1,1,282,0,1.494165," ","integrate((e*x^3+d)/(c*x^6+a),x, algorithm=""maxima"")","-\frac{e \log\left(c^{\frac{1}{3}} x^{2} + a^{\frac{1}{3}}\right)}{6 \, a^{\frac{1}{3}} c^{\frac{2}{3}}} + \frac{d \arctan\left(\frac{c^{\frac{1}{3}} x}{\sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}}\right)}{3 \, a^{\frac{2}{3}} \sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}} + \frac{{\left(\sqrt{3} a^{\frac{1}{6}} \sqrt{c} d + a^{\frac{2}{3}} e\right)} \log\left(c^{\frac{1}{3}} x^{2} + \sqrt{3} a^{\frac{1}{6}} c^{\frac{1}{6}} x + a^{\frac{1}{3}}\right)}{12 \, a c^{\frac{2}{3}}} - \frac{{\left(\sqrt{3} a^{\frac{1}{6}} \sqrt{c} d - a^{\frac{2}{3}} e\right)} \log\left(c^{\frac{1}{3}} x^{2} - \sqrt{3} a^{\frac{1}{6}} c^{\frac{1}{6}} x + a^{\frac{1}{3}}\right)}{12 \, a c^{\frac{2}{3}}} - \frac{{\left(\sqrt{3} a^{\frac{5}{6}} c^{\frac{1}{6}} e - a^{\frac{1}{3}} c^{\frac{2}{3}} d\right)} \arctan\left(\frac{2 \, c^{\frac{1}{3}} x + \sqrt{3} a^{\frac{1}{6}} c^{\frac{1}{6}}}{\sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}}\right)}{6 \, a c^{\frac{2}{3}} \sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}} + \frac{{\left(\sqrt{3} a^{\frac{5}{6}} c^{\frac{1}{6}} e + a^{\frac{1}{3}} c^{\frac{2}{3}} d\right)} \arctan\left(\frac{2 \, c^{\frac{1}{3}} x - \sqrt{3} a^{\frac{1}{6}} c^{\frac{1}{6}}}{\sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}}\right)}{6 \, a c^{\frac{2}{3}} \sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}}"," ",0,"-1/6*e*log(c^(1/3)*x^2 + a^(1/3))/(a^(1/3)*c^(2/3)) + 1/3*d*arctan(c^(1/3)*x/sqrt(a^(1/3)*c^(1/3)))/(a^(2/3)*sqrt(a^(1/3)*c^(1/3))) + 1/12*(sqrt(3)*a^(1/6)*sqrt(c)*d + a^(2/3)*e)*log(c^(1/3)*x^2 + sqrt(3)*a^(1/6)*c^(1/6)*x + a^(1/3))/(a*c^(2/3)) - 1/12*(sqrt(3)*a^(1/6)*sqrt(c)*d - a^(2/3)*e)*log(c^(1/3)*x^2 - sqrt(3)*a^(1/6)*c^(1/6)*x + a^(1/3))/(a*c^(2/3)) - 1/6*(sqrt(3)*a^(5/6)*c^(1/6)*e - a^(1/3)*c^(2/3)*d)*arctan((2*c^(1/3)*x + sqrt(3)*a^(1/6)*c^(1/6))/sqrt(a^(1/3)*c^(1/3)))/(a*c^(2/3)*sqrt(a^(1/3)*c^(1/3))) + 1/6*(sqrt(3)*a^(5/6)*c^(1/6)*e + a^(1/3)*c^(2/3)*d)*arctan((2*c^(1/3)*x - sqrt(3)*a^(1/6)*c^(1/6))/sqrt(a^(1/3)*c^(1/3)))/(a*c^(2/3)*sqrt(a^(1/3)*c^(1/3)))","A",0
2,1,313,0,1.341311," ","integrate((e*x^3+d)/(-c*x^6+a),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left(\sqrt{c} d + \sqrt{a} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{1}{3}}}\right)}{6 \, \sqrt{a} c \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{2}{3}}} + \frac{\sqrt{3} {\left(\sqrt{c} d - \sqrt{a} e\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{1}{3}}}\right)}{6 \, \sqrt{a} c \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{2}{3}}} + \frac{{\left(\sqrt{c} d + \sqrt{a} e\right)} \log\left(x^{2} + x \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{1}{3}} + \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{2}{3}}\right)}{12 \, \sqrt{a} c \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{2}{3}}} - \frac{{\left(\sqrt{c} d - \sqrt{a} e\right)} \log\left(x^{2} - x \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{1}{3}} + \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{2}{3}}\right)}{12 \, \sqrt{a} c \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{2}{3}}} + \frac{{\left(\sqrt{c} d - \sqrt{a} e\right)} \log\left(x + \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{1}{3}}\right)}{6 \, \sqrt{a} c \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{2}{3}}} - \frac{{\left(\sqrt{c} d + \sqrt{a} e\right)} \log\left(x - \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{1}{3}}\right)}{6 \, \sqrt{a} c \left(\frac{\sqrt{a}}{\sqrt{c}}\right)^{\frac{2}{3}}}"," ",0,"1/6*sqrt(3)*(sqrt(c)*d + sqrt(a)*e)*arctan(1/3*sqrt(3)*(2*x + (sqrt(a)/sqrt(c))^(1/3))/(sqrt(a)/sqrt(c))^(1/3))/(sqrt(a)*c*(sqrt(a)/sqrt(c))^(2/3)) + 1/6*sqrt(3)*(sqrt(c)*d - sqrt(a)*e)*arctan(1/3*sqrt(3)*(2*x - (sqrt(a)/sqrt(c))^(1/3))/(sqrt(a)/sqrt(c))^(1/3))/(sqrt(a)*c*(sqrt(a)/sqrt(c))^(2/3)) + 1/12*(sqrt(c)*d + sqrt(a)*e)*log(x^2 + x*(sqrt(a)/sqrt(c))^(1/3) + (sqrt(a)/sqrt(c))^(2/3))/(sqrt(a)*c*(sqrt(a)/sqrt(c))^(2/3)) - 1/12*(sqrt(c)*d - sqrt(a)*e)*log(x^2 - x*(sqrt(a)/sqrt(c))^(1/3) + (sqrt(a)/sqrt(c))^(2/3))/(sqrt(a)*c*(sqrt(a)/sqrt(c))^(2/3)) + 1/6*(sqrt(c)*d - sqrt(a)*e)*log(x + (sqrt(a)/sqrt(c))^(1/3))/(sqrt(a)*c*(sqrt(a)/sqrt(c))^(2/3)) - 1/6*(sqrt(c)*d + sqrt(a)*e)*log(x - (sqrt(a)/sqrt(c))^(1/3))/(sqrt(a)*c*(sqrt(a)/sqrt(c))^(2/3))","A",0
3,0,0,0,0.000000," ","integrate((e*x^4+d)/(c*x^8+a),x, algorithm=""maxima"")","\int \frac{e x^{4} + d}{c x^{8} + a}\,{d x}"," ",0,"integrate((e*x^4 + d)/(c*x^8 + a), x)","F",0
4,0,0,0,0.000000," ","integrate((e*x^4+d)/(-c*x^8+a),x, algorithm=""maxima"")","-\int \frac{e x^{4} + d}{c x^{8} - a}\,{d x}"," ",0,"-integrate((e*x^4 + d)/(c*x^8 - a), x)","F",0
5,0,0,0,0.000000," ","integrate((e*x^4+d)/(e^2*x^8+b*x^4+d^2),x, algorithm=""maxima"")","\int \frac{e x^{4} + d}{e^{2} x^{8} + b x^{4} + d^{2}}\,{d x}"," ",0,"integrate((e*x^4 + d)/(e^2*x^8 + b*x^4 + d^2), x)","F",0
6,0,0,0,0.000000," ","integrate((e*x^4+d)/(e^2*x^8+f*x^4+d^2),x, algorithm=""maxima"")","\int \frac{e x^{4} + d}{e^{2} x^{8} + f x^{4} + d^{2}}\,{d x}"," ",0,"integrate((e*x^4 + d)/(e^2*x^8 + f*x^4 + d^2), x)","F",0
7,0,0,0,0.000000," ","integrate((e*x^4+d)/(e^2*x^8-b*x^4+d^2),x, algorithm=""maxima"")","\int \frac{e x^{4} + d}{e^{2} x^{8} - b x^{4} + d^{2}}\,{d x}"," ",0,"integrate((e*x^4 + d)/(e^2*x^8 - b*x^4 + d^2), x)","F",0
8,0,0,0,0.000000," ","integrate((e*x^4+d)/(e^2*x^8-f*x^4+d^2),x, algorithm=""maxima"")","\int \frac{e x^{4} + d}{e^{2} x^{8} - f x^{4} + d^{2}}\,{d x}"," ",0,"integrate((e*x^4 + d)/(e^2*x^8 - f*x^4 + d^2), x)","F",0
9,0,0,0,0.000000," ","integrate((x^4+1)/(x^8+b*x^4+1),x, algorithm=""maxima"")","\int \frac{x^{4} + 1}{x^{8} + b x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 + 1)/(x^8 + b*x^4 + 1), x)","F",0
10,0,0,0,0.000000," ","integrate((x^4+1)/(x^8+3*x^4+1),x, algorithm=""maxima"")","\int \frac{x^{4} + 1}{x^{8} + 3 \, x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 + 1)/(x^8 + 3*x^4 + 1), x)","F",0
11,1,72,0,1.586752," ","integrate((x^4+1)/(x^8+2*x^4+1),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{8} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{8} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right)"," ",0,"1/4*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/4*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/8*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/8*sqrt(2)*log(x^2 - sqrt(2)*x + 1)","A",0
12,0,0,0,0.000000," ","integrate((x^4+1)/(x^8+x^4+1),x, algorithm=""maxima"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{2} \, \int \frac{1}{x^{4} - x^{2} + 1}\,{d x} + \frac{1}{8} \, \log\left(x^{2} + x + 1\right) - \frac{1}{8} \, \log\left(x^{2} - x + 1\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/2*integrate(1/(x^4 - x^2 + 1), x) + 1/8*log(x^2 + x + 1) - 1/8*log(x^2 - x + 1)","F",0
13,0,0,0,0.000000," ","integrate((x^4+1)/(x^8+1),x, algorithm=""maxima"")","\int \frac{x^{4} + 1}{x^{8} + 1}\,{d x}"," ",0,"integrate((x^4 + 1)/(x^8 + 1), x)","F",0
14,0,0,0,0.000000," ","integrate((x^4+1)/(x^8-x^4+1),x, algorithm=""maxima"")","\int \frac{x^{4} + 1}{x^{8} - x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 + 1)/(x^8 - x^4 + 1), x)","F",0
15,1,27,0,1.326032," ","integrate((x^4+1)/(x^8-2*x^4+1),x, algorithm=""maxima"")","-\frac{x}{2 \, {\left(x^{4} - 1\right)}} + \frac{1}{4} \, \arctan\left(x\right) + \frac{1}{8} \, \log\left(x + 1\right) - \frac{1}{8} \, \log\left(x - 1\right)"," ",0,"-1/2*x/(x^4 - 1) + 1/4*arctan(x) + 1/8*log(x + 1) - 1/8*log(x - 1)","A",0
16,0,0,0,0.000000," ","integrate((x^4+1)/(x^8-3*x^4+1),x, algorithm=""maxima"")","\int \frac{x^{4} + 1}{x^{8} - 3 \, x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 + 1)/(x^8 - 3*x^4 + 1), x)","F",0
17,0,0,0,0.000000," ","integrate((x^4+1)/(x^8-4*x^4+1),x, algorithm=""maxima"")","\int \frac{x^{4} + 1}{x^{8} - 4 \, x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 + 1)/(x^8 - 4*x^4 + 1), x)","F",0
18,0,0,0,0.000000," ","integrate((x^4+1)/(x^8-5*x^4+1),x, algorithm=""maxima"")","\int \frac{x^{4} + 1}{x^{8} - 5 \, x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 + 1)/(x^8 - 5*x^4 + 1), x)","F",0
19,0,0,0,0.000000," ","integrate((x^4+1)/(x^8-6*x^4+1),x, algorithm=""maxima"")","\int \frac{x^{4} + 1}{x^{8} - 6 \, x^{4} + 1}\,{d x}"," ",0,"integrate((x^4 + 1)/(x^8 - 6*x^4 + 1), x)","F",0
20,0,0,0,0.000000," ","integrate((-x^4+1)/(x^8+b*x^4+1),x, algorithm=""maxima"")","-\int \frac{x^{4} - 1}{x^{8} + b x^{4} + 1}\,{d x}"," ",0,"-integrate((x^4 - 1)/(x^8 + b*x^4 + 1), x)","F",0
21,0,0,0,0.000000," ","integrate((-x^4+1)/(x^8+3*x^4+1),x, algorithm=""maxima"")","-\int \frac{x^{4} - 1}{x^{8} + 3 \, x^{4} + 1}\,{d x}"," ",0,"-integrate((x^4 - 1)/(x^8 + 3*x^4 + 1), x)","F",0
22,1,82,0,1.556654," ","integrate((-x^4+1)/(x^8+2*x^4+1),x, algorithm=""maxima"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \sqrt{2}\right)}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \sqrt{2}\right)}\right) + \frac{1}{16} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{16} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right) + \frac{x}{2 \, {\left(x^{4} + 1\right)}}"," ",0,"1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2))) + 1/8*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2))) + 1/16*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/16*sqrt(2)*log(x^2 - sqrt(2)*x + 1) + 1/2*x/(x^4 + 1)","A",0
23,0,0,0,0.000000," ","integrate((-x^4+1)/(x^8+x^4+1),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - \frac{1}{2} \, \int \frac{2 \, x^{2} - 1}{x^{4} - x^{2} + 1}\,{d x} - \frac{1}{8} \, \log\left(x^{2} + x + 1\right) + \frac{1}{8} \, \log\left(x^{2} - x + 1\right)"," ",0,"1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) - 1/2*integrate((2*x^2 - 1)/(x^4 - x^2 + 1), x) - 1/8*log(x^2 + x + 1) + 1/8*log(x^2 - x + 1)","F",0
24,0,0,0,0.000000," ","integrate((-x^4+1)/(x^8+1),x, algorithm=""maxima"")","-\int \frac{x^{4} - 1}{x^{8} + 1}\,{d x}"," ",0,"-integrate((x^4 - 1)/(x^8 + 1), x)","F",0
25,0,0,0,0.000000," ","integrate((-x^4+1)/(x^8-x^4+1),x, algorithm=""maxima"")","-\int \frac{x^{4} - 1}{x^{8} - x^{4} + 1}\,{d x}"," ",0,"-integrate((x^4 - 1)/(x^8 - x^4 + 1), x)","F",0
26,1,17,0,1.595879," ","integrate((-x^4+1)/(x^8-2*x^4+1),x, algorithm=""maxima"")","\frac{1}{2} \, \arctan\left(x\right) + \frac{1}{4} \, \log\left(x + 1\right) - \frac{1}{4} \, \log\left(x - 1\right)"," ",0,"1/2*arctan(x) + 1/4*log(x + 1) - 1/4*log(x - 1)","A",0
27,0,0,0,0.000000," ","integrate((-x^4+1)/(x^8-3*x^4+1),x, algorithm=""maxima"")","-\int \frac{x^{4} - 1}{x^{8} - 3 \, x^{4} + 1}\,{d x}"," ",0,"-integrate((x^4 - 1)/(x^8 - 3*x^4 + 1), x)","F",0
28,0,0,0,0.000000," ","integrate((-x^4+1)/(x^8-4*x^4+1),x, algorithm=""maxima"")","-\int \frac{x^{4} - 1}{x^{8} - 4 \, x^{4} + 1}\,{d x}"," ",0,"-integrate((x^4 - 1)/(x^8 - 4*x^4 + 1), x)","F",0
29,0,0,0,0.000000," ","integrate((-x^4+1)/(x^8-5*x^4+1),x, algorithm=""maxima"")","-\int \frac{x^{4} - 1}{x^{8} - 5 \, x^{4} + 1}\,{d x}"," ",0,"-integrate((x^4 - 1)/(x^8 - 5*x^4 + 1), x)","F",0
30,0,0,0,0.000000," ","integrate((-x^4+1)/(x^8-6*x^4+1),x, algorithm=""maxima"")","-\int \frac{x^{4} - 1}{x^{8} - 6 \, x^{4} + 1}\,{d x}"," ",0,"-integrate((x^4 - 1)/(x^8 - 6*x^4 + 1), x)","F",0
31,0,0,0,0.000000," ","integrate((-1+2*x^4+3^(1/2))/(x^8-x^4+1),x, algorithm=""maxima"")","\int \frac{2 \, x^{4} + \sqrt{3} - 1}{x^{8} - x^{4} + 1}\,{d x}"," ",0,"integrate((2*x^4 + sqrt(3) - 1)/(x^8 - x^4 + 1), x)","F",0
32,0,0,0,0.000000," ","integrate((1+x^4*(1+3^(1/2)))/(x^8-x^4+1),x, algorithm=""maxima"")","\int \frac{x^{4} {\left(\sqrt{3} + 1\right)} + 1}{x^{8} - x^{4} + 1}\,{d x}"," ",0,"integrate((x^4*(sqrt(3) + 1) + 1)/(x^8 - x^4 + 1), x)","F",0
33,0,0,0,0.000000," ","integrate((3+x^4*(-3+3^(1/2))-2*3^(1/2))/(x^8-x^4+1),x, algorithm=""maxima"")","\int \frac{x^{4} {\left(\sqrt{3} - 3\right)} - 2 \, \sqrt{3} + 3}{x^{8} - x^{4} + 1}\,{d x}"," ",0,"integrate((x^4*(sqrt(3) - 3) - 2*sqrt(3) + 3)/(x^8 - x^4 + 1), x)","F",0
34,1,42,0,1.618566," ","integrate((d+e/x)/(c+a/x^2),x, algorithm=""maxima"")","-\frac{a d \arctan\left(\frac{c x}{\sqrt{a c}}\right)}{\sqrt{a c} c} + \frac{d x}{c} + \frac{e \log\left(c x^{2} + a\right)}{2 \, c}"," ",0,"-a*d*arctan(c*x/sqrt(a*c))/(sqrt(a*c)*c) + d*x/c + 1/2*e*log(c*x^2 + a)/c","A",0
