}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c^{5} - 16 \, a^{3} b^{7} c^{6} + 96 \, a^{4} b^{5} c^{7} - 256 \, a^{5} b^{3} c^{8} + 256 \, a^{6} b c^{9}\right)} x\right)}}, -\frac{13 \, a^{3} b^{9} - 199 \, a^{4} b^{7} c + 1123 \, a^{5} b^{5} c^{2} - 2730 \, a^{6} b^{3} c^{3} + 2360 \, a^{7} b c^{4} - 3 \, {\left(b^{8} c^{4} - 16 \, a b^{6} c^{5} + 96 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} + 256 \, a^{4} c^{8}\right)} x^{7} - 9 \, {\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{6} + 3 \, {\left(3 \, b^{10} c^{2} - 51 \, a b^{8} c^{3} + 340 \, a^{2} b^{6} c^{4} - 1112 \, a^{3} b^{4} c^{5} + 1812 \, a^{4} b^{2} c^{6} - 1232 \, a^{5} c^{7}\right)} x^{5} + 3 \, {\left(9 \, b^{11} c - 144 \, a b^{9} c^{2} + 874 \, a^{2} b^{7} c^{3} - 2444 \, a^{3} b^{5} c^{4} + 2994 \, a^{4} b^{3} c^{5} - 1160 \, a^{5} b c^{6}\right)} x^{4} + {\left(13 \, b^{12} - 157 \, a b^{10} c + 451 \, a^{2} b^{8} c^{2} + 1340 \, a^{3} b^{6} c^{3} - 8946 \, a^{4} b^{4} c^{4} + 13480 \, a^{5} b^{2} c^{5} - 4480 \, a^{6} c^{6}\right)} x^{3} + 3 \, {\left(13 \, a b^{11} - 198 \, a^{2} b^{9} c + 1106 \, a^{3} b^{7} c^{2} - 2619 \, a^{4} b^{5} c^{3} + 2012 \, a^{5} b^{3} c^{4} + 448 \, a^{6} b c^{5}\right)} x^{2} + 12 \, {\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 70 \, a^{5} b^{4} c^{2} - 140 \, a^{6} b^{2} c^{3} + 70 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 70 \, a^{2} b^{4} c^{5} - 140 \, a^{3} b^{2} c^{6} + 70 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 14 \, a b^{7} c^{3} + 70 \, a^{2} b^{5} c^{4} - 140 \, a^{3} b^{3} c^{5} + 70 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 13 \, a b^{8} c^{2} + 56 \, a^{2} b^{6} c^{3} - 70 \, a^{3} b^{4} c^{4} - 70 \, a^{4} b^{2} c^{5} + 70 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 8 \, a b^{9} c - 14 \, a^{2} b^{7} c^{2} + 280 \, a^{3} b^{5} c^{3} - 770 \, a^{4} b^{3} c^{4} + 420 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 13 \, a^{2} b^{8} c + 56 \, a^{3} b^{6} c^{2} - 70 \, a^{4} b^{4} c^{3} - 70 \, a^{5} b^{2} c^{4} + 70 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 14 \, a^{3} b^{7} c + 70 \, a^{4} b^{5} c^{2} - 140 \, a^{5} b^{3} c^{3} + 70 \, a^{6} b c^{4}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 3 \, {\left(13 \, a^{2} b^{10} - 203 \, a^{3} b^{8} c + 1183 \, a^{4} b^{6} c^{2} - 3058 \, a^{5} b^{4} c^{3} + 3108 \, a^{6} b^{2} c^{4} - 560 \, a^{7} c^{5}\right)} x + 6 \, {\left(a^{3} b^{9} - 16 \, a^{4} b^{7} c + 96 \, a^{5} b^{5} c^{2} - 256 \, a^{6} b^{3} c^{3} + 256 \, a^{7} b c^{4} + {\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{6} + 3 \, {\left(b^{10} c^{2} - 16 \, a b^{8} c^{3} + 96 \, a^{2} b^{6} c^{4} - 256 \, a^{3} b^{4} c^{5} + 256 \, a^{4} b^{2} c^{6}\right)} x^{5} + 3 \, {\left(b^{11} c - 15 \, a b^{9} c^{2} + 80 \, a^{2} b^{7} c^{3} - 160 \, a^{3} b^{5} c^{4} + 256 \, a^{5} b c^{6}\right)} x^{4} + {\left(b^{12} - 10 \, a b^{10} c + 320 \, a^{3} b^{6} c^{3} - 1280 \, a^{4} b^{4} c^{4} + 1536 \, a^{5} b^{2} c^{5}\right)} x^{3} + 3 \, {\left(a b^{11} - 15 \, a^{2} b^{9} c + 80 \, a^{3} b^{7} c^{2} - 160 \, a^{4} b^{5} c^{3} + 256 \, a^{6} b c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{10} - 16 \, a^{3} b^{8} c + 96 \, a^{4} b^{6} c^{2} - 256 \, a^{5} b^{4} c^{3} + 256 \, a^{6} b^{2} c^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{3 \, {\left(a^{3} b^{8} c^{5} - 16 \, a^{4} b^{6} c^{6} + 96 \, a^{5} b^{4} c^{7} - 256 \, a^{6} b^{2} c^{8} + 256 \, a^{7} c^{9} + {\left(b^{8} c^{8} - 16 \, a b^{6} c^{9} + 96 \, a^{2} b^{4} c^{10} - 256 \, a^{3} b^{2} c^{11} + 256 \, a^{4} c^{12}\right)} x^{6} + 3 \, {\left(b^{9} c^{7} - 16 \, a b^{7} c^{8} + 96 \, a^{2} b^{5} c^{9} - 256 \, a^{3} b^{3} c^{10} + 256 \, a^{4} b c^{11}\right)} x^{5} + 3 \, {\left(b^{10} c^{6} - 15 \, a b^{8} c^{7} + 80 \, a^{2} b^{6} c^{8} - 160 \, a^{3} b^{4} c^{9} + 256 \, a^{5} c^{11}\right)} x^{4} + {\left(b^{11} c^{5} - 10 \, a b^{9} c^{6} + 320 \, a^{3} b^{5} c^{8} - 1280 \, a^{4} b^{3} c^{9} + 1536 \, a^{5} b c^{10}\right)} x^{3} + 3 \, {\left(a b^{10} c^{5} - 15 \, a^{2} b^{8} c^{6} + 80 \, a^{3} b^{6} c^{7} - 160 \, a^{4} b^{4} c^{8} + 256 \, a^{6} c^{10}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c^{5} - 16 \, a^{3} b^{7} c^{6} + 96 \, a^{4} b^{5} c^{7} - 256 \, a^{5} b^{3} c^{8} + 256 \, a^{6} b c^{9}\right)} x\right)}}\right]"," ",0,"[-1/3*(13*a^3*b^9 - 199*a^4*b^7*c + 1123*a^5*b^5*c^2 - 2730*a^6*b^3*c^3 + 2360*a^7*b*c^4 - 3*(b^8*c^4 - 16*a*b^6*c^5 + 96*a^2*b^4*c^6 - 256*a^3*b^2*c^7 + 256*a^4*c^8)*x^7 - 9*(b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^6 + 3*(3*b^10*c^2 - 51*a*b^8*c^3 + 340*a^2*b^6*c^4 - 1112*a^3*b^4*c^5 + 1812*a^4*b^2*c^6 - 1232*a^5*c^7)*x^5 + 3*(9*b^11*c - 144*a*b^9*c^2 + 874*a^2*b^7*c^3 - 2444*a^3*b^5*c^4 + 2994*a^4*b^3*c^5 - 1160*a^5*b*c^6)*x^4 + (13*b^12 - 157*a*b^10*c + 451*a^2*b^8*c^2 + 1340*a^3*b^6*c^3 - 8946*a^4*b^4*c^4 + 13480*a^5*b^2*c^5 - 4480*a^6*c^6)*x^3 + 3*(13*a*b^11 - 198*a^2*b^9*c + 1106*a^3*b^7*c^2 - 2619*a^4*b^5*c^3 + 2012*a^5*b^3*c^4 + 448*a^6*b*c^5)*x^2 + 6*(a^3*b^8 - 14*a^4*b^6*c + 70*a^5*b^4*c^2 - 140*a^6*b^2*c^3 + 70*a^7*c^4 + (b^8*c^3 - 14*a*b^6*c^4 + 70*a^2*b^4*c^5 - 140*a^3*b^2*c^6 + 70*a^4*c^7)*x^6 + 3*(b^9*c^2 - 14*a*b^7*c^3 + 70*a^2*b^5*c^4 - 140*a^3*b^3*c^5 + 70*a^4*b*c^6)*x^5 + 3*(b^10*c - 13*a*b^8*c^2 + 56*a^2*b^6*c^3 - 70*a^3*b^4*c^4 - 70*a^4*b^2*c^5 + 70*a^5*c^6)*x^4 + (b^11 - 8*a*b^9*c - 14*a^2*b^7*c^2 + 280*a^3*b^5*c^3 - 770*a^4*b^3*c^4 + 420*a^5*b*c^5)*x^3 + 3*(a*b^10 - 13*a^2*b^8*c + 56*a^3*b^6*c^2 - 70*a^4*b^4*c^3 - 70*a^5*b^2*c^4 + 70*a^6*c^5)*x^2 + 3*(a^2*b^9 - 14*a^3*b^7*c + 70*a^4*b^5*c^2 - 140*a^5*b^3*c^3 + 70*a^6*b*c^4)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 3*(13*a^2*b^10 - 203*a^3*b^8*c + 1183*a^4*b^6*c^2 - 3058*a^5*b^4*c^3 + 3108*a^6*b^2*c^4 - 560*a^7*c^5)*x + 6*(a^3*b^9 - 16*a^4*b^7*c + 96*a^5*b^5*c^2 - 256*a^6*b^3*c^3 + 256*a^7*b*c^4 + (b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^6 + 3*(b^10*c^2 - 16*a*b^8*c^3 + 96*a^2*b^6*c^4 - 256*a^3*b^4*c^5 + 256*a^4*b^2*c^6)*x^5 + 3*(b^11*c - 15*a*b^9*c^2 + 80*a^2*b^7*c^3 - 160*a^3*b^5*c^4 + 256*a^5*b*c^6)*x^4 + (b^12 - 10*a*b^10*c + 320*a^3*b^6*c^3 - 1280*a^4*b^4*c^4 + 1536*a^5*b^2*c^5)*x^3 + 3*(a*b^11 - 15*a^2*b^9*c + 80*a^3*b^7*c^2 - 160*a^4*b^5*c^3 + 256*a^6*b*c^5)*x^2 + 3*(a^2*b^10 - 16*a^3*b^8*c + 96*a^4*b^6*c^2 - 256*a^5*b^4*c^3 + 256*a^6*b^2*c^4)*x)*log(c*x^2 + b*x + a))/(a^3*b^8*c^5 - 16*a^4*b^6*c^6 + 96*a^5*b^4*c^7 - 256*a^6*b^2*c^8 + 256*a^7*c^9 + (b^8*c^8 - 16*a*b^6*c^9 + 96*a^2*b^4*c^10 - 256*a^3*b^2*c^11 + 256*a^4*c^12)*x^6 + 3*(b^9*c^7 - 16*a*b^7*c^8 + 96*a^2*b^5*c^9 - 256*a^3*b^3*c^10 + 256*a^4*b*c^11)*x^5 + 3*(b^10*c^6 - 15*a*b^8*c^7 + 80*a^2*b^6*c^8 - 160*a^3*b^4*c^9 + 256*a^5*c^11)*x^4 + (b^11*c^5 - 10*a*b^9*c^6 + 320*a^3*b^5*c^8 - 1280*a^4*b^3*c^9 + 1536*a^5*b*c^10)*x^3 + 3*(a*b^10*c^5 - 15*a^2*b^8*c^6 + 80*a^3*b^6*c^7 - 160*a^4*b^4*c^8 + 256*a^6*c^10)*x^2 + 3*(a^2*b^9*c^5 - 16*a^3*b^7*c^6 + 96*a^4*b^5*c^7 - 256*a^5*b^3*c^8 + 256*a^6*b*c^9)*x), -1/3*(13*a^3*b^9 - 199*a^4*b^7*c + 1123*a^5*b^5*c^2 - 2730*a^6*b^3*c^3 + 2360*a^7*b*c^4 - 3*(b^8*c^4 - 16*a*b^6*c^5 + 96*a^2*b^4*c^6 - 256*a^3*b^2*c^7 + 256*a^4*c^8)*x^7 - 9*(b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^6 + 3*(3*b^10*c^2 - 51*a*b^8*c^3 + 340*a^2*b^6*c^4 - 1112*a^3*b^4*c^5 + 1812*a^4*b^2*c^6 - 1232*a^5*c^7)*x^5 + 3*(9*b^11*c - 144*a*b^9*c^2 + 874*a^2*b^7*c^3 - 2444*a^3*b^5*c^4 + 2994*a^4*b^3*c^5 - 1160*a^5*b*c^6)*x^4 + (13*b^12 - 157*a*b^10*c + 451*a^2*b^8*c^2 + 1340*a^3*b^6*c^3 - 8946*a^4*b^4*c^4 + 13480*a^5*b^2*c^5 - 4480*a^6*c^6)*x^3 + 3*(13*a*b^11 - 198*a^2*b^9*c + 1106*a^3*b^7*c^2 - 2619*a^4*b^5*c^3 + 2012*a^5*b^3*c^4 + 448*a^6*b*c^5)*x^2 + 12*(a^3*b^8 - 14*a^4*b^6*c + 70*a^5*b^4*c^2 - 140*a^6*b^2*c^3 + 70*a^7*c^4 + (b^8*c^3 - 14*a*b^6*c^4 + 70*a^2*b^4*c^5 - 140*a^3*b^2*c^6 + 70*a^4*c^7)*x^6 + 3*(b^9*c^2 - 14*a*b^7*c^3 + 70*a^2*b^5*c^4 - 140*a^3*b^3*c^5 + 70*a^4*b*c^6)*x^5 + 3*(b^10*c - 13*a*b^8*c^2 + 56*a^2*b^6*c^3 - 70*a^3*b^4*c^4 - 70*a^4*b^2*c^5 + 70*a^5*c^6)*x^4 + (b^11 - 8*a*b^9*c - 14*a^2*b^7*c^2 + 280*a^3*b^5*c^3 - 770*a^4*b^3*c^4 + 420*a^5*b*c^5)*x^3 + 3*(a*b^10 - 13*a^2*b^8*c + 56*a^3*b^6*c^2 - 70*a^4*b^4*c^3 - 70*a^5*b^2*c^4 + 70*a^6*c^5)*x^2 + 3*(a^2*b^9 - 14*a^3*b^7*c + 70*a^4*b^5*c^2 - 140*a^5*b^3*c^3 + 70*a^6*b*c^4)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 3*(13*a^2*b^10 - 203*a^3*b^8*c + 1183*a^4*b^6*c^2 - 3058*a^5*b^4*c^3 + 3108*a^6*b^2*c^4 - 560*a^7*c^5)*x + 6*(a^3*b^9 - 16*a^4*b^7*c + 96*a^5*b^5*c^2 - 256*a^6*b^3*c^3 + 256*a^7*b*c^4 + (b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^6 + 3*(b^10*c^2 - 16*a*b^8*c^3 + 96*a^2*b^6*c^4 - 256*a^3*b^4*c^5 + 256*a^4*b^2*c^6)*x^5 + 3*(b^11*c - 15*a*b^9*c^2 + 80*a^2*b^7*c^3 - 160*a^3*b^5*c^4 + 256*a^5*b*c^6)*x^4 + (b^12 - 10*a*b^10*c + 320*a^3*b^6*c^3 - 1280*a^4*b^4*c^4 + 1536*a^5*b^2*c^5)*x^3 + 3*(a*b^11 - 15*a^2*b^9*c + 80*a^3*b^7*c^2 - 160*a^4*b^5*c^3 + 256*a^6*b*c^5)*x^2 + 3*(a^2*b^10 - 16*a^3*b^8*c + 96*a^4*b^6*c^2 - 256*a^5*b^4*c^3 + 256*a^6*b^2*c^4)*x)*log(c*x^2 + b*x + a))/(a^3*b^8*c^5 - 16*a^4*b^6*c^6 + 96*a^5*b^4*c^7 - 256*a^6*b^2*c^8 + 256*a^7*c^9 + (b^8*c^8 - 16*a*b^6*c^9 + 96*a^2*b^4*c^10 - 256*a^3*b^2*c^11 + 256*a^4*c^12)*x^6 + 3*(b^9*c^7 - 16*a*b^7*c^8 + 96*a^2*b^5*c^9 - 256*a^3*b^3*c^10 + 256*a^4*b*c^11)*x^5 + 3*(b^10*c^6 - 15*a*b^8*c^7 + 80*a^2*b^6*c^8 - 160*a^3*b^4*c^9 + 256*a^5*c^11)*x^4 + (b^11*c^5 - 10*a*b^9*c^6 + 320*a^3*b^5*c^8 - 1280*a^4*b^3*c^9 + 1536*a^5*b*c^10)*x^3 + 3*(a*b^10*c^5 - 15*a^2*b^8*c^6 + 80*a^3*b^6*c^7 - 160*a^4*b^4*c^8 + 256*a^6*c^10)*x^2 + 3*(a^2*b^9*c^5 - 16*a^3*b^7*c^6 + 96*a^4*b^5*c^7 - 256*a^5*b^3*c^8 + 256*a^6*b*c^9)*x)]","B",0
2211,1,2884,0,0.475722," ","integrate(x^7/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[\frac{11 \, a^{3} b^{8} - 168 \, a^{4} b^{6} c + 934 \, a^{5} b^{4} c^{2} - 2104 \, a^{6} b^{2} c^{3} + 1408 \, a^{7} c^{4} + 6 \, {\left(3 \, b^{9} c^{2} - 47 \, a b^{7} c^{3} + 273 \, a^{2} b^{5} c^{4} - 686 \, a^{3} b^{3} c^{5} + 616 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(9 \, b^{10} c - 136 \, a b^{8} c^{2} + 741 \, a^{2} b^{6} c^{3} - 1606 \, a^{3} b^{4} c^{4} + 776 \, a^{4} b^{2} c^{5} + 768 \, a^{5} c^{6}\right)} x^{4} + {\left(11 \, b^{11} - 120 \, a b^{9} c + 187 \, a^{2} b^{7} c^{2} + 2166 \, a^{3} b^{5} c^{3} - 9064 \, a^{4} b^{3} c^{4} + 9088 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(11 \, a b^{10} - 163 \, a^{2} b^{8} c + 857 \, a^{3} b^{6} c^{2} - 1676 \, a^{4} b^{4} c^{3} + 320 \, a^{5} b^{2} c^{4} + 1152 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{3} b^{7} - 14 \, a^{4} b^{5} c + 70 \, a^{5} b^{3} c^{2} - 140 \, a^{6} b c^{3} + {\left(b^{7} c^{3} - 14 \, a b^{5} c^{4} + 70 \, a^{2} b^{3} c^{5} - 140 \, a^{3} b c^{6}\right)} x^{6} + 3 \, {\left(b^{8} c^{2} - 14 \, a b^{6} c^{3} + 70 \, a^{2} b^{4} c^{4} - 140 \, a^{3} b^{2} c^{5}\right)} x^{5} + 3 \, {\left(b^{9} c - 13 \, a b^{7} c^{2} + 56 \, a^{2} b^{5} c^{3} - 70 \, a^{3} b^{3} c^{4} - 140 \, a^{4} b c^{5}\right)} x^{4} + {\left(b^{10} - 8 \, a b^{8} c - 14 \, a^{2} b^{6} c^{2} + 280 \, a^{3} b^{4} c^{3} - 840 \, a^{4} b^{2} c^{4}\right)} x^{3} + 3 \, {\left(a b^{9} - 13 \, a^{2} b^{7} c + 56 \, a^{3} b^{5} c^{2} - 70 \, a^{4} b^{3} c^{3} - 140 \, a^{5} b c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{8} - 14 \, a^{3} b^{6} c + 70 \, a^{4} b^{4} c^{2} - 140 \, a^{5} b^{2} c^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 3 \, {\left(11 \, a^{2} b^{9} - 170 \, a^{3} b^{7} c + 964 \, a^{4} b^{5} c^{2} - 2268 \, a^{5} b^{3} c^{3} + 1712 \, a^{6} b c^{4}\right)} x + 3 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(a^{3} b^{8} c^{4} - 16 \, a^{4} b^{6} c^{5} + 96 \, a^{5} b^{4} c^{6} - 256 \, a^{6} b^{2} c^{7} + 256 \, a^{7} c^{8} + {\left(b^{8} c^{7} - 16 \, a b^{6} c^{8} + 96 \, a^{2} b^{4} c^{9} - 256 \, a^{3} b^{2} c^{10} + 256 \, a^{4} c^{11}\right)} x^{6} + 3 \, {\left(b^{9} c^{6} - 16 \, a b^{7} c^{7} + 96 \, a^{2} b^{5} c^{8} - 256 \, a^{3} b^{3} c^{9} + 256 \, a^{4} b c^{10}\right)} x^{5} + 3 \, {\left(b^{10} c^{5} - 15 \, a b^{8} c^{6} + 80 \, a^{2} b^{6} c^{7} - 160 \, a^{3} b^{4} c^{8} + 256 \, a^{5} c^{10}\right)} x^{4} + {\left(b^{11} c^{4} - 10 \, a b^{9} c^{5} + 320 \, a^{3} b^{5} c^{7} - 1280 \, a^{4} b^{3} c^{8} + 1536 \, a^{5} b c^{9}\right)} x^{3} + 3 \, {\left(a b^{10} c^{4} - 15 \, a^{2} b^{8} c^{5} + 80 \, a^{3} b^{6} c^{6} - 160 \, a^{4} b^{4} c^{7} + 256 \, a^{6} c^{9}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c^{4} - 16 \, a^{3} b^{7} c^{5} + 96 \, a^{4} b^{5} c^{6} - 256 \, a^{5} b^{3} c^{7} + 256 \, a^{6} b c^{8}\right)} x\right)}}, \frac{11 \, a^{3} b^{8} - 168 \, a^{4} b^{6} c + 934 \, a^{5} b^{4} c^{2} - 2104 \, a^{6} b^{2} c^{3} + 1408 \, a^{7} c^{4} + 6 \, {\left(3 \, b^{9} c^{2} - 47 \, a b^{7} c^{3} + 273 \, a^{2} b^{5} c^{4} - 686 \, a^{3} b^{3} c^{5} + 616 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(9 \, b^{10} c - 136 \, a b^{8} c^{2} + 741 \, a^{2} b^{6} c^{3} - 1606 \, a^{3} b^{4} c^{4} + 776 \, a^{4} b^{2} c^{5} + 768 \, a^{5} c^{6}\right)} x^{4} + {\left(11 \, b^{11} - 120 \, a b^{9} c + 187 \, a^{2} b^{7} c^{2} + 2166 \, a^{3} b^{5} c^{3} - 9064 \, a^{4} b^{3} c^{4} + 9088 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(11 \, a b^{10} - 163 \, a^{2} b^{8} c + 857 \, a^{3} b^{6} c^{2} - 1676 \, a^{4} b^{4} c^{3} + 320 \, a^{5} b^{2} c^{4} + 1152 \, a^{6} c^{5}\right)} x^{2} + 6 \, {\left(a^{3} b^{7} - 14 \, a^{4} b^{5} c + 70 \, a^{5} b^{3} c^{2} - 140 \, a^{6} b c^{3} + {\left(b^{7} c^{3} - 14 \, a b^{5} c^{4} + 70 \, a^{2} b^{3} c^{5} - 140 \, a^{3} b c^{6}\right)} x^{6} + 3 \, {\left(b^{8} c^{2} - 14 \, a b^{6} c^{3} + 70 \, a^{2} b^{4} c^{4} - 140 \, a^{3} b^{2} c^{5}\right)} x^{5} + 3 \, {\left(b^{9} c - 13 \, a b^{7} c^{2} + 56 \, a^{2} b^{5} c^{3} - 70 \, a^{3} b^{3} c^{4} - 140 \, a^{4} b c^{5}\right)} x^{4} + {\left(b^{10} - 8 \, a b^{8} c - 14 \, a^{2} b^{6} c^{2} + 280 \, a^{3} b^{4} c^{3} - 840 \, a^{4} b^{2} c^{4}\right)} x^{3} + 3 \, {\left(a b^{9} - 13 \, a^{2} b^{7} c + 56 \, a^{3} b^{5} c^{2} - 70 \, a^{4} b^{3} c^{3} - 140 \, a^{5} b c^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{8} - 14 \, a^{3} b^{6} c + 70 \, a^{4} b^{4} c^{2} - 140 \, a^{5} b^{2} c^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 3 \, {\left(11 \, a^{2} b^{9} - 170 \, a^{3} b^{7} c + 964 \, a^{4} b^{5} c^{2} - 2268 \, a^{5} b^{3} c^{3} + 1712 \, a^{6} b c^{4}\right)} x + 3 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right)}{6 \, {\left(a^{3} b^{8} c^{4} - 16 \, a^{4} b^{6} c^{5} + 96 \, a^{5} b^{4} c^{6} - 256 \, a^{6} b^{2} c^{7} + 256 \, a^{7} c^{8} + {\left(b^{8} c^{7} - 16 \, a b^{6} c^{8} + 96 \, a^{2} b^{4} c^{9} - 256 \, a^{3} b^{2} c^{10} + 256 \, a^{4} c^{11}\right)} x^{6} + 3 \, {\left(b^{9} c^{6} - 16 \, a b^{7} c^{7} + 96 \, a^{2} b^{5} c^{8} - 256 \, a^{3} b^{3} c^{9} + 256 \, a^{4} b c^{10}\right)} x^{5} + 3 \, {\left(b^{10} c^{5} - 15 \, a b^{8} c^{6} + 80 \, a^{2} b^{6} c^{7} - 160 \, a^{3} b^{4} c^{8} + 256 \, a^{5} c^{10}\right)} x^{4} + {\left(b^{11} c^{4} - 10 \, a b^{9} c^{5} + 320 \, a^{3} b^{5} c^{7} - 1280 \, a^{4} b^{3} c^{8} + 1536 \, a^{5} b c^{9}\right)} x^{3} + 3 \, {\left(a b^{10} c^{4} - 15 \, a^{2} b^{8} c^{5} + 80 \, a^{3} b^{6} c^{6} - 160 \, a^{4} b^{4} c^{7} + 256 \, a^{6} c^{9}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c^{4} - 16 \, a^{3} b^{7} c^{5} + 96 \, a^{4} b^{5} c^{6} - 256 \, a^{5} b^{3} c^{7} + 256 \, a^{6} b c^{8}\right)} x\right)}}\right]"," ",0,"[1/6*(11*a^3*b^8 - 168*a^4*b^6*c + 934*a^5*b^4*c^2 - 2104*a^6*b^2*c^3 + 1408*a^7*c^4 + 6*(3*b^9*c^2 - 47*a*b^7*c^3 + 273*a^2*b^5*c^4 - 686*a^3*b^3*c^5 + 616*a^4*b*c^6)*x^5 + 3*(9*b^10*c - 136*a*b^8*c^2 + 741*a^2*b^6*c^3 - 1606*a^3*b^4*c^4 + 776*a^4*b^2*c^5 + 768*a^5*c^6)*x^4 + (11*b^11 - 120*a*b^9*c + 187*a^2*b^7*c^2 + 2166*a^3*b^5*c^3 - 9064*a^4*b^3*c^4 + 9088*a^5*b*c^5)*x^3 + 3*(11*a*b^10 - 163*a^2*b^8*c + 857*a^3*b^6*c^2 - 1676*a^4*b^4*c^3 + 320*a^5*b^2*c^4 + 1152*a^6*c^5)*x^2 + 3*(a^3*b^7 - 14*a^4*b^5*c + 70*a^5*b^3*c^2 - 140*a^6*b*c^3 + (b^7*c^3 - 14*a*b^5*c^4 + 70*a^2*b^3*c^5 - 140*a^3*b*c^6)*x^6 + 3*(b^8*c^2 - 14*a*b^6*c^3 + 70*a^2*b^4*c^4 - 140*a^3*b^2*c^5)*x^5 + 3*(b^9*c - 13*a*b^7*c^2 + 56*a^2*b^5*c^3 - 70*a^3*b^3*c^4 - 140*a^4*b*c^5)*x^4 + (b^10 - 8*a*b^8*c - 14*a^2*b^6*c^2 + 280*a^3*b^4*c^3 - 840*a^4*b^2*c^4)*x^3 + 3*(a*b^9 - 13*a^2*b^7*c + 56*a^3*b^5*c^2 - 70*a^4*b^3*c^3 - 140*a^5*b*c^4)*x^2 + 3*(a^2*b^8 - 14*a^3*b^6*c + 70*a^4*b^4*c^2 - 140*a^5*b^2*c^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 3*(11*a^2*b^9 - 170*a^3*b^7*c + 964*a^4*b^5*c^2 - 2268*a^5*b^3*c^3 + 1712*a^6*b*c^4)*x + 3*(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x)*log(c*x^2 + b*x + a))/(a^3*b^8*c^4 - 16*a^4*b^6*c^5 + 96*a^5*b^4*c^6 - 256*a^6*b^2*c^7 + 256*a^7*c^8 + (b^8*c^7 - 16*a*b^6*c^8 + 96*a^2*b^4*c^9 - 256*a^3*b^2*c^10 + 256*a^4*c^11)*x^6 + 3*(b^9*c^6 - 16*a*b^7*c^7 + 96*a^2*b^5*c^8 - 256*a^3*b^3*c^9 + 256*a^4*b*c^10)*x^5 + 3*(b^10*c^5 - 15*a*b^8*c^6 + 80*a^2*b^6*c^7 - 160*a^3*b^4*c^8 + 256*a^5*c^10)*x^4 + (b^11*c^4 - 10*a*b^9*c^5 + 320*a^3*b^5*c^7 - 1280*a^4*b^3*c^8 + 1536*a^5*b*c^9)*x^3 + 3*(a*b^10*c^4 - 15*a^2*b^8*c^5 + 80*a^3*b^6*c^6 - 160*a^4*b^4*c^7 + 256*a^6*c^9)*x^2 + 3*(a^2*b^9*c^4 - 16*a^3*b^7*c^5 + 96*a^4*b^5*c^6 - 256*a^5*b^3*c^7 + 256*a^6*b*c^8)*x), 1/6*(11*a^3*b^8 - 168*a^4*b^6*c + 934*a^5*b^4*c^2 - 2104*a^6*b^2*c^3 + 1408*a^7*c^4 + 6*(3*b^9*c^2 - 47*a*b^7*c^3 + 273*a^2*b^5*c^4 - 686*a^3*b^3*c^5 + 616*a^4*b*c^6)*x^5 + 3*(9*b^10*c - 136*a*b^8*c^2 + 741*a^2*b^6*c^3 - 1606*a^3*b^4*c^4 + 776*a^4*b^2*c^5 + 768*a^5*c^6)*x^4 + (11*b^11 - 120*a*b^9*c + 187*a^2*b^7*c^2 + 2166*a^3*b^5*c^3 - 9064*a^4*b^3*c^4 + 9088*a^5*b*c^5)*x^3 + 3*(11*a*b^10 - 163*a^2*b^8*c + 857*a^3*b^6*c^2 - 1676*a^4*b^4*c^3 + 320*a^5*b^2*c^4 + 1152*a^6*c^5)*x^2 + 6*(a^3*b^7 - 14*a^4*b^5*c + 70*a^5*b^3*c^2 - 140*a^6*b*c^3 + (b^7*c^3 - 14*a*b^5*c^4 + 70*a^2*b^3*c^5 - 140*a^3*b*c^6)*x^6 + 3*(b^8*c^2 - 14*a*b^6*c^3 + 70*a^2*b^4*c^4 - 140*a^3*b^2*c^5)*x^5 + 3*(b^9*c - 13*a*b^7*c^2 + 56*a^2*b^5*c^3 - 70*a^3*b^3*c^4 - 140*a^4*b*c^5)*x^4 + (b^10 - 8*a*b^8*c - 14*a^2*b^6*c^2 + 280*a^3*b^4*c^3 - 840*a^4*b^2*c^4)*x^3 + 3*(a*b^9 - 13*a^2*b^7*c + 56*a^3*b^5*c^2 - 70*a^4*b^3*c^3 - 140*a^5*b*c^4)*x^2 + 3*(a^2*b^8 - 14*a^3*b^6*c + 70*a^4*b^4*c^2 - 140*a^5*b^2*c^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 3*(11*a^2*b^9 - 170*a^3*b^7*c + 964*a^4*b^5*c^2 - 2268*a^5*b^3*c^3 + 1712*a^6*b*c^4)*x + 3*(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x)*log(c*x^2 + b*x + a))/(a^3*b^8*c^4 - 16*a^4*b^6*c^5 + 96*a^5*b^4*c^6 - 256*a^6*b^2*c^7 + 256*a^7*c^8 + (b^8*c^7 - 16*a*b^6*c^8 + 96*a^2*b^4*c^9 - 256*a^3*b^2*c^10 + 256*a^4*c^11)*x^6 + 3*(b^9*c^6 - 16*a*b^7*c^7 + 96*a^2*b^5*c^8 - 256*a^3*b^3*c^9 + 256*a^4*b*c^10)*x^5 + 3*(b^10*c^5 - 15*a*b^8*c^6 + 80*a^2*b^6*c^7 - 160*a^3*b^4*c^8 + 256*a^5*c^10)*x^4 + (b^11*c^4 - 10*a*b^9*c^5 + 320*a^3*b^5*c^7 - 1280*a^4*b^3*c^8 + 1536*a^5*b*c^9)*x^3 + 3*(a*b^10*c^4 - 15*a^2*b^8*c^5 + 80*a^3*b^6*c^6 - 160*a^4*b^4*c^7 + 256*a^6*c^9)*x^2 + 3*(a^2*b^9*c^4 - 16*a^3*b^7*c^5 + 96*a^4*b^5*c^6 - 256*a^5*b^3*c^7 + 256*a^6*b*c^8)*x)]","B",0
2212,1,1675,0,0.444561," ","integrate(x^6/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[-\frac{a^{3} b^{7} - 17 \, a^{4} b^{5} c + 118 \, a^{5} b^{3} c^{2} - 264 \, a^{6} b c^{3} + 3 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} + 96 \, a^{2} b^{4} c^{4} - 236 \, a^{3} b^{2} c^{5} + 176 \, a^{4} c^{6}\right)} x^{5} + 3 \, {\left(b^{9} c - 16 \, a b^{7} c^{2} + 96 \, a^{2} b^{5} c^{3} - 206 \, a^{3} b^{3} c^{4} + 56 \, a^{4} b c^{5}\right)} x^{4} + {\left(b^{10} - 11 \, a b^{8} c + 16 \, a^{2} b^{6} c^{2} + 334 \, a^{3} b^{4} c^{3} - 1304 \, a^{4} b^{2} c^{4} + 640 \, a^{5} c^{5}\right)} x^{3} + 3 \, {\left(a b^{9} - 16 \, a^{2} b^{7} c + 101 \, a^{3} b^{5} c^{2} - 196 \, a^{4} b^{3} c^{3} - 64 \, a^{5} b c^{4}\right)} x^{2} + 60 \, {\left(a^{3} c^{6} x^{6} + 3 \, a^{3} b c^{5} x^{5} + 3 \, a^{5} b c^{3} x + a^{6} c^{3} + 3 \, {\left(a^{3} b^{2} c^{4} + a^{4} c^{5}\right)} x^{4} + {\left(a^{3} b^{3} c^{3} + 6 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a^{4} b^{2} c^{3} + a^{5} c^{4}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 3 \, {\left(a^{2} b^{8} - 17 \, a^{3} b^{6} c + 118 \, a^{4} b^{4} c^{2} - 284 \, a^{5} b^{2} c^{3} + 80 \, a^{6} c^{4}\right)} x}{3 \, {\left(a^{3} b^{8} c^{3} - 16 \, a^{4} b^{6} c^{4} + 96 \, a^{5} b^{4} c^{5} - 256 \, a^{6} b^{2} c^{6} + 256 \, a^{7} c^{7} + {\left(b^{8} c^{6} - 16 \, a b^{6} c^{7} + 96 \, a^{2} b^{4} c^{8} - 256 \, a^{3} b^{2} c^{9} + 256 \, a^{4} c^{10}\right)} x^{6} + 3 \, {\left(b^{9} c^{5} - 16 \, a b^{7} c^{6} + 96 \, a^{2} b^{5} c^{7} - 256 \, a^{3} b^{3} c^{8} + 256 \, a^{4} b c^{9}\right)} x^{5} + 3 \, {\left(b^{10} c^{4} - 15 \, a b^{8} c^{5} + 80 \, a^{2} b^{6} c^{6} - 160 \, a^{3} b^{4} c^{7} + 256 \, a^{5} c^{9}\right)} x^{4} + {\left(b^{11} c^{3} - 10 \, a b^{9} c^{4} + 320 \, a^{3} b^{5} c^{6} - 1280 \, a^{4} b^{3} c^{7} + 1536 \, a^{5} b c^{8}\right)} x^{3} + 3 \, {\left(a b^{10} c^{3} - 15 \, a^{2} b^{8} c^{4} + 80 \, a^{3} b^{6} c^{5} - 160 \, a^{4} b^{4} c^{6} + 256 \, a^{6} c^{8}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c^{3} - 16 \, a^{3} b^{7} c^{4} + 96 \, a^{4} b^{5} c^{5} - 256 \, a^{5} b^{3} c^{6} + 256 \, a^{6} b c^{7}\right)} x\right)}}, -\frac{a^{3} b^{7} - 17 \, a^{4} b^{5} c + 118 \, a^{5} b^{3} c^{2} - 264 \, a^{6} b c^{3} + 3 \, {\left(b^{8} c^{2} - 16 \, a b^{6} c^{3} + 96 \, a^{2} b^{4} c^{4} - 236 \, a^{3} b^{2} c^{5} + 176 \, a^{4} c^{6}\right)} x^{5} + 3 \, {\left(b^{9} c - 16 \, a b^{7} c^{2} + 96 \, a^{2} b^{5} c^{3} - 206 \, a^{3} b^{3} c^{4} + 56 \, a^{4} b c^{5}\right)} x^{4} + {\left(b^{10} - 11 \, a b^{8} c + 16 \, a^{2} b^{6} c^{2} + 334 \, a^{3} b^{4} c^{3} - 1304 \, a^{4} b^{2} c^{4} + 640 \, a^{5} c^{5}\right)} x^{3} + 3 \, {\left(a b^{9} - 16 \, a^{2} b^{7} c + 101 \, a^{3} b^{5} c^{2} - 196 \, a^{4} b^{3} c^{3} - 64 \, a^{5} b c^{4}\right)} x^{2} - 120 \, {\left(a^{3} c^{6} x^{6} + 3 \, a^{3} b c^{5} x^{5} + 3 \, a^{5} b c^{3} x + a^{6} c^{3} + 3 \, {\left(a^{3} b^{2} c^{4} + a^{4} c^{5}\right)} x^{4} + {\left(a^{3} b^{3} c^{3} + 6 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a^{4} b^{2} c^{3} + a^{5} c^{4}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 3 \, {\left(a^{2} b^{8} - 17 \, a^{3} b^{6} c + 118 \, a^{4} b^{4} c^{2} - 284 \, a^{5} b^{2} c^{3} + 80 \, a^{6} c^{4}\right)} x}{3 \, {\left(a^{3} b^{8} c^{3} - 16 \, a^{4} b^{6} c^{4} + 96 \, a^{5} b^{4} c^{5} - 256 \, a^{6} b^{2} c^{6} + 256 \, a^{7} c^{7} + {\left(b^{8} c^{6} - 16 \, a b^{6} c^{7} + 96 \, a^{2} b^{4} c^{8} - 256 \, a^{3} b^{2} c^{9} + 256 \, a^{4} c^{10}\right)} x^{6} + 3 \, {\left(b^{9} c^{5} - 16 \, a b^{7} c^{6} + 96 \, a^{2} b^{5} c^{7} - 256 \, a^{3} b^{3} c^{8} + 256 \, a^{4} b c^{9}\right)} x^{5} + 3 \, {\left(b^{10} c^{4} - 15 \, a b^{8} c^{5} + 80 \, a^{2} b^{6} c^{6} - 160 \, a^{3} b^{4} c^{7} + 256 \, a^{5} c^{9}\right)} x^{4} + {\left(b^{11} c^{3} - 10 \, a b^{9} c^{4} + 320 \, a^{3} b^{5} c^{6} - 1280 \, a^{4} b^{3} c^{7} + 1536 \, a^{5} b c^{8}\right)} x^{3} + 3 \, {\left(a b^{10} c^{3} - 15 \, a^{2} b^{8} c^{4} + 80 \, a^{3} b^{6} c^{5} - 160 \, a^{4} b^{4} c^{6} + 256 \, a^{6} c^{8}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c^{3} - 16 \, a^{3} b^{7} c^{4} + 96 \, a^{4} b^{5} c^{5} - 256 \, a^{5} b^{3} c^{6} + 256 \, a^{6} b c^{7}\right)} x\right)}}\right]"," ",0,"[-1/3*(a^3*b^7 - 17*a^4*b^5*c + 118*a^5*b^3*c^2 - 264*a^6*b*c^3 + 3*(b^8*c^2 - 16*a*b^6*c^3 + 96*a^2*b^4*c^4 - 236*a^3*b^2*c^5 + 176*a^4*c^6)*x^5 + 3*(b^9*c - 16*a*b^7*c^2 + 96*a^2*b^5*c^3 - 206*a^3*b^3*c^4 + 56*a^4*b*c^5)*x^4 + (b^10 - 11*a*b^8*c + 16*a^2*b^6*c^2 + 334*a^3*b^4*c^3 - 1304*a^4*b^2*c^4 + 640*a^5*c^5)*x^3 + 3*(a*b^9 - 16*a^2*b^7*c + 101*a^3*b^5*c^2 - 196*a^4*b^3*c^3 - 64*a^5*b*c^4)*x^2 + 60*(a^3*c^6*x^6 + 3*a^3*b*c^5*x^5 + 3*a^5*b*c^3*x + a^6*c^3 + 3*(a^3*b^2*c^4 + a^4*c^5)*x^4 + (a^3*b^3*c^3 + 6*a^4*b*c^4)*x^3 + 3*(a^4*b^2*c^3 + a^5*c^4)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 3*(a^2*b^8 - 17*a^3*b^6*c + 118*a^4*b^4*c^2 - 284*a^5*b^2*c^3 + 80*a^6*c^4)*x)/(a^3*b^8*c^3 - 16*a^4*b^6*c^4 + 96*a^5*b^4*c^5 - 256*a^6*b^2*c^6 + 256*a^7*c^7 + (b^8*c^6 - 16*a*b^6*c^7 + 96*a^2*b^4*c^8 - 256*a^3*b^2*c^9 + 256*a^4*c^10)*x^6 + 3*(b^9*c^5 - 16*a*b^7*c^6 + 96*a^2*b^5*c^7 - 256*a^3*b^3*c^8 + 256*a^4*b*c^9)*x^5 + 3*(b^10*c^4 - 15*a*b^8*c^5 + 80*a^2*b^6*c^6 - 160*a^3*b^4*c^7 + 256*a^5*c^9)*x^4 + (b^11*c^3 - 10*a*b^9*c^4 + 320*a^3*b^5*c^6 - 1280*a^4*b^3*c^7 + 1536*a^5*b*c^8)*x^3 + 3*(a*b^10*c^3 - 15*a^2*b^8*c^4 + 80*a^3*b^6*c^5 - 160*a^4*b^4*c^6 + 256*a^6*c^8)*x^2 + 3*(a^2*b^9*c^3 - 16*a^3*b^7*c^4 + 96*a^4*b^5*c^5 - 256*a^5*b^3*c^6 + 256*a^6*b*c^7)*x), -1/3*(a^3*b^7 - 17*a^4*b^5*c + 118*a^5*b^3*c^2 - 264*a^6*b*c^3 + 3*(b^8*c^2 - 16*a*b^6*c^3 + 96*a^2*b^4*c^4 - 236*a^3*b^2*c^5 + 176*a^4*c^6)*x^5 + 3*(b^9*c - 16*a*b^7*c^2 + 96*a^2*b^5*c^3 - 206*a^3*b^3*c^4 + 56*a^4*b*c^5)*x^4 + (b^10 - 11*a*b^8*c + 16*a^2*b^6*c^2 + 334*a^3*b^4*c^3 - 1304*a^4*b^2*c^4 + 640*a^5*c^5)*x^3 + 3*(a*b^9 - 16*a^2*b^7*c + 101*a^3*b^5*c^2 - 196*a^4*b^3*c^3 - 64*a^5*b*c^4)*x^2 - 120*(a^3*c^6*x^6 + 3*a^3*b*c^5*x^5 + 3*a^5*b*c^3*x + a^6*c^3 + 3*(a^3*b^2*c^4 + a^4*c^5)*x^4 + (a^3*b^3*c^3 + 6*a^4*b*c^4)*x^3 + 3*(a^4*b^2*c^3 + a^5*c^4)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 3*(a^2*b^8 - 17*a^3*b^6*c + 118*a^4*b^4*c^2 - 284*a^5*b^2*c^3 + 80*a^6*c^4)*x)/(a^3*b^8*c^3 - 16*a^4*b^6*c^4 + 96*a^5*b^4*c^5 - 256*a^6*b^2*c^6 + 256*a^7*c^7 + (b^8*c^6 - 16*a*b^6*c^7 + 96*a^2*b^4*c^8 - 256*a^3*b^2*c^9 + 256*a^4*c^10)*x^6 + 3*(b^9*c^5 - 16*a*b^7*c^6 + 96*a^2*b^5*c^7 - 256*a^3*b^3*c^8 + 256*a^4*b*c^9)*x^5 + 3*(b^10*c^4 - 15*a*b^8*c^5 + 80*a^2*b^6*c^6 - 160*a^3*b^4*c^7 + 256*a^5*c^9)*x^4 + (b^11*c^3 - 10*a*b^9*c^4 + 320*a^3*b^5*c^6 - 1280*a^4*b^3*c^7 + 1536*a^5*b*c^8)*x^3 + 3*(a*b^10*c^3 - 15*a^2*b^8*c^4 + 80*a^3*b^6*c^5 - 160*a^4*b^4*c^6 + 256*a^6*c^8)*x^2 + 3*(a^2*b^9*c^3 - 16*a^3*b^7*c^4 + 96*a^4*b^5*c^5 - 256*a^5*b^3*c^6 + 256*a^6*b*c^7)*x)]","B",0
2213,1,1594,0,0.436454," ","integrate(x^5/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[-\frac{a^{3} b^{6} - 22 \, a^{4} b^{4} c + 8 \, a^{5} b^{2} c^{2} + 256 \, a^{6} c^{3} - 60 \, {\left(a^{2} b^{3} c^{4} - 4 \, a^{3} b c^{5}\right)} x^{5} + 3 \, {\left(b^{8} c - 16 \, a b^{6} c^{2} + 46 \, a^{2} b^{4} c^{3} - 56 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} x^{4} + {\left(b^{9} - 16 \, a b^{7} c - 14 \, a^{2} b^{5} c^{2} + 24 \, a^{3} b^{3} c^{3} + 896 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a b^{8} - 21 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} + 64 \, a^{4} b^{2} c^{3} + 256 \, a^{5} c^{4}\right)} x^{2} + 60 \, {\left(a^{2} b c^{5} x^{6} + 3 \, a^{2} b^{2} c^{4} x^{5} + 3 \, a^{4} b^{2} c^{2} x + a^{5} b c^{2} + 3 \, {\left(a^{2} b^{3} c^{3} + a^{3} b c^{4}\right)} x^{4} + {\left(a^{2} b^{4} c^{2} + 6 \, a^{3} b^{2} c^{3}\right)} x^{3} + 3 \, {\left(a^{3} b^{3} c^{2} + a^{4} b c^{3}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 3 \, {\left(a^{2} b^{7} - 22 \, a^{3} b^{5} c + 28 \, a^{4} b^{3} c^{2} + 176 \, a^{5} b c^{3}\right)} x}{6 \, {\left(a^{3} b^{8} c^{2} - 16 \, a^{4} b^{6} c^{3} + 96 \, a^{5} b^{4} c^{4} - 256 \, a^{6} b^{2} c^{5} + 256 \, a^{7} c^{6} + {\left(b^{8} c^{5} - 16 \, a b^{6} c^{6} + 96 \, a^{2} b^{4} c^{7} - 256 \, a^{3} b^{2} c^{8} + 256 \, a^{4} c^{9}\right)} x^{6} + 3 \, {\left(b^{9} c^{4} - 16 \, a b^{7} c^{5} + 96 \, a^{2} b^{5} c^{6} - 256 \, a^{3} b^{3} c^{7} + 256 \, a^{4} b c^{8}\right)} x^{5} + 3 \, {\left(b^{10} c^{3} - 15 \, a b^{8} c^{4} + 80 \, a^{2} b^{6} c^{5} - 160 \, a^{3} b^{4} c^{6} + 256 \, a^{5} c^{8}\right)} x^{4} + {\left(b^{11} c^{2} - 10 \, a b^{9} c^{3} + 320 \, a^{3} b^{5} c^{5} - 1280 \, a^{4} b^{3} c^{6} + 1536 \, a^{5} b c^{7}\right)} x^{3} + 3 \, {\left(a b^{10} c^{2} - 15 \, a^{2} b^{8} c^{3} + 80 \, a^{3} b^{6} c^{4} - 160 \, a^{4} b^{4} c^{5} + 256 \, a^{6} c^{7}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c^{2} - 16 \, a^{3} b^{7} c^{3} + 96 \, a^{4} b^{5} c^{4} - 256 \, a^{5} b^{3} c^{5} + 256 \, a^{6} b c^{6}\right)} x\right)}}, -\frac{a^{3} b^{6} - 22 \, a^{4} b^{4} c + 8 \, a^{5} b^{2} c^{2} + 256 \, a^{6} c^{3} - 60 \, {\left(a^{2} b^{3} c^{4} - 4 \, a^{3} b c^{5}\right)} x^{5} + 3 \, {\left(b^{8} c - 16 \, a b^{6} c^{2} + 46 \, a^{2} b^{4} c^{3} - 56 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} x^{4} + {\left(b^{9} - 16 \, a b^{7} c - 14 \, a^{2} b^{5} c^{2} + 24 \, a^{3} b^{3} c^{3} + 896 \, a^{4} b c^{4}\right)} x^{3} + 3 \, {\left(a b^{8} - 21 \, a^{2} b^{6} c + 36 \, a^{3} b^{4} c^{2} + 64 \, a^{4} b^{2} c^{3} + 256 \, a^{5} c^{4}\right)} x^{2} + 120 \, {\left(a^{2} b c^{5} x^{6} + 3 \, a^{2} b^{2} c^{4} x^{5} + 3 \, a^{4} b^{2} c^{2} x + a^{5} b c^{2} + 3 \, {\left(a^{2} b^{3} c^{3} + a^{3} b c^{4}\right)} x^{4} + {\left(a^{2} b^{4} c^{2} + 6 \, a^{3} b^{2} c^{3}\right)} x^{3} + 3 \, {\left(a^{3} b^{3} c^{2} + a^{4} b c^{3}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 3 \, {\left(a^{2} b^{7} - 22 \, a^{3} b^{5} c + 28 \, a^{4} b^{3} c^{2} + 176 \, a^{5} b c^{3}\right)} x}{6 \, {\left(a^{3} b^{8} c^{2} - 16 \, a^{4} b^{6} c^{3} + 96 \, a^{5} b^{4} c^{4} - 256 \, a^{6} b^{2} c^{5} + 256 \, a^{7} c^{6} + {\left(b^{8} c^{5} - 16 \, a b^{6} c^{6} + 96 \, a^{2} b^{4} c^{7} - 256 \, a^{3} b^{2} c^{8} + 256 \, a^{4} c^{9}\right)} x^{6} + 3 \, {\left(b^{9} c^{4} - 16 \, a b^{7} c^{5} + 96 \, a^{2} b^{5} c^{6} - 256 \, a^{3} b^{3} c^{7} + 256 \, a^{4} b c^{8}\right)} x^{5} + 3 \, {\left(b^{10} c^{3} - 15 \, a b^{8} c^{4} + 80 \, a^{2} b^{6} c^{5} - 160 \, a^{3} b^{4} c^{6} + 256 \, a^{5} c^{8}\right)} x^{4} + {\left(b^{11} c^{2} - 10 \, a b^{9} c^{3} + 320 \, a^{3} b^{5} c^{5} - 1280 \, a^{4} b^{3} c^{6} + 1536 \, a^{5} b c^{7}\right)} x^{3} + 3 \, {\left(a b^{10} c^{2} - 15 \, a^{2} b^{8} c^{3} + 80 \, a^{3} b^{6} c^{4} - 160 \, a^{4} b^{4} c^{5} + 256 \, a^{6} c^{7}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c^{2} - 16 \, a^{3} b^{7} c^{3} + 96 \, a^{4} b^{5} c^{4} - 256 \, a^{5} b^{3} c^{5} + 256 \, a^{6} b c^{6}\right)} x\right)}}\right]"," ",0,"[-1/6*(a^3*b^6 - 22*a^4*b^4*c + 8*a^5*b^2*c^2 + 256*a^6*c^3 - 60*(a^2*b^3*c^4 - 4*a^3*b*c^5)*x^5 + 3*(b^8*c - 16*a*b^6*c^2 + 46*a^2*b^4*c^3 - 56*a^3*b^2*c^4 + 256*a^4*c^5)*x^4 + (b^9 - 16*a*b^7*c - 14*a^2*b^5*c^2 + 24*a^3*b^3*c^3 + 896*a^4*b*c^4)*x^3 + 3*(a*b^8 - 21*a^2*b^6*c + 36*a^3*b^4*c^2 + 64*a^4*b^2*c^3 + 256*a^5*c^4)*x^2 + 60*(a^2*b*c^5*x^6 + 3*a^2*b^2*c^4*x^5 + 3*a^4*b^2*c^2*x + a^5*b*c^2 + 3*(a^2*b^3*c^3 + a^3*b*c^4)*x^4 + (a^2*b^4*c^2 + 6*a^3*b^2*c^3)*x^3 + 3*(a^3*b^3*c^2 + a^4*b*c^3)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 3*(a^2*b^7 - 22*a^3*b^5*c + 28*a^4*b^3*c^2 + 176*a^5*b*c^3)*x)/(a^3*b^8*c^2 - 16*a^4*b^6*c^3 + 96*a^5*b^4*c^4 - 256*a^6*b^2*c^5 + 256*a^7*c^6 + (b^8*c^5 - 16*a*b^6*c^6 + 96*a^2*b^4*c^7 - 256*a^3*b^2*c^8 + 256*a^4*c^9)*x^6 + 3*(b^9*c^4 - 16*a*b^7*c^5 + 96*a^2*b^5*c^6 - 256*a^3*b^3*c^7 + 256*a^4*b*c^8)*x^5 + 3*(b^10*c^3 - 15*a*b^8*c^4 + 80*a^2*b^6*c^5 - 160*a^3*b^4*c^6 + 256*a^5*c^8)*x^4 + (b^11*c^2 - 10*a*b^9*c^3 + 320*a^3*b^5*c^5 - 1280*a^4*b^3*c^6 + 1536*a^5*b*c^7)*x^3 + 3*(a*b^10*c^2 - 15*a^2*b^8*c^3 + 80*a^3*b^6*c^4 - 160*a^4*b^4*c^5 + 256*a^6*c^7)*x^2 + 3*(a^2*b^9*c^2 - 16*a^3*b^7*c^3 + 96*a^4*b^5*c^4 - 256*a^5*b^3*c^5 + 256*a^6*b*c^6)*x), -1/6*(a^3*b^6 - 22*a^4*b^4*c + 8*a^5*b^2*c^2 + 256*a^6*c^3 - 60*(a^2*b^3*c^4 - 4*a^3*b*c^5)*x^5 + 3*(b^8*c - 16*a*b^6*c^2 + 46*a^2*b^4*c^3 - 56*a^3*b^2*c^4 + 256*a^4*c^5)*x^4 + (b^9 - 16*a*b^7*c - 14*a^2*b^5*c^2 + 24*a^3*b^3*c^3 + 896*a^4*b*c^4)*x^3 + 3*(a*b^8 - 21*a^2*b^6*c + 36*a^3*b^4*c^2 + 64*a^4*b^2*c^3 + 256*a^5*c^4)*x^2 + 120*(a^2*b*c^5*x^6 + 3*a^2*b^2*c^4*x^5 + 3*a^4*b^2*c^2*x + a^5*b*c^2 + 3*(a^2*b^3*c^3 + a^3*b*c^4)*x^4 + (a^2*b^4*c^2 + 6*a^3*b^2*c^3)*x^3 + 3*(a^3*b^3*c^2 + a^4*b*c^3)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 3*(a^2*b^7 - 22*a^3*b^5*c + 28*a^4*b^3*c^2 + 176*a^5*b*c^3)*x)/(a^3*b^8*c^2 - 16*a^4*b^6*c^3 + 96*a^5*b^4*c^4 - 256*a^6*b^2*c^5 + 256*a^7*c^6 + (b^8*c^5 - 16*a*b^6*c^6 + 96*a^2*b^4*c^7 - 256*a^3*b^2*c^8 + 256*a^4*c^9)*x^6 + 3*(b^9*c^4 - 16*a*b^7*c^5 + 96*a^2*b^5*c^6 - 256*a^3*b^3*c^7 + 256*a^4*b*c^8)*x^5 + 3*(b^10*c^3 - 15*a*b^8*c^4 + 80*a^2*b^6*c^5 - 160*a^3*b^4*c^6 + 256*a^5*c^8)*x^4 + (b^11*c^2 - 10*a*b^9*c^3 + 320*a^3*b^5*c^5 - 1280*a^4*b^3*c^6 + 1536*a^5*b*c^7)*x^3 + 3*(a*b^10*c^2 - 15*a^2*b^8*c^3 + 80*a^3*b^6*c^4 - 160*a^4*b^4*c^5 + 256*a^6*c^7)*x^2 + 3*(a^2*b^9*c^2 - 16*a^3*b^7*c^3 + 96*a^4*b^5*c^4 - 256*a^5*b^3*c^5 + 256*a^6*b*c^6)*x)]","B",0
2214,1,4631,0,0.495300," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(5 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 10 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + 6 \, {\left(b^{4} c^{4} - 3 \, a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} d^{2} e^{2} - {\left(b^{5} c^{3} + 2 \, a b^{3} c^{4} - 24 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a b^{4} c^{3} - 3 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}\right)} x^{5} + {\left(b^{7} c - 17 \, a b^{5} c^{2} + 118 \, a^{2} b^{3} c^{3} - 264 \, a^{3} b c^{4}\right)} d^{4} + 2 \, {\left(a b^{6} c - 22 \, a^{2} b^{4} c^{2} + 8 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} d^{3} e + 6 \, {\left(a^{2} b^{5} c + 22 \, a^{3} b^{3} c^{2} - 104 \, a^{4} b c^{3}\right)} d^{2} e^{2} - 4 \, {\left(11 \, a^{3} b^{4} c - 28 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d e^{3} + {\left(a^{3} b^{5} + 22 \, a^{4} b^{3} c - 104 \, a^{5} b c^{2}\right)} e^{4} + 30 \, {\left(5 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{4} - 10 \, {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5}\right)} d^{3} e + 6 \, {\left(b^{5} c^{3} - 3 \, a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{2} e^{2} - {\left(b^{6} c^{2} + 2 \, a b^{4} c^{3} - 24 \, a^{2} b^{2} c^{4}\right)} d e^{3} + {\left(a b^{5} c^{2} - 3 \, a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} e^{4}\right)} x^{4} + {\left(10 \, {\left(11 \, b^{4} c^{4} - 28 \, a b^{2} c^{5} - 64 \, a^{2} c^{6}\right)} d^{4} - 20 \, {\left(11 \, b^{5} c^{3} - 28 \, a b^{3} c^{4} - 64 \, a^{2} b c^{5}\right)} d^{3} e + 12 \, {\left(11 \, b^{6} c^{2} - 17 \, a b^{4} c^{3} - 92 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e^{2} - 2 \, {\left(11 \, b^{7} c + 38 \, a b^{5} c^{2} - 232 \, a^{2} b^{3} c^{3} - 384 \, a^{3} b c^{4}\right)} d e^{3} + {\left(b^{8} + 6 \, a b^{6} c + 62 \, a^{2} b^{4} c^{2} - 440 \, a^{3} b^{2} c^{3} + 128 \, a^{4} c^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(5 \, {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} - 64 \, a^{2} b c^{5}\right)} d^{4} - 10 \, {\left(b^{6} c^{2} + 12 \, a b^{4} c^{3} - 64 \, a^{2} b^{2} c^{4}\right)} d^{3} e + 6 \, {\left(b^{7} c + 13 \, a b^{5} c^{2} - 52 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2} e^{2} - 2 \, {\left(17 \, a b^{6} c - 44 \, a^{2} b^{4} c^{2} - 64 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d e^{3} + {\left(a b^{7} + 13 \, a^{2} b^{5} c - 52 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} e^{4}\right)} x^{2} + 12 \, {\left(5 \, a^{3} c^{4} d^{4} - 10 \, a^{3} b c^{3} d^{3} e + {\left(5 \, c^{7} d^{4} - 10 \, b c^{6} d^{3} e + 6 \, {\left(b^{2} c^{5} + a c^{6}\right)} d^{2} e^{2} - {\left(b^{3} c^{4} + 6 \, a b c^{5}\right)} d e^{3} + {\left(a b^{2} c^{4} + a^{2} c^{5}\right)} e^{4}\right)} x^{6} + 3 \, {\left(5 \, b c^{6} d^{4} - 10 \, b^{2} c^{5} d^{3} e + 6 \, {\left(b^{3} c^{4} + a b c^{5}\right)} d^{2} e^{2} - {\left(b^{4} c^{3} + 6 \, a b^{2} c^{4}\right)} d e^{3} + {\left(a b^{3} c^{3} + a^{2} b c^{4}\right)} e^{4}\right)} x^{5} + 6 \, {\left(a^{3} b^{2} c^{2} + a^{4} c^{3}\right)} d^{2} e^{2} - {\left(a^{3} b^{3} c + 6 \, a^{4} b c^{2}\right)} d e^{3} + {\left(a^{4} b^{2} c + a^{5} c^{2}\right)} e^{4} + 3 \, {\left(5 \, {\left(b^{2} c^{5} + a c^{6}\right)} d^{4} - 10 \, {\left(b^{3} c^{4} + a b c^{5}\right)} d^{3} e + 6 \, {\left(b^{4} c^{3} + 2 \, a b^{2} c^{4} + a^{2} c^{5}\right)} d^{2} e^{2} - {\left(b^{5} c^{2} + 7 \, a b^{3} c^{3} + 6 \, a^{2} b c^{4}\right)} d e^{3} + {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} e^{4}\right)} x^{4} + {\left(5 \, {\left(b^{3} c^{4} + 6 \, a b c^{5}\right)} d^{4} - 10 \, {\left(b^{4} c^{3} + 6 \, a b^{2} c^{4}\right)} d^{3} e + 6 \, {\left(b^{5} c^{2} + 7 \, a b^{3} c^{3} + 6 \, a^{2} b c^{4}\right)} d^{2} e^{2} - {\left(b^{6} c + 12 \, a b^{4} c^{2} + 36 \, a^{2} b^{2} c^{3}\right)} d e^{3} + {\left(a b^{5} c + 7 \, a^{2} b^{3} c^{2} + 6 \, a^{3} b c^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(5 \, {\left(a b^{2} c^{4} + a^{2} c^{5}\right)} d^{4} - 10 \, {\left(a b^{3} c^{3} + a^{2} b c^{4}\right)} d^{3} e + 6 \, {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} d^{2} e^{2} - {\left(a b^{5} c + 7 \, a^{2} b^{3} c^{2} + 6 \, a^{3} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{4} c + 2 \, a^{3} b^{2} c^{2} + a^{4} c^{3}\right)} e^{4}\right)} x^{2} + 3 \, {\left(5 \, a^{2} b c^{4} d^{4} - 10 \, a^{2} b^{2} c^{3} d^{3} e + 6 \, {\left(a^{2} b^{3} c^{2} + a^{3} b c^{3}\right)} d^{2} e^{2} - {\left(a^{2} b^{4} c + 6 \, a^{3} b^{2} c^{2}\right)} d e^{3} + {\left(a^{3} b^{3} c + a^{4} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 3 \, {\left({\left(b^{6} c^{2} - 22 \, a b^{4} c^{3} + 28 \, a^{2} b^{2} c^{4} + 176 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 22 \, a b^{5} c^{2} + 28 \, a^{2} b^{3} c^{3} + 176 \, a^{3} b c^{4}\right)} d^{3} e - 6 \, {\left(a b^{6} c + 18 \, a^{2} b^{4} c^{2} - 92 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{2} e^{2} + 40 \, {\left(a^{2} b^{5} c - 3 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{3} - {\left(a^{2} b^{6} + 18 \, a^{3} b^{4} c - 92 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} e^{4}\right)} x}{3 \, {\left(a^{3} b^{8} c - 16 \, a^{4} b^{6} c^{2} + 96 \, a^{5} b^{4} c^{3} - 256 \, a^{6} b^{2} c^{4} + 256 \, a^{7} c^{5} + {\left(b^{8} c^{4} - 16 \, a b^{6} c^{5} + 96 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} + 256 \, a^{4} c^{8}\right)} x^{6} + 3 \, {\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{5} + 3 \, {\left(b^{10} c^{2} - 15 \, a b^{8} c^{3} + 80 \, a^{2} b^{6} c^{4} - 160 \, a^{3} b^{4} c^{5} + 256 \, a^{5} c^{7}\right)} x^{4} + {\left(b^{11} c - 10 \, a b^{9} c^{2} + 320 \, a^{3} b^{5} c^{4} - 1280 \, a^{4} b^{3} c^{5} + 1536 \, a^{5} b c^{6}\right)} x^{3} + 3 \, {\left(a b^{10} c - 15 \, a^{2} b^{8} c^{2} + 80 \, a^{3} b^{6} c^{3} - 160 \, a^{4} b^{4} c^{4} + 256 \, a^{6} c^{6}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c - 16 \, a^{3} b^{7} c^{2} + 96 \, a^{4} b^{5} c^{3} - 256 \, a^{5} b^{3} c^{4} + 256 \, a^{6} b c^{5}\right)} x\right)}}, -\frac{12 \, {\left(5 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{4} - 10 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{3} e + 6 \, {\left(b^{4} c^{4} - 3 \, a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} d^{2} e^{2} - {\left(b^{5} c^{3} + 2 \, a b^{3} c^{4} - 24 \, a^{2} b c^{5}\right)} d e^{3} + {\left(a b^{4} c^{3} - 3 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} e^{4}\right)} x^{5} + {\left(b^{7} c - 17 \, a b^{5} c^{2} + 118 \, a^{2} b^{3} c^{3} - 264 \, a^{3} b c^{4}\right)} d^{4} + 2 \, {\left(a b^{6} c - 22 \, a^{2} b^{4} c^{2} + 8 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} d^{3} e + 6 \, {\left(a^{2} b^{5} c + 22 \, a^{3} b^{3} c^{2} - 104 \, a^{4} b c^{3}\right)} d^{2} e^{2} - 4 \, {\left(11 \, a^{3} b^{4} c - 28 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d e^{3} + {\left(a^{3} b^{5} + 22 \, a^{4} b^{3} c - 104 \, a^{5} b c^{2}\right)} e^{4} + 30 \, {\left(5 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{4} - 10 \, {\left(b^{4} c^{4} - 4 \, a b^{2} c^{5}\right)} d^{3} e + 6 \, {\left(b^{5} c^{3} - 3 \, a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{2} e^{2} - {\left(b^{6} c^{2} + 2 \, a b^{4} c^{3} - 24 \, a^{2} b^{2} c^{4}\right)} d e^{3} + {\left(a b^{5} c^{2} - 3 \, a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} e^{4}\right)} x^{4} + {\left(10 \, {\left(11 \, b^{4} c^{4} - 28 \, a b^{2} c^{5} - 64 \, a^{2} c^{6}\right)} d^{4} - 20 \, {\left(11 \, b^{5} c^{3} - 28 \, a b^{3} c^{4} - 64 \, a^{2} b c^{5}\right)} d^{3} e + 12 \, {\left(11 \, b^{6} c^{2} - 17 \, a b^{4} c^{3} - 92 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e^{2} - 2 \, {\left(11 \, b^{7} c + 38 \, a b^{5} c^{2} - 232 \, a^{2} b^{3} c^{3} - 384 \, a^{3} b c^{4}\right)} d e^{3} + {\left(b^{8} + 6 \, a b^{6} c + 62 \, a^{2} b^{4} c^{2} - 440 \, a^{3} b^{2} c^{3} + 128 \, a^{4} c^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(5 \, {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} - 64 \, a^{2} b c^{5}\right)} d^{4} - 10 \, {\left(b^{6} c^{2} + 12 \, a b^{4} c^{3} - 64 \, a^{2} b^{2} c^{4}\right)} d^{3} e + 6 \, {\left(b^{7} c + 13 \, a b^{5} c^{2} - 52 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2} e^{2} - 2 \, {\left(17 \, a b^{6} c - 44 \, a^{2} b^{4} c^{2} - 64 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d e^{3} + {\left(a b^{7} + 13 \, a^{2} b^{5} c - 52 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} e^{4}\right)} x^{2} - 24 \, {\left(5 \, a^{3} c^{4} d^{4} - 10 \, a^{3} b c^{3} d^{3} e + {\left(5 \, c^{7} d^{4} - 10 \, b c^{6} d^{3} e + 6 \, {\left(b^{2} c^{5} + a c^{6}\right)} d^{2} e^{2} - {\left(b^{3} c^{4} + 6 \, a b c^{5}\right)} d e^{3} + {\left(a b^{2} c^{4} + a^{2} c^{5}\right)} e^{4}\right)} x^{6} + 3 \, {\left(5 \, b c^{6} d^{4} - 10 \, b^{2} c^{5} d^{3} e + 6 \, {\left(b^{3} c^{4} + a b c^{5}\right)} d^{2} e^{2} - {\left(b^{4} c^{3} + 6 \, a b^{2} c^{4}\right)} d e^{3} + {\left(a b^{3} c^{3} + a^{2} b c^{4}\right)} e^{4}\right)} x^{5} + 6 \, {\left(a^{3} b^{2} c^{2} + a^{4} c^{3}\right)} d^{2} e^{2} - {\left(a^{3} b^{3} c + 6 \, a^{4} b c^{2}\right)} d e^{3} + {\left(a^{4} b^{2} c + a^{5} c^{2}\right)} e^{4} + 3 \, {\left(5 \, {\left(b^{2} c^{5} + a c^{6}\right)} d^{4} - 10 \, {\left(b^{3} c^{4} + a b c^{5}\right)} d^{3} e + 6 \, {\left(b^{4} c^{3} + 2 \, a b^{2} c^{4} + a^{2} c^{5}\right)} d^{2} e^{2} - {\left(b^{5} c^{2} + 7 \, a b^{3} c^{3} + 6 \, a^{2} b c^{4}\right)} d e^{3} + {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} e^{4}\right)} x^{4} + {\left(5 \, {\left(b^{3} c^{4} + 6 \, a b c^{5}\right)} d^{4} - 10 \, {\left(b^{4} c^{3} + 6 \, a b^{2} c^{4}\right)} d^{3} e + 6 \, {\left(b^{5} c^{2} + 7 \, a b^{3} c^{3} + 6 \, a^{2} b c^{4}\right)} d^{2} e^{2} - {\left(b^{6} c + 12 \, a b^{4} c^{2} + 36 \, a^{2} b^{2} c^{3}\right)} d e^{3} + {\left(a b^{5} c + 7 \, a^{2} b^{3} c^{2} + 6 \, a^{3} b c^{3}\right)} e^{4}\right)} x^{3} + 3 \, {\left(5 \, {\left(a b^{2} c^{4} + a^{2} c^{5}\right)} d^{4} - 10 \, {\left(a b^{3} c^{3} + a^{2} b c^{4}\right)} d^{3} e + 6 \, {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} + a^{3} c^{4}\right)} d^{2} e^{2} - {\left(a b^{5} c + 7 \, a^{2} b^{3} c^{2} + 6 \, a^{3} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{4} c + 2 \, a^{3} b^{2} c^{2} + a^{4} c^{3}\right)} e^{4}\right)} x^{2} + 3 \, {\left(5 \, a^{2} b c^{4} d^{4} - 10 \, a^{2} b^{2} c^{3} d^{3} e + 6 \, {\left(a^{2} b^{3} c^{2} + a^{3} b c^{3}\right)} d^{2} e^{2} - {\left(a^{2} b^{4} c + 6 \, a^{3} b^{2} c^{2}\right)} d e^{3} + {\left(a^{3} b^{3} c + a^{4} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 3 \, {\left({\left(b^{6} c^{2} - 22 \, a b^{4} c^{3} + 28 \, a^{2} b^{2} c^{4} + 176 \, a^{3} c^{5}\right)} d^{4} - 2 \, {\left(b^{7} c - 22 \, a b^{5} c^{2} + 28 \, a^{2} b^{3} c^{3} + 176 \, a^{3} b c^{4}\right)} d^{3} e - 6 \, {\left(a b^{6} c + 18 \, a^{2} b^{4} c^{2} - 92 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{2} e^{2} + 40 \, {\left(a^{2} b^{5} c - 3 \, a^{3} b^{3} c^{2} - 4 \, a^{4} b c^{3}\right)} d e^{3} - {\left(a^{2} b^{6} + 18 \, a^{3} b^{4} c - 92 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} e^{4}\right)} x}{3 \, {\left(a^{3} b^{8} c - 16 \, a^{4} b^{6} c^{2} + 96 \, a^{5} b^{4} c^{3} - 256 \, a^{6} b^{2} c^{4} + 256 \, a^{7} c^{5} + {\left(b^{8} c^{4} - 16 \, a b^{6} c^{5} + 96 \, a^{2} b^{4} c^{6} - 256 \, a^{3} b^{2} c^{7} + 256 \, a^{4} c^{8}\right)} x^{6} + 3 \, {\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{5} + 3 \, {\left(b^{10} c^{2} - 15 \, a b^{8} c^{3} + 80 \, a^{2} b^{6} c^{4} - 160 \, a^{3} b^{4} c^{5} + 256 \, a^{5} c^{7}\right)} x^{4} + {\left(b^{11} c - 10 \, a b^{9} c^{2} + 320 \, a^{3} b^{5} c^{4} - 1280 \, a^{4} b^{3} c^{5} + 1536 \, a^{5} b c^{6}\right)} x^{3} + 3 \, {\left(a b^{10} c - 15 \, a^{2} b^{8} c^{2} + 80 \, a^{3} b^{6} c^{3} - 160 \, a^{4} b^{4} c^{4} + 256 \, a^{6} c^{6}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c - 16 \, a^{3} b^{7} c^{2} + 96 \, a^{4} b^{5} c^{3} - 256 \, a^{5} b^{3} c^{4} + 256 \, a^{6} b c^{5}\right)} x\right)}}\right]"," ",0,"[-1/3*(12*(5*(b^2*c^6 - 4*a*c^7)*d^4 - 10*(b^3*c^5 - 4*a*b*c^6)*d^3*e + 6*(b^4*c^4 - 3*a*b^2*c^5 - 4*a^2*c^6)*d^2*e^2 - (b^5*c^3 + 2*a*b^3*c^4 - 24*a^2*b*c^5)*d*e^3 + (a*b^4*c^3 - 3*a^2*b^2*c^4 - 4*a^3*c^5)*e^4)*x^5 + (b^7*c - 17*a*b^5*c^2 + 118*a^2*b^3*c^3 - 264*a^3*b*c^4)*d^4 + 2*(a*b^6*c - 22*a^2*b^4*c^2 + 8*a^3*b^2*c^3 + 256*a^4*c^4)*d^3*e + 6*(a^2*b^5*c + 22*a^3*b^3*c^2 - 104*a^4*b*c^3)*d^2*e^2 - 4*(11*a^3*b^4*c - 28*a^4*b^2*c^2 - 64*a^5*c^3)*d*e^3 + (a^3*b^5 + 22*a^4*b^3*c - 104*a^5*b*c^2)*e^4 + 30*(5*(b^3*c^5 - 4*a*b*c^6)*d^4 - 10*(b^4*c^4 - 4*a*b^2*c^5)*d^3*e + 6*(b^5*c^3 - 3*a*b^3*c^4 - 4*a^2*b*c^5)*d^2*e^2 - (b^6*c^2 + 2*a*b^4*c^3 - 24*a^2*b^2*c^4)*d*e^3 + (a*b^5*c^2 - 3*a^2*b^3*c^3 - 4*a^3*b*c^4)*e^4)*x^4 + (10*(11*b^4*c^4 - 28*a*b^2*c^5 - 64*a^2*c^6)*d^4 - 20*(11*b^5*c^3 - 28*a*b^3*c^4 - 64*a^2*b*c^5)*d^3*e + 12*(11*b^6*c^2 - 17*a*b^4*c^3 - 92*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e^2 - 2*(11*b^7*c + 38*a*b^5*c^2 - 232*a^2*b^3*c^3 - 384*a^3*b*c^4)*d*e^3 + (b^8 + 6*a*b^6*c + 62*a^2*b^4*c^2 - 440*a^3*b^2*c^3 + 128*a^4*c^4)*e^4)*x^3 + 3*(5*(b^5*c^3 + 12*a*b^3*c^4 - 64*a^2*b*c^5)*d^4 - 10*(b^6*c^2 + 12*a*b^4*c^3 - 64*a^2*b^2*c^4)*d^3*e + 6*(b^7*c + 13*a*b^5*c^2 - 52*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2*e^2 - 2*(17*a*b^6*c - 44*a^2*b^4*c^2 - 64*a^3*b^2*c^3 - 128*a^4*c^4)*d*e^3 + (a*b^7 + 13*a^2*b^5*c - 52*a^3*b^3*c^2 - 64*a^4*b*c^3)*e^4)*x^2 + 12*(5*a^3*c^4*d^4 - 10*a^3*b*c^3*d^3*e + (5*c^7*d^4 - 10*b*c^6*d^3*e + 6*(b^2*c^5 + a*c^6)*d^2*e^2 - (b^3*c^4 + 6*a*b*c^5)*d*e^3 + (a*b^2*c^4 + a^2*c^5)*e^4)*x^6 + 3*(5*b*c^6*d^4 - 10*b^2*c^5*d^3*e + 6*(b^3*c^4 + a*b*c^5)*d^2*e^2 - (b^4*c^3 + 6*a*b^2*c^4)*d*e^3 + (a*b^3*c^3 + a^2*b*c^4)*e^4)*x^5 + 6*(a^3*b^2*c^2 + a^4*c^3)*d^2*e^2 - (a^3*b^3*c + 6*a^4*b*c^2)*d*e^3 + (a^4*b^2*c + a^5*c^2)*e^4 + 3*(5*(b^2*c^5 + a*c^6)*d^4 - 10*(b^3*c^4 + a*b*c^5)*d^3*e + 6*(b^4*c^3 + 2*a*b^2*c^4 + a^2*c^5)*d^2*e^2 - (b^5*c^2 + 7*a*b^3*c^3 + 6*a^2*b*c^4)*d*e^3 + (a*b^4*c^2 + 2*a^2*b^2*c^3 + a^3*c^4)*e^4)*x^4 + (5*(b^3*c^4 + 6*a*b*c^5)*d^4 - 10*(b^4*c^3 + 6*a*b^2*c^4)*d^3*e + 6*(b^5*c^2 + 7*a*b^3*c^3 + 6*a^2*b*c^4)*d^2*e^2 - (b^6*c + 12*a*b^4*c^2 + 36*a^2*b^2*c^3)*d*e^3 + (a*b^5*c + 7*a^2*b^3*c^2 + 6*a^3*b*c^3)*e^4)*x^3 + 3*(5*(a*b^2*c^4 + a^2*c^5)*d^4 - 10*(a*b^3*c^3 + a^2*b*c^4)*d^3*e + 6*(a*b^4*c^2 + 2*a^2*b^2*c^3 + a^3*c^4)*d^2*e^2 - (a*b^5*c + 7*a^2*b^3*c^2 + 6*a^3*b*c^3)*d*e^3 + (a^2*b^4*c + 2*a^3*b^2*c^2 + a^4*c^3)*e^4)*x^2 + 3*(5*a^2*b*c^4*d^4 - 10*a^2*b^2*c^3*d^3*e + 6*(a^2*b^3*c^2 + a^3*b*c^3)*d^2*e^2 - (a^2*b^4*c + 6*a^3*b^2*c^2)*d*e^3 + (a^3*b^3*c + a^4*b*c^2)*e^4)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 3*((b^6*c^2 - 22*a*b^4*c^3 + 28*a^2*b^2*c^4 + 176*a^3*c^5)*d^4 - 2*(b^7*c - 22*a*b^5*c^2 + 28*a^2*b^3*c^3 + 176*a^3*b*c^4)*d^3*e - 6*(a*b^6*c + 18*a^2*b^4*c^2 - 92*a^3*b^2*c^3 + 16*a^4*c^4)*d^2*e^2 + 40*(a^2*b^5*c - 3*a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^3 - (a^2*b^6 + 18*a^3*b^4*c - 92*a^4*b^2*c^2 + 16*a^5*c^3)*e^4)*x)/(a^3*b^8*c - 16*a^4*b^6*c^2 + 96*a^5*b^4*c^3 - 256*a^6*b^2*c^4 + 256*a^7*c^5 + (b^8*c^4 - 16*a*b^6*c^5 + 96*a^2*b^4*c^6 - 256*a^3*b^2*c^7 + 256*a^4*c^8)*x^6 + 3*(b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^5 + 3*(b^10*c^2 - 15*a*b^8*c^3 + 80*a^2*b^6*c^4 - 160*a^3*b^4*c^5 + 256*a^5*c^7)*x^4 + (b^11*c - 10*a*b^9*c^2 + 320*a^3*b^5*c^4 - 1280*a^4*b^3*c^5 + 1536*a^5*b*c^6)*x^3 + 3*(a*b^10*c - 15*a^2*b^8*c^2 + 80*a^3*b^6*c^3 - 160*a^4*b^4*c^4 + 256*a^6*c^6)*x^2 + 3*(a^2*b^9*c - 16*a^3*b^7*c^2 + 96*a^4*b^5*c^3 - 256*a^5*b^3*c^4 + 256*a^6*b*c^5)*x), -1/3*(12*(5*(b^2*c^6 - 4*a*c^7)*d^4 - 10*(b^3*c^5 - 4*a*b*c^6)*d^3*e + 6*(b^4*c^4 - 3*a*b^2*c^5 - 4*a^2*c^6)*d^2*e^2 - (b^5*c^3 + 2*a*b^3*c^4 - 24*a^2*b*c^5)*d*e^3 + (a*b^4*c^3 - 3*a^2*b^2*c^4 - 4*a^3*c^5)*e^4)*x^5 + (b^7*c - 17*a*b^5*c^2 + 118*a^2*b^3*c^3 - 264*a^3*b*c^4)*d^4 + 2*(a*b^6*c - 22*a^2*b^4*c^2 + 8*a^3*b^2*c^3 + 256*a^4*c^4)*d^3*e + 6*(a^2*b^5*c + 22*a^3*b^3*c^2 - 104*a^4*b*c^3)*d^2*e^2 - 4*(11*a^3*b^4*c - 28*a^4*b^2*c^2 - 64*a^5*c^3)*d*e^3 + (a^3*b^5 + 22*a^4*b^3*c - 104*a^5*b*c^2)*e^4 + 30*(5*(b^3*c^5 - 4*a*b*c^6)*d^4 - 10*(b^4*c^4 - 4*a*b^2*c^5)*d^3*e + 6*(b^5*c^3 - 3*a*b^3*c^4 - 4*a^2*b*c^5)*d^2*e^2 - (b^6*c^2 + 2*a*b^4*c^3 - 24*a^2*b^2*c^4)*d*e^3 + (a*b^5*c^2 - 3*a^2*b^3*c^3 - 4*a^3*b*c^4)*e^4)*x^4 + (10*(11*b^4*c^4 - 28*a*b^2*c^5 - 64*a^2*c^6)*d^4 - 20*(11*b^5*c^3 - 28*a*b^3*c^4 - 64*a^2*b*c^5)*d^3*e + 12*(11*b^6*c^2 - 17*a*b^4*c^3 - 92*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e^2 - 2*(11*b^7*c + 38*a*b^5*c^2 - 232*a^2*b^3*c^3 - 384*a^3*b*c^4)*d*e^3 + (b^8 + 6*a*b^6*c + 62*a^2*b^4*c^2 - 440*a^3*b^2*c^3 + 128*a^4*c^4)*e^4)*x^3 + 3*(5*(b^5*c^3 + 12*a*b^3*c^4 - 64*a^2*b*c^5)*d^4 - 10*(b^6*c^2 + 12*a*b^4*c^3 - 64*a^2*b^2*c^4)*d^3*e + 6*(b^7*c + 13*a*b^5*c^2 - 52*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2*e^2 - 2*(17*a*b^6*c - 44*a^2*b^4*c^2 - 64*a^3*b^2*c^3 - 128*a^4*c^4)*d*e^3 + (a*b^7 + 13*a^2*b^5*c - 52*a^3*b^3*c^2 - 64*a^4*b*c^3)*e^4)*x^2 - 24*(5*a^3*c^4*d^4 - 10*a^3*b*c^3*d^3*e + (5*c^7*d^4 - 10*b*c^6*d^3*e + 6*(b^2*c^5 + a*c^6)*d^2*e^2 - (b^3*c^4 + 6*a*b*c^5)*d*e^3 + (a*b^2*c^4 + a^2*c^5)*e^4)*x^6 + 3*(5*b*c^6*d^4 - 10*b^2*c^5*d^3*e + 6*(b^3*c^4 + a*b*c^5)*d^2*e^2 - (b^4*c^3 + 6*a*b^2*c^4)*d*e^3 + (a*b^3*c^3 + a^2*b*c^4)*e^4)*x^5 + 6*(a^3*b^2*c^2 + a^4*c^3)*d^2*e^2 - (a^3*b^3*c + 6*a^4*b*c^2)*d*e^3 + (a^4*b^2*c + a^5*c^2)*e^4 + 3*(5*(b^2*c^5 + a*c^6)*d^4 - 10*(b^3*c^4 + a*b*c^5)*d^3*e + 6*(b^4*c^3 + 2*a*b^2*c^4 + a^2*c^5)*d^2*e^2 - (b^5*c^2 + 7*a*b^3*c^3 + 6*a^2*b*c^4)*d*e^3 + (a*b^4*c^2 + 2*a^2*b^2*c^3 + a^3*c^4)*e^4)*x^4 + (5*(b^3*c^4 + 6*a*b*c^5)*d^4 - 10*(b^4*c^3 + 6*a*b^2*c^4)*d^3*e + 6*(b^5*c^2 + 7*a*b^3*c^3 + 6*a^2*b*c^4)*d^2*e^2 - (b^6*c + 12*a*b^4*c^2 + 36*a^2*b^2*c^3)*d*e^3 + (a*b^5*c + 7*a^2*b^3*c^2 + 6*a^3*b*c^3)*e^4)*x^3 + 3*(5*(a*b^2*c^4 + a^2*c^5)*d^4 - 10*(a*b^3*c^3 + a^2*b*c^4)*d^3*e + 6*(a*b^4*c^2 + 2*a^2*b^2*c^3 + a^3*c^4)*d^2*e^2 - (a*b^5*c + 7*a^2*b^3*c^2 + 6*a^3*b*c^3)*d*e^3 + (a^2*b^4*c + 2*a^3*b^2*c^2 + a^4*c^3)*e^4)*x^2 + 3*(5*a^2*b*c^4*d^4 - 10*a^2*b^2*c^3*d^3*e + 6*(a^2*b^3*c^2 + a^3*b*c^3)*d^2*e^2 - (a^2*b^4*c + 6*a^3*b^2*c^2)*d*e^3 + (a^3*b^3*c + a^4*b*c^2)*e^4)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 3*((b^6*c^2 - 22*a*b^4*c^3 + 28*a^2*b^2*c^4 + 176*a^3*c^5)*d^4 - 2*(b^7*c - 22*a*b^5*c^2 + 28*a^2*b^3*c^3 + 176*a^3*b*c^4)*d^3*e - 6*(a*b^6*c + 18*a^2*b^4*c^2 - 92*a^3*b^2*c^3 + 16*a^4*c^4)*d^2*e^2 + 40*(a^2*b^5*c - 3*a^3*b^3*c^2 - 4*a^4*b*c^3)*d*e^3 - (a^2*b^6 + 18*a^3*b^4*c - 92*a^4*b^2*c^2 + 16*a^5*c^3)*e^4)*x)/(a^3*b^8*c - 16*a^4*b^6*c^2 + 96*a^5*b^4*c^3 - 256*a^6*b^2*c^4 + 256*a^7*c^5 + (b^8*c^4 - 16*a*b^6*c^5 + 96*a^2*b^4*c^6 - 256*a^3*b^2*c^7 + 256*a^4*c^8)*x^6 + 3*(b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^5 + 3*(b^10*c^2 - 15*a*b^8*c^3 + 80*a^2*b^6*c^4 - 160*a^3*b^4*c^5 + 256*a^5*c^7)*x^4 + (b^11*c - 10*a*b^9*c^2 + 320*a^3*b^5*c^4 - 1280*a^4*b^3*c^5 + 1536*a^5*b*c^6)*x^3 + 3*(a*b^10*c - 15*a^2*b^8*c^2 + 80*a^3*b^6*c^3 - 160*a^4*b^4*c^4 + 256*a^6*c^6)*x^2 + 3*(a^2*b^9*c - 16*a^3*b^7*c^2 + 96*a^4*b^5*c^3 - 256*a^5*b^3*c^4 + 256*a^6*b*c^5)*x)]","B",0
2215,1,3608,0,0.473538," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(20 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{3} - 30 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{2} e + 12 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d e^{2} - {\left(b^{5} c^{2} + 2 \, a b^{3} c^{3} - 24 \, a^{2} b c^{4}\right)} e^{3}\right)} x^{5} + 15 \, {\left(20 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} - 30 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{2} e + 12 \, {\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e^{2} - {\left(b^{6} c + 2 \, a b^{4} c^{2} - 24 \, a^{2} b^{2} c^{3}\right)} e^{3}\right)} x^{4} + 2 \, {\left(b^{7} - 17 \, a b^{5} c + 118 \, a^{2} b^{3} c^{2} - 264 \, a^{3} b c^{3}\right)} d^{3} + 3 \, {\left(a b^{6} - 22 \, a^{2} b^{4} c + 8 \, a^{3} b^{2} c^{2} + 256 \, a^{4} c^{3}\right)} d^{2} e + 6 \, {\left(a^{2} b^{5} + 22 \, a^{3} b^{3} c - 104 \, a^{4} b c^{2}\right)} d e^{2} - 2 \, {\left(11 \, a^{3} b^{4} - 28 \, a^{4} b^{2} c - 64 \, a^{5} c^{2}\right)} e^{3} + {\left(20 \, {\left(11 \, b^{4} c^{3} - 28 \, a b^{2} c^{4} - 64 \, a^{2} c^{5}\right)} d^{3} - 30 \, {\left(11 \, b^{5} c^{2} - 28 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} d^{2} e + 12 \, {\left(11 \, b^{6} c - 17 \, a b^{4} c^{2} - 92 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{2} - {\left(11 \, b^{7} + 38 \, a b^{5} c - 232 \, a^{2} b^{3} c^{2} - 384 \, a^{3} b c^{3}\right)} e^{3}\right)} x^{3} + 3 \, {\left(10 \, {\left(b^{5} c^{2} + 12 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} d^{3} - 15 \, {\left(b^{6} c + 12 \, a b^{4} c^{2} - 64 \, a^{2} b^{2} c^{3}\right)} d^{2} e + 6 \, {\left(b^{7} + 13 \, a b^{5} c - 52 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e^{2} - {\left(17 \, a b^{6} - 44 \, a^{2} b^{4} c - 64 \, a^{3} b^{2} c^{2} - 128 \, a^{4} c^{3}\right)} e^{3}\right)} x^{2} - 6 \, {\left(20 \, a^{3} c^{3} d^{3} - 30 \, a^{3} b c^{2} d^{2} e + {\left(20 \, c^{6} d^{3} - 30 \, b c^{5} d^{2} e + 12 \, {\left(b^{2} c^{4} + a c^{5}\right)} d e^{2} - {\left(b^{3} c^{3} + 6 \, a b c^{4}\right)} e^{3}\right)} x^{6} + 3 \, {\left(20 \, b c^{5} d^{3} - 30 \, b^{2} c^{4} d^{2} e + 12 \, {\left(b^{3} c^{3} + a b c^{4}\right)} d e^{2} - {\left(b^{4} c^{2} + 6 \, a b^{2} c^{3}\right)} e^{3}\right)} x^{5} + 3 \, {\left(20 \, {\left(b^{2} c^{4} + a c^{5}\right)} d^{3} - 30 \, {\left(b^{3} c^{3} + a b c^{4}\right)} d^{2} e + 12 \, {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d e^{2} - {\left(b^{5} c + 7 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} e^{3}\right)} x^{4} + 12 \, {\left(a^{3} b^{2} c + a^{4} c^{2}\right)} d e^{2} - {\left(a^{3} b^{3} + 6 \, a^{4} b c\right)} e^{3} + {\left(20 \, {\left(b^{3} c^{3} + 6 \, a b c^{4}\right)} d^{3} - 30 \, {\left(b^{4} c^{2} + 6 \, a b^{2} c^{3}\right)} d^{2} e + 12 \, {\left(b^{5} c + 7 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} d e^{2} - {\left(b^{6} + 12 \, a b^{4} c + 36 \, a^{2} b^{2} c^{2}\right)} e^{3}\right)} x^{3} + 3 \, {\left(20 \, {\left(a b^{2} c^{3} + a^{2} c^{4}\right)} d^{3} - 30 \, {\left(a b^{3} c^{2} + a^{2} b c^{3}\right)} d^{2} e + 12 \, {\left(a b^{4} c + 2 \, a^{2} b^{2} c^{2} + a^{3} c^{3}\right)} d e^{2} - {\left(a b^{5} + 7 \, a^{2} b^{3} c + 6 \, a^{3} b c^{2}\right)} e^{3}\right)} x^{2} + 3 \, {\left(20 \, a^{2} b c^{3} d^{3} - 30 \, a^{2} b^{2} c^{2} d^{2} e + 12 \, {\left(a^{2} b^{3} c + a^{3} b c^{2}\right)} d e^{2} - {\left(a^{2} b^{4} + 6 \, a^{3} b^{2} c\right)} e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 3 \, {\left(2 \, {\left(b^{6} c - 22 \, a b^{4} c^{2} + 28 \, a^{2} b^{2} c^{3} + 176 \, a^{3} c^{4}\right)} d^{3} - 3 \, {\left(b^{7} - 22 \, a b^{5} c + 28 \, a^{2} b^{3} c^{2} + 176 \, a^{3} b c^{3}\right)} d^{2} e - 6 \, {\left(a b^{6} + 18 \, a^{2} b^{4} c - 92 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{2} + 20 \, {\left(a^{2} b^{5} - 3 \, a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} e^{3}\right)} x}{6 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)}}, -\frac{6 \, {\left(20 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{3} - 30 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{2} e + 12 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d e^{2} - {\left(b^{5} c^{2} + 2 \, a b^{3} c^{3} - 24 \, a^{2} b c^{4}\right)} e^{3}\right)} x^{5} + 15 \, {\left(20 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{3} - 30 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{2} e + 12 \, {\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e^{2} - {\left(b^{6} c + 2 \, a b^{4} c^{2} - 24 \, a^{2} b^{2} c^{3}\right)} e^{3}\right)} x^{4} + 2 \, {\left(b^{7} - 17 \, a b^{5} c + 118 \, a^{2} b^{3} c^{2} - 264 \, a^{3} b c^{3}\right)} d^{3} + 3 \, {\left(a b^{6} - 22 \, a^{2} b^{4} c + 8 \, a^{3} b^{2} c^{2} + 256 \, a^{4} c^{3}\right)} d^{2} e + 6 \, {\left(a^{2} b^{5} + 22 \, a^{3} b^{3} c - 104 \, a^{4} b c^{2}\right)} d e^{2} - 2 \, {\left(11 \, a^{3} b^{4} - 28 \, a^{4} b^{2} c - 64 \, a^{5} c^{2}\right)} e^{3} + {\left(20 \, {\left(11 \, b^{4} c^{3} - 28 \, a b^{2} c^{4} - 64 \, a^{2} c^{5}\right)} d^{3} - 30 \, {\left(11 \, b^{5} c^{2} - 28 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} d^{2} e + 12 \, {\left(11 \, b^{6} c - 17 \, a b^{4} c^{2} - 92 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{2} - {\left(11 \, b^{7} + 38 \, a b^{5} c - 232 \, a^{2} b^{3} c^{2} - 384 \, a^{3} b c^{3}\right)} e^{3}\right)} x^{3} + 3 \, {\left(10 \, {\left(b^{5} c^{2} + 12 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} d^{3} - 15 \, {\left(b^{6} c + 12 \, a b^{4} c^{2} - 64 \, a^{2} b^{2} c^{3}\right)} d^{2} e + 6 \, {\left(b^{7} + 13 \, a b^{5} c - 52 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e^{2} - {\left(17 \, a b^{6} - 44 \, a^{2} b^{4} c - 64 \, a^{3} b^{2} c^{2} - 128 \, a^{4} c^{3}\right)} e^{3}\right)} x^{2} - 12 \, {\left(20 \, a^{3} c^{3} d^{3} - 30 \, a^{3} b c^{2} d^{2} e + {\left(20 \, c^{6} d^{3} - 30 \, b c^{5} d^{2} e + 12 \, {\left(b^{2} c^{4} + a c^{5}\right)} d e^{2} - {\left(b^{3} c^{3} + 6 \, a b c^{4}\right)} e^{3}\right)} x^{6} + 3 \, {\left(20 \, b c^{5} d^{3} - 30 \, b^{2} c^{4} d^{2} e + 12 \, {\left(b^{3} c^{3} + a b c^{4}\right)} d e^{2} - {\left(b^{4} c^{2} + 6 \, a b^{2} c^{3}\right)} e^{3}\right)} x^{5} + 3 \, {\left(20 \, {\left(b^{2} c^{4} + a c^{5}\right)} d^{3} - 30 \, {\left(b^{3} c^{3} + a b c^{4}\right)} d^{2} e + 12 \, {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d e^{2} - {\left(b^{5} c + 7 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} e^{3}\right)} x^{4} + 12 \, {\left(a^{3} b^{2} c + a^{4} c^{2}\right)} d e^{2} - {\left(a^{3} b^{3} + 6 \, a^{4} b c\right)} e^{3} + {\left(20 \, {\left(b^{3} c^{3} + 6 \, a b c^{4}\right)} d^{3} - 30 \, {\left(b^{4} c^{2} + 6 \, a b^{2} c^{3}\right)} d^{2} e + 12 \, {\left(b^{5} c + 7 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} d e^{2} - {\left(b^{6} + 12 \, a b^{4} c + 36 \, a^{2} b^{2} c^{2}\right)} e^{3}\right)} x^{3} + 3 \, {\left(20 \, {\left(a b^{2} c^{3} + a^{2} c^{4}\right)} d^{3} - 30 \, {\left(a b^{3} c^{2} + a^{2} b c^{3}\right)} d^{2} e + 12 \, {\left(a b^{4} c + 2 \, a^{2} b^{2} c^{2} + a^{3} c^{3}\right)} d e^{2} - {\left(a b^{5} + 7 \, a^{2} b^{3} c + 6 \, a^{3} b c^{2}\right)} e^{3}\right)} x^{2} + 3 \, {\left(20 \, a^{2} b c^{3} d^{3} - 30 \, a^{2} b^{2} c^{2} d^{2} e + 12 \, {\left(a^{2} b^{3} c + a^{3} b c^{2}\right)} d e^{2} - {\left(a^{2} b^{4} + 6 \, a^{3} b^{2} c\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 3 \, {\left(2 \, {\left(b^{6} c - 22 \, a b^{4} c^{2} + 28 \, a^{2} b^{2} c^{3} + 176 \, a^{3} c^{4}\right)} d^{3} - 3 \, {\left(b^{7} - 22 \, a b^{5} c + 28 \, a^{2} b^{3} c^{2} + 176 \, a^{3} b c^{3}\right)} d^{2} e - 6 \, {\left(a b^{6} + 18 \, a^{2} b^{4} c - 92 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{2} + 20 \, {\left(a^{2} b^{5} - 3 \, a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} e^{3}\right)} x}{6 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/6*(6*(20*(b^2*c^5 - 4*a*c^6)*d^3 - 30*(b^3*c^4 - 4*a*b*c^5)*d^2*e + 12*(b^4*c^3 - 3*a*b^2*c^4 - 4*a^2*c^5)*d*e^2 - (b^5*c^2 + 2*a*b^3*c^3 - 24*a^2*b*c^4)*e^3)*x^5 + 15*(20*(b^3*c^4 - 4*a*b*c^5)*d^3 - 30*(b^4*c^3 - 4*a*b^2*c^4)*d^2*e + 12*(b^5*c^2 - 3*a*b^3*c^3 - 4*a^2*b*c^4)*d*e^2 - (b^6*c + 2*a*b^4*c^2 - 24*a^2*b^2*c^3)*e^3)*x^4 + 2*(b^7 - 17*a*b^5*c + 118*a^2*b^3*c^2 - 264*a^3*b*c^3)*d^3 + 3*(a*b^6 - 22*a^2*b^4*c + 8*a^3*b^2*c^2 + 256*a^4*c^3)*d^2*e + 6*(a^2*b^5 + 22*a^3*b^3*c - 104*a^4*b*c^2)*d*e^2 - 2*(11*a^3*b^4 - 28*a^4*b^2*c - 64*a^5*c^2)*e^3 + (20*(11*b^4*c^3 - 28*a*b^2*c^4 - 64*a^2*c^5)*d^3 - 30*(11*b^5*c^2 - 28*a*b^3*c^3 - 64*a^2*b*c^4)*d^2*e + 12*(11*b^6*c - 17*a*b^4*c^2 - 92*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^2 - (11*b^7 + 38*a*b^5*c - 232*a^2*b^3*c^2 - 384*a^3*b*c^3)*e^3)*x^3 + 3*(10*(b^5*c^2 + 12*a*b^3*c^3 - 64*a^2*b*c^4)*d^3 - 15*(b^6*c + 12*a*b^4*c^2 - 64*a^2*b^2*c^3)*d^2*e + 6*(b^7 + 13*a*b^5*c - 52*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e^2 - (17*a*b^6 - 44*a^2*b^4*c - 64*a^3*b^2*c^2 - 128*a^4*c^3)*e^3)*x^2 - 6*(20*a^3*c^3*d^3 - 30*a^3*b*c^2*d^2*e + (20*c^6*d^3 - 30*b*c^5*d^2*e + 12*(b^2*c^4 + a*c^5)*d*e^2 - (b^3*c^3 + 6*a*b*c^4)*e^3)*x^6 + 3*(20*b*c^5*d^3 - 30*b^2*c^4*d^2*e + 12*(b^3*c^3 + a*b*c^4)*d*e^2 - (b^4*c^2 + 6*a*b^2*c^3)*e^3)*x^5 + 3*(20*(b^2*c^4 + a*c^5)*d^3 - 30*(b^3*c^3 + a*b*c^4)*d^2*e + 12*(b^4*c^2 + 2*a*b^2*c^3 + a^2*c^4)*d*e^2 - (b^5*c + 7*a*b^3*c^2 + 6*a^2*b*c^3)*e^3)*x^4 + 12*(a^3*b^2*c + a^4*c^2)*d*e^2 - (a^3*b^3 + 6*a^4*b*c)*e^3 + (20*(b^3*c^3 + 6*a*b*c^4)*d^3 - 30*(b^4*c^2 + 6*a*b^2*c^3)*d^2*e + 12*(b^5*c + 7*a*b^3*c^2 + 6*a^2*b*c^3)*d*e^2 - (b^6 + 12*a*b^4*c + 36*a^2*b^2*c^2)*e^3)*x^3 + 3*(20*(a*b^2*c^3 + a^2*c^4)*d^3 - 30*(a*b^3*c^2 + a^2*b*c^3)*d^2*e + 12*(a*b^4*c + 2*a^2*b^2*c^2 + a^3*c^3)*d*e^2 - (a*b^5 + 7*a^2*b^3*c + 6*a^3*b*c^2)*e^3)*x^2 + 3*(20*a^2*b*c^3*d^3 - 30*a^2*b^2*c^2*d^2*e + 12*(a^2*b^3*c + a^3*b*c^2)*d*e^2 - (a^2*b^4 + 6*a^3*b^2*c)*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 3*(2*(b^6*c - 22*a*b^4*c^2 + 28*a^2*b^2*c^3 + 176*a^3*c^4)*d^3 - 3*(b^7 - 22*a*b^5*c + 28*a^2*b^3*c^2 + 176*a^3*b*c^3)*d^2*e - 6*(a*b^6 + 18*a^2*b^4*c - 92*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^2 + 20*(a^2*b^5 - 3*a^3*b^3*c - 4*a^4*b*c^2)*e^3)*x)/(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x), -1/6*(6*(20*(b^2*c^5 - 4*a*c^6)*d^3 - 30*(b^3*c^4 - 4*a*b*c^5)*d^2*e + 12*(b^4*c^3 - 3*a*b^2*c^4 - 4*a^2*c^5)*d*e^2 - (b^5*c^2 + 2*a*b^3*c^3 - 24*a^2*b*c^4)*e^3)*x^5 + 15*(20*(b^3*c^4 - 4*a*b*c^5)*d^3 - 30*(b^4*c^3 - 4*a*b^2*c^4)*d^2*e + 12*(b^5*c^2 - 3*a*b^3*c^3 - 4*a^2*b*c^4)*d*e^2 - (b^6*c + 2*a*b^4*c^2 - 24*a^2*b^2*c^3)*e^3)*x^4 + 2*(b^7 - 17*a*b^5*c + 118*a^2*b^3*c^2 - 264*a^3*b*c^3)*d^3 + 3*(a*b^6 - 22*a^2*b^4*c + 8*a^3*b^2*c^2 + 256*a^4*c^3)*d^2*e + 6*(a^2*b^5 + 22*a^3*b^3*c - 104*a^4*b*c^2)*d*e^2 - 2*(11*a^3*b^4 - 28*a^4*b^2*c - 64*a^5*c^2)*e^3 + (20*(11*b^4*c^3 - 28*a*b^2*c^4 - 64*a^2*c^5)*d^3 - 30*(11*b^5*c^2 - 28*a*b^3*c^3 - 64*a^2*b*c^4)*d^2*e + 12*(11*b^6*c - 17*a*b^4*c^2 - 92*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^2 - (11*b^7 + 38*a*b^5*c - 232*a^2*b^3*c^2 - 384*a^3*b*c^3)*e^3)*x^3 + 3*(10*(b^5*c^2 + 12*a*b^3*c^3 - 64*a^2*b*c^4)*d^3 - 15*(b^6*c + 12*a*b^4*c^2 - 64*a^2*b^2*c^3)*d^2*e + 6*(b^7 + 13*a*b^5*c - 52*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e^2 - (17*a*b^6 - 44*a^2*b^4*c - 64*a^3*b^2*c^2 - 128*a^4*c^3)*e^3)*x^2 - 12*(20*a^3*c^3*d^3 - 30*a^3*b*c^2*d^2*e + (20*c^6*d^3 - 30*b*c^5*d^2*e + 12*(b^2*c^4 + a*c^5)*d*e^2 - (b^3*c^3 + 6*a*b*c^4)*e^3)*x^6 + 3*(20*b*c^5*d^3 - 30*b^2*c^4*d^2*e + 12*(b^3*c^3 + a*b*c^4)*d*e^2 - (b^4*c^2 + 6*a*b^2*c^3)*e^3)*x^5 + 3*(20*(b^2*c^4 + a*c^5)*d^3 - 30*(b^3*c^3 + a*b*c^4)*d^2*e + 12*(b^4*c^2 + 2*a*b^2*c^3 + a^2*c^4)*d*e^2 - (b^5*c + 7*a*b^3*c^2 + 6*a^2*b*c^3)*e^3)*x^4 + 12*(a^3*b^2*c + a^4*c^2)*d*e^2 - (a^3*b^3 + 6*a^4*b*c)*e^3 + (20*(b^3*c^3 + 6*a*b*c^4)*d^3 - 30*(b^4*c^2 + 6*a*b^2*c^3)*d^2*e + 12*(b^5*c + 7*a*b^3*c^2 + 6*a^2*b*c^3)*d*e^2 - (b^6 + 12*a*b^4*c + 36*a^2*b^2*c^2)*e^3)*x^3 + 3*(20*(a*b^2*c^3 + a^2*c^4)*d^3 - 30*(a*b^3*c^2 + a^2*b*c^3)*d^2*e + 12*(a*b^4*c + 2*a^2*b^2*c^2 + a^3*c^3)*d*e^2 - (a*b^5 + 7*a^2*b^3*c + 6*a^3*b*c^2)*e^3)*x^2 + 3*(20*a^2*b*c^3*d^3 - 30*a^2*b^2*c^2*d^2*e + 12*(a^2*b^3*c + a^3*b*c^2)*d*e^2 - (a^2*b^4 + 6*a^3*b^2*c)*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 3*(2*(b^6*c - 22*a*b^4*c^2 + 28*a^2*b^2*c^3 + 176*a^3*c^4)*d^3 - 3*(b^7 - 22*a*b^5*c + 28*a^2*b^3*c^2 + 176*a^3*b*c^3)*d^2*e - 6*(a*b^6 + 18*a^2*b^4*c - 92*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^2 + 20*(a^2*b^5 - 3*a^3*b^3*c - 4*a^4*b*c^2)*e^3)*x)/(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x)]","B",0
2216,1,2761,0,0.445305," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(5 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{2} - 5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d e + {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} e^{2}\right)} x^{5} + 30 \, {\left(5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{2} - 5 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d e + {\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} e^{2}\right)} x^{4} + 2 \, {\left(5 \, {\left(11 \, b^{4} c^{3} - 28 \, a b^{2} c^{4} - 64 \, a^{2} c^{5}\right)} d^{2} - 5 \, {\left(11 \, b^{5} c^{2} - 28 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} d e + {\left(11 \, b^{6} c - 17 \, a b^{4} c^{2} - 92 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}\right)} x^{3} + {\left(b^{7} - 17 \, a b^{5} c + 118 \, a^{2} b^{3} c^{2} - 264 \, a^{3} b c^{3}\right)} d^{2} + {\left(a b^{6} - 22 \, a^{2} b^{4} c + 8 \, a^{3} b^{2} c^{2} + 256 \, a^{4} c^{3}\right)} d e + {\left(a^{2} b^{5} + 22 \, a^{3} b^{3} c - 104 \, a^{4} b c^{2}\right)} e^{2} + 3 \, {\left(5 \, {\left(b^{5} c^{2} + 12 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} d^{2} - 5 \, {\left(b^{6} c + 12 \, a b^{4} c^{2} - 64 \, a^{2} b^{2} c^{3}\right)} d e + {\left(b^{7} + 13 \, a b^{5} c - 52 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{2}\right)} x^{2} + 12 \, {\left(5 \, a^{3} c^{3} d^{2} - 5 \, a^{3} b c^{2} d e + {\left(5 \, c^{6} d^{2} - 5 \, b c^{5} d e + {\left(b^{2} c^{4} + a c^{5}\right)} e^{2}\right)} x^{6} + 3 \, {\left(5 \, b c^{5} d^{2} - 5 \, b^{2} c^{4} d e + {\left(b^{3} c^{3} + a b c^{4}\right)} e^{2}\right)} x^{5} + 3 \, {\left(5 \, {\left(b^{2} c^{4} + a c^{5}\right)} d^{2} - 5 \, {\left(b^{3} c^{3} + a b c^{4}\right)} d e + {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} e^{2}\right)} x^{4} + {\left(5 \, {\left(b^{3} c^{3} + 6 \, a b c^{4}\right)} d^{2} - 5 \, {\left(b^{4} c^{2} + 6 \, a b^{2} c^{3}\right)} d e + {\left(b^{5} c + 7 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} e^{2}\right)} x^{3} + {\left(a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2} + 3 \, {\left(5 \, {\left(a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 5 \, {\left(a b^{3} c^{2} + a^{2} b c^{3}\right)} d e + {\left(a b^{4} c + 2 \, a^{2} b^{2} c^{2} + a^{3} c^{3}\right)} e^{2}\right)} x^{2} + 3 \, {\left(5 \, a^{2} b c^{3} d^{2} - 5 \, a^{2} b^{2} c^{2} d e + {\left(a^{2} b^{3} c + a^{3} b c^{2}\right)} e^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 3 \, {\left({\left(b^{6} c - 22 \, a b^{4} c^{2} + 28 \, a^{2} b^{2} c^{3} + 176 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 22 \, a b^{5} c + 28 \, a^{2} b^{3} c^{2} + 176 \, a^{3} b c^{3}\right)} d e - {\left(a b^{6} + 18 \, a^{2} b^{4} c - 92 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} e^{2}\right)} x}{3 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)}}, -\frac{12 \, {\left(5 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{2} - 5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d e + {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} e^{2}\right)} x^{5} + 30 \, {\left(5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{2} - 5 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d e + {\left(b^{5} c^{2} - 3 \, a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} e^{2}\right)} x^{4} + 2 \, {\left(5 \, {\left(11 \, b^{4} c^{3} - 28 \, a b^{2} c^{4} - 64 \, a^{2} c^{5}\right)} d^{2} - 5 \, {\left(11 \, b^{5} c^{2} - 28 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} d e + {\left(11 \, b^{6} c - 17 \, a b^{4} c^{2} - 92 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} e^{2}\right)} x^{3} + {\left(b^{7} - 17 \, a b^{5} c + 118 \, a^{2} b^{3} c^{2} - 264 \, a^{3} b c^{3}\right)} d^{2} + {\left(a b^{6} - 22 \, a^{2} b^{4} c + 8 \, a^{3} b^{2} c^{2} + 256 \, a^{4} c^{3}\right)} d e + {\left(a^{2} b^{5} + 22 \, a^{3} b^{3} c - 104 \, a^{4} b c^{2}\right)} e^{2} + 3 \, {\left(5 \, {\left(b^{5} c^{2} + 12 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} d^{2} - 5 \, {\left(b^{6} c + 12 \, a b^{4} c^{2} - 64 \, a^{2} b^{2} c^{3}\right)} d e + {\left(b^{7} + 13 \, a b^{5} c - 52 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{2}\right)} x^{2} - 24 \, {\left(5 \, a^{3} c^{3} d^{2} - 5 \, a^{3} b c^{2} d e + {\left(5 \, c^{6} d^{2} - 5 \, b c^{5} d e + {\left(b^{2} c^{4} + a c^{5}\right)} e^{2}\right)} x^{6} + 3 \, {\left(5 \, b c^{5} d^{2} - 5 \, b^{2} c^{4} d e + {\left(b^{3} c^{3} + a b c^{4}\right)} e^{2}\right)} x^{5} + 3 \, {\left(5 \, {\left(b^{2} c^{4} + a c^{5}\right)} d^{2} - 5 \, {\left(b^{3} c^{3} + a b c^{4}\right)} d e + {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} e^{2}\right)} x^{4} + {\left(5 \, {\left(b^{3} c^{3} + 6 \, a b c^{4}\right)} d^{2} - 5 \, {\left(b^{4} c^{2} + 6 \, a b^{2} c^{3}\right)} d e + {\left(b^{5} c + 7 \, a b^{3} c^{2} + 6 \, a^{2} b c^{3}\right)} e^{2}\right)} x^{3} + {\left(a^{3} b^{2} c + a^{4} c^{2}\right)} e^{2} + 3 \, {\left(5 \, {\left(a b^{2} c^{3} + a^{2} c^{4}\right)} d^{2} - 5 \, {\left(a b^{3} c^{2} + a^{2} b c^{3}\right)} d e + {\left(a b^{4} c + 2 \, a^{2} b^{2} c^{2} + a^{3} c^{3}\right)} e^{2}\right)} x^{2} + 3 \, {\left(5 \, a^{2} b c^{3} d^{2} - 5 \, a^{2} b^{2} c^{2} d e + {\left(a^{2} b^{3} c + a^{3} b c^{2}\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 3 \, {\left({\left(b^{6} c - 22 \, a b^{4} c^{2} + 28 \, a^{2} b^{2} c^{3} + 176 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 22 \, a b^{5} c + 28 \, a^{2} b^{3} c^{2} + 176 \, a^{3} b c^{3}\right)} d e - {\left(a b^{6} + 18 \, a^{2} b^{4} c - 92 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} e^{2}\right)} x}{3 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/3*(12*(5*(b^2*c^5 - 4*a*c^6)*d^2 - 5*(b^3*c^4 - 4*a*b*c^5)*d*e + (b^4*c^3 - 3*a*b^2*c^4 - 4*a^2*c^5)*e^2)*x^5 + 30*(5*(b^3*c^4 - 4*a*b*c^5)*d^2 - 5*(b^4*c^3 - 4*a*b^2*c^4)*d*e + (b^5*c^2 - 3*a*b^3*c^3 - 4*a^2*b*c^4)*e^2)*x^4 + 2*(5*(11*b^4*c^3 - 28*a*b^2*c^4 - 64*a^2*c^5)*d^2 - 5*(11*b^5*c^2 - 28*a*b^3*c^3 - 64*a^2*b*c^4)*d*e + (11*b^6*c - 17*a*b^4*c^2 - 92*a^2*b^2*c^3 - 64*a^3*c^4)*e^2)*x^3 + (b^7 - 17*a*b^5*c + 118*a^2*b^3*c^2 - 264*a^3*b*c^3)*d^2 + (a*b^6 - 22*a^2*b^4*c + 8*a^3*b^2*c^2 + 256*a^4*c^3)*d*e + (a^2*b^5 + 22*a^3*b^3*c - 104*a^4*b*c^2)*e^2 + 3*(5*(b^5*c^2 + 12*a*b^3*c^3 - 64*a^2*b*c^4)*d^2 - 5*(b^6*c + 12*a*b^4*c^2 - 64*a^2*b^2*c^3)*d*e + (b^7 + 13*a*b^5*c - 52*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^2)*x^2 + 12*(5*a^3*c^3*d^2 - 5*a^3*b*c^2*d*e + (5*c^6*d^2 - 5*b*c^5*d*e + (b^2*c^4 + a*c^5)*e^2)*x^6 + 3*(5*b*c^5*d^2 - 5*b^2*c^4*d*e + (b^3*c^3 + a*b*c^4)*e^2)*x^5 + 3*(5*(b^2*c^4 + a*c^5)*d^2 - 5*(b^3*c^3 + a*b*c^4)*d*e + (b^4*c^2 + 2*a*b^2*c^3 + a^2*c^4)*e^2)*x^4 + (5*(b^3*c^3 + 6*a*b*c^4)*d^2 - 5*(b^4*c^2 + 6*a*b^2*c^3)*d*e + (b^5*c + 7*a*b^3*c^2 + 6*a^2*b*c^3)*e^2)*x^3 + (a^3*b^2*c + a^4*c^2)*e^2 + 3*(5*(a*b^2*c^3 + a^2*c^4)*d^2 - 5*(a*b^3*c^2 + a^2*b*c^3)*d*e + (a*b^4*c + 2*a^2*b^2*c^2 + a^3*c^3)*e^2)*x^2 + 3*(5*a^2*b*c^3*d^2 - 5*a^2*b^2*c^2*d*e + (a^2*b^3*c + a^3*b*c^2)*e^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 3*((b^6*c - 22*a*b^4*c^2 + 28*a^2*b^2*c^3 + 176*a^3*c^4)*d^2 - (b^7 - 22*a*b^5*c + 28*a^2*b^3*c^2 + 176*a^3*b*c^3)*d*e - (a*b^6 + 18*a^2*b^4*c - 92*a^3*b^2*c^2 + 16*a^4*c^3)*e^2)*x)/(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x), -1/3*(12*(5*(b^2*c^5 - 4*a*c^6)*d^2 - 5*(b^3*c^4 - 4*a*b*c^5)*d*e + (b^4*c^3 - 3*a*b^2*c^4 - 4*a^2*c^5)*e^2)*x^5 + 30*(5*(b^3*c^4 - 4*a*b*c^5)*d^2 - 5*(b^4*c^3 - 4*a*b^2*c^4)*d*e + (b^5*c^2 - 3*a*b^3*c^3 - 4*a^2*b*c^4)*e^2)*x^4 + 2*(5*(11*b^4*c^3 - 28*a*b^2*c^4 - 64*a^2*c^5)*d^2 - 5*(11*b^5*c^2 - 28*a*b^3*c^3 - 64*a^2*b*c^4)*d*e + (11*b^6*c - 17*a*b^4*c^2 - 92*a^2*b^2*c^3 - 64*a^3*c^4)*e^2)*x^3 + (b^7 - 17*a*b^5*c + 118*a^2*b^3*c^2 - 264*a^3*b*c^3)*d^2 + (a*b^6 - 22*a^2*b^4*c + 8*a^3*b^2*c^2 + 256*a^4*c^3)*d*e + (a^2*b^5 + 22*a^3*b^3*c - 104*a^4*b*c^2)*e^2 + 3*(5*(b^5*c^2 + 12*a*b^3*c^3 - 64*a^2*b*c^4)*d^2 - 5*(b^6*c + 12*a*b^4*c^2 - 64*a^2*b^2*c^3)*d*e + (b^7 + 13*a*b^5*c - 52*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^2)*x^2 - 24*(5*a^3*c^3*d^2 - 5*a^3*b*c^2*d*e + (5*c^6*d^2 - 5*b*c^5*d*e + (b^2*c^4 + a*c^5)*e^2)*x^6 + 3*(5*b*c^5*d^2 - 5*b^2*c^4*d*e + (b^3*c^3 + a*b*c^4)*e^2)*x^5 + 3*(5*(b^2*c^4 + a*c^5)*d^2 - 5*(b^3*c^3 + a*b*c^4)*d*e + (b^4*c^2 + 2*a*b^2*c^3 + a^2*c^4)*e^2)*x^4 + (5*(b^3*c^3 + 6*a*b*c^4)*d^2 - 5*(b^4*c^2 + 6*a*b^2*c^3)*d*e + (b^5*c + 7*a*b^3*c^2 + 6*a^2*b*c^3)*e^2)*x^3 + (a^3*b^2*c + a^4*c^2)*e^2 + 3*(5*(a*b^2*c^3 + a^2*c^4)*d^2 - 5*(a*b^3*c^2 + a^2*b*c^3)*d*e + (a*b^4*c + 2*a^2*b^2*c^2 + a^3*c^3)*e^2)*x^2 + 3*(5*a^2*b*c^3*d^2 - 5*a^2*b^2*c^2*d*e + (a^2*b^3*c + a^3*b*c^2)*e^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 3*((b^6*c - 22*a*b^4*c^2 + 28*a^2*b^2*c^3 + 176*a^3*c^4)*d^2 - (b^7 - 22*a*b^5*c + 28*a^2*b^3*c^2 + 176*a^3*b*c^3)*d*e - (a*b^6 + 18*a^2*b^4*c - 92*a^3*b^2*c^2 + 16*a^4*c^3)*e^2)*x)/(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x)]","B",0
2217,1,1960,0,0.437919," ","integrate((e*x+d)/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[-\frac{60 \, {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d - {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} e\right)} x^{5} + 150 \, {\left(2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d - {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} e\right)} x^{4} + 10 \, {\left(2 \, {\left(11 \, b^{4} c^{3} - 28 \, a b^{2} c^{4} - 64 \, a^{2} c^{5}\right)} d - {\left(11 \, b^{5} c^{2} - 28 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} e\right)} x^{3} + 15 \, {\left(2 \, {\left(b^{5} c^{2} + 12 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} d - {\left(b^{6} c + 12 \, a b^{4} c^{2} - 64 \, a^{2} b^{2} c^{3}\right)} e\right)} x^{2} - 60 \, {\left(2 \, a^{3} c^{3} d - a^{3} b c^{2} e + {\left(2 \, c^{6} d - b c^{5} e\right)} x^{6} + 3 \, {\left(2 \, b c^{5} d - b^{2} c^{4} e\right)} x^{5} + 3 \, {\left(2 \, {\left(b^{2} c^{4} + a c^{5}\right)} d - {\left(b^{3} c^{3} + a b c^{4}\right)} e\right)} x^{4} + {\left(2 \, {\left(b^{3} c^{3} + 6 \, a b c^{4}\right)} d - {\left(b^{4} c^{2} + 6 \, a b^{2} c^{3}\right)} e\right)} x^{3} + 3 \, {\left(2 \, {\left(a b^{2} c^{3} + a^{2} c^{4}\right)} d - {\left(a b^{3} c^{2} + a^{2} b c^{3}\right)} e\right)} x^{2} + 3 \, {\left(2 \, a^{2} b c^{3} d - a^{2} b^{2} c^{2} e\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 2 \, {\left(b^{7} - 17 \, a b^{5} c + 118 \, a^{2} b^{3} c^{2} - 264 \, a^{3} b c^{3}\right)} d + {\left(a b^{6} - 22 \, a^{2} b^{4} c + 8 \, a^{3} b^{2} c^{2} + 256 \, a^{4} c^{3}\right)} e - 3 \, {\left(2 \, {\left(b^{6} c - 22 \, a b^{4} c^{2} + 28 \, a^{2} b^{2} c^{3} + 176 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 22 \, a b^{5} c + 28 \, a^{2} b^{3} c^{2} + 176 \, a^{3} b c^{3}\right)} e\right)} x}{6 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)}}, -\frac{60 \, {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d - {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} e\right)} x^{5} + 150 \, {\left(2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d - {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} e\right)} x^{4} + 10 \, {\left(2 \, {\left(11 \, b^{4} c^{3} - 28 \, a b^{2} c^{4} - 64 \, a^{2} c^{5}\right)} d - {\left(11 \, b^{5} c^{2} - 28 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} e\right)} x^{3} + 15 \, {\left(2 \, {\left(b^{5} c^{2} + 12 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} d - {\left(b^{6} c + 12 \, a b^{4} c^{2} - 64 \, a^{2} b^{2} c^{3}\right)} e\right)} x^{2} - 120 \, {\left(2 \, a^{3} c^{3} d - a^{3} b c^{2} e + {\left(2 \, c^{6} d - b c^{5} e\right)} x^{6} + 3 \, {\left(2 \, b c^{5} d - b^{2} c^{4} e\right)} x^{5} + 3 \, {\left(2 \, {\left(b^{2} c^{4} + a c^{5}\right)} d - {\left(b^{3} c^{3} + a b c^{4}\right)} e\right)} x^{4} + {\left(2 \, {\left(b^{3} c^{3} + 6 \, a b c^{4}\right)} d - {\left(b^{4} c^{2} + 6 \, a b^{2} c^{3}\right)} e\right)} x^{3} + 3 \, {\left(2 \, {\left(a b^{2} c^{3} + a^{2} c^{4}\right)} d - {\left(a b^{3} c^{2} + a^{2} b c^{3}\right)} e\right)} x^{2} + 3 \, {\left(2 \, a^{2} b c^{3} d - a^{2} b^{2} c^{2} e\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 2 \, {\left(b^{7} - 17 \, a b^{5} c + 118 \, a^{2} b^{3} c^{2} - 264 \, a^{3} b c^{3}\right)} d + {\left(a b^{6} - 22 \, a^{2} b^{4} c + 8 \, a^{3} b^{2} c^{2} + 256 \, a^{4} c^{3}\right)} e - 3 \, {\left(2 \, {\left(b^{6} c - 22 \, a b^{4} c^{2} + 28 \, a^{2} b^{2} c^{3} + 176 \, a^{3} c^{4}\right)} d - {\left(b^{7} - 22 \, a b^{5} c + 28 \, a^{2} b^{3} c^{2} + 176 \, a^{3} b c^{3}\right)} e\right)} x}{6 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/6*(60*(2*(b^2*c^5 - 4*a*c^6)*d - (b^3*c^4 - 4*a*b*c^5)*e)*x^5 + 150*(2*(b^3*c^4 - 4*a*b*c^5)*d - (b^4*c^3 - 4*a*b^2*c^4)*e)*x^4 + 10*(2*(11*b^4*c^3 - 28*a*b^2*c^4 - 64*a^2*c^5)*d - (11*b^5*c^2 - 28*a*b^3*c^3 - 64*a^2*b*c^4)*e)*x^3 + 15*(2*(b^5*c^2 + 12*a*b^3*c^3 - 64*a^2*b*c^4)*d - (b^6*c + 12*a*b^4*c^2 - 64*a^2*b^2*c^3)*e)*x^2 - 60*(2*a^3*c^3*d - a^3*b*c^2*e + (2*c^6*d - b*c^5*e)*x^6 + 3*(2*b*c^5*d - b^2*c^4*e)*x^5 + 3*(2*(b^2*c^4 + a*c^5)*d - (b^3*c^3 + a*b*c^4)*e)*x^4 + (2*(b^3*c^3 + 6*a*b*c^4)*d - (b^4*c^2 + 6*a*b^2*c^3)*e)*x^3 + 3*(2*(a*b^2*c^3 + a^2*c^4)*d - (a*b^3*c^2 + a^2*b*c^3)*e)*x^2 + 3*(2*a^2*b*c^3*d - a^2*b^2*c^2*e)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 2*(b^7 - 17*a*b^5*c + 118*a^2*b^3*c^2 - 264*a^3*b*c^3)*d + (a*b^6 - 22*a^2*b^4*c + 8*a^3*b^2*c^2 + 256*a^4*c^3)*e - 3*(2*(b^6*c - 22*a*b^4*c^2 + 28*a^2*b^2*c^3 + 176*a^3*c^4)*d - (b^7 - 22*a*b^5*c + 28*a^2*b^3*c^2 + 176*a^3*b*c^3)*e)*x)/(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x), -1/6*(60*(2*(b^2*c^5 - 4*a*c^6)*d - (b^3*c^4 - 4*a*b*c^5)*e)*x^5 + 150*(2*(b^3*c^4 - 4*a*b*c^5)*d - (b^4*c^3 - 4*a*b^2*c^4)*e)*x^4 + 10*(2*(11*b^4*c^3 - 28*a*b^2*c^4 - 64*a^2*c^5)*d - (11*b^5*c^2 - 28*a*b^3*c^3 - 64*a^2*b*c^4)*e)*x^3 + 15*(2*(b^5*c^2 + 12*a*b^3*c^3 - 64*a^2*b*c^4)*d - (b^6*c + 12*a*b^4*c^2 - 64*a^2*b^2*c^3)*e)*x^2 - 120*(2*a^3*c^3*d - a^3*b*c^2*e + (2*c^6*d - b*c^5*e)*x^6 + 3*(2*b*c^5*d - b^2*c^4*e)*x^5 + 3*(2*(b^2*c^4 + a*c^5)*d - (b^3*c^3 + a*b*c^4)*e)*x^4 + (2*(b^3*c^3 + 6*a*b*c^4)*d - (b^4*c^2 + 6*a*b^2*c^3)*e)*x^3 + 3*(2*(a*b^2*c^3 + a^2*c^4)*d - (a*b^3*c^2 + a^2*b*c^3)*e)*x^2 + 3*(2*a^2*b*c^3*d - a^2*b^2*c^2*e)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 2*(b^7 - 17*a*b^5*c + 118*a^2*b^3*c^2 - 264*a^3*b*c^3)*d + (a*b^6 - 22*a^2*b^4*c + 8*a^3*b^2*c^2 + 256*a^4*c^3)*e - 3*(2*(b^6*c - 22*a*b^4*c^2 + 28*a^2*b^2*c^3 + 176*a^3*c^4)*d - (b^7 - 22*a*b^5*c + 28*a^2*b^3*c^2 + 176*a^3*b*c^3)*e)*x)/(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x)]","B",0
2218,1,1337,0,0.437588," ","integrate(1/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[-\frac{b^{7} - 17 \, a b^{5} c + 118 \, a^{2} b^{3} c^{2} - 264 \, a^{3} b c^{3} + 60 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{5} + 150 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{4} + 10 \, {\left(11 \, b^{4} c^{3} - 28 \, a b^{2} c^{4} - 64 \, a^{2} c^{5}\right)} x^{3} + 15 \, {\left(b^{5} c^{2} + 12 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} x^{2} + 60 \, {\left(c^{6} x^{6} + 3 \, b c^{5} x^{5} + 3 \, a^{2} b c^{3} x + a^{3} c^{3} + 3 \, {\left(b^{2} c^{4} + a c^{5}\right)} x^{4} + {\left(b^{3} c^{3} + 6 \, a b c^{4}\right)} x^{3} + 3 \, {\left(a b^{2} c^{3} + a^{2} c^{4}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 3 \, {\left(b^{6} c - 22 \, a b^{4} c^{2} + 28 \, a^{2} b^{2} c^{3} + 176 \, a^{3} c^{4}\right)} x}{3 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)}}, -\frac{b^{7} - 17 \, a b^{5} c + 118 \, a^{2} b^{3} c^{2} - 264 \, a^{3} b c^{3} + 60 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{5} + 150 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x^{4} + 10 \, {\left(11 \, b^{4} c^{3} - 28 \, a b^{2} c^{4} - 64 \, a^{2} c^{5}\right)} x^{3} + 15 \, {\left(b^{5} c^{2} + 12 \, a b^{3} c^{3} - 64 \, a^{2} b c^{4}\right)} x^{2} - 120 \, {\left(c^{6} x^{6} + 3 \, b c^{5} x^{5} + 3 \, a^{2} b c^{3} x + a^{3} c^{3} + 3 \, {\left(b^{2} c^{4} + a c^{5}\right)} x^{4} + {\left(b^{3} c^{3} + 6 \, a b c^{4}\right)} x^{3} + 3 \, {\left(a b^{2} c^{3} + a^{2} c^{4}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 3 \, {\left(b^{6} c - 22 \, a b^{4} c^{2} + 28 \, a^{2} b^{2} c^{3} + 176 \, a^{3} c^{4}\right)} x}{3 \, {\left(a^{3} b^{8} - 16 \, a^{4} b^{6} c + 96 \, a^{5} b^{4} c^{2} - 256 \, a^{6} b^{2} c^{3} + 256 \, a^{7} c^{4} + {\left(b^{8} c^{3} - 16 \, a b^{6} c^{4} + 96 \, a^{2} b^{4} c^{5} - 256 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} x^{6} + 3 \, {\left(b^{9} c^{2} - 16 \, a b^{7} c^{3} + 96 \, a^{2} b^{5} c^{4} - 256 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} x^{5} + 3 \, {\left(b^{10} c - 15 \, a b^{8} c^{2} + 80 \, a^{2} b^{6} c^{3} - 160 \, a^{3} b^{4} c^{4} + 256 \, a^{5} c^{6}\right)} x^{4} + {\left(b^{11} - 10 \, a b^{9} c + 320 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4} + 1536 \, a^{5} b c^{5}\right)} x^{3} + 3 \, {\left(a b^{10} - 15 \, a^{2} b^{8} c + 80 \, a^{3} b^{6} c^{2} - 160 \, a^{4} b^{4} c^{3} + 256 \, a^{6} c^{5}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} - 16 \, a^{3} b^{7} c + 96 \, a^{4} b^{5} c^{2} - 256 \, a^{5} b^{3} c^{3} + 256 \, a^{6} b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/3*(b^7 - 17*a*b^5*c + 118*a^2*b^3*c^2 - 264*a^3*b*c^3 + 60*(b^2*c^5 - 4*a*c^6)*x^5 + 150*(b^3*c^4 - 4*a*b*c^5)*x^4 + 10*(11*b^4*c^3 - 28*a*b^2*c^4 - 64*a^2*c^5)*x^3 + 15*(b^5*c^2 + 12*a*b^3*c^3 - 64*a^2*b*c^4)*x^2 + 60*(c^6*x^6 + 3*b*c^5*x^5 + 3*a^2*b*c^3*x + a^3*c^3 + 3*(b^2*c^4 + a*c^5)*x^4 + (b^3*c^3 + 6*a*b*c^4)*x^3 + 3*(a*b^2*c^3 + a^2*c^4)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 3*(b^6*c - 22*a*b^4*c^2 + 28*a^2*b^2*c^3 + 176*a^3*c^4)*x)/(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x), -1/3*(b^7 - 17*a*b^5*c + 118*a^2*b^3*c^2 - 264*a^3*b*c^3 + 60*(b^2*c^5 - 4*a*c^6)*x^5 + 150*(b^3*c^4 - 4*a*b*c^5)*x^4 + 10*(11*b^4*c^3 - 28*a*b^2*c^4 - 64*a^2*c^5)*x^3 + 15*(b^5*c^2 + 12*a*b^3*c^3 - 64*a^2*b*c^4)*x^2 - 120*(c^6*x^6 + 3*b*c^5*x^5 + 3*a^2*b*c^3*x + a^3*c^3 + 3*(b^2*c^4 + a*c^5)*x^4 + (b^3*c^3 + 6*a*b*c^4)*x^3 + 3*(a*b^2*c^3 + a^2*c^4)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 3*(b^6*c - 22*a*b^4*c^2 + 28*a^2*b^2*c^3 + 176*a^3*c^4)*x)/(a^3*b^8 - 16*a^4*b^6*c + 96*a^5*b^4*c^2 - 256*a^6*b^2*c^3 + 256*a^7*c^4 + (b^8*c^3 - 16*a*b^6*c^4 + 96*a^2*b^4*c^5 - 256*a^3*b^2*c^6 + 256*a^4*c^7)*x^6 + 3*(b^9*c^2 - 16*a*b^7*c^3 + 96*a^2*b^5*c^4 - 256*a^3*b^3*c^5 + 256*a^4*b*c^6)*x^5 + 3*(b^10*c - 15*a*b^8*c^2 + 80*a^2*b^6*c^3 - 160*a^3*b^4*c^4 + 256*a^5*c^6)*x^4 + (b^11 - 10*a*b^9*c + 320*a^3*b^5*c^3 - 1280*a^4*b^3*c^4 + 1536*a^5*b*c^5)*x^3 + 3*(a*b^10 - 15*a^2*b^8*c + 80*a^3*b^6*c^2 - 160*a^4*b^4*c^3 + 256*a^6*c^5)*x^2 + 3*(a^2*b^9 - 16*a^3*b^7*c + 96*a^4*b^5*c^2 - 256*a^5*b^3*c^3 + 256*a^6*b*c^4)*x)]","B",0
2219,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2220,1,3934,0,2.627861," ","integrate(1/x^2/(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\left[-\frac{3 \, a^{4} b^{8} - 48 \, a^{5} b^{6} c + 288 \, a^{6} b^{4} c^{2} - 768 \, a^{7} b^{2} c^{3} + 768 \, a^{8} c^{4} + 12 \, {\left(a b^{8} c^{3} - 15 \, a^{2} b^{6} c^{4} + 82 \, a^{3} b^{4} c^{5} - 187 \, a^{4} b^{2} c^{6} + 140 \, a^{5} c^{7}\right)} x^{6} + 6 \, {\left(6 \, a b^{9} c^{2} - 91 \, a^{2} b^{7} c^{3} + 506 \, a^{3} b^{5} c^{4} - 1191 \, a^{4} b^{3} c^{5} + 956 \, a^{5} b c^{6}\right)} x^{5} + 2 \, {\left(18 \, a b^{10} c - 261 \, a^{2} b^{8} c^{2} + 1334 \, a^{3} b^{6} c^{3} - 2537 \, a^{4} b^{4} c^{4} + 340 \, a^{5} b^{2} c^{5} + 2240 \, a^{6} c^{6}\right)} x^{4} + 3 \, {\left(4 \, a b^{11} - 42 \, a^{2} b^{9} c + 50 \, a^{3} b^{7} c^{2} + 837 \, a^{4} b^{5} c^{3} - 3364 \, a^{5} b^{3} c^{4} + 3520 \, a^{6} b c^{5}\right)} x^{3} + 3 \, {\left(10 \, a^{2} b^{10} - 148 \, a^{3} b^{8} c + 783 \, a^{4} b^{6} c^{2} - 1618 \, a^{5} b^{4} c^{3} + 548 \, a^{6} b^{2} c^{4} + 1232 \, a^{7} c^{5}\right)} x^{2} + 6 \, {\left({\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 70 \, a^{2} b^{4} c^{5} - 140 \, a^{3} b^{2} c^{6} + 70 \, a^{4} c^{7}\right)} x^{7} + 3 \, {\left(b^{9} c^{2} - 14 \, a b^{7} c^{3} + 70 \, a^{2} b^{5} c^{4} - 140 \, a^{3} b^{3} c^{5} + 70 \, a^{4} b c^{6}\right)} x^{6} + 3 \, {\left(b^{10} c - 13 \, a b^{8} c^{2} + 56 \, a^{2} b^{6} c^{3} - 70 \, a^{3} b^{4} c^{4} - 70 \, a^{4} b^{2} c^{5} + 70 \, a^{5} c^{6}\right)} x^{5} + {\left(b^{11} - 8 \, a b^{9} c - 14 \, a^{2} b^{7} c^{2} + 280 \, a^{3} b^{5} c^{3} - 770 \, a^{4} b^{3} c^{4} + 420 \, a^{5} b c^{5}\right)} x^{4} + 3 \, {\left(a b^{10} - 13 \, a^{2} b^{8} c + 56 \, a^{3} b^{6} c^{2} - 70 \, a^{4} b^{4} c^{3} - 70 \, a^{5} b^{2} c^{4} + 70 \, a^{6} c^{5}\right)} x^{3} + 3 \, {\left(a^{2} b^{9} - 14 \, a^{3} b^{7} c + 70 \, a^{4} b^{5} c^{2} - 140 \, a^{5} b^{3} c^{3} + 70 \, a^{6} b c^{4}\right)} x^{2} + {\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 70 \, a^{5} b^{4} c^{2} - 140 \, a^{6} b^{2} c^{3} + 70 \, a^{7} c^{4}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + {\left(22 \, a^{3} b^{9} - 343 \, a^{4} b^{7} c + 1987 \, a^{5} b^{5} c^{2} - 5034 \, a^{6} b^{3} c^{3} + 4664 \, a^{7} b c^{4}\right)} x - 6 \, {\left({\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{7} + 3 \, {\left(b^{10} c^{2} - 16 \, a b^{8} c^{3} + 96 \, a^{2} b^{6} c^{4} - 256 \, a^{3} b^{4} c^{5} + 256 \, a^{4} b^{2} c^{6}\right)} x^{6} + 3 \, {\left(b^{11} c - 15 \, a b^{9} c^{2} + 80 \, a^{2} b^{7} c^{3} - 160 \, a^{3} b^{5} c^{4} + 256 \, a^{5} b c^{6}\right)} x^{5} + {\left(b^{12} - 10 \, a b^{10} c + 320 \, a^{3} b^{6} c^{3} - 1280 \, a^{4} b^{4} c^{4} + 1536 \, a^{5} b^{2} c^{5}\right)} x^{4} + 3 \, {\left(a b^{11} - 15 \, a^{2} b^{9} c + 80 \, a^{3} b^{7} c^{2} - 160 \, a^{4} b^{5} c^{3} + 256 \, a^{6} b c^{5}\right)} x^{3} + 3 \, {\left(a^{2} b^{10} - 16 \, a^{3} b^{8} c + 96 \, a^{4} b^{6} c^{2} - 256 \, a^{5} b^{4} c^{3} + 256 \, a^{6} b^{2} c^{4}\right)} x^{2} + {\left(a^{3} b^{9} - 16 \, a^{4} b^{7} c + 96 \, a^{5} b^{5} c^{2} - 256 \, a^{6} b^{3} c^{3} + 256 \, a^{7} b c^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 12 \, {\left({\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{7} + 3 \, {\left(b^{10} c^{2} - 16 \, a b^{8} c^{3} + 96 \, a^{2} b^{6} c^{4} - 256 \, a^{3} b^{4} c^{5} + 256 \, a^{4} b^{2} c^{6}\right)} x^{6} + 3 \, {\left(b^{11} c - 15 \, a b^{9} c^{2} + 80 \, a^{2} b^{7} c^{3} - 160 \, a^{3} b^{5} c^{4} + 256 \, a^{5} b c^{6}\right)} x^{5} + {\left(b^{12} - 10 \, a b^{10} c + 320 \, a^{3} b^{6} c^{3} - 1280 \, a^{4} b^{4} c^{4} + 1536 \, a^{5} b^{2} c^{5}\right)} x^{4} + 3 \, {\left(a b^{11} - 15 \, a^{2} b^{9} c + 80 \, a^{3} b^{7} c^{2} - 160 \, a^{4} b^{5} c^{3} + 256 \, a^{6} b c^{5}\right)} x^{3} + 3 \, {\left(a^{2} b^{10} - 16 \, a^{3} b^{8} c + 96 \, a^{4} b^{6} c^{2} - 256 \, a^{5} b^{4} c^{3} + 256 \, a^{6} b^{2} c^{4}\right)} x^{2} + {\left(a^{3} b^{9} - 16 \, a^{4} b^{7} c + 96 \, a^{5} b^{5} c^{2} - 256 \, a^{6} b^{3} c^{3} + 256 \, a^{7} b c^{4}\right)} x\right)} \log\left(x\right)}{3 \, {\left({\left(a^{5} b^{8} c^{3} - 16 \, a^{6} b^{6} c^{4} + 96 \, a^{7} b^{4} c^{5} - 256 \, a^{8} b^{2} c^{6} + 256 \, a^{9} c^{7}\right)} x^{7} + 3 \, {\left(a^{5} b^{9} c^{2} - 16 \, a^{6} b^{7} c^{3} + 96 \, a^{7} b^{5} c^{4} - 256 \, a^{8} b^{3} c^{5} + 256 \, a^{9} b c^{6}\right)} x^{6} + 3 \, {\left(a^{5} b^{10} c - 15 \, a^{6} b^{8} c^{2} + 80 \, a^{7} b^{6} c^{3} - 160 \, a^{8} b^{4} c^{4} + 256 \, a^{10} c^{6}\right)} x^{5} + {\left(a^{5} b^{11} - 10 \, a^{6} b^{9} c + 320 \, a^{8} b^{5} c^{3} - 1280 \, a^{9} b^{3} c^{4} + 1536 \, a^{10} b c^{5}\right)} x^{4} + 3 \, {\left(a^{6} b^{10} - 15 \, a^{7} b^{8} c + 80 \, a^{8} b^{6} c^{2} - 160 \, a^{9} b^{4} c^{3} + 256 \, a^{11} c^{5}\right)} x^{3} + 3 \, {\left(a^{7} b^{9} - 16 \, a^{8} b^{7} c + 96 \, a^{9} b^{5} c^{2} - 256 \, a^{10} b^{3} c^{3} + 256 \, a^{11} b c^{4}\right)} x^{2} + {\left(a^{8} b^{8} - 16 \, a^{9} b^{6} c + 96 \, a^{10} b^{4} c^{2} - 256 \, a^{11} b^{2} c^{3} + 256 \, a^{12} c^{4}\right)} x\right)}}, -\frac{3 \, a^{4} b^{8} - 48 \, a^{5} b^{6} c + 288 \, a^{6} b^{4} c^{2} - 768 \, a^{7} b^{2} c^{3} + 768 \, a^{8} c^{4} + 12 \, {\left(a b^{8} c^{3} - 15 \, a^{2} b^{6} c^{4} + 82 \, a^{3} b^{4} c^{5} - 187 \, a^{4} b^{2} c^{6} + 140 \, a^{5} c^{7}\right)} x^{6} + 6 \, {\left(6 \, a b^{9} c^{2} - 91 \, a^{2} b^{7} c^{3} + 506 \, a^{3} b^{5} c^{4} - 1191 \, a^{4} b^{3} c^{5} + 956 \, a^{5} b c^{6}\right)} x^{5} + 2 \, {\left(18 \, a b^{10} c - 261 \, a^{2} b^{8} c^{2} + 1334 \, a^{3} b^{6} c^{3} - 2537 \, a^{4} b^{4} c^{4} + 340 \, a^{5} b^{2} c^{5} + 2240 \, a^{6} c^{6}\right)} x^{4} + 3 \, {\left(4 \, a b^{11} - 42 \, a^{2} b^{9} c + 50 \, a^{3} b^{7} c^{2} + 837 \, a^{4} b^{5} c^{3} - 3364 \, a^{5} b^{3} c^{4} + 3520 \, a^{6} b c^{5}\right)} x^{3} + 3 \, {\left(10 \, a^{2} b^{10} - 148 \, a^{3} b^{8} c + 783 \, a^{4} b^{6} c^{2} - 1618 \, a^{5} b^{4} c^{3} + 548 \, a^{6} b^{2} c^{4} + 1232 \, a^{7} c^{5}\right)} x^{2} + 12 \, {\left({\left(b^{8} c^{3} - 14 \, a b^{6} c^{4} + 70 \, a^{2} b^{4} c^{5} - 140 \, a^{3} b^{2} c^{6} + 70 \, a^{4} c^{7}\right)} x^{7} + 3 \, {\left(b^{9} c^{2} - 14 \, a b^{7} c^{3} + 70 \, a^{2} b^{5} c^{4} - 140 \, a^{3} b^{3} c^{5} + 70 \, a^{4} b c^{6}\right)} x^{6} + 3 \, {\left(b^{10} c - 13 \, a b^{8} c^{2} + 56 \, a^{2} b^{6} c^{3} - 70 \, a^{3} b^{4} c^{4} - 70 \, a^{4} b^{2} c^{5} + 70 \, a^{5} c^{6}\right)} x^{5} + {\left(b^{11} - 8 \, a b^{9} c - 14 \, a^{2} b^{7} c^{2} + 280 \, a^{3} b^{5} c^{3} - 770 \, a^{4} b^{3} c^{4} + 420 \, a^{5} b c^{5}\right)} x^{4} + 3 \, {\left(a b^{10} - 13 \, a^{2} b^{8} c + 56 \, a^{3} b^{6} c^{2} - 70 \, a^{4} b^{4} c^{3} - 70 \, a^{5} b^{2} c^{4} + 70 \, a^{6} c^{5}\right)} x^{3} + 3 \, {\left(a^{2} b^{9} - 14 \, a^{3} b^{7} c + 70 \, a^{4} b^{5} c^{2} - 140 \, a^{5} b^{3} c^{3} + 70 \, a^{6} b c^{4}\right)} x^{2} + {\left(a^{3} b^{8} - 14 \, a^{4} b^{6} c + 70 \, a^{5} b^{4} c^{2} - 140 \, a^{6} b^{2} c^{3} + 70 \, a^{7} c^{4}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(22 \, a^{3} b^{9} - 343 \, a^{4} b^{7} c + 1987 \, a^{5} b^{5} c^{2} - 5034 \, a^{6} b^{3} c^{3} + 4664 \, a^{7} b c^{4}\right)} x - 6 \, {\left({\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{7} + 3 \, {\left(b^{10} c^{2} - 16 \, a b^{8} c^{3} + 96 \, a^{2} b^{6} c^{4} - 256 \, a^{3} b^{4} c^{5} + 256 \, a^{4} b^{2} c^{6}\right)} x^{6} + 3 \, {\left(b^{11} c - 15 \, a b^{9} c^{2} + 80 \, a^{2} b^{7} c^{3} - 160 \, a^{3} b^{5} c^{4} + 256 \, a^{5} b c^{6}\right)} x^{5} + {\left(b^{12} - 10 \, a b^{10} c + 320 \, a^{3} b^{6} c^{3} - 1280 \, a^{4} b^{4} c^{4} + 1536 \, a^{5} b^{2} c^{5}\right)} x^{4} + 3 \, {\left(a b^{11} - 15 \, a^{2} b^{9} c + 80 \, a^{3} b^{7} c^{2} - 160 \, a^{4} b^{5} c^{3} + 256 \, a^{6} b c^{5}\right)} x^{3} + 3 \, {\left(a^{2} b^{10} - 16 \, a^{3} b^{8} c + 96 \, a^{4} b^{6} c^{2} - 256 \, a^{5} b^{4} c^{3} + 256 \, a^{6} b^{2} c^{4}\right)} x^{2} + {\left(a^{3} b^{9} - 16 \, a^{4} b^{7} c + 96 \, a^{5} b^{5} c^{2} - 256 \, a^{6} b^{3} c^{3} + 256 \, a^{7} b c^{4}\right)} x\right)} \log\left(c x^{2} + b x + a\right) + 12 \, {\left({\left(b^{9} c^{3} - 16 \, a b^{7} c^{4} + 96 \, a^{2} b^{5} c^{5} - 256 \, a^{3} b^{3} c^{6} + 256 \, a^{4} b c^{7}\right)} x^{7} + 3 \, {\left(b^{10} c^{2} - 16 \, a b^{8} c^{3} + 96 \, a^{2} b^{6} c^{4} - 256 \, a^{3} b^{4} c^{5} + 256 \, a^{4} b^{2} c^{6}\right)} x^{6} + 3 \, {\left(b^{11} c - 15 \, a b^{9} c^{2} + 80 \, a^{2} b^{7} c^{3} - 160 \, a^{3} b^{5} c^{4} + 256 \, a^{5} b c^{6}\right)} x^{5} + {\left(b^{12} - 10 \, a b^{10} c + 320 \, a^{3} b^{6} c^{3} - 1280 \, a^{4} b^{4} c^{4} + 1536 \, a^{5} b^{2} c^{5}\right)} x^{4} + 3 \, {\left(a b^{11} - 15 \, a^{2} b^{9} c + 80 \, a^{3} b^{7} c^{2} - 160 \, a^{4} b^{5} c^{3} + 256 \, a^{6} b c^{5}\right)} x^{3} + 3 \, {\left(a^{2} b^{10} - 16 \, a^{3} b^{8} c + 96 \, a^{4} b^{6} c^{2} - 256 \, a^{5} b^{4} c^{3} + 256 \, a^{6} b^{2} c^{4}\right)} x^{2} + {\left(a^{3} b^{9} - 16 \, a^{4} b^{7} c + 96 \, a^{5} b^{5} c^{2} - 256 \, a^{6} b^{3} c^{3} + 256 \, a^{7} b c^{4}\right)} x\right)} \log\left(x\right)}{3 \, {\left({\left(a^{5} b^{8} c^{3} - 16 \, a^{6} b^{6} c^{4} + 96 \, a^{7} b^{4} c^{5} - 256 \, a^{8} b^{2} c^{6} + 256 \, a^{9} c^{7}\right)} x^{7} + 3 \, {\left(a^{5} b^{9} c^{2} - 16 \, a^{6} b^{7} c^{3} + 96 \, a^{7} b^{5} c^{4} - 256 \, a^{8} b^{3} c^{5} + 256 \, a^{9} b c^{6}\right)} x^{6} + 3 \, {\left(a^{5} b^{10} c - 15 \, a^{6} b^{8} c^{2} + 80 \, a^{7} b^{6} c^{3} - 160 \, a^{8} b^{4} c^{4} + 256 \, a^{10} c^{6}\right)} x^{5} + {\left(a^{5} b^{11} - 10 \, a^{6} b^{9} c + 320 \, a^{8} b^{5} c^{3} - 1280 \, a^{9} b^{3} c^{4} + 1536 \, a^{10} b c^{5}\right)} x^{4} + 3 \, {\left(a^{6} b^{10} - 15 \, a^{7} b^{8} c + 80 \, a^{8} b^{6} c^{2} - 160 \, a^{9} b^{4} c^{3} + 256 \, a^{11} c^{5}\right)} x^{3} + 3 \, {\left(a^{7} b^{9} - 16 \, a^{8} b^{7} c + 96 \, a^{9} b^{5} c^{2} - 256 \, a^{10} b^{3} c^{3} + 256 \, a^{11} b c^{4}\right)} x^{2} + {\left(a^{8} b^{8} - 16 \, a^{9} b^{6} c + 96 \, a^{10} b^{4} c^{2} - 256 \, a^{11} b^{2} c^{3} + 256 \, a^{12} c^{4}\right)} x\right)}}\right]"," ",0,"[-1/3*(3*a^4*b^8 - 48*a^5*b^6*c + 288*a^6*b^4*c^2 - 768*a^7*b^2*c^3 + 768*a^8*c^4 + 12*(a*b^8*c^3 - 15*a^2*b^6*c^4 + 82*a^3*b^4*c^5 - 187*a^4*b^2*c^6 + 140*a^5*c^7)*x^6 + 6*(6*a*b^9*c^2 - 91*a^2*b^7*c^3 + 506*a^3*b^5*c^4 - 1191*a^4*b^3*c^5 + 956*a^5*b*c^6)*x^5 + 2*(18*a*b^10*c - 261*a^2*b^8*c^2 + 1334*a^3*b^6*c^3 - 2537*a^4*b^4*c^4 + 340*a^5*b^2*c^5 + 2240*a^6*c^6)*x^4 + 3*(4*a*b^11 - 42*a^2*b^9*c + 50*a^3*b^7*c^2 + 837*a^4*b^5*c^3 - 3364*a^5*b^3*c^4 + 3520*a^6*b*c^5)*x^3 + 3*(10*a^2*b^10 - 148*a^3*b^8*c + 783*a^4*b^6*c^2 - 1618*a^5*b^4*c^3 + 548*a^6*b^2*c^4 + 1232*a^7*c^5)*x^2 + 6*((b^8*c^3 - 14*a*b^6*c^4 + 70*a^2*b^4*c^5 - 140*a^3*b^2*c^6 + 70*a^4*c^7)*x^7 + 3*(b^9*c^2 - 14*a*b^7*c^3 + 70*a^2*b^5*c^4 - 140*a^3*b^3*c^5 + 70*a^4*b*c^6)*x^6 + 3*(b^10*c - 13*a*b^8*c^2 + 56*a^2*b^6*c^3 - 70*a^3*b^4*c^4 - 70*a^4*b^2*c^5 + 70*a^5*c^6)*x^5 + (b^11 - 8*a*b^9*c - 14*a^2*b^7*c^2 + 280*a^3*b^5*c^3 - 770*a^4*b^3*c^4 + 420*a^5*b*c^5)*x^4 + 3*(a*b^10 - 13*a^2*b^8*c + 56*a^3*b^6*c^2 - 70*a^4*b^4*c^3 - 70*a^5*b^2*c^4 + 70*a^6*c^5)*x^3 + 3*(a^2*b^9 - 14*a^3*b^7*c + 70*a^4*b^5*c^2 - 140*a^5*b^3*c^3 + 70*a^6*b*c^4)*x^2 + (a^3*b^8 - 14*a^4*b^6*c + 70*a^5*b^4*c^2 - 140*a^6*b^2*c^3 + 70*a^7*c^4)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + (22*a^3*b^9 - 343*a^4*b^7*c + 1987*a^5*b^5*c^2 - 5034*a^6*b^3*c^3 + 4664*a^7*b*c^4)*x - 6*((b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^7 + 3*(b^10*c^2 - 16*a*b^8*c^3 + 96*a^2*b^6*c^4 - 256*a^3*b^4*c^5 + 256*a^4*b^2*c^6)*x^6 + 3*(b^11*c - 15*a*b^9*c^2 + 80*a^2*b^7*c^3 - 160*a^3*b^5*c^4 + 256*a^5*b*c^6)*x^5 + (b^12 - 10*a*b^10*c + 320*a^3*b^6*c^3 - 1280*a^4*b^4*c^4 + 1536*a^5*b^2*c^5)*x^4 + 3*(a*b^11 - 15*a^2*b^9*c + 80*a^3*b^7*c^2 - 160*a^4*b^5*c^3 + 256*a^6*b*c^5)*x^3 + 3*(a^2*b^10 - 16*a^3*b^8*c + 96*a^4*b^6*c^2 - 256*a^5*b^4*c^3 + 256*a^6*b^2*c^4)*x^2 + (a^3*b^9 - 16*a^4*b^7*c + 96*a^5*b^5*c^2 - 256*a^6*b^3*c^3 + 256*a^7*b*c^4)*x)*log(c*x^2 + b*x + a) + 12*((b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^7 + 3*(b^10*c^2 - 16*a*b^8*c^3 + 96*a^2*b^6*c^4 - 256*a^3*b^4*c^5 + 256*a^4*b^2*c^6)*x^6 + 3*(b^11*c - 15*a*b^9*c^2 + 80*a^2*b^7*c^3 - 160*a^3*b^5*c^4 + 256*a^5*b*c^6)*x^5 + (b^12 - 10*a*b^10*c + 320*a^3*b^6*c^3 - 1280*a^4*b^4*c^4 + 1536*a^5*b^2*c^5)*x^4 + 3*(a*b^11 - 15*a^2*b^9*c + 80*a^3*b^7*c^2 - 160*a^4*b^5*c^3 + 256*a^6*b*c^5)*x^3 + 3*(a^2*b^10 - 16*a^3*b^8*c + 96*a^4*b^6*c^2 - 256*a^5*b^4*c^3 + 256*a^6*b^2*c^4)*x^2 + (a^3*b^9 - 16*a^4*b^7*c + 96*a^5*b^5*c^2 - 256*a^6*b^3*c^3 + 256*a^7*b*c^4)*x)*log(x))/((a^5*b^8*c^3 - 16*a^6*b^6*c^4 + 96*a^7*b^4*c^5 - 256*a^8*b^2*c^6 + 256*a^9*c^7)*x^7 + 3*(a^5*b^9*c^2 - 16*a^6*b^7*c^3 + 96*a^7*b^5*c^4 - 256*a^8*b^3*c^5 + 256*a^9*b*c^6)*x^6 + 3*(a^5*b^10*c - 15*a^6*b^8*c^2 + 80*a^7*b^6*c^3 - 160*a^8*b^4*c^4 + 256*a^10*c^6)*x^5 + (a^5*b^11 - 10*a^6*b^9*c + 320*a^8*b^5*c^3 - 1280*a^9*b^3*c^4 + 1536*a^10*b*c^5)*x^4 + 3*(a^6*b^10 - 15*a^7*b^8*c + 80*a^8*b^6*c^2 - 160*a^9*b^4*c^3 + 256*a^11*c^5)*x^3 + 3*(a^7*b^9 - 16*a^8*b^7*c + 96*a^9*b^5*c^2 - 256*a^10*b^3*c^3 + 256*a^11*b*c^4)*x^2 + (a^8*b^8 - 16*a^9*b^6*c + 96*a^10*b^4*c^2 - 256*a^11*b^2*c^3 + 256*a^12*c^4)*x), -1/3*(3*a^4*b^8 - 48*a^5*b^6*c + 288*a^6*b^4*c^2 - 768*a^7*b^2*c^3 + 768*a^8*c^4 + 12*(a*b^8*c^3 - 15*a^2*b^6*c^4 + 82*a^3*b^4*c^5 - 187*a^4*b^2*c^6 + 140*a^5*c^7)*x^6 + 6*(6*a*b^9*c^2 - 91*a^2*b^7*c^3 + 506*a^3*b^5*c^4 - 1191*a^4*b^3*c^5 + 956*a^5*b*c^6)*x^5 + 2*(18*a*b^10*c - 261*a^2*b^8*c^2 + 1334*a^3*b^6*c^3 - 2537*a^4*b^4*c^4 + 340*a^5*b^2*c^5 + 2240*a^6*c^6)*x^4 + 3*(4*a*b^11 - 42*a^2*b^9*c + 50*a^3*b^7*c^2 + 837*a^4*b^5*c^3 - 3364*a^5*b^3*c^4 + 3520*a^6*b*c^5)*x^3 + 3*(10*a^2*b^10 - 148*a^3*b^8*c + 783*a^4*b^6*c^2 - 1618*a^5*b^4*c^3 + 548*a^6*b^2*c^4 + 1232*a^7*c^5)*x^2 + 12*((b^8*c^3 - 14*a*b^6*c^4 + 70*a^2*b^4*c^5 - 140*a^3*b^2*c^6 + 70*a^4*c^7)*x^7 + 3*(b^9*c^2 - 14*a*b^7*c^3 + 70*a^2*b^5*c^4 - 140*a^3*b^3*c^5 + 70*a^4*b*c^6)*x^6 + 3*(b^10*c - 13*a*b^8*c^2 + 56*a^2*b^6*c^3 - 70*a^3*b^4*c^4 - 70*a^4*b^2*c^5 + 70*a^5*c^6)*x^5 + (b^11 - 8*a*b^9*c - 14*a^2*b^7*c^2 + 280*a^3*b^5*c^3 - 770*a^4*b^3*c^4 + 420*a^5*b*c^5)*x^4 + 3*(a*b^10 - 13*a^2*b^8*c + 56*a^3*b^6*c^2 - 70*a^4*b^4*c^3 - 70*a^5*b^2*c^4 + 70*a^6*c^5)*x^3 + 3*(a^2*b^9 - 14*a^3*b^7*c + 70*a^4*b^5*c^2 - 140*a^5*b^3*c^3 + 70*a^6*b*c^4)*x^2 + (a^3*b^8 - 14*a^4*b^6*c + 70*a^5*b^4*c^2 - 140*a^6*b^2*c^3 + 70*a^7*c^4)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + (22*a^3*b^9 - 343*a^4*b^7*c + 1987*a^5*b^5*c^2 - 5034*a^6*b^3*c^3 + 4664*a^7*b*c^4)*x - 6*((b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^7 + 3*(b^10*c^2 - 16*a*b^8*c^3 + 96*a^2*b^6*c^4 - 256*a^3*b^4*c^5 + 256*a^4*b^2*c^6)*x^6 + 3*(b^11*c - 15*a*b^9*c^2 + 80*a^2*b^7*c^3 - 160*a^3*b^5*c^4 + 256*a^5*b*c^6)*x^5 + (b^12 - 10*a*b^10*c + 320*a^3*b^6*c^3 - 1280*a^4*b^4*c^4 + 1536*a^5*b^2*c^5)*x^4 + 3*(a*b^11 - 15*a^2*b^9*c + 80*a^3*b^7*c^2 - 160*a^4*b^5*c^3 + 256*a^6*b*c^5)*x^3 + 3*(a^2*b^10 - 16*a^3*b^8*c + 96*a^4*b^6*c^2 - 256*a^5*b^4*c^3 + 256*a^6*b^2*c^4)*x^2 + (a^3*b^9 - 16*a^4*b^7*c + 96*a^5*b^5*c^2 - 256*a^6*b^3*c^3 + 256*a^7*b*c^4)*x)*log(c*x^2 + b*x + a) + 12*((b^9*c^3 - 16*a*b^7*c^4 + 96*a^2*b^5*c^5 - 256*a^3*b^3*c^6 + 256*a^4*b*c^7)*x^7 + 3*(b^10*c^2 - 16*a*b^8*c^3 + 96*a^2*b^6*c^4 - 256*a^3*b^4*c^5 + 256*a^4*b^2*c^6)*x^6 + 3*(b^11*c - 15*a*b^9*c^2 + 80*a^2*b^7*c^3 - 160*a^3*b^5*c^4 + 256*a^5*b*c^6)*x^5 + (b^12 - 10*a*b^10*c + 320*a^3*b^6*c^3 - 1280*a^4*b^4*c^4 + 1536*a^5*b^2*c^5)*x^4 + 3*(a*b^11 - 15*a^2*b^9*c + 80*a^3*b^7*c^2 - 160*a^4*b^5*c^3 + 256*a^6*b*c^5)*x^3 + 3*(a^2*b^10 - 16*a^3*b^8*c + 96*a^4*b^6*c^2 - 256*a^5*b^4*c^3 + 256*a^6*b^2*c^4)*x^2 + (a^3*b^9 - 16*a^4*b^7*c + 96*a^5*b^5*c^2 - 256*a^6*b^3*c^3 + 256*a^7*b*c^4)*x)*log(x))/((a^5*b^8*c^3 - 16*a^6*b^6*c^4 + 96*a^7*b^4*c^5 - 256*a^8*b^2*c^6 + 256*a^9*c^7)*x^7 + 3*(a^5*b^9*c^2 - 16*a^6*b^7*c^3 + 96*a^7*b^5*c^4 - 256*a^8*b^3*c^5 + 256*a^9*b*c^6)*x^6 + 3*(a^5*b^10*c - 15*a^6*b^8*c^2 + 80*a^7*b^6*c^3 - 160*a^8*b^4*c^4 + 256*a^10*c^6)*x^5 + (a^5*b^11 - 10*a^6*b^9*c + 320*a^8*b^5*c^3 - 1280*a^9*b^3*c^4 + 1536*a^10*b*c^5)*x^4 + 3*(a^6*b^10 - 15*a^7*b^8*c + 80*a^8*b^6*c^2 - 160*a^9*b^4*c^3 + 256*a^11*c^5)*x^3 + 3*(a^7*b^9 - 16*a^8*b^7*c + 96*a^9*b^5*c^2 - 256*a^10*b^3*c^3 + 256*a^11*b*c^4)*x^2 + (a^8*b^8 - 16*a^9*b^6*c + 96*a^10*b^4*c^2 - 256*a^11*b^2*c^3 + 256*a^12*c^4)*x)]","B",0
2221,1,8858,0,0.565653," ","integrate((e*x+d)^5/(c*x^2+b*x+a)^5,x, algorithm=""fricas"")","\left[\frac{60 \, {\left(14 \, {\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{5} - 35 \, {\left(b^{3} c^{7} - 4 \, a b c^{8}\right)} d^{4} e + 10 \, {\left(3 \, b^{4} c^{6} - 10 \, a b^{2} c^{7} - 8 \, a^{2} c^{8}\right)} d^{3} e^{2} - 10 \, {\left(b^{5} c^{5} - a b^{3} c^{6} - 12 \, a^{2} b c^{7}\right)} d^{2} e^{3} + {\left(b^{6} c^{4} + 8 \, a b^{4} c^{5} - 42 \, a^{2} b^{2} c^{6} - 24 \, a^{3} c^{7}\right)} d e^{4} - {\left(a b^{5} c^{4} - a^{2} b^{3} c^{5} - 12 \, a^{3} b c^{6}\right)} e^{5}\right)} x^{7} + 210 \, {\left(14 \, {\left(b^{3} c^{7} - 4 \, a b c^{8}\right)} d^{5} - 35 \, {\left(b^{4} c^{6} - 4 \, a b^{2} c^{7}\right)} d^{4} e + 10 \, {\left(3 \, b^{5} c^{5} - 10 \, a b^{3} c^{6} - 8 \, a^{2} b c^{7}\right)} d^{3} e^{2} - 10 \, {\left(b^{6} c^{4} - a b^{4} c^{5} - 12 \, a^{2} b^{2} c^{6}\right)} d^{2} e^{3} + {\left(b^{7} c^{3} + 8 \, a b^{5} c^{4} - 42 \, a^{2} b^{3} c^{5} - 24 \, a^{3} b c^{6}\right)} d e^{4} - {\left(a b^{6} c^{3} - a^{2} b^{4} c^{4} - 12 \, a^{3} b^{2} c^{5}\right)} e^{5}\right)} x^{6} - {\left(3 \, b^{9} c - 62 \, a b^{7} c^{2} + 526 \, a^{2} b^{5} c^{3} - 2420 \, a^{3} b^{3} c^{4} + 4464 \, a^{4} b c^{5}\right)} d^{5} - 5 \, {\left(a b^{8} c - 23 \, a^{2} b^{6} c^{2} + 250 \, a^{3} b^{4} c^{3} - 312 \, a^{4} b^{2} c^{4} - 1536 \, a^{5} c^{5}\right)} d^{4} e - 10 \, {\left(a^{2} b^{7} c - 32 \, a^{3} b^{5} c^{2} - 212 \, a^{4} b^{3} c^{3} + 1296 \, a^{5} b c^{4}\right)} d^{3} e^{2} - 10 \, {\left(3 \, a^{3} b^{6} c + 154 \, a^{4} b^{4} c^{2} - 536 \, a^{5} b^{2} c^{3} - 512 \, a^{6} c^{4}\right)} d^{2} e^{3} + 50 \, {\left(5 \, a^{4} b^{5} c + 2 \, a^{5} b^{3} c^{2} - 88 \, a^{6} b c^{3}\right)} d e^{4} - {\left(3 \, a^{4} b^{6} + 154 \, a^{5} b^{4} c - 536 \, a^{6} b^{2} c^{2} - 512 \, a^{7} c^{3}\right)} e^{5} + 20 \, {\left(14 \, {\left(13 \, b^{4} c^{6} - 41 \, a b^{2} c^{7} - 44 \, a^{2} c^{8}\right)} d^{5} - 35 \, {\left(13 \, b^{5} c^{5} - 41 \, a b^{3} c^{6} - 44 \, a^{2} b c^{7}\right)} d^{4} e + 10 \, {\left(39 \, b^{6} c^{4} - 97 \, a b^{4} c^{5} - 214 \, a^{2} b^{2} c^{6} - 88 \, a^{3} c^{7}\right)} d^{3} e^{2} - 10 \, {\left(13 \, b^{7} c^{3} - 2 \, a b^{5} c^{4} - 167 \, a^{2} b^{3} c^{5} - 132 \, a^{3} b c^{6}\right)} d^{2} e^{3} + {\left(13 \, b^{8} c^{2} + 115 \, a b^{6} c^{3} - 458 \, a^{2} b^{4} c^{4} - 774 \, a^{3} b^{2} c^{5} - 264 \, a^{4} c^{6}\right)} d e^{4} - {\left(13 \, a b^{7} c^{2} - 2 \, a^{2} b^{5} c^{3} - 167 \, a^{3} b^{3} c^{4} - 132 \, a^{4} b c^{5}\right)} e^{5}\right)} x^{5} + {\left(350 \, {\left(5 \, b^{5} c^{5} + 2 \, a b^{3} c^{6} - 88 \, a^{2} b c^{7}\right)} d^{5} - 875 \, {\left(5 \, b^{6} c^{4} + 2 \, a b^{4} c^{5} - 88 \, a^{2} b^{2} c^{6}\right)} d^{4} e + 250 \, {\left(15 \, b^{7} c^{3} + 16 \, a b^{5} c^{4} - 260 \, a^{2} b^{3} c^{5} - 176 \, a^{3} b c^{6}\right)} d^{3} e^{2} - 250 \, {\left(5 \, b^{8} c^{2} + 17 \, a b^{6} c^{3} - 82 \, a^{2} b^{4} c^{4} - 264 \, a^{3} b^{2} c^{5}\right)} d^{2} e^{3} + 25 \, {\left(5 \, b^{9} c + 62 \, a b^{7} c^{2} - 34 \, a^{2} b^{5} c^{3} - 1044 \, a^{3} b^{3} c^{4} - 528 \, a^{4} b c^{5}\right)} d e^{4} - {\left(3 \, b^{10} + 65 \, a b^{8} c + 905 \, a^{2} b^{6} c^{2} - 3970 \, a^{3} b^{4} c^{3} - 2760 \, a^{4} b^{2} c^{4} - 3072 \, a^{5} c^{5}\right)} e^{5}\right)} x^{4} + 4 \, {\left(14 \, {\left(3 \, b^{6} c^{4} + 89 \, a b^{4} c^{5} - 331 \, a^{2} b^{2} c^{6} - 292 \, a^{3} c^{7}\right)} d^{5} - 35 \, {\left(3 \, b^{7} c^{3} + 89 \, a b^{5} c^{4} - 331 \, a^{2} b^{3} c^{5} - 292 \, a^{3} b c^{6}\right)} d^{4} e + 10 \, {\left(9 \, b^{8} c^{2} + 273 \, a b^{6} c^{3} - 815 \, a^{2} b^{4} c^{4} - 1538 \, a^{3} b^{2} c^{5} - 584 \, a^{4} c^{6}\right)} d^{3} e^{2} - 10 \, {\left(3 \, b^{9} c + 98 \, a b^{7} c^{2} - 64 \, a^{2} b^{5} c^{3} - 1285 \, a^{3} b^{3} c^{4} - 876 \, a^{4} b c^{5}\right)} d^{2} e^{3} + 5 \, {\left(37 \, a b^{8} c + 55 \, a^{2} b^{6} c^{2} - 362 \, a^{3} b^{4} c^{3} - 1866 \, a^{4} b^{2} c^{4} + 264 \, a^{5} c^{5}\right)} d e^{4} - {\left(3 \, a b^{9} + 98 \, a^{2} b^{7} c - 64 \, a^{3} b^{5} c^{2} - 1285 \, a^{4} b^{3} c^{3} - 876 \, a^{5} b c^{4}\right)} e^{5}\right)} x^{3} - 2 \, {\left(14 \, {\left(b^{7} c^{3} - 32 \, a b^{5} c^{4} - 107 \, a^{2} b^{3} c^{5} + 876 \, a^{3} b c^{6}\right)} d^{5} - 35 \, {\left(b^{8} c^{2} - 32 \, a b^{6} c^{3} - 107 \, a^{2} b^{4} c^{4} + 876 \, a^{3} b^{2} c^{5}\right)} d^{4} e + 10 \, {\left(3 \, b^{9} c - 94 \, a b^{7} c^{2} - 385 \, a^{2} b^{5} c^{3} + 2414 \, a^{3} b^{3} c^{4} + 1752 \, a^{4} b c^{5}\right)} d^{3} e^{2} + 10 \, {\left(9 \, a b^{8} c + 363 \, a^{2} b^{6} c^{2} - 1195 \, a^{3} b^{4} c^{3} - 1348 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{2} e^{3} - 5 \, {\left(129 \, a^{2} b^{7} c - 8 \, a^{3} b^{5} c^{2} - 1718 \, a^{4} b^{3} c^{3} - 1256 \, a^{5} b c^{4}\right)} d e^{4} + {\left(9 \, a^{2} b^{8} + 363 \, a^{3} b^{6} c - 1195 \, a^{4} b^{4} c^{2} - 1348 \, a^{5} b^{2} c^{3} - 1024 \, a^{6} c^{4}\right)} e^{5}\right)} x^{2} - 60 \, {\left(14 \, a^{4} c^{5} d^{5} - 35 \, a^{4} b c^{4} d^{4} e + {\left(14 \, c^{9} d^{5} - 35 \, b c^{8} d^{4} e + 10 \, {\left(3 \, b^{2} c^{7} + 2 \, a c^{8}\right)} d^{3} e^{2} - 10 \, {\left(b^{3} c^{6} + 3 \, a b c^{7}\right)} d^{2} e^{3} + {\left(b^{4} c^{5} + 12 \, a b^{2} c^{6} + 6 \, a^{2} c^{7}\right)} d e^{4} - {\left(a b^{3} c^{5} + 3 \, a^{2} b c^{6}\right)} e^{5}\right)} x^{8} + 4 \, {\left(14 \, b c^{8} d^{5} - 35 \, b^{2} c^{7} d^{4} e + 10 \, {\left(3 \, b^{3} c^{6} + 2 \, a b c^{7}\right)} d^{3} e^{2} - 10 \, {\left(b^{4} c^{5} + 3 \, a b^{2} c^{6}\right)} d^{2} e^{3} + {\left(b^{5} c^{4} + 12 \, a b^{3} c^{5} + 6 \, a^{2} b c^{6}\right)} d e^{4} - {\left(a b^{4} c^{4} + 3 \, a^{2} b^{2} c^{5}\right)} e^{5}\right)} x^{7} + 2 \, {\left(14 \, {\left(3 \, b^{2} c^{7} + 2 \, a c^{8}\right)} d^{5} - 35 \, {\left(3 \, b^{3} c^{6} + 2 \, a b c^{7}\right)} d^{4} e + 10 \, {\left(9 \, b^{4} c^{5} + 12 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} d^{3} e^{2} - 10 \, {\left(3 \, b^{5} c^{4} + 11 \, a b^{3} c^{5} + 6 \, a^{2} b c^{6}\right)} d^{2} e^{3} + {\left(3 \, b^{6} c^{3} + 38 \, a b^{4} c^{4} + 42 \, a^{2} b^{2} c^{5} + 12 \, a^{3} c^{6}\right)} d e^{4} - {\left(3 \, a b^{5} c^{3} + 11 \, a^{2} b^{3} c^{4} + 6 \, a^{3} b c^{5}\right)} e^{5}\right)} x^{6} + 10 \, {\left(3 \, a^{4} b^{2} c^{3} + 2 \, a^{5} c^{4}\right)} d^{3} e^{2} - 10 \, {\left(a^{4} b^{3} c^{2} + 3 \, a^{5} b c^{3}\right)} d^{2} e^{3} + {\left(a^{4} b^{4} c + 12 \, a^{5} b^{2} c^{2} + 6 \, a^{6} c^{3}\right)} d e^{4} - {\left(a^{5} b^{3} c + 3 \, a^{6} b c^{2}\right)} e^{5} + 4 \, {\left(14 \, {\left(b^{3} c^{6} + 3 \, a b c^{7}\right)} d^{5} - 35 \, {\left(b^{4} c^{5} + 3 \, a b^{2} c^{6}\right)} d^{4} e + 10 \, {\left(3 \, b^{5} c^{4} + 11 \, a b^{3} c^{5} + 6 \, a^{2} b c^{6}\right)} d^{3} e^{2} - 10 \, {\left(b^{6} c^{3} + 6 \, a b^{4} c^{4} + 9 \, a^{2} b^{2} c^{5}\right)} d^{2} e^{3} + {\left(b^{7} c^{2} + 15 \, a b^{5} c^{3} + 42 \, a^{2} b^{3} c^{4} + 18 \, a^{3} b c^{5}\right)} d e^{4} - {\left(a b^{6} c^{2} + 6 \, a^{2} b^{4} c^{3} + 9 \, a^{3} b^{2} c^{4}\right)} e^{5}\right)} x^{5} + {\left(14 \, {\left(b^{4} c^{5} + 12 \, a b^{2} c^{6} + 6 \, a^{2} c^{7}\right)} d^{5} - 35 \, {\left(b^{5} c^{4} + 12 \, a b^{3} c^{5} + 6 \, a^{2} b c^{6}\right)} d^{4} e + 10 \, {\left(3 \, b^{6} c^{3} + 38 \, a b^{4} c^{4} + 42 \, a^{2} b^{2} c^{5} + 12 \, a^{3} c^{6}\right)} d^{3} e^{2} - 10 \, {\left(b^{7} c^{2} + 15 \, a b^{5} c^{3} + 42 \, a^{2} b^{3} c^{4} + 18 \, a^{3} b c^{5}\right)} d^{2} e^{3} + {\left(b^{8} c + 24 \, a b^{6} c^{2} + 156 \, a^{2} b^{4} c^{3} + 144 \, a^{3} b^{2} c^{4} + 36 \, a^{4} c^{5}\right)} d e^{4} - {\left(a b^{7} c + 15 \, a^{2} b^{5} c^{2} + 42 \, a^{3} b^{3} c^{3} + 18 \, a^{4} b c^{4}\right)} e^{5}\right)} x^{4} + 4 \, {\left(14 \, {\left(a b^{3} c^{5} + 3 \, a^{2} b c^{6}\right)} d^{5} - 35 \, {\left(a b^{4} c^{4} + 3 \, a^{2} b^{2} c^{5}\right)} d^{4} e + 10 \, {\left(3 \, a b^{5} c^{3} + 11 \, a^{2} b^{3} c^{4} + 6 \, a^{3} b c^{5}\right)} d^{3} e^{2} - 10 \, {\left(a b^{6} c^{2} + 6 \, a^{2} b^{4} c^{3} + 9 \, a^{3} b^{2} c^{4}\right)} d^{2} e^{3} + {\left(a b^{7} c + 15 \, a^{2} b^{5} c^{2} + 42 \, a^{3} b^{3} c^{3} + 18 \, a^{4} b c^{4}\right)} d e^{4} - {\left(a^{2} b^{6} c + 6 \, a^{3} b^{4} c^{2} + 9 \, a^{4} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + 2 \, {\left(14 \, {\left(3 \, a^{2} b^{2} c^{5} + 2 \, a^{3} c^{6}\right)} d^{5} - 35 \, {\left(3 \, a^{2} b^{3} c^{4} + 2 \, a^{3} b c^{5}\right)} d^{4} e + 10 \, {\left(9 \, a^{2} b^{4} c^{3} + 12 \, a^{3} b^{2} c^{4} + 4 \, a^{4} c^{5}\right)} d^{3} e^{2} - 10 \, {\left(3 \, a^{2} b^{5} c^{2} + 11 \, a^{3} b^{3} c^{3} + 6 \, a^{4} b c^{4}\right)} d^{2} e^{3} + {\left(3 \, a^{2} b^{6} c + 38 \, a^{3} b^{4} c^{2} + 42 \, a^{4} b^{2} c^{3} + 12 \, a^{5} c^{4}\right)} d e^{4} - {\left(3 \, a^{3} b^{5} c + 11 \, a^{4} b^{3} c^{2} + 6 \, a^{5} b c^{3}\right)} e^{5}\right)} x^{2} + 4 \, {\left(14 \, a^{3} b c^{5} d^{5} - 35 \, a^{3} b^{2} c^{4} d^{4} e + 10 \, {\left(3 \, a^{3} b^{3} c^{3} + 2 \, a^{4} b c^{4}\right)} d^{3} e^{2} - 10 \, {\left(a^{3} b^{4} c^{2} + 3 \, a^{4} b^{2} c^{3}\right)} d^{2} e^{3} + {\left(a^{3} b^{5} c + 12 \, a^{4} b^{3} c^{2} + 6 \, a^{5} b c^{3}\right)} d e^{4} - {\left(a^{4} b^{4} c + 3 \, a^{5} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 4 \, {\left(2 \, {\left(b^{8} c^{2} - 23 \, a b^{6} c^{3} + 250 \, a^{2} b^{4} c^{4} - 417 \, a^{3} b^{2} c^{5} - 1116 \, a^{4} c^{6}\right)} d^{5} - 5 \, {\left(b^{9} c - 23 \, a b^{7} c^{2} + 250 \, a^{2} b^{5} c^{3} - 417 \, a^{3} b^{3} c^{4} - 1116 \, a^{4} b c^{5}\right)} d^{4} e - 10 \, {\left(a b^{8} c - 32 \, a^{2} b^{6} c^{2} - 167 \, a^{3} b^{4} c^{3} + 1146 \, a^{4} b^{2} c^{4} - 120 \, a^{5} c^{5}\right)} d^{3} e^{2} - 10 \, {\left(3 \, a^{2} b^{7} c + 139 \, a^{3} b^{5} c^{2} - 521 \, a^{4} b^{3} c^{3} - 332 \, a^{5} b c^{4}\right)} d^{2} e^{3} + 5 \, {\left(47 \, a^{3} b^{6} c - 4 \, a^{4} b^{4} c^{2} - 754 \, a^{5} b^{2} c^{3} + 72 \, a^{6} c^{4}\right)} d e^{4} - {\left(3 \, a^{3} b^{7} + 139 \, a^{4} b^{5} c - 521 \, a^{5} b^{3} c^{2} - 332 \, a^{6} b c^{3}\right)} e^{5}\right)} x}{12 \, {\left(a^{4} b^{10} c - 20 \, a^{5} b^{8} c^{2} + 160 \, a^{6} b^{6} c^{3} - 640 \, a^{7} b^{4} c^{4} + 1280 \, a^{8} b^{2} c^{5} - 1024 \, a^{9} c^{6} + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} x^{8} + 4 \, {\left(b^{11} c^{4} - 20 \, a b^{9} c^{5} + 160 \, a^{2} b^{7} c^{6} - 640 \, a^{3} b^{5} c^{7} + 1280 \, a^{4} b^{3} c^{8} - 1024 \, a^{5} b c^{9}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{3} - 58 \, a b^{10} c^{4} + 440 \, a^{2} b^{8} c^{5} - 1600 \, a^{3} b^{6} c^{6} + 2560 \, a^{4} b^{4} c^{7} - 512 \, a^{5} b^{2} c^{8} - 2048 \, a^{6} c^{9}\right)} x^{6} + 4 \, {\left(b^{13} c^{2} - 17 \, a b^{11} c^{3} + 100 \, a^{2} b^{9} c^{4} - 160 \, a^{3} b^{7} c^{5} - 640 \, a^{4} b^{5} c^{6} + 2816 \, a^{5} b^{3} c^{7} - 3072 \, a^{6} b c^{8}\right)} x^{5} + {\left(b^{14} c - 8 \, a b^{12} c^{2} - 74 \, a^{2} b^{10} c^{3} + 1160 \, a^{3} b^{8} c^{4} - 5440 \, a^{4} b^{6} c^{5} + 10496 \, a^{5} b^{4} c^{6} - 4608 \, a^{6} b^{2} c^{7} - 6144 \, a^{7} c^{8}\right)} x^{4} + 4 \, {\left(a b^{13} c - 17 \, a^{2} b^{11} c^{2} + 100 \, a^{3} b^{9} c^{3} - 160 \, a^{4} b^{7} c^{4} - 640 \, a^{5} b^{5} c^{5} + 2816 \, a^{6} b^{3} c^{6} - 3072 \, a^{7} b c^{7}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} c - 58 \, a^{3} b^{10} c^{2} + 440 \, a^{4} b^{8} c^{3} - 1600 \, a^{5} b^{6} c^{4} + 2560 \, a^{6} b^{4} c^{5} - 512 \, a^{7} b^{2} c^{6} - 2048 \, a^{8} c^{7}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} c - 20 \, a^{4} b^{9} c^{2} + 160 \, a^{5} b^{7} c^{3} - 640 \, a^{6} b^{5} c^{4} + 1280 \, a^{7} b^{3} c^{5} - 1024 \, a^{8} b c^{6}\right)} x\right)}}, \frac{60 \, {\left(14 \, {\left(b^{2} c^{8} - 4 \, a c^{9}\right)} d^{5} - 35 \, {\left(b^{3} c^{7} - 4 \, a b c^{8}\right)} d^{4} e + 10 \, {\left(3 \, b^{4} c^{6} - 10 \, a b^{2} c^{7} - 8 \, a^{2} c^{8}\right)} d^{3} e^{2} - 10 \, {\left(b^{5} c^{5} - a b^{3} c^{6} - 12 \, a^{2} b c^{7}\right)} d^{2} e^{3} + {\left(b^{6} c^{4} + 8 \, a b^{4} c^{5} - 42 \, a^{2} b^{2} c^{6} - 24 \, a^{3} c^{7}\right)} d e^{4} - {\left(a b^{5} c^{4} - a^{2} b^{3} c^{5} - 12 \, a^{3} b c^{6}\right)} e^{5}\right)} x^{7} + 210 \, {\left(14 \, {\left(b^{3} c^{7} - 4 \, a b c^{8}\right)} d^{5} - 35 \, {\left(b^{4} c^{6} - 4 \, a b^{2} c^{7}\right)} d^{4} e + 10 \, {\left(3 \, b^{5} c^{5} - 10 \, a b^{3} c^{6} - 8 \, a^{2} b c^{7}\right)} d^{3} e^{2} - 10 \, {\left(b^{6} c^{4} - a b^{4} c^{5} - 12 \, a^{2} b^{2} c^{6}\right)} d^{2} e^{3} + {\left(b^{7} c^{3} + 8 \, a b^{5} c^{4} - 42 \, a^{2} b^{3} c^{5} - 24 \, a^{3} b c^{6}\right)} d e^{4} - {\left(a b^{6} c^{3} - a^{2} b^{4} c^{4} - 12 \, a^{3} b^{2} c^{5}\right)} e^{5}\right)} x^{6} - {\left(3 \, b^{9} c - 62 \, a b^{7} c^{2} + 526 \, a^{2} b^{5} c^{3} - 2420 \, a^{3} b^{3} c^{4} + 4464 \, a^{4} b c^{5}\right)} d^{5} - 5 \, {\left(a b^{8} c - 23 \, a^{2} b^{6} c^{2} + 250 \, a^{3} b^{4} c^{3} - 312 \, a^{4} b^{2} c^{4} - 1536 \, a^{5} c^{5}\right)} d^{4} e - 10 \, {\left(a^{2} b^{7} c - 32 \, a^{3} b^{5} c^{2} - 212 \, a^{4} b^{3} c^{3} + 1296 \, a^{5} b c^{4}\right)} d^{3} e^{2} - 10 \, {\left(3 \, a^{3} b^{6} c + 154 \, a^{4} b^{4} c^{2} - 536 \, a^{5} b^{2} c^{3} - 512 \, a^{6} c^{4}\right)} d^{2} e^{3} + 50 \, {\left(5 \, a^{4} b^{5} c + 2 \, a^{5} b^{3} c^{2} - 88 \, a^{6} b c^{3}\right)} d e^{4} - {\left(3 \, a^{4} b^{6} + 154 \, a^{5} b^{4} c - 536 \, a^{6} b^{2} c^{2} - 512 \, a^{7} c^{3}\right)} e^{5} + 20 \, {\left(14 \, {\left(13 \, b^{4} c^{6} - 41 \, a b^{2} c^{7} - 44 \, a^{2} c^{8}\right)} d^{5} - 35 \, {\left(13 \, b^{5} c^{5} - 41 \, a b^{3} c^{6} - 44 \, a^{2} b c^{7}\right)} d^{4} e + 10 \, {\left(39 \, b^{6} c^{4} - 97 \, a b^{4} c^{5} - 214 \, a^{2} b^{2} c^{6} - 88 \, a^{3} c^{7}\right)} d^{3} e^{2} - 10 \, {\left(13 \, b^{7} c^{3} - 2 \, a b^{5} c^{4} - 167 \, a^{2} b^{3} c^{5} - 132 \, a^{3} b c^{6}\right)} d^{2} e^{3} + {\left(13 \, b^{8} c^{2} + 115 \, a b^{6} c^{3} - 458 \, a^{2} b^{4} c^{4} - 774 \, a^{3} b^{2} c^{5} - 264 \, a^{4} c^{6}\right)} d e^{4} - {\left(13 \, a b^{7} c^{2} - 2 \, a^{2} b^{5} c^{3} - 167 \, a^{3} b^{3} c^{4} - 132 \, a^{4} b c^{5}\right)} e^{5}\right)} x^{5} + {\left(350 \, {\left(5 \, b^{5} c^{5} + 2 \, a b^{3} c^{6} - 88 \, a^{2} b c^{7}\right)} d^{5} - 875 \, {\left(5 \, b^{6} c^{4} + 2 \, a b^{4} c^{5} - 88 \, a^{2} b^{2} c^{6}\right)} d^{4} e + 250 \, {\left(15 \, b^{7} c^{3} + 16 \, a b^{5} c^{4} - 260 \, a^{2} b^{3} c^{5} - 176 \, a^{3} b c^{6}\right)} d^{3} e^{2} - 250 \, {\left(5 \, b^{8} c^{2} + 17 \, a b^{6} c^{3} - 82 \, a^{2} b^{4} c^{4} - 264 \, a^{3} b^{2} c^{5}\right)} d^{2} e^{3} + 25 \, {\left(5 \, b^{9} c + 62 \, a b^{7} c^{2} - 34 \, a^{2} b^{5} c^{3} - 1044 \, a^{3} b^{3} c^{4} - 528 \, a^{4} b c^{5}\right)} d e^{4} - {\left(3 \, b^{10} + 65 \, a b^{8} c + 905 \, a^{2} b^{6} c^{2} - 3970 \, a^{3} b^{4} c^{3} - 2760 \, a^{4} b^{2} c^{4} - 3072 \, a^{5} c^{5}\right)} e^{5}\right)} x^{4} + 4 \, {\left(14 \, {\left(3 \, b^{6} c^{4} + 89 \, a b^{4} c^{5} - 331 \, a^{2} b^{2} c^{6} - 292 \, a^{3} c^{7}\right)} d^{5} - 35 \, {\left(3 \, b^{7} c^{3} + 89 \, a b^{5} c^{4} - 331 \, a^{2} b^{3} c^{5} - 292 \, a^{3} b c^{6}\right)} d^{4} e + 10 \, {\left(9 \, b^{8} c^{2} + 273 \, a b^{6} c^{3} - 815 \, a^{2} b^{4} c^{4} - 1538 \, a^{3} b^{2} c^{5} - 584 \, a^{4} c^{6}\right)} d^{3} e^{2} - 10 \, {\left(3 \, b^{9} c + 98 \, a b^{7} c^{2} - 64 \, a^{2} b^{5} c^{3} - 1285 \, a^{3} b^{3} c^{4} - 876 \, a^{4} b c^{5}\right)} d^{2} e^{3} + 5 \, {\left(37 \, a b^{8} c + 55 \, a^{2} b^{6} c^{2} - 362 \, a^{3} b^{4} c^{3} - 1866 \, a^{4} b^{2} c^{4} + 264 \, a^{5} c^{5}\right)} d e^{4} - {\left(3 \, a b^{9} + 98 \, a^{2} b^{7} c - 64 \, a^{3} b^{5} c^{2} - 1285 \, a^{4} b^{3} c^{3} - 876 \, a^{5} b c^{4}\right)} e^{5}\right)} x^{3} - 2 \, {\left(14 \, {\left(b^{7} c^{3} - 32 \, a b^{5} c^{4} - 107 \, a^{2} b^{3} c^{5} + 876 \, a^{3} b c^{6}\right)} d^{5} - 35 \, {\left(b^{8} c^{2} - 32 \, a b^{6} c^{3} - 107 \, a^{2} b^{4} c^{4} + 876 \, a^{3} b^{2} c^{5}\right)} d^{4} e + 10 \, {\left(3 \, b^{9} c - 94 \, a b^{7} c^{2} - 385 \, a^{2} b^{5} c^{3} + 2414 \, a^{3} b^{3} c^{4} + 1752 \, a^{4} b c^{5}\right)} d^{3} e^{2} + 10 \, {\left(9 \, a b^{8} c + 363 \, a^{2} b^{6} c^{2} - 1195 \, a^{3} b^{4} c^{3} - 1348 \, a^{4} b^{2} c^{4} - 1024 \, a^{5} c^{5}\right)} d^{2} e^{3} - 5 \, {\left(129 \, a^{2} b^{7} c - 8 \, a^{3} b^{5} c^{2} - 1718 \, a^{4} b^{3} c^{3} - 1256 \, a^{5} b c^{4}\right)} d e^{4} + {\left(9 \, a^{2} b^{8} + 363 \, a^{3} b^{6} c - 1195 \, a^{4} b^{4} c^{2} - 1348 \, a^{5} b^{2} c^{3} - 1024 \, a^{6} c^{4}\right)} e^{5}\right)} x^{2} - 120 \, {\left(14 \, a^{4} c^{5} d^{5} - 35 \, a^{4} b c^{4} d^{4} e + {\left(14 \, c^{9} d^{5} - 35 \, b c^{8} d^{4} e + 10 \, {\left(3 \, b^{2} c^{7} + 2 \, a c^{8}\right)} d^{3} e^{2} - 10 \, {\left(b^{3} c^{6} + 3 \, a b c^{7}\right)} d^{2} e^{3} + {\left(b^{4} c^{5} + 12 \, a b^{2} c^{6} + 6 \, a^{2} c^{7}\right)} d e^{4} - {\left(a b^{3} c^{5} + 3 \, a^{2} b c^{6}\right)} e^{5}\right)} x^{8} + 4 \, {\left(14 \, b c^{8} d^{5} - 35 \, b^{2} c^{7} d^{4} e + 10 \, {\left(3 \, b^{3} c^{6} + 2 \, a b c^{7}\right)} d^{3} e^{2} - 10 \, {\left(b^{4} c^{5} + 3 \, a b^{2} c^{6}\right)} d^{2} e^{3} + {\left(b^{5} c^{4} + 12 \, a b^{3} c^{5} + 6 \, a^{2} b c^{6}\right)} d e^{4} - {\left(a b^{4} c^{4} + 3 \, a^{2} b^{2} c^{5}\right)} e^{5}\right)} x^{7} + 2 \, {\left(14 \, {\left(3 \, b^{2} c^{7} + 2 \, a c^{8}\right)} d^{5} - 35 \, {\left(3 \, b^{3} c^{6} + 2 \, a b c^{7}\right)} d^{4} e + 10 \, {\left(9 \, b^{4} c^{5} + 12 \, a b^{2} c^{6} + 4 \, a^{2} c^{7}\right)} d^{3} e^{2} - 10 \, {\left(3 \, b^{5} c^{4} + 11 \, a b^{3} c^{5} + 6 \, a^{2} b c^{6}\right)} d^{2} e^{3} + {\left(3 \, b^{6} c^{3} + 38 \, a b^{4} c^{4} + 42 \, a^{2} b^{2} c^{5} + 12 \, a^{3} c^{6}\right)} d e^{4} - {\left(3 \, a b^{5} c^{3} + 11 \, a^{2} b^{3} c^{4} + 6 \, a^{3} b c^{5}\right)} e^{5}\right)} x^{6} + 10 \, {\left(3 \, a^{4} b^{2} c^{3} + 2 \, a^{5} c^{4}\right)} d^{3} e^{2} - 10 \, {\left(a^{4} b^{3} c^{2} + 3 \, a^{5} b c^{3}\right)} d^{2} e^{3} + {\left(a^{4} b^{4} c + 12 \, a^{5} b^{2} c^{2} + 6 \, a^{6} c^{3}\right)} d e^{4} - {\left(a^{5} b^{3} c + 3 \, a^{6} b c^{2}\right)} e^{5} + 4 \, {\left(14 \, {\left(b^{3} c^{6} + 3 \, a b c^{7}\right)} d^{5} - 35 \, {\left(b^{4} c^{5} + 3 \, a b^{2} c^{6}\right)} d^{4} e + 10 \, {\left(3 \, b^{5} c^{4} + 11 \, a b^{3} c^{5} + 6 \, a^{2} b c^{6}\right)} d^{3} e^{2} - 10 \, {\left(b^{6} c^{3} + 6 \, a b^{4} c^{4} + 9 \, a^{2} b^{2} c^{5}\right)} d^{2} e^{3} + {\left(b^{7} c^{2} + 15 \, a b^{5} c^{3} + 42 \, a^{2} b^{3} c^{4} + 18 \, a^{3} b c^{5}\right)} d e^{4} - {\left(a b^{6} c^{2} + 6 \, a^{2} b^{4} c^{3} + 9 \, a^{3} b^{2} c^{4}\right)} e^{5}\right)} x^{5} + {\left(14 \, {\left(b^{4} c^{5} + 12 \, a b^{2} c^{6} + 6 \, a^{2} c^{7}\right)} d^{5} - 35 \, {\left(b^{5} c^{4} + 12 \, a b^{3} c^{5} + 6 \, a^{2} b c^{6}\right)} d^{4} e + 10 \, {\left(3 \, b^{6} c^{3} + 38 \, a b^{4} c^{4} + 42 \, a^{2} b^{2} c^{5} + 12 \, a^{3} c^{6}\right)} d^{3} e^{2} - 10 \, {\left(b^{7} c^{2} + 15 \, a b^{5} c^{3} + 42 \, a^{2} b^{3} c^{4} + 18 \, a^{3} b c^{5}\right)} d^{2} e^{3} + {\left(b^{8} c + 24 \, a b^{6} c^{2} + 156 \, a^{2} b^{4} c^{3} + 144 \, a^{3} b^{2} c^{4} + 36 \, a^{4} c^{5}\right)} d e^{4} - {\left(a b^{7} c + 15 \, a^{2} b^{5} c^{2} + 42 \, a^{3} b^{3} c^{3} + 18 \, a^{4} b c^{4}\right)} e^{5}\right)} x^{4} + 4 \, {\left(14 \, {\left(a b^{3} c^{5} + 3 \, a^{2} b c^{6}\right)} d^{5} - 35 \, {\left(a b^{4} c^{4} + 3 \, a^{2} b^{2} c^{5}\right)} d^{4} e + 10 \, {\left(3 \, a b^{5} c^{3} + 11 \, a^{2} b^{3} c^{4} + 6 \, a^{3} b c^{5}\right)} d^{3} e^{2} - 10 \, {\left(a b^{6} c^{2} + 6 \, a^{2} b^{4} c^{3} + 9 \, a^{3} b^{2} c^{4}\right)} d^{2} e^{3} + {\left(a b^{7} c + 15 \, a^{2} b^{5} c^{2} + 42 \, a^{3} b^{3} c^{3} + 18 \, a^{4} b c^{4}\right)} d e^{4} - {\left(a^{2} b^{6} c + 6 \, a^{3} b^{4} c^{2} + 9 \, a^{4} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + 2 \, {\left(14 \, {\left(3 \, a^{2} b^{2} c^{5} + 2 \, a^{3} c^{6}\right)} d^{5} - 35 \, {\left(3 \, a^{2} b^{3} c^{4} + 2 \, a^{3} b c^{5}\right)} d^{4} e + 10 \, {\left(9 \, a^{2} b^{4} c^{3} + 12 \, a^{3} b^{2} c^{4} + 4 \, a^{4} c^{5}\right)} d^{3} e^{2} - 10 \, {\left(3 \, a^{2} b^{5} c^{2} + 11 \, a^{3} b^{3} c^{3} + 6 \, a^{4} b c^{4}\right)} d^{2} e^{3} + {\left(3 \, a^{2} b^{6} c + 38 \, a^{3} b^{4} c^{2} + 42 \, a^{4} b^{2} c^{3} + 12 \, a^{5} c^{4}\right)} d e^{4} - {\left(3 \, a^{3} b^{5} c + 11 \, a^{4} b^{3} c^{2} + 6 \, a^{5} b c^{3}\right)} e^{5}\right)} x^{2} + 4 \, {\left(14 \, a^{3} b c^{5} d^{5} - 35 \, a^{3} b^{2} c^{4} d^{4} e + 10 \, {\left(3 \, a^{3} b^{3} c^{3} + 2 \, a^{4} b c^{4}\right)} d^{3} e^{2} - 10 \, {\left(a^{3} b^{4} c^{2} + 3 \, a^{4} b^{2} c^{3}\right)} d^{2} e^{3} + {\left(a^{3} b^{5} c + 12 \, a^{4} b^{3} c^{2} + 6 \, a^{5} b c^{3}\right)} d e^{4} - {\left(a^{4} b^{4} c + 3 \, a^{5} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 4 \, {\left(2 \, {\left(b^{8} c^{2} - 23 \, a b^{6} c^{3} + 250 \, a^{2} b^{4} c^{4} - 417 \, a^{3} b^{2} c^{5} - 1116 \, a^{4} c^{6}\right)} d^{5} - 5 \, {\left(b^{9} c - 23 \, a b^{7} c^{2} + 250 \, a^{2} b^{5} c^{3} - 417 \, a^{3} b^{3} c^{4} - 1116 \, a^{4} b c^{5}\right)} d^{4} e - 10 \, {\left(a b^{8} c - 32 \, a^{2} b^{6} c^{2} - 167 \, a^{3} b^{4} c^{3} + 1146 \, a^{4} b^{2} c^{4} - 120 \, a^{5} c^{5}\right)} d^{3} e^{2} - 10 \, {\left(3 \, a^{2} b^{7} c + 139 \, a^{3} b^{5} c^{2} - 521 \, a^{4} b^{3} c^{3} - 332 \, a^{5} b c^{4}\right)} d^{2} e^{3} + 5 \, {\left(47 \, a^{3} b^{6} c - 4 \, a^{4} b^{4} c^{2} - 754 \, a^{5} b^{2} c^{3} + 72 \, a^{6} c^{4}\right)} d e^{4} - {\left(3 \, a^{3} b^{7} + 139 \, a^{4} b^{5} c - 521 \, a^{5} b^{3} c^{2} - 332 \, a^{6} b c^{3}\right)} e^{5}\right)} x}{12 \, {\left(a^{4} b^{10} c - 20 \, a^{5} b^{8} c^{2} + 160 \, a^{6} b^{6} c^{3} - 640 \, a^{7} b^{4} c^{4} + 1280 \, a^{8} b^{2} c^{5} - 1024 \, a^{9} c^{6} + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} x^{8} + 4 \, {\left(b^{11} c^{4} - 20 \, a b^{9} c^{5} + 160 \, a^{2} b^{7} c^{6} - 640 \, a^{3} b^{5} c^{7} + 1280 \, a^{4} b^{3} c^{8} - 1024 \, a^{5} b c^{9}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{3} - 58 \, a b^{10} c^{4} + 440 \, a^{2} b^{8} c^{5} - 1600 \, a^{3} b^{6} c^{6} + 2560 \, a^{4} b^{4} c^{7} - 512 \, a^{5} b^{2} c^{8} - 2048 \, a^{6} c^{9}\right)} x^{6} + 4 \, {\left(b^{13} c^{2} - 17 \, a b^{11} c^{3} + 100 \, a^{2} b^{9} c^{4} - 160 \, a^{3} b^{7} c^{5} - 640 \, a^{4} b^{5} c^{6} + 2816 \, a^{5} b^{3} c^{7} - 3072 \, a^{6} b c^{8}\right)} x^{5} + {\left(b^{14} c - 8 \, a b^{12} c^{2} - 74 \, a^{2} b^{10} c^{3} + 1160 \, a^{3} b^{8} c^{4} - 5440 \, a^{4} b^{6} c^{5} + 10496 \, a^{5} b^{4} c^{6} - 4608 \, a^{6} b^{2} c^{7} - 6144 \, a^{7} c^{8}\right)} x^{4} + 4 \, {\left(a b^{13} c - 17 \, a^{2} b^{11} c^{2} + 100 \, a^{3} b^{9} c^{3} - 160 \, a^{4} b^{7} c^{4} - 640 \, a^{5} b^{5} c^{5} + 2816 \, a^{6} b^{3} c^{6} - 3072 \, a^{7} b c^{7}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} c - 58 \, a^{3} b^{10} c^{2} + 440 \, a^{4} b^{8} c^{3} - 1600 \, a^{5} b^{6} c^{4} + 2560 \, a^{6} b^{4} c^{5} - 512 \, a^{7} b^{2} c^{6} - 2048 \, a^{8} c^{7}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} c - 20 \, a^{4} b^{9} c^{2} + 160 \, a^{5} b^{7} c^{3} - 640 \, a^{6} b^{5} c^{4} + 1280 \, a^{7} b^{3} c^{5} - 1024 \, a^{8} b c^{6}\right)} x\right)}}\right]"," ",0,"[1/12*(60*(14*(b^2*c^8 - 4*a*c^9)*d^5 - 35*(b^3*c^7 - 4*a*b*c^8)*d^4*e + 10*(3*b^4*c^6 - 10*a*b^2*c^7 - 8*a^2*c^8)*d^3*e^2 - 10*(b^5*c^5 - a*b^3*c^6 - 12*a^2*b*c^7)*d^2*e^3 + (b^6*c^4 + 8*a*b^4*c^5 - 42*a^2*b^2*c^6 - 24*a^3*c^7)*d*e^4 - (a*b^5*c^4 - a^2*b^3*c^5 - 12*a^3*b*c^6)*e^5)*x^7 + 210*(14*(b^3*c^7 - 4*a*b*c^8)*d^5 - 35*(b^4*c^6 - 4*a*b^2*c^7)*d^4*e + 10*(3*b^5*c^5 - 10*a*b^3*c^6 - 8*a^2*b*c^7)*d^3*e^2 - 10*(b^6*c^4 - a*b^4*c^5 - 12*a^2*b^2*c^6)*d^2*e^3 + (b^7*c^3 + 8*a*b^5*c^4 - 42*a^2*b^3*c^5 - 24*a^3*b*c^6)*d*e^4 - (a*b^6*c^3 - a^2*b^4*c^4 - 12*a^3*b^2*c^5)*e^5)*x^6 - (3*b^9*c - 62*a*b^7*c^2 + 526*a^2*b^5*c^3 - 2420*a^3*b^3*c^4 + 4464*a^4*b*c^5)*d^5 - 5*(a*b^8*c - 23*a^2*b^6*c^2 + 250*a^3*b^4*c^3 - 312*a^4*b^2*c^4 - 1536*a^5*c^5)*d^4*e - 10*(a^2*b^7*c - 32*a^3*b^5*c^2 - 212*a^4*b^3*c^3 + 1296*a^5*b*c^4)*d^3*e^2 - 10*(3*a^3*b^6*c + 154*a^4*b^4*c^2 - 536*a^5*b^2*c^3 - 512*a^6*c^4)*d^2*e^3 + 50*(5*a^4*b^5*c + 2*a^5*b^3*c^2 - 88*a^6*b*c^3)*d*e^4 - (3*a^4*b^6 + 154*a^5*b^4*c - 536*a^6*b^2*c^2 - 512*a^7*c^3)*e^5 + 20*(14*(13*b^4*c^6 - 41*a*b^2*c^7 - 44*a^2*c^8)*d^5 - 35*(13*b^5*c^5 - 41*a*b^3*c^6 - 44*a^2*b*c^7)*d^4*e + 10*(39*b^6*c^4 - 97*a*b^4*c^5 - 214*a^2*b^2*c^6 - 88*a^3*c^7)*d^3*e^2 - 10*(13*b^7*c^3 - 2*a*b^5*c^4 - 167*a^2*b^3*c^5 - 132*a^3*b*c^6)*d^2*e^3 + (13*b^8*c^2 + 115*a*b^6*c^3 - 458*a^2*b^4*c^4 - 774*a^3*b^2*c^5 - 264*a^4*c^6)*d*e^4 - (13*a*b^7*c^2 - 2*a^2*b^5*c^3 - 167*a^3*b^3*c^4 - 132*a^4*b*c^5)*e^5)*x^5 + (350*(5*b^5*c^5 + 2*a*b^3*c^6 - 88*a^2*b*c^7)*d^5 - 875*(5*b^6*c^4 + 2*a*b^4*c^5 - 88*a^2*b^2*c^6)*d^4*e + 250*(15*b^7*c^3 + 16*a*b^5*c^4 - 260*a^2*b^3*c^5 - 176*a^3*b*c^6)*d^3*e^2 - 250*(5*b^8*c^2 + 17*a*b^6*c^3 - 82*a^2*b^4*c^4 - 264*a^3*b^2*c^5)*d^2*e^3 + 25*(5*b^9*c + 62*a*b^7*c^2 - 34*a^2*b^5*c^3 - 1044*a^3*b^3*c^4 - 528*a^4*b*c^5)*d*e^4 - (3*b^10 + 65*a*b^8*c + 905*a^2*b^6*c^2 - 3970*a^3*b^4*c^3 - 2760*a^4*b^2*c^4 - 3072*a^5*c^5)*e^5)*x^4 + 4*(14*(3*b^6*c^4 + 89*a*b^4*c^5 - 331*a^2*b^2*c^6 - 292*a^3*c^7)*d^5 - 35*(3*b^7*c^3 + 89*a*b^5*c^4 - 331*a^2*b^3*c^5 - 292*a^3*b*c^6)*d^4*e + 10*(9*b^8*c^2 + 273*a*b^6*c^3 - 815*a^2*b^4*c^4 - 1538*a^3*b^2*c^5 - 584*a^4*c^6)*d^3*e^2 - 10*(3*b^9*c + 98*a*b^7*c^2 - 64*a^2*b^5*c^3 - 1285*a^3*b^3*c^4 - 876*a^4*b*c^5)*d^2*e^3 + 5*(37*a*b^8*c + 55*a^2*b^6*c^2 - 362*a^3*b^4*c^3 - 1866*a^4*b^2*c^4 + 264*a^5*c^5)*d*e^4 - (3*a*b^9 + 98*a^2*b^7*c - 64*a^3*b^5*c^2 - 1285*a^4*b^3*c^3 - 876*a^5*b*c^4)*e^5)*x^3 - 2*(14*(b^7*c^3 - 32*a*b^5*c^4 - 107*a^2*b^3*c^5 + 876*a^3*b*c^6)*d^5 - 35*(b^8*c^2 - 32*a*b^6*c^3 - 107*a^2*b^4*c^4 + 876*a^3*b^2*c^5)*d^4*e + 10*(3*b^9*c - 94*a*b^7*c^2 - 385*a^2*b^5*c^3 + 2414*a^3*b^3*c^4 + 1752*a^4*b*c^5)*d^3*e^2 + 10*(9*a*b^8*c + 363*a^2*b^6*c^2 - 1195*a^3*b^4*c^3 - 1348*a^4*b^2*c^4 - 1024*a^5*c^5)*d^2*e^3 - 5*(129*a^2*b^7*c - 8*a^3*b^5*c^2 - 1718*a^4*b^3*c^3 - 1256*a^5*b*c^4)*d*e^4 + (9*a^2*b^8 + 363*a^3*b^6*c - 1195*a^4*b^4*c^2 - 1348*a^5*b^2*c^3 - 1024*a^6*c^4)*e^5)*x^2 - 60*(14*a^4*c^5*d^5 - 35*a^4*b*c^4*d^4*e + (14*c^9*d^5 - 35*b*c^8*d^4*e + 10*(3*b^2*c^7 + 2*a*c^8)*d^3*e^2 - 10*(b^3*c^6 + 3*a*b*c^7)*d^2*e^3 + (b^4*c^5 + 12*a*b^2*c^6 + 6*a^2*c^7)*d*e^4 - (a*b^3*c^5 + 3*a^2*b*c^6)*e^5)*x^8 + 4*(14*b*c^8*d^5 - 35*b^2*c^7*d^4*e + 10*(3*b^3*c^6 + 2*a*b*c^7)*d^3*e^2 - 10*(b^4*c^5 + 3*a*b^2*c^6)*d^2*e^3 + (b^5*c^4 + 12*a*b^3*c^5 + 6*a^2*b*c^6)*d*e^4 - (a*b^4*c^4 + 3*a^2*b^2*c^5)*e^5)*x^7 + 2*(14*(3*b^2*c^7 + 2*a*c^8)*d^5 - 35*(3*b^3*c^6 + 2*a*b*c^7)*d^4*e + 10*(9*b^4*c^5 + 12*a*b^2*c^6 + 4*a^2*c^7)*d^3*e^2 - 10*(3*b^5*c^4 + 11*a*b^3*c^5 + 6*a^2*b*c^6)*d^2*e^3 + (3*b^6*c^3 + 38*a*b^4*c^4 + 42*a^2*b^2*c^5 + 12*a^3*c^6)*d*e^4 - (3*a*b^5*c^3 + 11*a^2*b^3*c^4 + 6*a^3*b*c^5)*e^5)*x^6 + 10*(3*a^4*b^2*c^3 + 2*a^5*c^4)*d^3*e^2 - 10*(a^4*b^3*c^2 + 3*a^5*b*c^3)*d^2*e^3 + (a^4*b^4*c + 12*a^5*b^2*c^2 + 6*a^6*c^3)*d*e^4 - (a^5*b^3*c + 3*a^6*b*c^2)*e^5 + 4*(14*(b^3*c^6 + 3*a*b*c^7)*d^5 - 35*(b^4*c^5 + 3*a*b^2*c^6)*d^4*e + 10*(3*b^5*c^4 + 11*a*b^3*c^5 + 6*a^2*b*c^6)*d^3*e^2 - 10*(b^6*c^3 + 6*a*b^4*c^4 + 9*a^2*b^2*c^5)*d^2*e^3 + (b^7*c^2 + 15*a*b^5*c^3 + 42*a^2*b^3*c^4 + 18*a^3*b*c^5)*d*e^4 - (a*b^6*c^2 + 6*a^2*b^4*c^3 + 9*a^3*b^2*c^4)*e^5)*x^5 + (14*(b^4*c^5 + 12*a*b^2*c^6 + 6*a^2*c^7)*d^5 - 35*(b^5*c^4 + 12*a*b^3*c^5 + 6*a^2*b*c^6)*d^4*e + 10*(3*b^6*c^3 + 38*a*b^4*c^4 + 42*a^2*b^2*c^5 + 12*a^3*c^6)*d^3*e^2 - 10*(b^7*c^2 + 15*a*b^5*c^3 + 42*a^2*b^3*c^4 + 18*a^3*b*c^5)*d^2*e^3 + (b^8*c + 24*a*b^6*c^2 + 156*a^2*b^4*c^3 + 144*a^3*b^2*c^4 + 36*a^4*c^5)*d*e^4 - (a*b^7*c + 15*a^2*b^5*c^2 + 42*a^3*b^3*c^3 + 18*a^4*b*c^4)*e^5)*x^4 + 4*(14*(a*b^3*c^5 + 3*a^2*b*c^6)*d^5 - 35*(a*b^4*c^4 + 3*a^2*b^2*c^5)*d^4*e + 10*(3*a*b^5*c^3 + 11*a^2*b^3*c^4 + 6*a^3*b*c^5)*d^3*e^2 - 10*(a*b^6*c^2 + 6*a^2*b^4*c^3 + 9*a^3*b^2*c^4)*d^2*e^3 + (a*b^7*c + 15*a^2*b^5*c^2 + 42*a^3*b^3*c^3 + 18*a^4*b*c^4)*d*e^4 - (a^2*b^6*c + 6*a^3*b^4*c^2 + 9*a^4*b^2*c^3)*e^5)*x^3 + 2*(14*(3*a^2*b^2*c^5 + 2*a^3*c^6)*d^5 - 35*(3*a^2*b^3*c^4 + 2*a^3*b*c^5)*d^4*e + 10*(9*a^2*b^4*c^3 + 12*a^3*b^2*c^4 + 4*a^4*c^5)*d^3*e^2 - 10*(3*a^2*b^5*c^2 + 11*a^3*b^3*c^3 + 6*a^4*b*c^4)*d^2*e^3 + (3*a^2*b^6*c + 38*a^3*b^4*c^2 + 42*a^4*b^2*c^3 + 12*a^5*c^4)*d*e^4 - (3*a^3*b^5*c + 11*a^4*b^3*c^2 + 6*a^5*b*c^3)*e^5)*x^2 + 4*(14*a^3*b*c^5*d^5 - 35*a^3*b^2*c^4*d^4*e + 10*(3*a^3*b^3*c^3 + 2*a^4*b*c^4)*d^3*e^2 - 10*(a^3*b^4*c^2 + 3*a^4*b^2*c^3)*d^2*e^3 + (a^3*b^5*c + 12*a^4*b^3*c^2 + 6*a^5*b*c^3)*d*e^4 - (a^4*b^4*c + 3*a^5*b^2*c^2)*e^5)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 4*(2*(b^8*c^2 - 23*a*b^6*c^3 + 250*a^2*b^4*c^4 - 417*a^3*b^2*c^5 - 1116*a^4*c^6)*d^5 - 5*(b^9*c - 23*a*b^7*c^2 + 250*a^2*b^5*c^3 - 417*a^3*b^3*c^4 - 1116*a^4*b*c^5)*d^4*e - 10*(a*b^8*c - 32*a^2*b^6*c^2 - 167*a^3*b^4*c^3 + 1146*a^4*b^2*c^4 - 120*a^5*c^5)*d^3*e^2 - 10*(3*a^2*b^7*c + 139*a^3*b^5*c^2 - 521*a^4*b^3*c^3 - 332*a^5*b*c^4)*d^2*e^3 + 5*(47*a^3*b^6*c - 4*a^4*b^4*c^2 - 754*a^5*b^2*c^3 + 72*a^6*c^4)*d*e^4 - (3*a^3*b^7 + 139*a^4*b^5*c - 521*a^5*b^3*c^2 - 332*a^6*b*c^3)*e^5)*x)/(a^4*b^10*c - 20*a^5*b^8*c^2 + 160*a^6*b^6*c^3 - 640*a^7*b^4*c^4 + 1280*a^8*b^2*c^5 - 1024*a^9*c^6 + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*x^8 + 4*(b^11*c^4 - 20*a*b^9*c^5 + 160*a^2*b^7*c^6 - 640*a^3*b^5*c^7 + 1280*a^4*b^3*c^8 - 1024*a^5*b*c^9)*x^7 + 2*(3*b^12*c^3 - 58*a*b^10*c^4 + 440*a^2*b^8*c^5 - 1600*a^3*b^6*c^6 + 2560*a^4*b^4*c^7 - 512*a^5*b^2*c^8 - 2048*a^6*c^9)*x^6 + 4*(b^13*c^2 - 17*a*b^11*c^3 + 100*a^2*b^9*c^4 - 160*a^3*b^7*c^5 - 640*a^4*b^5*c^6 + 2816*a^5*b^3*c^7 - 3072*a^6*b*c^8)*x^5 + (b^14*c - 8*a*b^12*c^2 - 74*a^2*b^10*c^3 + 1160*a^3*b^8*c^4 - 5440*a^4*b^6*c^5 + 10496*a^5*b^4*c^6 - 4608*a^6*b^2*c^7 - 6144*a^7*c^8)*x^4 + 4*(a*b^13*c - 17*a^2*b^11*c^2 + 100*a^3*b^9*c^3 - 160*a^4*b^7*c^4 - 640*a^5*b^5*c^5 + 2816*a^6*b^3*c^6 - 3072*a^7*b*c^7)*x^3 + 2*(3*a^2*b^12*c - 58*a^3*b^10*c^2 + 440*a^4*b^8*c^3 - 1600*a^5*b^6*c^4 + 2560*a^6*b^4*c^5 - 512*a^7*b^2*c^6 - 2048*a^8*c^7)*x^2 + 4*(a^3*b^11*c - 20*a^4*b^9*c^2 + 160*a^5*b^7*c^3 - 640*a^6*b^5*c^4 + 1280*a^7*b^3*c^5 - 1024*a^8*b*c^6)*x), 1/12*(60*(14*(b^2*c^8 - 4*a*c^9)*d^5 - 35*(b^3*c^7 - 4*a*b*c^8)*d^4*e + 10*(3*b^4*c^6 - 10*a*b^2*c^7 - 8*a^2*c^8)*d^3*e^2 - 10*(b^5*c^5 - a*b^3*c^6 - 12*a^2*b*c^7)*d^2*e^3 + (b^6*c^4 + 8*a*b^4*c^5 - 42*a^2*b^2*c^6 - 24*a^3*c^7)*d*e^4 - (a*b^5*c^4 - a^2*b^3*c^5 - 12*a^3*b*c^6)*e^5)*x^7 + 210*(14*(b^3*c^7 - 4*a*b*c^8)*d^5 - 35*(b^4*c^6 - 4*a*b^2*c^7)*d^4*e + 10*(3*b^5*c^5 - 10*a*b^3*c^6 - 8*a^2*b*c^7)*d^3*e^2 - 10*(b^6*c^4 - a*b^4*c^5 - 12*a^2*b^2*c^6)*d^2*e^3 + (b^7*c^3 + 8*a*b^5*c^4 - 42*a^2*b^3*c^5 - 24*a^3*b*c^6)*d*e^4 - (a*b^6*c^3 - a^2*b^4*c^4 - 12*a^3*b^2*c^5)*e^5)*x^6 - (3*b^9*c - 62*a*b^7*c^2 + 526*a^2*b^5*c^3 - 2420*a^3*b^3*c^4 + 4464*a^4*b*c^5)*d^5 - 5*(a*b^8*c - 23*a^2*b^6*c^2 + 250*a^3*b^4*c^3 - 312*a^4*b^2*c^4 - 1536*a^5*c^5)*d^4*e - 10*(a^2*b^7*c - 32*a^3*b^5*c^2 - 212*a^4*b^3*c^3 + 1296*a^5*b*c^4)*d^3*e^2 - 10*(3*a^3*b^6*c + 154*a^4*b^4*c^2 - 536*a^5*b^2*c^3 - 512*a^6*c^4)*d^2*e^3 + 50*(5*a^4*b^5*c + 2*a^5*b^3*c^2 - 88*a^6*b*c^3)*d*e^4 - (3*a^4*b^6 + 154*a^5*b^4*c - 536*a^6*b^2*c^2 - 512*a^7*c^3)*e^5 + 20*(14*(13*b^4*c^6 - 41*a*b^2*c^7 - 44*a^2*c^8)*d^5 - 35*(13*b^5*c^5 - 41*a*b^3*c^6 - 44*a^2*b*c^7)*d^4*e + 10*(39*b^6*c^4 - 97*a*b^4*c^5 - 214*a^2*b^2*c^6 - 88*a^3*c^7)*d^3*e^2 - 10*(13*b^7*c^3 - 2*a*b^5*c^4 - 167*a^2*b^3*c^5 - 132*a^3*b*c^6)*d^2*e^3 + (13*b^8*c^2 + 115*a*b^6*c^3 - 458*a^2*b^4*c^4 - 774*a^3*b^2*c^5 - 264*a^4*c^6)*d*e^4 - (13*a*b^7*c^2 - 2*a^2*b^5*c^3 - 167*a^3*b^3*c^4 - 132*a^4*b*c^5)*e^5)*x^5 + (350*(5*b^5*c^5 + 2*a*b^3*c^6 - 88*a^2*b*c^7)*d^5 - 875*(5*b^6*c^4 + 2*a*b^4*c^5 - 88*a^2*b^2*c^6)*d^4*e + 250*(15*b^7*c^3 + 16*a*b^5*c^4 - 260*a^2*b^3*c^5 - 176*a^3*b*c^6)*d^3*e^2 - 250*(5*b^8*c^2 + 17*a*b^6*c^3 - 82*a^2*b^4*c^4 - 264*a^3*b^2*c^5)*d^2*e^3 + 25*(5*b^9*c + 62*a*b^7*c^2 - 34*a^2*b^5*c^3 - 1044*a^3*b^3*c^4 - 528*a^4*b*c^5)*d*e^4 - (3*b^10 + 65*a*b^8*c + 905*a^2*b^6*c^2 - 3970*a^3*b^4*c^3 - 2760*a^4*b^2*c^4 - 3072*a^5*c^5)*e^5)*x^4 + 4*(14*(3*b^6*c^4 + 89*a*b^4*c^5 - 331*a^2*b^2*c^6 - 292*a^3*c^7)*d^5 - 35*(3*b^7*c^3 + 89*a*b^5*c^4 - 331*a^2*b^3*c^5 - 292*a^3*b*c^6)*d^4*e + 10*(9*b^8*c^2 + 273*a*b^6*c^3 - 815*a^2*b^4*c^4 - 1538*a^3*b^2*c^5 - 584*a^4*c^6)*d^3*e^2 - 10*(3*b^9*c + 98*a*b^7*c^2 - 64*a^2*b^5*c^3 - 1285*a^3*b^3*c^4 - 876*a^4*b*c^5)*d^2*e^3 + 5*(37*a*b^8*c + 55*a^2*b^6*c^2 - 362*a^3*b^4*c^3 - 1866*a^4*b^2*c^4 + 264*a^5*c^5)*d*e^4 - (3*a*b^9 + 98*a^2*b^7*c - 64*a^3*b^5*c^2 - 1285*a^4*b^3*c^3 - 876*a^5*b*c^4)*e^5)*x^3 - 2*(14*(b^7*c^3 - 32*a*b^5*c^4 - 107*a^2*b^3*c^5 + 876*a^3*b*c^6)*d^5 - 35*(b^8*c^2 - 32*a*b^6*c^3 - 107*a^2*b^4*c^4 + 876*a^3*b^2*c^5)*d^4*e + 10*(3*b^9*c - 94*a*b^7*c^2 - 385*a^2*b^5*c^3 + 2414*a^3*b^3*c^4 + 1752*a^4*b*c^5)*d^3*e^2 + 10*(9*a*b^8*c + 363*a^2*b^6*c^2 - 1195*a^3*b^4*c^3 - 1348*a^4*b^2*c^4 - 1024*a^5*c^5)*d^2*e^3 - 5*(129*a^2*b^7*c - 8*a^3*b^5*c^2 - 1718*a^4*b^3*c^3 - 1256*a^5*b*c^4)*d*e^4 + (9*a^2*b^8 + 363*a^3*b^6*c - 1195*a^4*b^4*c^2 - 1348*a^5*b^2*c^3 - 1024*a^6*c^4)*e^5)*x^2 - 120*(14*a^4*c^5*d^5 - 35*a^4*b*c^4*d^4*e + (14*c^9*d^5 - 35*b*c^8*d^4*e + 10*(3*b^2*c^7 + 2*a*c^8)*d^3*e^2 - 10*(b^3*c^6 + 3*a*b*c^7)*d^2*e^3 + (b^4*c^5 + 12*a*b^2*c^6 + 6*a^2*c^7)*d*e^4 - (a*b^3*c^5 + 3*a^2*b*c^6)*e^5)*x^8 + 4*(14*b*c^8*d^5 - 35*b^2*c^7*d^4*e + 10*(3*b^3*c^6 + 2*a*b*c^7)*d^3*e^2 - 10*(b^4*c^5 + 3*a*b^2*c^6)*d^2*e^3 + (b^5*c^4 + 12*a*b^3*c^5 + 6*a^2*b*c^6)*d*e^4 - (a*b^4*c^4 + 3*a^2*b^2*c^5)*e^5)*x^7 + 2*(14*(3*b^2*c^7 + 2*a*c^8)*d^5 - 35*(3*b^3*c^6 + 2*a*b*c^7)*d^4*e + 10*(9*b^4*c^5 + 12*a*b^2*c^6 + 4*a^2*c^7)*d^3*e^2 - 10*(3*b^5*c^4 + 11*a*b^3*c^5 + 6*a^2*b*c^6)*d^2*e^3 + (3*b^6*c^3 + 38*a*b^4*c^4 + 42*a^2*b^2*c^5 + 12*a^3*c^6)*d*e^4 - (3*a*b^5*c^3 + 11*a^2*b^3*c^4 + 6*a^3*b*c^5)*e^5)*x^6 + 10*(3*a^4*b^2*c^3 + 2*a^5*c^4)*d^3*e^2 - 10*(a^4*b^3*c^2 + 3*a^5*b*c^3)*d^2*e^3 + (a^4*b^4*c + 12*a^5*b^2*c^2 + 6*a^6*c^3)*d*e^4 - (a^5*b^3*c + 3*a^6*b*c^2)*e^5 + 4*(14*(b^3*c^6 + 3*a*b*c^7)*d^5 - 35*(b^4*c^5 + 3*a*b^2*c^6)*d^4*e + 10*(3*b^5*c^4 + 11*a*b^3*c^5 + 6*a^2*b*c^6)*d^3*e^2 - 10*(b^6*c^3 + 6*a*b^4*c^4 + 9*a^2*b^2*c^5)*d^2*e^3 + (b^7*c^2 + 15*a*b^5*c^3 + 42*a^2*b^3*c^4 + 18*a^3*b*c^5)*d*e^4 - (a*b^6*c^2 + 6*a^2*b^4*c^3 + 9*a^3*b^2*c^4)*e^5)*x^5 + (14*(b^4*c^5 + 12*a*b^2*c^6 + 6*a^2*c^7)*d^5 - 35*(b^5*c^4 + 12*a*b^3*c^5 + 6*a^2*b*c^6)*d^4*e + 10*(3*b^6*c^3 + 38*a*b^4*c^4 + 42*a^2*b^2*c^5 + 12*a^3*c^6)*d^3*e^2 - 10*(b^7*c^2 + 15*a*b^5*c^3 + 42*a^2*b^3*c^4 + 18*a^3*b*c^5)*d^2*e^3 + (b^8*c + 24*a*b^6*c^2 + 156*a^2*b^4*c^3 + 144*a^3*b^2*c^4 + 36*a^4*c^5)*d*e^4 - (a*b^7*c + 15*a^2*b^5*c^2 + 42*a^3*b^3*c^3 + 18*a^4*b*c^4)*e^5)*x^4 + 4*(14*(a*b^3*c^5 + 3*a^2*b*c^6)*d^5 - 35*(a*b^4*c^4 + 3*a^2*b^2*c^5)*d^4*e + 10*(3*a*b^5*c^3 + 11*a^2*b^3*c^4 + 6*a^3*b*c^5)*d^3*e^2 - 10*(a*b^6*c^2 + 6*a^2*b^4*c^3 + 9*a^3*b^2*c^4)*d^2*e^3 + (a*b^7*c + 15*a^2*b^5*c^2 + 42*a^3*b^3*c^3 + 18*a^4*b*c^4)*d*e^4 - (a^2*b^6*c + 6*a^3*b^4*c^2 + 9*a^4*b^2*c^3)*e^5)*x^3 + 2*(14*(3*a^2*b^2*c^5 + 2*a^3*c^6)*d^5 - 35*(3*a^2*b^3*c^4 + 2*a^3*b*c^5)*d^4*e + 10*(9*a^2*b^4*c^3 + 12*a^3*b^2*c^4 + 4*a^4*c^5)*d^3*e^2 - 10*(3*a^2*b^5*c^2 + 11*a^3*b^3*c^3 + 6*a^4*b*c^4)*d^2*e^3 + (3*a^2*b^6*c + 38*a^3*b^4*c^2 + 42*a^4*b^2*c^3 + 12*a^5*c^4)*d*e^4 - (3*a^3*b^5*c + 11*a^4*b^3*c^2 + 6*a^5*b*c^3)*e^5)*x^2 + 4*(14*a^3*b*c^5*d^5 - 35*a^3*b^2*c^4*d^4*e + 10*(3*a^3*b^3*c^3 + 2*a^4*b*c^4)*d^3*e^2 - 10*(a^3*b^4*c^2 + 3*a^4*b^2*c^3)*d^2*e^3 + (a^3*b^5*c + 12*a^4*b^3*c^2 + 6*a^5*b*c^3)*d*e^4 - (a^4*b^4*c + 3*a^5*b^2*c^2)*e^5)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 4*(2*(b^8*c^2 - 23*a*b^6*c^3 + 250*a^2*b^4*c^4 - 417*a^3*b^2*c^5 - 1116*a^4*c^6)*d^5 - 5*(b^9*c - 23*a*b^7*c^2 + 250*a^2*b^5*c^3 - 417*a^3*b^3*c^4 - 1116*a^4*b*c^5)*d^4*e - 10*(a*b^8*c - 32*a^2*b^6*c^2 - 167*a^3*b^4*c^3 + 1146*a^4*b^2*c^4 - 120*a^5*c^5)*d^3*e^2 - 10*(3*a^2*b^7*c + 139*a^3*b^5*c^2 - 521*a^4*b^3*c^3 - 332*a^5*b*c^4)*d^2*e^3 + 5*(47*a^3*b^6*c - 4*a^4*b^4*c^2 - 754*a^5*b^2*c^3 + 72*a^6*c^4)*d*e^4 - (3*a^3*b^7 + 139*a^4*b^5*c - 521*a^5*b^3*c^2 - 332*a^6*b*c^3)*e^5)*x)/(a^4*b^10*c - 20*a^5*b^8*c^2 + 160*a^6*b^6*c^3 - 640*a^7*b^4*c^4 + 1280*a^8*b^2*c^5 - 1024*a^9*c^6 + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*x^8 + 4*(b^11*c^4 - 20*a*b^9*c^5 + 160*a^2*b^7*c^6 - 640*a^3*b^5*c^7 + 1280*a^4*b^3*c^8 - 1024*a^5*b*c^9)*x^7 + 2*(3*b^12*c^3 - 58*a*b^10*c^4 + 440*a^2*b^8*c^5 - 1600*a^3*b^6*c^6 + 2560*a^4*b^4*c^7 - 512*a^5*b^2*c^8 - 2048*a^6*c^9)*x^6 + 4*(b^13*c^2 - 17*a*b^11*c^3 + 100*a^2*b^9*c^4 - 160*a^3*b^7*c^5 - 640*a^4*b^5*c^6 + 2816*a^5*b^3*c^7 - 3072*a^6*b*c^8)*x^5 + (b^14*c - 8*a*b^12*c^2 - 74*a^2*b^10*c^3 + 1160*a^3*b^8*c^4 - 5440*a^4*b^6*c^5 + 10496*a^5*b^4*c^6 - 4608*a^6*b^2*c^7 - 6144*a^7*c^8)*x^4 + 4*(a*b^13*c - 17*a^2*b^11*c^2 + 100*a^3*b^9*c^3 - 160*a^4*b^7*c^4 - 640*a^5*b^5*c^5 + 2816*a^6*b^3*c^6 - 3072*a^7*b*c^7)*x^3 + 2*(3*a^2*b^12*c - 58*a^3*b^10*c^2 + 440*a^4*b^8*c^3 - 1600*a^5*b^6*c^4 + 2560*a^6*b^4*c^5 - 512*a^7*b^2*c^6 - 2048*a^8*c^7)*x^2 + 4*(a^3*b^11*c - 20*a^4*b^9*c^2 + 160*a^5*b^7*c^3 - 640*a^6*b^5*c^4 + 1280*a^7*b^3*c^5 - 1024*a^8*b*c^6)*x)]","B",0