35,-2,0,0,0.000000," ","integrate((d+e/x)/(c+a/x^2+b/x),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
36,1,240,0,1.297706," ","integrate((d+e/x^2)/(c+a/x^4),x, algorithm=""maxima"")","\frac{d x}{c} - \frac{\frac{2 \, \sqrt{2} {\left(a \sqrt{c} d - \sqrt{a} c e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{c} x + \sqrt{2} a^{\frac{1}{4}} c^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{c}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{c}} \sqrt{c}} + \frac{2 \, \sqrt{2} {\left(a \sqrt{c} d - \sqrt{a} c e\right)} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{c} x - \sqrt{2} a^{\frac{1}{4}} c^{\frac{1}{4}}\right)}}{2 \, \sqrt{\sqrt{a} \sqrt{c}}}\right)}{\sqrt{a} \sqrt{\sqrt{a} \sqrt{c}} \sqrt{c}} + \frac{\sqrt{2} {\left(a \sqrt{c} d + \sqrt{a} c e\right)} \log\left(\sqrt{c} x^{2} + \sqrt{2} a^{\frac{1}{4}} c^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} c^{\frac{3}{4}}} - \frac{\sqrt{2} {\left(a \sqrt{c} d + \sqrt{a} c e\right)} \log\left(\sqrt{c} x^{2} - \sqrt{2} a^{\frac{1}{4}} c^{\frac{1}{4}} x + \sqrt{a}\right)}{a^{\frac{3}{4}} c^{\frac{3}{4}}}}{8 \, c}"," ",0,"d*x/c - 1/8*(2*sqrt(2)*(a*sqrt(c)*d - sqrt(a)*c*e)*arctan(1/2*sqrt(2)*(2*sqrt(c)*x + sqrt(2)*a^(1/4)*c^(1/4))/sqrt(sqrt(a)*sqrt(c)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(c))*sqrt(c)) + 2*sqrt(2)*(a*sqrt(c)*d - sqrt(a)*c*e)*arctan(1/2*sqrt(2)*(2*sqrt(c)*x - sqrt(2)*a^(1/4)*c^(1/4))/sqrt(sqrt(a)*sqrt(c)))/(sqrt(a)*sqrt(sqrt(a)*sqrt(c))*sqrt(c)) + sqrt(2)*(a*sqrt(c)*d + sqrt(a)*c*e)*log(sqrt(c)*x^2 + sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(a))/(a^(3/4)*c^(3/4)) - sqrt(2)*(a*sqrt(c)*d + sqrt(a)*c*e)*log(sqrt(c)*x^2 - sqrt(2)*a^(1/4)*c^(1/4)*x + sqrt(a))/(a^(3/4)*c^(3/4)))/c","A",0
37,0,0,0,0.000000," ","integrate((d+e/x^2)/(c+a/x^4+b/x^2),x, algorithm=""maxima"")","\frac{d x}{c} + \frac{-\int \frac{{\left(b d - c e\right)} x^{2} + a d}{c x^{4} + b x^{2} + a}\,{d x}}{c}"," ",0,"d*x/c + integrate(-((b*d - c*e)*x^2 + a*d)/(c*x^4 + b*x^2 + a), x)/c","F",0
38,1,295,0,1.525116," ","integrate((d+e/x^3)/(c+a/x^6),x, algorithm=""maxima"")","\frac{d x}{c} - \frac{\frac{2 \, c^{\frac{1}{3}} e \log\left(c^{\frac{1}{3}} x^{2} + a^{\frac{1}{3}}\right)}{a^{\frac{1}{3}}} + \frac{4 \, a^{\frac{1}{3}} d \arctan\left(\frac{c^{\frac{1}{3}} x}{\sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}}\right)}{\sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}} + \frac{{\left(\sqrt{3} a^{\frac{7}{6}} \sqrt{c} d - a^{\frac{2}{3}} c e\right)} \log\left(c^{\frac{1}{3}} x^{2} + \sqrt{3} a^{\frac{1}{6}} c^{\frac{1}{6}} x + a^{\frac{1}{3}}\right)}{a c^{\frac{2}{3}}} - \frac{{\left(\sqrt{3} a^{\frac{7}{6}} \sqrt{c} d + a^{\frac{2}{3}} c e\right)} \log\left(c^{\frac{1}{3}} x^{2} - \sqrt{3} a^{\frac{1}{6}} c^{\frac{1}{6}} x + a^{\frac{1}{3}}\right)}{a c^{\frac{2}{3}}} + \frac{2 \, {\left(\sqrt{3} a^{\frac{5}{6}} c^{\frac{7}{6}} e + a^{\frac{4}{3}} c^{\frac{2}{3}} d\right)} \arctan\left(\frac{2 \, c^{\frac{1}{3}} x + \sqrt{3} a^{\frac{1}{6}} c^{\frac{1}{6}}}{\sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}}\right)}{a c^{\frac{2}{3}} \sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}} - \frac{2 \, {\left(\sqrt{3} a^{\frac{5}{6}} c^{\frac{7}{6}} e - a^{\frac{4}{3}} c^{\frac{2}{3}} d\right)} \arctan\left(\frac{2 \, c^{\frac{1}{3}} x - \sqrt{3} a^{\frac{1}{6}} c^{\frac{1}{6}}}{\sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}}\right)}{a c^{\frac{2}{3}} \sqrt{a^{\frac{1}{3}} c^{\frac{1}{3}}}}}{12 \, c}"," ",0,"d*x/c - 1/12*(2*c^(1/3)*e*log(c^(1/3)*x^2 + a^(1/3))/a^(1/3) + 4*a^(1/3)*d*arctan(c^(1/3)*x/sqrt(a^(1/3)*c^(1/3)))/sqrt(a^(1/3)*c^(1/3)) + (sqrt(3)*a^(7/6)*sqrt(c)*d - a^(2/3)*c*e)*log(c^(1/3)*x^2 + sqrt(3)*a^(1/6)*c^(1/6)*x + a^(1/3))/(a*c^(2/3)) - (sqrt(3)*a^(7/6)*sqrt(c)*d + a^(2/3)*c*e)*log(c^(1/3)*x^2 - sqrt(3)*a^(1/6)*c^(1/6)*x + a^(1/3))/(a*c^(2/3)) + 2*(sqrt(3)*a^(5/6)*c^(7/6)*e + a^(4/3)*c^(2/3)*d)*arctan((2*c^(1/3)*x + sqrt(3)*a^(1/6)*c^(1/6))/sqrt(a^(1/3)*c^(1/3)))/(a*c^(2/3)*sqrt(a^(1/3)*c^(1/3))) - 2*(sqrt(3)*a^(5/6)*c^(7/6)*e - a^(4/3)*c^(2/3)*d)*arctan((2*c^(1/3)*x - sqrt(3)*a^(1/6)*c^(1/6))/sqrt(a^(1/3)*c^(1/3)))/(a*c^(2/3)*sqrt(a^(1/3)*c^(1/3))))/c","A",0
39,0,0,0,0.000000," ","integrate((d+e/x^3)/(c+a/x^6+b/x^3),x, algorithm=""maxima"")","\frac{d x}{c} + \frac{-\int \frac{{\left(b d - c e\right)} x^{3} + a d}{c x^{6} + b x^{3} + a}\,{d x}}{c}"," ",0,"d*x/c + integrate(-((b*d - c*e)*x^3 + a*d)/(c*x^6 + b*x^3 + a), x)/c","F",0
40,0,0,0,0.000000," ","integrate((d+e/x^4)/(c+a/x^8),x, algorithm=""maxima"")","\frac{d x}{c} + \frac{-\frac{{\left(c \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + a d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x + \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} - \frac{{\left(c \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + a d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x - \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} + \frac{{\left(c \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - a d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x + \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} + \frac{{\left(c \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - a d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \arctan\left(\frac{2 \, x - \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}{\sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}}\right)}{8 \, a} - \frac{{\left(c \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + a d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a} + \frac{{\left(c \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e + a d \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a} + \frac{{\left(c \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - a d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a} - \frac{{\left(c \sqrt{\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{5}{8}} e - a d \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}}\right)} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} \left(\frac{a}{c}\right)^{\frac{1}{8}} + \left(\frac{a}{c}\right)^{\frac{1}{4}}\right)}{16 \, a}}{c}"," ",0,"d*x/c + integrate((c*e*x^4 - a*d)/(c*x^8 + a), x)/c","F",0
41,0,0,0,0.000000," ","integrate((d+e/x^4)/(c+a/x^8+b/x^4),x, algorithm=""maxima"")","\frac{d x}{c} + \frac{-\int \frac{{\left(b d - c e\right)} x^{4} + a d}{c x^{8} + b x^{4} + a}\,{d x}}{c}"," ",0,"d*x/c + integrate(-((b*d - c*e)*x^4 + a*d)/(c*x^8 + b*x^4 + a), x)/c","F",0
42,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+c*x^(2*n)),x, algorithm=""maxima"")","\frac{3 \, d e^{2} {\left(n + 1\right)} x + e^{3} x x^{n}}{c {\left(n + 1\right)}} - \int -\frac{c d^{3} - 3 \, a d e^{2} + {\left(3 \, c d^{2} e - a e^{3}\right)} x^{n}}{c^{2} x^{2 \, n} + a c}\,{d x}"," ",0,"(3*d*e^2*(n + 1)*x + e^3*x*x^n)/(c*(n + 1)) - integrate(-(c*d^3 - 3*a*d*e^2 + (3*c*d^2*e - a*e^3)*x^n)/(c^2*x^(2*n) + a*c), x)","F",0
43,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+c*x^(2*n)),x, algorithm=""maxima"")","\frac{e^{2} x}{c} + \int \frac{2 \, c d e x^{n} + c d^{2} - a e^{2}}{c^{2} x^{2 \, n} + a c}\,{d x}"," ",0,"e^2*x/c + integrate((2*c*d*e*x^n + c*d^2 - a*e^2)/(c^2*x^(2*n) + a*c), x)","F",0
44,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+c*x^(2*n)),x, algorithm=""maxima"")","\int \frac{e x^{n} + d}{c x^{2 \, n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + a), x)","F",0
45,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(c x^{2 \, n} + a\right)} {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + a)*(e*x^n + d)), x)","F",0
46,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+c*x^(2*n)),x, algorithm=""maxima"")","\frac{e^{2} x}{c d^{4} n + a d^{2} e^{2} n + {\left(c d^{3} e n + a d e^{3} n\right)} x^{n}} + {\left(c d^{2} e^{2} {\left(3 \, n - 1\right)} + a e^{4} {\left(n - 1\right)}\right)} \int \frac{1}{c^{2} d^{6} n + 2 \, a c d^{4} e^{2} n + a^{2} d^{2} e^{4} n + {\left(c^{2} d^{5} e n + 2 \, a c d^{3} e^{3} n + a^{2} d e^{5} n\right)} x^{n}}\,{d x} - \int \frac{2 \, c^{2} d e x^{n} - c^{2} d^{2} + a c e^{2}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4} + {\left(c^{3} d^{4} + 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} x^{2 \, n}}\,{d x}"," ",0,"e^2*x/(c*d^4*n + a*d^2*e^2*n + (c*d^3*e*n + a*d*e^3*n)*x^n) + (c*d^2*e^2*(3*n - 1) + a*e^4*(n - 1))*integrate(1/(c^2*d^6*n + 2*a*c*d^4*e^2*n + a^2*d^2*e^4*n + (c^2*d^5*e*n + 2*a*c*d^3*e^3*n + a^2*d*e^5*n)*x^n), x) - integrate((2*c^2*d*e*x^n - c^2*d^2 + a*c*e^2)/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4 + (c^3*d^4 + 2*a*c^2*d^2*e^2 + a^2*c*e^4)*x^(2*n)), x)","F",0
47,0,0,0,0.000000," ","integrate((d+e*x^n)/(a-c*x^(2*n)),x, algorithm=""maxima"")","-\int \frac{e x^{n} + d}{c x^{2 \, n} - a}\,{d x}"," ",0,"-integrate((e*x^n + d)/(c*x^(2*n) - a), x)","F",0
48,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+c*x^(2*n))^2,x, algorithm=""maxima"")","\frac{{\left(3 \, c d^{2} e - a e^{3}\right)} x x^{n} + {\left(c d^{3} - 3 \, a d e^{2}\right)} x}{2 \, {\left(a c^{2} n x^{2 \, n} + a^{2} c n\right)}} + \int \frac{c d^{3} {\left(2 \, n - 1\right)} + 3 \, a d e^{2} + {\left(a e^{3} {\left(n + 1\right)} + 3 \, c d^{2} e {\left(n - 1\right)}\right)} x^{n}}{2 \, {\left(a c^{2} n x^{2 \, n} + a^{2} c n\right)}}\,{d x}"," ",0,"1/2*((3*c*d^2*e - a*e^3)*x*x^n + (c*d^3 - 3*a*d*e^2)*x)/(a*c^2*n*x^(2*n) + a^2*c*n) + integrate(1/2*(c*d^3*(2*n - 1) + 3*a*d*e^2 + (a*e^3*(n + 1) + 3*c*d^2*e*(n - 1))*x^n)/(a*c^2*n*x^(2*n) + a^2*c*n), x)","F",0
49,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+c*x^(2*n))^2,x, algorithm=""maxima"")","\frac{2 \, c d e x x^{n} + {\left(c d^{2} - a e^{2}\right)} x}{2 \, {\left(a c^{2} n x^{2 \, n} + a^{2} c n\right)}} + \int \frac{2 \, c d e {\left(n - 1\right)} x^{n} + c d^{2} {\left(2 \, n - 1\right)} + a e^{2}}{2 \, {\left(a c^{2} n x^{2 \, n} + a^{2} c n\right)}}\,{d x}"," ",0,"1/2*(2*c*d*e*x*x^n + (c*d^2 - a*e^2)*x)/(a*c^2*n*x^(2*n) + a^2*c*n) + integrate(1/2*(2*c*d*e*(n - 1)*x^n + c*d^2*(2*n - 1) + a*e^2)/(a*c^2*n*x^(2*n) + a^2*c*n), x)","F",0
50,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+c*x^(2*n))^2,x, algorithm=""maxima"")","\frac{e x x^{n} + d x}{2 \, {\left(a c n x^{2 \, n} + a^{2} n\right)}} + \int \frac{e {\left(n - 1\right)} x^{n} + d {\left(2 \, n - 1\right)}}{2 \, {\left(a c n x^{2 \, n} + a^{2} n\right)}}\,{d x}"," ",0,"1/2*(e*x*x^n + d*x)/(a*c*n*x^(2*n) + a^2*n) + integrate(1/2*(e*(n - 1)*x^n + d*(2*n - 1))/(a*c*n*x^(2*n) + a^2*n), x)","F",0
51,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n))^2,x, algorithm=""maxima"")","e^{4} \int \frac{1}{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^{n}}\,{d x} - \frac{c e x x^{n} - c d x}{2 \, {\left(a^{2} c d^{2} n + a^{3} e^{2} n + {\left(a c^{2} d^{2} n + a^{2} c e^{2} n\right)} x^{2 \, n}\right)}} - \int -\frac{a c d e^{2} {\left(4 \, n - 1\right)} + c^{2} d^{3} {\left(2 \, n - 1\right)} - {\left(a c e^{3} {\left(3 \, n - 1\right)} + c^{2} d^{2} e {\left(n - 1\right)}\right)} x^{n}}{2 \, {\left(a^{2} c^{2} d^{4} n + 2 \, a^{3} c d^{2} e^{2} n + a^{4} e^{4} n + {\left(a c^{3} d^{4} n + 2 \, a^{2} c^{2} d^{2} e^{2} n + a^{3} c e^{4} n\right)} x^{2 \, n}\right)}}\,{d x}"," ",0,"e^4*integrate(1/(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^n), x) - 1/2*(c*e*x*x^n - c*d*x)/(a^2*c*d^2*n + a^3*e^2*n + (a*c^2*d^2*n + a^2*c*e^2*n)*x^(2*n)) - integrate(-1/2*(a*c*d*e^2*(4*n - 1) + c^2*d^3*(2*n - 1) - (a*c*e^3*(3*n - 1) + c^2*d^2*e*(n - 1))*x^n)/(a^2*c^2*d^4*n + 2*a^3*c*d^2*e^2*n + a^4*e^4*n + (a*c^3*d^4*n + 2*a^2*c^2*d^2*e^2*n + a^3*c*e^4*n)*x^(2*n)), x)","F",0