2222,1,7259,0,0.567817," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^5,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(70 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{4} - 140 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{3} e + 30 \, {\left(3 \, b^{4} c^{5} - 10 \, a b^{2} c^{6} - 8 \, a^{2} c^{7}\right)} d^{2} e^{2} - 20 \, {\left(b^{5} c^{4} - a b^{3} c^{5} - 12 \, a^{2} b c^{6}\right)} d e^{3} + {\left(b^{6} c^{3} + 8 \, a b^{4} c^{4} - 42 \, a^{2} b^{2} c^{5} - 24 \, a^{3} c^{6}\right)} e^{4}\right)} x^{7} + 42 \, {\left(70 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{4} - 140 \, {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} d^{3} e + 30 \, {\left(3 \, b^{5} c^{4} - 10 \, a b^{3} c^{5} - 8 \, a^{2} b c^{6}\right)} d^{2} e^{2} - 20 \, {\left(b^{6} c^{3} - a b^{4} c^{4} - 12 \, a^{2} b^{2} c^{5}\right)} d e^{3} + {\left(b^{7} c^{2} + 8 \, a b^{5} c^{3} - 42 \, a^{2} b^{3} c^{4} - 24 \, a^{3} b c^{5}\right)} e^{4}\right)} x^{6} + 4 \, {\left(70 \, {\left(13 \, b^{4} c^{5} - 41 \, a b^{2} c^{6} - 44 \, a^{2} c^{7}\right)} d^{4} - 140 \, {\left(13 \, b^{5} c^{4} - 41 \, a b^{3} c^{5} - 44 \, a^{2} b c^{6}\right)} d^{3} e + 30 \, {\left(39 \, b^{6} c^{3} - 97 \, a b^{4} c^{4} - 214 \, a^{2} b^{2} c^{5} - 88 \, a^{3} c^{6}\right)} d^{2} e^{2} - 20 \, {\left(13 \, b^{7} c^{2} - 2 \, a b^{5} c^{3} - 167 \, a^{2} b^{3} c^{4} - 132 \, a^{3} b c^{5}\right)} d e^{3} + {\left(13 \, b^{8} c + 115 \, a b^{6} c^{2} - 458 \, a^{2} b^{4} c^{3} - 774 \, a^{3} b^{2} c^{4} - 264 \, a^{4} c^{5}\right)} e^{4}\right)} x^{5} - {\left(3 \, b^{9} - 62 \, a b^{7} c + 526 \, a^{2} b^{5} c^{2} - 2420 \, a^{3} b^{3} c^{3} + 4464 \, a^{4} b c^{4}\right)} d^{4} - 4 \, {\left(a b^{8} - 23 \, a^{2} b^{6} c + 250 \, a^{3} b^{4} c^{2} - 312 \, a^{4} b^{2} c^{3} - 1536 \, a^{5} c^{4}\right)} d^{3} e - 6 \, {\left(a^{2} b^{7} - 32 \, a^{3} b^{5} c - 212 \, a^{4} b^{3} c^{2} + 1296 \, a^{5} b c^{3}\right)} d^{2} e^{2} - 4 \, {\left(3 \, a^{3} b^{6} + 154 \, a^{4} b^{4} c - 536 \, a^{5} b^{2} c^{2} - 512 \, a^{6} c^{3}\right)} d e^{3} + 10 \, {\left(5 \, a^{4} b^{5} + 2 \, a^{5} b^{3} c - 88 \, a^{6} b c^{2}\right)} e^{4} + 5 \, {\left(70 \, {\left(5 \, b^{5} c^{4} + 2 \, a b^{3} c^{5} - 88 \, a^{2} b c^{6}\right)} d^{4} - 140 \, {\left(5 \, b^{6} c^{3} + 2 \, a b^{4} c^{4} - 88 \, a^{2} b^{2} c^{5}\right)} d^{3} e + 30 \, {\left(15 \, b^{7} c^{2} + 16 \, a b^{5} c^{3} - 260 \, a^{2} b^{3} c^{4} - 176 \, a^{3} b c^{5}\right)} d^{2} e^{2} - 20 \, {\left(5 \, b^{8} c + 17 \, a b^{6} c^{2} - 82 \, a^{2} b^{4} c^{3} - 264 \, a^{3} b^{2} c^{4}\right)} d e^{3} + {\left(5 \, b^{9} + 62 \, a b^{7} c - 34 \, a^{2} b^{5} c^{2} - 1044 \, a^{3} b^{3} c^{3} - 528 \, a^{4} b c^{4}\right)} e^{4}\right)} x^{4} + 4 \, {\left(14 \, {\left(3 \, b^{6} c^{3} + 89 \, a b^{4} c^{4} - 331 \, a^{2} b^{2} c^{5} - 292 \, a^{3} c^{6}\right)} d^{4} - 28 \, {\left(3 \, b^{7} c^{2} + 89 \, a b^{5} c^{3} - 331 \, a^{2} b^{3} c^{4} - 292 \, a^{3} b c^{5}\right)} d^{3} e + 6 \, {\left(9 \, b^{8} c + 273 \, a b^{6} c^{2} - 815 \, a^{2} b^{4} c^{3} - 1538 \, a^{3} b^{2} c^{4} - 584 \, a^{4} c^{5}\right)} d^{2} e^{2} - 4 \, {\left(3 \, b^{9} + 98 \, a b^{7} c - 64 \, a^{2} b^{5} c^{2} - 1285 \, a^{3} b^{3} c^{3} - 876 \, a^{4} b c^{4}\right)} d e^{3} + {\left(37 \, a b^{8} + 55 \, a^{2} b^{6} c - 362 \, a^{3} b^{4} c^{2} - 1866 \, a^{4} b^{2} c^{3} + 264 \, a^{5} c^{4}\right)} e^{4}\right)} x^{3} - 2 \, {\left(14 \, {\left(b^{7} c^{2} - 32 \, a b^{5} c^{3} - 107 \, a^{2} b^{3} c^{4} + 876 \, a^{3} b c^{5}\right)} d^{4} - 28 \, {\left(b^{8} c - 32 \, a b^{6} c^{2} - 107 \, a^{2} b^{4} c^{3} + 876 \, a^{3} b^{2} c^{4}\right)} d^{3} e + 6 \, {\left(3 \, b^{9} - 94 \, a b^{7} c - 385 \, a^{2} b^{5} c^{2} + 2414 \, a^{3} b^{3} c^{3} + 1752 \, a^{4} b c^{4}\right)} d^{2} e^{2} + 4 \, {\left(9 \, a b^{8} + 363 \, a^{2} b^{6} c - 1195 \, a^{3} b^{4} c^{2} - 1348 \, a^{4} b^{2} c^{3} - 1024 \, a^{5} c^{4}\right)} d e^{3} - {\left(129 \, a^{2} b^{7} - 8 \, a^{3} b^{5} c - 1718 \, a^{4} b^{3} c^{2} - 1256 \, a^{5} b c^{3}\right)} e^{4}\right)} x^{2} + 12 \, {\left(70 \, a^{4} c^{4} d^{4} - 140 \, a^{4} b c^{3} d^{3} e + {\left(70 \, c^{8} d^{4} - 140 \, b c^{7} d^{3} e + 30 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d^{2} e^{2} - 20 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} d e^{3} + {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} e^{4}\right)} x^{8} + 4 \, {\left(70 \, b c^{7} d^{4} - 140 \, b^{2} c^{6} d^{3} e + 30 \, {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} d^{2} e^{2} - 20 \, {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} d e^{3} + {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} e^{4}\right)} x^{7} + 2 \, {\left(70 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d^{4} - 140 \, {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} d^{3} e + 30 \, {\left(9 \, b^{4} c^{4} + 12 \, a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} d^{2} e^{2} - 20 \, {\left(3 \, b^{5} c^{3} + 11 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d e^{3} + {\left(3 \, b^{6} c^{2} + 38 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} + 12 \, a^{3} c^{5}\right)} e^{4}\right)} x^{6} + 4 \, {\left(70 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} d^{4} - 140 \, {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} d^{3} e + 30 \, {\left(3 \, b^{5} c^{3} + 11 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d^{2} e^{2} - 20 \, {\left(b^{6} c^{2} + 6 \, a b^{4} c^{3} + 9 \, a^{2} b^{2} c^{4}\right)} d e^{3} + {\left(b^{7} c + 15 \, a b^{5} c^{2} + 42 \, a^{2} b^{3} c^{3} + 18 \, a^{3} b c^{4}\right)} e^{4}\right)} x^{5} + 30 \, {\left(3 \, a^{4} b^{2} c^{2} + 2 \, a^{5} c^{3}\right)} d^{2} e^{2} - 20 \, {\left(a^{4} b^{3} c + 3 \, a^{5} b c^{2}\right)} d e^{3} + {\left(a^{4} b^{4} + 12 \, a^{5} b^{2} c + 6 \, a^{6} c^{2}\right)} e^{4} + {\left(70 \, {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} d^{4} - 140 \, {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d^{3} e + 30 \, {\left(3 \, b^{6} c^{2} + 38 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} + 12 \, a^{3} c^{5}\right)} d^{2} e^{2} - 20 \, {\left(b^{7} c + 15 \, a b^{5} c^{2} + 42 \, a^{2} b^{3} c^{3} + 18 \, a^{3} b c^{4}\right)} d e^{3} + {\left(b^{8} + 24 \, a b^{6} c + 156 \, a^{2} b^{4} c^{2} + 144 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} e^{4}\right)} x^{4} + 4 \, {\left(70 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d^{4} - 140 \, {\left(a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} d^{3} e + 30 \, {\left(3 \, a b^{5} c^{2} + 11 \, a^{2} b^{3} c^{3} + 6 \, a^{3} b c^{4}\right)} d^{2} e^{2} - 20 \, {\left(a b^{6} c + 6 \, a^{2} b^{4} c^{2} + 9 \, a^{3} b^{2} c^{3}\right)} d e^{3} + {\left(a b^{7} + 15 \, a^{2} b^{5} c + 42 \, a^{3} b^{3} c^{2} + 18 \, a^{4} b c^{3}\right)} e^{4}\right)} x^{3} + 2 \, {\left(70 \, {\left(3 \, a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} d^{4} - 140 \, {\left(3 \, a^{2} b^{3} c^{3} + 2 \, a^{3} b c^{4}\right)} d^{3} e + 30 \, {\left(9 \, a^{2} b^{4} c^{2} + 12 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} d^{2} e^{2} - 20 \, {\left(3 \, a^{2} b^{5} c + 11 \, a^{3} b^{3} c^{2} + 6 \, a^{4} b c^{3}\right)} d e^{3} + {\left(3 \, a^{2} b^{6} + 38 \, a^{3} b^{4} c + 42 \, a^{4} b^{2} c^{2} + 12 \, a^{5} c^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(70 \, a^{3} b c^{4} d^{4} - 140 \, a^{3} b^{2} c^{3} d^{3} e + 30 \, {\left(3 \, a^{3} b^{3} c^{2} + 2 \, a^{4} b c^{3}\right)} d^{2} e^{2} - 20 \, {\left(a^{3} b^{4} c + 3 \, a^{4} b^{2} c^{2}\right)} d e^{3} + {\left(a^{3} b^{5} + 12 \, a^{4} b^{3} c + 6 \, a^{5} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 4 \, {\left(2 \, {\left(b^{8} c - 23 \, a b^{6} c^{2} + 250 \, a^{2} b^{4} c^{3} - 417 \, a^{3} b^{2} c^{4} - 1116 \, a^{4} c^{5}\right)} d^{4} - 4 \, {\left(b^{9} - 23 \, a b^{7} c + 250 \, a^{2} b^{5} c^{2} - 417 \, a^{3} b^{3} c^{3} - 1116 \, a^{4} b c^{4}\right)} d^{3} e - 6 \, {\left(a b^{8} - 32 \, a^{2} b^{6} c - 167 \, a^{3} b^{4} c^{2} + 1146 \, a^{4} b^{2} c^{3} - 120 \, a^{5} c^{4}\right)} d^{2} e^{2} - 4 \, {\left(3 \, a^{2} b^{7} + 139 \, a^{3} b^{5} c - 521 \, a^{4} b^{3} c^{2} - 332 \, a^{5} b c^{3}\right)} d e^{3} + {\left(47 \, a^{3} b^{6} - 4 \, a^{4} b^{4} c - 754 \, a^{5} b^{2} c^{2} + 72 \, a^{6} c^{3}\right)} e^{4}\right)} x}{12 \, {\left(a^{4} b^{10} - 20 \, a^{5} b^{8} c + 160 \, a^{6} b^{6} c^{2} - 640 \, a^{7} b^{4} c^{3} + 1280 \, a^{8} b^{2} c^{4} - 1024 \, a^{9} c^{5} + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} x^{8} + 4 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{2} - 58 \, a b^{10} c^{3} + 440 \, a^{2} b^{8} c^{4} - 1600 \, a^{3} b^{6} c^{5} + 2560 \, a^{4} b^{4} c^{6} - 512 \, a^{5} b^{2} c^{7} - 2048 \, a^{6} c^{8}\right)} x^{6} + 4 \, {\left(b^{13} c - 17 \, a b^{11} c^{2} + 100 \, a^{2} b^{9} c^{3} - 160 \, a^{3} b^{7} c^{4} - 640 \, a^{4} b^{5} c^{5} + 2816 \, a^{5} b^{3} c^{6} - 3072 \, a^{6} b c^{7}\right)} x^{5} + {\left(b^{14} - 8 \, a b^{12} c - 74 \, a^{2} b^{10} c^{2} + 1160 \, a^{3} b^{8} c^{3} - 5440 \, a^{4} b^{6} c^{4} + 10496 \, a^{5} b^{4} c^{5} - 4608 \, a^{6} b^{2} c^{6} - 6144 \, a^{7} c^{7}\right)} x^{4} + 4 \, {\left(a b^{13} - 17 \, a^{2} b^{11} c + 100 \, a^{3} b^{9} c^{2} - 160 \, a^{4} b^{7} c^{3} - 640 \, a^{5} b^{5} c^{4} + 2816 \, a^{6} b^{3} c^{5} - 3072 \, a^{7} b c^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} - 58 \, a^{3} b^{10} c + 440 \, a^{4} b^{8} c^{2} - 1600 \, a^{5} b^{6} c^{3} + 2560 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 2048 \, a^{8} c^{6}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} - 20 \, a^{4} b^{9} c + 160 \, a^{5} b^{7} c^{2} - 640 \, a^{6} b^{5} c^{3} + 1280 \, a^{7} b^{3} c^{4} - 1024 \, a^{8} b c^{5}\right)} x\right)}}, \frac{12 \, {\left(70 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{4} - 140 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{3} e + 30 \, {\left(3 \, b^{4} c^{5} - 10 \, a b^{2} c^{6} - 8 \, a^{2} c^{7}\right)} d^{2} e^{2} - 20 \, {\left(b^{5} c^{4} - a b^{3} c^{5} - 12 \, a^{2} b c^{6}\right)} d e^{3} + {\left(b^{6} c^{3} + 8 \, a b^{4} c^{4} - 42 \, a^{2} b^{2} c^{5} - 24 \, a^{3} c^{6}\right)} e^{4}\right)} x^{7} + 42 \, {\left(70 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{4} - 140 \, {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} d^{3} e + 30 \, {\left(3 \, b^{5} c^{4} - 10 \, a b^{3} c^{5} - 8 \, a^{2} b c^{6}\right)} d^{2} e^{2} - 20 \, {\left(b^{6} c^{3} - a b^{4} c^{4} - 12 \, a^{2} b^{2} c^{5}\right)} d e^{3} + {\left(b^{7} c^{2} + 8 \, a b^{5} c^{3} - 42 \, a^{2} b^{3} c^{4} - 24 \, a^{3} b c^{5}\right)} e^{4}\right)} x^{6} + 4 \, {\left(70 \, {\left(13 \, b^{4} c^{5} - 41 \, a b^{2} c^{6} - 44 \, a^{2} c^{7}\right)} d^{4} - 140 \, {\left(13 \, b^{5} c^{4} - 41 \, a b^{3} c^{5} - 44 \, a^{2} b c^{6}\right)} d^{3} e + 30 \, {\left(39 \, b^{6} c^{3} - 97 \, a b^{4} c^{4} - 214 \, a^{2} b^{2} c^{5} - 88 \, a^{3} c^{6}\right)} d^{2} e^{2} - 20 \, {\left(13 \, b^{7} c^{2} - 2 \, a b^{5} c^{3} - 167 \, a^{2} b^{3} c^{4} - 132 \, a^{3} b c^{5}\right)} d e^{3} + {\left(13 \, b^{8} c + 115 \, a b^{6} c^{2} - 458 \, a^{2} b^{4} c^{3} - 774 \, a^{3} b^{2} c^{4} - 264 \, a^{4} c^{5}\right)} e^{4}\right)} x^{5} - {\left(3 \, b^{9} - 62 \, a b^{7} c + 526 \, a^{2} b^{5} c^{2} - 2420 \, a^{3} b^{3} c^{3} + 4464 \, a^{4} b c^{4}\right)} d^{4} - 4 \, {\left(a b^{8} - 23 \, a^{2} b^{6} c + 250 \, a^{3} b^{4} c^{2} - 312 \, a^{4} b^{2} c^{3} - 1536 \, a^{5} c^{4}\right)} d^{3} e - 6 \, {\left(a^{2} b^{7} - 32 \, a^{3} b^{5} c - 212 \, a^{4} b^{3} c^{2} + 1296 \, a^{5} b c^{3}\right)} d^{2} e^{2} - 4 \, {\left(3 \, a^{3} b^{6} + 154 \, a^{4} b^{4} c - 536 \, a^{5} b^{2} c^{2} - 512 \, a^{6} c^{3}\right)} d e^{3} + 10 \, {\left(5 \, a^{4} b^{5} + 2 \, a^{5} b^{3} c - 88 \, a^{6} b c^{2}\right)} e^{4} + 5 \, {\left(70 \, {\left(5 \, b^{5} c^{4} + 2 \, a b^{3} c^{5} - 88 \, a^{2} b c^{6}\right)} d^{4} - 140 \, {\left(5 \, b^{6} c^{3} + 2 \, a b^{4} c^{4} - 88 \, a^{2} b^{2} c^{5}\right)} d^{3} e + 30 \, {\left(15 \, b^{7} c^{2} + 16 \, a b^{5} c^{3} - 260 \, a^{2} b^{3} c^{4} - 176 \, a^{3} b c^{5}\right)} d^{2} e^{2} - 20 \, {\left(5 \, b^{8} c + 17 \, a b^{6} c^{2} - 82 \, a^{2} b^{4} c^{3} - 264 \, a^{3} b^{2} c^{4}\right)} d e^{3} + {\left(5 \, b^{9} + 62 \, a b^{7} c - 34 \, a^{2} b^{5} c^{2} - 1044 \, a^{3} b^{3} c^{3} - 528 \, a^{4} b c^{4}\right)} e^{4}\right)} x^{4} + 4 \, {\left(14 \, {\left(3 \, b^{6} c^{3} + 89 \, a b^{4} c^{4} - 331 \, a^{2} b^{2} c^{5} - 292 \, a^{3} c^{6}\right)} d^{4} - 28 \, {\left(3 \, b^{7} c^{2} + 89 \, a b^{5} c^{3} - 331 \, a^{2} b^{3} c^{4} - 292 \, a^{3} b c^{5}\right)} d^{3} e + 6 \, {\left(9 \, b^{8} c + 273 \, a b^{6} c^{2} - 815 \, a^{2} b^{4} c^{3} - 1538 \, a^{3} b^{2} c^{4} - 584 \, a^{4} c^{5}\right)} d^{2} e^{2} - 4 \, {\left(3 \, b^{9} + 98 \, a b^{7} c - 64 \, a^{2} b^{5} c^{2} - 1285 \, a^{3} b^{3} c^{3} - 876 \, a^{4} b c^{4}\right)} d e^{3} + {\left(37 \, a b^{8} + 55 \, a^{2} b^{6} c - 362 \, a^{3} b^{4} c^{2} - 1866 \, a^{4} b^{2} c^{3} + 264 \, a^{5} c^{4}\right)} e^{4}\right)} x^{3} - 2 \, {\left(14 \, {\left(b^{7} c^{2} - 32 \, a b^{5} c^{3} - 107 \, a^{2} b^{3} c^{4} + 876 \, a^{3} b c^{5}\right)} d^{4} - 28 \, {\left(b^{8} c - 32 \, a b^{6} c^{2} - 107 \, a^{2} b^{4} c^{3} + 876 \, a^{3} b^{2} c^{4}\right)} d^{3} e + 6 \, {\left(3 \, b^{9} - 94 \, a b^{7} c - 385 \, a^{2} b^{5} c^{2} + 2414 \, a^{3} b^{3} c^{3} + 1752 \, a^{4} b c^{4}\right)} d^{2} e^{2} + 4 \, {\left(9 \, a b^{8} + 363 \, a^{2} b^{6} c - 1195 \, a^{3} b^{4} c^{2} - 1348 \, a^{4} b^{2} c^{3} - 1024 \, a^{5} c^{4}\right)} d e^{3} - {\left(129 \, a^{2} b^{7} - 8 \, a^{3} b^{5} c - 1718 \, a^{4} b^{3} c^{2} - 1256 \, a^{5} b c^{3}\right)} e^{4}\right)} x^{2} - 24 \, {\left(70 \, a^{4} c^{4} d^{4} - 140 \, a^{4} b c^{3} d^{3} e + {\left(70 \, c^{8} d^{4} - 140 \, b c^{7} d^{3} e + 30 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d^{2} e^{2} - 20 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} d e^{3} + {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} e^{4}\right)} x^{8} + 4 \, {\left(70 \, b c^{7} d^{4} - 140 \, b^{2} c^{6} d^{3} e + 30 \, {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} d^{2} e^{2} - 20 \, {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} d e^{3} + {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} e^{4}\right)} x^{7} + 2 \, {\left(70 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d^{4} - 140 \, {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} d^{3} e + 30 \, {\left(9 \, b^{4} c^{4} + 12 \, a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} d^{2} e^{2} - 20 \, {\left(3 \, b^{5} c^{3} + 11 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d e^{3} + {\left(3 \, b^{6} c^{2} + 38 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} + 12 \, a^{3} c^{5}\right)} e^{4}\right)} x^{6} + 4 \, {\left(70 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} d^{4} - 140 \, {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} d^{3} e + 30 \, {\left(3 \, b^{5} c^{3} + 11 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d^{2} e^{2} - 20 \, {\left(b^{6} c^{2} + 6 \, a b^{4} c^{3} + 9 \, a^{2} b^{2} c^{4}\right)} d e^{3} + {\left(b^{7} c + 15 \, a b^{5} c^{2} + 42 \, a^{2} b^{3} c^{3} + 18 \, a^{3} b c^{4}\right)} e^{4}\right)} x^{5} + 30 \, {\left(3 \, a^{4} b^{2} c^{2} + 2 \, a^{5} c^{3}\right)} d^{2} e^{2} - 20 \, {\left(a^{4} b^{3} c + 3 \, a^{5} b c^{2}\right)} d e^{3} + {\left(a^{4} b^{4} + 12 \, a^{5} b^{2} c + 6 \, a^{6} c^{2}\right)} e^{4} + {\left(70 \, {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} d^{4} - 140 \, {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d^{3} e + 30 \, {\left(3 \, b^{6} c^{2} + 38 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} + 12 \, a^{3} c^{5}\right)} d^{2} e^{2} - 20 \, {\left(b^{7} c + 15 \, a b^{5} c^{2} + 42 \, a^{2} b^{3} c^{3} + 18 \, a^{3} b c^{4}\right)} d e^{3} + {\left(b^{8} + 24 \, a b^{6} c + 156 \, a^{2} b^{4} c^{2} + 144 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} e^{4}\right)} x^{4} + 4 \, {\left(70 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d^{4} - 140 \, {\left(a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} d^{3} e + 30 \, {\left(3 \, a b^{5} c^{2} + 11 \, a^{2} b^{3} c^{3} + 6 \, a^{3} b c^{4}\right)} d^{2} e^{2} - 20 \, {\left(a b^{6} c + 6 \, a^{2} b^{4} c^{2} + 9 \, a^{3} b^{2} c^{3}\right)} d e^{3} + {\left(a b^{7} + 15 \, a^{2} b^{5} c + 42 \, a^{3} b^{3} c^{2} + 18 \, a^{4} b c^{3}\right)} e^{4}\right)} x^{3} + 2 \, {\left(70 \, {\left(3 \, a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} d^{4} - 140 \, {\left(3 \, a^{2} b^{3} c^{3} + 2 \, a^{3} b c^{4}\right)} d^{3} e + 30 \, {\left(9 \, a^{2} b^{4} c^{2} + 12 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} d^{2} e^{2} - 20 \, {\left(3 \, a^{2} b^{5} c + 11 \, a^{3} b^{3} c^{2} + 6 \, a^{4} b c^{3}\right)} d e^{3} + {\left(3 \, a^{2} b^{6} + 38 \, a^{3} b^{4} c + 42 \, a^{4} b^{2} c^{2} + 12 \, a^{5} c^{3}\right)} e^{4}\right)} x^{2} + 4 \, {\left(70 \, a^{3} b c^{4} d^{4} - 140 \, a^{3} b^{2} c^{3} d^{3} e + 30 \, {\left(3 \, a^{3} b^{3} c^{2} + 2 \, a^{4} b c^{3}\right)} d^{2} e^{2} - 20 \, {\left(a^{3} b^{4} c + 3 \, a^{4} b^{2} c^{2}\right)} d e^{3} + {\left(a^{3} b^{5} + 12 \, a^{4} b^{3} c + 6 \, a^{5} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 4 \, {\left(2 \, {\left(b^{8} c - 23 \, a b^{6} c^{2} + 250 \, a^{2} b^{4} c^{3} - 417 \, a^{3} b^{2} c^{4} - 1116 \, a^{4} c^{5}\right)} d^{4} - 4 \, {\left(b^{9} - 23 \, a b^{7} c + 250 \, a^{2} b^{5} c^{2} - 417 \, a^{3} b^{3} c^{3} - 1116 \, a^{4} b c^{4}\right)} d^{3} e - 6 \, {\left(a b^{8} - 32 \, a^{2} b^{6} c - 167 \, a^{3} b^{4} c^{2} + 1146 \, a^{4} b^{2} c^{3} - 120 \, a^{5} c^{4}\right)} d^{2} e^{2} - 4 \, {\left(3 \, a^{2} b^{7} + 139 \, a^{3} b^{5} c - 521 \, a^{4} b^{3} c^{2} - 332 \, a^{5} b c^{3}\right)} d e^{3} + {\left(47 \, a^{3} b^{6} - 4 \, a^{4} b^{4} c - 754 \, a^{5} b^{2} c^{2} + 72 \, a^{6} c^{3}\right)} e^{4}\right)} x}{12 \, {\left(a^{4} b^{10} - 20 \, a^{5} b^{8} c + 160 \, a^{6} b^{6} c^{2} - 640 \, a^{7} b^{4} c^{3} + 1280 \, a^{8} b^{2} c^{4} - 1024 \, a^{9} c^{5} + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} x^{8} + 4 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{2} - 58 \, a b^{10} c^{3} + 440 \, a^{2} b^{8} c^{4} - 1600 \, a^{3} b^{6} c^{5} + 2560 \, a^{4} b^{4} c^{6} - 512 \, a^{5} b^{2} c^{7} - 2048 \, a^{6} c^{8}\right)} x^{6} + 4 \, {\left(b^{13} c - 17 \, a b^{11} c^{2} + 100 \, a^{2} b^{9} c^{3} - 160 \, a^{3} b^{7} c^{4} - 640 \, a^{4} b^{5} c^{5} + 2816 \, a^{5} b^{3} c^{6} - 3072 \, a^{6} b c^{7}\right)} x^{5} + {\left(b^{14} - 8 \, a b^{12} c - 74 \, a^{2} b^{10} c^{2} + 1160 \, a^{3} b^{8} c^{3} - 5440 \, a^{4} b^{6} c^{4} + 10496 \, a^{5} b^{4} c^{5} - 4608 \, a^{6} b^{2} c^{6} - 6144 \, a^{7} c^{7}\right)} x^{4} + 4 \, {\left(a b^{13} - 17 \, a^{2} b^{11} c + 100 \, a^{3} b^{9} c^{2} - 160 \, a^{4} b^{7} c^{3} - 640 \, a^{5} b^{5} c^{4} + 2816 \, a^{6} b^{3} c^{5} - 3072 \, a^{7} b c^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} - 58 \, a^{3} b^{10} c + 440 \, a^{4} b^{8} c^{2} - 1600 \, a^{5} b^{6} c^{3} + 2560 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 2048 \, a^{8} c^{6}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} - 20 \, a^{4} b^{9} c + 160 \, a^{5} b^{7} c^{2} - 640 \, a^{6} b^{5} c^{3} + 1280 \, a^{7} b^{3} c^{4} - 1024 \, a^{8} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/12*(12*(70*(b^2*c^7 - 4*a*c^8)*d^4 - 140*(b^3*c^6 - 4*a*b*c^7)*d^3*e + 30*(3*b^4*c^5 - 10*a*b^2*c^6 - 8*a^2*c^7)*d^2*e^2 - 20*(b^5*c^4 - a*b^3*c^5 - 12*a^2*b*c^6)*d*e^3 + (b^6*c^3 + 8*a*b^4*c^4 - 42*a^2*b^2*c^5 - 24*a^3*c^6)*e^4)*x^7 + 42*(70*(b^3*c^6 - 4*a*b*c^7)*d^4 - 140*(b^4*c^5 - 4*a*b^2*c^6)*d^3*e + 30*(3*b^5*c^4 - 10*a*b^3*c^5 - 8*a^2*b*c^6)*d^2*e^2 - 20*(b^6*c^3 - a*b^4*c^4 - 12*a^2*b^2*c^5)*d*e^3 + (b^7*c^2 + 8*a*b^5*c^3 - 42*a^2*b^3*c^4 - 24*a^3*b*c^5)*e^4)*x^6 + 4*(70*(13*b^4*c^5 - 41*a*b^2*c^6 - 44*a^2*c^7)*d^4 - 140*(13*b^5*c^4 - 41*a*b^3*c^5 - 44*a^2*b*c^6)*d^3*e + 30*(39*b^6*c^3 - 97*a*b^4*c^4 - 214*a^2*b^2*c^5 - 88*a^3*c^6)*d^2*e^2 - 20*(13*b^7*c^2 - 2*a*b^5*c^3 - 167*a^2*b^3*c^4 - 132*a^3*b*c^5)*d*e^3 + (13*b^8*c + 115*a*b^6*c^2 - 458*a^2*b^4*c^3 - 774*a^3*b^2*c^4 - 264*a^4*c^5)*e^4)*x^5 - (3*b^9 - 62*a*b^7*c + 526*a^2*b^5*c^2 - 2420*a^3*b^3*c^3 + 4464*a^4*b*c^4)*d^4 - 4*(a*b^8 - 23*a^2*b^6*c + 250*a^3*b^4*c^2 - 312*a^4*b^2*c^3 - 1536*a^5*c^4)*d^3*e - 6*(a^2*b^7 - 32*a^3*b^5*c - 212*a^4*b^3*c^2 + 1296*a^5*b*c^3)*d^2*e^2 - 4*(3*a^3*b^6 + 154*a^4*b^4*c - 536*a^5*b^2*c^2 - 512*a^6*c^3)*d*e^3 + 10*(5*a^4*b^5 + 2*a^5*b^3*c - 88*a^6*b*c^2)*e^4 + 5*(70*(5*b^5*c^4 + 2*a*b^3*c^5 - 88*a^2*b*c^6)*d^4 - 140*(5*b^6*c^3 + 2*a*b^4*c^4 - 88*a^2*b^2*c^5)*d^3*e + 30*(15*b^7*c^2 + 16*a*b^5*c^3 - 260*a^2*b^3*c^4 - 176*a^3*b*c^5)*d^2*e^2 - 20*(5*b^8*c + 17*a*b^6*c^2 - 82*a^2*b^4*c^3 - 264*a^3*b^2*c^4)*d*e^3 + (5*b^9 + 62*a*b^7*c - 34*a^2*b^5*c^2 - 1044*a^3*b^3*c^3 - 528*a^4*b*c^4)*e^4)*x^4 + 4*(14*(3*b^6*c^3 + 89*a*b^4*c^4 - 331*a^2*b^2*c^5 - 292*a^3*c^6)*d^4 - 28*(3*b^7*c^2 + 89*a*b^5*c^3 - 331*a^2*b^3*c^4 - 292*a^3*b*c^5)*d^3*e + 6*(9*b^8*c + 273*a*b^6*c^2 - 815*a^2*b^4*c^3 - 1538*a^3*b^2*c^4 - 584*a^4*c^5)*d^2*e^2 - 4*(3*b^9 + 98*a*b^7*c - 64*a^2*b^5*c^2 - 1285*a^3*b^3*c^3 - 876*a^4*b*c^4)*d*e^3 + (37*a*b^8 + 55*a^2*b^6*c - 362*a^3*b^4*c^2 - 1866*a^4*b^2*c^3 + 264*a^5*c^4)*e^4)*x^3 - 2*(14*(b^7*c^2 - 32*a*b^5*c^3 - 107*a^2*b^3*c^4 + 876*a^3*b*c^5)*d^4 - 28*(b^8*c - 32*a*b^6*c^2 - 107*a^2*b^4*c^3 + 876*a^3*b^2*c^4)*d^3*e + 6*(3*b^9 - 94*a*b^7*c - 385*a^2*b^5*c^2 + 2414*a^3*b^3*c^3 + 1752*a^4*b*c^4)*d^2*e^2 + 4*(9*a*b^8 + 363*a^2*b^6*c - 1195*a^3*b^4*c^2 - 1348*a^4*b^2*c^3 - 1024*a^5*c^4)*d*e^3 - (129*a^2*b^7 - 8*a^3*b^5*c - 1718*a^4*b^3*c^2 - 1256*a^5*b*c^3)*e^4)*x^2 + 12*(70*a^4*c^4*d^4 - 140*a^4*b*c^3*d^3*e + (70*c^8*d^4 - 140*b*c^7*d^3*e + 30*(3*b^2*c^6 + 2*a*c^7)*d^2*e^2 - 20*(b^3*c^5 + 3*a*b*c^6)*d*e^3 + (b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*e^4)*x^8 + 4*(70*b*c^7*d^4 - 140*b^2*c^6*d^3*e + 30*(3*b^3*c^5 + 2*a*b*c^6)*d^2*e^2 - 20*(b^4*c^4 + 3*a*b^2*c^5)*d*e^3 + (b^5*c^3 + 12*a*b^3*c^4 + 6*a^2*b*c^5)*e^4)*x^7 + 2*(70*(3*b^2*c^6 + 2*a*c^7)*d^4 - 140*(3*b^3*c^5 + 2*a*b*c^6)*d^3*e + 30*(9*b^4*c^4 + 12*a*b^2*c^5 + 4*a^2*c^6)*d^2*e^2 - 20*(3*b^5*c^3 + 11*a*b^3*c^4 + 6*a^2*b*c^5)*d*e^3 + (3*b^6*c^2 + 38*a*b^4*c^3 + 42*a^2*b^2*c^4 + 12*a^3*c^5)*e^4)*x^6 + 4*(70*(b^3*c^5 + 3*a*b*c^6)*d^4 - 140*(b^4*c^4 + 3*a*b^2*c^5)*d^3*e + 30*(3*b^5*c^3 + 11*a*b^3*c^4 + 6*a^2*b*c^5)*d^2*e^2 - 20*(b^6*c^2 + 6*a*b^4*c^3 + 9*a^2*b^2*c^4)*d*e^3 + (b^7*c + 15*a*b^5*c^2 + 42*a^2*b^3*c^3 + 18*a^3*b*c^4)*e^4)*x^5 + 30*(3*a^4*b^2*c^2 + 2*a^5*c^3)*d^2*e^2 - 20*(a^4*b^3*c + 3*a^5*b*c^2)*d*e^3 + (a^4*b^4 + 12*a^5*b^2*c + 6*a^6*c^2)*e^4 + (70*(b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*d^4 - 140*(b^5*c^3 + 12*a*b^3*c^4 + 6*a^2*b*c^5)*d^3*e + 30*(3*b^6*c^2 + 38*a*b^4*c^3 + 42*a^2*b^2*c^4 + 12*a^3*c^5)*d^2*e^2 - 20*(b^7*c + 15*a*b^5*c^2 + 42*a^2*b^3*c^3 + 18*a^3*b*c^4)*d*e^3 + (b^8 + 24*a*b^6*c + 156*a^2*b^4*c^2 + 144*a^3*b^2*c^3 + 36*a^4*c^4)*e^4)*x^4 + 4*(70*(a*b^3*c^4 + 3*a^2*b*c^5)*d^4 - 140*(a*b^4*c^3 + 3*a^2*b^2*c^4)*d^3*e + 30*(3*a*b^5*c^2 + 11*a^2*b^3*c^3 + 6*a^3*b*c^4)*d^2*e^2 - 20*(a*b^6*c + 6*a^2*b^4*c^2 + 9*a^3*b^2*c^3)*d*e^3 + (a*b^7 + 15*a^2*b^5*c + 42*a^3*b^3*c^2 + 18*a^4*b*c^3)*e^4)*x^3 + 2*(70*(3*a^2*b^2*c^4 + 2*a^3*c^5)*d^4 - 140*(3*a^2*b^3*c^3 + 2*a^3*b*c^4)*d^3*e + 30*(9*a^2*b^4*c^2 + 12*a^3*b^2*c^3 + 4*a^4*c^4)*d^2*e^2 - 20*(3*a^2*b^5*c + 11*a^3*b^3*c^2 + 6*a^4*b*c^3)*d*e^3 + (3*a^2*b^6 + 38*a^3*b^4*c + 42*a^4*b^2*c^2 + 12*a^5*c^3)*e^4)*x^2 + 4*(70*a^3*b*c^4*d^4 - 140*a^3*b^2*c^3*d^3*e + 30*(3*a^3*b^3*c^2 + 2*a^4*b*c^3)*d^2*e^2 - 20*(a^3*b^4*c + 3*a^4*b^2*c^2)*d*e^3 + (a^3*b^5 + 12*a^4*b^3*c + 6*a^5*b*c^2)*e^4)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 4*(2*(b^8*c - 23*a*b^6*c^2 + 250*a^2*b^4*c^3 - 417*a^3*b^2*c^4 - 1116*a^4*c^5)*d^4 - 4*(b^9 - 23*a*b^7*c + 250*a^2*b^5*c^2 - 417*a^3*b^3*c^3 - 1116*a^4*b*c^4)*d^3*e - 6*(a*b^8 - 32*a^2*b^6*c - 167*a^3*b^4*c^2 + 1146*a^4*b^2*c^3 - 120*a^5*c^4)*d^2*e^2 - 4*(3*a^2*b^7 + 139*a^3*b^5*c - 521*a^4*b^3*c^2 - 332*a^5*b*c^3)*d*e^3 + (47*a^3*b^6 - 4*a^4*b^4*c - 754*a^5*b^2*c^2 + 72*a^6*c^3)*e^4)*x)/(a^4*b^10 - 20*a^5*b^8*c + 160*a^6*b^6*c^2 - 640*a^7*b^4*c^3 + 1280*a^8*b^2*c^4 - 1024*a^9*c^5 + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*x^8 + 4*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*x^7 + 2*(3*b^12*c^2 - 58*a*b^10*c^3 + 440*a^2*b^8*c^4 - 1600*a^3*b^6*c^5 + 2560*a^4*b^4*c^6 - 512*a^5*b^2*c^7 - 2048*a^6*c^8)*x^6 + 4*(b^13*c - 17*a*b^11*c^2 + 100*a^2*b^9*c^3 - 160*a^3*b^7*c^4 - 640*a^4*b^5*c^5 + 2816*a^5*b^3*c^6 - 3072*a^6*b*c^7)*x^5 + (b^14 - 8*a*b^12*c - 74*a^2*b^10*c^2 + 1160*a^3*b^8*c^3 - 5440*a^4*b^6*c^4 + 10496*a^5*b^4*c^5 - 4608*a^6*b^2*c^6 - 6144*a^7*c^7)*x^4 + 4*(a*b^13 - 17*a^2*b^11*c + 100*a^3*b^9*c^2 - 160*a^4*b^7*c^3 - 640*a^5*b^5*c^4 + 2816*a^6*b^3*c^5 - 3072*a^7*b*c^6)*x^3 + 2*(3*a^2*b^12 - 58*a^3*b^10*c + 440*a^4*b^8*c^2 - 1600*a^5*b^6*c^3 + 2560*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 2048*a^8*c^6)*x^2 + 4*(a^3*b^11 - 20*a^4*b^9*c + 160*a^5*b^7*c^2 - 640*a^6*b^5*c^3 + 1280*a^7*b^3*c^4 - 1024*a^8*b*c^5)*x), 1/12*(12*(70*(b^2*c^7 - 4*a*c^8)*d^4 - 140*(b^3*c^6 - 4*a*b*c^7)*d^3*e + 30*(3*b^4*c^5 - 10*a*b^2*c^6 - 8*a^2*c^7)*d^2*e^2 - 20*(b^5*c^4 - a*b^3*c^5 - 12*a^2*b*c^6)*d*e^3 + (b^6*c^3 + 8*a*b^4*c^4 - 42*a^2*b^2*c^5 - 24*a^3*c^6)*e^4)*x^7 + 42*(70*(b^3*c^6 - 4*a*b*c^7)*d^4 - 140*(b^4*c^5 - 4*a*b^2*c^6)*d^3*e + 30*(3*b^5*c^4 - 10*a*b^3*c^5 - 8*a^2*b*c^6)*d^2*e^2 - 20*(b^6*c^3 - a*b^4*c^4 - 12*a^2*b^2*c^5)*d*e^3 + (b^7*c^2 + 8*a*b^5*c^3 - 42*a^2*b^3*c^4 - 24*a^3*b*c^5)*e^4)*x^6 + 4*(70*(13*b^4*c^5 - 41*a*b^2*c^6 - 44*a^2*c^7)*d^4 - 140*(13*b^5*c^4 - 41*a*b^3*c^5 - 44*a^2*b*c^6)*d^3*e + 30*(39*b^6*c^3 - 97*a*b^4*c^4 - 214*a^2*b^2*c^5 - 88*a^3*c^6)*d^2*e^2 - 20*(13*b^7*c^2 - 2*a*b^5*c^3 - 167*a^2*b^3*c^4 - 132*a^3*b*c^5)*d*e^3 + (13*b^8*c + 115*a*b^6*c^2 - 458*a^2*b^4*c^3 - 774*a^3*b^2*c^4 - 264*a^4*c^5)*e^4)*x^5 - (3*b^9 - 62*a*b^7*c + 526*a^2*b^5*c^2 - 2420*a^3*b^3*c^3 + 4464*a^4*b*c^4)*d^4 - 4*(a*b^8 - 23*a^2*b^6*c + 250*a^3*b^4*c^2 - 312*a^4*b^2*c^3 - 1536*a^5*c^4)*d^3*e - 6*(a^2*b^7 - 32*a^3*b^5*c - 212*a^4*b^3*c^2 + 1296*a^5*b*c^3)*d^2*e^2 - 4*(3*a^3*b^6 + 154*a^4*b^4*c - 536*a^5*b^2*c^2 - 512*a^6*c^3)*d*e^3 + 10*(5*a^4*b^5 + 2*a^5*b^3*c - 88*a^6*b*c^2)*e^4 + 5*(70*(5*b^5*c^4 + 2*a*b^3*c^5 - 88*a^2*b*c^6)*d^4 - 140*(5*b^6*c^3 + 2*a*b^4*c^4 - 88*a^2*b^2*c^5)*d^3*e + 30*(15*b^7*c^2 + 16*a*b^5*c^3 - 260*a^2*b^3*c^4 - 176*a^3*b*c^5)*d^2*e^2 - 20*(5*b^8*c + 17*a*b^6*c^2 - 82*a^2*b^4*c^3 - 264*a^3*b^2*c^4)*d*e^3 + (5*b^9 + 62*a*b^7*c - 34*a^2*b^5*c^2 - 1044*a^3*b^3*c^3 - 528*a^4*b*c^4)*e^4)*x^4 + 4*(14*(3*b^6*c^3 + 89*a*b^4*c^4 - 331*a^2*b^2*c^5 - 292*a^3*c^6)*d^4 - 28*(3*b^7*c^2 + 89*a*b^5*c^3 - 331*a^2*b^3*c^4 - 292*a^3*b*c^5)*d^3*e + 6*(9*b^8*c + 273*a*b^6*c^2 - 815*a^2*b^4*c^3 - 1538*a^3*b^2*c^4 - 584*a^4*c^5)*d^2*e^2 - 4*(3*b^9 + 98*a*b^7*c - 64*a^2*b^5*c^2 - 1285*a^3*b^3*c^3 - 876*a^4*b*c^4)*d*e^3 + (37*a*b^8 + 55*a^2*b^6*c - 362*a^3*b^4*c^2 - 1866*a^4*b^2*c^3 + 264*a^5*c^4)*e^4)*x^3 - 2*(14*(b^7*c^2 - 32*a*b^5*c^3 - 107*a^2*b^3*c^4 + 876*a^3*b*c^5)*d^4 - 28*(b^8*c - 32*a*b^6*c^2 - 107*a^2*b^4*c^3 + 876*a^3*b^2*c^4)*d^3*e + 6*(3*b^9 - 94*a*b^7*c - 385*a^2*b^5*c^2 + 2414*a^3*b^3*c^3 + 1752*a^4*b*c^4)*d^2*e^2 + 4*(9*a*b^8 + 363*a^2*b^6*c - 1195*a^3*b^4*c^2 - 1348*a^4*b^2*c^3 - 1024*a^5*c^4)*d*e^3 - (129*a^2*b^7 - 8*a^3*b^5*c - 1718*a^4*b^3*c^2 - 1256*a^5*b*c^3)*e^4)*x^2 - 24*(70*a^4*c^4*d^4 - 140*a^4*b*c^3*d^3*e + (70*c^8*d^4 - 140*b*c^7*d^3*e + 30*(3*b^2*c^6 + 2*a*c^7)*d^2*e^2 - 20*(b^3*c^5 + 3*a*b*c^6)*d*e^3 + (b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*e^4)*x^8 + 4*(70*b*c^7*d^4 - 140*b^2*c^6*d^3*e + 30*(3*b^3*c^5 + 2*a*b*c^6)*d^2*e^2 - 20*(b^4*c^4 + 3*a*b^2*c^5)*d*e^3 + (b^5*c^3 + 12*a*b^3*c^4 + 6*a^2*b*c^5)*e^4)*x^7 + 2*(70*(3*b^2*c^6 + 2*a*c^7)*d^4 - 140*(3*b^3*c^5 + 2*a*b*c^6)*d^3*e + 30*(9*b^4*c^4 + 12*a*b^2*c^5 + 4*a^2*c^6)*d^2*e^2 - 20*(3*b^5*c^3 + 11*a*b^3*c^4 + 6*a^2*b*c^5)*d*e^3 + (3*b^6*c^2 + 38*a*b^4*c^3 + 42*a^2*b^2*c^4 + 12*a^3*c^5)*e^4)*x^6 + 4*(70*(b^3*c^5 + 3*a*b*c^6)*d^4 - 140*(b^4*c^4 + 3*a*b^2*c^5)*d^3*e + 30*(3*b^5*c^3 + 11*a*b^3*c^4 + 6*a^2*b*c^5)*d^2*e^2 - 20*(b^6*c^2 + 6*a*b^4*c^3 + 9*a^2*b^2*c^4)*d*e^3 + (b^7*c + 15*a*b^5*c^2 + 42*a^2*b^3*c^3 + 18*a^3*b*c^4)*e^4)*x^5 + 30*(3*a^4*b^2*c^2 + 2*a^5*c^3)*d^2*e^2 - 20*(a^4*b^3*c + 3*a^5*b*c^2)*d*e^3 + (a^4*b^4 + 12*a^5*b^2*c + 6*a^6*c^2)*e^4 + (70*(b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*d^4 - 140*(b^5*c^3 + 12*a*b^3*c^4 + 6*a^2*b*c^5)*d^3*e + 30*(3*b^6*c^2 + 38*a*b^4*c^3 + 42*a^2*b^2*c^4 + 12*a^3*c^5)*d^2*e^2 - 20*(b^7*c + 15*a*b^5*c^2 + 42*a^2*b^3*c^3 + 18*a^3*b*c^4)*d*e^3 + (b^8 + 24*a*b^6*c + 156*a^2*b^4*c^2 + 144*a^3*b^2*c^3 + 36*a^4*c^4)*e^4)*x^4 + 4*(70*(a*b^3*c^4 + 3*a^2*b*c^5)*d^4 - 140*(a*b^4*c^3 + 3*a^2*b^2*c^4)*d^3*e + 30*(3*a*b^5*c^2 + 11*a^2*b^3*c^3 + 6*a^3*b*c^4)*d^2*e^2 - 20*(a*b^6*c + 6*a^2*b^4*c^2 + 9*a^3*b^2*c^3)*d*e^3 + (a*b^7 + 15*a^2*b^5*c + 42*a^3*b^3*c^2 + 18*a^4*b*c^3)*e^4)*x^3 + 2*(70*(3*a^2*b^2*c^4 + 2*a^3*c^5)*d^4 - 140*(3*a^2*b^3*c^3 + 2*a^3*b*c^4)*d^3*e + 30*(9*a^2*b^4*c^2 + 12*a^3*b^2*c^3 + 4*a^4*c^4)*d^2*e^2 - 20*(3*a^2*b^5*c + 11*a^3*b^3*c^2 + 6*a^4*b*c^3)*d*e^3 + (3*a^2*b^6 + 38*a^3*b^4*c + 42*a^4*b^2*c^2 + 12*a^5*c^3)*e^4)*x^2 + 4*(70*a^3*b*c^4*d^4 - 140*a^3*b^2*c^3*d^3*e + 30*(3*a^3*b^3*c^2 + 2*a^4*b*c^3)*d^2*e^2 - 20*(a^3*b^4*c + 3*a^4*b^2*c^2)*d*e^3 + (a^3*b^5 + 12*a^4*b^3*c + 6*a^5*b*c^2)*e^4)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 4*(2*(b^8*c - 23*a*b^6*c^2 + 250*a^2*b^4*c^3 - 417*a^3*b^2*c^4 - 1116*a^4*c^5)*d^4 - 4*(b^9 - 23*a*b^7*c + 250*a^2*b^5*c^2 - 417*a^3*b^3*c^3 - 1116*a^4*b*c^4)*d^3*e - 6*(a*b^8 - 32*a^2*b^6*c - 167*a^3*b^4*c^2 + 1146*a^4*b^2*c^3 - 120*a^5*c^4)*d^2*e^2 - 4*(3*a^2*b^7 + 139*a^3*b^5*c - 521*a^4*b^3*c^2 - 332*a^5*b*c^3)*d*e^3 + (47*a^3*b^6 - 4*a^4*b^4*c - 754*a^5*b^2*c^2 + 72*a^6*c^3)*e^4)*x)/(a^4*b^10 - 20*a^5*b^8*c + 160*a^6*b^6*c^2 - 640*a^7*b^4*c^3 + 1280*a^8*b^2*c^4 - 1024*a^9*c^5 + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*x^8 + 4*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*x^7 + 2*(3*b^12*c^2 - 58*a*b^10*c^3 + 440*a^2*b^8*c^4 - 1600*a^3*b^6*c^5 + 2560*a^4*b^4*c^6 - 512*a^5*b^2*c^7 - 2048*a^6*c^8)*x^6 + 4*(b^13*c - 17*a*b^11*c^2 + 100*a^2*b^9*c^3 - 160*a^3*b^7*c^4 - 640*a^4*b^5*c^5 + 2816*a^5*b^3*c^6 - 3072*a^6*b*c^7)*x^5 + (b^14 - 8*a*b^12*c - 74*a^2*b^10*c^2 + 1160*a^3*b^8*c^3 - 5440*a^4*b^6*c^4 + 10496*a^5*b^4*c^5 - 4608*a^6*b^2*c^6 - 6144*a^7*c^7)*x^4 + 4*(a*b^13 - 17*a^2*b^11*c + 100*a^3*b^9*c^2 - 160*a^4*b^7*c^3 - 640*a^5*b^5*c^4 + 2816*a^6*b^3*c^5 - 3072*a^7*b*c^6)*x^3 + 2*(3*a^2*b^12 - 58*a^3*b^10*c + 440*a^4*b^8*c^2 - 1600*a^5*b^6*c^3 + 2560*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 2048*a^8*c^6)*x^2 + 4*(a^3*b^11 - 20*a^4*b^9*c + 160*a^5*b^7*c^2 - 640*a^6*b^5*c^3 + 1280*a^7*b^3*c^4 - 1024*a^8*b*c^5)*x)]","B",0
2223,1,5818,0,0.519609," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^5,x, algorithm=""fricas"")","\left[\frac{60 \, {\left(14 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{3} - 21 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{2} e + 3 \, {\left(3 \, b^{4} c^{5} - 10 \, a b^{2} c^{6} - 8 \, a^{2} c^{7}\right)} d e^{2} - {\left(b^{5} c^{4} - a b^{3} c^{5} - 12 \, a^{2} b c^{6}\right)} e^{3}\right)} x^{7} + 210 \, {\left(14 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{3} - 21 \, {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} d^{2} e + 3 \, {\left(3 \, b^{5} c^{4} - 10 \, a b^{3} c^{5} - 8 \, a^{2} b c^{6}\right)} d e^{2} - {\left(b^{6} c^{3} - a b^{4} c^{4} - 12 \, a^{2} b^{2} c^{5}\right)} e^{3}\right)} x^{6} + 20 \, {\left(14 \, {\left(13 \, b^{4} c^{5} - 41 \, a b^{2} c^{6} - 44 \, a^{2} c^{7}\right)} d^{3} - 21 \, {\left(13 \, b^{5} c^{4} - 41 \, a b^{3} c^{5} - 44 \, a^{2} b c^{6}\right)} d^{2} e + 3 \, {\left(39 \, b^{6} c^{3} - 97 \, a b^{4} c^{4} - 214 \, a^{2} b^{2} c^{5} - 88 \, a^{3} c^{6}\right)} d e^{2} - {\left(13 \, b^{7} c^{2} - 2 \, a b^{5} c^{3} - 167 \, a^{2} b^{3} c^{4} - 132 \, a^{3} b c^{5}\right)} e^{3}\right)} x^{5} + 25 \, {\left(14 \, {\left(5 \, b^{5} c^{4} + 2 \, a b^{3} c^{5} - 88 \, a^{2} b c^{6}\right)} d^{3} - 21 \, {\left(5 \, b^{6} c^{3} + 2 \, a b^{4} c^{4} - 88 \, a^{2} b^{2} c^{5}\right)} d^{2} e + 3 \, {\left(15 \, b^{7} c^{2} + 16 \, a b^{5} c^{3} - 260 \, a^{2} b^{3} c^{4} - 176 \, a^{3} b c^{5}\right)} d e^{2} - {\left(5 \, b^{8} c + 17 \, a b^{6} c^{2} - 82 \, a^{2} b^{4} c^{3} - 264 \, a^{3} b^{2} c^{4}\right)} e^{3}\right)} x^{4} - {\left(3 \, b^{9} - 62 \, a b^{7} c + 526 \, a^{2} b^{5} c^{2} - 2420 \, a^{3} b^{3} c^{3} + 4464 \, a^{4} b c^{4}\right)} d^{3} - 3 \, {\left(a b^{8} - 23 \, a^{2} b^{6} c + 250 \, a^{3} b^{4} c^{2} - 312 \, a^{4} b^{2} c^{3} - 1536 \, a^{5} c^{4}\right)} d^{2} e - 3 \, {\left(a^{2} b^{7} - 32 \, a^{3} b^{5} c - 212 \, a^{4} b^{3} c^{2} + 1296 \, a^{5} b c^{3}\right)} d e^{2} - {\left(3 \, a^{3} b^{6} + 154 \, a^{4} b^{4} c - 536 \, a^{5} b^{2} c^{2} - 512 \, a^{6} c^{3}\right)} e^{3} + 4 \, {\left(14 \, {\left(3 \, b^{6} c^{3} + 89 \, a b^{4} c^{4} - 331 \, a^{2} b^{2} c^{5} - 292 \, a^{3} c^{6}\right)} d^{3} - 21 \, {\left(3 \, b^{7} c^{2} + 89 \, a b^{5} c^{3} - 331 \, a^{2} b^{3} c^{4} - 292 \, a^{3} b c^{5}\right)} d^{2} e + 3 \, {\left(9 \, b^{8} c + 273 \, a b^{6} c^{2} - 815 \, a^{2} b^{4} c^{3} - 1538 \, a^{3} b^{2} c^{4} - 584 \, a^{4} c^{5}\right)} d e^{2} - {\left(3 \, b^{9} + 98 \, a b^{7} c - 64 \, a^{2} b^{5} c^{2} - 1285 \, a^{3} b^{3} c^{3} - 876 \, a^{4} b c^{4}\right)} e^{3}\right)} x^{3} - 2 \, {\left(14 \, {\left(b^{7} c^{2} - 32 \, a b^{5} c^{3} - 107 \, a^{2} b^{3} c^{4} + 876 \, a^{3} b c^{5}\right)} d^{3} - 21 \, {\left(b^{8} c - 32 \, a b^{6} c^{2} - 107 \, a^{2} b^{4} c^{3} + 876 \, a^{3} b^{2} c^{4}\right)} d^{2} e + 3 \, {\left(3 \, b^{9} - 94 \, a b^{7} c - 385 \, a^{2} b^{5} c^{2} + 2414 \, a^{3} b^{3} c^{3} + 1752 \, a^{4} b c^{4}\right)} d e^{2} + {\left(9 \, a b^{8} + 363 \, a^{2} b^{6} c - 1195 \, a^{3} b^{4} c^{2} - 1348 \, a^{4} b^{2} c^{3} - 1024 \, a^{5} c^{4}\right)} e^{3}\right)} x^{2} - 60 \, {\left(14 \, a^{4} c^{4} d^{3} - 21 \, a^{4} b c^{3} d^{2} e + {\left(14 \, c^{8} d^{3} - 21 \, b c^{7} d^{2} e + 3 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d e^{2} - {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} e^{3}\right)} x^{8} + 4 \, {\left(14 \, b c^{7} d^{3} - 21 \, b^{2} c^{6} d^{2} e + 3 \, {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} d e^{2} - {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} e^{3}\right)} x^{7} + 2 \, {\left(14 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d^{3} - 21 \, {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} d^{2} e + 3 \, {\left(9 \, b^{4} c^{4} + 12 \, a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} d e^{2} - {\left(3 \, b^{5} c^{3} + 11 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} e^{3}\right)} x^{6} + 4 \, {\left(14 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} d^{3} - 21 \, {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} d^{2} e + 3 \, {\left(3 \, b^{5} c^{3} + 11 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d e^{2} - {\left(b^{6} c^{2} + 6 \, a b^{4} c^{3} + 9 \, a^{2} b^{2} c^{4}\right)} e^{3}\right)} x^{5} + {\left(14 \, {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} d^{3} - 21 \, {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d^{2} e + 3 \, {\left(3 \, b^{6} c^{2} + 38 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} + 12 \, a^{3} c^{5}\right)} d e^{2} - {\left(b^{7} c + 15 \, a b^{5} c^{2} + 42 \, a^{2} b^{3} c^{3} + 18 \, a^{3} b c^{4}\right)} e^{3}\right)} x^{4} + 3 \, {\left(3 \, a^{4} b^{2} c^{2} + 2 \, a^{5} c^{3}\right)} d e^{2} - {\left(a^{4} b^{3} c + 3 \, a^{5} b c^{2}\right)} e^{3} + 4 \, {\left(14 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d^{3} - 21 \, {\left(a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} d^{2} e + 3 \, {\left(3 \, a b^{5} c^{2} + 11 \, a^{2} b^{3} c^{3} + 6 \, a^{3} b c^{4}\right)} d e^{2} - {\left(a b^{6} c + 6 \, a^{2} b^{4} c^{2} + 9 \, a^{3} b^{2} c^{3}\right)} e^{3}\right)} x^{3} + 2 \, {\left(14 \, {\left(3 \, a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} d^{3} - 21 \, {\left(3 \, a^{2} b^{3} c^{3} + 2 \, a^{3} b c^{4}\right)} d^{2} e + 3 \, {\left(9 \, a^{2} b^{4} c^{2} + 12 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} d e^{2} - {\left(3 \, a^{2} b^{5} c + 11 \, a^{3} b^{3} c^{2} + 6 \, a^{4} b c^{3}\right)} e^{3}\right)} x^{2} + 4 \, {\left(14 \, a^{3} b c^{4} d^{3} - 21 \, a^{3} b^{2} c^{3} d^{2} e + 3 \, {\left(3 \, a^{3} b^{3} c^{2} + 2 \, a^{4} b c^{3}\right)} d e^{2} - {\left(a^{3} b^{4} c + 3 \, a^{4} b^{2} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 4 \, {\left(2 \, {\left(b^{8} c - 23 \, a b^{6} c^{2} + 250 \, a^{2} b^{4} c^{3} - 417 \, a^{3} b^{2} c^{4} - 1116 \, a^{4} c^{5}\right)} d^{3} - 3 \, {\left(b^{9} - 23 \, a b^{7} c + 250 \, a^{2} b^{5} c^{2} - 417 \, a^{3} b^{3} c^{3} - 1116 \, a^{4} b c^{4}\right)} d^{2} e - 3 \, {\left(a b^{8} - 32 \, a^{2} b^{6} c - 167 \, a^{3} b^{4} c^{2} + 1146 \, a^{4} b^{2} c^{3} - 120 \, a^{5} c^{4}\right)} d e^{2} - {\left(3 \, a^{2} b^{7} + 139 \, a^{3} b^{5} c - 521 \, a^{4} b^{3} c^{2} - 332 \, a^{5} b c^{3}\right)} e^{3}\right)} x}{12 \, {\left(a^{4} b^{10} - 20 \, a^{5} b^{8} c + 160 \, a^{6} b^{6} c^{2} - 640 \, a^{7} b^{4} c^{3} + 1280 \, a^{8} b^{2} c^{4} - 1024 \, a^{9} c^{5} + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} x^{8} + 4 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{2} - 58 \, a b^{10} c^{3} + 440 \, a^{2} b^{8} c^{4} - 1600 \, a^{3} b^{6} c^{5} + 2560 \, a^{4} b^{4} c^{6} - 512 \, a^{5} b^{2} c^{7} - 2048 \, a^{6} c^{8}\right)} x^{6} + 4 \, {\left(b^{13} c - 17 \, a b^{11} c^{2} + 100 \, a^{2} b^{9} c^{3} - 160 \, a^{3} b^{7} c^{4} - 640 \, a^{4} b^{5} c^{5} + 2816 \, a^{5} b^{3} c^{6} - 3072 \, a^{6} b c^{7}\right)} x^{5} + {\left(b^{14} - 8 \, a b^{12} c - 74 \, a^{2} b^{10} c^{2} + 1160 \, a^{3} b^{8} c^{3} - 5440 \, a^{4} b^{6} c^{4} + 10496 \, a^{5} b^{4} c^{5} - 4608 \, a^{6} b^{2} c^{6} - 6144 \, a^{7} c^{7}\right)} x^{4} + 4 \, {\left(a b^{13} - 17 \, a^{2} b^{11} c + 100 \, a^{3} b^{9} c^{2} - 160 \, a^{4} b^{7} c^{3} - 640 \, a^{5} b^{5} c^{4} + 2816 \, a^{6} b^{3} c^{5} - 3072 \, a^{7} b c^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} - 58 \, a^{3} b^{10} c + 440 \, a^{4} b^{8} c^{2} - 1600 \, a^{5} b^{6} c^{3} + 2560 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 2048 \, a^{8} c^{6}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} - 20 \, a^{4} b^{9} c + 160 \, a^{5} b^{7} c^{2} - 640 \, a^{6} b^{5} c^{3} + 1280 \, a^{7} b^{3} c^{4} - 1024 \, a^{8} b c^{5}\right)} x\right)}}, \frac{60 \, {\left(14 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{3} - 21 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{2} e + 3 \, {\left(3 \, b^{4} c^{5} - 10 \, a b^{2} c^{6} - 8 \, a^{2} c^{7}\right)} d e^{2} - {\left(b^{5} c^{4} - a b^{3} c^{5} - 12 \, a^{2} b c^{6}\right)} e^{3}\right)} x^{7} + 210 \, {\left(14 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{3} - 21 \, {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} d^{2} e + 3 \, {\left(3 \, b^{5} c^{4} - 10 \, a b^{3} c^{5} - 8 \, a^{2} b c^{6}\right)} d e^{2} - {\left(b^{6} c^{3} - a b^{4} c^{4} - 12 \, a^{2} b^{2} c^{5}\right)} e^{3}\right)} x^{6} + 20 \, {\left(14 \, {\left(13 \, b^{4} c^{5} - 41 \, a b^{2} c^{6} - 44 \, a^{2} c^{7}\right)} d^{3} - 21 \, {\left(13 \, b^{5} c^{4} - 41 \, a b^{3} c^{5} - 44 \, a^{2} b c^{6}\right)} d^{2} e + 3 \, {\left(39 \, b^{6} c^{3} - 97 \, a b^{4} c^{4} - 214 \, a^{2} b^{2} c^{5} - 88 \, a^{3} c^{6}\right)} d e^{2} - {\left(13 \, b^{7} c^{2} - 2 \, a b^{5} c^{3} - 167 \, a^{2} b^{3} c^{4} - 132 \, a^{3} b c^{5}\right)} e^{3}\right)} x^{5} + 25 \, {\left(14 \, {\left(5 \, b^{5} c^{4} + 2 \, a b^{3} c^{5} - 88 \, a^{2} b c^{6}\right)} d^{3} - 21 \, {\left(5 \, b^{6} c^{3} + 2 \, a b^{4} c^{4} - 88 \, a^{2} b^{2} c^{5}\right)} d^{2} e + 3 \, {\left(15 \, b^{7} c^{2} + 16 \, a b^{5} c^{3} - 260 \, a^{2} b^{3} c^{4} - 176 \, a^{3} b c^{5}\right)} d e^{2} - {\left(5 \, b^{8} c + 17 \, a b^{6} c^{2} - 82 \, a^{2} b^{4} c^{3} - 264 \, a^{3} b^{2} c^{4}\right)} e^{3}\right)} x^{4} - {\left(3 \, b^{9} - 62 \, a b^{7} c + 526 \, a^{2} b^{5} c^{2} - 2420 \, a^{3} b^{3} c^{3} + 4464 \, a^{4} b c^{4}\right)} d^{3} - 3 \, {\left(a b^{8} - 23 \, a^{2} b^{6} c + 250 \, a^{3} b^{4} c^{2} - 312 \, a^{4} b^{2} c^{3} - 1536 \, a^{5} c^{4}\right)} d^{2} e - 3 \, {\left(a^{2} b^{7} - 32 \, a^{3} b^{5} c - 212 \, a^{4} b^{3} c^{2} + 1296 \, a^{5} b c^{3}\right)} d e^{2} - {\left(3 \, a^{3} b^{6} + 154 \, a^{4} b^{4} c - 536 \, a^{5} b^{2} c^{2} - 512 \, a^{6} c^{3}\right)} e^{3} + 4 \, {\left(14 \, {\left(3 \, b^{6} c^{3} + 89 \, a b^{4} c^{4} - 331 \, a^{2} b^{2} c^{5} - 292 \, a^{3} c^{6}\right)} d^{3} - 21 \, {\left(3 \, b^{7} c^{2} + 89 \, a b^{5} c^{3} - 331 \, a^{2} b^{3} c^{4} - 292 \, a^{3} b c^{5}\right)} d^{2} e + 3 \, {\left(9 \, b^{8} c + 273 \, a b^{6} c^{2} - 815 \, a^{2} b^{4} c^{3} - 1538 \, a^{3} b^{2} c^{4} - 584 \, a^{4} c^{5}\right)} d e^{2} - {\left(3 \, b^{9} + 98 \, a b^{7} c - 64 \, a^{2} b^{5} c^{2} - 1285 \, a^{3} b^{3} c^{3} - 876 \, a^{4} b c^{4}\right)} e^{3}\right)} x^{3} - 2 \, {\left(14 \, {\left(b^{7} c^{2} - 32 \, a b^{5} c^{3} - 107 \, a^{2} b^{3} c^{4} + 876 \, a^{3} b c^{5}\right)} d^{3} - 21 \, {\left(b^{8} c - 32 \, a b^{6} c^{2} - 107 \, a^{2} b^{4} c^{3} + 876 \, a^{3} b^{2} c^{4}\right)} d^{2} e + 3 \, {\left(3 \, b^{9} - 94 \, a b^{7} c - 385 \, a^{2} b^{5} c^{2} + 2414 \, a^{3} b^{3} c^{3} + 1752 \, a^{4} b c^{4}\right)} d e^{2} + {\left(9 \, a b^{8} + 363 \, a^{2} b^{6} c - 1195 \, a^{3} b^{4} c^{2} - 1348 \, a^{4} b^{2} c^{3} - 1024 \, a^{5} c^{4}\right)} e^{3}\right)} x^{2} - 120 \, {\left(14 \, a^{4} c^{4} d^{3} - 21 \, a^{4} b c^{3} d^{2} e + {\left(14 \, c^{8} d^{3} - 21 \, b c^{7} d^{2} e + 3 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d e^{2} - {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} e^{3}\right)} x^{8} + 4 \, {\left(14 \, b c^{7} d^{3} - 21 \, b^{2} c^{6} d^{2} e + 3 \, {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} d e^{2} - {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} e^{3}\right)} x^{7} + 2 \, {\left(14 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d^{3} - 21 \, {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} d^{2} e + 3 \, {\left(9 \, b^{4} c^{4} + 12 \, a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} d e^{2} - {\left(3 \, b^{5} c^{3} + 11 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} e^{3}\right)} x^{6} + 4 \, {\left(14 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} d^{3} - 21 \, {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} d^{2} e + 3 \, {\left(3 \, b^{5} c^{3} + 11 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d e^{2} - {\left(b^{6} c^{2} + 6 \, a b^{4} c^{3} + 9 \, a^{2} b^{2} c^{4}\right)} e^{3}\right)} x^{5} + {\left(14 \, {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} d^{3} - 21 \, {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d^{2} e + 3 \, {\left(3 \, b^{6} c^{2} + 38 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} + 12 \, a^{3} c^{5}\right)} d e^{2} - {\left(b^{7} c + 15 \, a b^{5} c^{2} + 42 \, a^{2} b^{3} c^{3} + 18 \, a^{3} b c^{4}\right)} e^{3}\right)} x^{4} + 3 \, {\left(3 \, a^{4} b^{2} c^{2} + 2 \, a^{5} c^{3}\right)} d e^{2} - {\left(a^{4} b^{3} c + 3 \, a^{5} b c^{2}\right)} e^{3} + 4 \, {\left(14 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d^{3} - 21 \, {\left(a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} d^{2} e + 3 \, {\left(3 \, a b^{5} c^{2} + 11 \, a^{2} b^{3} c^{3} + 6 \, a^{3} b c^{4}\right)} d e^{2} - {\left(a b^{6} c + 6 \, a^{2} b^{4} c^{2} + 9 \, a^{3} b^{2} c^{3}\right)} e^{3}\right)} x^{3} + 2 \, {\left(14 \, {\left(3 \, a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} d^{3} - 21 \, {\left(3 \, a^{2} b^{3} c^{3} + 2 \, a^{3} b c^{4}\right)} d^{2} e + 3 \, {\left(9 \, a^{2} b^{4} c^{2} + 12 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} d e^{2} - {\left(3 \, a^{2} b^{5} c + 11 \, a^{3} b^{3} c^{2} + 6 \, a^{4} b c^{3}\right)} e^{3}\right)} x^{2} + 4 \, {\left(14 \, a^{3} b c^{4} d^{3} - 21 \, a^{3} b^{2} c^{3} d^{2} e + 3 \, {\left(3 \, a^{3} b^{3} c^{2} + 2 \, a^{4} b c^{3}\right)} d e^{2} - {\left(a^{3} b^{4} c + 3 \, a^{4} b^{2} c^{2}\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 4 \, {\left(2 \, {\left(b^{8} c - 23 \, a b^{6} c^{2} + 250 \, a^{2} b^{4} c^{3} - 417 \, a^{3} b^{2} c^{4} - 1116 \, a^{4} c^{5}\right)} d^{3} - 3 \, {\left(b^{9} - 23 \, a b^{7} c + 250 \, a^{2} b^{5} c^{2} - 417 \, a^{3} b^{3} c^{3} - 1116 \, a^{4} b c^{4}\right)} d^{2} e - 3 \, {\left(a b^{8} - 32 \, a^{2} b^{6} c - 167 \, a^{3} b^{4} c^{2} + 1146 \, a^{4} b^{2} c^{3} - 120 \, a^{5} c^{4}\right)} d e^{2} - {\left(3 \, a^{2} b^{7} + 139 \, a^{3} b^{5} c - 521 \, a^{4} b^{3} c^{2} - 332 \, a^{5} b c^{3}\right)} e^{3}\right)} x}{12 \, {\left(a^{4} b^{10} - 20 \, a^{5} b^{8} c + 160 \, a^{6} b^{6} c^{2} - 640 \, a^{7} b^{4} c^{3} + 1280 \, a^{8} b^{2} c^{4} - 1024 \, a^{9} c^{5} + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} x^{8} + 4 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{2} - 58 \, a b^{10} c^{3} + 440 \, a^{2} b^{8} c^{4} - 1600 \, a^{3} b^{6} c^{5} + 2560 \, a^{4} b^{4} c^{6} - 512 \, a^{5} b^{2} c^{7} - 2048 \, a^{6} c^{8}\right)} x^{6} + 4 \, {\left(b^{13} c - 17 \, a b^{11} c^{2} + 100 \, a^{2} b^{9} c^{3} - 160 \, a^{3} b^{7} c^{4} - 640 \, a^{4} b^{5} c^{5} + 2816 \, a^{5} b^{3} c^{6} - 3072 \, a^{6} b c^{7}\right)} x^{5} + {\left(b^{14} - 8 \, a b^{12} c - 74 \, a^{2} b^{10} c^{2} + 1160 \, a^{3} b^{8} c^{3} - 5440 \, a^{4} b^{6} c^{4} + 10496 \, a^{5} b^{4} c^{5} - 4608 \, a^{6} b^{2} c^{6} - 6144 \, a^{7} c^{7}\right)} x^{4} + 4 \, {\left(a b^{13} - 17 \, a^{2} b^{11} c + 100 \, a^{3} b^{9} c^{2} - 160 \, a^{4} b^{7} c^{3} - 640 \, a^{5} b^{5} c^{4} + 2816 \, a^{6} b^{3} c^{5} - 3072 \, a^{7} b c^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} - 58 \, a^{3} b^{10} c + 440 \, a^{4} b^{8} c^{2} - 1600 \, a^{5} b^{6} c^{3} + 2560 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 2048 \, a^{8} c^{6}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} - 20 \, a^{4} b^{9} c + 160 \, a^{5} b^{7} c^{2} - 640 \, a^{6} b^{5} c^{3} + 1280 \, a^{7} b^{3} c^{4} - 1024 \, a^{8} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/12*(60*(14*(b^2*c^7 - 4*a*c^8)*d^3 - 21*(b^3*c^6 - 4*a*b*c^7)*d^2*e + 3*(3*b^4*c^5 - 10*a*b^2*c^6 - 8*a^2*c^7)*d*e^2 - (b^5*c^4 - a*b^3*c^5 - 12*a^2*b*c^6)*e^3)*x^7 + 210*(14*(b^3*c^6 - 4*a*b*c^7)*d^3 - 21*(b^4*c^5 - 4*a*b^2*c^6)*d^2*e + 3*(3*b^5*c^4 - 10*a*b^3*c^5 - 8*a^2*b*c^6)*d*e^2 - (b^6*c^3 - a*b^4*c^4 - 12*a^2*b^2*c^5)*e^3)*x^6 + 20*(14*(13*b^4*c^5 - 41*a*b^2*c^6 - 44*a^2*c^7)*d^3 - 21*(13*b^5*c^4 - 41*a*b^3*c^5 - 44*a^2*b*c^6)*d^2*e + 3*(39*b^6*c^3 - 97*a*b^4*c^4 - 214*a^2*b^2*c^5 - 88*a^3*c^6)*d*e^2 - (13*b^7*c^2 - 2*a*b^5*c^3 - 167*a^2*b^3*c^4 - 132*a^3*b*c^5)*e^3)*x^5 + 25*(14*(5*b^5*c^4 + 2*a*b^3*c^5 - 88*a^2*b*c^6)*d^3 - 21*(5*b^6*c^3 + 2*a*b^4*c^4 - 88*a^2*b^2*c^5)*d^2*e + 3*(15*b^7*c^2 + 16*a*b^5*c^3 - 260*a^2*b^3*c^4 - 176*a^3*b*c^5)*d*e^2 - (5*b^8*c + 17*a*b^6*c^2 - 82*a^2*b^4*c^3 - 264*a^3*b^2*c^4)*e^3)*x^4 - (3*b^9 - 62*a*b^7*c + 526*a^2*b^5*c^2 - 2420*a^3*b^3*c^3 + 4464*a^4*b*c^4)*d^3 - 3*(a*b^8 - 23*a^2*b^6*c + 250*a^3*b^4*c^2 - 312*a^4*b^2*c^3 - 1536*a^5*c^4)*d^2*e - 3*(a^2*b^7 - 32*a^3*b^5*c - 212*a^4*b^3*c^2 + 1296*a^5*b*c^3)*d*e^2 - (3*a^3*b^6 + 154*a^4*b^4*c - 536*a^5*b^2*c^2 - 512*a^6*c^3)*e^3 + 4*(14*(3*b^6*c^3 + 89*a*b^4*c^4 - 331*a^2*b^2*c^5 - 292*a^3*c^6)*d^3 - 21*(3*b^7*c^2 + 89*a*b^5*c^3 - 331*a^2*b^3*c^4 - 292*a^3*b*c^5)*d^2*e + 3*(9*b^8*c + 273*a*b^6*c^2 - 815*a^2*b^4*c^3 - 1538*a^3*b^2*c^4 - 584*a^4*c^5)*d*e^2 - (3*b^9 + 98*a*b^7*c - 64*a^2*b^5*c^2 - 1285*a^3*b^3*c^3 - 876*a^4*b*c^4)*e^3)*x^3 - 2*(14*(b^7*c^2 - 32*a*b^5*c^3 - 107*a^2*b^3*c^4 + 876*a^3*b*c^5)*d^3 - 21*(b^8*c - 32*a*b^6*c^2 - 107*a^2*b^4*c^3 + 876*a^3*b^2*c^4)*d^2*e + 3*(3*b^9 - 94*a*b^7*c - 385*a^2*b^5*c^2 + 2414*a^3*b^3*c^3 + 1752*a^4*b*c^4)*d*e^2 + (9*a*b^8 + 363*a^2*b^6*c - 1195*a^3*b^4*c^2 - 1348*a^4*b^2*c^3 - 1024*a^5*c^4)*e^3)*x^2 - 60*(14*a^4*c^4*d^3 - 21*a^4*b*c^3*d^2*e + (14*c^8*d^3 - 21*b*c^7*d^2*e + 3*(3*b^2*c^6 + 2*a*c^7)*d*e^2 - (b^3*c^5 + 3*a*b*c^6)*e^3)*x^8 + 4*(14*b*c^7*d^3 - 21*b^2*c^6*d^2*e + 3*(3*b^3*c^5 + 2*a*b*c^6)*d*e^2 - (b^4*c^4 + 3*a*b^2*c^5)*e^3)*x^7 + 2*(14*(3*b^2*c^6 + 2*a*c^7)*d^3 - 21*(3*b^3*c^5 + 2*a*b*c^6)*d^2*e + 3*(9*b^4*c^4 + 12*a*b^2*c^5 + 4*a^2*c^6)*d*e^2 - (3*b^5*c^3 + 11*a*b^3*c^4 + 6*a^2*b*c^5)*e^3)*x^6 + 4*(14*(b^3*c^5 + 3*a*b*c^6)*d^3 - 21*(b^4*c^4 + 3*a*b^2*c^5)*d^2*e + 3*(3*b^5*c^3 + 11*a*b^3*c^4 + 6*a^2*b*c^5)*d*e^2 - (b^6*c^2 + 6*a*b^4*c^3 + 9*a^2*b^2*c^4)*e^3)*x^5 + (14*(b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*d^3 - 21*(b^5*c^3 + 12*a*b^3*c^4 + 6*a^2*b*c^5)*d^2*e + 3*(3*b^6*c^2 + 38*a*b^4*c^3 + 42*a^2*b^2*c^4 + 12*a^3*c^5)*d*e^2 - (b^7*c + 15*a*b^5*c^2 + 42*a^2*b^3*c^3 + 18*a^3*b*c^4)*e^3)*x^4 + 3*(3*a^4*b^2*c^2 + 2*a^5*c^3)*d*e^2 - (a^4*b^3*c + 3*a^5*b*c^2)*e^3 + 4*(14*(a*b^3*c^4 + 3*a^2*b*c^5)*d^3 - 21*(a*b^4*c^3 + 3*a^2*b^2*c^4)*d^2*e + 3*(3*a*b^5*c^2 + 11*a^2*b^3*c^3 + 6*a^3*b*c^4)*d*e^2 - (a*b^6*c + 6*a^2*b^4*c^2 + 9*a^3*b^2*c^3)*e^3)*x^3 + 2*(14*(3*a^2*b^2*c^4 + 2*a^3*c^5)*d^3 - 21*(3*a^2*b^3*c^3 + 2*a^3*b*c^4)*d^2*e + 3*(9*a^2*b^4*c^2 + 12*a^3*b^2*c^3 + 4*a^4*c^4)*d*e^2 - (3*a^2*b^5*c + 11*a^3*b^3*c^2 + 6*a^4*b*c^3)*e^3)*x^2 + 4*(14*a^3*b*c^4*d^3 - 21*a^3*b^2*c^3*d^2*e + 3*(3*a^3*b^3*c^2 + 2*a^4*b*c^3)*d*e^2 - (a^3*b^4*c + 3*a^4*b^2*c^2)*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 4*(2*(b^8*c - 23*a*b^6*c^2 + 250*a^2*b^4*c^3 - 417*a^3*b^2*c^4 - 1116*a^4*c^5)*d^3 - 3*(b^9 - 23*a*b^7*c + 250*a^2*b^5*c^2 - 417*a^3*b^3*c^3 - 1116*a^4*b*c^4)*d^2*e - 3*(a*b^8 - 32*a^2*b^6*c - 167*a^3*b^4*c^2 + 1146*a^4*b^2*c^3 - 120*a^5*c^4)*d*e^2 - (3*a^2*b^7 + 139*a^3*b^5*c - 521*a^4*b^3*c^2 - 332*a^5*b*c^3)*e^3)*x)/(a^4*b^10 - 20*a^5*b^8*c + 160*a^6*b^6*c^2 - 640*a^7*b^4*c^3 + 1280*a^8*b^2*c^4 - 1024*a^9*c^5 + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*x^8 + 4*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*x^7 + 2*(3*b^12*c^2 - 58*a*b^10*c^3 + 440*a^2*b^8*c^4 - 1600*a^3*b^6*c^5 + 2560*a^4*b^4*c^6 - 512*a^5*b^2*c^7 - 2048*a^6*c^8)*x^6 + 4*(b^13*c - 17*a*b^11*c^2 + 100*a^2*b^9*c^3 - 160*a^3*b^7*c^4 - 640*a^4*b^5*c^5 + 2816*a^5*b^3*c^6 - 3072*a^6*b*c^7)*x^5 + (b^14 - 8*a*b^12*c - 74*a^2*b^10*c^2 + 1160*a^3*b^8*c^3 - 5440*a^4*b^6*c^4 + 10496*a^5*b^4*c^5 - 4608*a^6*b^2*c^6 - 6144*a^7*c^7)*x^4 + 4*(a*b^13 - 17*a^2*b^11*c + 100*a^3*b^9*c^2 - 160*a^4*b^7*c^3 - 640*a^5*b^5*c^4 + 2816*a^6*b^3*c^5 - 3072*a^7*b*c^6)*x^3 + 2*(3*a^2*b^12 - 58*a^3*b^10*c + 440*a^4*b^8*c^2 - 1600*a^5*b^6*c^3 + 2560*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 2048*a^8*c^6)*x^2 + 4*(a^3*b^11 - 20*a^4*b^9*c + 160*a^5*b^7*c^2 - 640*a^6*b^5*c^3 + 1280*a^7*b^3*c^4 - 1024*a^8*b*c^5)*x), 1/12*(60*(14*(b^2*c^7 - 4*a*c^8)*d^3 - 21*(b^3*c^6 - 4*a*b*c^7)*d^2*e + 3*(3*b^4*c^5 - 10*a*b^2*c^6 - 8*a^2*c^7)*d*e^2 - (b^5*c^4 - a*b^3*c^5 - 12*a^2*b*c^6)*e^3)*x^7 + 210*(14*(b^3*c^6 - 4*a*b*c^7)*d^3 - 21*(b^4*c^5 - 4*a*b^2*c^6)*d^2*e + 3*(3*b^5*c^4 - 10*a*b^3*c^5 - 8*a^2*b*c^6)*d*e^2 - (b^6*c^3 - a*b^4*c^4 - 12*a^2*b^2*c^5)*e^3)*x^6 + 20*(14*(13*b^4*c^5 - 41*a*b^2*c^6 - 44*a^2*c^7)*d^3 - 21*(13*b^5*c^4 - 41*a*b^3*c^5 - 44*a^2*b*c^6)*d^2*e + 3*(39*b^6*c^3 - 97*a*b^4*c^4 - 214*a^2*b^2*c^5 - 88*a^3*c^6)*d*e^2 - (13*b^7*c^2 - 2*a*b^5*c^3 - 167*a^2*b^3*c^4 - 132*a^3*b*c^5)*e^3)*x^5 + 25*(14*(5*b^5*c^4 + 2*a*b^3*c^5 - 88*a^2*b*c^6)*d^3 - 21*(5*b^6*c^3 + 2*a*b^4*c^4 - 88*a^2*b^2*c^5)*d^2*e + 3*(15*b^7*c^2 + 16*a*b^5*c^3 - 260*a^2*b^3*c^4 - 176*a^3*b*c^5)*d*e^2 - (5*b^8*c + 17*a*b^6*c^2 - 82*a^2*b^4*c^3 - 264*a^3*b^2*c^4)*e^3)*x^4 - (3*b^9 - 62*a*b^7*c + 526*a^2*b^5*c^2 - 2420*a^3*b^3*c^3 + 4464*a^4*b*c^4)*d^3 - 3*(a*b^8 - 23*a^2*b^6*c + 250*a^3*b^4*c^2 - 312*a^4*b^2*c^3 - 1536*a^5*c^4)*d^2*e - 3*(a^2*b^7 - 32*a^3*b^5*c - 212*a^4*b^3*c^2 + 1296*a^5*b*c^3)*d*e^2 - (3*a^3*b^6 + 154*a^4*b^4*c - 536*a^5*b^2*c^2 - 512*a^6*c^3)*e^3 + 4*(14*(3*b^6*c^3 + 89*a*b^4*c^4 - 331*a^2*b^2*c^5 - 292*a^3*c^6)*d^3 - 21*(3*b^7*c^2 + 89*a*b^5*c^3 - 331*a^2*b^3*c^4 - 292*a^3*b*c^5)*d^2*e + 3*(9*b^8*c + 273*a*b^6*c^2 - 815*a^2*b^4*c^3 - 1538*a^3*b^2*c^4 - 584*a^4*c^5)*d*e^2 - (3*b^9 + 98*a*b^7*c - 64*a^2*b^5*c^2 - 1285*a^3*b^3*c^3 - 876*a^4*b*c^4)*e^3)*x^3 - 2*(14*(b^7*c^2 - 32*a*b^5*c^3 - 107*a^2*b^3*c^4 + 876*a^3*b*c^5)*d^3 - 21*(b^8*c - 32*a*b^6*c^2 - 107*a^2*b^4*c^3 + 876*a^3*b^2*c^4)*d^2*e + 3*(3*b^9 - 94*a*b^7*c - 385*a^2*b^5*c^2 + 2414*a^3*b^3*c^3 + 1752*a^4*b*c^4)*d*e^2 + (9*a*b^8 + 363*a^2*b^6*c - 1195*a^3*b^4*c^2 - 1348*a^4*b^2*c^3 - 1024*a^5*c^4)*e^3)*x^2 - 120*(14*a^4*c^4*d^3 - 21*a^4*b*c^3*d^2*e + (14*c^8*d^3 - 21*b*c^7*d^2*e + 3*(3*b^2*c^6 + 2*a*c^7)*d*e^2 - (b^3*c^5 + 3*a*b*c^6)*e^3)*x^8 + 4*(14*b*c^7*d^3 - 21*b^2*c^6*d^2*e + 3*(3*b^3*c^5 + 2*a*b*c^6)*d*e^2 - (b^4*c^4 + 3*a*b^2*c^5)*e^3)*x^7 + 2*(14*(3*b^2*c^6 + 2*a*c^7)*d^3 - 21*(3*b^3*c^5 + 2*a*b*c^6)*d^2*e + 3*(9*b^4*c^4 + 12*a*b^2*c^5 + 4*a^2*c^6)*d*e^2 - (3*b^5*c^3 + 11*a*b^3*c^4 + 6*a^2*b*c^5)*e^3)*x^6 + 4*(14*(b^3*c^5 + 3*a*b*c^6)*d^3 - 21*(b^4*c^4 + 3*a*b^2*c^5)*d^2*e + 3*(3*b^5*c^3 + 11*a*b^3*c^4 + 6*a^2*b*c^5)*d*e^2 - (b^6*c^2 + 6*a*b^4*c^3 + 9*a^2*b^2*c^4)*e^3)*x^5 + (14*(b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*d^3 - 21*(b^5*c^3 + 12*a*b^3*c^4 + 6*a^2*b*c^5)*d^2*e + 3*(3*b^6*c^2 + 38*a*b^4*c^3 + 42*a^2*b^2*c^4 + 12*a^3*c^5)*d*e^2 - (b^7*c + 15*a*b^5*c^2 + 42*a^2*b^3*c^3 + 18*a^3*b*c^4)*e^3)*x^4 + 3*(3*a^4*b^2*c^2 + 2*a^5*c^3)*d*e^2 - (a^4*b^3*c + 3*a^5*b*c^2)*e^3 + 4*(14*(a*b^3*c^4 + 3*a^2*b*c^5)*d^3 - 21*(a*b^4*c^3 + 3*a^2*b^2*c^4)*d^2*e + 3*(3*a*b^5*c^2 + 11*a^2*b^3*c^3 + 6*a^3*b*c^4)*d*e^2 - (a*b^6*c + 6*a^2*b^4*c^2 + 9*a^3*b^2*c^3)*e^3)*x^3 + 2*(14*(3*a^2*b^2*c^4 + 2*a^3*c^5)*d^3 - 21*(3*a^2*b^3*c^3 + 2*a^3*b*c^4)*d^2*e + 3*(9*a^2*b^4*c^2 + 12*a^3*b^2*c^3 + 4*a^4*c^4)*d*e^2 - (3*a^2*b^5*c + 11*a^3*b^3*c^2 + 6*a^4*b*c^3)*e^3)*x^2 + 4*(14*a^3*b*c^4*d^3 - 21*a^3*b^2*c^3*d^2*e + 3*(3*a^3*b^3*c^2 + 2*a^4*b*c^3)*d*e^2 - (a^3*b^4*c + 3*a^4*b^2*c^2)*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 4*(2*(b^8*c - 23*a*b^6*c^2 + 250*a^2*b^4*c^3 - 417*a^3*b^2*c^4 - 1116*a^4*c^5)*d^3 - 3*(b^9 - 23*a*b^7*c + 250*a^2*b^5*c^2 - 417*a^3*b^3*c^3 - 1116*a^4*b*c^4)*d^2*e - 3*(a*b^8 - 32*a^2*b^6*c - 167*a^3*b^4*c^2 + 1146*a^4*b^2*c^3 - 120*a^5*c^4)*d*e^2 - (3*a^2*b^7 + 139*a^3*b^5*c - 521*a^4*b^3*c^2 - 332*a^5*b*c^3)*e^3)*x)/(a^4*b^10 - 20*a^5*b^8*c + 160*a^6*b^6*c^2 - 640*a^7*b^4*c^3 + 1280*a^8*b^2*c^4 - 1024*a^9*c^5 + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*x^8 + 4*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*x^7 + 2*(3*b^12*c^2 - 58*a*b^10*c^3 + 440*a^2*b^8*c^4 - 1600*a^3*b^6*c^5 + 2560*a^4*b^4*c^6 - 512*a^5*b^2*c^7 - 2048*a^6*c^8)*x^6 + 4*(b^13*c - 17*a*b^11*c^2 + 100*a^2*b^9*c^3 - 160*a^3*b^7*c^4 - 640*a^4*b^5*c^5 + 2816*a^5*b^3*c^6 - 3072*a^6*b*c^7)*x^5 + (b^14 - 8*a*b^12*c - 74*a^2*b^10*c^2 + 1160*a^3*b^8*c^3 - 5440*a^4*b^6*c^4 + 10496*a^5*b^4*c^5 - 4608*a^6*b^2*c^6 - 6144*a^7*c^7)*x^4 + 4*(a*b^13 - 17*a^2*b^11*c + 100*a^3*b^9*c^2 - 160*a^4*b^7*c^3 - 640*a^5*b^5*c^4 + 2816*a^6*b^3*c^5 - 3072*a^7*b*c^6)*x^3 + 2*(3*a^2*b^12 - 58*a^3*b^10*c + 440*a^4*b^8*c^2 - 1600*a^5*b^6*c^3 + 2560*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 2048*a^8*c^6)*x^2 + 4*(a^3*b^11 - 20*a^4*b^9*c + 160*a^5*b^7*c^2 - 640*a^6*b^5*c^3 + 1280*a^7*b^3*c^4 - 1024*a^8*b*c^5)*x)]","B",0
2224,1,4491,0,0.497229," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^5,x, algorithm=""fricas"")","\left[\frac{60 \, {\left(14 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{2} - 14 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d e + {\left(3 \, b^{4} c^{5} - 10 \, a b^{2} c^{6} - 8 \, a^{2} c^{7}\right)} e^{2}\right)} x^{7} + 210 \, {\left(14 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{2} - 14 \, {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} d e + {\left(3 \, b^{5} c^{4} - 10 \, a b^{3} c^{5} - 8 \, a^{2} b c^{6}\right)} e^{2}\right)} x^{6} + 20 \, {\left(14 \, {\left(13 \, b^{4} c^{5} - 41 \, a b^{2} c^{6} - 44 \, a^{2} c^{7}\right)} d^{2} - 14 \, {\left(13 \, b^{5} c^{4} - 41 \, a b^{3} c^{5} - 44 \, a^{2} b c^{6}\right)} d e + {\left(39 \, b^{6} c^{3} - 97 \, a b^{4} c^{4} - 214 \, a^{2} b^{2} c^{5} - 88 \, a^{3} c^{6}\right)} e^{2}\right)} x^{5} + 25 \, {\left(14 \, {\left(5 \, b^{5} c^{4} + 2 \, a b^{3} c^{5} - 88 \, a^{2} b c^{6}\right)} d^{2} - 14 \, {\left(5 \, b^{6} c^{3} + 2 \, a b^{4} c^{4} - 88 \, a^{2} b^{2} c^{5}\right)} d e + {\left(15 \, b^{7} c^{2} + 16 \, a b^{5} c^{3} - 260 \, a^{2} b^{3} c^{4} - 176 \, a^{3} b c^{5}\right)} e^{2}\right)} x^{4} + 4 \, {\left(14 \, {\left(3 \, b^{6} c^{3} + 89 \, a b^{4} c^{4} - 331 \, a^{2} b^{2} c^{5} - 292 \, a^{3} c^{6}\right)} d^{2} - 14 \, {\left(3 \, b^{7} c^{2} + 89 \, a b^{5} c^{3} - 331 \, a^{2} b^{3} c^{4} - 292 \, a^{3} b c^{5}\right)} d e + {\left(9 \, b^{8} c + 273 \, a b^{6} c^{2} - 815 \, a^{2} b^{4} c^{3} - 1538 \, a^{3} b^{2} c^{4} - 584 \, a^{4} c^{5}\right)} e^{2}\right)} x^{3} - {\left(3 \, b^{9} - 62 \, a b^{7} c + 526 \, a^{2} b^{5} c^{2} - 2420 \, a^{3} b^{3} c^{3} + 4464 \, a^{4} b c^{4}\right)} d^{2} - 2 \, {\left(a b^{8} - 23 \, a^{2} b^{6} c + 250 \, a^{3} b^{4} c^{2} - 312 \, a^{4} b^{2} c^{3} - 1536 \, a^{5} c^{4}\right)} d e - {\left(a^{2} b^{7} - 32 \, a^{3} b^{5} c - 212 \, a^{4} b^{3} c^{2} + 1296 \, a^{5} b c^{3}\right)} e^{2} - 2 \, {\left(14 \, {\left(b^{7} c^{2} - 32 \, a b^{5} c^{3} - 107 \, a^{2} b^{3} c^{4} + 876 \, a^{3} b c^{5}\right)} d^{2} - 14 \, {\left(b^{8} c - 32 \, a b^{6} c^{2} - 107 \, a^{2} b^{4} c^{3} + 876 \, a^{3} b^{2} c^{4}\right)} d e + {\left(3 \, b^{9} - 94 \, a b^{7} c - 385 \, a^{2} b^{5} c^{2} + 2414 \, a^{3} b^{3} c^{3} + 1752 \, a^{4} b c^{4}\right)} e^{2}\right)} x^{2} + 60 \, {\left(14 \, a^{4} c^{4} d^{2} - 14 \, a^{4} b c^{3} d e + {\left(14 \, c^{8} d^{2} - 14 \, b c^{7} d e + {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} e^{2}\right)} x^{8} + 4 \, {\left(14 \, b c^{7} d^{2} - 14 \, b^{2} c^{6} d e + {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} e^{2}\right)} x^{7} + 2 \, {\left(14 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d^{2} - 14 \, {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} d e + {\left(9 \, b^{4} c^{4} + 12 \, a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} e^{2}\right)} x^{6} + 4 \, {\left(14 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} d^{2} - 14 \, {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} d e + {\left(3 \, b^{5} c^{3} + 11 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} e^{2}\right)} x^{5} + {\left(14 \, {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} d^{2} - 14 \, {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d e + {\left(3 \, b^{6} c^{2} + 38 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} + 12 \, a^{3} c^{5}\right)} e^{2}\right)} x^{4} + 4 \, {\left(14 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d^{2} - 14 \, {\left(a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} d e + {\left(3 \, a b^{5} c^{2} + 11 \, a^{2} b^{3} c^{3} + 6 \, a^{3} b c^{4}\right)} e^{2}\right)} x^{3} + {\left(3 \, a^{4} b^{2} c^{2} + 2 \, a^{5} c^{3}\right)} e^{2} + 2 \, {\left(14 \, {\left(3 \, a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} d^{2} - 14 \, {\left(3 \, a^{2} b^{3} c^{3} + 2 \, a^{3} b c^{4}\right)} d e + {\left(9 \, a^{2} b^{4} c^{2} + 12 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} e^{2}\right)} x^{2} + 4 \, {\left(14 \, a^{3} b c^{4} d^{2} - 14 \, a^{3} b^{2} c^{3} d e + {\left(3 \, a^{3} b^{3} c^{2} + 2 \, a^{4} b c^{3}\right)} e^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) + 4 \, {\left(2 \, {\left(b^{8} c - 23 \, a b^{6} c^{2} + 250 \, a^{2} b^{4} c^{3} - 417 \, a^{3} b^{2} c^{4} - 1116 \, a^{4} c^{5}\right)} d^{2} - 2 \, {\left(b^{9} - 23 \, a b^{7} c + 250 \, a^{2} b^{5} c^{2} - 417 \, a^{3} b^{3} c^{3} - 1116 \, a^{4} b c^{4}\right)} d e - {\left(a b^{8} - 32 \, a^{2} b^{6} c - 167 \, a^{3} b^{4} c^{2} + 1146 \, a^{4} b^{2} c^{3} - 120 \, a^{5} c^{4}\right)} e^{2}\right)} x}{12 \, {\left(a^{4} b^{10} - 20 \, a^{5} b^{8} c + 160 \, a^{6} b^{6} c^{2} - 640 \, a^{7} b^{4} c^{3} + 1280 \, a^{8} b^{2} c^{4} - 1024 \, a^{9} c^{5} + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} x^{8} + 4 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{2} - 58 \, a b^{10} c^{3} + 440 \, a^{2} b^{8} c^{4} - 1600 \, a^{3} b^{6} c^{5} + 2560 \, a^{4} b^{4} c^{6} - 512 \, a^{5} b^{2} c^{7} - 2048 \, a^{6} c^{8}\right)} x^{6} + 4 \, {\left(b^{13} c - 17 \, a b^{11} c^{2} + 100 \, a^{2} b^{9} c^{3} - 160 \, a^{3} b^{7} c^{4} - 640 \, a^{4} b^{5} c^{5} + 2816 \, a^{5} b^{3} c^{6} - 3072 \, a^{6} b c^{7}\right)} x^{5} + {\left(b^{14} - 8 \, a b^{12} c - 74 \, a^{2} b^{10} c^{2} + 1160 \, a^{3} b^{8} c^{3} - 5440 \, a^{4} b^{6} c^{4} + 10496 \, a^{5} b^{4} c^{5} - 4608 \, a^{6} b^{2} c^{6} - 6144 \, a^{7} c^{7}\right)} x^{4} + 4 \, {\left(a b^{13} - 17 \, a^{2} b^{11} c + 100 \, a^{3} b^{9} c^{2} - 160 \, a^{4} b^{7} c^{3} - 640 \, a^{5} b^{5} c^{4} + 2816 \, a^{6} b^{3} c^{5} - 3072 \, a^{7} b c^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} - 58 \, a^{3} b^{10} c + 440 \, a^{4} b^{8} c^{2} - 1600 \, a^{5} b^{6} c^{3} + 2560 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 2048 \, a^{8} c^{6}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} - 20 \, a^{4} b^{9} c + 160 \, a^{5} b^{7} c^{2} - 640 \, a^{6} b^{5} c^{3} + 1280 \, a^{7} b^{3} c^{4} - 1024 \, a^{8} b c^{5}\right)} x\right)}}, \frac{60 \, {\left(14 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{2} - 14 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d e + {\left(3 \, b^{4} c^{5} - 10 \, a b^{2} c^{6} - 8 \, a^{2} c^{7}\right)} e^{2}\right)} x^{7} + 210 \, {\left(14 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d^{2} - 14 \, {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} d e + {\left(3 \, b^{5} c^{4} - 10 \, a b^{3} c^{5} - 8 \, a^{2} b c^{6}\right)} e^{2}\right)} x^{6} + 20 \, {\left(14 \, {\left(13 \, b^{4} c^{5} - 41 \, a b^{2} c^{6} - 44 \, a^{2} c^{7}\right)} d^{2} - 14 \, {\left(13 \, b^{5} c^{4} - 41 \, a b^{3} c^{5} - 44 \, a^{2} b c^{6}\right)} d e + {\left(39 \, b^{6} c^{3} - 97 \, a b^{4} c^{4} - 214 \, a^{2} b^{2} c^{5} - 88 \, a^{3} c^{6}\right)} e^{2}\right)} x^{5} + 25 \, {\left(14 \, {\left(5 \, b^{5} c^{4} + 2 \, a b^{3} c^{5} - 88 \, a^{2} b c^{6}\right)} d^{2} - 14 \, {\left(5 \, b^{6} c^{3} + 2 \, a b^{4} c^{4} - 88 \, a^{2} b^{2} c^{5}\right)} d e + {\left(15 \, b^{7} c^{2} + 16 \, a b^{5} c^{3} - 260 \, a^{2} b^{3} c^{4} - 176 \, a^{3} b c^{5}\right)} e^{2}\right)} x^{4} + 4 \, {\left(14 \, {\left(3 \, b^{6} c^{3} + 89 \, a b^{4} c^{4} - 331 \, a^{2} b^{2} c^{5} - 292 \, a^{3} c^{6}\right)} d^{2} - 14 \, {\left(3 \, b^{7} c^{2} + 89 \, a b^{5} c^{3} - 331 \, a^{2} b^{3} c^{4} - 292 \, a^{3} b c^{5}\right)} d e + {\left(9 \, b^{8} c + 273 \, a b^{6} c^{2} - 815 \, a^{2} b^{4} c^{3} - 1538 \, a^{3} b^{2} c^{4} - 584 \, a^{4} c^{5}\right)} e^{2}\right)} x^{3} - {\left(3 \, b^{9} - 62 \, a b^{7} c + 526 \, a^{2} b^{5} c^{2} - 2420 \, a^{3} b^{3} c^{3} + 4464 \, a^{4} b c^{4}\right)} d^{2} - 2 \, {\left(a b^{8} - 23 \, a^{2} b^{6} c + 250 \, a^{3} b^{4} c^{2} - 312 \, a^{4} b^{2} c^{3} - 1536 \, a^{5} c^{4}\right)} d e - {\left(a^{2} b^{7} - 32 \, a^{3} b^{5} c - 212 \, a^{4} b^{3} c^{2} + 1296 \, a^{5} b c^{3}\right)} e^{2} - 2 \, {\left(14 \, {\left(b^{7} c^{2} - 32 \, a b^{5} c^{3} - 107 \, a^{2} b^{3} c^{4} + 876 \, a^{3} b c^{5}\right)} d^{2} - 14 \, {\left(b^{8} c - 32 \, a b^{6} c^{2} - 107 \, a^{2} b^{4} c^{3} + 876 \, a^{3} b^{2} c^{4}\right)} d e + {\left(3 \, b^{9} - 94 \, a b^{7} c - 385 \, a^{2} b^{5} c^{2} + 2414 \, a^{3} b^{3} c^{3} + 1752 \, a^{4} b c^{4}\right)} e^{2}\right)} x^{2} - 120 \, {\left(14 \, a^{4} c^{4} d^{2} - 14 \, a^{4} b c^{3} d e + {\left(14 \, c^{8} d^{2} - 14 \, b c^{7} d e + {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} e^{2}\right)} x^{8} + 4 \, {\left(14 \, b c^{7} d^{2} - 14 \, b^{2} c^{6} d e + {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} e^{2}\right)} x^{7} + 2 \, {\left(14 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d^{2} - 14 \, {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} d e + {\left(9 \, b^{4} c^{4} + 12 \, a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} e^{2}\right)} x^{6} + 4 \, {\left(14 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} d^{2} - 14 \, {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} d e + {\left(3 \, b^{5} c^{3} + 11 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} e^{2}\right)} x^{5} + {\left(14 \, {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} d^{2} - 14 \, {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} d e + {\left(3 \, b^{6} c^{2} + 38 \, a b^{4} c^{3} + 42 \, a^{2} b^{2} c^{4} + 12 \, a^{3} c^{5}\right)} e^{2}\right)} x^{4} + 4 \, {\left(14 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d^{2} - 14 \, {\left(a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} d e + {\left(3 \, a b^{5} c^{2} + 11 \, a^{2} b^{3} c^{3} + 6 \, a^{3} b c^{4}\right)} e^{2}\right)} x^{3} + {\left(3 \, a^{4} b^{2} c^{2} + 2 \, a^{5} c^{3}\right)} e^{2} + 2 \, {\left(14 \, {\left(3 \, a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} d^{2} - 14 \, {\left(3 \, a^{2} b^{3} c^{3} + 2 \, a^{3} b c^{4}\right)} d e + {\left(9 \, a^{2} b^{4} c^{2} + 12 \, a^{3} b^{2} c^{3} + 4 \, a^{4} c^{4}\right)} e^{2}\right)} x^{2} + 4 \, {\left(14 \, a^{3} b c^{4} d^{2} - 14 \, a^{3} b^{2} c^{3} d e + {\left(3 \, a^{3} b^{3} c^{2} + 2 \, a^{4} b c^{3}\right)} e^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) + 4 \, {\left(2 \, {\left(b^{8} c - 23 \, a b^{6} c^{2} + 250 \, a^{2} b^{4} c^{3} - 417 \, a^{3} b^{2} c^{4} - 1116 \, a^{4} c^{5}\right)} d^{2} - 2 \, {\left(b^{9} - 23 \, a b^{7} c + 250 \, a^{2} b^{5} c^{2} - 417 \, a^{3} b^{3} c^{3} - 1116 \, a^{4} b c^{4}\right)} d e - {\left(a b^{8} - 32 \, a^{2} b^{6} c - 167 \, a^{3} b^{4} c^{2} + 1146 \, a^{4} b^{2} c^{3} - 120 \, a^{5} c^{4}\right)} e^{2}\right)} x}{12 \, {\left(a^{4} b^{10} - 20 \, a^{5} b^{8} c + 160 \, a^{6} b^{6} c^{2} - 640 \, a^{7} b^{4} c^{3} + 1280 \, a^{8} b^{2} c^{4} - 1024 \, a^{9} c^{5} + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} x^{8} + 4 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{2} - 58 \, a b^{10} c^{3} + 440 \, a^{2} b^{8} c^{4} - 1600 \, a^{3} b^{6} c^{5} + 2560 \, a^{4} b^{4} c^{6} - 512 \, a^{5} b^{2} c^{7} - 2048 \, a^{6} c^{8}\right)} x^{6} + 4 \, {\left(b^{13} c - 17 \, a b^{11} c^{2} + 100 \, a^{2} b^{9} c^{3} - 160 \, a^{3} b^{7} c^{4} - 640 \, a^{4} b^{5} c^{5} + 2816 \, a^{5} b^{3} c^{6} - 3072 \, a^{6} b c^{7}\right)} x^{5} + {\left(b^{14} - 8 \, a b^{12} c - 74 \, a^{2} b^{10} c^{2} + 1160 \, a^{3} b^{8} c^{3} - 5440 \, a^{4} b^{6} c^{4} + 10496 \, a^{5} b^{4} c^{5} - 4608 \, a^{6} b^{2} c^{6} - 6144 \, a^{7} c^{7}\right)} x^{4} + 4 \, {\left(a b^{13} - 17 \, a^{2} b^{11} c + 100 \, a^{3} b^{9} c^{2} - 160 \, a^{4} b^{7} c^{3} - 640 \, a^{5} b^{5} c^{4} + 2816 \, a^{6} b^{3} c^{5} - 3072 \, a^{7} b c^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} - 58 \, a^{3} b^{10} c + 440 \, a^{4} b^{8} c^{2} - 1600 \, a^{5} b^{6} c^{3} + 2560 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 2048 \, a^{8} c^{6}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} - 20 \, a^{4} b^{9} c + 160 \, a^{5} b^{7} c^{2} - 640 \, a^{6} b^{5} c^{3} + 1280 \, a^{7} b^{3} c^{4} - 1024 \, a^{8} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/12*(60*(14*(b^2*c^7 - 4*a*c^8)*d^2 - 14*(b^3*c^6 - 4*a*b*c^7)*d*e + (3*b^4*c^5 - 10*a*b^2*c^6 - 8*a^2*c^7)*e^2)*x^7 + 210*(14*(b^3*c^6 - 4*a*b*c^7)*d^2 - 14*(b^4*c^5 - 4*a*b^2*c^6)*d*e + (3*b^5*c^4 - 10*a*b^3*c^5 - 8*a^2*b*c^6)*e^2)*x^6 + 20*(14*(13*b^4*c^5 - 41*a*b^2*c^6 - 44*a^2*c^7)*d^2 - 14*(13*b^5*c^4 - 41*a*b^3*c^5 - 44*a^2*b*c^6)*d*e + (39*b^6*c^3 - 97*a*b^4*c^4 - 214*a^2*b^2*c^5 - 88*a^3*c^6)*e^2)*x^5 + 25*(14*(5*b^5*c^4 + 2*a*b^3*c^5 - 88*a^2*b*c^6)*d^2 - 14*(5*b^6*c^3 + 2*a*b^4*c^4 - 88*a^2*b^2*c^5)*d*e + (15*b^7*c^2 + 16*a*b^5*c^3 - 260*a^2*b^3*c^4 - 176*a^3*b*c^5)*e^2)*x^4 + 4*(14*(3*b^6*c^3 + 89*a*b^4*c^4 - 331*a^2*b^2*c^5 - 292*a^3*c^6)*d^2 - 14*(3*b^7*c^2 + 89*a*b^5*c^3 - 331*a^2*b^3*c^4 - 292*a^3*b*c^5)*d*e + (9*b^8*c + 273*a*b^6*c^2 - 815*a^2*b^4*c^3 - 1538*a^3*b^2*c^4 - 584*a^4*c^5)*e^2)*x^3 - (3*b^9 - 62*a*b^7*c + 526*a^2*b^5*c^2 - 2420*a^3*b^3*c^3 + 4464*a^4*b*c^4)*d^2 - 2*(a*b^8 - 23*a^2*b^6*c + 250*a^3*b^4*c^2 - 312*a^4*b^2*c^3 - 1536*a^5*c^4)*d*e - (a^2*b^7 - 32*a^3*b^5*c - 212*a^4*b^3*c^2 + 1296*a^5*b*c^3)*e^2 - 2*(14*(b^7*c^2 - 32*a*b^5*c^3 - 107*a^2*b^3*c^4 + 876*a^3*b*c^5)*d^2 - 14*(b^8*c - 32*a*b^6*c^2 - 107*a^2*b^4*c^3 + 876*a^3*b^2*c^4)*d*e + (3*b^9 - 94*a*b^7*c - 385*a^2*b^5*c^2 + 2414*a^3*b^3*c^3 + 1752*a^4*b*c^4)*e^2)*x^2 + 60*(14*a^4*c^4*d^2 - 14*a^4*b*c^3*d*e + (14*c^8*d^2 - 14*b*c^7*d*e + (3*b^2*c^6 + 2*a*c^7)*e^2)*x^8 + 4*(14*b*c^7*d^2 - 14*b^2*c^6*d*e + (3*b^3*c^5 + 2*a*b*c^6)*e^2)*x^7 + 2*(14*(3*b^2*c^6 + 2*a*c^7)*d^2 - 14*(3*b^3*c^5 + 2*a*b*c^6)*d*e + (9*b^4*c^4 + 12*a*b^2*c^5 + 4*a^2*c^6)*e^2)*x^6 + 4*(14*(b^3*c^5 + 3*a*b*c^6)*d^2 - 14*(b^4*c^4 + 3*a*b^2*c^5)*d*e + (3*b^5*c^3 + 11*a*b^3*c^4 + 6*a^2*b*c^5)*e^2)*x^5 + (14*(b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*d^2 - 14*(b^5*c^3 + 12*a*b^3*c^4 + 6*a^2*b*c^5)*d*e + (3*b^6*c^2 + 38*a*b^4*c^3 + 42*a^2*b^2*c^4 + 12*a^3*c^5)*e^2)*x^4 + 4*(14*(a*b^3*c^4 + 3*a^2*b*c^5)*d^2 - 14*(a*b^4*c^3 + 3*a^2*b^2*c^4)*d*e + (3*a*b^5*c^2 + 11*a^2*b^3*c^3 + 6*a^3*b*c^4)*e^2)*x^3 + (3*a^4*b^2*c^2 + 2*a^5*c^3)*e^2 + 2*(14*(3*a^2*b^2*c^4 + 2*a^3*c^5)*d^2 - 14*(3*a^2*b^3*c^3 + 2*a^3*b*c^4)*d*e + (9*a^2*b^4*c^2 + 12*a^3*b^2*c^3 + 4*a^4*c^4)*e^2)*x^2 + 4*(14*a^3*b*c^4*d^2 - 14*a^3*b^2*c^3*d*e + (3*a^3*b^3*c^2 + 2*a^4*b*c^3)*e^2)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) + 4*(2*(b^8*c - 23*a*b^6*c^2 + 250*a^2*b^4*c^3 - 417*a^3*b^2*c^4 - 1116*a^4*c^5)*d^2 - 2*(b^9 - 23*a*b^7*c + 250*a^2*b^5*c^2 - 417*a^3*b^3*c^3 - 1116*a^4*b*c^4)*d*e - (a*b^8 - 32*a^2*b^6*c - 167*a^3*b^4*c^2 + 1146*a^4*b^2*c^3 - 120*a^5*c^4)*e^2)*x)/(a^4*b^10 - 20*a^5*b^8*c + 160*a^6*b^6*c^2 - 640*a^7*b^4*c^3 + 1280*a^8*b^2*c^4 - 1024*a^9*c^5 + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*x^8 + 4*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*x^7 + 2*(3*b^12*c^2 - 58*a*b^10*c^3 + 440*a^2*b^8*c^4 - 1600*a^3*b^6*c^5 + 2560*a^4*b^4*c^6 - 512*a^5*b^2*c^7 - 2048*a^6*c^8)*x^6 + 4*(b^13*c - 17*a*b^11*c^2 + 100*a^2*b^9*c^3 - 160*a^3*b^7*c^4 - 640*a^4*b^5*c^5 + 2816*a^5*b^3*c^6 - 3072*a^6*b*c^7)*x^5 + (b^14 - 8*a*b^12*c - 74*a^2*b^10*c^2 + 1160*a^3*b^8*c^3 - 5440*a^4*b^6*c^4 + 10496*a^5*b^4*c^5 - 4608*a^6*b^2*c^6 - 6144*a^7*c^7)*x^4 + 4*(a*b^13 - 17*a^2*b^11*c + 100*a^3*b^9*c^2 - 160*a^4*b^7*c^3 - 640*a^5*b^5*c^4 + 2816*a^6*b^3*c^5 - 3072*a^7*b*c^6)*x^3 + 2*(3*a^2*b^12 - 58*a^3*b^10*c + 440*a^4*b^8*c^2 - 1600*a^5*b^6*c^3 + 2560*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 2048*a^8*c^6)*x^2 + 4*(a^3*b^11 - 20*a^4*b^9*c + 160*a^5*b^7*c^2 - 640*a^6*b^5*c^3 + 1280*a^7*b^3*c^4 - 1024*a^8*b*c^5)*x), 1/12*(60*(14*(b^2*c^7 - 4*a*c^8)*d^2 - 14*(b^3*c^6 - 4*a*b*c^7)*d*e + (3*b^4*c^5 - 10*a*b^2*c^6 - 8*a^2*c^7)*e^2)*x^7 + 210*(14*(b^3*c^6 - 4*a*b*c^7)*d^2 - 14*(b^4*c^5 - 4*a*b^2*c^6)*d*e + (3*b^5*c^4 - 10*a*b^3*c^5 - 8*a^2*b*c^6)*e^2)*x^6 + 20*(14*(13*b^4*c^5 - 41*a*b^2*c^6 - 44*a^2*c^7)*d^2 - 14*(13*b^5*c^4 - 41*a*b^3*c^5 - 44*a^2*b*c^6)*d*e + (39*b^6*c^3 - 97*a*b^4*c^4 - 214*a^2*b^2*c^5 - 88*a^3*c^6)*e^2)*x^5 + 25*(14*(5*b^5*c^4 + 2*a*b^3*c^5 - 88*a^2*b*c^6)*d^2 - 14*(5*b^6*c^3 + 2*a*b^4*c^4 - 88*a^2*b^2*c^5)*d*e + (15*b^7*c^2 + 16*a*b^5*c^3 - 260*a^2*b^3*c^4 - 176*a^3*b*c^5)*e^2)*x^4 + 4*(14*(3*b^6*c^3 + 89*a*b^4*c^4 - 331*a^2*b^2*c^5 - 292*a^3*c^6)*d^2 - 14*(3*b^7*c^2 + 89*a*b^5*c^3 - 331*a^2*b^3*c^4 - 292*a^3*b*c^5)*d*e + (9*b^8*c + 273*a*b^6*c^2 - 815*a^2*b^4*c^3 - 1538*a^3*b^2*c^4 - 584*a^4*c^5)*e^2)*x^3 - (3*b^9 - 62*a*b^7*c + 526*a^2*b^5*c^2 - 2420*a^3*b^3*c^3 + 4464*a^4*b*c^4)*d^2 - 2*(a*b^8 - 23*a^2*b^6*c + 250*a^3*b^4*c^2 - 312*a^4*b^2*c^3 - 1536*a^5*c^4)*d*e - (a^2*b^7 - 32*a^3*b^5*c - 212*a^4*b^3*c^2 + 1296*a^5*b*c^3)*e^2 - 2*(14*(b^7*c^2 - 32*a*b^5*c^3 - 107*a^2*b^3*c^4 + 876*a^3*b*c^5)*d^2 - 14*(b^8*c - 32*a*b^6*c^2 - 107*a^2*b^4*c^3 + 876*a^3*b^2*c^4)*d*e + (3*b^9 - 94*a*b^7*c - 385*a^2*b^5*c^2 + 2414*a^3*b^3*c^3 + 1752*a^4*b*c^4)*e^2)*x^2 - 120*(14*a^4*c^4*d^2 - 14*a^4*b*c^3*d*e + (14*c^8*d^2 - 14*b*c^7*d*e + (3*b^2*c^6 + 2*a*c^7)*e^2)*x^8 + 4*(14*b*c^7*d^2 - 14*b^2*c^6*d*e + (3*b^3*c^5 + 2*a*b*c^6)*e^2)*x^7 + 2*(14*(3*b^2*c^6 + 2*a*c^7)*d^2 - 14*(3*b^3*c^5 + 2*a*b*c^6)*d*e + (9*b^4*c^4 + 12*a*b^2*c^5 + 4*a^2*c^6)*e^2)*x^6 + 4*(14*(b^3*c^5 + 3*a*b*c^6)*d^2 - 14*(b^4*c^4 + 3*a*b^2*c^5)*d*e + (3*b^5*c^3 + 11*a*b^3*c^4 + 6*a^2*b*c^5)*e^2)*x^5 + (14*(b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*d^2 - 14*(b^5*c^3 + 12*a*b^3*c^4 + 6*a^2*b*c^5)*d*e + (3*b^6*c^2 + 38*a*b^4*c^3 + 42*a^2*b^2*c^4 + 12*a^3*c^5)*e^2)*x^4 + 4*(14*(a*b^3*c^4 + 3*a^2*b*c^5)*d^2 - 14*(a*b^4*c^3 + 3*a^2*b^2*c^4)*d*e + (3*a*b^5*c^2 + 11*a^2*b^3*c^3 + 6*a^3*b*c^4)*e^2)*x^3 + (3*a^4*b^2*c^2 + 2*a^5*c^3)*e^2 + 2*(14*(3*a^2*b^2*c^4 + 2*a^3*c^5)*d^2 - 14*(3*a^2*b^3*c^3 + 2*a^3*b*c^4)*d*e + (9*a^2*b^4*c^2 + 12*a^3*b^2*c^3 + 4*a^4*c^4)*e^2)*x^2 + 4*(14*a^3*b*c^4*d^2 - 14*a^3*b^2*c^3*d*e + (3*a^3*b^3*c^2 + 2*a^4*b*c^3)*e^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) + 4*(2*(b^8*c - 23*a*b^6*c^2 + 250*a^2*b^4*c^3 - 417*a^3*b^2*c^4 - 1116*a^4*c^5)*d^2 - 2*(b^9 - 23*a*b^7*c + 250*a^2*b^5*c^2 - 417*a^3*b^3*c^3 - 1116*a^4*b*c^4)*d*e - (a*b^8 - 32*a^2*b^6*c - 167*a^3*b^4*c^2 + 1146*a^4*b^2*c^3 - 120*a^5*c^4)*e^2)*x)/(a^4*b^10 - 20*a^5*b^8*c + 160*a^6*b^6*c^2 - 640*a^7*b^4*c^3 + 1280*a^8*b^2*c^4 - 1024*a^9*c^5 + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*x^8 + 4*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*x^7 + 2*(3*b^12*c^2 - 58*a*b^10*c^3 + 440*a^2*b^8*c^4 - 1600*a^3*b^6*c^5 + 2560*a^4*b^4*c^6 - 512*a^5*b^2*c^7 - 2048*a^6*c^8)*x^6 + 4*(b^13*c - 17*a*b^11*c^2 + 100*a^2*b^9*c^3 - 160*a^3*b^7*c^4 - 640*a^4*b^5*c^5 + 2816*a^5*b^3*c^6 - 3072*a^6*b*c^7)*x^5 + (b^14 - 8*a*b^12*c - 74*a^2*b^10*c^2 + 1160*a^3*b^8*c^3 - 5440*a^4*b^6*c^4 + 10496*a^5*b^4*c^5 - 4608*a^6*b^2*c^6 - 6144*a^7*c^7)*x^4 + 4*(a*b^13 - 17*a^2*b^11*c + 100*a^3*b^9*c^2 - 160*a^4*b^7*c^3 - 640*a^5*b^5*c^4 + 2816*a^6*b^3*c^5 - 3072*a^7*b*c^6)*x^3 + 2*(3*a^2*b^12 - 58*a^3*b^10*c + 440*a^4*b^8*c^2 - 1600*a^5*b^6*c^3 + 2560*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 2048*a^8*c^6)*x^2 + 4*(a^3*b^11 - 20*a^4*b^9*c + 160*a^5*b^7*c^2 - 640*a^6*b^5*c^3 + 1280*a^7*b^3*c^4 - 1024*a^8*b*c^5)*x)]","B",0
2225,1,3202,0,0.478702," ","integrate((e*x+d)/(c*x^2+b*x+a)^5,x, algorithm=""fricas"")","\left[\frac{420 \, {\left(2 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} e\right)} x^{7} + 1470 \, {\left(2 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d - {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} e\right)} x^{6} + 140 \, {\left(2 \, {\left(13 \, b^{4} c^{5} - 41 \, a b^{2} c^{6} - 44 \, a^{2} c^{7}\right)} d - {\left(13 \, b^{5} c^{4} - 41 \, a b^{3} c^{5} - 44 \, a^{2} b c^{6}\right)} e\right)} x^{5} + 175 \, {\left(2 \, {\left(5 \, b^{5} c^{4} + 2 \, a b^{3} c^{5} - 88 \, a^{2} b c^{6}\right)} d - {\left(5 \, b^{6} c^{3} + 2 \, a b^{4} c^{4} - 88 \, a^{2} b^{2} c^{5}\right)} e\right)} x^{4} + 28 \, {\left(2 \, {\left(3 \, b^{6} c^{3} + 89 \, a b^{4} c^{4} - 331 \, a^{2} b^{2} c^{5} - 292 \, a^{3} c^{6}\right)} d - {\left(3 \, b^{7} c^{2} + 89 \, a b^{5} c^{3} - 331 \, a^{2} b^{3} c^{4} - 292 \, a^{3} b c^{5}\right)} e\right)} x^{3} - 14 \, {\left(2 \, {\left(b^{7} c^{2} - 32 \, a b^{5} c^{3} - 107 \, a^{2} b^{3} c^{4} + 876 \, a^{3} b c^{5}\right)} d - {\left(b^{8} c - 32 \, a b^{6} c^{2} - 107 \, a^{2} b^{4} c^{3} + 876 \, a^{3} b^{2} c^{4}\right)} e\right)} x^{2} - 420 \, {\left(2 \, a^{4} c^{4} d - a^{4} b c^{3} e + {\left(2 \, c^{8} d - b c^{7} e\right)} x^{8} + 4 \, {\left(2 \, b c^{7} d - b^{2} c^{6} e\right)} x^{7} + 2 \, {\left(2 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d - {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} e\right)} x^{6} + 4 \, {\left(2 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} d - {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} e\right)} x^{5} + {\left(2 \, {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} d - {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} e\right)} x^{4} + 4 \, {\left(2 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} e\right)} x^{3} + 2 \, {\left(2 \, {\left(3 \, a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} d - {\left(3 \, a^{2} b^{3} c^{3} + 2 \, a^{3} b c^{4}\right)} e\right)} x^{2} + 4 \, {\left(2 \, a^{3} b c^{4} d - a^{3} b^{2} c^{3} e\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(3 \, b^{9} - 62 \, a b^{7} c + 526 \, a^{2} b^{5} c^{2} - 2420 \, a^{3} b^{3} c^{3} + 4464 \, a^{4} b c^{4}\right)} d - {\left(a b^{8} - 23 \, a^{2} b^{6} c + 250 \, a^{3} b^{4} c^{2} - 312 \, a^{4} b^{2} c^{3} - 1536 \, a^{5} c^{4}\right)} e + 4 \, {\left(2 \, {\left(b^{8} c - 23 \, a b^{6} c^{2} + 250 \, a^{2} b^{4} c^{3} - 417 \, a^{3} b^{2} c^{4} - 1116 \, a^{4} c^{5}\right)} d - {\left(b^{9} - 23 \, a b^{7} c + 250 \, a^{2} b^{5} c^{2} - 417 \, a^{3} b^{3} c^{3} - 1116 \, a^{4} b c^{4}\right)} e\right)} x}{12 \, {\left(a^{4} b^{10} - 20 \, a^{5} b^{8} c + 160 \, a^{6} b^{6} c^{2} - 640 \, a^{7} b^{4} c^{3} + 1280 \, a^{8} b^{2} c^{4} - 1024 \, a^{9} c^{5} + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} x^{8} + 4 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{2} - 58 \, a b^{10} c^{3} + 440 \, a^{2} b^{8} c^{4} - 1600 \, a^{3} b^{6} c^{5} + 2560 \, a^{4} b^{4} c^{6} - 512 \, a^{5} b^{2} c^{7} - 2048 \, a^{6} c^{8}\right)} x^{6} + 4 \, {\left(b^{13} c - 17 \, a b^{11} c^{2} + 100 \, a^{2} b^{9} c^{3} - 160 \, a^{3} b^{7} c^{4} - 640 \, a^{4} b^{5} c^{5} + 2816 \, a^{5} b^{3} c^{6} - 3072 \, a^{6} b c^{7}\right)} x^{5} + {\left(b^{14} - 8 \, a b^{12} c - 74 \, a^{2} b^{10} c^{2} + 1160 \, a^{3} b^{8} c^{3} - 5440 \, a^{4} b^{6} c^{4} + 10496 \, a^{5} b^{4} c^{5} - 4608 \, a^{6} b^{2} c^{6} - 6144 \, a^{7} c^{7}\right)} x^{4} + 4 \, {\left(a b^{13} - 17 \, a^{2} b^{11} c + 100 \, a^{3} b^{9} c^{2} - 160 \, a^{4} b^{7} c^{3} - 640 \, a^{5} b^{5} c^{4} + 2816 \, a^{6} b^{3} c^{5} - 3072 \, a^{7} b c^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} - 58 \, a^{3} b^{10} c + 440 \, a^{4} b^{8} c^{2} - 1600 \, a^{5} b^{6} c^{3} + 2560 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 2048 \, a^{8} c^{6}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} - 20 \, a^{4} b^{9} c + 160 \, a^{5} b^{7} c^{2} - 640 \, a^{6} b^{5} c^{3} + 1280 \, a^{7} b^{3} c^{4} - 1024 \, a^{8} b c^{5}\right)} x\right)}}, \frac{420 \, {\left(2 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d - {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} e\right)} x^{7} + 1470 \, {\left(2 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d - {\left(b^{4} c^{5} - 4 \, a b^{2} c^{6}\right)} e\right)} x^{6} + 140 \, {\left(2 \, {\left(13 \, b^{4} c^{5} - 41 \, a b^{2} c^{6} - 44 \, a^{2} c^{7}\right)} d - {\left(13 \, b^{5} c^{4} - 41 \, a b^{3} c^{5} - 44 \, a^{2} b c^{6}\right)} e\right)} x^{5} + 175 \, {\left(2 \, {\left(5 \, b^{5} c^{4} + 2 \, a b^{3} c^{5} - 88 \, a^{2} b c^{6}\right)} d - {\left(5 \, b^{6} c^{3} + 2 \, a b^{4} c^{4} - 88 \, a^{2} b^{2} c^{5}\right)} e\right)} x^{4} + 28 \, {\left(2 \, {\left(3 \, b^{6} c^{3} + 89 \, a b^{4} c^{4} - 331 \, a^{2} b^{2} c^{5} - 292 \, a^{3} c^{6}\right)} d - {\left(3 \, b^{7} c^{2} + 89 \, a b^{5} c^{3} - 331 \, a^{2} b^{3} c^{4} - 292 \, a^{3} b c^{5}\right)} e\right)} x^{3} - 14 \, {\left(2 \, {\left(b^{7} c^{2} - 32 \, a b^{5} c^{3} - 107 \, a^{2} b^{3} c^{4} + 876 \, a^{3} b c^{5}\right)} d - {\left(b^{8} c - 32 \, a b^{6} c^{2} - 107 \, a^{2} b^{4} c^{3} + 876 \, a^{3} b^{2} c^{4}\right)} e\right)} x^{2} - 840 \, {\left(2 \, a^{4} c^{4} d - a^{4} b c^{3} e + {\left(2 \, c^{8} d - b c^{7} e\right)} x^{8} + 4 \, {\left(2 \, b c^{7} d - b^{2} c^{6} e\right)} x^{7} + 2 \, {\left(2 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} d - {\left(3 \, b^{3} c^{5} + 2 \, a b c^{6}\right)} e\right)} x^{6} + 4 \, {\left(2 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} d - {\left(b^{4} c^{4} + 3 \, a b^{2} c^{5}\right)} e\right)} x^{5} + {\left(2 \, {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} d - {\left(b^{5} c^{3} + 12 \, a b^{3} c^{4} + 6 \, a^{2} b c^{5}\right)} e\right)} x^{4} + 4 \, {\left(2 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} d - {\left(a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} e\right)} x^{3} + 2 \, {\left(2 \, {\left(3 \, a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} d - {\left(3 \, a^{2} b^{3} c^{3} + 2 \, a^{3} b c^{4}\right)} e\right)} x^{2} + 4 \, {\left(2 \, a^{3} b c^{4} d - a^{3} b^{2} c^{3} e\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(3 \, b^{9} - 62 \, a b^{7} c + 526 \, a^{2} b^{5} c^{2} - 2420 \, a^{3} b^{3} c^{3} + 4464 \, a^{4} b c^{4}\right)} d - {\left(a b^{8} - 23 \, a^{2} b^{6} c + 250 \, a^{3} b^{4} c^{2} - 312 \, a^{4} b^{2} c^{3} - 1536 \, a^{5} c^{4}\right)} e + 4 \, {\left(2 \, {\left(b^{8} c - 23 \, a b^{6} c^{2} + 250 \, a^{2} b^{4} c^{3} - 417 \, a^{3} b^{2} c^{4} - 1116 \, a^{4} c^{5}\right)} d - {\left(b^{9} - 23 \, a b^{7} c + 250 \, a^{2} b^{5} c^{2} - 417 \, a^{3} b^{3} c^{3} - 1116 \, a^{4} b c^{4}\right)} e\right)} x}{12 \, {\left(a^{4} b^{10} - 20 \, a^{5} b^{8} c + 160 \, a^{6} b^{6} c^{2} - 640 \, a^{7} b^{4} c^{3} + 1280 \, a^{8} b^{2} c^{4} - 1024 \, a^{9} c^{5} + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} x^{8} + 4 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{2} - 58 \, a b^{10} c^{3} + 440 \, a^{2} b^{8} c^{4} - 1600 \, a^{3} b^{6} c^{5} + 2560 \, a^{4} b^{4} c^{6} - 512 \, a^{5} b^{2} c^{7} - 2048 \, a^{6} c^{8}\right)} x^{6} + 4 \, {\left(b^{13} c - 17 \, a b^{11} c^{2} + 100 \, a^{2} b^{9} c^{3} - 160 \, a^{3} b^{7} c^{4} - 640 \, a^{4} b^{5} c^{5} + 2816 \, a^{5} b^{3} c^{6} - 3072 \, a^{6} b c^{7}\right)} x^{5} + {\left(b^{14} - 8 \, a b^{12} c - 74 \, a^{2} b^{10} c^{2} + 1160 \, a^{3} b^{8} c^{3} - 5440 \, a^{4} b^{6} c^{4} + 10496 \, a^{5} b^{4} c^{5} - 4608 \, a^{6} b^{2} c^{6} - 6144 \, a^{7} c^{7}\right)} x^{4} + 4 \, {\left(a b^{13} - 17 \, a^{2} b^{11} c + 100 \, a^{3} b^{9} c^{2} - 160 \, a^{4} b^{7} c^{3} - 640 \, a^{5} b^{5} c^{4} + 2816 \, a^{6} b^{3} c^{5} - 3072 \, a^{7} b c^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} - 58 \, a^{3} b^{10} c + 440 \, a^{4} b^{8} c^{2} - 1600 \, a^{5} b^{6} c^{3} + 2560 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 2048 \, a^{8} c^{6}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} - 20 \, a^{4} b^{9} c + 160 \, a^{5} b^{7} c^{2} - 640 \, a^{6} b^{5} c^{3} + 1280 \, a^{7} b^{3} c^{4} - 1024 \, a^{8} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/12*(420*(2*(b^2*c^7 - 4*a*c^8)*d - (b^3*c^6 - 4*a*b*c^7)*e)*x^7 + 1470*(2*(b^3*c^6 - 4*a*b*c^7)*d - (b^4*c^5 - 4*a*b^2*c^6)*e)*x^6 + 140*(2*(13*b^4*c^5 - 41*a*b^2*c^6 - 44*a^2*c^7)*d - (13*b^5*c^4 - 41*a*b^3*c^5 - 44*a^2*b*c^6)*e)*x^5 + 175*(2*(5*b^5*c^4 + 2*a*b^3*c^5 - 88*a^2*b*c^6)*d - (5*b^6*c^3 + 2*a*b^4*c^4 - 88*a^2*b^2*c^5)*e)*x^4 + 28*(2*(3*b^6*c^3 + 89*a*b^4*c^4 - 331*a^2*b^2*c^5 - 292*a^3*c^6)*d - (3*b^7*c^2 + 89*a*b^5*c^3 - 331*a^2*b^3*c^4 - 292*a^3*b*c^5)*e)*x^3 - 14*(2*(b^7*c^2 - 32*a*b^5*c^3 - 107*a^2*b^3*c^4 + 876*a^3*b*c^5)*d - (b^8*c - 32*a*b^6*c^2 - 107*a^2*b^4*c^3 + 876*a^3*b^2*c^4)*e)*x^2 - 420*(2*a^4*c^4*d - a^4*b*c^3*e + (2*c^8*d - b*c^7*e)*x^8 + 4*(2*b*c^7*d - b^2*c^6*e)*x^7 + 2*(2*(3*b^2*c^6 + 2*a*c^7)*d - (3*b^3*c^5 + 2*a*b*c^6)*e)*x^6 + 4*(2*(b^3*c^5 + 3*a*b*c^6)*d - (b^4*c^4 + 3*a*b^2*c^5)*e)*x^5 + (2*(b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*d - (b^5*c^3 + 12*a*b^3*c^4 + 6*a^2*b*c^5)*e)*x^4 + 4*(2*(a*b^3*c^4 + 3*a^2*b*c^5)*d - (a*b^4*c^3 + 3*a^2*b^2*c^4)*e)*x^3 + 2*(2*(3*a^2*b^2*c^4 + 2*a^3*c^5)*d - (3*a^2*b^3*c^3 + 2*a^3*b*c^4)*e)*x^2 + 4*(2*a^3*b*c^4*d - a^3*b^2*c^3*e)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (3*b^9 - 62*a*b^7*c + 526*a^2*b^5*c^2 - 2420*a^3*b^3*c^3 + 4464*a^4*b*c^4)*d - (a*b^8 - 23*a^2*b^6*c + 250*a^3*b^4*c^2 - 312*a^4*b^2*c^3 - 1536*a^5*c^4)*e + 4*(2*(b^8*c - 23*a*b^6*c^2 + 250*a^2*b^4*c^3 - 417*a^3*b^2*c^4 - 1116*a^4*c^5)*d - (b^9 - 23*a*b^7*c + 250*a^2*b^5*c^2 - 417*a^3*b^3*c^3 - 1116*a^4*b*c^4)*e)*x)/(a^4*b^10 - 20*a^5*b^8*c + 160*a^6*b^6*c^2 - 640*a^7*b^4*c^3 + 1280*a^8*b^2*c^4 - 1024*a^9*c^5 + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*x^8 + 4*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*x^7 + 2*(3*b^12*c^2 - 58*a*b^10*c^3 + 440*a^2*b^8*c^4 - 1600*a^3*b^6*c^5 + 2560*a^4*b^4*c^6 - 512*a^5*b^2*c^7 - 2048*a^6*c^8)*x^6 + 4*(b^13*c - 17*a*b^11*c^2 + 100*a^2*b^9*c^3 - 160*a^3*b^7*c^4 - 640*a^4*b^5*c^5 + 2816*a^5*b^3*c^6 - 3072*a^6*b*c^7)*x^5 + (b^14 - 8*a*b^12*c - 74*a^2*b^10*c^2 + 1160*a^3*b^8*c^3 - 5440*a^4*b^6*c^4 + 10496*a^5*b^4*c^5 - 4608*a^6*b^2*c^6 - 6144*a^7*c^7)*x^4 + 4*(a*b^13 - 17*a^2*b^11*c + 100*a^3*b^9*c^2 - 160*a^4*b^7*c^3 - 640*a^5*b^5*c^4 + 2816*a^6*b^3*c^5 - 3072*a^7*b*c^6)*x^3 + 2*(3*a^2*b^12 - 58*a^3*b^10*c + 440*a^4*b^8*c^2 - 1600*a^5*b^6*c^3 + 2560*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 2048*a^8*c^6)*x^2 + 4*(a^3*b^11 - 20*a^4*b^9*c + 160*a^5*b^7*c^2 - 640*a^6*b^5*c^3 + 1280*a^7*b^3*c^4 - 1024*a^8*b*c^5)*x), 1/12*(420*(2*(b^2*c^7 - 4*a*c^8)*d - (b^3*c^6 - 4*a*b*c^7)*e)*x^7 + 1470*(2*(b^3*c^6 - 4*a*b*c^7)*d - (b^4*c^5 - 4*a*b^2*c^6)*e)*x^6 + 140*(2*(13*b^4*c^5 - 41*a*b^2*c^6 - 44*a^2*c^7)*d - (13*b^5*c^4 - 41*a*b^3*c^5 - 44*a^2*b*c^6)*e)*x^5 + 175*(2*(5*b^5*c^4 + 2*a*b^3*c^5 - 88*a^2*b*c^6)*d - (5*b^6*c^3 + 2*a*b^4*c^4 - 88*a^2*b^2*c^5)*e)*x^4 + 28*(2*(3*b^6*c^3 + 89*a*b^4*c^4 - 331*a^2*b^2*c^5 - 292*a^3*c^6)*d - (3*b^7*c^2 + 89*a*b^5*c^3 - 331*a^2*b^3*c^4 - 292*a^3*b*c^5)*e)*x^3 - 14*(2*(b^7*c^2 - 32*a*b^5*c^3 - 107*a^2*b^3*c^4 + 876*a^3*b*c^5)*d - (b^8*c - 32*a*b^6*c^2 - 107*a^2*b^4*c^3 + 876*a^3*b^2*c^4)*e)*x^2 - 840*(2*a^4*c^4*d - a^4*b*c^3*e + (2*c^8*d - b*c^7*e)*x^8 + 4*(2*b*c^7*d - b^2*c^6*e)*x^7 + 2*(2*(3*b^2*c^6 + 2*a*c^7)*d - (3*b^3*c^5 + 2*a*b*c^6)*e)*x^6 + 4*(2*(b^3*c^5 + 3*a*b*c^6)*d - (b^4*c^4 + 3*a*b^2*c^5)*e)*x^5 + (2*(b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*d - (b^5*c^3 + 12*a*b^3*c^4 + 6*a^2*b*c^5)*e)*x^4 + 4*(2*(a*b^3*c^4 + 3*a^2*b*c^5)*d - (a*b^4*c^3 + 3*a^2*b^2*c^4)*e)*x^3 + 2*(2*(3*a^2*b^2*c^4 + 2*a^3*c^5)*d - (3*a^2*b^3*c^3 + 2*a^3*b*c^4)*e)*x^2 + 4*(2*a^3*b*c^4*d - a^3*b^2*c^3*e)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (3*b^9 - 62*a*b^7*c + 526*a^2*b^5*c^2 - 2420*a^3*b^3*c^3 + 4464*a^4*b*c^4)*d - (a*b^8 - 23*a^2*b^6*c + 250*a^3*b^4*c^2 - 312*a^4*b^2*c^3 - 1536*a^5*c^4)*e + 4*(2*(b^8*c - 23*a*b^6*c^2 + 250*a^2*b^4*c^3 - 417*a^3*b^2*c^4 - 1116*a^4*c^5)*d - (b^9 - 23*a*b^7*c + 250*a^2*b^5*c^2 - 417*a^3*b^3*c^3 - 1116*a^4*b*c^4)*e)*x)/(a^4*b^10 - 20*a^5*b^8*c + 160*a^6*b^6*c^2 - 640*a^7*b^4*c^3 + 1280*a^8*b^2*c^4 - 1024*a^9*c^5 + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*x^8 + 4*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*x^7 + 2*(3*b^12*c^2 - 58*a*b^10*c^3 + 440*a^2*b^8*c^4 - 1600*a^3*b^6*c^5 + 2560*a^4*b^4*c^6 - 512*a^5*b^2*c^7 - 2048*a^6*c^8)*x^6 + 4*(b^13*c - 17*a*b^11*c^2 + 100*a^2*b^9*c^3 - 160*a^3*b^7*c^4 - 640*a^4*b^5*c^5 + 2816*a^5*b^3*c^6 - 3072*a^6*b*c^7)*x^5 + (b^14 - 8*a*b^12*c - 74*a^2*b^10*c^2 + 1160*a^3*b^8*c^3 - 5440*a^4*b^6*c^4 + 10496*a^5*b^4*c^5 - 4608*a^6*b^2*c^6 - 6144*a^7*c^7)*x^4 + 4*(a*b^13 - 17*a^2*b^11*c + 100*a^3*b^9*c^2 - 160*a^4*b^7*c^3 - 640*a^5*b^5*c^4 + 2816*a^6*b^3*c^5 - 3072*a^7*b*c^6)*x^3 + 2*(3*a^2*b^12 - 58*a^3*b^10*c + 440*a^4*b^8*c^2 - 1600*a^5*b^6*c^3 + 2560*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 2048*a^8*c^6)*x^2 + 4*(a^3*b^11 - 20*a^4*b^9*c + 160*a^5*b^7*c^2 - 640*a^6*b^5*c^3 + 1280*a^7*b^3*c^4 - 1024*a^8*b*c^5)*x)]","B",0
2226,1,2217,0,0.449119," ","integrate(1/(c*x^2+b*x+a)^5,x, algorithm=""fricas"")","\left[-\frac{3 \, b^{9} - 62 \, a b^{7} c + 526 \, a^{2} b^{5} c^{2} - 2420 \, a^{3} b^{3} c^{3} + 4464 \, a^{4} b c^{4} - 840 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} x^{7} - 2940 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} x^{6} - 280 \, {\left(13 \, b^{4} c^{5} - 41 \, a b^{2} c^{6} - 44 \, a^{2} c^{7}\right)} x^{5} - 350 \, {\left(5 \, b^{5} c^{4} + 2 \, a b^{3} c^{5} - 88 \, a^{2} b c^{6}\right)} x^{4} - 56 \, {\left(3 \, b^{6} c^{3} + 89 \, a b^{4} c^{4} - 331 \, a^{2} b^{2} c^{5} - 292 \, a^{3} c^{6}\right)} x^{3} + 28 \, {\left(b^{7} c^{2} - 32 \, a b^{5} c^{3} - 107 \, a^{2} b^{3} c^{4} + 876 \, a^{3} b c^{5}\right)} x^{2} - 840 \, {\left(c^{8} x^{8} + 4 \, b c^{7} x^{7} + 4 \, a^{3} b c^{4} x + a^{4} c^{4} + 2 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} x^{6} + 4 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} x^{5} + {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} x^{4} + 4 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} x^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - 8 \, {\left(b^{8} c - 23 \, a b^{6} c^{2} + 250 \, a^{2} b^{4} c^{3} - 417 \, a^{3} b^{2} c^{4} - 1116 \, a^{4} c^{5}\right)} x}{12 \, {\left(a^{4} b^{10} - 20 \, a^{5} b^{8} c + 160 \, a^{6} b^{6} c^{2} - 640 \, a^{7} b^{4} c^{3} + 1280 \, a^{8} b^{2} c^{4} - 1024 \, a^{9} c^{5} + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} x^{8} + 4 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{2} - 58 \, a b^{10} c^{3} + 440 \, a^{2} b^{8} c^{4} - 1600 \, a^{3} b^{6} c^{5} + 2560 \, a^{4} b^{4} c^{6} - 512 \, a^{5} b^{2} c^{7} - 2048 \, a^{6} c^{8}\right)} x^{6} + 4 \, {\left(b^{13} c - 17 \, a b^{11} c^{2} + 100 \, a^{2} b^{9} c^{3} - 160 \, a^{3} b^{7} c^{4} - 640 \, a^{4} b^{5} c^{5} + 2816 \, a^{5} b^{3} c^{6} - 3072 \, a^{6} b c^{7}\right)} x^{5} + {\left(b^{14} - 8 \, a b^{12} c - 74 \, a^{2} b^{10} c^{2} + 1160 \, a^{3} b^{8} c^{3} - 5440 \, a^{4} b^{6} c^{4} + 10496 \, a^{5} b^{4} c^{5} - 4608 \, a^{6} b^{2} c^{6} - 6144 \, a^{7} c^{7}\right)} x^{4} + 4 \, {\left(a b^{13} - 17 \, a^{2} b^{11} c + 100 \, a^{3} b^{9} c^{2} - 160 \, a^{4} b^{7} c^{3} - 640 \, a^{5} b^{5} c^{4} + 2816 \, a^{6} b^{3} c^{5} - 3072 \, a^{7} b c^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} - 58 \, a^{3} b^{10} c + 440 \, a^{4} b^{8} c^{2} - 1600 \, a^{5} b^{6} c^{3} + 2560 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 2048 \, a^{8} c^{6}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} - 20 \, a^{4} b^{9} c + 160 \, a^{5} b^{7} c^{2} - 640 \, a^{6} b^{5} c^{3} + 1280 \, a^{7} b^{3} c^{4} - 1024 \, a^{8} b c^{5}\right)} x\right)}}, -\frac{3 \, b^{9} - 62 \, a b^{7} c + 526 \, a^{2} b^{5} c^{2} - 2420 \, a^{3} b^{3} c^{3} + 4464 \, a^{4} b c^{4} - 840 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} x^{7} - 2940 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} x^{6} - 280 \, {\left(13 \, b^{4} c^{5} - 41 \, a b^{2} c^{6} - 44 \, a^{2} c^{7}\right)} x^{5} - 350 \, {\left(5 \, b^{5} c^{4} + 2 \, a b^{3} c^{5} - 88 \, a^{2} b c^{6}\right)} x^{4} - 56 \, {\left(3 \, b^{6} c^{3} + 89 \, a b^{4} c^{4} - 331 \, a^{2} b^{2} c^{5} - 292 \, a^{3} c^{6}\right)} x^{3} + 28 \, {\left(b^{7} c^{2} - 32 \, a b^{5} c^{3} - 107 \, a^{2} b^{3} c^{4} + 876 \, a^{3} b c^{5}\right)} x^{2} + 1680 \, {\left(c^{8} x^{8} + 4 \, b c^{7} x^{7} + 4 \, a^{3} b c^{4} x + a^{4} c^{4} + 2 \, {\left(3 \, b^{2} c^{6} + 2 \, a c^{7}\right)} x^{6} + 4 \, {\left(b^{3} c^{5} + 3 \, a b c^{6}\right)} x^{5} + {\left(b^{4} c^{4} + 12 \, a b^{2} c^{5} + 6 \, a^{2} c^{6}\right)} x^{4} + 4 \, {\left(a b^{3} c^{4} + 3 \, a^{2} b c^{5}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 2 \, a^{3} c^{5}\right)} x^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - 8 \, {\left(b^{8} c - 23 \, a b^{6} c^{2} + 250 \, a^{2} b^{4} c^{3} - 417 \, a^{3} b^{2} c^{4} - 1116 \, a^{4} c^{5}\right)} x}{12 \, {\left(a^{4} b^{10} - 20 \, a^{5} b^{8} c + 160 \, a^{6} b^{6} c^{2} - 640 \, a^{7} b^{4} c^{3} + 1280 \, a^{8} b^{2} c^{4} - 1024 \, a^{9} c^{5} + {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} x^{8} + 4 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} x^{7} + 2 \, {\left(3 \, b^{12} c^{2} - 58 \, a b^{10} c^{3} + 440 \, a^{2} b^{8} c^{4} - 1600 \, a^{3} b^{6} c^{5} + 2560 \, a^{4} b^{4} c^{6} - 512 \, a^{5} b^{2} c^{7} - 2048 \, a^{6} c^{8}\right)} x^{6} + 4 \, {\left(b^{13} c - 17 \, a b^{11} c^{2} + 100 \, a^{2} b^{9} c^{3} - 160 \, a^{3} b^{7} c^{4} - 640 \, a^{4} b^{5} c^{5} + 2816 \, a^{5} b^{3} c^{6} - 3072 \, a^{6} b c^{7}\right)} x^{5} + {\left(b^{14} - 8 \, a b^{12} c - 74 \, a^{2} b^{10} c^{2} + 1160 \, a^{3} b^{8} c^{3} - 5440 \, a^{4} b^{6} c^{4} + 10496 \, a^{5} b^{4} c^{5} - 4608 \, a^{6} b^{2} c^{6} - 6144 \, a^{7} c^{7}\right)} x^{4} + 4 \, {\left(a b^{13} - 17 \, a^{2} b^{11} c + 100 \, a^{3} b^{9} c^{2} - 160 \, a^{4} b^{7} c^{3} - 640 \, a^{5} b^{5} c^{4} + 2816 \, a^{6} b^{3} c^{5} - 3072 \, a^{7} b c^{6}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{12} - 58 \, a^{3} b^{10} c + 440 \, a^{4} b^{8} c^{2} - 1600 \, a^{5} b^{6} c^{3} + 2560 \, a^{6} b^{4} c^{4} - 512 \, a^{7} b^{2} c^{5} - 2048 \, a^{8} c^{6}\right)} x^{2} + 4 \, {\left(a^{3} b^{11} - 20 \, a^{4} b^{9} c + 160 \, a^{5} b^{7} c^{2} - 640 \, a^{6} b^{5} c^{3} + 1280 \, a^{7} b^{3} c^{4} - 1024 \, a^{8} b c^{5}\right)} x\right)}}\right]"," ",0,"[-1/12*(3*b^9 - 62*a*b^7*c + 526*a^2*b^5*c^2 - 2420*a^3*b^3*c^3 + 4464*a^4*b*c^4 - 840*(b^2*c^7 - 4*a*c^8)*x^7 - 2940*(b^3*c^6 - 4*a*b*c^7)*x^6 - 280*(13*b^4*c^5 - 41*a*b^2*c^6 - 44*a^2*c^7)*x^5 - 350*(5*b^5*c^4 + 2*a*b^3*c^5 - 88*a^2*b*c^6)*x^4 - 56*(3*b^6*c^3 + 89*a*b^4*c^4 - 331*a^2*b^2*c^5 - 292*a^3*c^6)*x^3 + 28*(b^7*c^2 - 32*a*b^5*c^3 - 107*a^2*b^3*c^4 + 876*a^3*b*c^5)*x^2 - 840*(c^8*x^8 + 4*b*c^7*x^7 + 4*a^3*b*c^4*x + a^4*c^4 + 2*(3*b^2*c^6 + 2*a*c^7)*x^6 + 4*(b^3*c^5 + 3*a*b*c^6)*x^5 + (b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*x^4 + 4*(a*b^3*c^4 + 3*a^2*b*c^5)*x^3 + 2*(3*a^2*b^2*c^4 + 2*a^3*c^5)*x^2)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - 8*(b^8*c - 23*a*b^6*c^2 + 250*a^2*b^4*c^3 - 417*a^3*b^2*c^4 - 1116*a^4*c^5)*x)/(a^4*b^10 - 20*a^5*b^8*c + 160*a^6*b^6*c^2 - 640*a^7*b^4*c^3 + 1280*a^8*b^2*c^4 - 1024*a^9*c^5 + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*x^8 + 4*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*x^7 + 2*(3*b^12*c^2 - 58*a*b^10*c^3 + 440*a^2*b^8*c^4 - 1600*a^3*b^6*c^5 + 2560*a^4*b^4*c^6 - 512*a^5*b^2*c^7 - 2048*a^6*c^8)*x^6 + 4*(b^13*c - 17*a*b^11*c^2 + 100*a^2*b^9*c^3 - 160*a^3*b^7*c^4 - 640*a^4*b^5*c^5 + 2816*a^5*b^3*c^6 - 3072*a^6*b*c^7)*x^5 + (b^14 - 8*a*b^12*c - 74*a^2*b^10*c^2 + 1160*a^3*b^8*c^3 - 5440*a^4*b^6*c^4 + 10496*a^5*b^4*c^5 - 4608*a^6*b^2*c^6 - 6144*a^7*c^7)*x^4 + 4*(a*b^13 - 17*a^2*b^11*c + 100*a^3*b^9*c^2 - 160*a^4*b^7*c^3 - 640*a^5*b^5*c^4 + 2816*a^6*b^3*c^5 - 3072*a^7*b*c^6)*x^3 + 2*(3*a^2*b^12 - 58*a^3*b^10*c + 440*a^4*b^8*c^2 - 1600*a^5*b^6*c^3 + 2560*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 2048*a^8*c^6)*x^2 + 4*(a^3*b^11 - 20*a^4*b^9*c + 160*a^5*b^7*c^2 - 640*a^6*b^5*c^3 + 1280*a^7*b^3*c^4 - 1024*a^8*b*c^5)*x), -1/12*(3*b^9 - 62*a*b^7*c + 526*a^2*b^5*c^2 - 2420*a^3*b^3*c^3 + 4464*a^4*b*c^4 - 840*(b^2*c^7 - 4*a*c^8)*x^7 - 2940*(b^3*c^6 - 4*a*b*c^7)*x^6 - 280*(13*b^4*c^5 - 41*a*b^2*c^6 - 44*a^2*c^7)*x^5 - 350*(5*b^5*c^4 + 2*a*b^3*c^5 - 88*a^2*b*c^6)*x^4 - 56*(3*b^6*c^3 + 89*a*b^4*c^4 - 331*a^2*b^2*c^5 - 292*a^3*c^6)*x^3 + 28*(b^7*c^2 - 32*a*b^5*c^3 - 107*a^2*b^3*c^4 + 876*a^3*b*c^5)*x^2 + 1680*(c^8*x^8 + 4*b*c^7*x^7 + 4*a^3*b*c^4*x + a^4*c^4 + 2*(3*b^2*c^6 + 2*a*c^7)*x^6 + 4*(b^3*c^5 + 3*a*b*c^6)*x^5 + (b^4*c^4 + 12*a*b^2*c^5 + 6*a^2*c^6)*x^4 + 4*(a*b^3*c^4 + 3*a^2*b*c^5)*x^3 + 2*(3*a^2*b^2*c^4 + 2*a^3*c^5)*x^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - 8*(b^8*c - 23*a*b^6*c^2 + 250*a^2*b^4*c^3 - 417*a^3*b^2*c^4 - 1116*a^4*c^5)*x)/(a^4*b^10 - 20*a^5*b^8*c + 160*a^6*b^6*c^2 - 640*a^7*b^4*c^3 + 1280*a^8*b^2*c^4 - 1024*a^9*c^5 + (b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*x^8 + 4*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*x^7 + 2*(3*b^12*c^2 - 58*a*b^10*c^3 + 440*a^2*b^8*c^4 - 1600*a^3*b^6*c^5 + 2560*a^4*b^4*c^6 - 512*a^5*b^2*c^7 - 2048*a^6*c^8)*x^6 + 4*(b^13*c - 17*a*b^11*c^2 + 100*a^2*b^9*c^3 - 160*a^3*b^7*c^4 - 640*a^4*b^5*c^5 + 2816*a^5*b^3*c^6 - 3072*a^6*b*c^7)*x^5 + (b^14 - 8*a*b^12*c - 74*a^2*b^10*c^2 + 1160*a^3*b^8*c^3 - 5440*a^4*b^6*c^4 + 10496*a^5*b^4*c^5 - 4608*a^6*b^2*c^6 - 6144*a^7*c^7)*x^4 + 4*(a*b^13 - 17*a^2*b^11*c + 100*a^3*b^9*c^2 - 160*a^4*b^7*c^3 - 640*a^5*b^5*c^4 + 2816*a^6*b^3*c^5 - 3072*a^7*b*c^6)*x^3 + 2*(3*a^2*b^12 - 58*a^3*b^10*c + 440*a^4*b^8*c^2 - 1600*a^5*b^6*c^3 + 2560*a^6*b^4*c^4 - 512*a^7*b^2*c^5 - 2048*a^8*c^6)*x^2 + 4*(a^3*b^11 - 20*a^4*b^9*c + 160*a^5*b^7*c^2 - 640*a^6*b^5*c^3 + 1280*a^7*b^3*c^4 - 1024*a^8*b*c^5)*x)]","B",0
2227,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2228,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2229,1,136,0,0.421447," ","integrate(1/(1+2*x)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{9938600 \, x^{3} + 251248 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 17286220 \, x^{2} - 953312 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) + 1906624 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \log\left(2 \, x + 1\right) + 11711056 \, x + 6271517}{20436626 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/20436626*(9938600*x^3 + 251248*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*arctan(1/31*sqrt(31)*(10*x + 3)) + 17286220*x^2 - 953312*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*log(5*x^2 + 3*x + 2) + 1906624*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*log(2*x + 1) + 11711056*x + 6271517)/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","A",0
2230,1,161,0,0.429419," ","integrate(1/(1+2*x)^2/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","-\frac{558948600 \, x^{4} + 582332520 \, x^{3} + 2130024 \, \sqrt{31} {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 497710766 \, x^{2} + 11439744 \, {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) - 22879488 \, {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)} \log\left(2 \, x + 1\right) + 167764870 \, x + 38185273}{143056382 \, {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"-1/143056382*(558948600*x^4 + 582332520*x^3 + 2130024*sqrt(31)*(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4)*arctan(1/31*sqrt(31)*(10*x + 3)) + 497710766*x^2 + 11439744*(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4)*log(5*x^2 + 3*x + 2) - 22879488*(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4)*log(2*x + 1) + 167764870*x + 38185273)/(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4)","A",0
2231,1,186,0,0.428862," ","integrate(1/(1+2*x)/(5*x^2+3*x+2)^4,x, algorithm=""fricas"")","\frac{13230273000 \, x^{5} + 27602985900 \, x^{4} + 31119019540 \, x^{3} + 57022128 \, \sqrt{31} {\left(125 \, x^{6} + 225 \, x^{5} + 285 \, x^{4} + 207 \, x^{3} + 114 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 22840952148 \, x^{2} - 177316032 \, {\left(125 \, x^{6} + 225 \, x^{5} + 285 \, x^{4} + 207 \, x^{3} + 114 \, x^{2} + 36 \, x + 8\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) + 354632064 \, {\left(125 \, x^{6} + 225 \, x^{5} + 285 \, x^{4} + 207 \, x^{3} + 114 \, x^{2} + 36 \, x + 8\right)} \log\left(2 \, x + 1\right) + 9750500928 \, x + 3001362805}{6652121763 \, {\left(125 \, x^{6} + 225 \, x^{5} + 285 \, x^{4} + 207 \, x^{3} + 114 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/6652121763*(13230273000*x^5 + 27602985900*x^4 + 31119019540*x^3 + 57022128*sqrt(31)*(125*x^6 + 225*x^5 + 285*x^4 + 207*x^3 + 114*x^2 + 36*x + 8)*arctan(1/31*sqrt(31)*(10*x + 3)) + 22840952148*x^2 - 177316032*(125*x^6 + 225*x^5 + 285*x^4 + 207*x^3 + 114*x^2 + 36*x + 8)*log(5*x^2 + 3*x + 2) + 354632064*(125*x^6 + 225*x^5 + 285*x^4 + 207*x^3 + 114*x^2 + 36*x + 8)*log(2*x + 1) + 9750500928*x + 3001362805)/(125*x^6 + 225*x^5 + 285*x^4 + 207*x^3 + 114*x^2 + 36*x + 8)","A",0
2232,1,211,0,0.428330," ","integrate(1/(1+2*x)^2/(5*x^2+3*x+2)^4,x, algorithm=""fricas"")","-\frac{553538139000 \, x^{6} + 858833833200 \, x^{5} + 982016294070 \, x^{4} + 605165058624 \, x^{3} + 348170952 \, \sqrt{31} {\left(250 \, x^{7} + 575 \, x^{6} + 795 \, x^{5} + 699 \, x^{4} + 435 \, x^{3} + 186 \, x^{2} + 52 \, x + 8\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 281968516011 \, x^{2} + 2837056512 \, {\left(250 \, x^{7} + 575 \, x^{6} + 795 \, x^{5} + 699 \, x^{4} + 435 \, x^{3} + 186 \, x^{2} + 52 \, x + 8\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) - 5674113024 \, {\left(250 \, x^{7} + 575 \, x^{6} + 795 \, x^{5} + 699 \, x^{4} + 435 \, x^{3} + 186 \, x^{2} + 52 \, x + 8\right)} \log\left(2 \, x + 1\right) + 66162113227 \, x + 8352308951}{46564852341 \, {\left(250 \, x^{7} + 575 \, x^{6} + 795 \, x^{5} + 699 \, x^{4} + 435 \, x^{3} + 186 \, x^{2} + 52 \, x + 8\right)}}"," ",0,"-1/46564852341*(553538139000*x^6 + 858833833200*x^5 + 982016294070*x^4 + 605165058624*x^3 + 348170952*sqrt(31)*(250*x^7 + 575*x^6 + 795*x^5 + 699*x^4 + 435*x^3 + 186*x^2 + 52*x + 8)*arctan(1/31*sqrt(31)*(10*x + 3)) + 281968516011*x^2 + 2837056512*(250*x^7 + 575*x^6 + 795*x^5 + 699*x^4 + 435*x^3 + 186*x^2 + 52*x + 8)*log(5*x^2 + 3*x + 2) - 5674113024*(250*x^7 + 575*x^6 + 795*x^5 + 699*x^4 + 435*x^3 + 186*x^2 + 52*x + 8)*log(2*x + 1) + 66162113227*x + 8352308951)/(250*x^7 + 575*x^6 + 795*x^5 + 699*x^4 + 435*x^3 + 186*x^2 + 52*x + 8)","A",0
2233,1,54,0,0.411737," ","integrate((7-3*x)/(x^2+2*x-5),x, algorithm=""fricas"")","\frac{5}{6} \, \sqrt{3} \sqrt{2} \log\left(-\frac{2 \, \sqrt{3} \sqrt{2} {\left(x + 1\right)} - x^{2} - 2 \, x - 7}{x^{2} + 2 \, x - 5}\right) - \frac{3}{2} \, \log\left(x^{2} + 2 \, x - 5\right)"," ",0,"5/6*sqrt(3)*sqrt(2)*log(-(2*sqrt(3)*sqrt(2)*(x + 1) - x^2 - 2*x - 7)/(x^2 + 2*x - 5)) - 3/2*log(x^2 + 2*x - 5)","A",0
2234,1,32,0,0.419805," ","integrate(1/(-1+x)/(x^2+x+1),x, algorithm=""fricas"")","-\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(x - 1\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/6*log(x^2 + x + 1) + 1/3*log(x - 1)","A",0
2235,1,162,0,0.449629," ","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=""fricas"")","-\cos\left(\frac{2 \, \pi k}{n} - \frac{\pi}{n}\right) \log\left(-\frac{2 \, {\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)}}{\cos\left(\frac{2 \, \pi k}{n} - \frac{\pi}{n}\right) + 1}\right) - 2 \, \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}{\left(\frac{a}{b}\right)^{\left(\frac{1}{n}\right)} \sin\left(\frac{2 \, \pi k}{n} - \frac{\pi}{n}\right)}\right) \sin\left(\frac{2 \, \pi k}{n} - \frac{\pi}{n}\right)"," ",0,"-cos(2*pi*k/n - pi/n)*log(-2*(2*x*(a/b)^(1/n)*cos(2*pi*k/n - pi/n) - x^2 - (a/b)^(2/n))/(cos(2*pi*k/n - pi/n) + 1)) - 2*arctan(((a/b)^(1/n)*cos(2*pi*k/n - pi/n) - x)/((a/b)^(1/n)*sin(2*pi*k/n - pi/n)))*sin(2*pi*k/n - pi/n)","A",0
2236,1,30,0,0.408077," ","integrate(x^4/(15*x^2+13*x+2),x, algorithm=""fricas"")","\frac{1}{45} \, x^{3} - \frac{13}{450} \, x^{2} + \frac{139}{3375} \, x + \frac{1}{4375} \, \log\left(5 \, x + 1\right) - \frac{16}{567} \, \log\left(3 \, x + 2\right)"," ",0,"1/45*x^3 - 13/450*x^2 + 139/3375*x + 1/4375*log(5*x + 1) - 16/567*log(3*x + 2)","A",0
2237,1,25,0,0.399523," ","integrate(x^3/(15*x^2+13*x+2),x, algorithm=""fricas"")","\frac{1}{30} \, x^{2} - \frac{13}{225} \, x - \frac{1}{875} \, \log\left(5 \, x + 1\right) + \frac{8}{189} \, \log\left(3 \, x + 2\right)"," ",0,"1/30*x^2 - 13/225*x - 1/875*log(5*x + 1) + 8/189*log(3*x + 2)","A",0
2238,1,20,0,0.396660," ","integrate(x^2/(15*x^2+13*x+2),x, algorithm=""fricas"")","\frac{1}{15} \, x + \frac{1}{175} \, \log\left(5 \, x + 1\right) - \frac{4}{63} \, \log\left(3 \, x + 2\right)"," ",0,"1/15*x + 1/175*log(5*x + 1) - 4/63*log(3*x + 2)","A",0
2239,1,17,0,0.404518," ","integrate(x/(15*x^2+13*x+2),x, algorithm=""fricas"")","-\frac{1}{35} \, \log\left(5 \, x + 1\right) + \frac{2}{21} \, \log\left(3 \, x + 2\right)"," ",0,"-1/35*log(5*x + 1) + 2/21*log(3*x + 2)","A",0
2240,1,17,0,0.407925," ","integrate(1/(15*x^2+13*x+2),x, algorithm=""fricas"")","\frac{1}{7} \, \log\left(5 \, x + 1\right) - \frac{1}{7} \, \log\left(3 \, x + 2\right)"," ",0,"1/7*log(5*x + 1) - 1/7*log(3*x + 2)","A",0
2241,1,21,0,0.414129," ","integrate(1/x/(15*x^2+13*x+2),x, algorithm=""fricas"")","-\frac{5}{7} \, \log\left(5 \, x + 1\right) + \frac{3}{14} \, \log\left(3 \, x + 2\right) + \frac{1}{2} \, \log\left(x\right)"," ",0,"-5/7*log(5*x + 1) + 3/14*log(3*x + 2) + 1/2*log(x)","A",0
2242,1,30,0,0.409188," ","integrate(1/x^2/(15*x^2+13*x+2),x, algorithm=""fricas"")","\frac{100 \, x \log\left(5 \, x + 1\right) - 9 \, x \log\left(3 \, x + 2\right) - 91 \, x \log\left(x\right) - 14}{28 \, x}"," ",0,"1/28*(100*x*log(5*x + 1) - 9*x*log(3*x + 2) - 91*x*log(x) - 14)/x","A",0
2243,1,39,0,0.410072," ","integrate(1/x^3/(15*x^2+13*x+2),x, algorithm=""fricas"")","-\frac{1000 \, x^{2} \log\left(5 \, x + 1\right) - 27 \, x^{2} \log\left(3 \, x + 2\right) - 973 \, x^{2} \log\left(x\right) - 182 \, x + 14}{56 \, x^{2}}"," ",0,"-1/56*(1000*x^2*log(5*x + 1) - 27*x^2*log(3*x + 2) - 973*x^2*log(x) - 182*x + 14)/x^2","A",0
2244,1,44,0,0.404696," ","integrate(1/x^4/(15*x^2+13*x+2),x, algorithm=""fricas"")","\frac{30000 \, x^{3} \log\left(5 \, x + 1\right) - 243 \, x^{3} \log\left(3 \, x + 2\right) - 29757 \, x^{3} \log\left(x\right) - 5838 \, x^{2} + 546 \, x - 56}{336 \, x^{3}}"," ",0,"1/336*(30000*x^3*log(5*x + 1) - 243*x^3*log(3*x + 2) - 29757*x^3*log(x) - 5838*x^2 + 546*x - 56)/x^3","A",0
2245,1,30,0,0.401937," ","integrate(x^5/(15*x^3+13*x^2+2*x),x, algorithm=""fricas"")","\frac{1}{45} \, x^{3} - \frac{13}{450} \, x^{2} + \frac{139}{3375} \, x + \frac{1}{4375} \, \log\left(5 \, x + 1\right) - \frac{16}{567} \, \log\left(3 \, x + 2\right)"," ",0,"1/45*x^3 - 13/450*x^2 + 139/3375*x + 1/4375*log(5*x + 1) - 16/567*log(3*x + 2)","A",0
2246,1,25,0,0.396285," ","integrate(x^4/(15*x^3+13*x^2+2*x),x, algorithm=""fricas"")","\frac{1}{30} \, x^{2} - \frac{13}{225} \, x - \frac{1}{875} \, \log\left(5 \, x + 1\right) + \frac{8}{189} \, \log\left(3 \, x + 2\right)"," ",0,"1/30*x^2 - 13/225*x - 1/875*log(5*x + 1) + 8/189*log(3*x + 2)","A",0
2247,1,20,0,0.399664," ","integrate(x^3/(15*x^3+13*x^2+2*x),x, algorithm=""fricas"")","\frac{1}{15} \, x + \frac{1}{175} \, \log\left(5 \, x + 1\right) - \frac{4}{63} \, \log\left(3 \, x + 2\right)"," ",0,"1/15*x + 1/175*log(5*x + 1) - 4/63*log(3*x + 2)","A",0
2248,1,17,0,0.420826," ","integrate(x^2/(15*x^3+13*x^2+2*x),x, algorithm=""fricas"")","-\frac{1}{35} \, \log\left(5 \, x + 1\right) + \frac{2}{21} \, \log\left(3 \, x + 2\right)"," ",0,"-1/35*log(5*x + 1) + 2/21*log(3*x + 2)","A",0
2249,1,17,0,0.399553," ","integrate(x/(15*x^3+13*x^2+2*x),x, algorithm=""fricas"")","\frac{1}{7} \, \log\left(5 \, x + 1\right) - \frac{1}{7} \, \log\left(3 \, x + 2\right)"," ",0,"1/7*log(5*x + 1) - 1/7*log(3*x + 2)","A",0
2250,1,21,0,0.421616," ","integrate(1/(15*x^3+13*x^2+2*x),x, algorithm=""fricas"")","-\frac{5}{7} \, \log\left(5 \, x + 1\right) + \frac{3}{14} \, \log\left(3 \, x + 2\right) + \frac{1}{2} \, \log\left(x\right)"," ",0,"-5/7*log(5*x + 1) + 3/14*log(3*x + 2) + 1/2*log(x)","A",0
2251,1,30,0,0.418853," ","integrate(1/x/(15*x^3+13*x^2+2*x),x, algorithm=""fricas"")","\frac{100 \, x \log\left(5 \, x + 1\right) - 9 \, x \log\left(3 \, x + 2\right) - 91 \, x \log\left(x\right) - 14}{28 \, x}"," ",0,"1/28*(100*x*log(5*x + 1) - 9*x*log(3*x + 2) - 91*x*log(x) - 14)/x","A",0
2252,1,39,0,0.409958," ","integrate(1/x^2/(15*x^3+13*x^2+2*x),x, algorithm=""fricas"")","-\frac{1000 \, x^{2} \log\left(5 \, x + 1\right) - 27 \, x^{2} \log\left(3 \, x + 2\right) - 973 \, x^{2} \log\left(x\right) - 182 \, x + 14}{56 \, x^{2}}"," ",0,"-1/56*(1000*x^2*log(5*x + 1) - 27*x^2*log(3*x + 2) - 973*x^2*log(x) - 182*x + 14)/x^2","A",0
2253,1,44,0,0.410240," ","integrate(1/x^3/(15*x^3+13*x^2+2*x),x, algorithm=""fricas"")","\frac{30000 \, x^{3} \log\left(5 \, x + 1\right) - 243 \, x^{3} \log\left(3 \, x + 2\right) - 29757 \, x^{3} \log\left(x\right) - 5838 \, x^{2} + 546 \, x - 56}{336 \, x^{3}}"," ",0,"1/336*(30000*x^3*log(5*x + 1) - 243*x^3*log(3*x + 2) - 29757*x^3*log(x) - 5838*x^2 + 546*x - 56)/x^3","A",0
2254,1,16,0,0.390201," ","integrate(x/(x^2+4*x+4),x, algorithm=""fricas"")","\frac{{\left(x + 2\right)} \log\left(x + 2\right) + 2}{x + 2}"," ",0,"((x + 2)*log(x + 2) + 2)/(x + 2)","A",0
2255,1,20,0,0.415557," ","integrate(x/(x^2+2*x+5),x, algorithm=""fricas"")","-\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
2256,1,13,0,0.394163," ","integrate(x/(x^2-5*x+6),x, algorithm=""fricas"")","-2 \, \log\left(x - 2\right) + 3 \, \log\left(x - 3\right)"," ",0,"-2*log(x - 2) + 3*log(x - 3)","A",0
2257,1,28,0,0.381660," ","integrate(x/(x^2+2*x+2)^2,x, algorithm=""fricas"")","-\frac{{\left(x^{2} + 2 \, x + 2\right)} \arctan\left(x + 1\right) + x + 2}{2 \, {\left(x^{2} + 2 \, x + 2\right)}}"," ",0,"-1/2*((x^2 + 2*x + 2)*arctan(x + 1) + x + 2)/(x^2 + 2*x + 2)","A",0
2258,1,71,0,0.389267," ","integrate(x/(x^2+x+1)^3,x, algorithm=""fricas"")","-\frac{6 \, x^{3} + 4 \, \sqrt{3} {\left(x^{4} + 2 \, x^{3} + 3 \, x^{2} + 2 \, x + 1\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + 9 \, x^{2} + 12 \, x + 9}{18 \, {\left(x^{4} + 2 \, x^{3} + 3 \, x^{2} + 2 \, x + 1\right)}}"," ",0,"-1/18*(6*x^3 + 4*sqrt(3)*(x^4 + 2*x^3 + 3*x^2 + 2*x + 1)*arctan(1/3*sqrt(3)*(2*x + 1)) + 9*x^2 + 12*x + 9)/(x^4 + 2*x^3 + 3*x^2 + 2*x + 1)","A",0
2259,1,27,0,0.407113," ","integrate(x^2/(x^2+x+1),x, algorithm=""fricas"")","-\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
2260,1,14,0,0.414789," ","integrate(x^2/(x^2-3*x+2),x, algorithm=""fricas"")","x - \log\left(x - 1\right) + 4 \, \log\left(x - 2\right)"," ",0,"x - log(x - 1) + 4*log(x - 2)","A",0
2261,1,14,0,0.394254," ","integrate(x^2/(x^2+x-6),x, algorithm=""fricas"")","x - \frac{9}{5} \, \log\left(x + 3\right) + \frac{4}{5} \, \log\left(x - 2\right)"," ",0,"x - 9/5*log(x + 3) + 4/5*log(x - 2)","A",0
2262,1,26,0,0.396995," ","integrate(x^2/(x^2+2*x+2)^2,x, algorithm=""fricas"")","\frac{{\left(x^{2} + 2 \, x + 2\right)} \arctan\left(x + 1\right) + 1}{x^{2} + 2 \, x + 2}"," ",0,"((x^2 + 2*x + 2)*arctan(x + 1) + 1)/(x^2 + 2*x + 2)","A",0
2263,1,21,0,0.414817," ","integrate(x^3/(x^2-3*x+2),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} + 3 \, x - \log\left(x - 1\right) + 8 \, \log\left(x - 2\right)"," ",0,"1/2*x^2 + 3*x - log(x - 1) + 8*log(x - 2)","A",0
2264,1,29,0,0.412405," ","integrate(x^3/(x^2+2*x+1),x, algorithm=""fricas"")","\frac{x^{3} - 3 \, x^{2} + 6 \, {\left(x + 1\right)} \log\left(x + 1\right) - 4 \, x + 2}{2 \, {\left(x + 1\right)}}"," ",0,"1/2*(x^3 - 3*x^2 + 6*(x + 1)*log(x + 1) - 4*x + 2)/(x + 1)","A",0
2265,1,29,0,0.404957," ","integrate(x^3/(x^2-2*x+1),x, algorithm=""fricas"")","\frac{x^{3} + 3 \, x^{2} + 6 \, {\left(x - 1\right)} \log\left(x - 1\right) - 4 \, x - 2}{2 \, {\left(x - 1\right)}}"," ",0,"1/2*(x^3 + 3*x^2 + 6*(x - 1)*log(x - 1) - 4*x - 2)/(x - 1)","A",0
2266,1,34,0,0.410352," ","integrate(x^4/(x^2+4*x+4),x, algorithm=""fricas"")","\frac{x^{4} - 4 \, x^{3} + 24 \, x^{2} - 96 \, {\left(x + 2\right)} \log\left(x + 2\right) + 72 \, x - 48}{3 \, {\left(x + 2\right)}}"," ",0,"1/3*(x^4 - 4*x^3 + 24*x^2 - 96*(x + 2)*log(x + 2) + 72*x - 48)/(x + 2)","A",0
2267,1,28,0,0.414271," ","integrate(1/x/(x^2+x+1),x, algorithm=""fricas"")","-\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(x\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 1/2*log(x^2 + x + 1) + log(x)","A",0
2268,1,149,0,0.412515," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, c e^{5} x^{5} + 8 \, c d^{5} - 22 \, b d^{4} e + 99 \, a d^{3} e^{2} + 7 \, {\left(23 \, c d e^{4} + 11 \, b e^{5}\right)} x^{4} + {\left(113 \, c d^{2} e^{3} + 209 \, b d e^{4} + 99 \, a e^{5}\right)} x^{3} + 3 \, {\left(c d^{3} e^{2} + 55 \, b d^{2} e^{3} + 99 \, a d e^{4}\right)} x^{2} - {\left(4 \, c d^{4} e - 11 \, b d^{3} e^{2} - 297 \, a d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{693 \, e^{3}}"," ",0,"2/693*(63*c*e^5*x^5 + 8*c*d^5 - 22*b*d^4*e + 99*a*d^3*e^2 + 7*(23*c*d*e^4 + 11*b*e^5)*x^4 + (113*c*d^2*e^3 + 209*b*d*e^4 + 99*a*e^5)*x^3 + 3*(c*d^3*e^2 + 55*b*d^2*e^3 + 99*a*d*e^4)*x^2 - (4*c*d^4*e - 11*b*d^3*e^2 - 297*a*d^2*e^3)*x)*sqrt(e*x + d)/e^3","B",0
2269,1,117,0,0.403725," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c e^{4} x^{4} + 8 \, c d^{4} - 18 \, b d^{3} e + 63 \, a d^{2} e^{2} + 5 \, {\left(10 \, c d e^{3} + 9 \, b e^{4}\right)} x^{3} + 3 \, {\left(c d^{2} e^{2} + 24 \, b d e^{3} + 21 \, a e^{4}\right)} x^{2} - {\left(4 \, c d^{3} e - 9 \, b d^{2} e^{2} - 126 \, a d e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{3}}"," ",0,"2/315*(35*c*e^4*x^4 + 8*c*d^4 - 18*b*d^3*e + 63*a*d^2*e^2 + 5*(10*c*d*e^3 + 9*b*e^4)*x^3 + 3*(c*d^2*e^2 + 24*b*d*e^3 + 21*a*e^4)*x^2 - (4*c*d^3*e - 9*b*d^2*e^2 - 126*a*d*e^3)*x)*sqrt(e*x + d)/e^3","A",0
2270,1,84,0,0.412835," ","integrate((c*x^2+b*x+a)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c e^{3} x^{3} + 8 \, c d^{3} - 14 \, b d^{2} e + 35 \, a d e^{2} + 3 \, {\left(c d e^{2} + 7 \, b e^{3}\right)} x^{2} - {\left(4 \, c d^{2} e - 7 \, b d e^{2} - 35 \, a e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, e^{3}}"," ",0,"2/105*(15*c*e^3*x^3 + 8*c*d^3 - 14*b*d^2*e + 35*a*d*e^2 + 3*(c*d*e^2 + 7*b*e^3)*x^2 - (4*c*d^2*e - 7*b*d*e^2 - 35*a*e^3)*x)*sqrt(e*x + d)/e^3","A",0
2271,1,54,0,0.402641," ","integrate((c*x^2+b*x+a)/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c e^{2} x^{2} + 8 \, c d^{2} - 10 \, b d e + 15 \, a e^{2} - {\left(4 \, c d e - 5 \, b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, e^{3}}"," ",0,"2/15*(3*c*e^2*x^2 + 8*c*d^2 - 10*b*d*e + 15*a*e^2 - (4*c*d*e - 5*b*e^2)*x)*sqrt(e*x + d)/e^3","A",0
2272,1,63,0,0.416252," ","integrate((c*x^2+b*x+a)/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(c e^{2} x^{2} - 8 \, c d^{2} + 6 \, b d e - 3 \, a e^{2} - {\left(4 \, c d e - 3 \, b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{4} x + d e^{3}\right)}}"," ",0,"2/3*(c*e^2*x^2 - 8*c*d^2 + 6*b*d*e - 3*a*e^2 - (4*c*d*e - 3*b*e^2)*x)*sqrt(e*x + d)/(e^4*x + d*e^3)","A",0
2273,1,75,0,0.414830," ","integrate((c*x^2+b*x+a)/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c e^{2} x^{2} + 8 \, c d^{2} - 2 \, b d e - a e^{2} + 3 \, {\left(4 \, c d e - b e^{2}\right)} x\right)} \sqrt{e x + d}}{3 \, {\left(e^{5} x^{2} + 2 \, d e^{4} x + d^{2} e^{3}\right)}}"," ",0,"2/3*(3*c*e^2*x^2 + 8*c*d^2 - 2*b*d*e - a*e^2 + 3*(4*c*d*e - b*e^2)*x)*sqrt(e*x + d)/(e^5*x^2 + 2*d*e^4*x + d^2*e^3)","A",0
2274,1,85,0,0.413047," ","integrate((c*x^2+b*x+a)/(e*x+d)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, c e^{2} x^{2} + 8 \, c d^{2} + 2 \, b d e + 3 \, a e^{2} + 5 \, {\left(4 \, c d e + b e^{2}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{6} x^{3} + 3 \, d e^{5} x^{2} + 3 \, d^{2} e^{4} x + d^{3} e^{3}\right)}}"," ",0,"-2/15*(15*c*e^2*x^2 + 8*c*d^2 + 2*b*d*e + 3*a*e^2 + 5*(4*c*d*e + b*e^2)*x)*sqrt(e*x + d)/(e^6*x^3 + 3*d*e^5*x^2 + 3*d^2*e^4*x + d^3*e^3)","A",0
2275,1,365,0,0.415518," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, c^{2} e^{7} x^{7} + 128 \, c^{2} d^{7} - 480 \, b c d^{6} e - 2860 \, a b d^{4} e^{3} + 6435 \, a^{2} d^{3} e^{4} + 520 \, {\left(b^{2} + 2 \, a c\right)} d^{5} e^{2} + 231 \, {\left(31 \, c^{2} d e^{6} + 30 \, b c e^{7}\right)} x^{6} + 63 \, {\left(71 \, c^{2} d^{2} e^{5} + 270 \, b c d e^{6} + 65 \, {\left(b^{2} + 2 \, a c\right)} e^{7}\right)} x^{5} + 35 \, {\left(c^{2} d^{3} e^{4} + 318 \, b c d^{2} e^{5} + 286 \, a b e^{7} + 299 \, {\left(b^{2} + 2 \, a c\right)} d e^{6}\right)} x^{4} - 5 \, {\left(8 \, c^{2} d^{4} e^{3} - 30 \, b c d^{3} e^{4} - 5434 \, a b d e^{6} - 1287 \, a^{2} e^{7} - 1469 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} x^{3} + 3 \, {\left(16 \, c^{2} d^{5} e^{2} - 60 \, b c d^{4} e^{3} + 7150 \, a b d^{2} e^{5} + 6435 \, a^{2} d e^{6} + 65 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} x^{2} - {\left(64 \, c^{2} d^{6} e - 240 \, b c d^{5} e^{2} - 1430 \, a b d^{3} e^{4} - 19305 \, a^{2} d^{2} e^{5} + 260 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{5}}"," ",0,"2/45045*(3003*c^2*e^7*x^7 + 128*c^2*d^7 - 480*b*c*d^6*e - 2860*a*b*d^4*e^3 + 6435*a^2*d^3*e^4 + 520*(b^2 + 2*a*c)*d^5*e^2 + 231*(31*c^2*d*e^6 + 30*b*c*e^7)*x^6 + 63*(71*c^2*d^2*e^5 + 270*b*c*d*e^6 + 65*(b^2 + 2*a*c)*e^7)*x^5 + 35*(c^2*d^3*e^4 + 318*b*c*d^2*e^5 + 286*a*b*e^7 + 299*(b^2 + 2*a*c)*d*e^6)*x^4 - 5*(8*c^2*d^4*e^3 - 30*b*c*d^3*e^4 - 5434*a*b*d*e^6 - 1287*a^2*e^7 - 1469*(b^2 + 2*a*c)*d^2*e^5)*x^3 + 3*(16*c^2*d^5*e^2 - 60*b*c*d^4*e^3 + 7150*a*b*d^2*e^5 + 6435*a^2*d*e^6 + 65*(b^2 + 2*a*c)*d^3*e^4)*x^2 - (64*c^2*d^6*e - 240*b*c*d^5*e^2 - 1430*a*b*d^3*e^4 - 19305*a^2*d^2*e^5 + 260*(b^2 + 2*a*c)*d^4*e^3)*x)*sqrt(e*x + d)/e^5","B",0
2276,1,302,0,0.410131," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, c^{2} e^{6} x^{6} + 384 \, c^{2} d^{6} - 1248 \, b c d^{5} e - 5148 \, a b d^{3} e^{3} + 9009 \, a^{2} d^{2} e^{4} + 1144 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{2} + 630 \, {\left(7 \, c^{2} d e^{5} + 13 \, b c e^{6}\right)} x^{5} + 35 \, {\left(3 \, c^{2} d^{2} e^{4} + 312 \, b c d e^{5} + 143 \, {\left(b^{2} + 2 \, a c\right)} e^{6}\right)} x^{4} - 10 \, {\left(12 \, c^{2} d^{3} e^{3} - 39 \, b c d^{2} e^{4} - 1287 \, a b e^{6} - 715 \, {\left(b^{2} + 2 \, a c\right)} d e^{5}\right)} x^{3} + 3 \, {\left(48 \, c^{2} d^{4} e^{2} - 156 \, b c d^{3} e^{3} + 6864 \, a b d e^{5} + 3003 \, a^{2} e^{6} + 143 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} x^{2} - 2 \, {\left(96 \, c^{2} d^{5} e - 312 \, b c d^{4} e^{2} - 1287 \, a b d^{2} e^{4} - 9009 \, a^{2} d e^{5} + 286 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{5}}"," ",0,"2/45045*(3465*c^2*e^6*x^6 + 384*c^2*d^6 - 1248*b*c*d^5*e - 5148*a*b*d^3*e^3 + 9009*a^2*d^2*e^4 + 1144*(b^2 + 2*a*c)*d^4*e^2 + 630*(7*c^2*d*e^5 + 13*b*c*e^6)*x^5 + 35*(3*c^2*d^2*e^4 + 312*b*c*d*e^5 + 143*(b^2 + 2*a*c)*e^6)*x^4 - 10*(12*c^2*d^3*e^3 - 39*b*c*d^2*e^4 - 1287*a*b*e^6 - 715*(b^2 + 2*a*c)*d*e^5)*x^3 + 3*(48*c^2*d^4*e^2 - 156*b*c*d^3*e^3 + 6864*a*b*d*e^5 + 3003*a^2*e^6 + 143*(b^2 + 2*a*c)*d^2*e^4)*x^2 - 2*(96*c^2*d^5*e - 312*b*c*d^4*e^2 - 1287*a*b*d^2*e^4 - 9009*a^2*d*e^5 + 286*(b^2 + 2*a*c)*d^3*e^3)*x)*sqrt(e*x + d)/e^5","B",0
2277,1,237,0,0.406692," ","integrate((c*x^2+b*x+a)^2*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, c^{2} e^{5} x^{5} + 128 \, c^{2} d^{5} - 352 \, b c d^{4} e - 924 \, a b d^{2} e^{3} + 1155 \, a^{2} d e^{4} + 264 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + 35 \, {\left(c^{2} d e^{4} + 22 \, b c e^{5}\right)} x^{4} - 5 \, {\left(8 \, c^{2} d^{2} e^{3} - 22 \, b c d e^{4} - 99 \, {\left(b^{2} + 2 \, a c\right)} e^{5}\right)} x^{3} + 3 \, {\left(16 \, c^{2} d^{3} e^{2} - 44 \, b c d^{2} e^{3} + 462 \, a b e^{5} + 33 \, {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} x^{2} - {\left(64 \, c^{2} d^{4} e - 176 \, b c d^{3} e^{2} - 462 \, a b d e^{4} - 1155 \, a^{2} e^{5} + 132 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{e x + d}}{3465 \, e^{5}}"," ",0,"2/3465*(315*c^2*e^5*x^5 + 128*c^2*d^5 - 352*b*c*d^4*e - 924*a*b*d^2*e^3 + 1155*a^2*d*e^4 + 264*(b^2 + 2*a*c)*d^3*e^2 + 35*(c^2*d*e^4 + 22*b*c*e^5)*x^4 - 5*(8*c^2*d^2*e^3 - 22*b*c*d*e^4 - 99*(b^2 + 2*a*c)*e^5)*x^3 + 3*(16*c^2*d^3*e^2 - 44*b*c*d^2*e^3 + 462*a*b*e^5 + 33*(b^2 + 2*a*c)*d*e^4)*x^2 - (64*c^2*d^4*e - 176*b*c*d^3*e^2 - 462*a*b*d*e^4 - 1155*a^2*e^5 + 132*(b^2 + 2*a*c)*d^2*e^3)*x)*sqrt(e*x + d)/e^5","A",0