52,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+c*x^(2*n))^2,x, algorithm=""maxima"")","{\left(c d^{2} e^{4} {\left(5 \, n - 1\right)} + a e^{6} {\left(n - 1\right)}\right)} \int \frac{1}{c^{3} d^{8} n + 3 \, a c^{2} d^{6} e^{2} n + 3 \, a^{2} c d^{4} e^{4} n + a^{3} d^{2} e^{6} n + {\left(c^{3} d^{7} e n + 3 \, a c^{2} d^{5} e^{3} n + 3 \, a^{2} c d^{3} e^{5} n + a^{3} d e^{7} n\right)} x^{n}}\,{d x} - \frac{2 \, {\left(c^{2} d^{2} e^{2} - a c e^{4}\right)} x x^{2 \, n} + {\left(c^{2} d^{3} e + a c d e^{3}\right)} x x^{n} - {\left(c^{2} d^{4} - a c d^{2} e^{2} + 2 \, a^{2} e^{4}\right)} x}{2 \, {\left(a^{2} c^{2} d^{6} n + 2 \, a^{3} c d^{4} e^{2} n + a^{4} d^{2} e^{4} n + {\left(a c^{3} d^{5} e n + 2 \, a^{2} c^{2} d^{3} e^{3} n + a^{3} c d e^{5} n\right)} x^{3 \, n} + {\left(a c^{3} d^{6} n + 2 \, a^{2} c^{2} d^{4} e^{2} n + a^{3} c d^{2} e^{4} n\right)} x^{2 \, n} + {\left(a^{2} c^{2} d^{5} e n + 2 \, a^{3} c d^{3} e^{3} n + a^{4} d e^{5} n\right)} x^{n}\right)}} - \int \frac{a^{2} c e^{4} {\left(4 \, n - 1\right)} - c^{3} d^{4} {\left(2 \, n - 1\right)} - 6 \, a c^{2} d^{2} e^{2} n + 2 \, {\left(a c^{2} d e^{3} {\left(5 \, n - 1\right)} + c^{3} d^{3} e {\left(n - 1\right)}\right)} x^{n}}{2 \, {\left(a^{2} c^{3} d^{6} n + 3 \, a^{3} c^{2} d^{4} e^{2} n + 3 \, a^{4} c d^{2} e^{4} n + a^{5} e^{6} n + {\left(a c^{4} d^{6} n + 3 \, a^{2} c^{3} d^{4} e^{2} n + 3 \, a^{3} c^{2} d^{2} e^{4} n + a^{4} c e^{6} n\right)} x^{2 \, n}\right)}}\,{d x}"," ",0,"(c*d^2*e^4*(5*n - 1) + a*e^6*(n - 1))*integrate(1/(c^3*d^8*n + 3*a*c^2*d^6*e^2*n + 3*a^2*c*d^4*e^4*n + a^3*d^2*e^6*n + (c^3*d^7*e*n + 3*a*c^2*d^5*e^3*n + 3*a^2*c*d^3*e^5*n + a^3*d*e^7*n)*x^n), x) - 1/2*(2*(c^2*d^2*e^2 - a*c*e^4)*x*x^(2*n) + (c^2*d^3*e + a*c*d*e^3)*x*x^n - (c^2*d^4 - a*c*d^2*e^2 + 2*a^2*e^4)*x)/(a^2*c^2*d^6*n + 2*a^3*c*d^4*e^2*n + a^4*d^2*e^4*n + (a*c^3*d^5*e*n + 2*a^2*c^2*d^3*e^3*n + a^3*c*d*e^5*n)*x^(3*n) + (a*c^3*d^6*n + 2*a^2*c^2*d^4*e^2*n + a^3*c*d^2*e^4*n)*x^(2*n) + (a^2*c^2*d^5*e*n + 2*a^3*c*d^3*e^3*n + a^4*d*e^5*n)*x^n) - integrate(1/2*(a^2*c*e^4*(4*n - 1) - c^3*d^4*(2*n - 1) - 6*a*c^2*d^2*e^2*n + 2*(a*c^2*d*e^3*(5*n - 1) + c^3*d^3*e*(n - 1))*x^n)/(a^2*c^3*d^6*n + 3*a^3*c^2*d^4*e^2*n + 3*a^4*c*d^2*e^4*n + a^5*e^6*n + (a*c^4*d^6*n + 3*a^2*c^3*d^4*e^2*n + 3*a^3*c^2*d^2*e^4*n + a^4*c*e^6*n)*x^(2*n)), x)","F",0
53,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+c*x^(2*n))^3,x, algorithm=""maxima"")","\frac{{\left(3 \, c^{2} d^{2} e {\left(3 \, n - 1\right)} + a c e^{3} {\left(n + 1\right)}\right)} x x^{3 \, n} + {\left(c^{2} d^{3} {\left(4 \, n - 1\right)} + 3 \, a c d e^{2}\right)} x x^{2 \, n} + {\left(3 \, a c d^{2} e {\left(5 \, n - 1\right)} - a^{2} e^{3} {\left(n - 1\right)}\right)} x x^{n} + {\left(a c d^{3} {\left(6 \, n - 1\right)} - 3 \, a^{2} d e^{2} {\left(2 \, n - 1\right)}\right)} x}{8 \, {\left(a^{2} c^{3} n^{2} x^{4 \, n} + 2 \, a^{3} c^{2} n^{2} x^{2 \, n} + a^{4} c n^{2}\right)}} + \int \frac{{\left(8 \, n^{2} - 6 \, n + 1\right)} c d^{3} + 3 \, a d e^{2} {\left(2 \, n - 1\right)} + {\left(3 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} c d^{2} e + {\left(n^{2} - 1\right)} a e^{3}\right)} x^{n}}{8 \, {\left(a^{2} c^{2} n^{2} x^{2 \, n} + a^{3} c n^{2}\right)}}\,{d x}"," ",0,"1/8*((3*c^2*d^2*e*(3*n - 1) + a*c*e^3*(n + 1))*x*x^(3*n) + (c^2*d^3*(4*n - 1) + 3*a*c*d*e^2)*x*x^(2*n) + (3*a*c*d^2*e*(5*n - 1) - a^2*e^3*(n - 1))*x*x^n + (a*c*d^3*(6*n - 1) - 3*a^2*d*e^2*(2*n - 1))*x)/(a^2*c^3*n^2*x^(4*n) + 2*a^3*c^2*n^2*x^(2*n) + a^4*c*n^2) + integrate(1/8*((8*n^2 - 6*n + 1)*c*d^3 + 3*a*d*e^2*(2*n - 1) + (3*(3*n^2 - 4*n + 1)*c*d^2*e + (n^2 - 1)*a*e^3)*x^n)/(a^2*c^2*n^2*x^(2*n) + a^3*c*n^2), x)","F",0
54,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+c*x^(2*n))^3,x, algorithm=""maxima"")","\frac{2 \, c^{2} d e {\left(3 \, n - 1\right)} x x^{3 \, n} + 2 \, a c d e {\left(5 \, n - 1\right)} x x^{n} + {\left(c^{2} d^{2} {\left(4 \, n - 1\right)} + a c e^{2}\right)} x x^{2 \, n} + {\left(a c d^{2} {\left(6 \, n - 1\right)} - a^{2} e^{2} {\left(2 \, n - 1\right)}\right)} x}{8 \, {\left(a^{2} c^{3} n^{2} x^{4 \, n} + 2 \, a^{3} c^{2} n^{2} x^{2 \, n} + a^{4} c n^{2}\right)}} + \int \frac{2 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} c d e x^{n} + {\left(8 \, n^{2} - 6 \, n + 1\right)} c d^{2} + a e^{2} {\left(2 \, n - 1\right)}}{8 \, {\left(a^{2} c^{2} n^{2} x^{2 \, n} + a^{3} c n^{2}\right)}}\,{d x}"," ",0,"1/8*(2*c^2*d*e*(3*n - 1)*x*x^(3*n) + 2*a*c*d*e*(5*n - 1)*x*x^n + (c^2*d^2*(4*n - 1) + a*c*e^2)*x*x^(2*n) + (a*c*d^2*(6*n - 1) - a^2*e^2*(2*n - 1))*x)/(a^2*c^3*n^2*x^(4*n) + 2*a^3*c^2*n^2*x^(2*n) + a^4*c*n^2) + integrate(1/8*(2*(3*n^2 - 4*n + 1)*c*d*e*x^n + (8*n^2 - 6*n + 1)*c*d^2 + a*e^2*(2*n - 1))/(a^2*c^2*n^2*x^(2*n) + a^3*c*n^2), x)","F",0
55,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+c*x^(2*n))^3,x, algorithm=""maxima"")","\frac{c e {\left(3 \, n - 1\right)} x x^{3 \, n} + c d {\left(4 \, n - 1\right)} x x^{2 \, n} + a e {\left(5 \, n - 1\right)} x x^{n} + a d {\left(6 \, n - 1\right)} x}{8 \, {\left(a^{2} c^{2} n^{2} x^{4 \, n} + 2 \, a^{3} c n^{2} x^{2 \, n} + a^{4} n^{2}\right)}} + \int \frac{{\left(3 \, n^{2} - 4 \, n + 1\right)} e x^{n} + {\left(8 \, n^{2} - 6 \, n + 1\right)} d}{8 \, {\left(a^{2} c n^{2} x^{2 \, n} + a^{3} n^{2}\right)}}\,{d x}"," ",0,"1/8*(c*e*(3*n - 1)*x*x^(3*n) + c*d*(4*n - 1)*x*x^(2*n) + a*e*(5*n - 1)*x*x^n + a*d*(6*n - 1)*x)/(a^2*c^2*n^2*x^(4*n) + 2*a^3*c*n^2*x^(2*n) + a^4*n^2) + integrate(1/8*((3*n^2 - 4*n + 1)*e*x^n + (8*n^2 - 6*n + 1)*d)/(a^2*c*n^2*x^(2*n) + a^3*n^2), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n))^3,x, algorithm=""maxima"")","e^{6} \int \frac{1}{c^{3} d^{7} + 3 \, a c^{2} d^{5} e^{2} + 3 \, a^{2} c d^{3} e^{4} + a^{3} d e^{6} + {\left(c^{3} d^{6} e + 3 \, a c^{2} d^{4} e^{3} + 3 \, a^{2} c d^{2} e^{5} + a^{3} e^{7}\right)} x^{n}}\,{d x} - \frac{{\left(a c^{2} e^{3} {\left(7 \, n - 1\right)} + c^{3} d^{2} e {\left(3 \, n - 1\right)}\right)} x x^{3 \, n} - {\left(a c^{2} d e^{2} {\left(8 \, n - 1\right)} + c^{3} d^{3} {\left(4 \, n - 1\right)}\right)} x x^{2 \, n} + {\left(a^{2} c e^{3} {\left(9 \, n - 1\right)} + a c^{2} d^{2} e {\left(5 \, n - 1\right)}\right)} x x^{n} - {\left(a^{2} c d e^{2} {\left(10 \, n - 1\right)} + a c^{2} d^{3} {\left(6 \, n - 1\right)}\right)} x}{8 \, {\left(a^{4} c^{2} d^{4} n^{2} + 2 \, a^{5} c d^{2} e^{2} n^{2} + a^{6} e^{4} n^{2} + {\left(a^{2} c^{4} d^{4} n^{2} + 2 \, a^{3} c^{3} d^{2} e^{2} n^{2} + a^{4} c^{2} e^{4} n^{2}\right)} x^{4 \, n} + 2 \, {\left(a^{3} c^{3} d^{4} n^{2} + 2 \, a^{4} c^{2} d^{2} e^{2} n^{2} + a^{5} c e^{4} n^{2}\right)} x^{2 \, n}\right)}} - \int -\frac{{\left(8 \, n^{2} - 6 \, n + 1\right)} c^{3} d^{5} + 2 \, {\left(12 \, n^{2} - 8 \, n + 1\right)} a c^{2} d^{3} e^{2} + {\left(24 \, n^{2} - 10 \, n + 1\right)} a^{2} c d e^{4} - {\left({\left(3 \, n^{2} - 4 \, n + 1\right)} c^{3} d^{4} e + 2 \, {\left(5 \, n^{2} - 6 \, n + 1\right)} a c^{2} d^{2} e^{3} + {\left(15 \, n^{2} - 8 \, n + 1\right)} a^{2} c e^{5}\right)} x^{n}}{8 \, {\left(a^{3} c^{3} d^{6} n^{2} + 3 \, a^{4} c^{2} d^{4} e^{2} n^{2} + 3 \, a^{5} c d^{2} e^{4} n^{2} + a^{6} e^{6} n^{2} + {\left(a^{2} c^{4} d^{6} n^{2} + 3 \, a^{3} c^{3} d^{4} e^{2} n^{2} + 3 \, a^{4} c^{2} d^{2} e^{4} n^{2} + a^{5} c e^{6} n^{2}\right)} x^{2 \, n}\right)}}\,{d x}"," ",0,"e^6*integrate(1/(c^3*d^7 + 3*a*c^2*d^5*e^2 + 3*a^2*c*d^3*e^4 + a^3*d*e^6 + (c^3*d^6*e + 3*a*c^2*d^4*e^3 + 3*a^2*c*d^2*e^5 + a^3*e^7)*x^n), x) - 1/8*((a*c^2*e^3*(7*n - 1) + c^3*d^2*e*(3*n - 1))*x*x^(3*n) - (a*c^2*d*e^2*(8*n - 1) + c^3*d^3*(4*n - 1))*x*x^(2*n) + (a^2*c*e^3*(9*n - 1) + a*c^2*d^2*e*(5*n - 1))*x*x^n - (a^2*c*d*e^2*(10*n - 1) + a*c^2*d^3*(6*n - 1))*x)/(a^4*c^2*d^4*n^2 + 2*a^5*c*d^2*e^2*n^2 + a^6*e^4*n^2 + (a^2*c^4*d^4*n^2 + 2*a^3*c^3*d^2*e^2*n^2 + a^4*c^2*e^4*n^2)*x^(4*n) + 2*(a^3*c^3*d^4*n^2 + 2*a^4*c^2*d^2*e^2*n^2 + a^5*c*e^4*n^2)*x^(2*n)) - integrate(-1/8*((8*n^2 - 6*n + 1)*c^3*d^5 + 2*(12*n^2 - 8*n + 1)*a*c^2*d^3*e^2 + (24*n^2 - 10*n + 1)*a^2*c*d*e^4 - ((3*n^2 - 4*n + 1)*c^3*d^4*e + 2*(5*n^2 - 6*n + 1)*a*c^2*d^2*e^3 + (15*n^2 - 8*n + 1)*a^2*c*e^5)*x^n)/(a^3*c^3*d^6*n^2 + 3*a^4*c^2*d^4*e^2*n^2 + 3*a^5*c*d^2*e^4*n^2 + a^6*e^6*n^2 + (a^2*c^4*d^6*n^2 + 3*a^3*c^3*d^4*e^2*n^2 + 3*a^4*c^2*d^2*e^4*n^2 + a^5*c*e^6*n^2)*x^(2*n)), x)","F",0
57,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+c*x^(2*n))^3,x, algorithm=""maxima"")","{\left(c d^{2} e^{6} {\left(7 \, n - 1\right)} + a e^{8} {\left(n - 1\right)}\right)} \int \frac{1}{c^{4} d^{10} n + 4 \, a c^{3} d^{8} e^{2} n + 6 \, a^{2} c^{2} d^{6} e^{4} n + 4 \, a^{3} c d^{4} e^{6} n + a^{4} d^{2} e^{8} n + {\left(c^{4} d^{9} e n + 4 \, a c^{3} d^{7} e^{3} n + 6 \, a^{2} c^{2} d^{5} e^{5} n + 4 \, a^{3} c d^{3} e^{7} n + a^{4} d e^{9} n\right)} x^{n}}\,{d x} - \frac{2 \, {\left(a c^{3} d^{2} e^{4} {\left(11 \, n - 1\right)} + c^{4} d^{4} e^{2} {\left(3 \, n - 1\right)} - 4 \, a^{2} c^{2} e^{6} n\right)} x x^{4 \, n} + {\left(a^{2} c^{2} d e^{5} {\left(8 \, n - 1\right)} + 2 \, a c^{3} d^{3} e^{3} {\left(5 \, n - 1\right)} + c^{4} d^{5} e {\left(2 \, n - 1\right)}\right)} x x^{3 \, n} + {\left(a^{2} c^{2} d^{2} e^{4} {\left(34 \, n - 3\right)} - c^{4} d^{6} {\left(4 \, n - 1\right)} - 2 \, a c^{3} d^{4} e^{2} {\left(n + 1\right)} - 16 \, a^{3} c e^{6} n\right)} x x^{2 \, n} + {\left(a^{3} c d e^{5} {\left(10 \, n - 1\right)} + 2 \, a^{2} c^{2} d^{3} e^{3} {\left(7 \, n - 1\right)} + a c^{3} d^{5} e {\left(4 \, n - 1\right)}\right)} x x^{n} + {\left(a^{3} c d^{2} e^{4} {\left(10 \, n - 1\right)} - a c^{3} d^{6} {\left(6 \, n - 1\right)} - 12 \, a^{2} c^{2} d^{4} e^{2} n - 8 \, a^{4} e^{6} n\right)} x}{8 \, {\left(a^{4} c^{3} d^{8} n^{2} + 3 \, a^{5} c^{2} d^{6} e^{2} n^{2} + 3 \, a^{6} c d^{4} e^{4} n^{2} + a^{7} d^{2} e^{6} n^{2} + {\left(a^{2} c^{5} d^{7} e n^{2} + 3 \, a^{3} c^{4} d^{5} e^{3} n^{2} + 3 \, a^{4} c^{3} d^{3} e^{5} n^{2} + a^{5} c^{2} d e^{7} n^{2}\right)} x^{5 \, n} + {\left(a^{2} c^{5} d^{8} n^{2} + 3 \, a^{3} c^{4} d^{6} e^{2} n^{2} + 3 \, a^{4} c^{3} d^{4} e^{4} n^{2} + a^{5} c^{2} d^{2} e^{6} n^{2}\right)} x^{4 \, n} + 2 \, {\left(a^{3} c^{4} d^{7} e n^{2} + 3 \, a^{4} c^{3} d^{5} e^{3} n^{2} + 3 \, a^{5} c^{2} d^{3} e^{5} n^{2} + a^{6} c d e^{7} n^{2}\right)} x^{3 \, n} + 2 \, {\left(a^{3} c^{4} d^{8} n^{2} + 3 \, a^{4} c^{3} d^{6} e^{2} n^{2} + 3 \, a^{5} c^{2} d^{4} e^{4} n^{2} + a^{6} c d^{2} e^{6} n^{2}\right)} x^{2 \, n} + {\left(a^{4} c^{3} d^{7} e n^{2} + 3 \, a^{5} c^{2} d^{5} e^{3} n^{2} + 3 \, a^{6} c d^{3} e^{5} n^{2} + a^{7} d e^{7} n^{2}\right)} x^{n}\right)}} - \int -\frac{{\left(8 \, n^{2} - 6 \, n + 1\right)} c^{4} d^{6} + {\left(32 \, n^{2} - 18 \, n + 1\right)} a c^{3} d^{4} e^{2} + {\left(48 \, n^{2} - 2 \, n - 1\right)} a^{2} c^{2} d^{2} e^{4} - {\left(24 \, n^{2} - 10 \, n + 1\right)} a^{3} c e^{6} - 2 \, {\left({\left(3 \, n^{2} - 4 \, n + 1\right)} c^{4} d^{5} e + 2 \, {\left(7 \, n^{2} - 8 \, n + 1\right)} a c^{3} d^{3} e^{3} + {\left(35 \, n^{2} - 12 \, n + 1\right)} a^{2} c^{2} d e^{5}\right)} x^{n}}{8 \, {\left(a^{3} c^{4} d^{8} n^{2} + 4 \, a^{4} c^{3} d^{6} e^{2} n^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} n^{2} + 4 \, a^{6} c d^{2} e^{6} n^{2} + a^{7} e^{8} n^{2} + {\left(a^{2} c^{5} d^{8} n^{2} + 4 \, a^{3} c^{4} d^{6} e^{2} n^{2} + 6 \, a^{4} c^{3} d^{4} e^{4} n^{2} + 4 \, a^{5} c^{2} d^{2} e^{6} n^{2} + a^{6} c e^{8} n^{2}\right)} x^{2 \, n}\right)}}\,{d x}"," ",0,"(c*d^2*e^6*(7*n - 1) + a*e^8*(n - 1))*integrate(1/(c^4*d^10*n + 4*a*c^3*d^8*e^2*n + 6*a^2*c^2*d^6*e^4*n + 4*a^3*c*d^4*e^6*n + a^4*d^2*e^8*n + (c^4*d^9*e*n + 4*a*c^3*d^7*e^3*n + 6*a^2*c^2*d^5*e^5*n + 4*a^3*c*d^3*e^7*n + a^4*d*e^9*n)*x^n), x) - 1/8*(2*(a*c^3*d^2*e^4*(11*n - 1) + c^4*d^4*e^2*(3*n - 1) - 4*a^2*c^2*e^6*n)*x*x^(4*n) + (a^2*c^2*d*e^5*(8*n - 1) + 2*a*c^3*d^3*e^3*(5*n - 1) + c^4*d^5*e*(2*n - 1))*x*x^(3*n) + (a^2*c^2*d^2*e^4*(34*n - 3) - c^4*d^6*(4*n - 1) - 2*a*c^3*d^4*e^2*(n + 1) - 16*a^3*c*e^6*n)*x*x^(2*n) + (a^3*c*d*e^5*(10*n - 1) + 2*a^2*c^2*d^3*e^3*(7*n - 1) + a*c^3*d^5*e*(4*n - 1))*x*x^n + (a^3*c*d^2*e^4*(10*n - 1) - a*c^3*d^6*(6*n - 1) - 12*a^2*c^2*d^4*e^2*n - 8*a^4*e^6*n)*x)/(a^4*c^3*d^8*n^2 + 3*a^5*c^2*d^6*e^2*n^2 + 3*a^6*c*d^4*e^4*n^2 + a^7*d^2*e^6*n^2 + (a^2*c^5*d^7*e*n^2 + 3*a^3*c^4*d^5*e^3*n^2 + 3*a^4*c^3*d^3*e^5*n^2 + a^5*c^2*d*e^7*n^2)*x^(5*n) + (a^2*c^5*d^8*n^2 + 3*a^3*c^4*d^6*e^2*n^2 + 3*a^4*c^3*d^4*e^4*n^2 + a^5*c^2*d^2*e^6*n^2)*x^(4*n) + 2*(a^3*c^4*d^7*e*n^2 + 3*a^4*c^3*d^5*e^3*n^2 + 3*a^5*c^2*d^3*e^5*n^2 + a^6*c*d*e^7*n^2)*x^(3*n) + 2*(a^3*c^4*d^8*n^2 + 3*a^4*c^3*d^6*e^2*n^2 + 3*a^5*c^2*d^4*e^4*n^2 + a^6*c*d^2*e^6*n^2)*x^(2*n) + (a^4*c^3*d^7*e*n^2 + 3*a^5*c^2*d^5*e^3*n^2 + 3*a^6*c*d^3*e^5*n^2 + a^7*d*e^7*n^2)*x^n) - integrate(-1/8*((8*n^2 - 6*n + 1)*c^4*d^6 + (32*n^2 - 18*n + 1)*a*c^3*d^4*e^2 + (48*n^2 - 2*n - 1)*a^2*c^2*d^2*e^4 - (24*n^2 - 10*n + 1)*a^3*c*e^6 - 2*((3*n^2 - 4*n + 1)*c^4*d^5*e + 2*(7*n^2 - 8*n + 1)*a*c^3*d^3*e^3 + (35*n^2 - 12*n + 1)*a^2*c^2*d*e^5)*x^n)/(a^3*c^4*d^8*n^2 + 4*a^4*c^3*d^6*e^2*n^2 + 6*a^5*c^2*d^4*e^4*n^2 + 4*a^6*c*d^2*e^6*n^2 + a^7*e^8*n^2 + (a^2*c^5*d^8*n^2 + 4*a^3*c^4*d^6*e^2*n^2 + 6*a^4*c^3*d^4*e^4*n^2 + 4*a^5*c^2*d^2*e^6*n^2 + a^6*c*e^8*n^2)*x^(2*n)), x)","F",0
58,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{c x^{2 \, n} + a} {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(c*x^(2*n) + a)*(e*x^n + d)), x)","F",0
59,0,0,0,0.000000," ","integrate((d+e*x^n)^q*(a+c*x^(2*n))^p,x, algorithm=""maxima"")","\int {\left(c x^{2 \, n} + a\right)}^{p} {\left(e x^{n} + d\right)}^{q}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p*(e*x^n + d)^q, x)","F",0
60,0,0,0,0.000000," ","integrate((d+e*x^n)^3*(a+c*x^(2*n))^p,x, algorithm=""maxima"")","\int {\left(e x^{n} + d\right)}^{3} {\left(c x^{2 \, n} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^n + d)^3*(c*x^(2*n) + a)^p, x)","F",0
61,0,0,0,0.000000," ","integrate((d+e*x^n)^2*(a+c*x^(2*n))^p,x, algorithm=""maxima"")","\int {\left(e x^{n} + d\right)}^{2} {\left(c x^{2 \, n} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^n + d)^2*(c*x^(2*n) + a)^p, x)","F",0
62,0,0,0,0.000000," ","integrate((d+e*x^n)*(a+c*x^(2*n))^p,x, algorithm=""maxima"")","\int {\left(e x^{n} + d\right)} {\left(c x^{2 \, n} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^n + d)*(c*x^(2*n) + a)^p, x)","F",0
63,0,0,0,0.000000," ","integrate((a+c*x^(2*n))^p/(d+e*x^n),x, algorithm=""maxima"")","\int \frac{{\left(c x^{2 \, n} + a\right)}^{p}}{e x^{n} + d}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p/(e*x^n + d), x)","F",0
64,0,0,0,0.000000," ","integrate((a+c*x^(2*n))^p/(d+e*x^n)^2,x, algorithm=""maxima"")","\int \frac{{\left(c x^{2 \, n} + a\right)}^{p}}{{\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p/(e*x^n + d)^2, x)","F",0
65,0,0,0,0.000000," ","integrate((a+c*x^(2*n))^p/(d+e*x^n)^3,x, algorithm=""maxima"")","\int \frac{{\left(c x^{2 \, n} + a\right)}^{p}}{{\left(e x^{n} + d\right)}^{3}}\,{d x}"," ",0,"integrate((c*x^(2*n) + a)^p/(e*x^n + d)^3, x)","F",0
66,1,82,0,0.549611," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n)),x, algorithm=""maxima"")","a d x + \frac{c e x^{3 \, n + 1}}{3 \, n + 1} + \frac{c d x^{2 \, n + 1}}{2 \, n + 1} + \frac{b e x^{2 \, n + 1}}{2 \, n + 1} + \frac{b d x^{n + 1}}{n + 1} + \frac{a e x^{n + 1}}{n + 1}"," ",0,"a*d*x + c*e*x^(3*n + 1)/(3*n + 1) + c*d*x^(2*n + 1)/(2*n + 1) + b*e*x^(2*n + 1)/(2*n + 1) + b*d*x^(n + 1)/(n + 1) + a*e*x^(n + 1)/(n + 1)","A",0
67,1,208,0,0.695035," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^2,x, algorithm=""maxima"")","a^{2} d x + \frac{c^{2} e x^{5 \, n + 1}}{5 \, n + 1} + \frac{c^{2} d x^{4 \, n + 1}}{4 \, n + 1} + \frac{2 \, b c e x^{4 \, n + 1}}{4 \, n + 1} + \frac{2 \, b c d x^{3 \, n + 1}}{3 \, n + 1} + \frac{b^{2} e x^{3 \, n + 1}}{3 \, n + 1} + \frac{2 \, a c e x^{3 \, n + 1}}{3 \, n + 1} + \frac{b^{2} d x^{2 \, n + 1}}{2 \, n + 1} + \frac{2 \, a c d x^{2 \, n + 1}}{2 \, n + 1} + \frac{2 \, a b e x^{2 \, n + 1}}{2 \, n + 1} + \frac{2 \, a b d x^{n + 1}}{n + 1} + \frac{a^{2} e x^{n + 1}}{n + 1}"," ",0,"a^2*d*x + c^2*e*x^(5*n + 1)/(5*n + 1) + c^2*d*x^(4*n + 1)/(4*n + 1) + 2*b*c*e*x^(4*n + 1)/(4*n + 1) + 2*b*c*d*x^(3*n + 1)/(3*n + 1) + b^2*e*x^(3*n + 1)/(3*n + 1) + 2*a*c*e*x^(3*n + 1)/(3*n + 1) + b^2*d*x^(2*n + 1)/(2*n + 1) + 2*a*c*d*x^(2*n + 1)/(2*n + 1) + 2*a*b*e*x^(2*n + 1)/(2*n + 1) + 2*a*b*d*x^(n + 1)/(n + 1) + a^2*e*x^(n + 1)/(n + 1)","A",0
68,1,386,0,0.882376," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^3,x, algorithm=""maxima"")","a^{3} d x + \frac{c^{3} e x^{7 \, n + 1}}{7 \, n + 1} + \frac{c^{3} d x^{6 \, n + 1}}{6 \, n + 1} + \frac{3 \, b c^{2} e x^{6 \, n + 1}}{6 \, n + 1} + \frac{3 \, b c^{2} d x^{5 \, n + 1}}{5 \, n + 1} + \frac{3 \, b^{2} c e x^{5 \, n + 1}}{5 \, n + 1} + \frac{3 \, a c^{2} e x^{5 \, n + 1}}{5 \, n + 1} + \frac{3 \, b^{2} c d x^{4 \, n + 1}}{4 \, n + 1} + \frac{3 \, a c^{2} d x^{4 \, n + 1}}{4 \, n + 1} + \frac{b^{3} e x^{4 \, n + 1}}{4 \, n + 1} + \frac{6 \, a b c e x^{4 \, n + 1}}{4 \, n + 1} + \frac{b^{3} d x^{3 \, n + 1}}{3 \, n + 1} + \frac{6 \, a b c d x^{3 \, n + 1}}{3 \, n + 1} + \frac{3 \, a b^{2} e x^{3 \, n + 1}}{3 \, n + 1} + \frac{3 \, a^{2} c e x^{3 \, n + 1}}{3 \, n + 1} + \frac{3 \, a b^{2} d x^{2 \, n + 1}}{2 \, n + 1} + \frac{3 \, a^{2} c d x^{2 \, n + 1}}{2 \, n + 1} + \frac{3 \, a^{2} b e x^{2 \, n + 1}}{2 \, n + 1} + \frac{3 \, a^{2} b d x^{n + 1}}{n + 1} + \frac{a^{3} e x^{n + 1}}{n + 1}"," ",0,"a^3*d*x + c^3*e*x^(7*n + 1)/(7*n + 1) + c^3*d*x^(6*n + 1)/(6*n + 1) + 3*b*c^2*e*x^(6*n + 1)/(6*n + 1) + 3*b*c^2*d*x^(5*n + 1)/(5*n + 1) + 3*b^2*c*e*x^(5*n + 1)/(5*n + 1) + 3*a*c^2*e*x^(5*n + 1)/(5*n + 1) + 3*b^2*c*d*x^(4*n + 1)/(4*n + 1) + 3*a*c^2*d*x^(4*n + 1)/(4*n + 1) + b^3*e*x^(4*n + 1)/(4*n + 1) + 6*a*b*c*e*x^(4*n + 1)/(4*n + 1) + b^3*d*x^(3*n + 1)/(3*n + 1) + 6*a*b*c*d*x^(3*n + 1)/(3*n + 1) + 3*a*b^2*e*x^(3*n + 1)/(3*n + 1) + 3*a^2*c*e*x^(3*n + 1)/(3*n + 1) + 3*a*b^2*d*x^(2*n + 1)/(2*n + 1) + 3*a^2*c*d*x^(2*n + 1)/(2*n + 1) + 3*a^2*b*e*x^(2*n + 1)/(2*n + 1) + 3*a^2*b*d*x^(n + 1)/(n + 1) + a^3*e*x^(n + 1)/(n + 1)","A",0
69,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+b*x^n+c*x^(2*n)),x, algorithm=""maxima"")","\frac{c e^{3} x x^{n} + {\left(3 \, c d e^{2} {\left(n + 1\right)} - b e^{3} {\left(n + 1\right)}\right)} x}{c^{2} {\left(n + 1\right)}} - \int -\frac{c^{2} d^{3} - {\left(3 \, c d e^{2} - b e^{3}\right)} a + {\left(3 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3} - a c e^{3}\right)} x^{n}}{c^{3} x^{2 \, n} + b c^{2} x^{n} + a c^{2}}\,{d x}"," ",0,"(c*e^3*x*x^n + (3*c*d*e^2*(n + 1) - b*e^3*(n + 1))*x)/(c^2*(n + 1)) - integrate(-(c^2*d^3 - (3*c*d*e^2 - b*e^3)*a + (3*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3 - a*c*e^3)*x^n)/(c^3*x^(2*n) + b*c^2*x^n + a*c^2), x)","F",0
70,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""maxima"")","\frac{e^{2} x}{c} - \int -\frac{c d^{2} - a e^{2} + {\left(2 \, c d e - b e^{2}\right)} x^{n}}{c^{2} x^{2 \, n} + b c x^{n} + a c}\,{d x}"," ",0,"e^2*x/c - integrate(-(c*d^2 - a*e^2 + (2*c*d*e - b*e^2)*x^n)/(c^2*x^(2*n) + b*c*x^n + a*c), x)","F",0
71,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""maxima"")","\int \frac{e x^{n} + d}{c x^{2 \, n} + b x^{n} + a}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + b*x^n + a), x)","F",0
72,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(c x^{2 \, n} + b x^{n} + a\right)} {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"integrate(1/((c*x^(2*n) + b*x^n + a)*(e*x^n + d)), x)","F",0
73,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""maxima"")","\frac{e^{2} x}{c d^{4} n - b d^{3} e n + a d^{2} e^{2} n + {\left(c d^{3} e n - b d^{2} e^{2} n + a d e^{3} n\right)} x^{n}} + {\left(c d^{2} e^{2} {\left(3 \, n - 1\right)} - b d e^{3} {\left(2 \, n - 1\right)} + a e^{4} {\left(n - 1\right)}\right)} \int \frac{1}{c^{2} d^{6} n - 2 \, b c d^{5} e n + b^{2} d^{4} e^{2} n + a^{2} d^{2} e^{4} n + 2 \, {\left(c d^{4} e^{2} n - b d^{3} e^{3} n\right)} a + {\left(c^{2} d^{5} e n - 2 \, b c d^{4} e^{2} n + b^{2} d^{3} e^{3} n + a^{2} d e^{5} n + 2 \, {\left(c d^{3} e^{3} n - b d^{2} e^{4} n\right)} a\right)} x^{n}}\,{d x} + \int \frac{c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - a c e^{2} - {\left(2 \, c^{2} d e - b c e^{2}\right)} x^{n}}{a^{3} e^{4} + 2 \, {\left(c d^{2} e^{2} - b d e^{3}\right)} a^{2} + {\left(c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2}\right)} a + {\left(c^{3} d^{4} - 2 \, b c^{2} d^{3} e + b^{2} c d^{2} e^{2} + a^{2} c e^{4} + 2 \, {\left(c^{2} d^{2} e^{2} - b c d e^{3}\right)} a\right)} x^{2 \, n} + {\left(b c^{2} d^{4} - 2 \, b^{2} c d^{3} e + b^{3} d^{2} e^{2} + a^{2} b e^{4} + 2 \, {\left(b c d^{2} e^{2} - b^{2} d e^{3}\right)} a\right)} x^{n}}\,{d x}"," ",0,"e^2*x/(c*d^4*n - b*d^3*e*n + a*d^2*e^2*n + (c*d^3*e*n - b*d^2*e^2*n + a*d*e^3*n)*x^n) + (c*d^2*e^2*(3*n - 1) - b*d*e^3*(2*n - 1) + a*e^4*(n - 1))*integrate(1/(c^2*d^6*n - 2*b*c*d^5*e*n + b^2*d^4*e^2*n + a^2*d^2*e^4*n + 2*(c*d^4*e^2*n - b*d^3*e^3*n)*a + (c^2*d^5*e*n - 2*b*c*d^4*e^2*n + b^2*d^3*e^3*n + a^2*d*e^5*n + 2*(c*d^3*e^3*n - b*d^2*e^4*n)*a)*x^n), x) + integrate((c^2*d^2 - 2*b*c*d*e + b^2*e^2 - a*c*e^2 - (2*c^2*d*e - b*c*e^2)*x^n)/(a^3*e^4 + 2*(c*d^2*e^2 - b*d*e^3)*a^2 + (c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2)*a + (c^3*d^4 - 2*b*c^2*d^3*e + b^2*c*d^2*e^2 + a^2*c*e^4 + 2*(c^2*d^2*e^2 - b*c*d*e^3)*a)*x^(2*n) + (b*c^2*d^4 - 2*b^2*c*d^3*e + b^3*d^2*e^2 + a^2*b*e^4 + 2*(b*c*d^2*e^2 - b^2*d*e^3)*a)*x^n), x)","F",0
74,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^3/(a+b*x^n+c*x^(2*n)),x, algorithm=""maxima"")","{\left({\left(12 \, n^{2} - 7 \, n + 1\right)} c^{2} d^{4} e^{2} - 2 \, {\left(8 \, n^{2} - 6 \, n + 1\right)} b c d^{3} e^{3} + {\left(6 \, n^{2} - 5 \, n + 1\right)} b^{2} d^{2} e^{4} + {\left(2 \, n^{2} - 3 \, n + 1\right)} a^{2} e^{6} + 2 \, {\left({\left(3 \, n^{2} - 5 \, n + 1\right)} c d^{2} e^{4} - {\left(3 \, n^{2} - 4 \, n + 1\right)} b d e^{5}\right)} a\right)} \int \frac{1}{2 \, {\left(c^{3} d^{9} n^{2} - 3 \, b c^{2} d^{8} e n^{2} + 3 \, b^{2} c d^{7} e^{2} n^{2} - b^{3} d^{6} e^{3} n^{2} + a^{3} d^{3} e^{6} n^{2} + 3 \, {\left(c d^{5} e^{4} n^{2} - b d^{4} e^{5} n^{2}\right)} a^{2} + 3 \, {\left(c^{2} d^{7} e^{2} n^{2} - 2 \, b c d^{6} e^{3} n^{2} + b^{2} d^{5} e^{4} n^{2}\right)} a + {\left(c^{3} d^{8} e n^{2} - 3 \, b c^{2} d^{7} e^{2} n^{2} + 3 \, b^{2} c d^{6} e^{3} n^{2} - b^{3} d^{5} e^{4} n^{2} + a^{3} d^{2} e^{7} n^{2} + 3 \, {\left(c d^{4} e^{5} n^{2} - b d^{3} e^{6} n^{2}\right)} a^{2} + 3 \, {\left(c^{2} d^{6} e^{3} n^{2} - 2 \, b c d^{5} e^{4} n^{2} + b^{2} d^{4} e^{5} n^{2}\right)} a\right)} x^{n}\right)}}\,{d x} + \frac{{\left(c d^{2} e^{3} {\left(6 \, n - 1\right)} - b d e^{4} {\left(4 \, n - 1\right)} + a e^{5} {\left(2 \, n - 1\right)}\right)} x x^{n} + {\left(c d^{3} e^{2} {\left(7 \, n - 1\right)} - b d^{2} e^{3} {\left(5 \, n - 1\right)} + a d e^{4} {\left(3 \, n - 1\right)}\right)} x}{2 \, {\left(c^{2} d^{8} n^{2} - 2 \, b c d^{7} e n^{2} + b^{2} d^{6} e^{2} n^{2} + a^{2} d^{4} e^{4} n^{2} + 2 \, {\left(c d^{6} e^{2} n^{2} - b d^{5} e^{3} n^{2}\right)} a + {\left(c^{2} d^{6} e^{2} n^{2} - 2 \, b c d^{5} e^{3} n^{2} + b^{2} d^{4} e^{4} n^{2} + a^{2} d^{2} e^{6} n^{2} + 2 \, {\left(c d^{4} e^{4} n^{2} - b d^{3} e^{5} n^{2}\right)} a\right)} x^{2 \, n} + 2 \, {\left(c^{2} d^{7} e n^{2} - 2 \, b c d^{6} e^{2} n^{2} + b^{2} d^{5} e^{3} n^{2} + a^{2} d^{3} e^{5} n^{2} + 2 \, {\left(c d^{5} e^{3} n^{2} - b d^{4} e^{4} n^{2}\right)} a\right)} x^{n}\right)}} + \int \frac{c^{3} d^{3} - 3 \, b c^{2} d^{2} e + 3 \, b^{2} c d e^{2} - b^{3} e^{3} - {\left(3 \, c^{2} d e^{2} - 2 \, b c e^{3}\right)} a - {\left(3 \, c^{3} d^{2} e - 3 \, b c^{2} d e^{2} + b^{2} c e^{3} - a c^{2} e^{3}\right)} x^{n}}{a^{4} e^{6} + 3 \, {\left(c d^{2} e^{4} - b d e^{5}\right)} a^{3} + 3 \, {\left(c^{2} d^{4} e^{2} - 2 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4}\right)} a^{2} + {\left(c^{3} d^{6} - 3 \, b c^{2} d^{5} e + 3 \, b^{2} c d^{4} e^{2} - b^{3} d^{3} e^{3}\right)} a + {\left(c^{4} d^{6} - 3 \, b c^{3} d^{5} e + 3 \, b^{2} c^{2} d^{4} e^{2} - b^{3} c d^{3} e^{3} + a^{3} c e^{6} + 3 \, {\left(c^{2} d^{2} e^{4} - b c d e^{5}\right)} a^{2} + 3 \, {\left(c^{3} d^{4} e^{2} - 2 \, b c^{2} d^{3} e^{3} + b^{2} c d^{2} e^{4}\right)} a\right)} x^{2 \, n} + {\left(b c^{3} d^{6} - 3 \, b^{2} c^{2} d^{5} e + 3 \, b^{3} c d^{4} e^{2} - b^{4} d^{3} e^{3} + a^{3} b e^{6} + 3 \, {\left(b c d^{2} e^{4} - b^{2} d e^{5}\right)} a^{2} + 3 \, {\left(b c^{2} d^{4} e^{2} - 2 \, b^{2} c d^{3} e^{3} + b^{3} d^{2} e^{4}\right)} a\right)} x^{n}}\,{d x}"," ",0,"((12*n^2 - 7*n + 1)*c^2*d^4*e^2 - 2*(8*n^2 - 6*n + 1)*b*c*d^3*e^3 + (6*n^2 - 5*n + 1)*b^2*d^2*e^4 + (2*n^2 - 3*n + 1)*a^2*e^6 + 2*((3*n^2 - 5*n + 1)*c*d^2*e^4 - (3*n^2 - 4*n + 1)*b*d*e^5)*a)*integrate(1/2/(c^3*d^9*n^2 - 3*b*c^2*d^8*e*n^2 + 3*b^2*c*d^7*e^2*n^2 - b^3*d^6*e^3*n^2 + a^3*d^3*e^6*n^2 + 3*(c*d^5*e^4*n^2 - b*d^4*e^5*n^2)*a^2 + 3*(c^2*d^7*e^2*n^2 - 2*b*c*d^6*e^3*n^2 + b^2*d^5*e^4*n^2)*a + (c^3*d^8*e*n^2 - 3*b*c^2*d^7*e^2*n^2 + 3*b^2*c*d^6*e^3*n^2 - b^3*d^5*e^4*n^2 + a^3*d^2*e^7*n^2 + 3*(c*d^4*e^5*n^2 - b*d^3*e^6*n^2)*a^2 + 3*(c^2*d^6*e^3*n^2 - 2*b*c*d^5*e^4*n^2 + b^2*d^4*e^5*n^2)*a)*x^n), x) + 1/2*((c*d^2*e^3*(6*n - 1) - b*d*e^4*(4*n - 1) + a*e^5*(2*n - 1))*x*x^n + (c*d^3*e^2*(7*n - 1) - b*d^2*e^3*(5*n - 1) + a*d*e^4*(3*n - 1))*x)/(c^2*d^8*n^2 - 2*b*c*d^7*e*n^2 + b^2*d^6*e^2*n^2 + a^2*d^4*e^4*n^2 + 2*(c*d^6*e^2*n^2 - b*d^5*e^3*n^2)*a + (c^2*d^6*e^2*n^2 - 2*b*c*d^5*e^3*n^2 + b^2*d^4*e^4*n^2 + a^2*d^2*e^6*n^2 + 2*(c*d^4*e^4*n^2 - b*d^3*e^5*n^2)*a)*x^(2*n) + 2*(c^2*d^7*e*n^2 - 2*b*c*d^6*e^2*n^2 + b^2*d^5*e^3*n^2 + a^2*d^3*e^5*n^2 + 2*(c*d^5*e^3*n^2 - b*d^4*e^4*n^2)*a)*x^n) + integrate((c^3*d^3 - 3*b*c^2*d^2*e + 3*b^2*c*d*e^2 - b^3*e^3 - (3*c^2*d*e^2 - 2*b*c*e^3)*a - (3*c^3*d^2*e - 3*b*c^2*d*e^2 + b^2*c*e^3 - a*c^2*e^3)*x^n)/(a^4*e^6 + 3*(c*d^2*e^4 - b*d*e^5)*a^3 + 3*(c^2*d^4*e^2 - 2*b*c*d^3*e^3 + b^2*d^2*e^4)*a^2 + (c^3*d^6 - 3*b*c^2*d^5*e + 3*b^2*c*d^4*e^2 - b^3*d^3*e^3)*a + (c^4*d^6 - 3*b*c^3*d^5*e + 3*b^2*c^2*d^4*e^2 - b^3*c*d^3*e^3 + a^3*c*e^6 + 3*(c^2*d^2*e^4 - b*c*d*e^5)*a^2 + 3*(c^3*d^4*e^2 - 2*b*c^2*d^3*e^3 + b^2*c*d^2*e^4)*a)*x^(2*n) + (b*c^3*d^6 - 3*b^2*c^2*d^5*e + 3*b^3*c*d^4*e^2 - b^4*d^3*e^3 + a^3*b*e^6 + 3*(b*c*d^2*e^4 - b^2*d*e^5)*a^2 + 3*(b*c^2*d^4*e^2 - 2*b^2*c*d^3*e^3 + b^3*d^2*e^4)*a)*x^n), x)","F",0