2278,1,176,0,0.419080," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{2} e^{4} x^{4} + 128 \, c^{2} d^{4} - 288 \, b c d^{3} e - 420 \, a b d e^{3} + 315 \, a^{2} e^{4} + 168 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} - 10 \, {\left(4 \, c^{2} d e^{3} - 9 \, b c e^{4}\right)} x^{3} + 3 \, {\left(16 \, c^{2} d^{2} e^{2} - 36 \, b c d e^{3} + 21 \, {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} - 2 \, {\left(32 \, c^{2} d^{3} e - 72 \, b c d^{2} e^{2} - 105 \, a b e^{4} + 42 \, {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{e x + d}}{315 \, e^{5}}"," ",0,"2/315*(35*c^2*e^4*x^4 + 128*c^2*d^4 - 288*b*c*d^3*e - 420*a*b*d*e^3 + 315*a^2*e^4 + 168*(b^2 + 2*a*c)*d^2*e^2 - 10*(4*c^2*d*e^3 - 9*b*c*e^4)*x^3 + 3*(16*c^2*d^2*e^2 - 36*b*c*d*e^3 + 21*(b^2 + 2*a*c)*e^4)*x^2 - 2*(32*c^2*d^3*e - 72*b*c*d^2*e^2 - 105*a*b*e^4 + 42*(b^2 + 2*a*c)*d*e^3)*x)*sqrt(e*x + d)/e^5","A",0
2279,1,185,0,0.415575," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, c^{2} e^{4} x^{4} - 384 \, c^{2} d^{4} + 672 \, b c d^{3} e + 420 \, a b d e^{3} - 105 \, a^{2} e^{4} - 280 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} - 6 \, {\left(4 \, c^{2} d e^{3} - 7 \, b c e^{4}\right)} x^{3} + {\left(48 \, c^{2} d^{2} e^{2} - 84 \, b c d e^{3} + 35 \, {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} - 2 \, {\left(96 \, c^{2} d^{3} e - 168 \, b c d^{2} e^{2} - 105 \, a b e^{4} + 70 \, {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{e x + d}}{105 \, {\left(e^{6} x + d e^{5}\right)}}"," ",0,"2/105*(15*c^2*e^4*x^4 - 384*c^2*d^4 + 672*b*c*d^3*e + 420*a*b*d*e^3 - 105*a^2*e^4 - 280*(b^2 + 2*a*c)*d^2*e^2 - 6*(4*c^2*d*e^3 - 7*b*c*e^4)*x^3 + (48*c^2*d^2*e^2 - 84*b*c*d*e^3 + 35*(b^2 + 2*a*c)*e^4)*x^2 - 2*(96*c^2*d^3*e - 168*b*c*d^2*e^2 - 105*a*b*e^4 + 70*(b^2 + 2*a*c)*d*e^3)*x)*sqrt(e*x + d)/(e^6*x + d*e^5)","A",0
2280,1,197,0,0.420865," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, c^{2} e^{4} x^{4} + 128 \, c^{2} d^{4} - 160 \, b c d^{3} e - 20 \, a b d e^{3} - 5 \, a^{2} e^{4} + 40 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} - 2 \, {\left(4 \, c^{2} d e^{3} - 5 \, b c e^{4}\right)} x^{3} + 3 \, {\left(16 \, c^{2} d^{2} e^{2} - 20 \, b c d e^{3} + 5 \, {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} + 6 \, {\left(32 \, c^{2} d^{3} e - 40 \, b c d^{2} e^{2} - 5 \, a b e^{4} + 10 \, {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{7} x^{2} + 2 \, d e^{6} x + d^{2} e^{5}\right)}}"," ",0,"2/15*(3*c^2*e^4*x^4 + 128*c^2*d^4 - 160*b*c*d^3*e - 20*a*b*d*e^3 - 5*a^2*e^4 + 40*(b^2 + 2*a*c)*d^2*e^2 - 2*(4*c^2*d*e^3 - 5*b*c*e^4)*x^3 + 3*(16*c^2*d^2*e^2 - 20*b*c*d*e^3 + 5*(b^2 + 2*a*c)*e^4)*x^2 + 6*(32*c^2*d^3*e - 40*b*c*d^2*e^2 - 5*a*b*e^4 + 10*(b^2 + 2*a*c)*d*e^3)*x)*sqrt(e*x + d)/(e^7*x^2 + 2*d*e^6*x + d^2*e^5)","A",0
2281,1,206,0,0.403398," ","integrate((c*x^2+b*x+a)^2/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{2} e^{4} x^{4} - 128 \, c^{2} d^{4} + 96 \, b c d^{3} e - 4 \, a b d e^{3} - 3 \, a^{2} e^{4} - 8 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2} - 10 \, {\left(4 \, c^{2} d e^{3} - 3 \, b c e^{4}\right)} x^{3} - 15 \, {\left(16 \, c^{2} d^{2} e^{2} - 12 \, b c d e^{3} + {\left(b^{2} + 2 \, a c\right)} e^{4}\right)} x^{2} - 10 \, {\left(32 \, c^{2} d^{3} e - 24 \, b c d^{2} e^{2} + a b e^{4} + 2 \, {\left(b^{2} + 2 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{e x + d}}{15 \, {\left(e^{8} x^{3} + 3 \, d e^{7} x^{2} + 3 \, d^{2} e^{6} x + d^{3} e^{5}\right)}}"," ",0,"2/15*(5*c^2*e^4*x^4 - 128*c^2*d^4 + 96*b*c*d^3*e - 4*a*b*d*e^3 - 3*a^2*e^4 - 8*(b^2 + 2*a*c)*d^2*e^2 - 10*(4*c^2*d*e^3 - 3*b*c*e^4)*x^3 - 15*(16*c^2*d^2*e^2 - 12*b*c*d*e^3 + (b^2 + 2*a*c)*e^4)*x^2 - 10*(32*c^2*d^3*e - 24*b*c*d^2*e^2 + a*b*e^4 + 2*(b^2 + 2*a*c)*d*e^3)*x)*sqrt(e*x + d)/(e^8*x^3 + 3*d*e^7*x^2 + 3*d^2*e^6*x + d^3*e^5)","A",0
2282,1,727,0,0.408195," ","integrate((e*x+d)^(5/2)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(255255 \, c^{3} e^{9} x^{9} + 5120 \, c^{3} d^{9} - 24320 \, b c^{2} d^{8} e - 461890 \, a^{2} b d^{4} e^{5} + 692835 \, a^{3} d^{3} e^{6} + 41344 \, {\left(b^{2} c + a c^{2}\right)} d^{7} e^{2} - 25840 \, {\left(b^{3} + 6 \, a b c\right)} d^{6} e^{3} + 167960 \, {\left(a b^{2} + a^{2} c\right)} d^{5} e^{4} + 45045 \, {\left(13 \, c^{3} d e^{8} + 19 \, b c^{2} e^{9}\right)} x^{8} + 3003 \, {\left(115 \, c^{3} d^{2} e^{7} + 665 \, b c^{2} d e^{8} + 323 \, {\left(b^{2} c + a c^{2}\right)} e^{9}\right)} x^{7} + 231 \, {\left(5 \, c^{3} d^{3} e^{6} + 5225 \, b c^{2} d^{2} e^{7} + 10013 \, {\left(b^{2} c + a c^{2}\right)} d e^{8} + 1615 \, {\left(b^{3} + 6 \, a b c\right)} e^{9}\right)} x^{6} - 63 \, {\left(20 \, c^{3} d^{4} e^{5} - 95 \, b c^{2} d^{3} e^{6} - 22933 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{7} - 14535 \, {\left(b^{3} + 6 \, a b c\right)} d e^{8} - 20995 \, {\left(a b^{2} + a^{2} c\right)} e^{9}\right)} x^{5} + 35 \, {\left(40 \, c^{3} d^{5} e^{4} - 190 \, b c^{2} d^{4} e^{5} + 46189 \, a^{2} b e^{9} + 323 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{6} + 17119 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{7} + 96577 \, {\left(a b^{2} + a^{2} c\right)} d e^{8}\right)} x^{4} - 5 \, {\left(320 \, c^{3} d^{6} e^{3} - 1520 \, b c^{2} d^{5} e^{4} - 877591 \, a^{2} b d e^{8} - 138567 \, a^{3} e^{9} + 2584 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{5} - 1615 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{6} - 474487 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{7}\right)} x^{3} + 3 \, {\left(640 \, c^{3} d^{7} e^{2} - 3040 \, b c^{2} d^{6} e^{3} + 1154725 \, a^{2} b d^{2} e^{7} + 692835 \, a^{3} d e^{8} + 5168 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{4} - 3230 \, {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{5} + 20995 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{6}\right)} x^{2} - {\left(2560 \, c^{3} d^{8} e - 12160 \, b c^{2} d^{7} e^{2} - 230945 \, a^{2} b d^{3} e^{6} - 2078505 \, a^{3} d^{2} e^{7} + 20672 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{3} - 12920 \, {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{4} + 83980 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{5}\right)} x\right)} \sqrt{e x + d}}{4849845 \, e^{7}}"," ",0,"2/4849845*(255255*c^3*e^9*x^9 + 5120*c^3*d^9 - 24320*b*c^2*d^8*e - 461890*a^2*b*d^4*e^5 + 692835*a^3*d^3*e^6 + 41344*(b^2*c + a*c^2)*d^7*e^2 - 25840*(b^3 + 6*a*b*c)*d^6*e^3 + 167960*(a*b^2 + a^2*c)*d^5*e^4 + 45045*(13*c^3*d*e^8 + 19*b*c^2*e^9)*x^8 + 3003*(115*c^3*d^2*e^7 + 665*b*c^2*d*e^8 + 323*(b^2*c + a*c^2)*e^9)*x^7 + 231*(5*c^3*d^3*e^6 + 5225*b*c^2*d^2*e^7 + 10013*(b^2*c + a*c^2)*d*e^8 + 1615*(b^3 + 6*a*b*c)*e^9)*x^6 - 63*(20*c^3*d^4*e^5 - 95*b*c^2*d^3*e^6 - 22933*(b^2*c + a*c^2)*d^2*e^7 - 14535*(b^3 + 6*a*b*c)*d*e^8 - 20995*(a*b^2 + a^2*c)*e^9)*x^5 + 35*(40*c^3*d^5*e^4 - 190*b*c^2*d^4*e^5 + 46189*a^2*b*e^9 + 323*(b^2*c + a*c^2)*d^3*e^6 + 17119*(b^3 + 6*a*b*c)*d^2*e^7 + 96577*(a*b^2 + a^2*c)*d*e^8)*x^4 - 5*(320*c^3*d^6*e^3 - 1520*b*c^2*d^5*e^4 - 877591*a^2*b*d*e^8 - 138567*a^3*e^9 + 2584*(b^2*c + a*c^2)*d^4*e^5 - 1615*(b^3 + 6*a*b*c)*d^3*e^6 - 474487*(a*b^2 + a^2*c)*d^2*e^7)*x^3 + 3*(640*c^3*d^7*e^2 - 3040*b*c^2*d^6*e^3 + 1154725*a^2*b*d^2*e^7 + 692835*a^3*d*e^8 + 5168*(b^2*c + a*c^2)*d^5*e^4 - 3230*(b^3 + 6*a*b*c)*d^4*e^5 + 20995*(a*b^2 + a^2*c)*d^3*e^6)*x^2 - (2560*c^3*d^8*e - 12160*b*c^2*d^7*e^2 - 230945*a^2*b*d^3*e^6 - 2078505*a^3*d^2*e^7 + 20672*(b^2*c + a*c^2)*d^6*e^3 - 12920*(b^3 + 6*a*b*c)*d^5*e^4 + 83980*(a*b^2 + a^2*c)*d^4*e^5)*x)*sqrt(e*x + d)/e^7","B",0
2283,1,619,0,0.403417," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(15015 \, c^{3} e^{8} x^{8} + 1024 \, c^{3} d^{8} - 4352 \, b c^{2} d^{7} e - 43758 \, a^{2} b d^{3} e^{5} + 51051 \, a^{3} d^{2} e^{6} + 6528 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{2} - 3536 \, {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{3} + 19448 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{4} + 3003 \, {\left(6 \, c^{3} d e^{7} + 17 \, b c^{2} e^{8}\right)} x^{7} + 231 \, {\left(c^{3} d^{2} e^{6} + 272 \, b c^{2} d e^{7} + 255 \, {\left(b^{2} c + a c^{2}\right)} e^{8}\right)} x^{6} - 21 \, {\left(12 \, c^{3} d^{3} e^{5} - 51 \, b c^{2} d^{2} e^{6} - 3570 \, {\left(b^{2} c + a c^{2}\right)} d e^{7} - 1105 \, {\left(b^{3} + 6 \, a b c\right)} e^{8}\right)} x^{5} + 35 \, {\left(8 \, c^{3} d^{4} e^{4} - 34 \, b c^{2} d^{3} e^{5} + 51 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{6} + 884 \, {\left(b^{3} + 6 \, a b c\right)} d e^{7} + 2431 \, {\left(a b^{2} + a^{2} c\right)} e^{8}\right)} x^{4} - 5 \, {\left(64 \, c^{3} d^{5} e^{3} - 272 \, b c^{2} d^{4} e^{4} - 21879 \, a^{2} b e^{8} + 408 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{5} - 221 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{6} - 24310 \, {\left(a b^{2} + a^{2} c\right)} d e^{7}\right)} x^{3} + 3 \, {\left(128 \, c^{3} d^{6} e^{2} - 544 \, b c^{2} d^{5} e^{3} + 58344 \, a^{2} b d e^{7} + 17017 \, a^{3} e^{8} + 816 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{4} - 442 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{5} + 2431 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{6}\right)} x^{2} - {\left(512 \, c^{3} d^{7} e - 2176 \, b c^{2} d^{6} e^{2} - 21879 \, a^{2} b d^{2} e^{6} - 102102 \, a^{3} d e^{7} + 3264 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{3} - 1768 \, {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{4} + 9724 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{5}\right)} x\right)} \sqrt{e x + d}}{255255 \, e^{7}}"," ",0,"2/255255*(15015*c^3*e^8*x^8 + 1024*c^3*d^8 - 4352*b*c^2*d^7*e - 43758*a^2*b*d^3*e^5 + 51051*a^3*d^2*e^6 + 6528*(b^2*c + a*c^2)*d^6*e^2 - 3536*(b^3 + 6*a*b*c)*d^5*e^3 + 19448*(a*b^2 + a^2*c)*d^4*e^4 + 3003*(6*c^3*d*e^7 + 17*b*c^2*e^8)*x^7 + 231*(c^3*d^2*e^6 + 272*b*c^2*d*e^7 + 255*(b^2*c + a*c^2)*e^8)*x^6 - 21*(12*c^3*d^3*e^5 - 51*b*c^2*d^2*e^6 - 3570*(b^2*c + a*c^2)*d*e^7 - 1105*(b^3 + 6*a*b*c)*e^8)*x^5 + 35*(8*c^3*d^4*e^4 - 34*b*c^2*d^3*e^5 + 51*(b^2*c + a*c^2)*d^2*e^6 + 884*(b^3 + 6*a*b*c)*d*e^7 + 2431*(a*b^2 + a^2*c)*e^8)*x^4 - 5*(64*c^3*d^5*e^3 - 272*b*c^2*d^4*e^4 - 21879*a^2*b*e^8 + 408*(b^2*c + a*c^2)*d^3*e^5 - 221*(b^3 + 6*a*b*c)*d^2*e^6 - 24310*(a*b^2 + a^2*c)*d*e^7)*x^3 + 3*(128*c^3*d^6*e^2 - 544*b*c^2*d^5*e^3 + 58344*a^2*b*d*e^7 + 17017*a^3*e^8 + 816*(b^2*c + a*c^2)*d^4*e^4 - 442*(b^3 + 6*a*b*c)*d^3*e^5 + 2431*(a*b^2 + a^2*c)*d^2*e^6)*x^2 - (512*c^3*d^7*e - 2176*b*c^2*d^6*e^2 - 21879*a^2*b*d^2*e^6 - 102102*a^3*d*e^7 + 3264*(b^2*c + a*c^2)*d^5*e^3 - 1768*(b^3 + 6*a*b*c)*d^4*e^4 + 9724*(a*b^2 + a^2*c)*d^3*e^5)*x)*sqrt(e*x + d)/e^7","B",0
2284,1,512,0,0.409337," ","integrate((c*x^2+b*x+a)^3*(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, c^{3} e^{7} x^{7} + 1024 \, c^{3} d^{7} - 3840 \, b c^{2} d^{6} e - 18018 \, a^{2} b d^{2} e^{5} + 15015 \, a^{3} d e^{6} + 4992 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{2} - 2288 \, {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{3} + 10296 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{4} + 231 \, {\left(c^{3} d e^{6} + 45 \, b c^{2} e^{7}\right)} x^{6} - 63 \, {\left(4 \, c^{3} d^{2} e^{5} - 15 \, b c^{2} d e^{6} - 195 \, {\left(b^{2} c + a c^{2}\right)} e^{7}\right)} x^{5} + 35 \, {\left(8 \, c^{3} d^{3} e^{4} - 30 \, b c^{2} d^{2} e^{5} + 39 \, {\left(b^{2} c + a c^{2}\right)} d e^{6} + 143 \, {\left(b^{3} + 6 \, a b c\right)} e^{7}\right)} x^{4} - 5 \, {\left(64 \, c^{3} d^{4} e^{3} - 240 \, b c^{2} d^{3} e^{4} + 312 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{5} - 143 \, {\left(b^{3} + 6 \, a b c\right)} d e^{6} - 3861 \, {\left(a b^{2} + a^{2} c\right)} e^{7}\right)} x^{3} + 3 \, {\left(128 \, c^{3} d^{5} e^{2} - 480 \, b c^{2} d^{4} e^{3} + 9009 \, a^{2} b e^{7} + 624 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{4} - 286 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{5} + 1287 \, {\left(a b^{2} + a^{2} c\right)} d e^{6}\right)} x^{2} - {\left(512 \, c^{3} d^{6} e - 1920 \, b c^{2} d^{5} e^{2} - 9009 \, a^{2} b d e^{6} - 15015 \, a^{3} e^{7} + 2496 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{3} - 1144 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{4} + 5148 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{5}\right)} x\right)} \sqrt{e x + d}}{45045 \, e^{7}}"," ",0,"2/45045*(3003*c^3*e^7*x^7 + 1024*c^3*d^7 - 3840*b*c^2*d^6*e - 18018*a^2*b*d^2*e^5 + 15015*a^3*d*e^6 + 4992*(b^2*c + a*c^2)*d^5*e^2 - 2288*(b^3 + 6*a*b*c)*d^4*e^3 + 10296*(a*b^2 + a^2*c)*d^3*e^4 + 231*(c^3*d*e^6 + 45*b*c^2*e^7)*x^6 - 63*(4*c^3*d^2*e^5 - 15*b*c^2*d*e^6 - 195*(b^2*c + a*c^2)*e^7)*x^5 + 35*(8*c^3*d^3*e^4 - 30*b*c^2*d^2*e^5 + 39*(b^2*c + a*c^2)*d*e^6 + 143*(b^3 + 6*a*b*c)*e^7)*x^4 - 5*(64*c^3*d^4*e^3 - 240*b*c^2*d^3*e^4 + 312*(b^2*c + a*c^2)*d^2*e^5 - 143*(b^3 + 6*a*b*c)*d*e^6 - 3861*(a*b^2 + a^2*c)*e^7)*x^3 + 3*(128*c^3*d^5*e^2 - 480*b*c^2*d^4*e^3 + 9009*a^2*b*e^7 + 624*(b^2*c + a*c^2)*d^3*e^4 - 286*(b^3 + 6*a*b*c)*d^2*e^5 + 1287*(a*b^2 + a^2*c)*d*e^6)*x^2 - (512*c^3*d^6*e - 1920*b*c^2*d^5*e^2 - 9009*a^2*b*d*e^6 - 15015*a^3*e^7 + 2496*(b^2*c + a*c^2)*d^4*e^3 - 1144*(b^3 + 6*a*b*c)*d^3*e^4 + 5148*(a*b^2 + a^2*c)*d^2*e^5)*x)*sqrt(e*x + d)/e^7","A",0
2285,1,408,0,0.409604," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, c^{3} e^{6} x^{6} + 5120 \, c^{3} d^{6} - 16640 \, b c^{2} d^{5} e - 30030 \, a^{2} b d e^{5} + 15015 \, a^{3} e^{6} + 18304 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - 6864 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 24024 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} - 315 \, {\left(4 \, c^{3} d e^{5} - 13 \, b c^{2} e^{6}\right)} x^{5} + 35 \, {\left(40 \, c^{3} d^{2} e^{4} - 130 \, b c^{2} d e^{5} + 143 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} - 5 \, {\left(320 \, c^{3} d^{3} e^{3} - 1040 \, b c^{2} d^{2} e^{4} + 1144 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} - 429 \, {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + 3 \, {\left(640 \, c^{3} d^{4} e^{2} - 2080 \, b c^{2} d^{3} e^{3} + 2288 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - 858 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 3003 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} - {\left(2560 \, c^{3} d^{5} e - 8320 \, b c^{2} d^{4} e^{2} - 15015 \, a^{2} b e^{6} + 9152 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - 3432 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 12012 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x\right)} \sqrt{e x + d}}{15015 \, e^{7}}"," ",0,"2/15015*(1155*c^3*e^6*x^6 + 5120*c^3*d^6 - 16640*b*c^2*d^5*e - 30030*a^2*b*d*e^5 + 15015*a^3*e^6 + 18304*(b^2*c + a*c^2)*d^4*e^2 - 6864*(b^3 + 6*a*b*c)*d^3*e^3 + 24024*(a*b^2 + a^2*c)*d^2*e^4 - 315*(4*c^3*d*e^5 - 13*b*c^2*e^6)*x^5 + 35*(40*c^3*d^2*e^4 - 130*b*c^2*d*e^5 + 143*(b^2*c + a*c^2)*e^6)*x^4 - 5*(320*c^3*d^3*e^3 - 1040*b*c^2*d^2*e^4 + 1144*(b^2*c + a*c^2)*d*e^5 - 429*(b^3 + 6*a*b*c)*e^6)*x^3 + 3*(640*c^3*d^4*e^2 - 2080*b*c^2*d^3*e^3 + 2288*(b^2*c + a*c^2)*d^2*e^4 - 858*(b^3 + 6*a*b*c)*d*e^5 + 3003*(a*b^2 + a^2*c)*e^6)*x^2 - (2560*c^3*d^5*e - 8320*b*c^2*d^4*e^2 - 15015*a^2*b*e^6 + 9152*(b^2*c + a*c^2)*d^3*e^3 - 3432*(b^3 + 6*a*b*c)*d^2*e^4 + 12012*(a*b^2 + a^2*c)*d*e^5)*x)*sqrt(e*x + d)/e^7","A",0
2286,1,417,0,0.409141," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, c^{3} e^{6} x^{6} - 5120 \, c^{3} d^{6} + 14080 \, b c^{2} d^{5} e + 6930 \, a^{2} b d e^{5} - 1155 \, a^{3} e^{6} - 12672 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + 3696 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 9240 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} - 35 \, {\left(4 \, c^{3} d e^{5} - 11 \, b c^{2} e^{6}\right)} x^{5} + 5 \, {\left(40 \, c^{3} d^{2} e^{4} - 110 \, b c^{2} d e^{5} + 99 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} - {\left(320 \, c^{3} d^{3} e^{3} - 880 \, b c^{2} d^{2} e^{4} + 792 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} - 231 \, {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + {\left(640 \, c^{3} d^{4} e^{2} - 1760 \, b c^{2} d^{3} e^{3} + 1584 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - 462 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 1155 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} - {\left(2560 \, c^{3} d^{5} e - 7040 \, b c^{2} d^{4} e^{2} - 3465 \, a^{2} b e^{6} + 6336 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - 1848 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 4620 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x\right)} \sqrt{e x + d}}{1155 \, {\left(e^{8} x + d e^{7}\right)}}"," ",0,"2/1155*(105*c^3*e^6*x^6 - 5120*c^3*d^6 + 14080*b*c^2*d^5*e + 6930*a^2*b*d*e^5 - 1155*a^3*e^6 - 12672*(b^2*c + a*c^2)*d^4*e^2 + 3696*(b^3 + 6*a*b*c)*d^3*e^3 - 9240*(a*b^2 + a^2*c)*d^2*e^4 - 35*(4*c^3*d*e^5 - 11*b*c^2*e^6)*x^5 + 5*(40*c^3*d^2*e^4 - 110*b*c^2*d*e^5 + 99*(b^2*c + a*c^2)*e^6)*x^4 - (320*c^3*d^3*e^3 - 880*b*c^2*d^2*e^4 + 792*(b^2*c + a*c^2)*d*e^5 - 231*(b^3 + 6*a*b*c)*e^6)*x^3 + (640*c^3*d^4*e^2 - 1760*b*c^2*d^3*e^3 + 1584*(b^2*c + a*c^2)*d^2*e^4 - 462*(b^3 + 6*a*b*c)*d*e^5 + 1155*(a*b^2 + a^2*c)*e^6)*x^2 - (2560*c^3*d^5*e - 7040*b*c^2*d^4*e^2 - 3465*a^2*b*e^6 + 6336*(b^2*c + a*c^2)*d^3*e^3 - 1848*(b^3 + 6*a*b*c)*d^2*e^4 + 4620*(a*b^2 + a^2*c)*d*e^5)*x)*sqrt(e*x + d)/(e^8*x + d*e^7)","A",0
2287,1,429,0,0.409530," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, c^{3} e^{6} x^{6} + 5120 \, c^{3} d^{6} - 11520 \, b c^{2} d^{5} e - 630 \, a^{2} b d e^{5} - 105 \, a^{3} e^{6} + 8064 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} - 1680 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} + 2520 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} - 15 \, {\left(4 \, c^{3} d e^{5} - 9 \, b c^{2} e^{6}\right)} x^{5} + 3 \, {\left(40 \, c^{3} d^{2} e^{4} - 90 \, b c^{2} d e^{5} + 63 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} - {\left(320 \, c^{3} d^{3} e^{3} - 720 \, b c^{2} d^{2} e^{4} + 504 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} - 105 \, {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} + 3 \, {\left(640 \, c^{3} d^{4} e^{2} - 1440 \, b c^{2} d^{3} e^{3} + 1008 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - 210 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 315 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} + 3 \, {\left(2560 \, c^{3} d^{5} e - 5760 \, b c^{2} d^{4} e^{2} - 315 \, a^{2} b e^{6} + 4032 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - 840 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 1260 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x\right)} \sqrt{e x + d}}{315 \, {\left(e^{9} x^{2} + 2 \, d e^{8} x + d^{2} e^{7}\right)}}"," ",0,"2/315*(35*c^3*e^6*x^6 + 5120*c^3*d^6 - 11520*b*c^2*d^5*e - 630*a^2*b*d*e^5 - 105*a^3*e^6 + 8064*(b^2*c + a*c^2)*d^4*e^2 - 1680*(b^3 + 6*a*b*c)*d^3*e^3 + 2520*(a*b^2 + a^2*c)*d^2*e^4 - 15*(4*c^3*d*e^5 - 9*b*c^2*e^6)*x^5 + 3*(40*c^3*d^2*e^4 - 90*b*c^2*d*e^5 + 63*(b^2*c + a*c^2)*e^6)*x^4 - (320*c^3*d^3*e^3 - 720*b*c^2*d^2*e^4 + 504*(b^2*c + a*c^2)*d*e^5 - 105*(b^3 + 6*a*b*c)*e^6)*x^3 + 3*(640*c^3*d^4*e^2 - 1440*b*c^2*d^3*e^3 + 1008*(b^2*c + a*c^2)*d^2*e^4 - 210*(b^3 + 6*a*b*c)*d*e^5 + 315*(a*b^2 + a^2*c)*e^6)*x^2 + 3*(2560*c^3*d^5*e - 5760*b*c^2*d^4*e^2 - 315*a^2*b*e^6 + 4032*(b^2*c + a*c^2)*d^3*e^3 - 840*(b^3 + 6*a*b*c)*d^2*e^4 + 1260*(a*b^2 + a^2*c)*d*e^5)*x)*sqrt(e*x + d)/(e^9*x^2 + 2*d*e^8*x + d^2*e^7)","A",0
2288,1,440,0,0.428476," ","integrate((c*x^2+b*x+a)^3/(e*x+d)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, c^{3} e^{6} x^{6} - 1024 \, c^{3} d^{6} + 1792 \, b c^{2} d^{5} e - 14 \, a^{2} b d e^{5} - 7 \, a^{3} e^{6} - 896 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{2} + 112 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{3} - 56 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{4} - 3 \, {\left(4 \, c^{3} d e^{5} - 7 \, b c^{2} e^{6}\right)} x^{5} + 5 \, {\left(8 \, c^{3} d^{2} e^{4} - 14 \, b c^{2} d e^{5} + 7 \, {\left(b^{2} c + a c^{2}\right)} e^{6}\right)} x^{4} - 5 \, {\left(64 \, c^{3} d^{3} e^{3} - 112 \, b c^{2} d^{2} e^{4} + 56 \, {\left(b^{2} c + a c^{2}\right)} d e^{5} - 7 \, {\left(b^{3} + 6 \, a b c\right)} e^{6}\right)} x^{3} - 15 \, {\left(128 \, c^{3} d^{4} e^{2} - 224 \, b c^{2} d^{3} e^{3} + 112 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{4} - 14 \, {\left(b^{3} + 6 \, a b c\right)} d e^{5} + 7 \, {\left(a b^{2} + a^{2} c\right)} e^{6}\right)} x^{2} - 5 \, {\left(512 \, c^{3} d^{5} e - 896 \, b c^{2} d^{4} e^{2} + 7 \, a^{2} b e^{6} + 448 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{3} - 56 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{4} + 28 \, {\left(a b^{2} + a^{2} c\right)} d e^{5}\right)} x\right)} \sqrt{e x + d}}{35 \, {\left(e^{10} x^{3} + 3 \, d e^{9} x^{2} + 3 \, d^{2} e^{8} x + d^{3} e^{7}\right)}}"," ",0,"2/35*(5*c^3*e^6*x^6 - 1024*c^3*d^6 + 1792*b*c^2*d^5*e - 14*a^2*b*d*e^5 - 7*a^3*e^6 - 896*(b^2*c + a*c^2)*d^4*e^2 + 112*(b^3 + 6*a*b*c)*d^3*e^3 - 56*(a*b^2 + a^2*c)*d^2*e^4 - 3*(4*c^3*d*e^5 - 7*b*c^2*e^6)*x^5 + 5*(8*c^3*d^2*e^4 - 14*b*c^2*d*e^5 + 7*(b^2*c + a*c^2)*e^6)*x^4 - 5*(64*c^3*d^3*e^3 - 112*b*c^2*d^2*e^4 + 56*(b^2*c + a*c^2)*d*e^5 - 7*(b^3 + 6*a*b*c)*e^6)*x^3 - 15*(128*c^3*d^4*e^2 - 224*b*c^2*d^3*e^3 + 112*(b^2*c + a*c^2)*d^2*e^4 - 14*(b^3 + 6*a*b*c)*d*e^5 + 7*(a*b^2 + a^2*c)*e^6)*x^2 - 5*(512*c^3*d^5*e - 896*b*c^2*d^4*e^2 + 7*a^2*b*e^6 + 448*(b^2*c + a*c^2)*d^3*e^3 - 56*(b^3 + 6*a*b*c)*d^2*e^4 + 28*(a*b^2 + a^2*c)*d*e^5)*x)*sqrt(e*x + d)/(e^10*x^3 + 3*d*e^9*x^2 + 3*d^2*e^8*x + d^3*e^7)","A",0
2289,1,6701,0,2.093325," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} c^{2} \sqrt{\frac{2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(\sqrt{2} {\left(10 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{5} e^{2} - 25 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e^{3} + 10 \, {\left(3 \, b^{4} c^{3} - 14 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} e^{4} - 10 \, {\left(2 \, b^{5} c^{2} - 11 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} d^{2} e^{5} + {\left(7 \, b^{6} c - 44 \, a b^{4} c^{2} + 66 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{7} - {\left(2 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{2} - 2 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d e + {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} + 4 \, {\left(5 \, c^{6} d^{8} e - 20 \, b c^{5} d^{7} e^{2} + 35 \, b^{2} c^{4} d^{6} e^{3} - 35 \, b^{3} c^{3} d^{5} e^{4} + 7 \, {\left(3 \, b^{4} c^{2} + a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{4} e^{5} - 7 \, {\left(b^{5} c + 2 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{6} + {\left(b^{6} + 9 \, a b^{4} c - 15 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{7} - {\left(2 \, a b^{5} - a^{2} b^{3} c - 8 \, a^{3} b c^{2}\right)} d e^{8} + {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{2} c^{2} \sqrt{\frac{2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\sqrt{2} {\left(10 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{5} e^{2} - 25 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e^{3} + 10 \, {\left(3 \, b^{4} c^{3} - 14 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} e^{4} - 10 \, {\left(2 \, b^{5} c^{2} - 11 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} d^{2} e^{5} + {\left(7 \, b^{6} c - 44 \, a b^{4} c^{2} + 66 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{7} - {\left(2 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{2} - 2 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d e + {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} + 4 \, {\left(5 \, c^{6} d^{8} e - 20 \, b c^{5} d^{7} e^{2} + 35 \, b^{2} c^{4} d^{6} e^{3} - 35 \, b^{3} c^{3} d^{5} e^{4} + 7 \, {\left(3 \, b^{4} c^{2} + a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{4} e^{5} - 7 \, {\left(b^{5} c + 2 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{6} + {\left(b^{6} + 9 \, a b^{4} c - 15 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{7} - {\left(2 \, a b^{5} - a^{2} b^{3} c - 8 \, a^{3} b c^{2}\right)} d e^{8} + {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) + 3 \, \sqrt{2} c^{2} \sqrt{\frac{2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{5} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(\sqrt{2} {\left(10 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{5} e^{2} - 25 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e^{3} + 10 \, {\left(3 \, b^{4} c^{3} - 14 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} e^{4} - 10 \, {\left(2 \, b^{5} c^{2} - 11 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} d^{2} e^{5} + {\left(7 \, b^{6} c - 44 \, a b^{4} c^{2} + 66 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{7} + {\left(2 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{2} - 2 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d e + {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{5} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} + 4 \, {\left(5 \, c^{6} d^{8} e - 20 \, b c^{5} d^{7} e^{2} + 35 \, b^{2} c^{4} d^{6} e^{3} - 35 \, b^{3} c^{3} d^{5} e^{4} + 7 \, {\left(3 \, b^{4} c^{2} + a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{4} e^{5} - 7 \, {\left(b^{5} c + 2 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{6} + {\left(b^{6} + 9 \, a b^{4} c - 15 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{7} - {\left(2 \, a b^{5} - a^{2} b^{3} c - 8 \, a^{3} b c^{2}\right)} d e^{8} + {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{2} c^{2} \sqrt{\frac{2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{5} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} \log\left(-\sqrt{2} {\left(10 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{5} e^{2} - 25 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{4} e^{3} + 10 \, {\left(3 \, b^{4} c^{3} - 14 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d^{3} e^{4} - 10 \, {\left(2 \, b^{5} c^{2} - 11 \, a b^{3} c^{3} + 12 \, a^{2} b c^{4}\right)} d^{2} e^{5} + {\left(7 \, b^{6} c - 44 \, a b^{4} c^{2} + 66 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 7 \, a b^{5} c + 13 \, a^{2} b^{3} c^{2} - 4 \, a^{3} b c^{3}\right)} e^{7} + {\left(2 \, {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{2} - 2 \, {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} d e + {\left(b^{4} c^{5} - 6 \, a b^{2} c^{6} + 8 \, a^{2} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}\right)} \sqrt{\frac{2 \, c^{5} d^{5} - 5 \, b c^{4} d^{4} e + 10 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{3} e^{2} - 10 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{2} e^{3} + 5 \, {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} e^{5} - {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} \sqrt{\frac{25 \, c^{8} d^{8} e^{2} - 100 \, b c^{7} d^{7} e^{3} + 100 \, {\left(2 \, b^{2} c^{6} - a c^{7}\right)} d^{6} e^{4} - 50 \, {\left(5 \, b^{3} c^{5} - 6 \, a b c^{6}\right)} d^{5} e^{5} + 10 \, {\left(21 \, b^{4} c^{4} - 43 \, a b^{2} c^{5} + 11 \, a^{2} c^{6}\right)} d^{4} e^{6} - 20 \, {\left(6 \, b^{5} c^{3} - 18 \, a b^{3} c^{4} + 11 \, a^{2} b c^{5}\right)} d^{3} e^{7} + 5 \, {\left(9 \, b^{6} c^{2} - 36 \, a b^{4} c^{3} + 36 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{2} e^{8} - 10 \, {\left(b^{7} c - 5 \, a b^{5} c^{2} + 7 \, a^{2} b^{3} c^{3} - 2 \, a^{3} b c^{4}\right)} d e^{9} + {\left(b^{8} - 6 \, a b^{6} c + 11 \, a^{2} b^{4} c^{2} - 6 \, a^{3} b^{2} c^{3} + a^{4} c^{4}\right)} e^{10}}{b^{2} c^{10} - 4 \, a c^{11}}}}{b^{2} c^{5} - 4 \, a c^{6}}} + 4 \, {\left(5 \, c^{6} d^{8} e - 20 \, b c^{5} d^{7} e^{2} + 35 \, b^{2} c^{4} d^{6} e^{3} - 35 \, b^{3} c^{3} d^{5} e^{4} + 7 \, {\left(3 \, b^{4} c^{2} + a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{4} e^{5} - 7 \, {\left(b^{5} c + 2 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{6} + {\left(b^{6} + 9 \, a b^{4} c - 15 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{7} - {\left(2 \, a b^{5} - a^{2} b^{3} c - 8 \, a^{3} b c^{2}\right)} d e^{8} + {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) + 4 \, {\left(c e^{2} x + 7 \, c d e - 3 \, b e^{2}\right)} \sqrt{e x + d}}{6 \, c^{2}}"," ",0,"1/6*(3*sqrt(2)*c^2*sqrt((2*c^5*d^5 - 5*b*c^4*d^4*e + 10*(b^2*c^3 - 2*a*c^4)*d^3*e^2 - 10*(b^3*c^2 - 3*a*b*c^3)*d^2*e^3 + 5*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^5 + (b^2*c^5 - 4*a*c^6)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(sqrt(2)*(10*(b^2*c^5 - 4*a*c^6)*d^5*e^2 - 25*(b^3*c^4 - 4*a*b*c^5)*d^4*e^3 + 10*(3*b^4*c^3 - 14*a*b^2*c^4 + 8*a^2*c^5)*d^3*e^4 - 10*(2*b^5*c^2 - 11*a*b^3*c^3 + 12*a^2*b*c^4)*d^2*e^5 + (7*b^6*c - 44*a*b^4*c^2 + 66*a^2*b^2*c^3 - 8*a^3*c^4)*d*e^6 - (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e^7 - (2*(b^2*c^7 - 4*a*c^8)*d^2 - 2*(b^3*c^6 - 4*a*b*c^7)*d*e + (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*e^2)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))*sqrt((2*c^5*d^5 - 5*b*c^4*d^4*e + 10*(b^2*c^3 - 2*a*c^4)*d^3*e^2 - 10*(b^3*c^2 - 3*a*b*c^3)*d^2*e^3 + 5*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^5 + (b^2*c^5 - 4*a*c^6)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) + 4*(5*c^6*d^8*e - 20*b*c^5*d^7*e^2 + 35*b^2*c^4*d^6*e^3 - 35*b^3*c^3*d^5*e^4 + 7*(3*b^4*c^2 + a*b^2*c^3 - 2*a^2*c^4)*d^4*e^5 - 7*(b^5*c + 2*a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^6 + (b^6 + 9*a*b^4*c - 15*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^7 - (2*a*b^5 - a^2*b^3*c - 8*a^3*b*c^2)*d*e^8 + (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e^9)*sqrt(e*x + d)) - 3*sqrt(2)*c^2*sqrt((2*c^5*d^5 - 5*b*c^4*d^4*e + 10*(b^2*c^3 - 2*a*c^4)*d^3*e^2 - 10*(b^3*c^2 - 3*a*b*c^3)*d^2*e^3 + 5*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^5 + (b^2*c^5 - 4*a*c^6)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-sqrt(2)*(10*(b^2*c^5 - 4*a*c^6)*d^5*e^2 - 25*(b^3*c^4 - 4*a*b*c^5)*d^4*e^3 + 10*(3*b^4*c^3 - 14*a*b^2*c^4 + 8*a^2*c^5)*d^3*e^4 - 10*(2*b^5*c^2 - 11*a*b^3*c^3 + 12*a^2*b*c^4)*d^2*e^5 + (7*b^6*c - 44*a*b^4*c^2 + 66*a^2*b^2*c^3 - 8*a^3*c^4)*d*e^6 - (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e^7 - (2*(b^2*c^7 - 4*a*c^8)*d^2 - 2*(b^3*c^6 - 4*a*b*c^7)*d*e + (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*e^2)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))*sqrt((2*c^5*d^5 - 5*b*c^4*d^4*e + 10*(b^2*c^3 - 2*a*c^4)*d^3*e^2 - 10*(b^3*c^2 - 3*a*b*c^3)*d^2*e^3 + 5*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^5 + (b^2*c^5 - 4*a*c^6)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) + 4*(5*c^6*d^8*e - 20*b*c^5*d^7*e^2 + 35*b^2*c^4*d^6*e^3 - 35*b^3*c^3*d^5*e^4 + 7*(3*b^4*c^2 + a*b^2*c^3 - 2*a^2*c^4)*d^4*e^5 - 7*(b^5*c + 2*a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^6 + (b^6 + 9*a*b^4*c - 15*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^7 - (2*a*b^5 - a^2*b^3*c - 8*a^3*b*c^2)*d*e^8 + (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e^9)*sqrt(e*x + d)) + 3*sqrt(2)*c^2*sqrt((2*c^5*d^5 - 5*b*c^4*d^4*e + 10*(b^2*c^3 - 2*a*c^4)*d^3*e^2 - 10*(b^3*c^2 - 3*a*b*c^3)*d^2*e^3 + 5*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^5 - (b^2*c^5 - 4*a*c^6)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(sqrt(2)*(10*(b^2*c^5 - 4*a*c^6)*d^5*e^2 - 25*(b^3*c^4 - 4*a*b*c^5)*d^4*e^3 + 10*(3*b^4*c^3 - 14*a*b^2*c^4 + 8*a^2*c^5)*d^3*e^4 - 10*(2*b^5*c^2 - 11*a*b^3*c^3 + 12*a^2*b*c^4)*d^2*e^5 + (7*b^6*c - 44*a*b^4*c^2 + 66*a^2*b^2*c^3 - 8*a^3*c^4)*d*e^6 - (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e^7 + (2*(b^2*c^7 - 4*a*c^8)*d^2 - 2*(b^3*c^6 - 4*a*b*c^7)*d*e + (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*e^2)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))*sqrt((2*c^5*d^5 - 5*b*c^4*d^4*e + 10*(b^2*c^3 - 2*a*c^4)*d^3*e^2 - 10*(b^3*c^2 - 3*a*b*c^3)*d^2*e^3 + 5*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^5 - (b^2*c^5 - 4*a*c^6)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) + 4*(5*c^6*d^8*e - 20*b*c^5*d^7*e^2 + 35*b^2*c^4*d^6*e^3 - 35*b^3*c^3*d^5*e^4 + 7*(3*b^4*c^2 + a*b^2*c^3 - 2*a^2*c^4)*d^4*e^5 - 7*(b^5*c + 2*a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^6 + (b^6 + 9*a*b^4*c - 15*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^7 - (2*a*b^5 - a^2*b^3*c - 8*a^3*b*c^2)*d*e^8 + (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e^9)*sqrt(e*x + d)) - 3*sqrt(2)*c^2*sqrt((2*c^5*d^5 - 5*b*c^4*d^4*e + 10*(b^2*c^3 - 2*a*c^4)*d^3*e^2 - 10*(b^3*c^2 - 3*a*b*c^3)*d^2*e^3 + 5*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^5 - (b^2*c^5 - 4*a*c^6)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6))*log(-sqrt(2)*(10*(b^2*c^5 - 4*a*c^6)*d^5*e^2 - 25*(b^3*c^4 - 4*a*b*c^5)*d^4*e^3 + 10*(3*b^4*c^3 - 14*a*b^2*c^4 + 8*a^2*c^5)*d^3*e^4 - 10*(2*b^5*c^2 - 11*a*b^3*c^3 + 12*a^2*b*c^4)*d^2*e^5 + (7*b^6*c - 44*a*b^4*c^2 + 66*a^2*b^2*c^3 - 8*a^3*c^4)*d*e^6 - (b^7 - 7*a*b^5*c + 13*a^2*b^3*c^2 - 4*a^3*b*c^3)*e^7 + (2*(b^2*c^7 - 4*a*c^8)*d^2 - 2*(b^3*c^6 - 4*a*b*c^7)*d*e + (b^4*c^5 - 6*a*b^2*c^6 + 8*a^2*c^7)*e^2)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))*sqrt((2*c^5*d^5 - 5*b*c^4*d^4*e + 10*(b^2*c^3 - 2*a*c^4)*d^3*e^2 - 10*(b^3*c^2 - 3*a*b*c^3)*d^2*e^3 + 5*(b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*e^5 - (b^2*c^5 - 4*a*c^6)*sqrt((25*c^8*d^8*e^2 - 100*b*c^7*d^7*e^3 + 100*(2*b^2*c^6 - a*c^7)*d^6*e^4 - 50*(5*b^3*c^5 - 6*a*b*c^6)*d^5*e^5 + 10*(21*b^4*c^4 - 43*a*b^2*c^5 + 11*a^2*c^6)*d^4*e^6 - 20*(6*b^5*c^3 - 18*a*b^3*c^4 + 11*a^2*b*c^5)*d^3*e^7 + 5*(9*b^6*c^2 - 36*a*b^4*c^3 + 36*a^2*b^2*c^4 - 4*a^3*c^5)*d^2*e^8 - 10*(b^7*c - 5*a*b^5*c^2 + 7*a^2*b^3*c^3 - 2*a^3*b*c^4)*d*e^9 + (b^8 - 6*a*b^6*c + 11*a^2*b^4*c^2 - 6*a^3*b^2*c^3 + a^4*c^4)*e^10)/(b^2*c^10 - 4*a*c^11)))/(b^2*c^5 - 4*a*c^6)) + 4*(5*c^6*d^8*e - 20*b*c^5*d^7*e^2 + 35*b^2*c^4*d^6*e^3 - 35*b^3*c^3*d^5*e^4 + 7*(3*b^4*c^2 + a*b^2*c^3 - 2*a^2*c^4)*d^4*e^5 - 7*(b^5*c + 2*a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^6 + (b^6 + 9*a*b^4*c - 15*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^7 - (2*a*b^5 - a^2*b^3*c - 8*a^3*b*c^2)*d*e^8 + (a^2*b^4 - 3*a^3*b^2*c + a^4*c^2)*e^9)*sqrt(e*x + d)) + 4*(c*e^2*x + 7*c*d*e - 3*b*e^2)*sqrt(e*x + d))/c^2","B",0
2290,1,2770,0,0.573215," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{\sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\sqrt{2} {\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} - {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 4 \, {\left(3 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 2 \, a b c\right)} d e^{4} + {\left(a b^{2} - a^{2} c\right)} e^{5}\right)} \sqrt{e x + d}\right) - \sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-\sqrt{2} {\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} - {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 4 \, {\left(3 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 2 \, a b c\right)} d e^{4} + {\left(a b^{2} - a^{2} c\right)} e^{5}\right)} \sqrt{e x + d}\right) + \sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(\sqrt{2} {\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} + {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 4 \, {\left(3 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 2 \, a b c\right)} d e^{4} + {\left(a b^{2} - a^{2} c\right)} e^{5}\right)} \sqrt{e x + d}\right) - \sqrt{2} c \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(-\sqrt{2} {\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} + {\left(2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d - {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} e\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} - 4 \, {\left(3 \, c^{3} d^{4} e - 6 \, b c^{2} d^{3} e^{2} + 2 \, {\left(2 \, b^{2} c + a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 2 \, a b c\right)} d e^{4} + {\left(a b^{2} - a^{2} c\right)} e^{5}\right)} \sqrt{e x + d}\right) - 4 \, \sqrt{e x + d} e}{2 \, c}"," ",0,"-1/2*(sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(sqrt(2)*(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 - (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 4*(3*c^3*d^4*e - 6*b*c^2*d^3*e^2 + 2*(2*b^2*c + a*c^2)*d^2*e^3 - (b^3 + 2*a*b*c)*d*e^4 + (a*b^2 - a^2*c)*e^5)*sqrt(e*x + d)) - sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-sqrt(2)*(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 - (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 4*(3*c^3*d^4*e - 6*b*c^2*d^3*e^2 + 2*(2*b^2*c + a*c^2)*d^2*e^3 - (b^3 + 2*a*b*c)*d*e^4 + (a*b^2 - a^2*c)*e^5)*sqrt(e*x + d)) + sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(sqrt(2)*(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 + (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 4*(3*c^3*d^4*e - 6*b*c^2*d^3*e^2 + 2*(2*b^2*c + a*c^2)*d^2*e^3 - (b^3 + 2*a*b*c)*d*e^4 + (a*b^2 - a^2*c)*e^5)*sqrt(e*x + d)) - sqrt(2)*c*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(-sqrt(2)*(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 + (2*(b^2*c^4 - 4*a*c^5)*d - (b^3*c^3 - 4*a*b*c^4)*e)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - (b^2*c^3 - 4*a*c^4)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4)) - 4*(3*c^3*d^4*e - 6*b*c^2*d^3*e^2 + 2*(2*b^2*c + a*c^2)*d^2*e^3 - (b^3 + 2*a*b*c)*d*e^4 + (a*b^2 - a^2*c)*e^5)*sqrt(e*x + d)) - 4*sqrt(e*x + d)*e)/c","B",0
2291,1,715,0,0.452560," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\sqrt{2} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} + 2 \, \sqrt{e x + d} e\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(-\sqrt{2} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}} \sqrt{\frac{2 \, c d - b e + {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} + 2 \, \sqrt{e x + d} e\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(\sqrt{2} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} + 2 \, \sqrt{e x + d} e\right) - \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} \log\left(-\sqrt{2} {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}} \sqrt{\frac{2 \, c d - b e - {\left(b^{2} c - 4 \, a c^{2}\right)} \sqrt{\frac{e^{2}}{b^{2} c^{2} - 4 \, a c^{3}}}}{b^{2} c - 4 \, a c^{2}}} + 2 \, \sqrt{e x + d} e\right)"," ",0,"-1/2*sqrt(2)*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log(sqrt(2)*(b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3))*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) + 2*sqrt(e*x + d)*e) + 1/2*sqrt(2)*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log(-sqrt(2)*(b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3))*sqrt((2*c*d - b*e + (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) + 2*sqrt(e*x + d)*e) + 1/2*sqrt(2)*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log(sqrt(2)*(b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3))*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) + 2*sqrt(e*x + d)*e) - 1/2*sqrt(2)*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2))*log(-sqrt(2)*(b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3))*sqrt((2*c*d - b*e - (b^2*c - 4*a*c^2)*sqrt(e^2/(b^2*c^2 - 4*a*c^3)))/(b^2*c - 4*a*c^2)) + 2*sqrt(e*x + d)*e)","B",0
2292,1,2641,0,0.487209," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(4 \, \sqrt{e x + d} c e + \sqrt{2} {\left({\left(b^{2} - 4 \, a c\right)} e^{2} - {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right)} \sqrt{\frac{2 \, c d - b e + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(4 \, \sqrt{e x + d} c e - \sqrt{2} {\left({\left(b^{2} - 4 \, a c\right)} e^{2} - {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right)} \sqrt{\frac{2 \, c d - b e + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}\right) - \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(4 \, \sqrt{e x + d} c e + \sqrt{2} {\left({\left(b^{2} - 4 \, a c\right)} e^{2} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right)} \sqrt{\frac{2 \, c d - b e - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\frac{2 \, c d - b e - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}} \log\left(4 \, \sqrt{e x + d} c e - \sqrt{2} {\left({\left(b^{2} - 4 \, a c\right)} e^{2} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} - 3 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}\right)} \sqrt{\frac{2 \, c d - b e - {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{\frac{e^{2}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}}}\right)"," ",0,"-1/2*sqrt(2)*sqrt((2*c*d - b*e + ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log(4*sqrt(e*x + d)*c*e + sqrt(2)*((b^2 - 4*a*c)*e^2 - (2*(b^2*c^2 - 4*a*c^3)*d^3 - 3*(b^3*c - 4*a*b*c^2)*d^2*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))*sqrt((2*c*d - b*e + ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))) + 1/2*sqrt(2)*sqrt((2*c*d - b*e + ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log(4*sqrt(e*x + d)*c*e - sqrt(2)*((b^2 - 4*a*c)*e^2 - (2*(b^2*c^2 - 4*a*c^3)*d^3 - 3*(b^3*c - 4*a*b*c^2)*d^2*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))*sqrt((2*c*d - b*e + ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))) - 1/2*sqrt(2)*sqrt((2*c*d - b*e - ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log(4*sqrt(e*x + d)*c*e + sqrt(2)*((b^2 - 4*a*c)*e^2 + (2*(b^2*c^2 - 4*a*c^3)*d^3 - 3*(b^3*c - 4*a*b*c^2)*d^2*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))*sqrt((2*c*d - b*e - ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))) + 1/2*sqrt(2)*sqrt((2*c*d - b*e - ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2))*log(4*sqrt(e*x + d)*c*e - sqrt(2)*((b^2 - 4*a*c)*e^2 + (2*(b^2*c^2 - 4*a*c^3)*d^3 - 3*(b^3*c - 4*a*b*c^2)*d^2*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))*sqrt((2*c*d - b*e - ((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)*sqrt(e^2/((b^2*c^2 - 4*a*c^3)*d^4 - 2*(b^3*c - 4*a*b*c^2)*d^3*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d*e^3 + (a^2*b^2 - 4*a^3*c)*e^4)))/((b^2*c - 4*a*c^2)*d^2 - (b^3 - 4*a*b*c)*d*e + (a*b^2 - 4*a^2*c)*e^2)))","B",0
2293,1,11293,0,0.833520," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} \log\left(\sqrt{2} {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{3} + {\left(5 \, b^{4} c - 22 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{5} - {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} - 8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e + {\left(13 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{6} e^{2} - {\left(11 \, b^{5} c^{2} - 32 \, a b^{3} c^{3} - 48 \, a^{2} b c^{4}\right)} d^{5} e^{3} + 5 \, {\left(b^{6} c - a b^{4} c^{2} - 12 \, a^{2} b^{2} c^{3}\right)} d^{4} e^{4} - {\left(b^{7} + 6 \, a b^{5} c - 40 \, a^{2} b^{3} c^{2}\right)} d^{3} e^{5} + {\left(3 \, a b^{6} - 9 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2} e^{6} - {\left(3 \, a^{2} b^{5} - 16 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{7} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{8}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} - 4 \, {\left(3 \, c^{4} d^{2} e - 3 \, b c^{3} d e^{2} + {\left(b^{2} c^{2} - a c^{3}\right)} e^{3}\right)} \sqrt{e x + d}\right) - \sqrt{2} {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} \log\left(-\sqrt{2} {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{3} + {\left(5 \, b^{4} c - 22 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{5} - {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} - 8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e + {\left(13 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{6} e^{2} - {\left(11 \, b^{5} c^{2} - 32 \, a b^{3} c^{3} - 48 \, a^{2} b c^{4}\right)} d^{5} e^{3} + 5 \, {\left(b^{6} c - a b^{4} c^{2} - 12 \, a^{2} b^{2} c^{3}\right)} d^{4} e^{4} - {\left(b^{7} + 6 \, a b^{5} c - 40 \, a^{2} b^{3} c^{2}\right)} d^{3} e^{5} + {\left(3 \, a b^{6} - 9 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2} e^{6} - {\left(3 \, a^{2} b^{5} - 16 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{7} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{8}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} - 4 \, {\left(3 \, c^{4} d^{2} e - 3 \, b c^{3} d e^{2} + {\left(b^{2} c^{2} - a c^{3}\right)} e^{3}\right)} \sqrt{e x + d}\right) + \sqrt{2} {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} \log\left(\sqrt{2} {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{3} + {\left(5 \, b^{4} c - 22 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{5} + {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} - 8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e + {\left(13 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{6} e^{2} - {\left(11 \, b^{5} c^{2} - 32 \, a b^{3} c^{3} - 48 \, a^{2} b c^{4}\right)} d^{5} e^{3} + 5 \, {\left(b^{6} c - a b^{4} c^{2} - 12 \, a^{2} b^{2} c^{3}\right)} d^{4} e^{4} - {\left(b^{7} + 6 \, a b^{5} c - 40 \, a^{2} b^{3} c^{2}\right)} d^{3} e^{5} + {\left(3 \, a b^{6} - 9 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2} e^{6} - {\left(3 \, a^{2} b^{5} - 16 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{7} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{8}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} - 4 \, {\left(3 \, c^{4} d^{2} e - 3 \, b c^{3} d e^{2} + {\left(b^{2} c^{2} - a c^{3}\right)} e^{3}\right)} \sqrt{e x + d}\right) - \sqrt{2} {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} \log\left(-\sqrt{2} {\left(6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{2} - 9 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{3} + {\left(5 \, b^{4} c - 22 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} e^{5} + {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} - 8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e + {\left(13 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{6} e^{2} - {\left(11 \, b^{5} c^{2} - 32 \, a b^{3} c^{3} - 48 \, a^{2} b c^{4}\right)} d^{5} e^{3} + 5 \, {\left(b^{6} c - a b^{4} c^{2} - 12 \, a^{2} b^{2} c^{3}\right)} d^{4} e^{4} - {\left(b^{7} + 6 \, a b^{5} c - 40 \, a^{2} b^{3} c^{2}\right)} d^{3} e^{5} + {\left(3 \, a b^{6} - 9 \, a^{2} b^{4} c - 16 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2} e^{6} - {\left(3 \, a^{2} b^{5} - 16 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{7} + {\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} e^{8}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}\right)} \sqrt{\frac{2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(b^{3} - 3 \, a b c\right)} e^{3} - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}\right)} \sqrt{\frac{9 \, c^{4} d^{4} e^{2} - 18 \, b c^{3} d^{3} e^{3} + 3 \, {\left(5 \, b^{2} c^{2} - 2 \, a c^{3}\right)} d^{2} e^{4} - 6 \, {\left(b^{3} c - a b c^{2}\right)} d e^{5} + {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} e^{6}}{{\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} - 6 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e + 3 \, {\left(5 \, b^{4} c^{4} - 18 \, a b^{2} c^{5} - 8 \, a^{2} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(2 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 12 \, a^{2} b c^{5}\right)} d^{9} e^{3} + 15 \, {\left(b^{6} c^{2} - 15 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{8} e^{4} - 6 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 30 \, a^{2} b^{3} c^{3} - 40 \, a^{3} b c^{4}\right)} d^{7} e^{5} + {\left(b^{8} + 26 \, a b^{6} c - 30 \, a^{2} b^{4} c^{2} - 340 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} d^{6} e^{6} - 6 \, {\left(a b^{7} + 6 \, a^{2} b^{5} c - 30 \, a^{3} b^{3} c^{2} - 40 \, a^{4} b c^{3}\right)} d^{5} e^{7} + 15 \, {\left(a^{2} b^{6} - 15 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{4} e^{8} - 10 \, {\left(2 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 12 \, a^{5} b c^{2}\right)} d^{3} e^{9} + 3 \, {\left(5 \, a^{4} b^{4} - 18 \, a^{5} b^{2} c - 8 \, a^{6} c^{2}\right)} d^{2} e^{10} - 6 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{11} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{12}}}}{{\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e + 3 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} + 2 \, a b^{3} c - 24 \, a^{2} b c^{2}\right)} d^{3} e^{3} + 3 \, {\left(a b^{4} - 3 \, a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{5} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{6}}} - 4 \, {\left(3 \, c^{4} d^{2} e - 3 \, b c^{3} d e^{2} + {\left(b^{2} c^{2} - a c^{3}\right)} e^{3}\right)} \sqrt{e x + d}\right) - 4 \, \sqrt{e x + d} e}{2 \, {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)}}"," ",0,"1/2*(sqrt(2)*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6))*log(sqrt(2)*(6*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - 9*(b^3*c^2 - 4*a*b*c^3)*d^2*e^3 + (5*b^4*c - 22*a*b^2*c^2 + 8*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^5 - (2*(b^2*c^5 - 4*a*c^6)*d^8 - 8*(b^3*c^4 - 4*a*b*c^5)*d^7*e + (13*b^4*c^3 - 48*a*b^2*c^4 - 16*a^2*c^5)*d^6*e^2 - (11*b^5*c^2 - 32*a*b^3*c^3 - 48*a^2*b*c^4)*d^5*e^3 + 5*(b^6*c - a*b^4*c^2 - 12*a^2*b^2*c^3)*d^4*e^4 - (b^7 + 6*a*b^5*c - 40*a^2*b^3*c^2)*d^3*e^5 + (3*a*b^6 - 9*a^2*b^4*c - 16*a^3*b^2*c^2 + 16*a^4*c^3)*d^2*e^6 - (3*a^2*b^5 - 16*a^3*b^3*c + 16*a^4*b*c^2)*d*e^7 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^8)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)) - 4*(3*c^4*d^2*e - 3*b*c^3*d*e^2 + (b^2*c^2 - a*c^3)*e^3)*sqrt(e*x + d)) - sqrt(2)*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6))*log(-sqrt(2)*(6*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - 9*(b^3*c^2 - 4*a*b*c^3)*d^2*e^3 + (5*b^4*c - 22*a*b^2*c^2 + 8*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^5 - (2*(b^2*c^5 - 4*a*c^6)*d^8 - 8*(b^3*c^4 - 4*a*b*c^5)*d^7*e + (13*b^4*c^3 - 48*a*b^2*c^4 - 16*a^2*c^5)*d^6*e^2 - (11*b^5*c^2 - 32*a*b^3*c^3 - 48*a^2*b*c^4)*d^5*e^3 + 5*(b^6*c - a*b^4*c^2 - 12*a^2*b^2*c^3)*d^4*e^4 - (b^7 + 6*a*b^5*c - 40*a^2*b^3*c^2)*d^3*e^5 + (3*a*b^6 - 9*a^2*b^4*c - 16*a^3*b^2*c^2 + 16*a^4*c^3)*d^2*e^6 - (3*a^2*b^5 - 16*a^3*b^3*c + 16*a^4*b*c^2)*d*e^7 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^8)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 + ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)) - 4*(3*c^4*d^2*e - 3*b*c^3*d*e^2 + (b^2*c^2 - a*c^3)*e^3)*sqrt(e*x + d)) + sqrt(2)*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6))*log(sqrt(2)*(6*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - 9*(b^3*c^2 - 4*a*b*c^3)*d^2*e^3 + (5*b^4*c - 22*a*b^2*c^2 + 8*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^5 + (2*(b^2*c^5 - 4*a*c^6)*d^8 - 8*(b^3*c^4 - 4*a*b*c^5)*d^7*e + (13*b^4*c^3 - 48*a*b^2*c^4 - 16*a^2*c^5)*d^6*e^2 - (11*b^5*c^2 - 32*a*b^3*c^3 - 48*a^2*b*c^4)*d^5*e^3 + 5*(b^6*c - a*b^4*c^2 - 12*a^2*b^2*c^3)*d^4*e^4 - (b^7 + 6*a*b^5*c - 40*a^2*b^3*c^2)*d^3*e^5 + (3*a*b^6 - 9*a^2*b^4*c - 16*a^3*b^2*c^2 + 16*a^4*c^3)*d^2*e^6 - (3*a^2*b^5 - 16*a^3*b^3*c + 16*a^4*b*c^2)*d*e^7 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^8)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)) - 4*(3*c^4*d^2*e - 3*b*c^3*d*e^2 + (b^2*c^2 - a*c^3)*e^3)*sqrt(e*x + d)) - sqrt(2)*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6))*log(-sqrt(2)*(6*(b^2*c^3 - 4*a*c^4)*d^3*e^2 - 9*(b^3*c^2 - 4*a*b*c^3)*d^2*e^3 + (5*b^4*c - 22*a*b^2*c^2 + 8*a^2*c^3)*d*e^4 - (b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*e^5 + (2*(b^2*c^5 - 4*a*c^6)*d^8 - 8*(b^3*c^4 - 4*a*b*c^5)*d^7*e + (13*b^4*c^3 - 48*a*b^2*c^4 - 16*a^2*c^5)*d^6*e^2 - (11*b^5*c^2 - 32*a*b^3*c^3 - 48*a^2*b*c^4)*d^5*e^3 + 5*(b^6*c - a*b^4*c^2 - 12*a^2*b^2*c^3)*d^4*e^4 - (b^7 + 6*a*b^5*c - 40*a^2*b^3*c^2)*d^3*e^5 + (3*a*b^6 - 9*a^2*b^4*c - 16*a^3*b^2*c^2 + 16*a^4*c^3)*d^2*e^6 - (3*a^2*b^5 - 16*a^3*b^3*c + 16*a^4*b*c^2)*d*e^7 + (a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*e^8)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))*sqrt((2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (b^3 - 3*a*b*c)*e^3 - ((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)*sqrt((9*c^4*d^4*e^2 - 18*b*c^3*d^3*e^3 + 3*(5*b^2*c^2 - 2*a*c^3)*d^2*e^4 - 6*(b^3*c - a*b*c^2)*d*e^5 + (b^4 - 2*a*b^2*c + a^2*c^2)*e^6)/((b^2*c^6 - 4*a*c^7)*d^12 - 6*(b^3*c^5 - 4*a*b*c^6)*d^11*e + 3*(5*b^4*c^4 - 18*a*b^2*c^5 - 8*a^2*c^6)*d^10*e^2 - 10*(2*b^5*c^3 - 5*a*b^3*c^4 - 12*a^2*b*c^5)*d^9*e^3 + 15*(b^6*c^2 - 15*a^2*b^2*c^4 - 4*a^3*c^5)*d^8*e^4 - 6*(b^7*c + 6*a*b^5*c^2 - 30*a^2*b^3*c^3 - 40*a^3*b*c^4)*d^7*e^5 + (b^8 + 26*a*b^6*c - 30*a^2*b^4*c^2 - 340*a^3*b^2*c^3 - 80*a^4*c^4)*d^6*e^6 - 6*(a*b^7 + 6*a^2*b^5*c - 30*a^3*b^3*c^2 - 40*a^4*b*c^3)*d^5*e^7 + 15*(a^2*b^6 - 15*a^4*b^2*c^2 - 4*a^5*c^3)*d^4*e^8 - 10*(2*a^3*b^5 - 5*a^4*b^3*c - 12*a^5*b*c^2)*d^3*e^9 + 3*(5*a^4*b^4 - 18*a^5*b^2*c - 8*a^6*c^2)*d^2*e^10 - 6*(a^5*b^3 - 4*a^6*b*c)*d*e^11 + (a^6*b^2 - 4*a^7*c)*e^12)))/((b^2*c^3 - 4*a*c^4)*d^6 - 3*(b^3*c^2 - 4*a*b*c^3)*d^5*e + 3*(b^4*c - 3*a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - (b^5 + 2*a*b^3*c - 24*a^2*b*c^2)*d^3*e^3 + 3*(a*b^4 - 3*a^2*b^2*c - 4*a^3*c^2)*d^2*e^4 - 3*(a^2*b^3 - 4*a^3*b*c)*d*e^5 + (a^3*b^2 - 4*a^4*c)*e^6)) - 4*(3*c^4*d^2*e - 3*b*c^3*d*e^2 + (b^2*c^2 - a*c^3)*e^3)*sqrt(e*x + d)) - 4*sqrt(e*x + d)*e)/(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)","B",0
2294,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2295,1,10077,0,7.962882," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{\frac{32 \, c^{7} d^{7} - 112 \, b c^{6} d^{6} e + 14 \, {\left(7 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} + 35 \, {\left(b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{4} e^{3} - 70 \, {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{3} e^{4} + 14 \, {\left(b^{5} c^{2} + 5 \, a b^{3} c^{3} - 60 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 7 \, {\left(3 \, b^{6} c - 40 \, a b^{4} c^{2} + 150 \, a^{2} b^{2} c^{3} - 120 \, a^{3} c^{4}\right)} d e^{6} - {\left(9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}\right)} e^{7} + {\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{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(\sqrt{\frac{1}{2}} {\left(70 \, {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{6} e^{4} - 210 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{5} e^{5} + 21 \, {\left(13 \, b^{6} c^{4} - 106 \, a b^{4} c^{5} + 224 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{4} e^{6} - 28 \, {\left(7 \, b^{7} c^{3} - 59 \, a b^{5} c^{4} + 136 \, a^{2} b^{3} c^{5} - 48 \, a^{3} b c^{6}\right)} d^{3} e^{7} - 6 \, {\left(3 \, b^{8} c^{2} - 146 \, a b^{6} c^{3} + 1289 \, a^{2} b^{4} c^{4} - 4072 \, a^{3} b^{2} c^{5} + 4240 \, a^{4} c^{6}\right)} d^{2} e^{8} + 3 \, {\left(27 \, b^{9} c - 474 \, a b^{7} c^{2} + 3026 \, a^{2} b^{5} c^{3} - 8368 \, a^{3} b^{3} c^{4} + 8480 \, a^{4} b c^{5}\right)} d e^{9} - {\left(27 \, b^{10} - 459 \, a b^{8} c + 2961 \, a^{2} b^{6} c^{2} - 8818 \, a^{3} b^{4} c^{3} + 11360 \, a^{4} b^{2} c^{4} - 4000 \, a^{5} c^{5}\right)} e^{10} - {\left(8 \, {\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{3} - 12 \, {\left(b^{7} c^{7} - 12 \, a b^{5} c^{8} + 48 \, a^{2} b^{3} c^{9} - 64 \, a^{3} b c^{10}\right)} d^{2} e - 2 \, {\left(b^{8} c^{6} - 28 \, a b^{6} c^{7} + 240 \, a^{2} b^{4} c^{8} - 832 \, a^{3} b^{2} c^{9} + 1024 \, a^{4} c^{10}\right)} d e^{2} + {\left(3 \, b^{9} c^{5} - 52 \, a b^{7} c^{6} + 336 \, a^{2} b^{5} c^{7} - 960 \, a^{3} b^{3} c^{8} + 1024 \, a^{4} b c^{9}\right)} e^{3}\right)} \sqrt{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\frac{32 \, c^{7} d^{7} - 112 \, b c^{6} d^{6} e + 14 \, {\left(7 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} + 35 \, {\left(b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{4} e^{3} - 70 \, {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{3} e^{4} + 14 \, {\left(b^{5} c^{2} + 5 \, a b^{3} c^{3} - 60 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 7 \, {\left(3 \, b^{6} c - 40 \, a b^{4} c^{2} + 150 \, a^{2} b^{2} c^{3} - 120 \, a^{3} c^{4}\right)} d e^{6} - {\left(9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}\right)} e^{7} + {\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{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} - 2 \, {\left(560 \, c^{8} d^{10} e^{3} - 2800 \, b c^{7} d^{9} e^{4} + 7 \, {\left(647 \, b^{2} c^{6} + 1012 \, a c^{7}\right)} d^{8} e^{5} - 28 \, {\left(47 \, b^{3} c^{5} + 1012 \, a b c^{6}\right)} d^{7} e^{6} - {\left(3329 \, b^{4} c^{4} - 35844 \, a b^{2} c^{5} - 27488 \, a^{2} c^{6}\right)} d^{6} e^{7} + {\left(2833 \, b^{5} c^{3} - 8356 \, a b^{3} c^{4} - 82464 \, a^{2} b c^{5}\right)} d^{5} e^{8} + {\left(9 \, b^{6} c^{2} - 14273 \, a b^{4} c^{3} + 77982 \, a^{2} b^{2} c^{4} + 33464 \, a^{3} c^{5}\right)} d^{4} e^{9} - {\left(675 \, b^{7} c - 9414 \, a b^{5} c^{2} + 18524 \, a^{2} b^{3} c^{3} + 66928 \, a^{3} b c^{4}\right)} d^{3} e^{10} + {\left(189 \, b^{8} - 999 \, a b^{6} c - 8127 \, a^{2} b^{4} c^{2} + 40196 \, a^{3} b^{2} c^{3} + 10000 \, a^{4} c^{4}\right)} d^{2} e^{11} - {\left(378 \, a b^{7} - 3645 \, a^{2} b^{5} c + 6732 \, a^{3} b^{3} c^{2} + 10000 \, a^{4} b c^{3}\right)} d e^{12} + {\left(189 \, a^{2} b^{6} - 1971 \, a^{3} b^{4} c + 5625 \, a^{4} b^{2} c^{2} - 2500 \, a^{5} c^{3}\right)} e^{13}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{\frac{32 \, c^{7} d^{7} - 112 \, b c^{6} d^{6} e + 14 \, {\left(7 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} + 35 \, {\left(b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{4} e^{3} - 70 \, {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{3} e^{4} + 14 \, {\left(b^{5} c^{2} + 5 \, a b^{3} c^{3} - 60 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 7 \, {\left(3 \, b^{6} c - 40 \, a b^{4} c^{2} + 150 \, a^{2} b^{2} c^{3} - 120 \, a^{3} c^{4}\right)} d e^{6} - {\left(9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}\right)} e^{7} + {\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{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(-\sqrt{\frac{1}{2}} {\left(70 \, {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{6} e^{4} - 210 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{5} e^{5} + 21 \, {\left(13 \, b^{6} c^{4} - 106 \, a b^{4} c^{5} + 224 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{4} e^{6} - 28 \, {\left(7 \, b^{7} c^{3} - 59 \, a b^{5} c^{4} + 136 \, a^{2} b^{3} c^{5} - 48 \, a^{3} b c^{6}\right)} d^{3} e^{7} - 6 \, {\left(3 \, b^{8} c^{2} - 146 \, a b^{6} c^{3} + 1289 \, a^{2} b^{4} c^{4} - 4072 \, a^{3} b^{2} c^{5} + 4240 \, a^{4} c^{6}\right)} d^{2} e^{8} + 3 \, {\left(27 \, b^{9} c - 474 \, a b^{7} c^{2} + 3026 \, a^{2} b^{5} c^{3} - 8368 \, a^{3} b^{3} c^{4} + 8480 \, a^{4} b c^{5}\right)} d e^{9} - {\left(27 \, b^{10} - 459 \, a b^{8} c + 2961 \, a^{2} b^{6} c^{2} - 8818 \, a^{3} b^{4} c^{3} + 11360 \, a^{4} b^{2} c^{4} - 4000 \, a^{5} c^{5}\right)} e^{10} - {\left(8 \, {\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{3} - 12 \, {\left(b^{7} c^{7} - 12 \, a b^{5} c^{8} + 48 \, a^{2} b^{3} c^{9} - 64 \, a^{3} b c^{10}\right)} d^{2} e - 2 \, {\left(b^{8} c^{6} - 28 \, a b^{6} c^{7} + 240 \, a^{2} b^{4} c^{8} - 832 \, a^{3} b^{2} c^{9} + 1024 \, a^{4} c^{10}\right)} d e^{2} + {\left(3 \, b^{9} c^{5} - 52 \, a b^{7} c^{6} + 336 \, a^{2} b^{5} c^{7} - 960 \, a^{3} b^{3} c^{8} + 1024 \, a^{4} b c^{9}\right)} e^{3}\right)} \sqrt{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\frac{32 \, c^{7} d^{7} - 112 \, b c^{6} d^{6} e + 14 \, {\left(7 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} + 35 \, {\left(b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{4} e^{3} - 70 \, {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{3} e^{4} + 14 \, {\left(b^{5} c^{2} + 5 \, a b^{3} c^{3} - 60 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 7 \, {\left(3 \, b^{6} c - 40 \, a b^{4} c^{2} + 150 \, a^{2} b^{2} c^{3} - 120 \, a^{3} c^{4}\right)} d e^{6} - {\left(9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}\right)} e^{7} + {\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{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} - 2 \, {\left(560 \, c^{8} d^{10} e^{3} - 2800 \, b c^{7} d^{9} e^{4} + 7 \, {\left(647 \, b^{2} c^{6} + 1012 \, a c^{7}\right)} d^{8} e^{5} - 28 \, {\left(47 \, b^{3} c^{5} + 1012 \, a b c^{6}\right)} d^{7} e^{6} - {\left(3329 \, b^{4} c^{4} - 35844 \, a b^{2} c^{5} - 27488 \, a^{2} c^{6}\right)} d^{6} e^{7} + {\left(2833 \, b^{5} c^{3} - 8356 \, a b^{3} c^{4} - 82464 \, a^{2} b c^{5}\right)} d^{5} e^{8} + {\left(9 \, b^{6} c^{2} - 14273 \, a b^{4} c^{3} + 77982 \, a^{2} b^{2} c^{4} + 33464 \, a^{3} c^{5}\right)} d^{4} e^{9} - {\left(675 \, b^{7} c - 9414 \, a b^{5} c^{2} + 18524 \, a^{2} b^{3} c^{3} + 66928 \, a^{3} b c^{4}\right)} d^{3} e^{10} + {\left(189 \, b^{8} - 999 \, a b^{6} c - 8127 \, a^{2} b^{4} c^{2} + 40196 \, a^{3} b^{2} c^{3} + 10000 \, a^{4} c^{4}\right)} d^{2} e^{11} - {\left(378 \, a b^{7} - 3645 \, a^{2} b^{5} c + 6732 \, a^{3} b^{3} c^{2} + 10000 \, a^{4} b c^{3}\right)} d e^{12} + {\left(189 \, a^{2} b^{6} - 1971 \, a^{3} b^{4} c + 5625 \, a^{4} b^{2} c^{2} - 2500 \, a^{5} c^{3}\right)} e^{13}\right)} \sqrt{e x + d}\right) + \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{\frac{32 \, c^{7} d^{7} - 112 \, b c^{6} d^{6} e + 14 \, {\left(7 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} + 35 \, {\left(b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{4} e^{3} - 70 \, {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{3} e^{4} + 14 \, {\left(b^{5} c^{2} + 5 \, a b^{3} c^{3} - 60 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 7 \, {\left(3 \, b^{6} c - 40 \, a b^{4} c^{2} + 150 \, a^{2} b^{2} c^{3} - 120 \, a^{3} c^{4}\right)} d e^{6} - {\left(9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}\right)} e^{7} - {\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{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(\sqrt{\frac{1}{2}} {\left(70 \, {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{6} e^{4} - 210 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{5} e^{5} + 21 \, {\left(13 \, b^{6} c^{4} - 106 \, a b^{4} c^{5} + 224 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{4} e^{6} - 28 \, {\left(7 \, b^{7} c^{3} - 59 \, a b^{5} c^{4} + 136 \, a^{2} b^{3} c^{5} - 48 \, a^{3} b c^{6}\right)} d^{3} e^{7} - 6 \, {\left(3 \, b^{8} c^{2} - 146 \, a b^{6} c^{3} + 1289 \, a^{2} b^{4} c^{4} - 4072 \, a^{3} b^{2} c^{5} + 4240 \, a^{4} c^{6}\right)} d^{2} e^{8} + 3 \, {\left(27 \, b^{9} c - 474 \, a b^{7} c^{2} + 3026 \, a^{2} b^{5} c^{3} - 8368 \, a^{3} b^{3} c^{4} + 8480 \, a^{4} b c^{5}\right)} d e^{9} - {\left(27 \, b^{10} - 459 \, a b^{8} c + 2961 \, a^{2} b^{6} c^{2} - 8818 \, a^{3} b^{4} c^{3} + 11360 \, a^{4} b^{2} c^{4} - 4000 \, a^{5} c^{5}\right)} e^{10} + {\left(8 \, {\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{3} - 12 \, {\left(b^{7} c^{7} - 12 \, a b^{5} c^{8} + 48 \, a^{2} b^{3} c^{9} - 64 \, a^{3} b c^{10}\right)} d^{2} e - 2 \, {\left(b^{8} c^{6} - 28 \, a b^{6} c^{7} + 240 \, a^{2} b^{4} c^{8} - 832 \, a^{3} b^{2} c^{9} + 1024 \, a^{4} c^{10}\right)} d e^{2} + {\left(3 \, b^{9} c^{5} - 52 \, a b^{7} c^{6} + 336 \, a^{2} b^{5} c^{7} - 960 \, a^{3} b^{3} c^{8} + 1024 \, a^{4} b c^{9}\right)} e^{3}\right)} \sqrt{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\frac{32 \, c^{7} d^{7} - 112 \, b c^{6} d^{6} e + 14 \, {\left(7 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} + 35 \, {\left(b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{4} e^{3} - 70 \, {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{3} e^{4} + 14 \, {\left(b^{5} c^{2} + 5 \, a b^{3} c^{3} - 60 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 7 \, {\left(3 \, b^{6} c - 40 \, a b^{4} c^{2} + 150 \, a^{2} b^{2} c^{3} - 120 \, a^{3} c^{4}\right)} d e^{6} - {\left(9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}\right)} e^{7} - {\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{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} - 2 \, {\left(560 \, c^{8} d^{10} e^{3} - 2800 \, b c^{7} d^{9} e^{4} + 7 \, {\left(647 \, b^{2} c^{6} + 1012 \, a c^{7}\right)} d^{8} e^{5} - 28 \, {\left(47 \, b^{3} c^{5} + 1012 \, a b c^{6}\right)} d^{7} e^{6} - {\left(3329 \, b^{4} c^{4} - 35844 \, a b^{2} c^{5} - 27488 \, a^{2} c^{6}\right)} d^{6} e^{7} + {\left(2833 \, b^{5} c^{3} - 8356 \, a b^{3} c^{4} - 82464 \, a^{2} b c^{5}\right)} d^{5} e^{8} + {\left(9 \, b^{6} c^{2} - 14273 \, a b^{4} c^{3} + 77982 \, a^{2} b^{2} c^{4} + 33464 \, a^{3} c^{5}\right)} d^{4} e^{9} - {\left(675 \, b^{7} c - 9414 \, a b^{5} c^{2} + 18524 \, a^{2} b^{3} c^{3} + 66928 \, a^{3} b c^{4}\right)} d^{3} e^{10} + {\left(189 \, b^{8} - 999 \, a b^{6} c - 8127 \, a^{2} b^{4} c^{2} + 40196 \, a^{3} b^{2} c^{3} + 10000 \, a^{4} c^{4}\right)} d^{2} e^{11} - {\left(378 \, a b^{7} - 3645 \, a^{2} b^{5} c + 6732 \, a^{3} b^{3} c^{2} + 10000 \, a^{4} b c^{3}\right)} d e^{12} + {\left(189 \, a^{2} b^{6} - 1971 \, a^{3} b^{4} c + 5625 \, a^{4} b^{2} c^{2} - 2500 \, a^{5} c^{3}\right)} e^{13}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)} \sqrt{\frac{32 \, c^{7} d^{7} - 112 \, b c^{6} d^{6} e + 14 \, {\left(7 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} + 35 \, {\left(b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{4} e^{3} - 70 \, {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{3} e^{4} + 14 \, {\left(b^{5} c^{2} + 5 \, a b^{3} c^{3} - 60 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 7 \, {\left(3 \, b^{6} c - 40 \, a b^{4} c^{2} + 150 \, a^{2} b^{2} c^{3} - 120 \, a^{3} c^{4}\right)} d e^{6} - {\left(9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}\right)} e^{7} - {\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{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} \log\left(-\sqrt{\frac{1}{2}} {\left(70 \, {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{6} e^{4} - 210 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{5} e^{5} + 21 \, {\left(13 \, b^{6} c^{4} - 106 \, a b^{4} c^{5} + 224 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{4} e^{6} - 28 \, {\left(7 \, b^{7} c^{3} - 59 \, a b^{5} c^{4} + 136 \, a^{2} b^{3} c^{5} - 48 \, a^{3} b c^{6}\right)} d^{3} e^{7} - 6 \, {\left(3 \, b^{8} c^{2} - 146 \, a b^{6} c^{3} + 1289 \, a^{2} b^{4} c^{4} - 4072 \, a^{3} b^{2} c^{5} + 4240 \, a^{4} c^{6}\right)} d^{2} e^{8} + 3 \, {\left(27 \, b^{9} c - 474 \, a b^{7} c^{2} + 3026 \, a^{2} b^{5} c^{3} - 8368 \, a^{3} b^{3} c^{4} + 8480 \, a^{4} b c^{5}\right)} d e^{9} - {\left(27 \, b^{10} - 459 \, a b^{8} c + 2961 \, a^{2} b^{6} c^{2} - 8818 \, a^{3} b^{4} c^{3} + 11360 \, a^{4} b^{2} c^{4} - 4000 \, a^{5} c^{5}\right)} e^{10} + {\left(8 \, {\left(b^{6} c^{8} - 12 \, a b^{4} c^{9} + 48 \, a^{2} b^{2} c^{10} - 64 \, a^{3} c^{11}\right)} d^{3} - 12 \, {\left(b^{7} c^{7} - 12 \, a b^{5} c^{8} + 48 \, a^{2} b^{3} c^{9} - 64 \, a^{3} b c^{10}\right)} d^{2} e - 2 \, {\left(b^{8} c^{6} - 28 \, a b^{6} c^{7} + 240 \, a^{2} b^{4} c^{8} - 832 \, a^{3} b^{2} c^{9} + 1024 \, a^{4} c^{10}\right)} d e^{2} + {\left(3 \, b^{9} c^{5} - 52 \, a b^{7} c^{6} + 336 \, a^{2} b^{5} c^{7} - 960 \, a^{3} b^{3} c^{8} + 1024 \, a^{4} b c^{9}\right)} e^{3}\right)} \sqrt{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}\right)} \sqrt{\frac{32 \, c^{7} d^{7} - 112 \, b c^{6} d^{6} e + 14 \, {\left(7 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} + 35 \, {\left(b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{4} e^{3} - 70 \, {\left(b^{4} c^{3} - 6 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{3} e^{4} + 14 \, {\left(b^{5} c^{2} + 5 \, a b^{3} c^{3} - 60 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 7 \, {\left(3 \, b^{6} c - 40 \, a b^{4} c^{2} + 150 \, a^{2} b^{2} c^{3} - 120 \, a^{3} c^{4}\right)} d e^{6} - {\left(9 \, b^{7} - 105 \, a b^{5} c + 385 \, a^{2} b^{3} c^{2} - 420 \, a^{3} b c^{3}\right)} e^{7} - {\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{\frac{1225 \, c^{8} d^{8} e^{6} - 4900 \, b c^{7} d^{7} e^{7} + 980 \, {\left(6 \, b^{2} c^{6} + 11 \, a c^{7}\right)} d^{6} e^{8} - 490 \, {\left(b^{3} c^{5} + 66 \, a b c^{6}\right)} d^{5} e^{9} - 14 \, {\left(241 \, b^{4} c^{4} - 2103 \, a b^{2} c^{5} - 1569 \, a^{2} c^{6}\right)} d^{4} e^{10} + 28 \, {\left(66 \, b^{5} c^{3} - 178 \, a b^{3} c^{4} - 1569 \, a^{2} b c^{5}\right)} d^{3} e^{11} + 7 \, {\left(27 \, b^{6} c^{2} - 1116 \, a b^{4} c^{3} + 5532 \, a^{2} b^{2} c^{4} - 1100 \, a^{3} c^{5}\right)} d^{2} e^{12} - 14 \, {\left(27 \, b^{7} c - 351 \, a b^{5} c^{2} + 1197 \, a^{2} b^{3} c^{3} - 550 \, a^{3} b c^{4}\right)} d e^{13} + {\left(81 \, b^{8} - 918 \, a b^{6} c + 3051 \, a^{2} b^{4} c^{2} - 2550 \, a^{3} b^{2} c^{3} + 625 \, a^{4} c^{4}\right)} e^{14}}{b^{6} c^{10} - 12 \, a b^{4} c^{11} + 48 \, a^{2} b^{2} c^{12} - 64 \, a^{3} c^{13}}}}{b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}}} - 2 \, {\left(560 \, c^{8} d^{10} e^{3} - 2800 \, b c^{7} d^{9} e^{4} + 7 \, {\left(647 \, b^{2} c^{6} + 1012 \, a c^{7}\right)} d^{8} e^{5} - 28 \, {\left(47 \, b^{3} c^{5} + 1012 \, a b c^{6}\right)} d^{7} e^{6} - {\left(3329 \, b^{4} c^{4} - 35844 \, a b^{2} c^{5} - 27488 \, a^{2} c^{6}\right)} d^{6} e^{7} + {\left(2833 \, b^{5} c^{3} - 8356 \, a b^{3} c^{4} - 82464 \, a^{2} b c^{5}\right)} d^{5} e^{8} + {\left(9 \, b^{6} c^{2} - 14273 \, a b^{4} c^{3} + 77982 \, a^{2} b^{2} c^{4} + 33464 \, a^{3} c^{5}\right)} d^{4} e^{9} - {\left(675 \, b^{7} c - 9414 \, a b^{5} c^{2} + 18524 \, a^{2} b^{3} c^{3} + 66928 \, a^{3} b c^{4}\right)} d^{3} e^{10} + {\left(189 \, b^{8} - 999 \, a b^{6} c - 8127 \, a^{2} b^{4} c^{2} + 40196 \, a^{3} b^{2} c^{3} + 10000 \, a^{4} c^{4}\right)} d^{2} e^{11} - {\left(378 \, a b^{7} - 3645 \, a^{2} b^{5} c + 6732 \, a^{3} b^{3} c^{2} + 10000 \, a^{4} b c^{3}\right)} d e^{12} + {\left(189 \, a^{2} b^{6} - 1971 \, a^{3} b^{4} c + 5625 \, a^{4} b^{2} c^{2} - 2500 \, a^{5} c^{3}\right)} e^{13}\right)} \sqrt{e x + d}\right) + 2 \, {\left(b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3} x^{2} - {\left(3 \, a b^{2} - 10 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{2} - {\left(3 \, b^{3} - 11 \, a b c\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)}}"," ",0,"-1/2*(sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)*sqrt((32*c^7*d^7 - 112*b*c^6*d^6*e + 14*(7*b^2*c^5 + 20*a*c^6)*d^5*e^2 + 35*(b^3*c^4 - 20*a*b*c^5)*d^4*e^3 - 70*(b^4*c^3 - 6*a*b^2*c^4 - 8*a^2*c^5)*d^3*e^4 + 14*(b^5*c^2 + 5*a*b^3*c^3 - 60*a^2*b*c^4)*d^2*e^5 + 7*(3*b^6*c - 40*a*b^4*c^2 + 150*a^2*b^2*c^3 - 120*a^3*c^4)*d*e^6 - (9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)*e^7 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(sqrt(1/2)*(70*(b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^6*e^4 - 210*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^5*e^5 + 21*(13*b^6*c^4 - 106*a*b^4*c^5 + 224*a^2*b^2*c^6 - 32*a^3*c^7)*d^4*e^6 - 28*(7*b^7*c^3 - 59*a*b^5*c^4 + 136*a^2*b^3*c^5 - 48*a^3*b*c^6)*d^3*e^7 - 6*(3*b^8*c^2 - 146*a*b^6*c^3 + 1289*a^2*b^4*c^4 - 4072*a^3*b^2*c^5 + 4240*a^4*c^6)*d^2*e^8 + 3*(27*b^9*c - 474*a*b^7*c^2 + 3026*a^2*b^5*c^3 - 8368*a^3*b^3*c^4 + 8480*a^4*b*c^5)*d*e^9 - (27*b^10 - 459*a*b^8*c + 2961*a^2*b^6*c^2 - 8818*a^3*b^4*c^3 + 11360*a^4*b^2*c^4 - 4000*a^5*c^5)*e^10 - (8*(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^3 - 12*(b^7*c^7 - 12*a*b^5*c^8 + 48*a^2*b^3*c^9 - 64*a^3*b*c^10)*d^2*e - 2*(b^8*c^6 - 28*a*b^6*c^7 + 240*a^2*b^4*c^8 - 832*a^3*b^2*c^9 + 1024*a^4*c^10)*d*e^2 + (3*b^9*c^5 - 52*a*b^7*c^6 + 336*a^2*b^5*c^7 - 960*a^3*b^3*c^8 + 1024*a^4*b*c^9)*e^3)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt((32*c^7*d^7 - 112*b*c^6*d^6*e + 14*(7*b^2*c^5 + 20*a*c^6)*d^5*e^2 + 35*(b^3*c^4 - 20*a*b*c^5)*d^4*e^3 - 70*(b^4*c^3 - 6*a*b^2*c^4 - 8*a^2*c^5)*d^3*e^4 + 14*(b^5*c^2 + 5*a*b^3*c^3 - 60*a^2*b*c^4)*d^2*e^5 + 7*(3*b^6*c - 40*a*b^4*c^2 + 150*a^2*b^2*c^3 - 120*a^3*c^4)*d*e^6 - (9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)*e^7 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)) - 2*(560*c^8*d^10*e^3 - 2800*b*c^7*d^9*e^4 + 7*(647*b^2*c^6 + 1012*a*c^7)*d^8*e^5 - 28*(47*b^3*c^5 + 1012*a*b*c^6)*d^7*e^6 - (3329*b^4*c^4 - 35844*a*b^2*c^5 - 27488*a^2*c^6)*d^6*e^7 + (2833*b^5*c^3 - 8356*a*b^3*c^4 - 82464*a^2*b*c^5)*d^5*e^8 + (9*b^6*c^2 - 14273*a*b^4*c^3 + 77982*a^2*b^2*c^4 + 33464*a^3*c^5)*d^4*e^9 - (675*b^7*c - 9414*a*b^5*c^2 + 18524*a^2*b^3*c^3 + 66928*a^3*b*c^4)*d^3*e^10 + (189*b^8 - 999*a*b^6*c - 8127*a^2*b^4*c^2 + 40196*a^3*b^2*c^3 + 10000*a^4*c^4)*d^2*e^11 - (378*a*b^7 - 3645*a^2*b^5*c + 6732*a^3*b^3*c^2 + 10000*a^4*b*c^3)*d*e^12 + (189*a^2*b^6 - 1971*a^3*b^4*c + 5625*a^4*b^2*c^2 - 2500*a^5*c^3)*e^13)*sqrt(e*x + d)) - sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)*sqrt((32*c^7*d^7 - 112*b*c^6*d^6*e + 14*(7*b^2*c^5 + 20*a*c^6)*d^5*e^2 + 35*(b^3*c^4 - 20*a*b*c^5)*d^4*e^3 - 70*(b^4*c^3 - 6*a*b^2*c^4 - 8*a^2*c^5)*d^3*e^4 + 14*(b^5*c^2 + 5*a*b^3*c^3 - 60*a^2*b*c^4)*d^2*e^5 + 7*(3*b^6*c - 40*a*b^4*c^2 + 150*a^2*b^2*c^3 - 120*a^3*c^4)*d*e^6 - (9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)*e^7 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(-sqrt(1/2)*(70*(b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^6*e^4 - 210*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^5*e^5 + 21*(13*b^6*c^4 - 106*a*b^4*c^5 + 224*a^2*b^2*c^6 - 32*a^3*c^7)*d^4*e^6 - 28*(7*b^7*c^3 - 59*a*b^5*c^4 + 136*a^2*b^3*c^5 - 48*a^3*b*c^6)*d^3*e^7 - 6*(3*b^8*c^2 - 146*a*b^6*c^3 + 1289*a^2*b^4*c^4 - 4072*a^3*b^2*c^5 + 4240*a^4*c^6)*d^2*e^8 + 3*(27*b^9*c - 474*a*b^7*c^2 + 3026*a^2*b^5*c^3 - 8368*a^3*b^3*c^4 + 8480*a^4*b*c^5)*d*e^9 - (27*b^10 - 459*a*b^8*c + 2961*a^2*b^6*c^2 - 8818*a^3*b^4*c^3 + 11360*a^4*b^2*c^4 - 4000*a^5*c^5)*e^10 - (8*(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^3 - 12*(b^7*c^7 - 12*a*b^5*c^8 + 48*a^2*b^3*c^9 - 64*a^3*b*c^10)*d^2*e - 2*(b^8*c^6 - 28*a*b^6*c^7 + 240*a^2*b^4*c^8 - 832*a^3*b^2*c^9 + 1024*a^4*c^10)*d*e^2 + (3*b^9*c^5 - 52*a*b^7*c^6 + 336*a^2*b^5*c^7 - 960*a^3*b^3*c^8 + 1024*a^4*b*c^9)*e^3)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt((32*c^7*d^7 - 112*b*c^6*d^6*e + 14*(7*b^2*c^5 + 20*a*c^6)*d^5*e^2 + 35*(b^3*c^4 - 20*a*b*c^5)*d^4*e^3 - 70*(b^4*c^3 - 6*a*b^2*c^4 - 8*a^2*c^5)*d^3*e^4 + 14*(b^5*c^2 + 5*a*b^3*c^3 - 60*a^2*b*c^4)*d^2*e^5 + 7*(3*b^6*c - 40*a*b^4*c^2 + 150*a^2*b^2*c^3 - 120*a^3*c^4)*d*e^6 - (9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)*e^7 + (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)) - 2*(560*c^8*d^10*e^3 - 2800*b*c^7*d^9*e^4 + 7*(647*b^2*c^6 + 1012*a*c^7)*d^8*e^5 - 28*(47*b^3*c^5 + 1012*a*b*c^6)*d^7*e^6 - (3329*b^4*c^4 - 35844*a*b^2*c^5 - 27488*a^2*c^6)*d^6*e^7 + (2833*b^5*c^3 - 8356*a*b^3*c^4 - 82464*a^2*b*c^5)*d^5*e^8 + (9*b^6*c^2 - 14273*a*b^4*c^3 + 77982*a^2*b^2*c^4 + 33464*a^3*c^5)*d^4*e^9 - (675*b^7*c - 9414*a*b^5*c^2 + 18524*a^2*b^3*c^3 + 66928*a^3*b*c^4)*d^3*e^10 + (189*b^8 - 999*a*b^6*c - 8127*a^2*b^4*c^2 + 40196*a^3*b^2*c^3 + 10000*a^4*c^4)*d^2*e^11 - (378*a*b^7 - 3645*a^2*b^5*c + 6732*a^3*b^3*c^2 + 10000*a^4*b*c^3)*d*e^12 + (189*a^2*b^6 - 1971*a^3*b^4*c + 5625*a^4*b^2*c^2 - 2500*a^5*c^3)*e^13)*sqrt(e*x + d)) + sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)*sqrt((32*c^7*d^7 - 112*b*c^6*d^6*e + 14*(7*b^2*c^5 + 20*a*c^6)*d^5*e^2 + 35*(b^3*c^4 - 20*a*b*c^5)*d^4*e^3 - 70*(b^4*c^3 - 6*a*b^2*c^4 - 8*a^2*c^5)*d^3*e^4 + 14*(b^5*c^2 + 5*a*b^3*c^3 - 60*a^2*b*c^4)*d^2*e^5 + 7*(3*b^6*c - 40*a*b^4*c^2 + 150*a^2*b^2*c^3 - 120*a^3*c^4)*d*e^6 - (9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)*e^7 - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(sqrt(1/2)*(70*(b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^6*e^4 - 210*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^5*e^5 + 21*(13*b^6*c^4 - 106*a*b^4*c^5 + 224*a^2*b^2*c^6 - 32*a^3*c^7)*d^4*e^6 - 28*(7*b^7*c^3 - 59*a*b^5*c^4 + 136*a^2*b^3*c^5 - 48*a^3*b*c^6)*d^3*e^7 - 6*(3*b^8*c^2 - 146*a*b^6*c^3 + 1289*a^2*b^4*c^4 - 4072*a^3*b^2*c^5 + 4240*a^4*c^6)*d^2*e^8 + 3*(27*b^9*c - 474*a*b^7*c^2 + 3026*a^2*b^5*c^3 - 8368*a^3*b^3*c^4 + 8480*a^4*b*c^5)*d*e^9 - (27*b^10 - 459*a*b^8*c + 2961*a^2*b^6*c^2 - 8818*a^3*b^4*c^3 + 11360*a^4*b^2*c^4 - 4000*a^5*c^5)*e^10 + (8*(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^3 - 12*(b^7*c^7 - 12*a*b^5*c^8 + 48*a^2*b^3*c^9 - 64*a^3*b*c^10)*d^2*e - 2*(b^8*c^6 - 28*a*b^6*c^7 + 240*a^2*b^4*c^8 - 832*a^3*b^2*c^9 + 1024*a^4*c^10)*d*e^2 + (3*b^9*c^5 - 52*a*b^7*c^6 + 336*a^2*b^5*c^7 - 960*a^3*b^3*c^8 + 1024*a^4*b*c^9)*e^3)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt((32*c^7*d^7 - 112*b*c^6*d^6*e + 14*(7*b^2*c^5 + 20*a*c^6)*d^5*e^2 + 35*(b^3*c^4 - 20*a*b*c^5)*d^4*e^3 - 70*(b^4*c^3 - 6*a*b^2*c^4 - 8*a^2*c^5)*d^3*e^4 + 14*(b^5*c^2 + 5*a*b^3*c^3 - 60*a^2*b*c^4)*d^2*e^5 + 7*(3*b^6*c - 40*a*b^4*c^2 + 150*a^2*b^2*c^3 - 120*a^3*c^4)*d*e^6 - (9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)*e^7 - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)) - 2*(560*c^8*d^10*e^3 - 2800*b*c^7*d^9*e^4 + 7*(647*b^2*c^6 + 1012*a*c^7)*d^8*e^5 - 28*(47*b^3*c^5 + 1012*a*b*c^6)*d^7*e^6 - (3329*b^4*c^4 - 35844*a*b^2*c^5 - 27488*a^2*c^6)*d^6*e^7 + (2833*b^5*c^3 - 8356*a*b^3*c^4 - 82464*a^2*b*c^5)*d^5*e^8 + (9*b^6*c^2 - 14273*a*b^4*c^3 + 77982*a^2*b^2*c^4 + 33464*a^3*c^5)*d^4*e^9 - (675*b^7*c - 9414*a*b^5*c^2 + 18524*a^2*b^3*c^3 + 66928*a^3*b*c^4)*d^3*e^10 + (189*b^8 - 999*a*b^6*c - 8127*a^2*b^4*c^2 + 40196*a^3*b^2*c^3 + 10000*a^4*c^4)*d^2*e^11 - (378*a*b^7 - 3645*a^2*b^5*c + 6732*a^3*b^3*c^2 + 10000*a^4*b*c^3)*d*e^12 + (189*a^2*b^6 - 1971*a^3*b^4*c + 5625*a^4*b^2*c^2 - 2500*a^5*c^3)*e^13)*sqrt(e*x + d)) - sqrt(1/2)*(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)*sqrt((32*c^7*d^7 - 112*b*c^6*d^6*e + 14*(7*b^2*c^5 + 20*a*c^6)*d^5*e^2 + 35*(b^3*c^4 - 20*a*b*c^5)*d^4*e^3 - 70*(b^4*c^3 - 6*a*b^2*c^4 - 8*a^2*c^5)*d^3*e^4 + 14*(b^5*c^2 + 5*a*b^3*c^3 - 60*a^2*b*c^4)*d^2*e^5 + 7*(3*b^6*c - 40*a*b^4*c^2 + 150*a^2*b^2*c^3 - 120*a^3*c^4)*d*e^6 - (9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)*e^7 - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8))*log(-sqrt(1/2)*(70*(b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^6*e^4 - 210*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^5*e^5 + 21*(13*b^6*c^4 - 106*a*b^4*c^5 + 224*a^2*b^2*c^6 - 32*a^3*c^7)*d^4*e^6 - 28*(7*b^7*c^3 - 59*a*b^5*c^4 + 136*a^2*b^3*c^5 - 48*a^3*b*c^6)*d^3*e^7 - 6*(3*b^8*c^2 - 146*a*b^6*c^3 + 1289*a^2*b^4*c^4 - 4072*a^3*b^2*c^5 + 4240*a^4*c^6)*d^2*e^8 + 3*(27*b^9*c - 474*a*b^7*c^2 + 3026*a^2*b^5*c^3 - 8368*a^3*b^3*c^4 + 8480*a^4*b*c^5)*d*e^9 - (27*b^10 - 459*a*b^8*c + 2961*a^2*b^6*c^2 - 8818*a^3*b^4*c^3 + 11360*a^4*b^2*c^4 - 4000*a^5*c^5)*e^10 + (8*(b^6*c^8 - 12*a*b^4*c^9 + 48*a^2*b^2*c^10 - 64*a^3*c^11)*d^3 - 12*(b^7*c^7 - 12*a*b^5*c^8 + 48*a^2*b^3*c^9 - 64*a^3*b*c^10)*d^2*e - 2*(b^8*c^6 - 28*a*b^6*c^7 + 240*a^2*b^4*c^8 - 832*a^3*b^2*c^9 + 1024*a^4*c^10)*d*e^2 + (3*b^9*c^5 - 52*a*b^7*c^6 + 336*a^2*b^5*c^7 - 960*a^3*b^3*c^8 + 1024*a^4*b*c^9)*e^3)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))*sqrt((32*c^7*d^7 - 112*b*c^6*d^6*e + 14*(7*b^2*c^5 + 20*a*c^6)*d^5*e^2 + 35*(b^3*c^4 - 20*a*b*c^5)*d^4*e^3 - 70*(b^4*c^3 - 6*a*b^2*c^4 - 8*a^2*c^5)*d^3*e^4 + 14*(b^5*c^2 + 5*a*b^3*c^3 - 60*a^2*b*c^4)*d^2*e^5 + 7*(3*b^6*c - 40*a*b^4*c^2 + 150*a^2*b^2*c^3 - 120*a^3*c^4)*d*e^6 - (9*b^7 - 105*a*b^5*c + 385*a^2*b^3*c^2 - 420*a^3*b*c^3)*e^7 - (b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*sqrt((1225*c^8*d^8*e^6 - 4900*b*c^7*d^7*e^7 + 980*(6*b^2*c^6 + 11*a*c^7)*d^6*e^8 - 490*(b^3*c^5 + 66*a*b*c^6)*d^5*e^9 - 14*(241*b^4*c^4 - 2103*a*b^2*c^5 - 1569*a^2*c^6)*d^4*e^10 + 28*(66*b^5*c^3 - 178*a*b^3*c^4 - 1569*a^2*b*c^5)*d^3*e^11 + 7*(27*b^6*c^2 - 1116*a*b^4*c^3 + 5532*a^2*b^2*c^4 - 1100*a^3*c^5)*d^2*e^12 - 14*(27*b^7*c - 351*a*b^5*c^2 + 1197*a^2*b^3*c^3 - 550*a^3*b*c^4)*d*e^13 + (81*b^8 - 918*a*b^6*c + 3051*a^2*b^4*c^2 - 2550*a^3*b^2*c^3 + 625*a^4*c^4)*e^14)/(b^6*c^10 - 12*a*b^4*c^11 + 48*a^2*b^2*c^12 - 64*a^3*c^13)))/(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)) - 2*(560*c^8*d^10*e^3 - 2800*b*c^7*d^9*e^4 + 7*(647*b^2*c^6 + 1012*a*c^7)*d^8*e^5 - 28*(47*b^3*c^5 + 1012*a*b*c^6)*d^7*e^6 - (3329*b^4*c^4 - 35844*a*b^2*c^5 - 27488*a^2*c^6)*d^6*e^7 + (2833*b^5*c^3 - 8356*a*b^3*c^4 - 82464*a^2*b*c^5)*d^5*e^8 + (9*b^6*c^2 - 14273*a*b^4*c^3 + 77982*a^2*b^2*c^4 + 33464*a^3*c^5)*d^4*e^9 - (675*b^7*c - 9414*a*b^5*c^2 + 18524*a^2*b^3*c^3 + 66928*a^3*b*c^4)*d^3*e^10 + (189*b^8 - 999*a*b^6*c - 8127*a^2*b^4*c^2 + 40196*a^3*b^2*c^3 + 10000*a^4*c^4)*d^2*e^11 - (378*a*b^7 - 3645*a^2*b^5*c + 6732*a^3*b^3*c^2 + 10000*a^4*b*c^3)*d*e^12 + (189*a^2*b^6 - 1971*a^3*b^4*c + 5625*a^4*b^2*c^2 - 2500*a^5*c^3)*e^13)*sqrt(e*x + d)) + 2*(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - 2*(b^2*c - 4*a*c^2)*e^3*x^2 - (3*a*b^2 - 10*a^2*c)*e^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e + 3*(b^2*c - 2*a*c^2)*d*e^2 - (3*b^3 - 11*a*b*c)*e^3)*x)*sqrt(e*x + d))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)","B",0
2296,1,5256,0,0.822182," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \sqrt{\frac{32 \, c^{5} d^{5} - 80 \, b c^{4} d^{4} e + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{2} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{3} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{5} + {\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{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(\sqrt{\frac{1}{2}} {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} e^{4} - 15 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 3 \, {\left(b^{6} c - 2 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} + 96 \, a^{3} c^{4}\right)} d e^{6} + {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3}\right)} e^{7} - {\left(8 \, {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} d^{2} - 8 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} d e - {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\frac{32 \, c^{5} d^{5} - 80 \, b c^{4} d^{4} e + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{2} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{3} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{5} + {\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{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} + 2 \, {\left(80 \, c^{5} d^{6} e^{3} - 240 \, b c^{4} d^{5} e^{4} + {\left(199 \, b^{2} c^{3} + 404 \, a c^{4}\right)} d^{4} e^{5} + 2 \, {\left(b^{3} c^{2} - 404 \, a b c^{3}\right)} d^{3} e^{6} - 6 \, {\left(6 \, b^{4} c - 47 \, a b^{2} c^{2} - 108 \, a^{2} c^{3}\right)} d^{2} e^{7} - {\left(5 \, b^{5} - 122 \, a b^{3} c + 648 \, a^{2} b c^{2}\right)} d e^{8} + {\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \sqrt{\frac{32 \, c^{5} d^{5} - 80 \, b c^{4} d^{4} e + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{2} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{3} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{5} + {\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{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(-\sqrt{\frac{1}{2}} {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} e^{4} - 15 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 3 \, {\left(b^{6} c - 2 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} + 96 \, a^{3} c^{4}\right)} d e^{6} + {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3}\right)} e^{7} - {\left(8 \, {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} d^{2} - 8 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} d e - {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\frac{32 \, c^{5} d^{5} - 80 \, b c^{4} d^{4} e + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{2} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{3} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{5} + {\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{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} + 2 \, {\left(80 \, c^{5} d^{6} e^{3} - 240 \, b c^{4} d^{5} e^{4} + {\left(199 \, b^{2} c^{3} + 404 \, a c^{4}\right)} d^{4} e^{5} + 2 \, {\left(b^{3} c^{2} - 404 \, a b c^{3}\right)} d^{3} e^{6} - 6 \, {\left(6 \, b^{4} c - 47 \, a b^{2} c^{2} - 108 \, a^{2} c^{3}\right)} d^{2} e^{7} - {\left(5 \, b^{5} - 122 \, a b^{3} c + 648 \, a^{2} b c^{2}\right)} d e^{8} + {\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) + \sqrt{\frac{1}{2}} {\left(a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \sqrt{\frac{32 \, c^{5} d^{5} - 80 \, b c^{4} d^{4} e + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{2} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{3} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{5} - {\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{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(\sqrt{\frac{1}{2}} {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} e^{4} - 15 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 3 \, {\left(b^{6} c - 2 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} + 96 \, a^{3} c^{4}\right)} d e^{6} + {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3}\right)} e^{7} + {\left(8 \, {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} d^{2} - 8 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} d e - {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\frac{32 \, c^{5} d^{5} - 80 \, b c^{4} d^{4} e + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{2} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{3} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{5} - {\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{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} + 2 \, {\left(80 \, c^{5} d^{6} e^{3} - 240 \, b c^{4} d^{5} e^{4} + {\left(199 \, b^{2} c^{3} + 404 \, a c^{4}\right)} d^{4} e^{5} + 2 \, {\left(b^{3} c^{2} - 404 \, a b c^{3}\right)} d^{3} e^{6} - 6 \, {\left(6 \, b^{4} c - 47 \, a b^{2} c^{2} - 108 \, a^{2} c^{3}\right)} d^{2} e^{7} - {\left(5 \, b^{5} - 122 \, a b^{3} c + 648 \, a^{2} b c^{2}\right)} d e^{8} + {\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)} \sqrt{\frac{32 \, c^{5} d^{5} - 80 \, b c^{4} d^{4} e + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{2} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{3} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{5} - {\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{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} \log\left(-\sqrt{\frac{1}{2}} {\left(10 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} e^{4} - 15 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{5} + 3 \, {\left(b^{6} c - 2 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} + 96 \, a^{3} c^{4}\right)} d e^{6} + {\left(b^{7} - 17 \, a b^{5} c + 88 \, a^{2} b^{3} c^{2} - 144 \, a^{3} b c^{3}\right)} e^{7} + {\left(8 \, {\left(b^{6} c^{5} - 12 \, a b^{4} c^{6} + 48 \, a^{2} b^{2} c^{7} - 64 \, a^{3} c^{8}\right)} d^{2} - 8 \, {\left(b^{7} c^{4} - 12 \, a b^{5} c^{5} + 48 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} d e - {\left(b^{8} c^{3} - 24 \, a b^{6} c^{4} + 192 \, a^{2} b^{4} c^{5} - 640 \, a^{3} b^{2} c^{6} + 768 \, a^{4} c^{7}\right)} e^{2}\right)} \sqrt{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}\right)} \sqrt{\frac{32 \, c^{5} d^{5} - 80 \, b c^{4} d^{4} e + 10 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{3} e^{2} + 5 \, {\left(b^{3} c^{2} - 36 \, a b c^{3}\right)} d^{2} e^{3} - 5 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} - 24 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} e^{5} - {\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{\frac{25 \, c^{4} d^{4} e^{6} - 50 \, b c^{3} d^{3} e^{7} + 15 \, {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{2} e^{8} + 10 \, {\left(b^{3} c - 9 \, a b c^{2}\right)} d e^{9} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} e^{10}}{b^{6} c^{6} - 12 \, a b^{4} c^{7} + 48 \, a^{2} b^{2} c^{8} - 64 \, a^{3} c^{9}}}}{b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}}} + 2 \, {\left(80 \, c^{5} d^{6} e^{3} - 240 \, b c^{4} d^{5} e^{4} + {\left(199 \, b^{2} c^{3} + 404 \, a c^{4}\right)} d^{4} e^{5} + 2 \, {\left(b^{3} c^{2} - 404 \, a b c^{3}\right)} d^{3} e^{6} - 6 \, {\left(6 \, b^{4} c - 47 \, a b^{2} c^{2} - 108 \, a^{2} c^{3}\right)} d^{2} e^{7} - {\left(5 \, b^{5} - 122 \, a b^{3} c + 648 \, a^{2} b c^{2}\right)} d e^{8} + {\left(5 \, a b^{4} - 81 \, a^{2} b^{2} c + 324 \, a^{3} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) - 2 \, {\left(b c d^{2} - 4 \, a c d e + a b e^{2} + {\left(2 \, c^{2} d^{2} - 2 \, b c d e + {\left(b^{2} - 2 \, a c\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} x^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} x\right)}}"," ",0,"1/2*(sqrt(1/2)*(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)*sqrt((32*c^5*d^5 - 80*b*c^4*d^4*e + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^2 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^3 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^4 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^5 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(sqrt(1/2)*(10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*e^4 - 15*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^5 + 3*(b^6*c - 2*a*b^4*c^2 - 32*a^2*b^2*c^3 + 96*a^3*c^4)*d*e^6 + (b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3)*e^7 - (8*(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*d^2 - 8*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*d*e - (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*e^2)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt((32*c^5*d^5 - 80*b*c^4*d^4*e + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^2 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^3 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^4 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^5 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) + 2*(80*c^5*d^6*e^3 - 240*b*c^4*d^5*e^4 + (199*b^2*c^3 + 404*a*c^4)*d^4*e^5 + 2*(b^3*c^2 - 404*a*b*c^3)*d^3*e^6 - 6*(6*b^4*c - 47*a*b^2*c^2 - 108*a^2*c^3)*d^2*e^7 - (5*b^5 - 122*a*b^3*c + 648*a^2*b*c^2)*d*e^8 + (5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*e^9)*sqrt(e*x + d)) - sqrt(1/2)*(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)*sqrt((32*c^5*d^5 - 80*b*c^4*d^4*e + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^2 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^3 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^4 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^5 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(-sqrt(1/2)*(10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*e^4 - 15*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^5 + 3*(b^6*c - 2*a*b^4*c^2 - 32*a^2*b^2*c^3 + 96*a^3*c^4)*d*e^6 + (b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3)*e^7 - (8*(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*d^2 - 8*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*d*e - (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*e^2)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt((32*c^5*d^5 - 80*b*c^4*d^4*e + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^2 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^3 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^4 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^5 + (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) + 2*(80*c^5*d^6*e^3 - 240*b*c^4*d^5*e^4 + (199*b^2*c^3 + 404*a*c^4)*d^4*e^5 + 2*(b^3*c^2 - 404*a*b*c^3)*d^3*e^6 - 6*(6*b^4*c - 47*a*b^2*c^2 - 108*a^2*c^3)*d^2*e^7 - (5*b^5 - 122*a*b^3*c + 648*a^2*b*c^2)*d*e^8 + (5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*e^9)*sqrt(e*x + d)) + sqrt(1/2)*(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)*sqrt((32*c^5*d^5 - 80*b*c^4*d^4*e + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^2 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^3 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^4 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^5 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(sqrt(1/2)*(10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*e^4 - 15*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^5 + 3*(b^6*c - 2*a*b^4*c^2 - 32*a^2*b^2*c^3 + 96*a^3*c^4)*d*e^6 + (b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3)*e^7 + (8*(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*d^2 - 8*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*d*e - (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*e^2)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt((32*c^5*d^5 - 80*b*c^4*d^4*e + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^2 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^3 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^4 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^5 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) + 2*(80*c^5*d^6*e^3 - 240*b*c^4*d^5*e^4 + (199*b^2*c^3 + 404*a*c^4)*d^4*e^5 + 2*(b^3*c^2 - 404*a*b*c^3)*d^3*e^6 - 6*(6*b^4*c - 47*a*b^2*c^2 - 108*a^2*c^3)*d^2*e^7 - (5*b^5 - 122*a*b^3*c + 648*a^2*b*c^2)*d*e^8 + (5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*e^9)*sqrt(e*x + d)) - sqrt(1/2)*(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)*sqrt((32*c^5*d^5 - 80*b*c^4*d^4*e + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^2 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^3 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^4 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^5 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6))*log(-sqrt(1/2)*(10*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3*e^4 - 15*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^5 + 3*(b^6*c - 2*a*b^4*c^2 - 32*a^2*b^2*c^3 + 96*a^3*c^4)*d*e^6 + (b^7 - 17*a*b^5*c + 88*a^2*b^3*c^2 - 144*a^3*b*c^3)*e^7 + (8*(b^6*c^5 - 12*a*b^4*c^6 + 48*a^2*b^2*c^7 - 64*a^3*c^8)*d^2 - 8*(b^7*c^4 - 12*a*b^5*c^5 + 48*a^2*b^3*c^6 - 64*a^3*b*c^7)*d*e - (b^8*c^3 - 24*a*b^6*c^4 + 192*a^2*b^4*c^5 - 640*a^3*b^2*c^6 + 768*a^4*c^7)*e^2)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))*sqrt((32*c^5*d^5 - 80*b*c^4*d^4*e + 10*(5*b^2*c^3 + 12*a*c^4)*d^3*e^2 + 5*(b^3*c^2 - 36*a*b*c^3)*d^2*e^3 - 5*(b^4*c - 6*a*b^2*c^2 - 24*a^2*c^3)*d*e^4 - (b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*e^5 - (b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*sqrt((25*c^4*d^4*e^6 - 50*b*c^3*d^3*e^7 + 15*(b^2*c^2 + 6*a*c^3)*d^2*e^8 + 10*(b^3*c - 9*a*b*c^2)*d*e^9 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*e^10)/(b^6*c^6 - 12*a*b^4*c^7 + 48*a^2*b^2*c^8 - 64*a^3*c^9)))/(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)) + 2*(80*c^5*d^6*e^3 - 240*b*c^4*d^5*e^4 + (199*b^2*c^3 + 404*a*c^4)*d^4*e^5 + 2*(b^3*c^2 - 404*a*b*c^3)*d^3*e^6 - 6*(6*b^4*c - 47*a*b^2*c^2 - 108*a^2*c^3)*d^2*e^7 - (5*b^5 - 122*a*b^3*c + 648*a^2*b*c^2)*d*e^8 + (5*a*b^4 - 81*a^2*b^2*c + 324*a^3*c^2)*e^9)*sqrt(e*x + d)) - 2*(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + (2*c^2*d^2 - 2*b*c*d*e + (b^2 - 2*a*c)*e^2)*x)*sqrt(e*x + d))/(a*b^2*c - 4*a^2*c^2 + (b^2*c^2 - 4*a*c^3)*x^2 + (b^3*c - 4*a*b*c^2)*x)","B",0
2297,1,2396,0,0.488793," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} + {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left(\sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{4} + 2 \, \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\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)} d - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} + {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} + {\left(16 \, c^{2} d^{2} e^{3} - 16 \, b c d e^{4} + {\left(3 \, b^{2} + 4 \, a c\right)} e^{5}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} + {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left(-\sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{4} + 2 \, \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\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)} d - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} + {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} + {\left(16 \, c^{2} d^{2} e^{3} - 16 \, b c d e^{4} + {\left(3 \, b^{2} + 4 \, a c\right)} e^{5}\right)} \sqrt{e x + d}\right) + \sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} - {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left(\sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{4} - 2 \, \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\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)} d - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} - {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} + {\left(16 \, c^{2} d^{2} e^{3} - 16 \, b c d e^{4} + {\left(3 \, b^{2} + 4 \, a c\right)} e^{5}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} - {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} \log\left(-\sqrt{\frac{1}{2}} {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{4} - 2 \, \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}} {\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)} d - {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e\right)}\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} - {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} \sqrt{\frac{e^{6}}{b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}}}}{b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}}} + {\left(16 \, c^{2} d^{2} e^{3} - 16 \, b c d e^{4} + {\left(3 \, b^{2} + 4 \, a c\right)} e^{5}\right)} \sqrt{e x + d}\right) - 2 \, {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} \sqrt{e x + d}}{2 \, {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)}}"," ",0,"1/2*(sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 + (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log(sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^4 + 2*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e))*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 + (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)) + (16*c^2*d^2*e^3 - 16*b*c*d*e^4 + (3*b^2 + 4*a*c)*e^5)*sqrt(e*x + d)) - sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 + (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log(-sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^4 + 2*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e))*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 + (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)) + (16*c^2*d^2*e^3 - 16*b*c*d*e^4 + (3*b^2 + 4*a*c)*e^5)*sqrt(e*x + d)) + sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 - (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log(sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^4 - 2*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e))*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 - (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)) + (16*c^2*d^2*e^3 - 16*b*c*d*e^4 + (3*b^2 + 4*a*c)*e^5)*sqrt(e*x + d)) - sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 - (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4))*log(-sqrt(1/2)*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^4 - 2*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5))*(2*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d - (b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*e))*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 - (b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*sqrt(e^6/(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)))/(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)) + (16*c^2*d^2*e^3 - 16*b*c*d*e^4 + (3*b^2 + 4*a*c)*e^5)*sqrt(e*x + d)) - 2*(b*d - 2*a*e + (2*c*d - b*e)*x)*sqrt(e*x + d))/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)","B",0
2298,1,6393,0,0.577122," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} + \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left(\sqrt{\frac{1}{2}} {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{5} - {\left(8 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{4} - 16 \, {\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)} d^{3} e + 3 \, {\left(3 \, b^{8} c - 32 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{4} c^{5}\right)} d^{2} e^{2} - {\left(b^{9} - 96 \, a^{2} b^{5} c^{2} + 512 \, a^{3} b^{3} c^{3} - 768 \, a^{4} b c^{4}\right)} d e^{3} + {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{4}\right)} \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}}\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} + \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} + 2 \, {\left(16 \, c^{3} d^{2} e^{3} - 16 \, b c^{2} d e^{4} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{5}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} + \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left(-\sqrt{\frac{1}{2}} {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{5} - {\left(8 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{4} - 16 \, {\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)} d^{3} e + 3 \, {\left(3 \, b^{8} c - 32 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{4} c^{5}\right)} d^{2} e^{2} - {\left(b^{9} - 96 \, a^{2} b^{5} c^{2} + 512 \, a^{3} b^{3} c^{3} - 768 \, a^{4} b c^{4}\right)} d e^{3} + {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{4}\right)} \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}}\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} + \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} + 2 \, {\left(16 \, c^{3} d^{2} e^{3} - 16 \, b c^{2} d e^{4} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{5}\right)} \sqrt{e x + d}\right) + \sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} - \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left(\sqrt{\frac{1}{2}} {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{5} + {\left(8 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{4} - 16 \, {\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)} d^{3} e + 3 \, {\left(3 \, b^{8} c - 32 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{4} c^{5}\right)} d^{2} e^{2} - {\left(b^{9} - 96 \, a^{2} b^{5} c^{2} + 512 \, a^{3} b^{3} c^{3} - 768 \, a^{4} b c^{4}\right)} d e^{3} + {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{4}\right)} \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}}\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} - \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} + 2 \, {\left(16 \, c^{3} d^{2} e^{3} - 16 \, b c^{2} d e^{4} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{5}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} - \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} \log\left(-\sqrt{\frac{1}{2}} {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{5} + {\left(8 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{4} - 16 \, {\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)} d^{3} e + 3 \, {\left(3 \, b^{8} c - 32 \, a b^{6} c^{2} + 96 \, a^{2} b^{4} c^{3} - 256 \, a^{4} c^{5}\right)} d^{2} e^{2} - {\left(b^{9} - 96 \, a^{2} b^{5} c^{2} + 512 \, a^{3} b^{3} c^{3} - 768 \, a^{4} b c^{4}\right)} d e^{3} + {\left(a b^{8} - 8 \, a^{2} b^{6} c + 128 \, a^{4} b^{2} c^{3} - 256 \, a^{5} c^{4}\right)} e^{4}\right)} \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}}\right)} \sqrt{\frac{32 \, c^{3} d^{3} - 48 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{2} - {\left(b^{3} + 12 \, a b c\right)} e^{3} - \sqrt{\frac{e^{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)} d^{4} - 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{3} e + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} e^{2} - 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d e^{3} + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{4}}} {\left({\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}\right)}}{{\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{2} - {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d e + {\left(a b^{6} - 12 \, a^{2} b^{4} c + 48 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} e^{2}}} + 2 \, {\left(16 \, c^{3} d^{2} e^{3} - 16 \, b c^{2} d e^{4} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{5}\right)} \sqrt{e x + d}\right) - 2 \, {\left(2 \, c x + b\right)} \sqrt{e x + d}}{2 \, {\left(a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x\right)}}"," ",0,"1/2*(sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 + sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log(sqrt(1/2)*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^5 - (8*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^4 - 16*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3*e + 3*(3*b^8*c - 32*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^4*c^5)*d^2*e^2 - (b^9 - 96*a^2*b^5*c^2 + 512*a^3*b^3*c^3 - 768*a^4*b*c^4)*d*e^3 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^4)*sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)))*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 + sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2)) + 2*(16*c^3*d^2*e^3 - 16*b*c^2*d*e^4 + (3*b^2*c + 4*a*c^2)*e^5)*sqrt(e*x + d)) - sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 + sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log(-sqrt(1/2)*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^5 - (8*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^4 - 16*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3*e + 3*(3*b^8*c - 32*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^4*c^5)*d^2*e^2 - (b^9 - 96*a^2*b^5*c^2 + 512*a^3*b^3*c^3 - 768*a^4*b*c^4)*d*e^3 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^4)*sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)))*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 + sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2)) + 2*(16*c^3*d^2*e^3 - 16*b*c^2*d*e^4 + (3*b^2*c + 4*a*c^2)*e^5)*sqrt(e*x + d)) + sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 - sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log(sqrt(1/2)*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^5 + (8*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^4 - 16*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3*e + 3*(3*b^8*c - 32*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^4*c^5)*d^2*e^2 - (b^9 - 96*a^2*b^5*c^2 + 512*a^3*b^3*c^3 - 768*a^4*b*c^4)*d*e^3 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^4)*sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)))*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 - sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2)) + 2*(16*c^3*d^2*e^3 - 16*b*c^2*d*e^4 + (3*b^2*c + 4*a*c^2)*e^5)*sqrt(e*x + d)) - sqrt(1/2)*(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 - sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))*log(-sqrt(1/2)*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^5 + (8*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^4 - 16*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^3*e + 3*(3*b^8*c - 32*a*b^6*c^2 + 96*a^2*b^4*c^3 - 256*a^4*c^5)*d^2*e^2 - (b^9 - 96*a^2*b^5*c^2 + 512*a^3*b^3*c^3 - 768*a^4*b*c^4)*d*e^3 + (a*b^8 - 8*a^2*b^6*c + 128*a^4*b^2*c^3 - 256*a^5*c^4)*e^4)*sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4)))*sqrt((32*c^3*d^3 - 48*b*c^2*d^2*e + 6*(3*b^2*c + 4*a*c^2)*d*e^2 - (b^3 + 12*a*b*c)*e^3 - sqrt(e^6/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^4 - 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^3*e + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*e^2 - 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*e^3 + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*e^4))*((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2))/((b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^2 - (b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*d*e + (a*b^6 - 12*a^2*b^4*c + 48*a^3*b^2*c^2 - 64*a^4*c^3)*e^2)) + 2*(16*c^3*d^2*e^3 - 16*b*c^2*d*e^4 + (3*b^2*c + 4*a*c^2)*e^5)*sqrt(e*x + d)) - 2*(2*c*x + b)*sqrt(e*x + d))/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)","B",0
2299,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2300,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2301,1,3449,0,1.181063," ","integrate(1/x^(5/2)/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left(\sqrt{\frac{1}{2}} {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7} - {\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} + 2 \, {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left(-\sqrt{\frac{1}{2}} {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7} - {\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} + {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} + 2 \, {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} \sqrt{x}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left(\sqrt{\frac{1}{2}} {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7} + {\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} + 2 \, {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} \log\left(-\sqrt{\frac{1}{2}} {\left(125 \, b^{14} - 2425 \, a b^{12} c + 18940 \, a^{2} b^{10} c^{2} - 75579 \, a^{3} b^{8} c^{3} + 160932 \, a^{4} b^{6} c^{4} - 172990 \, a^{5} b^{4} c^{5} + 79408 \, a^{6} b^{2} c^{6} - 10976 \, a^{7} c^{7} + {\left(5 \, a^{7} b^{11} - 94 \, a^{8} b^{9} c + 700 \, a^{9} b^{7} c^{2} - 2576 \, a^{10} b^{5} c^{3} + 4672 \, a^{11} b^{3} c^{4} - 3328 \, a^{12} b c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}\right)} \sqrt{-\frac{25 \, b^{9} - 315 \, a b^{7} c + 1386 \, a^{2} b^{5} c^{2} - 2415 \, a^{3} b^{3} c^{3} + 1260 \, a^{4} b c^{4} - {\left(a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}\right)} \sqrt{\frac{625 \, b^{12} - 8250 \, a b^{10} c + 39525 \, a^{2} b^{8} c^{2} - 83630 \, a^{3} b^{6} c^{3} + 76686 \, a^{4} b^{4} c^{4} - 24108 \, a^{5} b^{2} c^{5} + 2401 \, a^{6} c^{6}}{a^{14} b^{6} - 12 \, a^{15} b^{4} c + 48 \, a^{16} b^{2} c^{2} - 64 \, a^{17} c^{3}}}}{a^{7} b^{6} - 12 \, a^{8} b^{4} c + 48 \, a^{9} b^{2} c^{2} - 64 \, a^{10} c^{3}}} + 2 \, {\left(1125 \, b^{8} c^{4} - 12325 \, a b^{6} c^{5} + 43410 \, a^{2} b^{4} c^{6} - 50421 \, a^{3} b^{2} c^{7} + 9604 \, a^{4} c^{8}\right)} \sqrt{x}\right) - 2 \, {\left(2 \, a^{2} b^{2} - 8 \, a^{3} c - 3 \, {\left(5 \, b^{3} c - 19 \, a b c^{2}\right)} x^{3} - {\left(15 \, b^{4} - 62 \, a b^{2} c + 14 \, a^{2} c^{2}\right)} x^{2} - 10 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} x\right)} \sqrt{x}}{6 \, {\left({\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} x^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} x^{2}\right)}}"," ",0,"1/6*(3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log(sqrt(1/2)*(125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7 - (5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)) + 2*(1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*sqrt(x)) - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log(-sqrt(1/2)*(125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7 - (5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 + (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)) + 2*(1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*sqrt(x)) + 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log(sqrt(1/2)*(125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7 + (5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)) + 2*(1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*sqrt(x)) - 3*sqrt(1/2)*((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3))*log(-sqrt(1/2)*(125*b^14 - 2425*a*b^12*c + 18940*a^2*b^10*c^2 - 75579*a^3*b^8*c^3 + 160932*a^4*b^6*c^4 - 172990*a^5*b^4*c^5 + 79408*a^6*b^2*c^6 - 10976*a^7*c^7 + (5*a^7*b^11 - 94*a^8*b^9*c + 700*a^9*b^7*c^2 - 2576*a^10*b^5*c^3 + 4672*a^11*b^3*c^4 - 3328*a^12*b*c^5)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))*sqrt(-(25*b^9 - 315*a*b^7*c + 1386*a^2*b^5*c^2 - 2415*a^3*b^3*c^3 + 1260*a^4*b*c^4 - (a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)*sqrt((625*b^12 - 8250*a*b^10*c + 39525*a^2*b^8*c^2 - 83630*a^3*b^6*c^3 + 76686*a^4*b^4*c^4 - 24108*a^5*b^2*c^5 + 2401*a^6*c^6)/(a^14*b^6 - 12*a^15*b^4*c + 48*a^16*b^2*c^2 - 64*a^17*c^3)))/(a^7*b^6 - 12*a^8*b^4*c + 48*a^9*b^2*c^2 - 64*a^10*c^3)) + 2*(1125*b^8*c^4 - 12325*a*b^6*c^5 + 43410*a^2*b^4*c^6 - 50421*a^3*b^2*c^7 + 9604*a^4*c^8)*sqrt(x)) - 2*(2*a^2*b^2 - 8*a^3*c - 3*(5*b^3*c - 19*a*b*c^2)*x^3 - (15*b^4 - 62*a*b^2*c + 14*a^2*c^2)*x^2 - 10*(a*b^3 - 4*a^2*b*c)*x)*sqrt(x))/((a^3*b^2*c - 4*a^4*c^2)*x^4 + (a^3*b^3 - 4*a^4*b*c)*x^3 + (a^4*b^2 - 4*a^5*c)*x^2)","B",0
2302,1,8780,0,1.958695," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{\sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)} \sqrt{\frac{4608 \, c^{7} d^{7} - 16128 \, b c^{6} d^{6} e + 672 \, {\left(31 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} - 1680 \, {\left(7 \, b^{3} c^{4} + 20 \, a b c^{5}\right)} d^{4} e^{3} + 70 \, {\left(35 \, b^{4} c^{3} + 392 \, a b^{2} c^{4} + 176 \, a^{2} c^{5}\right)} d^{3} e^{4} + 21 \, {\left(b^{5} c^{2} - 360 \, a b^{3} c^{3} - 880 \, a^{2} b c^{4}\right)} d^{2} e^{5} - 21 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} - 320 \, a^{2} b^{2} c^{3} - 160 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} e^{7} + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(504 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{4} e^{6} - 1008 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{3} e^{7} + 3 \, {\left(167 \, b^{8} c^{2} - 1664 \, a b^{6} c^{3} + 3936 \, a^{2} b^{4} c^{4} + 5632 \, a^{3} b^{2} c^{5} - 21760 \, a^{4} c^{6}\right)} d^{2} e^{8} + 3 \, {\left(b^{9} c - 352 \, a b^{7} c^{2} + 4128 \, a^{2} b^{5} c^{3} - 16384 \, a^{3} b^{3} c^{4} + 21760 \, a^{4} b c^{5}\right)} d e^{9} - {\left(b^{10} - 17 \, a b^{8} c - 392 \, a^{2} b^{6} c^{2} + 5696 \, a^{3} b^{4} c^{3} - 23680 \, a^{4} b^{2} c^{4} + 32000 \, a^{5} c^{5}\right)} e^{10} - {\left(96 \, {\left(b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}\right)} d^{3} - 144 \, {\left(b^{11} c^{5} - 20 \, a b^{9} c^{6} + 160 \, a^{2} b^{7} c^{7} - 640 \, a^{3} b^{5} c^{8} + 1280 \, a^{4} b^{3} c^{9} - 1024 \, a^{5} b c^{10}\right)} d^{2} e + 2 \, {\left(23 \, b^{12} c^{4} - 408 \, a b^{10} c^{5} + 2640 \, a^{2} b^{8} c^{6} - 6400 \, a^{3} b^{6} c^{7} - 3840 \, a^{4} b^{4} c^{8} + 43008 \, a^{5} b^{2} c^{9} - 53248 \, a^{6} c^{10}\right)} d e^{2} + {\left(b^{13} c^{3} - 72 \, a b^{11} c^{4} + 1200 \, a^{2} b^{9} c^{5} - 8960 \, a^{3} b^{7} c^{6} + 34560 \, a^{4} b^{5} c^{7} - 67584 \, a^{5} b^{3} c^{8} + 53248 \, a^{6} b c^{9}\right)} e^{3}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{\frac{4608 \, c^{7} d^{7} - 16128 \, b c^{6} d^{6} e + 672 \, {\left(31 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} - 1680 \, {\left(7 \, b^{3} c^{4} + 20 \, a b c^{5}\right)} d^{4} e^{3} + 70 \, {\left(35 \, b^{4} c^{3} + 392 \, a b^{2} c^{4} + 176 \, a^{2} c^{5}\right)} d^{3} e^{4} + 21 \, {\left(b^{5} c^{2} - 360 \, a b^{3} c^{3} - 880 \, a^{2} b c^{4}\right)} d^{2} e^{5} - 21 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} - 320 \, a^{2} b^{2} c^{3} - 160 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} e^{7} + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} + {\left(48384 \, c^{7} d^{8} e^{5} - 193536 \, b c^{6} d^{7} e^{6} + 432 \, {\left(683 \, b^{2} c^{5} + 404 \, a c^{6}\right)} d^{6} e^{7} - 432 \, {\left(481 \, b^{3} c^{4} + 1212 \, a b c^{5}\right)} d^{5} e^{8} + 9 \, {\left(6841 \, b^{4} c^{3} + 60712 \, a b^{2} c^{4} + 24016 \, a^{2} c^{5}\right)} d^{4} e^{9} - 18 \, {\left(145 \, b^{5} c^{2} + 12232 \, a b^{3} c^{3} + 24016 \, a^{2} b c^{4}\right)} d^{3} e^{10} - 2 \, {\left(518 \, b^{6} c - 10131 \, a b^{4} c^{2} - 124608 \, a^{2} b^{2} c^{3} - 50000 \, a^{3} c^{4}\right)} d^{2} e^{11} - {\left(35 \, b^{7} - 2562 \, a b^{5} c + 33072 \, a^{2} b^{3} c^{2} + 100000 \, a^{3} b c^{3}\right)} d e^{12} + {\left(35 \, a b^{6} - 1491 \, a^{2} b^{4} c + 15000 \, a^{3} b^{2} c^{2} + 10000 \, a^{4} c^{3}\right)} e^{13}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)} \sqrt{\frac{4608 \, c^{7} d^{7} - 16128 \, b c^{6} d^{6} e + 672 \, {\left(31 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} - 1680 \, {\left(7 \, b^{3} c^{4} + 20 \, a b c^{5}\right)} d^{4} e^{3} + 70 \, {\left(35 \, b^{4} c^{3} + 392 \, a b^{2} c^{4} + 176 \, a^{2} c^{5}\right)} d^{3} e^{4} + 21 \, {\left(b^{5} c^{2} - 360 \, a b^{3} c^{3} - 880 \, a^{2} b c^{4}\right)} d^{2} e^{5} - 21 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} - 320 \, a^{2} b^{2} c^{3} - 160 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} e^{7} + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(504 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{4} e^{6} - 1008 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{3} e^{7} + 3 \, {\left(167 \, b^{8} c^{2} - 1664 \, a b^{6} c^{3} + 3936 \, a^{2} b^{4} c^{4} + 5632 \, a^{3} b^{2} c^{5} - 21760 \, a^{4} c^{6}\right)} d^{2} e^{8} + 3 \, {\left(b^{9} c - 352 \, a b^{7} c^{2} + 4128 \, a^{2} b^{5} c^{3} - 16384 \, a^{3} b^{3} c^{4} + 21760 \, a^{4} b c^{5}\right)} d e^{9} - {\left(b^{10} - 17 \, a b^{8} c - 392 \, a^{2} b^{6} c^{2} + 5696 \, a^{3} b^{4} c^{3} - 23680 \, a^{4} b^{2} c^{4} + 32000 \, a^{5} c^{5}\right)} e^{10} - {\left(96 \, {\left(b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}\right)} d^{3} - 144 \, {\left(b^{11} c^{5} - 20 \, a b^{9} c^{6} + 160 \, a^{2} b^{7} c^{7} - 640 \, a^{3} b^{5} c^{8} + 1280 \, a^{4} b^{3} c^{9} - 1024 \, a^{5} b c^{10}\right)} d^{2} e + 2 \, {\left(23 \, b^{12} c^{4} - 408 \, a b^{10} c^{5} + 2640 \, a^{2} b^{8} c^{6} - 6400 \, a^{3} b^{6} c^{7} - 3840 \, a^{4} b^{4} c^{8} + 43008 \, a^{5} b^{2} c^{9} - 53248 \, a^{6} c^{10}\right)} d e^{2} + {\left(b^{13} c^{3} - 72 \, a b^{11} c^{4} + 1200 \, a^{2} b^{9} c^{5} - 8960 \, a^{3} b^{7} c^{6} + 34560 \, a^{4} b^{5} c^{7} - 67584 \, a^{5} b^{3} c^{8} + 53248 \, a^{6} b c^{9}\right)} e^{3}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{\frac{4608 \, c^{7} d^{7} - 16128 \, b c^{6} d^{6} e + 672 \, {\left(31 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} - 1680 \, {\left(7 \, b^{3} c^{4} + 20 \, a b c^{5}\right)} d^{4} e^{3} + 70 \, {\left(35 \, b^{4} c^{3} + 392 \, a b^{2} c^{4} + 176 \, a^{2} c^{5}\right)} d^{3} e^{4} + 21 \, {\left(b^{5} c^{2} - 360 \, a b^{3} c^{3} - 880 \, a^{2} b c^{4}\right)} d^{2} e^{5} - 21 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} - 320 \, a^{2} b^{2} c^{3} - 160 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} e^{7} + {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} + {\left(48384 \, c^{7} d^{8} e^{5} - 193536 \, b c^{6} d^{7} e^{6} + 432 \, {\left(683 \, b^{2} c^{5} + 404 \, a c^{6}\right)} d^{6} e^{7} - 432 \, {\left(481 \, b^{3} c^{4} + 1212 \, a b c^{5}\right)} d^{5} e^{8} + 9 \, {\left(6841 \, b^{4} c^{3} + 60712 \, a b^{2} c^{4} + 24016 \, a^{2} c^{5}\right)} d^{4} e^{9} - 18 \, {\left(145 \, b^{5} c^{2} + 12232 \, a b^{3} c^{3} + 24016 \, a^{2} b c^{4}\right)} d^{3} e^{10} - 2 \, {\left(518 \, b^{6} c - 10131 \, a b^{4} c^{2} - 124608 \, a^{2} b^{2} c^{3} - 50000 \, a^{3} c^{4}\right)} d^{2} e^{11} - {\left(35 \, b^{7} - 2562 \, a b^{5} c + 33072 \, a^{2} b^{3} c^{2} + 100000 \, a^{3} b c^{3}\right)} d e^{12} + {\left(35 \, a b^{6} - 1491 \, a^{2} b^{4} c + 15000 \, a^{3} b^{2} c^{2} + 10000 \, a^{4} c^{3}\right)} e^{13}\right)} \sqrt{e x + d}\right) + \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)} \sqrt{\frac{4608 \, c^{7} d^{7} - 16128 \, b c^{6} d^{6} e + 672 \, {\left(31 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} - 1680 \, {\left(7 \, b^{3} c^{4} + 20 \, a b c^{5}\right)} d^{4} e^{3} + 70 \, {\left(35 \, b^{4} c^{3} + 392 \, a b^{2} c^{4} + 176 \, a^{2} c^{5}\right)} d^{3} e^{4} + 21 \, {\left(b^{5} c^{2} - 360 \, a b^{3} c^{3} - 880 \, a^{2} b c^{4}\right)} d^{2} e^{5} - 21 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} - 320 \, a^{2} b^{2} c^{3} - 160 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} e^{7} - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(504 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{4} e^{6} - 1008 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{3} e^{7} + 3 \, {\left(167 \, b^{8} c^{2} - 1664 \, a b^{6} c^{3} + 3936 \, a^{2} b^{4} c^{4} + 5632 \, a^{3} b^{2} c^{5} - 21760 \, a^{4} c^{6}\right)} d^{2} e^{8} + 3 \, {\left(b^{9} c - 352 \, a b^{7} c^{2} + 4128 \, a^{2} b^{5} c^{3} - 16384 \, a^{3} b^{3} c^{4} + 21760 \, a^{4} b c^{5}\right)} d e^{9} - {\left(b^{10} - 17 \, a b^{8} c - 392 \, a^{2} b^{6} c^{2} + 5696 \, a^{3} b^{4} c^{3} - 23680 \, a^{4} b^{2} c^{4} + 32000 \, a^{5} c^{5}\right)} e^{10} + {\left(96 \, {\left(b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}\right)} d^{3} - 144 \, {\left(b^{11} c^{5} - 20 \, a b^{9} c^{6} + 160 \, a^{2} b^{7} c^{7} - 640 \, a^{3} b^{5} c^{8} + 1280 \, a^{4} b^{3} c^{9} - 1024 \, a^{5} b c^{10}\right)} d^{2} e + 2 \, {\left(23 \, b^{12} c^{4} - 408 \, a b^{10} c^{5} + 2640 \, a^{2} b^{8} c^{6} - 6400 \, a^{3} b^{6} c^{7} - 3840 \, a^{4} b^{4} c^{8} + 43008 \, a^{5} b^{2} c^{9} - 53248 \, a^{6} c^{10}\right)} d e^{2} + {\left(b^{13} c^{3} - 72 \, a b^{11} c^{4} + 1200 \, a^{2} b^{9} c^{5} - 8960 \, a^{3} b^{7} c^{6} + 34560 \, a^{4} b^{5} c^{7} - 67584 \, a^{5} b^{3} c^{8} + 53248 \, a^{6} b c^{9}\right)} e^{3}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{\frac{4608 \, c^{7} d^{7} - 16128 \, b c^{6} d^{6} e + 672 \, {\left(31 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} - 1680 \, {\left(7 \, b^{3} c^{4} + 20 \, a b c^{5}\right)} d^{4} e^{3} + 70 \, {\left(35 \, b^{4} c^{3} + 392 \, a b^{2} c^{4} + 176 \, a^{2} c^{5}\right)} d^{3} e^{4} + 21 \, {\left(b^{5} c^{2} - 360 \, a b^{3} c^{3} - 880 \, a^{2} b c^{4}\right)} d^{2} e^{5} - 21 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} - 320 \, a^{2} b^{2} c^{3} - 160 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} e^{7} - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} + {\left(48384 \, c^{7} d^{8} e^{5} - 193536 \, b c^{6} d^{7} e^{6} + 432 \, {\left(683 \, b^{2} c^{5} + 404 \, a c^{6}\right)} d^{6} e^{7} - 432 \, {\left(481 \, b^{3} c^{4} + 1212 \, a b c^{5}\right)} d^{5} e^{8} + 9 \, {\left(6841 \, b^{4} c^{3} + 60712 \, a b^{2} c^{4} + 24016 \, a^{2} c^{5}\right)} d^{4} e^{9} - 18 \, {\left(145 \, b^{5} c^{2} + 12232 \, a b^{3} c^{3} + 24016 \, a^{2} b c^{4}\right)} d^{3} e^{10} - 2 \, {\left(518 \, b^{6} c - 10131 \, a b^{4} c^{2} - 124608 \, a^{2} b^{2} c^{3} - 50000 \, a^{3} c^{4}\right)} d^{2} e^{11} - {\left(35 \, b^{7} - 2562 \, a b^{5} c + 33072 \, a^{2} b^{3} c^{2} + 100000 \, a^{3} b c^{3}\right)} d e^{12} + {\left(35 \, a b^{6} - 1491 \, a^{2} b^{4} c + 15000 \, a^{3} b^{2} c^{2} + 10000 \, a^{4} c^{3}\right)} e^{13}\right)} \sqrt{e x + d}\right) - \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)} \sqrt{\frac{4608 \, c^{7} d^{7} - 16128 \, b c^{6} d^{6} e + 672 \, {\left(31 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} - 1680 \, {\left(7 \, b^{3} c^{4} + 20 \, a b c^{5}\right)} d^{4} e^{3} + 70 \, {\left(35 \, b^{4} c^{3} + 392 \, a b^{2} c^{4} + 176 \, a^{2} c^{5}\right)} d^{3} e^{4} + 21 \, {\left(b^{5} c^{2} - 360 \, a b^{3} c^{3} - 880 \, a^{2} b c^{4}\right)} d^{2} e^{5} - 21 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} - 320 \, a^{2} b^{2} c^{3} - 160 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} e^{7} - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(504 \, {\left(b^{6} c^{4} - 12 \, a b^{4} c^{5} + 48 \, a^{2} b^{2} c^{6} - 64 \, a^{3} c^{7}\right)} d^{4} e^{6} - 1008 \, {\left(b^{7} c^{3} - 12 \, a b^{5} c^{4} + 48 \, a^{2} b^{3} c^{5} - 64 \, a^{3} b c^{6}\right)} d^{3} e^{7} + 3 \, {\left(167 \, b^{8} c^{2} - 1664 \, a b^{6} c^{3} + 3936 \, a^{2} b^{4} c^{4} + 5632 \, a^{3} b^{2} c^{5} - 21760 \, a^{4} c^{6}\right)} d^{2} e^{8} + 3 \, {\left(b^{9} c - 352 \, a b^{7} c^{2} + 4128 \, a^{2} b^{5} c^{3} - 16384 \, a^{3} b^{3} c^{4} + 21760 \, a^{4} b c^{5}\right)} d e^{9} - {\left(b^{10} - 17 \, a b^{8} c - 392 \, a^{2} b^{6} c^{2} + 5696 \, a^{3} b^{4} c^{3} - 23680 \, a^{4} b^{2} c^{4} + 32000 \, a^{5} c^{5}\right)} e^{10} + {\left(96 \, {\left(b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}\right)} d^{3} - 144 \, {\left(b^{11} c^{5} - 20 \, a b^{9} c^{6} + 160 \, a^{2} b^{7} c^{7} - 640 \, a^{3} b^{5} c^{8} + 1280 \, a^{4} b^{3} c^{9} - 1024 \, a^{5} b c^{10}\right)} d^{2} e + 2 \, {\left(23 \, b^{12} c^{4} - 408 \, a b^{10} c^{5} + 2640 \, a^{2} b^{8} c^{6} - 6400 \, a^{3} b^{6} c^{7} - 3840 \, a^{4} b^{4} c^{8} + 43008 \, a^{5} b^{2} c^{9} - 53248 \, a^{6} c^{10}\right)} d e^{2} + {\left(b^{13} c^{3} - 72 \, a b^{11} c^{4} + 1200 \, a^{2} b^{9} c^{5} - 8960 \, a^{3} b^{7} c^{6} + 34560 \, a^{4} b^{5} c^{7} - 67584 \, a^{5} b^{3} c^{8} + 53248 \, a^{6} b c^{9}\right)} e^{3}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}\right)} \sqrt{\frac{4608 \, c^{7} d^{7} - 16128 \, b c^{6} d^{6} e + 672 \, {\left(31 \, b^{2} c^{5} + 20 \, a c^{6}\right)} d^{5} e^{2} - 1680 \, {\left(7 \, b^{3} c^{4} + 20 \, a b c^{5}\right)} d^{4} e^{3} + 70 \, {\left(35 \, b^{4} c^{3} + 392 \, a b^{2} c^{4} + 176 \, a^{2} c^{5}\right)} d^{3} e^{4} + 21 \, {\left(b^{5} c^{2} - 360 \, a b^{3} c^{3} - 880 \, a^{2} b c^{4}\right)} d^{2} e^{5} - 21 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} - 320 \, a^{2} b^{2} c^{3} - 160 \, a^{3} c^{4}\right)} d e^{6} - {\left(b^{7} - 35 \, a b^{5} c + 280 \, a^{2} b^{3} c^{2} + 1680 \, a^{3} b c^{3}\right)} e^{7} - {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} \sqrt{\frac{441 \, c^{4} d^{4} e^{10} - 882 \, b c^{3} d^{3} e^{11} + 21 \, {\left(19 \, b^{2} c^{2} + 50 \, a c^{3}\right)} d^{2} e^{12} + 42 \, {\left(b^{3} c - 25 \, a b c^{2}\right)} d e^{13} + {\left(b^{4} - 50 \, a b^{2} c + 625 \, a^{2} c^{2}\right)} e^{14}}{b^{10} c^{6} - 20 \, a b^{8} c^{7} + 160 \, a^{2} b^{6} c^{8} - 640 \, a^{3} b^{4} c^{9} + 1280 \, a^{4} b^{2} c^{10} - 1024 \, a^{5} c^{11}}}}{b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}}} + {\left(48384 \, c^{7} d^{8} e^{5} - 193536 \, b c^{6} d^{7} e^{6} + 432 \, {\left(683 \, b^{2} c^{5} + 404 \, a c^{6}\right)} d^{6} e^{7} - 432 \, {\left(481 \, b^{3} c^{4} + 1212 \, a b c^{5}\right)} d^{5} e^{8} + 9 \, {\left(6841 \, b^{4} c^{3} + 60712 \, a b^{2} c^{4} + 24016 \, a^{2} c^{5}\right)} d^{4} e^{9} - 18 \, {\left(145 \, b^{5} c^{2} + 12232 \, a b^{3} c^{3} + 24016 \, a^{2} b c^{4}\right)} d^{3} e^{10} - 2 \, {\left(518 \, b^{6} c - 10131 \, a b^{4} c^{2} - 124608 \, a^{2} b^{2} c^{3} - 50000 \, a^{3} c^{4}\right)} d^{2} e^{11} - {\left(35 \, b^{7} - 2562 \, a b^{5} c + 33072 \, a^{2} b^{3} c^{2} + 100000 \, a^{3} b c^{3}\right)} d e^{12} + {\left(35 \, a b^{6} - 1491 \, a^{2} b^{4} c + 15000 \, a^{3} b^{2} c^{2} + 10000 \, a^{4} c^{3}\right)} e^{13}\right)} \sqrt{e x + d}\right) - 2 \, {\left(36 \, a^{2} b c d e^{2} - 2 \, {\left(b^{3} c - 10 \, a b c^{2}\right)} d^{3} - {\left(7 \, a b^{2} c + 44 \, a^{2} c^{2}\right)} d^{2} e - {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} e^{3} + {\left(24 \, c^{4} d^{3} - 36 \, b c^{3} d^{2} e + 2 \, {\left(5 \, b^{2} c^{2} + 16 \, a c^{3}\right)} d e^{2} + {\left(b^{3} c - 16 \, a b c^{2}\right)} e^{3}\right)} x^{3} + {\left(36 \, b c^{3} d^{3} - {\left(55 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e + 4 \, {\left(4 \, b^{3} c + 11 \, a b c^{2}\right)} d e^{2} - {\left(b^{4} + 5 \, a b^{2} c + 36 \, a^{2} c^{2}\right)} e^{3}\right)} x^{2} + {\left(8 \, {\left(b^{2} c^{2} + 5 \, a c^{3}\right)} d^{3} - {\left(13 \, b^{3} c + 56 \, a b c^{2}\right)} d^{2} e + 2 \, {\left(29 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - 2 \, {\left(a b^{3} + 14 \, a^{2} b c\right)} e^{3}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3} + {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} x^{4} + 2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} x^{3} + {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} x^{2} + 2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} x\right)}}"," ",0,"-1/8*(sqrt(1/2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)*sqrt((4608*c^7*d^7 - 16128*b*c^6*d^6*e + 672*(31*b^2*c^5 + 20*a*c^6)*d^5*e^2 - 1680*(7*b^3*c^4 + 20*a*b*c^5)*d^4*e^3 + 70*(35*b^4*c^3 + 392*a*b^2*c^4 + 176*a^2*c^5)*d^3*e^4 + 21*(b^5*c^2 - 360*a*b^3*c^3 - 880*a^2*b*c^4)*d^2*e^5 - 21*(b^6*c - 10*a*b^4*c^2 - 320*a^2*b^2*c^3 - 160*a^3*c^4)*d*e^6 - (b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*e^7 + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(1/2*sqrt(1/2)*(504*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^4*e^6 - 1008*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^3*e^7 + 3*(167*b^8*c^2 - 1664*a*b^6*c^3 + 3936*a^2*b^4*c^4 + 5632*a^3*b^2*c^5 - 21760*a^4*c^6)*d^2*e^8 + 3*(b^9*c - 352*a*b^7*c^2 + 4128*a^2*b^5*c^3 - 16384*a^3*b^3*c^4 + 21760*a^4*b*c^5)*d*e^9 - (b^10 - 17*a*b^8*c - 392*a^2*b^6*c^2 + 5696*a^3*b^4*c^3 - 23680*a^4*b^2*c^4 + 32000*a^5*c^5)*e^10 - (96*(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)*d^3 - 144*(b^11*c^5 - 20*a*b^9*c^6 + 160*a^2*b^7*c^7 - 640*a^3*b^5*c^8 + 1280*a^4*b^3*c^9 - 1024*a^5*b*c^10)*d^2*e + 2*(23*b^12*c^4 - 408*a*b^10*c^5 + 2640*a^2*b^8*c^6 - 6400*a^3*b^6*c^7 - 3840*a^4*b^4*c^8 + 43008*a^5*b^2*c^9 - 53248*a^6*c^10)*d*e^2 + (b^13*c^3 - 72*a*b^11*c^4 + 1200*a^2*b^9*c^5 - 8960*a^3*b^7*c^6 + 34560*a^4*b^5*c^7 - 67584*a^5*b^3*c^8 + 53248*a^6*b*c^9)*e^3)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt((4608*c^7*d^7 - 16128*b*c^6*d^6*e + 672*(31*b^2*c^5 + 20*a*c^6)*d^5*e^2 - 1680*(7*b^3*c^4 + 20*a*b*c^5)*d^4*e^3 + 70*(35*b^4*c^3 + 392*a*b^2*c^4 + 176*a^2*c^5)*d^3*e^4 + 21*(b^5*c^2 - 360*a*b^3*c^3 - 880*a^2*b*c^4)*d^2*e^5 - 21*(b^6*c - 10*a*b^4*c^2 - 320*a^2*b^2*c^3 - 160*a^3*c^4)*d*e^6 - (b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*e^7 + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)) + (48384*c^7*d^8*e^5 - 193536*b*c^6*d^7*e^6 + 432*(683*b^2*c^5 + 404*a*c^6)*d^6*e^7 - 432*(481*b^3*c^4 + 1212*a*b*c^5)*d^5*e^8 + 9*(6841*b^4*c^3 + 60712*a*b^2*c^4 + 24016*a^2*c^5)*d^4*e^9 - 18*(145*b^5*c^2 + 12232*a*b^3*c^3 + 24016*a^2*b*c^4)*d^3*e^10 - 2*(518*b^6*c - 10131*a*b^4*c^2 - 124608*a^2*b^2*c^3 - 50000*a^3*c^4)*d^2*e^11 - (35*b^7 - 2562*a*b^5*c + 33072*a^2*b^3*c^2 + 100000*a^3*b*c^3)*d*e^12 + (35*a*b^6 - 1491*a^2*b^4*c + 15000*a^3*b^2*c^2 + 10000*a^4*c^3)*e^13)*sqrt(e*x + d)) - sqrt(1/2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)*sqrt((4608*c^7*d^7 - 16128*b*c^6*d^6*e + 672*(31*b^2*c^5 + 20*a*c^6)*d^5*e^2 - 1680*(7*b^3*c^4 + 20*a*b*c^5)*d^4*e^3 + 70*(35*b^4*c^3 + 392*a*b^2*c^4 + 176*a^2*c^5)*d^3*e^4 + 21*(b^5*c^2 - 360*a*b^3*c^3 - 880*a^2*b*c^4)*d^2*e^5 - 21*(b^6*c - 10*a*b^4*c^2 - 320*a^2*b^2*c^3 - 160*a^3*c^4)*d*e^6 - (b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*e^7 + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(-1/2*sqrt(1/2)*(504*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^4*e^6 - 1008*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^3*e^7 + 3*(167*b^8*c^2 - 1664*a*b^6*c^3 + 3936*a^2*b^4*c^4 + 5632*a^3*b^2*c^5 - 21760*a^4*c^6)*d^2*e^8 + 3*(b^9*c - 352*a*b^7*c^2 + 4128*a^2*b^5*c^3 - 16384*a^3*b^3*c^4 + 21760*a^4*b*c^5)*d*e^9 - (b^10 - 17*a*b^8*c - 392*a^2*b^6*c^2 + 5696*a^3*b^4*c^3 - 23680*a^4*b^2*c^4 + 32000*a^5*c^5)*e^10 - (96*(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)*d^3 - 144*(b^11*c^5 - 20*a*b^9*c^6 + 160*a^2*b^7*c^7 - 640*a^3*b^5*c^8 + 1280*a^4*b^3*c^9 - 1024*a^5*b*c^10)*d^2*e + 2*(23*b^12*c^4 - 408*a*b^10*c^5 + 2640*a^2*b^8*c^6 - 6400*a^3*b^6*c^7 - 3840*a^4*b^4*c^8 + 43008*a^5*b^2*c^9 - 53248*a^6*c^10)*d*e^2 + (b^13*c^3 - 72*a*b^11*c^4 + 1200*a^2*b^9*c^5 - 8960*a^3*b^7*c^6 + 34560*a^4*b^5*c^7 - 67584*a^5*b^3*c^8 + 53248*a^6*b*c^9)*e^3)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt((4608*c^7*d^7 - 16128*b*c^6*d^6*e + 672*(31*b^2*c^5 + 20*a*c^6)*d^5*e^2 - 1680*(7*b^3*c^4 + 20*a*b*c^5)*d^4*e^3 + 70*(35*b^4*c^3 + 392*a*b^2*c^4 + 176*a^2*c^5)*d^3*e^4 + 21*(b^5*c^2 - 360*a*b^3*c^3 - 880*a^2*b*c^4)*d^2*e^5 - 21*(b^6*c - 10*a*b^4*c^2 - 320*a^2*b^2*c^3 - 160*a^3*c^4)*d*e^6 - (b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*e^7 + (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)) + (48384*c^7*d^8*e^5 - 193536*b*c^6*d^7*e^6 + 432*(683*b^2*c^5 + 404*a*c^6)*d^6*e^7 - 432*(481*b^3*c^4 + 1212*a*b*c^5)*d^5*e^8 + 9*(6841*b^4*c^3 + 60712*a*b^2*c^4 + 24016*a^2*c^5)*d^4*e^9 - 18*(145*b^5*c^2 + 12232*a*b^3*c^3 + 24016*a^2*b*c^4)*d^3*e^10 - 2*(518*b^6*c - 10131*a*b^4*c^2 - 124608*a^2*b^2*c^3 - 50000*a^3*c^4)*d^2*e^11 - (35*b^7 - 2562*a*b^5*c + 33072*a^2*b^3*c^2 + 100000*a^3*b*c^3)*d*e^12 + (35*a*b^6 - 1491*a^2*b^4*c + 15000*a^3*b^2*c^2 + 10000*a^4*c^3)*e^13)*sqrt(e*x + d)) + sqrt(1/2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)*sqrt((4608*c^7*d^7 - 16128*b*c^6*d^6*e + 672*(31*b^2*c^5 + 20*a*c^6)*d^5*e^2 - 1680*(7*b^3*c^4 + 20*a*b*c^5)*d^4*e^3 + 70*(35*b^4*c^3 + 392*a*b^2*c^4 + 176*a^2*c^5)*d^3*e^4 + 21*(b^5*c^2 - 360*a*b^3*c^3 - 880*a^2*b*c^4)*d^2*e^5 - 21*(b^6*c - 10*a*b^4*c^2 - 320*a^2*b^2*c^3 - 160*a^3*c^4)*d*e^6 - (b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*e^7 - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(1/2*sqrt(1/2)*(504*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^4*e^6 - 1008*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^3*e^7 + 3*(167*b^8*c^2 - 1664*a*b^6*c^3 + 3936*a^2*b^4*c^4 + 5632*a^3*b^2*c^5 - 21760*a^4*c^6)*d^2*e^8 + 3*(b^9*c - 352*a*b^7*c^2 + 4128*a^2*b^5*c^3 - 16384*a^3*b^3*c^4 + 21760*a^4*b*c^5)*d*e^9 - (b^10 - 17*a*b^8*c - 392*a^2*b^6*c^2 + 5696*a^3*b^4*c^3 - 23680*a^4*b^2*c^4 + 32000*a^5*c^5)*e^10 + (96*(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)*d^3 - 144*(b^11*c^5 - 20*a*b^9*c^6 + 160*a^2*b^7*c^7 - 640*a^3*b^5*c^8 + 1280*a^4*b^3*c^9 - 1024*a^5*b*c^10)*d^2*e + 2*(23*b^12*c^4 - 408*a*b^10*c^5 + 2640*a^2*b^8*c^6 - 6400*a^3*b^6*c^7 - 3840*a^4*b^4*c^8 + 43008*a^5*b^2*c^9 - 53248*a^6*c^10)*d*e^2 + (b^13*c^3 - 72*a*b^11*c^4 + 1200*a^2*b^9*c^5 - 8960*a^3*b^7*c^6 + 34560*a^4*b^5*c^7 - 67584*a^5*b^3*c^8 + 53248*a^6*b*c^9)*e^3)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt((4608*c^7*d^7 - 16128*b*c^6*d^6*e + 672*(31*b^2*c^5 + 20*a*c^6)*d^5*e^2 - 1680*(7*b^3*c^4 + 20*a*b*c^5)*d^4*e^3 + 70*(35*b^4*c^3 + 392*a*b^2*c^4 + 176*a^2*c^5)*d^3*e^4 + 21*(b^5*c^2 - 360*a*b^3*c^3 - 880*a^2*b*c^4)*d^2*e^5 - 21*(b^6*c - 10*a*b^4*c^2 - 320*a^2*b^2*c^3 - 160*a^3*c^4)*d*e^6 - (b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*e^7 - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)) + (48384*c^7*d^8*e^5 - 193536*b*c^6*d^7*e^6 + 432*(683*b^2*c^5 + 404*a*c^6)*d^6*e^7 - 432*(481*b^3*c^4 + 1212*a*b*c^5)*d^5*e^8 + 9*(6841*b^4*c^3 + 60712*a*b^2*c^4 + 24016*a^2*c^5)*d^4*e^9 - 18*(145*b^5*c^2 + 12232*a*b^3*c^3 + 24016*a^2*b*c^4)*d^3*e^10 - 2*(518*b^6*c - 10131*a*b^4*c^2 - 124608*a^2*b^2*c^3 - 50000*a^3*c^4)*d^2*e^11 - (35*b^7 - 2562*a*b^5*c + 33072*a^2*b^3*c^2 + 100000*a^3*b*c^3)*d*e^12 + (35*a*b^6 - 1491*a^2*b^4*c + 15000*a^3*b^2*c^2 + 10000*a^4*c^3)*e^13)*sqrt(e*x + d)) - sqrt(1/2)*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)*sqrt((4608*c^7*d^7 - 16128*b*c^6*d^6*e + 672*(31*b^2*c^5 + 20*a*c^6)*d^5*e^2 - 1680*(7*b^3*c^4 + 20*a*b*c^5)*d^4*e^3 + 70*(35*b^4*c^3 + 392*a*b^2*c^4 + 176*a^2*c^5)*d^3*e^4 + 21*(b^5*c^2 - 360*a*b^3*c^3 - 880*a^2*b*c^4)*d^2*e^5 - 21*(b^6*c - 10*a*b^4*c^2 - 320*a^2*b^2*c^3 - 160*a^3*c^4)*d*e^6 - (b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*e^7 - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8))*log(-1/2*sqrt(1/2)*(504*(b^6*c^4 - 12*a*b^4*c^5 + 48*a^2*b^2*c^6 - 64*a^3*c^7)*d^4*e^6 - 1008*(b^7*c^3 - 12*a*b^5*c^4 + 48*a^2*b^3*c^5 - 64*a^3*b*c^6)*d^3*e^7 + 3*(167*b^8*c^2 - 1664*a*b^6*c^3 + 3936*a^2*b^4*c^4 + 5632*a^3*b^2*c^5 - 21760*a^4*c^6)*d^2*e^8 + 3*(b^9*c - 352*a*b^7*c^2 + 4128*a^2*b^5*c^3 - 16384*a^3*b^3*c^4 + 21760*a^4*b*c^5)*d*e^9 - (b^10 - 17*a*b^8*c - 392*a^2*b^6*c^2 + 5696*a^3*b^4*c^3 - 23680*a^4*b^2*c^4 + 32000*a^5*c^5)*e^10 + (96*(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)*d^3 - 144*(b^11*c^5 - 20*a*b^9*c^6 + 160*a^2*b^7*c^7 - 640*a^3*b^5*c^8 + 1280*a^4*b^3*c^9 - 1024*a^5*b*c^10)*d^2*e + 2*(23*b^12*c^4 - 408*a*b^10*c^5 + 2640*a^2*b^8*c^6 - 6400*a^3*b^6*c^7 - 3840*a^4*b^4*c^8 + 43008*a^5*b^2*c^9 - 53248*a^6*c^10)*d*e^2 + (b^13*c^3 - 72*a*b^11*c^4 + 1200*a^2*b^9*c^5 - 8960*a^3*b^7*c^6 + 34560*a^4*b^5*c^7 - 67584*a^5*b^3*c^8 + 53248*a^6*b*c^9)*e^3)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))*sqrt((4608*c^7*d^7 - 16128*b*c^6*d^6*e + 672*(31*b^2*c^5 + 20*a*c^6)*d^5*e^2 - 1680*(7*b^3*c^4 + 20*a*b*c^5)*d^4*e^3 + 70*(35*b^4*c^3 + 392*a*b^2*c^4 + 176*a^2*c^5)*d^3*e^4 + 21*(b^5*c^2 - 360*a*b^3*c^3 - 880*a^2*b*c^4)*d^2*e^5 - 21*(b^6*c - 10*a*b^4*c^2 - 320*a^2*b^2*c^3 - 160*a^3*c^4)*d*e^6 - (b^7 - 35*a*b^5*c + 280*a^2*b^3*c^2 + 1680*a^3*b*c^3)*e^7 - (b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*sqrt((441*c^4*d^4*e^10 - 882*b*c^3*d^3*e^11 + 21*(19*b^2*c^2 + 50*a*c^3)*d^2*e^12 + 42*(b^3*c - 25*a*b*c^2)*d*e^13 + (b^4 - 50*a*b^2*c + 625*a^2*c^2)*e^14)/(b^10*c^6 - 20*a*b^8*c^7 + 160*a^2*b^6*c^8 - 640*a^3*b^4*c^9 + 1280*a^4*b^2*c^10 - 1024*a^5*c^11)))/(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)) + (48384*c^7*d^8*e^5 - 193536*b*c^6*d^7*e^6 + 432*(683*b^2*c^5 + 404*a*c^6)*d^6*e^7 - 432*(481*b^3*c^4 + 1212*a*b*c^5)*d^5*e^8 + 9*(6841*b^4*c^3 + 60712*a*b^2*c^4 + 24016*a^2*c^5)*d^4*e^9 - 18*(145*b^5*c^2 + 12232*a*b^3*c^3 + 24016*a^2*b*c^4)*d^3*e^10 - 2*(518*b^6*c - 10131*a*b^4*c^2 - 124608*a^2*b^2*c^3 - 50000*a^3*c^4)*d^2*e^11 - (35*b^7 - 2562*a*b^5*c + 33072*a^2*b^3*c^2 + 100000*a^3*b*c^3)*d*e^12 + (35*a*b^6 - 1491*a^2*b^4*c + 15000*a^3*b^2*c^2 + 10000*a^4*c^3)*e^13)*sqrt(e*x + d)) - 2*(36*a^2*b*c*d*e^2 - 2*(b^3*c - 10*a*b*c^2)*d^3 - (7*a*b^2*c + 44*a^2*c^2)*d^2*e - (a^2*b^2 + 20*a^3*c)*e^3 + (24*c^4*d^3 - 36*b*c^3*d^2*e + 2*(5*b^2*c^2 + 16*a*c^3)*d*e^2 + (b^3*c - 16*a*b*c^2)*e^3)*x^3 + (36*b*c^3*d^3 - (55*b^2*c^2 - 4*a*c^3)*d^2*e + 4*(4*b^3*c + 11*a*b*c^2)*d*e^2 - (b^4 + 5*a*b^2*c + 36*a^2*c^2)*e^3)*x^2 + (8*(b^2*c^2 + 5*a*c^3)*d^3 - (13*b^3*c + 56*a*b*c^2)*d^2*e + 2*(29*a*b^2*c - 8*a^2*c^2)*d*e^2 - 2*(a*b^3 + 14*a^2*b*c)*e^3)*x)*sqrt(e*x + d))/(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3 + (b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*x^4 + 2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*x^3 + (b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*x^2 + 2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*x)","B",0