75,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""maxima"")","\frac{{\left(b c^{2} d^{3} + 2 \, a^{2} c e^{3} - {\left(6 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3}\right)} a\right)} x x^{n} + {\left(b^{2} c d^{3} + {\left(6 \, c d e^{2} - b e^{3}\right)} a^{2} - {\left(2 \, c^{2} d^{3} + 3 \, b c d^{2} e\right)} a\right)} x}{a^{2} b^{2} c n - 4 \, a^{3} c^{2} n + {\left(a b^{2} c^{2} n - 4 \, a^{2} c^{3} n\right)} x^{2 \, n} + {\left(a b^{3} c n - 4 \, a^{2} b c^{2} n\right)} x^{n}} + \int \frac{b^{2} c d^{3} {\left(n - 1\right)} - {\left(6 \, c d e^{2} - b e^{3}\right)} a^{2} - {\left(2 \, c^{2} d^{3} {\left(2 \, n - 1\right)} - 3 \, b c d^{2} e\right)} a - {\left(2 \, a^{2} c e^{3} {\left(n + 1\right)} - b c^{2} d^{3} {\left(n - 1\right)} + {\left(6 \, c^{2} d^{2} e {\left(n - 1\right)} - 3 \, b c d e^{2} {\left(n - 1\right)} - b^{2} e^{3}\right)} a\right)} x^{n}}{a^{2} b^{2} c n - 4 \, a^{3} c^{2} n + {\left(a b^{2} c^{2} n - 4 \, a^{2} c^{3} n\right)} x^{2 \, n} + {\left(a b^{3} c n - 4 \, a^{2} b c^{2} n\right)} x^{n}}\,{d x}"," ",0,"((b*c^2*d^3 + 2*a^2*c*e^3 - (6*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3)*a)*x*x^n + (b^2*c*d^3 + (6*c*d*e^2 - b*e^3)*a^2 - (2*c^2*d^3 + 3*b*c*d^2*e)*a)*x)/(a^2*b^2*c*n - 4*a^3*c^2*n + (a*b^2*c^2*n - 4*a^2*c^3*n)*x^(2*n) + (a*b^3*c*n - 4*a^2*b*c^2*n)*x^n) + integrate((b^2*c*d^3*(n - 1) - (6*c*d*e^2 - b*e^3)*a^2 - (2*c^2*d^3*(2*n - 1) - 3*b*c*d^2*e)*a - (2*a^2*c*e^3*(n + 1) - b*c^2*d^3*(n - 1) + (6*c^2*d^2*e*(n - 1) - 3*b*c*d*e^2*(n - 1) - b^2*e^3)*a)*x^n)/(a^2*b^2*c*n - 4*a^3*c^2*n + (a*b^2*c^2*n - 4*a^2*c^3*n)*x^(2*n) + (a*b^3*c*n - 4*a^2*b*c^2*n)*x^n), x)","F",0
76,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""maxima"")","\frac{{\left(b c d^{2} - {\left(4 \, c d e - b e^{2}\right)} a\right)} x x^{n} + {\left(b^{2} d^{2} + 2 \, a^{2} e^{2} - 2 \, {\left(c d^{2} + b d e\right)} a\right)} x}{a^{2} b^{2} n - 4 \, a^{3} c n + {\left(a b^{2} c n - 4 \, a^{2} c^{2} n\right)} x^{2 \, n} + {\left(a b^{3} n - 4 \, a^{2} b c n\right)} x^{n}} - \int -\frac{b^{2} d^{2} {\left(n - 1\right)} - 2 \, a^{2} e^{2} - 2 \, {\left(c d^{2} {\left(2 \, n - 1\right)} - b d e\right)} a + {\left(b c d^{2} {\left(n - 1\right)} - {\left(4 \, c d e {\left(n - 1\right)} - b e^{2} {\left(n - 1\right)}\right)} a\right)} x^{n}}{a^{2} b^{2} n - 4 \, a^{3} c n + {\left(a b^{2} c n - 4 \, a^{2} c^{2} n\right)} x^{2 \, n} + {\left(a b^{3} n - 4 \, a^{2} b c n\right)} x^{n}}\,{d x}"," ",0,"((b*c*d^2 - (4*c*d*e - b*e^2)*a)*x*x^n + (b^2*d^2 + 2*a^2*e^2 - 2*(c*d^2 + b*d*e)*a)*x)/(a^2*b^2*n - 4*a^3*c*n + (a*b^2*c*n - 4*a^2*c^2*n)*x^(2*n) + (a*b^3*n - 4*a^2*b*c*n)*x^n) - integrate(-(b^2*d^2*(n - 1) - 2*a^2*e^2 - 2*(c*d^2*(2*n - 1) - b*d*e)*a + (b*c*d^2*(n - 1) - (4*c*d*e*(n - 1) - b*e^2*(n - 1))*a)*x^n)/(a^2*b^2*n - 4*a^3*c*n + (a*b^2*c*n - 4*a^2*c^2*n)*x^(2*n) + (a*b^3*n - 4*a^2*b*c*n)*x^n), x)","F",0
77,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""maxima"")","\frac{{\left(b c d - 2 \, a c e\right)} x x^{n} + {\left(b^{2} d - {\left(2 \, c d + b e\right)} a\right)} x}{a^{2} b^{2} n - 4 \, a^{3} c n + {\left(a b^{2} c n - 4 \, a^{2} c^{2} n\right)} x^{2 \, n} + {\left(a b^{3} n - 4 \, a^{2} b c n\right)} x^{n}} + \int \frac{b^{2} d {\left(n - 1\right)} - {\left(2 \, c d {\left(2 \, n - 1\right)} - b e\right)} a + {\left(b c d {\left(n - 1\right)} - 2 \, a c e {\left(n - 1\right)}\right)} x^{n}}{a^{2} b^{2} n - 4 \, a^{3} c n + {\left(a b^{2} c n - 4 \, a^{2} c^{2} n\right)} x^{2 \, n} + {\left(a b^{3} n - 4 \, a^{2} b c n\right)} x^{n}}\,{d x}"," ",0,"((b*c*d - 2*a*c*e)*x*x^n + (b^2*d - (2*c*d + b*e)*a)*x)/(a^2*b^2*n - 4*a^3*c*n + (a*b^2*c*n - 4*a^2*c^2*n)*x^(2*n) + (a*b^3*n - 4*a^2*b*c*n)*x^n) + integrate((b^2*d*(n - 1) - (2*c*d*(2*n - 1) - b*e)*a + (b*c*d*(n - 1) - 2*a*c*e*(n - 1))*x^n)/(a^2*b^2*n - 4*a^3*c*n + (a*b^2*c*n - 4*a^2*c^2*n)*x^(2*n) + (a*b^3*n - 4*a^2*b*c*n)*x^n), x)","F",0
78,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""maxima"")","e^{4} \int \frac{1}{c^{2} d^{5} - 2 \, b c d^{4} e + b^{2} d^{3} e^{2} + a^{2} d e^{4} + 2 \, {\left(c d^{3} e^{2} - b d^{2} e^{3}\right)} a + {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} + b^{2} d^{2} e^{3} + a^{2} e^{5} + 2 \, {\left(c d^{2} e^{3} - b d e^{4}\right)} a\right)} x^{n}}\,{d x} - \frac{{\left(b c^{2} d - b^{2} c e + 2 \, a c^{2} e\right)} x x^{n} + {\left(b^{2} c d - b^{3} e - {\left(2 \, c^{2} d - 3 \, b c e\right)} a\right)} x}{4 \, a^{4} c e^{2} n + {\left(4 \, c^{2} d^{2} n - 4 \, b c d e n - b^{2} e^{2} n\right)} a^{3} - {\left(b^{2} c d^{2} n - b^{3} d e n\right)} a^{2} + {\left(4 \, a^{3} c^{2} e^{2} n + {\left(4 \, c^{3} d^{2} n - 4 \, b c^{2} d e n - b^{2} c e^{2} n\right)} a^{2} - {\left(b^{2} c^{2} d^{2} n - b^{3} c d e n\right)} a\right)} x^{2 \, n} + {\left(4 \, a^{3} b c e^{2} n + {\left(4 \, b c^{2} d^{2} n - 4 \, b^{2} c d e n - b^{3} e^{2} n\right)} a^{2} - {\left(b^{3} c d^{2} n - b^{4} d e n\right)} a\right)} x^{n}} - \int \frac{b^{2} c^{2} d^{3} {\left(n - 1\right)} - 2 \, b^{3} c d^{2} e {\left(n - 1\right)} + b^{4} d e^{2} {\left(n - 1\right)} + {\left(b c e^{3} {\left(8 \, n - 3\right)} - 2 \, c^{2} d e^{2} {\left(4 \, n - 1\right)}\right)} a^{2} + {\left(b c^{2} d^{2} e {\left(8 \, n - 5\right)} - 2 \, c^{3} d^{3} {\left(2 \, n - 1\right)} - b^{3} e^{3} {\left(2 \, n - 1\right)} - 2 \, b^{2} c d e^{2} {\left(n - 1\right)}\right)} a + {\left(2 \, a^{2} c^{2} e^{3} {\left(3 \, n - 1\right)} + b c^{3} d^{3} {\left(n - 1\right)} - 2 \, b^{2} c^{2} d^{2} e {\left(n - 1\right)} + b^{3} c d e^{2} {\left(n - 1\right)} - {\left(b^{2} c e^{3} {\left(2 \, n - 1\right)} - 2 \, c^{3} d^{2} e {\left(n - 1\right)} + b c^{2} d e^{2} {\left(n - 1\right)}\right)} a\right)} x^{n}}{4 \, a^{5} c e^{4} n + {\left(8 \, c^{2} d^{2} e^{2} n - 8 \, b c d e^{3} n - b^{2} e^{4} n\right)} a^{4} + 2 \, {\left(2 \, c^{3} d^{4} n - 4 \, b c^{2} d^{3} e n + b^{2} c d^{2} e^{2} n + b^{3} d e^{3} n\right)} a^{3} - {\left(b^{2} c^{2} d^{4} n - 2 \, b^{3} c d^{3} e n + b^{4} d^{2} e^{2} n\right)} a^{2} + {\left(4 \, a^{4} c^{2} e^{4} n + {\left(8 \, c^{3} d^{2} e^{2} n - 8 \, b c^{2} d e^{3} n - b^{2} c e^{4} n\right)} a^{3} + 2 \, {\left(2 \, c^{4} d^{4} n - 4 \, b c^{3} d^{3} e n + b^{2} c^{2} d^{2} e^{2} n + b^{3} c d e^{3} n\right)} a^{2} - {\left(b^{2} c^{3} d^{4} n - 2 \, b^{3} c^{2} d^{3} e n + b^{4} c d^{2} e^{2} n\right)} a\right)} x^{2 \, n} + {\left(4 \, a^{4} b c e^{4} n + {\left(8 \, b c^{2} d^{2} e^{2} n - 8 \, b^{2} c d e^{3} n - b^{3} e^{4} n\right)} a^{3} + 2 \, {\left(2 \, b c^{3} d^{4} n - 4 \, b^{2} c^{2} d^{3} e n + b^{3} c d^{2} e^{2} n + b^{4} d e^{3} n\right)} a^{2} - {\left(b^{3} c^{2} d^{4} n - 2 \, b^{4} c d^{3} e n + b^{5} d^{2} e^{2} n\right)} a\right)} x^{n}}\,{d x}"," ",0,"e^4*integrate(1/(c^2*d^5 - 2*b*c*d^4*e + b^2*d^3*e^2 + a^2*d*e^4 + 2*(c*d^3*e^2 - b*d^2*e^3)*a + (c^2*d^4*e - 2*b*c*d^3*e^2 + b^2*d^2*e^3 + a^2*e^5 + 2*(c*d^2*e^3 - b*d*e^4)*a)*x^n), x) - ((b*c^2*d - b^2*c*e + 2*a*c^2*e)*x*x^n + (b^2*c*d - b^3*e - (2*c^2*d - 3*b*c*e)*a)*x)/(4*a^4*c*e^2*n + (4*c^2*d^2*n - 4*b*c*d*e*n - b^2*e^2*n)*a^3 - (b^2*c*d^2*n - b^3*d*e*n)*a^2 + (4*a^3*c^2*e^2*n + (4*c^3*d^2*n - 4*b*c^2*d*e*n - b^2*c*e^2*n)*a^2 - (b^2*c^2*d^2*n - b^3*c*d*e*n)*a)*x^(2*n) + (4*a^3*b*c*e^2*n + (4*b*c^2*d^2*n - 4*b^2*c*d*e*n - b^3*e^2*n)*a^2 - (b^3*c*d^2*n - b^4*d*e*n)*a)*x^n) - integrate((b^2*c^2*d^3*(n - 1) - 2*b^3*c*d^2*e*(n - 1) + b^4*d*e^2*(n - 1) + (b*c*e^3*(8*n - 3) - 2*c^2*d*e^2*(4*n - 1))*a^2 + (b*c^2*d^2*e*(8*n - 5) - 2*c^3*d^3*(2*n - 1) - b^3*e^3*(2*n - 1) - 2*b^2*c*d*e^2*(n - 1))*a + (2*a^2*c^2*e^3*(3*n - 1) + b*c^3*d^3*(n - 1) - 2*b^2*c^2*d^2*e*(n - 1) + b^3*c*d*e^2*(n - 1) - (b^2*c*e^3*(2*n - 1) - 2*c^3*d^2*e*(n - 1) + b*c^2*d*e^2*(n - 1))*a)*x^n)/(4*a^5*c*e^4*n + (8*c^2*d^2*e^2*n - 8*b*c*d*e^3*n - b^2*e^4*n)*a^4 + 2*(2*c^3*d^4*n - 4*b*c^2*d^3*e*n + b^2*c*d^2*e^2*n + b^3*d*e^3*n)*a^3 - (b^2*c^2*d^4*n - 2*b^3*c*d^3*e*n + b^4*d^2*e^2*n)*a^2 + (4*a^4*c^2*e^4*n + (8*c^3*d^2*e^2*n - 8*b*c^2*d*e^3*n - b^2*c*e^4*n)*a^3 + 2*(2*c^4*d^4*n - 4*b*c^3*d^3*e*n + b^2*c^2*d^2*e^2*n + b^3*c*d*e^3*n)*a^2 - (b^2*c^3*d^4*n - 2*b^3*c^2*d^3*e*n + b^4*c*d^2*e^2*n)*a)*x^(2*n) + (4*a^4*b*c*e^4*n + (8*b*c^2*d^2*e^2*n - 8*b^2*c*d*e^3*n - b^3*e^4*n)*a^3 + 2*(2*b*c^3*d^4*n - 4*b^2*c^2*d^3*e*n + b^3*c*d^2*e^2*n + b^4*d*e^3*n)*a^2 - (b^3*c^2*d^4*n - 2*b^4*c*d^3*e*n + b^5*d^2*e^2*n)*a)*x^n), x)","F",0
79,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""maxima"")","{\left(c d^{2} e^{4} {\left(5 \, n - 1\right)} - b d e^{5} {\left(3 \, n - 1\right)} + a e^{6} {\left(n - 1\right)}\right)} \int \frac{1}{c^{3} d^{8} n - 3 \, b c^{2} d^{7} e n + 3 \, b^{2} c d^{6} e^{2} n - b^{3} d^{5} e^{3} n + a^{3} d^{2} e^{6} n + 3 \, {\left(c d^{4} e^{4} n - b d^{3} e^{5} n\right)} a^{2} + 3 \, {\left(c^{2} d^{6} e^{2} n - 2 \, b c d^{5} e^{3} n + b^{2} d^{4} e^{4} n\right)} a + {\left(c^{3} d^{7} e n - 3 \, b c^{2} d^{6} e^{2} n + 3 \, b^{2} c d^{5} e^{3} n - b^{3} d^{4} e^{4} n + a^{3} d e^{7} n + 3 \, {\left(c d^{3} e^{5} n - b d^{2} e^{6} n\right)} a^{2} + 3 \, {\left(c^{2} d^{5} e^{3} n - 2 \, b c d^{4} e^{4} n + b^{2} d^{3} e^{5} n\right)} a\right)} x^{n}}\,{d x} - \frac{{\left(b c^{3} d^{3} e - 2 \, b^{2} c^{2} d^{2} e^{2} + b^{3} c d e^{3} - 4 \, a^{2} c^{2} e^{4} + {\left(4 \, c^{3} d^{2} e^{2} - 3 \, b c^{2} d e^{3} + b^{2} c e^{4}\right)} a\right)} x x^{2 \, n} + {\left(b c^{3} d^{4} - b^{2} c^{2} d^{3} e - b^{3} c d^{2} e^{2} + b^{4} d e^{3} + 2 \, {\left(c^{2} d e^{3} - 2 \, b c e^{4}\right)} a^{2} + {\left(2 \, c^{3} d^{3} e + 3 \, b c^{2} d^{2} e^{2} - 4 \, b^{2} c d e^{3} + b^{3} e^{4}\right)} a\right)} x x^{n} + {\left(b^{2} c^{2} d^{4} - 2 \, b^{3} c d^{3} e + b^{4} d^{2} e^{2} - 4 \, a^{3} c e^{4} + {\left(2 \, c^{2} d^{2} e^{2} + b^{2} e^{4}\right)} a^{2} - 2 \, {\left(c^{3} d^{4} - 3 \, b c^{2} d^{3} e + 2 \, b^{2} c d^{2} e^{2}\right)} a\right)} x}{4 \, a^{5} c d^{2} e^{4} n + {\left(8 \, c^{2} d^{4} e^{2} n - 8 \, b c d^{3} e^{3} n - b^{2} d^{2} e^{4} n\right)} a^{4} + 2 \, {\left(2 \, c^{3} d^{6} n - 4 \, b c^{2} d^{5} e n + b^{2} c d^{4} e^{2} n + b^{3} d^{3} e^{3} n\right)} a^{3} - {\left(b^{2} c^{2} d^{6} n - 2 \, b^{3} c d^{5} e n + b^{4} d^{4} e^{2} n\right)} a^{2} + {\left(4 \, a^{4} c^{2} d e^{5} n + {\left(8 \, c^{3} d^{3} e^{3} n - 8 \, b c^{2} d^{2} e^{4} n - b^{2} c d e^{5} n\right)} a^{3} + 2 \, {\left(2 \, c^{4} d^{5} e n - 4 \, b c^{3} d^{4} e^{2} n + b^{2} c^{2} d^{3} e^{3} n + b^{3} c d^{2} e^{4} n\right)} a^{2} - {\left(b^{2} c^{3} d^{5} e n - 2 \, b^{3} c^{2} d^{4} e^{2} n + b^{4} c d^{3} e^{3} n\right)} a\right)} x^{3 \, n} + {\left(4 \, {\left(c^{2} d^{2} e^{4} n + b c d e^{5} n\right)} a^{4} + {\left(8 \, c^{3} d^{4} e^{2} n - 9 \, b^{2} c d^{2} e^{4} n - b^{3} d e^{5} n\right)} a^{3} + 2 \, {\left(2 \, c^{4} d^{6} n - 2 \, b c^{3} d^{5} e n - 3 \, b^{2} c^{2} d^{4} e^{2} n + 2 \, b^{3} c d^{3} e^{3} n + b^{4} d^{2} e^{4} n\right)} a^{2} - {\left(b^{2} c^{3} d^{6} n - b^{3} c^{2} d^{5} e n - b^{4} c d^{4} e^{2} n + b^{5} d^{3} e^{3} n\right)} a\right)} x^{2 \, n} + {\left(4 \, a^{5} c d e^{5} n + {\left(8 \, c^{2} d^{3} e^{3} n - 4 \, b c d^{2} e^{4} n - b^{2} d e^{5} n\right)} a^{4} + {\left(4 \, c^{3} d^{5} e n - 6 \, b^{2} c d^{3} e^{3} n + b^{3} d^{2} e^{4} n\right)} a^{3} + {\left(4 \, b c^{3} d^{6} n - 9 \, b^{2} c^{2} d^{5} e n + 4 \, b^{3} c d^{4} e^{2} n + b^{4} d^{3} e^{3} n\right)} a^{2} - {\left(b^{3} c^{2} d^{6} n - 2 \, b^{4} c d^{5} e n + b^{5} d^{4} e^{2} n\right)} a\right)} x^{n}} + \int -\frac{2 \, a^{3} c^{2} e^{4} {\left(4 \, n - 1\right)} + b^{2} c^{3} d^{4} {\left(n - 1\right)} - 3 \, b^{3} c^{2} d^{3} e {\left(n - 1\right)} + 3 \, b^{4} c d^{2} e^{2} {\left(n - 1\right)} - b^{5} d e^{3} {\left(n - 1\right)} - 2 \, {\left(b^{2} c e^{4} {\left(7 \, n - 2\right)} - 2 \, b c^{2} d e^{3} {\left(6 \, n - 1\right)} + 6 \, c^{3} d^{2} e^{2} n\right)} a^{2} + {\left(b^{4} e^{4} {\left(3 \, n - 1\right)} + 4 \, b c^{3} d^{3} e {\left(3 \, n - 2\right)} - 2 \, c^{4} d^{4} {\left(2 \, n - 1\right)} - 2 \, b^{3} c d e^{3} {\left(n + 1\right)} - 9 \, b^{2} c^{2} d^{2} e^{2} {\left(n - 1\right)}\right)} a + {\left(b c^{4} d^{4} {\left(n - 1\right)} - 3 \, b^{2} c^{3} d^{3} e {\left(n - 1\right)} + 3 \, b^{3} c^{2} d^{2} e^{2} {\left(n - 1\right)} - b^{4} c d e^{3} {\left(n - 1\right)} - {\left(b c^{2} e^{4} {\left(11 \, n - 3\right)} - 4 \, c^{3} d e^{3} {\left(5 \, n - 1\right)}\right)} a^{2} - {\left(b^{2} c^{2} d e^{3} {\left(3 \, n + 1\right)} - b^{3} c e^{4} {\left(3 \, n - 1\right)} - 4 \, c^{4} d^{3} e {\left(n - 1\right)} + 6 \, b c^{3} d^{2} e^{2} {\left(n - 1\right)}\right)} a\right)} x^{n}}{4 \, a^{6} c e^{6} n + {\left(12 \, c^{2} d^{2} e^{4} n - 12 \, b c d e^{5} n - b^{2} e^{6} n\right)} a^{5} + 3 \, {\left(4 \, c^{3} d^{4} e^{2} n - 8 \, b c^{2} d^{3} e^{3} n + 3 \, b^{2} c d^{2} e^{4} n + b^{3} d e^{5} n\right)} a^{4} + {\left(4 \, c^{4} d^{6} n - 12 \, b c^{3} d^{5} e n + 9 \, b^{2} c^{2} d^{4} e^{2} n + 2 \, b^{3} c d^{3} e^{3} n - 3 \, b^{4} d^{2} e^{4} n\right)} a^{3} - {\left(b^{2} c^{3} d^{6} n - 3 \, b^{3} c^{2} d^{5} e n + 3 \, b^{4} c d^{4} e^{2} n - b^{5} d^{3} e^{3} n\right)} a^{2} + {\left(4 \, a^{5} c^{2} e^{6} n + {\left(12 \, c^{3} d^{2} e^{4} n - 12 \, b c^{2} d e^{5} n - b^{2} c e^{6} n\right)} a^{4} + 3 \, {\left(4 \, c^{4} d^{4} e^{2} n - 8 \, b c^{3} d^{3} e^{3} n + 3 \, b^{2} c^{2} d^{2} e^{4} n + b^{3} c d e^{5} n\right)} a^{3} + {\left(4 \, c^{5} d^{6} n - 12 \, b c^{4} d^{5} e n + 9 \, b^{2} c^{3} d^{4} e^{2} n + 2 \, b^{3} c^{2} d^{3} e^{3} n - 3 \, b^{4} c d^{2} e^{4} n\right)} a^{2} - {\left(b^{2} c^{4} d^{6} n - 3 \, b^{3} c^{3} d^{5} e n + 3 \, b^{4} c^{2} d^{4} e^{2} n - b^{5} c d^{3} e^{3} n\right)} a\right)} x^{2 \, n} + {\left(4 \, a^{5} b c e^{6} n + {\left(12 \, b c^{2} d^{2} e^{4} n - 12 \, b^{2} c d e^{5} n - b^{3} e^{6} n\right)} a^{4} + 3 \, {\left(4 \, b c^{3} d^{4} e^{2} n - 8 \, b^{2} c^{2} d^{3} e^{3} n + 3 \, b^{3} c d^{2} e^{4} n + b^{4} d e^{5} n\right)} a^{3} + {\left(4 \, b c^{4} d^{6} n - 12 \, b^{2} c^{3} d^{5} e n + 9 \, b^{3} c^{2} d^{4} e^{2} n + 2 \, b^{4} c d^{3} e^{3} n - 3 \, b^{5} d^{2} e^{4} n\right)} a^{2} - {\left(b^{3} c^{3} d^{6} n - 3 \, b^{4} c^{2} d^{5} e n + 3 \, b^{5} c d^{4} e^{2} n - b^{6} d^{3} e^{3} n\right)} a\right)} x^{n}}\,{d x}"," ",0,"(c*d^2*e^4*(5*n - 1) - b*d*e^5*(3*n - 1) + a*e^6*(n - 1))*integrate(1/(c^3*d^8*n - 3*b*c^2*d^7*e*n + 3*b^2*c*d^6*e^2*n - b^3*d^5*e^3*n + a^3*d^2*e^6*n + 3*(c*d^4*e^4*n - b*d^3*e^5*n)*a^2 + 3*(c^2*d^6*e^2*n - 2*b*c*d^5*e^3*n + b^2*d^4*e^4*n)*a + (c^3*d^7*e*n - 3*b*c^2*d^6*e^2*n + 3*b^2*c*d^5*e^3*n - b^3*d^4*e^4*n + a^3*d*e^7*n + 3*(c*d^3*e^5*n - b*d^2*e^6*n)*a^2 + 3*(c^2*d^5*e^3*n - 2*b*c*d^4*e^4*n + b^2*d^3*e^5*n)*a)*x^n), x) - ((b*c^3*d^3*e - 2*b^2*c^2*d^2*e^2 + b^3*c*d*e^3 - 4*a^2*c^2*e^4 + (4*c^3*d^2*e^2 - 3*b*c^2*d*e^3 + b^2*c*e^4)*a)*x*x^(2*n) + (b*c^3*d^4 - b^2*c^2*d^3*e - b^3*c*d^2*e^2 + b^4*d*e^3 + 2*(c^2*d*e^3 - 2*b*c*e^4)*a^2 + (2*c^3*d^3*e + 3*b*c^2*d^2*e^2 - 4*b^2*c*d*e^3 + b^3*e^4)*a)*x*x^n + (b^2*c^2*d^4 - 2*b^3*c*d^3*e + b^4*d^2*e^2 - 4*a^3*c*e^4 + (2*c^2*d^2*e^2 + b^2*e^4)*a^2 - 2*(c^3*d^4 - 3*b*c^2*d^3*e + 2*b^2*c*d^2*e^2)*a)*x)/(4*a^5*c*d^2*e^4*n + (8*c^2*d^4*e^2*n - 8*b*c*d^3*e^3*n - b^2*d^2*e^4*n)*a^4 + 2*(2*c^3*d^6*n - 4*b*c^2*d^5*e*n + b^2*c*d^4*e^2*n + b^3*d^3*e^3*n)*a^3 - (b^2*c^2*d^6*n - 2*b^3*c*d^5*e*n + b^4*d^4*e^2*n)*a^2 + (4*a^4*c^2*d*e^5*n + (8*c^3*d^3*e^3*n - 8*b*c^2*d^2*e^4*n - b^2*c*d*e^5*n)*a^3 + 2*(2*c^4*d^5*e*n - 4*b*c^3*d^4*e^2*n + b^2*c^2*d^3*e^3*n + b^3*c*d^2*e^4*n)*a^2 - (b^2*c^3*d^5*e*n - 2*b^3*c^2*d^4*e^2*n + b^4*c*d^3*e^3*n)*a)*x^(3*n) + (4*(c^2*d^2*e^4*n + b*c*d*e^5*n)*a^4 + (8*c^3*d^4*e^2*n - 9*b^2*c*d^2*e^4*n - b^3*d*e^5*n)*a^3 + 2*(2*c^4*d^6*n - 2*b*c^3*d^5*e*n - 3*b^2*c^2*d^4*e^2*n + 2*b^3*c*d^3*e^3*n + b^4*d^2*e^4*n)*a^2 - (b^2*c^3*d^6*n - b^3*c^2*d^5*e*n - b^4*c*d^4*e^2*n + b^5*d^3*e^3*n)*a)*x^(2*n) + (4*a^5*c*d*e^5*n + (8*c^2*d^3*e^3*n - 4*b*c*d^2*e^4*n - b^2*d*e^5*n)*a^4 + (4*c^3*d^5*e*n - 6*b^2*c*d^3*e^3*n + b^3*d^2*e^4*n)*a^3 + (4*b*c^3*d^6*n - 9*b^2*c^2*d^5*e*n + 4*b^3*c*d^4*e^2*n + b^4*d^3*e^3*n)*a^2 - (b^3*c^2*d^6*n - 2*b^4*c*d^5*e*n + b^5*d^4*e^2*n)*a)*x^n) + integrate(-(2*a^3*c^2*e^4*(4*n - 1) + b^2*c^3*d^4*(n - 1) - 3*b^3*c^2*d^3*e*(n - 1) + 3*b^4*c*d^2*e^2*(n - 1) - b^5*d*e^3*(n - 1) - 2*(b^2*c*e^4*(7*n - 2) - 2*b*c^2*d*e^3*(6*n - 1) + 6*c^3*d^2*e^2*n)*a^2 + (b^4*e^4*(3*n - 1) + 4*b*c^3*d^3*e*(3*n - 2) - 2*c^4*d^4*(2*n - 1) - 2*b^3*c*d*e^3*(n + 1) - 9*b^2*c^2*d^2*e^2*(n - 1))*a + (b*c^4*d^4*(n - 1) - 3*b^2*c^3*d^3*e*(n - 1) + 3*b^3*c^2*d^2*e^2*(n - 1) - b^4*c*d*e^3*(n - 1) - (b*c^2*e^4*(11*n - 3) - 4*c^3*d*e^3*(5*n - 1))*a^2 - (b^2*c^2*d*e^3*(3*n + 1) - b^3*c*e^4*(3*n - 1) - 4*c^4*d^3*e*(n - 1) + 6*b*c^3*d^2*e^2*(n - 1))*a)*x^n)/(4*a^6*c*e^6*n + (12*c^2*d^2*e^4*n - 12*b*c*d*e^5*n - b^2*e^6*n)*a^5 + 3*(4*c^3*d^4*e^2*n - 8*b*c^2*d^3*e^3*n + 3*b^2*c*d^2*e^4*n + b^3*d*e^5*n)*a^4 + (4*c^4*d^6*n - 12*b*c^3*d^5*e*n + 9*b^2*c^2*d^4*e^2*n + 2*b^3*c*d^3*e^3*n - 3*b^4*d^2*e^4*n)*a^3 - (b^2*c^3*d^6*n - 3*b^3*c^2*d^5*e*n + 3*b^4*c*d^4*e^2*n - b^5*d^3*e^3*n)*a^2 + (4*a^5*c^2*e^6*n + (12*c^3*d^2*e^4*n - 12*b*c^2*d*e^5*n - b^2*c*e^6*n)*a^4 + 3*(4*c^4*d^4*e^2*n - 8*b*c^3*d^3*e^3*n + 3*b^2*c^2*d^2*e^4*n + b^3*c*d*e^5*n)*a^3 + (4*c^5*d^6*n - 12*b*c^4*d^5*e*n + 9*b^2*c^3*d^4*e^2*n + 2*b^3*c^2*d^3*e^3*n - 3*b^4*c*d^2*e^4*n)*a^2 - (b^2*c^4*d^6*n - 3*b^3*c^3*d^5*e*n + 3*b^4*c^2*d^4*e^2*n - b^5*c*d^3*e^3*n)*a)*x^(2*n) + (4*a^5*b*c*e^6*n + (12*b*c^2*d^2*e^4*n - 12*b^2*c*d*e^5*n - b^3*e^6*n)*a^4 + 3*(4*b*c^3*d^4*e^2*n - 8*b^2*c^2*d^3*e^3*n + 3*b^3*c*d^2*e^4*n + b^4*d*e^5*n)*a^3 + (4*b*c^4*d^6*n - 12*b^2*c^3*d^5*e*n + 9*b^3*c^2*d^4*e^2*n + 2*b^4*c*d^3*e^3*n - 3*b^5*d^2*e^4*n)*a^2 - (b^3*c^3*d^6*n - 3*b^4*c^2*d^5*e*n + 3*b^5*c*d^4*e^2*n - b^6*d^3*e^3*n)*a)*x^n), x)","F",0
80,0,0,0,0.000000," ","integrate((d+e*x^n)^3/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""maxima"")","\frac{{\left(b^{3} c^{2} d^{3} {\left(2 \, n - 1\right)} + 4 \, a^{3} c^{2} e^{3} {\left(n + 1\right)} + {\left(12 \, c^{3} d^{2} e {\left(3 \, n - 1\right)} + b^{2} c e^{3} {\left(2 \, n - 1\right)} - 18 \, b c^{2} d e^{2} n\right)} a^{2} - {\left(2 \, b c^{3} d^{3} {\left(7 \, n - 2\right)} - 3 \, b^{2} c^{2} d^{2} e\right)} a\right)} x x^{3 \, n} + {\left(2 \, b^{4} c d^{3} {\left(2 \, n - 1\right)} + 2 \, {\left(b c e^{3} {\left(3 \, n + 2\right)} + 6 \, c^{2} d e^{2}\right)} a^{3} - {\left(3 \, b^{2} c d e^{2} {\left(9 \, n + 1\right)} - 6 \, b c^{2} d^{2} e {\left(9 \, n - 4\right)} - 4 \, c^{3} d^{3} {\left(4 \, n - 1\right)} - b^{3} e^{3} {\left(3 \, n - 1\right)}\right)} a^{2} - {\left(b^{2} c^{2} d^{3} {\left(29 \, n - 9\right)} - 6 \, b^{3} c d^{2} e\right)} a\right)} x x^{2 \, n} + {\left(b^{5} d^{3} {\left(2 \, n - 1\right)} - 4 \, a^{4} c e^{3} {\left(n - 1\right)} + {\left(b^{2} e^{3} {\left(10 \, n - 1\right)} + 12 \, c^{2} d^{2} e {\left(5 \, n - 1\right)} - 6 \, b c d e^{2} {\left(5 \, n - 2\right)}\right)} a^{3} + {\left(3 \, b^{2} c d^{2} e {\left(4 \, n - 3\right)} - 3 \, b^{3} d e^{2} {\left(2 \, n + 1\right)} - 2 \, b c^{2} d^{3} n\right)} a^{2} - {\left(4 \, b^{3} c d^{3} {\left(3 \, n - 1\right)} - 3 \, b^{4} d^{2} e\right)} a\right)} x x^{n} + {\left(a b^{4} d^{3} {\left(3 \, n - 1\right)} - 6 \, {\left(2 \, c d e^{2} {\left(2 \, n - 1\right)} - b e^{3} n\right)} a^{4} + {\left(4 \, c^{2} d^{3} {\left(6 \, n - 1\right)} + 6 \, b c d^{2} e {\left(5 \, n - 2\right)} - 3 \, b^{2} d e^{2} {\left(n + 1\right)}\right)} a^{3} - {\left(b^{2} c d^{3} {\left(21 \, n - 5\right)} + 3 \, b^{3} d^{2} e {\left(n - 1\right)}\right)} a^{2}\right)} x}{2 \, {\left(a^{4} b^{4} n^{2} - 8 \, a^{5} b^{2} c n^{2} + 16 \, a^{6} c^{2} n^{2} + {\left(a^{2} b^{4} c^{2} n^{2} - 8 \, a^{3} b^{2} c^{3} n^{2} + 16 \, a^{4} c^{4} n^{2}\right)} x^{4 \, n} + 2 \, {\left(a^{2} b^{5} c n^{2} - 8 \, a^{3} b^{3} c^{2} n^{2} + 16 \, a^{4} b c^{3} n^{2}\right)} x^{3 \, n} + {\left(a^{2} b^{6} n^{2} - 6 \, a^{3} b^{4} c n^{2} + 32 \, a^{5} c^{3} n^{2}\right)} x^{2 \, n} + 2 \, {\left(a^{3} b^{5} n^{2} - 8 \, a^{4} b^{3} c n^{2} + 16 \, a^{5} b c^{2} n^{2}\right)} x^{n}\right)}} + \int \frac{{\left(2 \, n^{2} - 3 \, n + 1\right)} b^{4} d^{3} + 6 \, {\left(2 \, c d e^{2} {\left(2 \, n - 1\right)} - b e^{3} n\right)} a^{3} + {\left(4 \, {\left(8 \, n^{2} - 6 \, n + 1\right)} c^{2} d^{3} - 6 \, b c d^{2} e {\left(5 \, n - 2\right)} + 3 \, b^{2} d e^{2} {\left(n + 1\right)}\right)} a^{2} - {\left({\left(16 \, n^{2} - 21 \, n + 5\right)} b^{2} c d^{3} - 3 \, b^{3} d^{2} e {\left(n - 1\right)}\right)} a + {\left({\left(2 \, n^{2} - 3 \, n + 1\right)} b^{3} c d^{3} + 4 \, {\left(n^{2} - 1\right)} a^{3} c e^{3} + {\left(12 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} c^{2} d^{2} e - 18 \, {\left(n^{2} - n\right)} b c d e^{2} + {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{2} e^{3}\right)} a^{2} - {\left(2 \, {\left(7 \, n^{2} - 9 \, n + 2\right)} b c^{2} d^{3} - 3 \, b^{2} c d^{2} e {\left(n - 1\right)}\right)} a\right)} x^{n}}{2 \, {\left(a^{3} b^{4} n^{2} - 8 \, a^{4} b^{2} c n^{2} + 16 \, a^{5} c^{2} n^{2} + {\left(a^{2} b^{4} c n^{2} - 8 \, a^{3} b^{2} c^{2} n^{2} + 16 \, a^{4} c^{3} n^{2}\right)} x^{2 \, n} + {\left(a^{2} b^{5} n^{2} - 8 \, a^{3} b^{3} c n^{2} + 16 \, a^{4} b c^{2} n^{2}\right)} x^{n}\right)}}\,{d x}"," ",0,"1/2*((b^3*c^2*d^3*(2*n - 1) + 4*a^3*c^2*e^3*(n + 1) + (12*c^3*d^2*e*(3*n - 1) + b^2*c*e^3*(2*n - 1) - 18*b*c^2*d*e^2*n)*a^2 - (2*b*c^3*d^3*(7*n - 2) - 3*b^2*c^2*d^2*e)*a)*x*x^(3*n) + (2*b^4*c*d^3*(2*n - 1) + 2*(b*c*e^3*(3*n + 2) + 6*c^2*d*e^2)*a^3 - (3*b^2*c*d*e^2*(9*n + 1) - 6*b*c^2*d^2*e*(9*n - 4) - 4*c^3*d^3*(4*n - 1) - b^3*e^3*(3*n - 1))*a^2 - (b^2*c^2*d^3*(29*n - 9) - 6*b^3*c*d^2*e)*a)*x*x^(2*n) + (b^5*d^3*(2*n - 1) - 4*a^4*c*e^3*(n - 1) + (b^2*e^3*(10*n - 1) + 12*c^2*d^2*e*(5*n - 1) - 6*b*c*d*e^2*(5*n - 2))*a^3 + (3*b^2*c*d^2*e*(4*n - 3) - 3*b^3*d*e^2*(2*n + 1) - 2*b*c^2*d^3*n)*a^2 - (4*b^3*c*d^3*(3*n - 1) - 3*b^4*d^2*e)*a)*x*x^n + (a*b^4*d^3*(3*n - 1) - 6*(2*c*d*e^2*(2*n - 1) - b*e^3*n)*a^4 + (4*c^2*d^3*(6*n - 1) + 6*b*c*d^2*e*(5*n - 2) - 3*b^2*d*e^2*(n + 1))*a^3 - (b^2*c*d^3*(21*n - 5) + 3*b^3*d^2*e*(n - 1))*a^2)*x)/(a^4*b^4*n^2 - 8*a^5*b^2*c*n^2 + 16*a^6*c^2*n^2 + (a^2*b^4*c^2*n^2 - 8*a^3*b^2*c^3*n^2 + 16*a^4*c^4*n^2)*x^(4*n) + 2*(a^2*b^5*c*n^2 - 8*a^3*b^3*c^2*n^2 + 16*a^4*b*c^3*n^2)*x^(3*n) + (a^2*b^6*n^2 - 6*a^3*b^4*c*n^2 + 32*a^5*c^3*n^2)*x^(2*n) + 2*(a^3*b^5*n^2 - 8*a^4*b^3*c*n^2 + 16*a^5*b*c^2*n^2)*x^n) + integrate(1/2*((2*n^2 - 3*n + 1)*b^4*d^3 + 6*(2*c*d*e^2*(2*n - 1) - b*e^3*n)*a^3 + (4*(8*n^2 - 6*n + 1)*c^2*d^3 - 6*b*c*d^2*e*(5*n - 2) + 3*b^2*d*e^2*(n + 1))*a^2 - ((16*n^2 - 21*n + 5)*b^2*c*d^3 - 3*b^3*d^2*e*(n - 1))*a + ((2*n^2 - 3*n + 1)*b^3*c*d^3 + 4*(n^2 - 1)*a^3*c*e^3 + (12*(3*n^2 - 4*n + 1)*c^2*d^2*e - 18*(n^2 - n)*b*c*d*e^2 + (2*n^2 - 3*n + 1)*b^2*e^3)*a^2 - (2*(7*n^2 - 9*n + 2)*b*c^2*d^3 - 3*b^2*c*d^2*e*(n - 1))*a)*x^n)/(a^3*b^4*n^2 - 8*a^4*b^2*c*n^2 + 16*a^5*c^2*n^2 + (a^2*b^4*c*n^2 - 8*a^3*b^2*c^2*n^2 + 16*a^4*c^3*n^2)*x^(2*n) + (a^2*b^5*n^2 - 8*a^3*b^3*c*n^2 + 16*a^4*b*c^2*n^2)*x^n), x)","F",0