2303,1,5124,0,0.671374," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} + {\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} \log\left(27 \, \sqrt{\frac{1}{2}} {\left(4 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{6} - 2 \, {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{7} + \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}} {\left(16 \, {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} d^{2} - 16 \, {\left(b^{11} c^{2} - 20 \, a b^{9} c^{3} + 160 \, a^{2} b^{7} c^{4} - 640 \, a^{3} b^{5} c^{5} + 1280 \, a^{4} b^{3} c^{6} - 1024 \, a^{5} b c^{7}\right)} d e + {\left(3 \, b^{12} c - 56 \, a b^{10} c^{2} + 400 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 1280 \, a^{4} b^{4} c^{5} + 2048 \, a^{5} b^{2} c^{6} - 4096 \, a^{6} c^{7}\right)} e^{2}\right)}\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} + {\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} + 27 \, {\left(256 \, c^{4} d^{4} e^{5} - 512 \, b c^{3} d^{3} e^{6} + 48 \, {\left(7 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{2} e^{7} - 16 \, {\left(5 \, b^{3} c + 12 \, a b c^{2}\right)} d e^{8} + {\left(5 \, b^{4} + 40 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} + {\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} \log\left(-27 \, \sqrt{\frac{1}{2}} {\left(4 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{6} - 2 \, {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{7} + \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}} {\left(16 \, {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} d^{2} - 16 \, {\left(b^{11} c^{2} - 20 \, a b^{9} c^{3} + 160 \, a^{2} b^{7} c^{4} - 640 \, a^{3} b^{5} c^{5} + 1280 \, a^{4} b^{3} c^{6} - 1024 \, a^{5} b c^{7}\right)} d e + {\left(3 \, b^{12} c - 56 \, a b^{10} c^{2} + 400 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 1280 \, a^{4} b^{4} c^{5} + 2048 \, a^{5} b^{2} c^{6} - 4096 \, a^{6} c^{7}\right)} e^{2}\right)}\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} + {\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} + 27 \, {\left(256 \, c^{4} d^{4} e^{5} - 512 \, b c^{3} d^{3} e^{6} + 48 \, {\left(7 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{2} e^{7} - 16 \, {\left(5 \, b^{3} c + 12 \, a b c^{2}\right)} d e^{8} + {\left(5 \, b^{4} + 40 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) + 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} - {\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} \log\left(27 \, \sqrt{\frac{1}{2}} {\left(4 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{6} - 2 \, {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{7} - \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}} {\left(16 \, {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} d^{2} - 16 \, {\left(b^{11} c^{2} - 20 \, a b^{9} c^{3} + 160 \, a^{2} b^{7} c^{4} - 640 \, a^{3} b^{5} c^{5} + 1280 \, a^{4} b^{3} c^{6} - 1024 \, a^{5} b c^{7}\right)} d e + {\left(3 \, b^{12} c - 56 \, a b^{10} c^{2} + 400 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 1280 \, a^{4} b^{4} c^{5} + 2048 \, a^{5} b^{2} c^{6} - 4096 \, a^{6} c^{7}\right)} e^{2}\right)}\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} - {\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} + 27 \, {\left(256 \, c^{4} d^{4} e^{5} - 512 \, b c^{3} d^{3} e^{6} + 48 \, {\left(7 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{2} e^{7} - 16 \, {\left(5 \, b^{3} c + 12 \, a b c^{2}\right)} d e^{8} + {\left(5 \, b^{4} + 40 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} - {\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} \log\left(-27 \, \sqrt{\frac{1}{2}} {\left(4 \, {\left(b^{6} c - 12 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{6} - 2 \, {\left(b^{7} - 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{7} - \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}} {\left(16 \, {\left(b^{10} c^{3} - 20 \, a b^{8} c^{4} + 160 \, a^{2} b^{6} c^{5} - 640 \, a^{3} b^{4} c^{6} + 1280 \, a^{4} b^{2} c^{7} - 1024 \, a^{5} c^{8}\right)} d^{2} - 16 \, {\left(b^{11} c^{2} - 20 \, a b^{9} c^{3} + 160 \, a^{2} b^{7} c^{4} - 640 \, a^{3} b^{5} c^{5} + 1280 \, a^{4} b^{3} c^{6} - 1024 \, a^{5} b c^{7}\right)} d e + {\left(3 \, b^{12} c - 56 \, a b^{10} c^{2} + 400 \, a^{2} b^{8} c^{3} - 1280 \, a^{3} b^{6} c^{4} + 1280 \, a^{4} b^{4} c^{5} + 2048 \, a^{5} b^{2} c^{6} - 4096 \, a^{6} c^{7}\right)} e^{2}\right)}\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} - {\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} \sqrt{\frac{e^{10}}{b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}}}}{b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}}} + 27 \, {\left(256 \, c^{4} d^{4} e^{5} - 512 \, b c^{3} d^{3} e^{6} + 48 \, {\left(7 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{2} e^{7} - 16 \, {\left(5 \, b^{3} c + 12 \, a b c^{2}\right)} d e^{8} + {\left(5 \, b^{4} + 40 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{9}\right)} \sqrt{e x + d}\right) - 2 \, {\left(12 \, a^{2} b e^{2} + 3 \, {\left(8 \, c^{3} d^{2} - 8 \, b c^{2} d e + {\left(b^{2} c + 4 \, a c^{2}\right)} e^{2}\right)} x^{3} - 2 \, {\left(b^{3} - 10 \, a b c\right)} d^{2} - {\left(5 \, a b^{2} + 28 \, a^{2} c\right)} d e + {\left(36 \, b c^{2} d^{2} - {\left(37 \, b^{2} c - 4 \, a c^{2}\right)} d e + {\left(5 \, b^{3} + 16 \, a b c\right)} e^{2}\right)} x^{2} + {\left(8 \, {\left(b^{2} c + 5 \, a c^{2}\right)} d^{2} - 9 \, {\left(b^{3} + 4 \, a b c\right)} d e + {\left(19 \, a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"-1/8*(3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 + (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))*log(27*sqrt(1/2)*(4*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^6 - 2*(b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^7 + sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))*(16*(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*d^2 - 16*(b^11*c^2 - 20*a*b^9*c^3 + 160*a^2*b^7*c^4 - 640*a^3*b^5*c^5 + 1280*a^4*b^3*c^6 - 1024*a^5*b*c^7)*d*e + (3*b^12*c - 56*a*b^10*c^2 + 400*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 1280*a^4*b^4*c^5 + 2048*a^5*b^2*c^6 - 4096*a^6*c^7)*e^2))*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 + (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)) + 27*(256*c^4*d^4*e^5 - 512*b*c^3*d^3*e^6 + 48*(7*b^2*c^2 + 4*a*c^3)*d^2*e^7 - 16*(5*b^3*c + 12*a*b*c^2)*d*e^8 + (5*b^4 + 40*a*b^2*c + 16*a^2*c^2)*e^9)*sqrt(e*x + d)) - 3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 + (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))*log(-27*sqrt(1/2)*(4*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^6 - 2*(b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^7 + sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))*(16*(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*d^2 - 16*(b^11*c^2 - 20*a*b^9*c^3 + 160*a^2*b^7*c^4 - 640*a^3*b^5*c^5 + 1280*a^4*b^3*c^6 - 1024*a^5*b*c^7)*d*e + (3*b^12*c - 56*a*b^10*c^2 + 400*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 1280*a^4*b^4*c^5 + 2048*a^5*b^2*c^6 - 4096*a^6*c^7)*e^2))*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 + (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)) + 27*(256*c^4*d^4*e^5 - 512*b*c^3*d^3*e^6 + 48*(7*b^2*c^2 + 4*a*c^3)*d^2*e^7 - 16*(5*b^3*c + 12*a*b*c^2)*d*e^8 + (5*b^4 + 40*a*b^2*c + 16*a^2*c^2)*e^9)*sqrt(e*x + d)) + 3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 - (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))*log(27*sqrt(1/2)*(4*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^6 - 2*(b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^7 - sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))*(16*(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*d^2 - 16*(b^11*c^2 - 20*a*b^9*c^3 + 160*a^2*b^7*c^4 - 640*a^3*b^5*c^5 + 1280*a^4*b^3*c^6 - 1024*a^5*b*c^7)*d*e + (3*b^12*c - 56*a*b^10*c^2 + 400*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 1280*a^4*b^4*c^5 + 2048*a^5*b^2*c^6 - 4096*a^6*c^7)*e^2))*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 - (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)) + 27*(256*c^4*d^4*e^5 - 512*b*c^3*d^3*e^6 + 48*(7*b^2*c^2 + 4*a*c^3)*d^2*e^7 - 16*(5*b^3*c + 12*a*b*c^2)*d*e^8 + (5*b^4 + 40*a*b^2*c + 16*a^2*c^2)*e^9)*sqrt(e*x + d)) - 3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 - (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6))*log(-27*sqrt(1/2)*(4*(b^6*c - 12*a*b^4*c^2 + 48*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^6 - 2*(b^7 - 12*a*b^5*c + 48*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^7 - sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7))*(16*(b^10*c^3 - 20*a*b^8*c^4 + 160*a^2*b^6*c^5 - 640*a^3*b^4*c^6 + 1280*a^4*b^2*c^7 - 1024*a^5*c^8)*d^2 - 16*(b^11*c^2 - 20*a*b^9*c^3 + 160*a^2*b^7*c^4 - 640*a^3*b^5*c^5 + 1280*a^4*b^3*c^6 - 1024*a^5*b*c^7)*d*e + (3*b^12*c - 56*a*b^10*c^2 + 400*a^2*b^8*c^3 - 1280*a^3*b^6*c^4 + 1280*a^4*b^4*c^5 + 2048*a^5*b^2*c^6 - 4096*a^6*c^7)*e^2))*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 - (b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*sqrt(e^10/(b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)))/(b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)) + 27*(256*c^4*d^4*e^5 - 512*b*c^3*d^3*e^6 + 48*(7*b^2*c^2 + 4*a*c^3)*d^2*e^7 - 16*(5*b^3*c + 12*a*b*c^2)*d*e^8 + (5*b^4 + 40*a*b^2*c + 16*a^2*c^2)*e^9)*sqrt(e*x + d)) - 2*(12*a^2*b*e^2 + 3*(8*c^3*d^2 - 8*b*c^2*d*e + (b^2*c + 4*a*c^2)*e^2)*x^3 - 2*(b^3 - 10*a*b*c)*d^2 - (5*a*b^2 + 28*a^2*c)*d*e + (36*b*c^2*d^2 - (37*b^2*c - 4*a*c^2)*d*e + (5*b^3 + 16*a*b*c)*e^2)*x^2 + (8*(b^2*c + 5*a*c^2)*d^2 - 9*(b^3 + 4*a*b*c)*d*e + (19*a*b^2 - 4*a^2*c)*e^2)*x)*sqrt(e*x + d))/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
2304,1,11128,0,0.857483," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} + \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left({\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}\right)}}{{\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e^{6} - 8 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d e^{7} + {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e^{8} - \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left(32 \, {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{5} - 80 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} d^{4} e + 2 \, {\left(33 \, b^{12} c^{2} - 632 \, a b^{10} c^{3} + 4720 \, a^{2} b^{8} c^{4} - 16640 \, a^{3} b^{6} c^{5} + 24320 \, a^{4} b^{4} c^{6} + 2048 \, a^{5} b^{2} c^{7} - 28672 \, a^{6} c^{8}\right)} d^{3} e^{2} - {\left(19 \, b^{13} c - 296 \, a b^{11} c^{2} + 1360 \, a^{2} b^{9} c^{3} + 1280 \, a^{3} b^{7} c^{4} - 29440 \, a^{4} b^{5} c^{5} + 88064 \, a^{5} b^{3} c^{6} - 86016 \, a^{6} b c^{7}\right)} d^{2} e^{3} + {\left(b^{14} + 10 \, a b^{12} c - 416 \, a^{2} b^{10} c^{2} + 3680 \, a^{3} b^{8} c^{3} - 14080 \, a^{4} b^{6} c^{4} + 22016 \, a^{5} b^{4} c^{5} - 24576 \, a^{7} c^{7}\right)} d e^{4} - {\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} e^{5}\right)}\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} + \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left({\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}\right)}}{{\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} + 27 \, {\left(256 \, c^{5} d^{4} e^{5} - 512 \, b c^{4} d^{3} e^{6} + 48 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{2} e^{7} - 16 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d e^{8} + {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{9}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} + \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left({\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}\right)}}{{\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e^{6} - 8 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d e^{7} + {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e^{8} - \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left(32 \, {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{5} - 80 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} d^{4} e + 2 \, {\left(33 \, b^{12} c^{2} - 632 \, a b^{10} c^{3} + 4720 \, a^{2} b^{8} c^{4} - 16640 \, a^{3} b^{6} c^{5} + 24320 \, a^{4} b^{4} c^{6} + 2048 \, a^{5} b^{2} c^{7} - 28672 \, a^{6} c^{8}\right)} d^{3} e^{2} - {\left(19 \, b^{13} c - 296 \, a b^{11} c^{2} + 1360 \, a^{2} b^{9} c^{3} + 1280 \, a^{3} b^{7} c^{4} - 29440 \, a^{4} b^{5} c^{5} + 88064 \, a^{5} b^{3} c^{6} - 86016 \, a^{6} b c^{7}\right)} d^{2} e^{3} + {\left(b^{14} + 10 \, a b^{12} c - 416 \, a^{2} b^{10} c^{2} + 3680 \, a^{3} b^{8} c^{3} - 14080 \, a^{4} b^{6} c^{4} + 22016 \, a^{5} b^{4} c^{5} - 24576 \, a^{7} c^{7}\right)} d e^{4} - {\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} e^{5}\right)}\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} + \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left({\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}\right)}}{{\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} + 27 \, {\left(256 \, c^{5} d^{4} e^{5} - 512 \, b c^{4} d^{3} e^{6} + 48 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{2} e^{7} - 16 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d e^{8} + {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{9}\right)} \sqrt{e x + d}\right) + 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} - \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left({\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}\right)}}{{\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e^{6} - 8 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d e^{7} + {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e^{8} + \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left(32 \, {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{5} - 80 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} d^{4} e + 2 \, {\left(33 \, b^{12} c^{2} - 632 \, a b^{10} c^{3} + 4720 \, a^{2} b^{8} c^{4} - 16640 \, a^{3} b^{6} c^{5} + 24320 \, a^{4} b^{4} c^{6} + 2048 \, a^{5} b^{2} c^{7} - 28672 \, a^{6} c^{8}\right)} d^{3} e^{2} - {\left(19 \, b^{13} c - 296 \, a b^{11} c^{2} + 1360 \, a^{2} b^{9} c^{3} + 1280 \, a^{3} b^{7} c^{4} - 29440 \, a^{4} b^{5} c^{5} + 88064 \, a^{5} b^{3} c^{6} - 86016 \, a^{6} b c^{7}\right)} d^{2} e^{3} + {\left(b^{14} + 10 \, a b^{12} c - 416 \, a^{2} b^{10} c^{2} + 3680 \, a^{3} b^{8} c^{3} - 14080 \, a^{4} b^{6} c^{4} + 22016 \, a^{5} b^{4} c^{5} - 24576 \, a^{7} c^{7}\right)} d e^{4} - {\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} e^{5}\right)}\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} - \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left({\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}\right)}}{{\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} + 27 \, {\left(256 \, c^{5} d^{4} e^{5} - 512 \, b c^{4} d^{3} e^{6} + 48 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{2} e^{7} - 16 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d e^{8} + {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{9}\right)} \sqrt{e x + d}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} - \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left({\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}\right)}}{{\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(8 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} e^{6} - 8 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d e^{7} + {\left(b^{8} - 8 \, a b^{6} c + 128 \, a^{3} b^{2} c^{3} - 256 \, a^{4} c^{4}\right)} e^{8} + \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left(32 \, {\left(b^{10} c^{4} - 20 \, a b^{8} c^{5} + 160 \, a^{2} b^{6} c^{6} - 640 \, a^{3} b^{4} c^{7} + 1280 \, a^{4} b^{2} c^{8} - 1024 \, a^{5} c^{9}\right)} d^{5} - 80 \, {\left(b^{11} c^{3} - 20 \, a b^{9} c^{4} + 160 \, a^{2} b^{7} c^{5} - 640 \, a^{3} b^{5} c^{6} + 1280 \, a^{4} b^{3} c^{7} - 1024 \, a^{5} b c^{8}\right)} d^{4} e + 2 \, {\left(33 \, b^{12} c^{2} - 632 \, a b^{10} c^{3} + 4720 \, a^{2} b^{8} c^{4} - 16640 \, a^{3} b^{6} c^{5} + 24320 \, a^{4} b^{4} c^{6} + 2048 \, a^{5} b^{2} c^{7} - 28672 \, a^{6} c^{8}\right)} d^{3} e^{2} - {\left(19 \, b^{13} c - 296 \, a b^{11} c^{2} + 1360 \, a^{2} b^{9} c^{3} + 1280 \, a^{3} b^{7} c^{4} - 29440 \, a^{4} b^{5} c^{5} + 88064 \, a^{5} b^{3} c^{6} - 86016 \, a^{6} b c^{7}\right)} d^{2} e^{3} + {\left(b^{14} + 10 \, a b^{12} c - 416 \, a^{2} b^{10} c^{2} + 3680 \, a^{3} b^{8} c^{3} - 14080 \, a^{4} b^{6} c^{4} + 22016 \, a^{5} b^{4} c^{5} - 24576 \, a^{7} c^{7}\right)} d e^{4} - {\left(a b^{13} - 8 \, a^{2} b^{11} c - 80 \, a^{3} b^{9} c^{2} + 1280 \, a^{4} b^{7} c^{3} - 6400 \, a^{5} b^{5} c^{4} + 14336 \, a^{6} b^{3} c^{5} - 12288 \, a^{7} b c^{6}\right)} e^{5}\right)}\right)} \sqrt{\frac{512 \, c^{5} d^{5} - 1280 \, b c^{4} d^{4} e + 160 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{3} e^{2} - 80 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d^{2} e^{3} + 10 \, {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{4} - {\left(b^{5} + 40 \, a b^{3} c + 80 \, a^{2} b c^{2}\right)} e^{5} - \sqrt{\frac{e^{10}}{{\left(b^{10} c^{2} - 20 \, a b^{8} c^{3} + 160 \, a^{2} b^{6} c^{4} - 640 \, a^{3} b^{4} c^{5} + 1280 \, a^{4} b^{2} c^{6} - 1024 \, a^{5} c^{7}\right)} d^{4} - 2 \, {\left(b^{11} c - 20 \, a b^{9} c^{2} + 160 \, a^{2} b^{7} c^{3} - 640 \, a^{3} b^{5} c^{4} + 1280 \, a^{4} b^{3} c^{5} - 1024 \, a^{5} b c^{6}\right)} d^{3} e + {\left(b^{12} - 18 \, a b^{10} c + 120 \, a^{2} b^{8} c^{2} - 320 \, a^{3} b^{6} c^{3} + 1536 \, a^{5} b^{2} c^{5} - 2048 \, a^{6} c^{6}\right)} d^{2} e^{2} - 2 \, {\left(a b^{11} - 20 \, a^{2} b^{9} c + 160 \, a^{3} b^{7} c^{2} - 640 \, a^{4} b^{5} c^{3} + 1280 \, a^{5} b^{3} c^{4} - 1024 \, a^{6} b c^{5}\right)} d e^{3} + {\left(a^{2} b^{10} - 20 \, a^{3} b^{8} c + 160 \, a^{4} b^{6} c^{2} - 640 \, a^{5} b^{4} c^{3} + 1280 \, a^{6} b^{2} c^{4} - 1024 \, a^{7} c^{5}\right)} e^{4}}} {\left({\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}\right)}}{{\left(b^{10} c - 20 \, a b^{8} c^{2} + 160 \, a^{2} b^{6} c^{3} - 640 \, a^{3} b^{4} c^{4} + 1280 \, a^{4} b^{2} c^{5} - 1024 \, a^{5} c^{6}\right)} d^{2} - {\left(b^{11} - 20 \, a b^{9} c + 160 \, a^{2} b^{7} c^{2} - 640 \, a^{3} b^{5} c^{3} + 1280 \, a^{4} b^{3} c^{4} - 1024 \, a^{5} b c^{5}\right)} d e + {\left(a b^{10} - 20 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} - 640 \, a^{4} b^{4} c^{3} + 1280 \, a^{5} b^{2} c^{4} - 1024 \, a^{6} c^{5}\right)} e^{2}}} + 27 \, {\left(256 \, c^{5} d^{4} e^{5} - 512 \, b c^{4} d^{3} e^{6} + 48 \, {\left(7 \, b^{2} c^{3} + 4 \, a c^{4}\right)} d^{2} e^{7} - 16 \, {\left(5 \, b^{3} c^{2} + 12 \, a b c^{3}\right)} d e^{8} + {\left(5 \, b^{4} c + 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{9}\right)} \sqrt{e x + d}\right) - 2 \, {\left(12 \, {\left(2 \, c^{3} d - b c^{2} e\right)} x^{3} + {\left(36 \, b c^{2} d - {\left(19 \, b^{2} c - 4 \, a c^{2}\right)} e\right)} x^{2} - 2 \, {\left(b^{3} - 10 \, a b c\right)} d - 3 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e + {\left(8 \, {\left(b^{2} c + 5 \, a c^{2}\right)} d - {\left(5 \, b^{3} + 16 \, a b c\right)} e\right)} x\right)} \sqrt{e x + d}}{8 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"-1/8*(3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 + sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))/((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(27/2*sqrt(1/2)*(8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e^6 - 8*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*e^7 + (b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e^8 - sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*(32*(b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^5 - 80*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*d^4*e + 2*(33*b^12*c^2 - 632*a*b^10*c^3 + 4720*a^2*b^8*c^4 - 16640*a^3*b^6*c^5 + 24320*a^4*b^4*c^6 + 2048*a^5*b^2*c^7 - 28672*a^6*c^8)*d^3*e^2 - (19*b^13*c - 296*a*b^11*c^2 + 1360*a^2*b^9*c^3 + 1280*a^3*b^7*c^4 - 29440*a^4*b^5*c^5 + 88064*a^5*b^3*c^6 - 86016*a^6*b*c^7)*d^2*e^3 + (b^14 + 10*a*b^12*c - 416*a^2*b^10*c^2 + 3680*a^3*b^8*c^3 - 14080*a^4*b^6*c^4 + 22016*a^5*b^4*c^5 - 24576*a^7*c^7)*d*e^4 - (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*e^5))*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 + sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))/((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2)) + 27*(256*c^5*d^4*e^5 - 512*b*c^4*d^3*e^6 + 48*(7*b^2*c^3 + 4*a*c^4)*d^2*e^7 - 16*(5*b^3*c^2 + 12*a*b*c^3)*d*e^8 + (5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e^9)*sqrt(e*x + d)) - 3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 + sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))/((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(-27/2*sqrt(1/2)*(8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e^6 - 8*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*e^7 + (b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e^8 - sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*(32*(b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^5 - 80*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*d^4*e + 2*(33*b^12*c^2 - 632*a*b^10*c^3 + 4720*a^2*b^8*c^4 - 16640*a^3*b^6*c^5 + 24320*a^4*b^4*c^6 + 2048*a^5*b^2*c^7 - 28672*a^6*c^8)*d^3*e^2 - (19*b^13*c - 296*a*b^11*c^2 + 1360*a^2*b^9*c^3 + 1280*a^3*b^7*c^4 - 29440*a^4*b^5*c^5 + 88064*a^5*b^3*c^6 - 86016*a^6*b*c^7)*d^2*e^3 + (b^14 + 10*a*b^12*c - 416*a^2*b^10*c^2 + 3680*a^3*b^8*c^3 - 14080*a^4*b^6*c^4 + 22016*a^5*b^4*c^5 - 24576*a^7*c^7)*d*e^4 - (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*e^5))*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 + sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))/((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2)) + 27*(256*c^5*d^4*e^5 - 512*b*c^4*d^3*e^6 + 48*(7*b^2*c^3 + 4*a*c^4)*d^2*e^7 - 16*(5*b^3*c^2 + 12*a*b*c^3)*d*e^8 + (5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e^9)*sqrt(e*x + d)) + 3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 - sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))/((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(27/2*sqrt(1/2)*(8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e^6 - 8*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*e^7 + (b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e^8 + sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*(32*(b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^5 - 80*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*d^4*e + 2*(33*b^12*c^2 - 632*a*b^10*c^3 + 4720*a^2*b^8*c^4 - 16640*a^3*b^6*c^5 + 24320*a^4*b^4*c^6 + 2048*a^5*b^2*c^7 - 28672*a^6*c^8)*d^3*e^2 - (19*b^13*c - 296*a*b^11*c^2 + 1360*a^2*b^9*c^3 + 1280*a^3*b^7*c^4 - 29440*a^4*b^5*c^5 + 88064*a^5*b^3*c^6 - 86016*a^6*b*c^7)*d^2*e^3 + (b^14 + 10*a*b^12*c - 416*a^2*b^10*c^2 + 3680*a^3*b^8*c^3 - 14080*a^4*b^6*c^4 + 22016*a^5*b^4*c^5 - 24576*a^7*c^7)*d*e^4 - (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*e^5))*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 - sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))/((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2)) + 27*(256*c^5*d^4*e^5 - 512*b*c^4*d^3*e^6 + 48*(7*b^2*c^3 + 4*a*c^4)*d^2*e^7 - 16*(5*b^3*c^2 + 12*a*b*c^3)*d*e^8 + (5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e^9)*sqrt(e*x + d)) - 3*sqrt(1/2)*(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 - sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))/((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))*log(-27/2*sqrt(1/2)*(8*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*e^6 - 8*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*e^7 + (b^8 - 8*a*b^6*c + 128*a^3*b^2*c^3 - 256*a^4*c^4)*e^8 + sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*(32*(b^10*c^4 - 20*a*b^8*c^5 + 160*a^2*b^6*c^6 - 640*a^3*b^4*c^7 + 1280*a^4*b^2*c^8 - 1024*a^5*c^9)*d^5 - 80*(b^11*c^3 - 20*a*b^9*c^4 + 160*a^2*b^7*c^5 - 640*a^3*b^5*c^6 + 1280*a^4*b^3*c^7 - 1024*a^5*b*c^8)*d^4*e + 2*(33*b^12*c^2 - 632*a*b^10*c^3 + 4720*a^2*b^8*c^4 - 16640*a^3*b^6*c^5 + 24320*a^4*b^4*c^6 + 2048*a^5*b^2*c^7 - 28672*a^6*c^8)*d^3*e^2 - (19*b^13*c - 296*a*b^11*c^2 + 1360*a^2*b^9*c^3 + 1280*a^3*b^7*c^4 - 29440*a^4*b^5*c^5 + 88064*a^5*b^3*c^6 - 86016*a^6*b*c^7)*d^2*e^3 + (b^14 + 10*a*b^12*c - 416*a^2*b^10*c^2 + 3680*a^3*b^8*c^3 - 14080*a^4*b^6*c^4 + 22016*a^5*b^4*c^5 - 24576*a^7*c^7)*d*e^4 - (a*b^13 - 8*a^2*b^11*c - 80*a^3*b^9*c^2 + 1280*a^4*b^7*c^3 - 6400*a^5*b^5*c^4 + 14336*a^6*b^3*c^5 - 12288*a^7*b*c^6)*e^5))*sqrt((512*c^5*d^5 - 1280*b*c^4*d^4*e + 160*(7*b^2*c^3 + 4*a*c^4)*d^3*e^2 - 80*(5*b^3*c^2 + 12*a*b*c^3)*d^2*e^3 + 10*(5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*d*e^4 - (b^5 + 40*a*b^3*c + 80*a^2*b*c^2)*e^5 - sqrt(e^10/((b^10*c^2 - 20*a*b^8*c^3 + 160*a^2*b^6*c^4 - 640*a^3*b^4*c^5 + 1280*a^4*b^2*c^6 - 1024*a^5*c^7)*d^4 - 2*(b^11*c - 20*a*b^9*c^2 + 160*a^2*b^7*c^3 - 640*a^3*b^5*c^4 + 1280*a^4*b^3*c^5 - 1024*a^5*b*c^6)*d^3*e + (b^12 - 18*a*b^10*c + 120*a^2*b^8*c^2 - 320*a^3*b^6*c^3 + 1536*a^5*b^2*c^5 - 2048*a^6*c^6)*d^2*e^2 - 2*(a*b^11 - 20*a^2*b^9*c + 160*a^3*b^7*c^2 - 640*a^4*b^5*c^3 + 1280*a^5*b^3*c^4 - 1024*a^6*b*c^5)*d*e^3 + (a^2*b^10 - 20*a^3*b^8*c + 160*a^4*b^6*c^2 - 640*a^5*b^4*c^3 + 1280*a^6*b^2*c^4 - 1024*a^7*c^5)*e^4))*((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2))/((b^10*c - 20*a*b^8*c^2 + 160*a^2*b^6*c^3 - 640*a^3*b^4*c^4 + 1280*a^4*b^2*c^5 - 1024*a^5*c^6)*d^2 - (b^11 - 20*a*b^9*c + 160*a^2*b^7*c^2 - 640*a^3*b^5*c^3 + 1280*a^4*b^3*c^4 - 1024*a^5*b*c^5)*d*e + (a*b^10 - 20*a^2*b^8*c + 160*a^3*b^6*c^2 - 640*a^4*b^4*c^3 + 1280*a^5*b^2*c^4 - 1024*a^6*c^5)*e^2)) + 27*(256*c^5*d^4*e^5 - 512*b*c^4*d^3*e^6 + 48*(7*b^2*c^3 + 4*a*c^4)*d^2*e^7 - 16*(5*b^3*c^2 + 12*a*b*c^3)*d*e^8 + (5*b^4*c + 40*a*b^2*c^2 + 16*a^2*c^3)*e^9)*sqrt(e*x + d)) - 2*(12*(2*c^3*d - b*c^2*e)*x^3 + (36*b*c^2*d - (19*b^2*c - 4*a*c^2)*e)*x^2 - 2*(b^3 - 10*a*b*c)*d - 3*(a*b^2 + 4*a^2*c)*e + (8*(b^2*c + 5*a*c^2)*d - (5*b^3 + 16*a*b*c)*e)*x)*sqrt(e*x + d))/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
2305,-1,0,0,0.000000," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2306,-1,0,0,0.000000," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2307,1,733,0,0.433405," ","integrate((e*x+d)^(1/2)/(a+I*b*x+c*x^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-\frac{4 \, c d - 2 i \, b e + 2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}}}{b^{2} c + 4 \, a c^{2}}} \log\left(\frac{{\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}} \sqrt{-\frac{4 \, c d - 2 i \, b e + 2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}}}{b^{2} c + 4 \, a c^{2}}} + 2 \, \sqrt{e x + d} e}{2 \, e}\right) + \frac{1}{2} \, \sqrt{-\frac{4 \, c d - 2 i \, b e + 2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}}}{b^{2} c + 4 \, a c^{2}}} \log\left(-\frac{{\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}} \sqrt{-\frac{4 \, c d - 2 i \, b e + 2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}}}{b^{2} c + 4 \, a c^{2}}} - 2 \, \sqrt{e x + d} e}{2 \, e}\right) + \frac{1}{2} \, \sqrt{-\frac{4 \, c d - 2 i \, b e - 2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}}}{b^{2} c + 4 \, a c^{2}}} \log\left(\frac{{\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}} \sqrt{-\frac{4 \, c d - 2 i \, b e - 2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}}}{b^{2} c + 4 \, a c^{2}}} + 2 \, \sqrt{e x + d} e}{2 \, e}\right) - \frac{1}{2} \, \sqrt{-\frac{4 \, c d - 2 i \, b e - 2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}}}{b^{2} c + 4 \, a c^{2}}} \log\left(-\frac{{\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}} \sqrt{-\frac{4 \, c d - 2 i \, b e - 2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} \sqrt{-\frac{e^{2}}{b^{2} c^{2} + 4 \, a c^{3}}}}{b^{2} c + 4 \, a c^{2}}} - 2 \, \sqrt{e x + d} e}{2 \, e}\right)"," ",0,"-1/2*sqrt(-(4*c*d - 2*I*b*e + 2*(b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3)))/(b^2*c + 4*a*c^2))*log(1/2*((b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3))*sqrt(-(4*c*d - 2*I*b*e + 2*(b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3)))/(b^2*c + 4*a*c^2)) + 2*sqrt(e*x + d)*e)/e) + 1/2*sqrt(-(4*c*d - 2*I*b*e + 2*(b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3)))/(b^2*c + 4*a*c^2))*log(-1/2*((b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3))*sqrt(-(4*c*d - 2*I*b*e + 2*(b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3)))/(b^2*c + 4*a*c^2)) - 2*sqrt(e*x + d)*e)/e) + 1/2*sqrt(-(4*c*d - 2*I*b*e - 2*(b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3)))/(b^2*c + 4*a*c^2))*log(1/2*((b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3))*sqrt(-(4*c*d - 2*I*b*e - 2*(b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3)))/(b^2*c + 4*a*c^2)) + 2*sqrt(e*x + d)*e)/e) - 1/2*sqrt(-(4*c*d - 2*I*b*e - 2*(b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3)))/(b^2*c + 4*a*c^2))*log(-1/2*((b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3))*sqrt(-(4*c*d - 2*I*b*e - 2*(b^2*c + 4*a*c^2)*sqrt(-e^2/(b^2*c^2 + 4*a*c^3)))/(b^2*c + 4*a*c^2)) - 2*sqrt(e*x + d)*e)/e)","A",0
2308,1,2725,0,0.489492," ","integrate(1/(e*x+d)^(1/2)/(a+I*b*x+c*x^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-\frac{4 \, c d - 2 i \, b e + {\left(2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} - {\left(2 i \, b^{3} + 8 i \, a b c\right)} d e + 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-i \, b^{3} - 4 i \, a b c\right)} d e + {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}}} \log\left(\frac{4 \, \sqrt{e x + d} c e - {\left({\left(b^{2} + 4 \, a c\right)} e^{2} + {\left(2 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{3} - {\left(3 i \, b^{3} c + 12 i \, a b c^{2}\right)} d^{2} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - {\left(i \, a b^{3} + 4 i \, a^{2} b c\right)} e^{3}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}\right)} \sqrt{-\frac{4 \, c d - 2 i \, b e + {\left(2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} - {\left(2 i \, b^{3} + 8 i \, a b c\right)} d e + 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-i \, b^{3} - 4 i \, a b c\right)} d e + {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}}}}{4 \, c e}\right) + \frac{1}{2} \, \sqrt{-\frac{4 \, c d - 2 i \, b e + {\left(2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} - {\left(2 i \, b^{3} + 8 i \, a b c\right)} d e + 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-i \, b^{3} - 4 i \, a b c\right)} d e + {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}}} \log\left(\frac{4 \, \sqrt{e x + d} c e + {\left({\left(b^{2} + 4 \, a c\right)} e^{2} + {\left(2 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{3} + {\left(-3 i \, b^{3} c - 12 i \, a b c^{2}\right)} d^{2} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} + {\left(-i \, a b^{3} - 4 i \, a^{2} b c\right)} e^{3}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}\right)} \sqrt{-\frac{4 \, c d - 2 i \, b e + {\left(2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} - {\left(2 i \, b^{3} + 8 i \, a b c\right)} d e + 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-i \, b^{3} - 4 i \, a b c\right)} d e + {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}}}}{4 \, c e}\right) + \frac{1}{2} \, \sqrt{-\frac{4 \, c d - 2 i \, b e - {\left(2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-2 i \, b^{3} - 8 i \, a b c\right)} d e + 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-i \, b^{3} - 4 i \, a b c\right)} d e + {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}}} \log\left(\frac{4 \, \sqrt{e x + d} c e + {\left({\left(b^{2} + 4 \, a c\right)} e^{2} - {\left(2 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{3} - {\left(3 i \, b^{3} c + 12 i \, a b c^{2}\right)} d^{2} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} - {\left(i \, a b^{3} + 4 i \, a^{2} b c\right)} e^{3}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}\right)} \sqrt{-\frac{4 \, c d - 2 i \, b e - {\left(2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-2 i \, b^{3} - 8 i \, a b c\right)} d e + 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-i \, b^{3} - 4 i \, a b c\right)} d e + {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}}}}{4 \, c e}\right) - \frac{1}{2} \, \sqrt{-\frac{4 \, c d - 2 i \, b e - {\left(2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-2 i \, b^{3} - 8 i \, a b c\right)} d e + 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-i \, b^{3} - 4 i \, a b c\right)} d e + {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}}} \log\left(\frac{4 \, \sqrt{e x + d} c e - {\left({\left(b^{2} + 4 \, a c\right)} e^{2} - {\left(2 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{3} + {\left(-3 i \, b^{3} c - 12 i \, a b c^{2}\right)} d^{2} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d e^{2} + {\left(-i \, a b^{3} - 4 i \, a^{2} b c\right)} e^{3}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}\right)} \sqrt{-\frac{4 \, c d - 2 i \, b e - {\left(2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-2 i \, b^{3} - 8 i \, a b c\right)} d e + 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-\frac{e^{2}}{{\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{4} + {\left(-2 i \, b^{3} c - 8 i \, a b c^{2}\right)} d^{3} e - {\left(b^{4} + 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{2} + {\left(-2 i \, a b^{3} - 8 i \, a^{2} b c\right)} d e^{3} + {\left(a^{2} b^{2} + 4 \, a^{3} c\right)} e^{4}}}}{{\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} + {\left(-i \, b^{3} - 4 i \, a b c\right)} d e + {\left(a b^{2} + 4 \, a^{2} c\right)} e^{2}}}}{4 \, c e}\right)"," ",0,"-1/2*sqrt(-(4*c*d - 2*I*b*e + (2*(b^2*c + 4*a*c^2)*d^2 - (2*I*b^3 + 8*I*a*b*c)*d*e + 2*(a*b^2 + 4*a^2*c)*e^2)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))/((b^2*c + 4*a*c^2)*d^2 + (-I*b^3 - 4*I*a*b*c)*d*e + (a*b^2 + 4*a^2*c)*e^2))*log(1/4*(4*sqrt(e*x + d)*c*e - ((b^2 + 4*a*c)*e^2 + (2*(b^2*c^2 + 4*a*c^3)*d^3 - (3*I*b^3*c + 12*I*a*b*c^2)*d^2*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d*e^2 - (I*a*b^3 + 4*I*a^2*b*c)*e^3)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))*sqrt(-(4*c*d - 2*I*b*e + (2*(b^2*c + 4*a*c^2)*d^2 - (2*I*b^3 + 8*I*a*b*c)*d*e + 2*(a*b^2 + 4*a^2*c)*e^2)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))/((b^2*c + 4*a*c^2)*d^2 + (-I*b^3 - 4*I*a*b*c)*d*e + (a*b^2 + 4*a^2*c)*e^2)))/(c*e)) + 1/2*sqrt(-(4*c*d - 2*I*b*e + (2*(b^2*c + 4*a*c^2)*d^2 - (2*I*b^3 + 8*I*a*b*c)*d*e + 2*(a*b^2 + 4*a^2*c)*e^2)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))/((b^2*c + 4*a*c^2)*d^2 + (-I*b^3 - 4*I*a*b*c)*d*e + (a*b^2 + 4*a^2*c)*e^2))*log(1/4*(4*sqrt(e*x + d)*c*e + ((b^2 + 4*a*c)*e^2 + (2*(b^2*c^2 + 4*a*c^3)*d^3 + (-3*I*b^3*c - 12*I*a*b*c^2)*d^2*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d*e^2 + (-I*a*b^3 - 4*I*a^2*b*c)*e^3)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))*sqrt(-(4*c*d - 2*I*b*e + (2*(b^2*c + 4*a*c^2)*d^2 - (2*I*b^3 + 8*I*a*b*c)*d*e + 2*(a*b^2 + 4*a^2*c)*e^2)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))/((b^2*c + 4*a*c^2)*d^2 + (-I*b^3 - 4*I*a*b*c)*d*e + (a*b^2 + 4*a^2*c)*e^2)))/(c*e)) + 1/2*sqrt(-(4*c*d - 2*I*b*e - (2*(b^2*c + 4*a*c^2)*d^2 + (-2*I*b^3 - 8*I*a*b*c)*d*e + 2*(a*b^2 + 4*a^2*c)*e^2)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))/((b^2*c + 4*a*c^2)*d^2 + (-I*b^3 - 4*I*a*b*c)*d*e + (a*b^2 + 4*a^2*c)*e^2))*log(1/4*(4*sqrt(e*x + d)*c*e + ((b^2 + 4*a*c)*e^2 - (2*(b^2*c^2 + 4*a*c^3)*d^3 - (3*I*b^3*c + 12*I*a*b*c^2)*d^2*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d*e^2 - (I*a*b^3 + 4*I*a^2*b*c)*e^3)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))*sqrt(-(4*c*d - 2*I*b*e - (2*(b^2*c + 4*a*c^2)*d^2 + (-2*I*b^3 - 8*I*a*b*c)*d*e + 2*(a*b^2 + 4*a^2*c)*e^2)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))/((b^2*c + 4*a*c^2)*d^2 + (-I*b^3 - 4*I*a*b*c)*d*e + (a*b^2 + 4*a^2*c)*e^2)))/(c*e)) - 1/2*sqrt(-(4*c*d - 2*I*b*e - (2*(b^2*c + 4*a*c^2)*d^2 + (-2*I*b^3 - 8*I*a*b*c)*d*e + 2*(a*b^2 + 4*a^2*c)*e^2)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))/((b^2*c + 4*a*c^2)*d^2 + (-I*b^3 - 4*I*a*b*c)*d*e + (a*b^2 + 4*a^2*c)*e^2))*log(1/4*(4*sqrt(e*x + d)*c*e - ((b^2 + 4*a*c)*e^2 - (2*(b^2*c^2 + 4*a*c^3)*d^3 + (-3*I*b^3*c - 12*I*a*b*c^2)*d^2*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d*e^2 + (-I*a*b^3 - 4*I*a^2*b*c)*e^3)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))*sqrt(-(4*c*d - 2*I*b*e - (2*(b^2*c + 4*a*c^2)*d^2 + (-2*I*b^3 - 8*I*a*b*c)*d*e + 2*(a*b^2 + 4*a^2*c)*e^2)*sqrt(-e^2/((b^2*c^2 + 4*a*c^3)*d^4 + (-2*I*b^3*c - 8*I*a*b*c^2)*d^3*e - (b^4 + 2*a*b^2*c - 8*a^2*c^2)*d^2*e^2 + (-2*I*a*b^3 - 8*I*a^2*b*c)*d*e^3 + (a^2*b^2 + 4*a^3*c)*e^4)))/((b^2*c + 4*a*c^2)*d^2 + (-I*b^3 - 4*I*a*b*c)*d*e + (a*b^2 + 4*a^2*c)*e^2)))/(c*e))","B",0
2309,1,468,0,0.445817," ","integrate((1+2*x)^(7/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{1}{1752203762968750} \cdot 42875^{\frac{1}{4}} \sqrt{155} {\left(168698 \, \sqrt{35} \sqrt{31} + 1500625 \, \sqrt{31}\right)} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} \log\left(\frac{26582500}{34021} \cdot 42875^{\frac{1}{4}} \sqrt{155} {\left(216 \, \sqrt{35} \sqrt{31} + 665 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} + 353314653125000 \, x + 35331465312500 \, \sqrt{35} + 176657326562500\right) - \frac{1}{1752203762968750} \cdot 42875^{\frac{1}{4}} \sqrt{155} {\left(168698 \, \sqrt{35} \sqrt{31} + 1500625 \, \sqrt{31}\right)} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} \log\left(-\frac{26582500}{34021} \cdot 42875^{\frac{1}{4}} \sqrt{155} {\left(216 \, \sqrt{35} \sqrt{31} + 665 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} + 353314653125000 \, x + 35331465312500 \, \sqrt{35} + 176657326562500\right) + \frac{2}{830703125} \cdot 42875^{\frac{1}{4}} \sqrt{155} \sqrt{35} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} \arctan\left(\frac{1}{2044682140744622640625} \cdot 42875^{\frac{3}{4}} \sqrt{34021} \sqrt{217} \sqrt{155} \sqrt{42875^{\frac{1}{4}} \sqrt{155} {\left(216 \, \sqrt{35} \sqrt{31} + 665 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} + 452181616250 \, x + 45218161625 \, \sqrt{35} + 226090808125} {\left(19 \, \sqrt{35} + 216\right)} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} - \frac{1}{1582635656875} \cdot 42875^{\frac{3}{4}} \sqrt{155} \sqrt{2 \, x + 1} {\left(19 \, \sqrt{35} + 216\right)} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + \frac{2}{830703125} \cdot 42875^{\frac{1}{4}} \sqrt{155} \sqrt{35} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} \arctan\left(\frac{1}{715638749260617924218750} \cdot 42875^{\frac{3}{4}} \sqrt{34021} \sqrt{155} \sqrt{-26582500 \cdot 42875^{\frac{1}{4}} \sqrt{155} {\left(216 \, \sqrt{35} \sqrt{31} + 665 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} + 12020117813965625000 \, x + 1202011781396562500 \, \sqrt{35} + 6010058906982812500} {\left(19 \, \sqrt{35} + 216\right)} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} - \frac{1}{1582635656875} \cdot 42875^{\frac{3}{4}} \sqrt{155} \sqrt{2 \, x + 1} {\left(19 \, \sqrt{35} + 216\right)} \sqrt{-14465853500 \, \sqrt{35} + 128678593750} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + \frac{8}{375} \, {\left(30 \, x^{2} + 50 \, x - 11\right)} \sqrt{2 \, x + 1}"," ",0,"1/1752203762968750*42875^(1/4)*sqrt(155)*(168698*sqrt(35)*sqrt(31) + 1500625*sqrt(31))*sqrt(-14465853500*sqrt(35) + 128678593750)*log(26582500/34021*42875^(1/4)*sqrt(155)*(216*sqrt(35)*sqrt(31) + 665*sqrt(31))*sqrt(2*x + 1)*sqrt(-14465853500*sqrt(35) + 128678593750) + 353314653125000*x + 35331465312500*sqrt(35) + 176657326562500) - 1/1752203762968750*42875^(1/4)*sqrt(155)*(168698*sqrt(35)*sqrt(31) + 1500625*sqrt(31))*sqrt(-14465853500*sqrt(35) + 128678593750)*log(-26582500/34021*42875^(1/4)*sqrt(155)*(216*sqrt(35)*sqrt(31) + 665*sqrt(31))*sqrt(2*x + 1)*sqrt(-14465853500*sqrt(35) + 128678593750) + 353314653125000*x + 35331465312500*sqrt(35) + 176657326562500) + 2/830703125*42875^(1/4)*sqrt(155)*sqrt(35)*sqrt(-14465853500*sqrt(35) + 128678593750)*arctan(1/2044682140744622640625*42875^(3/4)*sqrt(34021)*sqrt(217)*sqrt(155)*sqrt(42875^(1/4)*sqrt(155)*(216*sqrt(35)*sqrt(31) + 665*sqrt(31))*sqrt(2*x + 1)*sqrt(-14465853500*sqrt(35) + 128678593750) + 452181616250*x + 45218161625*sqrt(35) + 226090808125)*(19*sqrt(35) + 216)*sqrt(-14465853500*sqrt(35) + 128678593750) - 1/1582635656875*42875^(3/4)*sqrt(155)*sqrt(2*x + 1)*(19*sqrt(35) + 216)*sqrt(-14465853500*sqrt(35) + 128678593750) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 2/830703125*42875^(1/4)*sqrt(155)*sqrt(35)*sqrt(-14465853500*sqrt(35) + 128678593750)*arctan(1/715638749260617924218750*42875^(3/4)*sqrt(34021)*sqrt(155)*sqrt(-26582500*42875^(1/4)*sqrt(155)*(216*sqrt(35)*sqrt(31) + 665*sqrt(31))*sqrt(2*x + 1)*sqrt(-14465853500*sqrt(35) + 128678593750) + 12020117813965625000*x + 1202011781396562500*sqrt(35) + 6010058906982812500)*(19*sqrt(35) + 216)*sqrt(-14465853500*sqrt(35) + 128678593750) - 1/1582635656875*42875^(3/4)*sqrt(155)*sqrt(2*x + 1)*(19*sqrt(35) + 216)*sqrt(-14465853500*sqrt(35) + 128678593750) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 8/375*(30*x^2 + 50*x - 11)*sqrt(2*x + 1)","B",0
2310,1,493,0,0.445661," ","integrate((1+2*x)^(5/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","-\frac{1}{1673341250} \, \sqrt{155} 35^{\frac{1}{4}} \sqrt{2} {\left(7162 \, \sqrt{35} \sqrt{31} - 42875 \, \sqrt{31}\right)} \sqrt{7162 \, \sqrt{35} + 42875} \log\left(\frac{26582500}{199} \, \sqrt{155} 35^{\frac{1}{4}} \sqrt{2} {\left(19 \, \sqrt{35} \sqrt{31} - 140 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} + 288420125000 \, x + 28842012500 \, \sqrt{35} + 144210062500\right) + \frac{1}{1673341250} \, \sqrt{155} 35^{\frac{1}{4}} \sqrt{2} {\left(7162 \, \sqrt{35} \sqrt{31} - 42875 \, \sqrt{31}\right)} \sqrt{7162 \, \sqrt{35} + 42875} \log\left(-\frac{26582500}{199} \, \sqrt{155} 35^{\frac{1}{4}} \sqrt{2} {\left(19 \, \sqrt{35} \sqrt{31} - 140 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} + 288420125000 \, x + 28842012500 \, \sqrt{35} + 144210062500\right) + \frac{2}{135625} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{2} \sqrt{7162 \, \sqrt{35} + 42875} \arctan\left(\frac{1}{46619287225} \, \sqrt{217} \sqrt{199} \sqrt{155} 35^{\frac{3}{4}} \sqrt{2} \sqrt{\sqrt{155} 35^{\frac{1}{4}} \sqrt{2} {\left(19 \, \sqrt{35} \sqrt{31} - 140 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} + 2159150 \, x + 215915 \, \sqrt{35} + 1079575} \sqrt{7162 \, \sqrt{35} + 42875} {\left(4 \, \sqrt{35} - 19\right)} - \frac{1}{215915} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} {\left(4 \, \sqrt{35} - 19\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + \frac{2}{135625} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{2} \sqrt{7162 \, \sqrt{35} + 42875} \arctan\left(\frac{1}{16316750528750} \, \sqrt{199} \sqrt{155} 35^{\frac{3}{4}} \sqrt{2} \sqrt{-26582500 \, \sqrt{155} 35^{\frac{1}{4}} \sqrt{2} {\left(19 \, \sqrt{35} \sqrt{31} - 140 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} + 57395604875000 \, x + 5739560487500 \, \sqrt{35} + 28697802437500} \sqrt{7162 \, \sqrt{35} + 42875} {\left(4 \, \sqrt{35} - 19\right)} - \frac{1}{215915} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} {\left(4 \, \sqrt{35} - 19\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + \frac{4}{75} \, {\left(10 \, x + 17\right)} \sqrt{2 \, x + 1}"," ",0,"-1/1673341250*sqrt(155)*35^(1/4)*sqrt(2)*(7162*sqrt(35)*sqrt(31) - 42875*sqrt(31))*sqrt(7162*sqrt(35) + 42875)*log(26582500/199*sqrt(155)*35^(1/4)*sqrt(2)*(19*sqrt(35)*sqrt(31) - 140*sqrt(31))*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875) + 288420125000*x + 28842012500*sqrt(35) + 144210062500) + 1/1673341250*sqrt(155)*35^(1/4)*sqrt(2)*(7162*sqrt(35)*sqrt(31) - 42875*sqrt(31))*sqrt(7162*sqrt(35) + 42875)*log(-26582500/199*sqrt(155)*35^(1/4)*sqrt(2)*(19*sqrt(35)*sqrt(31) - 140*sqrt(31))*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875) + 288420125000*x + 28842012500*sqrt(35) + 144210062500) + 2/135625*sqrt(155)*35^(3/4)*sqrt(2)*sqrt(7162*sqrt(35) + 42875)*arctan(1/46619287225*sqrt(217)*sqrt(199)*sqrt(155)*35^(3/4)*sqrt(2)*sqrt(sqrt(155)*35^(1/4)*sqrt(2)*(19*sqrt(35)*sqrt(31) - 140*sqrt(31))*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875) + 2159150*x + 215915*sqrt(35) + 1079575)*sqrt(7162*sqrt(35) + 42875)*(4*sqrt(35) - 19) - 1/215915*sqrt(155)*35^(3/4)*sqrt(2)*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875)*(4*sqrt(35) - 19) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 2/135625*sqrt(155)*35^(3/4)*sqrt(2)*sqrt(7162*sqrt(35) + 42875)*arctan(1/16316750528750*sqrt(199)*sqrt(155)*35^(3/4)*sqrt(2)*sqrt(-26582500*sqrt(155)*35^(1/4)*sqrt(2)*(19*sqrt(35)*sqrt(31) - 140*sqrt(31))*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875) + 57395604875000*x + 5739560487500*sqrt(35) + 28697802437500)*sqrt(7162*sqrt(35) + 42875)*(4*sqrt(35) - 19) - 1/215915*sqrt(155)*35^(3/4)*sqrt(2)*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875)*(4*sqrt(35) - 19) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 4/75*(10*x + 17)*sqrt(2*x + 1)","B",0
2311,1,454,0,0.444468," ","integrate((1+2*x)^(3/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","-\frac{1}{1118363750} \cdot 42875^{\frac{1}{4}} \sqrt{155} {\left(178 \, \sqrt{35} \sqrt{31} + 1225 \, \sqrt{31}\right)} \sqrt{-12460 \, \sqrt{35} + 85750} \log\left(\frac{620}{19} \cdot 42875^{\frac{1}{4}} \sqrt{155} {\left(4 \, \sqrt{35} \sqrt{31} + 35 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-12460 \, \sqrt{35} + 85750} + 235445000 \, x + 23544500 \, \sqrt{35} + 117722500\right) + \frac{1}{1118363750} \cdot 42875^{\frac{1}{4}} \sqrt{155} {\left(178 \, \sqrt{35} \sqrt{31} + 1225 \, \sqrt{31}\right)} \sqrt{-12460 \, \sqrt{35} + 85750} \log\left(-\frac{620}{19} \cdot 42875^{\frac{1}{4}} \sqrt{155} {\left(4 \, \sqrt{35} \sqrt{31} + 35 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-12460 \, \sqrt{35} + 85750} + 235445000 \, x + 23544500 \, \sqrt{35} + 117722500\right) + \frac{2}{949375} \cdot 42875^{\frac{1}{4}} \sqrt{155} \sqrt{35} \sqrt{-12460 \, \sqrt{35} + 85750} \arctan\left(\frac{1}{5205983256250} \cdot 42875^{\frac{3}{4}} \sqrt{155} \sqrt{-620 \cdot 42875^{\frac{1}{4}} \sqrt{155} {\left(4 \, \sqrt{35} \sqrt{31} + 35 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-12460 \, \sqrt{35} + 85750} + 4473455000 \, x + 447345500 \, \sqrt{35} + 2236727500} {\left(\sqrt{35} \sqrt{19} + 4 \, \sqrt{19}\right)} \sqrt{-12460 \, \sqrt{35} + 85750} - \frac{1}{25253375} \cdot 42875^{\frac{3}{4}} \sqrt{155} \sqrt{2 \, x + 1} {\left(\sqrt{35} + 4\right)} \sqrt{-12460 \, \sqrt{35} + 85750} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + \frac{2}{949375} \cdot 42875^{\frac{1}{4}} \sqrt{155} \sqrt{35} \sqrt{-12460 \, \sqrt{35} + 85750} \arctan\left(-\frac{1}{25253375} \cdot 42875^{\frac{3}{4}} \sqrt{155} \sqrt{2 \, x + 1} {\left(\sqrt{35} + 4\right)} \sqrt{-12460 \, \sqrt{35} + 85750} + \frac{1}{16793494375} \cdot 42875^{\frac{3}{4}} \sqrt{42875^{\frac{1}{4}} \sqrt{155} {\left(4 \, \sqrt{35} \sqrt{31} + 35 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-12460 \, \sqrt{35} + 85750} + 7215250 \, x + 721525 \, \sqrt{35} + 3607625} {\left(\sqrt{35} \sqrt{19} + 4 \, \sqrt{19}\right)} \sqrt{-12460 \, \sqrt{35} + 85750} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + \frac{4}{5} \, \sqrt{2 \, x + 1}"," ",0,"-1/1118363750*42875^(1/4)*sqrt(155)*(178*sqrt(35)*sqrt(31) + 1225*sqrt(31))*sqrt(-12460*sqrt(35) + 85750)*log(620/19*42875^(1/4)*sqrt(155)*(4*sqrt(35)*sqrt(31) + 35*sqrt(31))*sqrt(2*x + 1)*sqrt(-12460*sqrt(35) + 85750) + 235445000*x + 23544500*sqrt(35) + 117722500) + 1/1118363750*42875^(1/4)*sqrt(155)*(178*sqrt(35)*sqrt(31) + 1225*sqrt(31))*sqrt(-12460*sqrt(35) + 85750)*log(-620/19*42875^(1/4)*sqrt(155)*(4*sqrt(35)*sqrt(31) + 35*sqrt(31))*sqrt(2*x + 1)*sqrt(-12460*sqrt(35) + 85750) + 235445000*x + 23544500*sqrt(35) + 117722500) + 2/949375*42875^(1/4)*sqrt(155)*sqrt(35)*sqrt(-12460*sqrt(35) + 85750)*arctan(1/5205983256250*42875^(3/4)*sqrt(155)*sqrt(-620*42875^(1/4)*sqrt(155)*(4*sqrt(35)*sqrt(31) + 35*sqrt(31))*sqrt(2*x + 1)*sqrt(-12460*sqrt(35) + 85750) + 4473455000*x + 447345500*sqrt(35) + 2236727500)*(sqrt(35)*sqrt(19) + 4*sqrt(19))*sqrt(-12460*sqrt(35) + 85750) - 1/25253375*42875^(3/4)*sqrt(155)*sqrt(2*x + 1)*(sqrt(35) + 4)*sqrt(-12460*sqrt(35) + 85750) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 2/949375*42875^(1/4)*sqrt(155)*sqrt(35)*sqrt(-12460*sqrt(35) + 85750)*arctan(-1/25253375*42875^(3/4)*sqrt(155)*sqrt(2*x + 1)*(sqrt(35) + 4)*sqrt(-12460*sqrt(35) + 85750) + 1/16793494375*42875^(3/4)*sqrt(42875^(1/4)*sqrt(155)*(4*sqrt(35)*sqrt(31) + 35*sqrt(31))*sqrt(2*x + 1)*sqrt(-12460*sqrt(35) + 85750) + 7215250*x + 721525*sqrt(35) + 3607625)*(sqrt(35)*sqrt(19) + 4*sqrt(19))*sqrt(-12460*sqrt(35) + 85750) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 4/5*sqrt(2*x + 1)","B",0
2312,1,371,0,0.428711," ","integrate((1+2*x)^(1/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{1}{336350} \, \sqrt{155} 35^{\frac{1}{4}} {\left(2 \, \sqrt{35} \sqrt{31} - 35 \, \sqrt{31}\right)} \sqrt{4 \, \sqrt{35} + 70} \log\left(\frac{124}{7} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{31} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} + 192200 \, x + 19220 \, \sqrt{35} + 96100\right) - \frac{1}{336350} \, \sqrt{155} 35^{\frac{1}{4}} {\left(2 \, \sqrt{35} \sqrt{31} - 35 \, \sqrt{31}\right)} \sqrt{4 \, \sqrt{35} + 70} \log\left(-\frac{124}{7} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{31} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} + 192200 \, x + 19220 \, \sqrt{35} + 96100\right) - \frac{2}{5425} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{4 \, \sqrt{35} + 70} \arctan\left(\frac{1}{1177225} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{31} \sqrt{7} \sqrt{\sqrt{155} 35^{\frac{3}{4}} \sqrt{31} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} + 10850 \, x + 1085 \, \sqrt{35} + 5425} \sqrt{4 \, \sqrt{35} + 70} - \frac{1}{1085} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) - \frac{2}{5425} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{4 \, \sqrt{35} + 70} \arctan\left(\frac{1}{2354450} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{7} \sqrt{-124 \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{31} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} + 1345400 \, x + 134540 \, \sqrt{35} + 672700} \sqrt{4 \, \sqrt{35} + 70} - \frac{1}{1085} \, \sqrt{155} 35^{\frac{3}{4}} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right)"," ",0,"1/336350*sqrt(155)*35^(1/4)*(2*sqrt(35)*sqrt(31) - 35*sqrt(31))*sqrt(4*sqrt(35) + 70)*log(124/7*sqrt(155)*35^(3/4)*sqrt(31)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) + 192200*x + 19220*sqrt(35) + 96100) - 1/336350*sqrt(155)*35^(1/4)*(2*sqrt(35)*sqrt(31) - 35*sqrt(31))*sqrt(4*sqrt(35) + 70)*log(-124/7*sqrt(155)*35^(3/4)*sqrt(31)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) + 192200*x + 19220*sqrt(35) + 96100) - 2/5425*sqrt(155)*35^(3/4)*sqrt(4*sqrt(35) + 70)*arctan(1/1177225*sqrt(155)*35^(3/4)*sqrt(31)*sqrt(7)*sqrt(sqrt(155)*35^(3/4)*sqrt(31)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) + 10850*x + 1085*sqrt(35) + 5425)*sqrt(4*sqrt(35) + 70) - 1/1085*sqrt(155)*35^(3/4)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) - 2/5425*sqrt(155)*35^(3/4)*sqrt(4*sqrt(35) + 70)*arctan(1/2354450*sqrt(155)*35^(3/4)*sqrt(7)*sqrt(-124*sqrt(155)*35^(3/4)*sqrt(31)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) + 1345400*x + 134540*sqrt(35) + 672700)*sqrt(4*sqrt(35) + 70) - 1/1085*sqrt(155)*35^(3/4)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31))","B",0
2313,1,365,0,0.437455," ","integrate(1/(1+2*x)^(1/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","-\frac{1}{470890} \, \sqrt{217} 35^{\frac{1}{4}} {\left(2 \, \sqrt{35} \sqrt{31} - 35 \, \sqrt{31}\right)} \sqrt{4 \, \sqrt{35} + 70} \log\left(4340 \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{31} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} + 9417800 \, x + 941780 \, \sqrt{35} + 4708900\right) + \frac{1}{470890} \, \sqrt{217} 35^{\frac{1}{4}} {\left(2 \, \sqrt{35} \sqrt{31} - 35 \, \sqrt{31}\right)} \sqrt{4 \, \sqrt{35} + 70} \log\left(-4340 \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{31} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} + 9417800 \, x + 941780 \, \sqrt{35} + 4708900\right) - \frac{2}{7595} \, \sqrt{217} 35^{\frac{3}{4}} \sqrt{4 \, \sqrt{35} + 70} \arctan\left(\frac{1}{235445} \, \sqrt{1085} \sqrt{217} 35^{\frac{1}{4}} \sqrt{\sqrt{217} 35^{\frac{1}{4}} \sqrt{31} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} + 2170 \, x + 217 \, \sqrt{35} + 1085} \sqrt{4 \, \sqrt{35} + 70} - \frac{1}{217} \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) - \frac{2}{7595} \, \sqrt{217} 35^{\frac{3}{4}} \sqrt{4 \, \sqrt{35} + 70} \arctan\left(\frac{1}{470890} \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{-4340 \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{31} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} + 9417800 \, x + 941780 \, \sqrt{35} + 4708900} \sqrt{4 \, \sqrt{35} + 70} - \frac{1}{217} \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{2 \, x + 1} \sqrt{4 \, \sqrt{35} + 70} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right)"," ",0,"-1/470890*sqrt(217)*35^(1/4)*(2*sqrt(35)*sqrt(31) - 35*sqrt(31))*sqrt(4*sqrt(35) + 70)*log(4340*sqrt(217)*35^(1/4)*sqrt(31)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) + 9417800*x + 941780*sqrt(35) + 4708900) + 1/470890*sqrt(217)*35^(1/4)*(2*sqrt(35)*sqrt(31) - 35*sqrt(31))*sqrt(4*sqrt(35) + 70)*log(-4340*sqrt(217)*35^(1/4)*sqrt(31)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) + 9417800*x + 941780*sqrt(35) + 4708900) - 2/7595*sqrt(217)*35^(3/4)*sqrt(4*sqrt(35) + 70)*arctan(1/235445*sqrt(1085)*sqrt(217)*35^(1/4)*sqrt(sqrt(217)*35^(1/4)*sqrt(31)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) + 2170*x + 217*sqrt(35) + 1085)*sqrt(4*sqrt(35) + 70) - 1/217*sqrt(217)*35^(1/4)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) - 2/7595*sqrt(217)*35^(3/4)*sqrt(4*sqrt(35) + 70)*arctan(1/470890*sqrt(217)*35^(1/4)*sqrt(-4340*sqrt(217)*35^(1/4)*sqrt(31)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) + 9417800*x + 941780*sqrt(35) + 4708900)*sqrt(4*sqrt(35) + 70) - 1/217*sqrt(217)*35^(1/4)*sqrt(2*x + 1)*sqrt(4*sqrt(35) + 70) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31))","B",0
2314,1,500,0,0.437985," ","integrate(1/(1+2*x)^(3/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{2356 \cdot 42875^{\frac{1}{4}} \sqrt{217} \sqrt{35} {\left(2 \, x + 1\right)} \sqrt{-12460 \, \sqrt{35} + 85750} \arctan\left(\frac{1}{3644188279375} \cdot 42875^{\frac{3}{4}} \sqrt{217} \sqrt{31} \sqrt{42875^{\frac{1}{4}} \sqrt{217} {\left(\sqrt{35} \sqrt{31} + 4 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-12460 \, \sqrt{35} + 85750} + 1443050 \, x + 144305 \, \sqrt{35} + 721525} {\left(4 \, \sqrt{35} \sqrt{19} + 35 \, \sqrt{19}\right)} \sqrt{-12460 \, \sqrt{35} + 85750} - \frac{1}{176773625} \cdot 42875^{\frac{3}{4}} \sqrt{217} \sqrt{2 \, x + 1} {\left(4 \, \sqrt{35} + 35\right)} \sqrt{-12460 \, \sqrt{35} + 85750} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 2356 \cdot 42875^{\frac{1}{4}} \sqrt{217} \sqrt{35} {\left(2 \, x + 1\right)} \sqrt{-12460 \, \sqrt{35} + 85750} \arctan\left(\frac{1}{255093179556250} \cdot 42875^{\frac{3}{4}} \sqrt{217} \sqrt{-151900 \cdot 42875^{\frac{1}{4}} \sqrt{217} {\left(\sqrt{35} \sqrt{31} + 4 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-12460 \, \sqrt{35} + 85750} + 219199295000 \, x + 21919929500 \, \sqrt{35} + 109599647500} {\left(4 \, \sqrt{35} \sqrt{19} + 35 \, \sqrt{19}\right)} \sqrt{-12460 \, \sqrt{35} + 85750} - \frac{1}{176773625} \cdot 42875^{\frac{3}{4}} \sqrt{217} \sqrt{2 \, x + 1} {\left(4 \, \sqrt{35} + 35\right)} \sqrt{-12460 \, \sqrt{35} + 85750} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 42875^{\frac{1}{4}} \sqrt{217} {\left(178 \, \sqrt{35} \sqrt{31} {\left(2 \, x + 1\right)} + 1225 \, \sqrt{31} {\left(2 \, x + 1\right)}\right)} \sqrt{-12460 \, \sqrt{35} + 85750} \log\left(\frac{151900}{19} \cdot 42875^{\frac{1}{4}} \sqrt{217} {\left(\sqrt{35} \sqrt{31} + 4 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-12460 \, \sqrt{35} + 85750} + 11536805000 \, x + 1153680500 \, \sqrt{35} + 5768402500\right) - 42875^{\frac{1}{4}} \sqrt{217} {\left(178 \, \sqrt{35} \sqrt{31} {\left(2 \, x + 1\right)} + 1225 \, \sqrt{31} {\left(2 \, x + 1\right)}\right)} \sqrt{-12460 \, \sqrt{35} + 85750} \log\left(-\frac{151900}{19} \cdot 42875^{\frac{1}{4}} \sqrt{217} {\left(\sqrt{35} \sqrt{31} + 4 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-12460 \, \sqrt{35} + 85750} + 11536805000 \, x + 1153680500 \, \sqrt{35} + 5768402500\right) - 1252567400 \, \sqrt{2 \, x + 1}}{2191992950 \, {\left(2 \, x + 1\right)}}"," ",0,"1/2191992950*(2356*42875^(1/4)*sqrt(217)*sqrt(35)*(2*x + 1)*sqrt(-12460*sqrt(35) + 85750)*arctan(1/3644188279375*42875^(3/4)*sqrt(217)*sqrt(31)*sqrt(42875^(1/4)*sqrt(217)*(sqrt(35)*sqrt(31) + 4*sqrt(31))*sqrt(2*x + 1)*sqrt(-12460*sqrt(35) + 85750) + 1443050*x + 144305*sqrt(35) + 721525)*(4*sqrt(35)*sqrt(19) + 35*sqrt(19))*sqrt(-12460*sqrt(35) + 85750) - 1/176773625*42875^(3/4)*sqrt(217)*sqrt(2*x + 1)*(4*sqrt(35) + 35)*sqrt(-12460*sqrt(35) + 85750) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 2356*42875^(1/4)*sqrt(217)*sqrt(35)*(2*x + 1)*sqrt(-12460*sqrt(35) + 85750)*arctan(1/255093179556250*42875^(3/4)*sqrt(217)*sqrt(-151900*42875^(1/4)*sqrt(217)*(sqrt(35)*sqrt(31) + 4*sqrt(31))*sqrt(2*x + 1)*sqrt(-12460*sqrt(35) + 85750) + 219199295000*x + 21919929500*sqrt(35) + 109599647500)*(4*sqrt(35)*sqrt(19) + 35*sqrt(19))*sqrt(-12460*sqrt(35) + 85750) - 1/176773625*42875^(3/4)*sqrt(217)*sqrt(2*x + 1)*(4*sqrt(35) + 35)*sqrt(-12460*sqrt(35) + 85750) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 42875^(1/4)*sqrt(217)*(178*sqrt(35)*sqrt(31)*(2*x + 1) + 1225*sqrt(31)*(2*x + 1))*sqrt(-12460*sqrt(35) + 85750)*log(151900/19*42875^(1/4)*sqrt(217)*(sqrt(35)*sqrt(31) + 4*sqrt(31))*sqrt(2*x + 1)*sqrt(-12460*sqrt(35) + 85750) + 11536805000*x + 1153680500*sqrt(35) + 5768402500) - 42875^(1/4)*sqrt(217)*(178*sqrt(35)*sqrt(31)*(2*x + 1) + 1225*sqrt(31)*(2*x + 1))*sqrt(-12460*sqrt(35) + 85750)*log(-151900/19*42875^(1/4)*sqrt(217)*(sqrt(35)*sqrt(31) + 4*sqrt(31))*sqrt(2*x + 1)*sqrt(-12460*sqrt(35) + 85750) + 11536805000*x + 1153680500*sqrt(35) + 5768402500) - 1252567400*sqrt(2*x + 1))/(2*x + 1)","B",0
2315,1,567,0,0.441282," ","integrate(1/(1+2*x)^(5/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","-\frac{74028 \, \sqrt{217} 35^{\frac{3}{4}} \sqrt{2} {\left(4 \, x^{2} + 4 \, x + 1\right)} \sqrt{7162 \, \sqrt{35} + 42875} \arctan\left(\frac{1}{326335010575} \, \sqrt{1085} \sqrt{217} \sqrt{199} 35^{\frac{3}{4}} \sqrt{2} \sqrt{\sqrt{217} 35^{\frac{1}{4}} \sqrt{2} {\left(4 \, \sqrt{35} \sqrt{31} - 19 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} + 431830 \, x + 43183 \, \sqrt{35} + 215915} \sqrt{7162 \, \sqrt{35} + 42875} {\left(19 \, \sqrt{35} - 140\right)} - \frac{1}{1511405} \, \sqrt{217} 35^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} {\left(19 \, \sqrt{35} - 140\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 74028 \, \sqrt{217} 35^{\frac{3}{4}} \sqrt{2} {\left(4 \, x^{2} + 4 \, x + 1\right)} \sqrt{7162 \, \sqrt{35} + 42875} \arctan\left(\frac{1}{799520775908750} \, \sqrt{217} \sqrt{199} 35^{\frac{3}{4}} \sqrt{2} \sqrt{-6512712500 \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{2} {\left(4 \, \sqrt{35} \sqrt{31} - 19 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} + 2812384638875000 \, x + 281238463887500 \, \sqrt{35} + 1406192319437500} \sqrt{7162 \, \sqrt{35} + 42875} {\left(19 \, \sqrt{35} - 140\right)} - \frac{1}{1511405} \, \sqrt{217} 35^{\frac{3}{4}} \sqrt{2} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} {\left(19 \, \sqrt{35} - 140\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 3 \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{2} {\left(7162 \, \sqrt{35} \sqrt{31} {\left(4 \, x^{2} + 4 \, x + 1\right)} - 42875 \, \sqrt{31} {\left(4 \, x^{2} + 4 \, x + 1\right)}\right)} \sqrt{7162 \, \sqrt{35} + 42875} \log\left(\frac{6512712500}{199} \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{2} {\left(4 \, \sqrt{35} \sqrt{31} - 19 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} + 14132586125000 \, x + 1413258612500 \, \sqrt{35} + 7066293062500\right) - 3 \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{2} {\left(7162 \, \sqrt{35} \sqrt{31} {\left(4 \, x^{2} + 4 \, x + 1\right)} - 42875 \, \sqrt{31} {\left(4 \, x^{2} + 4 \, x + 1\right)}\right)} \sqrt{7162 \, \sqrt{35} + 42875} \log\left(-\frac{6512712500}{199} \, \sqrt{217} 35^{\frac{1}{4}} \sqrt{2} {\left(4 \, \sqrt{35} \sqrt{31} - 19 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{7162 \, \sqrt{35} + 42875} + 14132586125000 \, x + 1413258612500 \, \sqrt{35} + 7066293062500\right) + 374828440 \, {\left(24 \, x + 19\right)} \sqrt{2 \, x + 1}}{13774945170 \, {\left(4 \, x^{2} + 4 \, x + 1\right)}}"," ",0,"-1/13774945170*(74028*sqrt(217)*35^(3/4)*sqrt(2)*(4*x^2 + 4*x + 1)*sqrt(7162*sqrt(35) + 42875)*arctan(1/326335010575*sqrt(1085)*sqrt(217)*sqrt(199)*35^(3/4)*sqrt(2)*sqrt(sqrt(217)*35^(1/4)*sqrt(2)*(4*sqrt(35)*sqrt(31) - 19*sqrt(31))*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875) + 431830*x + 43183*sqrt(35) + 215915)*sqrt(7162*sqrt(35) + 42875)*(19*sqrt(35) - 140) - 1/1511405*sqrt(217)*35^(3/4)*sqrt(2)*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875)*(19*sqrt(35) - 140) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 74028*sqrt(217)*35^(3/4)*sqrt(2)*(4*x^2 + 4*x + 1)*sqrt(7162*sqrt(35) + 42875)*arctan(1/799520775908750*sqrt(217)*sqrt(199)*35^(3/4)*sqrt(2)*sqrt(-6512712500*sqrt(217)*35^(1/4)*sqrt(2)*(4*sqrt(35)*sqrt(31) - 19*sqrt(31))*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875) + 2812384638875000*x + 281238463887500*sqrt(35) + 1406192319437500)*sqrt(7162*sqrt(35) + 42875)*(19*sqrt(35) - 140) - 1/1511405*sqrt(217)*35^(3/4)*sqrt(2)*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875)*(19*sqrt(35) - 140) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 3*sqrt(217)*35^(1/4)*sqrt(2)*(7162*sqrt(35)*sqrt(31)*(4*x^2 + 4*x + 1) - 42875*sqrt(31)*(4*x^2 + 4*x + 1))*sqrt(7162*sqrt(35) + 42875)*log(6512712500/199*sqrt(217)*35^(1/4)*sqrt(2)*(4*sqrt(35)*sqrt(31) - 19*sqrt(31))*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875) + 14132586125000*x + 1413258612500*sqrt(35) + 7066293062500) - 3*sqrt(217)*35^(1/4)*sqrt(2)*(7162*sqrt(35)*sqrt(31)*(4*x^2 + 4*x + 1) - 42875*sqrt(31)*(4*x^2 + 4*x + 1))*sqrt(7162*sqrt(35) + 42875)*log(-6512712500/199*sqrt(217)*35^(1/4)*sqrt(2)*(4*sqrt(35)*sqrt(31) - 19*sqrt(31))*sqrt(2*x + 1)*sqrt(7162*sqrt(35) + 42875) + 14132586125000*x + 1413258612500*sqrt(35) + 7066293062500) + 374828440*(24*x + 19)*sqrt(2*x + 1))/(4*x^2 + 4*x + 1)","B",0
2316,1,541,0,0.446523," ","integrate((1+2*x)^(7/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{16794436 \cdot 21898835^{\frac{1}{4}} \sqrt{155} \sqrt{35} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} \arctan\left(\frac{1}{60332699662225359002939375} \cdot 21898835^{\frac{3}{4}} \sqrt{4369} \sqrt{3955} \sqrt{155} \sqrt{21898835^{\frac{1}{4}} \sqrt{155} {\left(814 \, \sqrt{35} \sqrt{31} + 5285 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} + 40683471557750 \, x + 4068347155775 \, \sqrt{35} + 20341735778875} {\left(151 \, \sqrt{35} + 814\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} - \frac{1}{3218062600218025} \cdot 21898835^{\frac{3}{4}} \sqrt{155} \sqrt{2 \, x + 1} {\left(151 \, \sqrt{35} + 814\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 16794436 \cdot 21898835^{\frac{1}{4}} \sqrt{155} \sqrt{35} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} \arctan\left(\frac{1}{4223288976355775130205756250} \cdot 21898835^{\frac{3}{4}} \sqrt{4369} \sqrt{155} \sqrt{-19379500 \cdot 21898835^{\frac{1}{4}} \sqrt{155} {\left(814 \, \sqrt{35} \sqrt{31} + 5285 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} + 788425337053416125000 \, x + 78842533705341612500 \, \sqrt{35} + 394212668526708062500} {\left(151 \, \sqrt{35} + 814\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} - \frac{1}{3218062600218025} \cdot 21898835^{\frac{3}{4}} \sqrt{155} \sqrt{2 \, x + 1} {\left(151 \, \sqrt{35} + 814\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) - 21898835^{\frac{1}{4}} \sqrt{155} {\left(5682718 \, \sqrt{35} \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} + 33914125 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)}\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} \log\left(\frac{19379500}{4369} \cdot 21898835^{\frac{1}{4}} \sqrt{155} {\left(814 \, \sqrt{35} \sqrt{31} + 5285 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} + 180458992230125000 \, x + 18045899223012500 \, \sqrt{35} + 90229496115062500\right) + 21898835^{\frac{1}{4}} \sqrt{155} {\left(5682718 \, \sqrt{35} \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} + 33914125 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)}\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} \log\left(-\frac{19379500}{4369} \cdot 21898835^{\frac{1}{4}} \sqrt{155} {\left(814 \, \sqrt{35} \sqrt{31} + 5285 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} + 180458992230125000 \, x + 18045899223012500 \, \sqrt{35} + 90229496115062500\right) + 1261187618290250 \, {\left(2480 \, x^{2} + 1132 \, x + 1003\right)} \sqrt{2 \, x + 1}}{977420404174943750 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"1/977420404174943750*(16794436*21898835^(1/4)*sqrt(155)*sqrt(35)*(5*x^2 + 3*x + 2)*sqrt(-11012823348100*sqrt(35) + 65723878543750)*arctan(1/60332699662225359002939375*21898835^(3/4)*sqrt(4369)*sqrt(3955)*sqrt(155)*sqrt(21898835^(1/4)*sqrt(155)*(814*sqrt(35)*sqrt(31) + 5285*sqrt(31))*sqrt(2*x + 1)*sqrt(-11012823348100*sqrt(35) + 65723878543750) + 40683471557750*x + 4068347155775*sqrt(35) + 20341735778875)*(151*sqrt(35) + 814)*sqrt(-11012823348100*sqrt(35) + 65723878543750) - 1/3218062600218025*21898835^(3/4)*sqrt(155)*sqrt(2*x + 1)*(151*sqrt(35) + 814)*sqrt(-11012823348100*sqrt(35) + 65723878543750) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 16794436*21898835^(1/4)*sqrt(155)*sqrt(35)*(5*x^2 + 3*x + 2)*sqrt(-11012823348100*sqrt(35) + 65723878543750)*arctan(1/4223288976355775130205756250*21898835^(3/4)*sqrt(4369)*sqrt(155)*sqrt(-19379500*21898835^(1/4)*sqrt(155)*(814*sqrt(35)*sqrt(31) + 5285*sqrt(31))*sqrt(2*x + 1)*sqrt(-11012823348100*sqrt(35) + 65723878543750) + 788425337053416125000*x + 78842533705341612500*sqrt(35) + 394212668526708062500)*(151*sqrt(35) + 814)*sqrt(-11012823348100*sqrt(35) + 65723878543750) - 1/3218062600218025*21898835^(3/4)*sqrt(155)*sqrt(2*x + 1)*(151*sqrt(35) + 814)*sqrt(-11012823348100*sqrt(35) + 65723878543750) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) - 21898835^(1/4)*sqrt(155)*(5682718*sqrt(35)*sqrt(31)*(5*x^2 + 3*x + 2) + 33914125*sqrt(31)*(5*x^2 + 3*x + 2))*sqrt(-11012823348100*sqrt(35) + 65723878543750)*log(19379500/4369*21898835^(1/4)*sqrt(155)*(814*sqrt(35)*sqrt(31) + 5285*sqrt(31))*sqrt(2*x + 1)*sqrt(-11012823348100*sqrt(35) + 65723878543750) + 180458992230125000*x + 18045899223012500*sqrt(35) + 90229496115062500) + 21898835^(1/4)*sqrt(155)*(5682718*sqrt(35)*sqrt(31)*(5*x^2 + 3*x + 2) + 33914125*sqrt(31)*(5*x^2 + 3*x + 2))*sqrt(-11012823348100*sqrt(35) + 65723878543750)*log(-19379500/4369*21898835^(1/4)*sqrt(155)*(814*sqrt(35)*sqrt(31) + 5285*sqrt(31))*sqrt(2*x + 1)*sqrt(-11012823348100*sqrt(35) + 65723878543750) + 180458992230125000*x + 18045899223012500*sqrt(35) + 90229496115062500) + 1261187618290250*(2480*x^2 + 1132*x + 1003)*sqrt(2*x + 1))/(5*x^2 + 3*x + 2)","B",0
2317,1,572,0,0.453700," ","integrate((1+2*x)^(5/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{1149356 \cdot 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{155} \sqrt{35} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{32678 \, \sqrt{35} + 361375} \arctan\left(\frac{1}{32833385198242899725} \cdot 5969915^{\frac{3}{4}} \sqrt{826} \sqrt{299} \sqrt{155} \sqrt{59} \sqrt{5969915^{\frac{1}{4}} \sqrt{826} \sqrt{155} {\left(97 \, \sqrt{35} \sqrt{31} - 70 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} + 41534852450 \, x + 4153485245 \, \sqrt{35} + 20767426225} \sqrt{32678 \, \sqrt{35} + 361375} {\left(2 \, \sqrt{35} - 97\right)} - \frac{1}{1715389406185} \cdot 5969915^{\frac{3}{4}} \sqrt{826} \sqrt{155} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} {\left(2 \, \sqrt{35} - 97\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 1149356 \cdot 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{155} \sqrt{35} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{32678 \, \sqrt{35} + 361375} \arctan\left(\frac{1}{1641669259912144986250} \cdot 5969915^{\frac{3}{4}} \sqrt{826} \sqrt{299} \sqrt{155} \sqrt{-147500 \cdot 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{155} {\left(97 \, \sqrt{35} \sqrt{31} - 70 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} + 6126390736375000 \, x + 612639073637500 \, \sqrt{35} + 3063195368187500} \sqrt{32678 \, \sqrt{35} + 361375} {\left(2 \, \sqrt{35} - 97\right)} - \frac{1}{1715389406185} \cdot 5969915^{\frac{3}{4}} \sqrt{826} \sqrt{155} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} {\left(2 \, \sqrt{35} - 97\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{155} {\left(32678 \, \sqrt{35} \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} - 361375 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)}\right)} \sqrt{32678 \, \sqrt{35} + 361375} \log\left(\frac{147500}{299} \cdot 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{155} {\left(97 \, \sqrt{35} \sqrt{31} - 70 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} + 20489601125000 \, x + 2048960112500 \, \sqrt{35} + 10244800562500\right) - 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{155} {\left(32678 \, \sqrt{35} \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} - 361375 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)}\right)} \sqrt{32678 \, \sqrt{35} + 361375} \log\left(-\frac{147500}{299} \cdot 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{155} {\left(97 \, \sqrt{35} \sqrt{31} - 70 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} + 20489601125000 \, x + 2048960112500 \, \sqrt{35} + 10244800562500\right) - 1287580425950 \, {\left(54 \, x + 41\right)} \sqrt{2 \, x + 1}}{199574966022250 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"1/199574966022250*(1149356*5969915^(1/4)*sqrt(826)*sqrt(155)*sqrt(35)*(5*x^2 + 3*x + 2)*sqrt(32678*sqrt(35) + 361375)*arctan(1/32833385198242899725*5969915^(3/4)*sqrt(826)*sqrt(299)*sqrt(155)*sqrt(59)*sqrt(5969915^(1/4)*sqrt(826)*sqrt(155)*(97*sqrt(35)*sqrt(31) - 70*sqrt(31))*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375) + 41534852450*x + 4153485245*sqrt(35) + 20767426225)*sqrt(32678*sqrt(35) + 361375)*(2*sqrt(35) - 97) - 1/1715389406185*5969915^(3/4)*sqrt(826)*sqrt(155)*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375)*(2*sqrt(35) - 97) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 1149356*5969915^(1/4)*sqrt(826)*sqrt(155)*sqrt(35)*(5*x^2 + 3*x + 2)*sqrt(32678*sqrt(35) + 361375)*arctan(1/1641669259912144986250*5969915^(3/4)*sqrt(826)*sqrt(299)*sqrt(155)*sqrt(-147500*5969915^(1/4)*sqrt(826)*sqrt(155)*(97*sqrt(35)*sqrt(31) - 70*sqrt(31))*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375) + 6126390736375000*x + 612639073637500*sqrt(35) + 3063195368187500)*sqrt(32678*sqrt(35) + 361375)*(2*sqrt(35) - 97) - 1/1715389406185*5969915^(3/4)*sqrt(826)*sqrt(155)*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375)*(2*sqrt(35) - 97) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 5969915^(1/4)*sqrt(826)*sqrt(155)*(32678*sqrt(35)*sqrt(31)*(5*x^2 + 3*x + 2) - 361375*sqrt(31)*(5*x^2 + 3*x + 2))*sqrt(32678*sqrt(35) + 361375)*log(147500/299*5969915^(1/4)*sqrt(826)*sqrt(155)*(97*sqrt(35)*sqrt(31) - 70*sqrt(31))*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375) + 20489601125000*x + 2048960112500*sqrt(35) + 10244800562500) - 5969915^(1/4)*sqrt(826)*sqrt(155)*(32678*sqrt(35)*sqrt(31)*(5*x^2 + 3*x + 2) - 361375*sqrt(31)*(5*x^2 + 3*x + 2))*sqrt(32678*sqrt(35) + 361375)*log(-147500/299*5969915^(1/4)*sqrt(826)*sqrt(155)*(97*sqrt(35)*sqrt(31) - 70*sqrt(31))*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375) + 20489601125000*x + 2048960112500*sqrt(35) + 10244800562500) - 1287580425950*(54*x + 41)*sqrt(2*x + 1))/(5*x^2 + 3*x + 2)","B",0
2318,1,538,0,0.441885," ","integrate((1+2*x)^(3/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","-\frac{3844 \cdot 77315^{\frac{1}{4}} \sqrt{155} \sqrt{35} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{20492 \, \sqrt{35} + 154630} \arctan\left(\frac{1}{3788913966425} \cdot 77315^{\frac{3}{4}} \sqrt{155} \sqrt{47} \sqrt{77315^{\frac{1}{4}} \sqrt{155} {\left(2 \, \sqrt{35} \sqrt{31} - 35 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} + 15808450 \, x + 1580845 \, \sqrt{35} + 7904225} {\left(\sqrt{35} \sqrt{7} - 2 \, \sqrt{7}\right)} \sqrt{20492 \, \sqrt{35} + 154630} - \frac{1}{74299715} \cdot 77315^{\frac{3}{4}} \sqrt{155} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} {\left(\sqrt{35} - 2\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 3844 \cdot 77315^{\frac{1}{4}} \sqrt{155} \sqrt{35} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{20492 \, \sqrt{35} + 154630} \arctan\left(\frac{1}{7577827932850} \cdot 77315^{\frac{3}{4}} \sqrt{155} \sqrt{-188 \cdot 77315^{\frac{1}{4}} \sqrt{155} {\left(2 \, \sqrt{35} \sqrt{31} - 35 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} + 2971988600 \, x + 297198860 \, \sqrt{35} + 1485994300} {\left(\sqrt{35} \sqrt{7} - 2 \, \sqrt{7}\right)} \sqrt{20492 \, \sqrt{35} + 154630} - \frac{1}{74299715} \cdot 77315^{\frac{3}{4}} \sqrt{155} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} {\left(\sqrt{35} - 2\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) - 77315^{\frac{1}{4}} \sqrt{155} {\left(218 \, \sqrt{35} \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} - 1645 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)}\right)} \sqrt{20492 \, \sqrt{35} + 154630} \log\left(\frac{188}{7} \cdot 77315^{\frac{1}{4}} \sqrt{155} {\left(2 \, \sqrt{35} \sqrt{31} - 35 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} + 424569800 \, x + 42456980 \, \sqrt{35} + 212284900\right) + 77315^{\frac{1}{4}} \sqrt{155} {\left(218 \, \sqrt{35} \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} - 1645 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)}\right)} \sqrt{20492 \, \sqrt{35} + 154630} \log\left(-\frac{188}{7} \cdot 77315^{\frac{1}{4}} \sqrt{155} {\left(2 \, \sqrt{35} \sqrt{31} - 35 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} + 424569800 \, x + 42456980 \, \sqrt{35} + 212284900\right) - 490061950 \, {\left(4 \, x - 5\right)} \sqrt{2 \, x + 1}}{15191920450 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"-1/15191920450*(3844*77315^(1/4)*sqrt(155)*sqrt(35)*(5*x^2 + 3*x + 2)*sqrt(20492*sqrt(35) + 154630)*arctan(1/3788913966425*77315^(3/4)*sqrt(155)*sqrt(47)*sqrt(77315^(1/4)*sqrt(155)*(2*sqrt(35)*sqrt(31) - 35*sqrt(31))*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630) + 15808450*x + 1580845*sqrt(35) + 7904225)*(sqrt(35)*sqrt(7) - 2*sqrt(7))*sqrt(20492*sqrt(35) + 154630) - 1/74299715*77315^(3/4)*sqrt(155)*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630)*(sqrt(35) - 2) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 3844*77315^(1/4)*sqrt(155)*sqrt(35)*(5*x^2 + 3*x + 2)*sqrt(20492*sqrt(35) + 154630)*arctan(1/7577827932850*77315^(3/4)*sqrt(155)*sqrt(-188*77315^(1/4)*sqrt(155)*(2*sqrt(35)*sqrt(31) - 35*sqrt(31))*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630) + 2971988600*x + 297198860*sqrt(35) + 1485994300)*(sqrt(35)*sqrt(7) - 2*sqrt(7))*sqrt(20492*sqrt(35) + 154630) - 1/74299715*77315^(3/4)*sqrt(155)*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630)*(sqrt(35) - 2) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) - 77315^(1/4)*sqrt(155)*(218*sqrt(35)*sqrt(31)*(5*x^2 + 3*x + 2) - 1645*sqrt(31)*(5*x^2 + 3*x + 2))*sqrt(20492*sqrt(35) + 154630)*log(188/7*77315^(1/4)*sqrt(155)*(2*sqrt(35)*sqrt(31) - 35*sqrt(31))*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630) + 424569800*x + 42456980*sqrt(35) + 212284900) + 77315^(1/4)*sqrt(155)*(218*sqrt(35)*sqrt(31)*(5*x^2 + 3*x + 2) - 1645*sqrt(31)*(5*x^2 + 3*x + 2))*sqrt(20492*sqrt(35) + 154630)*log(-188/7*77315^(1/4)*sqrt(155)*(2*sqrt(35)*sqrt(31) - 35*sqrt(31))*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630) + 424569800*x + 42456980*sqrt(35) + 212284900) - 490061950*(4*x - 5)*sqrt(2*x + 1))/(5*x^2 + 3*x + 2)","B",0
2319,1,526,0,0.442693," ","integrate((1+2*x)^(1/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{3844 \cdot 77315^{\frac{1}{4}} \sqrt{217} \sqrt{35} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{20492 \, \sqrt{35} + 154630} \arctan\left(\frac{1}{26522397764975} \cdot 77315^{\frac{3}{4}} \sqrt{1645} \sqrt{217} \sqrt{77315^{\frac{1}{4}} \sqrt{217} {\left(\sqrt{35} \sqrt{31} - 2 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} + 3161690 \, x + 316169 \, \sqrt{35} + 1580845} \sqrt{20492 \, \sqrt{35} + 154630} {\left(2 \, \sqrt{35} - 35\right)} - \frac{1}{520098005} \cdot 77315^{\frac{3}{4}} \sqrt{217} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} {\left(2 \, \sqrt{35} - 35\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 3844 \cdot 77315^{\frac{1}{4}} \sqrt{217} \sqrt{35} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{20492 \, \sqrt{35} + 154630} \arctan\left(\frac{1}{53044795529950} \cdot 77315^{\frac{3}{4}} \sqrt{217} \sqrt{-6580 \cdot 77315^{\frac{1}{4}} \sqrt{217} {\left(\sqrt{35} \sqrt{31} - 2 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} + 20803920200 \, x + 2080392020 \, \sqrt{35} + 10401960100} \sqrt{20492 \, \sqrt{35} + 154630} {\left(2 \, \sqrt{35} - 35\right)} - \frac{1}{520098005} \cdot 77315^{\frac{3}{4}} \sqrt{217} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} {\left(2 \, \sqrt{35} - 35\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 77315^{\frac{1}{4}} \sqrt{217} {\left(218 \, \sqrt{35} \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} - 1645 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)}\right)} \sqrt{20492 \, \sqrt{35} + 154630} \log\left(6580 \cdot 77315^{\frac{1}{4}} \sqrt{217} {\left(\sqrt{35} \sqrt{31} - 2 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} + 20803920200 \, x + 2080392020 \, \sqrt{35} + 10401960100\right) - 77315^{\frac{1}{4}} \sqrt{217} {\left(218 \, \sqrt{35} \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} - 1645 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)}\right)} \sqrt{20492 \, \sqrt{35} + 154630} \log\left(-6580 \cdot 77315^{\frac{1}{4}} \sqrt{217} {\left(\sqrt{35} \sqrt{31} - 2 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{20492 \, \sqrt{35} + 154630} + 20803920200 \, x + 2080392020 \, \sqrt{35} + 10401960100\right) + 686086730 \, {\left(10 \, x + 3\right)} \sqrt{2 \, x + 1}}{21268688630 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"1/21268688630*(3844*77315^(1/4)*sqrt(217)*sqrt(35)*(5*x^2 + 3*x + 2)*sqrt(20492*sqrt(35) + 154630)*arctan(1/26522397764975*77315^(3/4)*sqrt(1645)*sqrt(217)*sqrt(77315^(1/4)*sqrt(217)*(sqrt(35)*sqrt(31) - 2*sqrt(31))*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630) + 3161690*x + 316169*sqrt(35) + 1580845)*sqrt(20492*sqrt(35) + 154630)*(2*sqrt(35) - 35) - 1/520098005*77315^(3/4)*sqrt(217)*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630)*(2*sqrt(35) - 35) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 3844*77315^(1/4)*sqrt(217)*sqrt(35)*(5*x^2 + 3*x + 2)*sqrt(20492*sqrt(35) + 154630)*arctan(1/53044795529950*77315^(3/4)*sqrt(217)*sqrt(-6580*77315^(1/4)*sqrt(217)*(sqrt(35)*sqrt(31) - 2*sqrt(31))*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630) + 20803920200*x + 2080392020*sqrt(35) + 10401960100)*sqrt(20492*sqrt(35) + 154630)*(2*sqrt(35) - 35) - 1/520098005*77315^(3/4)*sqrt(217)*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630)*(2*sqrt(35) - 35) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 77315^(1/4)*sqrt(217)*(218*sqrt(35)*sqrt(31)*(5*x^2 + 3*x + 2) - 1645*sqrt(31)*(5*x^2 + 3*x + 2))*sqrt(20492*sqrt(35) + 154630)*log(6580*77315^(1/4)*sqrt(217)*(sqrt(35)*sqrt(31) - 2*sqrt(31))*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630) + 20803920200*x + 2080392020*sqrt(35) + 10401960100) - 77315^(1/4)*sqrt(217)*(218*sqrt(35)*sqrt(31)*(5*x^2 + 3*x + 2) - 1645*sqrt(31)*(5*x^2 + 3*x + 2))*sqrt(20492*sqrt(35) + 154630)*log(-6580*77315^(1/4)*sqrt(217)*(sqrt(35)*sqrt(31) - 2*sqrt(31))*sqrt(2*x + 1)*sqrt(20492*sqrt(35) + 154630) + 20803920200*x + 2080392020*sqrt(35) + 10401960100) + 686086730*(10*x + 3)*sqrt(2*x + 1))/(5*x^2 + 3*x + 2)","B",0
2320,1,572,0,0.436319," ","integrate(1/(1+2*x)^(1/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","-\frac{1149356 \cdot 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{217} \sqrt{35} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{32678 \, \sqrt{35} + 361375} \arctan\left(\frac{1}{229833696387700298075} \cdot 5969915^{\frac{3}{4}} \sqrt{826} \sqrt{299} \sqrt{295} \sqrt{217} \sqrt{5969915^{\frac{1}{4}} \sqrt{826} \sqrt{217} {\left(2 \, \sqrt{35} \sqrt{31} - 97 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} + 8306970490 \, x + 830697049 \, \sqrt{35} + 4153485245} \sqrt{32678 \, \sqrt{35} + 361375} {\left(97 \, \sqrt{35} - 70\right)} - \frac{1}{12007725843295} \cdot 5969915^{\frac{3}{4}} \sqrt{826} \sqrt{217} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} {\left(97 \, \sqrt{35} - 70\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 1149356 \cdot 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{217} \sqrt{35} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{32678 \, \sqrt{35} + 361375} \arctan\left(\frac{1}{80441793735695104326250} \cdot 5969915^{\frac{3}{4}} \sqrt{826} \sqrt{299} \sqrt{217} \sqrt{-36137500 \cdot 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{217} {\left(2 \, \sqrt{35} \sqrt{31} - 97 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} + 300193146082375000 \, x + 30019314608237500 \, \sqrt{35} + 150096573041187500} \sqrt{32678 \, \sqrt{35} + 361375} {\left(97 \, \sqrt{35} - 70\right)} - \frac{1}{12007725843295} \cdot 5969915^{\frac{3}{4}} \sqrt{826} \sqrt{217} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} {\left(97 \, \sqrt{35} - 70\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) - 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{217} {\left(32678 \, \sqrt{35} \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} - 361375 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)}\right)} \sqrt{32678 \, \sqrt{35} + 361375} \log\left(\frac{36137500}{299} \cdot 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{217} {\left(2 \, \sqrt{35} \sqrt{31} - 97 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} + 1003990455125000 \, x + 100399045512500 \, \sqrt{35} + 501995227562500\right) + 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{217} {\left(32678 \, \sqrt{35} \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} - 361375 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)}\right)} \sqrt{32678 \, \sqrt{35} + 361375} \log\left(-\frac{36137500}{299} \cdot 5969915^{\frac{1}{4}} \sqrt{826} \sqrt{217} {\left(2 \, \sqrt{35} \sqrt{31} - 97 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{32678 \, \sqrt{35} + 361375} + 1003990455125000 \, x + 100399045512500 \, \sqrt{35} + 501995227562500\right) - 1802612596330 \, {\left(20 \, x + 37\right)} \sqrt{2 \, x + 1}}{391166933403610 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"-1/391166933403610*(1149356*5969915^(1/4)*sqrt(826)*sqrt(217)*sqrt(35)*(5*x^2 + 3*x + 2)*sqrt(32678*sqrt(35) + 361375)*arctan(1/229833696387700298075*5969915^(3/4)*sqrt(826)*sqrt(299)*sqrt(295)*sqrt(217)*sqrt(5969915^(1/4)*sqrt(826)*sqrt(217)*(2*sqrt(35)*sqrt(31) - 97*sqrt(31))*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375) + 8306970490*x + 830697049*sqrt(35) + 4153485245)*sqrt(32678*sqrt(35) + 361375)*(97*sqrt(35) - 70) - 1/12007725843295*5969915^(3/4)*sqrt(826)*sqrt(217)*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375)*(97*sqrt(35) - 70) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 1149356*5969915^(1/4)*sqrt(826)*sqrt(217)*sqrt(35)*(5*x^2 + 3*x + 2)*sqrt(32678*sqrt(35) + 361375)*arctan(1/80441793735695104326250*5969915^(3/4)*sqrt(826)*sqrt(299)*sqrt(217)*sqrt(-36137500*5969915^(1/4)*sqrt(826)*sqrt(217)*(2*sqrt(35)*sqrt(31) - 97*sqrt(31))*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375) + 300193146082375000*x + 30019314608237500*sqrt(35) + 150096573041187500)*sqrt(32678*sqrt(35) + 361375)*(97*sqrt(35) - 70) - 1/12007725843295*5969915^(3/4)*sqrt(826)*sqrt(217)*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375)*(97*sqrt(35) - 70) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) - 5969915^(1/4)*sqrt(826)*sqrt(217)*(32678*sqrt(35)*sqrt(31)*(5*x^2 + 3*x + 2) - 361375*sqrt(31)*(5*x^2 + 3*x + 2))*sqrt(32678*sqrt(35) + 361375)*log(36137500/299*5969915^(1/4)*sqrt(826)*sqrt(217)*(2*sqrt(35)*sqrt(31) - 97*sqrt(31))*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375) + 1003990455125000*x + 100399045512500*sqrt(35) + 501995227562500) + 5969915^(1/4)*sqrt(826)*sqrt(217)*(32678*sqrt(35)*sqrt(31)*(5*x^2 + 3*x + 2) - 361375*sqrt(31)*(5*x^2 + 3*x + 2))*sqrt(32678*sqrt(35) + 361375)*log(-36137500/299*5969915^(1/4)*sqrt(826)*sqrt(217)*(2*sqrt(35)*sqrt(31) - 97*sqrt(31))*sqrt(2*x + 1)*sqrt(32678*sqrt(35) + 361375) + 1003990455125000*x + 100399045512500*sqrt(35) + 501995227562500) - 1802612596330*(20*x + 37)*sqrt(2*x + 1))/(5*x^2 + 3*x + 2)","B",0
2321,1,576,0,0.451291," ","integrate(1/(1+2*x)^(3/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{16794436 \cdot 21898835^{\frac{1}{4}} \sqrt{217} \sqrt{35} {\left(10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} \arctan\left(\frac{1}{84465779527115502604115125} \cdot 21898835^{\frac{3}{4}} \sqrt{4369} \sqrt{791} \sqrt{217} \sqrt{21898835^{\frac{1}{4}} \sqrt{217} {\left(151 \, \sqrt{35} \sqrt{31} + 814 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} + 8136694311550 \, x + 813669431155 \, \sqrt{35} + 4068347155775} {\left(814 \, \sqrt{35} + 5285\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} - \frac{1}{22526438201526175} \cdot 21898835^{\frac{3}{4}} \sqrt{217} \sqrt{2 \, x + 1} {\left(814 \, \sqrt{35} + 5285\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 16794436 \cdot 21898835^{\frac{1}{4}} \sqrt{217} \sqrt{35} {\left(10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} \arctan\left(\frac{1}{206941159841432981380082056250} \cdot 21898835^{\frac{3}{4}} \sqrt{4369} \sqrt{217} \sqrt{-4747977500 \cdot 21898835^{\frac{1}{4}} \sqrt{217} {\left(151 \, \sqrt{35} \sqrt{31} + 814 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} + 38632841515617390125000 \, x + 3863284151561739012500 \, \sqrt{35} + 19316420757808695062500} {\left(814 \, \sqrt{35} + 5285\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} - \frac{1}{22526438201526175} \cdot 21898835^{\frac{3}{4}} \sqrt{217} \sqrt{2 \, x + 1} {\left(814 \, \sqrt{35} + 5285\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 21898835^{\frac{1}{4}} \sqrt{217} {\left(5682718 \, \sqrt{35} \sqrt{31} {\left(10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right)} + 33914125 \, \sqrt{31} {\left(10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right)}\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} \log\left(\frac{4747977500}{4369} \cdot 21898835^{\frac{1}{4}} \sqrt{217} {\left(151 \, \sqrt{35} \sqrt{31} + 814 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} + 8842490619276125000 \, x + 884249061927612500 \, \sqrt{35} + 4421245309638062500\right) - 21898835^{\frac{1}{4}} \sqrt{217} {\left(5682718 \, \sqrt{35} \sqrt{31} {\left(10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right)} + 33914125 \, \sqrt{31} {\left(10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right)}\right)} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} \log\left(-\frac{4747977500}{4369} \cdot 21898835^{\frac{1}{4}} \sqrt{217} {\left(151 \, \sqrt{35} \sqrt{31} + 814 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-11012823348100 \, \sqrt{35} + 65723878543750} + 8842490619276125000 \, x + 884249061927612500 \, \sqrt{35} + 4421245309638062500\right) - 1765662665606350 \, {\left(3020 \, x^{2} + 1672 \, x + 949\right)} \sqrt{2 \, x + 1}}{2682041589056045650 \, {\left(10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right)}}"," ",0,"1/2682041589056045650*(16794436*21898835^(1/4)*sqrt(217)*sqrt(35)*(10*x^3 + 11*x^2 + 7*x + 2)*sqrt(-11012823348100*sqrt(35) + 65723878543750)*arctan(1/84465779527115502604115125*21898835^(3/4)*sqrt(4369)*sqrt(791)*sqrt(217)*sqrt(21898835^(1/4)*sqrt(217)*(151*sqrt(35)*sqrt(31) + 814*sqrt(31))*sqrt(2*x + 1)*sqrt(-11012823348100*sqrt(35) + 65723878543750) + 8136694311550*x + 813669431155*sqrt(35) + 4068347155775)*(814*sqrt(35) + 5285)*sqrt(-11012823348100*sqrt(35) + 65723878543750) - 1/22526438201526175*21898835^(3/4)*sqrt(217)*sqrt(2*x + 1)*(814*sqrt(35) + 5285)*sqrt(-11012823348100*sqrt(35) + 65723878543750) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 16794436*21898835^(1/4)*sqrt(217)*sqrt(35)*(10*x^3 + 11*x^2 + 7*x + 2)*sqrt(-11012823348100*sqrt(35) + 65723878543750)*arctan(1/206941159841432981380082056250*21898835^(3/4)*sqrt(4369)*sqrt(217)*sqrt(-4747977500*21898835^(1/4)*sqrt(217)*(151*sqrt(35)*sqrt(31) + 814*sqrt(31))*sqrt(2*x + 1)*sqrt(-11012823348100*sqrt(35) + 65723878543750) + 38632841515617390125000*x + 3863284151561739012500*sqrt(35) + 19316420757808695062500)*(814*sqrt(35) + 5285)*sqrt(-11012823348100*sqrt(35) + 65723878543750) - 1/22526438201526175*21898835^(3/4)*sqrt(217)*sqrt(2*x + 1)*(814*sqrt(35) + 5285)*sqrt(-11012823348100*sqrt(35) + 65723878543750) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 21898835^(1/4)*sqrt(217)*(5682718*sqrt(35)*sqrt(31)*(10*x^3 + 11*x^2 + 7*x + 2) + 33914125*sqrt(31)*(10*x^3 + 11*x^2 + 7*x + 2))*sqrt(-11012823348100*sqrt(35) + 65723878543750)*log(4747977500/4369*21898835^(1/4)*sqrt(217)*(151*sqrt(35)*sqrt(31) + 814*sqrt(31))*sqrt(2*x + 1)*sqrt(-11012823348100*sqrt(35) + 65723878543750) + 8842490619276125000*x + 884249061927612500*sqrt(35) + 4421245309638062500) - 21898835^(1/4)*sqrt(217)*(5682718*sqrt(35)*sqrt(31)*(10*x^3 + 11*x^2 + 7*x + 2) + 33914125*sqrt(31)*(10*x^3 + 11*x^2 + 7*x + 2))*sqrt(-11012823348100*sqrt(35) + 65723878543750)*log(-4747977500/4369*21898835^(1/4)*sqrt(217)*(151*sqrt(35)*sqrt(31) + 814*sqrt(31))*sqrt(2*x + 1)*sqrt(-11012823348100*sqrt(35) + 65723878543750) + 8842490619276125000*x + 884249061927612500*sqrt(35) + 4421245309638062500) - 1765662665606350*(3020*x^2 + 1672*x + 949)*sqrt(2*x + 1))/(10*x^3 + 11*x^2 + 7*x + 2)","B",0
2322,1,653,0,0.454417," ","integrate(1/(1+2*x)^(5/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","-\frac{620294748 \cdot 161637035^{\frac{1}{4}} \sqrt{4298} \sqrt{217} \sqrt{35} {\left(20 \, x^{4} + 32 \, x^{3} + 25 \, x^{2} + 11 \, x + 2\right)} \sqrt{12504542 \, \sqrt{35} + 92138375} \arctan\left(\frac{1}{55152316249116723757744225} \cdot 161637035^{\frac{3}{4}} \sqrt{4298} \sqrt{1535} \sqrt{217} \sqrt{149} \sqrt{161637035^{\frac{1}{4}} \sqrt{4298} \sqrt{217} {\left(234 \, \sqrt{35} \sqrt{31} - 499 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{12504542 \, \sqrt{35} + 92138375} + 7775911578470 \, x + 777591157847 \, \sqrt{35} + 3887955789235} \sqrt{12504542 \, \sqrt{35} + 92138375} {\left(499 \, \sqrt{35} - 8190\right)} - \frac{1}{58486518937462105} \cdot 161637035^{\frac{3}{4}} \sqrt{4298} \sqrt{217} \sqrt{2 \, x + 1} \sqrt{12504542 \, \sqrt{35} + 92138375} {\left(499 \, \sqrt{35} - 8190\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 620294748 \cdot 161637035^{\frac{1}{4}} \sqrt{4298} \sqrt{217} \sqrt{35} {\left(20 \, x^{4} + 32 \, x^{3} + 25 \, x^{2} + 11 \, x + 2\right)} \sqrt{12504542 \, \sqrt{35} + 92138375} \arctan\left(\frac{1}{4729311118361759062226567293750} \cdot 161637035^{\frac{3}{4}} \sqrt{4298} \sqrt{217} \sqrt{149} \sqrt{-11286950937500 \cdot 161637035^{\frac{1}{4}} \sqrt{4298} \sqrt{217} {\left(234 \, \sqrt{35} \sqrt{31} - 499 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{12504542 \, \sqrt{35} + 92138375} + 87766332480529071315625000 \, x + 8776633248052907131562500 \, \sqrt{35} + 43883166240264535657812500} \sqrt{12504542 \, \sqrt{35} + 92138375} {\left(499 \, \sqrt{35} - 8190\right)} - \frac{1}{58486518937462105} \cdot 161637035^{\frac{3}{4}} \sqrt{4298} \sqrt{217} \sqrt{2 \, x + 1} \sqrt{12504542 \, \sqrt{35} + 92138375} {\left(499 \, \sqrt{35} - 8190\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 3 \cdot 161637035^{\frac{1}{4}} \sqrt{4298} \sqrt{217} {\left(12504542 \, \sqrt{35} \sqrt{31} {\left(20 \, x^{4} + 32 \, x^{3} + 25 \, x^{2} + 11 \, x + 2\right)} - 92138375 \, \sqrt{31} {\left(20 \, x^{4} + 32 \, x^{3} + 25 \, x^{2} + 11 \, x + 2\right)}\right)} \sqrt{12504542 \, \sqrt{35} + 92138375} \log\left(\frac{11286950937500}{53789} \cdot 161637035^{\frac{1}{4}} \sqrt{4298} \sqrt{217} {\left(234 \, \sqrt{35} \sqrt{31} - 499 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{12504542 \, \sqrt{35} + 92138375} + 1631678084376528125000 \, x + 163167808437652812500 \, \sqrt{35} + 815839042188264062500\right) - 3 \cdot 161637035^{\frac{1}{4}} \sqrt{4298} \sqrt{217} {\left(12504542 \, \sqrt{35} \sqrt{31} {\left(20 \, x^{4} + 32 \, x^{3} + 25 \, x^{2} + 11 \, x + 2\right)} - 92138375 \, \sqrt{31} {\left(20 \, x^{4} + 32 \, x^{3} + 25 \, x^{2} + 11 \, x + 2\right)}\right)} \sqrt{12504542 \, \sqrt{35} + 92138375} \log\left(-\frac{11286950937500}{53789} \cdot 161637035^{\frac{1}{4}} \sqrt{4298} \sqrt{217} {\left(234 \, \sqrt{35} \sqrt{31} - 499 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{12504542 \, \sqrt{35} + 92138375} + 1631678084376528125000 \, x + 163167808437652812500 \, \sqrt{35} + 815839042188264062500\right) + 337474562505598 \, {\left(140400 \, x^{3} + 183140 \, x^{2} + 112560 \, x + 34121\right)} \sqrt{2 \, x + 1}}{10765101069366070602 \, {\left(20 \, x^{4} + 32 \, x^{3} + 25 \, x^{2} + 11 \, x + 2\right)}}"," ",0,"-1/10765101069366070602*(620294748*161637035^(1/4)*sqrt(4298)*sqrt(217)*sqrt(35)*(20*x^4 + 32*x^3 + 25*x^2 + 11*x + 2)*sqrt(12504542*sqrt(35) + 92138375)*arctan(1/55152316249116723757744225*161637035^(3/4)*sqrt(4298)*sqrt(1535)*sqrt(217)*sqrt(149)*sqrt(161637035^(1/4)*sqrt(4298)*sqrt(217)*(234*sqrt(35)*sqrt(31) - 499*sqrt(31))*sqrt(2*x + 1)*sqrt(12504542*sqrt(35) + 92138375) + 7775911578470*x + 777591157847*sqrt(35) + 3887955789235)*sqrt(12504542*sqrt(35) + 92138375)*(499*sqrt(35) - 8190) - 1/58486518937462105*161637035^(3/4)*sqrt(4298)*sqrt(217)*sqrt(2*x + 1)*sqrt(12504542*sqrt(35) + 92138375)*(499*sqrt(35) - 8190) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 620294748*161637035^(1/4)*sqrt(4298)*sqrt(217)*sqrt(35)*(20*x^4 + 32*x^3 + 25*x^2 + 11*x + 2)*sqrt(12504542*sqrt(35) + 92138375)*arctan(1/4729311118361759062226567293750*161637035^(3/4)*sqrt(4298)*sqrt(217)*sqrt(149)*sqrt(-11286950937500*161637035^(1/4)*sqrt(4298)*sqrt(217)*(234*sqrt(35)*sqrt(31) - 499*sqrt(31))*sqrt(2*x + 1)*sqrt(12504542*sqrt(35) + 92138375) + 87766332480529071315625000*x + 8776633248052907131562500*sqrt(35) + 43883166240264535657812500)*sqrt(12504542*sqrt(35) + 92138375)*(499*sqrt(35) - 8190) - 1/58486518937462105*161637035^(3/4)*sqrt(4298)*sqrt(217)*sqrt(2*x + 1)*sqrt(12504542*sqrt(35) + 92138375)*(499*sqrt(35) - 8190) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 3*161637035^(1/4)*sqrt(4298)*sqrt(217)*(12504542*sqrt(35)*sqrt(31)*(20*x^4 + 32*x^3 + 25*x^2 + 11*x + 2) - 92138375*sqrt(31)*(20*x^4 + 32*x^3 + 25*x^2 + 11*x + 2))*sqrt(12504542*sqrt(35) + 92138375)*log(11286950937500/53789*161637035^(1/4)*sqrt(4298)*sqrt(217)*(234*sqrt(35)*sqrt(31) - 499*sqrt(31))*sqrt(2*x + 1)*sqrt(12504542*sqrt(35) + 92138375) + 1631678084376528125000*x + 163167808437652812500*sqrt(35) + 815839042188264062500) - 3*161637035^(1/4)*sqrt(4298)*sqrt(217)*(12504542*sqrt(35)*sqrt(31)*(20*x^4 + 32*x^3 + 25*x^2 + 11*x + 2) - 92138375*sqrt(31)*(20*x^4 + 32*x^3 + 25*x^2 + 11*x + 2))*sqrt(12504542*sqrt(35) + 92138375)*log(-11286950937500/53789*161637035^(1/4)*sqrt(4298)*sqrt(217)*(234*sqrt(35)*sqrt(31) - 499*sqrt(31))*sqrt(2*x + 1)*sqrt(12504542*sqrt(35) + 92138375) + 1631678084376528125000*x + 163167808437652812500*sqrt(35) + 815839042188264062500) + 337474562505598*(140400*x^3 + 183140*x^2 + 112560*x + 34121)*sqrt(2*x + 1))/(20*x^4 + 32*x^3 + 25*x^2 + 11*x + 2)","B",0
2323,1,653,0,0.457360," ","integrate((1+2*x)^(9/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{19347824532 \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{155} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{250141922 \, \sqrt{35} + 2263842875} \arctan\left(\frac{1}{2160252846511970217131322639383425} \cdot 97578096035^{\frac{3}{4}} \sqrt{1677751} \sqrt{105602} \sqrt{7543} \sqrt{155} \sqrt{97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{155} {\left(7379 \, \sqrt{35} \sqrt{31} - 9240 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} + 29796214090828850 \, x + 2979621409082885 \, \sqrt{35} + 14898107045414425} \sqrt{250141922 \, \sqrt{35} + 2263842875} {\left(264 \, \sqrt{35} - 7379\right)} - \frac{1}{157326990020985410885} \cdot 97578096035^{\frac{3}{4}} \sqrt{105602} \sqrt{155} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} {\left(264 \, \sqrt{35} - 7379\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 19347824532 \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{155} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{250141922 \, \sqrt{35} + 2263842875} \arctan\left(\frac{1}{7938929210931490547957610699734086875} \cdot 97578096035^{\frac{3}{4}} \sqrt{1677751} \sqrt{105602} \sqrt{155} \sqrt{-101872929375 \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{155} {\left(7379 \, \sqrt{35} \sqrt{31} - 9240 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} + 3035427613717387271262468750 \, x + 303542761371738727126246875 \, \sqrt{35} + 1517713806858693635631234375} \sqrt{250141922 \, \sqrt{35} + 2263842875} {\left(264 \, \sqrt{35} - 7379\right)} - \frac{1}{157326990020985410885} \cdot 97578096035^{\frac{3}{4}} \sqrt{105602} \sqrt{155} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} {\left(264 \, \sqrt{35} - 7379\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 3 \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{155} {\left(250141922 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 2263842875 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{250141922 \, \sqrt{35} + 2263842875} \log\left(\frac{101872929375}{1677751} \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{155} {\left(7379 \, \sqrt{35} \sqrt{31} - 9240 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} + 1809224142150645281250 \, x + 180922414215064528125 \, \sqrt{35} + 904612071075322640625\right) - 3 \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{155} {\left(250141922 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 2263842875 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{250141922 \, \sqrt{35} + 2263842875} \log\left(-\frac{101872929375}{1677751} \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{155} {\left(7379 \, \sqrt{35} \sqrt{31} - 9240 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} + 1809224142150645281250 \, x + 180922414215064528125 \, \sqrt{35} + 904612071075322640625\right) - 923682636815694350 \, {\left(86150 \, x^{3} + 144557 \, x^{2} + 87291 \, x + 27977\right)} \sqrt{2 \, x + 1}}{44382950698994113517500 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/44382950698994113517500*(19347824532*97578096035^(1/4)*sqrt(105602)*sqrt(155)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(250141922*sqrt(35) + 2263842875)*arctan(1/2160252846511970217131322639383425*97578096035^(3/4)*sqrt(1677751)*sqrt(105602)*sqrt(7543)*sqrt(155)*sqrt(97578096035^(1/4)*sqrt(105602)*sqrt(155)*(7379*sqrt(35)*sqrt(31) - 9240*sqrt(31))*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875) + 29796214090828850*x + 2979621409082885*sqrt(35) + 14898107045414425)*sqrt(250141922*sqrt(35) + 2263842875)*(264*sqrt(35) - 7379) - 1/157326990020985410885*97578096035^(3/4)*sqrt(105602)*sqrt(155)*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875)*(264*sqrt(35) - 7379) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 19347824532*97578096035^(1/4)*sqrt(105602)*sqrt(155)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(250141922*sqrt(35) + 2263842875)*arctan(1/7938929210931490547957610699734086875*97578096035^(3/4)*sqrt(1677751)*sqrt(105602)*sqrt(155)*sqrt(-101872929375*97578096035^(1/4)*sqrt(105602)*sqrt(155)*(7379*sqrt(35)*sqrt(31) - 9240*sqrt(31))*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875) + 3035427613717387271262468750*x + 303542761371738727126246875*sqrt(35) + 1517713806858693635631234375)*sqrt(250141922*sqrt(35) + 2263842875)*(264*sqrt(35) - 7379) - 1/157326990020985410885*97578096035^(3/4)*sqrt(105602)*sqrt(155)*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875)*(264*sqrt(35) - 7379) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 3*97578096035^(1/4)*sqrt(105602)*sqrt(155)*(250141922*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 2263842875*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(250141922*sqrt(35) + 2263842875)*log(101872929375/1677751*97578096035^(1/4)*sqrt(105602)*sqrt(155)*(7379*sqrt(35)*sqrt(31) - 9240*sqrt(31))*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875) + 1809224142150645281250*x + 180922414215064528125*sqrt(35) + 904612071075322640625) - 3*97578096035^(1/4)*sqrt(105602)*sqrt(155)*(250141922*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 2263842875*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(250141922*sqrt(35) + 2263842875)*log(-101872929375/1677751*97578096035^(1/4)*sqrt(105602)*sqrt(155)*(7379*sqrt(35)*sqrt(31) - 9240*sqrt(31))*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875) + 1809224142150645281250*x + 180922414215064528125*sqrt(35) + 904612071075322640625) - 923682636815694350*(86150*x^3 + 144557*x^2 + 87291*x + 27977)*sqrt(2*x + 1))/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","B",0
2324,1,652,0,0.450996," ","integrate((1+2*x)^(7/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","-\frac{102361876 \cdot 121835^{\frac{1}{4}} \sqrt{155} \sqrt{118} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{9651062 \, \sqrt{35} + 63240625} \arctan\left(\frac{1}{5314799928145246742525} \cdot 121835^{\frac{3}{4}} \sqrt{26629} \sqrt{413} \sqrt{155} \sqrt{118} \sqrt{121835^{\frac{1}{4}} \sqrt{155} \sqrt{118} {\left(544 \, \sqrt{35} \sqrt{31} - 6265 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} + 528443184850 \, x + 52844318485 \, \sqrt{35} + 264221592425} \sqrt{9651062 \, \sqrt{35} + 63240625} {\left(179 \, \sqrt{35} - 544\right)} - \frac{1}{3117814790615} \cdot 121835^{\frac{3}{4}} \sqrt{155} \sqrt{118} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} {\left(179 \, \sqrt{35} - 544\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 102361876 \cdot 121835^{\frac{1}{4}} \sqrt{155} \sqrt{118} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{9651062 \, \sqrt{35} + 63240625} \arctan\left(\frac{1}{23252249685635454498546875} \cdot 121835^{\frac{3}{4}} \sqrt{26629} \sqrt{155} \sqrt{118} \sqrt{-7905078125 \cdot 121835^{\frac{1}{4}} \sqrt{155} \sqrt{118} {\left(544 \, \sqrt{35} \sqrt{31} - 6265 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} + 4177384660863066406250 \, x + 417738466086306640625 \, \sqrt{35} + 2088692330431533203125} \sqrt{9651062 \, \sqrt{35} + 63240625} {\left(179 \, \sqrt{35} - 544\right)} - \frac{1}{3117814790615} \cdot 121835^{\frac{3}{4}} \sqrt{155} \sqrt{118} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} {\left(179 \, \sqrt{35} - 544\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) - 121835^{\frac{1}{4}} \sqrt{155} \sqrt{118} {\left(9651062 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 63240625 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{9651062 \, \sqrt{35} + 63240625} \log\left(\frac{7905078125}{26629} \cdot 121835^{\frac{1}{4}} \sqrt{155} \sqrt{118} {\left(544 \, \sqrt{35} \sqrt{31} - 6265 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} + 156873508613281250 \, x + 15687350861328125 \, \sqrt{35} + 78436754306640625\right) + 121835^{\frac{1}{4}} \sqrt{155} \sqrt{118} {\left(9651062 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 63240625 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{9651062 \, \sqrt{35} + 63240625} \log\left(-\frac{7905078125}{26629} \cdot 121835^{\frac{1}{4}} \sqrt{155} \sqrt{118} {\left(544 \, \sqrt{35} \sqrt{31} - 6265 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} + 156873508613281250 \, x + 15687350861328125 \, \sqrt{35} + 78436754306640625\right) - 16381738730350 \, {\left(5440 \, x^{3} - 3629 \, x^{2} - 4167 \, x - 2689\right)} \sqrt{2 \, x + 1}}{157428509198663500 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/157428509198663500*(102361876*121835^(1/4)*sqrt(155)*sqrt(118)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(9651062*sqrt(35) + 63240625)*arctan(1/5314799928145246742525*121835^(3/4)*sqrt(26629)*sqrt(413)*sqrt(155)*sqrt(118)*sqrt(121835^(1/4)*sqrt(155)*sqrt(118)*(544*sqrt(35)*sqrt(31) - 6265*sqrt(31))*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625) + 528443184850*x + 52844318485*sqrt(35) + 264221592425)*sqrt(9651062*sqrt(35) + 63240625)*(179*sqrt(35) - 544) - 1/3117814790615*121835^(3/4)*sqrt(155)*sqrt(118)*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625)*(179*sqrt(35) - 544) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 102361876*121835^(1/4)*sqrt(155)*sqrt(118)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(9651062*sqrt(35) + 63240625)*arctan(1/23252249685635454498546875*121835^(3/4)*sqrt(26629)*sqrt(155)*sqrt(118)*sqrt(-7905078125*121835^(1/4)*sqrt(155)*sqrt(118)*(544*sqrt(35)*sqrt(31) - 6265*sqrt(31))*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625) + 4177384660863066406250*x + 417738466086306640625*sqrt(35) + 2088692330431533203125)*sqrt(9651062*sqrt(35) + 63240625)*(179*sqrt(35) - 544) - 1/3117814790615*121835^(3/4)*sqrt(155)*sqrt(118)*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625)*(179*sqrt(35) - 544) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) - 121835^(1/4)*sqrt(155)*sqrt(118)*(9651062*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 63240625*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(9651062*sqrt(35) + 63240625)*log(7905078125/26629*121835^(1/4)*sqrt(155)*sqrt(118)*(544*sqrt(35)*sqrt(31) - 6265*sqrt(31))*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625) + 156873508613281250*x + 15687350861328125*sqrt(35) + 78436754306640625) + 121835^(1/4)*sqrt(155)*sqrt(118)*(9651062*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 63240625*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(9651062*sqrt(35) + 63240625)*log(-7905078125/26629*121835^(1/4)*sqrt(155)*sqrt(118)*(544*sqrt(35)*sqrt(31) - 6265*sqrt(31))*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625) + 156873508613281250*x + 15687350861328125*sqrt(35) + 78436754306640625) - 16381738730350*(5440*x^3 - 3629*x^2 - 4167*x - 2689)*sqrt(2*x + 1))/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","B",0
2325,1,617,0,0.449660," ","integrate((1+2*x)^(5/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{357492 \cdot 256095875^{\frac{1}{4}} \sqrt{155} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{81593620 \, \sqrt{35} + 512191750} \arctan\left(\frac{1}{694138872776299934375} \cdot 256095875^{\frac{3}{4}} \sqrt{2705} \sqrt{217} \sqrt{155} \sqrt{256095875^{\frac{1}{4}} \sqrt{155} {\left(39 \, \sqrt{35} \sqrt{31} - 140 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} + 28204629250 \, x + 2820462925 \, \sqrt{35} + 14102314625} \sqrt{81593620 \, \sqrt{35} + 512191750} {\left(4 \, \sqrt{35} - 39\right)} - \frac{1}{7629352212125} \cdot 256095875^{\frac{3}{4}} \sqrt{155} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} {\left(4 \, \sqrt{35} - 39\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 357492 \cdot 256095875^{\frac{1}{4}} \sqrt{155} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{81593620 \, \sqrt{35} + 512191750} \arctan\left(\frac{1}{2082416618328899803125} \cdot 256095875^{\frac{3}{4}} \sqrt{217} \sqrt{155} \sqrt{-24345 \cdot 256095875^{\frac{1}{4}} \sqrt{155} {\left(39 \, \sqrt{35} \sqrt{31} - 140 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} + 686641699091250 \, x + 68664169909125 \, \sqrt{35} + 343320849545625} \sqrt{81593620 \, \sqrt{35} + 512191750} {\left(4 \, \sqrt{35} - 39\right)} - \frac{1}{7629352212125} \cdot 256095875^{\frac{3}{4}} \sqrt{155} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} {\left(4 \, \sqrt{35} - 39\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 3 \cdot 256095875^{\frac{1}{4}} \sqrt{155} {\left(15082 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 94675 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{81593620 \, \sqrt{35} + 512191750} \log\left(\frac{24345}{217} \cdot 256095875^{\frac{1}{4}} \sqrt{155} {\left(39 \, \sqrt{35} \sqrt{31} - 140 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} + 3164247461250 \, x + 316424746125 \, \sqrt{35} + 1582123730625\right) - 3 \cdot 256095875^{\frac{1}{4}} \sqrt{155} {\left(15082 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 94675 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{81593620 \, \sqrt{35} + 512191750} \log\left(-\frac{24345}{217} \cdot 256095875^{\frac{1}{4}} \sqrt{155} {\left(39 \, \sqrt{35} \sqrt{31} - 140 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} + 3164247461250 \, x + 316424746125 \, \sqrt{35} + 1582123730625\right) + 874343506750 \, {\left(1170 \, x^{3} + 1115 \, x^{2} + 381 \, x - 89\right)} \sqrt{2 \, x + 1}}{1680488219973500 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/1680488219973500*(357492*256095875^(1/4)*sqrt(155)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(81593620*sqrt(35) + 512191750)*arctan(1/694138872776299934375*256095875^(3/4)*sqrt(2705)*sqrt(217)*sqrt(155)*sqrt(256095875^(1/4)*sqrt(155)*(39*sqrt(35)*sqrt(31) - 140*sqrt(31))*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750) + 28204629250*x + 2820462925*sqrt(35) + 14102314625)*sqrt(81593620*sqrt(35) + 512191750)*(4*sqrt(35) - 39) - 1/7629352212125*256095875^(3/4)*sqrt(155)*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750)*(4*sqrt(35) - 39) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 357492*256095875^(1/4)*sqrt(155)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(81593620*sqrt(35) + 512191750)*arctan(1/2082416618328899803125*256095875^(3/4)*sqrt(217)*sqrt(155)*sqrt(-24345*256095875^(1/4)*sqrt(155)*(39*sqrt(35)*sqrt(31) - 140*sqrt(31))*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750) + 686641699091250*x + 68664169909125*sqrt(35) + 343320849545625)*sqrt(81593620*sqrt(35) + 512191750)*(4*sqrt(35) - 39) - 1/7629352212125*256095875^(3/4)*sqrt(155)*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750)*(4*sqrt(35) - 39) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 3*256095875^(1/4)*sqrt(155)*(15082*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 94675*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(81593620*sqrt(35) + 512191750)*log(24345/217*256095875^(1/4)*sqrt(155)*(39*sqrt(35)*sqrt(31) - 140*sqrt(31))*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750) + 3164247461250*x + 316424746125*sqrt(35) + 1582123730625) - 3*256095875^(1/4)*sqrt(155)*(15082*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 94675*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(81593620*sqrt(35) + 512191750)*log(-24345/217*256095875^(1/4)*sqrt(155)*(39*sqrt(35)*sqrt(31) - 140*sqrt(31))*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750) + 3164247461250*x + 316424746125*sqrt(35) + 1582123730625) + 874343506750*(1170*x^3 + 1115*x^2 + 381*x - 89)*sqrt(2*x + 1))/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","B",0
2326,1,625,0,0.458192," ","integrate((1+2*x)^(3/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","-\frac{357492 \cdot 256095875^{\frac{1}{4}} \sqrt{217} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{81593620 \, \sqrt{35} + 512191750} \arctan\left(\frac{1}{971794421886819908125} \cdot 256095875^{\frac{3}{4}} \sqrt{3787} \sqrt{217} \sqrt{256095875^{\frac{1}{4}} \sqrt{217} {\left(4 \, \sqrt{35} \sqrt{31} - 39 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} + 5640925850 \, x + 564092585 \, \sqrt{35} + 2820462925} {\left(39 \, \sqrt{35} \sqrt{31} - 140 \, \sqrt{31}\right)} \sqrt{81593620 \, \sqrt{35} + 512191750} - \frac{1}{53405465484875} \cdot 256095875^{\frac{3}{4}} \sqrt{217} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} {\left(39 \, \sqrt{35} - 140\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 357492 \cdot 256095875^{\frac{1}{4}} \sqrt{217} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{81593620 \, \sqrt{35} + 512191750} \arctan\left(\frac{1}{14576916328302298621875} \cdot 256095875^{\frac{3}{4}} \sqrt{217} \sqrt{-852075 \cdot 256095875^{\frac{1}{4}} \sqrt{217} {\left(4 \, \sqrt{35} \sqrt{31} - 39 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} + 4806491893638750 \, x + 480649189363875 \, \sqrt{35} + 2403245946819375} {\left(39 \, \sqrt{35} \sqrt{31} - 140 \, \sqrt{31}\right)} \sqrt{81593620 \, \sqrt{35} + 512191750} - \frac{1}{53405465484875} \cdot 256095875^{\frac{3}{4}} \sqrt{217} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} {\left(39 \, \sqrt{35} - 140\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) - 3 \cdot 256095875^{\frac{1}{4}} \sqrt{217} {\left(15082 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 94675 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{81593620 \, \sqrt{35} + 512191750} \log\left(\frac{852075}{31} \cdot 256095875^{\frac{1}{4}} \sqrt{217} {\left(4 \, \sqrt{35} \sqrt{31} - 39 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} + 155048125601250 \, x + 15504812560125 \, \sqrt{35} + 77524062800625\right) + 3 \cdot 256095875^{\frac{1}{4}} \sqrt{217} {\left(15082 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 94675 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{81593620 \, \sqrt{35} + 512191750} \log\left(-\frac{852075}{31} \cdot 256095875^{\frac{1}{4}} \sqrt{217} {\left(4 \, \sqrt{35} \sqrt{31} - 39 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{81593620 \, \sqrt{35} + 512191750} + 155048125601250 \, x + 15504812560125 \, \sqrt{35} + 77524062800625\right) - 1224080909450 \, {\left(600 \, x^{3} + 695 \, x^{2} + 565 \, x - 21\right)} \sqrt{2 \, x + 1}}{2352683507962900 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/2352683507962900*(357492*256095875^(1/4)*sqrt(217)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(81593620*sqrt(35) + 512191750)*arctan(1/971794421886819908125*256095875^(3/4)*sqrt(3787)*sqrt(217)*sqrt(256095875^(1/4)*sqrt(217)*(4*sqrt(35)*sqrt(31) - 39*sqrt(31))*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750) + 5640925850*x + 564092585*sqrt(35) + 2820462925)*(39*sqrt(35)*sqrt(31) - 140*sqrt(31))*sqrt(81593620*sqrt(35) + 512191750) - 1/53405465484875*256095875^(3/4)*sqrt(217)*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750)*(39*sqrt(35) - 140) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 357492*256095875^(1/4)*sqrt(217)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(81593620*sqrt(35) + 512191750)*arctan(1/14576916328302298621875*256095875^(3/4)*sqrt(217)*sqrt(-852075*256095875^(1/4)*sqrt(217)*(4*sqrt(35)*sqrt(31) - 39*sqrt(31))*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750) + 4806491893638750*x + 480649189363875*sqrt(35) + 2403245946819375)*(39*sqrt(35)*sqrt(31) - 140*sqrt(31))*sqrt(81593620*sqrt(35) + 512191750) - 1/53405465484875*256095875^(3/4)*sqrt(217)*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750)*(39*sqrt(35) - 140) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) - 3*256095875^(1/4)*sqrt(217)*(15082*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 94675*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(81593620*sqrt(35) + 512191750)*log(852075/31*256095875^(1/4)*sqrt(217)*(4*sqrt(35)*sqrt(31) - 39*sqrt(31))*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750) + 155048125601250*x + 15504812560125*sqrt(35) + 77524062800625) + 3*256095875^(1/4)*sqrt(217)*(15082*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 94675*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(81593620*sqrt(35) + 512191750)*log(-852075/31*256095875^(1/4)*sqrt(217)*(4*sqrt(35)*sqrt(31) - 39*sqrt(31))*sqrt(2*x + 1)*sqrt(81593620*sqrt(35) + 512191750) + 155048125601250*x + 15504812560125*sqrt(35) + 77524062800625) - 1224080909450*(600*x^3 + 695*x^2 + 565*x - 21)*sqrt(2*x + 1))/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","B",0
2327,1,652,0,0.447845," ","integrate((1+2*x)^(1/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{102361876 \cdot 121835^{\frac{1}{4}} \sqrt{217} \sqrt{118} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{9651062 \, \sqrt{35} + 63240625} \arctan\left(\frac{1}{37203599497016727197675} \cdot 121835^{\frac{3}{4}} \sqrt{26629} \sqrt{2065} \sqrt{217} \sqrt{118} \sqrt{121835^{\frac{1}{4}} \sqrt{217} \sqrt{118} {\left(179 \, \sqrt{35} \sqrt{31} - 544 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} + 105688636970 \, x + 10568863697 \, \sqrt{35} + 52844318485} \sqrt{9651062 \, \sqrt{35} + 63240625} {\left(544 \, \sqrt{35} - 6265\right)} - \frac{1}{21824703534305} \cdot 121835^{\frac{3}{4}} \sqrt{217} \sqrt{118} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} {\left(544 \, \sqrt{35} - 6265\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 102361876 \cdot 121835^{\frac{1}{4}} \sqrt{217} \sqrt{118} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{9651062 \, \sqrt{35} + 63240625} \arctan\left(\frac{1}{1139360234596137270428796875} \cdot 121835^{\frac{3}{4}} \sqrt{26629} \sqrt{217} \sqrt{118} \sqrt{-1936744140625 \cdot 121835^{\frac{1}{4}} \sqrt{217} \sqrt{118} {\left(179 \, \sqrt{35} \sqrt{31} - 544 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} + 204691848382290253906250 \, x + 20469184838229025390625 \, \sqrt{35} + 102345924191145126953125} \sqrt{9651062 \, \sqrt{35} + 63240625} {\left(544 \, \sqrt{35} - 6265\right)} - \frac{1}{21824703534305} \cdot 121835^{\frac{3}{4}} \sqrt{217} \sqrt{118} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} {\left(544 \, \sqrt{35} - 6265\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 121835^{\frac{1}{4}} \sqrt{217} \sqrt{118} {\left(9651062 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 63240625 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{9651062 \, \sqrt{35} + 63240625} \log\left(\frac{1936744140625}{26629} \cdot 121835^{\frac{1}{4}} \sqrt{217} \sqrt{118} {\left(179 \, \sqrt{35} \sqrt{31} - 544 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} + 7686801922050781250 \, x + 768680192205078125 \, \sqrt{35} + 3843400961025390625\right) - 121835^{\frac{1}{4}} \sqrt{217} \sqrt{118} {\left(9651062 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 63240625 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{9651062 \, \sqrt{35} + 63240625} \log\left(-\frac{1936744140625}{26629} \cdot 121835^{\frac{1}{4}} \sqrt{217} \sqrt{118} {\left(179 \, \sqrt{35} \sqrt{31} - 544 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{9651062 \, \sqrt{35} + 63240625} + 7686801922050781250 \, x + 768680192205078125 \, \sqrt{35} + 3843400961025390625\right) + 22934434222490 \, {\left(8950 \, x^{3} + 8365 \, x^{2} + 7547 \, x + 1849\right)} \sqrt{2 \, x + 1}}{308559878029380460 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/308559878029380460*(102361876*121835^(1/4)*sqrt(217)*sqrt(118)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(9651062*sqrt(35) + 63240625)*arctan(1/37203599497016727197675*121835^(3/4)*sqrt(26629)*sqrt(2065)*sqrt(217)*sqrt(118)*sqrt(121835^(1/4)*sqrt(217)*sqrt(118)*(179*sqrt(35)*sqrt(31) - 544*sqrt(31))*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625) + 105688636970*x + 10568863697*sqrt(35) + 52844318485)*sqrt(9651062*sqrt(35) + 63240625)*(544*sqrt(35) - 6265) - 1/21824703534305*121835^(3/4)*sqrt(217)*sqrt(118)*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625)*(544*sqrt(35) - 6265) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 102361876*121835^(1/4)*sqrt(217)*sqrt(118)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(9651062*sqrt(35) + 63240625)*arctan(1/1139360234596137270428796875*121835^(3/4)*sqrt(26629)*sqrt(217)*sqrt(118)*sqrt(-1936744140625*121835^(1/4)*sqrt(217)*sqrt(118)*(179*sqrt(35)*sqrt(31) - 544*sqrt(31))*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625) + 204691848382290253906250*x + 20469184838229025390625*sqrt(35) + 102345924191145126953125)*sqrt(9651062*sqrt(35) + 63240625)*(544*sqrt(35) - 6265) - 1/21824703534305*121835^(3/4)*sqrt(217)*sqrt(118)*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625)*(544*sqrt(35) - 6265) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 121835^(1/4)*sqrt(217)*sqrt(118)*(9651062*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 63240625*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(9651062*sqrt(35) + 63240625)*log(1936744140625/26629*121835^(1/4)*sqrt(217)*sqrt(118)*(179*sqrt(35)*sqrt(31) - 544*sqrt(31))*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625) + 7686801922050781250*x + 768680192205078125*sqrt(35) + 3843400961025390625) - 121835^(1/4)*sqrt(217)*sqrt(118)*(9651062*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 63240625*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(9651062*sqrt(35) + 63240625)*log(-1936744140625/26629*121835^(1/4)*sqrt(217)*sqrt(118)*(179*sqrt(35)*sqrt(31) - 544*sqrt(31))*sqrt(2*x + 1)*sqrt(9651062*sqrt(35) + 63240625) + 7686801922050781250*x + 768680192205078125*sqrt(35) + 3843400961025390625) + 22934434222490*(8950*x^3 + 8365*x^2 + 7547*x + 1849)*sqrt(2*x + 1))/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","B",0