81,0,0,0,0.000000," ","integrate((d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""maxima"")","\frac{{\left(b^{3} c^{2} d^{2} {\left(2 \, n - 1\right)} + 2 \, {\left(4 \, c^{3} d e {\left(3 \, n - 1\right)} - 3 \, b c^{2} e^{2} n\right)} a^{2} - 2 \, {\left(b c^{3} d^{2} {\left(7 \, n - 2\right)} - b^{2} c^{2} d e\right)} a\right)} x x^{3 \, n} + {\left(2 \, b^{4} c d^{2} {\left(2 \, n - 1\right)} + 4 \, a^{3} c^{2} e^{2} - {\left(b^{2} c e^{2} {\left(9 \, n + 1\right)} - 4 \, b c^{2} d e {\left(9 \, n - 4\right)} - 4 \, c^{3} d^{2} {\left(4 \, n - 1\right)}\right)} a^{2} - {\left(b^{2} c^{2} d^{2} {\left(29 \, n - 9\right)} - 4 \, b^{3} c d e\right)} a\right)} x x^{2 \, n} + {\left(b^{5} d^{2} {\left(2 \, n - 1\right)} + 2 \, {\left(4 \, c^{2} d e {\left(5 \, n - 1\right)} - b c e^{2} {\left(5 \, n - 2\right)}\right)} a^{3} + {\left(2 \, b^{2} c d e {\left(4 \, n - 3\right)} - b^{3} e^{2} {\left(2 \, n + 1\right)} - 2 \, b c^{2} d^{2} n\right)} a^{2} - 2 \, {\left(2 \, b^{3} c d^{2} {\left(3 \, n - 1\right)} - b^{4} d e\right)} a\right)} x x^{n} + {\left(a b^{4} d^{2} {\left(3 \, n - 1\right)} - 4 \, a^{4} c e^{2} {\left(2 \, n - 1\right)} + {\left(4 \, c^{2} d^{2} {\left(6 \, n - 1\right)} + 4 \, b c d e {\left(5 \, n - 2\right)} - b^{2} e^{2} {\left(n + 1\right)}\right)} a^{3} - {\left(b^{2} c d^{2} {\left(21 \, n - 5\right)} + 2 \, b^{3} d e {\left(n - 1\right)}\right)} a^{2}\right)} x}{2 \, {\left(a^{4} b^{4} n^{2} - 8 \, a^{5} b^{2} c n^{2} + 16 \, a^{6} c^{2} n^{2} + {\left(a^{2} b^{4} c^{2} n^{2} - 8 \, a^{3} b^{2} c^{3} n^{2} + 16 \, a^{4} c^{4} n^{2}\right)} x^{4 \, n} + 2 \, {\left(a^{2} b^{5} c n^{2} - 8 \, a^{3} b^{3} c^{2} n^{2} + 16 \, a^{4} b c^{3} n^{2}\right)} x^{3 \, n} + {\left(a^{2} b^{6} n^{2} - 6 \, a^{3} b^{4} c n^{2} + 32 \, a^{5} c^{3} n^{2}\right)} x^{2 \, n} + 2 \, {\left(a^{3} b^{5} n^{2} - 8 \, a^{4} b^{3} c n^{2} + 16 \, a^{5} b c^{2} n^{2}\right)} x^{n}\right)}} - \int -\frac{{\left(2 \, n^{2} - 3 \, n + 1\right)} b^{4} d^{2} + 4 \, a^{3} c e^{2} {\left(2 \, n - 1\right)} + {\left(4 \, {\left(8 \, n^{2} - 6 \, n + 1\right)} c^{2} d^{2} - 4 \, b c d e {\left(5 \, n - 2\right)} + b^{2} e^{2} {\left(n + 1\right)}\right)} a^{2} - {\left({\left(16 \, n^{2} - 21 \, n + 5\right)} b^{2} c d^{2} - 2 \, b^{3} d e {\left(n - 1\right)}\right)} a + {\left({\left(2 \, n^{2} - 3 \, n + 1\right)} b^{3} c d^{2} + 2 \, {\left(4 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} c^{2} d e - 3 \, {\left(n^{2} - n\right)} b c e^{2}\right)} a^{2} - 2 \, {\left({\left(7 \, n^{2} - 9 \, n + 2\right)} b c^{2} d^{2} - b^{2} c d e {\left(n - 1\right)}\right)} a\right)} x^{n}}{2 \, {\left(a^{3} b^{4} n^{2} - 8 \, a^{4} b^{2} c n^{2} + 16 \, a^{5} c^{2} n^{2} + {\left(a^{2} b^{4} c n^{2} - 8 \, a^{3} b^{2} c^{2} n^{2} + 16 \, a^{4} c^{3} n^{2}\right)} x^{2 \, n} + {\left(a^{2} b^{5} n^{2} - 8 \, a^{3} b^{3} c n^{2} + 16 \, a^{4} b c^{2} n^{2}\right)} x^{n}\right)}}\,{d x}"," ",0,"1/2*((b^3*c^2*d^2*(2*n - 1) + 2*(4*c^3*d*e*(3*n - 1) - 3*b*c^2*e^2*n)*a^2 - 2*(b*c^3*d^2*(7*n - 2) - b^2*c^2*d*e)*a)*x*x^(3*n) + (2*b^4*c*d^2*(2*n - 1) + 4*a^3*c^2*e^2 - (b^2*c*e^2*(9*n + 1) - 4*b*c^2*d*e*(9*n - 4) - 4*c^3*d^2*(4*n - 1))*a^2 - (b^2*c^2*d^2*(29*n - 9) - 4*b^3*c*d*e)*a)*x*x^(2*n) + (b^5*d^2*(2*n - 1) + 2*(4*c^2*d*e*(5*n - 1) - b*c*e^2*(5*n - 2))*a^3 + (2*b^2*c*d*e*(4*n - 3) - b^3*e^2*(2*n + 1) - 2*b*c^2*d^2*n)*a^2 - 2*(2*b^3*c*d^2*(3*n - 1) - b^4*d*e)*a)*x*x^n + (a*b^4*d^2*(3*n - 1) - 4*a^4*c*e^2*(2*n - 1) + (4*c^2*d^2*(6*n - 1) + 4*b*c*d*e*(5*n - 2) - b^2*e^2*(n + 1))*a^3 - (b^2*c*d^2*(21*n - 5) + 2*b^3*d*e*(n - 1))*a^2)*x)/(a^4*b^4*n^2 - 8*a^5*b^2*c*n^2 + 16*a^6*c^2*n^2 + (a^2*b^4*c^2*n^2 - 8*a^3*b^2*c^3*n^2 + 16*a^4*c^4*n^2)*x^(4*n) + 2*(a^2*b^5*c*n^2 - 8*a^3*b^3*c^2*n^2 + 16*a^4*b*c^3*n^2)*x^(3*n) + (a^2*b^6*n^2 - 6*a^3*b^4*c*n^2 + 32*a^5*c^3*n^2)*x^(2*n) + 2*(a^3*b^5*n^2 - 8*a^4*b^3*c*n^2 + 16*a^5*b*c^2*n^2)*x^n) - integrate(-1/2*((2*n^2 - 3*n + 1)*b^4*d^2 + 4*a^3*c*e^2*(2*n - 1) + (4*(8*n^2 - 6*n + 1)*c^2*d^2 - 4*b*c*d*e*(5*n - 2) + b^2*e^2*(n + 1))*a^2 - ((16*n^2 - 21*n + 5)*b^2*c*d^2 - 2*b^3*d*e*(n - 1))*a + ((2*n^2 - 3*n + 1)*b^3*c*d^2 + 2*(4*(3*n^2 - 4*n + 1)*c^2*d*e - 3*(n^2 - n)*b*c*e^2)*a^2 - 2*((7*n^2 - 9*n + 2)*b*c^2*d^2 - b^2*c*d*e*(n - 1))*a)*x^n)/(a^3*b^4*n^2 - 8*a^4*b^2*c*n^2 + 16*a^5*c^2*n^2 + (a^2*b^4*c*n^2 - 8*a^3*b^2*c^2*n^2 + 16*a^4*c^3*n^2)*x^(2*n) + (a^2*b^5*n^2 - 8*a^3*b^3*c*n^2 + 16*a^4*b*c^2*n^2)*x^n), x)","F",0
82,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""maxima"")","\frac{{\left(4 \, a^{2} c^{3} e {\left(3 \, n - 1\right)} + b^{3} c^{2} d {\left(2 \, n - 1\right)} - {\left(2 \, b c^{3} d {\left(7 \, n - 2\right)} - b^{2} c^{2} e\right)} a\right)} x x^{3 \, n} + {\left(2 \, b^{4} c d {\left(2 \, n - 1\right)} + 2 \, {\left(b c^{2} e {\left(9 \, n - 4\right)} + 2 \, c^{3} d {\left(4 \, n - 1\right)}\right)} a^{2} - {\left(b^{2} c^{2} d {\left(29 \, n - 9\right)} - 2 \, b^{3} c e\right)} a\right)} x x^{2 \, n} + {\left(4 \, a^{3} c^{2} e {\left(5 \, n - 1\right)} + b^{5} d {\left(2 \, n - 1\right)} + {\left(b^{2} c e {\left(4 \, n - 3\right)} - 2 \, b c^{2} d n\right)} a^{2} - {\left(4 \, b^{3} c d {\left(3 \, n - 1\right)} - b^{4} e\right)} a\right)} x x^{n} + {\left(a b^{4} d {\left(3 \, n - 1\right)} + 2 \, {\left(2 \, c^{2} d {\left(6 \, n - 1\right)} + b c e {\left(5 \, n - 2\right)}\right)} a^{3} - {\left(b^{2} c d {\left(21 \, n - 5\right)} + b^{3} e {\left(n - 1\right)}\right)} a^{2}\right)} x}{2 \, {\left(a^{4} b^{4} n^{2} - 8 \, a^{5} b^{2} c n^{2} + 16 \, a^{6} c^{2} n^{2} + {\left(a^{2} b^{4} c^{2} n^{2} - 8 \, a^{3} b^{2} c^{3} n^{2} + 16 \, a^{4} c^{4} n^{2}\right)} x^{4 \, n} + 2 \, {\left(a^{2} b^{5} c n^{2} - 8 \, a^{3} b^{3} c^{2} n^{2} + 16 \, a^{4} b c^{3} n^{2}\right)} x^{3 \, n} + {\left(a^{2} b^{6} n^{2} - 6 \, a^{3} b^{4} c n^{2} + 32 \, a^{5} c^{3} n^{2}\right)} x^{2 \, n} + 2 \, {\left(a^{3} b^{5} n^{2} - 8 \, a^{4} b^{3} c n^{2} + 16 \, a^{5} b c^{2} n^{2}\right)} x^{n}\right)}} + \int \frac{{\left(2 \, n^{2} - 3 \, n + 1\right)} b^{4} d + 2 \, {\left(2 \, {\left(8 \, n^{2} - 6 \, n + 1\right)} c^{2} d - b c e {\left(5 \, n - 2\right)}\right)} a^{2} - {\left({\left(16 \, n^{2} - 21 \, n + 5\right)} b^{2} c d - b^{3} e {\left(n - 1\right)}\right)} a + {\left({\left(2 \, n^{2} - 3 \, n + 1\right)} b^{3} c d + 4 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} a^{2} c^{2} e - {\left(2 \, {\left(7 \, n^{2} - 9 \, n + 2\right)} b c^{2} d - b^{2} c e {\left(n - 1\right)}\right)} a\right)} x^{n}}{2 \, {\left(a^{3} b^{4} n^{2} - 8 \, a^{4} b^{2} c n^{2} + 16 \, a^{5} c^{2} n^{2} + {\left(a^{2} b^{4} c n^{2} - 8 \, a^{3} b^{2} c^{2} n^{2} + 16 \, a^{4} c^{3} n^{2}\right)} x^{2 \, n} + {\left(a^{2} b^{5} n^{2} - 8 \, a^{3} b^{3} c n^{2} + 16 \, a^{4} b c^{2} n^{2}\right)} x^{n}\right)}}\,{d x}"," ",0,"1/2*((4*a^2*c^3*e*(3*n - 1) + b^3*c^2*d*(2*n - 1) - (2*b*c^3*d*(7*n - 2) - b^2*c^2*e)*a)*x*x^(3*n) + (2*b^4*c*d*(2*n - 1) + 2*(b*c^2*e*(9*n - 4) + 2*c^3*d*(4*n - 1))*a^2 - (b^2*c^2*d*(29*n - 9) - 2*b^3*c*e)*a)*x*x^(2*n) + (4*a^3*c^2*e*(5*n - 1) + b^5*d*(2*n - 1) + (b^2*c*e*(4*n - 3) - 2*b*c^2*d*n)*a^2 - (4*b^3*c*d*(3*n - 1) - b^4*e)*a)*x*x^n + (a*b^4*d*(3*n - 1) + 2*(2*c^2*d*(6*n - 1) + b*c*e*(5*n - 2))*a^3 - (b^2*c*d*(21*n - 5) + b^3*e*(n - 1))*a^2)*x)/(a^4*b^4*n^2 - 8*a^5*b^2*c*n^2 + 16*a^6*c^2*n^2 + (a^2*b^4*c^2*n^2 - 8*a^3*b^2*c^3*n^2 + 16*a^4*c^4*n^2)*x^(4*n) + 2*(a^2*b^5*c*n^2 - 8*a^3*b^3*c^2*n^2 + 16*a^4*b*c^3*n^2)*x^(3*n) + (a^2*b^6*n^2 - 6*a^3*b^4*c*n^2 + 32*a^5*c^3*n^2)*x^(2*n) + 2*(a^3*b^5*n^2 - 8*a^4*b^3*c*n^2 + 16*a^5*b*c^2*n^2)*x^n) + integrate(1/2*((2*n^2 - 3*n + 1)*b^4*d + 2*(2*(8*n^2 - 6*n + 1)*c^2*d - b*c*e*(5*n - 2))*a^2 - ((16*n^2 - 21*n + 5)*b^2*c*d - b^3*e*(n - 1))*a + ((2*n^2 - 3*n + 1)*b^3*c*d + 4*(3*n^2 - 4*n + 1)*a^2*c^2*e - (2*(7*n^2 - 9*n + 2)*b*c^2*d - b^2*c*e*(n - 1))*a)*x^n)/(a^3*b^4*n^2 - 8*a^4*b^2*c*n^2 + 16*a^5*c^2*n^2 + (a^2*b^4*c*n^2 - 8*a^3*b^2*c^2*n^2 + 16*a^4*c^3*n^2)*x^(2*n) + (a^2*b^5*n^2 - 8*a^3*b^3*c*n^2 + 16*a^4*b*c^2*n^2)*x^n), x)","F",0
83,0,0,0,0.000000," ","integrate(1/(d+e*x^n)/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""maxima"")","e^{6} \int \frac{1}{c^{3} d^{7} - 3 \, b c^{2} d^{6} e + 3 \, b^{2} c d^{5} e^{2} - b^{3} d^{4} e^{3} + a^{3} d e^{6} + 3 \, {\left(c d^{3} e^{4} - b d^{2} e^{5}\right)} a^{2} + 3 \, {\left(c^{2} d^{5} e^{2} - 2 \, b c d^{4} e^{3} + b^{2} d^{3} e^{4}\right)} a + {\left(c^{3} d^{6} e - 3 \, b c^{2} d^{5} e^{2} + 3 \, b^{2} c d^{4} e^{3} - b^{3} d^{3} e^{4} + a^{3} e^{7} + 3 \, {\left(c d^{2} e^{5} - b d e^{6}\right)} a^{2} + 3 \, {\left(c^{2} d^{4} e^{3} - 2 \, b c d^{3} e^{4} + b^{2} d^{2} e^{5}\right)} a\right)} x^{n}}\,{d x} - \frac{{\left(4 \, a^{3} c^{4} e^{3} {\left(7 \, n - 1\right)} - b^{3} c^{4} d^{3} {\left(2 \, n - 1\right)} + 2 \, b^{4} c^{3} d^{2} e {\left(2 \, n - 1\right)} - b^{5} c^{2} d e^{2} {\left(2 \, n - 1\right)} - {\left(b^{2} c^{3} e^{3} {\left(26 \, n - 5\right)} - 4 \, c^{5} d^{2} e {\left(3 \, n - 1\right)} - 10 \, b c^{4} d e^{2} n\right)} a^{2} - {\left(b^{2} c^{4} d^{2} e {\left(28 \, n - 9\right)} - 2 \, b c^{5} d^{3} {\left(7 \, n - 2\right)} - 2 \, b^{3} c^{3} d e^{2} {\left(5 \, n - 2\right)} - b^{4} c^{2} e^{3} {\left(4 \, n - 1\right)}\right)} a\right)} x x^{3 \, n} - {\left(2 \, b^{4} c^{3} d^{3} {\left(2 \, n - 1\right)} - 4 \, b^{5} c^{2} d^{2} e {\left(2 \, n - 1\right)} + 2 \, b^{6} c d e^{2} {\left(2 \, n - 1\right)} - 2 \, {\left(b c^{3} e^{3} {\left(37 \, n - 6\right)} - 2 \, c^{4} d e^{2} {\left(8 \, n - 1\right)}\right)} a^{3} - {\left(2 \, b c^{4} d^{2} e {\left(25 \, n - 8\right)} + 3 \, b^{2} c^{3} d e^{2} {\left(5 \, n + 1\right)} - 11 \, b^{3} c^{2} e^{3} {\left(5 \, n - 1\right)} - 4 \, c^{5} d^{3} {\left(4 \, n - 1\right)}\right)} a^{2} - {\left(b^{2} c^{4} d^{3} {\left(29 \, n - 9\right)} - 2 \, b^{3} c^{3} d^{2} e {\left(29 \, n - 10\right)} + 3 \, b^{4} c^{2} d e^{2} {\left(7 \, n - 3\right)} + 2 \, b^{5} c e^{3} {\left(4 \, n - 1\right)}\right)} a\right)} x x^{2 \, n} + {\left(4 \, a^{4} c^{3} e^{3} {\left(9 \, n - 1\right)} - b^{5} c^{2} d^{3} {\left(2 \, n - 1\right)} + 2 \, b^{6} c d^{2} e {\left(2 \, n - 1\right)} - b^{7} d e^{2} {\left(2 \, n - 1\right)} + {\left(b^{2} c^{2} e^{3} {\left(14 \, n - 3\right)} - 2 \, b c^{3} d e^{2} {\left(13 \, n - 2\right)} + 4 \, c^{4} d^{2} e {\left(5 \, n - 1\right)}\right)} a^{3} - {\left(b^{4} c e^{3} {\left(24 \, n - 5\right)} - b^{3} c^{2} d e^{2} {\left(20 \, n - 1\right)} - 2 \, b c^{4} d^{3} n + 3 \, b^{2} c^{3} d^{2} e\right)} a^{2} - {\left(3 \, b^{4} c^{2} d^{2} e {\left(8 \, n - 3\right)} - b^{6} e^{3} {\left(4 \, n - 1\right)} - 4 \, b^{3} c^{3} d^{3} {\left(3 \, n - 1\right)} - 4 \, b^{5} c d e^{2} {\left(2 \, n - 1\right)}\right)} a\right)} x x^{n} + {\left(2 \, {\left(b c^{2} e^{3} {\left(29 \, n - 4\right)} - 2 \, c^{3} d e^{2} {\left(10 \, n - 1\right)}\right)} a^{4} + {\left(2 \, b c^{3} d^{2} e {\left(29 \, n - 6\right)} - 4 \, c^{4} d^{3} {\left(6 \, n - 1\right)} - 6 \, b^{3} c e^{3} {\left(6 \, n - 1\right)} - b^{2} c^{2} d e^{2} {\left(n - 3\right)}\right)} a^{3} - {\left(b^{3} c^{2} d^{2} e {\left(43 \, n - 11\right)} - b^{2} c^{3} d^{3} {\left(21 \, n - 5\right)} - b^{4} c d e^{2} {\left(17 \, n - 5\right)} - b^{5} e^{3} {\left(5 \, n - 1\right)}\right)} a^{2} - {\left(b^{4} c^{2} d^{3} {\left(3 \, n - 1\right)} - 2 \, b^{5} c d^{2} e {\left(3 \, n - 1\right)} + b^{6} d e^{2} {\left(3 \, n - 1\right)}\right)} a\right)} x}{2 \, {\left(16 \, a^{8} c^{2} e^{4} n^{2} + 8 \, {\left(4 \, c^{3} d^{2} e^{2} n^{2} - 4 \, b c^{2} d e^{3} n^{2} - b^{2} c e^{4} n^{2}\right)} a^{7} + {\left(16 \, c^{4} d^{4} n^{2} - 32 \, b c^{3} d^{3} e n^{2} + 16 \, b^{3} c d e^{3} n^{2} + b^{4} e^{4} n^{2}\right)} a^{6} - 2 \, {\left(4 \, b^{2} c^{3} d^{4} n^{2} - 8 \, b^{3} c^{2} d^{3} e n^{2} + 3 \, b^{4} c d^{2} e^{2} n^{2} + b^{5} d e^{3} n^{2}\right)} a^{5} + {\left(b^{4} c^{2} d^{4} n^{2} - 2 \, b^{5} c d^{3} e n^{2} + b^{6} d^{2} e^{2} n^{2}\right)} a^{4} + {\left(16 \, a^{6} c^{4} e^{4} n^{2} + 8 \, {\left(4 \, c^{5} d^{2} e^{2} n^{2} - 4 \, b c^{4} d e^{3} n^{2} - b^{2} c^{3} e^{4} n^{2}\right)} a^{5} + {\left(16 \, c^{6} d^{4} n^{2} - 32 \, b c^{5} d^{3} e n^{2} + 16 \, b^{3} c^{3} d e^{3} n^{2} + b^{4} c^{2} e^{4} n^{2}\right)} a^{4} - 2 \, {\left(4 \, b^{2} c^{5} d^{4} n^{2} - 8 \, b^{3} c^{4} d^{3} e n^{2} + 3 \, b^{4} c^{3} d^{2} e^{2} n^{2} + b^{5} c^{2} d e^{3} n^{2}\right)} a^{3} + {\left(b^{4} c^{4} d^{4} n^{2} - 2 \, b^{5} c^{3} d^{3} e n^{2} + b^{6} c^{2} d^{2} e^{2} n^{2}\right)} a^{2}\right)} x^{4 \, n} + 2 \, {\left(16 \, a^{6} b c^{3} e^{4} n^{2} + 8 \, {\left(4 \, b c^{4} d^{2} e^{2} n^{2} - 4 \, b^{2} c^{3} d e^{3} n^{2} - b^{3} c^{2} e^{4} n^{2}\right)} a^{5} + {\left(16 \, b c^{5} d^{4} n^{2} - 32 \, b^{2} c^{4} d^{3} e n^{2} + 16 \, b^{4} c^{2} d e^{3} n^{2} + b^{5} c e^{4} n^{2}\right)} a^{4} - 2 \, {\left(4 \, b^{3} c^{4} d^{4} n^{2} - 8 \, b^{4} c^{3} d^{3} e n^{2} + 3 \, b^{5} c^{2} d^{2} e^{2} n^{2} + b^{6} c d