2328,1,653,0,0.448792," ","integrate(1/(1+2*x)^(1/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","-\frac{19347824532 \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{217} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{250141922 \, \sqrt{35} + 2263842875} \arctan\left(\frac{1}{15121769925583791519919258475683975} \cdot 97578096035^{\frac{3}{4}} \sqrt{1677751} \sqrt{105602} \sqrt{37715} \sqrt{217} \sqrt{97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{217} {\left(264 \, \sqrt{35} \sqrt{31} - 7379 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} + 5959242818165770 \, x + 595924281816577 \, \sqrt{35} + 2979621409082885} \sqrt{250141922 \, \sqrt{35} + 2263842875} {\left(7379 \, \sqrt{35} - 9240\right)} - \frac{1}{1101288930146897876195} \cdot 97578096035^{\frac{3}{4}} \sqrt{105602} \sqrt{217} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} {\left(7379 \, \sqrt{35} - 9240\right)} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) + 19347824532 \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{217} \sqrt{35} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{250141922 \, \sqrt{35} + 2263842875} \arctan\left(\frac{1}{389007531335643036849922924286970256875} \cdot 97578096035^{\frac{3}{4}} \sqrt{1677751} \sqrt{105602} \sqrt{217} \sqrt{-24958867696875 \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{217} {\left(264 \, \sqrt{35} \sqrt{31} - 7379 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} + 148735953072151976291860968750 \, x + 14873595307215197629186096875 \, \sqrt{35} + 74367976536075988145930484375} \sqrt{250141922 \, \sqrt{35} + 2263842875} {\left(7379 \, \sqrt{35} - 9240\right)} - \frac{1}{1101288930146897876195} \cdot 97578096035^{\frac{3}{4}} \sqrt{105602} \sqrt{217} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} {\left(7379 \, \sqrt{35} - 9240\right)} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) - 3 \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{217} {\left(250141922 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 2263842875 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{250141922 \, \sqrt{35} + 2263842875} \log\left(\frac{24958867696875}{1677751} \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{217} {\left(264 \, \sqrt{35} \sqrt{31} - 7379 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} + 88651982965381618781250 \, x + 8865198296538161878125 \, \sqrt{35} + 44325991482690809390625\right) + 3 \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{217} {\left(250141922 \, \sqrt{35} \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} - 2263842875 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}\right)} \sqrt{250141922 \, \sqrt{35} + 2263842875} \log\left(-\frac{24958867696875}{1677751} \cdot 97578096035^{\frac{1}{4}} \sqrt{105602} \sqrt{217} {\left(264 \, \sqrt{35} \sqrt{31} - 7379 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{250141922 \, \sqrt{35} + 2263842875} + 88651982965381618781250 \, x + 8865198296538161878125 \, \sqrt{35} + 44325991482690809390625\right) - 1293155691541972090 \, {\left(39600 \, x^{3} + 69895 \, x^{2} + 47861 \, x + 26483\right)} \sqrt{2 \, x + 1}}{121786816718039847492020 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/121786816718039847492020*(19347824532*97578096035^(1/4)*sqrt(105602)*sqrt(217)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(250141922*sqrt(35) + 2263842875)*arctan(1/15121769925583791519919258475683975*97578096035^(3/4)*sqrt(1677751)*sqrt(105602)*sqrt(37715)*sqrt(217)*sqrt(97578096035^(1/4)*sqrt(105602)*sqrt(217)*(264*sqrt(35)*sqrt(31) - 7379*sqrt(31))*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875) + 5959242818165770*x + 595924281816577*sqrt(35) + 2979621409082885)*sqrt(250141922*sqrt(35) + 2263842875)*(7379*sqrt(35) - 9240) - 1/1101288930146897876195*97578096035^(3/4)*sqrt(105602)*sqrt(217)*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875)*(7379*sqrt(35) - 9240) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) + 19347824532*97578096035^(1/4)*sqrt(105602)*sqrt(217)*sqrt(35)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(250141922*sqrt(35) + 2263842875)*arctan(1/389007531335643036849922924286970256875*97578096035^(3/4)*sqrt(1677751)*sqrt(105602)*sqrt(217)*sqrt(-24958867696875*97578096035^(1/4)*sqrt(105602)*sqrt(217)*(264*sqrt(35)*sqrt(31) - 7379*sqrt(31))*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875) + 148735953072151976291860968750*x + 14873595307215197629186096875*sqrt(35) + 74367976536075988145930484375)*sqrt(250141922*sqrt(35) + 2263842875)*(7379*sqrt(35) - 9240) - 1/1101288930146897876195*97578096035^(3/4)*sqrt(105602)*sqrt(217)*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875)*(7379*sqrt(35) - 9240) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) - 3*97578096035^(1/4)*sqrt(105602)*sqrt(217)*(250141922*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 2263842875*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(250141922*sqrt(35) + 2263842875)*log(24958867696875/1677751*97578096035^(1/4)*sqrt(105602)*sqrt(217)*(264*sqrt(35)*sqrt(31) - 7379*sqrt(31))*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875) + 88651982965381618781250*x + 8865198296538161878125*sqrt(35) + 44325991482690809390625) + 3*97578096035^(1/4)*sqrt(105602)*sqrt(217)*(250141922*sqrt(35)*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) - 2263842875*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4))*sqrt(250141922*sqrt(35) + 2263842875)*log(-24958867696875/1677751*97578096035^(1/4)*sqrt(105602)*sqrt(217)*(264*sqrt(35)*sqrt(31) - 7379*sqrt(31))*sqrt(2*x + 1)*sqrt(250141922*sqrt(35) + 2263842875) + 88651982965381618781250*x + 8865198296538161878125*sqrt(35) + 44325991482690809390625) - 1293155691541972090*(39600*x^3 + 69895*x^2 + 47861*x + 26483)*sqrt(2*x + 1))/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","B",0
2329,1,657,0,0.457929," ","integrate(1/(1+2*x)^(3/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","-\frac{26636371428 \cdot 3500868535115^{\frac{1}{4}} \sqrt{217} \sqrt{35} {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} \arctan\left(\frac{1}{1509001768301691738567787671747064606625} \cdot 3500868535115^{\frac{3}{4}} \sqrt{2309779} \sqrt{316267} \sqrt{217} \sqrt{3500868535115^{\frac{1}{4}} \sqrt{217} {\left(2703 \, \sqrt{35} \sqrt{31} + 18092 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} + 1719941911827268850 \, x + 171994191182726885 \, \sqrt{35} + 859970955913634425} {\left(18092 \, \sqrt{35} + 94605\right)} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} - \frac{1}{1903863040197561930840325} \cdot 3500868535115^{\frac{3}{4}} \sqrt{217} \sqrt{2 \, x + 1} {\left(18092 \, \sqrt{35} + 94605\right)} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} - \frac{1}{31} \, \sqrt{35} \sqrt{31} - \frac{2}{31} \, \sqrt{31}\right) + 26636371428 \cdot 3500868535115^{\frac{1}{4}} \sqrt{217} \sqrt{35} {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} \arctan\left(\frac{1}{27727907492543585696183098468352312146734375} \cdot 3500868535115^{\frac{3}{4}} \sqrt{2309779} \sqrt{217} \sqrt{-106784587546875 \cdot 3500868535115^{\frac{1}{4}} \sqrt{217} {\left(2703 \, \sqrt{35} \sqrt{31} + 18092 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} + 183663287659058552515752602343750 \, x + 18366328765905855251575260234375 \, \sqrt{35} + 91831643829529276257876301171875} {\left(18092 \, \sqrt{35} + 94605\right)} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} - \frac{1}{1903863040197561930840325} \cdot 3500868535115^{\frac{3}{4}} \sqrt{217} \sqrt{2 \, x + 1} {\left(18092 \, \sqrt{35} + 94605\right)} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} + \frac{1}{31} \, \sqrt{35} \sqrt{31} + \frac{2}{31} \, \sqrt{31}\right) - 3 \cdot 3500868535115^{\frac{1}{4}} \sqrt{217} {\left(2257111762 \, \sqrt{35} \sqrt{31} {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)} + 13559947625 \, \sqrt{31} {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)}\right)} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} \log\left(\frac{106784587546875}{2309779} \cdot 3500868535115^{\frac{1}{4}} \sqrt{217} {\left(2703 \, \sqrt{35} \sqrt{31} + 18092 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} + 79515524064881771163281250 \, x + 7951552406488177116328125 \, \sqrt{35} + 39757762032440885581640625\right) + 3 \cdot 3500868535115^{\frac{1}{4}} \sqrt{217} {\left(2257111762 \, \sqrt{35} \sqrt{31} {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)} + 13559947625 \, \sqrt{31} {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)}\right)} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} \log\left(-\frac{106784587546875}{2309779} \cdot 3500868535115^{\frac{1}{4}} \sqrt{217} {\left(2703 \, \sqrt{35} \sqrt{31} + 18092 \, \sqrt{31}\right)} \sqrt{2 \, x + 1} \sqrt{-1748932415799512300 \, \sqrt{35} + 10506981691013893750} + 79515524064881771163281250 \, x + 7951552406488177116328125 \, \sqrt{35} + 39757762032440885581640625\right) + 74645478973303468090 \, {\left(4054500 \, x^{4} + 4501400 \, x^{3} + 4077245 \, x^{2} + 1525635 \, x + 429487\right)} \sqrt{2 \, x + 1}}{49209733431234418124460140 \, {\left(50 \, x^{5} + 85 \, x^{4} + 88 \, x^{3} + 53 \, x^{2} + 20 \, x + 4\right)}}"," ",0,"-1/49209733431234418124460140*(26636371428*3500868535115^(1/4)*sqrt(217)*sqrt(35)*(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4)*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750)*arctan(1/1509001768301691738567787671747064606625*3500868535115^(3/4)*sqrt(2309779)*sqrt(316267)*sqrt(217)*sqrt(3500868535115^(1/4)*sqrt(217)*(2703*sqrt(35)*sqrt(31) + 18092*sqrt(31))*sqrt(2*x + 1)*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750) + 1719941911827268850*x + 171994191182726885*sqrt(35) + 859970955913634425)*(18092*sqrt(35) + 94605)*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750) - 1/1903863040197561930840325*3500868535115^(3/4)*sqrt(217)*sqrt(2*x + 1)*(18092*sqrt(35) + 94605)*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750) - 1/31*sqrt(35)*sqrt(31) - 2/31*sqrt(31)) + 26636371428*3500868535115^(1/4)*sqrt(217)*sqrt(35)*(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4)*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750)*arctan(1/27727907492543585696183098468352312146734375*3500868535115^(3/4)*sqrt(2309779)*sqrt(217)*sqrt(-106784587546875*3500868535115^(1/4)*sqrt(217)*(2703*sqrt(35)*sqrt(31) + 18092*sqrt(31))*sqrt(2*x + 1)*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750) + 183663287659058552515752602343750*x + 18366328765905855251575260234375*sqrt(35) + 91831643829529276257876301171875)*(18092*sqrt(35) + 94605)*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750) - 1/1903863040197561930840325*3500868535115^(3/4)*sqrt(217)*sqrt(2*x + 1)*(18092*sqrt(35) + 94605)*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750) + 1/31*sqrt(35)*sqrt(31) + 2/31*sqrt(31)) - 3*3500868535115^(1/4)*sqrt(217)*(2257111762*sqrt(35)*sqrt(31)*(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4) + 13559947625*sqrt(31)*(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4))*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750)*log(106784587546875/2309779*3500868535115^(1/4)*sqrt(217)*(2703*sqrt(35)*sqrt(31) + 18092*sqrt(31))*sqrt(2*x + 1)*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750) + 79515524064881771163281250*x + 7951552406488177116328125*sqrt(35) + 39757762032440885581640625) + 3*3500868535115^(1/4)*sqrt(217)*(2257111762*sqrt(35)*sqrt(31)*(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4) + 13559947625*sqrt(31)*(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4))*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750)*log(-106784587546875/2309779*3500868535115^(1/4)*sqrt(217)*(2703*sqrt(35)*sqrt(31) + 18092*sqrt(31))*sqrt(2*x + 1)*sqrt(-1748932415799512300*sqrt(35) + 10506981691013893750) + 79515524064881771163281250*x + 7951552406488177116328125*sqrt(35) + 39757762032440885581640625) + 74645478973303468090*(4054500*x^4 + 4501400*x^3 + 4077245*x^2 + 1525635*x + 429487)*sqrt(2*x + 1))/(50*x^5 + 85*x^4 + 88*x^3 + 53*x^2 + 20*x + 4)","B",0
2330,1,4275,0,0.905941," ","integrate(x^(9/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{13} - 31 \, a b^{11} c + 413 \, a^{2} b^{9} c^{2} - 3012 \, a^{3} b^{7} c^{3} + 12496 \, a^{4} b^{5} c^{4} - 27584 \, a^{5} b^{3} c^{5} + 25088 \, a^{6} b c^{6} - {\left(b^{14} c^{5} - 30 \, a b^{12} c^{6} + 416 \, a^{2} b^{10} c^{7} - 3360 \, a^{3} b^{8} c^{8} + 16640 \, a^{4} b^{6} c^{9} - 49664 \, a^{5} b^{4} c^{10} + 81920 \, a^{6} b^{2} c^{11} - 57344 \, a^{7} c^{12}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} + 27 \, {\left(21 \, a^{2} b^{8} - 447 \, a^{3} b^{6} c + 4189 \, a^{4} b^{4} c^{2} - 19208 \, a^{5} b^{2} c^{3} + 38416 \, a^{6} c^{4}\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{13} - 31 \, a b^{11} c + 413 \, a^{2} b^{9} c^{2} - 3012 \, a^{3} b^{7} c^{3} + 12496 \, a^{4} b^{5} c^{4} - 27584 \, a^{5} b^{3} c^{5} + 25088 \, a^{6} b c^{6} - {\left(b^{14} c^{5} - 30 \, a b^{12} c^{6} + 416 \, a^{2} b^{10} c^{7} - 3360 \, a^{3} b^{8} c^{8} + 16640 \, a^{4} b^{6} c^{9} - 49664 \, a^{5} b^{4} c^{10} + 81920 \, a^{6} b^{2} c^{11} - 57344 \, a^{7} c^{12}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} + {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} + 27 \, {\left(21 \, a^{2} b^{8} - 447 \, a^{3} b^{6} c + 4189 \, a^{4} b^{4} c^{2} - 19208 \, a^{5} b^{2} c^{3} + 38416 \, a^{6} c^{4}\right)} \sqrt{x}\right) + 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{13} - 31 \, a b^{11} c + 413 \, a^{2} b^{9} c^{2} - 3012 \, a^{3} b^{7} c^{3} + 12496 \, a^{4} b^{5} c^{4} - 27584 \, a^{5} b^{3} c^{5} + 25088 \, a^{6} b c^{6} + {\left(b^{14} c^{5} - 30 \, a b^{12} c^{6} + 416 \, a^{2} b^{10} c^{7} - 3360 \, a^{3} b^{8} c^{8} + 16640 \, a^{4} b^{6} c^{9} - 49664 \, a^{5} b^{4} c^{10} + 81920 \, a^{6} b^{2} c^{11} - 57344 \, a^{7} c^{12}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} + 27 \, {\left(21 \, a^{2} b^{8} - 447 \, a^{3} b^{6} c + 4189 \, a^{4} b^{4} c^{2} - 19208 \, a^{5} b^{2} c^{3} + 38416 \, a^{6} c^{4}\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(b^{13} - 31 \, a b^{11} c + 413 \, a^{2} b^{9} c^{2} - 3012 \, a^{3} b^{7} c^{3} + 12496 \, a^{4} b^{5} c^{4} - 27584 \, a^{5} b^{3} c^{5} + 25088 \, a^{6} b c^{6} + {\left(b^{14} c^{5} - 30 \, a b^{12} c^{6} + 416 \, a^{2} b^{10} c^{7} - 3360 \, a^{3} b^{8} c^{8} + 16640 \, a^{4} b^{6} c^{9} - 49664 \, a^{5} b^{4} c^{10} + 81920 \, a^{6} b^{2} c^{11} - 57344 \, a^{7} c^{12}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}\right)} \sqrt{-\frac{b^{9} - 21 \, a b^{7} c + 189 \, a^{2} b^{5} c^{2} - 840 \, a^{3} b^{3} c^{3} + 1680 \, a^{4} b c^{4} - {\left(b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}\right)} \sqrt{\frac{b^{8} - 22 \, a b^{6} c + 219 \, a^{2} b^{4} c^{2} - 1078 \, a^{3} b^{2} c^{3} + 2401 \, a^{4} c^{4}}{b^{10} c^{10} - 20 \, a b^{8} c^{11} + 160 \, a^{2} b^{6} c^{12} - 640 \, a^{3} b^{4} c^{13} + 1280 \, a^{4} b^{2} c^{14} - 1024 \, a^{5} c^{15}}}}{b^{10} c^{5} - 20 \, a b^{8} c^{6} + 160 \, a^{2} b^{6} c^{7} - 640 \, a^{3} b^{4} c^{8} + 1280 \, a^{4} b^{2} c^{9} - 1024 \, a^{5} c^{10}}} + 27 \, {\left(21 \, a^{2} b^{8} - 447 \, a^{3} b^{6} c + 4189 \, a^{4} b^{4} c^{2} - 19208 \, a^{5} b^{2} c^{3} + 38416 \, a^{6} c^{4}\right)} \sqrt{x}\right) + 2 \, {\left(3 \, a^{2} b^{3} - 24 \, a^{3} b c + {\left(5 \, b^{4} c - 37 \, a b^{2} c^{2} + 44 \, a^{2} c^{3}\right)} x^{3} + {\left(3 \, b^{5} - 20 \, a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{2} + {\left(6 \, a b^{4} - 49 \, a^{2} b^{2} c + 28 \, a^{3} c^{2}\right)} x\right)} \sqrt{x}}{8 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4} + {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} x^{4} + 2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} x^{3} + {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} x\right)}}"," ",0,"-1/8*(3*sqrt(1/2)*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(27/2*sqrt(1/2)*(b^13 - 31*a*b^11*c + 413*a^2*b^9*c^2 - 3012*a^3*b^7*c^3 + 12496*a^4*b^5*c^4 - 27584*a^5*b^3*c^5 + 25088*a^6*b*c^6 - (b^14*c^5 - 30*a*b^12*c^6 + 416*a^2*b^10*c^7 - 3360*a^3*b^8*c^8 + 16640*a^4*b^6*c^9 - 49664*a^5*b^4*c^10 + 81920*a^6*b^2*c^11 - 57344*a^7*c^12)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)) + 27*(21*a^2*b^8 - 447*a^3*b^6*c + 4189*a^4*b^4*c^2 - 19208*a^5*b^2*c^3 + 38416*a^6*c^4)*sqrt(x)) - 3*sqrt(1/2)*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(-27/2*sqrt(1/2)*(b^13 - 31*a*b^11*c + 413*a^2*b^9*c^2 - 3012*a^3*b^7*c^3 + 12496*a^4*b^5*c^4 - 27584*a^5*b^3*c^5 + 25088*a^6*b*c^6 - (b^14*c^5 - 30*a*b^12*c^6 + 416*a^2*b^10*c^7 - 3360*a^3*b^8*c^8 + 16640*a^4*b^6*c^9 - 49664*a^5*b^4*c^10 + 81920*a^6*b^2*c^11 - 57344*a^7*c^12)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 + (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)) + 27*(21*a^2*b^8 - 447*a^3*b^6*c + 4189*a^4*b^4*c^2 - 19208*a^5*b^2*c^3 + 38416*a^6*c^4)*sqrt(x)) + 3*sqrt(1/2)*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(27/2*sqrt(1/2)*(b^13 - 31*a*b^11*c + 413*a^2*b^9*c^2 - 3012*a^3*b^7*c^3 + 12496*a^4*b^5*c^4 - 27584*a^5*b^3*c^5 + 25088*a^6*b*c^6 + (b^14*c^5 - 30*a*b^12*c^6 + 416*a^2*b^10*c^7 - 3360*a^3*b^8*c^8 + 16640*a^4*b^6*c^9 - 49664*a^5*b^4*c^10 + 81920*a^6*b^2*c^11 - 57344*a^7*c^12)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)) + 27*(21*a^2*b^8 - 447*a^3*b^6*c + 4189*a^4*b^4*c^2 - 19208*a^5*b^2*c^3 + 38416*a^6*c^4)*sqrt(x)) - 3*sqrt(1/2)*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10))*log(-27/2*sqrt(1/2)*(b^13 - 31*a*b^11*c + 413*a^2*b^9*c^2 - 3012*a^3*b^7*c^3 + 12496*a^4*b^5*c^4 - 27584*a^5*b^3*c^5 + 25088*a^6*b*c^6 + (b^14*c^5 - 30*a*b^12*c^6 + 416*a^2*b^10*c^7 - 3360*a^3*b^8*c^8 + 16640*a^4*b^6*c^9 - 49664*a^5*b^4*c^10 + 81920*a^6*b^2*c^11 - 57344*a^7*c^12)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))*sqrt(-(b^9 - 21*a*b^7*c + 189*a^2*b^5*c^2 - 840*a^3*b^3*c^3 + 1680*a^4*b*c^4 - (b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)*sqrt((b^8 - 22*a*b^6*c + 219*a^2*b^4*c^2 - 1078*a^3*b^2*c^3 + 2401*a^4*c^4)/(b^10*c^10 - 20*a*b^8*c^11 + 160*a^2*b^6*c^12 - 640*a^3*b^4*c^13 + 1280*a^4*b^2*c^14 - 1024*a^5*c^15)))/(b^10*c^5 - 20*a*b^8*c^6 + 160*a^2*b^6*c^7 - 640*a^3*b^4*c^8 + 1280*a^4*b^2*c^9 - 1024*a^5*c^10)) + 27*(21*a^2*b^8 - 447*a^3*b^6*c + 4189*a^4*b^4*c^2 - 19208*a^5*b^2*c^3 + 38416*a^6*c^4)*sqrt(x)) + 2*(3*a^2*b^3 - 24*a^3*b*c + (5*b^4*c - 37*a*b^2*c^2 + 44*a^2*c^3)*x^3 + (3*b^5 - 20*a*b^3*c - 4*a^2*b*c^2)*x^2 + (6*a*b^4 - 49*a^2*b^2*c + 28*a^3*c^2)*x)*sqrt(x))/(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4 + (b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*x^4 + 2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*x^3 + (b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*x^2 + 2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*x)","B",0
2331,1,4933,0,2.123102," ","integrate(1/x^(3/2)/(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{5} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{4} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{3} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8} - {\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{5} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{4} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{3} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8} - {\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} + {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} \sqrt{x}\right) + 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{5} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{4} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{3} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8} + {\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} \sqrt{x}\right) - 3 \, \sqrt{\frac{1}{2}} {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{5} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{4} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{3} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} \log\left(-\frac{27}{2} \, \sqrt{\frac{1}{2}} {\left(125 \, b^{17} - 3775 \, a b^{15} c + 49360 \, a^{2} b^{13} c^{2} - 362733 \, a^{3} b^{11} c^{3} + 1623534 \, a^{4} b^{9} c^{4} - 4463140 \, a^{5} b^{7} c^{5} + 7146736 \, a^{6} b^{5} c^{6} - 5684672 \, a^{7} b^{3} c^{7} + 1324800 \, a^{8} b c^{8} + {\left(5 \, a^{7} b^{16} - 152 \, a^{8} b^{14} c + 2006 \, a^{9} b^{12} c^{2} - 14960 \, a^{10} b^{10} c^{3} + 68640 \, a^{11} b^{8} c^{4} - 197120 \, a^{12} b^{6} c^{5} + 342528 \, a^{13} b^{4} c^{6} - 323584 \, a^{14} b^{2} c^{7} + 122880 \, a^{15} c^{8}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}\right)} \sqrt{-\frac{25 \, b^{11} - 495 \, a b^{9} c + 3894 \, a^{2} b^{7} c^{2} - 15015 \, a^{3} b^{5} c^{3} + 27720 \, a^{4} b^{3} c^{4} - 18480 \, a^{5} b c^{5} - {\left(a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}\right)} \sqrt{\frac{625 \, b^{12} - 12250 \, a b^{10} c + 94725 \, a^{2} b^{8} c^{2} - 351310 \, a^{3} b^{6} c^{3} + 591886 \, a^{4} b^{4} c^{4} - 312300 \, a^{5} b^{2} c^{5} + 50625 \, a^{6} c^{6}}{a^{14} b^{10} - 20 \, a^{15} b^{8} c + 160 \, a^{16} b^{6} c^{2} - 640 \, a^{17} b^{4} c^{3} + 1280 \, a^{18} b^{2} c^{4} - 1024 \, a^{19} c^{5}}}}{a^{7} b^{10} - 20 \, a^{8} b^{8} c + 160 \, a^{9} b^{6} c^{2} - 640 \, a^{10} b^{4} c^{3} + 1280 \, a^{11} b^{2} c^{4} - 1024 \, a^{12} c^{5}}} - 27 \, {\left(4125 \, b^{10} c^{4} - 77825 \, a b^{8} c^{5} + 571030 \, a^{2} b^{6} c^{6} - 1957349 \, a^{3} b^{4} c^{7} + 2835000 \, a^{4} b^{2} c^{8} - 810000 \, a^{5} c^{9}\right)} \sqrt{x}\right) + 2 \, {\left(8 \, a^{2} b^{4} - 64 \, a^{3} b^{2} c + 128 \, a^{4} c^{2} + 3 \, {\left(5 \, b^{4} c^{2} - 37 \, a b^{2} c^{3} + 60 \, a^{2} c^{4}\right)} x^{4} + {\left(30 \, b^{5} c - 227 \, a b^{3} c^{2} + 392 \, a^{2} b c^{3}\right)} x^{3} + {\left(15 \, b^{6} - 91 \, a b^{4} c + 25 \, a^{2} b^{2} c^{2} + 324 \, a^{3} c^{3}\right)} x^{2} + {\left(25 \, a b^{5} - 194 \, a^{2} b^{3} c + 364 \, a^{3} b c^{2}\right)} x\right)} \sqrt{x}}{8 \, {\left({\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} x^{5} + 2 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} x^{4} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} x^{3} + 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} x^{2} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} x\right)}}"," ",0,"-1/8*(3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^5 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^4 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^3 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(27/2*sqrt(1/2)*(125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8 - (5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)) - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*sqrt(x)) - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^5 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^4 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^3 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(-27/2*sqrt(1/2)*(125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8 - (5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 + (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)) - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*sqrt(x)) + 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^5 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^4 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^3 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(27/2*sqrt(1/2)*(125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8 + (5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)) - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*sqrt(x)) - 3*sqrt(1/2)*((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^5 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^4 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^3 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x)*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5))*log(-27/2*sqrt(1/2)*(125*b^17 - 3775*a*b^15*c + 49360*a^2*b^13*c^2 - 362733*a^3*b^11*c^3 + 1623534*a^4*b^9*c^4 - 4463140*a^5*b^7*c^5 + 7146736*a^6*b^5*c^6 - 5684672*a^7*b^3*c^7 + 1324800*a^8*b*c^8 + (5*a^7*b^16 - 152*a^8*b^14*c + 2006*a^9*b^12*c^2 - 14960*a^10*b^10*c^3 + 68640*a^11*b^8*c^4 - 197120*a^12*b^6*c^5 + 342528*a^13*b^4*c^6 - 323584*a^14*b^2*c^7 + 122880*a^15*c^8)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))*sqrt(-(25*b^11 - 495*a*b^9*c + 3894*a^2*b^7*c^2 - 15015*a^3*b^5*c^3 + 27720*a^4*b^3*c^4 - 18480*a^5*b*c^5 - (a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)*sqrt((625*b^12 - 12250*a*b^10*c + 94725*a^2*b^8*c^2 - 351310*a^3*b^6*c^3 + 591886*a^4*b^4*c^4 - 312300*a^5*b^2*c^5 + 50625*a^6*c^6)/(a^14*b^10 - 20*a^15*b^8*c + 160*a^16*b^6*c^2 - 640*a^17*b^4*c^3 + 1280*a^18*b^2*c^4 - 1024*a^19*c^5)))/(a^7*b^10 - 20*a^8*b^8*c + 160*a^9*b^6*c^2 - 640*a^10*b^4*c^3 + 1280*a^11*b^2*c^4 - 1024*a^12*c^5)) - 27*(4125*b^10*c^4 - 77825*a*b^8*c^5 + 571030*a^2*b^6*c^6 - 1957349*a^3*b^4*c^7 + 2835000*a^4*b^2*c^8 - 810000*a^5*c^9)*sqrt(x)) + 2*(8*a^2*b^4 - 64*a^3*b^2*c + 128*a^4*c^2 + 3*(5*b^4*c^2 - 37*a*b^2*c^3 + 60*a^2*c^4)*x^4 + (30*b^5*c - 227*a*b^3*c^2 + 392*a^2*b*c^3)*x^3 + (15*b^6 - 91*a*b^4*c + 25*a^2*b^2*c^2 + 324*a^3*c^3)*x^2 + (25*a*b^5 - 194*a^2*b^3*c + 364*a^3*b*c^2)*x)*sqrt(x))/((a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*x^5 + 2*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*x^4 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*x^3 + 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*x^2 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*x)","B",0
2332,1,15,0,0.397705," ","integrate((x^2-x+3)/x^(1/3),x, algorithm=""fricas"")","\frac{3}{40} \, {\left(5 \, x^{2} - 8 \, x + 60\right)} x^{\frac{2}{3}}"," ",0,"3/40*(5*x^2 - 8*x + 60)*x^(2/3)","A",0
2333,1,787,0,0.481617," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{2} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(384 \, c^{5} e^{3} x^{4} + 480 \, b c^{4} d^{3} - 240 \, {\left(3 \, b^{2} c^{3} - 8 \, a c^{4}\right)} d^{2} e + 30 \, {\left(15 \, b^{3} c^{2} - 52 \, a b c^{3}\right)} d e^{2} - {\left(105 \, b^{4} c - 460 \, a b^{2} c^{2} + 256 \, a^{2} c^{3}\right)} e^{3} + 48 \, {\left(30 \, c^{5} d e^{2} + b c^{4} e^{3}\right)} x^{3} + 8 \, {\left(240 \, c^{5} d^{2} e + 30 \, b c^{4} d e^{2} - {\left(7 \, b^{2} c^{3} - 16 \, a c^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(480 \, c^{5} d^{3} + 240 \, b c^{4} d^{2} e - 30 \, {\left(5 \, b^{2} c^{3} - 12 \, a c^{4}\right)} d e^{2} + {\left(35 \, b^{3} c^{2} - 116 \, a b c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{5}}, \frac{15 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{2} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(384 \, c^{5} e^{3} x^{4} + 480 \, b c^{4} d^{3} - 240 \, {\left(3 \, b^{2} c^{3} - 8 \, a c^{4}\right)} d^{2} e + 30 \, {\left(15 \, b^{3} c^{2} - 52 \, a b c^{3}\right)} d e^{2} - {\left(105 \, b^{4} c - 460 \, a b^{2} c^{2} + 256 \, a^{2} c^{3}\right)} e^{3} + 48 \, {\left(30 \, c^{5} d e^{2} + b c^{4} e^{3}\right)} x^{3} + 8 \, {\left(240 \, c^{5} d^{2} e + 30 \, b c^{4} d e^{2} - {\left(7 \, b^{2} c^{3} - 16 \, a c^{4}\right)} e^{3}\right)} x^{2} + 2 \, {\left(480 \, c^{5} d^{3} + 240 \, b c^{4} d^{2} e - 30 \, {\left(5 \, b^{2} c^{3} - 12 \, a c^{4}\right)} d e^{2} + {\left(35 \, b^{3} c^{2} - 116 \, a b c^{3}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, c^{5}}\right]"," ",0,"[-1/7680*(15*(32*(b^2*c^3 - 4*a*c^4)*d^3 - 48*(b^3*c^2 - 4*a*b*c^3)*d^2*e + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d*e^2 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(384*c^5*e^3*x^4 + 480*b*c^4*d^3 - 240*(3*b^2*c^3 - 8*a*c^4)*d^2*e + 30*(15*b^3*c^2 - 52*a*b*c^3)*d*e^2 - (105*b^4*c - 460*a*b^2*c^2 + 256*a^2*c^3)*e^3 + 48*(30*c^5*d*e^2 + b*c^4*e^3)*x^3 + 8*(240*c^5*d^2*e + 30*b*c^4*d*e^2 - (7*b^2*c^3 - 16*a*c^4)*e^3)*x^2 + 2*(480*c^5*d^3 + 240*b*c^4*d^2*e - 30*(5*b^2*c^3 - 12*a*c^4)*d*e^2 + (35*b^3*c^2 - 116*a*b*c^3)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^5, 1/3840*(15*(32*(b^2*c^3 - 4*a*c^4)*d^3 - 48*(b^3*c^2 - 4*a*b*c^3)*d^2*e + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d*e^2 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(384*c^5*e^3*x^4 + 480*b*c^4*d^3 - 240*(3*b^2*c^3 - 8*a*c^4)*d^2*e + 30*(15*b^3*c^2 - 52*a*b*c^3)*d*e^2 - (105*b^4*c - 460*a*b^2*c^2 + 256*a^2*c^3)*e^3 + 48*(30*c^5*d*e^2 + b*c^4*e^3)*x^3 + 8*(240*c^5*d^2*e + 30*b*c^4*d*e^2 - (7*b^2*c^3 - 16*a*c^4)*e^3)*x^2 + 2*(480*c^5*d^3 + 240*b*c^4*d^2*e - 30*(5*b^2*c^3 - 12*a*c^4)*d*e^2 + (35*b^3*c^2 - 116*a*b*c^3)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
2334,1,505,0,0.450774," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, c^{4} e^{2} x^{3} + 48 \, b c^{3} d^{2} - 16 \, {\left(3 \, b^{2} c^{2} - 8 \, a c^{3}\right)} d e + {\left(15 \, b^{3} c - 52 \, a b c^{2}\right)} e^{2} + 8 \, {\left(16 \, c^{4} d e + b c^{3} e^{2}\right)} x^{2} + 2 \, {\left(48 \, c^{4} d^{2} + 16 \, b c^{3} d e - {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{4}}, \frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(48 \, c^{4} e^{2} x^{3} + 48 \, b c^{3} d^{2} - 16 \, {\left(3 \, b^{2} c^{2} - 8 \, a c^{3}\right)} d e + {\left(15 \, b^{3} c - 52 \, a b c^{2}\right)} e^{2} + 8 \, {\left(16 \, c^{4} d e + b c^{3} e^{2}\right)} x^{2} + 2 \, {\left(48 \, c^{4} d^{2} + 16 \, b c^{3} d e - {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{4}}\right]"," ",0,"[1/768*(3*(16*(b^2*c^2 - 4*a*c^3)*d^2 - 16*(b^3*c - 4*a*b*c^2)*d*e + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(48*c^4*e^2*x^3 + 48*b*c^3*d^2 - 16*(3*b^2*c^2 - 8*a*c^3)*d*e + (15*b^3*c - 52*a*b*c^2)*e^2 + 8*(16*c^4*d*e + b*c^3*e^2)*x^2 + 2*(48*c^4*d^2 + 16*b*c^3*d*e - (5*b^2*c^2 - 12*a*c^3)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/384*(3*(16*(b^2*c^2 - 4*a*c^3)*d^2 - 16*(b^3*c - 4*a*b*c^2)*d*e + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(48*c^4*e^2*x^3 + 48*b*c^3*d^2 - 16*(3*b^2*c^2 - 8*a*c^3)*d*e + (15*b^3*c - 52*a*b*c^2)*e^2 + 8*(16*c^4*d*e + b*c^3*e^2)*x^2 + 2*(48*c^4*d^2 + 16*b*c^3*d*e - (5*b^2*c^2 - 12*a*c^3)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
2335,1,297,0,0.438735," ","integrate((e*x+d)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, c^{3} e x^{2} + 6 \, b c^{2} d - {\left(3 \, b^{2} c - 8 \, a c^{2}\right)} e + 2 \, {\left(6 \, c^{3} d + b c^{2} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, c^{3}}, \frac{3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(8 \, c^{3} e x^{2} + 6 \, b c^{2} d - {\left(3 \, b^{2} c - 8 \, a c^{2}\right)} e + 2 \, {\left(6 \, c^{3} d + b c^{2} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, c^{3}}\right]"," ",0,"[1/96*(3*(2*(b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(8*c^3*e*x^2 + 6*b*c^2*d - (3*b^2*c - 8*a*c^2)*e + 2*(6*c^3*d + b*c^2*e)*x)*sqrt(c*x^2 + b*x + a))/c^3, 1/48*(3*(2*(b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(8*c^3*e*x^2 + 6*b*c^2*d - (3*b^2*c - 8*a*c^2)*e + 2*(6*c^3*d + b*c^2*e)*x)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
2336,1,177,0,0.432133," ","integrate((c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, c^{2} x + b c\right)} \sqrt{c x^{2} + b x + a}}{16 \, c^{2}}, \frac{{\left(b^{2} - 4 \, a c\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(2 \, c^{2} x + b c\right)} \sqrt{c x^{2} + b x + a}}{8 \, c^{2}}\right]"," ",0,"[-1/16*((b^2 - 4*a*c)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(2*c^2*x + b*c)*sqrt(c*x^2 + b*x + a))/c^2, 1/8*((b^2 - 4*a*c)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(2*c^2*x + b*c)*sqrt(c*x^2 + b*x + a))/c^2]","A",0
2337,1,992,0,1.463435," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c x^{2} + b x + a} c e - {\left(2 \, c d - b e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, \sqrt{c d^{2} - b d e + a e^{2}} c \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{4 \, c e^{2}}, \frac{2 \, \sqrt{c x^{2} + b x + a} c e + {\left(2 \, c d - b e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + \sqrt{c d^{2} - b d e + a e^{2}} c \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, c e^{2}}, \frac{4 \, \sqrt{c x^{2} + b x + a} c e + 4 \, \sqrt{-c d^{2} + b d e - a e^{2}} c \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - {\left(2 \, c d - b e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right)}{4 \, c e^{2}}, \frac{2 \, \sqrt{c x^{2} + b x + a} c e + 2 \, \sqrt{-c d^{2} + b d e - a e^{2}} c \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + {\left(2 \, c d - b e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{2 \, c e^{2}}\right]"," ",0,"[1/4*(4*sqrt(c*x^2 + b*x + a)*c*e - (2*c*d - b*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 2*sqrt(c*d^2 - b*d*e + a*e^2)*c*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/(c*e^2), 1/2*(2*sqrt(c*x^2 + b*x + a)*c*e + (2*c*d - b*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + sqrt(c*d^2 - b*d*e + a*e^2)*c*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)))/(c*e^2), 1/4*(4*sqrt(c*x^2 + b*x + a)*c*e + 4*sqrt(-c*d^2 + b*d*e - a*e^2)*c*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - (2*c*d - b*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c))/(c*e^2), 1/2*(2*sqrt(c*x^2 + b*x + a)*c*e + 2*sqrt(-c*d^2 + b*d*e - a*e^2)*c*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + (2*c*d - b*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)))/(c*e^2)]","A",0
2338,1,1456,0,2.183367," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - {\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(c d^{3} e^{2} - b d^{2} e^{3} + a d e^{4} + {\left(c d^{2} e^{3} - b d e^{4} + a e^{5}\right)} x\right)}}, -\frac{{\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c d^{3} e^{2} - b d^{2} e^{3} + a d e^{4} + {\left(c d^{2} e^{3} - b d e^{4} + a e^{5}\right)} x\right)}}, -\frac{4 \, {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + {\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(c d^{3} e^{2} - b d^{2} e^{3} + a d e^{4} + {\left(c d^{2} e^{3} - b d e^{4} + a e^{5}\right)} x\right)}}, -\frac{{\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(c d^{3} - b d^{2} e + a d e^{2} + {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c d^{3} e^{2} - b d^{2} e^{3} + a d e^{4} + {\left(c d^{2} e^{3} - b d e^{4} + a e^{5}\right)} x\right)}}\right]"," ",0,"[1/4*(2*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - (2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(c*d^2*e - b*d*e^2 + a*e^3)*sqrt(c*x^2 + b*x + a))/(c*d^3*e^2 - b*d^2*e^3 + a*d*e^4 + (c*d^2*e^3 - b*d*e^4 + a*e^5)*x), -1/2*((2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - (c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 2*(c*d^2*e - b*d*e^2 + a*e^3)*sqrt(c*x^2 + b*x + a))/(c*d^3*e^2 - b*d^2*e^3 + a*d*e^4 + (c*d^2*e^3 - b*d*e^4 + a*e^5)*x), -1/4*(4*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + (2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(c*d^2*e - b*d*e^2 + a*e^3)*sqrt(c*x^2 + b*x + a))/(c*d^3*e^2 - b*d^2*e^3 + a*d*e^4 + (c*d^2*e^3 - b*d*e^4 + a*e^5)*x), -1/2*((2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(c*d^3 - b*d^2*e + a*d*e^2 + (c*d^2*e - b*d*e^2 + a*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(c*d^2*e - b*d*e^2 + a*e^3)*sqrt(c*x^2 + b*x + a))/(c*d^3*e^2 - b*d^2*e^3 + a*d*e^4 + (c*d^2*e^3 - b*d*e^4 + a*e^5)*x)]","B",0
2339,1,918,0,1.121337," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(b^{2} - 4 \, a c\right)} e^{2} x^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} d e x + {\left(b^{2} - 4 \, a c\right)} d^{2}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(b c d^{3} + 3 \, a b d e^{2} - 2 \, a^{2} e^{3} - {\left(b^{2} + 2 \, a c\right)} d^{2} e + {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e - a b e^{3} + {\left(b^{2} + 2 \, a c\right)} d e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(c^{2} d^{6} - 2 \, b c d^{5} e - 2 \, a b d^{3} e^{3} + a^{2} d^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{4} e^{2} + {\left(c^{2} d^{4} e^{2} - 2 \, b c d^{3} e^{3} - 2 \, a b d e^{5} + a^{2} e^{6} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e - 2 \, b c d^{4} e^{2} - 2 \, a b d^{2} e^{4} + a^{2} d e^{5} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} x\right)}}, -\frac{{\left({\left(b^{2} - 4 \, a c\right)} e^{2} x^{2} + 2 \, {\left(b^{2} - 4 \, a c\right)} d e x + {\left(b^{2} - 4 \, a c\right)} d^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(b c d^{3} + 3 \, a b d e^{2} - 2 \, a^{2} e^{3} - {\left(b^{2} + 2 \, a c\right)} d^{2} e + {\left(2 \, c^{2} d^{3} - 3 \, b c d^{2} e - a b e^{3} + {\left(b^{2} + 2 \, a c\right)} d e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(c^{2} d^{6} - 2 \, b c d^{5} e - 2 \, a b d^{3} e^{3} + a^{2} d^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{4} e^{2} + {\left(c^{2} d^{4} e^{2} - 2 \, b c d^{3} e^{3} - 2 \, a b d e^{5} + a^{2} e^{6} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(c^{2} d^{5} e - 2 \, b c d^{4} e^{2} - 2 \, a b d^{2} e^{4} + a^{2} d e^{5} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/16*(((b^2 - 4*a*c)*e^2*x^2 + 2*(b^2 - 4*a*c)*d*e*x + (b^2 - 4*a*c)*d^2)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(b*c*d^3 + 3*a*b*d*e^2 - 2*a^2*e^3 - (b^2 + 2*a*c)*d^2*e + (2*c^2*d^3 - 3*b*c*d^2*e - a*b*e^3 + (b^2 + 2*a*c)*d*e^2)*x)*sqrt(c*x^2 + b*x + a))/(c^2*d^6 - 2*b*c*d^5*e - 2*a*b*d^3*e^3 + a^2*d^2*e^4 + (b^2 + 2*a*c)*d^4*e^2 + (c^2*d^4*e^2 - 2*b*c*d^3*e^3 - 2*a*b*d*e^5 + a^2*e^6 + (b^2 + 2*a*c)*d^2*e^4)*x^2 + 2*(c^2*d^5*e - 2*b*c*d^4*e^2 - 2*a*b*d^2*e^4 + a^2*d*e^5 + (b^2 + 2*a*c)*d^3*e^3)*x), -1/8*(((b^2 - 4*a*c)*e^2*x^2 + 2*(b^2 - 4*a*c)*d*e*x + (b^2 - 4*a*c)*d^2)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(b*c*d^3 + 3*a*b*d*e^2 - 2*a^2*e^3 - (b^2 + 2*a*c)*d^2*e + (2*c^2*d^3 - 3*b*c*d^2*e - a*b*e^3 + (b^2 + 2*a*c)*d*e^2)*x)*sqrt(c*x^2 + b*x + a))/(c^2*d^6 - 2*b*c*d^5*e - 2*a*b*d^3*e^3 + a^2*d^2*e^4 + (b^2 + 2*a*c)*d^4*e^2 + (c^2*d^4*e^2 - 2*b*c*d^3*e^3 - 2*a*b*d*e^5 + a^2*e^6 + (b^2 + 2*a*c)*d^2*e^4)*x^2 + 2*(c^2*d^5*e - 2*b*c*d^4*e^2 - 2*a*b*d^2*e^4 + a^2*d*e^5 + (b^2 + 2*a*c)*d^3*e^3)*x)]","B",0
2340,1,1950,0,3.652648," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^4,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} - {\left(b^{3} - 4 \, a b c\right)} d^{3} e + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{3} - {\left(b^{3} - 4 \, a b c\right)} e^{4}\right)} x^{3} + 3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} - 4 \, a b c\right)} d e^{3}\right)} x^{2} + 3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} e - {\left(b^{3} - 4 \, a b c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(6 \, b c^{2} d^{5} + 22 \, a^{2} b d e^{4} - 8 \, a^{3} e^{5} - {\left(9 \, b^{2} c + 20 \, a c^{2}\right)} d^{4} e + {\left(3 \, b^{3} + 40 \, a b c\right)} d^{3} e^{2} - {\left(17 \, a b^{2} + 28 \, a^{2} c\right)} d^{2} e^{3} + {\left(4 \, c^{3} d^{4} e - 8 \, b c^{2} d^{3} e^{2} + {\left(7 \, b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{3} - {\left(3 \, b^{3} - 4 \, a b c\right)} d e^{4} + {\left(3 \, a b^{2} - 8 \, a^{2} c\right)} e^{5}\right)} x^{2} + 2 \, {\left(6 \, c^{3} d^{5} - 13 \, b c^{2} d^{4} e + 11 \, b^{2} c d^{3} e^{2} - a^{2} b e^{5} - 2 \, {\left(2 \, b^{3} + a b c\right)} d^{2} e^{3} + {\left(5 \, a b^{2} - 6 \, a^{2} c\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(c^{3} d^{9} - 3 \, b c^{2} d^{8} e - 3 \, a^{2} b d^{4} e^{5} + a^{3} d^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{7} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{6} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{5} e^{4} + {\left(c^{3} d^{6} e^{3} - 3 \, b c^{2} d^{5} e^{4} - 3 \, a^{2} b d e^{8} + a^{3} e^{9} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{5} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{7}\right)} x^{3} + 3 \, {\left(c^{3} d^{7} e^{2} - 3 \, b c^{2} d^{6} e^{3} - 3 \, a^{2} b d^{2} e^{7} + a^{3} d e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{6}\right)} x^{2} + 3 \, {\left(c^{3} d^{8} e - 3 \, b c^{2} d^{7} e^{2} - 3 \, a^{2} b d^{3} e^{6} + a^{3} d^{2} e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{5}\right)} x\right)}}, -\frac{3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{4} - {\left(b^{3} - 4 \, a b c\right)} d^{3} e + {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{3} - {\left(b^{3} - 4 \, a b c\right)} e^{4}\right)} x^{3} + 3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{2} - {\left(b^{3} - 4 \, a b c\right)} d e^{3}\right)} x^{2} + 3 \, {\left(2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} e - {\left(b^{3} - 4 \, a b c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(6 \, b c^{2} d^{5} + 22 \, a^{2} b d e^{4} - 8 \, a^{3} e^{5} - {\left(9 \, b^{2} c + 20 \, a c^{2}\right)} d^{4} e + {\left(3 \, b^{3} + 40 \, a b c\right)} d^{3} e^{2} - {\left(17 \, a b^{2} + 28 \, a^{2} c\right)} d^{2} e^{3} + {\left(4 \, c^{3} d^{4} e - 8 \, b c^{2} d^{3} e^{2} + {\left(7 \, b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{3} - {\left(3 \, b^{3} - 4 \, a b c\right)} d e^{4} + {\left(3 \, a b^{2} - 8 \, a^{2} c\right)} e^{5}\right)} x^{2} + 2 \, {\left(6 \, c^{3} d^{5} - 13 \, b c^{2} d^{4} e + 11 \, b^{2} c d^{3} e^{2} - a^{2} b e^{5} - 2 \, {\left(2 \, b^{3} + a b c\right)} d^{2} e^{3} + {\left(5 \, a b^{2} - 6 \, a^{2} c\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(c^{3} d^{9} - 3 \, b c^{2} d^{8} e - 3 \, a^{2} b d^{4} e^{5} + a^{3} d^{3} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{7} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{6} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{5} e^{4} + {\left(c^{3} d^{6} e^{3} - 3 \, b c^{2} d^{5} e^{4} - 3 \, a^{2} b d e^{8} + a^{3} e^{9} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{5} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{7}\right)} x^{3} + 3 \, {\left(c^{3} d^{7} e^{2} - 3 \, b c^{2} d^{6} e^{3} - 3 \, a^{2} b d^{2} e^{7} + a^{3} d e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{6}\right)} x^{2} + 3 \, {\left(c^{3} d^{8} e - 3 \, b c^{2} d^{7} e^{2} - 3 \, a^{2} b d^{3} e^{6} + a^{3} d^{2} e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{5}\right)} x\right)}}\right]"," ",0,"[1/96*(3*(2*(b^2*c - 4*a*c^2)*d^4 - (b^3 - 4*a*b*c)*d^3*e + (2*(b^2*c - 4*a*c^2)*d*e^3 - (b^3 - 4*a*b*c)*e^4)*x^3 + 3*(2*(b^2*c - 4*a*c^2)*d^2*e^2 - (b^3 - 4*a*b*c)*d*e^3)*x^2 + 3*(2*(b^2*c - 4*a*c^2)*d^3*e - (b^3 - 4*a*b*c)*d^2*e^2)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(6*b*c^2*d^5 + 22*a^2*b*d*e^4 - 8*a^3*e^5 - (9*b^2*c + 20*a*c^2)*d^4*e + (3*b^3 + 40*a*b*c)*d^3*e^2 - (17*a*b^2 + 28*a^2*c)*d^2*e^3 + (4*c^3*d^4*e - 8*b*c^2*d^3*e^2 + (7*b^2*c - 4*a*c^2)*d^2*e^3 - (3*b^3 - 4*a*b*c)*d*e^4 + (3*a*b^2 - 8*a^2*c)*e^5)*x^2 + 2*(6*c^3*d^5 - 13*b*c^2*d^4*e + 11*b^2*c*d^3*e^2 - a^2*b*e^5 - 2*(2*b^3 + a*b*c)*d^2*e^3 + (5*a*b^2 - 6*a^2*c)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^9 - 3*b*c^2*d^8*e - 3*a^2*b*d^4*e^5 + a^3*d^3*e^6 + 3*(b^2*c + a*c^2)*d^7*e^2 - (b^3 + 6*a*b*c)*d^6*e^3 + 3*(a*b^2 + a^2*c)*d^5*e^4 + (c^3*d^6*e^3 - 3*b*c^2*d^5*e^4 - 3*a^2*b*d*e^8 + a^3*e^9 + 3*(b^2*c + a*c^2)*d^4*e^5 - (b^3 + 6*a*b*c)*d^3*e^6 + 3*(a*b^2 + a^2*c)*d^2*e^7)*x^3 + 3*(c^3*d^7*e^2 - 3*b*c^2*d^6*e^3 - 3*a^2*b*d^2*e^7 + a^3*d*e^8 + 3*(b^2*c + a*c^2)*d^5*e^4 - (b^3 + 6*a*b*c)*d^4*e^5 + 3*(a*b^2 + a^2*c)*d^3*e^6)*x^2 + 3*(c^3*d^8*e - 3*b*c^2*d^7*e^2 - 3*a^2*b*d^3*e^6 + a^3*d^2*e^7 + 3*(b^2*c + a*c^2)*d^6*e^3 - (b^3 + 6*a*b*c)*d^5*e^4 + 3*(a*b^2 + a^2*c)*d^4*e^5)*x), -1/48*(3*(2*(b^2*c - 4*a*c^2)*d^4 - (b^3 - 4*a*b*c)*d^3*e + (2*(b^2*c - 4*a*c^2)*d*e^3 - (b^3 - 4*a*b*c)*e^4)*x^3 + 3*(2*(b^2*c - 4*a*c^2)*d^2*e^2 - (b^3 - 4*a*b*c)*d*e^3)*x^2 + 3*(2*(b^2*c - 4*a*c^2)*d^3*e - (b^3 - 4*a*b*c)*d^2*e^2)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(6*b*c^2*d^5 + 22*a^2*b*d*e^4 - 8*a^3*e^5 - (9*b^2*c + 20*a*c^2)*d^4*e + (3*b^3 + 40*a*b*c)*d^3*e^2 - (17*a*b^2 + 28*a^2*c)*d^2*e^3 + (4*c^3*d^4*e - 8*b*c^2*d^3*e^2 + (7*b^2*c - 4*a*c^2)*d^2*e^3 - (3*b^3 - 4*a*b*c)*d*e^4 + (3*a*b^2 - 8*a^2*c)*e^5)*x^2 + 2*(6*c^3*d^5 - 13*b*c^2*d^4*e + 11*b^2*c*d^3*e^2 - a^2*b*e^5 - 2*(2*b^3 + a*b*c)*d^2*e^3 + (5*a*b^2 - 6*a^2*c)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^9 - 3*b*c^2*d^8*e - 3*a^2*b*d^4*e^5 + a^3*d^3*e^6 + 3*(b^2*c + a*c^2)*d^7*e^2 - (b^3 + 6*a*b*c)*d^6*e^3 + 3*(a*b^2 + a^2*c)*d^5*e^4 + (c^3*d^6*e^3 - 3*b*c^2*d^5*e^4 - 3*a^2*b*d*e^8 + a^3*e^9 + 3*(b^2*c + a*c^2)*d^4*e^5 - (b^3 + 6*a*b*c)*d^3*e^6 + 3*(a*b^2 + a^2*c)*d^2*e^7)*x^3 + 3*(c^3*d^7*e^2 - 3*b*c^2*d^6*e^3 - 3*a^2*b*d^2*e^7 + a^3*d*e^8 + 3*(b^2*c + a*c^2)*d^5*e^4 - (b^3 + 6*a*b*c)*d^4*e^5 + 3*(a*b^2 + a^2*c)*d^3*e^6)*x^2 + 3*(c^3*d^8*e - 3*b*c^2*d^7*e^2 - 3*a^2*b*d^3*e^6 + a^3*d^2*e^7 + 3*(b^2*c + a*c^2)*d^6*e^3 - (b^3 + 6*a*b*c)*d^5*e^4 + 3*(a*b^2 + a^2*c)*d^4*e^5)*x)]","B",0
2341,1,3780,0,20.819005," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{6} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{5} e + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{4} e^{2} + {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{4} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{5} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{6}\right)} x^{4} + 4 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} e^{3} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{4} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d e^{5}\right)} x^{3} + 6 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e^{2} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{3} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{5} e - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} e^{2} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(48 \, b c^{3} d^{7} + 184 \, a^{3} b d e^{6} - 48 \, a^{4} e^{7} - 32 \, {\left(3 \, b^{2} c^{2} + 7 \, a c^{3}\right)} d^{6} e + {\left(63 \, b^{3} c + 572 \, a b c^{2}\right)} d^{5} e^{2} - {\left(15 \, b^{4} + 466 \, a b^{2} c + 376 \, a^{2} c^{2}\right)} d^{4} e^{3} + 7 \, {\left(19 \, a b^{3} + 84 \, a^{2} b c\right)} d^{3} e^{4} - 2 \, {\left(127 \, a^{2} b^{2} + 100 \, a^{3} c\right)} d^{2} e^{5} + {\left(16 \, c^{4} d^{5} e^{2} - 40 \, b c^{3} d^{4} e^{3} + 2 \, {\left(31 \, b^{2} c^{2} - 44 \, a c^{3}\right)} d^{3} e^{4} - {\left(53 \, b^{3} c - 132 \, a b c^{2}\right)} d^{2} e^{5} + {\left(15 \, b^{4} - 14 \, a b^{2} c - 104 \, a^{2} c^{2}\right)} d e^{6} - {\left(15 \, a b^{3} - 52 \, a^{2} b c\right)} e^{7}\right)} x^{3} + {\left(64 \, c^{4} d^{6} e - 168 \, b c^{3} d^{5} e^{2} + 4 \, {\left(61 \, b^{2} c^{2} - 64 \, a c^{3}\right)} d^{4} e^{3} - 5 \, {\left(39 \, b^{3} c - 76 \, a b c^{2}\right)} d^{3} e^{4} + {\left(55 \, b^{4} - 14 \, a b^{2} c - 344 \, a^{2} c^{2}\right)} d^{2} e^{5} - {\left(65 \, a b^{3} - 188 \, a^{2} b c\right)} d e^{6} + 2 \, {\left(5 \, a^{2} b^{2} - 12 \, a^{3} c\right)} e^{7}\right)} x^{2} + {\left(96 \, c^{4} d^{7} - 272 \, b c^{3} d^{6} e - 8 \, a^{3} b e^{7} + 2 \, {\left(187 \, b^{2} c^{2} - 100 \, a c^{3}\right)} d^{5} e^{2} - {\left(271 \, b^{3} c - 244 \, a b c^{2}\right)} d^{4} e^{3} + {\left(73 \, b^{4} + 110 \, a b^{2} c - 328 \, a^{2} c^{2}\right)} d^{3} e^{4} - {\left(109 \, a b^{3} - 148 \, a^{2} b c\right)} d^{2} e^{5} + 4 \, {\left(11 \, a^{2} b^{2} - 8 \, a^{3} c\right)} d e^{6}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, {\left(c^{4} d^{12} - 4 \, b c^{3} d^{11} e - 4 \, a^{3} b d^{5} e^{7} + a^{4} d^{4} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{10} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{9} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{8} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{7} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{6} e^{6} + {\left(c^{4} d^{8} e^{4} - 4 \, b c^{3} d^{7} e^{5} - 4 \, a^{3} b d e^{11} + a^{4} e^{12} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{6} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{8} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{9} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{10}\right)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, b c^{3} d^{8} e^{4} - 4 \, a^{3} b d^{2} e^{10} + a^{4} d e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{9}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, b c^{3} d^{9} e^{3} - 4 \, a^{3} b d^{3} e^{9} + a^{4} d^{2} e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{8}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, b c^{3} d^{10} e^{2} - 4 \, a^{3} b d^{4} e^{8} + a^{4} d^{3} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{7}\right)} x\right)}}, -\frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{6} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{5} e + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{4} e^{2} + {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{4} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{5} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{6}\right)} x^{4} + 4 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{3} e^{3} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{4} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d e^{5}\right)} x^{3} + 6 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e^{2} - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{3} e^{3} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} e^{4}\right)} x^{2} + 4 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{5} e - 16 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{4} e^{2} + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, b c^{3} d^{7} + 184 \, a^{3} b d e^{6} - 48 \, a^{4} e^{7} - 32 \, {\left(3 \, b^{2} c^{2} + 7 \, a c^{3}\right)} d^{6} e + {\left(63 \, b^{3} c + 572 \, a b c^{2}\right)} d^{5} e^{2} - {\left(15 \, b^{4} + 466 \, a b^{2} c + 376 \, a^{2} c^{2}\right)} d^{4} e^{3} + 7 \, {\left(19 \, a b^{3} + 84 \, a^{2} b c\right)} d^{3} e^{4} - 2 \, {\left(127 \, a^{2} b^{2} + 100 \, a^{3} c\right)} d^{2} e^{5} + {\left(16 \, c^{4} d^{5} e^{2} - 40 \, b c^{3} d^{4} e^{3} + 2 \, {\left(31 \, b^{2} c^{2} - 44 \, a c^{3}\right)} d^{3} e^{4} - {\left(53 \, b^{3} c - 132 \, a b c^{2}\right)} d^{2} e^{5} + {\left(15 \, b^{4} - 14 \, a b^{2} c - 104 \, a^{2} c^{2}\right)} d e^{6} - {\left(15 \, a b^{3} - 52 \, a^{2} b c\right)} e^{7}\right)} x^{3} + {\left(64 \, c^{4} d^{6} e - 168 \, b c^{3} d^{5} e^{2} + 4 \, {\left(61 \, b^{2} c^{2} - 64 \, a c^{3}\right)} d^{4} e^{3} - 5 \, {\left(39 \, b^{3} c - 76 \, a b c^{2}\right)} d^{3} e^{4} + {\left(55 \, b^{4} - 14 \, a b^{2} c - 344 \, a^{2} c^{2}\right)} d^{2} e^{5} - {\left(65 \, a b^{3} - 188 \, a^{2} b c\right)} d e^{6} + 2 \, {\left(5 \, a^{2} b^{2} - 12 \, a^{3} c\right)} e^{7}\right)} x^{2} + {\left(96 \, c^{4} d^{7} - 272 \, b c^{3} d^{6} e - 8 \, a^{3} b e^{7} + 2 \, {\left(187 \, b^{2} c^{2} - 100 \, a c^{3}\right)} d^{5} e^{2} - {\left(271 \, b^{3} c - 244 \, a b c^{2}\right)} d^{4} e^{3} + {\left(73 \, b^{4} + 110 \, a b^{2} c - 328 \, a^{2} c^{2}\right)} d^{3} e^{4} - {\left(109 \, a b^{3} - 148 \, a^{2} b c\right)} d^{2} e^{5} + 4 \, {\left(11 \, a^{2} b^{2} - 8 \, a^{3} c\right)} d e^{6}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, {\left(c^{4} d^{12} - 4 \, b c^{3} d^{11} e - 4 \, a^{3} b d^{5} e^{7} + a^{4} d^{4} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{10} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{9} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{8} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{7} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{6} e^{6} + {\left(c^{4} d^{8} e^{4} - 4 \, b c^{3} d^{7} e^{5} - 4 \, a^{3} b d e^{11} + a^{4} e^{12} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{6} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{8} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{9} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{10}\right)} x^{4} + 4 \, {\left(c^{4} d^{9} e^{3} - 4 \, b c^{3} d^{8} e^{4} - 4 \, a^{3} b d^{2} e^{10} + a^{4} d e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{9}\right)} x^{3} + 6 \, {\left(c^{4} d^{10} e^{2} - 4 \, b c^{3} d^{9} e^{3} - 4 \, a^{3} b d^{3} e^{9} + a^{4} d^{2} e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{8}\right)} x^{2} + 4 \, {\left(c^{4} d^{11} e - 4 \, b c^{3} d^{10} e^{2} - 4 \, a^{3} b d^{4} e^{8} + a^{4} d^{3} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{7}\right)} x\right)}}\right]"," ",0,"[1/768*(3*(16*(b^2*c^2 - 4*a*c^3)*d^6 - 16*(b^3*c - 4*a*b*c^2)*d^5*e + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d^4*e^2 + (16*(b^2*c^2 - 4*a*c^3)*d^2*e^4 - 16*(b^3*c - 4*a*b*c^2)*d*e^5 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*e^6)*x^4 + 4*(16*(b^2*c^2 - 4*a*c^3)*d^3*e^3 - 16*(b^3*c - 4*a*b*c^2)*d^2*e^4 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d*e^5)*x^3 + 6*(16*(b^2*c^2 - 4*a*c^3)*d^4*e^2 - 16*(b^3*c - 4*a*b*c^2)*d^3*e^3 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d^2*e^4)*x^2 + 4*(16*(b^2*c^2 - 4*a*c^3)*d^5*e - 16*(b^3*c - 4*a*b*c^2)*d^4*e^2 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d^3*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(48*b*c^3*d^7 + 184*a^3*b*d*e^6 - 48*a^4*e^7 - 32*(3*b^2*c^2 + 7*a*c^3)*d^6*e + (63*b^3*c + 572*a*b*c^2)*d^5*e^2 - (15*b^4 + 466*a*b^2*c + 376*a^2*c^2)*d^4*e^3 + 7*(19*a*b^3 + 84*a^2*b*c)*d^3*e^4 - 2*(127*a^2*b^2 + 100*a^3*c)*d^2*e^5 + (16*c^4*d^5*e^2 - 40*b*c^3*d^4*e^3 + 2*(31*b^2*c^2 - 44*a*c^3)*d^3*e^4 - (53*b^3*c - 132*a*b*c^2)*d^2*e^5 + (15*b^4 - 14*a*b^2*c - 104*a^2*c^2)*d*e^6 - (15*a*b^3 - 52*a^2*b*c)*e^7)*x^3 + (64*c^4*d^6*e - 168*b*c^3*d^5*e^2 + 4*(61*b^2*c^2 - 64*a*c^3)*d^4*e^3 - 5*(39*b^3*c - 76*a*b*c^2)*d^3*e^4 + (55*b^4 - 14*a*b^2*c - 344*a^2*c^2)*d^2*e^5 - (65*a*b^3 - 188*a^2*b*c)*d*e^6 + 2*(5*a^2*b^2 - 12*a^3*c)*e^7)*x^2 + (96*c^4*d^7 - 272*b*c^3*d^6*e - 8*a^3*b*e^7 + 2*(187*b^2*c^2 - 100*a*c^3)*d^5*e^2 - (271*b^3*c - 244*a*b*c^2)*d^4*e^3 + (73*b^4 + 110*a*b^2*c - 328*a^2*c^2)*d^3*e^4 - (109*a*b^3 - 148*a^2*b*c)*d^2*e^5 + 4*(11*a^2*b^2 - 8*a^3*c)*d*e^6)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^12 - 4*b*c^3*d^11*e - 4*a^3*b*d^5*e^7 + a^4*d^4*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^10*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^9*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^8*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^7*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^6*e^6 + (c^4*d^8*e^4 - 4*b*c^3*d^7*e^5 - 4*a^3*b*d*e^11 + a^4*e^12 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^6 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^8 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^9 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^10)*x^4 + 4*(c^4*d^9*e^3 - 4*b*c^3*d^8*e^4 - 4*a^3*b*d^2*e^10 + a^4*d*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^9)*x^3 + 6*(c^4*d^10*e^2 - 4*b*c^3*d^9*e^3 - 4*a^3*b*d^3*e^9 + a^4*d^2*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^8)*x^2 + 4*(c^4*d^11*e - 4*b*c^3*d^10*e^2 - 4*a^3*b*d^4*e^8 + a^4*d^3*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^7)*x), -1/384*(3*(16*(b^2*c^2 - 4*a*c^3)*d^6 - 16*(b^3*c - 4*a*b*c^2)*d^5*e + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d^4*e^2 + (16*(b^2*c^2 - 4*a*c^3)*d^2*e^4 - 16*(b^3*c - 4*a*b*c^2)*d*e^5 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*e^6)*x^4 + 4*(16*(b^2*c^2 - 4*a*c^3)*d^3*e^3 - 16*(b^3*c - 4*a*b*c^2)*d^2*e^4 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d*e^5)*x^3 + 6*(16*(b^2*c^2 - 4*a*c^3)*d^4*e^2 - 16*(b^3*c - 4*a*b*c^2)*d^3*e^3 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d^2*e^4)*x^2 + 4*(16*(b^2*c^2 - 4*a*c^3)*d^5*e - 16*(b^3*c - 4*a*b*c^2)*d^4*e^2 + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*d^3*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(48*b*c^3*d^7 + 184*a^3*b*d*e^6 - 48*a^4*e^7 - 32*(3*b^2*c^2 + 7*a*c^3)*d^6*e + (63*b^3*c + 572*a*b*c^2)*d^5*e^2 - (15*b^4 + 466*a*b^2*c + 376*a^2*c^2)*d^4*e^3 + 7*(19*a*b^3 + 84*a^2*b*c)*d^3*e^4 - 2*(127*a^2*b^2 + 100*a^3*c)*d^2*e^5 + (16*c^4*d^5*e^2 - 40*b*c^3*d^4*e^3 + 2*(31*b^2*c^2 - 44*a*c^3)*d^3*e^4 - (53*b^3*c - 132*a*b*c^2)*d^2*e^5 + (15*b^4 - 14*a*b^2*c - 104*a^2*c^2)*d*e^6 - (15*a*b^3 - 52*a^2*b*c)*e^7)*x^3 + (64*c^4*d^6*e - 168*b*c^3*d^5*e^2 + 4*(61*b^2*c^2 - 64*a*c^3)*d^4*e^3 - 5*(39*b^3*c - 76*a*b*c^2)*d^3*e^4 + (55*b^4 - 14*a*b^2*c - 344*a^2*c^2)*d^2*e^5 - (65*a*b^3 - 188*a^2*b*c)*d*e^6 + 2*(5*a^2*b^2 - 12*a^3*c)*e^7)*x^2 + (96*c^4*d^7 - 272*b*c^3*d^6*e - 8*a^3*b*e^7 + 2*(187*b^2*c^2 - 100*a*c^3)*d^5*e^2 - (271*b^3*c - 244*a*b*c^2)*d^4*e^3 + (73*b^4 + 110*a*b^2*c - 328*a^2*c^2)*d^3*e^4 - (109*a*b^3 - 148*a^2*b*c)*d^2*e^5 + 4*(11*a^2*b^2 - 8*a^3*c)*d*e^6)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^12 - 4*b*c^3*d^11*e - 4*a^3*b*d^5*e^7 + a^4*d^4*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^10*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^9*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^8*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^7*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^6*e^6 + (c^4*d^8*e^4 - 4*b*c^3*d^7*e^5 - 4*a^3*b*d*e^11 + a^4*e^12 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^6 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^8 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^9 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^10)*x^4 + 4*(c^4*d^9*e^3 - 4*b*c^3*d^8*e^4 - 4*a^3*b*d^2*e^10 + a^4*d*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^9)*x^3 + 6*(c^4*d^10*e^2 - 4*b*c^3*d^9*e^3 - 4*a^3*b*d^3*e^9 + a^4*d^2*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^8)*x^2 + 4*(c^4*d^11*e - 4*b*c^3*d^10*e^2 - 4*a^3*b*d^4*e^8 + a^4*d^3*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^7)*x)]","B",0
2342,1,6374,0,91.007711," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{8} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{7} e + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{6} e^{2} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d^{5} e^{3} + {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{5} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{6} + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{7} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} e^{8}\right)} x^{5} + 5 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} e^{4} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{5} + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} e^{6} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d e^{7}\right)} x^{4} + 10 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} e^{3} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e^{4} + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} e^{5} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d^{2} e^{6}\right)} x^{3} + 10 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e^{3} + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{4} e^{4} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d^{3} e^{5}\right)} x^{2} + 5 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{7} e - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} e^{2} + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{5} e^{3} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d^{4} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(480 \, b c^{4} d^{9} + 1872 \, a^{4} b d e^{8} - 384 \, a^{5} e^{9} - 240 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{8} e + 90 \, {\left(13 \, b^{3} c^{2} + 100 \, a b c^{3}\right)} d^{7} e^{2} - {\left(555 \, b^{4} c + 10720 \, a b^{2} c^{2} + 5264 \, a^{2} c^{3}\right)} d^{6} e^{3} + {\left(105 \, b^{5} + 6020 \, a b^{3} c + 12592 \, a^{2} b c^{2}\right)} d^{5} e^{4} - {\left(1315 \, a b^{4} + 11032 \, a^{2} b^{2} c + 3952 \, a^{3} c^{2}\right)} d^{4} e^{5} + 2 \, {\left(1657 \, a^{2} b^{3} + 3812 \, a^{3} b c\right)} d^{3} e^{6} - 8 \, {\left(449 \, a^{3} b^{2} + 244 \, a^{4} c\right)} d^{2} e^{7} + {\left(96 \, c^{5} d^{6} e^{3} - 288 \, b c^{4} d^{5} e^{4} + 4 \, {\left(167 \, b^{2} c^{3} - 308 \, a c^{4}\right)} d^{4} e^{5} - 8 \, {\left(107 \, b^{3} c^{2} - 308 \, a b c^{3}\right)} d^{3} e^{6} + {\left(485 \, b^{4} c - 1312 \, a b^{2} c^{2} - 1072 \, a^{2} c^{3}\right)} d^{2} e^{7} - {\left(105 \, b^{5} - 80 \, a b^{3} c - 1072 \, a^{2} b c^{2}\right)} d e^{8} + {\left(105 \, a b^{4} - 460 \, a^{2} b^{2} c + 256 \, a^{3} c^{2}\right)} e^{9}\right)} x^{4} + 2 \, {\left(240 \, c^{5} d^{7} e^{2} - 744 \, b c^{4} d^{6} e^{3} + 2 \, {\left(811 \, b^{2} c^{3} - 1300 \, a c^{4}\right)} d^{5} e^{4} - 3 \, {\left(669 \, b^{3} c^{2} - 1756 \, a b c^{3}\right)} d^{4} e^{5} + 2 \, {\left(567 \, b^{4} c - 1378 \, a b^{2} c^{2} - 1280 \, a^{2} c^{3}\right)} d^{3} e^{6} - {\left(245 \, b^{5} - 18 \, a b^{3} c - 2768 \, a^{2} b c^{2}\right)} d^{2} e^{7} + 2 \, {\left(140 \, a b^{4} - 529 \, a^{2} b^{2} c + 140 \, a^{3} c^{2}\right)} d e^{8} - {\left(35 \, a^{2} b^{3} - 116 \, a^{3} b c\right)} e^{9}\right)} x^{3} + 2 \, {\left(480 \, c^{5} d^{8} e - 1560 \, b c^{4} d^{7} e^{2} + 2 \, {\left(1589 \, b^{2} c^{3} - 2012 \, a c^{4}\right)} d^{6} e^{3} - 3 \, {\left(1243 \, b^{3} c^{2} - 2724 \, a b c^{3}\right)} d^{5} e^{4} + 3 \, {\left(693 \, b^{4} c - 1336 \, a b^{2} c^{2} - 1504 \, a^{2} c^{3}\right)} d^{4} e^{5} - 2 \, {\left(224 \, b^{5} + 217 \, a b^{3} c - 2592 \, a^{2} b c^{2}\right)} d^{3} e^{6} + 3 \, {\left(203 \, a b^{4} - 586 \, a^{2} b^{2} c - 24 \, a^{3} c^{2}\right)} d^{2} e^{7} - 3 \, {\left(63 \, a^{2} b^{3} - 164 \, a^{3} b c\right)} d e^{8} + 4 \, {\left(7 \, a^{3} b^{2} - 16 \, a^{4} c\right)} e^{9}\right)} x^{2} + 2 \, {\left(480 \, c^{5} d^{9} - 1680 \, b c^{4} d^{8} e - 24 \, a^{4} b e^{9} + 30 \, {\left(107 \, b^{2} c^{3} - 84 \, a c^{4}\right)} d^{7} e^{2} - {\left(3485 \, b^{3} c^{2} - 4796 \, a b c^{3}\right)} d^{6} e^{3} + 2 \, {\left(935 \, b^{4} c - 754 \, a b^{2} c^{2} - 1600 \, a^{2} c^{3}\right)} d^{5} e^{4} - {\left(395 \, b^{5} + 1242 \, a b^{3} c - 3488 \, a^{2} b c^{2}\right)} d^{4} e^{5} + 2 \, {\left(342 \, a b^{4} - 343 \, a^{2} b^{2} c - 140 \, a^{3} c^{2}\right)} d^{3} e^{6} - 3 \, {\left(139 \, a^{2} b^{3} - 116 \, a^{3} b c\right)} d^{2} e^{7} + 8 \, {\left(19 \, a^{3} b^{2} - 10 \, a^{4} c\right)} d e^{8}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, {\left(c^{5} d^{15} - 5 \, b c^{4} d^{14} e - 5 \, a^{4} b d^{6} e^{9} + a^{5} d^{5} e^{10} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{13} e^{2} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{12} e^{3} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{11} e^{4} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{10} e^{5} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{9} e^{6} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{8} e^{7} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{7} e^{8} + {\left(c^{5} d^{10} e^{5} - 5 \, b c^{4} d^{9} e^{6} - 5 \, a^{4} b d e^{14} + a^{5} e^{15} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{8} e^{7} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{7} e^{8} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{6} e^{9} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{5} e^{10} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{4} e^{11} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{3} e^{12} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{2} e^{13}\right)} x^{5} + 5 \, {\left(c^{5} d^{11} e^{4} - 5 \, b c^{4} d^{10} e^{5} - 5 \, a^{4} b d^{2} e^{13} + a^{5} d e^{14} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{9} e^{6} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{8} e^{7} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{7} e^{8} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{6} e^{9} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{5} e^{10} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{4} e^{11} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{3} e^{12}\right)} x^{4} + 10 \, {\left(c^{5} d^{12} e^{3} - 5 \, b c^{4} d^{11} e^{4} - 5 \, a^{4} b d^{3} e^{12} + a^{5} d^{2} e^{13} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{10} e^{5} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{9} e^{6} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{8} e^{7} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{7} e^{8} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{6} e^{9} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{5} e^{10} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{4} e^{11}\right)} x^{3} + 10 \, {\left(c^{5} d^{13} e^{2} - 5 \, b c^{4} d^{12} e^{3} - 5 \, a^{4} b d^{4} e^{11} + a^{5} d^{3} e^{12} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{11} e^{4} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{10} e^{5} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{9} e^{6} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{8} e^{7} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{7} e^{8} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{6} e^{9} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{5} e^{10}\right)} x^{2} + 5 \, {\left(c^{5} d^{14} e - 5 \, b c^{4} d^{13} e^{2} - 5 \, a^{4} b d^{5} e^{10} + a^{5} d^{4} e^{11} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{12} e^{3} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{11} e^{4} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{10} e^{5} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{9} e^{6} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{8} e^{7} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{7} e^{8} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{6} e^{9}\right)} x\right)}}, -\frac{15 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{8} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{7} e + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{6} e^{2} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d^{5} e^{3} + {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{5} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{6} + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{7} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} e^{8}\right)} x^{5} + 5 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} e^{4} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{5} + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} e^{6} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d e^{7}\right)} x^{4} + 10 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} e^{3} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e^{4} + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} e^{5} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d^{2} e^{6}\right)} x^{3} + 10 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e^{3} + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{4} e^{4} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d^{3} e^{5}\right)} x^{2} + 5 \, {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{7} e - 48 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{6} e^{2} + 6 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{5} e^{3} - {\left(7 \, b^{5} - 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d^{4} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(480 \, b c^{4} d^{9} + 1872 \, a^{4} b d e^{8} - 384 \, a^{5} e^{9} - 240 \, {\left(5 \, b^{2} c^{3} + 12 \, a c^{4}\right)} d^{8} e + 90 \, {\left(13 \, b^{3} c^{2} + 100 \, a b c^{3}\right)} d^{7} e^{2} - {\left(555 \, b^{4} c + 10720 \, a b^{2} c^{2} + 5264 \, a^{2} c^{3}\right)} d^{6} e^{3} + {\left(105 \, b^{5} + 6020 \, a b^{3} c + 12592 \, a^{2} b c^{2}\right)} d^{5} e^{4} - {\left(1315 \, a b^{4} + 11032 \, a^{2} b^{2} c + 3952 \, a^{3} c^{2}\right)} d^{4} e^{5} + 2 \, {\left(1657 \, a^{2} b^{3} + 3812 \, a^{3} b c\right)} d^{3} e^{6} - 8 \, {\left(449 \, a^{3} b^{2} + 244 \, a^{4} c\right)} d^{2} e^{7} + {\left(96 \, c^{5} d^{6} e^{3} - 288 \, b c^{4} d^{5} e^{4} + 4 \, {\left(167 \, b^{2} c^{3} - 308 \, a c^{4}\right)} d^{4} e^{5} - 8 \, {\left(107 \, b^{3} c^{2} - 308 \, a b c^{3}\right)} d^{3} e^{6} + {\left(485 \, b^{4} c - 1312 \, a b^{2} c^{2} - 1072 \, a^{2} c^{3}\right)} d^{2} e^{7} - {\left(105 \, b^{5} - 80 \, a b^{3} c - 1072 \, a^{2} b c^{2}\right)} d e^{8} + {\left(105 \, a b^{4} - 460 \, a^{2} b^{2} c + 256 \, a^{3} c^{2}\right)} e^{9}\right)} x^{4} + 2 \, {\left(240 \, c^{5} d^{7} e^{2} - 744 \, b c^{4} d^{6} e^{3} + 2 \, {\left(811 \, b^{2} c^{3} - 1300 \, a c^{4}\right)} d^{5} e^{4} - 3 \, {\left(669 \, b^{3} c^{2} - 1756 \, a b c^{3}\right)} d^{4} e^{5} + 2 \, {\left(567 \, b^{4} c - 1378 \, a b^{2} c^{2} - 1280 \, a^{2} c^{3}\right)} d^{3} e^{6} - {\left(245 \, b^{5} - 18 \, a b^{3} c - 2768 \, a^{2} b c^{2}\right)} d^{2} e^{7} + 2 \, {\left(140 \, a b^{4} - 529 \, a^{2} b^{2} c + 140 \, a^{3} c^{2}\right)} d e^{8} - {\left(35 \, a^{2} b^{3} - 116 \, a^{3} b c\right)} e^{9}\right)} x^{3} + 2 \, {\left(480 \, c^{5} d^{8} e - 1560 \, b c^{4} d^{7} e^{2} + 2 \, {\left(1589 \, b^{2} c^{3} - 2012 \, a c^{4}\right)} d^{6} e^{3} - 3 \, {\left(1243 \, b^{3} c^{2} - 2724 \, a b c^{3}\right)} d^{5} e^{4} + 3 \, {\left(693 \, b^{4} c - 1336 \, a b^{2} c^{2} - 1504 \, a^{2} c^{3}\right)} d^{4} e^{5} - 2 \, {\left(224 \, b^{5} + 217 \, a b^{3} c - 2592 \, a^{2} b c^{2}\right)} d^{3} e^{6} + 3 \, {\left(203 \, a b^{4} - 586 \, a^{2} b^{2} c - 24 \, a^{3} c^{2}\right)} d^{2} e^{7} - 3 \, {\left(63 \, a^{2} b^{3} - 164 \, a^{3} b c\right)} d e^{8} + 4 \, {\left(7 \, a^{3} b^{2} - 16 \, a^{4} c\right)} e^{9}\right)} x^{2} + 2 \, {\left(480 \, c^{5} d^{9} - 1680 \, b c^{4} d^{8} e - 24 \, a^{4} b e^{9} + 30 \, {\left(107 \, b^{2} c^{3} - 84 \, a c^{4}\right)} d^{7} e^{2} - {\left(3485 \, b^{3} c^{2} - 4796 \, a b c^{3}\right)} d^{6} e^{3} + 2 \, {\left(935 \, b^{4} c - 754 \, a b^{2} c^{2} - 1600 \, a^{2} c^{3}\right)} d^{5} e^{4} - {\left(395 \, b^{5} + 1242 \, a b^{3} c - 3488 \, a^{2} b c^{2}\right)} d^{4} e^{5} + 2 \, {\left(342 \, a b^{4} - 343 \, a^{2} b^{2} c - 140 \, a^{3} c^{2}\right)} d^{3} e^{6} - 3 \, {\left(139 \, a^{2} b^{3} - 116 \, a^{3} b c\right)} d^{2} e^{7} + 8 \, {\left(19 \, a^{3} b^{2} - 10 \, a^{4} c\right)} d e^{8}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, {\left(c^{5} d^{15} - 5 \, b c^{4} d^{14} e - 5 \, a^{4} b d^{6} e^{9} + a^{5} d^{5} e^{10} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{13} e^{2} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{12} e^{3} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{11} e^{4} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{10} e^{5} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{9} e^{6} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{8} e^{7} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{7} e^{8} + {\left(c^{5} d^{10} e^{5} - 5 \, b c^{4} d^{9} e^{6} - 5 \, a^{4} b d e^{14} + a^{5} e^{15} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{8} e^{7} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{7} e^{8} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{6} e^{9} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{5} e^{10} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{4} e^{11} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{3} e^{12} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{2} e^{13}\right)} x^{5} + 5 \, {\left(c^{5} d^{11} e^{4} - 5 \, b c^{4} d^{10} e^{5} - 5 \, a^{4} b d^{2} e^{13} + a^{5} d e^{14} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{9} e^{6} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{8} e^{7} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{7} e^{8} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{6} e^{9} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{5} e^{10} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{4} e^{11} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{3} e^{12}\right)} x^{4} + 10 \, {\left(c^{5} d^{12} e^{3} - 5 \, b c^{4} d^{11} e^{4} - 5 \, a^{4} b d^{3} e^{12} + a^{5} d^{2} e^{13} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{10} e^{5} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{9} e^{6} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{8} e^{7} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{7} e^{8} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{6} e^{9} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{5} e^{10} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{4} e^{11}\right)} x^{3} + 10 \, {\left(c^{5} d^{13} e^{2} - 5 \, b c^{4} d^{12} e^{3} - 5 \, a^{4} b d^{4} e^{11} + a^{5} d^{3} e^{12} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{11} e^{4} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{10} e^{5} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{9} e^{6} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{8} e^{7} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{7} e^{8} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{6} e^{9} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{5} e^{10}\right)} x^{2} + 5 \, {\left(c^{5} d^{14} e - 5 \, b c^{4} d^{13} e^{2} - 5 \, a^{4} b d^{5} e^{10} + a^{5} d^{4} e^{11} + 5 \, {\left(2 \, b^{2} c^{3} + a c^{4}\right)} d^{12} e^{3} - 10 \, {\left(b^{3} c^{2} + 2 \, a b c^{3}\right)} d^{11} e^{4} + 5 \, {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{10} e^{5} - {\left(b^{5} + 20 \, a b^{3} c + 30 \, a^{2} b c^{2}\right)} d^{9} e^{6} + 5 \, {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{8} e^{7} - 10 \, {\left(a^{2} b^{3} + 2 \, a^{3} b c\right)} d^{7} e^{8} + 5 \, {\left(2 \, a^{3} b^{2} + a^{4} c\right)} d^{6} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/7680*(15*(32*(b^2*c^3 - 4*a*c^4)*d^8 - 48*(b^3*c^2 - 4*a*b*c^3)*d^7*e + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d^6*e^2 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*d^5*e^3 + (32*(b^2*c^3 - 4*a*c^4)*d^3*e^5 - 48*(b^3*c^2 - 4*a*b*c^3)*d^2*e^6 + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d*e^7 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*e^8)*x^5 + 5*(32*(b^2*c^3 - 4*a*c^4)*d^4*e^4 - 48*(b^3*c^2 - 4*a*b*c^3)*d^3*e^5 + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d^2*e^6 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*d*e^7)*x^4 + 10*(32*(b^2*c^3 - 4*a*c^4)*d^5*e^3 - 48*(b^3*c^2 - 4*a*b*c^3)*d^4*e^4 + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d^3*e^5 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*d^2*e^6)*x^3 + 10*(32*(b^2*c^3 - 4*a*c^4)*d^6*e^2 - 48*(b^3*c^2 - 4*a*b*c^3)*d^5*e^3 + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d^4*e^4 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*d^3*e^5)*x^2 + 5*(32*(b^2*c^3 - 4*a*c^4)*d^7*e - 48*(b^3*c^2 - 4*a*b*c^3)*d^6*e^2 + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d^5*e^3 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*d^4*e^4)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(480*b*c^4*d^9 + 1872*a^4*b*d*e^8 - 384*a^5*e^9 - 240*(5*b^2*c^3 + 12*a*c^4)*d^8*e + 90*(13*b^3*c^2 + 100*a*b*c^3)*d^7*e^2 - (555*b^4*c + 10720*a*b^2*c^2 + 5264*a^2*c^3)*d^6*e^3 + (105*b^5 + 6020*a*b^3*c + 12592*a^2*b*c^2)*d^5*e^4 - (1315*a*b^4 + 11032*a^2*b^2*c + 3952*a^3*c^2)*d^4*e^5 + 2*(1657*a^2*b^3 + 3812*a^3*b*c)*d^3*e^6 - 8*(449*a^3*b^2 + 244*a^4*c)*d^2*e^7 + (96*c^5*d^6*e^3 - 288*b*c^4*d^5*e^4 + 4*(167*b^2*c^3 - 308*a*c^4)*d^4*e^5 - 8*(107*b^3*c^2 - 308*a*b*c^3)*d^3*e^6 + (485*b^4*c - 1312*a*b^2*c^2 - 1072*a^2*c^3)*d^2*e^7 - (105*b^5 - 80*a*b^3*c - 1072*a^2*b*c^2)*d*e^8 + (105*a*b^4 - 460*a^2*b^2*c + 256*a^3*c^2)*e^9)*x^4 + 2*(240*c^5*d^7*e^2 - 744*b*c^4*d^6*e^3 + 2*(811*b^2*c^3 - 1300*a*c^4)*d^5*e^4 - 3*(669*b^3*c^2 - 1756*a*b*c^3)*d^4*e^5 + 2*(567*b^4*c - 1378*a*b^2*c^2 - 1280*a^2*c^3)*d^3*e^6 - (245*b^5 - 18*a*b^3*c - 2768*a^2*b*c^2)*d^2*e^7 + 2*(140*a*b^4 - 529*a^2*b^2*c + 140*a^3*c^2)*d*e^8 - (35*a^2*b^3 - 116*a^3*b*c)*e^9)*x^3 + 2*(480*c^5*d^8*e - 1560*b*c^4*d^7*e^2 + 2*(1589*b^2*c^3 - 2012*a*c^4)*d^6*e^3 - 3*(1243*b^3*c^2 - 2724*a*b*c^3)*d^5*e^4 + 3*(693*b^4*c - 1336*a*b^2*c^2 - 1504*a^2*c^3)*d^4*e^5 - 2*(224*b^5 + 217*a*b^3*c - 2592*a^2*b*c^2)*d^3*e^6 + 3*(203*a*b^4 - 586*a^2*b^2*c - 24*a^3*c^2)*d^2*e^7 - 3*(63*a^2*b^3 - 164*a^3*b*c)*d*e^8 + 4*(7*a^3*b^2 - 16*a^4*c)*e^9)*x^2 + 2*(480*c^5*d^9 - 1680*b*c^4*d^8*e - 24*a^4*b*e^9 + 30*(107*b^2*c^3 - 84*a*c^4)*d^7*e^2 - (3485*b^3*c^2 - 4796*a*b*c^3)*d^6*e^3 + 2*(935*b^4*c - 754*a*b^2*c^2 - 1600*a^2*c^3)*d^5*e^4 - (395*b^5 + 1242*a*b^3*c - 3488*a^2*b*c^2)*d^4*e^5 + 2*(342*a*b^4 - 343*a^2*b^2*c - 140*a^3*c^2)*d^3*e^6 - 3*(139*a^2*b^3 - 116*a^3*b*c)*d^2*e^7 + 8*(19*a^3*b^2 - 10*a^4*c)*d*e^8)*x)*sqrt(c*x^2 + b*x + a))/(c^5*d^15 - 5*b*c^4*d^14*e - 5*a^4*b*d^6*e^9 + a^5*d^5*e^10 + 5*(2*b^2*c^3 + a*c^4)*d^13*e^2 - 10*(b^3*c^2 + 2*a*b*c^3)*d^12*e^3 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^11*e^4 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^10*e^5 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^9*e^6 - 10*(a^2*b^3 + 2*a^3*b*c)*d^8*e^7 + 5*(2*a^3*b^2 + a^4*c)*d^7*e^8 + (c^5*d^10*e^5 - 5*b*c^4*d^9*e^6 - 5*a^4*b*d*e^14 + a^5*e^15 + 5*(2*b^2*c^3 + a*c^4)*d^8*e^7 - 10*(b^3*c^2 + 2*a*b*c^3)*d^7*e^8 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^6*e^9 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^5*e^10 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^4*e^11 - 10*(a^2*b^3 + 2*a^3*b*c)*d^3*e^12 + 5*(2*a^3*b^2 + a^4*c)*d^2*e^13)*x^5 + 5*(c^5*d^11*e^4 - 5*b*c^4*d^10*e^5 - 5*a^4*b*d^2*e^13 + a^5*d*e^14 + 5*(2*b^2*c^3 + a*c^4)*d^9*e^6 - 10*(b^3*c^2 + 2*a*b*c^3)*d^8*e^7 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^7*e^8 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^6*e^9 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^5*e^10 - 10*(a^2*b^3 + 2*a^3*b*c)*d^4*e^11 + 5*(2*a^3*b^2 + a^4*c)*d^3*e^12)*x^4 + 10*(c^5*d^12*e^3 - 5*b*c^4*d^11*e^4 - 5*a^4*b*d^3*e^12 + a^5*d^2*e^13 + 5*(2*b^2*c^3 + a*c^4)*d^10*e^5 - 10*(b^3*c^2 + 2*a*b*c^3)*d^9*e^6 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^8*e^7 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^7*e^8 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^6*e^9 - 10*(a^2*b^3 + 2*a^3*b*c)*d^5*e^10 + 5*(2*a^3*b^2 + a^4*c)*d^4*e^11)*x^3 + 10*(c^5*d^13*e^2 - 5*b*c^4*d^12*e^3 - 5*a^4*b*d^4*e^11 + a^5*d^3*e^12 + 5*(2*b^2*c^3 + a*c^4)*d^11*e^4 - 10*(b^3*c^2 + 2*a*b*c^3)*d^10*e^5 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^9*e^6 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^8*e^7 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^7*e^8 - 10*(a^2*b^3 + 2*a^3*b*c)*d^6*e^9 + 5*(2*a^3*b^2 + a^4*c)*d^5*e^10)*x^2 + 5*(c^5*d^14*e - 5*b*c^4*d^13*e^2 - 5*a^4*b*d^5*e^10 + a^5*d^4*e^11 + 5*(2*b^2*c^3 + a*c^4)*d^12*e^3 - 10*(b^3*c^2 + 2*a*b*c^3)*d^11*e^4 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^10*e^5 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^9*e^6 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^8*e^7 - 10*(a^2*b^3 + 2*a^3*b*c)*d^7*e^8 + 5*(2*a^3*b^2 + a^4*c)*d^6*e^9)*x), -1/3840*(15*(32*(b^2*c^3 - 4*a*c^4)*d^8 - 48*(b^3*c^2 - 4*a*b*c^3)*d^7*e + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d^6*e^2 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*d^5*e^3 + (32*(b^2*c^3 - 4*a*c^4)*d^3*e^5 - 48*(b^3*c^2 - 4*a*b*c^3)*d^2*e^6 + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d*e^7 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*e^8)*x^5 + 5*(32*(b^2*c^3 - 4*a*c^4)*d^4*e^4 - 48*(b^3*c^2 - 4*a*b*c^3)*d^3*e^5 + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d^2*e^6 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*d*e^7)*x^4 + 10*(32*(b^2*c^3 - 4*a*c^4)*d^5*e^3 - 48*(b^3*c^2 - 4*a*b*c^3)*d^4*e^4 + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d^3*e^5 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*d^2*e^6)*x^3 + 10*(32*(b^2*c^3 - 4*a*c^4)*d^6*e^2 - 48*(b^3*c^2 - 4*a*b*c^3)*d^5*e^3 + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d^4*e^4 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*d^3*e^5)*x^2 + 5*(32*(b^2*c^3 - 4*a*c^4)*d^7*e - 48*(b^3*c^2 - 4*a*b*c^3)*d^6*e^2 + 6*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*d^5*e^3 - (7*b^5 - 40*a*b^3*c + 48*a^2*b*c^2)*d^4*e^4)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(480*b*c^4*d^9 + 1872*a^4*b*d*e^8 - 384*a^5*e^9 - 240*(5*b^2*c^3 + 12*a*c^4)*d^8*e + 90*(13*b^3*c^2 + 100*a*b*c^3)*d^7*e^2 - (555*b^4*c + 10720*a*b^2*c^2 + 5264*a^2*c^3)*d^6*e^3 + (105*b^5 + 6020*a*b^3*c + 12592*a^2*b*c^2)*d^5*e^4 - (1315*a*b^4 + 11032*a^2*b^2*c + 3952*a^3*c^2)*d^4*e^5 + 2*(1657*a^2*b^3 + 3812*a^3*b*c)*d^3*e^6 - 8*(449*a^3*b^2 + 244*a^4*c)*d^2*e^7 + (96*c^5*d^6*e^3 - 288*b*c^4*d^5*e^4 + 4*(167*b^2*c^3 - 308*a*c^4)*d^4*e^5 - 8*(107*b^3*c^2 - 308*a*b*c^3)*d^3*e^6 + (485*b^4*c - 1312*a*b^2*c^2 - 1072*a^2*c^3)*d^2*e^7 - (105*b^5 - 80*a*b^3*c - 1072*a^2*b*c^2)*d*e^8 + (105*a*b^4 - 460*a^2*b^2*c + 256*a^3*c^2)*e^9)*x^4 + 2*(240*c^5*d^7*e^2 - 744*b*c^4*d^6*e^3 + 2*(811*b^2*c^3 - 1300*a*c^4)*d^5*e^4 - 3*(669*b^3*c^2 - 1756*a*b*c^3)*d^4*e^5 + 2*(567*b^4*c - 1378*a*b^2*c^2 - 1280*a^2*c^3)*d^3*e^6 - (245*b^5 - 18*a*b^3*c - 2768*a^2*b*c^2)*d^2*e^7 + 2*(140*a*b^4 - 529*a^2*b^2*c + 140*a^3*c^2)*d*e^8 - (35*a^2*b^3 - 116*a^3*b*c)*e^9)*x^3 + 2*(480*c^5*d^8*e - 1560*b*c^4*d^7*e^2 + 2*(1589*b^2*c^3 - 2012*a*c^4)*d^6*e^3 - 3*(1243*b^3*c^2 - 2724*a*b*c^3)*d^5*e^4 + 3*(693*b^4*c - 1336*a*b^2*c^2 - 1504*a^2*c^3)*d^4*e^5 - 2*(224*b^5 + 217*a*b^3*c - 2592*a^2*b*c^2)*d^3*e^6 + 3*(203*a*b^4 - 586*a^2*b^2*c - 24*a^3*c^2)*d^2*e^7 - 3*(63*a^2*b^3 - 164*a^3*b*c)*d*e^8 + 4*(7*a^3*b^2 - 16*a^4*c)*e^9)*x^2 + 2*(480*c^5*d^9 - 1680*b*c^4*d^8*e - 24*a^4*b*e^9 + 30*(107*b^2*c^3 - 84*a*c^4)*d^7*e^2 - (3485*b^3*c^2 - 4796*a*b*c^3)*d^6*e^3 + 2*(935*b^4*c - 754*a*b^2*c^2 - 1600*a^2*c^3)*d^5*e^4 - (395*b^5 + 1242*a*b^3*c - 3488*a^2*b*c^2)*d^4*e^5 + 2*(342*a*b^4 - 343*a^2*b^2*c - 140*a^3*c^2)*d^3*e^6 - 3*(139*a^2*b^3 - 116*a^3*b*c)*d^2*e^7 + 8*(19*a^3*b^2 - 10*a^4*c)*d*e^8)*x)*sqrt(c*x^2 + b*x + a))/(c^5*d^15 - 5*b*c^4*d^14*e - 5*a^4*b*d^6*e^9 + a^5*d^5*e^10 + 5*(2*b^2*c^3 + a*c^4)*d^13*e^2 - 10*(b^3*c^2 + 2*a*b*c^3)*d^12*e^3 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^11*e^4 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^10*e^5 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^9*e^6 - 10*(a^2*b^3 + 2*a^3*b*c)*d^8*e^7 + 5*(2*a^3*b^2 + a^4*c)*d^7*e^8 + (c^5*d^10*e^5 - 5*b*c^4*d^9*e^6 - 5*a^4*b*d*e^14 + a^5*e^15 + 5*(2*b^2*c^3 + a*c^4)*d^8*e^7 - 10*(b^3*c^2 + 2*a*b*c^3)*d^7*e^8 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^6*e^9 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^5*e^10 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^4*e^11 - 10*(a^2*b^3 + 2*a^3*b*c)*d^3*e^12 + 5*(2*a^3*b^2 + a^4*c)*d^2*e^13)*x^5 + 5*(c^5*d^11*e^4 - 5*b*c^4*d^10*e^5 - 5*a^4*b*d^2*e^13 + a^5*d*e^14 + 5*(2*b^2*c^3 + a*c^4)*d^9*e^6 - 10*(b^3*c^2 + 2*a*b*c^3)*d^8*e^7 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^7*e^8 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^6*e^9 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^5*e^10 - 10*(a^2*b^3 + 2*a^3*b*c)*d^4*e^11 + 5*(2*a^3*b^2 + a^4*c)*d^3*e^12)*x^4 + 10*(c^5*d^12*e^3 - 5*b*c^4*d^11*e^4 - 5*a^4*b*d^3*e^12 + a^5*d^2*e^13 + 5*(2*b^2*c^3 + a*c^4)*d^10*e^5 - 10*(b^3*c^2 + 2*a*b*c^3)*d^9*e^6 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^8*e^7 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^7*e^8 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^6*e^9 - 10*(a^2*b^3 + 2*a^3*b*c)*d^5*e^10 + 5*(2*a^3*b^2 + a^4*c)*d^4*e^11)*x^3 + 10*(c^5*d^13*e^2 - 5*b*c^4*d^12*e^3 - 5*a^4*b*d^4*e^11 + a^5*d^3*e^12 + 5*(2*b^2*c^3 + a*c^4)*d^11*e^4 - 10*(b^3*c^2 + 2*a*b*c^3)*d^10*e^5 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^9*e^6 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^8*e^7 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^7*e^8 - 10*(a^2*b^3 + 2*a^3*b*c)*d^6*e^9 + 5*(2*a^3*b^2 + a^4*c)*d^5*e^10)*x^2 + 5*(c^5*d^14*e - 5*b*c^4*d^13*e^2 - 5*a^4*b*d^5*e^10 + a^5*d^4*e^11 + 5*(2*b^2*c^3 + a*c^4)*d^12*e^3 - 10*(b^3*c^2 + 2*a*b*c^3)*d^11*e^4 + 5*(b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^10*e^5 - (b^5 + 20*a*b^3*c + 30*a^2*b*c^2)*d^9*e^6 + 5*(a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^8*e^7 - 10*(a^2*b^3 + 2*a^3*b*c)*d^7*e^8 + 5*(2*a^3*b^2 + a^4*c)*d^6*e^9)*x)]","B",0
2343,1,1359,0,0.582461," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(16 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} - 24 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e + 2 \, {\left(7 \, b^{6} c - 60 \, a b^{4} c^{2} + 144 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{2} - {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(5120 \, c^{7} e^{3} x^{6} + 1280 \, {\left(14 \, c^{7} d e^{2} + 5 \, b c^{6} e^{3}\right)} x^{5} + 128 \, {\left(168 \, c^{7} d^{2} e + 182 \, b c^{6} d e^{2} + {\left(b^{2} c^{5} + 64 \, a c^{6}\right)} e^{3}\right)} x^{4} - 560 \, {\left(3 \, b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{3} + 168 \, {\left(15 \, b^{4} c^{3} - 100 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} d^{2} e - 14 \, {\left(105 \, b^{5} c^{2} - 760 \, a b^{3} c^{3} + 1296 \, a^{2} b c^{4}\right)} d e^{2} + {\left(315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4}\right)} e^{3} + 16 \, {\left(560 \, c^{7} d^{3} + 1848 \, b c^{6} d^{2} e + 14 \, {\left(3 \, b^{2} c^{5} + 140 \, a c^{6}\right)} d e^{2} - {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} e^{3}\right)} x^{3} + 8 \, {\left(1680 \, b c^{6} d^{3} + 168 \, {\left(b^{2} c^{5} + 32 \, a c^{6}\right)} d^{2} e - 14 \, {\left(7 \, b^{3} c^{4} - 36 \, a b c^{5}\right)} d e^{2} + {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} e^{3}\right)} x^{2} + 2 \, {\left(560 \, {\left(b^{2} c^{5} + 20 \, a c^{6}\right)} d^{3} - 168 \, {\left(5 \, b^{3} c^{4} - 28 \, a b c^{5}\right)} d^{2} e + 14 \, {\left(35 \, b^{4} c^{3} - 216 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} d e^{2} - {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{143360 \, c^{6}}, -\frac{105 \, {\left(16 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{3} - 24 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e + 2 \, {\left(7 \, b^{6} c - 60 \, a b^{4} c^{2} + 144 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d e^{2} - {\left(3 \, b^{7} - 28 \, a b^{5} c + 80 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(5120 \, c^{7} e^{3} x^{6} + 1280 \, {\left(14 \, c^{7} d e^{2} + 5 \, b c^{6} e^{3}\right)} x^{5} + 128 \, {\left(168 \, c^{7} d^{2} e + 182 \, b c^{6} d e^{2} + {\left(b^{2} c^{5} + 64 \, a c^{6}\right)} e^{3}\right)} x^{4} - 560 \, {\left(3 \, b^{3} c^{4} - 20 \, a b c^{5}\right)} d^{3} + 168 \, {\left(15 \, b^{4} c^{3} - 100 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} d^{2} e - 14 \, {\left(105 \, b^{5} c^{2} - 760 \, a b^{3} c^{3} + 1296 \, a^{2} b c^{4}\right)} d e^{2} + {\left(315 \, b^{6} c - 2520 \, a b^{4} c^{2} + 5488 \, a^{2} b^{2} c^{3} - 2048 \, a^{3} c^{4}\right)} e^{3} + 16 \, {\left(560 \, c^{7} d^{3} + 1848 \, b c^{6} d^{2} e + 14 \, {\left(3 \, b^{2} c^{5} + 140 \, a c^{6}\right)} d e^{2} - {\left(9 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} e^{3}\right)} x^{3} + 8 \, {\left(1680 \, b c^{6} d^{3} + 168 \, {\left(b^{2} c^{5} + 32 \, a c^{6}\right)} d^{2} e - 14 \, {\left(7 \, b^{3} c^{4} - 36 \, a b c^{5}\right)} d e^{2} + {\left(21 \, b^{4} c^{3} - 124 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} e^{3}\right)} x^{2} + 2 \, {\left(560 \, {\left(b^{2} c^{5} + 20 \, a c^{6}\right)} d^{3} - 168 \, {\left(5 \, b^{3} c^{4} - 28 \, a b c^{5}\right)} d^{2} e + 14 \, {\left(35 \, b^{4} c^{3} - 216 \, a b^{2} c^{4} + 240 \, a^{2} c^{5}\right)} d e^{2} - {\left(105 \, b^{5} c^{2} - 728 \, a b^{3} c^{3} + 1168 \, a^{2} b c^{4}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{71680 \, c^{6}}\right]"," ",0,"[1/143360*(105*(16*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3 - 24*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e + 2*(7*b^6*c - 60*a*b^4*c^2 + 144*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^2 - (3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(5120*c^7*e^3*x^6 + 1280*(14*c^7*d*e^2 + 5*b*c^6*e^3)*x^5 + 128*(168*c^7*d^2*e + 182*b*c^6*d*e^2 + (b^2*c^5 + 64*a*c^6)*e^3)*x^4 - 560*(3*b^3*c^4 - 20*a*b*c^5)*d^3 + 168*(15*b^4*c^3 - 100*a*b^2*c^4 + 128*a^2*c^5)*d^2*e - 14*(105*b^5*c^2 - 760*a*b^3*c^3 + 1296*a^2*b*c^4)*d*e^2 + (315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4)*e^3 + 16*(560*c^7*d^3 + 1848*b*c^6*d^2*e + 14*(3*b^2*c^5 + 140*a*c^6)*d*e^2 - (9*b^3*c^4 - 44*a*b*c^5)*e^3)*x^3 + 8*(1680*b*c^6*d^3 + 168*(b^2*c^5 + 32*a*c^6)*d^2*e - 14*(7*b^3*c^4 - 36*a*b*c^5)*d*e^2 + (21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*e^3)*x^2 + 2*(560*(b^2*c^5 + 20*a*c^6)*d^3 - 168*(5*b^3*c^4 - 28*a*b*c^5)*d^2*e + 14*(35*b^4*c^3 - 216*a*b^2*c^4 + 240*a^2*c^5)*d*e^2 - (105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^6, -1/71680*(105*(16*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^3 - 24*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e + 2*(7*b^6*c - 60*a*b^4*c^2 + 144*a^2*b^2*c^3 - 64*a^3*c^4)*d*e^2 - (3*b^7 - 28*a*b^5*c + 80*a^2*b^3*c^2 - 64*a^3*b*c^3)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(5120*c^7*e^3*x^6 + 1280*(14*c^7*d*e^2 + 5*b*c^6*e^3)*x^5 + 128*(168*c^7*d^2*e + 182*b*c^6*d*e^2 + (b^2*c^5 + 64*a*c^6)*e^3)*x^4 - 560*(3*b^3*c^4 - 20*a*b*c^5)*d^3 + 168*(15*b^4*c^3 - 100*a*b^2*c^4 + 128*a^2*c^5)*d^2*e - 14*(105*b^5*c^2 - 760*a*b^3*c^3 + 1296*a^2*b*c^4)*d*e^2 + (315*b^6*c - 2520*a*b^4*c^2 + 5488*a^2*b^2*c^3 - 2048*a^3*c^4)*e^3 + 16*(560*c^7*d^3 + 1848*b*c^6*d^2*e + 14*(3*b^2*c^5 + 140*a*c^6)*d*e^2 - (9*b^3*c^4 - 44*a*b*c^5)*e^3)*x^3 + 8*(1680*b*c^6*d^3 + 168*(b^2*c^5 + 32*a*c^6)*d^2*e - 14*(7*b^3*c^4 - 36*a*b*c^5)*d*e^2 + (21*b^4*c^3 - 124*a*b^2*c^4 + 128*a^2*c^5)*e^3)*x^2 + 2*(560*(b^2*c^5 + 20*a*c^6)*d^3 - 168*(5*b^3*c^4 - 28*a*b*c^5)*d^2*e + 14*(35*b^4*c^3 - 216*a*b^2*c^4 + 240*a^2*c^5)*d*e^2 - (105*b^5*c^2 - 728*a*b^3*c^3 + 1168*a^2*b*c^4)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^6]","B",0
2344,1,899,0,0.515243," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1280 \, c^{6} e^{2} x^{5} + 128 \, {\left(24 \, c^{6} d e + 13 \, b c^{5} e^{2}\right)} x^{4} + 16 \, {\left(120 \, c^{6} d^{2} + 264 \, b c^{5} d e + {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} e^{2}\right)} x^{3} - 120 \, {\left(3 \, b^{3} c^{3} - 20 \, a b c^{4}\right)} d^{2} + 24 \, {\left(15 \, b^{4} c^{2} - 100 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right)} d e - {\left(105 \, b^{5} c - 760 \, a b^{3} c^{2} + 1296 \, a^{2} b c^{3}\right)} e^{2} + 8 \, {\left(360 \, b c^{5} d^{2} + 24 \, {\left(b^{2} c^{4} + 32 \, a c^{5}\right)} d e - {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} e^{2}\right)} x^{2} + 2 \, {\left(120 \, {\left(b^{2} c^{4} + 20 \, a c^{5}\right)} d^{2} - 24 \, {\left(5 \, b^{3} c^{3} - 28 \, a b c^{4}\right)} d e + {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{5}}, -\frac{15 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d^{2} - 24 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d e + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(1280 \, c^{6} e^{2} x^{5} + 128 \, {\left(24 \, c^{6} d e + 13 \, b c^{5} e^{2}\right)} x^{4} + 16 \, {\left(120 \, c^{6} d^{2} + 264 \, b c^{5} d e + {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} e^{2}\right)} x^{3} - 120 \, {\left(3 \, b^{3} c^{3} - 20 \, a b c^{4}\right)} d^{2} + 24 \, {\left(15 \, b^{4} c^{2} - 100 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right)} d e - {\left(105 \, b^{5} c - 760 \, a b^{3} c^{2} + 1296 \, a^{2} b c^{3}\right)} e^{2} + 8 \, {\left(360 \, b c^{5} d^{2} + 24 \, {\left(b^{2} c^{4} + 32 \, a c^{5}\right)} d e - {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} e^{2}\right)} x^{2} + 2 \, {\left(120 \, {\left(b^{2} c^{4} + 20 \, a c^{5}\right)} d^{2} - 24 \, {\left(5 \, b^{3} c^{3} - 28 \, a b c^{4}\right)} d e + {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{5}}\right]"," ",0,"[-1/30720*(15*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(1280*c^6*e^2*x^5 + 128*(24*c^6*d*e + 13*b*c^5*e^2)*x^4 + 16*(120*c^6*d^2 + 264*b*c^5*d*e + (3*b^2*c^4 + 140*a*c^5)*e^2)*x^3 - 120*(3*b^3*c^3 - 20*a*b*c^4)*d^2 + 24*(15*b^4*c^2 - 100*a*b^2*c^3 + 128*a^2*c^4)*d*e - (105*b^5*c - 760*a*b^3*c^2 + 1296*a^2*b*c^3)*e^2 + 8*(360*b*c^5*d^2 + 24*(b^2*c^4 + 32*a*c^5)*d*e - (7*b^3*c^3 - 36*a*b*c^4)*e^2)*x^2 + 2*(120*(b^2*c^4 + 20*a*c^5)*d^2 - 24*(5*b^3*c^3 - 28*a*b*c^4)*d*e + (35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/15360*(15*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d^2 - 24*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*d*e + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(1280*c^6*e^2*x^5 + 128*(24*c^6*d*e + 13*b*c^5*e^2)*x^4 + 16*(120*c^6*d^2 + 264*b*c^5*d*e + (3*b^2*c^4 + 140*a*c^5)*e^2)*x^3 - 120*(3*b^3*c^3 - 20*a*b*c^4)*d^2 + 24*(15*b^4*c^2 - 100*a*b^2*c^3 + 128*a^2*c^4)*d*e - (105*b^5*c - 760*a*b^3*c^2 + 1296*a^2*b*c^3)*e^2 + 8*(360*b*c^5*d^2 + 24*(b^2*c^4 + 32*a*c^5)*d*e - (7*b^3*c^3 - 36*a*b*c^4)*e^2)*x^2 + 2*(120*(b^2*c^4 + 20*a*c^5)*d^2 - 24*(5*b^3*c^3 - 28*a*b*c^4)*d*e + (35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
2345,1,529,0,0.459443," ","integrate((e*x+d)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(128 \, c^{5} e x^{4} + 16 \, {\left(10 \, c^{5} d + 11 \, b c^{4} e\right)} x^{3} + 8 \, {\left(30 \, b c^{4} d + {\left(b^{2} c^{3} + 32 \, a c^{4}\right)} e\right)} x^{2} - 10 \, {\left(3 \, b^{3} c^{2} - 20 \, a b c^{3}\right)} d + {\left(15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3}\right)} e + 2 \, {\left(10 \, {\left(b^{2} c^{3} + 20 \, a c^{4}\right)} d - {\left(5 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2560 \, c^{4}}, -\frac{15 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(128 \, c^{5} e x^{4} + 16 \, {\left(10 \, c^{5} d + 11 \, b c^{4} e\right)} x^{3} + 8 \, {\left(30 \, b c^{4} d + {\left(b^{2} c^{3} + 32 \, a c^{4}\right)} e\right)} x^{2} - 10 \, {\left(3 \, b^{3} c^{2} - 20 \, a b c^{3}\right)} d + {\left(15 \, b^{4} c - 100 \, a b^{2} c^{2} + 128 \, a^{2} c^{3}\right)} e + 2 \, {\left(10 \, {\left(b^{2} c^{3} + 20 \, a c^{4}\right)} d - {\left(5 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1280 \, c^{4}}\right]"," ",0,"[-1/2560*(15*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(128*c^5*e*x^4 + 16*(10*c^5*d + 11*b*c^4*e)*x^3 + 8*(30*b*c^4*d + (b^2*c^3 + 32*a*c^4)*e)*x^2 - 10*(3*b^3*c^2 - 20*a*b*c^3)*d + (15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3)*e + 2*(10*(b^2*c^3 + 20*a*c^4)*d - (5*b^3*c^2 - 28*a*b*c^3)*e)*x)*sqrt(c*x^2 + b*x + a))/c^4, -1/1280*(15*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(128*c^5*e*x^4 + 16*(10*c^5*d + 11*b*c^4*e)*x^3 + 8*(30*b*c^4*d + (b^2*c^3 + 32*a*c^4)*e)*x^2 - 10*(3*b^3*c^2 - 20*a*b*c^3)*d + (15*b^4*c - 100*a*b^2*c^2 + 128*a^2*c^3)*e + 2*(10*(b^2*c^3 + 20*a*c^4)*d - (5*b^3*c^2 - 28*a*b*c^3)*e)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
2346,1,277,0,0.437587," ","integrate((c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(16 \, c^{4} x^{3} + 24 \, b c^{3} x^{2} - 3 \, b^{3} c + 20 \, a b c^{2} + 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{256 \, c^{3}}, -\frac{3 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(16 \, c^{4} x^{3} + 24 \, b c^{3} x^{2} - 3 \, b^{3} c + 20 \, a b c^{2} + 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{128 \, c^{3}}\right]"," ",0,"[1/256*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(16*c^4*x^3 + 24*b*c^3*x^2 - 3*b^3*c + 20*a*b*c^2 + 2*(b^2*c^2 + 20*a*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^3, -1/128*(3*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(16*c^4*x^3 + 24*b*c^3*x^2 - 3*b^3*c + 20*a*b*c^2 + 2*(b^2*c^2 + 20*a*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
2347,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2348,1,1583,0,12.817912," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + {\left(b^{2} + 4 \, a c\right)} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + {\left(b^{2} + 4 \, a c\right)} e^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 12 \, {\left(2 \, c^{2} d^{2} - b c d e + {\left(2 \, c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(2 \, c^{2} e^{3} x^{2} - 12 \, c^{2} d^{2} e + 9 \, b c d e^{2} - 4 \, a c e^{3} - {\left(6 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(c e^{5} x + c d e^{4}\right)}}, -\frac{24 \, {\left(2 \, c^{2} d^{2} - b c d e + {\left(2 \, c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 3 \, {\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + {\left(b^{2} + 4 \, a c\right)} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + {\left(b^{2} + 4 \, a c\right)} e^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, c^{2} e^{3} x^{2} - 12 \, c^{2} d^{2} e + 9 \, b c d e^{2} - 4 \, a c e^{3} - {\left(6 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(c e^{5} x + c d e^{4}\right)}}, -\frac{3 \, {\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + {\left(b^{2} + 4 \, a c\right)} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + {\left(b^{2} + 4 \, a c\right)} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 6 \, {\left(2 \, c^{2} d^{2} - b c d e + {\left(2 \, c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 2 \, {\left(2 \, c^{2} e^{3} x^{2} - 12 \, c^{2} d^{2} e + 9 \, b c d e^{2} - 4 \, a c e^{3} - {\left(6 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(c e^{5} x + c d e^{4}\right)}}, -\frac{12 \, {\left(2 \, c^{2} d^{2} - b c d e + {\left(2 \, c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 3 \, {\left(8 \, c^{2} d^{3} - 8 \, b c d^{2} e + {\left(b^{2} + 4 \, a c\right)} d e^{2} + {\left(8 \, c^{2} d^{2} e - 8 \, b c d e^{2} + {\left(b^{2} + 4 \, a c\right)} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(2 \, c^{2} e^{3} x^{2} - 12 \, c^{2} d^{2} e + 9 \, b c d e^{2} - 4 \, a c e^{3} - {\left(6 \, c^{2} d e^{2} - 5 \, b c e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(c e^{5} x + c d e^{4}\right)}}\right]"," ",0,"[1/16*(3*(8*c^2*d^3 - 8*b*c*d^2*e + (b^2 + 4*a*c)*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + (b^2 + 4*a*c)*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 12*(2*c^2*d^2 - b*c*d*e + (2*c^2*d*e - b*c*e^2)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(2*c^2*e^3*x^2 - 12*c^2*d^2*e + 9*b*c*d*e^2 - 4*a*c*e^3 - (6*c^2*d*e^2 - 5*b*c*e^3)*x)*sqrt(c*x^2 + b*x + a))/(c*e^5*x + c*d*e^4), -1/16*(24*(2*c^2*d^2 - b*c*d*e + (2*c^2*d*e - b*c*e^2)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 3*(8*c^2*d^3 - 8*b*c*d^2*e + (b^2 + 4*a*c)*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + (b^2 + 4*a*c)*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(2*c^2*e^3*x^2 - 12*c^2*d^2*e + 9*b*c*d*e^2 - 4*a*c*e^3 - (6*c^2*d*e^2 - 5*b*c*e^3)*x)*sqrt(c*x^2 + b*x + a))/(c*e^5*x + c*d*e^4), -1/8*(3*(8*c^2*d^3 - 8*b*c*d^2*e + (b^2 + 4*a*c)*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + (b^2 + 4*a*c)*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 6*(2*c^2*d^2 - b*c*d*e + (2*c^2*d*e - b*c*e^2)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 2*(2*c^2*e^3*x^2 - 12*c^2*d^2*e + 9*b*c*d*e^2 - 4*a*c*e^3 - (6*c^2*d*e^2 - 5*b*c*e^3)*x)*sqrt(c*x^2 + b*x + a))/(c*e^5*x + c*d*e^4), -1/8*(12*(2*c^2*d^2 - b*c*d*e + (2*c^2*d*e - b*c*e^2)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 3*(8*c^2*d^3 - 8*b*c*d^2*e + (b^2 + 4*a*c)*d*e^2 + (8*c^2*d^2*e - 8*b*c*d*e^2 + (b^2 + 4*a*c)*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(2*c^2*e^3*x^2 - 12*c^2*d^2*e + 9*b*c*d*e^2 - 4*a*c*e^3 - (6*c^2*d*e^2 - 5*b*c*e^3)*x)*sqrt(c*x^2 + b*x + a))/(c*e^5*x + c*d*e^4)]","A",0
2349,1,2711,0,20.428094," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(2 \, c^{2} d^{5} - 3 \, b c d^{4} e - a b d^{2} e^{3} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} - a b e^{5} + {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{4} e - 3 \, b c d^{3} e^{2} - a b d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 3 \, {\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + {\left(b^{2} + 4 \, a c\right)} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + {\left(b^{2} + 4 \, a c\right)} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(12 \, c^{2} d^{4} e - 15 \, b c d^{3} e^{2} - a b d e^{4} - 2 \, a^{2} e^{5} + {\left(3 \, b^{2} + 10 \, a c\right)} d^{2} e^{3} + 4 \, {\left(c^{2} d^{2} e^{3} - b c d e^{4} + a c e^{5}\right)} x^{2} + {\left(18 \, c^{2} d^{3} e^{2} - 23 \, b c d^{2} e^{3} - 5 \, a b e^{5} + {\left(5 \, b^{2} + 18 \, a c\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(c d^{4} e^{4} - b d^{3} e^{5} + a d^{2} e^{6} + {\left(c d^{2} e^{6} - b d e^{7} + a e^{8}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} - b d^{2} e^{6} + a d e^{7}\right)} x\right)}}, \frac{24 \, {\left(2 \, c^{2} d^{5} - 3 \, b c d^{4} e - a b d^{2} e^{3} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} - a b e^{5} + {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{4} e - 3 \, b c d^{3} e^{2} - a b d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 3 \, {\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + {\left(b^{2} + 4 \, a c\right)} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + {\left(b^{2} + 4 \, a c\right)} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(12 \, c^{2} d^{4} e - 15 \, b c d^{3} e^{2} - a b d e^{4} - 2 \, a^{2} e^{5} + {\left(3 \, b^{2} + 10 \, a c\right)} d^{2} e^{3} + 4 \, {\left(c^{2} d^{2} e^{3} - b c d e^{4} + a c e^{5}\right)} x^{2} + {\left(18 \, c^{2} d^{3} e^{2} - 23 \, b c d^{2} e^{3} - 5 \, a b e^{5} + {\left(5 \, b^{2} + 18 \, a c\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(c d^{4} e^{4} - b d^{3} e^{5} + a d^{2} e^{6} + {\left(c d^{2} e^{6} - b d e^{7} + a e^{8}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} - b d^{2} e^{6} + a d e^{7}\right)} x\right)}}, \frac{3 \, {\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + {\left(b^{2} + 4 \, a c\right)} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + {\left(b^{2} + 4 \, a c\right)} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 6 \, {\left(2 \, c^{2} d^{5} - 3 \, b c d^{4} e - a b d^{2} e^{3} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} - a b e^{5} + {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{4} e - 3 \, b c d^{3} e^{2} - a b d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 2 \, {\left(12 \, c^{2} d^{4} e - 15 \, b c d^{3} e^{2} - a b d e^{4} - 2 \, a^{2} e^{5} + {\left(3 \, b^{2} + 10 \, a c\right)} d^{2} e^{3} + 4 \, {\left(c^{2} d^{2} e^{3} - b c d e^{4} + a c e^{5}\right)} x^{2} + {\left(18 \, c^{2} d^{3} e^{2} - 23 \, b c d^{2} e^{3} - 5 \, a b e^{5} + {\left(5 \, b^{2} + 18 \, a c\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(c d^{4} e^{4} - b d^{3} e^{5} + a d^{2} e^{6} + {\left(c d^{2} e^{6} - b d e^{7} + a e^{8}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} - b d^{2} e^{6} + a d e^{7}\right)} x\right)}}, \frac{3 \, {\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + {\left(b^{2} + 4 \, a c\right)} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + {\left(b^{2} + 4 \, a c\right)} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + {\left(b^{2} + 4 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 12 \, {\left(2 \, c^{2} d^{5} - 3 \, b c d^{4} e - a b d^{2} e^{3} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} - a b e^{5} + {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} x^{2} + 2 \, {\left(2 \, c^{2} d^{4} e - 3 \, b c d^{3} e^{2} - a b d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(12 \, c^{2} d^{4} e - 15 \, b c d^{3} e^{2} - a b d e^{4} - 2 \, a^{2} e^{5} + {\left(3 \, b^{2} + 10 \, a c\right)} d^{2} e^{3} + 4 \, {\left(c^{2} d^{2} e^{3} - b c d e^{4} + a c e^{5}\right)} x^{2} + {\left(18 \, c^{2} d^{3} e^{2} - 23 \, b c d^{2} e^{3} - 5 \, a b e^{5} + {\left(5 \, b^{2} + 18 \, a c\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(c d^{4} e^{4} - b d^{3} e^{5} + a d^{2} e^{6} + {\left(c d^{2} e^{6} - b d e^{7} + a e^{8}\right)} x^{2} + 2 \, {\left(c d^{3} e^{5} - b d^{2} e^{6} + a d e^{7}\right)} x\right)}}\right]"," ",0,"[-1/16*(12*(2*c^2*d^5 - 3*b*c*d^4*e - a*b*d^2*e^3 + (b^2 + 2*a*c)*d^3*e^2 + (2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 - a*b*e^5 + (b^2 + 2*a*c)*d*e^4)*x^2 + 2*(2*c^2*d^4*e - 3*b*c*d^3*e^2 - a*b*d*e^4 + (b^2 + 2*a*c)*d^2*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 3*(8*c^2*d^4 - 8*b*c*d^3*e + (b^2 + 4*a*c)*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + (b^2 + 4*a*c)*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + (b^2 + 4*a*c)*d*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(12*c^2*d^4*e - 15*b*c*d^3*e^2 - a*b*d*e^4 - 2*a^2*e^5 + (3*b^2 + 10*a*c)*d^2*e^3 + 4*(c^2*d^2*e^3 - b*c*d*e^4 + a*c*e^5)*x^2 + (18*c^2*d^3*e^2 - 23*b*c*d^2*e^3 - 5*a*b*e^5 + (5*b^2 + 18*a*c)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*d^4*e^4 - b*d^3*e^5 + a*d^2*e^6 + (c*d^2*e^6 - b*d*e^7 + a*e^8)*x^2 + 2*(c*d^3*e^5 - b*d^2*e^6 + a*d*e^7)*x), 1/16*(24*(2*c^2*d^5 - 3*b*c*d^4*e - a*b*d^2*e^3 + (b^2 + 2*a*c)*d^3*e^2 + (2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 - a*b*e^5 + (b^2 + 2*a*c)*d*e^4)*x^2 + 2*(2*c^2*d^4*e - 3*b*c*d^3*e^2 - a*b*d*e^4 + (b^2 + 2*a*c)*d^2*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 3*(8*c^2*d^4 - 8*b*c*d^3*e + (b^2 + 4*a*c)*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + (b^2 + 4*a*c)*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + (b^2 + 4*a*c)*d*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(12*c^2*d^4*e - 15*b*c*d^3*e^2 - a*b*d*e^4 - 2*a^2*e^5 + (3*b^2 + 10*a*c)*d^2*e^3 + 4*(c^2*d^2*e^3 - b*c*d*e^4 + a*c*e^5)*x^2 + (18*c^2*d^3*e^2 - 23*b*c*d^2*e^3 - 5*a*b*e^5 + (5*b^2 + 18*a*c)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*d^4*e^4 - b*d^3*e^5 + a*d^2*e^6 + (c*d^2*e^6 - b*d*e^7 + a*e^8)*x^2 + 2*(c*d^3*e^5 - b*d^2*e^6 + a*d*e^7)*x), 1/8*(3*(8*c^2*d^4 - 8*b*c*d^3*e + (b^2 + 4*a*c)*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + (b^2 + 4*a*c)*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + (b^2 + 4*a*c)*d*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 6*(2*c^2*d^5 - 3*b*c*d^4*e - a*b*d^2*e^3 + (b^2 + 2*a*c)*d^3*e^2 + (2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 - a*b*e^5 + (b^2 + 2*a*c)*d*e^4)*x^2 + 2*(2*c^2*d^4*e - 3*b*c*d^3*e^2 - a*b*d*e^4 + (b^2 + 2*a*c)*d^2*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 2*(12*c^2*d^4*e - 15*b*c*d^3*e^2 - a*b*d*e^4 - 2*a^2*e^5 + (3*b^2 + 10*a*c)*d^2*e^3 + 4*(c^2*d^2*e^3 - b*c*d*e^4 + a*c*e^5)*x^2 + (18*c^2*d^3*e^2 - 23*b*c*d^2*e^3 - 5*a*b*e^5 + (5*b^2 + 18*a*c)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*d^4*e^4 - b*d^3*e^5 + a*d^2*e^6 + (c*d^2*e^6 - b*d*e^7 + a*e^8)*x^2 + 2*(c*d^3*e^5 - b*d^2*e^6 + a*d*e^7)*x), 1/8*(3*(8*c^2*d^4 - 8*b*c*d^3*e + (b^2 + 4*a*c)*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + (b^2 + 4*a*c)*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + (b^2 + 4*a*c)*d*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 12*(2*c^2*d^5 - 3*b*c*d^4*e - a*b*d^2*e^3 + (b^2 + 2*a*c)*d^3*e^2 + (2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 - a*b*e^5 + (b^2 + 2*a*c)*d*e^4)*x^2 + 2*(2*c^2*d^4*e - 3*b*c*d^3*e^2 - a*b*d*e^4 + (b^2 + 2*a*c)*d^2*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(12*c^2*d^4*e - 15*b*c*d^3*e^2 - a*b*d*e^4 - 2*a^2*e^5 + (3*b^2 + 10*a*c)*d^2*e^3 + 4*(c^2*d^2*e^3 - b*c*d*e^4 + a*c*e^5)*x^2 + (18*c^2*d^3*e^2 - 23*b*c*d^2*e^3 - 5*a*b*e^5 + (5*b^2 + 18*a*c)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*d^4*e^4 - b*d^3*e^5 + a*d^2*e^6 + (c*d^2*e^6 - b*d*e^7 + a*e^8)*x^2 + 2*(c*d^3*e^5 - b*d^2*e^6 + a*d*e^7)*x)]","B",0
2350,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2351,1,2570,0,17.673955," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{4} x^{4} + 4 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d e^{3} x^{3} + 6 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} e^{2} x^{2} + 4 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} e x + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{4}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(40 \, a^{3} b d e^{4} - 16 \, a^{4} e^{5} - {\left(3 \, b^{3} c - 20 \, a b c^{2}\right)} d^{5} + {\left(3 \, b^{4} - 22 \, a b^{2} c - 40 \, a^{2} c^{2}\right)} d^{4} e - {\left(a b^{3} - 84 \, a^{2} b c\right)} d^{3} e^{2} - 2 \, {\left(13 \, a^{2} b^{2} + 28 \, a^{3} c\right)} d^{2} e^{3} + {\left(16 \, c^{4} d^{5} - 40 \, b c^{3} d^{4} e + 2 \, {\left(13 \, b^{2} c^{2} + 28 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 84 \, a b c^{2}\right)} d^{2} e^{3} - {\left(3 \, b^{4} - 22 \, a b^{2} c - 40 \, a^{2} c^{2}\right)} d e^{4} + {\left(3 \, a b^{3} - 20 \, a^{2} b c\right)} e^{5}\right)} x^{3} + {\left(24 \, b c^{3} d^{5} - 4 \, {\left(17 \, b^{2} c^{2} - 8 \, a c^{3}\right)} d^{4} e + 5 \, {\left(11 \, b^{3} c + 4 \, a b c^{2}\right)} d^{3} e^{2} - {\left(11 \, b^{4} + 74 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2} e^{3} + {\left(13 \, a b^{3} + 68 \, a^{2} b c\right)} d e^{4} - 2 \, {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} e^{5}\right)} x^{2} - {\left(24 \, a^{3} b e^{5} - 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{5} + {\left(13 \, b^{3} c + 68 \, a b c^{2}\right)} d^{4} e - {\left(11 \, b^{4} + 74 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{3} e^{2} + 5 \, {\left(11 \, a b^{3} + 4 \, a^{2} b c\right)} d^{2} e^{3} - 4 \, {\left(17 \, a^{2} b^{2} - 8 \, a^{3} c\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{256 \, {\left(c^{3} d^{10} - 3 \, b c^{2} d^{9} e - 3 \, a^{2} b d^{5} e^{5} + a^{3} d^{4} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{8} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{7} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{6} e^{4} + {\left(c^{3} d^{6} e^{4} - 3 \, b c^{2} d^{5} e^{5} - 3 \, a^{2} b d e^{9} + a^{3} e^{10} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{6} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{7} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{8}\right)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{3} - 3 \, b c^{2} d^{6} e^{4} - 3 \, a^{2} b d^{2} e^{8} + a^{3} d e^{9} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{5} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{7}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{2} - 3 \, b c^{2} d^{7} e^{3} - 3 \, a^{2} b d^{3} e^{7} + a^{3} d^{2} e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{6}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e - 3 \, b c^{2} d^{8} e^{2} - 3 \, a^{2} b d^{4} e^{6} + a^{3} d^{3} e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{7} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{6} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{5} e^{5}\right)} x\right)}}, \frac{3 \, {\left({\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} e^{4} x^{4} + 4 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d e^{3} x^{3} + 6 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} e^{2} x^{2} + 4 \, {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} e x + {\left(b^{4} - 8 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{4}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(40 \, a^{3} b d e^{4} - 16 \, a^{4} e^{5} - {\left(3 \, b^{3} c - 20 \, a b c^{2}\right)} d^{5} + {\left(3 \, b^{4} - 22 \, a b^{2} c - 40 \, a^{2} c^{2}\right)} d^{4} e - {\left(a b^{3} - 84 \, a^{2} b c\right)} d^{3} e^{2} - 2 \, {\left(13 \, a^{2} b^{2} + 28 \, a^{3} c\right)} d^{2} e^{3} + {\left(16 \, c^{4} d^{5} - 40 \, b c^{3} d^{4} e + 2 \, {\left(13 \, b^{2} c^{2} + 28 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 84 \, a b c^{2}\right)} d^{2} e^{3} - {\left(3 \, b^{4} - 22 \, a b^{2} c - 40 \, a^{2} c^{2}\right)} d e^{4} + {\left(3 \, a b^{3} - 20 \, a^{2} b c\right)} e^{5}\right)} x^{3} + {\left(24 \, b c^{3} d^{5} - 4 \, {\left(17 \, b^{2} c^{2} - 8 \, a c^{3}\right)} d^{4} e + 5 \, {\left(11 \, b^{3} c + 4 \, a b c^{2}\right)} d^{3} e^{2} - {\left(11 \, b^{4} + 74 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{2} e^{3} + {\left(13 \, a b^{3} + 68 \, a^{2} b c\right)} d e^{4} - 2 \, {\left(a^{2} b^{2} + 20 \, a^{3} c\right)} e^{5}\right)} x^{2} - {\left(24 \, a^{3} b e^{5} - 2 \, {\left(b^{2} c^{2} + 20 \, a c^{3}\right)} d^{5} + {\left(13 \, b^{3} c + 68 \, a b c^{2}\right)} d^{4} e - {\left(11 \, b^{4} + 74 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d^{3} e^{2} + 5 \, {\left(11 \, a b^{3} + 4 \, a^{2} b c\right)} d^{2} e^{3} - 4 \, {\left(17 \, a^{2} b^{2} - 8 \, a^{3} c\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{128 \, {\left(c^{3} d^{10} - 3 \, b c^{2} d^{9} e - 3 \, a^{2} b d^{5} e^{5} + a^{3} d^{4} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{8} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{7} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{6} e^{4} + {\left(c^{3} d^{6} e^{4} - 3 \, b c^{2} d^{5} e^{5} - 3 \, a^{2} b d e^{9} + a^{3} e^{10} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{6} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{7} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{8}\right)} x^{4} + 4 \, {\left(c^{3} d^{7} e^{3} - 3 \, b c^{2} d^{6} e^{4} - 3 \, a^{2} b d^{2} e^{8} + a^{3} d e^{9} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{5} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{7}\right)} x^{3} + 6 \, {\left(c^{3} d^{8} e^{2} - 3 \, b c^{2} d^{7} e^{3} - 3 \, a^{2} b d^{3} e^{7} + a^{3} d^{2} e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{6}\right)} x^{2} + 4 \, {\left(c^{3} d^{9} e - 3 \, b c^{2} d^{8} e^{2} - 3 \, a^{2} b d^{4} e^{6} + a^{3} d^{3} e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{7} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{6} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{5} e^{5}\right)} x\right)}}\right]"," ",0,"[1/256*(3*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^4*x^4 + 4*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d*e^3*x^3 + 6*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^2*e^2*x^2 + 4*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^3*e*x + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^4)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(40*a^3*b*d*e^4 - 16*a^4*e^5 - (3*b^3*c - 20*a*b*c^2)*d^5 + (3*b^4 - 22*a*b^2*c - 40*a^2*c^2)*d^4*e - (a*b^3 - 84*a^2*b*c)*d^3*e^2 - 2*(13*a^2*b^2 + 28*a^3*c)*d^2*e^3 + (16*c^4*d^5 - 40*b*c^3*d^4*e + 2*(13*b^2*c^2 + 28*a*c^3)*d^3*e^2 + (b^3*c - 84*a*b*c^2)*d^2*e^3 - (3*b^4 - 22*a*b^2*c - 40*a^2*c^2)*d*e^4 + (3*a*b^3 - 20*a^2*b*c)*e^5)*x^3 + (24*b*c^3*d^5 - 4*(17*b^2*c^2 - 8*a*c^3)*d^4*e + 5*(11*b^3*c + 4*a*b*c^2)*d^3*e^2 - (11*b^4 + 74*a*b^2*c + 8*a^2*c^2)*d^2*e^3 + (13*a*b^3 + 68*a^2*b*c)*d*e^4 - 2*(a^2*b^2 + 20*a^3*c)*e^5)*x^2 - (24*a^3*b*e^5 - 2*(b^2*c^2 + 20*a*c^3)*d^5 + (13*b^3*c + 68*a*b*c^2)*d^4*e - (11*b^4 + 74*a*b^2*c + 8*a^2*c^2)*d^3*e^2 + 5*(11*a*b^3 + 4*a^2*b*c)*d^2*e^3 - 4*(17*a^2*b^2 - 8*a^3*c)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^10 - 3*b*c^2*d^9*e - 3*a^2*b*d^5*e^5 + a^3*d^4*e^6 + 3*(b^2*c + a*c^2)*d^8*e^2 - (b^3 + 6*a*b*c)*d^7*e^3 + 3*(a*b^2 + a^2*c)*d^6*e^4 + (c^3*d^6*e^4 - 3*b*c^2*d^5*e^5 - 3*a^2*b*d*e^9 + a^3*e^10 + 3*(b^2*c + a*c^2)*d^4*e^6 - (b^3 + 6*a*b*c)*d^3*e^7 + 3*(a*b^2 + a^2*c)*d^2*e^8)*x^4 + 4*(c^3*d^7*e^3 - 3*b*c^2*d^6*e^4 - 3*a^2*b*d^2*e^8 + a^3*d*e^9 + 3*(b^2*c + a*c^2)*d^5*e^5 - (b^3 + 6*a*b*c)*d^4*e^6 + 3*(a*b^2 + a^2*c)*d^3*e^7)*x^3 + 6*(c^3*d^8*e^2 - 3*b*c^2*d^7*e^3 - 3*a^2*b*d^3*e^7 + a^3*d^2*e^8 + 3*(b^2*c + a*c^2)*d^6*e^4 - (b^3 + 6*a*b*c)*d^5*e^5 + 3*(a*b^2 + a^2*c)*d^4*e^6)*x^2 + 4*(c^3*d^9*e - 3*b*c^2*d^8*e^2 - 3*a^2*b*d^4*e^6 + a^3*d^3*e^7 + 3*(b^2*c + a*c^2)*d^7*e^3 - (b^3 + 6*a*b*c)*d^6*e^4 + 3*(a*b^2 + a^2*c)*d^5*e^5)*x), 1/128*(3*((b^4 - 8*a*b^2*c + 16*a^2*c^2)*e^4*x^4 + 4*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d*e^3*x^3 + 6*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^2*e^2*x^2 + 4*(b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^3*e*x + (b^4 - 8*a*b^2*c + 16*a^2*c^2)*d^4)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(40*a^3*b*d*e^4 - 16*a^4*e^5 - (3*b^3*c - 20*a*b*c^2)*d^5 + (3*b^4 - 22*a*b^2*c - 40*a^2*c^2)*d^4*e - (a*b^3 - 84*a^2*b*c)*d^3*e^2 - 2*(13*a^2*b^2 + 28*a^3*c)*d^2*e^3 + (16*c^4*d^5 - 40*b*c^3*d^4*e + 2*(13*b^2*c^2 + 28*a*c^3)*d^3*e^2 + (b^3*c - 84*a*b*c^2)*d^2*e^3 - (3*b^4 - 22*a*b^2*c - 40*a^2*c^2)*d*e^4 + (3*a*b^3 - 20*a^2*b*c)*e^5)*x^3 + (24*b*c^3*d^5 - 4*(17*b^2*c^2 - 8*a*c^3)*d^4*e + 5*(11*b^3*c + 4*a*b*c^2)*d^3*e^2 - (11*b^4 + 74*a*b^2*c + 8*a^2*c^2)*d^2*e^3 + (13*a*b^3 + 68*a^2*b*c)*d*e^4 - 2*(a^2*b^2 + 20*a^3*c)*e^5)*x^2 - (24*a^3*b*e^5 - 2*(b^2*c^2 + 20*a*c^3)*d^5 + (13*b^3*c + 68*a*b*c^2)*d^4*e - (11*b^4 + 74*a*b^2*c + 8*a^2*c^2)*d^3*e^2 + 5*(11*a*b^3 + 4*a^2*b*c)*d^2*e^3 - 4*(17*a^2*b^2 - 8*a^3*c)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^10 - 3*b*c^2*d^9*e - 3*a^2*b*d^5*e^5 + a^3*d^4*e^6 + 3*(b^2*c + a*c^2)*d^8*e^2 - (b^3 + 6*a*b*c)*d^7*e^3 + 3*(a*b^2 + a^2*c)*d^6*e^4 + (c^3*d^6*e^4 - 3*b*c^2*d^5*e^5 - 3*a^2*b*d*e^9 + a^3*e^10 + 3*(b^2*c + a*c^2)*d^4*e^6 - (b^3 + 6*a*b*c)*d^3*e^7 + 3*(a*b^2 + a^2*c)*d^2*e^8)*x^4 + 4*(c^3*d^7*e^3 - 3*b*c^2*d^6*e^4 - 3*a^2*b*d^2*e^8 + a^3*d*e^9 + 3*(b^2*c + a*c^2)*d^5*e^5 - (b^3 + 6*a*b*c)*d^4*e^6 + 3*(a*b^2 + a^2*c)*d^3*e^7)*x^3 + 6*(c^3*d^8*e^2 - 3*b*c^2*d^7*e^3 - 3*a^2*b*d^3*e^7 + a^3*d^2*e^8 + 3*(b^2*c + a*c^2)*d^6*e^4 - (b^3 + 6*a*b*c)*d^5*e^5 + 3*(a*b^2 + a^2*c)*d^4*e^6)*x^2 + 4*(c^3*d^9*e - 3*b*c^2*d^8*e^2 - 3*a^2*b*d^4*e^6 + a^3*d^3*e^7 + 3*(b^2*c + a*c^2)*d^7*e^3 - (b^3 + 6*a*b*c)*d^6*e^4 + 3*(a*b^2 + a^2*c)*d^5*e^5)*x)]","B",0
2352,1,4830,0,75.935161," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^6,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{6} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{5} e + {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{5} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{6}\right)} x^{5} + 5 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} e^{4} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d e^{5}\right)} x^{4} + 10 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} e^{3} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} e^{4}\right)} x^{3} + 10 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{3} e^{3}\right)} x^{2} + 5 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{5} e - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{4} e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(464 \, a^{4} b d e^{6} - 128 \, a^{5} e^{7} - 10 \, {\left(3 \, b^{3} c^{2} - 20 \, a b c^{3}\right)} d^{7} + {\left(45 \, b^{4} c - 320 \, a b^{2} c^{2} - 528 \, a^{2} c^{3}\right)} d^{6} e - {\left(15 \, b^{5} - 100 \, a b^{3} c - 1424 \, a^{2} b c^{2}\right)} d^{5} e^{2} + {\left(5 \, a b^{4} - 1064 \, a^{2} b^{2} c - 944 \, a^{3} c^{2}\right)} d^{4} e^{3} + 2 \, {\left(129 \, a^{2} b^{3} + 724 \, a^{3} b c\right)} d^{3} e^{4} - 8 \, {\left(73 \, a^{3} b^{2} + 68 \, a^{4} c\right)} d^{2} e^{5} + {\left(32 \, c^{5} d^{6} e - 96 \, b c^{4} d^{5} e^{2} + 4 \, {\left(19 \, b^{2} c^{3} + 44 \, a c^{4}\right)} d^{4} e^{3} + 8 \, {\left(b^{3} c^{2} - 44 \, a b c^{3}\right)} d^{3} e^{4} - {\left(35 \, b^{4} c - 256 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d^{2} e^{5} + {\left(15 \, b^{5} - 80 \, a b^{3} c - 16 \, a^{2} b c^{2}\right)} d e^{6} - {\left(15 \, a b^{4} - 100 \, a^{2} b^{2} c + 128 \, a^{3} c^{2}\right)} e^{7}\right)} x^{4} + 2 \, {\left(80 \, c^{5} d^{7} - 248 \, b c^{4} d^{6} e + 2 \, {\left(107 \, b^{2} c^{3} + 220 \, a c^{4}\right)} d^{5} e^{2} + {\left(b^{3} c^{2} - 924 \, a b c^{3}\right)} d^{4} e^{3} - 2 \, {\left(41 \, b^{4} c - 334 \, a b^{2} c^{2} - 80 \, a^{2} c^{3}\right)} d^{3} e^{4} + {\left(35 \, b^{5} - 174 \, a b^{3} c - 224 \, a^{2} b c^{2}\right)} d^{2} e^{5} - 2 \, {\left(20 \, a b^{4} - 127 \, a^{2} b^{2} c + 100 \, a^{3} c^{2}\right)} d e^{6} + {\left(5 \, a^{2} b^{3} - 28 \, a^{3} b c\right)} e^{7}\right)} x^{3} + 2 \, {\left(120 \, b c^{4} d^{7} - 2 \, {\left(227 \, b^{2} c^{3} - 116 \, a c^{4}\right)} d^{6} e + 9 \, {\left(63 \, b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e^{2} - 3 \, {\left(99 \, b^{4} c + 152 \, a b^{2} c^{2} + 128 \, a^{2} c^{3}\right)} d^{4} e^{3} + 2 \, {\left(32 \, b^{5} + 151 \, a b^{3} c + 504 \, a^{2} b c^{2}\right)} d^{3} e^{4} - 3 \, {\left(29 \, a b^{4} + 122 \, a^{2} b^{2} c + 248 \, a^{3} c^{2}\right)} d^{2} e^{5} + 3 \, {\left(9 \, a^{2} b^{3} + 148 \, a^{3} b c\right)} d e^{6} - 4 \, {\left(a^{3} b^{2} + 32 \, a^{4} c\right)} e^{7}\right)} x^{2} - 2 \, {\left(88 \, a^{4} b e^{7} - 10 \, {\left(b^{2} c^{3} + 20 \, a c^{4}\right)} d^{7} + {\left(85 \, b^{3} c^{2} + 468 \, a b c^{3}\right)} d^{6} e - 2 \, {\left(55 \, b^{4} c + 382 \, a b^{2} c^{2} - 80 \, a^{2} c^{3}\right)} d^{5} e^{2} + {\left(35 \, b^{5} + 794 \, a b^{3} c - 16 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 2 \, {\left(134 \, a b^{4} + 409 \, a^{2} b^{2} c - 220 \, a^{3} c^{2}\right)} d^{3} e^{4} + 3 \, {\left(163 \, a^{2} b^{3} + 28 \, a^{3} b c\right)} d^{2} e^{5} - 8 \, {\left(43 \, a^{3} b^{2} - 10 \, a^{4} c\right)} d e^{6}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2560 \, {\left(c^{4} d^{13} - 4 \, b c^{3} d^{12} e - 4 \, a^{3} b d^{6} e^{7} + a^{4} d^{5} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{11} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{10} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{9} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{8} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{7} e^{6} + {\left(c^{4} d^{8} e^{5} - 4 \, b c^{3} d^{7} e^{6} - 4 \, a^{3} b d e^{12} + a^{4} e^{13} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{7} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{8} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{9} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{10} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{11}\right)} x^{5} + 5 \, {\left(c^{4} d^{9} e^{4} - 4 \, b c^{3} d^{8} e^{5} - 4 \, a^{3} b d^{2} e^{11} + a^{4} d e^{12} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{6} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{8} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{9} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{10}\right)} x^{4} + 10 \, {\left(c^{4} d^{10} e^{3} - 4 \, b c^{3} d^{9} e^{4} - 4 \, a^{3} b d^{3} e^{10} + a^{4} d^{2} e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{9}\right)} x^{3} + 10 \, {\left(c^{4} d^{11} e^{2} - 4 \, b c^{3} d^{10} e^{3} - 4 \, a^{3} b d^{4} e^{9} + a^{4} d^{3} e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{8}\right)} x^{2} + 5 \, {\left(c^{4} d^{12} e - 4 \, b c^{3} d^{11} e^{2} - 4 \, a^{3} b d^{5} e^{8} + a^{4} d^{4} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{10} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{9} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{8} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{7} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{6} e^{7}\right)} x\right)}}, \frac{15 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{6} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{5} e + {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d e^{5} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{6}\right)} x^{5} + 5 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} e^{4} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d e^{5}\right)} x^{4} + 10 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{3} e^{3} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} e^{4}\right)} x^{3} + 10 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{4} e^{2} - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{3} e^{3}\right)} x^{2} + 5 \, {\left(2 \, {\left(b^{4} c - 8 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{5} e - {\left(b^{5} - 8 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{4} e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 2 \, {\left(464 \, a^{4} b d e^{6} - 128 \, a^{5} e^{7} - 10 \, {\left(3 \, b^{3} c^{2} - 20 \, a b c^{3}\right)} d^{7} + {\left(45 \, b^{4} c - 320 \, a b^{2} c^{2} - 528 \, a^{2} c^{3}\right)} d^{6} e - {\left(15 \, b^{5} - 100 \, a b^{3} c - 1424 \, a^{2} b c^{2}\right)} d^{5} e^{2} + {\left(5 \, a b^{4} - 1064 \, a^{2} b^{2} c - 944 \, a^{3} c^{2}\right)} d^{4} e^{3} + 2 \, {\left(129 \, a^{2} b^{3} + 724 \, a^{3} b c\right)} d^{3} e^{4} - 8 \, {\left(73 \, a^{3} b^{2} + 68 \, a^{4} c\right)} d^{2} e^{5} + {\left(32 \, c^{5} d^{6} e - 96 \, b c^{4} d^{5} e^{2} + 4 \, {\left(19 \, b^{2} c^{3} + 44 \, a c^{4}\right)} d^{4} e^{3} + 8 \, {\left(b^{3} c^{2} - 44 \, a b c^{3}\right)} d^{3} e^{4} - {\left(35 \, b^{4} c - 256 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d^{2} e^{5} + {\left(15 \, b^{5} - 80 \, a b^{3} c - 16 \, a^{2} b c^{2}\right)} d e^{6} - {\left(15 \, a b^{4} - 100 \, a^{2} b^{2} c + 128 \, a^{3} c^{2}\right)} e^{7}\right)} x^{4} + 2 \, {\left(80 \, c^{5} d^{7} - 248 \, b c^{4} d^{6} e + 2 \, {\left(107 \, b^{2} c^{3} + 220 \, a c^{4}\right)} d^{5} e^{2} + {\left(b^{3} c^{2} - 924 \, a b c^{3}\right)} d^{4} e^{3} - 2 \, {\left(41 \, b^{4} c - 334 \, a b^{2} c^{2} - 80 \, a^{2} c^{3}\right)} d^{3} e^{4} + {\left(35 \, b^{5} - 174 \, a b^{3} c - 224 \, a^{2} b c^{2}\right)} d^{2} e^{5} - 2 \, {\left(20 \, a b^{4} - 127 \, a^{2} b^{2} c + 100 \, a^{3} c^{2}\right)} d e^{6} + {\left(5 \, a^{2} b^{3} - 28 \, a^{3} b c\right)} e^{7}\right)} x^{3} + 2 \, {\left(120 \, b c^{4} d^{7} - 2 \, {\left(227 \, b^{2} c^{3} - 116 \, a c^{4}\right)} d^{6} e + 9 \, {\left(63 \, b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{5} e^{2} - 3 \, {\left(99 \, b^{4} c + 152 \, a b^{2} c^{2} + 128 \, a^{2} c^{3}\right)} d^{4} e^{3} + 2 \, {\left(32 \, b^{5} + 151 \, a b^{3} c + 504 \, a^{2} b c^{2}\right)} d^{3} e^{4} - 3 \, {\left(29 \, a b^{4} + 122 \, a^{2} b^{2} c + 248 \, a^{3} c^{2}\right)} d^{2} e^{5} + 3 \, {\left(9 \, a^{2} b^{3} + 148 \, a^{3} b c\right)} d e^{6} - 4 \, {\left(a^{3} b^{2} + 32 \, a^{4} c\right)} e^{7}\right)} x^{2} - 2 \, {\left(88 \, a^{4} b e^{7} - 10 \, {\left(b^{2} c^{3} + 20 \, a c^{4}\right)} d^{7} + {\left(85 \, b^{3} c^{2} + 468 \, a b c^{3}\right)} d^{6} e - 2 \, {\left(55 \, b^{4} c + 382 \, a b^{2} c^{2} - 80 \, a^{2} c^{3}\right)} d^{5} e^{2} + {\left(35 \, b^{5} + 794 \, a b^{3} c - 16 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 2 \, {\left(134 \, a b^{4} + 409 \, a^{2} b^{2} c - 220 \, a^{3} c^{2}\right)} d^{3} e^{4} + 3 \, {\left(163 \, a^{2} b^{3} + 28 \, a^{3} b c\right)} d^{2} e^{5} - 8 \, {\left(43 \, a^{3} b^{2} - 10 \, a^{4} c\right)} d e^{6}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1280 \, {\left(c^{4} d^{13} - 4 \, b c^{3} d^{12} e - 4 \, a^{3} b d^{6} e^{7} + a^{4} d^{5} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{11} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{10} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{9} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{8} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{7} e^{6} + {\left(c^{4} d^{8} e^{5} - 4 \, b c^{3} d^{7} e^{6} - 4 \, a^{3} b d e^{12} + a^{4} e^{13} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{7} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{8} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{9} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{10} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{11}\right)} x^{5} + 5 \, {\left(c^{4} d^{9} e^{4} - 4 \, b c^{3} d^{8} e^{5} - 4 \, a^{3} b d^{2} e^{11} + a^{4} d e^{12} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{6} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{7} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{8} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{9} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{10}\right)} x^{4} + 10 \, {\left(c^{4} d^{10} e^{3} - 4 \, b c^{3} d^{9} e^{4} - 4 \, a^{3} b d^{3} e^{10} + a^{4} d^{2} e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{9}\right)} x^{3} + 10 \, {\left(c^{4} d^{11} e^{2} - 4 \, b c^{3} d^{10} e^{3} - 4 \, a^{3} b d^{4} e^{9} + a^{4} d^{3} e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{8}\right)} x^{2} + 5 \, {\left(c^{4} d^{12} e - 4 \, b c^{3} d^{11} e^{2} - 4 \, a^{3} b d^{5} e^{8} + a^{4} d^{4} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{10} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{9} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{8} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{7} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{6} e^{7}\right)} x\right)}}\right]"," ",0,"[-1/2560*(15*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^6 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^5*e + (2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^5 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^6)*x^5 + 5*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2*e^4 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*e^5)*x^4 + 10*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3*e^3 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2*e^4)*x^3 + 10*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^4*e^2 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^3*e^3)*x^2 + 5*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^5*e - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^4*e^2)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(464*a^4*b*d*e^6 - 128*a^5*e^7 - 10*(3*b^3*c^2 - 20*a*b*c^3)*d^7 + (45*b^4*c - 320*a*b^2*c^2 - 528*a^2*c^3)*d^6*e - (15*b^5 - 100*a*b^3*c - 1424*a^2*b*c^2)*d^5*e^2 + (5*a*b^4 - 1064*a^2*b^2*c - 944*a^3*c^2)*d^4*e^3 + 2*(129*a^2*b^3 + 724*a^3*b*c)*d^3*e^4 - 8*(73*a^3*b^2 + 68*a^4*c)*d^2*e^5 + (32*c^5*d^6*e - 96*b*c^4*d^5*e^2 + 4*(19*b^2*c^3 + 44*a*c^4)*d^4*e^3 + 8*(b^3*c^2 - 44*a*b*c^3)*d^3*e^4 - (35*b^4*c - 256*a*b^2*c^2 - 16*a^2*c^3)*d^2*e^5 + (15*b^5 - 80*a*b^3*c - 16*a^2*b*c^2)*d*e^6 - (15*a*b^4 - 100*a^2*b^2*c + 128*a^3*c^2)*e^7)*x^4 + 2*(80*c^5*d^7 - 248*b*c^4*d^6*e + 2*(107*b^2*c^3 + 220*a*c^4)*d^5*e^2 + (b^3*c^2 - 924*a*b*c^3)*d^4*e^3 - 2*(41*b^4*c - 334*a*b^2*c^2 - 80*a^2*c^3)*d^3*e^4 + (35*b^5 - 174*a*b^3*c - 224*a^2*b*c^2)*d^2*e^5 - 2*(20*a*b^4 - 127*a^2*b^2*c + 100*a^3*c^2)*d*e^6 + (5*a^2*b^3 - 28*a^3*b*c)*e^7)*x^3 + 2*(120*b*c^4*d^7 - 2*(227*b^2*c^3 - 116*a*c^4)*d^6*e + 9*(63*b^3*c^2 - 4*a*b*c^3)*d^5*e^2 - 3*(99*b^4*c + 152*a*b^2*c^2 + 128*a^2*c^3)*d^4*e^3 + 2*(32*b^5 + 151*a*b^3*c + 504*a^2*b*c^2)*d^3*e^4 - 3*(29*a*b^4 + 122*a^2*b^2*c + 248*a^3*c^2)*d^2*e^5 + 3*(9*a^2*b^3 + 148*a^3*b*c)*d*e^6 - 4*(a^3*b^2 + 32*a^4*c)*e^7)*x^2 - 2*(88*a^4*b*e^7 - 10*(b^2*c^3 + 20*a*c^4)*d^7 + (85*b^3*c^2 + 468*a*b*c^3)*d^6*e - 2*(55*b^4*c + 382*a*b^2*c^2 - 80*a^2*c^3)*d^5*e^2 + (35*b^5 + 794*a*b^3*c - 16*a^2*b*c^2)*d^4*e^3 - 2*(134*a*b^4 + 409*a^2*b^2*c - 220*a^3*c^2)*d^3*e^4 + 3*(163*a^2*b^3 + 28*a^3*b*c)*d^2*e^5 - 8*(43*a^3*b^2 - 10*a^4*c)*d*e^6)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^13 - 4*b*c^3*d^12*e - 4*a^3*b*d^6*e^7 + a^4*d^5*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^11*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^10*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^9*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^8*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^7*e^6 + (c^4*d^8*e^5 - 4*b*c^3*d^7*e^6 - 4*a^3*b*d*e^12 + a^4*e^13 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^7 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^8 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^9 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^10 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^11)*x^5 + 5*(c^4*d^9*e^4 - 4*b*c^3*d^8*e^5 - 4*a^3*b*d^2*e^11 + a^4*d*e^12 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^6 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^8 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^9 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^10)*x^4 + 10*(c^4*d^10*e^3 - 4*b*c^3*d^9*e^4 - 4*a^3*b*d^3*e^10 + a^4*d^2*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^9)*x^3 + 10*(c^4*d^11*e^2 - 4*b*c^3*d^10*e^3 - 4*a^3*b*d^4*e^9 + a^4*d^3*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^8)*x^2 + 5*(c^4*d^12*e - 4*b*c^3*d^11*e^2 - 4*a^3*b*d^5*e^8 + a^4*d^4*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^10*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^9*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^8*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^7*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^6*e^7)*x), 1/1280*(15*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^6 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^5*e + (2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d*e^5 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*e^6)*x^5 + 5*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^2*e^4 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d*e^5)*x^4 + 10*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^3*e^3 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^2*e^4)*x^3 + 10*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^4*e^2 - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^3*e^3)*x^2 + 5*(2*(b^4*c - 8*a*b^2*c^2 + 16*a^2*c^3)*d^5*e - (b^5 - 8*a*b^3*c + 16*a^2*b*c^2)*d^4*e^2)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 2*(464*a^4*b*d*e^6 - 128*a^5*e^7 - 10*(3*b^3*c^2 - 20*a*b*c^3)*d^7 + (45*b^4*c - 320*a*b^2*c^2 - 528*a^2*c^3)*d^6*e - (15*b^5 - 100*a*b^3*c - 1424*a^2*b*c^2)*d^5*e^2 + (5*a*b^4 - 1064*a^2*b^2*c - 944*a^3*c^2)*d^4*e^3 + 2*(129*a^2*b^3 + 724*a^3*b*c)*d^3*e^4 - 8*(73*a^3*b^2 + 68*a^4*c)*d^2*e^5 + (32*c^5*d^6*e - 96*b*c^4*d^5*e^2 + 4*(19*b^2*c^3 + 44*a*c^4)*d^4*e^3 + 8*(b^3*c^2 - 44*a*b*c^3)*d^3*e^4 - (35*b^4*c - 256*a*b^2*c^2 - 16*a^2*c^3)*d^2*e^5 + (15*b^5 - 80*a*b^3*c - 16*a^2*b*c^2)*d*e^6 - (15*a*b^4 - 100*a^2*b^2*c + 128*a^3*c^2)*e^7)*x^4 + 2*(80*c^5*d^7 - 248*b*c^4*d^6*e + 2*(107*b^2*c^3 + 220*a*c^4)*d^5*e^2 + (b^3*c^2 - 924*a*b*c^3)*d^4*e^3 - 2*(41*b^4*c - 334*a*b^2*c^2 - 80*a^2*c^3)*d^3*e^4 + (35*b^5 - 174*a*b^3*c - 224*a^2*b*c^2)*d^2*e^5 - 2*(20*a*b^4 - 127*a^2*b^2*c + 100*a^3*c^2)*d*e^6 + (5*a^2*b^3 - 28*a^3*b*c)*e^7)*x^3 + 2*(120*b*c^4*d^7 - 2*(227*b^2*c^3 - 116*a*c^4)*d^6*e + 9*(63*b^3*c^2 - 4*a*b*c^3)*d^5*e^2 - 3*(99*b^4*c + 152*a*b^2*c^2 + 128*a^2*c^3)*d^4*e^3 + 2*(32*b^5 + 151*a*b^3*c + 504*a^2*b*c^2)*d^3*e^4 - 3*(29*a*b^4 + 122*a^2*b^2*c + 248*a^3*c^2)*d^2*e^5 + 3*(9*a^2*b^3 + 148*a^3*b*c)*d*e^6 - 4*(a^3*b^2 + 32*a^4*c)*e^7)*x^2 - 2*(88*a^4*b*e^7 - 10*(b^2*c^3 + 20*a*c^4)*d^7 + (85*b^3*c^2 + 468*a*b*c^3)*d^6*e - 2*(55*b^4*c + 382*a*b^2*c^2 - 80*a^2*c^3)*d^5*e^2 + (35*b^5 + 794*a*b^3*c - 16*a^2*b*c^2)*d^4*e^3 - 2*(134*a*b^4 + 409*a^2*b^2*c - 220*a^3*c^2)*d^3*e^4 + 3*(163*a^2*b^3 + 28*a^3*b*c)*d^2*e^5 - 8*(43*a^3*b^2 - 10*a^4*c)*d*e^6)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^13 - 4*b*c^3*d^12*e - 4*a^3*b*d^6*e^7 + a^4*d^5*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^11*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^10*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^9*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^8*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^7*e^6 + (c^4*d^8*e^5 - 4*b*c^3*d^7*e^6 - 4*a^3*b*d*e^12 + a^4*e^13 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^7 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^8 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^9 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^10 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^11)*x^5 + 5*(c^4*d^9*e^4 - 4*b*c^3*d^8*e^5 - 4*a^3*b*d^2*e^11 + a^4*d*e^12 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^6 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^7 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^8 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^9 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^10)*x^4 + 10*(c^4*d^10*e^3 - 4*b*c^3*d^9*e^4 - 4*a^3*b*d^3*e^10 + a^4*d^2*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^9)*x^3 + 10*(c^4*d^11*e^2 - 4*b*c^3*d^10*e^3 - 4*a^3*b*d^4*e^9 + a^4*d^3*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^8)*x^2 + 5*(c^4*d^12*e - 4*b*c^3*d^11*e^2 - 4*a^3*b*d^5*e^8 + a^4*d^4*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^10*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^9*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^8*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^7*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^6*e^7)*x)]","B",0
2353,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^7,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2354,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^8,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2355,1,2119,0,0.770257," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{315 \, {\left(64 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{3} - 96 \, {\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)} d^{2} e + 6 \, {\left(9 \, b^{8} c - 112 \, a b^{6} c^{2} + 480 \, a^{2} b^{4} c^{3} - 768 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} d e^{2} - {\left(11 \, b^{9} - 144 \, a b^{7} c + 672 \, a^{2} b^{5} c^{2} - 1280 \, a^{3} b^{3} c^{3} + 768 \, a^{4} b c^{4}\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(229376 \, c^{9} e^{3} x^{8} + 14336 \, {\left(54 \, c^{9} d e^{2} + 37 \, b c^{8} e^{3}\right)} x^{7} + 1024 \, {\left(864 \, c^{9} d^{2} e + 1782 \, b c^{8} d e^{2} + {\left(309 \, b^{2} c^{7} + 608 \, a c^{8}\right)} e^{3}\right)} x^{6} + 256 \, {\left(1344 \, c^{9} d^{3} + 8352 \, b c^{8} d^{2} e + 18 \, {\left(243 \, b^{2} c^{7} + 476 \, a c^{8}\right)} d e^{2} + {\left(5 \, b^{3} c^{6} + 3012 \, a b c^{7}\right)} e^{3}\right)} x^{5} + 128 \, {\left(6720 \, b c^{8} d^{3} + 288 \, {\left(37 \, b^{2} c^{7} + 72 \, a c^{8}\right)} d^{2} e + 18 \, {\left(3 \, b^{3} c^{6} + 1228 \, a b c^{7}\right)} d e^{2} - {\left(11 \, b^{4} c^{5} - 84 \, a b^{2} c^{6} - 3840 \, a^{2} c^{7}\right)} e^{3}\right)} x^{4} + 1344 \, {\left(15 \, b^{5} c^{4} - 160 \, a b^{3} c^{5} + 528 \, a^{2} b c^{6}\right)} d^{3} - 288 \, {\left(105 \, b^{6} c^{3} - 1120 \, a b^{4} c^{4} + 3696 \, a^{2} b^{2} c^{5} - 3072 \, a^{3} c^{6}\right)} d^{2} e + 18 \, {\left(945 \, b^{7} c^{2} - 10500 \, a b^{5} c^{3} + 37744 \, a^{2} b^{3} c^{4} - 42432 \, a^{3} b c^{5}\right)} d e^{2} - {\left(3465 \, b^{8} c - 40740 \, a b^{6} c^{2} + 162288 \, a^{2} b^{4} c^{3} - 234432 \, a^{3} b^{2} c^{4} + 65536 \, a^{4} c^{5}\right)} e^{3} + 16 \, {\left(1344 \, {\left(27 \, b^{2} c^{7} + 52 \, a c^{8}\right)} d^{3} + 288 \, {\left(3 \, b^{3} c^{6} + 788 \, a b c^{7}\right)} d^{2} e - 18 \, {\left(27 \, b^{4} c^{5} - 216 \, a b^{2} c^{6} - 6608 \, a^{2} c^{7}\right)} d e^{2} + {\left(99 \, b^{5} c^{4} - 856 \, a b^{3} c^{5} + 1968 \, a^{2} b c^{6}\right)} e^{3}\right)} x^{3} + 8 \, {\left(1344 \, {\left(b^{3} c^{6} + 156 \, a b c^{7}\right)} d^{3} - 288 \, {\left(7 \, b^{4} c^{5} - 60 \, a b^{2} c^{6} - 1152 \, a^{2} c^{7}\right)} d^{2} e + 18 \, {\left(63 \, b^{5} c^{4} - 568 \, a b^{3} c^{5} + 1392 \, a^{2} b c^{6}\right)} d e^{2} - {\left(231 \, b^{6} c^{3} - 2232 \, a b^{4} c^{4} + 6384 \, a^{2} b^{2} c^{5} - 4096 \, a^{3} c^{6}\right)} e^{3}\right)} x^{2} - 2 \, {\left(1344 \, {\left(5 \, b^{4} c^{5} - 48 \, a b^{2} c^{6} - 528 \, a^{2} c^{7}\right)} d^{3} - 288 \, {\left(35 \, b^{5} c^{4} - 336 \, a b^{3} c^{5} + 912 \, a^{2} b c^{6}\right)} d^{2} e + 18 \, {\left(315 \, b^{6} c^{3} - 3164 \, a b^{4} c^{4} + 9552 \, a^{2} b^{2} c^{5} - 6720 \, a^{3} c^{6}\right)} d e^{2} - {\left(1155 \, b^{7} c^{2} - 12348 \, a b^{5} c^{3} + 42192 \, a^{2} b^{3} c^{4} - 44096 \, a^{3} b c^{5}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8257536 \, c^{7}}, \frac{315 \, {\left(64 \, {\left(b^{6} c^{3} - 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} - 64 \, a^{3} c^{6}\right)} d^{3} - 96 \, {\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)} d^{2} e + 6 \, {\left(9 \, b^{8} c - 112 \, a b^{6} c^{2} + 480 \, a^{2} b^{4} c^{3} - 768 \, a^{3} b^{2} c^{4} + 256 \, a^{4} c^{5}\right)} d e^{2} - {\left(11 \, b^{9} - 144 \, a b^{7} c + 672 \, a^{2} b^{5} c^{2} - 1280 \, a^{3} b^{3} c^{3} + 768 \, a^{4} b c^{4}\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(229376 \, c^{9} e^{3} x^{8} + 14336 \, {\left(54 \, c^{9} d e^{2} + 37 \, b c^{8} e^{3}\right)} x^{7} + 1024 \, {\left(864 \, c^{9} d^{2} e + 1782 \, b c^{8} d e^{2} + {\left(309 \, b^{2} c^{7} + 608 \, a c^{8}\right)} e^{3}\right)} x^{6} + 256 \, {\left(1344 \, c^{9} d^{3} + 8352 \, b c^{8} d^{2} e + 18 \, {\left(243 \, b^{2} c^{7} + 476 \, a c^{8}\right)} d e^{2} + {\left(5 \, b^{3} c^{6} + 3012 \, a b c^{7}\right)} e^{3}\right)} x^{5} + 128 \, {\left(6720 \, b c^{8} d^{3} + 288 \, {\left(37 \, b^{2} c^{7} + 72 \, a c^{8}\right)} d^{2} e + 18 \, {\left(3 \, b^{3} c^{6} + 1228 \, a b c^{7}\right)} d e^{2} - {\left(11 \, b^{4} c^{5} - 84 \, a b^{2} c^{6} - 3840 \, a^{2} c^{7}\right)} e^{3}\right)} x^{4} + 1344 \, {\left(15 \, b^{5} c^{4} - 160 \, a b^{3} c^{5} + 528 \, a^{2} b c^{6}\right)} d^{3} - 288 \, {\left(105 \, b^{6} c^{3} - 1120 \, a b^{4} c^{4} + 3696 \, a^{2} b^{2} c^{5} - 3072 \, a^{3} c^{6}\right)} d^{2} e + 18 \, {\left(945 \, b^{7} c^{2} - 10500 \, a b^{5} c^{3} + 37744 \, a^{2} b^{3} c^{4} - 42432 \, a^{3} b c^{5}\right)} d e^{2} - {\left(3465 \, b^{8} c - 40740 \, a b^{6} c^{2} + 162288 \, a^{2} b^{4} c^{3} - 234432 \, a^{3} b^{2} c^{4} + 65536 \, a^{4} c^{5}\right)} e^{3} + 16 \, {\left(1344 \, {\left(27 \, b^{2} c^{7} + 52 \, a c^{8}\right)} d^{3} + 288 \, {\left(3 \, b^{3} c^{6} + 788 \, a b c^{7}\right)} d^{2} e - 18 \, {\left(27 \, b^{4} c^{5} - 216 \, a b^{2} c^{6} - 6608 \, a^{2} c^{7}\right)} d e^{2} + {\left(99 \, b^{5} c^{4} - 856 \, a b^{3} c^{5} + 1968 \, a^{2} b c^{6}\right)} e^{3}\right)} x^{3} + 8 \, {\left(1344 \, {\left(b^{3} c^{6} + 156 \, a b c^{7}\right)} d^{3} - 288 \, {\left(7 \, b^{4} c^{5} - 60 \, a b^{2} c^{6} - 1152 \, a^{2} c^{7}\right)} d^{2} e + 18 \, {\left(63 \, b^{5} c^{4} - 568 \, a b^{3} c^{5} + 1392 \, a^{2} b c^{6}\right)} d e^{2} - {\left(231 \, b^{6} c^{3} - 2232 \, a b^{4} c^{4} + 6384 \, a^{2} b^{2} c^{5} - 4096 \, a^{3} c^{6}\right)} e^{3}\right)} x^{2} - 2 \, {\left(1344 \, {\left(5 \, b^{4} c^{5} - 48 \, a b^{2} c^{6} - 528 \, a^{2} c^{7}\right)} d^{3} - 288 \, {\left(35 \, b^{5} c^{4} - 336 \, a b^{3} c^{5} + 912 \, a^{2} b c^{6}\right)} d^{2} e + 18 \, {\left(315 \, b^{6} c^{3} - 3164 \, a b^{4} c^{4} + 9552 \, a^{2} b^{2} c^{5} - 6720 \, a^{3} c^{6}\right)} d e^{2} - {\left(1155 \, b^{7} c^{2} - 12348 \, a b^{5} c^{3} + 42192 \, a^{2} b^{3} c^{4} - 44096 \, a^{3} b c^{5}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4128768 \, c^{7}}\right]"," ",0,"[-1/8257536*(315*(64*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^3 - 96*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2*e + 6*(9*b^8*c - 112*a*b^6*c^2 + 480*a^2*b^4*c^3 - 768*a^3*b^2*c^4 + 256*a^4*c^5)*d*e^2 - (11*b^9 - 144*a*b^7*c + 672*a^2*b^5*c^2 - 1280*a^3*b^3*c^3 + 768*a^4*b*c^4)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(229376*c^9*e^3*x^8 + 14336*(54*c^9*d*e^2 + 37*b*c^8*e^3)*x^7 + 1024*(864*c^9*d^2*e + 1782*b*c^8*d*e^2 + (309*b^2*c^7 + 608*a*c^8)*e^3)*x^6 + 256*(1344*c^9*d^3 + 8352*b*c^8*d^2*e + 18*(243*b^2*c^7 + 476*a*c^8)*d*e^2 + (5*b^3*c^6 + 3012*a*b*c^7)*e^3)*x^5 + 128*(6720*b*c^8*d^3 + 288*(37*b^2*c^7 + 72*a*c^8)*d^2*e + 18*(3*b^3*c^6 + 1228*a*b*c^7)*d*e^2 - (11*b^4*c^5 - 84*a*b^2*c^6 - 3840*a^2*c^7)*e^3)*x^4 + 1344*(15*b^5*c^4 - 160*a*b^3*c^5 + 528*a^2*b*c^6)*d^3 - 288*(105*b^6*c^3 - 1120*a*b^4*c^4 + 3696*a^2*b^2*c^5 - 3072*a^3*c^6)*d^2*e + 18*(945*b^7*c^2 - 10500*a*b^5*c^3 + 37744*a^2*b^3*c^4 - 42432*a^3*b*c^5)*d*e^2 - (3465*b^8*c - 40740*a*b^6*c^2 + 162288*a^2*b^4*c^3 - 234432*a^3*b^2*c^4 + 65536*a^4*c^5)*e^3 + 16*(1344*(27*b^2*c^7 + 52*a*c^8)*d^3 + 288*(3*b^3*c^6 + 788*a*b*c^7)*d^2*e - 18*(27*b^4*c^5 - 216*a*b^2*c^6 - 6608*a^2*c^7)*d*e^2 + (99*b^5*c^4 - 856*a*b^3*c^5 + 1968*a^2*b*c^6)*e^3)*x^3 + 8*(1344*(b^3*c^6 + 156*a*b*c^7)*d^3 - 288*(7*b^4*c^5 - 60*a*b^2*c^6 - 1152*a^2*c^7)*d^2*e + 18*(63*b^5*c^4 - 568*a*b^3*c^5 + 1392*a^2*b*c^6)*d*e^2 - (231*b^6*c^3 - 2232*a*b^4*c^4 + 6384*a^2*b^2*c^5 - 4096*a^3*c^6)*e^3)*x^2 - 2*(1344*(5*b^4*c^5 - 48*a*b^2*c^6 - 528*a^2*c^7)*d^3 - 288*(35*b^5*c^4 - 336*a*b^3*c^5 + 912*a^2*b*c^6)*d^2*e + 18*(315*b^6*c^3 - 3164*a*b^4*c^4 + 9552*a^2*b^2*c^5 - 6720*a^3*c^6)*d*e^2 - (1155*b^7*c^2 - 12348*a*b^5*c^3 + 42192*a^2*b^3*c^4 - 44096*a^3*b*c^5)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^7, 1/4128768*(315*(64*(b^6*c^3 - 12*a*b^4*c^4 + 48*a^2*b^2*c^5 - 64*a^3*c^6)*d^3 - 96*(b^7*c^2 - 12*a*b^5*c^3 + 48*a^2*b^3*c^4 - 64*a^3*b*c^5)*d^2*e + 6*(9*b^8*c - 112*a*b^6*c^2 + 480*a^2*b^4*c^3 - 768*a^3*b^2*c^4 + 256*a^4*c^5)*d*e^2 - (11*b^9 - 144*a*b^7*c + 672*a^2*b^5*c^2 - 1280*a^3*b^3*c^3 + 768*a^4*b*c^4)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(229376*c^9*e^3*x^8 + 14336*(54*c^9*d*e^2 + 37*b*c^8*e^3)*x^7 + 1024*(864*c^9*d^2*e + 1782*b*c^8*d*e^2 + (309*b^2*c^7 + 608*a*c^8)*e^3)*x^6 + 256*(1344*c^9*d^3 + 8352*b*c^8*d^2*e + 18*(243*b^2*c^7 + 476*a*c^8)*d*e^2 + (5*b^3*c^6 + 3012*a*b*c^7)*e^3)*x^5 + 128*(6720*b*c^8*d^3 + 288*(37*b^2*c^7 + 72*a*c^8)*d^2*e + 18*(3*b^3*c^6 + 1228*a*b*c^7)*d*e^2 - (11*b^4*c^5 - 84*a*b^2*c^6 - 3840*a^2*c^7)*e^3)*x^4 + 1344*(15*b^5*c^4 - 160*a*b^3*c^5 + 528*a^2*b*c^6)*d^3 - 288*(105*b^6*c^3 - 1120*a*b^4*c^4 + 3696*a^2*b^2*c^5 - 3072*a^3*c^6)*d^2*e + 18*(945*b^7*c^2 - 10500*a*b^5*c^3 + 37744*a^2*b^3*c^4 - 42432*a^3*b*c^5)*d*e^2 - (3465*b^8*c - 40740*a*b^6*c^2 + 162288*a^2*b^4*c^3 - 234432*a^3*b^2*c^4 + 65536*a^4*c^5)*e^3 + 16*(1344*(27*b^2*c^7 + 52*a*c^8)*d^3 + 288*(3*b^3*c^6 + 788*a*b*c^7)*d^2*e - 18*(27*b^4*c^5 - 216*a*b^2*c^6 - 6608*a^2*c^7)*d*e^2 + (99*b^5*c^4 - 856*a*b^3*c^5 + 1968*a^2*b*c^6)*e^3)*x^3 + 8*(1344*(b^3*c^6 + 156*a*b*c^7)*d^3 - 288*(7*b^4*c^5 - 60*a*b^2*c^6 - 1152*a^2*c^7)*d^2*e + 18*(63*b^5*c^4 - 568*a*b^3*c^5 + 1392*a^2*b*c^6)*d*e^2 - (231*b^6*c^3 - 2232*a*b^4*c^4 + 6384*a^2*b^2*c^5 - 4096*a^3*c^6)*e^3)*x^2 - 2*(1344*(5*b^4*c^5 - 48*a*b^2*c^6 - 528*a^2*c^7)*d^3 - 288*(35*b^5*c^4 - 336*a*b^3*c^5 + 912*a^2*b*c^6)*d^2*e + 18*(315*b^6*c^3 - 3164*a*b^4*c^4 + 9552*a^2*b^2*c^5 - 6720*a^3*c^6)*d*e^2 - (1155*b^7*c^2 - 12348*a*b^5*c^3 + 42192*a^2*b^3*c^4 - 44096*a^3*b*c^5)*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^7]","B",0
2356,1,1425,0,0.644162," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(32 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} - 32 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d e + {\left(9 \, b^{8} - 112 \, a b^{6} c + 480 \, a^{2} b^{4} c^{2} - 768 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(43008 \, c^{8} e^{2} x^{7} + 3072 \, {\left(32 \, c^{8} d e + 33 \, b c^{7} e^{2}\right)} x^{6} + 256 \, {\left(224 \, c^{8} d^{2} + 928 \, b c^{7} d e + {\left(243 \, b^{2} c^{6} + 476 \, a c^{7}\right)} e^{2}\right)} x^{5} + 128 \, {\left(1120 \, b c^{7} d^{2} + 32 \, {\left(37 \, b^{2} c^{6} + 72 \, a c^{7}\right)} d e + {\left(3 \, b^{3} c^{5} + 1228 \, a b c^{6}\right)} e^{2}\right)} x^{4} + 16 \, {\left(224 \, {\left(27 \, b^{2} c^{6} + 52 \, a c^{7}\right)} d^{2} + 32 \, {\left(3 \, b^{3} c^{5} + 788 \, a b c^{6}\right)} d e - {\left(27 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} - 6608 \, a^{2} c^{6}\right)} e^{2}\right)} x^{3} + 224 \, {\left(15 \, b^{5} c^{3} - 160 \, a b^{3} c^{4} + 528 \, a^{2} b c^{5}\right)} d^{2} - 32 \, {\left(105 \, b^{6} c^{2} - 1120 \, a b^{4} c^{3} + 3696 \, a^{2} b^{2} c^{4} - 3072 \, a^{3} c^{5}\right)} d e + {\left(945 \, b^{7} c - 10500 \, a b^{5} c^{2} + 37744 \, a^{2} b^{3} c^{3} - 42432 \, a^{3} b c^{4}\right)} e^{2} + 8 \, {\left(224 \, {\left(b^{3} c^{5} + 156 \, a b c^{6}\right)} d^{2} - 32 \, {\left(7 \, b^{4} c^{4} - 60 \, a b^{2} c^{5} - 1152 \, a^{2} c^{6}\right)} d e + {\left(63 \, b^{5} c^{3} - 568 \, a b^{3} c^{4} + 1392 \, a^{2} b c^{5}\right)} e^{2}\right)} x^{2} - 2 \, {\left(224 \, {\left(5 \, b^{4} c^{4} - 48 \, a b^{2} c^{5} - 528 \, a^{2} c^{6}\right)} d^{2} - 32 \, {\left(35 \, b^{5} c^{3} - 336 \, a b^{3} c^{4} + 912 \, a^{2} b c^{5}\right)} d e + {\left(315 \, b^{6} c^{2} - 3164 \, a b^{4} c^{3} + 9552 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{1376256 \, c^{6}}, \frac{105 \, {\left(32 \, {\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} - 32 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d e + {\left(9 \, b^{8} - 112 \, a b^{6} c + 480 \, a^{2} b^{4} c^{2} - 768 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(43008 \, c^{8} e^{2} x^{7} + 3072 \, {\left(32 \, c^{8} d e + 33 \, b c^{7} e^{2}\right)} x^{6} + 256 \, {\left(224 \, c^{8} d^{2} + 928 \, b c^{7} d e + {\left(243 \, b^{2} c^{6} + 476 \, a c^{7}\right)} e^{2}\right)} x^{5} + 128 \, {\left(1120 \, b c^{7} d^{2} + 32 \, {\left(37 \, b^{2} c^{6} + 72 \, a c^{7}\right)} d e + {\left(3 \, b^{3} c^{5} + 1228 \, a b c^{6}\right)} e^{2}\right)} x^{4} + 16 \, {\left(224 \, {\left(27 \, b^{2} c^{6} + 52 \, a c^{7}\right)} d^{2} + 32 \, {\left(3 \, b^{3} c^{5} + 788 \, a b c^{6}\right)} d e - {\left(27 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} - 6608 \, a^{2} c^{6}\right)} e^{2}\right)} x^{3} + 224 \, {\left(15 \, b^{5} c^{3} - 160 \, a b^{3} c^{4} + 528 \, a^{2} b c^{5}\right)} d^{2} - 32 \, {\left(105 \, b^{6} c^{2} - 1120 \, a b^{4} c^{3} + 3696 \, a^{2} b^{2} c^{4} - 3072 \, a^{3} c^{5}\right)} d e + {\left(945 \, b^{7} c - 10500 \, a b^{5} c^{2} + 37744 \, a^{2} b^{3} c^{3} - 42432 \, a^{3} b c^{4}\right)} e^{2} + 8 \, {\left(224 \, {\left(b^{3} c^{5} + 156 \, a b c^{6}\right)} d^{2} - 32 \, {\left(7 \, b^{4} c^{4} - 60 \, a b^{2} c^{5} - 1152 \, a^{2} c^{6}\right)} d e + {\left(63 \, b^{5} c^{3} - 568 \, a b^{3} c^{4} + 1392 \, a^{2} b c^{5}\right)} e^{2}\right)} x^{2} - 2 \, {\left(224 \, {\left(5 \, b^{4} c^{4} - 48 \, a b^{2} c^{5} - 528 \, a^{2} c^{6}\right)} d^{2} - 32 \, {\left(35 \, b^{5} c^{3} - 336 \, a b^{3} c^{4} + 912 \, a^{2} b c^{5}\right)} d e + {\left(315 \, b^{6} c^{2} - 3164 \, a b^{4} c^{3} + 9552 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{688128 \, c^{6}}\right]"," ",0,"[1/1376256*(105*(32*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2 - 32*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*e + (9*b^8 - 112*a*b^6*c + 480*a^2*b^4*c^2 - 768*a^3*b^2*c^3 + 256*a^4*c^4)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(43008*c^8*e^2*x^7 + 3072*(32*c^8*d*e + 33*b*c^7*e^2)*x^6 + 256*(224*c^8*d^2 + 928*b*c^7*d*e + (243*b^2*c^6 + 476*a*c^7)*e^2)*x^5 + 128*(1120*b*c^7*d^2 + 32*(37*b^2*c^6 + 72*a*c^7)*d*e + (3*b^3*c^5 + 1228*a*b*c^6)*e^2)*x^4 + 16*(224*(27*b^2*c^6 + 52*a*c^7)*d^2 + 32*(3*b^3*c^5 + 788*a*b*c^6)*d*e - (27*b^4*c^4 - 216*a*b^2*c^5 - 6608*a^2*c^6)*e^2)*x^3 + 224*(15*b^5*c^3 - 160*a*b^3*c^4 + 528*a^2*b*c^5)*d^2 - 32*(105*b^6*c^2 - 1120*a*b^4*c^3 + 3696*a^2*b^2*c^4 - 3072*a^3*c^5)*d*e + (945*b^7*c - 10500*a*b^5*c^2 + 37744*a^2*b^3*c^3 - 42432*a^3*b*c^4)*e^2 + 8*(224*(b^3*c^5 + 156*a*b*c^6)*d^2 - 32*(7*b^4*c^4 - 60*a*b^2*c^5 - 1152*a^2*c^6)*d*e + (63*b^5*c^3 - 568*a*b^3*c^4 + 1392*a^2*b*c^5)*e^2)*x^2 - 2*(224*(5*b^4*c^4 - 48*a*b^2*c^5 - 528*a^2*c^6)*d^2 - 32*(35*b^5*c^3 - 336*a*b^3*c^4 + 912*a^2*b*c^5)*d*e + (315*b^6*c^2 - 3164*a*b^4*c^3 + 9552*a^2*b^2*c^4 - 6720*a^3*c^5)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/688128*(105*(32*(b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2 - 32*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*e + (9*b^8 - 112*a*b^6*c + 480*a^2*b^4*c^2 - 768*a^3*b^2*c^3 + 256*a^4*c^4)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(43008*c^8*e^2*x^7 + 3072*(32*c^8*d*e + 33*b*c^7*e^2)*x^6 + 256*(224*c^8*d^2 + 928*b*c^7*d*e + (243*b^2*c^6 + 476*a*c^7)*e^2)*x^5 + 128*(1120*b*c^7*d^2 + 32*(37*b^2*c^6 + 72*a*c^7)*d*e + (3*b^3*c^5 + 1228*a*b*c^6)*e^2)*x^4 + 16*(224*(27*b^2*c^6 + 52*a*c^7)*d^2 + 32*(3*b^3*c^5 + 788*a*b*c^6)*d*e - (27*b^4*c^4 - 216*a*b^2*c^5 - 6608*a^2*c^6)*e^2)*x^3 + 224*(15*b^5*c^3 - 160*a*b^3*c^4 + 528*a^2*b*c^5)*d^2 - 32*(105*b^6*c^2 - 1120*a*b^4*c^3 + 3696*a^2*b^2*c^4 - 3072*a^3*c^5)*d*e + (945*b^7*c - 10500*a*b^5*c^2 + 37744*a^2*b^3*c^3 - 42432*a^3*b*c^4)*e^2 + 8*(224*(b^3*c^5 + 156*a*b*c^6)*d^2 - 32*(7*b^4*c^4 - 60*a*b^2*c^5 - 1152*a^2*c^6)*d*e + (63*b^5*c^3 - 568*a*b^3*c^4 + 1392*a^2*b*c^5)*e^2)*x^2 - 2*(224*(5*b^4*c^4 - 48*a*b^2*c^5 - 528*a^2*c^6)*d^2 - 32*(35*b^5*c^3 - 336*a*b^3*c^4 + 912*a^2*b*c^5)*d*e + (315*b^6*c^2 - 3164*a*b^4*c^3 + 9552*a^2*b^2*c^4 - 6720*a^3*c^5)*e^2)*x)*sqrt(c*x^2 + b*x + a))/c^6]","B",0
2357,1,857,0,0.518187," ","integrate((e*x+d)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\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}\right)} e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(3072 \, c^{7} e x^{6} + 256 \, {\left(14 \, c^{7} d + 29 \, b c^{6} e\right)} x^{5} + 128 \, {\left(70 \, b c^{6} d + {\left(37 \, b^{2} c^{5} + 72 \, a c^{6}\right)} e\right)} x^{4} + 16 \, {\left(14 \, {\left(27 \, b^{2} c^{5} + 52 \, a c^{6}\right)} d + {\left(3 \, b^{3} c^{4} + 788 \, a b c^{5}\right)} e\right)} x^{3} + 8 \, {\left(14 \, {\left(b^{3} c^{4} + 156 \, a b c^{5}\right)} d - {\left(7 \, b^{4} c^{3} - 60 \, a b^{2} c^{4} - 1152 \, a^{2} c^{5}\right)} e\right)} x^{2} + 14 \, {\left(15 \, b^{5} c^{2} - 160 \, a b^{3} c^{3} + 528 \, a^{2} b c^{4}\right)} d - {\left(105 \, b^{6} c - 1120 \, a b^{4} c^{2} + 3696 \, a^{2} b^{2} c^{3} - 3072 \, a^{3} c^{4}\right)} e - 2 \, {\left(14 \, {\left(5 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 528 \, a^{2} c^{5}\right)} d - {\left(35 \, b^{5} c^{2} - 336 \, a b^{3} c^{3} + 912 \, a^{2} b c^{4}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{86016 \, c^{5}}, \frac{105 \, {\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}\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(3072 \, c^{7} e x^{6} + 256 \, {\left(14 \, c^{7} d + 29 \, b c^{6} e\right)} x^{5} + 128 \, {\left(70 \, b c^{6} d + {\left(37 \, b^{2} c^{5} + 72 \, a c^{6}\right)} e\right)} x^{4} + 16 \, {\left(14 \, {\left(27 \, b^{2} c^{5} + 52 \, a c^{6}\right)} d + {\left(3 \, b^{3} c^{4} + 788 \, a b c^{5}\right)} e\right)} x^{3} + 8 \, {\left(14 \, {\left(b^{3} c^{4} + 156 \, a b c^{5}\right)} d - {\left(7 \, b^{4} c^{3} - 60 \, a b^{2} c^{4} - 1152 \, a^{2} c^{5}\right)} e\right)} x^{2} + 14 \, {\left(15 \, b^{5} c^{2} - 160 \, a b^{3} c^{3} + 528 \, a^{2} b c^{4}\right)} d - {\left(105 \, b^{6} c - 1120 \, a b^{4} c^{2} + 3696 \, a^{2} b^{2} c^{3} - 3072 \, a^{3} c^{4}\right)} e - 2 \, {\left(14 \, {\left(5 \, b^{4} c^{3} - 48 \, a b^{2} c^{4} - 528 \, a^{2} c^{5}\right)} d - {\left(35 \, b^{5} c^{2} - 336 \, a b^{3} c^{3} + 912 \, a^{2} b c^{4}\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{43008 \, c^{5}}\right]"," ",0,"[1/86016*(105*(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)*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(3072*c^7*e*x^6 + 256*(14*c^7*d + 29*b*c^6*e)*x^5 + 128*(70*b*c^6*d + (37*b^2*c^5 + 72*a*c^6)*e)*x^4 + 16*(14*(27*b^2*c^5 + 52*a*c^6)*d + (3*b^3*c^4 + 788*a*b*c^5)*e)*x^3 + 8*(14*(b^3*c^4 + 156*a*b*c^5)*d - (7*b^4*c^3 - 60*a*b^2*c^4 - 1152*a^2*c^5)*e)*x^2 + 14*(15*b^5*c^2 - 160*a*b^3*c^3 + 528*a^2*b*c^4)*d - (105*b^6*c - 1120*a*b^4*c^2 + 3696*a^2*b^2*c^3 - 3072*a^3*c^4)*e - 2*(14*(5*b^4*c^3 - 48*a*b^2*c^4 - 528*a^2*c^5)*d - (35*b^5*c^2 - 336*a*b^3*c^3 + 912*a^2*b*c^4)*e)*x)*sqrt(c*x^2 + b*x + a))/c^5, 1/43008*(105*(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)*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(3072*c^7*e*x^6 + 256*(14*c^7*d + 29*b*c^6*e)*x^5 + 128*(70*b*c^6*d + (37*b^2*c^5 + 72*a*c^6)*e)*x^4 + 16*(14*(27*b^2*c^5 + 52*a*c^6)*d + (3*b^3*c^4 + 788*a*b*c^5)*e)*x^3 + 8*(14*(b^3*c^4 + 156*a*b*c^5)*d - (7*b^4*c^3 - 60*a*b^2*c^4 - 1152*a^2*c^5)*e)*x^2 + 14*(15*b^5*c^2 - 160*a*b^3*c^3 + 528*a^2*b*c^4)*d - (105*b^6*c - 1120*a*b^4*c^2 + 3696*a^2*b^2*c^3 - 3072*a^3*c^4)*e - 2*(14*(5*b^4*c^3 - 48*a*b^2*c^4 - 528*a^2*c^5)*d - (35*b^5*c^2 - 336*a*b^3*c^3 + 912*a^2*b*c^4)*e)*x)*sqrt(c*x^2 + b*x + a))/c^5]","B",0
2358,1,425,0,0.468070," ","integrate((c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(256 \, c^{6} x^{5} + 640 \, b c^{5} x^{4} + 15 \, b^{5} c - 160 \, a b^{3} c^{2} + 528 \, a^{2} b c^{3} + 16 \, {\left(27 \, b^{2} c^{4} + 52 \, a c^{5}\right)} x^{3} + 8 \, {\left(b^{3} c^{3} + 156 \, a b c^{4}\right)} x^{2} - 2 \, {\left(5 \, b^{4} c^{2} - 48 \, a b^{2} c^{3} - 528 \, a^{2} c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6144 \, c^{4}}, \frac{15 \, {\left(b^{6} - 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(256 \, c^{6} x^{5} + 640 \, b c^{5} x^{4} + 15 \, b^{5} c - 160 \, a b^{3} c^{2} + 528 \, a^{2} b c^{3} + 16 \, {\left(27 \, b^{2} c^{4} + 52 \, a c^{5}\right)} x^{3} + 8 \, {\left(b^{3} c^{3} + 156 \, a b c^{4}\right)} x^{2} - 2 \, {\left(5 \, b^{4} c^{2} - 48 \, a b^{2} c^{3} - 528 \, a^{2} c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3072 \, c^{4}}\right]"," ",0,"[-1/6144*(15*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(256*c^6*x^5 + 640*b*c^5*x^4 + 15*b^5*c - 160*a*b^3*c^2 + 528*a^2*b*c^3 + 16*(27*b^2*c^4 + 52*a*c^5)*x^3 + 8*(b^3*c^3 + 156*a*b*c^4)*x^2 - 2*(5*b^4*c^2 - 48*a*b^2*c^3 - 528*a^2*c^4)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/3072*(15*(b^6 - 12*a*b^4*c + 48*a^2*b^2*c^2 - 64*a^3*c^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(256*c^6*x^5 + 640*b*c^5*x^4 + 15*b^5*c - 160*a*b^3*c^2 + 528*a^2*b*c^3 + 16*(27*b^2*c^4 + 52*a*c^5)*x^3 + 8*(b^3*c^3 + 156*a*b*c^4)*x^2 - 2*(5*b^4*c^2 - 48*a*b^2*c^3 - 528*a^2*c^4)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
2359,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2360,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2361,1,3019,0,112.931834," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^3,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(32 \, c^{3} d^{5} - 48 \, b c^{2} d^{4} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} + 12 \, a b c\right)} d^{2} e^{3} + {\left(32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(32 \, c^{3} d^{4} e - 48 \, b c^{2} d^{3} e^{2} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 12 \, a b c\right)} d e^{4}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 30 \, {\left(16 \, c^{3} d^{4} - 16 \, b c^{2} d^{3} e + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{2} + {\left(16 \, c^{3} d^{2} e^{2} - 16 \, b c^{2} d e^{3} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(16 \, c^{3} d^{3} e - 16 \, b c^{2} d^{2} e^{2} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(8 \, c^{3} e^{5} x^{4} + 240 \, c^{3} d^{4} e - 300 \, b c^{2} d^{3} e^{2} - 30 \, a b c d e^{4} - 12 \, a^{2} c e^{5} + 5 \, {\left(15 \, b^{2} c + 28 \, a c^{2}\right)} d^{2} e^{3} - 2 \, {\left(10 \, c^{3} d e^{4} - 13 \, b c^{2} e^{5}\right)} x^{3} + {\left(80 \, c^{3} d^{2} e^{3} - 110 \, b c^{2} d e^{4} + {\left(33 \, b^{2} c + 56 \, a c^{2}\right)} e^{5}\right)} x^{2} + 2 \, {\left(180 \, c^{3} d^{3} e^{2} - 230 \, b c^{2} d^{2} e^{3} - 27 \, a b c e^{5} + 10 \, {\left(6 \, b^{2} c + 11 \, a c^{2}\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(c e^{8} x^{2} + 2 \, c d e^{7} x + c d^{2} e^{6}\right)}}, \frac{15 \, {\left(32 \, c^{3} d^{5} - 48 \, b c^{2} d^{4} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} + 12 \, a b c\right)} d^{2} e^{3} + {\left(32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(32 \, c^{3} d^{4} e - 48 \, b c^{2} d^{3} e^{2} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 12 \, a b c\right)} d e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 15 \, {\left(16 \, c^{3} d^{4} - 16 \, b c^{2} d^{3} e + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{2} + {\left(16 \, c^{3} d^{2} e^{2} - 16 \, b c^{2} d e^{3} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(16 \, c^{3} d^{3} e - 16 \, b c^{2} d^{2} e^{2} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 2 \, {\left(8 \, c^{3} e^{5} x^{4} + 240 \, c^{3} d^{4} e - 300 \, b c^{2} d^{3} e^{2} - 30 \, a b c d e^{4} - 12 \, a^{2} c e^{5} + 5 \, {\left(15 \, b^{2} c + 28 \, a c^{2}\right)} d^{2} e^{3} - 2 \, {\left(10 \, c^{3} d e^{4} - 13 \, b c^{2} e^{5}\right)} x^{3} + {\left(80 \, c^{3} d^{2} e^{3} - 110 \, b c^{2} d e^{4} + {\left(33 \, b^{2} c + 56 \, a c^{2}\right)} e^{5}\right)} x^{2} + 2 \, {\left(180 \, c^{3} d^{3} e^{2} - 230 \, b c^{2} d^{2} e^{3} - 27 \, a b c e^{5} + 10 \, {\left(6 \, b^{2} c + 11 \, a c^{2}\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(c e^{8} x^{2} + 2 \, c d e^{7} x + c d^{2} e^{6}\right)}}, \frac{60 \, {\left(16 \, c^{3} d^{4} - 16 \, b c^{2} d^{3} e + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{2} + {\left(16 \, c^{3} d^{2} e^{2} - 16 \, b c^{2} d e^{3} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(16 \, c^{3} d^{3} e - 16 \, b c^{2} d^{2} e^{2} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 15 \, {\left(32 \, c^{3} d^{5} - 48 \, b c^{2} d^{4} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} + 12 \, a b c\right)} d^{2} e^{3} + {\left(32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(32 \, c^{3} d^{4} e - 48 \, b c^{2} d^{3} e^{2} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 12 \, a b c\right)} d e^{4}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, c^{3} e^{5} x^{4} + 240 \, c^{3} d^{4} e - 300 \, b c^{2} d^{3} e^{2} - 30 \, a b c d e^{4} - 12 \, a^{2} c e^{5} + 5 \, {\left(15 \, b^{2} c + 28 \, a c^{2}\right)} d^{2} e^{3} - 2 \, {\left(10 \, c^{3} d e^{4} - 13 \, b c^{2} e^{5}\right)} x^{3} + {\left(80 \, c^{3} d^{2} e^{3} - 110 \, b c^{2} d e^{4} + {\left(33 \, b^{2} c + 56 \, a c^{2}\right)} e^{5}\right)} x^{2} + 2 \, {\left(180 \, c^{3} d^{3} e^{2} - 230 \, b c^{2} d^{2} e^{3} - 27 \, a b c e^{5} + 10 \, {\left(6 \, b^{2} c + 11 \, a c^{2}\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(c e^{8} x^{2} + 2 \, c d e^{7} x + c d^{2} e^{6}\right)}}, \frac{30 \, {\left(16 \, c^{3} d^{4} - 16 \, b c^{2} d^{3} e + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{2} + {\left(16 \, c^{3} d^{2} e^{2} - 16 \, b c^{2} d e^{3} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} e^{4}\right)} x^{2} + 2 \, {\left(16 \, c^{3} d^{3} e - 16 \, b c^{2} d^{2} e^{2} + {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) + 15 \, {\left(32 \, c^{3} d^{5} - 48 \, b c^{2} d^{4} e + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{3} e^{2} - {\left(b^{3} + 12 \, a b c\right)} d^{2} e^{3} + {\left(32 \, c^{3} d^{3} e^{2} - 48 \, b c^{2} d^{2} e^{3} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d e^{4} - {\left(b^{3} + 12 \, a b c\right)} e^{5}\right)} x^{2} + 2 \, {\left(32 \, c^{3} d^{4} e - 48 \, b c^{2} d^{3} e^{2} + 6 \, {\left(3 \, b^{2} c + 4 \, a c^{2}\right)} d^{2} e^{3} - {\left(b^{3} + 12 \, a b c\right)} d e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(8 \, c^{3} e^{5} x^{4} + 240 \, c^{3} d^{4} e - 300 \, b c^{2} d^{3} e^{2} - 30 \, a b c d e^{4} - 12 \, a^{2} c e^{5} + 5 \, {\left(15 \, b^{2} c + 28 \, a c^{2}\right)} d^{2} e^{3} - 2 \, {\left(10 \, c^{3} d e^{4} - 13 \, b c^{2} e^{5}\right)} x^{3} + {\left(80 \, c^{3} d^{2} e^{3} - 110 \, b c^{2} d e^{4} + {\left(33 \, b^{2} c + 56 \, a c^{2}\right)} e^{5}\right)} x^{2} + 2 \, {\left(180 \, c^{3} d^{3} e^{2} - 230 \, b c^{2} d^{2} e^{3} - 27 \, a b c e^{5} + 10 \, {\left(6 \, b^{2} c + 11 \, a c^{2}\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(c e^{8} x^{2} + 2 \, c d e^{7} x + c d^{2} e^{6}\right)}}\right]"," ",0,"[-1/96*(15*(32*c^3*d^5 - 48*b*c^2*d^4*e + 6*(3*b^2*c + 4*a*c^2)*d^3*e^2 - (b^3 + 12*a*b*c)*d^2*e^3 + (32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5)*x^2 + 2*(32*c^3*d^4*e - 48*b*c^2*d^3*e^2 + 6*(3*b^2*c + 4*a*c^2)*d^2*e^3 - (b^3 + 12*a*b*c)*d*e^4)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 30*(16*c^3*d^4 - 16*b*c^2*d^3*e + (3*b^2*c + 4*a*c^2)*d^2*e^2 + (16*c^3*d^2*e^2 - 16*b*c^2*d*e^3 + (3*b^2*c + 4*a*c^2)*e^4)*x^2 + 2*(16*c^3*d^3*e - 16*b*c^2*d^2*e^2 + (3*b^2*c + 4*a*c^2)*d*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(8*c^3*e^5*x^4 + 240*c^3*d^4*e - 300*b*c^2*d^3*e^2 - 30*a*b*c*d*e^4 - 12*a^2*c*e^5 + 5*(15*b^2*c + 28*a*c^2)*d^2*e^3 - 2*(10*c^3*d*e^4 - 13*b*c^2*e^5)*x^3 + (80*c^3*d^2*e^3 - 110*b*c^2*d*e^4 + (33*b^2*c + 56*a*c^2)*e^5)*x^2 + 2*(180*c^3*d^3*e^2 - 230*b*c^2*d^2*e^3 - 27*a*b*c*e^5 + 10*(6*b^2*c + 11*a*c^2)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*e^8*x^2 + 2*c*d*e^7*x + c*d^2*e^6), 1/48*(15*(32*c^3*d^5 - 48*b*c^2*d^4*e + 6*(3*b^2*c + 4*a*c^2)*d^3*e^2 - (b^3 + 12*a*b*c)*d^2*e^3 + (32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5)*x^2 + 2*(32*c^3*d^4*e - 48*b*c^2*d^3*e^2 + 6*(3*b^2*c + 4*a*c^2)*d^2*e^3 - (b^3 + 12*a*b*c)*d*e^4)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 15*(16*c^3*d^4 - 16*b*c^2*d^3*e + (3*b^2*c + 4*a*c^2)*d^2*e^2 + (16*c^3*d^2*e^2 - 16*b*c^2*d*e^3 + (3*b^2*c + 4*a*c^2)*e^4)*x^2 + 2*(16*c^3*d^3*e - 16*b*c^2*d^2*e^2 + (3*b^2*c + 4*a*c^2)*d*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 2*(8*c^3*e^5*x^4 + 240*c^3*d^4*e - 300*b*c^2*d^3*e^2 - 30*a*b*c*d*e^4 - 12*a^2*c*e^5 + 5*(15*b^2*c + 28*a*c^2)*d^2*e^3 - 2*(10*c^3*d*e^4 - 13*b*c^2*e^5)*x^3 + (80*c^3*d^2*e^3 - 110*b*c^2*d*e^4 + (33*b^2*c + 56*a*c^2)*e^5)*x^2 + 2*(180*c^3*d^3*e^2 - 230*b*c^2*d^2*e^3 - 27*a*b*c*e^5 + 10*(6*b^2*c + 11*a*c^2)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*e^8*x^2 + 2*c*d*e^7*x + c*d^2*e^6), 1/96*(60*(16*c^3*d^4 - 16*b*c^2*d^3*e + (3*b^2*c + 4*a*c^2)*d^2*e^2 + (16*c^3*d^2*e^2 - 16*b*c^2*d*e^3 + (3*b^2*c + 4*a*c^2)*e^4)*x^2 + 2*(16*c^3*d^3*e - 16*b*c^2*d^2*e^2 + (3*b^2*c + 4*a*c^2)*d*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 15*(32*c^3*d^5 - 48*b*c^2*d^4*e + 6*(3*b^2*c + 4*a*c^2)*d^3*e^2 - (b^3 + 12*a*b*c)*d^2*e^3 + (32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5)*x^2 + 2*(32*c^3*d^4*e - 48*b*c^2*d^3*e^2 + 6*(3*b^2*c + 4*a*c^2)*d^2*e^3 - (b^3 + 12*a*b*c)*d*e^4)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(8*c^3*e^5*x^4 + 240*c^3*d^4*e - 300*b*c^2*d^3*e^2 - 30*a*b*c*d*e^4 - 12*a^2*c*e^5 + 5*(15*b^2*c + 28*a*c^2)*d^2*e^3 - 2*(10*c^3*d*e^4 - 13*b*c^2*e^5)*x^3 + (80*c^3*d^2*e^3 - 110*b*c^2*d*e^4 + (33*b^2*c + 56*a*c^2)*e^5)*x^2 + 2*(180*c^3*d^3*e^2 - 230*b*c^2*d^2*e^3 - 27*a*b*c*e^5 + 10*(6*b^2*c + 11*a*c^2)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*e^8*x^2 + 2*c*d*e^7*x + c*d^2*e^6), 1/48*(30*(16*c^3*d^4 - 16*b*c^2*d^3*e + (3*b^2*c + 4*a*c^2)*d^2*e^2 + (16*c^3*d^2*e^2 - 16*b*c^2*d*e^3 + (3*b^2*c + 4*a*c^2)*e^4)*x^2 + 2*(16*c^3*d^3*e - 16*b*c^2*d^2*e^2 + (3*b^2*c + 4*a*c^2)*d*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) + 15*(32*c^3*d^5 - 48*b*c^2*d^4*e + 6*(3*b^2*c + 4*a*c^2)*d^3*e^2 - (b^3 + 12*a*b*c)*d^2*e^3 + (32*c^3*d^3*e^2 - 48*b*c^2*d^2*e^3 + 6*(3*b^2*c + 4*a*c^2)*d*e^4 - (b^3 + 12*a*b*c)*e^5)*x^2 + 2*(32*c^3*d^4*e - 48*b*c^2*d^3*e^2 + 6*(3*b^2*c + 4*a*c^2)*d^2*e^3 - (b^3 + 12*a*b*c)*d*e^4)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(8*c^3*e^5*x^4 + 240*c^3*d^4*e - 300*b*c^2*d^3*e^2 - 30*a*b*c*d*e^4 - 12*a^2*c*e^5 + 5*(15*b^2*c + 28*a*c^2)*d^2*e^3 - 2*(10*c^3*d*e^4 - 13*b*c^2*e^5)*x^3 + (80*c^3*d^2*e^3 - 110*b*c^2*d*e^4 + (33*b^2*c + 56*a*c^2)*e^5)*x^2 + 2*(180*c^3*d^3*e^2 - 230*b*c^2*d^2*e^3 - 27*a*b*c*e^5 + 10*(6*b^2*c + 11*a*c^2)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c*e^8*x^2 + 2*c*d*e^7*x + c*d^2*e^6)]","B",0
2362,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2363,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^5,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2364,1,78,0,0.441056," ","integrate((5*x^2-3*x-2)^(1/2)/x,x, algorithm=""fricas"")","\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(3 \, x + 4\right)}}{4 \, \sqrt{5 \, x^{2} - 3 \, x - 2}}\right) + \frac{3}{20} \, \sqrt{5} \log\left(-4 \, \sqrt{5} \sqrt{5 \, x^{2} - 3 \, x - 2} {\left(10 \, x - 3\right)} + 200 \, x^{2} - 120 \, x - 31\right) + \sqrt{5 \, x^{2} - 3 \, x - 2}"," ",0,"sqrt(2)*arctan(1/4*sqrt(2)*(3*x + 4)/sqrt(5*x^2 - 3*x - 2)) + 3/20*sqrt(5)*log(-4*sqrt(5)*sqrt(5*x^2 - 3*x - 2)*(10*x - 3) + 200*x^2 - 120*x - 31) + sqrt(5*x^2 - 3*x - 2)","A",0
2365,1,92,0,0.459525," ","integrate((-x^2-x+2)^(1/2)/x^2,x, algorithm=""fricas"")","\frac{\sqrt{2} x \log\left(-\frac{4 \, \sqrt{2} \sqrt{-x^{2} - x + 2} {\left(x - 4\right)} + 7 \, x^{2} + 16 \, x - 32}{x^{2}}\right) + 8 \, x \arctan\left(\frac{\sqrt{-x^{2} - x + 2} {\left(2 \, x + 1\right)}}{2 \, {\left(x^{2} + x - 2\right)}}\right) - 8 \, \sqrt{-x^{2} - x + 2}}{8 \, x}"," ",0,"1/8*(sqrt(2)*x*log(-(4*sqrt(2)*sqrt(-x^2 - x + 2)*(x - 4) + 7*x^2 + 16*x - 32)/x^2) + 8*x*arctan(1/2*sqrt(-x^2 - x + 2)*(2*x + 1)/(x^2 + x - 2)) - 8*sqrt(-x^2 - x + 2))/x","A",0
2366,1,32,0,0.404950," ","integrate((1+x)^3*(x^2+2*x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{15} \, {\left(3 \, x^{4} + 12 \, x^{3} + 19 \, x^{2} + 14 \, x + 2\right)} \sqrt{x^{2} + 2 \, x + 2}"," ",0,"1/15*(3*x^4 + 12*x^3 + 19*x^2 + 14*x + 2)*sqrt(x^2 + 2*x + 2)","A",0
2367,1,45,0,0.431115," ","integrate((-2+3*x)*(9*x^2+12*x+8)^(1/2),x, algorithm=""fricas"")","\frac{1}{9} \, \sqrt{9 \, x^{2} + 12 \, x + 8} {\left(9 \, x^{2} - 6 \, x - 4\right)} + \frac{8}{3} \, \log\left(-3 \, x + \sqrt{9 \, x^{2} + 12 \, x + 8} - 2\right)"," ",0,"1/9*sqrt(9*x^2 + 12*x + 8)*(9*x^2 - 6*x - 4) + 8/3*log(-3*x + sqrt(9*x^2 + 12*x + 8) - 2)","A",0
2368,1,47,0,0.420735," ","integrate((7-2*x)*(-4*x^2+16*x+9)^(1/2),x, algorithm=""fricas"")","-\frac{1}{6} \, {\left(4 \, x^{2} - 25 \, x + 9\right)} \sqrt{-4 \, x^{2} + 16 \, x + 9} - \frac{75}{2} \, \arctan\left(\frac{\sqrt{-4 \, x^{2} + 16 \, x + 9} - 3}{2 \, x}\right)"," ",0,"-1/6*(4*x^2 - 25*x + 9)*sqrt(-4*x^2 + 16*x + 9) - 75/2*arctan(1/2*(sqrt(-4*x^2 + 16*x + 9) - 3)/x)","A",0
2369,1,64,0,0.407816," ","integrate((x^2-x-1)^(1/2)/(1+x),x, algorithm=""fricas"")","\sqrt{x^{2} - x - 1} - \log\left(-x + \sqrt{x^{2} - x - 1}\right) + \log\left(-x + \sqrt{x^{2} - x - 1} - 2\right) + \frac{3}{2} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} - x - 1} + 1\right)"," ",0,"sqrt(x^2 - x - 1) - log(-x + sqrt(x^2 - x - 1)) + log(-x + sqrt(x^2 - x - 1) - 2) + 3/2*log(-2*x + 2*sqrt(x^2 - x - 1) + 1)","A",0
2370,1,51,0,0.416019," ","integrate((x^2-x-1)^(1/2)/(1-x),x, algorithm=""fricas"")","-\sqrt{x^{2} - x - 1} + 2 \, \arctan\left(-x + \sqrt{x^{2} - x - 1} + 1\right) + \frac{1}{2} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} - x - 1} + 1\right)"," ",0,"-sqrt(x^2 - x - 1) + 2*arctan(-x + sqrt(x^2 - x - 1) + 1) + 1/2*log(-2*x + 2*sqrt(x^2 - x - 1) + 1)","A",0
2371,1,431,0,0.448968," ","integrate(x^6/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(231 \, b^{6} - 1260 \, a b^{4} c + 1680 \, a^{2} b^{2} c^{2} - 320 \, a^{3} c^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(1280 \, c^{6} x^{5} - 1408 \, b c^{5} x^{4} - 3465 \, b^{5} c + 14280 \, a b^{3} c^{2} - 11088 \, a^{2} b c^{3} + 16 \, {\left(99 \, b^{2} c^{4} - 100 \, a c^{5}\right)} x^{3} - 24 \, {\left(77 \, b^{3} c^{3} - 156 \, a b c^{4}\right)} x^{2} + 6 \, {\left(385 \, b^{4} c^{2} - 1176 \, a b^{2} c^{3} + 400 \, a^{2} c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{7}}, -\frac{15 \, {\left(231 \, b^{6} - 1260 \, a b^{4} c + 1680 \, a^{2} b^{2} c^{2} - 320 \, a^{3} c^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(1280 \, c^{6} x^{5} - 1408 \, b c^{5} x^{4} - 3465 \, b^{5} c + 14280 \, a b^{3} c^{2} - 11088 \, a^{2} b c^{3} + 16 \, {\left(99 \, b^{2} c^{4} - 100 \, a c^{5}\right)} x^{3} - 24 \, {\left(77 \, b^{3} c^{3} - 156 \, a b c^{4}\right)} x^{2} + 6 \, {\left(385 \, b^{4} c^{2} - 1176 \, a b^{2} c^{3} + 400 \, a^{2} c^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{7}}\right]"," ",0,"[-1/30720*(15*(231*b^6 - 1260*a*b^4*c + 1680*a^2*b^2*c^2 - 320*a^3*c^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(1280*c^6*x^5 - 1408*b*c^5*x^4 - 3465*b^5*c + 14280*a*b^3*c^2 - 11088*a^2*b*c^3 + 16*(99*b^2*c^4 - 100*a*c^5)*x^3 - 24*(77*b^3*c^3 - 156*a*b*c^4)*x^2 + 6*(385*b^4*c^2 - 1176*a*b^2*c^3 + 400*a^2*c^4)*x)*sqrt(c*x^2 + b*x + a))/c^7, -1/15360*(15*(231*b^6 - 1260*a*b^4*c + 1680*a^2*b^2*c^2 - 320*a^3*c^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(1280*c^6*x^5 - 1408*b*c^5*x^4 - 3465*b^5*c + 14280*a*b^3*c^2 - 11088*a^2*b*c^3 + 16*(99*b^2*c^4 - 100*a*c^5)*x^3 - 24*(77*b^3*c^3 - 156*a*b*c^4)*x^2 + 6*(385*b^4*c^2 - 1176*a*b^2*c^3 + 400*a^2*c^4)*x)*sqrt(c*x^2 + b*x + a))/c^7]","A",0
2372,1,347,0,0.448961," ","integrate(x^5/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(63 \, b^{5} - 280 \, a b^{3} c + 240 \, a^{2} b c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(384 \, c^{5} x^{4} - 432 \, b c^{4} x^{3} + 945 \, b^{4} c - 2940 \, a b^{2} c^{2} + 1024 \, a^{2} c^{3} + 8 \, {\left(63 \, b^{2} c^{3} - 64 \, a c^{4}\right)} x^{2} - 14 \, {\left(45 \, b^{3} c^{2} - 92 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{7680 \, c^{6}}, \frac{15 \, {\left(63 \, b^{5} - 280 \, a b^{3} c + 240 \, a^{2} b c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(384 \, c^{5} x^{4} - 432 \, b c^{4} x^{3} + 945 \, b^{4} c - 2940 \, a b^{2} c^{2} + 1024 \, a^{2} c^{3} + 8 \, {\left(63 \, b^{2} c^{3} - 64 \, a c^{4}\right)} x^{2} - 14 \, {\left(45 \, b^{3} c^{2} - 92 \, a b c^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3840 \, c^{6}}\right]"," ",0,"[1/7680*(15*(63*b^5 - 280*a*b^3*c + 240*a^2*b*c^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(384*c^5*x^4 - 432*b*c^4*x^3 + 945*b^4*c - 2940*a*b^2*c^2 + 1024*a^2*c^3 + 8*(63*b^2*c^3 - 64*a*c^4)*x^2 - 14*(45*b^3*c^2 - 92*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/3840*(15*(63*b^5 - 280*a*b^3*c + 240*a^2*b*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(384*c^5*x^4 - 432*b*c^4*x^3 + 945*b^4*c - 2940*a*b^2*c^2 + 1024*a^2*c^3 + 8*(63*b^2*c^3 - 64*a*c^4)*x^2 - 14*(45*b^3*c^2 - 92*a*b*c^3)*x)*sqrt(c*x^2 + b*x + a))/c^6]","A",0
2373,1,599,0,0.531794," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(128 \, c^{4} d^{4} - 256 \, b c^{3} d^{3} e + 96 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} - 32 \, {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} d e^{3} + {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} e^{4}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, c^{4} e^{4} x^{3} + 768 \, c^{4} d^{3} e - 864 \, b c^{3} d^{2} e^{2} + 32 \, {\left(15 \, b^{2} c^{2} - 16 \, a c^{3}\right)} d e^{3} - 5 \, {\left(21 \, b^{3} c - 44 \, a b c^{2}\right)} e^{4} + 8 \, {\left(32 \, c^{4} d e^{3} - 7 \, b c^{3} e^{4}\right)} x^{2} + 2 \, {\left(288 \, c^{4} d^{2} e^{2} - 160 \, b c^{3} d e^{3} + {\left(35 \, b^{2} c^{2} - 36 \, a c^{3}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{5}}, -\frac{3 \, {\left(128 \, c^{4} d^{4} - 256 \, b c^{3} d^{3} e + 96 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} - 32 \, {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} d e^{3} + {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(48 \, c^{4} e^{4} x^{3} + 768 \, c^{4} d^{3} e - 864 \, b c^{3} d^{2} e^{2} + 32 \, {\left(15 \, b^{2} c^{2} - 16 \, a c^{3}\right)} d e^{3} - 5 \, {\left(21 \, b^{3} c - 44 \, a b c^{2}\right)} e^{4} + 8 \, {\left(32 \, c^{4} d e^{3} - 7 \, b c^{3} e^{4}\right)} x^{2} + 2 \, {\left(288 \, c^{4} d^{2} e^{2} - 160 \, b c^{3} d e^{3} + {\left(35 \, b^{2} c^{2} - 36 \, a c^{3}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{5}}\right]"," ",0,"[1/768*(3*(128*c^4*d^4 - 256*b*c^3*d^3*e + 96*(3*b^2*c^2 - 4*a*c^3)*d^2*e^2 - 32*(5*b^3*c - 12*a*b*c^2)*d*e^3 + (35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*e^4)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(48*c^4*e^4*x^3 + 768*c^4*d^3*e - 864*b*c^3*d^2*e^2 + 32*(15*b^2*c^2 - 16*a*c^3)*d*e^3 - 5*(21*b^3*c - 44*a*b*c^2)*e^4 + 8*(32*c^4*d*e^3 - 7*b*c^3*e^4)*x^2 + 2*(288*c^4*d^2*e^2 - 160*b*c^3*d*e^3 + (35*b^2*c^2 - 36*a*c^3)*e^4)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/384*(3*(128*c^4*d^4 - 256*b*c^3*d^3*e + 96*(3*b^2*c^2 - 4*a*c^3)*d^2*e^2 - 32*(5*b^3*c - 12*a*b*c^2)*d*e^3 + (35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*e^4)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(48*c^4*e^4*x^3 + 768*c^4*d^3*e - 864*b*c^3*d^2*e^2 + 32*(15*b^2*c^2 - 16*a*c^3)*d*e^3 - 5*(21*b^3*c - 44*a*b*c^2)*e^4 + 8*(32*c^4*d*e^3 - 7*b*c^3*e^4)*x^2 + 2*(288*c^4*d^2*e^2 - 160*b*c^3*d*e^3 + (35*b^2*c^2 - 36*a*c^3)*e^4)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
2374,1,391,0,0.448164," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, c^{3} d^{3} - 24 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d e^{2} - {\left(5 \, b^{3} - 12 \, a b c\right)} e^{3}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, c^{3} e^{3} x^{2} + 72 \, c^{3} d^{2} e - 54 \, b c^{2} d e^{2} + {\left(15 \, b^{2} c - 16 \, a c^{2}\right)} e^{3} + 2 \, {\left(18 \, c^{3} d e^{2} - 5 \, b c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, c^{4}}, -\frac{3 \, {\left(16 \, c^{3} d^{3} - 24 \, b c^{2} d^{2} e + 6 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d e^{2} - {\left(5 \, b^{3} - 12 \, a b c\right)} e^{3}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(8 \, c^{3} e^{3} x^{2} + 72 \, c^{3} d^{2} e - 54 \, b c^{2} d e^{2} + {\left(15 \, b^{2} c - 16 \, a c^{2}\right)} e^{3} + 2 \, {\left(18 \, c^{3} d e^{2} - 5 \, b c^{2} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, c^{4}}\right]"," ",0,"[1/96*(3*(16*c^3*d^3 - 24*b*c^2*d^2*e + 6*(3*b^2*c - 4*a*c^2)*d*e^2 - (5*b^3 - 12*a*b*c)*e^3)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(8*c^3*e^3*x^2 + 72*c^3*d^2*e - 54*b*c^2*d*e^2 + (15*b^2*c - 16*a*c^2)*e^3 + 2*(18*c^3*d*e^2 - 5*b*c^2*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^4, -1/48*(3*(16*c^3*d^3 - 24*b*c^2*d^2*e + 6*(3*b^2*c - 4*a*c^2)*d*e^2 - (5*b^3 - 12*a*b*c)*e^3)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(8*c^3*e^3*x^2 + 72*c^3*d^2*e - 54*b*c^2*d*e^2 + (15*b^2*c - 16*a*c^2)*e^3 + 2*(18*c^3*d*e^2 - 5*b*c^2*e^3)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
2375,1,247,0,0.436272," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(3 \, b^{2} - 4 \, a c\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(2 \, c^{2} e^{2} x + 8 \, c^{2} d e - 3 \, b c e^{2}\right)} \sqrt{c x^{2} + b x + a}}{16 \, c^{3}}, -\frac{{\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(3 \, b^{2} - 4 \, a c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(2 \, c^{2} e^{2} x + 8 \, c^{2} d e - 3 \, b c e^{2}\right)} \sqrt{c x^{2} + b x + a}}{8 \, c^{3}}\right]"," ",0,"[-1/16*((8*c^2*d^2 - 8*b*c*d*e + (3*b^2 - 4*a*c)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(2*c^2*e^2*x + 8*c^2*d*e - 3*b*c*e^2)*sqrt(c*x^2 + b*x + a))/c^3, -1/8*((8*c^2*d^2 - 8*b*c*d*e + (3*b^2 - 4*a*c)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(2*c^2*e^2*x + 8*c^2*d*e - 3*b*c*e^2)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
2376,1,165,0,0.432355," ","integrate((e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{c x^{2} + b x + a} c e - {\left(2 \, c d - b e\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right)}{4 \, c^{2}}, \frac{2 \, \sqrt{c x^{2} + b x + a} c e - {\left(2 \, c d - b e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{2 \, c^{2}}\right]"," ",0,"[1/4*(4*sqrt(c*x^2 + b*x + a)*c*e - (2*c*d - b*e)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c))/c^2, 1/2*(2*sqrt(c*x^2 + b*x + a)*c*e - (2*c*d - b*e)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)))/c^2]","A",0
2377,1,106,0,0.427393," ","integrate(1/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right)}{2 \, \sqrt{c}}, -\frac{\sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{c}\right]"," ",0,"[1/2*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c)/sqrt(c), -sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c))/c]","A",0
2378,1,343,0,0.497253," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right)}{2 \, \sqrt{c d^{2} - b d e + a e^{2}}}, \frac{\sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right)}{c d^{2} - b d e + a e^{2}}\right]"," ",0,"[1/2*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2))/sqrt(c*d^2 - b*d*e + a*e^2), sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x))/(c*d^2 - b*d*e + a*e^2)]","B",0
2379,1,652,0,0.638181," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e - 2 \, a b d^{2} e^{3} + a^{2} d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} - 2 \, a b d e^{4} + a^{2} e^{5} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)}}, \frac{{\left(2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(c d^{2} e - b d e^{2} + a e^{3}\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(c^{2} d^{5} - 2 \, b c d^{4} e - 2 \, a b d^{2} e^{3} + a^{2} d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} - 2 \, a b d e^{4} + a^{2} e^{5} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x\right)}}\right]"," ",0,"[-1/4*((2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(c*d^2*e - b*d*e^2 + a*e^3)*sqrt(c*x^2 + b*x + a))/(c^2*d^5 - 2*b*c*d^4*e - 2*a*b*d^2*e^3 + a^2*d*e^4 + (b^2 + 2*a*c)*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 - 2*a*b*d*e^4 + a^2*e^5 + (b^2 + 2*a*c)*d^2*e^3)*x), 1/2*((2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(c*d^2*e - b*d*e^2 + a*e^3)*sqrt(c*x^2 + b*x + a))/(c^2*d^5 - 2*b*c*d^4*e - 2*a*b*d^2*e^3 + a^2*d*e^4 + (b^2 + 2*a*c)*d^3*e^2 + (c^2*d^4*e - 2*b*c*d^3*e^2 - 2*a*b*d*e^4 + a^2*e^5 + (b^2 + 2*a*c)*d^2*e^3)*x)]","B",0
2380,1,1362,0,1.893870," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + {\left(3 \, b^{2} - 4 \, a c\right)} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + {\left(3 \, b^{2} - 4 \, a c\right)} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + {\left(3 \, b^{2} - 4 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(8 \, c^{2} d^{4} e - 13 \, b c d^{3} e^{2} - 7 \, a b d e^{4} + 2 \, a^{2} e^{5} + 5 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3} + 3 \, {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} - a b e^{5} + {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e - 3 \, a^{2} b d^{3} e^{5} + a^{3} d^{2} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{4} + {\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} - 3 \, a^{2} b d e^{7} + a^{3} e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} - 3 \, a^{2} b d^{2} e^{6} + a^{3} d e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{5}\right)} x\right)}}, \frac{{\left(8 \, c^{2} d^{4} - 8 \, b c d^{3} e + {\left(3 \, b^{2} - 4 \, a c\right)} d^{2} e^{2} + {\left(8 \, c^{2} d^{2} e^{2} - 8 \, b c d e^{3} + {\left(3 \, b^{2} - 4 \, a c\right)} e^{4}\right)} x^{2} + 2 \, {\left(8 \, c^{2} d^{3} e - 8 \, b c d^{2} e^{2} + {\left(3 \, b^{2} - 4 \, a c\right)} d e^{3}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, c^{2} d^{4} e - 13 \, b c d^{3} e^{2} - 7 \, a b d e^{4} + 2 \, a^{2} e^{5} + 5 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3} + 3 \, {\left(2 \, c^{2} d^{3} e^{2} - 3 \, b c d^{2} e^{3} - a b e^{5} + {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(c^{3} d^{8} - 3 \, b c^{2} d^{7} e - 3 \, a^{2} b d^{3} e^{5} + a^{3} d^{2} e^{6} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{6} e^{2} - {\left(b^{3} + 6 \, a b c\right)} d^{5} e^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{4} e^{4} + {\left(c^{3} d^{6} e^{2} - 3 \, b c^{2} d^{5} e^{3} - 3 \, a^{2} b d e^{7} + a^{3} e^{8} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{4} - {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{5} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{6}\right)} x^{2} + 2 \, {\left(c^{3} d^{7} e - 3 \, b c^{2} d^{6} e^{2} - 3 \, a^{2} b d^{2} e^{6} + a^{3} d e^{7} + 3 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{3} - {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{4} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/16*((8*c^2*d^4 - 8*b*c*d^3*e + (3*b^2 - 4*a*c)*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + (3*b^2 - 4*a*c)*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + (3*b^2 - 4*a*c)*d*e^3)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(8*c^2*d^4*e - 13*b*c*d^3*e^2 - 7*a*b*d*e^4 + 2*a^2*e^5 + 5*(b^2 + 2*a*c)*d^2*e^3 + 3*(2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 - a*b*e^5 + (b^2 + 2*a*c)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^8 - 3*b*c^2*d^7*e - 3*a^2*b*d^3*e^5 + a^3*d^2*e^6 + 3*(b^2*c + a*c^2)*d^6*e^2 - (b^3 + 6*a*b*c)*d^5*e^3 + 3*(a*b^2 + a^2*c)*d^4*e^4 + (c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 - 3*a^2*b*d*e^7 + a^3*e^8 + 3*(b^2*c + a*c^2)*d^4*e^4 - (b^3 + 6*a*b*c)*d^3*e^5 + 3*(a*b^2 + a^2*c)*d^2*e^6)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 - 3*a^2*b*d^2*e^6 + a^3*d*e^7 + 3*(b^2*c + a*c^2)*d^5*e^3 - (b^3 + 6*a*b*c)*d^4*e^4 + 3*(a*b^2 + a^2*c)*d^3*e^5)*x), 1/8*((8*c^2*d^4 - 8*b*c*d^3*e + (3*b^2 - 4*a*c)*d^2*e^2 + (8*c^2*d^2*e^2 - 8*b*c*d*e^3 + (3*b^2 - 4*a*c)*e^4)*x^2 + 2*(8*c^2*d^3*e - 8*b*c*d^2*e^2 + (3*b^2 - 4*a*c)*d*e^3)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(8*c^2*d^4*e - 13*b*c*d^3*e^2 - 7*a*b*d*e^4 + 2*a^2*e^5 + 5*(b^2 + 2*a*c)*d^2*e^3 + 3*(2*c^2*d^3*e^2 - 3*b*c*d^2*e^3 - a*b*e^5 + (b^2 + 2*a*c)*d*e^4)*x)*sqrt(c*x^2 + b*x + a))/(c^3*d^8 - 3*b*c^2*d^7*e - 3*a^2*b*d^3*e^5 + a^3*d^2*e^6 + 3*(b^2*c + a*c^2)*d^6*e^2 - (b^3 + 6*a*b*c)*d^5*e^3 + 3*(a*b^2 + a^2*c)*d^4*e^4 + (c^3*d^6*e^2 - 3*b*c^2*d^5*e^3 - 3*a^2*b*d*e^7 + a^3*e^8 + 3*(b^2*c + a*c^2)*d^4*e^4 - (b^3 + 6*a*b*c)*d^3*e^5 + 3*(a*b^2 + a^2*c)*d^2*e^6)*x^2 + 2*(c^3*d^7*e - 3*b*c^2*d^6*e^2 - 3*a^2*b*d^2*e^6 + a^3*d*e^7 + 3*(b^2*c + a*c^2)*d^5*e^3 - (b^3 + 6*a*b*c)*d^4*e^4 + 3*(a*b^2 + a^2*c)*d^3*e^5)*x)]","B",0
2381,1,2688,0,9.017815," ","integrate(1/(e*x+d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, c^{3} d^{6} - 24 \, b c^{2} d^{5} e + 6 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d^{4} e^{2} - {\left(5 \, b^{3} - 12 \, a b c\right)} d^{3} e^{3} + {\left(16 \, c^{3} d^{3} e^{3} - 24 \, b c^{2} d^{2} e^{4} + 6 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d e^{5} - {\left(5 \, b^{3} - 12 \, a b c\right)} e^{6}\right)} x^{3} + 3 \, {\left(16 \, c^{3} d^{4} e^{2} - 24 \, b c^{2} d^{3} e^{3} + 6 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{4} - {\left(5 \, b^{3} - 12 \, a b c\right)} d e^{5}\right)} x^{2} + 3 \, {\left(16 \, c^{3} d^{5} e - 24 \, b c^{2} d^{4} e^{2} + 6 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d^{3} e^{3} - {\left(5 \, b^{3} - 12 \, a b c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(72 \, c^{3} d^{6} e - 162 \, b c^{2} d^{5} e^{2} - 34 \, a^{2} b d e^{6} + 8 \, a^{3} e^{7} + {\left(123 \, b^{2} c + 92 \, a c^{2}\right)} d^{4} e^{3} - {\left(33 \, b^{3} + 136 \, a b c\right)} d^{3} e^{4} + {\left(59 \, a b^{2} + 28 \, a^{2} c\right)} d^{2} e^{5} + {\left(44 \, c^{3} d^{4} e^{3} - 88 \, b c^{2} d^{3} e^{4} + {\left(59 \, b^{2} c + 28 \, a c^{2}\right)} d^{2} e^{5} - {\left(15 \, b^{3} + 28 \, a b c\right)} d e^{6} + {\left(15 \, a b^{2} - 16 \, a^{2} c\right)} e^{7}\right)} x^{2} + 2 \, {\left(54 \, c^{3} d^{5} e^{2} - 113 \, b c^{2} d^{4} e^{3} - 5 \, a^{2} b e^{7} + {\left(79 \, b^{2} c + 48 \, a c^{2}\right)} d^{3} e^{4} - 2 \, {\left(10 \, b^{3} + 29 \, a b c\right)} d^{2} e^{5} + {\left(25 \, a b^{2} - 6 \, a^{2} c\right)} d e^{6}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(c^{4} d^{11} - 4 \, b c^{3} d^{10} e - 4 \, a^{3} b d^{4} e^{7} + a^{4} d^{3} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{6} + {\left(c^{4} d^{8} e^{3} - 4 \, b c^{3} d^{7} e^{4} - 4 \, a^{3} b d e^{10} + a^{4} e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{9}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} - 4 \, b c^{3} d^{8} e^{3} - 4 \, a^{3} b d^{2} e^{9} + a^{4} d e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{8}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e - 4 \, b c^{3} d^{9} e^{2} - 4 \, a^{3} b d^{3} e^{8} + a^{4} d^{2} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{7}\right)} x\right)}}, \frac{3 \, {\left(16 \, c^{3} d^{6} - 24 \, b c^{2} d^{5} e + 6 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d^{4} e^{2} - {\left(5 \, b^{3} - 12 \, a b c\right)} d^{3} e^{3} + {\left(16 \, c^{3} d^{3} e^{3} - 24 \, b c^{2} d^{2} e^{4} + 6 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d e^{5} - {\left(5 \, b^{3} - 12 \, a b c\right)} e^{6}\right)} x^{3} + 3 \, {\left(16 \, c^{3} d^{4} e^{2} - 24 \, b c^{2} d^{3} e^{3} + 6 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{4} - {\left(5 \, b^{3} - 12 \, a b c\right)} d e^{5}\right)} x^{2} + 3 \, {\left(16 \, c^{3} d^{5} e - 24 \, b c^{2} d^{4} e^{2} + 6 \, {\left(3 \, b^{2} c - 4 \, a c^{2}\right)} d^{3} e^{3} - {\left(5 \, b^{3} - 12 \, a b c\right)} d^{2} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(72 \, c^{3} d^{6} e - 162 \, b c^{2} d^{5} e^{2} - 34 \, a^{2} b d e^{6} + 8 \, a^{3} e^{7} + {\left(123 \, b^{2} c + 92 \, a c^{2}\right)} d^{4} e^{3} - {\left(33 \, b^{3} + 136 \, a b c\right)} d^{3} e^{4} + {\left(59 \, a b^{2} + 28 \, a^{2} c\right)} d^{2} e^{5} + {\left(44 \, c^{3} d^{4} e^{3} - 88 \, b c^{2} d^{3} e^{4} + {\left(59 \, b^{2} c + 28 \, a c^{2}\right)} d^{2} e^{5} - {\left(15 \, b^{3} + 28 \, a b c\right)} d e^{6} + {\left(15 \, a b^{2} - 16 \, a^{2} c\right)} e^{7}\right)} x^{2} + 2 \, {\left(54 \, c^{3} d^{5} e^{2} - 113 \, b c^{2} d^{4} e^{3} - 5 \, a^{2} b e^{7} + {\left(79 \, b^{2} c + 48 \, a c^{2}\right)} d^{3} e^{4} - 2 \, {\left(10 \, b^{3} + 29 \, a b c\right)} d^{2} e^{5} + {\left(25 \, a b^{2} - 6 \, a^{2} c\right)} d e^{6}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(c^{4} d^{11} - 4 \, b c^{3} d^{10} e - 4 \, a^{3} b d^{4} e^{7} + a^{4} d^{3} e^{8} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{9} e^{2} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{8} e^{3} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{7} e^{4} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{6} e^{5} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{5} e^{6} + {\left(c^{4} d^{8} e^{3} - 4 \, b c^{3} d^{7} e^{4} - 4 \, a^{3} b d e^{10} + a^{4} e^{11} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{5} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{6} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{7} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{8} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{9}\right)} x^{3} + 3 \, {\left(c^{4} d^{9} e^{2} - 4 \, b c^{3} d^{8} e^{3} - 4 \, a^{3} b d^{2} e^{9} + a^{4} d e^{10} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{4} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{5} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{6} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{7} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{8}\right)} x^{2} + 3 \, {\left(c^{4} d^{10} e - 4 \, b c^{3} d^{9} e^{2} - 4 \, a^{3} b d^{3} e^{8} + a^{4} d^{2} e^{9} + 2 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{8} e^{3} - 4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{7} e^{4} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{6} e^{5} - 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{5} e^{6} + 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{4} e^{7}\right)} x\right)}}\right]"," ",0,"[1/96*(3*(16*c^3*d^6 - 24*b*c^2*d^5*e + 6*(3*b^2*c - 4*a*c^2)*d^4*e^2 - (5*b^3 - 12*a*b*c)*d^3*e^3 + (16*c^3*d^3*e^3 - 24*b*c^2*d^2*e^4 + 6*(3*b^2*c - 4*a*c^2)*d*e^5 - (5*b^3 - 12*a*b*c)*e^6)*x^3 + 3*(16*c^3*d^4*e^2 - 24*b*c^2*d^3*e^3 + 6*(3*b^2*c - 4*a*c^2)*d^2*e^4 - (5*b^3 - 12*a*b*c)*d*e^5)*x^2 + 3*(16*c^3*d^5*e - 24*b*c^2*d^4*e^2 + 6*(3*b^2*c - 4*a*c^2)*d^3*e^3 - (5*b^3 - 12*a*b*c)*d^2*e^4)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(72*c^3*d^6*e - 162*b*c^2*d^5*e^2 - 34*a^2*b*d*e^6 + 8*a^3*e^7 + (123*b^2*c + 92*a*c^2)*d^4*e^3 - (33*b^3 + 136*a*b*c)*d^3*e^4 + (59*a*b^2 + 28*a^2*c)*d^2*e^5 + (44*c^3*d^4*e^3 - 88*b*c^2*d^3*e^4 + (59*b^2*c + 28*a*c^2)*d^2*e^5 - (15*b^3 + 28*a*b*c)*d*e^6 + (15*a*b^2 - 16*a^2*c)*e^7)*x^2 + 2*(54*c^3*d^5*e^2 - 113*b*c^2*d^4*e^3 - 5*a^2*b*e^7 + (79*b^2*c + 48*a*c^2)*d^3*e^4 - 2*(10*b^3 + 29*a*b*c)*d^2*e^5 + (25*a*b^2 - 6*a^2*c)*d*e^6)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^11 - 4*b*c^3*d^10*e - 4*a^3*b*d^4*e^7 + a^4*d^3*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^6 + (c^4*d^8*e^3 - 4*b*c^3*d^7*e^4 - 4*a^3*b*d*e^10 + a^4*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^9)*x^3 + 3*(c^4*d^9*e^2 - 4*b*c^3*d^8*e^3 - 4*a^3*b*d^2*e^9 + a^4*d*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^8)*x^2 + 3*(c^4*d^10*e - 4*b*c^3*d^9*e^2 - 4*a^3*b*d^3*e^8 + a^4*d^2*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^7)*x), 1/48*(3*(16*c^3*d^6 - 24*b*c^2*d^5*e + 6*(3*b^2*c - 4*a*c^2)*d^4*e^2 - (5*b^3 - 12*a*b*c)*d^3*e^3 + (16*c^3*d^3*e^3 - 24*b*c^2*d^2*e^4 + 6*(3*b^2*c - 4*a*c^2)*d*e^5 - (5*b^3 - 12*a*b*c)*e^6)*x^3 + 3*(16*c^3*d^4*e^2 - 24*b*c^2*d^3*e^3 + 6*(3*b^2*c - 4*a*c^2)*d^2*e^4 - (5*b^3 - 12*a*b*c)*d*e^5)*x^2 + 3*(16*c^3*d^5*e - 24*b*c^2*d^4*e^2 + 6*(3*b^2*c - 4*a*c^2)*d^3*e^3 - (5*b^3 - 12*a*b*c)*d^2*e^4)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(72*c^3*d^6*e - 162*b*c^2*d^5*e^2 - 34*a^2*b*d*e^6 + 8*a^3*e^7 + (123*b^2*c + 92*a*c^2)*d^4*e^3 - (33*b^3 + 136*a*b*c)*d^3*e^4 + (59*a*b^2 + 28*a^2*c)*d^2*e^5 + (44*c^3*d^4*e^3 - 88*b*c^2*d^3*e^4 + (59*b^2*c + 28*a*c^2)*d^2*e^5 - (15*b^3 + 28*a*b*c)*d*e^6 + (15*a*b^2 - 16*a^2*c)*e^7)*x^2 + 2*(54*c^3*d^5*e^2 - 113*b*c^2*d^4*e^3 - 5*a^2*b*e^7 + (79*b^2*c + 48*a*c^2)*d^3*e^4 - 2*(10*b^3 + 29*a*b*c)*d^2*e^5 + (25*a*b^2 - 6*a^2*c)*d*e^6)*x)*sqrt(c*x^2 + b*x + a))/(c^4*d^11 - 4*b*c^3*d^10*e - 4*a^3*b*d^4*e^7 + a^4*d^3*e^8 + 2*(3*b^2*c^2 + 2*a*c^3)*d^9*e^2 - 4*(b^3*c + 3*a*b*c^2)*d^8*e^3 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^7*e^4 - 4*(a*b^3 + 3*a^2*b*c)*d^6*e^5 + 2*(3*a^2*b^2 + 2*a^3*c)*d^5*e^6 + (c^4*d^8*e^3 - 4*b*c^3*d^7*e^4 - 4*a^3*b*d*e^10 + a^4*e^11 + 2*(3*b^2*c^2 + 2*a*c^3)*d^6*e^5 - 4*(b^3*c + 3*a*b*c^2)*d^5*e^6 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^7 - 4*(a*b^3 + 3*a^2*b*c)*d^3*e^8 + 2*(3*a^2*b^2 + 2*a^3*c)*d^2*e^9)*x^3 + 3*(c^4*d^9*e^2 - 4*b*c^3*d^8*e^3 - 4*a^3*b*d^2*e^9 + a^4*d*e^10 + 2*(3*b^2*c^2 + 2*a*c^3)*d^7*e^4 - 4*(b^3*c + 3*a*b*c^2)*d^6*e^5 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^6 - 4*(a*b^3 + 3*a^2*b*c)*d^4*e^7 + 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^8)*x^2 + 3*(c^4*d^10*e - 4*b*c^3*d^9*e^2 - 4*a^3*b*d^3*e^8 + a^4*d^2*e^9 + 2*(3*b^2*c^2 + 2*a*c^3)*d^8*e^3 - 4*(b^3*c + 3*a*b*c^2)*d^7*e^4 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^6*e^5 - 4*(a*b^3 + 3*a^2*b*c)*d^5*e^6 + 2*(3*a^2*b^2 + 2*a^3*c)*d^4*e^7)*x)]","B",0
2382,1,1173,0,0.748857," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(16 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{2} - 16 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e^{4} + {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{2} - 16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} + {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{4}\right)} x^{2} + {\left(16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{2} - 16 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d e^{3} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(8 \, b c^{4} d^{4} - 64 \, a c^{4} d^{3} e + 48 \, a b c^{3} d^{2} e^{2} - 2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{4} x^{3} - 16 \, {\left(3 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d e^{3} + {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} e^{4} - {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{3} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{4}\right)} x^{2} + {\left(16 \, c^{5} d^{4} - 32 \, b c^{4} d^{3} e + 48 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{2} e^{2} - 16 \, {\left(3 \, b^{3} c^{2} - 10 \, a b c^{3}\right)} d e^{3} + {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{2} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x\right)}}, -\frac{3 \, {\left(16 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{2} - 16 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e^{4} + {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{2} - 16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{3} + {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{4}\right)} x^{2} + {\left(16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{2} - 16 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d e^{3} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{4}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(8 \, b c^{4} d^{4} - 64 \, a c^{4} d^{3} e + 48 \, a b c^{3} d^{2} e^{2} - 2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{4} x^{3} - 16 \, {\left(3 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d e^{3} + {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} e^{4} - {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d e^{3} - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{4}\right)} x^{2} + {\left(16 \, c^{5} d^{4} - 32 \, b c^{4} d^{3} e + 48 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{2} e^{2} - 16 \, {\left(3 \, b^{3} c^{2} - 10 \, a b c^{3}\right)} d e^{3} + {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{2} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x\right)}}\right]"," ",0,"[-1/16*(3*(16*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^2 - 16*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*e^4 + (16*(b^2*c^3 - 4*a*c^4)*d^2*e^2 - 16*(b^3*c^2 - 4*a*b*c^3)*d*e^3 + (5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*e^4)*x^2 + (16*(b^3*c^2 - 4*a*b*c^3)*d^2*e^2 - 16*(b^4*c - 4*a*b^2*c^2)*d*e^3 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*e^4)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(8*b*c^4*d^4 - 64*a*c^4*d^3*e + 48*a*b*c^3*d^2*e^2 - 2*(b^2*c^3 - 4*a*c^4)*e^4*x^3 - 16*(3*a*b^2*c^2 - 8*a^2*c^3)*d*e^3 + (15*a*b^3*c - 52*a^2*b*c^2)*e^4 - (16*(b^2*c^3 - 4*a*c^4)*d*e^3 - 5*(b^3*c^2 - 4*a*b*c^3)*e^4)*x^2 + (16*c^5*d^4 - 32*b*c^4*d^3*e + 48*(b^2*c^3 - 2*a*c^4)*d^2*e^2 - 16*(3*b^3*c^2 - 10*a*b*c^3)*d*e^3 + (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^2 + (b^3*c^4 - 4*a*b*c^5)*x), -1/8*(3*(16*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^2 - 16*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*e^4 + (16*(b^2*c^3 - 4*a*c^4)*d^2*e^2 - 16*(b^3*c^2 - 4*a*b*c^3)*d*e^3 + (5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*e^4)*x^2 + (16*(b^3*c^2 - 4*a*b*c^3)*d^2*e^2 - 16*(b^4*c - 4*a*b^2*c^2)*d*e^3 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*e^4)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(8*b*c^4*d^4 - 64*a*c^4*d^3*e + 48*a*b*c^3*d^2*e^2 - 2*(b^2*c^3 - 4*a*c^4)*e^4*x^3 - 16*(3*a*b^2*c^2 - 8*a^2*c^3)*d*e^3 + (15*a*b^3*c - 52*a^2*b*c^2)*e^4 - (16*(b^2*c^3 - 4*a*c^4)*d*e^3 - 5*(b^3*c^2 - 4*a*b*c^3)*e^4)*x^2 + (16*c^5*d^4 - 32*b*c^4*d^3*e + 48*(b^2*c^3 - 2*a*c^4)*d^2*e^2 - 16*(3*b^3*c^2 - 10*a*b*c^3)*d*e^3 + (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^2 + (b^3*c^4 - 4*a*b*c^5)*x)]","B",0
2383,1,755,0,0.638856," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\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)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, b c^{3} d^{3} - 12 \, a c^{3} d^{2} e + 6 \, a b c^{2} d e^{2} - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{3} x^{2} - {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} e^{3} + {\left(4 \, c^{4} d^{3} - 6 \, b c^{3} d^{2} e + 6 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{2} - {\left(3 \, b^{3} c - 10 \, a b c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x\right)}}, -\frac{3 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} x^{2} + {\left(2 \, {\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)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(2 \, b c^{3} d^{3} - 12 \, a c^{3} d^{2} e + 6 \, a b c^{2} d e^{2} - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{3} x^{2} - {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} e^{3} + {\left(4 \, c^{4} d^{3} - 6 \, b c^{3} d^{2} e + 6 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{2} - {\left(3 \, b^{3} c - 10 \, a b c^{2}\right)} e^{3}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4} + {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} x^{2} + {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} x\right)}}\right]"," ",0,"[-1/4*(3*(2*(a*b^2*c - 4*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3 + (2*(b^2*c^2 - 4*a*c^3)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*x^2 + (2*(b^3*c - 4*a*b*c^2)*d*e^2 - (b^4 - 4*a*b^2*c)*e^3)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(2*b*c^3*d^3 - 12*a*c^3*d^2*e + 6*a*b*c^2*d*e^2 - (b^2*c^2 - 4*a*c^3)*e^3*x^2 - (3*a*b^2*c - 8*a^2*c^2)*e^3 + (4*c^4*d^3 - 6*b*c^3*d^2*e + 6*(b^2*c^2 - 2*a*c^3)*d*e^2 - (3*b^3*c - 10*a*b*c^2)*e^3)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^2 + (b^3*c^3 - 4*a*b*c^4)*x), -1/2*(3*(2*(a*b^2*c - 4*a^2*c^2)*d*e^2 - (a*b^3 - 4*a^2*b*c)*e^3 + (2*(b^2*c^2 - 4*a*c^3)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*x^2 + (2*(b^3*c - 4*a*b*c^2)*d*e^2 - (b^4 - 4*a*b^2*c)*e^3)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(2*b*c^3*d^3 - 12*a*c^3*d^2*e + 6*a*b*c^2*d*e^2 - (b^2*c^2 - 4*a*c^3)*e^3*x^2 - (3*a*b^2*c - 8*a^2*c^2)*e^3 + (4*c^4*d^3 - 6*b*c^3*d^2*e + 6*(b^2*c^2 - 2*a*c^3)*d*e^2 - (3*b^3*c - 10*a*b*c^2)*e^3)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^3 - 4*a^2*c^4 + (b^2*c^4 - 4*a*c^5)*x^2 + (b^3*c^3 - 4*a*b*c^4)*x)]","B",0
2384,1,461,0,0.564482," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{2} + {\left(b^{3} - 4 \, a b c\right)} e^{2} x + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(b c^{2} d^{2} - 4 \, a c^{2} d e + a b c e^{2} + {\left(2 \, c^{3} d^{2} - 2 \, b c^{2} d e + {\left(b^{2} c - 2 \, a c^{2}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)}}, -\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{2} + {\left(b^{3} - 4 \, a b c\right)} e^{2} x + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(b c^{2} d^{2} - 4 \, a c^{2} d e + a b c e^{2} + {\left(2 \, c^{3} d^{2} - 2 \, b c^{2} d e + {\left(b^{2} c - 2 \, a c^{2}\right)} e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x}\right]"," ",0,"[1/2*(((b^2*c - 4*a*c^2)*e^2*x^2 + (b^3 - 4*a*b*c)*e^2*x + (a*b^2 - 4*a^2*c)*e^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(b*c^2*d^2 - 4*a*c^2*d*e + a*b*c*e^2 + (2*c^3*d^2 - 2*b*c^2*d*e + (b^2*c - 2*a*c^2)*e^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x), -(((b^2*c - 4*a*c^2)*e^2*x^2 + (b^3 - 4*a*b*c)*e^2*x + (a*b^2 - 4*a^2*c)*e^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(b*c^2*d^2 - 4*a*c^2*d*e + a*b*c*e^2 + (2*c^3*d^2 - 2*b*c^2*d*e + (b^2*c - 2*a*c^2)*e^2)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)]","A",0
2385,1,74,0,0.498391," ","integrate((e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x}"," ",0,"-2*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)","A",0
2386,1,61,0,0.431885," ","integrate(1/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)}}{a b^{2} - 4 \, a^{2} c + {\left(b^{2} c - 4 \, a c^{2}\right)} x^{2} + {\left(b^{3} - 4 \, a b c\right)} x}"," ",0,"-2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)/(a*b^2 - 4*a^2*c + (b^2*c - 4*a*c^2)*x^2 + (b^3 - 4*a*b*c)*x)","B",0
2387,1,1349,0,0.893326," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{2} + {\left(b^{3} - 4 \, a b c\right)} e^{2} x + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(b c^{2} d^{3} - 2 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e + {\left(b^{3} - a b c\right)} d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e - a b c e^{3} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left({\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x\right)}}, \frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} e^{2} x^{2} + {\left(b^{3} - 4 \, a b c\right)} e^{2} x + {\left(a b^{2} - 4 \, a^{2} c\right)} e^{2}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(b c^{2} d^{3} - 2 \, {\left(b^{2} c - a c^{2}\right)} d^{2} e + {\left(b^{3} - a b c\right)} d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3} + {\left(2 \, c^{3} d^{3} - 3 \, b c^{2} d^{2} e - a b c e^{3} + {\left(b^{2} c + 2 \, a c^{2}\right)} d e^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{{\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{4} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} - 2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e + {\left(b^{4} c - 2 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} d^{2} e^{2} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} - 2 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} d^{3} e + {\left(b^{5} - 2 \, a b^{3} c - 8 \, a^{2} b c^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b^{4} - 4 \, a^{2} b^{2} c\right)} d e^{3} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{4}\right)} x}\right]"," ",0,"[1/2*(((b^2*c - 4*a*c^2)*e^2*x^2 + (b^3 - 4*a*b*c)*e^2*x + (a*b^2 - 4*a^2*c)*e^2)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(b*c^2*d^3 - 2*(b^2*c - a*c^2)*d^2*e + (b^3 - a*b*c)*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e - a*b*c*e^3 + (b^2*c + 2*a*c^2)*d*e^2)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x), (((b^2*c - 4*a*c^2)*e^2*x^2 + (b^3 - 4*a*b*c)*e^2*x + (a*b^2 - 4*a^2*c)*e^2)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(b*c^2*d^3 - 2*(b^2*c - a*c^2)*d^2*e + (b^3 - a*b*c)*d*e^2 - (a*b^2 - 2*a^2*c)*e^3 + (2*c^3*d^3 - 3*b*c^2*d^2*e - a*b*c*e^3 + (b^2*c + 2*a*c^2)*d*e^2)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^2 - 4*a^2*c^3)*d^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^3*b^2 - 4*a^4*c)*e^4 + ((b^2*c^3 - 4*a*c^4)*d^4 - 2*(b^3*c^2 - 4*a*b*c^3)*d^3*e + (b^4*c - 2*a*b^2*c^2 - 8*a^2*c^3)*d^2*e^2 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^3*c^2 - 4*a*b*c^3)*d^4 - 2*(b^4*c - 4*a*b^2*c^2)*d^3*e + (b^5 - 2*a*b^3*c - 8*a^2*b*c^2)*d^2*e^2 - 2*(a*b^4 - 4*a^2*b^2*c)*d*e^3 + (a^2*b^3 - 4*a^3*b*c)*e^4)*x)]","B",0
2388,1,3004,0,1.872750," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{3} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{4}\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{3} - {\left(b^{4} - 4 \, a b^{2} c\right)} e^{4}\right)} x^{2} + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{2} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d e^{3} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{4}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(2 \, b c^{3} d^{5} - 2 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e + 6 \, {\left(b^{3} c - 2 \, a b c^{2}\right)} d^{3} e^{2} - {\left(2 \, b^{4} - 3 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} e^{3} + {\left(a b^{3} - 2 \, a^{2} b c\right)} d e^{4} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{5} + {\left(4 \, c^{4} d^{4} e - 8 \, b c^{3} d^{3} e^{2} + {\left(7 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{3} - {\left(3 \, b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} e^{5}\right)} x^{2} + {\left(4 \, c^{4} d^{5} - 6 \, b c^{3} d^{4} e + 8 \, a c^{3} d^{3} e^{2} + {\left(5 \, b^{3} c - 16 \, a b c^{2}\right)} d^{2} e^{3} - {\left(3 \, b^{4} - 8 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{4} + {\left(3 \, a b^{3} - 10 \, a^{2} b c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{7} - 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{6} e + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{5} e^{2} - {\left(a b^{5} + 2 \, a^{2} b^{3} c - 24 \, a^{3} b c^{2}\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{6} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} e^{2} + 3 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{3} - {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{5} - 3 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{6} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{7}\right)} x^{3} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{7} - 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} e + 3 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{5} e^{2} + {\left(2 \, b^{5} c - 11 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d^{4} e^{3} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{5} - 4 \, a^{2} b^{3} c\right)} d^{2} e^{5} - {\left(3 \, a^{2} b^{4} - 13 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{7}\right)} x^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} - {\left(3 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} e + 3 \, {\left(b^{5} c - 4 \, a b^{3} c^{2}\right)} d^{5} e^{2} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{4} e^{3} + {\left(2 \, a b^{5} - 11 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} d^{3} e^{4} + 3 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{6} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{7}\right)} x\right)}}, \frac{3 \, {\left(2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} e^{2} - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{3} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{4}\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{2} + {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{3} - {\left(b^{4} - 4 \, a b^{2} c\right)} e^{4}\right)} x^{2} + {\left(2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{2} - {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d e^{3} - {\left(a b^{3} - 4 \, a^{2} b c\right)} e^{4}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, b c^{3} d^{5} - 2 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d^{4} e + 6 \, {\left(b^{3} c - 2 \, a b c^{2}\right)} d^{3} e^{2} - {\left(2 \, b^{4} - 3 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} e^{3} + {\left(a b^{3} - 2 \, a^{2} b c\right)} d e^{4} + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} e^{5} + {\left(4 \, c^{4} d^{4} e - 8 \, b c^{3} d^{3} e^{2} + {\left(7 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} e^{3} - {\left(3 \, b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(3 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} e^{5}\right)} x^{2} + {\left(4 \, c^{4} d^{5} - 6 \, b c^{3} d^{4} e + 8 \, a c^{3} d^{3} e^{2} + {\left(5 \, b^{3} c - 16 \, a b c^{2}\right)} d^{2} e^{3} - {\left(3 \, b^{4} - 8 \, a b^{2} c - 4 \, a^{2} c^{2}\right)} d e^{4} + {\left(3 \, a b^{3} - 10 \, a^{2} b c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left({\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{7} - 3 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{6} e + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{5} e^{2} - {\left(a b^{5} + 2 \, a^{2} b^{3} c - 24 \, a^{3} b c^{2}\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{4} - 3 \, a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{3} e^{4} - 3 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{2} e^{5} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d e^{6} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} e - 3 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} e^{2} + 3 \, {\left(b^{4} c^{2} - 3 \, a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{3} - {\left(b^{5} c + 2 \, a b^{3} c^{2} - 24 \, a^{2} b c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{2} e^{5} - 3 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{6} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{7}\right)} x^{3} + {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{7} - 2 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} e + 3 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{5} e^{2} + {\left(2 \, b^{5} c - 11 \, a b^{3} c^{2} + 12 \, a^{2} b c^{3}\right)} d^{4} e^{3} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{3} e^{4} + 3 \, {\left(a b^{5} - 4 \, a^{2} b^{3} c\right)} d^{2} e^{5} - {\left(3 \, a^{2} b^{4} - 13 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{6} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{7}\right)} x^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{7} - {\left(3 \, b^{4} c^{2} - 13 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} e + 3 \, {\left(b^{5} c - 4 \, a b^{3} c^{2}\right)} d^{5} e^{2} - {\left(b^{6} - a b^{4} c - 15 \, a^{2} b^{2} c^{2} + 12 \, a^{3} c^{3}\right)} d^{4} e^{3} + {\left(2 \, a b^{5} - 11 \, a^{2} b^{3} c + 12 \, a^{3} b c^{2}\right)} d^{3} e^{4} + 3 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{6} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{7}\right)} x\right)}}\right]"," ",0,"[-1/4*(3*(2*(a*b^2*c - 4*a^2*c^2)*d^2*e^2 - (a*b^3 - 4*a^2*b*c)*d*e^3 + (2*(b^2*c^2 - 4*a*c^3)*d*e^3 - (b^3*c - 4*a*b*c^2)*e^4)*x^3 + (2*(b^2*c^2 - 4*a*c^3)*d^2*e^2 + (b^3*c - 4*a*b*c^2)*d*e^3 - (b^4 - 4*a*b^2*c)*e^4)*x^2 + (2*(b^3*c - 4*a*b*c^2)*d^2*e^2 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*e^3 - (a*b^3 - 4*a^2*b*c)*e^4)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(2*b*c^3*d^5 - 2*(3*b^2*c^2 - 4*a*c^3)*d^4*e + 6*(b^3*c - 2*a*b*c^2)*d^3*e^2 - (2*b^4 - 3*a*b^2*c - 4*a^2*c^2)*d^2*e^3 + (a*b^3 - 2*a^2*b*c)*d*e^4 + (a^2*b^2 - 4*a^3*c)*e^5 + (4*c^4*d^4*e - 8*b*c^3*d^3*e^2 + (7*b^2*c^2 - 4*a*c^3)*d^2*e^3 - (3*b^3*c - 4*a*b*c^2)*d*e^4 + (3*a*b^2*c - 8*a^2*c^2)*e^5)*x^2 + (4*c^4*d^5 - 6*b*c^3*d^4*e + 8*a*c^3*d^3*e^2 + (5*b^3*c - 16*a*b*c^2)*d^2*e^3 - (3*b^4 - 8*a*b^2*c - 4*a^2*c^2)*d*e^4 + (3*a*b^3 - 10*a^2*b*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^3 - 4*a^2*c^4)*d^7 - 3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^6*e + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^5*e^2 - (a*b^5 + 2*a^2*b^3*c - 24*a^3*b*c^2)*d^4*e^3 + 3*(a^2*b^4 - 3*a^3*b^2*c - 4*a^4*c^2)*d^3*e^4 - 3*(a^3*b^3 - 4*a^4*b*c)*d^2*e^5 + (a^4*b^2 - 4*a^5*c)*d*e^6 + ((b^2*c^4 - 4*a*c^5)*d^6*e - 3*(b^3*c^3 - 4*a*b*c^4)*d^5*e^2 + 3*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e^3 - (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^4 + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^5 - 3*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^6 + (a^3*b^2*c - 4*a^4*c^2)*e^7)*x^3 + ((b^2*c^4 - 4*a*c^5)*d^7 - 2*(b^3*c^3 - 4*a*b*c^4)*d^6*e + 3*(a*b^2*c^3 - 4*a^2*c^4)*d^5*e^2 + (2*b^5*c - 11*a*b^3*c^2 + 12*a^2*b*c^3)*d^4*e^3 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^3*e^4 + 3*(a*b^5 - 4*a^2*b^3*c)*d^2*e^5 - (3*a^2*b^4 - 13*a^3*b^2*c + 4*a^4*c^2)*d*e^6 + (a^3*b^3 - 4*a^4*b*c)*e^7)*x^2 + ((b^3*c^3 - 4*a*b*c^4)*d^7 - (3*b^4*c^2 - 13*a*b^2*c^3 + 4*a^2*c^4)*d^6*e + 3*(b^5*c - 4*a*b^3*c^2)*d^5*e^2 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^4*e^3 + (2*a*b^5 - 11*a^2*b^3*c + 12*a^3*b*c^2)*d^3*e^4 + 3*(a^3*b^2*c - 4*a^4*c^2)*d^2*e^5 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^6 + (a^4*b^2 - 4*a^5*c)*e^7)*x), 1/2*(3*(2*(a*b^2*c - 4*a^2*c^2)*d^2*e^2 - (a*b^3 - 4*a^2*b*c)*d*e^3 + (2*(b^2*c^2 - 4*a*c^3)*d*e^3 - (b^3*c - 4*a*b*c^2)*e^4)*x^3 + (2*(b^2*c^2 - 4*a*c^3)*d^2*e^2 + (b^3*c - 4*a*b*c^2)*d*e^3 - (b^4 - 4*a*b^2*c)*e^4)*x^2 + (2*(b^3*c - 4*a*b*c^2)*d^2*e^2 - (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*e^3 - (a*b^3 - 4*a^2*b*c)*e^4)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(2*b*c^3*d^5 - 2*(3*b^2*c^2 - 4*a*c^3)*d^4*e + 6*(b^3*c - 2*a*b*c^2)*d^3*e^2 - (2*b^4 - 3*a*b^2*c - 4*a^2*c^2)*d^2*e^3 + (a*b^3 - 2*a^2*b*c)*d*e^4 + (a^2*b^2 - 4*a^3*c)*e^5 + (4*c^4*d^4*e - 8*b*c^3*d^3*e^2 + (7*b^2*c^2 - 4*a*c^3)*d^2*e^3 - (3*b^3*c - 4*a*b*c^2)*d*e^4 + (3*a*b^2*c - 8*a^2*c^2)*e^5)*x^2 + (4*c^4*d^5 - 6*b*c^3*d^4*e + 8*a*c^3*d^3*e^2 + (5*b^3*c - 16*a*b*c^2)*d^2*e^3 - (3*b^4 - 8*a*b^2*c - 4*a^2*c^2)*d*e^4 + (3*a*b^3 - 10*a^2*b*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^3 - 4*a^2*c^4)*d^7 - 3*(a*b^3*c^2 - 4*a^2*b*c^3)*d^6*e + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^5*e^2 - (a*b^5 + 2*a^2*b^3*c - 24*a^3*b*c^2)*d^4*e^3 + 3*(a^2*b^4 - 3*a^3*b^2*c - 4*a^4*c^2)*d^3*e^4 - 3*(a^3*b^3 - 4*a^4*b*c)*d^2*e^5 + (a^4*b^2 - 4*a^5*c)*d*e^6 + ((b^2*c^4 - 4*a*c^5)*d^6*e - 3*(b^3*c^3 - 4*a*b*c^4)*d^5*e^2 + 3*(b^4*c^2 - 3*a*b^2*c^3 - 4*a^2*c^4)*d^4*e^3 - (b^5*c + 2*a*b^3*c^2 - 24*a^2*b*c^3)*d^3*e^4 + 3*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^2*e^5 - 3*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^6 + (a^3*b^2*c - 4*a^4*c^2)*e^7)*x^3 + ((b^2*c^4 - 4*a*c^5)*d^7 - 2*(b^3*c^3 - 4*a*b*c^4)*d^6*e + 3*(a*b^2*c^3 - 4*a^2*c^4)*d^5*e^2 + (2*b^5*c - 11*a*b^3*c^2 + 12*a^2*b*c^3)*d^4*e^3 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^3*e^4 + 3*(a*b^5 - 4*a^2*b^3*c)*d^2*e^5 - (3*a^2*b^4 - 13*a^3*b^2*c + 4*a^4*c^2)*d*e^6 + (a^3*b^3 - 4*a^4*b*c)*e^7)*x^2 + ((b^3*c^3 - 4*a*b*c^4)*d^7 - (3*b^4*c^2 - 13*a*b^2*c^3 + 4*a^2*c^4)*d^6*e + 3*(b^5*c - 4*a*b^3*c^2)*d^5*e^2 - (b^6 - a*b^4*c - 15*a^2*b^2*c^2 + 12*a^3*c^3)*d^4*e^3 + (2*a*b^5 - 11*a^2*b^3*c + 12*a^3*b*c^2)*d^3*e^4 + 3*(a^3*b^2*c - 4*a^4*c^2)*d^2*e^5 - 2*(a^3*b^3 - 4*a^4*b*c)*d*e^6 + (a^4*b^2 - 4*a^5*c)*e^7)*x)]","B",0
2389,1,5732,0,7.678048," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(16 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - 16 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e^{3} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} d^{2} e^{4} + {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{4} - 16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{5} + {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{6}\right)} x^{4} + {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{3} - 16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{4} - 2 \, {\left(3 \, b^{4} c - 8 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d e^{5} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{6}\right)} x^{3} + {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} e^{2} + 16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{3} - 3 \, {\left(9 \, b^{4} c - 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} e^{4} + 2 \, {\left(5 \, b^{5} - 32 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d e^{5} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e^{6}\right)} x^{2} + {\left(16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e^{2} - 16 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{3} e^{3} + {\left(5 \, b^{5} - 56 \, a b^{3} c + 144 \, a^{2} b c^{2}\right)} d^{2} e^{4} + 2 \, {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} d e^{5}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(8 \, b c^{4} d^{7} - 16 \, {\left(2 \, b^{2} c^{3} - 3 \, a c^{4}\right)} d^{6} e + 16 \, {\left(3 \, b^{3} c^{2} - 7 \, a b c^{3}\right)} d^{5} e^{2} - 32 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} + a^{2} c^{3}\right)} d^{4} e^{3} + {\left(8 \, b^{5} - 33 \, a b^{3} c + 44 \, a^{2} b c^{2}\right)} d^{3} e^{4} + {\left(a b^{4} + 14 \, a^{2} b^{2} c - 88 \, a^{3} c^{2}\right)} d^{2} e^{5} - 11 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{6} + 2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{7} + {\left(16 \, c^{5} d^{5} e^{2} - 40 \, b c^{4} d^{4} e^{3} + 2 \, {\left(31 \, b^{2} c^{3} - 44 \, a c^{4}\right)} d^{3} e^{4} - {\left(53 \, b^{3} c^{2} - 132 \, a b c^{3}\right)} d^{2} e^{5} + {\left(15 \, b^{4} c - 14 \, a b^{2} c^{2} - 104 \, a^{2} c^{3}\right)} d e^{6} - {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} e^{7}\right)} x^{3} + {\left(32 \, c^{5} d^{6} e - 72 \, b c^{4} d^{5} e^{2} + 80 \, {\left(b^{2} c^{3} - a c^{4}\right)} d^{4} e^{3} - {\left(27 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} d^{3} e^{4} - 2 \, {\left(14 \, b^{4} c - 73 \, a b^{2} c^{2} + 68 \, a^{2} c^{3}\right)} d^{2} e^{5} + {\left(15 \, b^{5} - 49 \, a b^{3} c - 20 \, a^{2} b c^{2}\right)} d e^{6} - {\left(15 \, a b^{4} - 62 \, a^{2} b^{2} c + 24 \, a^{3} c^{2}\right)} e^{7}\right)} x^{2} + {\left(16 \, c^{5} d^{7} - 24 \, b c^{4} d^{6} e - 16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} e^{2} + 80 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{4} e^{3} - {\left(81 \, b^{4} c - 274 \, a b^{2} c^{2} + 40 \, a^{2} c^{3}\right)} d^{3} e^{4} + {\left(25 \, b^{5} - 63 \, a b^{3} c - 76 \, a^{2} b c^{2}\right)} d^{2} e^{5} - 2 \, {\left(10 \, a b^{4} - 47 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} d e^{6} - 5 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left({\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{10} - 4 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{9} e + 2 \, {\left(3 \, a b^{4} c^{2} - 10 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{8} e^{2} - 4 \, {\left(a b^{5} c - a^{2} b^{3} c^{2} - 12 \, a^{3} b c^{3}\right)} d^{7} e^{3} + {\left(a b^{6} + 8 \, a^{2} b^{4} c - 42 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} d^{6} e^{4} - 4 \, {\left(a^{2} b^{5} - a^{3} b^{3} c - 12 \, a^{4} b c^{2}\right)} d^{5} e^{5} + 2 \, {\left(3 \, a^{3} b^{4} - 10 \, a^{4} b^{2} c - 8 \, a^{5} c^{2}\right)} d^{4} e^{6} - 4 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{3} e^{7} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d^{2} e^{8} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} e^{2} - 4 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e^{3} + 2 \, {\left(3 \, b^{4} c^{3} - 10 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{6} e^{4} - 4 \, {\left(b^{5} c^{2} - a b^{3} c^{3} - 12 \, a^{2} b c^{4}\right)} d^{5} e^{5} + {\left(b^{6} c + 8 \, a b^{4} c^{2} - 42 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{4} e^{6} - 4 \, {\left(a b^{5} c - a^{2} b^{3} c^{2} - 12 \, a^{3} b c^{3}\right)} d^{3} e^{7} + 2 \, {\left(3 \, a^{2} b^{4} c - 10 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} d^{2} e^{8} - 4 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d e^{9} + {\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} e^{10}\right)} x^{4} + {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{9} e - 7 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{8} e^{2} + 8 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{7} e^{3} - 2 \, {\left(b^{5} c^{2} + 6 \, a b^{3} c^{3} - 40 \, a^{2} b c^{4}\right)} d^{6} e^{4} - 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 18 \, a^{2} b^{2} c^{3} + 24 \, a^{3} c^{4}\right)} d^{5} e^{5} + {\left(b^{7} - 34 \, a^{2} b^{3} c^{2} + 72 \, a^{3} b c^{3}\right)} d^{4} e^{6} - 4 \, {\left(a b^{6} - 4 \, a^{2} b^{4} c - 2 \, a^{3} b^{2} c^{2} + 8 \, a^{4} c^{3}\right)} d^{3} e^{7} + 2 \, {\left(3 \, a^{2} b^{5} - 14 \, a^{3} b^{3} c + 8 \, a^{4} b c^{2}\right)} d^{2} e^{8} - 2 \, {\left(2 \, a^{3} b^{4} - 9 \, a^{4} b^{2} c + 4 \, a^{5} c^{2}\right)} d e^{9} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e^{10}\right)} x^{3} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{10} - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{9} e - {\left(2 \, b^{4} c^{3} - 13 \, a b^{2} c^{4} + 20 \, a^{2} c^{5}\right)} d^{8} e^{2} + 8 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{7} e^{3} - {\left(7 \, b^{6} c - 22 \, a b^{4} c^{2} - 34 \, a^{2} b^{2} c^{3} + 40 \, a^{3} c^{4}\right)} d^{6} e^{4} + 2 \, {\left(b^{7} + 4 \, a b^{5} c - 38 \, a^{2} b^{3} c^{2} + 24 \, a^{3} b c^{3}\right)} d^{5} e^{5} - {\left(7 \, a b^{6} - 22 \, a^{2} b^{4} c - 34 \, a^{3} b^{2} c^{2} + 40 \, a^{4} c^{3}\right)} d^{4} e^{6} + 8 \, {\left(a^{2} b^{5} - 5 \, a^{3} b^{3} c + 4 \, a^{4} b c^{2}\right)} d^{3} e^{7} - {\left(2 \, a^{3} b^{4} - 13 \, a^{4} b^{2} c + 20 \, a^{5} c^{2}\right)} d^{2} e^{8} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{9} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{10}\right)} x^{2} + {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{10} - 2 \, {\left(2 \, b^{4} c^{3} - 9 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{9} e + 2 \, {\left(3 \, b^{5} c^{2} - 14 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{8} e^{2} - 4 \, {\left(b^{6} c - 4 \, a b^{4} c^{2} - 2 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{7} e^{3} + {\left(b^{7} - 34 \, a^{2} b^{3} c^{2} + 72 \, a^{3} b c^{3}\right)} d^{6} e^{4} - 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} + 24 \, a^{4} c^{3}\right)} d^{5} e^{5} - 2 \, {\left(a^{2} b^{5} + 6 \, a^{3} b^{3} c - 40 \, a^{4} b c^{2}\right)} d^{4} e^{6} + 8 \, {\left(a^{3} b^{4} - 3 \, a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} d^{3} e^{7} - 7 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{2} e^{8} + 2 \, {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d e^{9}\right)} x\right)}}, \frac{3 \, {\left(16 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{4} e^{2} - 16 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e^{3} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} d^{2} e^{4} + {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{2} e^{4} - 16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{5} + {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} e^{6}\right)} x^{4} + {\left(32 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{3} e^{3} - 16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{2} e^{4} - 2 \, {\left(3 \, b^{4} c - 8 \, a b^{2} c^{2} - 16 \, a^{2} c^{3}\right)} d e^{5} + {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} e^{6}\right)} x^{3} + {\left(16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} e^{2} + 16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e^{3} - 3 \, {\left(9 \, b^{4} c - 40 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} e^{4} + 2 \, {\left(5 \, b^{5} - 32 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d e^{5} + {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} e^{6}\right)} x^{2} + {\left(16 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{4} e^{2} - 16 \, {\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{3} e^{3} + {\left(5 \, b^{5} - 56 \, a b^{3} c + 144 \, a^{2} b c^{2}\right)} d^{2} e^{4} + 2 \, {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} d e^{5}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, b c^{4} d^{7} - 16 \, {\left(2 \, b^{2} c^{3} - 3 \, a c^{4}\right)} d^{6} e + 16 \, {\left(3 \, b^{3} c^{2} - 7 \, a b c^{3}\right)} d^{5} e^{2} - 32 \, {\left(b^{4} c - 3 \, a b^{2} c^{2} + a^{2} c^{3}\right)} d^{4} e^{3} + {\left(8 \, b^{5} - 33 \, a b^{3} c + 44 \, a^{2} b c^{2}\right)} d^{3} e^{4} + {\left(a b^{4} + 14 \, a^{2} b^{2} c - 88 \, a^{3} c^{2}\right)} d^{2} e^{5} - 11 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{6} + 2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{7} + {\left(16 \, c^{5} d^{5} e^{2} - 40 \, b c^{4} d^{4} e^{3} + 2 \, {\left(31 \, b^{2} c^{3} - 44 \, a c^{4}\right)} d^{3} e^{4} - {\left(53 \, b^{3} c^{2} - 132 \, a b c^{3}\right)} d^{2} e^{5} + {\left(15 \, b^{4} c - 14 \, a b^{2} c^{2} - 104 \, a^{2} c^{3}\right)} d e^{6} - {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} e^{7}\right)} x^{3} + {\left(32 \, c^{5} d^{6} e - 72 \, b c^{4} d^{5} e^{2} + 80 \, {\left(b^{2} c^{3} - a c^{4}\right)} d^{4} e^{3} - {\left(27 \, b^{3} c^{2} - 28 \, a b c^{3}\right)} d^{3} e^{4} - 2 \, {\left(14 \, b^{4} c - 73 \, a b^{2} c^{2} + 68 \, a^{2} c^{3}\right)} d^{2} e^{5} + {\left(15 \, b^{5} - 49 \, a b^{3} c - 20 \, a^{2} b c^{2}\right)} d e^{6} - {\left(15 \, a b^{4} - 62 \, a^{2} b^{2} c + 24 \, a^{3} c^{2}\right)} e^{7}\right)} x^{2} + {\left(16 \, c^{5} d^{7} - 24 \, b c^{4} d^{6} e - 16 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{5} e^{2} + 80 \, {\left(b^{3} c^{2} - 3 \, a b c^{3}\right)} d^{4} e^{3} - {\left(81 \, b^{4} c - 274 \, a b^{2} c^{2} + 40 \, a^{2} c^{3}\right)} d^{3} e^{4} + {\left(25 \, b^{5} - 63 \, a b^{3} c - 76 \, a^{2} b c^{2}\right)} d^{2} e^{5} - 2 \, {\left(10 \, a b^{4} - 47 \, a^{2} b^{2} c + 44 \, a^{3} c^{2}\right)} d e^{6} - 5 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left({\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{10} - 4 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{9} e + 2 \, {\left(3 \, a b^{4} c^{2} - 10 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{8} e^{2} - 4 \, {\left(a b^{5} c - a^{2} b^{3} c^{2} - 12 \, a^{3} b c^{3}\right)} d^{7} e^{3} + {\left(a b^{6} + 8 \, a^{2} b^{4} c - 42 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} d^{6} e^{4} - 4 \, {\left(a^{2} b^{5} - a^{3} b^{3} c - 12 \, a^{4} b c^{2}\right)} d^{5} e^{5} + 2 \, {\left(3 \, a^{3} b^{4} - 10 \, a^{4} b^{2} c - 8 \, a^{5} c^{2}\right)} d^{4} e^{6} - 4 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{3} e^{7} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d^{2} e^{8} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{8} e^{2} - 4 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{7} e^{3} + 2 \, {\left(3 \, b^{4} c^{3} - 10 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d^{6} e^{4} - 4 \, {\left(b^{5} c^{2} - a b^{3} c^{3} - 12 \, a^{2} b c^{4}\right)} d^{5} e^{5} + {\left(b^{6} c + 8 \, a b^{4} c^{2} - 42 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{4} e^{6} - 4 \, {\left(a b^{5} c - a^{2} b^{3} c^{2} - 12 \, a^{3} b c^{3}\right)} d^{3} e^{7} + 2 \, {\left(3 \, a^{2} b^{4} c - 10 \, a^{3} b^{2} c^{2} - 8 \, a^{4} c^{3}\right)} d^{2} e^{8} - 4 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d e^{9} + {\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} e^{10}\right)} x^{4} + {\left(2 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{9} e - 7 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{8} e^{2} + 8 \, {\left(b^{4} c^{3} - 3 \, a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{7} e^{3} - 2 \, {\left(b^{5} c^{2} + 6 \, a b^{3} c^{3} - 40 \, a^{2} b c^{4}\right)} d^{6} e^{4} - 2 \, {\left(b^{6} c - 10 \, a b^{4} c^{2} + 18 \, a^{2} b^{2} c^{3} + 24 \, a^{3} c^{4}\right)} d^{5} e^{5} + {\left(b^{7} - 34 \, a^{2} b^{3} c^{2} + 72 \, a^{3} b c^{3}\right)} d^{4} e^{6} - 4 \, {\left(a b^{6} - 4 \, a^{2} b^{4} c - 2 \, a^{3} b^{2} c^{2} + 8 \, a^{4} c^{3}\right)} d^{3} e^{7} + 2 \, {\left(3 \, a^{2} b^{5} - 14 \, a^{3} b^{3} c + 8 \, a^{4} b c^{2}\right)} d^{2} e^{8} - 2 \, {\left(2 \, a^{3} b^{4} - 9 \, a^{4} b^{2} c + 4 \, a^{5} c^{2}\right)} d e^{9} + {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e^{10}\right)} x^{3} + {\left({\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{10} - 2 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{9} e - {\left(2 \, b^{4} c^{3} - 13 \, a b^{2} c^{4} + 20 \, a^{2} c^{5}\right)} d^{8} e^{2} + 8 \, {\left(b^{5} c^{2} - 5 \, a b^{3} c^{3} + 4 \, a^{2} b c^{4}\right)} d^{7} e^{3} - {\left(7 \, b^{6} c - 22 \, a b^{4} c^{2} - 34 \, a^{2} b^{2} c^{3} + 40 \, a^{3} c^{4}\right)} d^{6} e^{4} + 2 \, {\left(b^{7} + 4 \, a b^{5} c - 38 \, a^{2} b^{3} c^{2} + 24 \, a^{3} b c^{3}\right)} d^{5} e^{5} - {\left(7 \, a b^{6} - 22 \, a^{2} b^{4} c - 34 \, a^{3} b^{2} c^{2} + 40 \, a^{4} c^{3}\right)} d^{4} e^{6} + 8 \, {\left(a^{2} b^{5} - 5 \, a^{3} b^{3} c + 4 \, a^{4} b c^{2}\right)} d^{3} e^{7} - {\left(2 \, a^{3} b^{4} - 13 \, a^{4} b^{2} c + 20 \, a^{5} c^{2}\right)} d^{2} e^{8} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{9} + {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{10}\right)} x^{2} + {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{10} - 2 \, {\left(2 \, b^{4} c^{3} - 9 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{9} e + 2 \, {\left(3 \, b^{5} c^{2} - 14 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{8} e^{2} - 4 \, {\left(b^{6} c - 4 \, a b^{4} c^{2} - 2 \, a^{2} b^{2} c^{3} + 8 \, a^{3} c^{4}\right)} d^{7} e^{3} + {\left(b^{7} - 34 \, a^{2} b^{3} c^{2} + 72 \, a^{3} b c^{3}\right)} d^{6} e^{4} - 2 \, {\left(a b^{6} - 10 \, a^{2} b^{4} c + 18 \, a^{3} b^{2} c^{2} + 24 \, a^{4} c^{3}\right)} d^{5} e^{5} - 2 \, {\left(a^{2} b^{5} + 6 \, a^{3} b^{3} c - 40 \, a^{4} b c^{2}\right)} d^{4} e^{6} + 8 \, {\left(a^{3} b^{4} - 3 \, a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} d^{3} e^{7} - 7 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d^{2} e^{8} + 2 \, {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d e^{9}\right)} x\right)}}\right]"," ",0,"[-1/16*(3*(16*(a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - 16*(a*b^3*c - 4*a^2*b*c^2)*d^3*e^3 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*d^2*e^4 + (16*(b^2*c^3 - 4*a*c^4)*d^2*e^4 - 16*(b^3*c^2 - 4*a*b*c^3)*d*e^5 + (5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*e^6)*x^4 + (32*(b^2*c^3 - 4*a*c^4)*d^3*e^3 - 16*(b^3*c^2 - 4*a*b*c^3)*d^2*e^4 - 2*(3*b^4*c - 8*a*b^2*c^2 - 16*a^2*c^3)*d*e^5 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*e^6)*x^3 + (16*(b^2*c^3 - 4*a*c^4)*d^4*e^2 + 16*(b^3*c^2 - 4*a*b*c^3)*d^3*e^3 - 3*(9*b^4*c - 40*a*b^2*c^2 + 16*a^2*c^3)*d^2*e^4 + 2*(5*b^5 - 32*a*b^3*c + 48*a^2*b*c^2)*d*e^5 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*e^6)*x^2 + (16*(b^3*c^2 - 4*a*b*c^3)*d^4*e^2 - 16*(b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^3*e^3 + (5*b^5 - 56*a*b^3*c + 144*a^2*b*c^2)*d^2*e^4 + 2*(5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*d*e^5)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(8*b*c^4*d^7 - 16*(2*b^2*c^3 - 3*a*c^4)*d^6*e + 16*(3*b^3*c^2 - 7*a*b*c^3)*d^5*e^2 - 32*(b^4*c - 3*a*b^2*c^2 + a^2*c^3)*d^4*e^3 + (8*b^5 - 33*a*b^3*c + 44*a^2*b*c^2)*d^3*e^4 + (a*b^4 + 14*a^2*b^2*c - 88*a^3*c^2)*d^2*e^5 - 11*(a^2*b^3 - 4*a^3*b*c)*d*e^6 + 2*(a^3*b^2 - 4*a^4*c)*e^7 + (16*c^5*d^5*e^2 - 40*b*c^4*d^4*e^3 + 2*(31*b^2*c^3 - 44*a*c^4)*d^3*e^4 - (53*b^3*c^2 - 132*a*b*c^3)*d^2*e^5 + (15*b^4*c - 14*a*b^2*c^2 - 104*a^2*c^3)*d*e^6 - (15*a*b^3*c - 52*a^2*b*c^2)*e^7)*x^3 + (32*c^5*d^6*e - 72*b*c^4*d^5*e^2 + 80*(b^2*c^3 - a*c^4)*d^4*e^3 - (27*b^3*c^2 - 28*a*b*c^3)*d^3*e^4 - 2*(14*b^4*c - 73*a*b^2*c^2 + 68*a^2*c^3)*d^2*e^5 + (15*b^5 - 49*a*b^3*c - 20*a^2*b*c^2)*d*e^6 - (15*a*b^4 - 62*a^2*b^2*c + 24*a^3*c^2)*e^7)*x^2 + (16*c^5*d^7 - 24*b*c^4*d^6*e - 16*(b^2*c^3 - 4*a*c^4)*d^5*e^2 + 80*(b^3*c^2 - 3*a*b*c^3)*d^4*e^3 - (81*b^4*c - 274*a*b^2*c^2 + 40*a^2*c^3)*d^3*e^4 + (25*b^5 - 63*a*b^3*c - 76*a^2*b*c^2)*d^2*e^5 - 2*(10*a*b^4 - 47*a^2*b^2*c + 44*a^3*c^2)*d*e^6 - 5*(a^2*b^3 - 4*a^3*b*c)*e^7)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^4 - 4*a^2*c^5)*d^10 - 4*(a*b^3*c^3 - 4*a^2*b*c^4)*d^9*e + 2*(3*a*b^4*c^2 - 10*a^2*b^2*c^3 - 8*a^3*c^4)*d^8*e^2 - 4*(a*b^5*c - a^2*b^3*c^2 - 12*a^3*b*c^3)*d^7*e^3 + (a*b^6 + 8*a^2*b^4*c - 42*a^3*b^2*c^2 - 24*a^4*c^3)*d^6*e^4 - 4*(a^2*b^5 - a^3*b^3*c - 12*a^4*b*c^2)*d^5*e^5 + 2*(3*a^3*b^4 - 10*a^4*b^2*c - 8*a^5*c^2)*d^4*e^6 - 4*(a^4*b^3 - 4*a^5*b*c)*d^3*e^7 + (a^5*b^2 - 4*a^6*c)*d^2*e^8 + ((b^2*c^5 - 4*a*c^6)*d^8*e^2 - 4*(b^3*c^4 - 4*a*b*c^5)*d^7*e^3 + 2*(3*b^4*c^3 - 10*a*b^2*c^4 - 8*a^2*c^5)*d^6*e^4 - 4*(b^5*c^2 - a*b^3*c^3 - 12*a^2*b*c^4)*d^5*e^5 + (b^6*c + 8*a*b^4*c^2 - 42*a^2*b^2*c^3 - 24*a^3*c^4)*d^4*e^6 - 4*(a*b^5*c - a^2*b^3*c^2 - 12*a^3*b*c^3)*d^3*e^7 + 2*(3*a^2*b^4*c - 10*a^3*b^2*c^2 - 8*a^4*c^3)*d^2*e^8 - 4*(a^3*b^3*c - 4*a^4*b*c^2)*d*e^9 + (a^4*b^2*c - 4*a^5*c^2)*e^10)*x^4 + (2*(b^2*c^5 - 4*a*c^6)*d^9*e - 7*(b^3*c^4 - 4*a*b*c^5)*d^8*e^2 + 8*(b^4*c^3 - 3*a*b^2*c^4 - 4*a^2*c^5)*d^7*e^3 - 2*(b^5*c^2 + 6*a*b^3*c^3 - 40*a^2*b*c^4)*d^6*e^4 - 2*(b^6*c - 10*a*b^4*c^2 + 18*a^2*b^2*c^3 + 24*a^3*c^4)*d^5*e^5 + (b^7 - 34*a^2*b^3*c^2 + 72*a^3*b*c^3)*d^4*e^6 - 4*(a*b^6 - 4*a^2*b^4*c - 2*a^3*b^2*c^2 + 8*a^4*c^3)*d^3*e^7 + 2*(3*a^2*b^5 - 14*a^3*b^3*c + 8*a^4*b*c^2)*d^2*e^8 - 2*(2*a^3*b^4 - 9*a^4*b^2*c + 4*a^5*c^2)*d*e^9 + (a^4*b^3 - 4*a^5*b*c)*e^10)*x^3 + ((b^2*c^5 - 4*a*c^6)*d^10 - 2*(b^3*c^4 - 4*a*b*c^5)*d^9*e - (2*b^4*c^3 - 13*a*b^2*c^4 + 20*a^2*c^5)*d^8*e^2 + 8*(b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^7*e^3 - (7*b^6*c - 22*a*b^4*c^2 - 34*a^2*b^2*c^3 + 40*a^3*c^4)*d^6*e^4 + 2*(b^7 + 4*a*b^5*c - 38*a^2*b^3*c^2 + 24*a^3*b*c^3)*d^5*e^5 - (7*a*b^6 - 22*a^2*b^4*c - 34*a^3*b^2*c^2 + 40*a^4*c^3)*d^4*e^6 + 8*(a^2*b^5 - 5*a^3*b^3*c + 4*a^4*b*c^2)*d^3*e^7 - (2*a^3*b^4 - 13*a^4*b^2*c + 20*a^5*c^2)*d^2*e^8 - 2*(a^4*b^3 - 4*a^5*b*c)*d*e^9 + (a^5*b^2 - 4*a^6*c)*e^10)*x^2 + ((b^3*c^4 - 4*a*b*c^5)*d^10 - 2*(2*b^4*c^3 - 9*a*b^2*c^4 + 4*a^2*c^5)*d^9*e + 2*(3*b^5*c^2 - 14*a*b^3*c^3 + 8*a^2*b*c^4)*d^8*e^2 - 4*(b^6*c - 4*a*b^4*c^2 - 2*a^2*b^2*c^3 + 8*a^3*c^4)*d^7*e^3 + (b^7 - 34*a^2*b^3*c^2 + 72*a^3*b*c^3)*d^6*e^4 - 2*(a*b^6 - 10*a^2*b^4*c + 18*a^3*b^2*c^2 + 24*a^4*c^3)*d^5*e^5 - 2*(a^2*b^5 + 6*a^3*b^3*c - 40*a^4*b*c^2)*d^4*e^6 + 8*(a^3*b^4 - 3*a^4*b^2*c - 4*a^5*c^2)*d^3*e^7 - 7*(a^4*b^3 - 4*a^5*b*c)*d^2*e^8 + 2*(a^5*b^2 - 4*a^6*c)*d*e^9)*x), 1/8*(3*(16*(a*b^2*c^2 - 4*a^2*c^3)*d^4*e^2 - 16*(a*b^3*c - 4*a^2*b*c^2)*d^3*e^3 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*d^2*e^4 + (16*(b^2*c^3 - 4*a*c^4)*d^2*e^4 - 16*(b^3*c^2 - 4*a*b*c^3)*d*e^5 + (5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*e^6)*x^4 + (32*(b^2*c^3 - 4*a*c^4)*d^3*e^3 - 16*(b^3*c^2 - 4*a*b*c^3)*d^2*e^4 - 2*(3*b^4*c - 8*a*b^2*c^2 - 16*a^2*c^3)*d*e^5 + (5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*e^6)*x^3 + (16*(b^2*c^3 - 4*a*c^4)*d^4*e^2 + 16*(b^3*c^2 - 4*a*b*c^3)*d^3*e^3 - 3*(9*b^4*c - 40*a*b^2*c^2 + 16*a^2*c^3)*d^2*e^4 + 2*(5*b^5 - 32*a*b^3*c + 48*a^2*b*c^2)*d*e^5 + (5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*e^6)*x^2 + (16*(b^3*c^2 - 4*a*b*c^3)*d^4*e^2 - 16*(b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^3*e^3 + (5*b^5 - 56*a*b^3*c + 144*a^2*b*c^2)*d^2*e^4 + 2*(5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*d*e^5)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(8*b*c^4*d^7 - 16*(2*b^2*c^3 - 3*a*c^4)*d^6*e + 16*(3*b^3*c^2 - 7*a*b*c^3)*d^5*e^2 - 32*(b^4*c - 3*a*b^2*c^2 + a^2*c^3)*d^4*e^3 + (8*b^5 - 33*a*b^3*c + 44*a^2*b*c^2)*d^3*e^4 + (a*b^4 + 14*a^2*b^2*c - 88*a^3*c^2)*d^2*e^5 - 11*(a^2*b^3 - 4*a^3*b*c)*d*e^6 + 2*(a^3*b^2 - 4*a^4*c)*e^7 + (16*c^5*d^5*e^2 - 40*b*c^4*d^4*e^3 + 2*(31*b^2*c^3 - 44*a*c^4)*d^3*e^4 - (53*b^3*c^2 - 132*a*b*c^3)*d^2*e^5 + (15*b^4*c - 14*a*b^2*c^2 - 104*a^2*c^3)*d*e^6 - (15*a*b^3*c - 52*a^2*b*c^2)*e^7)*x^3 + (32*c^5*d^6*e - 72*b*c^4*d^5*e^2 + 80*(b^2*c^3 - a*c^4)*d^4*e^3 - (27*b^3*c^2 - 28*a*b*c^3)*d^3*e^4 - 2*(14*b^4*c - 73*a*b^2*c^2 + 68*a^2*c^3)*d^2*e^5 + (15*b^5 - 49*a*b^3*c - 20*a^2*b*c^2)*d*e^6 - (15*a*b^4 - 62*a^2*b^2*c + 24*a^3*c^2)*e^7)*x^2 + (16*c^5*d^7 - 24*b*c^4*d^6*e - 16*(b^2*c^3 - 4*a*c^4)*d^5*e^2 + 80*(b^3*c^2 - 3*a*b*c^3)*d^4*e^3 - (81*b^4*c - 274*a*b^2*c^2 + 40*a^2*c^3)*d^3*e^4 + (25*b^5 - 63*a*b^3*c - 76*a^2*b*c^2)*d^2*e^5 - 2*(10*a*b^4 - 47*a^2*b^2*c + 44*a^3*c^2)*d*e^6 - 5*(a^2*b^3 - 4*a^3*b*c)*e^7)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^4 - 4*a^2*c^5)*d^10 - 4*(a*b^3*c^3 - 4*a^2*b*c^4)*d^9*e + 2*(3*a*b^4*c^2 - 10*a^2*b^2*c^3 - 8*a^3*c^4)*d^8*e^2 - 4*(a*b^5*c - a^2*b^3*c^2 - 12*a^3*b*c^3)*d^7*e^3 + (a*b^6 + 8*a^2*b^4*c - 42*a^3*b^2*c^2 - 24*a^4*c^3)*d^6*e^4 - 4*(a^2*b^5 - a^3*b^3*c - 12*a^4*b*c^2)*d^5*e^5 + 2*(3*a^3*b^4 - 10*a^4*b^2*c - 8*a^5*c^2)*d^4*e^6 - 4*(a^4*b^3 - 4*a^5*b*c)*d^3*e^7 + (a^5*b^2 - 4*a^6*c)*d^2*e^8 + ((b^2*c^5 - 4*a*c^6)*d^8*e^2 - 4*(b^3*c^4 - 4*a*b*c^5)*d^7*e^3 + 2*(3*b^4*c^3 - 10*a*b^2*c^4 - 8*a^2*c^5)*d^6*e^4 - 4*(b^5*c^2 - a*b^3*c^3 - 12*a^2*b*c^4)*d^5*e^5 + (b^6*c + 8*a*b^4*c^2 - 42*a^2*b^2*c^3 - 24*a^3*c^4)*d^4*e^6 - 4*(a*b^5*c - a^2*b^3*c^2 - 12*a^3*b*c^3)*d^3*e^7 + 2*(3*a^2*b^4*c - 10*a^3*b^2*c^2 - 8*a^4*c^3)*d^2*e^8 - 4*(a^3*b^3*c - 4*a^4*b*c^2)*d*e^9 + (a^4*b^2*c - 4*a^5*c^2)*e^10)*x^4 + (2*(b^2*c^5 - 4*a*c^6)*d^9*e - 7*(b^3*c^4 - 4*a*b*c^5)*d^8*e^2 + 8*(b^4*c^3 - 3*a*b^2*c^4 - 4*a^2*c^5)*d^7*e^3 - 2*(b^5*c^2 + 6*a*b^3*c^3 - 40*a^2*b*c^4)*d^6*e^4 - 2*(b^6*c - 10*a*b^4*c^2 + 18*a^2*b^2*c^3 + 24*a^3*c^4)*d^5*e^5 + (b^7 - 34*a^2*b^3*c^2 + 72*a^3*b*c^3)*d^4*e^6 - 4*(a*b^6 - 4*a^2*b^4*c - 2*a^3*b^2*c^2 + 8*a^4*c^3)*d^3*e^7 + 2*(3*a^2*b^5 - 14*a^3*b^3*c + 8*a^4*b*c^2)*d^2*e^8 - 2*(2*a^3*b^4 - 9*a^4*b^2*c + 4*a^5*c^2)*d*e^9 + (a^4*b^3 - 4*a^5*b*c)*e^10)*x^3 + ((b^2*c^5 - 4*a*c^6)*d^10 - 2*(b^3*c^4 - 4*a*b*c^5)*d^9*e - (2*b^4*c^3 - 13*a*b^2*c^4 + 20*a^2*c^5)*d^8*e^2 + 8*(b^5*c^2 - 5*a*b^3*c^3 + 4*a^2*b*c^4)*d^7*e^3 - (7*b^6*c - 22*a*b^4*c^2 - 34*a^2*b^2*c^3 + 40*a^3*c^4)*d^6*e^4 + 2*(b^7 + 4*a*b^5*c - 38*a^2*b^3*c^2 + 24*a^3*b*c^3)*d^5*e^5 - (7*a*b^6 - 22*a^2*b^4*c - 34*a^3*b^2*c^2 + 40*a^4*c^3)*d^4*e^6 + 8*(a^2*b^5 - 5*a^3*b^3*c + 4*a^4*b*c^2)*d^3*e^7 - (2*a^3*b^4 - 13*a^4*b^2*c + 20*a^5*c^2)*d^2*e^8 - 2*(a^4*b^3 - 4*a^5*b*c)*d*e^9 + (a^5*b^2 - 4*a^6*c)*e^10)*x^2 + ((b^3*c^4 - 4*a*b*c^5)*d^10 - 2*(2*b^4*c^3 - 9*a*b^2*c^4 + 4*a^2*c^5)*d^9*e + 2*(3*b^5*c^2 - 14*a*b^3*c^3 + 8*a^2*b*c^4)*d^8*e^2 - 4*(b^6*c - 4*a*b^4*c^2 - 2*a^2*b^2*c^3 + 8*a^3*c^4)*d^7*e^3 + (b^7 - 34*a^2*b^3*c^2 + 72*a^3*b*c^3)*d^6*e^4 - 2*(a*b^6 - 10*a^2*b^4*c + 18*a^3*b^2*c^2 + 24*a^4*c^3)*d^5*e^5 - 2*(a^2*b^5 + 6*a^3*b^3*c - 40*a^4*b*c^2)*d^4*e^6 + 8*(a^3*b^4 - 3*a^4*b^2*c - 4*a^5*c^2)*d^3*e^7 - 7*(a^4*b^3 - 4*a^5*b*c)*d^2*e^8 + 2*(a^5*b^2 - 4*a^6*c)*d*e^9)*x)]","B",0
2390,1,9408,0,46.364062," ","integrate(1/(e*x+d)^4/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(32 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{6} e^{2} - 48 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{5} e^{3} + 6 \, {\left(5 \, a b^{4} c - 24 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d^{4} e^{4} - {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} d^{3} e^{5} + {\left(32 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} e^{5} - 48 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e^{6} + 6 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{7} - {\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} e^{8}\right)} x^{5} + {\left(96 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{4} - 112 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{5} + 6 \, {\left(7 \, b^{4} c^{2} - 40 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d^{2} e^{6} + 3 \, {\left(3 \, b^{5} c - 8 \, a b^{3} c^{2} - 16 \, a^{2} b c^{3}\right)} d e^{7} - {\left(7 \, b^{6} - 40 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2}\right)} e^{8}\right)} x^{4} + {\left(96 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{5} e^{3} - 48 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{4} e^{4} - 2 \, {\left(27 \, b^{4} c^{2} - 88 \, a b^{2} c^{3} - 80 \, a^{2} c^{4}\right)} d^{3} e^{5} + 3 \, {\left(23 \, b^{5} c - 120 \, a b^{3} c^{2} + 112 \, a^{2} b c^{3}\right)} d^{2} e^{6} - 3 \, {\left(7 \, b^{6} - 50 \, a b^{4} c + 96 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d e^{7} - {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} e^{8}\right)} x^{3} + {\left(32 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} e^{2} + 48 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} e^{3} - 6 \, {\left(19 \, b^{4} c^{2} - 88 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d^{4} e^{4} + {\left(83 \, b^{5} c - 536 \, a b^{3} c^{2} + 816 \, a^{2} b c^{3}\right)} d^{3} e^{5} - 3 \, {\left(7 \, b^{6} - 70 \, a b^{4} c + 192 \, a^{2} b^{2} c^{2} - 96 \, a^{3} c^{3}\right)} d^{2} e^{6} - 3 \, {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} d e^{7}\right)} x^{2} + {\left(32 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} e^{2} - 48 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{5} e^{3} + 6 \, {\left(5 \, b^{5} c - 48 \, a b^{3} c^{2} + 112 \, a^{2} b c^{3}\right)} d^{4} e^{4} - {\left(7 \, b^{6} - 130 \, a b^{4} c + 480 \, a^{2} b^{2} c^{2} - 288 \, a^{3} c^{3}\right)} d^{3} e^{5} - 3 \, {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} d^{2} e^{6}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left(48 \, b c^{5} d^{9} - 48 \, {\left(5 \, b^{2} c^{4} - 8 \, a c^{5}\right)} d^{8} e + 240 \, {\left(2 \, b^{3} c^{3} - 5 \, a b c^{4}\right)} d^{7} e^{2} - 240 \, {\left(2 \, b^{4} c^{2} - 7 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} e^{3} + 30 \, {\left(8 \, b^{5} c - 41 \, a b^{3} c^{2} + 60 \, a^{2} b c^{3}\right)} d^{5} e^{4} - {\left(48 \, b^{6} - 405 \, a b^{4} c + 640 \, a^{2} b^{2} c^{2} + 1424 \, a^{3} c^{3}\right)} d^{4} e^{5} - {\left(39 \, a b^{5} + 220 \, a^{2} b^{3} c - 1552 \, a^{3} b c^{2}\right)} d^{3} e^{6} + {\left(125 \, a^{2} b^{4} - 472 \, a^{3} b^{2} c - 112 \, a^{4} c^{2}\right)} d^{2} e^{7} - 46 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{8} + 8 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{9} + {\left(96 \, c^{6} d^{6} e^{3} - 288 \, b c^{5} d^{5} e^{4} + 4 \, {\left(167 \, b^{2} c^{4} - 308 \, a c^{5}\right)} d^{4} e^{5} - 8 \, {\left(107 \, b^{3} c^{3} - 308 \, a b c^{4}\right)} d^{3} e^{6} + {\left(485 \, b^{4} c^{2} - 1312 \, a b^{2} c^{3} - 1072 \, a^{2} c^{4}\right)} d^{2} e^{7} - {\left(105 \, b^{5} c - 80 \, a b^{3} c^{2} - 1072 \, a^{2} b c^{3}\right)} d e^{8} + {\left(105 \, a b^{4} c - 460 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3}\right)} e^{9}\right)} x^{4} + {\left(288 \, c^{6} d^{7} e^{2} - 816 \, b c^{5} d^{6} e^{3} + 36 \, {\left(45 \, b^{2} c^{4} - 76 \, a c^{5}\right)} d^{5} e^{4} - 2 \, {\left(817 \, b^{3} c^{3} - 2188 \, a b c^{4}\right)} d^{4} e^{5} + 2 \, {\left(221 \, b^{4} c^{2} - 212 \, a b^{2} c^{3} - 1488 \, a^{2} c^{4}\right)} d^{3} e^{6} + {\left(205 \, b^{5} c - 1436 \, a b^{3} c^{2} + 2320 \, a^{2} b c^{3}\right)} d^{2} e^{7} - {\left(105 \, b^{6} - 430 \, a b^{4} c + 124 \, a^{2} b^{2} c^{2} - 48 \, a^{3} c^{3}\right)} d e^{8} + {\left(105 \, a b^{5} - 530 \, a^{2} b^{3} c + 488 \, a^{3} b c^{2}\right)} e^{9}\right)} x^{3} + {\left(288 \, c^{6} d^{8} e - 720 \, b c^{5} d^{7} e^{2} + 96 \, {\left(10 \, b^{2} c^{4} - 13 \, a c^{5}\right)} d^{6} e^{3} - 90 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{5} e^{4} - {\left(1225 \, b^{4} c^{2} - 5348 \, a b^{2} c^{3} + 3232 \, a^{2} c^{4}\right)} d^{4} e^{5} + {\left(1067 \, b^{5} c - 4444 \, a b^{3} c^{2} + 2000 \, a^{2} b c^{3}\right)} d^{3} e^{6} - 2 \, {\left(140 \, b^{6} - 387 \, a b^{4} c - 708 \, a^{2} b^{2} c^{2} + 784 \, a^{3} c^{3}\right)} d^{2} e^{7} + {\left(245 \, a b^{5} - 1354 \, a^{2} b^{3} c + 1640 \, a^{3} b c^{2}\right)} d e^{8} + {\left(35 \, a^{2} b^{4} - 172 \, a^{3} b^{2} c + 128 \, a^{4} c^{2}\right)} e^{9}\right)} x^{2} + {\left(96 \, c^{6} d^{9} - 144 \, b c^{5} d^{8} e - 48 \, {\left(5 \, b^{2} c^{4} - 14 \, a c^{5}\right)} d^{7} e^{2} + 1200 \, {\left(b^{3} c^{3} - 3 \, a b c^{4}\right)} d^{6} e^{3} - 90 \, {\left(19 \, b^{4} c^{2} - 70 \, a b^{2} c^{3} + 24 \, a^{2} c^{4}\right)} d^{5} e^{4} + {\left(1029 \, b^{5} c - 4190 \, a b^{3} c^{2} + 2168 \, a^{2} b c^{3}\right)} d^{4} e^{5} - {\left(231 \, b^{6} - 790 \, a b^{4} c - 776 \, a^{2} b^{2} c^{2} + 2592 \, a^{3} c^{3}\right)} d^{3} e^{6} + {\left(133 \, a b^{5} - 1076 \, a^{2} b^{3} c + 2320 \, a^{3} b c^{2}\right)} d^{2} e^{7} + 4 \, {\left(28 \, a^{2} b^{4} - 121 \, a^{3} b^{2} c + 36 \, a^{4} c^{2}\right)} d e^{8} - 14 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{9}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left({\left(a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} d^{13} - 5 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{12} e + 5 \, {\left(2 \, a b^{4} c^{3} - 7 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{11} e^{2} - 10 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b c^{4}\right)} d^{10} e^{3} + 5 \, {\left(a b^{6} c + 2 \, a^{2} b^{4} c^{2} - 22 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{9} e^{4} - {\left(a b^{7} + 16 \, a^{2} b^{5} c - 50 \, a^{3} b^{3} c^{2} - 120 \, a^{4} b c^{3}\right)} d^{8} e^{5} + 5 \, {\left(a^{2} b^{6} + 2 \, a^{3} b^{4} c - 22 \, a^{4} b^{2} c^{2} - 8 \, a^{5} c^{3}\right)} d^{7} e^{6} - 10 \, {\left(a^{3} b^{5} - 2 \, a^{4} b^{3} c - 8 \, a^{5} b c^{2}\right)} d^{6} e^{7} + 5 \, {\left(2 \, a^{4} b^{4} - 7 \, a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} d^{5} e^{8} - 5 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{4} e^{9} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d^{3} e^{10} + {\left({\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{10} e^{3} - 5 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{9} e^{4} + 5 \, {\left(2 \, b^{4} c^{4} - 7 \, a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} d^{8} e^{5} - 10 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} d^{7} e^{6} + 5 \, {\left(b^{6} c^{2} + 2 \, a b^{4} c^{3} - 22 \, a^{2} b^{2} c^{4} - 8 \, a^{3} c^{5}\right)} d^{6} e^{7} - {\left(b^{7} c + 16 \, a b^{5} c^{2} - 50 \, a^{2} b^{3} c^{3} - 120 \, a^{3} b c^{4}\right)} d^{5} e^{8} + 5 \, {\left(a b^{6} c + 2 \, a^{2} b^{4} c^{2} - 22 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{4} e^{9} - 10 \, {\left(a^{2} b^{5} c - 2 \, a^{3} b^{3} c^{2} - 8 \, a^{4} b c^{3}\right)} d^{3} e^{10} + 5 \, {\left(2 \, a^{3} b^{4} c - 7 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{2} e^{11} - 5 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d e^{12} + {\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} e^{13}\right)} x^{5} + {\left(3 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{11} e^{2} - 14 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{10} e^{3} + 5 \, {\left(5 \, b^{4} c^{4} - 17 \, a b^{2} c^{5} - 12 \, a^{2} c^{6}\right)} d^{9} e^{4} - 5 \, {\left(4 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 44 \, a^{2} b c^{5}\right)} d^{8} e^{5} + 5 \, {\left(b^{6} c^{2} + 10 \, a b^{4} c^{3} - 50 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{7} e^{6} + 2 \, {\left(b^{7} c - 19 \, a b^{5} c^{2} + 20 \, a^{2} b^{3} c^{3} + 160 \, a^{3} b c^{4}\right)} d^{6} e^{7} - {\left(b^{8} + a b^{6} c - 80 \, a^{2} b^{4} c^{2} + 210 \, a^{3} b^{2} c^{3} + 120 \, a^{4} c^{4}\right)} d^{5} e^{8} + 5 \, {\left(a b^{7} - 4 \, a^{2} b^{5} c - 10 \, a^{3} b^{3} c^{2} + 40 \, a^{4} b c^{3}\right)} d^{4} e^{9} - 5 \, {\left(2 \, a^{2} b^{6} - 10 \, a^{3} b^{4} c + 5 \, a^{4} b^{2} c^{2} + 12 \, a^{5} c^{3}\right)} d^{3} e^{10} + 10 \, {\left(a^{3} b^{5} - 5 \, a^{4} b^{3} c + 4 \, a^{5} b c^{2}\right)} d^{2} e^{11} - {\left(5 \, a^{4} b^{4} - 23 \, a^{5} b^{2} c + 12 \, a^{6} c^{2}\right)} d e^{12} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e^{13}\right)} x^{4} + {\left(3 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} e - 12 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e^{2} + {\left(15 \, b^{4} c^{4} - 44 \, a b^{2} c^{5} - 64 \, a^{2} c^{6}\right)} d^{10} e^{3} - 50 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{9} e^{4} - 5 \, {\left(3 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 25 \, a^{2} b^{2} c^{4} + 28 \, a^{3} c^{5}\right)} d^{8} e^{5} + 4 \, {\left(3 \, b^{7} c - 7 \, a b^{5} c^{2} - 40 \, a^{2} b^{3} c^{3} + 80 \, a^{3} b c^{4}\right)} d^{7} e^{6} - {\left(3 \, b^{8} + 28 \, a b^{6} c - 190 \, a^{2} b^{4} c^{2} + 80 \, a^{3} b^{2} c^{3} + 160 \, a^{4} c^{4}\right)} d^{6} e^{7} + 2 \, {\left(7 \, a b^{7} - 8 \, a^{2} b^{5} c - 110 \, a^{3} b^{3} c^{2} + 120 \, a^{4} b c^{3}\right)} d^{5} e^{8} - 25 \, {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c - a^{4} b^{2} c^{2} + 4 \, a^{5} c^{3}\right)} d^{4} e^{9} + 20 \, {\left(a^{3} b^{5} - 5 \, a^{4} b^{3} c + 4 \, a^{5} b c^{2}\right)} d^{3} e^{10} - {\left(5 \, a^{4} b^{4} - 28 \, a^{5} b^{2} c + 32 \, a^{6} c^{2}\right)} d^{2} e^{11} - 2 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{12} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{13}\right)} x^{3} + {\left({\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{13} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{12} e - {\left(5 \, b^{4} c^{4} - 28 \, a b^{2} c^{5} + 32 \, a^{2} c^{6}\right)} d^{11} e^{2} + 20 \, {\left(b^{5} c^{3} - 5 \, a b^{3} c^{4} + 4 \, a^{2} b c^{5}\right)} d^{10} e^{3} - 25 \, {\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} - a^{2} b^{2} c^{4} + 4 \, a^{3} c^{5}\right)} d^{9} e^{4} + 2 \, {\left(7 \, b^{7} c - 8 \, a b^{5} c^{2} - 110 \, a^{2} b^{3} c^{3} + 120 \, a^{3} b c^{4}\right)} d^{8} e^{5} - {\left(3 \, b^{8} + 28 \, a b^{6} c - 190 \, a^{2} b^{4} c^{2} + 80 \, a^{3} b^{2} c^{3} + 160 \, a^{4} c^{4}\right)} d^{7} e^{6} + 4 \, {\left(3 \, a b^{7} - 7 \, a^{2} b^{5} c - 40 \, a^{3} b^{3} c^{2} + 80 \, a^{4} b c^{3}\right)} d^{6} e^{7} - 5 \, {\left(3 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 25 \, a^{4} b^{2} c^{2} + 28 \, a^{5} c^{3}\right)} d^{5} e^{8} - 50 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d^{4} e^{9} + {\left(15 \, a^{4} b^{4} - 44 \, a^{5} b^{2} c - 64 \, a^{6} c^{2}\right)} d^{3} e^{10} - 12 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{2} e^{11} + 3 \, {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d e^{12}\right)} x^{2} + {\left({\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{13} - {\left(5 \, b^{4} c^{4} - 23 \, a b^{2} c^{5} + 12 \, a^{2} c^{6}\right)} d^{12} e + 10 \, {\left(b^{5} c^{3} - 5 \, a b^{3} c^{4} + 4 \, a^{2} b c^{5}\right)} d^{11} e^{2} - 5 \, {\left(2 \, b^{6} c^{2} - 10 \, a b^{4} c^{3} + 5 \, a^{2} b^{2} c^{4} + 12 \, a^{3} c^{5}\right)} d^{10} e^{3} + 5 \, {\left(b^{7} c - 4 \, a b^{5} c^{2} - 10 \, a^{2} b^{3} c^{3} + 40 \, a^{3} b c^{4}\right)} d^{9} e^{4} - {\left(b^{8} + a b^{6} c - 80 \, a^{2} b^{4} c^{2} + 210 \, a^{3} b^{2} c^{3} + 120 \, a^{4} c^{4}\right)} d^{8} e^{5} + 2 \, {\left(a b^{7} - 19 \, a^{2} b^{5} c + 20 \, a^{3} b^{3} c^{2} + 160 \, a^{4} b c^{3}\right)} d^{7} e^{6} + 5 \, {\left(a^{2} b^{6} + 10 \, a^{3} b^{4} c - 50 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d^{6} e^{7} - 5 \, {\left(4 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 44 \, a^{5} b c^{2}\right)} d^{5} e^{8} + 5 \, {\left(5 \, a^{4} b^{4} - 17 \, a^{5} b^{2} c - 12 \, a^{6} c^{2}\right)} d^{4} e^{9} - 14 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{3} e^{10} + 3 \, {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d^{2} e^{11}\right)} x\right)}}, \frac{15 \, {\left(32 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{6} e^{2} - 48 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{5} e^{3} + 6 \, {\left(5 \, a b^{4} c - 24 \, a^{2} b^{2} c^{2} + 16 \, a^{3} c^{3}\right)} d^{4} e^{4} - {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} d^{3} e^{5} + {\left(32 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{3} e^{5} - 48 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{2} e^{6} + 6 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d e^{7} - {\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} e^{8}\right)} x^{5} + {\left(96 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} e^{4} - 112 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{3} e^{5} + 6 \, {\left(7 \, b^{4} c^{2} - 40 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d^{2} e^{6} + 3 \, {\left(3 \, b^{5} c - 8 \, a b^{3} c^{2} - 16 \, a^{2} b c^{3}\right)} d e^{7} - {\left(7 \, b^{6} - 40 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2}\right)} e^{8}\right)} x^{4} + {\left(96 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{5} e^{3} - 48 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{4} e^{4} - 2 \, {\left(27 \, b^{4} c^{2} - 88 \, a b^{2} c^{3} - 80 \, a^{2} c^{4}\right)} d^{3} e^{5} + 3 \, {\left(23 \, b^{5} c - 120 \, a b^{3} c^{2} + 112 \, a^{2} b c^{3}\right)} d^{2} e^{6} - 3 \, {\left(7 \, b^{6} - 50 \, a b^{4} c + 96 \, a^{2} b^{2} c^{2} - 32 \, a^{3} c^{3}\right)} d e^{7} - {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} e^{8}\right)} x^{3} + {\left(32 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} e^{2} + 48 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{5} e^{3} - 6 \, {\left(19 \, b^{4} c^{2} - 88 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d^{4} e^{4} + {\left(83 \, b^{5} c - 536 \, a b^{3} c^{2} + 816 \, a^{2} b c^{3}\right)} d^{3} e^{5} - 3 \, {\left(7 \, b^{6} - 70 \, a b^{4} c + 192 \, a^{2} b^{2} c^{2} - 96 \, a^{3} c^{3}\right)} d^{2} e^{6} - 3 \, {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} d e^{7}\right)} x^{2} + {\left(32 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} e^{2} - 48 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{5} e^{3} + 6 \, {\left(5 \, b^{5} c - 48 \, a b^{3} c^{2} + 112 \, a^{2} b c^{3}\right)} d^{4} e^{4} - {\left(7 \, b^{6} - 130 \, a b^{4} c + 480 \, a^{2} b^{2} c^{2} - 288 \, a^{3} c^{3}\right)} d^{3} e^{5} - 3 \, {\left(7 \, a b^{5} - 40 \, a^{2} b^{3} c + 48 \, a^{3} b c^{2}\right)} d^{2} e^{6}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(48 \, b c^{5} d^{9} - 48 \, {\left(5 \, b^{2} c^{4} - 8 \, a c^{5}\right)} d^{8} e + 240 \, {\left(2 \, b^{3} c^{3} - 5 \, a b c^{4}\right)} d^{7} e^{2} - 240 \, {\left(2 \, b^{4} c^{2} - 7 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} e^{3} + 30 \, {\left(8 \, b^{5} c - 41 \, a b^{3} c^{2} + 60 \, a^{2} b c^{3}\right)} d^{5} e^{4} - {\left(48 \, b^{6} - 405 \, a b^{4} c + 640 \, a^{2} b^{2} c^{2} + 1424 \, a^{3} c^{3}\right)} d^{4} e^{5} - {\left(39 \, a b^{5} + 220 \, a^{2} b^{3} c - 1552 \, a^{3} b c^{2}\right)} d^{3} e^{6} + {\left(125 \, a^{2} b^{4} - 472 \, a^{3} b^{2} c - 112 \, a^{4} c^{2}\right)} d^{2} e^{7} - 46 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{8} + 8 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} e^{9} + {\left(96 \, c^{6} d^{6} e^{3} - 288 \, b c^{5} d^{5} e^{4} + 4 \, {\left(167 \, b^{2} c^{4} - 308 \, a c^{5}\right)} d^{4} e^{5} - 8 \, {\left(107 \, b^{3} c^{3} - 308 \, a b c^{4}\right)} d^{3} e^{6} + {\left(485 \, b^{4} c^{2} - 1312 \, a b^{2} c^{3} - 1072 \, a^{2} c^{4}\right)} d^{2} e^{7} - {\left(105 \, b^{5} c - 80 \, a b^{3} c^{2} - 1072 \, a^{2} b c^{3}\right)} d e^{8} + {\left(105 \, a b^{4} c - 460 \, a^{2} b^{2} c^{2} + 256 \, a^{3} c^{3}\right)} e^{9}\right)} x^{4} + {\left(288 \, c^{6} d^{7} e^{2} - 816 \, b c^{5} d^{6} e^{3} + 36 \, {\left(45 \, b^{2} c^{4} - 76 \, a c^{5}\right)} d^{5} e^{4} - 2 \, {\left(817 \, b^{3} c^{3} - 2188 \, a b c^{4}\right)} d^{4} e^{5} + 2 \, {\left(221 \, b^{4} c^{2} - 212 \, a b^{2} c^{3} - 1488 \, a^{2} c^{4}\right)} d^{3} e^{6} + {\left(205 \, b^{5} c - 1436 \, a b^{3} c^{2} + 2320 \, a^{2} b c^{3}\right)} d^{2} e^{7} - {\left(105 \, b^{6} - 430 \, a b^{4} c + 124 \, a^{2} b^{2} c^{2} - 48 \, a^{3} c^{3}\right)} d e^{8} + {\left(105 \, a b^{5} - 530 \, a^{2} b^{3} c + 488 \, a^{3} b c^{2}\right)} e^{9}\right)} x^{3} + {\left(288 \, c^{6} d^{8} e - 720 \, b c^{5} d^{7} e^{2} + 96 \, {\left(10 \, b^{2} c^{4} - 13 \, a c^{5}\right)} d^{6} e^{3} - 90 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{5} e^{4} - {\left(1225 \, b^{4} c^{2} - 5348 \, a b^{2} c^{3} + 3232 \, a^{2} c^{4}\right)} d^{4} e^{5} + {\left(1067 \, b^{5} c - 4444 \, a b^{3} c^{2} + 2000 \, a^{2} b c^{3}\right)} d^{3} e^{6} - 2 \, {\left(140 \, b^{6} - 387 \, a b^{4} c - 708 \, a^{2} b^{2} c^{2} + 784 \, a^{3} c^{3}\right)} d^{2} e^{7} + {\left(245 \, a b^{5} - 1354 \, a^{2} b^{3} c + 1640 \, a^{3} b c^{2}\right)} d e^{8} + {\left(35 \, a^{2} b^{4} - 172 \, a^{3} b^{2} c + 128 \, a^{4} c^{2}\right)} e^{9}\right)} x^{2} + {\left(96 \, c^{6} d^{9} - 144 \, b c^{5} d^{8} e - 48 \, {\left(5 \, b^{2} c^{4} - 14 \, a c^{5}\right)} d^{7} e^{2} + 1200 \, {\left(b^{3} c^{3} - 3 \, a b c^{4}\right)} d^{6} e^{3} - 90 \, {\left(19 \, b^{4} c^{2} - 70 \, a b^{2} c^{3} + 24 \, a^{2} c^{4}\right)} d^{5} e^{4} + {\left(1029 \, b^{5} c - 4190 \, a b^{3} c^{2} + 2168 \, a^{2} b c^{3}\right)} d^{4} e^{5} - {\left(231 \, b^{6} - 790 \, a b^{4} c - 776 \, a^{2} b^{2} c^{2} + 2592 \, a^{3} c^{3}\right)} d^{3} e^{6} + {\left(133 \, a b^{5} - 1076 \, a^{2} b^{3} c + 2320 \, a^{3} b c^{2}\right)} d^{2} e^{7} + 4 \, {\left(28 \, a^{2} b^{4} - 121 \, a^{3} b^{2} c + 36 \, a^{4} c^{2}\right)} d e^{8} - 14 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} e^{9}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left({\left(a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} d^{13} - 5 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{12} e + 5 \, {\left(2 \, a b^{4} c^{3} - 7 \, a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d^{11} e^{2} - 10 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{3} c^{3} - 8 \, a^{3} b c^{4}\right)} d^{10} e^{3} + 5 \, {\left(a b^{6} c + 2 \, a^{2} b^{4} c^{2} - 22 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{9} e^{4} - {\left(a b^{7} + 16 \, a^{2} b^{5} c - 50 \, a^{3} b^{3} c^{2} - 120 \, a^{4} b c^{3}\right)} d^{8} e^{5} + 5 \, {\left(a^{2} b^{6} + 2 \, a^{3} b^{4} c - 22 \, a^{4} b^{2} c^{2} - 8 \, a^{5} c^{3}\right)} d^{7} e^{6} - 10 \, {\left(a^{3} b^{5} - 2 \, a^{4} b^{3} c - 8 \, a^{5} b c^{2}\right)} d^{6} e^{7} + 5 \, {\left(2 \, a^{4} b^{4} - 7 \, a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} d^{5} e^{8} - 5 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{4} e^{9} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d^{3} e^{10} + {\left({\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{10} e^{3} - 5 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{9} e^{4} + 5 \, {\left(2 \, b^{4} c^{4} - 7 \, a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} d^{8} e^{5} - 10 \, {\left(b^{5} c^{3} - 2 \, a b^{3} c^{4} - 8 \, a^{2} b c^{5}\right)} d^{7} e^{6} + 5 \, {\left(b^{6} c^{2} + 2 \, a b^{4} c^{3} - 22 \, a^{2} b^{2} c^{4} - 8 \, a^{3} c^{5}\right)} d^{6} e^{7} - {\left(b^{7} c + 16 \, a b^{5} c^{2} - 50 \, a^{2} b^{3} c^{3} - 120 \, a^{3} b c^{4}\right)} d^{5} e^{8} + 5 \, {\left(a b^{6} c + 2 \, a^{2} b^{4} c^{2} - 22 \, a^{3} b^{2} c^{3} - 8 \, a^{4} c^{4}\right)} d^{4} e^{9} - 10 \, {\left(a^{2} b^{5} c - 2 \, a^{3} b^{3} c^{2} - 8 \, a^{4} b c^{3}\right)} d^{3} e^{10} + 5 \, {\left(2 \, a^{3} b^{4} c - 7 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{2} e^{11} - 5 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d e^{12} + {\left(a^{5} b^{2} c - 4 \, a^{6} c^{2}\right)} e^{13}\right)} x^{5} + {\left(3 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{11} e^{2} - 14 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{10} e^{3} + 5 \, {\left(5 \, b^{4} c^{4} - 17 \, a b^{2} c^{5} - 12 \, a^{2} c^{6}\right)} d^{9} e^{4} - 5 \, {\left(4 \, b^{5} c^{3} - 5 \, a b^{3} c^{4} - 44 \, a^{2} b c^{5}\right)} d^{8} e^{5} + 5 \, {\left(b^{6} c^{2} + 10 \, a b^{4} c^{3} - 50 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{7} e^{6} + 2 \, {\left(b^{7} c - 19 \, a b^{5} c^{2} + 20 \, a^{2} b^{3} c^{3} + 160 \, a^{3} b c^{4}\right)} d^{6} e^{7} - {\left(b^{8} + a b^{6} c - 80 \, a^{2} b^{4} c^{2} + 210 \, a^{3} b^{2} c^{3} + 120 \, a^{4} c^{4}\right)} d^{5} e^{8} + 5 \, {\left(a b^{7} - 4 \, a^{2} b^{5} c - 10 \, a^{3} b^{3} c^{2} + 40 \, a^{4} b c^{3}\right)} d^{4} e^{9} - 5 \, {\left(2 \, a^{2} b^{6} - 10 \, a^{3} b^{4} c + 5 \, a^{4} b^{2} c^{2} + 12 \, a^{5} c^{3}\right)} d^{3} e^{10} + 10 \, {\left(a^{3} b^{5} - 5 \, a^{4} b^{3} c + 4 \, a^{5} b c^{2}\right)} d^{2} e^{11} - {\left(5 \, a^{4} b^{4} - 23 \, a^{5} b^{2} c + 12 \, a^{6} c^{2}\right)} d e^{12} + {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} e^{13}\right)} x^{4} + {\left(3 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{12} e - 12 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{11} e^{2} + {\left(15 \, b^{4} c^{4} - 44 \, a b^{2} c^{5} - 64 \, a^{2} c^{6}\right)} d^{10} e^{3} - 50 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{9} e^{4} - 5 \, {\left(3 \, b^{6} c^{2} - 20 \, a b^{4} c^{3} + 25 \, a^{2} b^{2} c^{4} + 28 \, a^{3} c^{5}\right)} d^{8} e^{5} + 4 \, {\left(3 \, b^{7} c - 7 \, a b^{5} c^{2} - 40 \, a^{2} b^{3} c^{3} + 80 \, a^{3} b c^{4}\right)} d^{7} e^{6} - {\left(3 \, b^{8} + 28 \, a b^{6} c - 190 \, a^{2} b^{4} c^{2} + 80 \, a^{3} b^{2} c^{3} + 160 \, a^{4} c^{4}\right)} d^{6} e^{7} + 2 \, {\left(7 \, a b^{7} - 8 \, a^{2} b^{5} c - 110 \, a^{3} b^{3} c^{2} + 120 \, a^{4} b c^{3}\right)} d^{5} e^{8} - 25 \, {\left(a^{2} b^{6} - 4 \, a^{3} b^{4} c - a^{4} b^{2} c^{2} + 4 \, a^{5} c^{3}\right)} d^{4} e^{9} + 20 \, {\left(a^{3} b^{5} - 5 \, a^{4} b^{3} c + 4 \, a^{5} b c^{2}\right)} d^{3} e^{10} - {\left(5 \, a^{4} b^{4} - 28 \, a^{5} b^{2} c + 32 \, a^{6} c^{2}\right)} d^{2} e^{11} - 2 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d e^{12} + {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} e^{13}\right)} x^{3} + {\left({\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{13} - 2 \, {\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{12} e - {\left(5 \, b^{4} c^{4} - 28 \, a b^{2} c^{5} + 32 \, a^{2} c^{6}\right)} d^{11} e^{2} + 20 \, {\left(b^{5} c^{3} - 5 \, a b^{3} c^{4} + 4 \, a^{2} b c^{5}\right)} d^{10} e^{3} - 25 \, {\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} - a^{2} b^{2} c^{4} + 4 \, a^{3} c^{5}\right)} d^{9} e^{4} + 2 \, {\left(7 \, b^{7} c - 8 \, a b^{5} c^{2} - 110 \, a^{2} b^{3} c^{3} + 120 \, a^{3} b c^{4}\right)} d^{8} e^{5} - {\left(3 \, b^{8} + 28 \, a b^{6} c - 190 \, a^{2} b^{4} c^{2} + 80 \, a^{3} b^{2} c^{3} + 160 \, a^{4} c^{4}\right)} d^{7} e^{6} + 4 \, {\left(3 \, a b^{7} - 7 \, a^{2} b^{5} c - 40 \, a^{3} b^{3} c^{2} + 80 \, a^{4} b c^{3}\right)} d^{6} e^{7} - 5 \, {\left(3 \, a^{2} b^{6} - 20 \, a^{3} b^{4} c + 25 \, a^{4} b^{2} c^{2} + 28 \, a^{5} c^{3}\right)} d^{5} e^{8} - 50 \, {\left(a^{4} b^{3} c - 4 \, a^{5} b c^{2}\right)} d^{4} e^{9} + {\left(15 \, a^{4} b^{4} - 44 \, a^{5} b^{2} c - 64 \, a^{6} c^{2}\right)} d^{3} e^{10} - 12 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{2} e^{11} + 3 \, {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d e^{12}\right)} x^{2} + {\left({\left(b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{13} - {\left(5 \, b^{4} c^{4} - 23 \, a b^{2} c^{5} + 12 \, a^{2} c^{6}\right)} d^{12} e + 10 \, {\left(b^{5} c^{3} - 5 \, a b^{3} c^{4} + 4 \, a^{2} b c^{5}\right)} d^{11} e^{2} - 5 \, {\left(2 \, b^{6} c^{2} - 10 \, a b^{4} c^{3} + 5 \, a^{2} b^{2} c^{4} + 12 \, a^{3} c^{5}\right)} d^{10} e^{3} + 5 \, {\left(b^{7} c - 4 \, a b^{5} c^{2} - 10 \, a^{2} b^{3} c^{3} + 40 \, a^{3} b c^{4}\right)} d^{9} e^{4} - {\left(b^{8} + a b^{6} c - 80 \, a^{2} b^{4} c^{2} + 210 \, a^{3} b^{2} c^{3} + 120 \, a^{4} c^{4}\right)} d^{8} e^{5} + 2 \, {\left(a b^{7} - 19 \, a^{2} b^{5} c + 20 \, a^{3} b^{3} c^{2} + 160 \, a^{4} b c^{3}\right)} d^{7} e^{6} + 5 \, {\left(a^{2} b^{6} + 10 \, a^{3} b^{4} c - 50 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d^{6} e^{7} - 5 \, {\left(4 \, a^{3} b^{5} - 5 \, a^{4} b^{3} c - 44 \, a^{5} b c^{2}\right)} d^{5} e^{8} + 5 \, {\left(5 \, a^{4} b^{4} - 17 \, a^{5} b^{2} c - 12 \, a^{6} c^{2}\right)} d^{4} e^{9} - 14 \, {\left(a^{5} b^{3} - 4 \, a^{6} b c\right)} d^{3} e^{10} + 3 \, {\left(a^{6} b^{2} - 4 \, a^{7} c\right)} d^{2} e^{11}\right)} x\right)}}\right]"," ",0,"[1/96*(15*(32*(a*b^2*c^3 - 4*a^2*c^4)*d^6*e^2 - 48*(a*b^3*c^2 - 4*a^2*b*c^3)*d^5*e^3 + 6*(5*a*b^4*c - 24*a^2*b^2*c^2 + 16*a^3*c^3)*d^4*e^4 - (7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*d^3*e^5 + (32*(b^2*c^4 - 4*a*c^5)*d^3*e^5 - 48*(b^3*c^3 - 4*a*b*c^4)*d^2*e^6 + 6*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*d*e^7 - (7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*e^8)*x^5 + (96*(b^2*c^4 - 4*a*c^5)*d^4*e^4 - 112*(b^3*c^3 - 4*a*b*c^4)*d^3*e^5 + 6*(7*b^4*c^2 - 40*a*b^2*c^3 + 48*a^2*c^4)*d^2*e^6 + 3*(3*b^5*c - 8*a*b^3*c^2 - 16*a^2*b*c^3)*d*e^7 - (7*b^6 - 40*a*b^4*c + 48*a^2*b^2*c^2)*e^8)*x^4 + (96*(b^2*c^4 - 4*a*c^5)*d^5*e^3 - 48*(b^3*c^3 - 4*a*b*c^4)*d^4*e^4 - 2*(27*b^4*c^2 - 88*a*b^2*c^3 - 80*a^2*c^4)*d^3*e^5 + 3*(23*b^5*c - 120*a*b^3*c^2 + 112*a^2*b*c^3)*d^2*e^6 - 3*(7*b^6 - 50*a*b^4*c + 96*a^2*b^2*c^2 - 32*a^3*c^3)*d*e^7 - (7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*e^8)*x^3 + (32*(b^2*c^4 - 4*a*c^5)*d^6*e^2 + 48*(b^3*c^3 - 4*a*b*c^4)*d^5*e^3 - 6*(19*b^4*c^2 - 88*a*b^2*c^3 + 48*a^2*c^4)*d^4*e^4 + (83*b^5*c - 536*a*b^3*c^2 + 816*a^2*b*c^3)*d^3*e^5 - 3*(7*b^6 - 70*a*b^4*c + 192*a^2*b^2*c^2 - 96*a^3*c^3)*d^2*e^6 - 3*(7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*d*e^7)*x^2 + (32*(b^3*c^3 - 4*a*b*c^4)*d^6*e^2 - 48*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^5*e^3 + 6*(5*b^5*c - 48*a*b^3*c^2 + 112*a^2*b*c^3)*d^4*e^4 - (7*b^6 - 130*a*b^4*c + 480*a^2*b^2*c^2 - 288*a^3*c^3)*d^3*e^5 - 3*(7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*d^2*e^6)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*(48*b*c^5*d^9 - 48*(5*b^2*c^4 - 8*a*c^5)*d^8*e + 240*(2*b^3*c^3 - 5*a*b*c^4)*d^7*e^2 - 240*(2*b^4*c^2 - 7*a*b^2*c^3 + 4*a^2*c^4)*d^6*e^3 + 30*(8*b^5*c - 41*a*b^3*c^2 + 60*a^2*b*c^3)*d^5*e^4 - (48*b^6 - 405*a*b^4*c + 640*a^2*b^2*c^2 + 1424*a^3*c^3)*d^4*e^5 - (39*a*b^5 + 220*a^2*b^3*c - 1552*a^3*b*c^2)*d^3*e^6 + (125*a^2*b^4 - 472*a^3*b^2*c - 112*a^4*c^2)*d^2*e^7 - 46*(a^3*b^3 - 4*a^4*b*c)*d*e^8 + 8*(a^4*b^2 - 4*a^5*c)*e^9 + (96*c^6*d^6*e^3 - 288*b*c^5*d^5*e^4 + 4*(167*b^2*c^4 - 308*a*c^5)*d^4*e^5 - 8*(107*b^3*c^3 - 308*a*b*c^4)*d^3*e^6 + (485*b^4*c^2 - 1312*a*b^2*c^3 - 1072*a^2*c^4)*d^2*e^7 - (105*b^5*c - 80*a*b^3*c^2 - 1072*a^2*b*c^3)*d*e^8 + (105*a*b^4*c - 460*a^2*b^2*c^2 + 256*a^3*c^3)*e^9)*x^4 + (288*c^6*d^7*e^2 - 816*b*c^5*d^6*e^3 + 36*(45*b^2*c^4 - 76*a*c^5)*d^5*e^4 - 2*(817*b^3*c^3 - 2188*a*b*c^4)*d^4*e^5 + 2*(221*b^4*c^2 - 212*a*b^2*c^3 - 1488*a^2*c^4)*d^3*e^6 + (205*b^5*c - 1436*a*b^3*c^2 + 2320*a^2*b*c^3)*d^2*e^7 - (105*b^6 - 430*a*b^4*c + 124*a^2*b^2*c^2 - 48*a^3*c^3)*d*e^8 + (105*a*b^5 - 530*a^2*b^3*c + 488*a^3*b*c^2)*e^9)*x^3 + (288*c^6*d^8*e - 720*b*c^5*d^7*e^2 + 96*(10*b^2*c^4 - 13*a*c^5)*d^6*e^3 - 90*(b^3*c^3 + 4*a*b*c^4)*d^5*e^4 - (1225*b^4*c^2 - 5348*a*b^2*c^3 + 3232*a^2*c^4)*d^4*e^5 + (1067*b^5*c - 4444*a*b^3*c^2 + 2000*a^2*b*c^3)*d^3*e^6 - 2*(140*b^6 - 387*a*b^4*c - 708*a^2*b^2*c^2 + 784*a^3*c^3)*d^2*e^7 + (245*a*b^5 - 1354*a^2*b^3*c + 1640*a^3*b*c^2)*d*e^8 + (35*a^2*b^4 - 172*a^3*b^2*c + 128*a^4*c^2)*e^9)*x^2 + (96*c^6*d^9 - 144*b*c^5*d^8*e - 48*(5*b^2*c^4 - 14*a*c^5)*d^7*e^2 + 1200*(b^3*c^3 - 3*a*b*c^4)*d^6*e^3 - 90*(19*b^4*c^2 - 70*a*b^2*c^3 + 24*a^2*c^4)*d^5*e^4 + (1029*b^5*c - 4190*a*b^3*c^2 + 2168*a^2*b*c^3)*d^4*e^5 - (231*b^6 - 790*a*b^4*c - 776*a^2*b^2*c^2 + 2592*a^3*c^3)*d^3*e^6 + (133*a*b^5 - 1076*a^2*b^3*c + 2320*a^3*b*c^2)*d^2*e^7 + 4*(28*a^2*b^4 - 121*a^3*b^2*c + 36*a^4*c^2)*d*e^8 - 14*(a^3*b^3 - 4*a^4*b*c)*e^9)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^5 - 4*a^2*c^6)*d^13 - 5*(a*b^3*c^4 - 4*a^2*b*c^5)*d^12*e + 5*(2*a*b^4*c^3 - 7*a^2*b^2*c^4 - 4*a^3*c^5)*d^11*e^2 - 10*(a*b^5*c^2 - 2*a^2*b^3*c^3 - 8*a^3*b*c^4)*d^10*e^3 + 5*(a*b^6*c + 2*a^2*b^4*c^2 - 22*a^3*b^2*c^3 - 8*a^4*c^4)*d^9*e^4 - (a*b^7 + 16*a^2*b^5*c - 50*a^3*b^3*c^2 - 120*a^4*b*c^3)*d^8*e^5 + 5*(a^2*b^6 + 2*a^3*b^4*c - 22*a^4*b^2*c^2 - 8*a^5*c^3)*d^7*e^6 - 10*(a^3*b^5 - 2*a^4*b^3*c - 8*a^5*b*c^2)*d^6*e^7 + 5*(2*a^4*b^4 - 7*a^5*b^2*c - 4*a^6*c^2)*d^5*e^8 - 5*(a^5*b^3 - 4*a^6*b*c)*d^4*e^9 + (a^6*b^2 - 4*a^7*c)*d^3*e^10 + ((b^2*c^6 - 4*a*c^7)*d^10*e^3 - 5*(b^3*c^5 - 4*a*b*c^6)*d^9*e^4 + 5*(2*b^4*c^4 - 7*a*b^2*c^5 - 4*a^2*c^6)*d^8*e^5 - 10*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*d^7*e^6 + 5*(b^6*c^2 + 2*a*b^4*c^3 - 22*a^2*b^2*c^4 - 8*a^3*c^5)*d^6*e^7 - (b^7*c + 16*a*b^5*c^2 - 50*a^2*b^3*c^3 - 120*a^3*b*c^4)*d^5*e^8 + 5*(a*b^6*c + 2*a^2*b^4*c^2 - 22*a^3*b^2*c^3 - 8*a^4*c^4)*d^4*e^9 - 10*(a^2*b^5*c - 2*a^3*b^3*c^2 - 8*a^4*b*c^3)*d^3*e^10 + 5*(2*a^3*b^4*c - 7*a^4*b^2*c^2 - 4*a^5*c^3)*d^2*e^11 - 5*(a^4*b^3*c - 4*a^5*b*c^2)*d*e^12 + (a^5*b^2*c - 4*a^6*c^2)*e^13)*x^5 + (3*(b^2*c^6 - 4*a*c^7)*d^11*e^2 - 14*(b^3*c^5 - 4*a*b*c^6)*d^10*e^3 + 5*(5*b^4*c^4 - 17*a*b^2*c^5 - 12*a^2*c^6)*d^9*e^4 - 5*(4*b^5*c^3 - 5*a*b^3*c^4 - 44*a^2*b*c^5)*d^8*e^5 + 5*(b^6*c^2 + 10*a*b^4*c^3 - 50*a^2*b^2*c^4 - 24*a^3*c^5)*d^7*e^6 + 2*(b^7*c - 19*a*b^5*c^2 + 20*a^2*b^3*c^3 + 160*a^3*b*c^4)*d^6*e^7 - (b^8 + a*b^6*c - 80*a^2*b^4*c^2 + 210*a^3*b^2*c^3 + 120*a^4*c^4)*d^5*e^8 + 5*(a*b^7 - 4*a^2*b^5*c - 10*a^3*b^3*c^2 + 40*a^4*b*c^3)*d^4*e^9 - 5*(2*a^2*b^6 - 10*a^3*b^4*c + 5*a^4*b^2*c^2 + 12*a^5*c^3)*d^3*e^10 + 10*(a^3*b^5 - 5*a^4*b^3*c + 4*a^5*b*c^2)*d^2*e^11 - (5*a^4*b^4 - 23*a^5*b^2*c + 12*a^6*c^2)*d*e^12 + (a^5*b^3 - 4*a^6*b*c)*e^13)*x^4 + (3*(b^2*c^6 - 4*a*c^7)*d^12*e - 12*(b^3*c^5 - 4*a*b*c^6)*d^11*e^2 + (15*b^4*c^4 - 44*a*b^2*c^5 - 64*a^2*c^6)*d^10*e^3 - 50*(a*b^3*c^4 - 4*a^2*b*c^5)*d^9*e^4 - 5*(3*b^6*c^2 - 20*a*b^4*c^3 + 25*a^2*b^2*c^4 + 28*a^3*c^5)*d^8*e^5 + 4*(3*b^7*c - 7*a*b^5*c^2 - 40*a^2*b^3*c^3 + 80*a^3*b*c^4)*d^7*e^6 - (3*b^8 + 28*a*b^6*c - 190*a^2*b^4*c^2 + 80*a^3*b^2*c^3 + 160*a^4*c^4)*d^6*e^7 + 2*(7*a*b^7 - 8*a^2*b^5*c - 110*a^3*b^3*c^2 + 120*a^4*b*c^3)*d^5*e^8 - 25*(a^2*b^6 - 4*a^3*b^4*c - a^4*b^2*c^2 + 4*a^5*c^3)*d^4*e^9 + 20*(a^3*b^5 - 5*a^4*b^3*c + 4*a^5*b*c^2)*d^3*e^10 - (5*a^4*b^4 - 28*a^5*b^2*c + 32*a^6*c^2)*d^2*e^11 - 2*(a^5*b^3 - 4*a^6*b*c)*d*e^12 + (a^6*b^2 - 4*a^7*c)*e^13)*x^3 + ((b^2*c^6 - 4*a*c^7)*d^13 - 2*(b^3*c^5 - 4*a*b*c^6)*d^12*e - (5*b^4*c^4 - 28*a*b^2*c^5 + 32*a^2*c^6)*d^11*e^2 + 20*(b^5*c^3 - 5*a*b^3*c^4 + 4*a^2*b*c^5)*d^10*e^3 - 25*(b^6*c^2 - 4*a*b^4*c^3 - a^2*b^2*c^4 + 4*a^3*c^5)*d^9*e^4 + 2*(7*b^7*c - 8*a*b^5*c^2 - 110*a^2*b^3*c^3 + 120*a^3*b*c^4)*d^8*e^5 - (3*b^8 + 28*a*b^6*c - 190*a^2*b^4*c^2 + 80*a^3*b^2*c^3 + 160*a^4*c^4)*d^7*e^6 + 4*(3*a*b^7 - 7*a^2*b^5*c - 40*a^3*b^3*c^2 + 80*a^4*b*c^3)*d^6*e^7 - 5*(3*a^2*b^6 - 20*a^3*b^4*c + 25*a^4*b^2*c^2 + 28*a^5*c^3)*d^5*e^8 - 50*(a^4*b^3*c - 4*a^5*b*c^2)*d^4*e^9 + (15*a^4*b^4 - 44*a^5*b^2*c - 64*a^6*c^2)*d^3*e^10 - 12*(a^5*b^3 - 4*a^6*b*c)*d^2*e^11 + 3*(a^6*b^2 - 4*a^7*c)*d*e^12)*x^2 + ((b^3*c^5 - 4*a*b*c^6)*d^13 - (5*b^4*c^4 - 23*a*b^2*c^5 + 12*a^2*c^6)*d^12*e + 10*(b^5*c^3 - 5*a*b^3*c^4 + 4*a^2*b*c^5)*d^11*e^2 - 5*(2*b^6*c^2 - 10*a*b^4*c^3 + 5*a^2*b^2*c^4 + 12*a^3*c^5)*d^10*e^3 + 5*(b^7*c - 4*a*b^5*c^2 - 10*a^2*b^3*c^3 + 40*a^3*b*c^4)*d^9*e^4 - (b^8 + a*b^6*c - 80*a^2*b^4*c^2 + 210*a^3*b^2*c^3 + 120*a^4*c^4)*d^8*e^5 + 2*(a*b^7 - 19*a^2*b^5*c + 20*a^3*b^3*c^2 + 160*a^4*b*c^3)*d^7*e^6 + 5*(a^2*b^6 + 10*a^3*b^4*c - 50*a^4*b^2*c^2 - 24*a^5*c^3)*d^6*e^7 - 5*(4*a^3*b^5 - 5*a^4*b^3*c - 44*a^5*b*c^2)*d^5*e^8 + 5*(5*a^4*b^4 - 17*a^5*b^2*c - 12*a^6*c^2)*d^4*e^9 - 14*(a^5*b^3 - 4*a^6*b*c)*d^3*e^10 + 3*(a^6*b^2 - 4*a^7*c)*d^2*e^11)*x), 1/48*(15*(32*(a*b^2*c^3 - 4*a^2*c^4)*d^6*e^2 - 48*(a*b^3*c^2 - 4*a^2*b*c^3)*d^5*e^3 + 6*(5*a*b^4*c - 24*a^2*b^2*c^2 + 16*a^3*c^3)*d^4*e^4 - (7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*d^3*e^5 + (32*(b^2*c^4 - 4*a*c^5)*d^3*e^5 - 48*(b^3*c^3 - 4*a*b*c^4)*d^2*e^6 + 6*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*d*e^7 - (7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*e^8)*x^5 + (96*(b^2*c^4 - 4*a*c^5)*d^4*e^4 - 112*(b^3*c^3 - 4*a*b*c^4)*d^3*e^5 + 6*(7*b^4*c^2 - 40*a*b^2*c^3 + 48*a^2*c^4)*d^2*e^6 + 3*(3*b^5*c - 8*a*b^3*c^2 - 16*a^2*b*c^3)*d*e^7 - (7*b^6 - 40*a*b^4*c + 48*a^2*b^2*c^2)*e^8)*x^4 + (96*(b^2*c^4 - 4*a*c^5)*d^5*e^3 - 48*(b^3*c^3 - 4*a*b*c^4)*d^4*e^4 - 2*(27*b^4*c^2 - 88*a*b^2*c^3 - 80*a^2*c^4)*d^3*e^5 + 3*(23*b^5*c - 120*a*b^3*c^2 + 112*a^2*b*c^3)*d^2*e^6 - 3*(7*b^6 - 50*a*b^4*c + 96*a^2*b^2*c^2 - 32*a^3*c^3)*d*e^7 - (7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*e^8)*x^3 + (32*(b^2*c^4 - 4*a*c^5)*d^6*e^2 + 48*(b^3*c^3 - 4*a*b*c^4)*d^5*e^3 - 6*(19*b^4*c^2 - 88*a*b^2*c^3 + 48*a^2*c^4)*d^4*e^4 + (83*b^5*c - 536*a*b^3*c^2 + 816*a^2*b*c^3)*d^3*e^5 - 3*(7*b^6 - 70*a*b^4*c + 192*a^2*b^2*c^2 - 96*a^3*c^3)*d^2*e^6 - 3*(7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*d*e^7)*x^2 + (32*(b^3*c^3 - 4*a*b*c^4)*d^6*e^2 - 48*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^5*e^3 + 6*(5*b^5*c - 48*a*b^3*c^2 + 112*a^2*b*c^3)*d^4*e^4 - (7*b^6 - 130*a*b^4*c + 480*a^2*b^2*c^2 - 288*a^3*c^3)*d^3*e^5 - 3*(7*a*b^5 - 40*a^2*b^3*c + 48*a^3*b*c^2)*d^2*e^6)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(48*b*c^5*d^9 - 48*(5*b^2*c^4 - 8*a*c^5)*d^8*e + 240*(2*b^3*c^3 - 5*a*b*c^4)*d^7*e^2 - 240*(2*b^4*c^2 - 7*a*b^2*c^3 + 4*a^2*c^4)*d^6*e^3 + 30*(8*b^5*c - 41*a*b^3*c^2 + 60*a^2*b*c^3)*d^5*e^4 - (48*b^6 - 405*a*b^4*c + 640*a^2*b^2*c^2 + 1424*a^3*c^3)*d^4*e^5 - (39*a*b^5 + 220*a^2*b^3*c - 1552*a^3*b*c^2)*d^3*e^6 + (125*a^2*b^4 - 472*a^3*b^2*c - 112*a^4*c^2)*d^2*e^7 - 46*(a^3*b^3 - 4*a^4*b*c)*d*e^8 + 8*(a^4*b^2 - 4*a^5*c)*e^9 + (96*c^6*d^6*e^3 - 288*b*c^5*d^5*e^4 + 4*(167*b^2*c^4 - 308*a*c^5)*d^4*e^5 - 8*(107*b^3*c^3 - 308*a*b*c^4)*d^3*e^6 + (485*b^4*c^2 - 1312*a*b^2*c^3 - 1072*a^2*c^4)*d^2*e^7 - (105*b^5*c - 80*a*b^3*c^2 - 1072*a^2*b*c^3)*d*e^8 + (105*a*b^4*c - 460*a^2*b^2*c^2 + 256*a^3*c^3)*e^9)*x^4 + (288*c^6*d^7*e^2 - 816*b*c^5*d^6*e^3 + 36*(45*b^2*c^4 - 76*a*c^5)*d^5*e^4 - 2*(817*b^3*c^3 - 2188*a*b*c^4)*d^4*e^5 + 2*(221*b^4*c^2 - 212*a*b^2*c^3 - 1488*a^2*c^4)*d^3*e^6 + (205*b^5*c - 1436*a*b^3*c^2 + 2320*a^2*b*c^3)*d^2*e^7 - (105*b^6 - 430*a*b^4*c + 124*a^2*b^2*c^2 - 48*a^3*c^3)*d*e^8 + (105*a*b^5 - 530*a^2*b^3*c + 488*a^3*b*c^2)*e^9)*x^3 + (288*c^6*d^8*e - 720*b*c^5*d^7*e^2 + 96*(10*b^2*c^4 - 13*a*c^5)*d^6*e^3 - 90*(b^3*c^3 + 4*a*b*c^4)*d^5*e^4 - (1225*b^4*c^2 - 5348*a*b^2*c^3 + 3232*a^2*c^4)*d^4*e^5 + (1067*b^5*c - 4444*a*b^3*c^2 + 2000*a^2*b*c^3)*d^3*e^6 - 2*(140*b^6 - 387*a*b^4*c - 708*a^2*b^2*c^2 + 784*a^3*c^3)*d^2*e^7 + (245*a*b^5 - 1354*a^2*b^3*c + 1640*a^3*b*c^2)*d*e^8 + (35*a^2*b^4 - 172*a^3*b^2*c + 128*a^4*c^2)*e^9)*x^2 + (96*c^6*d^9 - 144*b*c^5*d^8*e - 48*(5*b^2*c^4 - 14*a*c^5)*d^7*e^2 + 1200*(b^3*c^3 - 3*a*b*c^4)*d^6*e^3 - 90*(19*b^4*c^2 - 70*a*b^2*c^3 + 24*a^2*c^4)*d^5*e^4 + (1029*b^5*c - 4190*a*b^3*c^2 + 2168*a^2*b*c^3)*d^4*e^5 - (231*b^6 - 790*a*b^4*c - 776*a^2*b^2*c^2 + 2592*a^3*c^3)*d^3*e^6 + (133*a*b^5 - 1076*a^2*b^3*c + 2320*a^3*b*c^2)*d^2*e^7 + 4*(28*a^2*b^4 - 121*a^3*b^2*c + 36*a^4*c^2)*d*e^8 - 14*(a^3*b^3 - 4*a^4*b*c)*e^9)*x)*sqrt(c*x^2 + b*x + a))/((a*b^2*c^5 - 4*a^2*c^6)*d^13 - 5*(a*b^3*c^4 - 4*a^2*b*c^5)*d^12*e + 5*(2*a*b^4*c^3 - 7*a^2*b^2*c^4 - 4*a^3*c^5)*d^11*e^2 - 10*(a*b^5*c^2 - 2*a^2*b^3*c^3 - 8*a^3*b*c^4)*d^10*e^3 + 5*(a*b^6*c + 2*a^2*b^4*c^2 - 22*a^3*b^2*c^3 - 8*a^4*c^4)*d^9*e^4 - (a*b^7 + 16*a^2*b^5*c - 50*a^3*b^3*c^2 - 120*a^4*b*c^3)*d^8*e^5 + 5*(a^2*b^6 + 2*a^3*b^4*c - 22*a^4*b^2*c^2 - 8*a^5*c^3)*d^7*e^6 - 10*(a^3*b^5 - 2*a^4*b^3*c - 8*a^5*b*c^2)*d^6*e^7 + 5*(2*a^4*b^4 - 7*a^5*b^2*c - 4*a^6*c^2)*d^5*e^8 - 5*(a^5*b^3 - 4*a^6*b*c)*d^4*e^9 + (a^6*b^2 - 4*a^7*c)*d^3*e^10 + ((b^2*c^6 - 4*a*c^7)*d^10*e^3 - 5*(b^3*c^5 - 4*a*b*c^6)*d^9*e^4 + 5*(2*b^4*c^4 - 7*a*b^2*c^5 - 4*a^2*c^6)*d^8*e^5 - 10*(b^5*c^3 - 2*a*b^3*c^4 - 8*a^2*b*c^5)*d^7*e^6 + 5*(b^6*c^2 + 2*a*b^4*c^3 - 22*a^2*b^2*c^4 - 8*a^3*c^5)*d^6*e^7 - (b^7*c + 16*a*b^5*c^2 - 50*a^2*b^3*c^3 - 120*a^3*b*c^4)*d^5*e^8 + 5*(a*b^6*c + 2*a^2*b^4*c^2 - 22*a^3*b^2*c^3 - 8*a^4*c^4)*d^4*e^9 - 10*(a^2*b^5*c - 2*a^3*b^3*c^2 - 8*a^4*b*c^3)*d^3*e^10 + 5*(2*a^3*b^4*c - 7*a^4*b^2*c^2 - 4*a^5*c^3)*d^2*e^11 - 5*(a^4*b^3*c - 4*a^5*b*c^2)*d*e^12 + (a^5*b^2*c - 4*a^6*c^2)*e^13)*x^5 + (3*(b^2*c^6 - 4*a*c^7)*d^11*e^2 - 14*(b^3*c^5 - 4*a*b*c^6)*d^10*e^3 + 5*(5*b^4*c^4 - 17*a*b^2*c^5 - 12*a^2*c^6)*d^9*e^4 - 5*(4*b^5*c^3 - 5*a*b^3*c^4 - 44*a^2*b*c^5)*d^8*e^5 + 5*(b^6*c^2 + 10*a*b^4*c^3 - 50*a^2*b^2*c^4 - 24*a^3*c^5)*d^7*e^6 + 2*(b^7*c - 19*a*b^5*c^2 + 20*a^2*b^3*c^3 + 160*a^3*b*c^4)*d^6*e^7 - (b^8 + a*b^6*c - 80*a^2*b^4*c^2 + 210*a^3*b^2*c^3 + 120*a^4*c^4)*d^5*e^8 + 5*(a*b^7 - 4*a^2*b^5*c - 10*a^3*b^3*c^2 + 40*a^4*b*c^3)*d^4*e^9 - 5*(2*a^2*b^6 - 10*a^3*b^4*c + 5*a^4*b^2*c^2 + 12*a^5*c^3)*d^3*e^10 + 10*(a^3*b^5 - 5*a^4*b^3*c + 4*a^5*b*c^2)*d^2*e^11 - (5*a^4*b^4 - 23*a^5*b^2*c + 12*a^6*c^2)*d*e^12 + (a^5*b^3 - 4*a^6*b*c)*e^13)*x^4 + (3*(b^2*c^6 - 4*a*c^7)*d^12*e - 12*(b^3*c^5 - 4*a*b*c^6)*d^11*e^2 + (15*b^4*c^4 - 44*a*b^2*c^5 - 64*a^2*c^6)*d^10*e^3 - 50*(a*b^3*c^4 - 4*a^2*b*c^5)*d^9*e^4 - 5*(3*b^6*c^2 - 20*a*b^4*c^3 + 25*a^2*b^2*c^4 + 28*a^3*c^5)*d^8*e^5 + 4*(3*b^7*c - 7*a*b^5*c^2 - 40*a^2*b^3*c^3 + 80*a^3*b*c^4)*d^7*e^6 - (3*b^8 + 28*a*b^6*c - 190*a^2*b^4*c^2 + 80*a^3*b^2*c^3 + 160*a^4*c^4)*d^6*e^7 + 2*(7*a*b^7 - 8*a^2*b^5*c - 110*a^3*b^3*c^2 + 120*a^4*b*c^3)*d^5*e^8 - 25*(a^2*b^6 - 4*a^3*b^4*c - a^4*b^2*c^2 + 4*a^5*c^3)*d^4*e^9 + 20*(a^3*b^5 - 5*a^4*b^3*c + 4*a^5*b*c^2)*d^3*e^10 - (5*a^4*b^4 - 28*a^5*b^2*c + 32*a^6*c^2)*d^2*e^11 - 2*(a^5*b^3 - 4*a^6*b*c)*d*e^12 + (a^6*b^2 - 4*a^7*c)*e^13)*x^3 + ((b^2*c^6 - 4*a*c^7)*d^13 - 2*(b^3*c^5 - 4*a*b*c^6)*d^12*e - (5*b^4*c^4 - 28*a*b^2*c^5 + 32*a^2*c^6)*d^11*e^2 + 20*(b^5*c^3 - 5*a*b^3*c^4 + 4*a^2*b*c^5)*d^10*e^3 - 25*(b^6*c^2 - 4*a*b^4*c^3 - a^2*b^2*c^4 + 4*a^3*c^5)*d^9*e^4 + 2*(7*b^7*c - 8*a*b^5*c^2 - 110*a^2*b^3*c^3 + 120*a^3*b*c^4)*d^8*e^5 - (3*b^8 + 28*a*b^6*c - 190*a^2*b^4*c^2 + 80*a^3*b^2*c^3 + 160*a^4*c^4)*d^7*e^6 + 4*(3*a*b^7 - 7*a^2*b^5*c - 40*a^3*b^3*c^2 + 80*a^4*b*c^3)*d^6*e^7 - 5*(3*a^2*b^6 - 20*a^3*b^4*c + 25*a^4*b^2*c^2 + 28*a^5*c^3)*d^5*e^8 - 50*(a^4*b^3*c - 4*a^5*b*c^2)*d^4*e^9 + (15*a^4*b^4 - 44*a^5*b^2*c - 64*a^6*c^2)*d^3*e^10 - 12*(a^5*b^3 - 4*a^6*b*c)*d^2*e^11 + 3*(a^6*b^2 - 4*a^7*c)*d*e^12)*x^2 + ((b^3*c^5 - 4*a*b*c^6)*d^13 - (5*b^4*c^4 - 23*a*b^2*c^5 + 12*a^2*c^6)*d^12*e + 10*(b^5*c^3 - 5*a*b^3*c^4 + 4*a^2*b*c^5)*d^11*e^2 - 5*(2*b^6*c^2 - 10*a*b^4*c^3 + 5*a^2*b^2*c^4 + 12*a^3*c^5)*d^10*e^3 + 5*(b^7*c - 4*a*b^5*c^2 - 10*a^2*b^3*c^3 + 40*a^3*b*c^4)*d^9*e^4 - (b^8 + a*b^6*c - 80*a^2*b^4*c^2 + 210*a^3*b^2*c^3 + 120*a^4*c^4)*d^8*e^5 + 2*(a*b^7 - 19*a^2*b^5*c + 20*a^3*b^3*c^2 + 160*a^4*b*c^3)*d^7*e^6 + 5*(a^2*b^6 + 10*a^3*b^4*c - 50*a^4*b^2*c^2 - 24*a^5*c^3)*d^6*e^7 - 5*(4*a^3*b^5 - 5*a^4*b^3*c - 44*a^5*b*c^2)*d^5*e^8 + 5*(5*a^4*b^4 - 17*a^5*b^2*c - 12*a^6*c^2)*d^4*e^9 - 14*(a^5*b^3 - 4*a^6*b*c)*d^3*e^10 + 3*(a^6*b^2 - 4*a^7*c)*d^2*e^11)*x)]","B",0
2391,1,2249,0,1.659987," ","integrate((e*x+d)^5/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{4} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} - {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{4} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left(160 \, a^{2} b c^{4} d^{3} e^{2} - 320 \, a^{3} c^{4} d^{2} e^{3} + 3 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e^{5} x^{4} - 2 \, {\left(b^{3} c^{4} - 12 \, a b c^{5}\right)} d^{5} - 20 \, {\left(a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{4} e - 10 \, {\left(3 \, a^{2} b^{3} c^{2} - 20 \, a^{3} b c^{3}\right)} d e^{4} + {\left(15 \, a^{2} b^{4} c - 100 \, a^{3} b^{2} c^{2} + 128 \, a^{4} c^{3}\right)} e^{5} + 4 \, {\left(8 \, c^{7} d^{5} - 20 \, b c^{6} d^{4} e + 10 \, {\left(b^{2} c^{5} + 4 \, a c^{6}\right)} d^{3} e^{2} + 5 \, {\left(b^{3} c^{4} - 12 \, a b c^{5}\right)} d^{2} e^{3} - 10 \, {\left(b^{4} c^{3} - 7 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d e^{4} + {\left(5 \, b^{5} c^{2} - 37 \, a b^{3} c^{3} + 64 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{3} + 3 \, {\left(16 \, b c^{6} d^{5} - 40 \, b^{2} c^{5} d^{4} e + 20 \, {\left(b^{3} c^{4} + 4 \, a b c^{5}\right)} d^{3} e^{2} - 40 \, {\left(a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{2} e^{3} - 10 \, {\left(b^{5} c^{2} - 6 \, a b^{3} c^{3}\right)} d e^{4} + {\left(5 \, b^{6} c - 30 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} e^{5}\right)} x^{2} + 6 \, {\left(40 \, a b^{2} c^{4} d^{3} e^{2} - 80 \, a^{2} b c^{4} d^{2} e^{3} + 2 \, {\left(b^{2} c^{5} + 4 \, a c^{6}\right)} d^{5} - 5 \, {\left(b^{3} c^{4} + 4 \, a b c^{5}\right)} d^{4} e - 10 \, {\left(a b^{4} c^{2} - 7 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e^{4} + {\left(5 \, a b^{5} c - 35 \, a^{2} b^{3} c^{2} + 52 \, a^{3} b c^{3}\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, {\left(a^{2} b^{4} c^{4} - 8 \, a^{3} b^{2} c^{5} + 16 \, a^{4} c^{6} + {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} x^{4} + 2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} x^{3} + {\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 32 \, a^{3} c^{7}\right)} x^{2} + 2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x\right)}}, -\frac{15 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{4} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{4} + 2 \, {\left(2 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{4} - {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} e^{5}\right)} x^{3} + {\left(2 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d e^{4} - {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} e^{5}\right)} x^{2} + 2 \, {\left(2 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d e^{4} - {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(160 \, a^{2} b c^{4} d^{3} e^{2} - 320 \, a^{3} c^{4} d^{2} e^{3} + 3 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e^{5} x^{4} - 2 \, {\left(b^{3} c^{4} - 12 \, a b c^{5}\right)} d^{5} - 20 \, {\left(a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{4} e - 10 \, {\left(3 \, a^{2} b^{3} c^{2} - 20 \, a^{3} b c^{3}\right)} d e^{4} + {\left(15 \, a^{2} b^{4} c - 100 \, a^{3} b^{2} c^{2} + 128 \, a^{4} c^{3}\right)} e^{5} + 4 \, {\left(8 \, c^{7} d^{5} - 20 \, b c^{6} d^{4} e + 10 \, {\left(b^{2} c^{5} + 4 \, a c^{6}\right)} d^{3} e^{2} + 5 \, {\left(b^{3} c^{4} - 12 \, a b c^{5}\right)} d^{2} e^{3} - 10 \, {\left(b^{4} c^{3} - 7 \, a b^{2} c^{4} + 8 \, a^{2} c^{5}\right)} d e^{4} + {\left(5 \, b^{5} c^{2} - 37 \, a b^{3} c^{3} + 64 \, a^{2} b c^{4}\right)} e^{5}\right)} x^{3} + 3 \, {\left(16 \, b c^{6} d^{5} - 40 \, b^{2} c^{5} d^{4} e + 20 \, {\left(b^{3} c^{4} + 4 \, a b c^{5}\right)} d^{3} e^{2} - 40 \, {\left(a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{2} e^{3} - 10 \, {\left(b^{5} c^{2} - 6 \, a b^{3} c^{3}\right)} d e^{4} + {\left(5 \, b^{6} c - 30 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} e^{5}\right)} x^{2} + 6 \, {\left(40 \, a b^{2} c^{4} d^{3} e^{2} - 80 \, a^{2} b c^{4} d^{2} e^{3} + 2 \, {\left(b^{2} c^{5} + 4 \, a c^{6}\right)} d^{5} - 5 \, {\left(b^{3} c^{4} + 4 \, a b c^{5}\right)} d^{4} e - 10 \, {\left(a b^{4} c^{2} - 7 \, a^{2} b^{2} c^{3} + 4 \, a^{3} c^{4}\right)} d e^{4} + {\left(5 \, a b^{5} c - 35 \, a^{2} b^{3} c^{2} + 52 \, a^{3} b c^{3}\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left(a^{2} b^{4} c^{4} - 8 \, a^{3} b^{2} c^{5} + 16 \, a^{4} c^{6} + {\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} x^{4} + 2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} x^{3} + {\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 32 \, a^{3} c^{7}\right)} x^{2} + 2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} x\right)}}\right]"," ",0,"[-1/12*(15*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^4 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5)*x^4 + 2*(2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 - (b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*e^5)*x^3 + (2*(b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d*e^4 - (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*e^5)*x^2 + 2*(2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^4 - (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e^5)*x)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*(160*a^2*b*c^4*d^3*e^2 - 320*a^3*c^4*d^2*e^3 + 3*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*e^5*x^4 - 2*(b^3*c^4 - 12*a*b*c^5)*d^5 - 20*(a*b^2*c^4 + 4*a^2*c^5)*d^4*e - 10*(3*a^2*b^3*c^2 - 20*a^3*b*c^3)*d*e^4 + (15*a^2*b^4*c - 100*a^3*b^2*c^2 + 128*a^4*c^3)*e^5 + 4*(8*c^7*d^5 - 20*b*c^6*d^4*e + 10*(b^2*c^5 + 4*a*c^6)*d^3*e^2 + 5*(b^3*c^4 - 12*a*b*c^5)*d^2*e^3 - 10*(b^4*c^3 - 7*a*b^2*c^4 + 8*a^2*c^5)*d*e^4 + (5*b^5*c^2 - 37*a*b^3*c^3 + 64*a^2*b*c^4)*e^5)*x^3 + 3*(16*b*c^6*d^5 - 40*b^2*c^5*d^4*e + 20*(b^3*c^4 + 4*a*b*c^5)*d^3*e^2 - 40*(a*b^2*c^4 + 4*a^2*c^5)*d^2*e^3 - 10*(b^5*c^2 - 6*a*b^3*c^3)*d*e^4 + (5*b^6*c - 30*a*b^4*c^2 + 16*a^2*b^2*c^3 + 64*a^3*c^4)*e^5)*x^2 + 6*(40*a*b^2*c^4*d^3*e^2 - 80*a^2*b*c^4*d^2*e^3 + 2*(b^2*c^5 + 4*a*c^6)*d^5 - 5*(b^3*c^4 + 4*a*b*c^5)*d^4*e - 10*(a*b^4*c^2 - 7*a^2*b^2*c^3 + 4*a^3*c^4)*d*e^4 + (5*a*b^5*c - 35*a^2*b^3*c^2 + 52*a^3*b*c^3)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^4 - 8*a^3*b^2*c^5 + 16*a^4*c^6 + (b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*x^4 + 2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*x^3 + (b^6*c^4 - 6*a*b^4*c^5 + 32*a^3*c^7)*x^2 + 2*(a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x), -1/6*(15*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d*e^4 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^4 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^5)*x^4 + 2*(2*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^4 - (b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*e^5)*x^3 + (2*(b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d*e^4 - (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*e^5)*x^2 + 2*(2*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d*e^4 - (a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e^5)*x)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(160*a^2*b*c^4*d^3*e^2 - 320*a^3*c^4*d^2*e^3 + 3*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*e^5*x^4 - 2*(b^3*c^4 - 12*a*b*c^5)*d^5 - 20*(a*b^2*c^4 + 4*a^2*c^5)*d^4*e - 10*(3*a^2*b^3*c^2 - 20*a^3*b*c^3)*d*e^4 + (15*a^2*b^4*c - 100*a^3*b^2*c^2 + 128*a^4*c^3)*e^5 + 4*(8*c^7*d^5 - 20*b*c^6*d^4*e + 10*(b^2*c^5 + 4*a*c^6)*d^3*e^2 + 5*(b^3*c^4 - 12*a*b*c^5)*d^2*e^3 - 10*(b^4*c^3 - 7*a*b^2*c^4 + 8*a^2*c^5)*d*e^4 + (5*b^5*c^2 - 37*a*b^3*c^3 + 64*a^2*b*c^4)*e^5)*x^3 + 3*(16*b*c^6*d^5 - 40*b^2*c^5*d^4*e + 20*(b^3*c^4 + 4*a*b*c^5)*d^3*e^2 - 40*(a*b^2*c^4 + 4*a^2*c^5)*d^2*e^3 - 10*(b^5*c^2 - 6*a*b^3*c^3)*d*e^4 + (5*b^6*c - 30*a*b^4*c^2 + 16*a^2*b^2*c^3 + 64*a^3*c^4)*e^5)*x^2 + 6*(40*a*b^2*c^4*d^3*e^2 - 80*a^2*b*c^4*d^2*e^3 + 2*(b^2*c^5 + 4*a*c^6)*d^5 - 5*(b^3*c^4 + 4*a*b*c^5)*d^4*e - 10*(a*b^4*c^2 - 7*a^2*b^2*c^3 + 4*a^3*c^4)*d*e^4 + (5*a*b^5*c - 35*a^2*b^3*c^2 + 52*a^3*b*c^3)*e^5)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^4 - 8*a^3*b^2*c^5 + 16*a^4*c^6 + (b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*x^4 + 2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*x^3 + (b^6*c^4 - 6*a*b^4*c^5 + 32*a^3*c^7)*x^2 + 2*(a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*x)]","B",0
2392,1,1515,0,1.386291," ","integrate((e*x+d)^4/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{4} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{4} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} e^{4} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{4} x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e^{4}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(48 \, a^{2} b c^{3} d^{2} e^{2} - 64 \, a^{3} c^{3} d e^{3} - {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} d^{4} - 8 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{3} e - {\left(3 \, a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} e^{4} + 4 \, {\left(4 \, c^{6} d^{4} - 8 \, b c^{5} d^{3} e + 3 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d^{2} e^{2} + {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} d e^{3} - {\left(b^{4} c^{2} - 7 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(8 \, b c^{5} d^{4} - 16 \, b^{2} c^{4} d^{3} e + 6 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{2} e^{2} - 8 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d e^{3} - {\left(b^{5} c - 6 \, a b^{3} c^{2}\right)} e^{4}\right)} x^{2} + 6 \, {\left(12 \, a b^{2} c^{3} d^{2} e^{2} - 16 \, a^{2} b c^{3} d e^{3} + {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d^{4} - 2 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{3} e - {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}, -\frac{3 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{4} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{4} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} e^{4} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{4} x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e^{4}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left(48 \, a^{2} b c^{3} d^{2} e^{2} - 64 \, a^{3} c^{3} d e^{3} - {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} d^{4} - 8 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{3} e - {\left(3 \, a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} e^{4} + 4 \, {\left(4 \, c^{6} d^{4} - 8 \, b c^{5} d^{3} e + 3 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d^{2} e^{2} + {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} d e^{3} - {\left(b^{4} c^{2} - 7 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} e^{4}\right)} x^{3} + 3 \, {\left(8 \, b c^{5} d^{4} - 16 \, b^{2} c^{4} d^{3} e + 6 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{2} e^{2} - 8 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d e^{3} - {\left(b^{5} c - 6 \, a b^{3} c^{2}\right)} e^{4}\right)} x^{2} + 6 \, {\left(12 \, a b^{2} c^{3} d^{2} e^{2} - 16 \, a^{2} b c^{3} d e^{3} + {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d^{4} - 2 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{3} e - {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} e^{4}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/6*(3*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^4*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^4*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*e^4*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^4*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e^4)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 - 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(48*a^2*b*c^3*d^2*e^2 - 64*a^3*c^3*d*e^3 - (b^3*c^3 - 12*a*b*c^4)*d^4 - 8*(a*b^2*c^3 + 4*a^2*c^4)*d^3*e - (3*a^2*b^3*c - 20*a^3*b*c^2)*e^4 + 4*(4*c^6*d^4 - 8*b*c^5*d^3*e + 3*(b^2*c^4 + 4*a*c^5)*d^2*e^2 + (b^3*c^3 - 12*a*b*c^4)*d*e^3 - (b^4*c^2 - 7*a*b^2*c^3 + 8*a^2*c^4)*e^4)*x^3 + 3*(8*b*c^5*d^4 - 16*b^2*c^4*d^3*e + 6*(b^3*c^3 + 4*a*b*c^4)*d^2*e^2 - 8*(a*b^2*c^3 + 4*a^2*c^4)*d*e^3 - (b^5*c - 6*a*b^3*c^2)*e^4)*x^2 + 6*(12*a*b^2*c^3*d^2*e^2 - 16*a^2*b*c^3*d*e^3 + (b^2*c^4 + 4*a*c^5)*d^4 - 2*(b^3*c^3 + 4*a*b*c^4)*d^3*e - (a*b^4*c - 7*a^2*b^2*c^2 + 4*a^3*c^3)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x), -1/3*(3*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^4*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^4*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*e^4*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^4*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e^4)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*(48*a^2*b*c^3*d^2*e^2 - 64*a^3*c^3*d*e^3 - (b^3*c^3 - 12*a*b*c^4)*d^4 - 8*(a*b^2*c^3 + 4*a^2*c^4)*d^3*e - (3*a^2*b^3*c - 20*a^3*b*c^2)*e^4 + 4*(4*c^6*d^4 - 8*b*c^5*d^3*e + 3*(b^2*c^4 + 4*a*c^5)*d^2*e^2 + (b^3*c^3 - 12*a*b*c^4)*d*e^3 - (b^4*c^2 - 7*a*b^2*c^3 + 8*a^2*c^4)*e^4)*x^3 + 3*(8*b*c^5*d^4 - 16*b^2*c^4*d^3*e + 6*(b^3*c^3 + 4*a*b*c^4)*d^2*e^2 - 8*(a*b^2*c^3 + 4*a^2*c^4)*d*e^3 - (b^5*c - 6*a*b^3*c^2)*e^4)*x^2 + 6*(12*a*b^2*c^3*d^2*e^2 - 16*a^2*b*c^3*d*e^3 + (b^2*c^4 + 4*a*c^5)*d^4 - 2*(b^3*c^3 + 4*a*b*c^4)*d^3*e - (a*b^4*c - 7*a^2*b^2*c^2 + 4*a^3*c^3)*e^4)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x)]","B",0
2393,1,366,0,1.192536," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(24 \, a^{2} b d e^{2} - 16 \, a^{3} e^{3} - {\left(b^{3} - 12 \, a b c\right)} d^{3} - 6 \, {\left(a b^{2} + 4 \, a^{2} c\right)} d^{2} e + {\left(16 \, c^{3} d^{3} - 24 \, b c^{2} d^{2} e + 6 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d e^{2} + {\left(b^{3} - 12 \, a b c\right)} e^{3}\right)} x^{3} + 3 \, {\left(8 \, b c^{2} d^{3} - 12 \, b^{2} c d^{2} e + 3 \, {\left(b^{3} + 4 \, a b c\right)} d e^{2} - 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e^{3}\right)} x^{2} + 3 \, {\left(12 \, a b^{2} d e^{2} - 8 \, a^{2} b e^{3} + 2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{3} - 3 \, {\left(b^{3} + 4 \, a b c\right)} d^{2} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"2/3*(24*a^2*b*d*e^2 - 16*a^3*e^3 - (b^3 - 12*a*b*c)*d^3 - 6*(a*b^2 + 4*a^2*c)*d^2*e + (16*c^3*d^3 - 24*b*c^2*d^2*e + 6*(b^2*c + 4*a*c^2)*d*e^2 + (b^3 - 12*a*b*c)*e^3)*x^3 + 3*(8*b*c^2*d^3 - 12*b^2*c*d^2*e + 3*(b^3 + 4*a*b*c)*d*e^2 - 2*(a*b^2 + 4*a^2*c)*e^3)*x^2 + 3*(12*a*b^2*d*e^2 - 8*a^2*b*e^3 + 2*(b^2*c + 4*a*c^2)*d^3 - 3*(b^3 + 4*a*b*c)*d^2*e)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
2394,1,305,0,1.178393," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{2} b e^{2} + 2 \, {\left(8 \, c^{3} d^{2} - 8 \, b c^{2} d e + {\left(b^{2} c + 4 \, a c^{2}\right)} e^{2}\right)} x^{3} - {\left(b^{3} - 12 \, a b c\right)} d^{2} - 4 \, {\left(a b^{2} + 4 \, a^{2} c\right)} d e + 3 \, {\left(8 \, b c^{2} d^{2} - 8 \, b^{2} c d e + {\left(b^{3} + 4 \, a b c\right)} e^{2}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} e^{2} + {\left(b^{2} c + 4 \, a c^{2}\right)} d^{2} - {\left(b^{3} + 4 \, a b c\right)} d e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"2/3*(8*a^2*b*e^2 + 2*(8*c^3*d^2 - 8*b*c^2*d*e + (b^2*c + 4*a*c^2)*e^2)*x^3 - (b^3 - 12*a*b*c)*d^2 - 4*(a*b^2 + 4*a^2*c)*d*e + 3*(8*b*c^2*d^2 - 8*b^2*c*d*e + (b^3 + 4*a*b*c)*e^2)*x^2 + 6*(2*a*b^2*e^2 + (b^2*c + 4*a*c^2)*d^2 - (b^3 + 4*a*b*c)*d*e)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
2395,1,247,0,1.093585," ","integrate((e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, {\left(2 \, c^{3} d - b c^{2} e\right)} x^{3} + 12 \, {\left(2 \, b c^{2} d - b^{2} c e\right)} x^{2} - {\left(b^{3} - 12 \, a b c\right)} d - 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e + 3 \, {\left(2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d - {\left(b^{3} + 4 \, a b c\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"2/3*(8*(2*c^3*d - b*c^2*e)*x^3 + 12*(2*b*c^2*d - b^2*c*e)*x^2 - (b^3 - 12*a*b*c)*d - 2*(a*b^2 + 4*a^2*c)*e + 3*(2*(b^2*c + 4*a*c^2)*d - (b^3 + 4*a*b*c)*e)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
2396,1,192,0,0.532504," ","integrate(1/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, c^{3} x^{3} + 24 \, b c^{2} x^{2} - b^{3} + 12 \, a b c + 6 \, {\left(b^{2} c + 4 \, a c^{2}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"2/3*(16*c^3*x^3 + 24*b*c^2*x^2 - b^3 + 12*a*b*c + 6*(b^2*c + 4*a*c^2)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
2397,1,4612,0,2.612956," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{4} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{4} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} e^{4} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{4} x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e^{4}\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} - 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) - 4 \, {\left({\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} d^{5} - {\left(3 \, b^{4} c^{2} - 34 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{4} e + {\left(3 \, b^{5} c - 27 \, a b^{3} c^{2} - 20 \, a^{2} b c^{3}\right)} d^{3} e^{2} - {\left(b^{6} - 66 \, a^{2} b^{2} c^{2} + 40 \, a^{3} c^{3}\right)} d^{2} e^{3} + {\left(5 \, a b^{5} - 34 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d e^{4} - 4 \, {\left(a^{2} b^{4} - 7 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} e^{5} - {\left(16 \, c^{6} d^{5} - 40 \, b c^{5} d^{4} e + 2 \, {\left(13 \, b^{2} c^{4} + 28 \, a c^{5}\right)} d^{3} e^{2} + {\left(b^{3} c^{3} - 84 \, a b c^{4}\right)} d^{2} e^{3} - {\left(3 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} - 40 \, a^{2} c^{4}\right)} d e^{4} + {\left(3 \, a b^{3} c^{2} - 20 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{3} - 3 \, {\left(8 \, b c^{5} d^{5} - 20 \, b^{2} c^{4} d^{4} e + {\left(13 \, b^{3} c^{3} + 28 \, a b c^{4}\right)} d^{3} e^{2} + {\left(b^{4} c^{2} - 46 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{3} - {\left(2 \, b^{5} c - 15 \, a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d e^{4} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} e^{5}\right)} x^{2} - 3 \, {\left(2 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d^{5} - 5 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{4} e + {\left(3 \, b^{4} c^{2} + 22 \, a b^{2} c^{3} + 24 \, a^{2} c^{4}\right)} d^{3} e^{2} + {\left(b^{5} c - 17 \, a b^{3} c^{2} - 28 \, a^{2} b c^{3}\right)} d^{2} e^{3} - {\left(b^{6} - 6 \, a b^{4} c - 8 \, a^{2} b^{2} c^{2} - 16 \, a^{3} c^{3}\right)} d e^{4} + {\left(a b^{5} - 6 \, a^{2} b^{3} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left({\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{6} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{5} e + 3 \, {\left(a^{2} b^{6} c - 7 \, a^{3} b^{4} c^{2} + 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} e^{2} - {\left(a^{2} b^{7} - 2 \, a^{3} b^{5} c - 32 \, a^{4} b^{3} c^{2} + 96 \, a^{5} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} b^{6} - 7 \, a^{4} b^{4} c + 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d e^{5} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{6} + {\left({\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{6} - 3 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{5} e + 3 \, {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{4} e^{2} - {\left(b^{7} c^{2} - 2 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 96 \, a^{3} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(a b^{6} c^{2} - 7 \, a^{2} b^{4} c^{3} + 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d e^{5} + {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{6}\right)} x^{4} + 2 \, {\left({\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{6} - 3 \, {\left(b^{6} c^{3} - 8 \, a b^{4} c^{4} + 16 \, a^{2} b^{2} c^{5}\right)} d^{5} e + 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{4} e^{2} - {\left(b^{8} c - 2 \, a b^{6} c^{2} - 32 \, a^{2} b^{4} c^{3} + 96 \, a^{3} b^{2} c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{6} c - 8 \, a^{3} b^{4} c^{2} + 16 \, a^{4} b^{2} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} e^{6}\right)} x^{3} + {\left({\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} d^{6} - 3 \, {\left(b^{7} c^{2} - 6 \, a b^{5} c^{3} + 32 \, a^{3} b c^{5}\right)} d^{5} e + 3 \, {\left(b^{8} c - 5 \, a b^{6} c^{2} - 6 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} + 32 \, a^{4} c^{5}\right)} d^{4} e^{2} - {\left(b^{9} - 36 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} + 192 \, a^{4} b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{8} - 5 \, a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{4} b^{2} c^{3} + 32 \, a^{5} c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{7} - 6 \, a^{3} b^{5} c + 32 \, a^{5} b c^{3}\right)} d e^{5} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{6} - 3 \, {\left(a b^{6} c^{2} - 8 \, a^{2} b^{4} c^{3} + 16 \, a^{3} b^{2} c^{4}\right)} d^{5} e + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{4} e^{2} - {\left(a b^{8} - 2 \, a^{2} b^{6} c - 32 \, a^{3} b^{4} c^{2} + 96 \, a^{4} b^{2} c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{2} b^{7} - 7 \, a^{3} b^{5} c + 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{3} b^{6} - 8 \, a^{4} b^{4} c + 16 \, a^{5} b^{2} c^{2}\right)} d e^{5} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} e^{6}\right)} x\right)}}, \frac{3 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{4} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e^{4} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} e^{4} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} e^{4} x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} e^{4}\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left({\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} d^{5} - {\left(3 \, b^{4} c^{2} - 34 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{4} e + {\left(3 \, b^{5} c - 27 \, a b^{3} c^{2} - 20 \, a^{2} b c^{3}\right)} d^{3} e^{2} - {\left(b^{6} - 66 \, a^{2} b^{2} c^{2} + 40 \, a^{3} c^{3}\right)} d^{2} e^{3} + {\left(5 \, a b^{5} - 34 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d e^{4} - 4 \, {\left(a^{2} b^{4} - 7 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} e^{5} - {\left(16 \, c^{6} d^{5} - 40 \, b c^{5} d^{4} e + 2 \, {\left(13 \, b^{2} c^{4} + 28 \, a c^{5}\right)} d^{3} e^{2} + {\left(b^{3} c^{3} - 84 \, a b c^{4}\right)} d^{2} e^{3} - {\left(3 \, b^{4} c^{2} - 22 \, a b^{2} c^{3} - 40 \, a^{2} c^{4}\right)} d e^{4} + {\left(3 \, a b^{3} c^{2} - 20 \, a^{2} b c^{3}\right)} e^{5}\right)} x^{3} - 3 \, {\left(8 \, b c^{5} d^{5} - 20 \, b^{2} c^{4} d^{4} e + {\left(13 \, b^{3} c^{3} + 28 \, a b c^{4}\right)} d^{3} e^{2} + {\left(b^{4} c^{2} - 46 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{2} e^{3} - {\left(2 \, b^{5} c - 15 \, a b^{3} c^{2} - 12 \, a^{2} b c^{3}\right)} d e^{4} + 2 \, {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} e^{5}\right)} x^{2} - 3 \, {\left(2 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d^{5} - 5 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{4} e + {\left(3 \, b^{4} c^{2} + 22 \, a b^{2} c^{3} + 24 \, a^{2} c^{4}\right)} d^{3} e^{2} + {\left(b^{5} c - 17 \, a b^{3} c^{2} - 28 \, a^{2} b c^{3}\right)} d^{2} e^{3} - {\left(b^{6} - 6 \, a b^{4} c - 8 \, a^{2} b^{2} c^{2} - 16 \, a^{3} c^{3}\right)} d e^{4} + {\left(a b^{5} - 6 \, a^{2} b^{3} c\right)} e^{5}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left({\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{6} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{5} e + 3 \, {\left(a^{2} b^{6} c - 7 \, a^{3} b^{4} c^{2} + 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} d^{4} e^{2} - {\left(a^{2} b^{7} - 2 \, a^{3} b^{5} c - 32 \, a^{4} b^{3} c^{2} + 96 \, a^{5} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} b^{6} - 7 \, a^{4} b^{4} c + 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d e^{5} + {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{6} + {\left({\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{6} - 3 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{5} e + 3 \, {\left(b^{6} c^{3} - 7 \, a b^{4} c^{4} + 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{4} e^{2} - {\left(b^{7} c^{2} - 2 \, a b^{5} c^{3} - 32 \, a^{2} b^{3} c^{4} + 96 \, a^{3} b c^{5}\right)} d^{3} e^{3} + 3 \, {\left(a b^{6} c^{2} - 7 \, a^{2} b^{4} c^{3} + 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d e^{5} + {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{6}\right)} x^{4} + 2 \, {\left({\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} d^{6} - 3 \, {\left(b^{6} c^{3} - 8 \, a b^{4} c^{4} + 16 \, a^{2} b^{2} c^{5}\right)} d^{5} e + 3 \, {\left(b^{7} c^{2} - 7 \, a b^{5} c^{3} + 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{4} e^{2} - {\left(b^{8} c - 2 \, a b^{6} c^{2} - 32 \, a^{2} b^{4} c^{3} + 96 \, a^{3} b^{2} c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{6} c - 8 \, a^{3} b^{4} c^{2} + 16 \, a^{4} b^{2} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} e^{6}\right)} x^{3} + {\left({\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} d^{6} - 3 \, {\left(b^{7} c^{2} - 6 \, a b^{5} c^{3} + 32 \, a^{3} b c^{5}\right)} d^{5} e + 3 \, {\left(b^{8} c - 5 \, a b^{6} c^{2} - 6 \, a^{2} b^{4} c^{3} + 32 \, a^{3} b^{2} c^{4} + 32 \, a^{4} c^{5}\right)} d^{4} e^{2} - {\left(b^{9} - 36 \, a^{2} b^{5} c^{2} + 32 \, a^{3} b^{3} c^{3} + 192 \, a^{4} b c^{4}\right)} d^{3} e^{3} + 3 \, {\left(a b^{8} - 5 \, a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{4} b^{2} c^{3} + 32 \, a^{5} c^{4}\right)} d^{2} e^{4} - 3 \, {\left(a^{2} b^{7} - 6 \, a^{3} b^{5} c + 32 \, a^{5} b c^{3}\right)} d e^{5} + {\left(a^{3} b^{6} - 6 \, a^{4} b^{4} c + 32 \, a^{6} c^{3}\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{6} - 3 \, {\left(a b^{6} c^{2} - 8 \, a^{2} b^{4} c^{3} + 16 \, a^{3} b^{2} c^{4}\right)} d^{5} e + 3 \, {\left(a b^{7} c - 7 \, a^{2} b^{5} c^{2} + 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{4} e^{2} - {\left(a b^{8} - 2 \, a^{2} b^{6} c - 32 \, a^{3} b^{4} c^{2} + 96 \, a^{4} b^{2} c^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{2} b^{7} - 7 \, a^{3} b^{5} c + 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{2} e^{4} - 3 \, {\left(a^{3} b^{6} - 8 \, a^{4} b^{4} c + 16 \, a^{5} b^{2} c^{2}\right)} d e^{5} + {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} e^{6}\right)} x\right)}}\right]"," ",0,"[1/6*(3*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^4*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^4*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*e^4*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^4*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e^4)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 - 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) - 4*((b^3*c^3 - 12*a*b*c^4)*d^5 - (3*b^4*c^2 - 34*a*b^2*c^3 + 8*a^2*c^4)*d^4*e + (3*b^5*c - 27*a*b^3*c^2 - 20*a^2*b*c^3)*d^3*e^2 - (b^6 - 66*a^2*b^2*c^2 + 40*a^3*c^3)*d^2*e^3 + (5*a*b^5 - 34*a^2*b^3*c + 16*a^3*b*c^2)*d*e^4 - 4*(a^2*b^4 - 7*a^3*b^2*c + 8*a^4*c^2)*e^5 - (16*c^6*d^5 - 40*b*c^5*d^4*e + 2*(13*b^2*c^4 + 28*a*c^5)*d^3*e^2 + (b^3*c^3 - 84*a*b*c^4)*d^2*e^3 - (3*b^4*c^2 - 22*a*b^2*c^3 - 40*a^2*c^4)*d*e^4 + (3*a*b^3*c^2 - 20*a^2*b*c^3)*e^5)*x^3 - 3*(8*b*c^5*d^5 - 20*b^2*c^4*d^4*e + (13*b^3*c^3 + 28*a*b*c^4)*d^3*e^2 + (b^4*c^2 - 46*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^3 - (2*b^5*c - 15*a*b^3*c^2 - 12*a^2*b*c^3)*d*e^4 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 4*a^3*c^3)*e^5)*x^2 - 3*(2*(b^2*c^4 + 4*a*c^5)*d^5 - 5*(b^3*c^3 + 4*a*b*c^4)*d^4*e + (3*b^4*c^2 + 22*a*b^2*c^3 + 24*a^2*c^4)*d^3*e^2 + (b^5*c - 17*a*b^3*c^2 - 28*a^2*b*c^3)*d^2*e^3 - (b^6 - 6*a*b^4*c - 8*a^2*b^2*c^2 - 16*a^3*c^3)*d*e^4 + (a*b^5 - 6*a^2*b^3*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^6 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^5*e + 3*(a^2*b^6*c - 7*a^3*b^4*c^2 + 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4*e^2 - (a^2*b^7 - 2*a^3*b^5*c - 32*a^4*b^3*c^2 + 96*a^5*b*c^3)*d^3*e^3 + 3*(a^3*b^6 - 7*a^4*b^4*c + 8*a^5*b^2*c^2 + 16*a^6*c^3)*d^2*e^4 - 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d*e^5 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^6 + ((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^6 - 3*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^5*e + 3*(b^6*c^3 - 7*a*b^4*c^4 + 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^4*e^2 - (b^7*c^2 - 2*a*b^5*c^3 - 32*a^2*b^3*c^4 + 96*a^3*b*c^5)*d^3*e^3 + 3*(a*b^6*c^2 - 7*a^2*b^4*c^3 + 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^2*e^4 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d*e^5 + (a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^6)*x^4 + 2*((b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^6 - 3*(b^6*c^3 - 8*a*b^4*c^4 + 16*a^2*b^2*c^5)*d^5*e + 3*(b^7*c^2 - 7*a*b^5*c^3 + 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^4*e^2 - (b^8*c - 2*a*b^6*c^2 - 32*a^2*b^4*c^3 + 96*a^3*b^2*c^4)*d^3*e^3 + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^2*e^4 - 3*(a^2*b^6*c - 8*a^3*b^4*c^2 + 16*a^4*b^2*c^3)*d*e^5 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*e^6)*x^3 + ((b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*d^6 - 3*(b^7*c^2 - 6*a*b^5*c^3 + 32*a^3*b*c^5)*d^5*e + 3*(b^8*c - 5*a*b^6*c^2 - 6*a^2*b^4*c^3 + 32*a^3*b^2*c^4 + 32*a^4*c^5)*d^4*e^2 - (b^9 - 36*a^2*b^5*c^2 + 32*a^3*b^3*c^3 + 192*a^4*b*c^4)*d^3*e^3 + 3*(a*b^8 - 5*a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^4*b^2*c^3 + 32*a^5*c^4)*d^2*e^4 - 3*(a^2*b^7 - 6*a^3*b^5*c + 32*a^5*b*c^3)*d*e^5 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*e^6)*x^2 + 2*((a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^6 - 3*(a*b^6*c^2 - 8*a^2*b^4*c^3 + 16*a^3*b^2*c^4)*d^5*e + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^4*e^2 - (a*b^8 - 2*a^2*b^6*c - 32*a^3*b^4*c^2 + 96*a^4*b^2*c^3)*d^3*e^3 + 3*(a^2*b^7 - 7*a^3*b^5*c + 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2*e^4 - 3*(a^3*b^6 - 8*a^4*b^4*c + 16*a^5*b^2*c^2)*d*e^5 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*e^6)*x), 1/3*(3*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*e^4*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e^4*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*e^4*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*e^4*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*e^4)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*((b^3*c^3 - 12*a*b*c^4)*d^5 - (3*b^4*c^2 - 34*a*b^2*c^3 + 8*a^2*c^4)*d^4*e + (3*b^5*c - 27*a*b^3*c^2 - 20*a^2*b*c^3)*d^3*e^2 - (b^6 - 66*a^2*b^2*c^2 + 40*a^3*c^3)*d^2*e^3 + (5*a*b^5 - 34*a^2*b^3*c + 16*a^3*b*c^2)*d*e^4 - 4*(a^2*b^4 - 7*a^3*b^2*c + 8*a^4*c^2)*e^5 - (16*c^6*d^5 - 40*b*c^5*d^4*e + 2*(13*b^2*c^4 + 28*a*c^5)*d^3*e^2 + (b^3*c^3 - 84*a*b*c^4)*d^2*e^3 - (3*b^4*c^2 - 22*a*b^2*c^3 - 40*a^2*c^4)*d*e^4 + (3*a*b^3*c^2 - 20*a^2*b*c^3)*e^5)*x^3 - 3*(8*b*c^5*d^5 - 20*b^2*c^4*d^4*e + (13*b^3*c^3 + 28*a*b*c^4)*d^3*e^2 + (b^4*c^2 - 46*a*b^2*c^3 + 8*a^2*c^4)*d^2*e^3 - (2*b^5*c - 15*a*b^3*c^2 - 12*a^2*b*c^3)*d*e^4 + 2*(a*b^4*c - 7*a^2*b^2*c^2 + 4*a^3*c^3)*e^5)*x^2 - 3*(2*(b^2*c^4 + 4*a*c^5)*d^5 - 5*(b^3*c^3 + 4*a*b*c^4)*d^4*e + (3*b^4*c^2 + 22*a*b^2*c^3 + 24*a^2*c^4)*d^3*e^2 + (b^5*c - 17*a*b^3*c^2 - 28*a^2*b*c^3)*d^2*e^3 - (b^6 - 6*a*b^4*c - 8*a^2*b^2*c^2 - 16*a^3*c^3)*d*e^4 + (a*b^5 - 6*a^2*b^3*c)*e^5)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^6 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^5*e + 3*(a^2*b^6*c - 7*a^3*b^4*c^2 + 8*a^4*b^2*c^3 + 16*a^5*c^4)*d^4*e^2 - (a^2*b^7 - 2*a^3*b^5*c - 32*a^4*b^3*c^2 + 96*a^5*b*c^3)*d^3*e^3 + 3*(a^3*b^6 - 7*a^4*b^4*c + 8*a^5*b^2*c^2 + 16*a^6*c^3)*d^2*e^4 - 3*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d*e^5 + (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^6 + ((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^6 - 3*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^5*e + 3*(b^6*c^3 - 7*a*b^4*c^4 + 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^4*e^2 - (b^7*c^2 - 2*a*b^5*c^3 - 32*a^2*b^3*c^4 + 96*a^3*b*c^5)*d^3*e^3 + 3*(a*b^6*c^2 - 7*a^2*b^4*c^3 + 8*a^3*b^2*c^4 + 16*a^4*c^5)*d^2*e^4 - 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d*e^5 + (a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^6)*x^4 + 2*((b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*d^6 - 3*(b^6*c^3 - 8*a*b^4*c^4 + 16*a^2*b^2*c^5)*d^5*e + 3*(b^7*c^2 - 7*a*b^5*c^3 + 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^4*e^2 - (b^8*c - 2*a*b^6*c^2 - 32*a^2*b^4*c^3 + 96*a^3*b^2*c^4)*d^3*e^3 + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^2*e^4 - 3*(a^2*b^6*c - 8*a^3*b^4*c^2 + 16*a^4*b^2*c^3)*d*e^5 + (a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*e^6)*x^3 + ((b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*d^6 - 3*(b^7*c^2 - 6*a*b^5*c^3 + 32*a^3*b*c^5)*d^5*e + 3*(b^8*c - 5*a*b^6*c^2 - 6*a^2*b^4*c^3 + 32*a^3*b^2*c^4 + 32*a^4*c^5)*d^4*e^2 - (b^9 - 36*a^2*b^5*c^2 + 32*a^3*b^3*c^3 + 192*a^4*b*c^4)*d^3*e^3 + 3*(a*b^8 - 5*a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^4*b^2*c^3 + 32*a^5*c^4)*d^2*e^4 - 3*(a^2*b^7 - 6*a^3*b^5*c + 32*a^5*b*c^3)*d*e^5 + (a^3*b^6 - 6*a^4*b^4*c + 32*a^6*c^3)*e^6)*x^2 + 2*((a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^6 - 3*(a*b^6*c^2 - 8*a^2*b^4*c^3 + 16*a^3*b^2*c^4)*d^5*e + 3*(a*b^7*c - 7*a^2*b^5*c^2 + 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^4*e^2 - (a*b^8 - 2*a^2*b^6*c - 32*a^3*b^4*c^2 + 96*a^4*b^2*c^3)*d^3*e^3 + 3*(a^2*b^7 - 7*a^3*b^5*c + 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^2*e^4 - 3*(a^3*b^6 - 8*a^4*b^4*c + 16*a^5*b^2*c^2)*d*e^5 + (a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*e^6)*x)]","B",0
2398,1,8874,0,8.883442," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2} e^{4} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{5} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{6}\right)} x^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{2} e^{4} + 3 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{5} - 2 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} e^{6}\right)} x^{4} + {\left(4 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{4} + 4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{5} - {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} e^{6}\right)} x^{3} + {\left(2 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d^{2} e^{4} - {\left(b^{7} - 10 \, a b^{5} c + 32 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} d e^{5} - 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e^{6}\right)} x^{2} + {\left(4 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2} e^{4} - 2 \, {\left(a b^{6} - 9 \, a^{2} b^{4} c + 24 \, a^{3} b^{2} c^{2} - 16 \, a^{4} c^{3}\right)} d e^{5} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{6}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(2 \, {\left(b^{3} c^{4} - 12 \, a b c^{5}\right)} d^{7} - 8 \, {\left(b^{4} c^{3} - 11 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{6} e + 4 \, {\left(3 \, b^{5} c^{2} - 26 \, a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{5} e^{2} - 8 \, {\left(b^{6} c - 3 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} + 32 \, a^{3} c^{4}\right)} d^{4} e^{3} + 2 \, {\left(b^{7} + 16 \, a b^{5} c - 155 \, a^{2} b^{3} c^{2} + 180 \, a^{3} b c^{3}\right)} d^{3} e^{4} - {\left(16 \, a b^{6} - 91 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2} + 176 \, a^{4} c^{3}\right)} d^{2} e^{5} + {\left(11 \, a^{2} b^{5} - 76 \, a^{3} b^{3} c + 112 \, a^{4} b c^{2}\right)} d e^{6} + 3 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} e^{7} - {\left(32 \, c^{7} d^{6} e - 96 \, b c^{6} d^{5} e^{2} + 4 \, {\left(19 \, b^{2} c^{5} + 44 \, a c^{6}\right)} d^{4} e^{3} + 8 \, {\left(b^{3} c^{4} - 44 \, a b c^{5}\right)} d^{3} e^{4} - {\left(35 \, b^{4} c^{3} - 256 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{2} e^{5} + {\left(15 \, b^{5} c^{2} - 80 \, a b^{3} c^{3} - 16 \, a^{2} b c^{4}\right)} d e^{6} - {\left(15 \, a b^{4} c^{2} - 100 \, a^{2} b^{2} c^{3} + 128 \, a^{3} c^{4}\right)} e^{7}\right)} x^{4} - 2 \, {\left(16 \, c^{7} d^{7} - 24 \, b c^{6} d^{6} e - 2 \, {\left(17 \, b^{2} c^{5} - 44 \, a c^{6}\right)} d^{5} e^{2} + {\left(61 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} d^{4} e^{3} - 4 \, {\left(b^{4} c^{3} + 49 \, a b^{2} c^{4} - 32 \, a^{2} c^{5}\right)} d^{3} e^{4} - 2 \, {\left(15 \, b^{5} c^{2} - 121 \, a b^{3} c^{3} + 88 \, a^{2} b c^{4}\right)} d^{2} e^{5} + {\left(15 \, b^{6} c - 90 \, a b^{4} c^{2} + 38 \, a^{2} b^{2} c^{3} + 56 \, a^{3} c^{4}\right)} d e^{6} - 3 \, {\left(5 \, a b^{5} c - 35 \, a^{2} b^{3} c^{2} + 52 \, a^{3} b c^{3}\right)} e^{7}\right)} x^{3} - 3 \, {\left(16 \, b c^{6} d^{7} - 4 \, {\left(11 \, b^{2} c^{5} - 4 \, a c^{6}\right)} d^{6} e + 2 \, {\left(13 \, b^{3} c^{4} + 20 \, a b c^{5}\right)} d^{5} e^{2} + 8 \, {\left(2 \, b^{4} c^{3} - 17 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} e^{3} - 2 \, {\left(7 \, b^{5} c^{2} - 34 \, a b^{3} c^{3} + 64 \, a^{2} b c^{4}\right)} d^{3} e^{4} - {\left(5 \, b^{6} c - 42 \, a b^{4} c^{2} + 28 \, a^{2} b^{2} c^{3} - 48 \, a^{3} c^{4}\right)} d^{2} e^{5} + {\left(5 \, b^{7} - 30 \, a b^{5} c + 18 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} d e^{6} - {\left(5 \, a b^{6} - 30 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2} + 64 \, a^{4} c^{3}\right)} e^{7}\right)} x^{2} - 2 \, {\left(6 \, {\left(b^{2} c^{5} + 4 \, a c^{6}\right)} d^{7} - {\left(19 \, b^{3} c^{4} + 60 \, a b c^{5}\right)} d^{6} e + 16 \, {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} + 7 \, a^{2} c^{5}\right)} d^{5} e^{2} + 2 \, {\left(3 \, b^{5} c^{2} - 46 \, a b^{3} c^{3} - 44 \, a^{2} b c^{4}\right)} d^{4} e^{3} - 2 \, {\left(7 \, b^{6} c - 51 \, a b^{4} c^{2} + 61 \, a^{2} b^{2} c^{3} - 76 \, a^{3} c^{4}\right)} d^{3} e^{4} + {\left(5 \, b^{7} - 43 \, a b^{5} c + 125 \, a^{2} b^{3} c^{2} - 156 \, a^{3} b c^{3}\right)} d^{2} e^{5} + {\left(5 \, a b^{6} - 32 \, a^{2} b^{4} c + 20 \, a^{3} b^{2} c^{2} + 64 \, a^{4} c^{3}\right)} d e^{6} - 2 \, {\left(5 \, a^{2} b^{5} - 37 \, a^{3} b^{3} c + 64 \, a^{4} b c^{2}\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{12 \, {\left({\left(a^{2} b^{4} c^{4} - 8 \, a^{3} b^{2} c^{5} + 16 \, a^{4} c^{6}\right)} d^{9} - 4 \, {\left(a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5}\right)} d^{8} e + 2 \, {\left(3 \, a^{2} b^{6} c^{2} - 22 \, a^{3} b^{4} c^{3} + 32 \, a^{4} b^{2} c^{4} + 32 \, a^{5} c^{5}\right)} d^{7} e^{2} - 4 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} - 8 \, a^{4} b^{3} c^{3} + 48 \, a^{5} b c^{4}\right)} d^{6} e^{3} + {\left(a^{2} b^{8} + 4 \, a^{3} b^{6} c - 74 \, a^{4} b^{4} c^{2} + 144 \, a^{5} b^{2} c^{3} + 96 \, a^{6} c^{4}\right)} d^{5} e^{4} - 4 \, {\left(a^{3} b^{7} - 5 \, a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 48 \, a^{6} b c^{3}\right)} d^{4} e^{5} + 2 \, {\left(3 \, a^{4} b^{6} - 22 \, a^{5} b^{4} c + 32 \, a^{6} b^{2} c^{2} + 32 \, a^{7} c^{3}\right)} d^{3} e^{6} - 4 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} d^{2} e^{7} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} d e^{8} + {\left({\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{8} e - 4 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{7} e^{2} + 2 \, {\left(3 \, b^{6} c^{4} - 22 \, a b^{4} c^{5} + 32 \, a^{2} b^{2} c^{6} + 32 \, a^{3} c^{7}\right)} d^{6} e^{3} - 4 \, {\left(b^{7} c^{3} - 5 \, a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 48 \, a^{3} b c^{6}\right)} d^{5} e^{4} + {\left(b^{8} c^{2} + 4 \, a b^{6} c^{3} - 74 \, a^{2} b^{4} c^{4} + 144 \, a^{3} b^{2} c^{5} + 96 \, a^{4} c^{6}\right)} d^{4} e^{5} - 4 \, {\left(a b^{7} c^{2} - 5 \, a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} + 48 \, a^{4} b c^{5}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{6} c^{2} - 22 \, a^{3} b^{4} c^{3} + 32 \, a^{4} b^{2} c^{4} + 32 \, a^{5} c^{5}\right)} d^{2} e^{7} - 4 \, {\left(a^{3} b^{5} c^{2} - 8 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4}\right)} d e^{8} + {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)} e^{9}\right)} x^{5} + {\left({\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{9} - 2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{8} e - 2 \, {\left(b^{6} c^{4} - 10 \, a b^{4} c^{5} + 32 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{7} e^{2} + 4 \, {\left(2 \, b^{7} c^{3} - 17 \, a b^{5} c^{4} + 40 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{6} e^{3} - {\left(7 \, b^{8} c^{2} - 44 \, a b^{6} c^{3} + 10 \, a^{2} b^{4} c^{4} + 240 \, a^{3} b^{2} c^{5} - 96 \, a^{4} c^{6}\right)} d^{5} e^{4} + 2 \, {\left(b^{9} c + 2 \, a b^{7} c^{2} - 64 \, a^{2} b^{5} c^{3} + 160 \, a^{3} b^{3} c^{4}\right)} d^{4} e^{5} - 2 \, {\left(4 \, a b^{8} c - 23 \, a^{2} b^{6} c^{2} - 10 \, a^{3} b^{4} c^{3} + 160 \, a^{4} b^{2} c^{4} - 32 \, a^{5} c^{5}\right)} d^{3} e^{6} + 4 \, {\left(3 \, a^{2} b^{7} c - 23 \, a^{3} b^{5} c^{2} + 40 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4}\right)} d^{2} e^{7} - {\left(8 \, a^{3} b^{6} c - 65 \, a^{4} b^{4} c^{2} + 136 \, a^{5} b^{2} c^{3} - 16 \, a^{6} c^{4}\right)} d e^{8} + 2 \, {\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)} e^{9}\right)} x^{4} + {\left(2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{9} - {\left(7 \, b^{6} c^{4} - 58 \, a b^{4} c^{5} + 128 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{8} e + 8 \, {\left(b^{7} c^{3} - 8 \, a b^{5} c^{4} + 16 \, a^{2} b^{3} c^{5}\right)} d^{7} e^{2} - 2 \, {\left(b^{8} c^{2} - 4 \, a b^{6} c^{3} - 20 \, a^{2} b^{4} c^{4} + 96 \, a^{3} b^{2} c^{5} - 64 \, a^{4} c^{6}\right)} d^{6} e^{3} - 2 \, {\left(b^{9} c - 10 \, a b^{7} c^{2} + 38 \, a^{2} b^{5} c^{3} - 80 \, a^{3} b^{3} c^{4} + 96 \, a^{4} b c^{5}\right)} d^{5} e^{4} + {\left(b^{10} - 2 \, a b^{8} c - 26 \, a^{2} b^{6} c^{2} + 60 \, a^{3} b^{4} c^{3} + 192 \, a^{5} c^{5}\right)} d^{4} e^{5} - 4 \, {\left(a b^{9} - 6 \, a^{2} b^{7} c + 4 \, a^{3} b^{5} c^{2} + 64 \, a^{5} b c^{4}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{8} - 20 \, a^{3} b^{6} c + 20 \, a^{4} b^{4} c^{2} + 32 \, a^{5} b^{2} c^{3} + 64 \, a^{6} c^{4}\right)} d^{2} e^{7} - 2 \, {\left(2 \, a^{3} b^{7} - 13 \, a^{4} b^{5} c + 8 \, a^{5} b^{3} c^{2} + 48 \, a^{6} b c^{3}\right)} d e^{8} + {\left(a^{4} b^{6} - 6 \, a^{5} b^{4} c + 32 \, a^{7} c^{3}\right)} e^{9}\right)} x^{3} + {\left({\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 32 \, a^{3} c^{7}\right)} d^{9} - 2 \, {\left(2 \, b^{7} c^{3} - 13 \, a b^{5} c^{4} + 8 \, a^{2} b^{3} c^{5} + 48 \, a^{3} b c^{6}\right)} d^{8} e + 2 \, {\left(3 \, b^{8} c^{2} - 20 \, a b^{6} c^{3} + 20 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} + 64 \, a^{4} c^{6}\right)} d^{7} e^{2} - 4 \, {\left(b^{9} c - 6 \, a b^{7} c^{2} + 4 \, a^{2} b^{5} c^{3} + 64 \, a^{4} b c^{5}\right)} d^{6} e^{3} + {\left(b^{10} - 2 \, a b^{8} c - 26 \, a^{2} b^{6} c^{2} + 60 \, a^{3} b^{4} c^{3} + 192 \, a^{5} c^{5}\right)} d^{5} e^{4} - 2 \, {\left(a b^{9} - 10 \, a^{2} b^{7} c + 38 \, a^{3} b^{5} c^{2} - 80 \, a^{4} b^{3} c^{3} + 96 \, a^{5} b c^{4}\right)} d^{4} e^{5} - 2 \, {\left(a^{2} b^{8} - 4 \, a^{3} b^{6} c - 20 \, a^{4} b^{4} c^{2} + 96 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} d^{3} e^{6} + 8 \, {\left(a^{3} b^{7} - 8 \, a^{4} b^{5} c + 16 \, a^{5} b^{3} c^{2}\right)} d^{2} e^{7} - {\left(7 \, a^{4} b^{6} - 58 \, a^{5} b^{4} c + 128 \, a^{6} b^{2} c^{2} - 32 \, a^{7} c^{3}\right)} d e^{8} + 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} e^{9}\right)} x^{2} + {\left(2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} d^{9} - {\left(8 \, a b^{6} c^{3} - 65 \, a^{2} b^{4} c^{4} + 136 \, a^{3} b^{2} c^{5} - 16 \, a^{4} c^{6}\right)} d^{8} e + 4 \, {\left(3 \, a b^{7} c^{2} - 23 \, a^{2} b^{5} c^{3} + 40 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5}\right)} d^{7} e^{2} - 2 \, {\left(4 \, a b^{8} c - 23 \, a^{2} b^{6} c^{2} - 10 \, a^{3} b^{4} c^{3} + 160 \, a^{4} b^{2} c^{4} - 32 \, a^{5} c^{5}\right)} d^{6} e^{3} + 2 \, {\left(a b^{9} + 2 \, a^{2} b^{7} c - 64 \, a^{3} b^{5} c^{2} + 160 \, a^{4} b^{3} c^{3}\right)} d^{5} e^{4} - {\left(7 \, a^{2} b^{8} - 44 \, a^{3} b^{6} c + 10 \, a^{4} b^{4} c^{2} + 240 \, a^{5} b^{2} c^{3} - 96 \, a^{6} c^{4}\right)} d^{4} e^{5} + 4 \, {\left(2 \, a^{3} b^{7} - 17 \, a^{4} b^{5} c + 40 \, a^{5} b^{3} c^{2} - 16 \, a^{6} b c^{3}\right)} d^{3} e^{6} - 2 \, {\left(a^{4} b^{6} - 10 \, a^{5} b^{4} c + 32 \, a^{6} b^{2} c^{2} - 32 \, a^{7} c^{3}\right)} d^{2} e^{7} - 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} d e^{8} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} e^{9}\right)} x\right)}}, \frac{15 \, {\left(2 \, {\left(a^{2} b^{4} c - 8 \, a^{3} b^{2} c^{2} + 16 \, a^{4} c^{3}\right)} d^{2} e^{4} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} d e^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d e^{5} - {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{6}\right)} x^{5} + {\left(2 \, {\left(b^{4} c^{3} - 8 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{2} e^{4} + 3 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d e^{5} - 2 \, {\left(b^{6} c - 8 \, a b^{4} c^{2} + 16 \, a^{2} b^{2} c^{3}\right)} e^{6}\right)} x^{4} + {\left(4 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{2} e^{4} + 4 \, {\left(a b^{4} c^{2} - 8 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d e^{5} - {\left(b^{7} - 6 \, a b^{5} c + 32 \, a^{3} b c^{3}\right)} e^{6}\right)} x^{3} + {\left(2 \, {\left(b^{6} c - 6 \, a b^{4} c^{2} + 32 \, a^{3} c^{4}\right)} d^{2} e^{4} - {\left(b^{7} - 10 \, a b^{5} c + 32 \, a^{2} b^{3} c^{2} - 32 \, a^{3} b c^{3}\right)} d e^{5} - 2 \, {\left(a b^{6} - 8 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} e^{6}\right)} x^{2} + {\left(4 \, {\left(a b^{5} c - 8 \, a^{2} b^{3} c^{2} + 16 \, a^{3} b c^{3}\right)} d^{2} e^{4} - 2 \, {\left(a b^{6} - 9 \, a^{2} b^{4} c + 24 \, a^{3} b^{2} c^{2} - 16 \, a^{4} c^{3}\right)} d e^{5} - {\left(a^{2} b^{5} - 8 \, a^{3} b^{3} c + 16 \, a^{4} b c^{2}\right)} e^{6}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(2 \, {\left(b^{3} c^{4} - 12 \, a b c^{5}\right)} d^{7} - 8 \, {\left(b^{4} c^{3} - 11 \, a b^{2} c^{4} + 4 \, a^{2} c^{5}\right)} d^{6} e + 4 \, {\left(3 \, b^{5} c^{2} - 26 \, a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{5} e^{2} - 8 \, {\left(b^{6} c - 3 \, a b^{4} c^{2} - 32 \, a^{2} b^{2} c^{3} + 32 \, a^{3} c^{4}\right)} d^{4} e^{3} + 2 \, {\left(b^{7} + 16 \, a b^{5} c - 155 \, a^{2} b^{3} c^{2} + 180 \, a^{3} b c^{3}\right)} d^{3} e^{4} - {\left(16 \, a b^{6} - 91 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2} + 176 \, a^{4} c^{3}\right)} d^{2} e^{5} + {\left(11 \, a^{2} b^{5} - 76 \, a^{3} b^{3} c + 112 \, a^{4} b c^{2}\right)} d e^{6} + 3 \, {\left(a^{3} b^{4} - 8 \, a^{4} b^{2} c + 16 \, a^{5} c^{2}\right)} e^{7} - {\left(32 \, c^{7} d^{6} e - 96 \, b c^{6} d^{5} e^{2} + 4 \, {\left(19 \, b^{2} c^{5} + 44 \, a c^{6}\right)} d^{4} e^{3} + 8 \, {\left(b^{3} c^{4} - 44 \, a b c^{5}\right)} d^{3} e^{4} - {\left(35 \, b^{4} c^{3} - 256 \, a b^{2} c^{4} - 16 \, a^{2} c^{5}\right)} d^{2} e^{5} + {\left(15 \, b^{5} c^{2} - 80 \, a b^{3} c^{3} - 16 \, a^{2} b c^{4}\right)} d e^{6} - {\left(15 \, a b^{4} c^{2} - 100 \, a^{2} b^{2} c^{3} + 128 \, a^{3} c^{4}\right)} e^{7}\right)} x^{4} - 2 \, {\left(16 \, c^{7} d^{7} - 24 \, b c^{6} d^{6} e - 2 \, {\left(17 \, b^{2} c^{5} - 44 \, a c^{6}\right)} d^{5} e^{2} + {\left(61 \, b^{3} c^{4} - 44 \, a b c^{5}\right)} d^{4} e^{3} - 4 \, {\left(b^{4} c^{3} + 49 \, a b^{2} c^{4} - 32 \, a^{2} c^{5}\right)} d^{3} e^{4} - 2 \, {\left(15 \, b^{5} c^{2} - 121 \, a b^{3} c^{3} + 88 \, a^{2} b c^{4}\right)} d^{2} e^{5} + {\left(15 \, b^{6} c - 90 \, a b^{4} c^{2} + 38 \, a^{2} b^{2} c^{3} + 56 \, a^{3} c^{4}\right)} d e^{6} - 3 \, {\left(5 \, a b^{5} c - 35 \, a^{2} b^{3} c^{2} + 52 \, a^{3} b c^{3}\right)} e^{7}\right)} x^{3} - 3 \, {\left(16 \, b c^{6} d^{7} - 4 \, {\left(11 \, b^{2} c^{5} - 4 \, a c^{6}\right)} d^{6} e + 2 \, {\left(13 \, b^{3} c^{4} + 20 \, a b c^{5}\right)} d^{5} e^{2} + 8 \, {\left(2 \, b^{4} c^{3} - 17 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} e^{3} - 2 \, {\left(7 \, b^{5} c^{2} - 34 \, a b^{3} c^{3} + 64 \, a^{2} b c^{4}\right)} d^{3} e^{4} - {\left(5 \, b^{6} c - 42 \, a b^{4} c^{2} + 28 \, a^{2} b^{2} c^{3} - 48 \, a^{3} c^{4}\right)} d^{2} e^{5} + {\left(5 \, b^{7} - 30 \, a b^{5} c + 18 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} d e^{6} - {\left(5 \, a b^{6} - 30 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2} + 64 \, a^{4} c^{3}\right)} e^{7}\right)} x^{2} - 2 \, {\left(6 \, {\left(b^{2} c^{5} + 4 \, a c^{6}\right)} d^{7} - {\left(19 \, b^{3} c^{4} + 60 \, a b c^{5}\right)} d^{6} e + 16 \, {\left(b^{4} c^{3} + 4 \, a b^{2} c^{4} + 7 \, a^{2} c^{5}\right)} d^{5} e^{2} + 2 \, {\left(3 \, b^{5} c^{2} - 46 \, a b^{3} c^{3} - 44 \, a^{2} b c^{4}\right)} d^{4} e^{3} - 2 \, {\left(7 \, b^{6} c - 51 \, a b^{4} c^{2} + 61 \, a^{2} b^{2} c^{3} - 76 \, a^{3} c^{4}\right)} d^{3} e^{4} + {\left(5 \, b^{7} - 43 \, a b^{5} c + 125 \, a^{2} b^{3} c^{2} - 156 \, a^{3} b c^{3}\right)} d^{2} e^{5} + {\left(5 \, a b^{6} - 32 \, a^{2} b^{4} c + 20 \, a^{3} b^{2} c^{2} + 64 \, a^{4} c^{3}\right)} d e^{6} - 2 \, {\left(5 \, a^{2} b^{5} - 37 \, a^{3} b^{3} c + 64 \, a^{4} b c^{2}\right)} e^{7}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left({\left(a^{2} b^{4} c^{4} - 8 \, a^{3} b^{2} c^{5} + 16 \, a^{4} c^{6}\right)} d^{9} - 4 \, {\left(a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5}\right)} d^{8} e + 2 \, {\left(3 \, a^{2} b^{6} c^{2} - 22 \, a^{3} b^{4} c^{3} + 32 \, a^{4} b^{2} c^{4} + 32 \, a^{5} c^{5}\right)} d^{7} e^{2} - 4 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} - 8 \, a^{4} b^{3} c^{3} + 48 \, a^{5} b c^{4}\right)} d^{6} e^{3} + {\left(a^{2} b^{8} + 4 \, a^{3} b^{6} c - 74 \, a^{4} b^{4} c^{2} + 144 \, a^{5} b^{2} c^{3} + 96 \, a^{6} c^{4}\right)} d^{5} e^{4} - 4 \, {\left(a^{3} b^{7} - 5 \, a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 48 \, a^{6} b c^{3}\right)} d^{4} e^{5} + 2 \, {\left(3 \, a^{4} b^{6} - 22 \, a^{5} b^{4} c + 32 \, a^{6} b^{2} c^{2} + 32 \, a^{7} c^{3}\right)} d^{3} e^{6} - 4 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} d^{2} e^{7} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} d e^{8} + {\left({\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{8} e - 4 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{7} e^{2} + 2 \, {\left(3 \, b^{6} c^{4} - 22 \, a b^{4} c^{5} + 32 \, a^{2} b^{2} c^{6} + 32 \, a^{3} c^{7}\right)} d^{6} e^{3} - 4 \, {\left(b^{7} c^{3} - 5 \, a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 48 \, a^{3} b c^{6}\right)} d^{5} e^{4} + {\left(b^{8} c^{2} + 4 \, a b^{6} c^{3} - 74 \, a^{2} b^{4} c^{4} + 144 \, a^{3} b^{2} c^{5} + 96 \, a^{4} c^{6}\right)} d^{4} e^{5} - 4 \, {\left(a b^{7} c^{2} - 5 \, a^{2} b^{5} c^{3} - 8 \, a^{3} b^{3} c^{4} + 48 \, a^{4} b c^{5}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{6} c^{2} - 22 \, a^{3} b^{4} c^{3} + 32 \, a^{4} b^{2} c^{4} + 32 \, a^{5} c^{5}\right)} d^{2} e^{7} - 4 \, {\left(a^{3} b^{5} c^{2} - 8 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4}\right)} d e^{8} + {\left(a^{4} b^{4} c^{2} - 8 \, a^{5} b^{2} c^{3} + 16 \, a^{6} c^{4}\right)} e^{9}\right)} x^{5} + {\left({\left(b^{4} c^{6} - 8 \, a b^{2} c^{7} + 16 \, a^{2} c^{8}\right)} d^{9} - 2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{8} e - 2 \, {\left(b^{6} c^{4} - 10 \, a b^{4} c^{5} + 32 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{7} e^{2} + 4 \, {\left(2 \, b^{7} c^{3} - 17 \, a b^{5} c^{4} + 40 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{6} e^{3} - {\left(7 \, b^{8} c^{2} - 44 \, a b^{6} c^{3} + 10 \, a^{2} b^{4} c^{4} + 240 \, a^{3} b^{2} c^{5} - 96 \, a^{4} c^{6}\right)} d^{5} e^{4} + 2 \, {\left(b^{9} c + 2 \, a b^{7} c^{2} - 64 \, a^{2} b^{5} c^{3} + 160 \, a^{3} b^{3} c^{4}\right)} d^{4} e^{5} - 2 \, {\left(4 \, a b^{8} c - 23 \, a^{2} b^{6} c^{2} - 10 \, a^{3} b^{4} c^{3} + 160 \, a^{4} b^{2} c^{4} - 32 \, a^{5} c^{5}\right)} d^{3} e^{6} + 4 \, {\left(3 \, a^{2} b^{7} c - 23 \, a^{3} b^{5} c^{2} + 40 \, a^{4} b^{3} c^{3} + 16 \, a^{5} b c^{4}\right)} d^{2} e^{7} - {\left(8 \, a^{3} b^{6} c - 65 \, a^{4} b^{4} c^{2} + 136 \, a^{5} b^{2} c^{3} - 16 \, a^{6} c^{4}\right)} d e^{8} + 2 \, {\left(a^{4} b^{5} c - 8 \, a^{5} b^{3} c^{2} + 16 \, a^{6} b c^{3}\right)} e^{9}\right)} x^{4} + {\left(2 \, {\left(b^{5} c^{5} - 8 \, a b^{3} c^{6} + 16 \, a^{2} b c^{7}\right)} d^{9} - {\left(7 \, b^{6} c^{4} - 58 \, a b^{4} c^{5} + 128 \, a^{2} b^{2} c^{6} - 32 \, a^{3} c^{7}\right)} d^{8} e + 8 \, {\left(b^{7} c^{3} - 8 \, a b^{5} c^{4} + 16 \, a^{2} b^{3} c^{5}\right)} d^{7} e^{2} - 2 \, {\left(b^{8} c^{2} - 4 \, a b^{6} c^{3} - 20 \, a^{2} b^{4} c^{4} + 96 \, a^{3} b^{2} c^{5} - 64 \, a^{4} c^{6}\right)} d^{6} e^{3} - 2 \, {\left(b^{9} c - 10 \, a b^{7} c^{2} + 38 \, a^{2} b^{5} c^{3} - 80 \, a^{3} b^{3} c^{4} + 96 \, a^{4} b c^{5}\right)} d^{5} e^{4} + {\left(b^{10} - 2 \, a b^{8} c - 26 \, a^{2} b^{6} c^{2} + 60 \, a^{3} b^{4} c^{3} + 192 \, a^{5} c^{5}\right)} d^{4} e^{5} - 4 \, {\left(a b^{9} - 6 \, a^{2} b^{7} c + 4 \, a^{3} b^{5} c^{2} + 64 \, a^{5} b c^{4}\right)} d^{3} e^{6} + 2 \, {\left(3 \, a^{2} b^{8} - 20 \, a^{3} b^{6} c + 20 \, a^{4} b^{4} c^{2} + 32 \, a^{5} b^{2} c^{3} + 64 \, a^{6} c^{4}\right)} d^{2} e^{7} - 2 \, {\left(2 \, a^{3} b^{7} - 13 \, a^{4} b^{5} c + 8 \, a^{5} b^{3} c^{2} + 48 \, a^{6} b c^{3}\right)} d e^{8} + {\left(a^{4} b^{6} - 6 \, a^{5} b^{4} c + 32 \, a^{7} c^{3}\right)} e^{9}\right)} x^{3} + {\left({\left(b^{6} c^{4} - 6 \, a b^{4} c^{5} + 32 \, a^{3} c^{7}\right)} d^{9} - 2 \, {\left(2 \, b^{7} c^{3} - 13 \, a b^{5} c^{4} + 8 \, a^{2} b^{3} c^{5} + 48 \, a^{3} b c^{6}\right)} d^{8} e + 2 \, {\left(3 \, b^{8} c^{2} - 20 \, a b^{6} c^{3} + 20 \, a^{2} b^{4} c^{4} + 32 \, a^{3} b^{2} c^{5} + 64 \, a^{4} c^{6}\right)} d^{7} e^{2} - 4 \, {\left(b^{9} c - 6 \, a b^{7} c^{2} + 4 \, a^{2} b^{5} c^{3} + 64 \, a^{4} b c^{5}\right)} d^{6} e^{3} + {\left(b^{10} - 2 \, a b^{8} c - 26 \, a^{2} b^{6} c^{2} + 60 \, a^{3} b^{4} c^{3} + 192 \, a^{5} c^{5}\right)} d^{5} e^{4} - 2 \, {\left(a b^{9} - 10 \, a^{2} b^{7} c + 38 \, a^{3} b^{5} c^{2} - 80 \, a^{4} b^{3} c^{3} + 96 \, a^{5} b c^{4}\right)} d^{4} e^{5} - 2 \, {\left(a^{2} b^{8} - 4 \, a^{3} b^{6} c - 20 \, a^{4} b^{4} c^{2} + 96 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} d^{3} e^{6} + 8 \, {\left(a^{3} b^{7} - 8 \, a^{4} b^{5} c + 16 \, a^{5} b^{3} c^{2}\right)} d^{2} e^{7} - {\left(7 \, a^{4} b^{6} - 58 \, a^{5} b^{4} c + 128 \, a^{6} b^{2} c^{2} - 32 \, a^{7} c^{3}\right)} d e^{8} + 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} e^{9}\right)} x^{2} + {\left(2 \, {\left(a b^{5} c^{4} - 8 \, a^{2} b^{3} c^{5} + 16 \, a^{3} b c^{6}\right)} d^{9} - {\left(8 \, a b^{6} c^{3} - 65 \, a^{2} b^{4} c^{4} + 136 \, a^{3} b^{2} c^{5} - 16 \, a^{4} c^{6}\right)} d^{8} e + 4 \, {\left(3 \, a b^{7} c^{2} - 23 \, a^{2} b^{5} c^{3} + 40 \, a^{3} b^{3} c^{4} + 16 \, a^{4} b c^{5}\right)} d^{7} e^{2} - 2 \, {\left(4 \, a b^{8} c - 23 \, a^{2} b^{6} c^{2} - 10 \, a^{3} b^{4} c^{3} + 160 \, a^{4} b^{2} c^{4} - 32 \, a^{5} c^{5}\right)} d^{6} e^{3} + 2 \, {\left(a b^{9} + 2 \, a^{2} b^{7} c - 64 \, a^{3} b^{5} c^{2} + 160 \, a^{4} b^{3} c^{3}\right)} d^{5} e^{4} - {\left(7 \, a^{2} b^{8} - 44 \, a^{3} b^{6} c + 10 \, a^{4} b^{4} c^{2} + 240 \, a^{5} b^{2} c^{3} - 96 \, a^{6} c^{4}\right)} d^{4} e^{5} + 4 \, {\left(2 \, a^{3} b^{7} - 17 \, a^{4} b^{5} c + 40 \, a^{5} b^{3} c^{2} - 16 \, a^{6} b c^{3}\right)} d^{3} e^{6} - 2 \, {\left(a^{4} b^{6} - 10 \, a^{5} b^{4} c + 32 \, a^{6} b^{2} c^{2} - 32 \, a^{7} c^{3}\right)} d^{2} e^{7} - 2 \, {\left(a^{5} b^{5} - 8 \, a^{6} b^{3} c + 16 \, a^{7} b c^{2}\right)} d e^{8} + {\left(a^{6} b^{4} - 8 \, a^{7} b^{2} c + 16 \, a^{8} c^{2}\right)} e^{9}\right)} x\right)}}\right]"," ",0,"[-1/12*(15*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d^2*e^4 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d*e^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^5 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^6)*x^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^2*e^4 + 3*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^5 - 2*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*e^6)*x^4 + (4*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^4 + 4*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^5 - (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*e^6)*x^3 + (2*(b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d^2*e^4 - (b^7 - 10*a*b^5*c + 32*a^2*b^3*c^2 - 32*a^3*b*c^3)*d*e^5 - 2*(a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e^6)*x^2 + (4*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2*e^4 - 2*(a*b^6 - 9*a^2*b^4*c + 24*a^3*b^2*c^2 - 16*a^4*c^3)*d*e^5 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^6)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(2*(b^3*c^4 - 12*a*b*c^5)*d^7 - 8*(b^4*c^3 - 11*a*b^2*c^4 + 4*a^2*c^5)*d^6*e + 4*(3*b^5*c^2 - 26*a*b^3*c^3 - 4*a^2*b*c^4)*d^5*e^2 - 8*(b^6*c - 3*a*b^4*c^2 - 32*a^2*b^2*c^3 + 32*a^3*c^4)*d^4*e^3 + 2*(b^7 + 16*a*b^5*c - 155*a^2*b^3*c^2 + 180*a^3*b*c^3)*d^3*e^4 - (16*a*b^6 - 91*a^2*b^4*c + 16*a^3*b^2*c^2 + 176*a^4*c^3)*d^2*e^5 + (11*a^2*b^5 - 76*a^3*b^3*c + 112*a^4*b*c^2)*d*e^6 + 3*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*e^7 - (32*c^7*d^6*e - 96*b*c^6*d^5*e^2 + 4*(19*b^2*c^5 + 44*a*c^6)*d^4*e^3 + 8*(b^3*c^4 - 44*a*b*c^5)*d^3*e^4 - (35*b^4*c^3 - 256*a*b^2*c^4 - 16*a^2*c^5)*d^2*e^5 + (15*b^5*c^2 - 80*a*b^3*c^3 - 16*a^2*b*c^4)*d*e^6 - (15*a*b^4*c^2 - 100*a^2*b^2*c^3 + 128*a^3*c^4)*e^7)*x^4 - 2*(16*c^7*d^7 - 24*b*c^6*d^6*e - 2*(17*b^2*c^5 - 44*a*c^6)*d^5*e^2 + (61*b^3*c^4 - 44*a*b*c^5)*d^4*e^3 - 4*(b^4*c^3 + 49*a*b^2*c^4 - 32*a^2*c^5)*d^3*e^4 - 2*(15*b^5*c^2 - 121*a*b^3*c^3 + 88*a^2*b*c^4)*d^2*e^5 + (15*b^6*c - 90*a*b^4*c^2 + 38*a^2*b^2*c^3 + 56*a^3*c^4)*d*e^6 - 3*(5*a*b^5*c - 35*a^2*b^3*c^2 + 52*a^3*b*c^3)*e^7)*x^3 - 3*(16*b*c^6*d^7 - 4*(11*b^2*c^5 - 4*a*c^6)*d^6*e + 2*(13*b^3*c^4 + 20*a*b*c^5)*d^5*e^2 + 8*(2*b^4*c^3 - 17*a*b^2*c^4 + 16*a^2*c^5)*d^4*e^3 - 2*(7*b^5*c^2 - 34*a*b^3*c^3 + 64*a^2*b*c^4)*d^3*e^4 - (5*b^6*c - 42*a*b^4*c^2 + 28*a^2*b^2*c^3 - 48*a^3*c^4)*d^2*e^5 + (5*b^7 - 30*a*b^5*c + 18*a^2*b^3*c^2 + 8*a^3*b*c^3)*d*e^6 - (5*a*b^6 - 30*a^2*b^4*c + 16*a^3*b^2*c^2 + 64*a^4*c^3)*e^7)*x^2 - 2*(6*(b^2*c^5 + 4*a*c^6)*d^7 - (19*b^3*c^4 + 60*a*b*c^5)*d^6*e + 16*(b^4*c^3 + 4*a*b^2*c^4 + 7*a^2*c^5)*d^5*e^2 + 2*(3*b^5*c^2 - 46*a*b^3*c^3 - 44*a^2*b*c^4)*d^4*e^3 - 2*(7*b^6*c - 51*a*b^4*c^2 + 61*a^2*b^2*c^3 - 76*a^3*c^4)*d^3*e^4 + (5*b^7 - 43*a*b^5*c + 125*a^2*b^3*c^2 - 156*a^3*b*c^3)*d^2*e^5 + (5*a*b^6 - 32*a^2*b^4*c + 20*a^3*b^2*c^2 + 64*a^4*c^3)*d*e^6 - 2*(5*a^2*b^5 - 37*a^3*b^3*c + 64*a^4*b*c^2)*e^7)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^4*c^4 - 8*a^3*b^2*c^5 + 16*a^4*c^6)*d^9 - 4*(a^2*b^5*c^3 - 8*a^3*b^3*c^4 + 16*a^4*b*c^5)*d^8*e + 2*(3*a^2*b^6*c^2 - 22*a^3*b^4*c^3 + 32*a^4*b^2*c^4 + 32*a^5*c^5)*d^7*e^2 - 4*(a^2*b^7*c - 5*a^3*b^5*c^2 - 8*a^4*b^3*c^3 + 48*a^5*b*c^4)*d^6*e^3 + (a^2*b^8 + 4*a^3*b^6*c - 74*a^4*b^4*c^2 + 144*a^5*b^2*c^3 + 96*a^6*c^4)*d^5*e^4 - 4*(a^3*b^7 - 5*a^4*b^5*c - 8*a^5*b^3*c^2 + 48*a^6*b*c^3)*d^4*e^5 + 2*(3*a^4*b^6 - 22*a^5*b^4*c + 32*a^6*b^2*c^2 + 32*a^7*c^3)*d^3*e^6 - 4*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*d^2*e^7 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*d*e^8 + ((b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^8*e - 4*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^7*e^2 + 2*(3*b^6*c^4 - 22*a*b^4*c^5 + 32*a^2*b^2*c^6 + 32*a^3*c^7)*d^6*e^3 - 4*(b^7*c^3 - 5*a*b^5*c^4 - 8*a^2*b^3*c^5 + 48*a^3*b*c^6)*d^5*e^4 + (b^8*c^2 + 4*a*b^6*c^3 - 74*a^2*b^4*c^4 + 144*a^3*b^2*c^5 + 96*a^4*c^6)*d^4*e^5 - 4*(a*b^7*c^2 - 5*a^2*b^5*c^3 - 8*a^3*b^3*c^4 + 48*a^4*b*c^5)*d^3*e^6 + 2*(3*a^2*b^6*c^2 - 22*a^3*b^4*c^3 + 32*a^4*b^2*c^4 + 32*a^5*c^5)*d^2*e^7 - 4*(a^3*b^5*c^2 - 8*a^4*b^3*c^3 + 16*a^5*b*c^4)*d*e^8 + (a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)*e^9)*x^5 + ((b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^9 - 2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^8*e - 2*(b^6*c^4 - 10*a*b^4*c^5 + 32*a^2*b^2*c^6 - 32*a^3*c^7)*d^7*e^2 + 4*(2*b^7*c^3 - 17*a*b^5*c^4 + 40*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^6*e^3 - (7*b^8*c^2 - 44*a*b^6*c^3 + 10*a^2*b^4*c^4 + 240*a^3*b^2*c^5 - 96*a^4*c^6)*d^5*e^4 + 2*(b^9*c + 2*a*b^7*c^2 - 64*a^2*b^5*c^3 + 160*a^3*b^3*c^4)*d^4*e^5 - 2*(4*a*b^8*c - 23*a^2*b^6*c^2 - 10*a^3*b^4*c^3 + 160*a^4*b^2*c^4 - 32*a^5*c^5)*d^3*e^6 + 4*(3*a^2*b^7*c - 23*a^3*b^5*c^2 + 40*a^4*b^3*c^3 + 16*a^5*b*c^4)*d^2*e^7 - (8*a^3*b^6*c - 65*a^4*b^4*c^2 + 136*a^5*b^2*c^3 - 16*a^6*c^4)*d*e^8 + 2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)*e^9)*x^4 + (2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^9 - (7*b^6*c^4 - 58*a*b^4*c^5 + 128*a^2*b^2*c^6 - 32*a^3*c^7)*d^8*e + 8*(b^7*c^3 - 8*a*b^5*c^4 + 16*a^2*b^3*c^5)*d^7*e^2 - 2*(b^8*c^2 - 4*a*b^6*c^3 - 20*a^2*b^4*c^4 + 96*a^3*b^2*c^5 - 64*a^4*c^6)*d^6*e^3 - 2*(b^9*c - 10*a*b^7*c^2 + 38*a^2*b^5*c^3 - 80*a^3*b^3*c^4 + 96*a^4*b*c^5)*d^5*e^4 + (b^10 - 2*a*b^8*c - 26*a^2*b^6*c^2 + 60*a^3*b^4*c^3 + 192*a^5*c^5)*d^4*e^5 - 4*(a*b^9 - 6*a^2*b^7*c + 4*a^3*b^5*c^2 + 64*a^5*b*c^4)*d^3*e^6 + 2*(3*a^2*b^8 - 20*a^3*b^6*c + 20*a^4*b^4*c^2 + 32*a^5*b^2*c^3 + 64*a^6*c^4)*d^2*e^7 - 2*(2*a^3*b^7 - 13*a^4*b^5*c + 8*a^5*b^3*c^2 + 48*a^6*b*c^3)*d*e^8 + (a^4*b^6 - 6*a^5*b^4*c + 32*a^7*c^3)*e^9)*x^3 + ((b^6*c^4 - 6*a*b^4*c^5 + 32*a^3*c^7)*d^9 - 2*(2*b^7*c^3 - 13*a*b^5*c^4 + 8*a^2*b^3*c^5 + 48*a^3*b*c^6)*d^8*e + 2*(3*b^8*c^2 - 20*a*b^6*c^3 + 20*a^2*b^4*c^4 + 32*a^3*b^2*c^5 + 64*a^4*c^6)*d^7*e^2 - 4*(b^9*c - 6*a*b^7*c^2 + 4*a^2*b^5*c^3 + 64*a^4*b*c^5)*d^6*e^3 + (b^10 - 2*a*b^8*c - 26*a^2*b^6*c^2 + 60*a^3*b^4*c^3 + 192*a^5*c^5)*d^5*e^4 - 2*(a*b^9 - 10*a^2*b^7*c + 38*a^3*b^5*c^2 - 80*a^4*b^3*c^3 + 96*a^5*b*c^4)*d^4*e^5 - 2*(a^2*b^8 - 4*a^3*b^6*c - 20*a^4*b^4*c^2 + 96*a^5*b^2*c^3 - 64*a^6*c^4)*d^3*e^6 + 8*(a^3*b^7 - 8*a^4*b^5*c + 16*a^5*b^3*c^2)*d^2*e^7 - (7*a^4*b^6 - 58*a^5*b^4*c + 128*a^6*b^2*c^2 - 32*a^7*c^3)*d*e^8 + 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*e^9)*x^2 + (2*(a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*d^9 - (8*a*b^6*c^3 - 65*a^2*b^4*c^4 + 136*a^3*b^2*c^5 - 16*a^4*c^6)*d^8*e + 4*(3*a*b^7*c^2 - 23*a^2*b^5*c^3 + 40*a^3*b^3*c^4 + 16*a^4*b*c^5)*d^7*e^2 - 2*(4*a*b^8*c - 23*a^2*b^6*c^2 - 10*a^3*b^4*c^3 + 160*a^4*b^2*c^4 - 32*a^5*c^5)*d^6*e^3 + 2*(a*b^9 + 2*a^2*b^7*c - 64*a^3*b^5*c^2 + 160*a^4*b^3*c^3)*d^5*e^4 - (7*a^2*b^8 - 44*a^3*b^6*c + 10*a^4*b^4*c^2 + 240*a^5*b^2*c^3 - 96*a^6*c^4)*d^4*e^5 + 4*(2*a^3*b^7 - 17*a^4*b^5*c + 40*a^5*b^3*c^2 - 16*a^6*b*c^3)*d^3*e^6 - 2*(a^4*b^6 - 10*a^5*b^4*c + 32*a^6*b^2*c^2 - 32*a^7*c^3)*d^2*e^7 - 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*d*e^8 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*e^9)*x), 1/6*(15*(2*(a^2*b^4*c - 8*a^3*b^2*c^2 + 16*a^4*c^3)*d^2*e^4 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*d*e^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d*e^5 - (b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*e^6)*x^5 + (2*(b^4*c^3 - 8*a*b^2*c^4 + 16*a^2*c^5)*d^2*e^4 + 3*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d*e^5 - 2*(b^6*c - 8*a*b^4*c^2 + 16*a^2*b^2*c^3)*e^6)*x^4 + (4*(b^5*c^2 - 8*a*b^3*c^3 + 16*a^2*b*c^4)*d^2*e^4 + 4*(a*b^4*c^2 - 8*a^2*b^2*c^3 + 16*a^3*c^4)*d*e^5 - (b^7 - 6*a*b^5*c + 32*a^3*b*c^3)*e^6)*x^3 + (2*(b^6*c - 6*a*b^4*c^2 + 32*a^3*c^4)*d^2*e^4 - (b^7 - 10*a*b^5*c + 32*a^2*b^3*c^2 - 32*a^3*b*c^3)*d*e^5 - 2*(a*b^6 - 8*a^2*b^4*c + 16*a^3*b^2*c^2)*e^6)*x^2 + (4*(a*b^5*c - 8*a^2*b^3*c^2 + 16*a^3*b*c^3)*d^2*e^4 - 2*(a*b^6 - 9*a^2*b^4*c + 24*a^3*b^2*c^2 - 16*a^4*c^3)*d*e^5 - (a^2*b^5 - 8*a^3*b^3*c + 16*a^4*b*c^2)*e^6)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(2*(b^3*c^4 - 12*a*b*c^5)*d^7 - 8*(b^4*c^3 - 11*a*b^2*c^4 + 4*a^2*c^5)*d^6*e + 4*(3*b^5*c^2 - 26*a*b^3*c^3 - 4*a^2*b*c^4)*d^5*e^2 - 8*(b^6*c - 3*a*b^4*c^2 - 32*a^2*b^2*c^3 + 32*a^3*c^4)*d^4*e^3 + 2*(b^7 + 16*a*b^5*c - 155*a^2*b^3*c^2 + 180*a^3*b*c^3)*d^3*e^4 - (16*a*b^6 - 91*a^2*b^4*c + 16*a^3*b^2*c^2 + 176*a^4*c^3)*d^2*e^5 + (11*a^2*b^5 - 76*a^3*b^3*c + 112*a^4*b*c^2)*d*e^6 + 3*(a^3*b^4 - 8*a^4*b^2*c + 16*a^5*c^2)*e^7 - (32*c^7*d^6*e - 96*b*c^6*d^5*e^2 + 4*(19*b^2*c^5 + 44*a*c^6)*d^4*e^3 + 8*(b^3*c^4 - 44*a*b*c^5)*d^3*e^4 - (35*b^4*c^3 - 256*a*b^2*c^4 - 16*a^2*c^5)*d^2*e^5 + (15*b^5*c^2 - 80*a*b^3*c^3 - 16*a^2*b*c^4)*d*e^6 - (15*a*b^4*c^2 - 100*a^2*b^2*c^3 + 128*a^3*c^4)*e^7)*x^4 - 2*(16*c^7*d^7 - 24*b*c^6*d^6*e - 2*(17*b^2*c^5 - 44*a*c^6)*d^5*e^2 + (61*b^3*c^4 - 44*a*b*c^5)*d^4*e^3 - 4*(b^4*c^3 + 49*a*b^2*c^4 - 32*a^2*c^5)*d^3*e^4 - 2*(15*b^5*c^2 - 121*a*b^3*c^3 + 88*a^2*b*c^4)*d^2*e^5 + (15*b^6*c - 90*a*b^4*c^2 + 38*a^2*b^2*c^3 + 56*a^3*c^4)*d*e^6 - 3*(5*a*b^5*c - 35*a^2*b^3*c^2 + 52*a^3*b*c^3)*e^7)*x^3 - 3*(16*b*c^6*d^7 - 4*(11*b^2*c^5 - 4*a*c^6)*d^6*e + 2*(13*b^3*c^4 + 20*a*b*c^5)*d^5*e^2 + 8*(2*b^4*c^3 - 17*a*b^2*c^4 + 16*a^2*c^5)*d^4*e^3 - 2*(7*b^5*c^2 - 34*a*b^3*c^3 + 64*a^2*b*c^4)*d^3*e^4 - (5*b^6*c - 42*a*b^4*c^2 + 28*a^2*b^2*c^3 - 48*a^3*c^4)*d^2*e^5 + (5*b^7 - 30*a*b^5*c + 18*a^2*b^3*c^2 + 8*a^3*b*c^3)*d*e^6 - (5*a*b^6 - 30*a^2*b^4*c + 16*a^3*b^2*c^2 + 64*a^4*c^3)*e^7)*x^2 - 2*(6*(b^2*c^5 + 4*a*c^6)*d^7 - (19*b^3*c^4 + 60*a*b*c^5)*d^6*e + 16*(b^4*c^3 + 4*a*b^2*c^4 + 7*a^2*c^5)*d^5*e^2 + 2*(3*b^5*c^2 - 46*a*b^3*c^3 - 44*a^2*b*c^4)*d^4*e^3 - 2*(7*b^6*c - 51*a*b^4*c^2 + 61*a^2*b^2*c^3 - 76*a^3*c^4)*d^3*e^4 + (5*b^7 - 43*a*b^5*c + 125*a^2*b^3*c^2 - 156*a^3*b*c^3)*d^2*e^5 + (5*a*b^6 - 32*a^2*b^4*c + 20*a^3*b^2*c^2 + 64*a^4*c^3)*d*e^6 - 2*(5*a^2*b^5 - 37*a^3*b^3*c + 64*a^4*b*c^2)*e^7)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^4*c^4 - 8*a^3*b^2*c^5 + 16*a^4*c^6)*d^9 - 4*(a^2*b^5*c^3 - 8*a^3*b^3*c^4 + 16*a^4*b*c^5)*d^8*e + 2*(3*a^2*b^6*c^2 - 22*a^3*b^4*c^3 + 32*a^4*b^2*c^4 + 32*a^5*c^5)*d^7*e^2 - 4*(a^2*b^7*c - 5*a^3*b^5*c^2 - 8*a^4*b^3*c^3 + 48*a^5*b*c^4)*d^6*e^3 + (a^2*b^8 + 4*a^3*b^6*c - 74*a^4*b^4*c^2 + 144*a^5*b^2*c^3 + 96*a^6*c^4)*d^5*e^4 - 4*(a^3*b^7 - 5*a^4*b^5*c - 8*a^5*b^3*c^2 + 48*a^6*b*c^3)*d^4*e^5 + 2*(3*a^4*b^6 - 22*a^5*b^4*c + 32*a^6*b^2*c^2 + 32*a^7*c^3)*d^3*e^6 - 4*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*d^2*e^7 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*d*e^8 + ((b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^8*e - 4*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^7*e^2 + 2*(3*b^6*c^4 - 22*a*b^4*c^5 + 32*a^2*b^2*c^6 + 32*a^3*c^7)*d^6*e^3 - 4*(b^7*c^3 - 5*a*b^5*c^4 - 8*a^2*b^3*c^5 + 48*a^3*b*c^6)*d^5*e^4 + (b^8*c^2 + 4*a*b^6*c^3 - 74*a^2*b^4*c^4 + 144*a^3*b^2*c^5 + 96*a^4*c^6)*d^4*e^5 - 4*(a*b^7*c^2 - 5*a^2*b^5*c^3 - 8*a^3*b^3*c^4 + 48*a^4*b*c^5)*d^3*e^6 + 2*(3*a^2*b^6*c^2 - 22*a^3*b^4*c^3 + 32*a^4*b^2*c^4 + 32*a^5*c^5)*d^2*e^7 - 4*(a^3*b^5*c^2 - 8*a^4*b^3*c^3 + 16*a^5*b*c^4)*d*e^8 + (a^4*b^4*c^2 - 8*a^5*b^2*c^3 + 16*a^6*c^4)*e^9)*x^5 + ((b^4*c^6 - 8*a*b^2*c^7 + 16*a^2*c^8)*d^9 - 2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^8*e - 2*(b^6*c^4 - 10*a*b^4*c^5 + 32*a^2*b^2*c^6 - 32*a^3*c^7)*d^7*e^2 + 4*(2*b^7*c^3 - 17*a*b^5*c^4 + 40*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^6*e^3 - (7*b^8*c^2 - 44*a*b^6*c^3 + 10*a^2*b^4*c^4 + 240*a^3*b^2*c^5 - 96*a^4*c^6)*d^5*e^4 + 2*(b^9*c + 2*a*b^7*c^2 - 64*a^2*b^5*c^3 + 160*a^3*b^3*c^4)*d^4*e^5 - 2*(4*a*b^8*c - 23*a^2*b^6*c^2 - 10*a^3*b^4*c^3 + 160*a^4*b^2*c^4 - 32*a^5*c^5)*d^3*e^6 + 4*(3*a^2*b^7*c - 23*a^3*b^5*c^2 + 40*a^4*b^3*c^3 + 16*a^5*b*c^4)*d^2*e^7 - (8*a^3*b^6*c - 65*a^4*b^4*c^2 + 136*a^5*b^2*c^3 - 16*a^6*c^4)*d*e^8 + 2*(a^4*b^5*c - 8*a^5*b^3*c^2 + 16*a^6*b*c^3)*e^9)*x^4 + (2*(b^5*c^5 - 8*a*b^3*c^6 + 16*a^2*b*c^7)*d^9 - (7*b^6*c^4 - 58*a*b^4*c^5 + 128*a^2*b^2*c^6 - 32*a^3*c^7)*d^8*e + 8*(b^7*c^3 - 8*a*b^5*c^4 + 16*a^2*b^3*c^5)*d^7*e^2 - 2*(b^8*c^2 - 4*a*b^6*c^3 - 20*a^2*b^4*c^4 + 96*a^3*b^2*c^5 - 64*a^4*c^6)*d^6*e^3 - 2*(b^9*c - 10*a*b^7*c^2 + 38*a^2*b^5*c^3 - 80*a^3*b^3*c^4 + 96*a^4*b*c^5)*d^5*e^4 + (b^10 - 2*a*b^8*c - 26*a^2*b^6*c^2 + 60*a^3*b^4*c^3 + 192*a^5*c^5)*d^4*e^5 - 4*(a*b^9 - 6*a^2*b^7*c + 4*a^3*b^5*c^2 + 64*a^5*b*c^4)*d^3*e^6 + 2*(3*a^2*b^8 - 20*a^3*b^6*c + 20*a^4*b^4*c^2 + 32*a^5*b^2*c^3 + 64*a^6*c^4)*d^2*e^7 - 2*(2*a^3*b^7 - 13*a^4*b^5*c + 8*a^5*b^3*c^2 + 48*a^6*b*c^3)*d*e^8 + (a^4*b^6 - 6*a^5*b^4*c + 32*a^7*c^3)*e^9)*x^3 + ((b^6*c^4 - 6*a*b^4*c^5 + 32*a^3*c^7)*d^9 - 2*(2*b^7*c^3 - 13*a*b^5*c^4 + 8*a^2*b^3*c^5 + 48*a^3*b*c^6)*d^8*e + 2*(3*b^8*c^2 - 20*a*b^6*c^3 + 20*a^2*b^4*c^4 + 32*a^3*b^2*c^5 + 64*a^4*c^6)*d^7*e^2 - 4*(b^9*c - 6*a*b^7*c^2 + 4*a^2*b^5*c^3 + 64*a^4*b*c^5)*d^6*e^3 + (b^10 - 2*a*b^8*c - 26*a^2*b^6*c^2 + 60*a^3*b^4*c^3 + 192*a^5*c^5)*d^5*e^4 - 2*(a*b^9 - 10*a^2*b^7*c + 38*a^3*b^5*c^2 - 80*a^4*b^3*c^3 + 96*a^5*b*c^4)*d^4*e^5 - 2*(a^2*b^8 - 4*a^3*b^6*c - 20*a^4*b^4*c^2 + 96*a^5*b^2*c^3 - 64*a^6*c^4)*d^3*e^6 + 8*(a^3*b^7 - 8*a^4*b^5*c + 16*a^5*b^3*c^2)*d^2*e^7 - (7*a^4*b^6 - 58*a^5*b^4*c + 128*a^6*b^2*c^2 - 32*a^7*c^3)*d*e^8 + 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*e^9)*x^2 + (2*(a*b^5*c^4 - 8*a^2*b^3*c^5 + 16*a^3*b*c^6)*d^9 - (8*a*b^6*c^3 - 65*a^2*b^4*c^4 + 136*a^3*b^2*c^5 - 16*a^4*c^6)*d^8*e + 4*(3*a*b^7*c^2 - 23*a^2*b^5*c^3 + 40*a^3*b^3*c^4 + 16*a^4*b*c^5)*d^7*e^2 - 2*(4*a*b^8*c - 23*a^2*b^6*c^2 - 10*a^3*b^4*c^3 + 160*a^4*b^2*c^4 - 32*a^5*c^5)*d^6*e^3 + 2*(a*b^9 + 2*a^2*b^7*c - 64*a^3*b^5*c^2 + 160*a^4*b^3*c^3)*d^5*e^4 - (7*a^2*b^8 - 44*a^3*b^6*c + 10*a^4*b^4*c^2 + 240*a^5*b^2*c^3 - 96*a^6*c^4)*d^4*e^5 + 4*(2*a^3*b^7 - 17*a^4*b^5*c + 40*a^5*b^3*c^2 - 16*a^6*b*c^3)*d^3*e^6 - 2*(a^4*b^6 - 10*a^5*b^4*c + 32*a^6*b^2*c^2 - 32*a^7*c^3)*d^2*e^7 - 2*(a^5*b^5 - 8*a^6*b^3*c + 16*a^7*b*c^2)*d*e^8 + (a^6*b^4 - 8*a^7*b^2*c + 16*a^8*c^2)*e^9)*x)]","B",0
2399,1,14440,0,52.919431," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(24 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{4} e^{4} - 24 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{3} e^{5} + {\left(7 \, a^{2} b^{6} - 60 \, a^{3} b^{4} c + 144 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d^{2} e^{6} + {\left(24 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{2} e^{6} - 24 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d e^{7} + {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{8}\right)} x^{6} + 2 \, {\left(24 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{3} e^{5} - {\left(17 \, b^{6} c^{2} - 132 \, a b^{4} c^{3} + 240 \, a^{2} b^{2} c^{4} + 64 \, a^{3} c^{5}\right)} d e^{7} + {\left(7 \, b^{7} c - 60 \, a b^{5} c^{2} + 144 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e^{8}\right)} x^{5} + {\left(24 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{4} e^{4} + 72 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{3} e^{5} - {\left(65 \, b^{6} c^{2} - 564 \, a b^{4} c^{3} + 1392 \, a^{2} b^{2} c^{4} - 704 \, a^{3} c^{5}\right)} d^{2} e^{6} + 4 \, {\left(b^{7} c - 24 \, a b^{5} c^{2} + 144 \, a^{2} b^{3} c^{3} - 256 \, a^{3} b c^{4}\right)} d e^{7} + {\left(7 \, b^{8} - 46 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 224 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} e^{8}\right)} x^{4} + 2 \, {\left(24 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{4} e^{4} + 48 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d^{3} e^{5} - {\left(17 \, b^{7} c - 108 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} + 448 \, a^{3} b c^{4}\right)} d^{2} e^{6} + {\left(7 \, b^{8} - 70 \, a b^{6} c + 216 \, a^{2} b^{4} c^{2} - 160 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d e^{7} + {\left(7 \, a b^{7} - 60 \, a^{2} b^{5} c + 144 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} e^{8}\right)} x^{3} + {\left(24 \, {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} d^{4} e^{4} - 24 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 32 \, a^{2} b^{3} c^{3} - 32 \, a^{3} b c^{4}\right)} d^{3} e^{5} + {\left(7 \, b^{8} - 142 \, a b^{6} c + 816 \, a^{2} b^{4} c^{2} - 1504 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} d^{2} e^{6} + 4 \, {\left(7 \, a b^{7} - 66 \, a^{2} b^{5} c + 192 \, a^{3} b^{3} c^{2} - 160 \, a^{4} b c^{3}\right)} d e^{7} + {\left(7 \, a^{2} b^{6} - 60 \, a^{3} b^{4} c + 144 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{8}\right)} x^{2} + 2 \, {\left(24 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} d^{4} e^{4} - 24 \, {\left(a b^{6} c - 9 \, a^{2} b^{4} c^{2} + 24 \, a^{3} b^{2} c^{3} - 16 \, a^{4} c^{4}\right)} d^{3} e^{5} + 7 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d^{2} e^{6} + {\left(7 \, a^{2} b^{6} - 60 \, a^{3} b^{4} c + 144 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d e^{7}\right)} x\right)} \sqrt{c d^{2} - b d e + a e^{2}} \log\left(\frac{8 \, a b d e - 8 \, a^{2} e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} - {\left(8 \, c^{2} d^{2} - 8 \, b c d e + {\left(b^{2} + 4 \, a c\right)} e^{2}\right)} x^{2} + 4 \, \sqrt{c d^{2} - b d e + a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)} - 2 \, {\left(4 \, b c d^{2} + 4 \, a b e^{2} - {\left(3 \, b^{2} + 4 \, a c\right)} d e\right)} x}{e^{2} x^{2} + 2 \, d e x + d^{2}}\right) + 4 \, {\left(8 \, {\left(b^{3} c^{5} - 12 \, a b c^{6}\right)} d^{9} - 8 \, {\left(5 \, b^{4} c^{4} - 54 \, a b^{2} c^{5} + 24 \, a^{2} c^{6}\right)} d^{8} e + 8 \, {\left(10 \, b^{5} c^{3} - 85 \, a b^{3} c^{4} + 12 \, a^{2} b c^{5}\right)} d^{7} e^{2} - 80 \, {\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} - 21 \, a^{2} b^{2} c^{4} + 28 \, a^{3} c^{5}\right)} d^{6} e^{3} + 40 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 85 \, a^{2} b^{3} c^{3} + 124 \, a^{3} b c^{4}\right)} d^{5} e^{4} - 8 \, {\left(b^{8} + 38 \, a b^{6} c - 300 \, a^{2} b^{4} c^{2} + 430 \, a^{3} b^{2} c^{3} + 56 \, a^{4} c^{4}\right)} d^{4} e^{5} + {\left(88 \, a b^{7} - 543 \, a^{2} b^{5} c + 480 \, a^{3} b^{3} c^{2} + 688 \, a^{4} b c^{3}\right)} d^{3} e^{6} - {\left(41 \, a^{2} b^{6} - 390 \, a^{3} b^{4} c + 1296 \, a^{4} b^{2} c^{2} - 1696 \, a^{5} c^{3}\right)} d^{2} e^{7} - 45 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d e^{8} + 6 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} e^{9} - {\left(128 \, c^{8} d^{7} e^{2} - 448 \, b c^{7} d^{6} e^{3} + 32 \, {\left(13 \, b^{2} c^{6} + 32 \, a c^{7}\right)} d^{5} e^{4} + 80 \, {\left(b^{3} c^{5} - 32 \, a b c^{6}\right)} d^{4} e^{5} - 2 \, {\left(233 \, b^{4} c^{4} - 1704 \, a b^{2} c^{5} + 848 \, a^{2} c^{6}\right)} d^{3} e^{6} + {\left(395 \, b^{5} c^{3} - 2552 \, a b^{3} c^{4} + 2544 \, a^{2} b c^{5}\right)} d^{2} e^{7} - {\left(105 \, b^{6} c^{2} - 470 \, a b^{4} c^{3} - 672 \, a^{2} b^{2} c^{4} + 2592 \, a^{3} c^{5}\right)} d e^{8} + {\left(105 \, a b^{5} c^{2} - 760 \, a^{2} b^{3} c^{3} + 1296 \, a^{3} b c^{4}\right)} e^{9}\right)} x^{5} - {\left(256 \, c^{8} d^{8} e - 704 \, b c^{7} d^{7} e^{2} + 32 \, {\left(5 \, b^{2} c^{6} + 64 \, a c^{7}\right)} d^{6} e^{3} + 112 \, {\left(7 \, b^{3} c^{5} - 32 \, a b c^{6}\right)} d^{5} e^{4} - 8 \, {\left(79 \, b^{4} c^{4} - 192 \, a b^{2} c^{5} + 64 \, a^{2} c^{6}\right)} d^{4} e^{5} - {\left(269 \, b^{5} c^{3} - 2888 \, a b^{3} c^{4} + 3216 \, a^{2} b c^{5}\right)} d^{3} e^{6} + {\left(615 \, b^{6} c^{2} - 4598 \, a b^{4} c^{3} + 7680 \, a^{2} b^{2} c^{4} - 2784 \, a^{3} c^{5}\right)} d^{2} e^{7} - {\left(210 \, b^{7} c - 1185 \, a b^{5} c^{2} + 152 \, a^{2} b^{3} c^{3} + 3696 \, a^{3} b c^{4}\right)} d e^{8} + 6 \, {\left(35 \, a b^{6} c - 265 \, a^{2} b^{4} c^{2} + 504 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} e^{9}\right)} x^{4} - {\left(128 \, c^{8} d^{9} - 64 \, b c^{7} d^{8} e - 16 \, {\left(55 \, b^{2} c^{6} - 76 \, a c^{7}\right)} d^{7} e^{2} + 40 \, {\left(29 \, b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{6} e^{3} + 8 \, {\left(25 \, b^{4} c^{4} - 678 \, a b^{2} c^{5} + 520 \, a^{2} c^{6}\right)} d^{5} e^{4} - 56 \, {\left(23 \, b^{5} c^{3} - 167 \, a b^{3} c^{4} + 204 \, a^{2} b c^{5}\right)} d^{4} e^{5} + 4 \, {\left(201 \, b^{6} c^{2} - 1393 \, a b^{4} c^{3} + 2340 \, a^{2} b^{2} c^{4} - 384 \, a^{3} c^{5}\right)} d^{3} e^{6} + {\left(45 \, b^{7} c - 582 \, a b^{5} c^{2} + 2072 \, a^{2} b^{3} c^{3} - 3264 \, a^{3} b c^{4}\right)} d^{2} e^{7} - 3 \, {\left(35 \, b^{8} - 250 \, a b^{6} c + 516 \, a^{2} b^{4} c^{2} - 848 \, a^{3} b^{2} c^{3} + 1536 \, a^{4} c^{4}\right)} d e^{8} + 3 \, {\left(35 \, a b^{7} - 230 \, a^{2} b^{5} c + 232 \, a^{3} b^{3} c^{2} + 448 \, a^{4} b c^{3}\right)} e^{9}\right)} x^{3} - {\left(192 \, b c^{7} d^{9} - 192 \, {\left(3 \, b^{2} c^{6} - 2 \, a c^{7}\right)} d^{8} e + 8 \, {\left(35 \, b^{3} c^{5} + 36 \, a b c^{6}\right)} d^{7} e^{2} + 8 \, {\left(65 \, b^{4} c^{4} - 330 \, a b^{2} c^{5} + 504 \, a^{2} c^{6}\right)} d^{6} e^{3} - 8 \, {\left(55 \, b^{5} c^{3} - 235 \, a b^{3} c^{4} + 732 \, a^{2} b c^{5}\right)} d^{5} e^{4} - 16 \, {\left(22 \, b^{6} c^{2} - 160 \, a b^{4} c^{3} + 57 \, a^{2} b^{2} c^{4} + 28 \, a^{3} c^{5}\right)} d^{4} e^{5} + {\left(551 \, b^{7} c - 3894 \, a b^{5} c^{2} + 5992 \, a^{2} b^{3} c^{3} - 1408 \, a^{3} b c^{4}\right)} d^{3} e^{6} - {\left(175 \, b^{8} - 1282 \, a b^{6} c + 2724 \, a^{2} b^{4} c^{2} - 3344 \, a^{3} b^{2} c^{3} + 4736 \, a^{4} c^{4}\right)} d^{2} e^{7} + {\left(35 \, a b^{7} - 402 \, a^{2} b^{5} c + 1608 \, a^{3} b^{3} c^{2} - 2176 \, a^{4} b c^{3}\right)} d e^{8} + 4 \, {\left(35 \, a^{2} b^{6} - 279 \, a^{3} b^{4} c + 588 \, a^{4} b^{2} c^{2} - 160 \, a^{5} c^{3}\right)} e^{9}\right)} x^{2} - {\left(48 \, {\left(b^{2} c^{6} + 4 \, a c^{7}\right)} d^{9} - 8 \, {\left(23 \, b^{3} c^{5} + 60 \, a b c^{6}\right)} d^{8} e + 8 \, {\left(25 \, b^{4} c^{4} + 54 \, a b^{2} c^{5} + 168 \, a^{2} c^{6}\right)} d^{7} e^{2} + 8 \, {\left(10 \, b^{5} c^{3} - 145 \, a b^{3} c^{4} - 84 \, a^{2} b c^{5}\right)} d^{6} e^{3} - 80 \, {\left(4 \, b^{6} c^{2} - 31 \, a b^{4} c^{3} + 57 \, a^{2} b^{2} c^{4} - 44 \, a^{3} c^{5}\right)} d^{5} e^{4} + 8 \, {\left(29 \, b^{7} c - 294 \, a b^{5} c^{2} + 1015 \, a^{2} b^{3} c^{3} - 1156 \, a^{3} b c^{4}\right)} d^{4} e^{5} - 2 \, {\left(28 \, b^{8} - 535 \, a b^{6} c + 2805 \, a^{2} b^{4} c^{2} - 4064 \, a^{3} b^{2} c^{3} - 208 \, a^{4} c^{4}\right)} d^{3} e^{6} - {\left(182 \, a b^{7} - 951 \, a^{2} b^{5} c - 624 \, a^{3} b^{3} c^{2} + 5360 \, a^{4} b c^{3}\right)} d^{2} e^{7} + {\left(217 \, a^{2} b^{6} - 1770 \, a^{3} b^{4} c + 4032 \, a^{4} b^{2} c^{2} - 1952 \, a^{5} c^{3}\right)} d e^{8} + 21 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} e^{9}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left({\left(a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} + 16 \, a^{4} c^{7}\right)} d^{12} - 5 \, {\left(a^{2} b^{5} c^{4} - 8 \, a^{3} b^{3} c^{5} + 16 \, a^{4} b c^{6}\right)} d^{11} e + 5 \, {\left(2 \, a^{2} b^{6} c^{3} - 15 \, a^{3} b^{4} c^{4} + 24 \, a^{4} b^{2} c^{5} + 16 \, a^{5} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(a^{2} b^{7} c^{2} - 6 \, a^{3} b^{5} c^{3} + 32 \, a^{5} b c^{5}\right)} d^{9} e^{3} + 5 \, {\left(a^{2} b^{8} c - 2 \, a^{3} b^{6} c^{2} - 30 \, a^{4} b^{4} c^{3} + 80 \, a^{5} b^{2} c^{4} + 32 \, a^{6} c^{5}\right)} d^{8} e^{4} - {\left(a^{2} b^{9} + 12 \, a^{3} b^{7} c - 114 \, a^{4} b^{5} c^{2} + 80 \, a^{5} b^{3} c^{3} + 480 \, a^{6} b c^{4}\right)} d^{7} e^{5} + 5 \, {\left(a^{3} b^{8} - 2 \, a^{4} b^{6} c - 30 \, a^{5} b^{4} c^{2} + 80 \, a^{6} b^{2} c^{3} + 32 \, a^{7} c^{4}\right)} d^{6} e^{6} - 10 \, {\left(a^{4} b^{7} - 6 \, a^{5} b^{5} c + 32 \, a^{7} b c^{3}\right)} d^{5} e^{7} + 5 \, {\left(2 \, a^{5} b^{6} - 15 \, a^{6} b^{4} c + 24 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3}\right)} d^{4} e^{8} - 5 \, {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} d^{3} e^{9} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} d^{2} e^{10} + {\left({\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} d^{10} e^{2} - 5 \, {\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} d^{9} e^{3} + 5 \, {\left(2 \, b^{6} c^{5} - 15 \, a b^{4} c^{6} + 24 \, a^{2} b^{2} c^{7} + 16 \, a^{3} c^{8}\right)} d^{8} e^{4} - 10 \, {\left(b^{7} c^{4} - 6 \, a b^{5} c^{5} + 32 \, a^{3} b c^{7}\right)} d^{7} e^{5} + 5 \, {\left(b^{8} c^{3} - 2 \, a b^{6} c^{4} - 30 \, a^{2} b^{4} c^{5} + 80 \, a^{3} b^{2} c^{6} + 32 \, a^{4} c^{7}\right)} d^{6} e^{6} - {\left(b^{9} c^{2} + 12 \, a b^{7} c^{3} - 114 \, a^{2} b^{5} c^{4} + 80 \, a^{3} b^{3} c^{5} + 480 \, a^{4} b c^{6}\right)} d^{5} e^{7} + 5 \, {\left(a b^{8} c^{2} - 2 \, a^{2} b^{6} c^{3} - 30 \, a^{3} b^{4} c^{4} + 80 \, a^{4} b^{2} c^{5} + 32 \, a^{5} c^{6}\right)} d^{4} e^{8} - 10 \, {\left(a^{2} b^{7} c^{2} - 6 \, a^{3} b^{5} c^{3} + 32 \, a^{5} b c^{5}\right)} d^{3} e^{9} + 5 \, {\left(2 \, a^{3} b^{6} c^{2} - 15 \, a^{4} b^{4} c^{3} + 24 \, a^{5} b^{2} c^{4} + 16 \, a^{6} c^{5}\right)} d^{2} e^{10} - 5 \, {\left(a^{4} b^{5} c^{2} - 8 \, a^{5} b^{3} c^{3} + 16 \, a^{6} b c^{4}\right)} d e^{11} + {\left(a^{5} b^{4} c^{2} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} e^{12}\right)} x^{6} + 2 \, {\left({\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} d^{11} e - 4 \, {\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} d^{10} e^{2} + 5 \, {\left(b^{6} c^{5} - 7 \, a b^{4} c^{6} + 8 \, a^{2} b^{2} c^{7} + 16 \, a^{3} c^{8}\right)} d^{9} e^{3} - 15 \, {\left(a b^{5} c^{5} - 8 \, a^{2} b^{3} c^{6} + 16 \, a^{3} b c^{7}\right)} d^{8} e^{4} - 5 \, {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 30 \, a^{2} b^{4} c^{5} - 16 \, a^{3} b^{2} c^{6} - 32 \, a^{4} c^{7}\right)} d^{7} e^{5} + 2 \, {\left(2 \, b^{9} c^{2} - 11 \, a b^{7} c^{3} - 18 \, a^{2} b^{5} c^{4} + 160 \, a^{3} b^{3} c^{5} - 160 \, a^{4} b c^{6}\right)} d^{6} e^{6} - {\left(b^{10} c + 7 \, a b^{8} c^{2} - 104 \, a^{2} b^{6} c^{3} + 230 \, a^{3} b^{4} c^{4} + 80 \, a^{4} b^{2} c^{5} - 160 \, a^{5} c^{6}\right)} d^{5} e^{7} + 5 \, {\left(a b^{9} c - 4 \, a^{2} b^{7} c^{2} - 18 \, a^{3} b^{5} c^{3} + 80 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5}\right)} d^{4} e^{8} - 5 \, {\left(2 \, a^{2} b^{8} c - 14 \, a^{3} b^{6} c^{2} + 15 \, a^{4} b^{4} c^{3} + 40 \, a^{5} b^{2} c^{4} - 16 \, a^{6} c^{5}\right)} d^{3} e^{9} + 10 \, {\left(a^{3} b^{7} c - 8 \, a^{4} b^{5} c^{2} + 16 \, a^{5} b^{3} c^{3}\right)} d^{2} e^{10} - {\left(5 \, a^{4} b^{6} c - 41 \, a^{5} b^{4} c^{2} + 88 \, a^{6} b^{2} c^{3} - 16 \, a^{7} c^{4}\right)} d e^{11} + {\left(a^{5} b^{5} c - 8 \, a^{6} b^{3} c^{2} + 16 \, a^{7} b c^{3}\right)} e^{12}\right)} x^{5} + {\left({\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} d^{12} - {\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} d^{11} e - {\left(9 \, b^{6} c^{5} - 79 \, a b^{4} c^{6} + 200 \, a^{2} b^{2} c^{7} - 112 \, a^{3} c^{8}\right)} d^{10} e^{2} + 5 \, {\left(5 \, b^{7} c^{4} - 42 \, a b^{5} c^{5} + 96 \, a^{2} b^{3} c^{6} - 32 \, a^{3} b c^{7}\right)} d^{9} e^{3} - 5 \, {\left(5 \, b^{8} c^{3} - 35 \, a b^{6} c^{4} + 36 \, a^{2} b^{4} c^{5} + 112 \, a^{3} b^{2} c^{6} - 64 \, a^{4} c^{7}\right)} d^{8} e^{4} + 3 \, {\left(3 \, b^{9} c^{2} - 4 \, a b^{7} c^{3} - 122 \, a^{2} b^{5} c^{4} + 400 \, a^{3} b^{3} c^{5} - 160 \, a^{4} b c^{6}\right)} d^{7} e^{5} + {\left(b^{10} c - 43 \, a b^{8} c^{2} + 276 \, a^{2} b^{6} c^{3} - 370 \, a^{3} b^{4} c^{4} - 560 \, a^{4} b^{2} c^{5} + 480 \, a^{5} c^{6}\right)} d^{6} e^{6} - {\left(b^{11} - 6 \, a b^{9} c - 40 \, a^{2} b^{7} c^{2} + 392 \, a^{3} b^{5} c^{3} - 960 \, a^{4} b^{3} c^{4} + 640 \, a^{5} b c^{5}\right)} d^{5} e^{7} + 5 \, {\left(a b^{10} - 8 \, a^{2} b^{8} c + 16 \, a^{3} b^{6} c^{2} + 5 \, a^{4} b^{4} c^{3} - 40 \, a^{5} b^{2} c^{4} + 80 \, a^{6} c^{5}\right)} d^{4} e^{8} - 5 \, {\left(2 \, a^{2} b^{9} - 16 \, a^{3} b^{7} c + 37 \, a^{4} b^{5} c^{2} - 40 \, a^{5} b^{3} c^{3} + 80 \, a^{6} b c^{4}\right)} d^{3} e^{9} + {\left(10 \, a^{3} b^{8} - 75 \, a^{4} b^{6} c + 131 \, a^{5} b^{4} c^{2} - 8 \, a^{6} b^{2} c^{3} + 176 \, a^{7} c^{4}\right)} d^{2} e^{10} - {\left(5 \, a^{4} b^{7} - 34 \, a^{5} b^{5} c + 32 \, a^{6} b^{3} c^{2} + 96 \, a^{7} b c^{3}\right)} d e^{11} + {\left(a^{5} b^{6} - 6 \, a^{6} b^{4} c + 32 \, a^{8} c^{3}\right)} e^{12}\right)} x^{4} + 2 \, {\left({\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} d^{12} - 2 \, {\left(2 \, b^{6} c^{5} - 17 \, a b^{4} c^{6} + 40 \, a^{2} b^{2} c^{7} - 16 \, a^{3} c^{8}\right)} d^{11} e + {\left(5 \, b^{7} c^{4} - 44 \, a b^{5} c^{5} + 112 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} d^{10} e^{2} + 10 \, {\left(a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} + 16 \, a^{4} c^{7}\right)} d^{9} e^{3} - 5 \, {\left(b^{9} c^{2} - 8 \, a b^{7} c^{3} + 21 \, a^{2} b^{5} c^{4} - 40 \, a^{3} b^{3} c^{5} + 80 \, a^{4} b c^{6}\right)} d^{8} e^{4} + 2 \, {\left(2 \, b^{10} c - 11 \, a b^{8} c^{2} + 2 \, a^{2} b^{6} c^{3} + 10 \, a^{3} b^{4} c^{4} + 80 \, a^{4} b^{2} c^{5} + 160 \, a^{5} c^{6}\right)} d^{7} e^{5} - {\left(b^{11} + 4 \, a b^{9} c - 70 \, a^{2} b^{7} c^{2} + 152 \, a^{3} b^{5} c^{3} - 160 \, a^{4} b^{3} c^{4} + 640 \, a^{5} b c^{5}\right)} d^{6} e^{6} + 2 \, {\left(2 \, a b^{10} - 11 \, a^{2} b^{8} c + 2 \, a^{3} b^{6} c^{2} + 10 \, a^{4} b^{4} c^{3} + 80 \, a^{5} b^{2} c^{4} + 160 \, a^{6} c^{5}\right)} d^{5} e^{7} - 5 \, {\left(a^{2} b^{9} - 8 \, a^{3} b^{7} c + 21 \, a^{4} b^{5} c^{2} - 40 \, a^{5} b^{3} c^{3} + 80 \, a^{6} b c^{4}\right)} d^{4} e^{8} + 10 \, {\left(a^{5} b^{4} c^{2} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} d^{3} e^{9} + {\left(5 \, a^{4} b^{7} - 44 \, a^{5} b^{5} c + 112 \, a^{6} b^{3} c^{2} - 64 \, a^{7} b c^{3}\right)} d^{2} e^{10} - 2 \, {\left(2 \, a^{5} b^{6} - 17 \, a^{6} b^{4} c + 40 \, a^{7} b^{2} c^{2} - 16 \, a^{8} c^{3}\right)} d e^{11} + {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} e^{12}\right)} x^{3} + {\left({\left(b^{6} c^{5} - 6 \, a b^{4} c^{6} + 32 \, a^{3} c^{8}\right)} d^{12} - {\left(5 \, b^{7} c^{4} - 34 \, a b^{5} c^{5} + 32 \, a^{2} b^{3} c^{6} + 96 \, a^{3} b c^{7}\right)} d^{11} e + {\left(10 \, b^{8} c^{3} - 75 \, a b^{6} c^{4} + 131 \, a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} + 176 \, a^{4} c^{7}\right)} d^{10} e^{2} - 5 \, {\left(2 \, b^{9} c^{2} - 16 \, a b^{7} c^{3} + 37 \, a^{2} b^{5} c^{4} - 40 \, a^{3} b^{3} c^{5} + 80 \, a^{4} b c^{6}\right)} d^{9} e^{3} + 5 \, {\left(b^{10} c - 8 \, a b^{8} c^{2} + 16 \, a^{2} b^{6} c^{3} + 5 \, a^{3} b^{4} c^{4} - 40 \, a^{4} b^{2} c^{5} + 80 \, a^{5} c^{6}\right)} d^{8} e^{4} - {\left(b^{11} - 6 \, a b^{9} c - 40 \, a^{2} b^{7} c^{2} + 392 \, a^{3} b^{5} c^{3} - 960 \, a^{4} b^{3} c^{4} + 640 \, a^{5} b c^{5}\right)} d^{7} e^{5} + {\left(a b^{10} - 43 \, a^{2} b^{8} c + 276 \, a^{3} b^{6} c^{2} - 370 \, a^{4} b^{4} c^{3} - 560 \, a^{5} b^{2} c^{4} + 480 \, a^{6} c^{5}\right)} d^{6} e^{6} + 3 \, {\left(3 \, a^{2} b^{9} - 4 \, a^{3} b^{7} c - 122 \, a^{4} b^{5} c^{2} + 400 \, a^{5} b^{3} c^{3} - 160 \, a^{6} b c^{4}\right)} d^{5} e^{7} - 5 \, {\left(5 \, a^{3} b^{8} - 35 \, a^{4} b^{6} c + 36 \, a^{5} b^{4} c^{2} + 112 \, a^{6} b^{2} c^{3} - 64 \, a^{7} c^{4}\right)} d^{4} e^{8} + 5 \, {\left(5 \, a^{4} b^{7} - 42 \, a^{5} b^{5} c + 96 \, a^{6} b^{3} c^{2} - 32 \, a^{7} b c^{3}\right)} d^{3} e^{9} - {\left(9 \, a^{5} b^{6} - 79 \, a^{6} b^{4} c + 200 \, a^{7} b^{2} c^{2} - 112 \, a^{8} c^{3}\right)} d^{2} e^{10} - {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} d e^{11} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} e^{12}\right)} x^{2} + 2 \, {\left({\left(a b^{5} c^{5} - 8 \, a^{2} b^{3} c^{6} + 16 \, a^{3} b c^{7}\right)} d^{12} - {\left(5 \, a b^{6} c^{4} - 41 \, a^{2} b^{4} c^{5} + 88 \, a^{3} b^{2} c^{6} - 16 \, a^{4} c^{7}\right)} d^{11} e + 10 \, {\left(a b^{7} c^{3} - 8 \, a^{2} b^{5} c^{4} + 16 \, a^{3} b^{3} c^{5}\right)} d^{10} e^{2} - 5 \, {\left(2 \, a b^{8} c^{2} - 14 \, a^{2} b^{6} c^{3} + 15 \, a^{3} b^{4} c^{4} + 40 \, a^{4} b^{2} c^{5} - 16 \, a^{5} c^{6}\right)} d^{9} e^{3} + 5 \, {\left(a b^{9} c - 4 \, a^{2} b^{7} c^{2} - 18 \, a^{3} b^{5} c^{3} + 80 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5}\right)} d^{8} e^{4} - {\left(a b^{10} + 7 \, a^{2} b^{8} c - 104 \, a^{3} b^{6} c^{2} + 230 \, a^{4} b^{4} c^{3} + 80 \, a^{5} b^{2} c^{4} - 160 \, a^{6} c^{5}\right)} d^{7} e^{5} + 2 \, {\left(2 \, a^{2} b^{9} - 11 \, a^{3} b^{7} c - 18 \, a^{4} b^{5} c^{2} + 160 \, a^{5} b^{3} c^{3} - 160 \, a^{6} b c^{4}\right)} d^{6} e^{6} - 5 \, {\left(a^{3} b^{8} - 10 \, a^{4} b^{6} c + 30 \, a^{5} b^{4} c^{2} - 16 \, a^{6} b^{2} c^{3} - 32 \, a^{7} c^{4}\right)} d^{5} e^{7} - 15 \, {\left(a^{5} b^{5} c - 8 \, a^{6} b^{3} c^{2} + 16 \, a^{7} b c^{3}\right)} d^{4} e^{8} + 5 \, {\left(a^{5} b^{6} - 7 \, a^{6} b^{4} c + 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3}\right)} d^{3} e^{9} - 4 \, {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} d^{2} e^{10} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} d e^{11}\right)} x\right)}}, \frac{15 \, {\left(24 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d^{4} e^{4} - 24 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d^{3} e^{5} + {\left(7 \, a^{2} b^{6} - 60 \, a^{3} b^{4} c + 144 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d^{2} e^{6} + {\left(24 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{2} e^{6} - 24 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d e^{7} + {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{8}\right)} x^{6} + 2 \, {\left(24 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{3} e^{5} - {\left(17 \, b^{6} c^{2} - 132 \, a b^{4} c^{3} + 240 \, a^{2} b^{2} c^{4} + 64 \, a^{3} c^{5}\right)} d e^{7} + {\left(7 \, b^{7} c - 60 \, a b^{5} c^{2} + 144 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e^{8}\right)} x^{5} + {\left(24 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{4} e^{4} + 72 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{3} e^{5} - {\left(65 \, b^{6} c^{2} - 564 \, a b^{4} c^{3} + 1392 \, a^{2} b^{2} c^{4} - 704 \, a^{3} c^{5}\right)} d^{2} e^{6} + 4 \, {\left(b^{7} c - 24 \, a b^{5} c^{2} + 144 \, a^{2} b^{3} c^{3} - 256 \, a^{3} b c^{4}\right)} d e^{7} + {\left(7 \, b^{8} - 46 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 224 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} e^{8}\right)} x^{4} + 2 \, {\left(24 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d^{4} e^{4} + 48 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d^{3} e^{5} - {\left(17 \, b^{7} c - 108 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} + 448 \, a^{3} b c^{4}\right)} d^{2} e^{6} + {\left(7 \, b^{8} - 70 \, a b^{6} c + 216 \, a^{2} b^{4} c^{2} - 160 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d e^{7} + {\left(7 \, a b^{7} - 60 \, a^{2} b^{5} c + 144 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} e^{8}\right)} x^{3} + {\left(24 \, {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} d^{4} e^{4} - 24 \, {\left(b^{7} c - 10 \, a b^{5} c^{2} + 32 \, a^{2} b^{3} c^{3} - 32 \, a^{3} b c^{4}\right)} d^{3} e^{5} + {\left(7 \, b^{8} - 142 \, a b^{6} c + 816 \, a^{2} b^{4} c^{2} - 1504 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} d^{2} e^{6} + 4 \, {\left(7 \, a b^{7} - 66 \, a^{2} b^{5} c + 192 \, a^{3} b^{3} c^{2} - 160 \, a^{4} b c^{3}\right)} d e^{7} + {\left(7 \, a^{2} b^{6} - 60 \, a^{3} b^{4} c + 144 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} e^{8}\right)} x^{2} + 2 \, {\left(24 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} d^{4} e^{4} - 24 \, {\left(a b^{6} c - 9 \, a^{2} b^{4} c^{2} + 24 \, a^{3} b^{2} c^{3} - 16 \, a^{4} c^{4}\right)} d^{3} e^{5} + 7 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d^{2} e^{6} + {\left(7 \, a^{2} b^{6} - 60 \, a^{3} b^{4} c + 144 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d e^{7}\right)} x\right)} \sqrt{-c d^{2} + b d e - a e^{2}} \arctan\left(-\frac{\sqrt{-c d^{2} + b d e - a e^{2}} \sqrt{c x^{2} + b x + a} {\left(b d - 2 \, a e + {\left(2 \, c d - b e\right)} x\right)}}{2 \, {\left(a c d^{2} - a b d e + a^{2} e^{2} + {\left(c^{2} d^{2} - b c d e + a c e^{2}\right)} x^{2} + {\left(b c d^{2} - b^{2} d e + a b e^{2}\right)} x\right)}}\right) - 2 \, {\left(8 \, {\left(b^{3} c^{5} - 12 \, a b c^{6}\right)} d^{9} - 8 \, {\left(5 \, b^{4} c^{4} - 54 \, a b^{2} c^{5} + 24 \, a^{2} c^{6}\right)} d^{8} e + 8 \, {\left(10 \, b^{5} c^{3} - 85 \, a b^{3} c^{4} + 12 \, a^{2} b c^{5}\right)} d^{7} e^{2} - 80 \, {\left(b^{6} c^{2} - 4 \, a b^{4} c^{3} - 21 \, a^{2} b^{2} c^{4} + 28 \, a^{3} c^{5}\right)} d^{6} e^{3} + 40 \, {\left(b^{7} c + 6 \, a b^{5} c^{2} - 85 \, a^{2} b^{3} c^{3} + 124 \, a^{3} b c^{4}\right)} d^{5} e^{4} - 8 \, {\left(b^{8} + 38 \, a b^{6} c - 300 \, a^{2} b^{4} c^{2} + 430 \, a^{3} b^{2} c^{3} + 56 \, a^{4} c^{4}\right)} d^{4} e^{5} + {\left(88 \, a b^{7} - 543 \, a^{2} b^{5} c + 480 \, a^{3} b^{3} c^{2} + 688 \, a^{4} b c^{3}\right)} d^{3} e^{6} - {\left(41 \, a^{2} b^{6} - 390 \, a^{3} b^{4} c + 1296 \, a^{4} b^{2} c^{2} - 1696 \, a^{5} c^{3}\right)} d^{2} e^{7} - 45 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} d e^{8} + 6 \, {\left(a^{4} b^{4} - 8 \, a^{5} b^{2} c + 16 \, a^{6} c^{2}\right)} e^{9} - {\left(128 \, c^{8} d^{7} e^{2} - 448 \, b c^{7} d^{6} e^{3} + 32 \, {\left(13 \, b^{2} c^{6} + 32 \, a c^{7}\right)} d^{5} e^{4} + 80 \, {\left(b^{3} c^{5} - 32 \, a b c^{6}\right)} d^{4} e^{5} - 2 \, {\left(233 \, b^{4} c^{4} - 1704 \, a b^{2} c^{5} + 848 \, a^{2} c^{6}\right)} d^{3} e^{6} + {\left(395 \, b^{5} c^{3} - 2552 \, a b^{3} c^{4} + 2544 \, a^{2} b c^{5}\right)} d^{2} e^{7} - {\left(105 \, b^{6} c^{2} - 470 \, a b^{4} c^{3} - 672 \, a^{2} b^{2} c^{4} + 2592 \, a^{3} c^{5}\right)} d e^{8} + {\left(105 \, a b^{5} c^{2} - 760 \, a^{2} b^{3} c^{3} + 1296 \, a^{3} b c^{4}\right)} e^{9}\right)} x^{5} - {\left(256 \, c^{8} d^{8} e - 704 \, b c^{7} d^{7} e^{2} + 32 \, {\left(5 \, b^{2} c^{6} + 64 \, a c^{7}\right)} d^{6} e^{3} + 112 \, {\left(7 \, b^{3} c^{5} - 32 \, a b c^{6}\right)} d^{5} e^{4} - 8 \, {\left(79 \, b^{4} c^{4} - 192 \, a b^{2} c^{5} + 64 \, a^{2} c^{6}\right)} d^{4} e^{5} - {\left(269 \, b^{5} c^{3} - 2888 \, a b^{3} c^{4} + 3216 \, a^{2} b c^{5}\right)} d^{3} e^{6} + {\left(615 \, b^{6} c^{2} - 4598 \, a b^{4} c^{3} + 7680 \, a^{2} b^{2} c^{4} - 2784 \, a^{3} c^{5}\right)} d^{2} e^{7} - {\left(210 \, b^{7} c - 1185 \, a b^{5} c^{2} + 152 \, a^{2} b^{3} c^{3} + 3696 \, a^{3} b c^{4}\right)} d e^{8} + 6 \, {\left(35 \, a b^{6} c - 265 \, a^{2} b^{4} c^{2} + 504 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} e^{9}\right)} x^{4} - {\left(128 \, c^{8} d^{9} - 64 \, b c^{7} d^{8} e - 16 \, {\left(55 \, b^{2} c^{6} - 76 \, a c^{7}\right)} d^{7} e^{2} + 40 \, {\left(29 \, b^{3} c^{5} - 4 \, a b c^{6}\right)} d^{6} e^{3} + 8 \, {\left(25 \, b^{4} c^{4} - 678 \, a b^{2} c^{5} + 520 \, a^{2} c^{6}\right)} d^{5} e^{4} - 56 \, {\left(23 \, b^{5} c^{3} - 167 \, a b^{3} c^{4} + 204 \, a^{2} b c^{5}\right)} d^{4} e^{5} + 4 \, {\left(201 \, b^{6} c^{2} - 1393 \, a b^{4} c^{3} + 2340 \, a^{2} b^{2} c^{4} - 384 \, a^{3} c^{5}\right)} d^{3} e^{6} + {\left(45 \, b^{7} c - 582 \, a b^{5} c^{2} + 2072 \, a^{2} b^{3} c^{3} - 3264 \, a^{3} b c^{4}\right)} d^{2} e^{7} - 3 \, {\left(35 \, b^{8} - 250 \, a b^{6} c + 516 \, a^{2} b^{4} c^{2} - 848 \, a^{3} b^{2} c^{3} + 1536 \, a^{4} c^{4}\right)} d e^{8} + 3 \, {\left(35 \, a b^{7} - 230 \, a^{2} b^{5} c + 232 \, a^{3} b^{3} c^{2} + 448 \, a^{4} b c^{3}\right)} e^{9}\right)} x^{3} - {\left(192 \, b c^{7} d^{9} - 192 \, {\left(3 \, b^{2} c^{6} - 2 \, a c^{7}\right)} d^{8} e + 8 \, {\left(35 \, b^{3} c^{5} + 36 \, a b c^{6}\right)} d^{7} e^{2} + 8 \, {\left(65 \, b^{4} c^{4} - 330 \, a b^{2} c^{5} + 504 \, a^{2} c^{6}\right)} d^{6} e^{3} - 8 \, {\left(55 \, b^{5} c^{3} - 235 \, a b^{3} c^{4} + 732 \, a^{2} b c^{5}\right)} d^{5} e^{4} - 16 \, {\left(22 \, b^{6} c^{2} - 160 \, a b^{4} c^{3} + 57 \, a^{2} b^{2} c^{4} + 28 \, a^{3} c^{5}\right)} d^{4} e^{5} + {\left(551 \, b^{7} c - 3894 \, a b^{5} c^{2} + 5992 \, a^{2} b^{3} c^{3} - 1408 \, a^{3} b c^{4}\right)} d^{3} e^{6} - {\left(175 \, b^{8} - 1282 \, a b^{6} c + 2724 \, a^{2} b^{4} c^{2} - 3344 \, a^{3} b^{2} c^{3} + 4736 \, a^{4} c^{4}\right)} d^{2} e^{7} + {\left(35 \, a b^{7} - 402 \, a^{2} b^{5} c + 1608 \, a^{3} b^{3} c^{2} - 2176 \, a^{4} b c^{3}\right)} d e^{8} + 4 \, {\left(35 \, a^{2} b^{6} - 279 \, a^{3} b^{4} c + 588 \, a^{4} b^{2} c^{2} - 160 \, a^{5} c^{3}\right)} e^{9}\right)} x^{2} - {\left(48 \, {\left(b^{2} c^{6} + 4 \, a c^{7}\right)} d^{9} - 8 \, {\left(23 \, b^{3} c^{5} + 60 \, a b c^{6}\right)} d^{8} e + 8 \, {\left(25 \, b^{4} c^{4} + 54 \, a b^{2} c^{5} + 168 \, a^{2} c^{6}\right)} d^{7} e^{2} + 8 \, {\left(10 \, b^{5} c^{3} - 145 \, a b^{3} c^{4} - 84 \, a^{2} b c^{5}\right)} d^{6} e^{3} - 80 \, {\left(4 \, b^{6} c^{2} - 31 \, a b^{4} c^{3} + 57 \, a^{2} b^{2} c^{4} - 44 \, a^{3} c^{5}\right)} d^{5} e^{4} + 8 \, {\left(29 \, b^{7} c - 294 \, a b^{5} c^{2} + 1015 \, a^{2} b^{3} c^{3} - 1156 \, a^{3} b c^{4}\right)} d^{4} e^{5} - 2 \, {\left(28 \, b^{8} - 535 \, a b^{6} c + 2805 \, a^{2} b^{4} c^{2} - 4064 \, a^{3} b^{2} c^{3} - 208 \, a^{4} c^{4}\right)} d^{3} e^{6} - {\left(182 \, a b^{7} - 951 \, a^{2} b^{5} c - 624 \, a^{3} b^{3} c^{2} + 5360 \, a^{4} b c^{3}\right)} d^{2} e^{7} + {\left(217 \, a^{2} b^{6} - 1770 \, a^{3} b^{4} c + 4032 \, a^{4} b^{2} c^{2} - 1952 \, a^{5} c^{3}\right)} d e^{8} + 21 \, {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} e^{9}\right)} x\right)} \sqrt{c x^{2} + b x + a}}{24 \, {\left({\left(a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} + 16 \, a^{4} c^{7}\right)} d^{12} - 5 \, {\left(a^{2} b^{5} c^{4} - 8 \, a^{3} b^{3} c^{5} + 16 \, a^{4} b c^{6}\right)} d^{11} e + 5 \, {\left(2 \, a^{2} b^{6} c^{3} - 15 \, a^{3} b^{4} c^{4} + 24 \, a^{4} b^{2} c^{5} + 16 \, a^{5} c^{6}\right)} d^{10} e^{2} - 10 \, {\left(a^{2} b^{7} c^{2} - 6 \, a^{3} b^{5} c^{3} + 32 \, a^{5} b c^{5}\right)} d^{9} e^{3} + 5 \, {\left(a^{2} b^{8} c - 2 \, a^{3} b^{6} c^{2} - 30 \, a^{4} b^{4} c^{3} + 80 \, a^{5} b^{2} c^{4} + 32 \, a^{6} c^{5}\right)} d^{8} e^{4} - {\left(a^{2} b^{9} + 12 \, a^{3} b^{7} c - 114 \, a^{4} b^{5} c^{2} + 80 \, a^{5} b^{3} c^{3} + 480 \, a^{6} b c^{4}\right)} d^{7} e^{5} + 5 \, {\left(a^{3} b^{8} - 2 \, a^{4} b^{6} c - 30 \, a^{5} b^{4} c^{2} + 80 \, a^{6} b^{2} c^{3} + 32 \, a^{7} c^{4}\right)} d^{6} e^{6} - 10 \, {\left(a^{4} b^{7} - 6 \, a^{5} b^{5} c + 32 \, a^{7} b c^{3}\right)} d^{5} e^{7} + 5 \, {\left(2 \, a^{5} b^{6} - 15 \, a^{6} b^{4} c + 24 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3}\right)} d^{4} e^{8} - 5 \, {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} d^{3} e^{9} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} d^{2} e^{10} + {\left({\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} d^{10} e^{2} - 5 \, {\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} d^{9} e^{3} + 5 \, {\left(2 \, b^{6} c^{5} - 15 \, a b^{4} c^{6} + 24 \, a^{2} b^{2} c^{7} + 16 \, a^{3} c^{8}\right)} d^{8} e^{4} - 10 \, {\left(b^{7} c^{4} - 6 \, a b^{5} c^{5} + 32 \, a^{3} b c^{7}\right)} d^{7} e^{5} + 5 \, {\left(b^{8} c^{3} - 2 \, a b^{6} c^{4} - 30 \, a^{2} b^{4} c^{5} + 80 \, a^{3} b^{2} c^{6} + 32 \, a^{4} c^{7}\right)} d^{6} e^{6} - {\left(b^{9} c^{2} + 12 \, a b^{7} c^{3} - 114 \, a^{2} b^{5} c^{4} + 80 \, a^{3} b^{3} c^{5} + 480 \, a^{4} b c^{6}\right)} d^{5} e^{7} + 5 \, {\left(a b^{8} c^{2} - 2 \, a^{2} b^{6} c^{3} - 30 \, a^{3} b^{4} c^{4} + 80 \, a^{4} b^{2} c^{5} + 32 \, a^{5} c^{6}\right)} d^{4} e^{8} - 10 \, {\left(a^{2} b^{7} c^{2} - 6 \, a^{3} b^{5} c^{3} + 32 \, a^{5} b c^{5}\right)} d^{3} e^{9} + 5 \, {\left(2 \, a^{3} b^{6} c^{2} - 15 \, a^{4} b^{4} c^{3} + 24 \, a^{5} b^{2} c^{4} + 16 \, a^{6} c^{5}\right)} d^{2} e^{10} - 5 \, {\left(a^{4} b^{5} c^{2} - 8 \, a^{5} b^{3} c^{3} + 16 \, a^{6} b c^{4}\right)} d e^{11} + {\left(a^{5} b^{4} c^{2} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} e^{12}\right)} x^{6} + 2 \, {\left({\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} d^{11} e - 4 \, {\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} d^{10} e^{2} + 5 \, {\left(b^{6} c^{5} - 7 \, a b^{4} c^{6} + 8 \, a^{2} b^{2} c^{7} + 16 \, a^{3} c^{8}\right)} d^{9} e^{3} - 15 \, {\left(a b^{5} c^{5} - 8 \, a^{2} b^{3} c^{6} + 16 \, a^{3} b c^{7}\right)} d^{8} e^{4} - 5 \, {\left(b^{8} c^{3} - 10 \, a b^{6} c^{4} + 30 \, a^{2} b^{4} c^{5} - 16 \, a^{3} b^{2} c^{6} - 32 \, a^{4} c^{7}\right)} d^{7} e^{5} + 2 \, {\left(2 \, b^{9} c^{2} - 11 \, a b^{7} c^{3} - 18 \, a^{2} b^{5} c^{4} + 160 \, a^{3} b^{3} c^{5} - 160 \, a^{4} b c^{6}\right)} d^{6} e^{6} - {\left(b^{10} c + 7 \, a b^{8} c^{2} - 104 \, a^{2} b^{6} c^{3} + 230 \, a^{3} b^{4} c^{4} + 80 \, a^{4} b^{2} c^{5} - 160 \, a^{5} c^{6}\right)} d^{5} e^{7} + 5 \, {\left(a b^{9} c - 4 \, a^{2} b^{7} c^{2} - 18 \, a^{3} b^{5} c^{3} + 80 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5}\right)} d^{4} e^{8} - 5 \, {\left(2 \, a^{2} b^{8} c - 14 \, a^{3} b^{6} c^{2} + 15 \, a^{4} b^{4} c^{3} + 40 \, a^{5} b^{2} c^{4} - 16 \, a^{6} c^{5}\right)} d^{3} e^{9} + 10 \, {\left(a^{3} b^{7} c - 8 \, a^{4} b^{5} c^{2} + 16 \, a^{5} b^{3} c^{3}\right)} d^{2} e^{10} - {\left(5 \, a^{4} b^{6} c - 41 \, a^{5} b^{4} c^{2} + 88 \, a^{6} b^{2} c^{3} - 16 \, a^{7} c^{4}\right)} d e^{11} + {\left(a^{5} b^{5} c - 8 \, a^{6} b^{3} c^{2} + 16 \, a^{7} b c^{3}\right)} e^{12}\right)} x^{5} + {\left({\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} d^{12} - {\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} d^{11} e - {\left(9 \, b^{6} c^{5} - 79 \, a b^{4} c^{6} + 200 \, a^{2} b^{2} c^{7} - 112 \, a^{3} c^{8}\right)} d^{10} e^{2} + 5 \, {\left(5 \, b^{7} c^{4} - 42 \, a b^{5} c^{5} + 96 \, a^{2} b^{3} c^{6} - 32 \, a^{3} b c^{7}\right)} d^{9} e^{3} - 5 \, {\left(5 \, b^{8} c^{3} - 35 \, a b^{6} c^{4} + 36 \, a^{2} b^{4} c^{5} + 112 \, a^{3} b^{2} c^{6} - 64 \, a^{4} c^{7}\right)} d^{8} e^{4} + 3 \, {\left(3 \, b^{9} c^{2} - 4 \, a b^{7} c^{3} - 122 \, a^{2} b^{5} c^{4} + 400 \, a^{3} b^{3} c^{5} - 160 \, a^{4} b c^{6}\right)} d^{7} e^{5} + {\left(b^{10} c - 43 \, a b^{8} c^{2} + 276 \, a^{2} b^{6} c^{3} - 370 \, a^{3} b^{4} c^{4} - 560 \, a^{4} b^{2} c^{5} + 480 \, a^{5} c^{6}\right)} d^{6} e^{6} - {\left(b^{11} - 6 \, a b^{9} c - 40 \, a^{2} b^{7} c^{2} + 392 \, a^{3} b^{5} c^{3} - 960 \, a^{4} b^{3} c^{4} + 640 \, a^{5} b c^{5}\right)} d^{5} e^{7} + 5 \, {\left(a b^{10} - 8 \, a^{2} b^{8} c + 16 \, a^{3} b^{6} c^{2} + 5 \, a^{4} b^{4} c^{3} - 40 \, a^{5} b^{2} c^{4} + 80 \, a^{6} c^{5}\right)} d^{4} e^{8} - 5 \, {\left(2 \, a^{2} b^{9} - 16 \, a^{3} b^{7} c + 37 \, a^{4} b^{5} c^{2} - 40 \, a^{5} b^{3} c^{3} + 80 \, a^{6} b c^{4}\right)} d^{3} e^{9} + {\left(10 \, a^{3} b^{8} - 75 \, a^{4} b^{6} c + 131 \, a^{5} b^{4} c^{2} - 8 \, a^{6} b^{2} c^{3} + 176 \, a^{7} c^{4}\right)} d^{2} e^{10} - {\left(5 \, a^{4} b^{7} - 34 \, a^{5} b^{5} c + 32 \, a^{6} b^{3} c^{2} + 96 \, a^{7} b c^{3}\right)} d e^{11} + {\left(a^{5} b^{6} - 6 \, a^{6} b^{4} c + 32 \, a^{8} c^{3}\right)} e^{12}\right)} x^{4} + 2 \, {\left({\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} d^{12} - 2 \, {\left(2 \, b^{6} c^{5} - 17 \, a b^{4} c^{6} + 40 \, a^{2} b^{2} c^{7} - 16 \, a^{3} c^{8}\right)} d^{11} e + {\left(5 \, b^{7} c^{4} - 44 \, a b^{5} c^{5} + 112 \, a^{2} b^{3} c^{6} - 64 \, a^{3} b c^{7}\right)} d^{10} e^{2} + 10 \, {\left(a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} + 16 \, a^{4} c^{7}\right)} d^{9} e^{3} - 5 \, {\left(b^{9} c^{2} - 8 \, a b^{7} c^{3} + 21 \, a^{2} b^{5} c^{4} - 40 \, a^{3} b^{3} c^{5} + 80 \, a^{4} b c^{6}\right)} d^{8} e^{4} + 2 \, {\left(2 \, b^{10} c - 11 \, a b^{8} c^{2} + 2 \, a^{2} b^{6} c^{3} + 10 \, a^{3} b^{4} c^{4} + 80 \, a^{4} b^{2} c^{5} + 160 \, a^{5} c^{6}\right)} d^{7} e^{5} - {\left(b^{11} + 4 \, a b^{9} c - 70 \, a^{2} b^{7} c^{2} + 152 \, a^{3} b^{5} c^{3} - 160 \, a^{4} b^{3} c^{4} + 640 \, a^{5} b c^{5}\right)} d^{6} e^{6} + 2 \, {\left(2 \, a b^{10} - 11 \, a^{2} b^{8} c + 2 \, a^{3} b^{6} c^{2} + 10 \, a^{4} b^{4} c^{3} + 80 \, a^{5} b^{2} c^{4} + 160 \, a^{6} c^{5}\right)} d^{5} e^{7} - 5 \, {\left(a^{2} b^{9} - 8 \, a^{3} b^{7} c + 21 \, a^{4} b^{5} c^{2} - 40 \, a^{5} b^{3} c^{3} + 80 \, a^{6} b c^{4}\right)} d^{4} e^{8} + 10 \, {\left(a^{5} b^{4} c^{2} - 8 \, a^{6} b^{2} c^{3} + 16 \, a^{7} c^{4}\right)} d^{3} e^{9} + {\left(5 \, a^{4} b^{7} - 44 \, a^{5} b^{5} c + 112 \, a^{6} b^{3} c^{2} - 64 \, a^{7} b c^{3}\right)} d^{2} e^{10} - 2 \, {\left(2 \, a^{5} b^{6} - 17 \, a^{6} b^{4} c + 40 \, a^{7} b^{2} c^{2} - 16 \, a^{8} c^{3}\right)} d e^{11} + {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} e^{12}\right)} x^{3} + {\left({\left(b^{6} c^{5} - 6 \, a b^{4} c^{6} + 32 \, a^{3} c^{8}\right)} d^{12} - {\left(5 \, b^{7} c^{4} - 34 \, a b^{5} c^{5} + 32 \, a^{2} b^{3} c^{6} + 96 \, a^{3} b c^{7}\right)} d^{11} e + {\left(10 \, b^{8} c^{3} - 75 \, a b^{6} c^{4} + 131 \, a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} + 176 \, a^{4} c^{7}\right)} d^{10} e^{2} - 5 \, {\left(2 \, b^{9} c^{2} - 16 \, a b^{7} c^{3} + 37 \, a^{2} b^{5} c^{4} - 40 \, a^{3} b^{3} c^{5} + 80 \, a^{4} b c^{6}\right)} d^{9} e^{3} + 5 \, {\left(b^{10} c - 8 \, a b^{8} c^{2} + 16 \, a^{2} b^{6} c^{3} + 5 \, a^{3} b^{4} c^{4} - 40 \, a^{4} b^{2} c^{5} + 80 \, a^{5} c^{6}\right)} d^{8} e^{4} - {\left(b^{11} - 6 \, a b^{9} c - 40 \, a^{2} b^{7} c^{2} + 392 \, a^{3} b^{5} c^{3} - 960 \, a^{4} b^{3} c^{4} + 640 \, a^{5} b c^{5}\right)} d^{7} e^{5} + {\left(a b^{10} - 43 \, a^{2} b^{8} c + 276 \, a^{3} b^{6} c^{2} - 370 \, a^{4} b^{4} c^{3} - 560 \, a^{5} b^{2} c^{4} + 480 \, a^{6} c^{5}\right)} d^{6} e^{6} + 3 \, {\left(3 \, a^{2} b^{9} - 4 \, a^{3} b^{7} c - 122 \, a^{4} b^{5} c^{2} + 400 \, a^{5} b^{3} c^{3} - 160 \, a^{6} b c^{4}\right)} d^{5} e^{7} - 5 \, {\left(5 \, a^{3} b^{8} - 35 \, a^{4} b^{6} c + 36 \, a^{5} b^{4} c^{2} + 112 \, a^{6} b^{2} c^{3} - 64 \, a^{7} c^{4}\right)} d^{4} e^{8} + 5 \, {\left(5 \, a^{4} b^{7} - 42 \, a^{5} b^{5} c + 96 \, a^{6} b^{3} c^{2} - 32 \, a^{7} b c^{3}\right)} d^{3} e^{9} - {\left(9 \, a^{5} b^{6} - 79 \, a^{6} b^{4} c + 200 \, a^{7} b^{2} c^{2} - 112 \, a^{8} c^{3}\right)} d^{2} e^{10} - {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} d e^{11} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} e^{12}\right)} x^{2} + 2 \, {\left({\left(a b^{5} c^{5} - 8 \, a^{2} b^{3} c^{6} + 16 \, a^{3} b c^{7}\right)} d^{12} - {\left(5 \, a b^{6} c^{4} - 41 \, a^{2} b^{4} c^{5} + 88 \, a^{3} b^{2} c^{6} - 16 \, a^{4} c^{7}\right)} d^{11} e + 10 \, {\left(a b^{7} c^{3} - 8 \, a^{2} b^{5} c^{4} + 16 \, a^{3} b^{3} c^{5}\right)} d^{10} e^{2} - 5 \, {\left(2 \, a b^{8} c^{2} - 14 \, a^{2} b^{6} c^{3} + 15 \, a^{3} b^{4} c^{4} + 40 \, a^{4} b^{2} c^{5} - 16 \, a^{5} c^{6}\right)} d^{9} e^{3} + 5 \, {\left(a b^{9} c - 4 \, a^{2} b^{7} c^{2} - 18 \, a^{3} b^{5} c^{3} + 80 \, a^{4} b^{3} c^{4} - 32 \, a^{5} b c^{5}\right)} d^{8} e^{4} - {\left(a b^{10} + 7 \, a^{2} b^{8} c - 104 \, a^{3} b^{6} c^{2} + 230 \, a^{4} b^{4} c^{3} + 80 \, a^{5} b^{2} c^{4} - 160 \, a^{6} c^{5}\right)} d^{7} e^{5} + 2 \, {\left(2 \, a^{2} b^{9} - 11 \, a^{3} b^{7} c - 18 \, a^{4} b^{5} c^{2} + 160 \, a^{5} b^{3} c^{3} - 160 \, a^{6} b c^{4}\right)} d^{6} e^{6} - 5 \, {\left(a^{3} b^{8} - 10 \, a^{4} b^{6} c + 30 \, a^{5} b^{4} c^{2} - 16 \, a^{6} b^{2} c^{3} - 32 \, a^{7} c^{4}\right)} d^{5} e^{7} - 15 \, {\left(a^{5} b^{5} c - 8 \, a^{6} b^{3} c^{2} + 16 \, a^{7} b c^{3}\right)} d^{4} e^{8} + 5 \, {\left(a^{5} b^{6} - 7 \, a^{6} b^{4} c + 8 \, a^{7} b^{2} c^{2} + 16 \, a^{8} c^{3}\right)} d^{3} e^{9} - 4 \, {\left(a^{6} b^{5} - 8 \, a^{7} b^{3} c + 16 \, a^{8} b c^{2}\right)} d^{2} e^{10} + {\left(a^{7} b^{4} - 8 \, a^{8} b^{2} c + 16 \, a^{9} c^{2}\right)} d e^{11}\right)} x\right)}}\right]"," ",0,"[-1/48*(15*(24*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^4*e^4 - 24*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^3*e^5 + (7*a^2*b^6 - 60*a^3*b^4*c + 144*a^4*b^2*c^2 - 64*a^5*c^3)*d^2*e^6 + (24*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^2*e^6 - 24*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d*e^7 + (7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*e^8)*x^6 + 2*(24*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^3*e^5 - (17*b^6*c^2 - 132*a*b^4*c^3 + 240*a^2*b^2*c^4 + 64*a^3*c^5)*d*e^7 + (7*b^7*c - 60*a*b^5*c^2 + 144*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^8)*x^5 + (24*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^4*e^4 + 72*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^3*e^5 - (65*b^6*c^2 - 564*a*b^4*c^3 + 1392*a^2*b^2*c^4 - 704*a^3*c^5)*d^2*e^6 + 4*(b^7*c - 24*a*b^5*c^2 + 144*a^2*b^3*c^3 - 256*a^3*b*c^4)*d*e^7 + (7*b^8 - 46*a*b^6*c + 24*a^2*b^4*c^2 + 224*a^3*b^2*c^3 - 128*a^4*c^4)*e^8)*x^4 + 2*(24*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^4*e^4 + 48*(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*d^3*e^5 - (17*b^7*c - 108*a*b^5*c^2 + 48*a^2*b^3*c^3 + 448*a^3*b*c^4)*d^2*e^6 + (7*b^8 - 70*a*b^6*c + 216*a^2*b^4*c^2 - 160*a^3*b^2*c^3 - 128*a^4*c^4)*d*e^7 + (7*a*b^7 - 60*a^2*b^5*c + 144*a^3*b^3*c^2 - 64*a^4*b*c^3)*e^8)*x^3 + (24*(b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*d^4*e^4 - 24*(b^7*c - 10*a*b^5*c^2 + 32*a^2*b^3*c^3 - 32*a^3*b*c^4)*d^3*e^5 + (7*b^8 - 142*a*b^6*c + 816*a^2*b^4*c^2 - 1504*a^3*b^2*c^3 + 256*a^4*c^4)*d^2*e^6 + 4*(7*a*b^7 - 66*a^2*b^5*c + 192*a^3*b^3*c^2 - 160*a^4*b*c^3)*d*e^7 + (7*a^2*b^6 - 60*a^3*b^4*c + 144*a^4*b^2*c^2 - 64*a^5*c^3)*e^8)*x^2 + 2*(24*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*d^4*e^4 - 24*(a*b^6*c - 9*a^2*b^4*c^2 + 24*a^3*b^2*c^3 - 16*a^4*c^4)*d^3*e^5 + 7*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2*e^6 + (7*a^2*b^6 - 60*a^3*b^4*c + 144*a^4*b^2*c^2 - 64*a^5*c^3)*d*e^7)*x)*sqrt(c*d^2 - b*d*e + a*e^2)*log((8*a*b*d*e - 8*a^2*e^2 - (b^2 + 4*a*c)*d^2 - (8*c^2*d^2 - 8*b*c*d*e + (b^2 + 4*a*c)*e^2)*x^2 + 4*sqrt(c*d^2 - b*d*e + a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x) - 2*(4*b*c*d^2 + 4*a*b*e^2 - (3*b^2 + 4*a*c)*d*e)*x)/(e^2*x^2 + 2*d*e*x + d^2)) + 4*(8*(b^3*c^5 - 12*a*b*c^6)*d^9 - 8*(5*b^4*c^4 - 54*a*b^2*c^5 + 24*a^2*c^6)*d^8*e + 8*(10*b^5*c^3 - 85*a*b^3*c^4 + 12*a^2*b*c^5)*d^7*e^2 - 80*(b^6*c^2 - 4*a*b^4*c^3 - 21*a^2*b^2*c^4 + 28*a^3*c^5)*d^6*e^3 + 40*(b^7*c + 6*a*b^5*c^2 - 85*a^2*b^3*c^3 + 124*a^3*b*c^4)*d^5*e^4 - 8*(b^8 + 38*a*b^6*c - 300*a^2*b^4*c^2 + 430*a^3*b^2*c^3 + 56*a^4*c^4)*d^4*e^5 + (88*a*b^7 - 543*a^2*b^5*c + 480*a^3*b^3*c^2 + 688*a^4*b*c^3)*d^3*e^6 - (41*a^2*b^6 - 390*a^3*b^4*c + 1296*a^4*b^2*c^2 - 1696*a^5*c^3)*d^2*e^7 - 45*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d*e^8 + 6*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*e^9 - (128*c^8*d^7*e^2 - 448*b*c^7*d^6*e^3 + 32*(13*b^2*c^6 + 32*a*c^7)*d^5*e^4 + 80*(b^3*c^5 - 32*a*b*c^6)*d^4*e^5 - 2*(233*b^4*c^4 - 1704*a*b^2*c^5 + 848*a^2*c^6)*d^3*e^6 + (395*b^5*c^3 - 2552*a*b^3*c^4 + 2544*a^2*b*c^5)*d^2*e^7 - (105*b^6*c^2 - 470*a*b^4*c^3 - 672*a^2*b^2*c^4 + 2592*a^3*c^5)*d*e^8 + (105*a*b^5*c^2 - 760*a^2*b^3*c^3 + 1296*a^3*b*c^4)*e^9)*x^5 - (256*c^8*d^8*e - 704*b*c^7*d^7*e^2 + 32*(5*b^2*c^6 + 64*a*c^7)*d^6*e^3 + 112*(7*b^3*c^5 - 32*a*b*c^6)*d^5*e^4 - 8*(79*b^4*c^4 - 192*a*b^2*c^5 + 64*a^2*c^6)*d^4*e^5 - (269*b^5*c^3 - 2888*a*b^3*c^4 + 3216*a^2*b*c^5)*d^3*e^6 + (615*b^6*c^2 - 4598*a*b^4*c^3 + 7680*a^2*b^2*c^4 - 2784*a^3*c^5)*d^2*e^7 - (210*b^7*c - 1185*a*b^5*c^2 + 152*a^2*b^3*c^3 + 3696*a^3*b*c^4)*d*e^8 + 6*(35*a*b^6*c - 265*a^2*b^4*c^2 + 504*a^3*b^2*c^3 - 80*a^4*c^4)*e^9)*x^4 - (128*c^8*d^9 - 64*b*c^7*d^8*e - 16*(55*b^2*c^6 - 76*a*c^7)*d^7*e^2 + 40*(29*b^3*c^5 - 4*a*b*c^6)*d^6*e^3 + 8*(25*b^4*c^4 - 678*a*b^2*c^5 + 520*a^2*c^6)*d^5*e^4 - 56*(23*b^5*c^3 - 167*a*b^3*c^4 + 204*a^2*b*c^5)*d^4*e^5 + 4*(201*b^6*c^2 - 1393*a*b^4*c^3 + 2340*a^2*b^2*c^4 - 384*a^3*c^5)*d^3*e^6 + (45*b^7*c - 582*a*b^5*c^2 + 2072*a^2*b^3*c^3 - 3264*a^3*b*c^4)*d^2*e^7 - 3*(35*b^8 - 250*a*b^6*c + 516*a^2*b^4*c^2 - 848*a^3*b^2*c^3 + 1536*a^4*c^4)*d*e^8 + 3*(35*a*b^7 - 230*a^2*b^5*c + 232*a^3*b^3*c^2 + 448*a^4*b*c^3)*e^9)*x^3 - (192*b*c^7*d^9 - 192*(3*b^2*c^6 - 2*a*c^7)*d^8*e + 8*(35*b^3*c^5 + 36*a*b*c^6)*d^7*e^2 + 8*(65*b^4*c^4 - 330*a*b^2*c^5 + 504*a^2*c^6)*d^6*e^3 - 8*(55*b^5*c^3 - 235*a*b^3*c^4 + 732*a^2*b*c^5)*d^5*e^4 - 16*(22*b^6*c^2 - 160*a*b^4*c^3 + 57*a^2*b^2*c^4 + 28*a^3*c^5)*d^4*e^5 + (551*b^7*c - 3894*a*b^5*c^2 + 5992*a^2*b^3*c^3 - 1408*a^3*b*c^4)*d^3*e^6 - (175*b^8 - 1282*a*b^6*c + 2724*a^2*b^4*c^2 - 3344*a^3*b^2*c^3 + 4736*a^4*c^4)*d^2*e^7 + (35*a*b^7 - 402*a^2*b^5*c + 1608*a^3*b^3*c^2 - 2176*a^4*b*c^3)*d*e^8 + 4*(35*a^2*b^6 - 279*a^3*b^4*c + 588*a^4*b^2*c^2 - 160*a^5*c^3)*e^9)*x^2 - (48*(b^2*c^6 + 4*a*c^7)*d^9 - 8*(23*b^3*c^5 + 60*a*b*c^6)*d^8*e + 8*(25*b^4*c^4 + 54*a*b^2*c^5 + 168*a^2*c^6)*d^7*e^2 + 8*(10*b^5*c^3 - 145*a*b^3*c^4 - 84*a^2*b*c^5)*d^6*e^3 - 80*(4*b^6*c^2 - 31*a*b^4*c^3 + 57*a^2*b^2*c^4 - 44*a^3*c^5)*d^5*e^4 + 8*(29*b^7*c - 294*a*b^5*c^2 + 1015*a^2*b^3*c^3 - 1156*a^3*b*c^4)*d^4*e^5 - 2*(28*b^8 - 535*a*b^6*c + 2805*a^2*b^4*c^2 - 4064*a^3*b^2*c^3 - 208*a^4*c^4)*d^3*e^6 - (182*a*b^7 - 951*a^2*b^5*c - 624*a^3*b^3*c^2 + 5360*a^4*b*c^3)*d^2*e^7 + (217*a^2*b^6 - 1770*a^3*b^4*c + 4032*a^4*b^2*c^2 - 1952*a^5*c^3)*d*e^8 + 21*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*e^9)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^4*c^5 - 8*a^3*b^2*c^6 + 16*a^4*c^7)*d^12 - 5*(a^2*b^5*c^4 - 8*a^3*b^3*c^5 + 16*a^4*b*c^6)*d^11*e + 5*(2*a^2*b^6*c^3 - 15*a^3*b^4*c^4 + 24*a^4*b^2*c^5 + 16*a^5*c^6)*d^10*e^2 - 10*(a^2*b^7*c^2 - 6*a^3*b^5*c^3 + 32*a^5*b*c^5)*d^9*e^3 + 5*(a^2*b^8*c - 2*a^3*b^6*c^2 - 30*a^4*b^4*c^3 + 80*a^5*b^2*c^4 + 32*a^6*c^5)*d^8*e^4 - (a^2*b^9 + 12*a^3*b^7*c - 114*a^4*b^5*c^2 + 80*a^5*b^3*c^3 + 480*a^6*b*c^4)*d^7*e^5 + 5*(a^3*b^8 - 2*a^4*b^6*c - 30*a^5*b^4*c^2 + 80*a^6*b^2*c^3 + 32*a^7*c^4)*d^6*e^6 - 10*(a^4*b^7 - 6*a^5*b^5*c + 32*a^7*b*c^3)*d^5*e^7 + 5*(2*a^5*b^6 - 15*a^6*b^4*c + 24*a^7*b^2*c^2 + 16*a^8*c^3)*d^4*e^8 - 5*(a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*d^3*e^9 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*d^2*e^10 + ((b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*d^10*e^2 - 5*(b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*d^9*e^3 + 5*(2*b^6*c^5 - 15*a*b^4*c^6 + 24*a^2*b^2*c^7 + 16*a^3*c^8)*d^8*e^4 - 10*(b^7*c^4 - 6*a*b^5*c^5 + 32*a^3*b*c^7)*d^7*e^5 + 5*(b^8*c^3 - 2*a*b^6*c^4 - 30*a^2*b^4*c^5 + 80*a^3*b^2*c^6 + 32*a^4*c^7)*d^6*e^6 - (b^9*c^2 + 12*a*b^7*c^3 - 114*a^2*b^5*c^4 + 80*a^3*b^3*c^5 + 480*a^4*b*c^6)*d^5*e^7 + 5*(a*b^8*c^2 - 2*a^2*b^6*c^3 - 30*a^3*b^4*c^4 + 80*a^4*b^2*c^5 + 32*a^5*c^6)*d^4*e^8 - 10*(a^2*b^7*c^2 - 6*a^3*b^5*c^3 + 32*a^5*b*c^5)*d^3*e^9 + 5*(2*a^3*b^6*c^2 - 15*a^4*b^4*c^3 + 24*a^5*b^2*c^4 + 16*a^6*c^5)*d^2*e^10 - 5*(a^4*b^5*c^2 - 8*a^5*b^3*c^3 + 16*a^6*b*c^4)*d*e^11 + (a^5*b^4*c^2 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*e^12)*x^6 + 2*((b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*d^11*e - 4*(b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*d^10*e^2 + 5*(b^6*c^5 - 7*a*b^4*c^6 + 8*a^2*b^2*c^7 + 16*a^3*c^8)*d^9*e^3 - 15*(a*b^5*c^5 - 8*a^2*b^3*c^6 + 16*a^3*b*c^7)*d^8*e^4 - 5*(b^8*c^3 - 10*a*b^6*c^4 + 30*a^2*b^4*c^5 - 16*a^3*b^2*c^6 - 32*a^4*c^7)*d^7*e^5 + 2*(2*b^9*c^2 - 11*a*b^7*c^3 - 18*a^2*b^5*c^4 + 160*a^3*b^3*c^5 - 160*a^4*b*c^6)*d^6*e^6 - (b^10*c + 7*a*b^8*c^2 - 104*a^2*b^6*c^3 + 230*a^3*b^4*c^4 + 80*a^4*b^2*c^5 - 160*a^5*c^6)*d^5*e^7 + 5*(a*b^9*c - 4*a^2*b^7*c^2 - 18*a^3*b^5*c^3 + 80*a^4*b^3*c^4 - 32*a^5*b*c^5)*d^4*e^8 - 5*(2*a^2*b^8*c - 14*a^3*b^6*c^2 + 15*a^4*b^4*c^3 + 40*a^5*b^2*c^4 - 16*a^6*c^5)*d^3*e^9 + 10*(a^3*b^7*c - 8*a^4*b^5*c^2 + 16*a^5*b^3*c^3)*d^2*e^10 - (5*a^4*b^6*c - 41*a^5*b^4*c^2 + 88*a^6*b^2*c^3 - 16*a^7*c^4)*d*e^11 + (a^5*b^5*c - 8*a^6*b^3*c^2 + 16*a^7*b*c^3)*e^12)*x^5 + ((b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*d^12 - (b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*d^11*e - (9*b^6*c^5 - 79*a*b^4*c^6 + 200*a^2*b^2*c^7 - 112*a^3*c^8)*d^10*e^2 + 5*(5*b^7*c^4 - 42*a*b^5*c^5 + 96*a^2*b^3*c^6 - 32*a^3*b*c^7)*d^9*e^3 - 5*(5*b^8*c^3 - 35*a*b^6*c^4 + 36*a^2*b^4*c^5 + 112*a^3*b^2*c^6 - 64*a^4*c^7)*d^8*e^4 + 3*(3*b^9*c^2 - 4*a*b^7*c^3 - 122*a^2*b^5*c^4 + 400*a^3*b^3*c^5 - 160*a^4*b*c^6)*d^7*e^5 + (b^10*c - 43*a*b^8*c^2 + 276*a^2*b^6*c^3 - 370*a^3*b^4*c^4 - 560*a^4*b^2*c^5 + 480*a^5*c^6)*d^6*e^6 - (b^11 - 6*a*b^9*c - 40*a^2*b^7*c^2 + 392*a^3*b^5*c^3 - 960*a^4*b^3*c^4 + 640*a^5*b*c^5)*d^5*e^7 + 5*(a*b^10 - 8*a^2*b^8*c + 16*a^3*b^6*c^2 + 5*a^4*b^4*c^3 - 40*a^5*b^2*c^4 + 80*a^6*c^5)*d^4*e^8 - 5*(2*a^2*b^9 - 16*a^3*b^7*c + 37*a^4*b^5*c^2 - 40*a^5*b^3*c^3 + 80*a^6*b*c^4)*d^3*e^9 + (10*a^3*b^8 - 75*a^4*b^6*c + 131*a^5*b^4*c^2 - 8*a^6*b^2*c^3 + 176*a^7*c^4)*d^2*e^10 - (5*a^4*b^7 - 34*a^5*b^5*c + 32*a^6*b^3*c^2 + 96*a^7*b*c^3)*d*e^11 + (a^5*b^6 - 6*a^6*b^4*c + 32*a^8*c^3)*e^12)*x^4 + 2*((b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*d^12 - 2*(2*b^6*c^5 - 17*a*b^4*c^6 + 40*a^2*b^2*c^7 - 16*a^3*c^8)*d^11*e + (5*b^7*c^4 - 44*a*b^5*c^5 + 112*a^2*b^3*c^6 - 64*a^3*b*c^7)*d^10*e^2 + 10*(a^2*b^4*c^5 - 8*a^3*b^2*c^6 + 16*a^4*c^7)*d^9*e^3 - 5*(b^9*c^2 - 8*a*b^7*c^3 + 21*a^2*b^5*c^4 - 40*a^3*b^3*c^5 + 80*a^4*b*c^6)*d^8*e^4 + 2*(2*b^10*c - 11*a*b^8*c^2 + 2*a^2*b^6*c^3 + 10*a^3*b^4*c^4 + 80*a^4*b^2*c^5 + 160*a^5*c^6)*d^7*e^5 - (b^11 + 4*a*b^9*c - 70*a^2*b^7*c^2 + 152*a^3*b^5*c^3 - 160*a^4*b^3*c^4 + 640*a^5*b*c^5)*d^6*e^6 + 2*(2*a*b^10 - 11*a^2*b^8*c + 2*a^3*b^6*c^2 + 10*a^4*b^4*c^3 + 80*a^5*b^2*c^4 + 160*a^6*c^5)*d^5*e^7 - 5*(a^2*b^9 - 8*a^3*b^7*c + 21*a^4*b^5*c^2 - 40*a^5*b^3*c^3 + 80*a^6*b*c^4)*d^4*e^8 + 10*(a^5*b^4*c^2 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*d^3*e^9 + (5*a^4*b^7 - 44*a^5*b^5*c + 112*a^6*b^3*c^2 - 64*a^7*b*c^3)*d^2*e^10 - 2*(2*a^5*b^6 - 17*a^6*b^4*c + 40*a^7*b^2*c^2 - 16*a^8*c^3)*d*e^11 + (a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*e^12)*x^3 + ((b^6*c^5 - 6*a*b^4*c^6 + 32*a^3*c^8)*d^12 - (5*b^7*c^4 - 34*a*b^5*c^5 + 32*a^2*b^3*c^6 + 96*a^3*b*c^7)*d^11*e + (10*b^8*c^3 - 75*a*b^6*c^4 + 131*a^2*b^4*c^5 - 8*a^3*b^2*c^6 + 176*a^4*c^7)*d^10*e^2 - 5*(2*b^9*c^2 - 16*a*b^7*c^3 + 37*a^2*b^5*c^4 - 40*a^3*b^3*c^5 + 80*a^4*b*c^6)*d^9*e^3 + 5*(b^10*c - 8*a*b^8*c^2 + 16*a^2*b^6*c^3 + 5*a^3*b^4*c^4 - 40*a^4*b^2*c^5 + 80*a^5*c^6)*d^8*e^4 - (b^11 - 6*a*b^9*c - 40*a^2*b^7*c^2 + 392*a^3*b^5*c^3 - 960*a^4*b^3*c^4 + 640*a^5*b*c^5)*d^7*e^5 + (a*b^10 - 43*a^2*b^8*c + 276*a^3*b^6*c^2 - 370*a^4*b^4*c^3 - 560*a^5*b^2*c^4 + 480*a^6*c^5)*d^6*e^6 + 3*(3*a^2*b^9 - 4*a^3*b^7*c - 122*a^4*b^5*c^2 + 400*a^5*b^3*c^3 - 160*a^6*b*c^4)*d^5*e^7 - 5*(5*a^3*b^8 - 35*a^4*b^6*c + 36*a^5*b^4*c^2 + 112*a^6*b^2*c^3 - 64*a^7*c^4)*d^4*e^8 + 5*(5*a^4*b^7 - 42*a^5*b^5*c + 96*a^6*b^3*c^2 - 32*a^7*b*c^3)*d^3*e^9 - (9*a^5*b^6 - 79*a^6*b^4*c + 200*a^7*b^2*c^2 - 112*a^8*c^3)*d^2*e^10 - (a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*d*e^11 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*e^12)*x^2 + 2*((a*b^5*c^5 - 8*a^2*b^3*c^6 + 16*a^3*b*c^7)*d^12 - (5*a*b^6*c^4 - 41*a^2*b^4*c^5 + 88*a^3*b^2*c^6 - 16*a^4*c^7)*d^11*e + 10*(a*b^7*c^3 - 8*a^2*b^5*c^4 + 16*a^3*b^3*c^5)*d^10*e^2 - 5*(2*a*b^8*c^2 - 14*a^2*b^6*c^3 + 15*a^3*b^4*c^4 + 40*a^4*b^2*c^5 - 16*a^5*c^6)*d^9*e^3 + 5*(a*b^9*c - 4*a^2*b^7*c^2 - 18*a^3*b^5*c^3 + 80*a^4*b^3*c^4 - 32*a^5*b*c^5)*d^8*e^4 - (a*b^10 + 7*a^2*b^8*c - 104*a^3*b^6*c^2 + 230*a^4*b^4*c^3 + 80*a^5*b^2*c^4 - 160*a^6*c^5)*d^7*e^5 + 2*(2*a^2*b^9 - 11*a^3*b^7*c - 18*a^4*b^5*c^2 + 160*a^5*b^3*c^3 - 160*a^6*b*c^4)*d^6*e^6 - 5*(a^3*b^8 - 10*a^4*b^6*c + 30*a^5*b^4*c^2 - 16*a^6*b^2*c^3 - 32*a^7*c^4)*d^5*e^7 - 15*(a^5*b^5*c - 8*a^6*b^3*c^2 + 16*a^7*b*c^3)*d^4*e^8 + 5*(a^5*b^6 - 7*a^6*b^4*c + 8*a^7*b^2*c^2 + 16*a^8*c^3)*d^3*e^9 - 4*(a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*d^2*e^10 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*d*e^11)*x), 1/24*(15*(24*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d^4*e^4 - 24*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d^3*e^5 + (7*a^2*b^6 - 60*a^3*b^4*c + 144*a^4*b^2*c^2 - 64*a^5*c^3)*d^2*e^6 + (24*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^2*e^6 - 24*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d*e^7 + (7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*e^8)*x^6 + 2*(24*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^3*e^5 - (17*b^6*c^2 - 132*a*b^4*c^3 + 240*a^2*b^2*c^4 + 64*a^3*c^5)*d*e^7 + (7*b^7*c - 60*a*b^5*c^2 + 144*a^2*b^3*c^3 - 64*a^3*b*c^4)*e^8)*x^5 + (24*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^4*e^4 + 72*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^3*e^5 - (65*b^6*c^2 - 564*a*b^4*c^3 + 1392*a^2*b^2*c^4 - 704*a^3*c^5)*d^2*e^6 + 4*(b^7*c - 24*a*b^5*c^2 + 144*a^2*b^3*c^3 - 256*a^3*b*c^4)*d*e^7 + (7*b^8 - 46*a*b^6*c + 24*a^2*b^4*c^2 + 224*a^3*b^2*c^3 - 128*a^4*c^4)*e^8)*x^4 + 2*(24*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d^4*e^4 + 48*(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*d^3*e^5 - (17*b^7*c - 108*a*b^5*c^2 + 48*a^2*b^3*c^3 + 448*a^3*b*c^4)*d^2*e^6 + (7*b^8 - 70*a*b^6*c + 216*a^2*b^4*c^2 - 160*a^3*b^2*c^3 - 128*a^4*c^4)*d*e^7 + (7*a*b^7 - 60*a^2*b^5*c + 144*a^3*b^3*c^2 - 64*a^4*b*c^3)*e^8)*x^3 + (24*(b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*d^4*e^4 - 24*(b^7*c - 10*a*b^5*c^2 + 32*a^2*b^3*c^3 - 32*a^3*b*c^4)*d^3*e^5 + (7*b^8 - 142*a*b^6*c + 816*a^2*b^4*c^2 - 1504*a^3*b^2*c^3 + 256*a^4*c^4)*d^2*e^6 + 4*(7*a*b^7 - 66*a^2*b^5*c + 192*a^3*b^3*c^2 - 160*a^4*b*c^3)*d*e^7 + (7*a^2*b^6 - 60*a^3*b^4*c + 144*a^4*b^2*c^2 - 64*a^5*c^3)*e^8)*x^2 + 2*(24*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*d^4*e^4 - 24*(a*b^6*c - 9*a^2*b^4*c^2 + 24*a^3*b^2*c^3 - 16*a^4*c^4)*d^3*e^5 + 7*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2*e^6 + (7*a^2*b^6 - 60*a^3*b^4*c + 144*a^4*b^2*c^2 - 64*a^5*c^3)*d*e^7)*x)*sqrt(-c*d^2 + b*d*e - a*e^2)*arctan(-1/2*sqrt(-c*d^2 + b*d*e - a*e^2)*sqrt(c*x^2 + b*x + a)*(b*d - 2*a*e + (2*c*d - b*e)*x)/(a*c*d^2 - a*b*d*e + a^2*e^2 + (c^2*d^2 - b*c*d*e + a*c*e^2)*x^2 + (b*c*d^2 - b^2*d*e + a*b*e^2)*x)) - 2*(8*(b^3*c^5 - 12*a*b*c^6)*d^9 - 8*(5*b^4*c^4 - 54*a*b^2*c^5 + 24*a^2*c^6)*d^8*e + 8*(10*b^5*c^3 - 85*a*b^3*c^4 + 12*a^2*b*c^5)*d^7*e^2 - 80*(b^6*c^2 - 4*a*b^4*c^3 - 21*a^2*b^2*c^4 + 28*a^3*c^5)*d^6*e^3 + 40*(b^7*c + 6*a*b^5*c^2 - 85*a^2*b^3*c^3 + 124*a^3*b*c^4)*d^5*e^4 - 8*(b^8 + 38*a*b^6*c - 300*a^2*b^4*c^2 + 430*a^3*b^2*c^3 + 56*a^4*c^4)*d^4*e^5 + (88*a*b^7 - 543*a^2*b^5*c + 480*a^3*b^3*c^2 + 688*a^4*b*c^3)*d^3*e^6 - (41*a^2*b^6 - 390*a^3*b^4*c + 1296*a^4*b^2*c^2 - 1696*a^5*c^3)*d^2*e^7 - 45*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*d*e^8 + 6*(a^4*b^4 - 8*a^5*b^2*c + 16*a^6*c^2)*e^9 - (128*c^8*d^7*e^2 - 448*b*c^7*d^6*e^3 + 32*(13*b^2*c^6 + 32*a*c^7)*d^5*e^4 + 80*(b^3*c^5 - 32*a*b*c^6)*d^4*e^5 - 2*(233*b^4*c^4 - 1704*a*b^2*c^5 + 848*a^2*c^6)*d^3*e^6 + (395*b^5*c^3 - 2552*a*b^3*c^4 + 2544*a^2*b*c^5)*d^2*e^7 - (105*b^6*c^2 - 470*a*b^4*c^3 - 672*a^2*b^2*c^4 + 2592*a^3*c^5)*d*e^8 + (105*a*b^5*c^2 - 760*a^2*b^3*c^3 + 1296*a^3*b*c^4)*e^9)*x^5 - (256*c^8*d^8*e - 704*b*c^7*d^7*e^2 + 32*(5*b^2*c^6 + 64*a*c^7)*d^6*e^3 + 112*(7*b^3*c^5 - 32*a*b*c^6)*d^5*e^4 - 8*(79*b^4*c^4 - 192*a*b^2*c^5 + 64*a^2*c^6)*d^4*e^5 - (269*b^5*c^3 - 2888*a*b^3*c^4 + 3216*a^2*b*c^5)*d^3*e^6 + (615*b^6*c^2 - 4598*a*b^4*c^3 + 7680*a^2*b^2*c^4 - 2784*a^3*c^5)*d^2*e^7 - (210*b^7*c - 1185*a*b^5*c^2 + 152*a^2*b^3*c^3 + 3696*a^3*b*c^4)*d*e^8 + 6*(35*a*b^6*c - 265*a^2*b^4*c^2 + 504*a^3*b^2*c^3 - 80*a^4*c^4)*e^9)*x^4 - (128*c^8*d^9 - 64*b*c^7*d^8*e - 16*(55*b^2*c^6 - 76*a*c^7)*d^7*e^2 + 40*(29*b^3*c^5 - 4*a*b*c^6)*d^6*e^3 + 8*(25*b^4*c^4 - 678*a*b^2*c^5 + 520*a^2*c^6)*d^5*e^4 - 56*(23*b^5*c^3 - 167*a*b^3*c^4 + 204*a^2*b*c^5)*d^4*e^5 + 4*(201*b^6*c^2 - 1393*a*b^4*c^3 + 2340*a^2*b^2*c^4 - 384*a^3*c^5)*d^3*e^6 + (45*b^7*c - 582*a*b^5*c^2 + 2072*a^2*b^3*c^3 - 3264*a^3*b*c^4)*d^2*e^7 - 3*(35*b^8 - 250*a*b^6*c + 516*a^2*b^4*c^2 - 848*a^3*b^2*c^3 + 1536*a^4*c^4)*d*e^8 + 3*(35*a*b^7 - 230*a^2*b^5*c + 232*a^3*b^3*c^2 + 448*a^4*b*c^3)*e^9)*x^3 - (192*b*c^7*d^9 - 192*(3*b^2*c^6 - 2*a*c^7)*d^8*e + 8*(35*b^3*c^5 + 36*a*b*c^6)*d^7*e^2 + 8*(65*b^4*c^4 - 330*a*b^2*c^5 + 504*a^2*c^6)*d^6*e^3 - 8*(55*b^5*c^3 - 235*a*b^3*c^4 + 732*a^2*b*c^5)*d^5*e^4 - 16*(22*b^6*c^2 - 160*a*b^4*c^3 + 57*a^2*b^2*c^4 + 28*a^3*c^5)*d^4*e^5 + (551*b^7*c - 3894*a*b^5*c^2 + 5992*a^2*b^3*c^3 - 1408*a^3*b*c^4)*d^3*e^6 - (175*b^8 - 1282*a*b^6*c + 2724*a^2*b^4*c^2 - 3344*a^3*b^2*c^3 + 4736*a^4*c^4)*d^2*e^7 + (35*a*b^7 - 402*a^2*b^5*c + 1608*a^3*b^3*c^2 - 2176*a^4*b*c^3)*d*e^8 + 4*(35*a^2*b^6 - 279*a^3*b^4*c + 588*a^4*b^2*c^2 - 160*a^5*c^3)*e^9)*x^2 - (48*(b^2*c^6 + 4*a*c^7)*d^9 - 8*(23*b^3*c^5 + 60*a*b*c^6)*d^8*e + 8*(25*b^4*c^4 + 54*a*b^2*c^5 + 168*a^2*c^6)*d^7*e^2 + 8*(10*b^5*c^3 - 145*a*b^3*c^4 - 84*a^2*b*c^5)*d^6*e^3 - 80*(4*b^6*c^2 - 31*a*b^4*c^3 + 57*a^2*b^2*c^4 - 44*a^3*c^5)*d^5*e^4 + 8*(29*b^7*c - 294*a*b^5*c^2 + 1015*a^2*b^3*c^3 - 1156*a^3*b*c^4)*d^4*e^5 - 2*(28*b^8 - 535*a*b^6*c + 2805*a^2*b^4*c^2 - 4064*a^3*b^2*c^3 - 208*a^4*c^4)*d^3*e^6 - (182*a*b^7 - 951*a^2*b^5*c - 624*a^3*b^3*c^2 + 5360*a^4*b*c^3)*d^2*e^7 + (217*a^2*b^6 - 1770*a^3*b^4*c + 4032*a^4*b^2*c^2 - 1952*a^5*c^3)*d*e^8 + 21*(a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*e^9)*x)*sqrt(c*x^2 + b*x + a))/((a^2*b^4*c^5 - 8*a^3*b^2*c^6 + 16*a^4*c^7)*d^12 - 5*(a^2*b^5*c^4 - 8*a^3*b^3*c^5 + 16*a^4*b*c^6)*d^11*e + 5*(2*a^2*b^6*c^3 - 15*a^3*b^4*c^4 + 24*a^4*b^2*c^5 + 16*a^5*c^6)*d^10*e^2 - 10*(a^2*b^7*c^2 - 6*a^3*b^5*c^3 + 32*a^5*b*c^5)*d^9*e^3 + 5*(a^2*b^8*c - 2*a^3*b^6*c^2 - 30*a^4*b^4*c^3 + 80*a^5*b^2*c^4 + 32*a^6*c^5)*d^8*e^4 - (a^2*b^9 + 12*a^3*b^7*c - 114*a^4*b^5*c^2 + 80*a^5*b^3*c^3 + 480*a^6*b*c^4)*d^7*e^5 + 5*(a^3*b^8 - 2*a^4*b^6*c - 30*a^5*b^4*c^2 + 80*a^6*b^2*c^3 + 32*a^7*c^4)*d^6*e^6 - 10*(a^4*b^7 - 6*a^5*b^5*c + 32*a^7*b*c^3)*d^5*e^7 + 5*(2*a^5*b^6 - 15*a^6*b^4*c + 24*a^7*b^2*c^2 + 16*a^8*c^3)*d^4*e^8 - 5*(a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*d^3*e^9 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*d^2*e^10 + ((b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*d^10*e^2 - 5*(b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*d^9*e^3 + 5*(2*b^6*c^5 - 15*a*b^4*c^6 + 24*a^2*b^2*c^7 + 16*a^3*c^8)*d^8*e^4 - 10*(b^7*c^4 - 6*a*b^5*c^5 + 32*a^3*b*c^7)*d^7*e^5 + 5*(b^8*c^3 - 2*a*b^6*c^4 - 30*a^2*b^4*c^5 + 80*a^3*b^2*c^6 + 32*a^4*c^7)*d^6*e^6 - (b^9*c^2 + 12*a*b^7*c^3 - 114*a^2*b^5*c^4 + 80*a^3*b^3*c^5 + 480*a^4*b*c^6)*d^5*e^7 + 5*(a*b^8*c^2 - 2*a^2*b^6*c^3 - 30*a^3*b^4*c^4 + 80*a^4*b^2*c^5 + 32*a^5*c^6)*d^4*e^8 - 10*(a^2*b^7*c^2 - 6*a^3*b^5*c^3 + 32*a^5*b*c^5)*d^3*e^9 + 5*(2*a^3*b^6*c^2 - 15*a^4*b^4*c^3 + 24*a^5*b^2*c^4 + 16*a^6*c^5)*d^2*e^10 - 5*(a^4*b^5*c^2 - 8*a^5*b^3*c^3 + 16*a^6*b*c^4)*d*e^11 + (a^5*b^4*c^2 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*e^12)*x^6 + 2*((b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*d^11*e - 4*(b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*d^10*e^2 + 5*(b^6*c^5 - 7*a*b^4*c^6 + 8*a^2*b^2*c^7 + 16*a^3*c^8)*d^9*e^3 - 15*(a*b^5*c^5 - 8*a^2*b^3*c^6 + 16*a^3*b*c^7)*d^8*e^4 - 5*(b^8*c^3 - 10*a*b^6*c^4 + 30*a^2*b^4*c^5 - 16*a^3*b^2*c^6 - 32*a^4*c^7)*d^7*e^5 + 2*(2*b^9*c^2 - 11*a*b^7*c^3 - 18*a^2*b^5*c^4 + 160*a^3*b^3*c^5 - 160*a^4*b*c^6)*d^6*e^6 - (b^10*c + 7*a*b^8*c^2 - 104*a^2*b^6*c^3 + 230*a^3*b^4*c^4 + 80*a^4*b^2*c^5 - 160*a^5*c^6)*d^5*e^7 + 5*(a*b^9*c - 4*a^2*b^7*c^2 - 18*a^3*b^5*c^3 + 80*a^4*b^3*c^4 - 32*a^5*b*c^5)*d^4*e^8 - 5*(2*a^2*b^8*c - 14*a^3*b^6*c^2 + 15*a^4*b^4*c^3 + 40*a^5*b^2*c^4 - 16*a^6*c^5)*d^3*e^9 + 10*(a^3*b^7*c - 8*a^4*b^5*c^2 + 16*a^5*b^3*c^3)*d^2*e^10 - (5*a^4*b^6*c - 41*a^5*b^4*c^2 + 88*a^6*b^2*c^3 - 16*a^7*c^4)*d*e^11 + (a^5*b^5*c - 8*a^6*b^3*c^2 + 16*a^7*b*c^3)*e^12)*x^5 + ((b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*d^12 - (b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*d^11*e - (9*b^6*c^5 - 79*a*b^4*c^6 + 200*a^2*b^2*c^7 - 112*a^3*c^8)*d^10*e^2 + 5*(5*b^7*c^4 - 42*a*b^5*c^5 + 96*a^2*b^3*c^6 - 32*a^3*b*c^7)*d^9*e^3 - 5*(5*b^8*c^3 - 35*a*b^6*c^4 + 36*a^2*b^4*c^5 + 112*a^3*b^2*c^6 - 64*a^4*c^7)*d^8*e^4 + 3*(3*b^9*c^2 - 4*a*b^7*c^3 - 122*a^2*b^5*c^4 + 400*a^3*b^3*c^5 - 160*a^4*b*c^6)*d^7*e^5 + (b^10*c - 43*a*b^8*c^2 + 276*a^2*b^6*c^3 - 370*a^3*b^4*c^4 - 560*a^4*b^2*c^5 + 480*a^5*c^6)*d^6*e^6 - (b^11 - 6*a*b^9*c - 40*a^2*b^7*c^2 + 392*a^3*b^5*c^3 - 960*a^4*b^3*c^4 + 640*a^5*b*c^5)*d^5*e^7 + 5*(a*b^10 - 8*a^2*b^8*c + 16*a^3*b^6*c^2 + 5*a^4*b^4*c^3 - 40*a^5*b^2*c^4 + 80*a^6*c^5)*d^4*e^8 - 5*(2*a^2*b^9 - 16*a^3*b^7*c + 37*a^4*b^5*c^2 - 40*a^5*b^3*c^3 + 80*a^6*b*c^4)*d^3*e^9 + (10*a^3*b^8 - 75*a^4*b^6*c + 131*a^5*b^4*c^2 - 8*a^6*b^2*c^3 + 176*a^7*c^4)*d^2*e^10 - (5*a^4*b^7 - 34*a^5*b^5*c + 32*a^6*b^3*c^2 + 96*a^7*b*c^3)*d*e^11 + (a^5*b^6 - 6*a^6*b^4*c + 32*a^8*c^3)*e^12)*x^4 + 2*((b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*d^12 - 2*(2*b^6*c^5 - 17*a*b^4*c^6 + 40*a^2*b^2*c^7 - 16*a^3*c^8)*d^11*e + (5*b^7*c^4 - 44*a*b^5*c^5 + 112*a^2*b^3*c^6 - 64*a^3*b*c^7)*d^10*e^2 + 10*(a^2*b^4*c^5 - 8*a^3*b^2*c^6 + 16*a^4*c^7)*d^9*e^3 - 5*(b^9*c^2 - 8*a*b^7*c^3 + 21*a^2*b^5*c^4 - 40*a^3*b^3*c^5 + 80*a^4*b*c^6)*d^8*e^4 + 2*(2*b^10*c - 11*a*b^8*c^2 + 2*a^2*b^6*c^3 + 10*a^3*b^4*c^4 + 80*a^4*b^2*c^5 + 160*a^5*c^6)*d^7*e^5 - (b^11 + 4*a*b^9*c - 70*a^2*b^7*c^2 + 152*a^3*b^5*c^3 - 160*a^4*b^3*c^4 + 640*a^5*b*c^5)*d^6*e^6 + 2*(2*a*b^10 - 11*a^2*b^8*c + 2*a^3*b^6*c^2 + 10*a^4*b^4*c^3 + 80*a^5*b^2*c^4 + 160*a^6*c^5)*d^5*e^7 - 5*(a^2*b^9 - 8*a^3*b^7*c + 21*a^4*b^5*c^2 - 40*a^5*b^3*c^3 + 80*a^6*b*c^4)*d^4*e^8 + 10*(a^5*b^4*c^2 - 8*a^6*b^2*c^3 + 16*a^7*c^4)*d^3*e^9 + (5*a^4*b^7 - 44*a^5*b^5*c + 112*a^6*b^3*c^2 - 64*a^7*b*c^3)*d^2*e^10 - 2*(2*a^5*b^6 - 17*a^6*b^4*c + 40*a^7*b^2*c^2 - 16*a^8*c^3)*d*e^11 + (a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*e^12)*x^3 + ((b^6*c^5 - 6*a*b^4*c^6 + 32*a^3*c^8)*d^12 - (5*b^7*c^4 - 34*a*b^5*c^5 + 32*a^2*b^3*c^6 + 96*a^3*b*c^7)*d^11*e + (10*b^8*c^3 - 75*a*b^6*c^4 + 131*a^2*b^4*c^5 - 8*a^3*b^2*c^6 + 176*a^4*c^7)*d^10*e^2 - 5*(2*b^9*c^2 - 16*a*b^7*c^3 + 37*a^2*b^5*c^4 - 40*a^3*b^3*c^5 + 80*a^4*b*c^6)*d^9*e^3 + 5*(b^10*c - 8*a*b^8*c^2 + 16*a^2*b^6*c^3 + 5*a^3*b^4*c^4 - 40*a^4*b^2*c^5 + 80*a^5*c^6)*d^8*e^4 - (b^11 - 6*a*b^9*c - 40*a^2*b^7*c^2 + 392*a^3*b^5*c^3 - 960*a^4*b^3*c^4 + 640*a^5*b*c^5)*d^7*e^5 + (a*b^10 - 43*a^2*b^8*c + 276*a^3*b^6*c^2 - 370*a^4*b^4*c^3 - 560*a^5*b^2*c^4 + 480*a^6*c^5)*d^6*e^6 + 3*(3*a^2*b^9 - 4*a^3*b^7*c - 122*a^4*b^5*c^2 + 400*a^5*b^3*c^3 - 160*a^6*b*c^4)*d^5*e^7 - 5*(5*a^3*b^8 - 35*a^4*b^6*c + 36*a^5*b^4*c^2 + 112*a^6*b^2*c^3 - 64*a^7*c^4)*d^4*e^8 + 5*(5*a^4*b^7 - 42*a^5*b^5*c + 96*a^6*b^3*c^2 - 32*a^7*b*c^3)*d^3*e^9 - (9*a^5*b^6 - 79*a^6*b^4*c + 200*a^7*b^2*c^2 - 112*a^8*c^3)*d^2*e^10 - (a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*d*e^11 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*e^12)*x^2 + 2*((a*b^5*c^5 - 8*a^2*b^3*c^6 + 16*a^3*b*c^7)*d^12 - (5*a*b^6*c^4 - 41*a^2*b^4*c^5 + 88*a^3*b^2*c^6 - 16*a^4*c^7)*d^11*e + 10*(a*b^7*c^3 - 8*a^2*b^5*c^4 + 16*a^3*b^3*c^5)*d^10*e^2 - 5*(2*a*b^8*c^2 - 14*a^2*b^6*c^3 + 15*a^3*b^4*c^4 + 40*a^4*b^2*c^5 - 16*a^5*c^6)*d^9*e^3 + 5*(a*b^9*c - 4*a^2*b^7*c^2 - 18*a^3*b^5*c^3 + 80*a^4*b^3*c^4 - 32*a^5*b*c^5)*d^8*e^4 - (a*b^10 + 7*a^2*b^8*c - 104*a^3*b^6*c^2 + 230*a^4*b^4*c^3 + 80*a^5*b^2*c^4 - 160*a^6*c^5)*d^7*e^5 + 2*(2*a^2*b^9 - 11*a^3*b^7*c - 18*a^4*b^5*c^2 + 160*a^5*b^3*c^3 - 160*a^6*b*c^4)*d^6*e^6 - 5*(a^3*b^8 - 10*a^4*b^6*c + 30*a^5*b^4*c^2 - 16*a^6*b^2*c^3 - 32*a^7*c^4)*d^5*e^7 - 15*(a^5*b^5*c - 8*a^6*b^3*c^2 + 16*a^7*b*c^3)*d^4*e^8 + 5*(a^5*b^6 - 7*a^6*b^4*c + 8*a^7*b^2*c^2 + 16*a^8*c^3)*d^3*e^9 - 4*(a^6*b^5 - 8*a^7*b^3*c + 16*a^8*b*c^2)*d^2*e^10 + (a^7*b^4 - 8*a^8*b^2*c + 16*a^9*c^2)*d*e^11)*x)]","B",0
2400,1,44,0,0.410781," ","integrate((3+x)/(-x^2-4*x+5)^(1/2),x, algorithm=""fricas"")","-\sqrt{-x^{2} - 4 \, x + 5} - \arctan\left(\frac{\sqrt{-x^{2} - 4 \, x + 5} {\left(x + 2\right)}}{x^{2} + 4 \, x - 5}\right)"," ",0,"-sqrt(-x^2 - 4*x + 5) - arctan(sqrt(-x^2 - 4*x + 5)*(x + 2)/(x^2 + 4*x - 5))","B",0
2401,1,47,0,0.412231," ","integrate(1/2*(5-4*x)/(-x^2+3*x-2)^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{-x^{2} + 3 \, x - 2} + \frac{1}{2} \, \arctan\left(\frac{\sqrt{-x^{2} + 3 \, x - 2} {\left(2 \, x - 3\right)}}{2 \, {\left(x^{2} - 3 \, x + 2\right)}}\right)"," ",0,"2*sqrt(-x^2 + 3*x - 2) + 1/2*arctan(1/2*sqrt(-x^2 + 3*x - 2)*(2*x - 3)/(x^2 - 3*x + 2))","B",0
2402,1,31,0,0.394774," ","integrate((3+2*x)/(x^2+2*x+5)^(1/2),x, algorithm=""fricas"")","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
2403,1,29,0,0.407518," ","integrate((-1+x)/(x^2-4*x+3)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} - 4 \, x + 3} - \log\left(-x + \sqrt{x^{2} - 4 \, x + 3} + 2\right)"," ",0,"sqrt(x^2 - 4*x + 3) - log(-x + sqrt(x^2 - 4*x + 3) + 2)","A",0
2404,1,18,0,0.394033," ","integrate(1/(1-x)/(x^2+2*x-4)^(1/2),x, algorithm=""fricas"")","-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
2405,1,18,0,0.403101," ","integrate(1/(-2+x)/(x^2-4*x+3)^(1/2),x, algorithm=""fricas"")","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
2406,1,20,0,0.418827," ","integrate((1+x)/(x^2+3*x+2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(x + \sqrt{x^{2} + 3 \, x + 2} + 2\right)}}{x + 2}"," ",0,"2*(x + sqrt(x^2 + 3*x + 2) + 2)/(x + 2)","A",0
2407,1,294,0,0.427013," ","integrate(2/(e*x+d)/(1/c*b^2+4*b*x+4*c*x^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{c} \log\left(\frac{16 \, c^{3} e^{2} x^{3} + 4 \, b c^{2} d^{2} + b^{3} e^{2} + 16 \, {\left(c^{3} d e + b c^{2} e^{2}\right)} x^{2} + 2 \, {\left(4 \, c^{3} d^{2} + 4 \, b c^{2} d e + 3 \, b^{2} c e^{2}\right)} x + {\left(4 \, c^{2} d^{2} - b^{2} e^{2} + 4 \, {\left(2 \, c^{2} d e - b c e^{2}\right)} x\right)} \sqrt{c} \sqrt{\frac{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}{c}}}{4 \, c^{2} e x^{3} + b^{2} d + 4 \, {\left(c^{2} d + b c e\right)} x^{2} + {\left(4 \, b c d + b^{2} e\right)} x}\right)}{2 \, c d - b e}, -\frac{4 \, \sqrt{-c} \arctan\left(-\frac{{\left(4 \, c e x + 2 \, c d + b e\right)} \sqrt{-c} \sqrt{\frac{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}{c}}}{2 \, b c d - b^{2} e + 2 \, {\left(2 \, c^{2} d - b c e\right)} x}\right)}{2 \, c d - b e}\right]"," ",0,"[-2*sqrt(c)*log((16*c^3*e^2*x^3 + 4*b*c^2*d^2 + b^3*e^2 + 16*(c^3*d*e + b*c^2*e^2)*x^2 + 2*(4*c^3*d^2 + 4*b*c^2*d*e + 3*b^2*c*e^2)*x + (4*c^2*d^2 - b^2*e^2 + 4*(2*c^2*d*e - b*c*e^2)*x)*sqrt(c)*sqrt((4*c^2*x^2 + 4*b*c*x + b^2)/c))/(4*c^2*e*x^3 + b^2*d + 4*(c^2*d + b*c*e)*x^2 + (4*b*c*d + b^2*e)*x))/(2*c*d - b*e), -4*sqrt(-c)*arctan(-(4*c*e*x + 2*c*d + b*e)*sqrt(-c)*sqrt((4*c^2*x^2 + 4*b*c*x + b^2)/c)/(2*b*c*d - b^2*e + 2*(2*c^2*d - b*c*e)*x))/(2*c*d - b*e)]","A",0
2408,1,175,0,0.453010," ","integrate(1/(1/2*b*e/c+e*x)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{c}{b^{2} - 4 \, a c}} \log\left(-\frac{4 \, c^{2} x^{2} + 4 \, b c x - b^{2} + 8 \, a c + 4 \, \sqrt{c x^{2} + b x + a} {\left(b^{2} - 4 \, a c\right)} \sqrt{-\frac{c}{b^{2} - 4 \, a c}}}{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}\right)}{e}, \frac{2 \, \sqrt{\frac{c}{b^{2} - 4 \, a c}} \arctan\left(-\frac{\sqrt{c x^{2} + b x + a} {\left(b^{2} - 4 \, a c\right)} \sqrt{\frac{c}{b^{2} - 4 \, a c}}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{e}\right]"," ",0,"[sqrt(-c/(b^2 - 4*a*c))*log(-(4*c^2*x^2 + 4*b*c*x - b^2 + 8*a*c + 4*sqrt(c*x^2 + b*x + a)*(b^2 - 4*a*c)*sqrt(-c/(b^2 - 4*a*c)))/(4*c^2*x^2 + 4*b*c*x + b^2))/e, 2*sqrt(c/(b^2 - 4*a*c))*arctan(-1/2*sqrt(c*x^2 + b*x + a)*(b^2 - 4*a*c)*sqrt(c/(b^2 - 4*a*c))/(c^2*x^2 + b*c*x + a*c))/e]","A",0
2409,1,62,0,0.482100," ","integrate(1/(e*x+d)/((b*d*e-c*d^2)/e^2+b*x+c*x^2)^(1/2),x, algorithm=""fricas"")","\frac{2 \, e \sqrt{\frac{c e^{2} x^{2} + b e^{2} x - c d^{2} + b d e}{e^{2}}}}{2 \, c d^{2} - b d e + {\left(2 \, c d e - b e^{2}\right)} x}"," ",0,"2*e*sqrt((c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)/e^2)/(2*c*d^2 - b*d*e + (2*c*d*e - b*e^2)*x)","A",0
2410,1,49,0,0.408432," ","integrate(2/(1/2*b*e/c+e*x)/(1/c*b^2+4*b*x+4*c*x^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, c \sqrt{\frac{4 \, c^{2} x^{2} + 4 \, b c x + b^{2}}{c}}}{4 \, c^{2} e x^{2} + 4 \, b c e x + b^{2} e}"," ",0,"-2*c*sqrt((4*c^2*x^2 + 4*b*c*x + b^2)/c)/(4*c^2*e*x^2 + 4*b*c*e*x + b^2*e)","A",0
2411,1,52,0,0.410742," ","integrate(x/(3*x^2+4*x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{9} \, \sqrt{3} \log\left(\sqrt{3} \sqrt{3 \, x^{2} + 4 \, x + 2} {\left(3 \, x + 2\right)} - 9 \, x^{2} - 12 \, x - 5\right) + \frac{1}{3} \, \sqrt{3 \, x^{2} + 4 \, x + 2}"," ",0,"1/9*sqrt(3)*log(sqrt(3)*sqrt(3*x^2 + 4*x + 2)*(3*x + 2) - 9*x^2 - 12*x - 5) + 1/3*sqrt(3*x^2 + 4*x + 2)","A",0
2412,1,55,0,0.412474," ","integrate(x/(-3*x^2+4*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{2}{9} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} \sqrt{-3 \, x^{2} + 4 \, x + 2} {\left(3 \, x - 2\right)}}{3 \, {\left(3 \, x^{2} - 4 \, x - 2\right)}}\right) - \frac{1}{3} \, \sqrt{-3 \, x^{2} + 4 \, x + 2}"," ",0,"-2/9*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(-3*x^2 + 4*x + 2)*(3*x - 2)/(3*x^2 - 4*x - 2)) - 1/3*sqrt(-3*x^2 + 4*x + 2)","A",0
2413,1,53,0,0.411034," ","integrate(x/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","\frac{5}{36} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 49\right) + \frac{1}{3} \, \sqrt{3 \, x^{2} + 5 \, x + 2}"," ",0,"5/36*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x + 2)*(6*x + 5) + 72*x^2 + 120*x + 49) + 1/3*sqrt(3*x^2 + 5*x + 2)","A",0
2414,1,55,0,0.407570," ","integrate(x/(-3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","-\frac{5}{18} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} \sqrt{-3 \, x^{2} + 5 \, x + 2} {\left(6 \, x - 5\right)}}{6 \, {\left(3 \, x^{2} - 5 \, x - 2\right)}}\right) - \frac{1}{3} \, \sqrt{-3 \, x^{2} + 5 \, x + 2}"," ",0,"-5/18*sqrt(3)*arctan(1/6*sqrt(3)*sqrt(-3*x^2 + 5*x + 2)*(6*x - 5)/(3*x^2 - 5*x - 2)) - 1/3*sqrt(-3*x^2 + 5*x + 2)","B",0
2415,1,53,0,0.418287," ","integrate(x/(3*x^2+4*x-2)^(1/2),x, algorithm=""fricas"")","\frac{1}{9} \, \sqrt{3} \log\left(-\sqrt{3} \sqrt{3 \, x^{2} + 4 \, x - 2} {\left(3 \, x + 2\right)} + 9 \, x^{2} + 12 \, x - 1\right) + \frac{1}{3} \, \sqrt{3 \, x^{2} + 4 \, x - 2}"," ",0,"1/9*sqrt(3)*log(-sqrt(3)*sqrt(3*x^2 + 4*x - 2)*(3*x + 2) + 9*x^2 + 12*x - 1) + 1/3*sqrt(3*x^2 + 4*x - 2)","A",0
2416,1,79,0,0.415074," ","integrate(x/(-3*x^2+4*x-2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{9} i \, \sqrt{3} \log\left(\frac{2 i \, \sqrt{3} \sqrt{-3 \, x^{2} + 4 \, x - 2} - 6 \, x + 4}{x}\right) + \frac{1}{9} i \, \sqrt{3} \log\left(\frac{-2 i \, \sqrt{3} \sqrt{-3 \, x^{2} + 4 \, x - 2} - 6 \, x + 4}{x}\right) - \frac{1}{3} \, \sqrt{-3 \, x^{2} + 4 \, x - 2}"," ",0,"-1/9*I*sqrt(3)*log((2*I*sqrt(3)*sqrt(-3*x^2 + 4*x - 2) - 6*x + 4)/x) + 1/9*I*sqrt(3)*log((-2*I*sqrt(3)*sqrt(-3*x^2 + 4*x - 2) - 6*x + 4)/x) - 1/3*sqrt(-3*x^2 + 4*x - 2)","C",0
2417,1,53,0,0.427661," ","integrate(x/(3*x^2+5*x-2)^(1/2),x, algorithm=""fricas"")","\frac{5}{36} \, \sqrt{3} \log\left(-4 \, \sqrt{3} \sqrt{3 \, x^{2} + 5 \, x - 2} {\left(6 \, x + 5\right)} + 72 \, x^{2} + 120 \, x + 1\right) + \frac{1}{3} \, \sqrt{3 \, x^{2} + 5 \, x - 2}"," ",0,"5/36*sqrt(3)*log(-4*sqrt(3)*sqrt(3*x^2 + 5*x - 2)*(6*x + 5) + 72*x^2 + 120*x + 1) + 1/3*sqrt(3*x^2 + 5*x - 2)","A",0
2418,1,55,0,0.409025," ","integrate(x/(-3*x^2+5*x-2)^(1/2),x, algorithm=""fricas"")","-\frac{5}{18} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} \sqrt{-3 \, x^{2} + 5 \, x - 2} {\left(6 \, x - 5\right)}}{6 \, {\left(3 \, x^{2} - 5 \, x + 2\right)}}\right) - \frac{1}{3} \, \sqrt{-3 \, x^{2} + 5 \, x - 2}"," ",0,"-5/18*sqrt(3)*arctan(1/6*sqrt(3)*sqrt(-3*x^2 + 5*x - 2)*(6*x - 5)/(3*x^2 - 5*x + 2)) - 1/3*sqrt(-3*x^2 + 5*x - 2)","B",0
2419,1,13,0,0.392321," ","integrate(1/x/((2+3*x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(3 \, x + 2\right) + \frac{1}{2} \, \log\left(x\right)"," ",0,"-1/2*log(3*x + 2) + 1/2*log(x)","A",0
2420,1,13,0,0.392401," ","integrate(1/x/((-2+3*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(3 \, x - 2\right) - \frac{1}{2} \, \log\left(x\right)"," ",0,"1/2*log(3*x - 2) - 1/2*log(x)","A",0
2421,1,11,0,0.392470," ","integrate(1/x/(-(-2+3*x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} i \, \log\left(x - \frac{2}{3}\right) + \frac{1}{2} i \, \log\left(x\right)"," ",0,"-1/2*I*log(x - 2/3) + 1/2*I*log(x)","C",0
2422,1,11,0,0.406934," ","integrate(1/x/(-(2+3*x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} i \, \log\left(x + \frac{2}{3}\right) - \frac{1}{2} i \, \log\left(x\right)"," ",0,"1/2*I*log(x + 2/3) - 1/2*I*log(x)","C",0
2423,1,16,0,0.414501," ","integrate(1/x/((b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\frac{\log\left(b x + a\right) - \log\left(x\right)}{a}"," ",0,"-(log(b*x + a) - log(x))/a","A",0
2424,1,17,0,0.413944," ","integrate(1/x/((b*x-a)^2)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(b x - a\right) - \log\left(x\right)}{a}"," ",0,"(log(b*x - a) - log(x))/a","A",0
2425,1,70,0,0.411287," ","integrate(1/x/(-(b*x-a)^2)^(1/2),x, algorithm=""fricas"")","-\sqrt{-\frac{1}{a^{2}}} \log\left(\frac{i \, a^{2} \sqrt{-\frac{1}{a^{2}}} + 2 \, b x - a}{2 \, b}\right) + \sqrt{-\frac{1}{a^{2}}} \log\left(\frac{-i \, a^{2} \sqrt{-\frac{1}{a^{2}}} + 2 \, b x - a}{2 \, b}\right)"," ",0,"-sqrt(-1/a^2)*log(1/2*(I*a^2*sqrt(-1/a^2) + 2*b*x - a)/b) + sqrt(-1/a^2)*log(1/2*(-I*a^2*sqrt(-1/a^2) + 2*b*x - a)/b)","C",0
2426,1,66,0,0.392723," ","integrate(1/x/(-(b*x+a)^2)^(1/2),x, algorithm=""fricas"")","-\sqrt{-\frac{1}{a^{2}}} \log\left(\frac{i \, a^{2} \sqrt{-\frac{1}{a^{2}}} + 2 \, b x + a}{2 \, b}\right) + \sqrt{-\frac{1}{a^{2}}} \log\left(\frac{-i \, a^{2} \sqrt{-\frac{1}{a^{2}}} + 2 \, b x + a}{2 \, b}\right)"," ",0,"-sqrt(-1/a^2)*log(1/2*(I*a^2*sqrt(-1/a^2) + 2*b*x + a)/b) + sqrt(-1/a^2)*log(1/2*(-I*a^2*sqrt(-1/a^2) + 2*b*x + a)/b)","C",0
2427,1,52,0,0.409466," ","integrate(x*(-x^2-2*x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(2 \, x^{2} + x - 9\right)} \sqrt{-x^{2} - 2 \, x + 3} + 2 \, \arctan\left(\frac{\sqrt{-x^{2} - 2 \, x + 3} {\left(x + 1\right)}}{x^{2} + 2 \, x - 3}\right)"," ",0,"1/6*(2*x^2 + x - 9)*sqrt(-x^2 - 2*x + 3) + 2*arctan(sqrt(-x^2 - 2*x + 3)*(x + 1)/(x^2 + 2*x - 3))","A",0
2428,1,54,0,0.393640," ","integrate(x*(-x^2+2*x+8)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(2 \, x^{2} - x - 19\right)} \sqrt{-x^{2} + 2 \, x + 8} - \frac{9}{2} \, \arctan\left(\frac{\sqrt{-x^{2} + 2 \, x + 8} {\left(x - 1\right)}}{x^{2} - 2 \, x - 8}\right)"," ",0,"1/6*(2*x^2 - x - 19)*sqrt(-x^2 + 2*x + 8) - 9/2*arctan(sqrt(-x^2 + 2*x + 8)*(x - 1)/(x^2 - 2*x - 8))","A",0
2429,1,39,0,0.409866," ","integrate(x*(x^2+2*x+4)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(2 \, x^{2} + 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^2 + x + 5)*sqrt(x^2 + 2*x + 4) + 3/2*log(-x + sqrt(x^2 + 2*x + 4) - 1)","A",0
2430,1,40,0,0.399690," ","integrate(1/x/(3*x^2+4*x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{2 \, \sqrt{2} \sqrt{3 \, x^{2} + 4 \, x + 2} {\left(x + 1\right)} - 5 \, x^{2} - 8 \, x - 4}{x^{2}}\right)"," ",0,"1/4*sqrt(2)*log((2*sqrt(2)*sqrt(3*x^2 + 4*x + 2)*(x + 1) - 5*x^2 - 8*x - 4)/x^2)","A",0
2431,1,39,0,0.413674," ","integrate(1/x/(-3*x^2+4*x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-3 \, x^{2} + 4 \, x + 2} {\left(x + 1\right)} + x^{2} - 8 \, x - 4}{x^{2}}\right)"," ",0,"1/4*sqrt(2)*log(-(2*sqrt(2)*sqrt(-3*x^2 + 4*x + 2)*(x + 1) + x^2 - 8*x - 4)/x^2)","A",0
2432,1,43,0,0.400144," ","integrate(1/x/(3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{4 \, \sqrt{2} \sqrt{3 \, x^{2} + 5 \, x + 2} {\left(5 \, x + 4\right)} - 49 \, x^{2} - 80 \, x - 32}{x^{2}}\right)"," ",0,"1/4*sqrt(2)*log(-(4*sqrt(2)*sqrt(3*x^2 + 5*x + 2)*(5*x + 4) - 49*x^2 - 80*x - 32)/x^2)","A",0
2433,1,43,0,0.394876," ","integrate(1/x/(-3*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{4 \, \sqrt{2} \sqrt{-3 \, x^{2} + 5 \, x + 2} {\left(5 \, x + 4\right)} - x^{2} - 80 \, x - 32}{x^{2}}\right)"," ",0,"1/4*sqrt(2)*log(-(4*sqrt(2)*sqrt(-3*x^2 + 5*x + 2)*(5*x + 4) - x^2 - 80*x - 32)/x^2)","A",0
2434,1,25,0,0.398721," ","integrate(1/x/(3*x^2+4*x-2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(x - 1\right)}}{\sqrt{3 \, x^{2} + 4 \, x - 2}}\right)"," ",0,"1/2*sqrt(2)*arctan(sqrt(2)*(x - 1)/sqrt(3*x^2 + 4*x - 2))","A",0
2435,1,64,0,0.387628," ","integrate(1/x/(-3*x^2+4*x-2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-2} \log\left(\frac{\sqrt{-2} \sqrt{-3 \, x^{2} + 4 \, x - 2} + 2 \, x - 2}{x}\right) - \frac{1}{4} \, \sqrt{-2} \log\left(-\frac{\sqrt{-2} \sqrt{-3 \, x^{2} + 4 \, x - 2} - 2 \, x + 2}{x}\right)"," ",0,"1/4*sqrt(-2)*log((sqrt(-2)*sqrt(-3*x^2 + 4*x - 2) + 2*x - 2)/x) - 1/4*sqrt(-2)*log(-(sqrt(-2)*sqrt(-3*x^2 + 4*x - 2) - 2*x + 2)/x)","B",0
2436,1,28,0,0.409753," ","integrate(1/x/(3*x^2+5*x-2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(5 \, x - 4\right)}}{4 \, \sqrt{3 \, x^{2} + 5 \, x - 2}}\right)"," ",0,"1/2*sqrt(2)*arctan(1/4*sqrt(2)*(5*x - 4)/sqrt(3*x^2 + 5*x - 2))","A",0
2437,1,40,0,0.393061," ","integrate(1/x/(-3*x^2+5*x-2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-3 \, x^{2} + 5 \, x - 2} {\left(5 \, x - 4\right)}}{4 \, {\left(3 \, x^{2} - 5 \, x + 2\right)}}\right)"," ",0,"-1/2*sqrt(2)*arctan(1/4*sqrt(2)*sqrt(-3*x^2 + 5*x - 2)*(5*x - 4)/(3*x^2 - 5*x + 2))","A",0
2438,1,63,0,0.413995," ","integrate(1/x^3/(x^2+x+1)^(1/2),x, algorithm=""fricas"")","\frac{x^{2} \log\left(-x + \sqrt{x^{2} + x + 1} + 1\right) - x^{2} \log\left(-x + \sqrt{x^{2} + x + 1} - 1\right) + 6 \, x^{2} + 2 \, \sqrt{x^{2} + x + 1} {\left(3 \, x - 2\right)}}{8 \, x^{2}}"," ",0,"1/8*(x^2*log(-x + sqrt(x^2 + x + 1) + 1) - x^2*log(-x + sqrt(x^2 + x + 1) - 1) + 6*x^2 + 2*sqrt(x^2 + x + 1)*(3*x - 2))/x^2","A",0
2439,1,30,0,0.404170," ","integrate(1/x-1/x/(c*x^2+b*x+1)^(1/2),x, algorithm=""fricas"")","\log\left(x\right) - \log\left(-\frac{b x - 2 \, \sqrt{c x^{2} + b x + 1} + 2}{x}\right)"," ",0,"log(x) - log(-(b*x - 2*sqrt(c*x^2 + b*x + 1) + 2)/x)","A",0
2440,0,0,0,0.444369," ","integrate((d*x)^(5/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} \sqrt{d x} d^{2} x^{2}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(d*x)*d^2*x^2, x)","F",0
2441,0,0,0,0.425931," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)^(3/2), x)","F",0
2442,0,0,0,0.422377," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} \sqrt{e x + d}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d), x)","F",0
2443,0,0,0,0.436380," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a}}{\sqrt{e x + d}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)/sqrt(e*x + d), x)","F",0
2444,0,0,0,0.444690," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
2445,0,0,0,0.418239," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
2446,0,0,0,0.428971," ","integrate((c*x^2+b*x+a)^(1/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
2447,0,0,0,0.449495," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e x^{3} + {\left(c d + b e\right)} x^{2} + a d + {\left(b d + a e\right)} x\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}, x\right)"," ",0,"integral((c*e*x^3 + (c*d + b*e)*x^2 + a*d + (b*d + a*e)*x)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d), x)","F",0
2448,0,0,0,0.435606," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} \sqrt{e x + d}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/2)*sqrt(e*x + d), x)","F",0
2449,0,0,0,0.447183," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/2)/sqrt(e*x + d), x)","F",0
2450,0,0,0,0.448120," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/2)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
2451,0,0,0,0.447303," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/2)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
2452,0,0,0,0.464186," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/2)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
2453,0,0,0,0.449989," ","integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} \sqrt{e x + d}}{e^{5} x^{5} + 5 \, d e^{4} x^{4} + 10 \, d^{2} e^{3} x^{3} + 10 \, d^{3} e^{2} x^{2} + 5 \, d^{4} e x + d^{5}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/2)*sqrt(e*x + d)/(e^5*x^5 + 5*d*e^4*x^4 + 10*d^2*e^3*x^3 + 10*d^3*e^2*x^2 + 5*d^4*e*x + d^5), x)","F",0
2454,0,0,0,0.467328," ","integrate((d*x)^(1/2)*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a} \sqrt{d x}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)*sqrt(d*x), x)","F",0
2455,0,0,0,0.456214," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)/sqrt(e*x + d), x)","F",0
2456,0,0,0,0.464457," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
2457,0,0,0,0.460520," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
2458,0,0,0,0.456902," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{4} x^{4} + 4 \, d e^{3} x^{3} + 6 \, d^{2} e^{2} x^{2} + 4 \, d^{3} e x + d^{4}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^4*x^4 + 4*d*e^3*x^3 + 6*d^2*e^2*x^2 + 4*d^3*e*x + d^4), x)","F",0
2459,0,0,0,0.483766," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{5} x^{5} + 5 \, d e^{4} x^{4} + 10 \, d^{2} e^{3} x^{3} + 10 \, d^{3} e^{2} x^{2} + 5 \, d^{4} e x + d^{5}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^5*x^5 + 5*d*e^4*x^4 + 10*d^2*e^3*x^3 + 10*d^3*e^2*x^2 + 5*d^4*e*x + d^5), x)","F",0
2460,0,0,0,0.502400," ","integrate((c*x^2+b*x+a)^(5/2)/(e*x+d)^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{e^{6} x^{6} + 6 \, d e^{5} x^{5} + 15 \, d^{2} e^{4} x^{4} + 20 \, d^{3} e^{3} x^{3} + 15 \, d^{4} e^{2} x^{2} + 6 \, d^{5} e x + d^{6}}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(e^6*x^6 + 6*d*e^5*x^5 + 15*d^2*e^4*x^4 + 20*d^3*e^3*x^3 + 15*d^4*e^2*x^2 + 6*d^5*e*x + d^6), x)","F",0
2461,0,0,0,0.447942," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
2462,0,0,0,0.426058," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
2463,0,0,0,0.447515," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{\frac{3}{2}}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((e*x + d)^(3/2)/sqrt(c*x^2 + b*x + a), x)","F",0
2464,0,0,0,0.413995," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x + d}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral(sqrt(e*x + d)/sqrt(c*x^2 + b*x + a), x)","F",0
2465,0,0,0,0.426093," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c e x^{3} + {\left(c d + b e\right)} x^{2} + a d + {\left(b d + a e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c*e*x^3 + (c*d + b*e)*x^2 + a*d + (b*d + a*e)*x), x)","F",0
2466,0,0,0,0.415595," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c e^{2} x^{4} + {\left(2 \, c d e + b e^{2}\right)} x^{3} + a d^{2} + {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{2} + {\left(b d^{2} + 2 \, a d e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c*e^2*x^4 + (2*c*d*e + b*e^2)*x^3 + a*d^2 + (c*d^2 + 2*b*d*e + a*e^2)*x^2 + (b*d^2 + 2*a*d*e)*x), x)","F",0
2467,0,0,0,0.435093," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c e^{3} x^{5} + {\left(3 \, c d e^{2} + b e^{3}\right)} x^{4} + a d^{3} + {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} x^{3} + {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} x^{2} + {\left(b d^{3} + 3 \, a d^{2} e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c*e^3*x^5 + (3*c*d*e^2 + b*e^3)*x^4 + a*d^3 + (3*c*d^2*e + 3*b*d*e^2 + a*e^3)*x^3 + (c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*x^2 + (b*d^3 + 3*a*d^2*e)*x), x)","F",0
2468,0,0,0,0.449695," ","integrate(1/(e*x+d)^(7/2)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c e^{4} x^{6} + {\left(4 \, c d e^{3} + b e^{4}\right)} x^{5} + a d^{4} + {\left(6 \, c d^{2} e^{2} + 4 \, b d e^{3} + a e^{4}\right)} x^{4} + 2 \, {\left(2 \, c d^{3} e + 3 \, b d^{2} e^{2} + 2 \, a d e^{3}\right)} x^{3} + {\left(c d^{4} + 4 \, b d^{3} e + 6 \, a d^{2} e^{2}\right)} x^{2} + {\left(b d^{4} + 4 \, a d^{3} e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c*e^4*x^6 + (4*c*d*e^3 + b*e^4)*x^5 + a*d^4 + (6*c*d^2*e^2 + 4*b*d*e^3 + a*e^4)*x^4 + 2*(2*c*d^3*e + 3*b*d^2*e^2 + 2*a*d*e^3)*x^3 + (c*d^4 + 4*b*d^3*e + 6*a*d^2*e^2)*x^2 + (b*d^4 + 4*a*d^3*e)*x), x)","F",0
2469,0,0,0,0.465075," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2470,0,0,0,0.472687," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2471,0,0,0,0.413293," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{3}{2}}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)^(3/2)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2472,0,0,0,0.435535," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2473,0,0,0,0.443796," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} e x^{5} + {\left(c^{2} d + 2 \, b c e\right)} x^{4} + {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} x^{3} + a^{2} d + {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} x^{2} + {\left(2 \, a b d + a^{2} e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*e*x^5 + (c^2*d + 2*b*c*e)*x^4 + (2*b*c*d + (b^2 + 2*a*c)*e)*x^3 + a^2*d + (2*a*b*e + (b^2 + 2*a*c)*d)*x^2 + (2*a*b*d + a^2*e)*x), x)","F",0
2474,0,0,0,0.452942," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} e^{2} x^{6} + 2 \, {\left(c^{2} d e + b c e^{2}\right)} x^{5} + {\left(c^{2} d^{2} + 4 \, b c d e + {\left(b^{2} + 2 \, a c\right)} e^{2}\right)} x^{4} + a^{2} d^{2} + 2 \, {\left(b c d^{2} + a b e^{2} + {\left(b^{2} + 2 \, a c\right)} d e\right)} x^{3} + {\left(4 \, a b d e + a^{2} e^{2} + {\left(b^{2} + 2 \, a c\right)} d^{2}\right)} x^{2} + 2 \, {\left(a b d^{2} + a^{2} d e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*e^2*x^6 + 2*(c^2*d*e + b*c*e^2)*x^5 + (c^2*d^2 + 4*b*c*d*e + (b^2 + 2*a*c)*e^2)*x^4 + a^2*d^2 + 2*(b*c*d^2 + a*b*e^2 + (b^2 + 2*a*c)*d*e)*x^3 + (4*a*b*d*e + a^2*e^2 + (b^2 + 2*a*c)*d^2)*x^2 + 2*(a*b*d^2 + a^2*d*e)*x), x)","F",0
2475,0,0,0,0.500424," ","integrate(1/(e*x+d)^(5/2)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{2} e^{3} x^{7} + {\left(3 \, c^{2} d e^{2} + 2 \, b c e^{3}\right)} x^{6} + {\left(3 \, c^{2} d^{2} e + 6 \, b c d e^{2} + {\left(b^{2} + 2 \, a c\right)} e^{3}\right)} x^{5} + a^{2} d^{3} + {\left(c^{2} d^{3} + 6 \, b c d^{2} e + 2 \, a b e^{3} + 3 \, {\left(b^{2} + 2 \, a c\right)} d e^{2}\right)} x^{4} + {\left(2 \, b c d^{3} + 6 \, a b d e^{2} + a^{2} e^{3} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e\right)} x^{3} + {\left(6 \, a b d^{2} e + 3 \, a^{2} d e^{2} + {\left(b^{2} + 2 \, a c\right)} d^{3}\right)} x^{2} + {\left(2 \, a b d^{3} + 3 \, a^{2} d^{2} e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^2*e^3*x^7 + (3*c^2*d*e^2 + 2*b*c*e^3)*x^6 + (3*c^2*d^2*e + 6*b*c*d*e^2 + (b^2 + 2*a*c)*e^3)*x^5 + a^2*d^3 + (c^2*d^3 + 6*b*c*d^2*e + 2*a*b*e^3 + 3*(b^2 + 2*a*c)*d*e^2)*x^4 + (2*b*c*d^3 + 6*a*b*d*e^2 + a^2*e^3 + 3*(b^2 + 2*a*c)*d^2*e)*x^3 + (6*a*b*d^2*e + 3*a^2*d*e^2 + (b^2 + 2*a*c)*d^3)*x^2 + (2*a*b*d^3 + 3*a^2*d^2*e)*x), x)","F",0
2476,0,0,0,0.452370," ","integrate((e*x+d)^(7/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
2477,0,0,0,0.448920," ","integrate((e*x+d)^(5/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} \sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
2478,0,0,0,0.441204," ","integrate((e*x+d)^(3/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{\frac{3}{2}}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)^(3/2)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
2479,0,0,0,0.449444," ","integrate((e*x+d)^(1/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
2480,0,0,0,0.491483," ","integrate(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{3} e x^{7} + {\left(c^{3} d + 3 \, b c^{2} e\right)} x^{6} + 3 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} x^{5} + {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} x^{4} + a^{3} d + {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} x^{3} + 3 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} x^{2} + {\left(3 \, a^{2} b d + a^{3} e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^3*e*x^7 + (c^3*d + 3*b*c^2*e)*x^6 + 3*(b*c^2*d + (b^2*c + a*c^2)*e)*x^5 + (3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*x^4 + a^3*d + ((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*x^3 + 3*(a^2*b*e + (a*b^2 + a^2*c)*d)*x^2 + (3*a^2*b*d + a^3*e)*x), x)","F",0
2481,0,0,0,0.569182," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{e x + d}}{c^{3} e^{2} x^{8} + {\left(2 \, c^{3} d e + 3 \, b c^{2} e^{2}\right)} x^{7} + {\left(c^{3} d^{2} + 6 \, b c^{2} d e + 3 \, {\left(b^{2} c + a c^{2}\right)} e^{2}\right)} x^{6} + {\left(3 \, b c^{2} d^{2} + 6 \, {\left(b^{2} c + a c^{2}\right)} d e + {\left(b^{3} + 6 \, a b c\right)} e^{2}\right)} x^{5} + a^{3} d^{2} + {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d^{2} + 2 \, {\left(b^{3} + 6 \, a b c\right)} d e + 3 \, {\left(a b^{2} + a^{2} c\right)} e^{2}\right)} x^{4} + {\left(3 \, a^{2} b e^{2} + {\left(b^{3} + 6 \, a b c\right)} d^{2} + 6 \, {\left(a b^{2} + a^{2} c\right)} d e\right)} x^{3} + {\left(6 \, a^{2} b d e + a^{3} e^{2} + 3 \, {\left(a b^{2} + a^{2} c\right)} d^{2}\right)} x^{2} + {\left(3 \, a^{2} b d^{2} + 2 \, a^{3} d e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(e*x + d)/(c^3*e^2*x^8 + (2*c^3*d*e + 3*b*c^2*e^2)*x^7 + (c^3*d^2 + 6*b*c^2*d*e + 3*(b^2*c + a*c^2)*e^2)*x^6 + (3*b*c^2*d^2 + 6*(b^2*c + a*c^2)*d*e + (b^3 + 6*a*b*c)*e^2)*x^5 + a^3*d^2 + (3*(b^2*c + a*c^2)*d^2 + 2*(b^3 + 6*a*b*c)*d*e + 3*(a*b^2 + a^2*c)*e^2)*x^4 + (3*a^2*b*e^2 + (b^3 + 6*a*b*c)*d^2 + 6*(a*b^2 + a^2*c)*d*e)*x^3 + (6*a^2*b*d*e + a^3*e^2 + 3*(a*b^2 + a^2*c)*d^2)*x^2 + (3*a^2*b*d^2 + 2*a^3*d*e)*x), x)","F",0
2482,0,0,0,0.414596," ","integrate((3+5*x)^(1/2)/(-12*x^2+5*x+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-12 \, x^{2} + 5 \, x + 2} \sqrt{5 \, x + 3}}{12 \, x^{2} - 5 \, x - 2}, x\right)"," ",0,"integral(-sqrt(-12*x^2 + 5*x + 2)*sqrt(5*x + 3)/(12*x^2 - 5*x - 2), x)","F",0
2483,0,0,0,0.433512," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e^{2} x^{4} + {\left(2 \, c d e + b e^{2}\right)} x^{3} + a d^{2} + {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{2} + {\left(b d^{2} + 2 \, a d e\right)} x\right)} {\left(c x^{2} + b x + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((c*e^2*x^4 + (2*c*d*e + b*e^2)*x^3 + a*d^2 + (c*d^2 + 2*b*d*e + a*e^2)*x^2 + (b*d^2 + 2*a*d*e)*x)*(c*x^2 + b*x + a)^(1/3), x)","F",0
2484,0,0,0,0.426332," ","integrate((e*x+d)*(c*x^2+b*x+a)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e x^{3} + {\left(c d + b e\right)} x^{2} + a d + {\left(b d + a e\right)} x\right)} {\left(c x^{2} + b x + a\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((c*e*x^3 + (c*d + b*e)*x^2 + a*d + (b*d + a*e)*x)*(c*x^2 + b*x + a)^(1/3), x)","F",0
2485,0,0,0,0.421469," ","integrate((c*x^2+b*x+a)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{\frac{4}{3}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(4/3), x)","F",0
2486,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2487,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2488,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(4/3)/(e*x+d)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2489,0,0,0,0.702536," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(c x^{2} + b x + a\right)}^{\frac{2}{3}}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(c*x^2 + b*x + a)^(2/3)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
2490,0,0,0,0.621400," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(c x^{2} + b x + a\right)}^{\frac{2}{3}}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(c*x^2 + b*x + a)^(2/3)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
2491,0,0,0,0.773811," ","integrate((e*x+d)/(c*x^2+b*x+a)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{2}{3}} {\left(e x + d\right)}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(2/3)*(e*x + d)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
2492,0,0,0,0.764594," ","integrate(1/(c*x^2+b*x+a)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{2}{3}}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(2/3)/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
2493,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(7/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2494,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(7/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2495,-1,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(7/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2496,-1,0,0,0.000000," ","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=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2497,0,0,0,0.701916," ","integrate((2+3*x)^3/(27*x^2-54*x+52)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)/(27*x^2 - 54*x + 52)^(1/3), x)","F",0
2498,0,0,0,0.538735," ","integrate((2+3*x)^2/(27*x^2-54*x+52)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{9 \, x^{2} + 12 \, x + 4}{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)/(27*x^2 - 54*x + 52)^(1/3), x)","F",0
2499,0,0,0,0.797426," ","integrate((2+3*x)/(27*x^2-54*x+52)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{3 \, x + 2}{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((3*x + 2)/(27*x^2 - 54*x + 52)^(1/3), x)","F",0
2500,1,214,0,3.912006," ","integrate(1/(2+3*x)/(27*x^2-54*x+52)^(1/3),x, algorithm=""fricas"")","-\frac{1}{90} \cdot 100^{\frac{1}{6}} \sqrt{3} \arctan\left(\frac{100^{\frac{1}{6}} {\left(2 \cdot 100^{\frac{2}{3}} \sqrt{3} {\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{2}{3}} {\left(3 \, x - 8\right)} + 100^{\frac{1}{3}} \sqrt{3} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} + 20 \, \sqrt{3} {\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}} {\left(9 \, x^{2} - 48 \, x + 64\right)}\right)}}{90 \, {\left(9 \, x^{3} - 162 \, x^{2} + 372 \, x - 344\right)}}\right) - \frac{1}{1800} \cdot 100^{\frac{2}{3}} \log\left(\frac{100^{\frac{2}{3}} {\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{2}{3}} + 100^{\frac{1}{3}} {\left(9 \, x^{2} - 48 \, x + 64\right)} - 10 \, {\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}} {\left(3 \, x - 8\right)}}{9 \, x^{2} + 12 \, x + 4}\right) + \frac{1}{900} \cdot 100^{\frac{2}{3}} \log\left(\frac{100^{\frac{1}{3}} {\left(3 \, x - 8\right)} + 10 \, {\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{1}{3}}}{3 \, x + 2}\right)"," ",0,"-1/90*100^(1/6)*sqrt(3)*arctan(1/90*100^(1/6)*(2*100^(2/3)*sqrt(3)*(27*x^2 - 54*x + 52)^(2/3)*(3*x - 8) + 100^(1/3)*sqrt(3)*(27*x^3 + 54*x^2 + 36*x + 8) + 20*sqrt(3)*(27*x^2 - 54*x + 52)^(1/3)*(9*x^2 - 48*x + 64))/(9*x^3 - 162*x^2 + 372*x - 344)) - 1/1800*100^(2/3)*log((100^(2/3)*(27*x^2 - 54*x + 52)^(2/3) + 100^(1/3)*(9*x^2 - 48*x + 64) - 10*(27*x^2 - 54*x + 52)^(1/3)*(3*x - 8))/(9*x^2 + 12*x + 4)) + 1/900*100^(2/3)*log((100^(1/3)*(3*x - 8) + 10*(27*x^2 - 54*x + 52)^(1/3))/(3*x + 2))","B",0
2501,0,0,0,2.979196," ","integrate(1/(2+3*x)^2/(27*x^2-54*x+52)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{2}{3}}}{243 \, x^{4} - 162 \, x^{3} - 72 \, x^{2} + 408 \, x + 208}, x\right)"," ",0,"integral((27*x^2 - 54*x + 52)^(2/3)/(243*x^4 - 162*x^3 - 72*x^2 + 408*x + 208), x)","F",0
2502,0,0,0,3.153582," ","integrate(1/(2+3*x)^3/(27*x^2-54*x+52)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{2} - 54 \, x + 52\right)}^{\frac{2}{3}}}{729 \, x^{5} - 540 \, x^{3} + 1080 \, x^{2} + 1440 \, x + 416}, x\right)"," ",0,"integral((27*x^2 - 54*x + 52)^(2/3)/(729*x^5 - 540*x^3 + 1080*x^2 + 1440*x + 416), x)","F",0
2503,0,0,0,0.401954," ","integrate((2+3*x)^3/(27*x^2+54*x+28)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8}{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((27*x^3 + 54*x^2 + 36*x + 8)/(27*x^2 + 54*x + 28)^(1/3), x)","F",0
2504,0,0,0,0.433883," ","integrate((2+3*x)^2/(27*x^2+54*x+28)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{9 \, x^{2} + 12 \, x + 4}{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((9*x^2 + 12*x + 4)/(27*x^2 + 54*x + 28)^(1/3), x)","F",0
2505,0,0,0,0.403327," ","integrate((2+3*x)/(27*x^2+54*x+28)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{3 \, x + 2}{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((3*x + 2)/(27*x^2 + 54*x + 28)^(1/3), x)","F",0
2506,1,214,0,2.864667," ","integrate(1/(2+3*x)/(27*x^2+54*x+28)^(1/3),x, algorithm=""fricas"")","-\frac{1}{18} \cdot 4^{\frac{1}{6}} \sqrt{3} \arctan\left(\frac{4^{\frac{1}{6}} {\left(2 \cdot 4^{\frac{2}{3}} \sqrt{3} {\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{2}{3}} {\left(3 \, x + 4\right)} + 4^{\frac{1}{3}} \sqrt{3} {\left(27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right)} - 4 \, \sqrt{3} {\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}} {\left(9 \, x^{2} + 24 \, x + 16\right)}\right)}}{18 \, {\left(9 \, x^{3} + 54 \, x^{2} + 84 \, x + 40\right)}}\right) - \frac{1}{72} \cdot 4^{\frac{2}{3}} \log\left(\frac{4^{\frac{2}{3}} {\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{2}{3}} + 4^{\frac{1}{3}} {\left(9 \, x^{2} + 24 \, x + 16\right)} + 2 \, {\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}} {\left(3 \, x + 4\right)}}{9 \, x^{2} + 12 \, x + 4}\right) + \frac{1}{36} \cdot 4^{\frac{2}{3}} \log\left(\frac{4^{\frac{1}{3}} {\left(3 \, x + 4\right)} - 2 \, {\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{1}{3}}}{3 \, x + 2}\right)"," ",0,"-1/18*4^(1/6)*sqrt(3)*arctan(1/18*4^(1/6)*(2*4^(2/3)*sqrt(3)*(27*x^2 + 54*x + 28)^(2/3)*(3*x + 4) + 4^(1/3)*sqrt(3)*(27*x^3 + 54*x^2 + 36*x + 8) - 4*sqrt(3)*(27*x^2 + 54*x + 28)^(1/3)*(9*x^2 + 24*x + 16))/(9*x^3 + 54*x^2 + 84*x + 40)) - 1/72*4^(2/3)*log((4^(2/3)*(27*x^2 + 54*x + 28)^(2/3) + 4^(1/3)*(9*x^2 + 24*x + 16) + 2*(27*x^2 + 54*x + 28)^(1/3)*(3*x + 4))/(9*x^2 + 12*x + 4)) + 1/36*4^(2/3)*log((4^(1/3)*(3*x + 4) - 2*(27*x^2 + 54*x + 28)^(1/3))/(3*x + 2))","B",0
2507,0,0,0,2.813502," ","integrate(1/(2+3*x)^2/(27*x^2+54*x+28)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{2}{3}}}{243 \, x^{4} + 810 \, x^{3} + 1008 \, x^{2} + 552 \, x + 112}, x\right)"," ",0,"integral((27*x^2 + 54*x + 28)^(2/3)/(243*x^4 + 810*x^3 + 1008*x^2 + 552*x + 112), x)","F",0
2508,0,0,0,2.899946," ","integrate(1/(2+3*x)^3/(27*x^2+54*x+28)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(27 \, x^{2} + 54 \, x + 28\right)}^{\frac{2}{3}}}{729 \, x^{5} + 2916 \, x^{4} + 4644 \, x^{3} + 3672 \, x^{2} + 1440 \, x + 224}, x\right)"," ",0,"integral((27*x^2 + 54*x + 28)^(2/3)/(729*x^5 + 2916*x^4 + 4644*x^3 + 3672*x^2 + 1440*x + 224), x)","F",0
2509,-1,0,0,0.000000," ","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=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2510,0,0,0,0.423774," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(c*x^2 + b*x + a)^(1/4), x)","F",0
2511,0,0,0,0.415085," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(c*x^2 + b*x + a)^(1/4), x)","F",0
2512,0,0,0,0.406100," ","integrate((e*x+d)*(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{\frac{1}{4}} {\left(e x + d\right)}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(1/4)*(e*x + d), x)","F",0
2513,0,0,0,0.409058," ","integrate((c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(1/4), x)","F",0
2514,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/4)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2515,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/4)/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2516,0,0,0,0.922330," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(c*x^2 + b*x + a)^(3/4), x)","F",0
2517,0,0,0,0.955991," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(c*x^2 + b*x + a)^(3/4), x)","F",0
2518,0,0,0,0.800127," ","integrate((e*x+d)*(c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{\frac{3}{4}} {\left(e x + d\right)}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/4)*(e*x + d), x)","F",0
2519,0,0,0,0.606778," ","integrate((c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/4), x)","F",0
2520,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/4)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2521,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/4)/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2522,0,0,0,0.744726," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e^{3} x^{5} + {\left(3 \, c d e^{2} + b e^{3}\right)} x^{4} + a d^{3} + {\left(3 \, c d^{2} e + 3 \, b d e^{2} + a e^{3}\right)} x^{3} + {\left(c d^{3} + 3 \, b d^{2} e + 3 \, a d e^{2}\right)} x^{2} + {\left(b d^{3} + 3 \, a d^{2} e\right)} x\right)} {\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((c*e^3*x^5 + (3*c*d*e^2 + b*e^3)*x^4 + a*d^3 + (3*c*d^2*e + 3*b*d*e^2 + a*e^3)*x^3 + (c*d^3 + 3*b*d^2*e + 3*a*d*e^2)*x^2 + (b*d^3 + 3*a*d^2*e)*x)*(c*x^2 + b*x + a)^(1/4), x)","F",0
2523,0,0,0,0.684350," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e^{2} x^{4} + {\left(2 \, c d e + b e^{2}\right)} x^{3} + a d^{2} + {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{2} + {\left(b d^{2} + 2 \, a d e\right)} x\right)} {\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((c*e^2*x^4 + (2*c*d*e + b*e^2)*x^3 + a*d^2 + (c*d^2 + 2*b*d*e + a*e^2)*x^2 + (b*d^2 + 2*a*d*e)*x)*(c*x^2 + b*x + a)^(1/4), x)","F",0
2524,0,0,0,0.531612," ","integrate((e*x+d)*(c*x^2+b*x+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e x^{3} + {\left(c d + b e\right)} x^{2} + a d + {\left(b d + a e\right)} x\right)} {\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}, x\right)"," ",0,"integral((c*e*x^3 + (c*d + b*e)*x^2 + a*d + (b*d + a*e)*x)*(c*x^2 + b*x + a)^(1/4), x)","F",0
2525,0,0,0,0.619952," ","integrate((c*x^2+b*x+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{\frac{5}{4}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(5/4), x)","F",0
2526,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/4)/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2527,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(5/4)/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2528,0,0,0,0.696471," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)/(c*x^2 + b*x + a)^(1/4), x)","F",0
2529,0,0,0,0.498063," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{2} + 2 \, d e x + d^{2}}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)/(c*x^2 + b*x + a)^(1/4), x)","F",0
2530,0,0,0,0.453348," ","integrate((e*x+d)/(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x + d}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral((e*x + d)/(c*x^2 + b*x + a)^(1/4), x)","F",0
2531,0,0,0,0.439653," ","integrate(1/(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{1}{4}}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(-1/4), x)","F",0
2532,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2533,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2534,-1,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2535,0,0,0,0.644182," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)/(c*x^2 + b*x + a)^(3/4), x)","F",0
2536,0,0,0,0.681244," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{2} + 2 \, d e x + d^{2}}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)/(c*x^2 + b*x + a)^(3/4), x)","F",0
2537,0,0,0,0.558922," ","integrate((e*x+d)/(c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x + d}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral((e*x + d)/(c*x^2 + b*x + a)^(3/4), x)","F",0
2538,0,0,0,0.607492," ","integrate(1/(c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(-3/4), x)","F",0
2539,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2540,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2541,-1,0,0,0.000000," ","integrate(1/(e*x+d)^3/(c*x^2+b*x+a)^(3/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2542,0,0,0,0.555664," ","integrate((e*x+d)^3/(c*x^2+b*x+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(c*x^2 + b*x + a)^(3/4)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2543,0,0,0,0.500657," ","integrate((e*x+d)^2/(c*x^2+b*x+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(c*x^2 + b*x + a)^(3/4)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2544,0,0,0,0.453467," ","integrate((e*x+d)/(c*x^2+b*x+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}} {\left(e x + d\right)}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/4)*(e*x + d)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2545,0,0,0,0.431178," ","integrate(1/(c*x^2+b*x+a)^(5/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/4)/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2546,-1,0,0,0.000000," ","integrate(1/(e*x+d)/(c*x^2+b*x+a)^(5/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2547,-1,0,0,0.000000," ","integrate(1/(e*x+d)^2/(c*x^2+b*x+a)^(5/4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2548,0,0,0,0.848576," ","integrate(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)^(1/4),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{\frac{3}{4}} \sqrt{e x + d}}{c e^{2} x^{4} + {\left(2 \, c d e + b e^{2}\right)} x^{3} + a d^{2} + {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{2} + {\left(b d^{2} + 2 \, a d e\right)} x}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/4)*sqrt(e*x + d)/(c*e^2*x^4 + (2*c*d*e + b*e^2)*x^3 + a*d^2 + (c*d^2 + 2*b*d*e + a*e^2)*x^2 + (b*d^2 + 2*a*d*e)*x), x)","F",0
2549,1,6186,0,0.862576," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^4,x, algorithm=""fricas"")","\frac{{\left(a^{4} d e^{8} m^{8} + 40320 \, c^{4} d^{9} - 181440 \, b c^{3} d^{8} e - 725760 \, a^{3} b d^{2} e^{7} + 362880 \, a^{4} d e^{8} + 103680 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{2} - 241920 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{3} + 72576 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{4} - 362880 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{5} + 241920 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{6} + {\left(c^{4} e^{9} m^{8} + 36 \, c^{4} e^{9} m^{7} + 546 \, c^{4} e^{9} m^{6} + 4536 \, c^{4} e^{9} m^{5} + 22449 \, c^{4} e^{9} m^{4} + 67284 \, c^{4} e^{9} m^{3} + 118124 \, c^{4} e^{9} m^{2} + 109584 \, c^{4} e^{9} m + 40320 \, c^{4} e^{9}\right)} x^{9} + {\left(181440 \, b c^{3} e^{9} + {\left(c^{4} d e^{8} + 4 \, b c^{3} e^{9}\right)} m^{8} + 4 \, {\left(7 \, c^{4} d e^{8} + 37 \, b c^{3} e^{9}\right)} m^{7} + 14 \, {\left(23 \, c^{4} d e^{8} + 164 \, b c^{3} e^{9}\right)} m^{6} + 56 \, {\left(35 \, c^{4} d e^{8} + 347 \, b c^{3} e^{9}\right)} m^{5} + 7 \, {\left(967 \, c^{4} d e^{8} + 13948 \, b c^{3} e^{9}\right)} m^{4} + 28 \, {\left(469 \, c^{4} d e^{8} + 10579 \, b c^{3} e^{9}\right)} m^{3} + 36 \, {\left(363 \, c^{4} d e^{8} + 14584 \, b c^{3} e^{9}\right)} m^{2} + 144 \, {\left(35 \, c^{4} d e^{8} + 3407 \, b c^{3} e^{9}\right)} m\right)} x^{8} - 4 \, {\left(a^{3} b d^{2} e^{7} - 11 \, a^{4} d e^{8}\right)} m^{7} + 2 \, {\left(51840 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{9} + {\left(2 \, b c^{3} d e^{8} + {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{9}\right)} m^{8} - 2 \, {\left(2 \, c^{4} d^{2} e^{7} - 30 \, b c^{3} d e^{8} - 19 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{9}\right)} m^{7} - 4 \, {\left(21 \, c^{4} d^{2} e^{7} - 182 \, b c^{3} d e^{8} - 151 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{9}\right)} m^{6} - 14 \, {\left(50 \, c^{4} d^{2} e^{7} - 330 \, b c^{3} d e^{8} - 373 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{9}\right)} m^{5} - 7 \, {\left(420 \, c^{4} d^{2} e^{7} - 2354 \, b c^{3} d e^{8} - 3817 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{9}\right)} m^{4} - 28 \, {\left(232 \, c^{4} d^{2} e^{7} - 1170 \, b c^{3} d e^{8} - 2939 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{9}\right)} m^{3} - 36 \, {\left(196 \, c^{4} d^{2} e^{7} - 922 \, b c^{3} d e^{8} - 4101 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{9}\right)} m^{2} - 144 \, {\left(20 \, c^{4} d^{2} e^{7} - 90 \, b c^{3} d e^{8} - 967 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} e^{9}\right)} m\right)} x^{7} - 2 \, {\left(84 \, a^{3} b d^{2} e^{7} - 413 \, a^{4} d e^{8} - 2 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{6}\right)} m^{6} + 2 \, {\left(120960 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{9} + {\left({\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{8} + 2 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{9}\right)} m^{8} - 2 \, {\left(7 \, b c^{3} d^{2} e^{7} - 16 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{8} - 39 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{9}\right)} m^{7} + 4 \, {\left(7 \, c^{4} d^{3} e^{6} - 84 \, b c^{3} d^{2} e^{7} + 103 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{8} + 318 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{9}\right)} m^{6} + 2 \, {\left(210 \, c^{4} d^{3} e^{6} - 1540 \, b c^{3} d^{2} e^{7} + 1375 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{8} + 5634 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{9}\right)} m^{5} + {\left(2380 \, c^{4} d^{3} e^{6} - 13860 \, b c^{3} d^{2} e^{7} + 10219 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{8} + 58938 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{9}\right)} m^{4} + 2 \, {\left(3150 \, c^{4} d^{3} e^{6} - 16093 \, b c^{3} d^{2} e^{7} + 10489 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{8} + 92511 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{9}\right)} m^{3} + 4 \, {\left(1918 \, c^{4} d^{3} e^{6} - 9051 \, b c^{3} d^{2} e^{7} + 5442 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{8} + 84307 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{9}\right)} m^{2} + 48 \, {\left(70 \, c^{4} d^{3} e^{6} - 315 \, b c^{3} d^{2} e^{7} + 180 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d e^{8} + 6709 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} e^{9}\right)} m\right)} x^{6} - 4 \, {\left(742 \, a^{3} b d^{2} e^{7} - 2156 \, a^{4} d e^{8} + 6 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{5} - 39 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{6}\right)} m^{5} + {\left(72576 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{9} + {\left(4 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{8} + {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{9}\right)} m^{8} - 4 \, {\left(3 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{7} - 34 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{8} - 10 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{9}\right)} m^{7} + 2 \, {\left(84 \, b c^{3} d^{3} e^{6} - 162 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{7} + 932 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{8} + 335 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{9}\right)} m^{6} - 4 \, {\left(84 \, c^{4} d^{4} e^{5} - 798 \, b c^{3} d^{3} e^{6} + 831 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{7} - 3304 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{8} - 1525 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{9}\right)} m^{5} - {\left(3360 \, c^{4} d^{4} e^{5} - 21000 \, b c^{3} d^{3} e^{6} + 16380 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{7} - 51796 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{8} - 32773 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{9}\right)} m^{4} - 4 \, {\left(2940 \, c^{4} d^{4} e^{5} - 15330 \, b c^{3} d^{3} e^{6} + 10182 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{7} - 27766 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{8} - 26365 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{9}\right)} m^{3} - 12 \, {\left(1400 \, c^{4} d^{4} e^{5} - 6636 \, b c^{3} d^{3} e^{6} + 4008 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{7} - 9928 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{8} - 16365 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{9}\right)} m^{2} - 144 \, {\left(56 \, c^{4} d^{4} e^{5} - 252 \, b c^{3} d^{3} e^{6} + 144 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{7} - 336 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d e^{8} - 1325 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} e^{9}\right)} m\right)} x^{5} - {\left(28560 \, a^{3} b d^{2} e^{7} - 54649 \, a^{4} d e^{8} - 24 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{4} + 840 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{5} - 2500 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{6}\right)} m^{4} + {\left(362880 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{9} + {\left({\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{8} + 4 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{9}\right)} m^{8} - 4 \, {\left(5 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{7} - 9 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{8} - 41 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{9}\right)} m^{7} + 2 \, {\left(30 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{6} - 300 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{7} + 263 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{8} + 1412 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{9}\right)} m^{6} - 4 \, {\left(210 \, b c^{3} d^{4} e^{5} - 345 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{6} + 1730 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{7} - 999 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{8} - 6626 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{9}\right)} m^{5} + {\left(1680 \, c^{4} d^{5} e^{4} - 12600 \, b c^{3} d^{4} e^{5} + 11100 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{6} - 38400 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{7} + 16789 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{8} + 147076 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{9}\right)} m^{4} + 4 \, {\left(2520 \, c^{4} d^{5} e^{4} - 13650 \, b c^{3} d^{4} e^{5} + 9375 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{6} - 26345 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{7} + 9576 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{8} + 122249 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{9}\right)} m^{3} + 12 \, {\left(1540 \, c^{4} d^{5} e^{4} - 7350 \, b c^{3} d^{4} e^{5} + 4470 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{6} - 11150 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{7} + 3597 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{8} + 78228 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{9}\right)} m^{2} + 144 \, {\left(70 \, c^{4} d^{5} e^{4} - 315 \, b c^{3} d^{4} e^{5} + 180 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{3} e^{6} - 420 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{2} e^{7} + 126 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d e^{8} + 6499 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} e^{9}\right)} m\right)} x^{4} - 4 \, {\left(40369 \, a^{3} b d^{2} e^{7} - 53669 \, a^{4} d e^{8} + 120 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{3} - 180 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{4} + 2910 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{5} - 5265 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{6}\right)} m^{3} + 2 \, {\left(120960 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{9} + {\left(2 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{8} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{9}\right)} m^{8} - 2 \, {\left({\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{7} - 38 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{8} - 21 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{9}\right)} m^{7} + 2 \, {\left(20 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{6} - 33 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{7} + 592 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{8} + 372 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{9}\right)} m^{6} - 2 \, {\left(60 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{5} - 540 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{6} + 427 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{7} - 4850 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{8} - 3609 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{9}\right)} m^{5} + {\left(1680 \, b c^{3} d^{5} e^{4} - 2400 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{5} + 10600 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{6} - 5430 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{7} + 44438 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{8} + 41619 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{9}\right)} m^{4} - 4 \, {\left(840 \, c^{4} d^{6} e^{3} - 5040 \, b c^{3} d^{5} e^{4} + 3750 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{5} - 11250 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{6} + 4322 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{7} - 27796 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{8} - 36117 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{9}\right)} m^{3} - 4 \, {\left(2520 \, c^{4} d^{6} e^{3} - 12180 \, b c^{3} d^{5} e^{4} + 7500 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{5} - 18940 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{6} + 6186 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{7} - 33954 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{8} - 72569 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{9}\right)} m^{2} - 48 \, {\left(140 \, c^{4} d^{6} e^{3} - 630 \, b c^{3} d^{5} e^{4} + 360 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{4} e^{5} - 840 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{3} e^{6} + 252 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} e^{7} - 1260 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{8} - 6289 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} e^{9}\right)} m\right)} x^{3} - 4 \, {\left(133938 \, a^{3} b d^{2} e^{7} - 127251 \, a^{4} d e^{8} - 360 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{2} + 2880 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{3} - 2010 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{4} + 19950 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{5} - 24574 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{6}\right)} m^{2} + 2 \, {\left(362880 \, a^{3} b e^{9} + {\left(2 \, a^{3} b e^{9} + {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{8}\right)} m^{8} + 2 \, {\left(43 \, a^{3} b e^{9} - 3 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{7} + 20 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{8}\right)} m^{7} + 2 \, {\left(784 \, a^{3} b e^{9} + 3 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{6} - 108 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{7} + 332 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{8}\right)} m^{6} + 2 \, {\left(7882 \, a^{3} b e^{9} - 60 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{5} + 93 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{6} - 1560 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{7} + 2945 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{8}\right)} m^{5} + {\left(95018 \, a^{3} b e^{9} + 360 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{4} - 3000 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{5} + 2190 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{6} - 22860 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{7} + 29839 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{8}\right)} m^{4} - 2 \, {\left(2520 \, b c^{3} d^{6} e^{3} - 174307 \, a^{3} b e^{9} - 3240 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{4} + 12900 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{5} - 5955 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{6} + 43797 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{7} - 42395 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{8}\right)} m^{3} + 12 \, {\left(840 \, c^{4} d^{7} e^{2} - 4200 \, b c^{3} d^{6} e^{3} + 62511 \, a^{3} b e^{9} + 2670 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{4} - 6950 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{5} + 2337 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{6} - 13197 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{7} + 10058 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{8}\right)} m^{2} + 144 \, {\left(70 \, c^{4} d^{7} e^{2} - 315 \, b c^{3} d^{6} e^{3} + 5869 \, a^{3} b e^{9} + 180 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{5} e^{4} - 420 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{4} e^{5} + 126 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} e^{6} - 630 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{2} e^{7} + 420 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d e^{8}\right)} m\right)} x^{2} - 48 \, {\left(420 \, b c^{3} d^{8} e + 20094 \, a^{3} b d^{2} e^{7} - 13827 \, a^{4} d e^{8} - 510 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{7} e^{2} + 1910 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{6} e^{3} - 825 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} e^{4} + 5637 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{4} e^{5} - 5018 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{3} e^{6}\right)} m + {\left(362880 \, a^{4} e^{9} + {\left(4 \, a^{3} b d e^{8} + a^{4} e^{9}\right)} m^{8} + 4 \, {\left(42 \, a^{3} b d e^{8} + 11 \, a^{4} e^{9} - {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{7}\right)} m^{7} + 2 \, {\left(1484 \, a^{3} b d e^{8} + 413 \, a^{4} e^{9} + 12 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{6} - 78 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{7}\right)} m^{6} + 4 \, {\left(7140 \, a^{3} b d e^{8} + 2156 \, a^{4} e^{9} - 6 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{5} + 210 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{6} - 625 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{7}\right)} m^{5} + {\left(161476 \, a^{3} b d e^{8} + 54649 \, a^{4} e^{9} + 480 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{4} - 720 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{5} + 11640 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{6} - 21060 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{7}\right)} m^{4} + 4 \, {\left(133938 \, a^{3} b d e^{8} + 53669 \, a^{4} e^{9} - 360 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{3} + 2880 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{4} - 2010 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{5} + 19950 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{6} - 24574 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{7}\right)} m^{3} + 12 \, {\left(1680 \, b c^{3} d^{7} e^{2} + 80376 \, a^{3} b d e^{8} + 42417 \, a^{4} e^{9} - 2040 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{3} + 7640 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{4} - 3300 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{5} + 22548 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{6} - 20072 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{7}\right)} m^{2} - 144 \, {\left(280 \, c^{4} d^{8} e - 1260 \, b c^{3} d^{7} e^{2} - 5040 \, a^{3} b d e^{8} - 4609 \, a^{4} e^{9} + 720 \, {\left(3 \, b^{2} c^{2} + 2 \, a c^{3}\right)} d^{6} e^{3} - 1680 \, {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e^{4} + 504 \, {\left(b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{4} e^{5} - 2520 \, {\left(a b^{3} + 3 \, a^{2} b c\right)} d^{3} e^{6} + 1680 \, {\left(3 \, a^{2} b^{2} + 2 \, a^{3} c\right)} d^{2} e^{7}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{9} m^{9} + 45 \, e^{9} m^{8} + 870 \, e^{9} m^{7} + 9450 \, e^{9} m^{6} + 63273 \, e^{9} m^{5} + 269325 \, e^{9} m^{4} + 723680 \, e^{9} m^{3} + 1172700 \, e^{9} m^{2} + 1026576 \, e^{9} m + 362880 \, e^{9}}"," ",0,"(a^4*d*e^8*m^8 + 40320*c^4*d^9 - 181440*b*c^3*d^8*e - 725760*a^3*b*d^2*e^7 + 362880*a^4*d*e^8 + 103680*(3*b^2*c^2 + 2*a*c^3)*d^7*e^2 - 241920*(b^3*c + 3*a*b*c^2)*d^6*e^3 + 72576*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^4 - 362880*(a*b^3 + 3*a^2*b*c)*d^4*e^5 + 241920*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6 + (c^4*e^9*m^8 + 36*c^4*e^9*m^7 + 546*c^4*e^9*m^6 + 4536*c^4*e^9*m^5 + 22449*c^4*e^9*m^4 + 67284*c^4*e^9*m^3 + 118124*c^4*e^9*m^2 + 109584*c^4*e^9*m + 40320*c^4*e^9)*x^9 + (181440*b*c^3*e^9 + (c^4*d*e^8 + 4*b*c^3*e^9)*m^8 + 4*(7*c^4*d*e^8 + 37*b*c^3*e^9)*m^7 + 14*(23*c^4*d*e^8 + 164*b*c^3*e^9)*m^6 + 56*(35*c^4*d*e^8 + 347*b*c^3*e^9)*m^5 + 7*(967*c^4*d*e^8 + 13948*b*c^3*e^9)*m^4 + 28*(469*c^4*d*e^8 + 10579*b*c^3*e^9)*m^3 + 36*(363*c^4*d*e^8 + 14584*b*c^3*e^9)*m^2 + 144*(35*c^4*d*e^8 + 3407*b*c^3*e^9)*m)*x^8 - 4*(a^3*b*d^2*e^7 - 11*a^4*d*e^8)*m^7 + 2*(51840*(3*b^2*c^2 + 2*a*c^3)*e^9 + (2*b*c^3*d*e^8 + (3*b^2*c^2 + 2*a*c^3)*e^9)*m^8 - 2*(2*c^4*d^2*e^7 - 30*b*c^3*d*e^8 - 19*(3*b^2*c^2 + 2*a*c^3)*e^9)*m^7 - 4*(21*c^4*d^2*e^7 - 182*b*c^3*d*e^8 - 151*(3*b^2*c^2 + 2*a*c^3)*e^9)*m^6 - 14*(50*c^4*d^2*e^7 - 330*b*c^3*d*e^8 - 373*(3*b^2*c^2 + 2*a*c^3)*e^9)*m^5 - 7*(420*c^4*d^2*e^7 - 2354*b*c^3*d*e^8 - 3817*(3*b^2*c^2 + 2*a*c^3)*e^9)*m^4 - 28*(232*c^4*d^2*e^7 - 1170*b*c^3*d*e^8 - 2939*(3*b^2*c^2 + 2*a*c^3)*e^9)*m^3 - 36*(196*c^4*d^2*e^7 - 922*b*c^3*d*e^8 - 4101*(3*b^2*c^2 + 2*a*c^3)*e^9)*m^2 - 144*(20*c^4*d^2*e^7 - 90*b*c^3*d*e^8 - 967*(3*b^2*c^2 + 2*a*c^3)*e^9)*m)*x^7 - 2*(84*a^3*b*d^2*e^7 - 413*a^4*d*e^8 - 2*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)*m^6 + 2*(120960*(b^3*c + 3*a*b*c^2)*e^9 + ((3*b^2*c^2 + 2*a*c^3)*d*e^8 + 2*(b^3*c + 3*a*b*c^2)*e^9)*m^8 - 2*(7*b*c^3*d^2*e^7 - 16*(3*b^2*c^2 + 2*a*c^3)*d*e^8 - 39*(b^3*c + 3*a*b*c^2)*e^9)*m^7 + 4*(7*c^4*d^3*e^6 - 84*b*c^3*d^2*e^7 + 103*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 318*(b^3*c + 3*a*b*c^2)*e^9)*m^6 + 2*(210*c^4*d^3*e^6 - 1540*b*c^3*d^2*e^7 + 1375*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 5634*(b^3*c + 3*a*b*c^2)*e^9)*m^5 + (2380*c^4*d^3*e^6 - 13860*b*c^3*d^2*e^7 + 10219*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 58938*(b^3*c + 3*a*b*c^2)*e^9)*m^4 + 2*(3150*c^4*d^3*e^6 - 16093*b*c^3*d^2*e^7 + 10489*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 92511*(b^3*c + 3*a*b*c^2)*e^9)*m^3 + 4*(1918*c^4*d^3*e^6 - 9051*b*c^3*d^2*e^7 + 5442*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 84307*(b^3*c + 3*a*b*c^2)*e^9)*m^2 + 48*(70*c^4*d^3*e^6 - 315*b*c^3*d^2*e^7 + 180*(3*b^2*c^2 + 2*a*c^3)*d*e^8 + 6709*(b^3*c + 3*a*b*c^2)*e^9)*m)*x^6 - 4*(742*a^3*b*d^2*e^7 - 2156*a^4*d*e^8 + 6*(a*b^3 + 3*a^2*b*c)*d^4*e^5 - 39*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)*m^5 + (72576*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9 + (4*(b^3*c + 3*a*b*c^2)*d*e^8 + (b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m^8 - 4*(3*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 34*(b^3*c + 3*a*b*c^2)*d*e^8 - 10*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m^7 + 2*(84*b*c^3*d^3*e^6 - 162*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 + 932*(b^3*c + 3*a*b*c^2)*d*e^8 + 335*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m^6 - 4*(84*c^4*d^4*e^5 - 798*b*c^3*d^3*e^6 + 831*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 3304*(b^3*c + 3*a*b*c^2)*d*e^8 - 1525*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m^5 - (3360*c^4*d^4*e^5 - 21000*b*c^3*d^3*e^6 + 16380*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 51796*(b^3*c + 3*a*b*c^2)*d*e^8 - 32773*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m^4 - 4*(2940*c^4*d^4*e^5 - 15330*b*c^3*d^3*e^6 + 10182*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 27766*(b^3*c + 3*a*b*c^2)*d*e^8 - 26365*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m^3 - 12*(1400*c^4*d^4*e^5 - 6636*b*c^3*d^3*e^6 + 4008*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 9928*(b^3*c + 3*a*b*c^2)*d*e^8 - 16365*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m^2 - 144*(56*c^4*d^4*e^5 - 252*b*c^3*d^3*e^6 + 144*(3*b^2*c^2 + 2*a*c^3)*d^2*e^7 - 336*(b^3*c + 3*a*b*c^2)*d*e^8 - 1325*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*e^9)*m)*x^5 - (28560*a^3*b*d^2*e^7 - 54649*a^4*d*e^8 - 24*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^4 + 840*(a*b^3 + 3*a^2*b*c)*d^4*e^5 - 2500*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)*m^4 + (362880*(a*b^3 + 3*a^2*b*c)*e^9 + ((b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 + 4*(a*b^3 + 3*a^2*b*c)*e^9)*m^8 - 4*(5*(b^3*c + 3*a*b*c^2)*d^2*e^7 - 9*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 - 41*(a*b^3 + 3*a^2*b*c)*e^9)*m^7 + 2*(30*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 - 300*(b^3*c + 3*a*b*c^2)*d^2*e^7 + 263*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 + 1412*(a*b^3 + 3*a^2*b*c)*e^9)*m^6 - 4*(210*b*c^3*d^4*e^5 - 345*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 + 1730*(b^3*c + 3*a*b*c^2)*d^2*e^7 - 999*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 - 6626*(a*b^3 + 3*a^2*b*c)*e^9)*m^5 + (1680*c^4*d^5*e^4 - 12600*b*c^3*d^4*e^5 + 11100*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 - 38400*(b^3*c + 3*a*b*c^2)*d^2*e^7 + 16789*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 + 147076*(a*b^3 + 3*a^2*b*c)*e^9)*m^4 + 4*(2520*c^4*d^5*e^4 - 13650*b*c^3*d^4*e^5 + 9375*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 - 26345*(b^3*c + 3*a*b*c^2)*d^2*e^7 + 9576*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 + 122249*(a*b^3 + 3*a^2*b*c)*e^9)*m^3 + 12*(1540*c^4*d^5*e^4 - 7350*b*c^3*d^4*e^5 + 4470*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 - 11150*(b^3*c + 3*a*b*c^2)*d^2*e^7 + 3597*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 + 78228*(a*b^3 + 3*a^2*b*c)*e^9)*m^2 + 144*(70*c^4*d^5*e^4 - 315*b*c^3*d^4*e^5 + 180*(3*b^2*c^2 + 2*a*c^3)*d^3*e^6 - 420*(b^3*c + 3*a*b*c^2)*d^2*e^7 + 126*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d*e^8 + 6499*(a*b^3 + 3*a^2*b*c)*e^9)*m)*x^4 - 4*(40369*a^3*b*d^2*e^7 - 53669*a^4*d*e^8 + 120*(b^3*c + 3*a*b*c^2)*d^6*e^3 - 180*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^4 + 2910*(a*b^3 + 3*a^2*b*c)*d^4*e^5 - 5265*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)*m^3 + 2*(120960*(3*a^2*b^2 + 2*a^3*c)*e^9 + (2*(a*b^3 + 3*a^2*b*c)*d*e^8 + (3*a^2*b^2 + 2*a^3*c)*e^9)*m^8 - 2*((b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 - 38*(a*b^3 + 3*a^2*b*c)*d*e^8 - 21*(3*a^2*b^2 + 2*a^3*c)*e^9)*m^7 + 2*(20*(b^3*c + 3*a*b*c^2)*d^3*e^6 - 33*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 + 592*(a*b^3 + 3*a^2*b*c)*d*e^8 + 372*(3*a^2*b^2 + 2*a^3*c)*e^9)*m^6 - 2*(60*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 - 540*(b^3*c + 3*a*b*c^2)*d^3*e^6 + 427*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 - 4850*(a*b^3 + 3*a^2*b*c)*d*e^8 - 3609*(3*a^2*b^2 + 2*a^3*c)*e^9)*m^5 + (1680*b*c^3*d^5*e^4 - 2400*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 + 10600*(b^3*c + 3*a*b*c^2)*d^3*e^6 - 5430*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 + 44438*(a*b^3 + 3*a^2*b*c)*d*e^8 + 41619*(3*a^2*b^2 + 2*a^3*c)*e^9)*m^4 - 4*(840*c^4*d^6*e^3 - 5040*b*c^3*d^5*e^4 + 3750*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 - 11250*(b^3*c + 3*a*b*c^2)*d^3*e^6 + 4322*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 - 27796*(a*b^3 + 3*a^2*b*c)*d*e^8 - 36117*(3*a^2*b^2 + 2*a^3*c)*e^9)*m^3 - 4*(2520*c^4*d^6*e^3 - 12180*b*c^3*d^5*e^4 + 7500*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 - 18940*(b^3*c + 3*a*b*c^2)*d^3*e^6 + 6186*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 - 33954*(a*b^3 + 3*a^2*b*c)*d*e^8 - 72569*(3*a^2*b^2 + 2*a^3*c)*e^9)*m^2 - 48*(140*c^4*d^6*e^3 - 630*b*c^3*d^5*e^4 + 360*(3*b^2*c^2 + 2*a*c^3)*d^4*e^5 - 840*(b^3*c + 3*a*b*c^2)*d^3*e^6 + 252*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^2*e^7 - 1260*(a*b^3 + 3*a^2*b*c)*d*e^8 - 6289*(3*a^2*b^2 + 2*a^3*c)*e^9)*m)*x^3 - 4*(133938*a^3*b*d^2*e^7 - 127251*a^4*d*e^8 - 360*(3*b^2*c^2 + 2*a*c^3)*d^7*e^2 + 2880*(b^3*c + 3*a*b*c^2)*d^6*e^3 - 2010*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^4 + 19950*(a*b^3 + 3*a^2*b*c)*d^4*e^5 - 24574*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)*m^2 + 2*(362880*a^3*b*e^9 + (2*a^3*b*e^9 + (3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^8 + 2*(43*a^3*b*e^9 - 3*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 20*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^7 + 2*(784*a^3*b*e^9 + 3*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 - 108*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 332*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^6 + 2*(7882*a^3*b*e^9 - 60*(b^3*c + 3*a*b*c^2)*d^4*e^5 + 93*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 - 1560*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 2945*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^5 + (95018*a^3*b*e^9 + 360*(3*b^2*c^2 + 2*a*c^3)*d^5*e^4 - 3000*(b^3*c + 3*a*b*c^2)*d^4*e^5 + 2190*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 - 22860*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 29839*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^4 - 2*(2520*b*c^3*d^6*e^3 - 174307*a^3*b*e^9 - 3240*(3*b^2*c^2 + 2*a*c^3)*d^5*e^4 + 12900*(b^3*c + 3*a*b*c^2)*d^4*e^5 - 5955*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 + 43797*(a*b^3 + 3*a^2*b*c)*d^2*e^7 - 42395*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^3 + 12*(840*c^4*d^7*e^2 - 4200*b*c^3*d^6*e^3 + 62511*a^3*b*e^9 + 2670*(3*b^2*c^2 + 2*a*c^3)*d^5*e^4 - 6950*(b^3*c + 3*a*b*c^2)*d^4*e^5 + 2337*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 - 13197*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 10058*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m^2 + 144*(70*c^4*d^7*e^2 - 315*b*c^3*d^6*e^3 + 5869*a^3*b*e^9 + 180*(3*b^2*c^2 + 2*a*c^3)*d^5*e^4 - 420*(b^3*c + 3*a*b*c^2)*d^4*e^5 + 126*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^3*e^6 - 630*(a*b^3 + 3*a^2*b*c)*d^2*e^7 + 420*(3*a^2*b^2 + 2*a^3*c)*d*e^8)*m)*x^2 - 48*(420*b*c^3*d^8*e + 20094*a^3*b*d^2*e^7 - 13827*a^4*d*e^8 - 510*(3*b^2*c^2 + 2*a*c^3)*d^7*e^2 + 1910*(b^3*c + 3*a*b*c^2)*d^6*e^3 - 825*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^5*e^4 + 5637*(a*b^3 + 3*a^2*b*c)*d^4*e^5 - 5018*(3*a^2*b^2 + 2*a^3*c)*d^3*e^6)*m + (362880*a^4*e^9 + (4*a^3*b*d*e^8 + a^4*e^9)*m^8 + 4*(42*a^3*b*d*e^8 + 11*a^4*e^9 - (3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m^7 + 2*(1484*a^3*b*d*e^8 + 413*a^4*e^9 + 12*(a*b^3 + 3*a^2*b*c)*d^3*e^6 - 78*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m^6 + 4*(7140*a^3*b*d*e^8 + 2156*a^4*e^9 - 6*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^5 + 210*(a*b^3 + 3*a^2*b*c)*d^3*e^6 - 625*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m^5 + (161476*a^3*b*d*e^8 + 54649*a^4*e^9 + 480*(b^3*c + 3*a*b*c^2)*d^5*e^4 - 720*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^5 + 11640*(a*b^3 + 3*a^2*b*c)*d^3*e^6 - 21060*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m^4 + 4*(133938*a^3*b*d*e^8 + 53669*a^4*e^9 - 360*(3*b^2*c^2 + 2*a*c^3)*d^6*e^3 + 2880*(b^3*c + 3*a*b*c^2)*d^5*e^4 - 2010*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^5 + 19950*(a*b^3 + 3*a^2*b*c)*d^3*e^6 - 24574*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m^3 + 12*(1680*b*c^3*d^7*e^2 + 80376*a^3*b*d*e^8 + 42417*a^4*e^9 - 2040*(3*b^2*c^2 + 2*a*c^3)*d^6*e^3 + 7640*(b^3*c + 3*a*b*c^2)*d^5*e^4 - 3300*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^5 + 22548*(a*b^3 + 3*a^2*b*c)*d^3*e^6 - 20072*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m^2 - 144*(280*c^4*d^8*e - 1260*b*c^3*d^7*e^2 - 5040*a^3*b*d*e^8 - 4609*a^4*e^9 + 720*(3*b^2*c^2 + 2*a*c^3)*d^6*e^3 - 1680*(b^3*c + 3*a*b*c^2)*d^5*e^4 + 504*(b^4 + 12*a*b^2*c + 6*a^2*c^2)*d^4*e^5 - 2520*(a*b^3 + 3*a^2*b*c)*d^3*e^6 + 1680*(3*a^2*b^2 + 2*a^3*c)*d^2*e^7)*m)*x)*(e*x + d)^m/(e^9*m^9 + 45*e^9*m^8 + 870*e^9*m^7 + 9450*e^9*m^6 + 63273*e^9*m^5 + 269325*e^9*m^4 + 723680*e^9*m^3 + 1172700*e^9*m^2 + 1026576*e^9*m + 362880*e^9)","B",0
2550,1,2550,0,0.662092," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} d e^{6} m^{6} + 720 \, c^{3} d^{7} - 2520 \, b c^{2} d^{6} e - 7560 \, a^{2} b d^{2} e^{5} + 5040 \, a^{3} d e^{6} + 3024 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{2} - 1260 \, {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{3} + 5040 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{4} + {\left(c^{3} e^{7} m^{6} + 21 \, c^{3} e^{7} m^{5} + 175 \, c^{3} e^{7} m^{4} + 735 \, c^{3} e^{7} m^{3} + 1624 \, c^{3} e^{7} m^{2} + 1764 \, c^{3} e^{7} m + 720 \, c^{3} e^{7}\right)} x^{7} + {\left(2520 \, b c^{2} e^{7} + {\left(c^{3} d e^{6} + 3 \, b c^{2} e^{7}\right)} m^{6} + 3 \, {\left(5 \, c^{3} d e^{6} + 22 \, b c^{2} e^{7}\right)} m^{5} + 5 \, {\left(17 \, c^{3} d e^{6} + 114 \, b c^{2} e^{7}\right)} m^{4} + 15 \, {\left(15 \, c^{3} d e^{6} + 164 \, b c^{2} e^{7}\right)} m^{3} + {\left(274 \, c^{3} d e^{6} + 5547 \, b c^{2} e^{7}\right)} m^{2} + 6 \, {\left(20 \, c^{3} d e^{6} + 1019 \, b c^{2} e^{7}\right)} m\right)} x^{6} - 3 \, {\left(a^{2} b d^{2} e^{5} - 9 \, a^{3} d e^{6}\right)} m^{5} + 3 \, {\left(1008 \, {\left(b^{2} c + a c^{2}\right)} e^{7} + {\left(b c^{2} d e^{6} + {\left(b^{2} c + a c^{2}\right)} e^{7}\right)} m^{6} - {\left(2 \, c^{3} d^{2} e^{5} - 17 \, b c^{2} d e^{6} - 23 \, {\left(b^{2} c + a c^{2}\right)} e^{7}\right)} m^{5} - {\left(20 \, c^{3} d^{2} e^{5} - 105 \, b c^{2} d e^{6} - 207 \, {\left(b^{2} c + a c^{2}\right)} e^{7}\right)} m^{4} - 5 \, {\left(14 \, c^{3} d^{2} e^{5} - 59 \, b c^{2} d e^{6} - 185 \, {\left(b^{2} c + a c^{2}\right)} e^{7}\right)} m^{3} - 2 \, {\left(50 \, c^{3} d^{2} e^{5} - 187 \, b c^{2} d e^{6} - 1072 \, {\left(b^{2} c + a c^{2}\right)} e^{7}\right)} m^{2} - 12 \, {\left(4 \, c^{3} d^{2} e^{5} - 14 \, b c^{2} d e^{6} - 201 \, {\left(b^{2} c + a c^{2}\right)} e^{7}\right)} m\right)} x^{5} - {\left(75 \, a^{2} b d^{2} e^{5} - 295 \, a^{3} d e^{6} - 6 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{4}\right)} m^{4} + {\left(1260 \, {\left(b^{3} + 6 \, a b c\right)} e^{7} + {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d e^{6} + {\left(b^{3} + 6 \, a b c\right)} e^{7}\right)} m^{6} - 3 \, {\left(5 \, b c^{2} d^{2} e^{5} - 19 \, {\left(b^{2} c + a c^{2}\right)} d e^{6} - 8 \, {\left(b^{3} + 6 \, a b c\right)} e^{7}\right)} m^{5} + {\left(30 \, c^{3} d^{3} e^{4} - 195 \, b c^{2} d^{2} e^{5} + 393 \, {\left(b^{2} c + a c^{2}\right)} d e^{6} + 226 \, {\left(b^{3} + 6 \, a b c\right)} e^{7}\right)} m^{4} + 3 \, {\left(60 \, c^{3} d^{3} e^{4} - 265 \, b c^{2} d^{2} e^{5} + 401 \, {\left(b^{2} c + a c^{2}\right)} d e^{6} + 352 \, {\left(b^{3} + 6 \, a b c\right)} e^{7}\right)} m^{3} + 5 \, {\left(66 \, c^{3} d^{3} e^{4} - 249 \, b c^{2} d^{2} e^{5} + 324 \, {\left(b^{2} c + a c^{2}\right)} d e^{6} + 509 \, {\left(b^{3} + 6 \, a b c\right)} e^{7}\right)} m^{2} + 18 \, {\left(10 \, c^{3} d^{3} e^{4} - 35 \, b c^{2} d^{2} e^{5} + 42 \, {\left(b^{2} c + a c^{2}\right)} d e^{6} + 164 \, {\left(b^{3} + 6 \, a b c\right)} e^{7}\right)} m\right)} x^{4} - 3 \, {\left(245 \, a^{2} b d^{2} e^{5} - 555 \, a^{3} d e^{6} + 2 \, {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{3} - 44 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{4}\right)} m^{3} + {\left(5040 \, {\left(a b^{2} + a^{2} c\right)} e^{7} + {\left({\left(b^{3} + 6 \, a b c\right)} d e^{6} + 3 \, {\left(a b^{2} + a^{2} c\right)} e^{7}\right)} m^{6} - 3 \, {\left(4 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{5} - 7 \, {\left(b^{3} + 6 \, a b c\right)} d e^{6} - 25 \, {\left(a b^{2} + a^{2} c\right)} e^{7}\right)} m^{5} + {\left(60 \, b c^{2} d^{3} e^{4} - 192 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{5} + 163 \, {\left(b^{3} + 6 \, a b c\right)} d e^{6} + 741 \, {\left(a b^{2} + a^{2} c\right)} e^{7}\right)} m^{4} - 3 \, {\left(40 \, c^{3} d^{4} e^{3} - 200 \, b c^{2} d^{3} e^{4} + 332 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{5} - 189 \, {\left(b^{3} + 6 \, a b c\right)} d e^{6} - 1219 \, {\left(a b^{2} + a^{2} c\right)} e^{7}\right)} m^{3} - 4 \, {\left(90 \, c^{3} d^{4} e^{3} - 345 \, b c^{2} d^{3} e^{4} + 456 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{5} - 211 \, {\left(b^{3} + 6 \, a b c\right)} d e^{6} - 2334 \, {\left(a b^{2} + a^{2} c\right)} e^{7}\right)} m^{2} - 12 \, {\left(20 \, c^{3} d^{4} e^{3} - 70 \, b c^{2} d^{3} e^{4} + 84 \, {\left(b^{2} c + a c^{2}\right)} d^{2} e^{5} - 35 \, {\left(b^{3} + 6 \, a b c\right)} d e^{6} - 949 \, {\left(a b^{2} + a^{2} c\right)} e^{7}\right)} m\right)} x^{3} - {\left(3525 \, a^{2} b d^{2} e^{5} - 5104 \, a^{3} d e^{6} - 72 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{2} + 108 \, {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{3} - 1074 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{4}\right)} m^{2} + 3 \, {\left(2520 \, a^{2} b e^{7} + {\left(a^{2} b e^{7} + {\left(a b^{2} + a^{2} c\right)} d e^{6}\right)} m^{6} + {\left(26 \, a^{2} b e^{7} - {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{5} + 23 \, {\left(a b^{2} + a^{2} c\right)} d e^{6}\right)} m^{5} + {\left(270 \, a^{2} b e^{7} + 12 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{4} - 19 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{5} + 201 \, {\left(a b^{2} + a^{2} c\right)} d e^{6}\right)} m^{4} - {\left(60 \, b c^{2} d^{4} e^{3} - 1420 \, a^{2} b e^{7} - 168 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{4} + 125 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{5} - 817 \, {\left(a b^{2} + a^{2} c\right)} d e^{6}\right)} m^{3} + {\left(120 \, c^{3} d^{5} e^{2} - 480 \, b c^{2} d^{4} e^{3} + 3929 \, a^{2} b e^{7} + 660 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{4} - 317 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{5} + 1478 \, {\left(a b^{2} + a^{2} c\right)} d e^{6}\right)} m^{2} + 6 \, {\left(20 \, c^{3} d^{5} e^{2} - 70 \, b c^{2} d^{4} e^{3} + 879 \, a^{2} b e^{7} + 84 \, {\left(b^{2} c + a c^{2}\right)} d^{3} e^{4} - 35 \, {\left(b^{3} + 6 \, a b c\right)} d^{2} e^{5} + 140 \, {\left(a b^{2} + a^{2} c\right)} d e^{6}\right)} m\right)} x^{2} - 6 \, {\left(60 \, b c^{2} d^{6} e + 1377 \, a^{2} b d^{2} e^{5} - 1338 \, a^{3} d e^{6} - 156 \, {\left(b^{2} c + a c^{2}\right)} d^{5} e^{2} + 107 \, {\left(b^{3} + 6 \, a b c\right)} d^{4} e^{3} - 638 \, {\left(a b^{2} + a^{2} c\right)} d^{3} e^{4}\right)} m + {\left(5040 \, a^{3} e^{7} + {\left(3 \, a^{2} b d e^{6} + a^{3} e^{7}\right)} m^{6} + 3 \, {\left(25 \, a^{2} b d e^{6} + 9 \, a^{3} e^{7} - 2 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{5}\right)} m^{5} + {\left(735 \, a^{2} b d e^{6} + 295 \, a^{3} e^{7} + 6 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{4} - 132 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{5}\right)} m^{4} + 3 \, {\left(1175 \, a^{2} b d e^{6} + 555 \, a^{3} e^{7} - 24 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{3} + 36 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{4} - 358 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{5}\right)} m^{3} + 2 \, {\left(180 \, b c^{2} d^{5} e^{2} + 4131 \, a^{2} b d e^{6} + 2552 \, a^{3} e^{7} - 468 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{3} + 321 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{4} - 1914 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{5}\right)} m^{2} - 36 \, {\left(20 \, c^{3} d^{6} e - 70 \, b c^{2} d^{5} e^{2} - 210 \, a^{2} b d e^{6} - 223 \, a^{3} e^{7} + 84 \, {\left(b^{2} c + a c^{2}\right)} d^{4} e^{3} - 35 \, {\left(b^{3} + 6 \, a b c\right)} d^{3} e^{4} + 140 \, {\left(a b^{2} + a^{2} c\right)} d^{2} e^{5}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{7} m^{7} + 28 \, e^{7} m^{6} + 322 \, e^{7} m^{5} + 1960 \, e^{7} m^{4} + 6769 \, e^{7} m^{3} + 13132 \, e^{7} m^{2} + 13068 \, e^{7} m + 5040 \, e^{7}}"," ",0,"(a^3*d*e^6*m^6 + 720*c^3*d^7 - 2520*b*c^2*d^6*e - 7560*a^2*b*d^2*e^5 + 5040*a^3*d*e^6 + 3024*(b^2*c + a*c^2)*d^5*e^2 - 1260*(b^3 + 6*a*b*c)*d^4*e^3 + 5040*(a*b^2 + a^2*c)*d^3*e^4 + (c^3*e^7*m^6 + 21*c^3*e^7*m^5 + 175*c^3*e^7*m^4 + 735*c^3*e^7*m^3 + 1624*c^3*e^7*m^2 + 1764*c^3*e^7*m + 720*c^3*e^7)*x^7 + (2520*b*c^2*e^7 + (c^3*d*e^6 + 3*b*c^2*e^7)*m^6 + 3*(5*c^3*d*e^6 + 22*b*c^2*e^7)*m^5 + 5*(17*c^3*d*e^6 + 114*b*c^2*e^7)*m^4 + 15*(15*c^3*d*e^6 + 164*b*c^2*e^7)*m^3 + (274*c^3*d*e^6 + 5547*b*c^2*e^7)*m^2 + 6*(20*c^3*d*e^6 + 1019*b*c^2*e^7)*m)*x^6 - 3*(a^2*b*d^2*e^5 - 9*a^3*d*e^6)*m^5 + 3*(1008*(b^2*c + a*c^2)*e^7 + (b*c^2*d*e^6 + (b^2*c + a*c^2)*e^7)*m^6 - (2*c^3*d^2*e^5 - 17*b*c^2*d*e^6 - 23*(b^2*c + a*c^2)*e^7)*m^5 - (20*c^3*d^2*e^5 - 105*b*c^2*d*e^6 - 207*(b^2*c + a*c^2)*e^7)*m^4 - 5*(14*c^3*d^2*e^5 - 59*b*c^2*d*e^6 - 185*(b^2*c + a*c^2)*e^7)*m^3 - 2*(50*c^3*d^2*e^5 - 187*b*c^2*d*e^6 - 1072*(b^2*c + a*c^2)*e^7)*m^2 - 12*(4*c^3*d^2*e^5 - 14*b*c^2*d*e^6 - 201*(b^2*c + a*c^2)*e^7)*m)*x^5 - (75*a^2*b*d^2*e^5 - 295*a^3*d*e^6 - 6*(a*b^2 + a^2*c)*d^3*e^4)*m^4 + (1260*(b^3 + 6*a*b*c)*e^7 + (3*(b^2*c + a*c^2)*d*e^6 + (b^3 + 6*a*b*c)*e^7)*m^6 - 3*(5*b*c^2*d^2*e^5 - 19*(b^2*c + a*c^2)*d*e^6 - 8*(b^3 + 6*a*b*c)*e^7)*m^5 + (30*c^3*d^3*e^4 - 195*b*c^2*d^2*e^5 + 393*(b^2*c + a*c^2)*d*e^6 + 226*(b^3 + 6*a*b*c)*e^7)*m^4 + 3*(60*c^3*d^3*e^4 - 265*b*c^2*d^2*e^5 + 401*(b^2*c + a*c^2)*d*e^6 + 352*(b^3 + 6*a*b*c)*e^7)*m^3 + 5*(66*c^3*d^3*e^4 - 249*b*c^2*d^2*e^5 + 324*(b^2*c + a*c^2)*d*e^6 + 509*(b^3 + 6*a*b*c)*e^7)*m^2 + 18*(10*c^3*d^3*e^4 - 35*b*c^2*d^2*e^5 + 42*(b^2*c + a*c^2)*d*e^6 + 164*(b^3 + 6*a*b*c)*e^7)*m)*x^4 - 3*(245*a^2*b*d^2*e^5 - 555*a^3*d*e^6 + 2*(b^3 + 6*a*b*c)*d^4*e^3 - 44*(a*b^2 + a^2*c)*d^3*e^4)*m^3 + (5040*(a*b^2 + a^2*c)*e^7 + ((b^3 + 6*a*b*c)*d*e^6 + 3*(a*b^2 + a^2*c)*e^7)*m^6 - 3*(4*(b^2*c + a*c^2)*d^2*e^5 - 7*(b^3 + 6*a*b*c)*d*e^6 - 25*(a*b^2 + a^2*c)*e^7)*m^5 + (60*b*c^2*d^3*e^4 - 192*(b^2*c + a*c^2)*d^2*e^5 + 163*(b^3 + 6*a*b*c)*d*e^6 + 741*(a*b^2 + a^2*c)*e^7)*m^4 - 3*(40*c^3*d^4*e^3 - 200*b*c^2*d^3*e^4 + 332*(b^2*c + a*c^2)*d^2*e^5 - 189*(b^3 + 6*a*b*c)*d*e^6 - 1219*(a*b^2 + a^2*c)*e^7)*m^3 - 4*(90*c^3*d^4*e^3 - 345*b*c^2*d^3*e^4 + 456*(b^2*c + a*c^2)*d^2*e^5 - 211*(b^3 + 6*a*b*c)*d*e^6 - 2334*(a*b^2 + a^2*c)*e^7)*m^2 - 12*(20*c^3*d^4*e^3 - 70*b*c^2*d^3*e^4 + 84*(b^2*c + a*c^2)*d^2*e^5 - 35*(b^3 + 6*a*b*c)*d*e^6 - 949*(a*b^2 + a^2*c)*e^7)*m)*x^3 - (3525*a^2*b*d^2*e^5 - 5104*a^3*d*e^6 - 72*(b^2*c + a*c^2)*d^5*e^2 + 108*(b^3 + 6*a*b*c)*d^4*e^3 - 1074*(a*b^2 + a^2*c)*d^3*e^4)*m^2 + 3*(2520*a^2*b*e^7 + (a^2*b*e^7 + (a*b^2 + a^2*c)*d*e^6)*m^6 + (26*a^2*b*e^7 - (b^3 + 6*a*b*c)*d^2*e^5 + 23*(a*b^2 + a^2*c)*d*e^6)*m^5 + (270*a^2*b*e^7 + 12*(b^2*c + a*c^2)*d^3*e^4 - 19*(b^3 + 6*a*b*c)*d^2*e^5 + 201*(a*b^2 + a^2*c)*d*e^6)*m^4 - (60*b*c^2*d^4*e^3 - 1420*a^2*b*e^7 - 168*(b^2*c + a*c^2)*d^3*e^4 + 125*(b^3 + 6*a*b*c)*d^2*e^5 - 817*(a*b^2 + a^2*c)*d*e^6)*m^3 + (120*c^3*d^5*e^2 - 480*b*c^2*d^4*e^3 + 3929*a^2*b*e^7 + 660*(b^2*c + a*c^2)*d^3*e^4 - 317*(b^3 + 6*a*b*c)*d^2*e^5 + 1478*(a*b^2 + a^2*c)*d*e^6)*m^2 + 6*(20*c^3*d^5*e^2 - 70*b*c^2*d^4*e^3 + 879*a^2*b*e^7 + 84*(b^2*c + a*c^2)*d^3*e^4 - 35*(b^3 + 6*a*b*c)*d^2*e^5 + 140*(a*b^2 + a^2*c)*d*e^6)*m)*x^2 - 6*(60*b*c^2*d^6*e + 1377*a^2*b*d^2*e^5 - 1338*a^3*d*e^6 - 156*(b^2*c + a*c^2)*d^5*e^2 + 107*(b^3 + 6*a*b*c)*d^4*e^3 - 638*(a*b^2 + a^2*c)*d^3*e^4)*m + (5040*a^3*e^7 + (3*a^2*b*d*e^6 + a^3*e^7)*m^6 + 3*(25*a^2*b*d*e^6 + 9*a^3*e^7 - 2*(a*b^2 + a^2*c)*d^2*e^5)*m^5 + (735*a^2*b*d*e^6 + 295*a^3*e^7 + 6*(b^3 + 6*a*b*c)*d^3*e^4 - 132*(a*b^2 + a^2*c)*d^2*e^5)*m^4 + 3*(1175*a^2*b*d*e^6 + 555*a^3*e^7 - 24*(b^2*c + a*c^2)*d^4*e^3 + 36*(b^3 + 6*a*b*c)*d^3*e^4 - 358*(a*b^2 + a^2*c)*d^2*e^5)*m^3 + 2*(180*b*c^2*d^5*e^2 + 4131*a^2*b*d*e^6 + 2552*a^3*e^7 - 468*(b^2*c + a*c^2)*d^4*e^3 + 321*(b^3 + 6*a*b*c)*d^3*e^4 - 1914*(a*b^2 + a^2*c)*d^2*e^5)*m^2 - 36*(20*c^3*d^6*e - 70*b*c^2*d^5*e^2 - 210*a^2*b*d*e^6 - 223*a^3*e^7 + 84*(b^2*c + a*c^2)*d^4*e^3 - 35*(b^3 + 6*a*b*c)*d^3*e^4 + 140*(a*b^2 + a^2*c)*d^2*e^5)*m)*x)*(e*x + d)^m/(e^7*m^7 + 28*e^7*m^6 + 322*e^7*m^5 + 1960*e^7*m^4 + 6769*e^7*m^3 + 13132*e^7*m^2 + 13068*e^7*m + 5040*e^7)","B",0
2551,1,869,0,0.679537," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} d e^{4} m^{4} + 24 \, c^{2} d^{5} - 60 \, b c d^{4} e - 120 \, a b d^{2} e^{3} + 120 \, a^{2} d e^{4} + 40 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(c^{2} e^{5} m^{4} + 10 \, c^{2} e^{5} m^{3} + 35 \, c^{2} e^{5} m^{2} + 50 \, c^{2} e^{5} m + 24 \, c^{2} e^{5}\right)} x^{5} + {\left(60 \, b c e^{5} + {\left(c^{2} d e^{4} + 2 \, b c e^{5}\right)} m^{4} + 2 \, {\left(3 \, c^{2} d e^{4} + 11 \, b c e^{5}\right)} m^{3} + {\left(11 \, c^{2} d e^{4} + 82 \, b c e^{5}\right)} m^{2} + 2 \, {\left(3 \, c^{2} d e^{4} + 61 \, b c e^{5}\right)} m\right)} x^{4} - 2 \, {\left(a b d^{2} e^{3} - 7 \, a^{2} d e^{4}\right)} m^{3} + {\left(40 \, {\left(b^{2} + 2 \, a c\right)} e^{5} + {\left(2 \, b c d e^{4} + {\left(b^{2} + 2 \, a c\right)} e^{5}\right)} m^{4} - 4 \, {\left(c^{2} d^{2} e^{3} - 4 \, b c d e^{4} - 3 \, {\left(b^{2} + 2 \, a c\right)} e^{5}\right)} m^{3} - {\left(12 \, c^{2} d^{2} e^{3} - 34 \, b c d e^{4} - 49 \, {\left(b^{2} + 2 \, a c\right)} e^{5}\right)} m^{2} - 2 \, {\left(4 \, c^{2} d^{2} e^{3} - 10 \, b c d e^{4} - 39 \, {\left(b^{2} + 2 \, a c\right)} e^{5}\right)} m\right)} x^{3} - {\left(24 \, a b d^{2} e^{3} - 71 \, a^{2} d e^{4} - 2 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2}\right)} m^{2} + {\left(120 \, a b e^{5} + {\left(2 \, a b e^{5} + {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} m^{4} - 2 \, {\left(3 \, b c d^{2} e^{3} - 13 \, a b e^{5} - 5 \, {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} m^{3} + {\left(12 \, c^{2} d^{3} e^{2} - 36 \, b c d^{2} e^{3} + 118 \, a b e^{5} + 29 \, {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} m^{2} + 2 \, {\left(6 \, c^{2} d^{3} e^{2} - 15 \, b c d^{2} e^{3} + 107 \, a b e^{5} + 10 \, {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} m\right)} x^{2} - 2 \, {\left(6 \, b c d^{4} e + 47 \, a b d^{2} e^{3} - 77 \, a^{2} d e^{4} - 9 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2}\right)} m + {\left(120 \, a^{2} e^{5} + {\left(2 \, a b d e^{4} + a^{2} e^{5}\right)} m^{4} + 2 \, {\left(12 \, a b d e^{4} + 7 \, a^{2} e^{5} - {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} m^{3} + {\left(12 \, b c d^{3} e^{2} + 94 \, a b d e^{4} + 71 \, a^{2} e^{5} - 18 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} m^{2} - 2 \, {\left(12 \, c^{2} d^{4} e - 30 \, b c d^{3} e^{2} - 60 \, a b d e^{4} - 77 \, a^{2} e^{5} + 20 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{5} m^{5} + 15 \, e^{5} m^{4} + 85 \, e^{5} m^{3} + 225 \, e^{5} m^{2} + 274 \, e^{5} m + 120 \, e^{5}}"," ",0,"(a^2*d*e^4*m^4 + 24*c^2*d^5 - 60*b*c*d^4*e - 120*a*b*d^2*e^3 + 120*a^2*d*e^4 + 40*(b^2 + 2*a*c)*d^3*e^2 + (c^2*e^5*m^4 + 10*c^2*e^5*m^3 + 35*c^2*e^5*m^2 + 50*c^2*e^5*m + 24*c^2*e^5)*x^5 + (60*b*c*e^5 + (c^2*d*e^4 + 2*b*c*e^5)*m^4 + 2*(3*c^2*d*e^4 + 11*b*c*e^5)*m^3 + (11*c^2*d*e^4 + 82*b*c*e^5)*m^2 + 2*(3*c^2*d*e^4 + 61*b*c*e^5)*m)*x^4 - 2*(a*b*d^2*e^3 - 7*a^2*d*e^4)*m^3 + (40*(b^2 + 2*a*c)*e^5 + (2*b*c*d*e^4 + (b^2 + 2*a*c)*e^5)*m^4 - 4*(c^2*d^2*e^3 - 4*b*c*d*e^4 - 3*(b^2 + 2*a*c)*e^5)*m^3 - (12*c^2*d^2*e^3 - 34*b*c*d*e^4 - 49*(b^2 + 2*a*c)*e^5)*m^2 - 2*(4*c^2*d^2*e^3 - 10*b*c*d*e^4 - 39*(b^2 + 2*a*c)*e^5)*m)*x^3 - (24*a*b*d^2*e^3 - 71*a^2*d*e^4 - 2*(b^2 + 2*a*c)*d^3*e^2)*m^2 + (120*a*b*e^5 + (2*a*b*e^5 + (b^2 + 2*a*c)*d*e^4)*m^4 - 2*(3*b*c*d^2*e^3 - 13*a*b*e^5 - 5*(b^2 + 2*a*c)*d*e^4)*m^3 + (12*c^2*d^3*e^2 - 36*b*c*d^2*e^3 + 118*a*b*e^5 + 29*(b^2 + 2*a*c)*d*e^4)*m^2 + 2*(6*c^2*d^3*e^2 - 15*b*c*d^2*e^3 + 107*a*b*e^5 + 10*(b^2 + 2*a*c)*d*e^4)*m)*x^2 - 2*(6*b*c*d^4*e + 47*a*b*d^2*e^3 - 77*a^2*d*e^4 - 9*(b^2 + 2*a*c)*d^3*e^2)*m + (120*a^2*e^5 + (2*a*b*d*e^4 + a^2*e^5)*m^4 + 2*(12*a*b*d*e^4 + 7*a^2*e^5 - (b^2 + 2*a*c)*d^2*e^3)*m^3 + (12*b*c*d^3*e^2 + 94*a*b*d*e^4 + 71*a^2*e^5 - 18*(b^2 + 2*a*c)*d^2*e^3)*m^2 - 2*(12*c^2*d^4*e - 30*b*c*d^3*e^2 - 60*a*b*d*e^4 - 77*a^2*e^5 + 20*(b^2 + 2*a*c)*d^2*e^3)*m)*x)*(e*x + d)^m/(e^5*m^5 + 15*e^5*m^4 + 85*e^5*m^3 + 225*e^5*m^2 + 274*e^5*m + 120*e^5)","B",0
2552,1,201,0,0.421768," ","integrate((e*x+d)^m*(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{{\left(a d e^{2} m^{2} + 2 \, c d^{3} - 3 \, b d^{2} e + 6 \, a d e^{2} + {\left(c e^{3} m^{2} + 3 \, c e^{3} m + 2 \, c e^{3}\right)} x^{3} + {\left(3 \, b e^{3} + {\left(c d e^{2} + b e^{3}\right)} m^{2} + {\left(c d e^{2} + 4 \, b e^{3}\right)} m\right)} x^{2} - {\left(b d^{2} e - 5 \, a d e^{2}\right)} m + {\left(6 \, a e^{3} + {\left(b d e^{2} + a e^{3}\right)} m^{2} - {\left(2 \, c d^{2} e - 3 \, b d e^{2} - 5 \, a e^{3}\right)} m\right)} x\right)} {\left(e x + d\right)}^{m}}{e^{3} m^{3} + 6 \, e^{3} m^{2} + 11 \, e^{3} m + 6 \, e^{3}}"," ",0,"(a*d*e^2*m^2 + 2*c*d^3 - 3*b*d^2*e + 6*a*d*e^2 + (c*e^3*m^2 + 3*c*e^3*m + 2*c*e^3)*x^3 + (3*b*e^3 + (c*d*e^2 + b*e^3)*m^2 + (c*d*e^2 + 4*b*e^3)*m)*x^2 - (b*d^2*e - 5*a*d*e^2)*m + (6*a*e^3 + (b*d*e^2 + a*e^3)*m^2 - (2*c*d^2*e - 3*b*d*e^2 - 5*a*e^3)*m)*x)*(e*x + d)^m/(e^3*m^3 + 6*e^3*m^2 + 11*e^3*m + 6*e^3)","B",0
2553,0,0,0,0.414800," ","integrate((e*x+d)^m/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c x^{2} + b x + a}, x\right)"," ",0,"integral((e*x + d)^m/(c*x^2 + b*x + a), x)","F",0
2554,0,0,0,0.440322," ","integrate((e*x+d)^m/(c*x^2+b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral((e*x + d)^m/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2555,0,0,0,0.498503," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}\right)} \sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2)*sqrt(c*x^2 + b*x + a)*(e*x + d)^m, x)","F",0
2556,0,0,0,0.492071," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{\frac{3}{2}} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(3/2)*(e*x + d)^m, x)","F",0
2557,0,0,0,0.435659," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)^m, x)","F",0
2558,0,0,0,0.443208," ","integrate((e*x+d)^m/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x + d\right)}^{m}}{\sqrt{c x^{2} + b x + a}}, x\right)"," ",0,"integral((e*x + d)^m/sqrt(c*x^2 + b*x + a), x)","F",0
2559,0,0,0,0.441933," ","integrate((e*x+d)^m/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{m}}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, a b x + {\left(b^{2} + 2 \, a c\right)} x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)^m/(c^2*x^4 + 2*b*c*x^3 + 2*a*b*x + (b^2 + 2*a*c)*x^2 + a^2), x)","F",0
2560,0,0,0,0.449690," ","integrate((e*x+d)^m/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} {\left(e x + d\right)}^{m}}{c^{3} x^{6} + 3 \, b c^{2} x^{5} + 3 \, {\left(b^{2} c + a c^{2}\right)} x^{4} + 3 \, a^{2} b x + {\left(b^{3} + 6 \, a b c\right)} x^{3} + a^{3} + 3 \, {\left(a b^{2} + a^{2} c\right)} x^{2}}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*(e*x + d)^m/(c^3*x^6 + 3*b*c^2*x^5 + 3*(b^2*c + a*c^2)*x^4 + 3*a^2*b*x + (b^3 + 6*a*b*c)*x^3 + a^3 + 3*(a*b^2 + a^2*c)*x^2), x)","F",0
2561,0,0,0,0.429476," ","integrate((d*x)^m*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{p} \left(d x\right)^{m}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p*(d*x)^m, x)","F",0
2562,0,0,0,0.451987," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p*(e*x + d)^m, x)","F",0
2563,0,0,0,0.426836," ","integrate((e*x+d)^3*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}\right)} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3)*(c*x^2 + b*x + a)^p, x)","F",0
2564,0,0,0,0.429443," ","integrate((e*x+d)^2*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2} + 2 \, d e x + d^{2}\right)} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((e^2*x^2 + 2*d*e*x + d^2)*(c*x^2 + b*x + a)^p, x)","F",0
2565,0,0,0,0.420770," ","integrate((e*x+d)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((e*x + d)*(c*x^2 + b*x + a)^p, x)","F",0
2566,0,0,0,0.418934," ","integrate((c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p, x)","F",0
2567,0,0,0,0.415049," ","integrate((c*x^2+b*x+a)^p/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{e x + d}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/(e*x + d), x)","F",0
2568,0,0,0,0.441726," ","integrate((c*x^2+b*x+a)^p/(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
2569,0,0,0,0.450464," ","integrate((c*x^2+b*x+a)^p/(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
2570,0,0,0,0.444722," ","integrate((e*x+d)^(3/2)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)}^{\frac{3}{2}} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral((e*x + d)^(3/2)*(c*x^2 + b*x + a)^p, x)","F",0
2571,0,0,0,0.438614," ","integrate((e*x+d)^(1/2)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x + d} {\left(c x^{2} + b x + a\right)}^{p}, x\right)"," ",0,"integral(sqrt(e*x + d)*(c*x^2 + b*x + a)^p, x)","F",0
2572,0,0,0,0.443973," ","integrate((c*x^2+b*x+a)^p/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{\sqrt{e x + d}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/sqrt(e*x + d), x)","F",0
2573,0,0,0,0.451278," ","integrate((c*x^2+b*x+a)^p/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x + d} {\left(c x^{2} + b x + a\right)}^{p}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral(sqrt(e*x + d)*(c*x^2 + b*x + a)^p/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
2574,0,0,0,0.450650," ","integrate((c*x^2+b*x+a)^p/((e*x+d)^(2*p)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2} + b x + a\right)}^{p}}{{\left(e x + d\right)}^{2 \, p}}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p/(e*x + d)^(2*p), x)","F",0
2575,0,0,0,0.467840," ","integrate((e*x+d)^(-1-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 1}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 1), x)","F",0
2576,0,0,0,0.471840," ","integrate((e*x+d)^(-2-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 2}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 2), x)","F",0
2577,0,0,0,0.481164," ","integrate((e*x+d)^(-3-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 3}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 3), x)","F",0
2578,0,0,0,0.526128," ","integrate((e*x+d)^(-4-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 4}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 4), x)","F",0
2579,0,0,0,0.524899," ","integrate((e*x+d)^(-5-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 5}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 5), x)","F",0
2580,0,0,0,0.671499," ","integrate((e*x+d)^(-6-2*p)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{p} {\left(e x + d\right)}^{-2 \, p - 6}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^p*(e*x + d)^(-2*p - 6), x)","F",0
2581,0,0,0,0.507632," ","integrate((e*x+d)^m*(c*x^2+b*x+a)^(-2-1/2*m),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2} + b x + a\right)}^{-\frac{1}{2} \, m - 2} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((c*x^2 + b*x + a)^(-1/2*m - 2)*(e*x + d)^m, x)","F",0
2582,1,115,0,0.620726," ","integrate(1/(1+x)^(1/3)/(x^2-x+1)^(1/3),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(-\frac{4 \, \sqrt{3} {\left(x^{2} - x + 1\right)}^{\frac{1}{3}} {\left(x + 1\right)}^{\frac{1}{3}} x^{2} - 2 \, \sqrt{3} {\left(x^{2} - x + 1\right)}^{\frac{2}{3}} {\left(x + 1\right)}^{\frac{2}{3}} x + \sqrt{3} {\left(x^{3} + 1\right)}}{9 \, x^{3} + 1}\right) - \frac{1}{6} \, \log\left(3 \, {\left(x^{2} - x + 1\right)}^{\frac{1}{3}} {\left(x + 1\right)}^{\frac{1}{3}} x^{2} - 3 \, {\left(x^{2} - x + 1\right)}^{\frac{2}{3}} {\left(x + 1\right)}^{\frac{2}{3}} x + 1\right)"," ",0,"1/3*sqrt(3)*arctan(-(4*sqrt(3)*(x^2 - x + 1)^(1/3)*(x + 1)^(1/3)*x^2 - 2*sqrt(3)*(x^2 - x + 1)^(2/3)*(x + 1)^(2/3)*x + sqrt(3)*(x^3 + 1))/(9*x^3 + 1)) - 1/6*log(3*(x^2 - x + 1)^(1/3)*(x + 1)^(1/3)*x^2 - 3*(x^2 - x + 1)^(2/3)*(x + 1)^(2/3)*x + 1)","A",0
2583,0,0,0,0.399598," ","integrate(1/(1+x)^(2/3)/(x^2-x+1)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{2} - x + 1\right)}^{\frac{1}{3}} {\left(x + 1\right)}^{\frac{1}{3}}}{x^{3} + 1}, x\right)"," ",0,"integral((x^2 - x + 1)^(1/3)*(x + 1)^(1/3)/(x^3 + 1), x)","F",0
2584,0,0,0,0.432453," ","integrate((1+x)^p*(x^2-x+1)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{2} - x + 1\right)}^{p} {\left(x + 1\right)}^{p}, x\right)"," ",0,"integral((x^2 - x + 1)^p*(x + 1)^p, x)","F",0
2585,1,115,0,0.599997," ","integrate(1/(1-x)^(1/3)/(x^2+x+1)^(1/3),x, algorithm=""fricas"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{4 \, \sqrt{3} {\left(x^{2} + x + 1\right)}^{\frac{1}{3}} x^{2} {\left(-x + 1\right)}^{\frac{1}{3}} + 2 \, \sqrt{3} {\left(x^{2} + x + 1\right)}^{\frac{2}{3}} x {\left(-x + 1\right)}^{\frac{2}{3}} - \sqrt{3} {\left(x^{3} - 1\right)}}{9 \, x^{3} - 1}\right) + \frac{1}{6} \, \log\left(3 \, {\left(x^{2} + x + 1\right)}^{\frac{1}{3}} x^{2} {\left(-x + 1\right)}^{\frac{1}{3}} + 3 \, {\left(x^{2} + x + 1\right)}^{\frac{2}{3}} x {\left(-x + 1\right)}^{\frac{2}{3}} + 1\right)"," ",0,"-1/3*sqrt(3)*arctan((4*sqrt(3)*(x^2 + x + 1)^(1/3)*x^2*(-x + 1)^(1/3) + 2*sqrt(3)*(x^2 + x + 1)^(2/3)*x*(-x + 1)^(2/3) - sqrt(3)*(x^3 - 1))/(9*x^3 - 1)) + 1/6*log(3*(x^2 + x + 1)^(1/3)*x^2*(-x + 1)^(1/3) + 3*(x^2 + x + 1)^(2/3)*x*(-x + 1)^(2/3) + 1)","A",0
2586,0,0,0,0.415036," ","integrate(1/(1-x)^(2/3)/(x^2+x+1)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(x^{2} + x + 1\right)}^{\frac{1}{3}} {\left(-x + 1\right)}^{\frac{1}{3}}}{x^{3} - 1}, x\right)"," ",0,"integral(-(x^2 + x + 1)^(1/3)*(-x + 1)^(1/3)/(x^3 - 1), x)","F",0
2587,0,0,0,0.441480," ","integrate((1-x)^p*(x^2+x+1)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{2} + x + 1\right)}^{p} {\left(-x + 1\right)}^{p}, x\right)"," ",0,"integral((x^2 + x + 1)^p*(-x + 1)^p, x)","F",0
2588,1,523,0,52.781435," ","integrate(1/(-c*e*x+b*e)^(1/3)/(c^2*x^2+b*c*x+b^2)^(1/3),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} e \sqrt{-\frac{1}{e^{\frac{2}{3}}}} \log\left(3 \, c^{3} e x^{3} - b^{3} e - 3 \, {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{2}{3}} {\left(-c e x + b e\right)}^{\frac{2}{3}} c e^{\frac{1}{3}} x + \sqrt{3} {\left(2 \, {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{1}{3}} {\left(-c e x + b e\right)}^{\frac{1}{3}} c^{2} e x^{2} + {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{2}{3}} {\left(-c e x + b e\right)}^{\frac{2}{3}} c e^{\frac{2}{3}} x + {\left(c^{3} e x^{3} - b^{3} e\right)} e^{\frac{1}{3}}\right)} \sqrt{-\frac{1}{e^{\frac{2}{3}}}}\right) - e^{\frac{2}{3}} \log\left(c^{2} e x^{2} - {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{1}{3}} {\left(-c e x + b e\right)}^{\frac{1}{3}} c e^{\frac{2}{3}} x + {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{2}{3}} {\left(-c e x + b e\right)}^{\frac{2}{3}} e^{\frac{1}{3}}\right) + 2 \, e^{\frac{2}{3}} \log\left(c e x + {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{1}{3}} {\left(-c e x + b e\right)}^{\frac{1}{3}} e^{\frac{2}{3}}\right)}{6 \, c e}, -\frac{2 \, \sqrt{3} e^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{2}{3}} {\left(-c e x + b e\right)}^{\frac{2}{3}} c e^{\frac{2}{3}} x + {\left(c^{3} e x^{3} - b^{3} e\right)} e^{\frac{1}{3}}\right)}}{3 \, {\left(c^{3} e x^{3} - b^{3} e\right)} e^{\frac{1}{3}}}\right) + e^{\frac{2}{3}} \log\left(c^{2} e x^{2} - {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{1}{3}} {\left(-c e x + b e\right)}^{\frac{1}{3}} c e^{\frac{2}{3}} x + {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{2}{3}} {\left(-c e x + b e\right)}^{\frac{2}{3}} e^{\frac{1}{3}}\right) - 2 \, e^{\frac{2}{3}} \log\left(c e x + {\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{1}{3}} {\left(-c e x + b e\right)}^{\frac{1}{3}} e^{\frac{2}{3}}\right)}{6 \, c e}\right]"," ",0,"[1/6*(sqrt(3)*e*sqrt(-1/e^(2/3))*log(3*c^3*e*x^3 - b^3*e - 3*(c^2*x^2 + b*c*x + b^2)^(2/3)*(-c*e*x + b*e)^(2/3)*c*e^(1/3)*x + sqrt(3)*(2*(c^2*x^2 + b*c*x + b^2)^(1/3)*(-c*e*x + b*e)^(1/3)*c^2*e*x^2 + (c^2*x^2 + b*c*x + b^2)^(2/3)*(-c*e*x + b*e)^(2/3)*c*e^(2/3)*x + (c^3*e*x^3 - b^3*e)*e^(1/3))*sqrt(-1/e^(2/3))) - e^(2/3)*log(c^2*e*x^2 - (c^2*x^2 + b*c*x + b^2)^(1/3)*(-c*e*x + b*e)^(1/3)*c*e^(2/3)*x + (c^2*x^2 + b*c*x + b^2)^(2/3)*(-c*e*x + b*e)^(2/3)*e^(1/3)) + 2*e^(2/3)*log(c*e*x + (c^2*x^2 + b*c*x + b^2)^(1/3)*(-c*e*x + b*e)^(1/3)*e^(2/3)))/(c*e), -1/6*(2*sqrt(3)*e^(2/3)*arctan(1/3*sqrt(3)*(2*(c^2*x^2 + b*c*x + b^2)^(2/3)*(-c*e*x + b*e)^(2/3)*c*e^(2/3)*x + (c^3*e*x^3 - b^3*e)*e^(1/3))/((c^3*e*x^3 - b^3*e)*e^(1/3))) + e^(2/3)*log(c^2*e*x^2 - (c^2*x^2 + b*c*x + b^2)^(1/3)*(-c*e*x + b*e)^(1/3)*c*e^(2/3)*x + (c^2*x^2 + b*c*x + b^2)^(2/3)*(-c*e*x + b*e)^(2/3)*e^(1/3)) - 2*e^(2/3)*log(c*e*x + (c^2*x^2 + b*c*x + b^2)^(1/3)*(-c*e*x + b*e)^(1/3)*e^(2/3)))/(c*e)]","A",0
2589,0,0,0,0.421043," ","integrate(1/(-c*e*x+b*e)^(2/3)/(c^2*x^2+b*c*x+b^2)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} x^{2} + b c x + b^{2}\right)}^{\frac{1}{3}} {\left(-c e x + b e\right)}^{\frac{1}{3}}}{c^{3} e x^{3} - b^{3} e}, x\right)"," ",0,"integral(-(c^2*x^2 + b*c*x + b^2)^(1/3)*(-c*e*x + b*e)^(1/3)/(c^3*e*x^3 - b^3*e), x)","F",0
2590,0,0,0,0.444827," ","integrate((-c*e*x+b*e)^p*(c^2*x^2+b*c*x+b^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{2} x^{2} + b c x + b^{2}\right)}^{p} {\left(-c e x + b e\right)}^{p}, x\right)"," ",0,"integral((c^2*x^2 + b*c*x + b^2)^p*(-c*e*x + b*e)^p, x)","F",0