e^{3} n^{2}\right)} a^{3} + {\left(b^{5} c^{3} d^{4} n^{2} - 2 \, b^{6} c^{2} d^{3} e n^{2} + b^{7} c d^{2} e^{2} n^{2}\right)} a^{2}\right)} x^{3 \, n} + {\left(32 \, a^{7} c^{3} e^{4} n^{2} + 64 \, {\left(c^{4} d^{2} e^{2} n^{2} - b c^{3} d e^{3} n^{2}\right)} a^{6} + 2 \, {\left(16 \, c^{5} d^{4} n^{2} - 32 \, b c^{4} d^{3} e n^{2} + 16 \, b^{2} c^{3} d^{2} e^{2} n^{2} - 3 \, b^{4} c e^{4} n^{2}\right)} a^{5} - {\left(12 \, b^{4} c^{2} d^{2} e^{2} n^{2} - 12 \, b^{5} c d e^{3} n^{2} - b^{6} e^{4} n^{2}\right)} a^{4} - 2 \, {\left(3 \, b^{4} c^{3} d^{4} n^{2} - 6 \, b^{5} c^{2} d^{3} e n^{2} + 2 \, b^{6} c d^{2} e^{2} n^{2} + b^{7} d e^{3} n^{2}\right)} a^{3} + {\left(b^{6} c^{2} d^{4} n^{2} - 2 \, b^{7} c d^{3} e n^{2} + b^{8} d^{2} e^{2} n^{2}\right)} a^{2}\right)} x^{2 \, n} + 2 \, {\left(16 \, a^{7} b c^{2} e^{4} n^{2} + 8 \, {\left(4 \, b c^{3} d^{2} e^{2} n^{2} - 4 \, b^{2} c^{2} d e^{3} n^{2} - b^{3} c e^{4} n^{2}\right)} a^{6} + {\left(16 \, b c^{4} d^{4} n^{2} - 32 \, b^{2} c^{3} d^{3} e n^{2} + 16 \, b^{4} c d e^{3} n^{2} + b^{5} e^{4} n^{2}\right)} a^{5} - 2 \, {\left(4 \, b^{3} c^{3} d^{4} n^{2} - 8 \, b^{4} c^{2} d^{3} e n^{2} + 3 \, b^{5} c d^{2} e^{2} n^{2} + b^{6} d e^{3} n^{2}\right)} a^{4} + {\left(b^{5} c^{2} d^{4} n^{2} - 2 \, b^{6} c d^{3} e n^{2} + b^{7} d^{2} e^{2} n^{2}\right)} a^{3}\right)} x^{n}\right)}} - \int -\frac{{\left(2 \, n^{2} - 3 \, n + 1\right)} b^{4} c^{3} d^{5} - 3 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{5} c^{2} d^{4} e + 3 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{6} c d^{3} e^{2} - {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{7} d^{2} e^{3} + 2 \, {\left(2 \, {\left(24 \, n^{2} - 10 \, n + 1\right)} c^{3} d e^{4} - {\left(48 \, n^{2} - 29 \, n + 4\right)} b c^{2} e^{5}\right)} a^{4} + {\left(8 \, {\left(12 \, n^{2} - 8 \, n + 1\right)} c^{4} d^{3} e^{2} - 12 \, {\left(16 \, n^{2} - 13 \, n + 2\right)} b c^{3} d^{2} e^{3} + {\left(48 \, n^{2} - 59 \, n + 11\right)} b^{2} c^{2} d e^{4} + 6 \, {\left(8 \, n^{2} - 6 \, n + 1\right)} b^{3} c e^{5}\right)} a^{3} + {\left(4 \, {\left(8 \, n^{2} - 6 \, n + 1\right)} c^{5} d^{5} - 2 \, {\left(48 \, n^{2} - 41 \, n + 8\right)} b c^{4} d^{4} e + 2 \, {\left(24 \, n^{2} - 19 \, n + 5\right)} b^{2} c^{3} d^{3} e^{2} + 2 \, {\left(32 \, n^{2} - 39 \, n + 7\right)} b^{3} c^{2} d^{2} e^{3} - {\left(42 \, n^{2} - 53 \, n + 11\right)} b^{4} c d e^{4} - {\left(6 \, n^{2} - 5 \, n + 1\right)} b^{5} e^{5}\right)} a^{2} - {\left({\left(16 \, n^{2} - 21 \, n + 5\right)} b^{2} c^{4} d^{5} - 16 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} b^{3} c^{3} d^{4} e + 3 \, {\left(14 \, n^{2} - 19 \, n + 5\right)} b^{4} c^{2} d^{3} e^{2} - 2 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{5} c d^{2} e^{3} - 2 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} b^{6} d e^{4}\right)} a + {\left({\left(2 \, n^{2} - 3 \, n + 1\right)} b^{3} c^{4} d^{5} - 3 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{4} c^{3} d^{4} e + 3 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{5} c^{2} d^{3} e^{2} - {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{6} c d^{2} e^{3} - 4 \, {\left(15 \, n^{2} - 8 \, n + 1\right)} a^{4} c^{3} e^{5} - {\left(8 \, {\left(5 \, n^{2} - 6 \, n + 1\right)} c^{4} d^{2} e^{3} - 2 \, {\left(9 \, n^{2} - 11 \, n + 2\right)} b c^{3} d e^{4} - {\left(42 \, n^{2} - 31 \, n + 5\right)} b^{2} c^{2} e^{5}\right)} a^{3} - {\left(4 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} c^{5} d^{4} e + 12 \, {\left(n^{2} - n\right)} b c^{4} d^{3} e^{2} - 2 \, {\left(32 \, n^{2} - 39 \, n + 7\right)} b^{2} c^{3} d^{2} e^{3} + 9 \, {\left(4 \, n^{2} - 5 \, n + 1\right)} b^{3} c^{2} d e^{4} + {\left(6 \, n^{2} - 5 \, n + 1\right)} b^{4} c e^{5}\right)} a^{2} - {\left(2 \, {\left(7 \, n^{2} - 9 \, n + 2\right)} b c^{5} d^{5} - {\left(42 \, n^{2} - 55 \, n + 13\right)} b^{2} c^{4} d^{4} e + 12 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} b^{3} c^{3} d^{3} e^{2} - {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{4} c^{2} d^{2} e^{3} - 2 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} b^{5} c d e^{4}\right)} a\right)} x^{n}}{2 \, {\left(16 \, a^{8} c^{2} e^{6} n^{2} + 8 \, {\left(6 \, c^{3} d^{2} e^{4} n^{2} - 6 \, b c^{2} d e^{5} n^{2} - b^{2} c e^{6} n^{2}\right)} a^{7} + {\left(48 \, c^{4} d^{4} e^{2} n^{2} - 96 \, b c^{3} d^{3} e^{3} n^{2} + 24 \, b^{2} c^{2} d^{2} e^{4} n^{2} + 24 \, b^{3} c d e^{5} n^{2} + b^{4} e^{6} n^{2}\right)} a^{6} + {\left(16 \, c^{5} d^{6} n^{2} - 48 \, b c^{4} d^{5} e n^{2} + 24 \, b^{2} c^{3} d^{4} e^{2} n^{2} + 32 \, b^{3} c^{2} d^{3} e^{3} n^{2} - 21 \, b^{4} c d^{2} e^{4} n^{2} - 3 \, b^{5} d e^{5} n^{2}\right)} a^{5} - {\left(8 \, b^{2} c^{4} d^{6} n^{2} - 24 \, b^{3} c^{3} d^{5} e n^{2} + 21 \, b^{4} c^{2} d^{4} e^{2} n^{2} - 2 \, b^{5} c d^{3} e^{3} n^{2} - 3 \, b^{6} d^{2} e^{4} n^{2}\right)} a^{4} + {\left(b^{4} c^{3} d^{6} n^{2} - 3 \, b^{5} c^{2} d^{5} e n^{2} + 3 \, b^{6} c d^{4} e^{2} n^{2} - b^{7} d^{3} e^{3} n^{2}\right)} a^{3} + {\left(16 \, a^{7} c^{3} e^{6} n^{2} + 8 \, {\left(6 \, c^{4} d^{2} e^{4} n^{2} - 6 \, b c^{3} d e^{5} n^{2} - b^{2} c^{2} e^{6} n^{2}\right)} a^{6} + {\left(48 \, c^{5} d^{4} e^{2} n^{2} - 96 \, b c^{4} d^{3} e^{3} n^{2} + 24 \, b^{2} c^{3} d^{2} e^{4} n^{2} + 24 \, b^{3} c^{2} d e^{5} n^{2} + b^{4} c e^{6} n^{2}\right)} a^{5} + {\left(16 \, c^{6} d^{6} n^{2} - 48 \, b c^{5} d^{5} e n^{2} + 24 \, b^{2} c^{4} d^{4} e^{2} n^{2} + 32 \, b^{3} c^{3} d^{3} e^{3} n^{2} - 21 \, b^{4} c^{2} d^{2} e^{4} n^{2} - 3 \, b^{5} c d e^{5} n^{2}\right)} a^{4} - {\left(8 \, b^{2} c^{5} d^{6} n^{2} - 24 \, b^{3} c^{4} d^{5} e n^{2} + 21 \, b^{4} c^{3} d^{4} e^{2} n^{2} - 2 \, b^{5} c^{2} d^{3} e^{3} n^{2} - 3 \, b^{6} c d^{2} e^{4} n^{2}\right)} a^{3} + {\left(b^{4} c^{4} d^{6} n^{2} - 3 \, b^{5} c^{3} d^{5} e n^{2} + 3 \, b^{6} c^{2} d^{4} e^{2} n^{2} - b^{7} c d^{3} e^{3} n^{2}\right)} a^{2}\right)} x^{2 \, n} + {\left(16 \, a^{7} b c^{2} e^{6} n^{2} + 8 \, {\left(6 \, b c^{3} d^{2} e^{4} n^{2} - 6 \, b^{2} c^{2} d e^{5} n^{2} - b^{3} c e^{6} n^{2}\right)} a^{6} + {\left(48 \, b c^{4} d^{4} e^{2} n^{2} - 96 \, b^{2} c^{3} d^{3} e^{3} n^{2} + 24 \, b^{3} c^{2} d^{2} e^{4} n^{2} + 24 \, b^{4} c d e^{5} n^{2} + b^{5} e^{6} n^{2}\right)} a^{5} + {\left(16 \, b c^{5} d^{6} n^{2} - 48 \, b^{2} c^{4} d^{5} e n^{2} + 24 \, b^{3} c^{3} d^{4} e^{2} n^{2} + 32 \, b^{4} c^{2} d^{3} e^{3} n^{2} - 21 \, b^{5} c d^{2} e^{4} n^{2} - 3 \, b^{6} d e^{5} n^{2}\right)} a^{4} - {\left(8 \, b^{3} c^{4} d^{6} n^{2} - 24 \, b^{4} c^{3} d^{5} e n^{2} + 21 \, b^{5} c^{2} d^{4} e^{2} n^{2} - 2 \, b^{6} c d^{3} e^{3} n^{2} - 3 \, b^{7} d^{2} e^{4} n^{2}\right)} a^{3} + {\left(b^{5} c^{3} d^{6} n^{2} - 3 \, b^{6} c^{2} d^{5} e n^{2} + 3 \, b^{7} c d^{4} e^{2} n^{2} - b^{8} d^{3} e^{3} n^{2}\right)} a^{2}\right)} x^{n}\right)}}\,{d x}"," ",0,"e^6*integrate(1/(c^3*d^7 - 3*b*c^2*d^6*e + 3*b^2*c*d^5*e^2 - b^3*d^4*e^3 + a^3*d*e^6 + 3*(c*d^3*e^4 - b*d^2*e^5)*a^2 + 3*(c^2*d^5*e^2 - 2*b*c*d^4*e^3 + b^2*d^3*e^4)*a + (c^3*d^6*e - 3*b*c^2*d^5*e^2 + 3*b^2*c*d^4*e^3 - b^3*d^3*e^4 + a^3*e^7 + 3*(c*d^2*e^5 - b*d*e^6)*a^2 + 3*(c^2*d^4*e^3 - 2*b*c*d^3*e^4 + b^2*d^2*e^5)*a)*x^n), x) - 1/2*((4*a^3*c^4*e^3*(7*n - 1) - b^3*c^4*d^3*(2*n - 1) + 2*b^4*c^3*d^2*e*(2*n - 1) - b^5*c^2*d*e^2*(2*n - 1) - (b^2*c^3*e^3*(26*n - 5) - 4*c^5*d^2*e*(3*n - 1) - 10*b*c^4*d*e^2*n)*a^2 - (b^2*c^4*d^2*e*(28*n - 9) - 2*b*c^5*d^3*(7*n - 2) - 2*b^3*c^3*d*e^2*(5*n - 2) - b^4*c^2*e^3*(4*n - 1))*a)*x*x^(3*n) - (2*b^4*c^3*d^3*(2*n - 1) - 4*b^5*c^2*d^2*e*(2*n - 1) + 2*b^6*c*d*e^2*(2*n - 1) - 2*(b*c^3*e^3*(37*n - 6) - 2*c^4*d*e^2*(8*n - 1))*a^3 - (2*b*c^4*d^2*e*(25*n - 8) + 3*b^2*c^3*d*e^2*(5*n + 1) - 11*b^3*c^2*e^3*(5*n - 1) - 4*c^5*d^3*(4*n - 1))*a^2 - (b^2*c^4*d^3*(29*n - 9) - 2*b^3*c^3*d^2*e*(29*n - 10) + 3*b^4*c^2*d*e^2*(7*n - 3) + 2*b^5*c*e^3*(4*n - 1))*a)*x*x^(2*n) + (4*a^4*c^3*e^3*(9*n - 1) - b^5*c^2*d^3*(2*n - 1) + 2*b^6*c*d^2*e*(2*n - 1) - b^7*d*e^2*(2*n - 1) + (b^2*c^2*e^3*(14*n - 3) - 2*b*c^3*d*e^2*(13*n - 2) + 4*c^4*d^2*e*(5*n - 1))*a^3 - (b^4*c*e^3*(24*n - 5) - b^3*c^2*d*e^2*(20*n - 1) - 2*b*c^4*d^3*n + 3*b^2*c^3*d^2*e)*a^2 - (3*b^4*c^2*d^2*e*(8*n - 3) - b^6*e^3*(4*n - 1) - 4*b^3*c^3*d^3*(3*n - 1) - 4*b^5*c*d*e^2*(2*n - 1))*a)*x*x^n + (2*(b*c^2*e^3*(29*n - 4) - 2*c^3*d*e^2*(10*n - 1))*a^4 + (2*b*c^3*d^2*e*(29*n - 6) - 4*c^4*d^3*(6*n - 1) - 6*b^3*c*e^3*(6*n - 1) - b^2*c^2*d*e^2*(n - 3))*a^3 - (b^3*c^2*d^2*e*(43*n - 11) - b^2*c^3*d^3*(21*n - 5) - b^4*c*d*e^2*(17*n - 5) - b^5*e^3*(5*n - 1))*a^2 - (b^4*c^2*d^3*(3*n - 1) - 2*b^5*c*d^2*e*(3*n - 1) + b^6*d*e^2*(3*n - 1))*a)*x)/(16*a^8*c^2*e^4*n^2 + 8*(4*c^3*d^2*e^2*n^2 - 4*b*c^2*d*e^3*n^2 - b^2*c*e^4*n^2)*a^7 + (16*c^4*d^4*n^2 - 32*b*c^3*d^3*e*n^2 + 16*b^3*c*d*e^3*n^2 + b^4*e^4*n^2)*a^6 - 2*(4*b^2*c^3*d^4*n^2 - 8*b^3*c^2*d^3*e*n^2 + 3*b^4*c*d^2*e^2*n^2 + b^5*d*e^3*n^2)*a^5 + (b^4*c^2*d^4*n^2 - 2*b^5*c*d^3*e*n^2 + b^6*d^2*e^2*n^2)*a^4 + (16*a^6*c^4*e^4*n^2 + 8*(4*c^5*d^2*e^2*n^2 - 4*b*c^4*d*e^3*n^2 - b^2*c^3*e^4*n^2)*a^5 + (16*c^6*d^4*n^2 - 32*b*c^5*d^3*e*n^2 + 16*b^3*c^3*d*e^3*n^2 + b^4*c^2*e^4*n^2)*a^4 - 2*(4*b^2*c^5*d^4*n^2 - 8*b^3*c^4*d^3*e*n^2 + 3*b^4*c^3*d^2*e^2*n^2 + b^5*c^2*d*e^3*n^2)*a^3 + (b^4*c^4*d^4*n^2 - 2*b^5*c^3*d^3*e*n^2 + b^6*c^2*d^2*e^2*n^2)*a^2)*x^(4*n) + 2*(16*a^6*b*c^3*e^4*n^2 + 8*(4*b*c^4*d^2*e^2*n^2 - 4*b^2*c^3*d*e^3*n^2 - b^3*c^2*e^4*n^2)*a^5 + (16*b*c^5*d^4*n^2 - 32*b^2*c^4*d^3*e*n^2 + 16*b^4*c^2*d*e^3*n^2 + b^5*c*e^4*n^2)*a^4 - 2*(4*b^3*c^4*d^4*n^2 - 8*b^4*c^3*d^3*e*n^2 + 3*b^5*c^2*d^2*e^2*n^2 + b^6*c*d*e^3*n^2)*a^3 + (b^5*c^3*d^4*n^2 - 2*b^6*c^2*d^3*e*n^2 + b^7*c*d^2*e^2*n^2)*a^2)*x^(3*n) + (32*a^7*c^3*e^4*n^2 + 64*(c^4*d^2*e^2*n^2 - b*c^3*d*e^3*n^2)*a^6 + 2*(16*c^5*d^4*n^2 - 32*b*c^4*d^3*e*n^2 + 16*b^2*c^3*d^2*e^2*n^2 - 3*b^4*c*e^4*n^2)*a^5 - (12*b^4*c^2*d^2*e^2*n^2 - 12*b^5*c*d*e^3*n^2 - b^6*e^4*n^2)*a^4 - 2*(3*b^4*c^3*d^4*n^2 - 6*b^5*c^2*d^3*e*n^2 + 2*b^6*c*d^2*e^2*n^2 + b^7*d*e^3*n^2)*a^3 + (b^6*c^2*d^4*n^2 - 2*b^7*c*d^3*e*n^2 + b^8*d^2*e^2*n^2)*a^2)*x^(2*n) + 2*(16*a^7*b*c^2*e^4*n^2 + 8*(4*b*c^3*d^2*e^2*n^2 - 4*b^2*c^2*d*e^3*n^2 - b^3*c*e^4*n^2)*a^6 + (16*b*c^4*d^4*n^2 - 32*b^2*c^3*d^3*e*n^2 + 16*b^4*c*d*e^3*n^2 + b^5*e^4*n^2)*a^5 - 2*(4*b^3*c^3*d^4*n^2 - 8*b^4*c^2*d^3*e*n^2 + 3*b^5*c*d^2*e^2*n^2 + b^6*d*e^3*n^2)*a^4 + (b^5*c^2*d^4*n^2 - 2*b^6*c*d^3*e*n^2 + b^7*d^2*e^2*n^2)*a^3)*x^n) - integrate(-1/2*((2*n^2 - 3*n + 1)*b^4*c^3*d^5 - 3*(2*n^2 - 3*n + 1)*b^5*c^2*d^4*e + 3*(2*n^2 - 3*n + 1)*b^6*c*d^3*e^2 - (2*n^2 - 3*n + 1)*b^7*d^2*e^3 + 2*(2*(24*n^2 - 10*n + 1)*c^3*d*e^4 - (48*n^2 - 29*n + 4)*b*c^2*e^5)*a^4 + (8*(12*n^2 - 8*n + 1)*c^4*d^3*e^2 - 12*(16*n^2 - 13*n + 2)*b*c^3*d^2*e^3 + (48*n^2 - 59*n + 11)*b^2*c^2*d*e^4 + 6*(8*n^2 - 6*n + 1)*b^3*c*e^5)*a^3 + (4*(8*n^2 - 6*n + 1)*c^5*d^5 - 2*(48*n^2 - 41*n + 8)*b*c^4*d^4*e + 2*(24*n^2 - 19*n + 5)*b^2*c^3*d^3*e^2 + 2*(32*n^2 - 39*n + 7)*b^3*c^2*d^2*e^3 - (42*n^2 - 53*n + 11)*b^4*c*d*e^4 - (6*n^2 - 5*n + 1)*b^5*e^5)*a^2 - ((16*n^2 - 21*n + 5)*b^2*c^4*d^5 - 16*(3*n^2 - 4*n + 1)*b^3*c^3*d^4*e + 3*(14*n^2 - 19*n + 5)*b^4*c^2*d^3*e^2 - 2*(2*n^2 - 3*n + 1)*b^5*c*d^2*e^3 - 2*(3*n^2 - 4*n + 1)*b^6*d*e^4)*a + ((2*n^2 - 3*n + 1)*b^3*c^4*d^5 - 3*(2*n^2 - 3*n + 1)*b^4*c^3*d^4*e + 3*(2*n^2 - 3*n + 1)*b^5*c^2*d^3*e^2 - (2*n^2 - 3*n + 1)*b^6*c*d^2*e^3 - 4*(15*n^2 - 8*n + 1)*a^4*c^3*e^5 - (8*(5*n^2 - 6*n + 1)*c^4*d^2*e^3 - 2*(9*n^2 - 11*n + 2)*b*c^3*d*e^4 - (42*n^2 - 31*n + 5)*b^2*c^2*e^5)*a^3 - (4*(3*n^2 - 4*n + 1)*c^5*d^4*e + 12*(n^2 - n)*b*c^4*d^3*e^2 - 2*(32*n^2 - 39*n + 7)*b^2*c^3*d^2*e^3 + 9*(4*n^2 - 5*n + 1)*b^3*c^2*d*e^4 + (6*n^2 - 5*n + 1)*b^4*c*e^5)*a^2 - (2*(7*n^2 - 9*n + 2)*b*c^5*d^5 - (42*n^2 - 55*n + 13)*b^2*c^4*d^4*e + 12*(3*n^2 - 4*n + 1)*b^3*c^3*d^3*e^2 - (2*n^2 - 3*n + 1)*b^4*c^2*d^2*e^3 - 2*(3*n^2 - 4*n + 1)*b^5*c*d*e^4)*a)*x^n)/(16*a^8*c^2*e^6*n^2 + 8*(6*c^3*d^2*e^4*n^2 - 6*b*c^2*d*e^5*n^2 - b^2*c*e^6*n^2)*a^7 + (48*c^4*d^4*e^2*n^2 - 96*b*c^3*d^3*e^3*n^2 + 24*b^2*c^2*d^2*e^4*n^2 + 24*b^3*c*d*e^5*n^2 + b^4*e^6*n^2)*a^6 + (16*c^5*d^6*n^2 - 48*b*c^4*d^5*e*n^2 + 24*b^2*c^3*d^4*e^2*n^2 + 32*b^3*c^2*d^3*e^3*n^2 - 21*b^4*c*d^2*e^4*n^2 - 3*b^5*d*e^5*n^2)*a^5 - (8*b^2*c^4*d^6*n^2 - 24*b^3*c^3*d^5*e*n^2 + 21*b^4*c^2*d^4*e^2*n^2 - 2*b^5*c*d^3*e^3*n^2 - 3*b^6*d^2*e^4*n^2)*a^4 + (b^4*c^3*d^6*n^2 - 3*b^5*c^2*d^5*e*n^2 + 3*b^6*c*d^4*e^2*n^2 - b^7*d^3*e^3*n^2)*a^3 + (16*a^7*c^3*e^6*n^2 + 8*(6*c^4*d^2*e^4*n^2 - 6*b*c^3*d*e^5*n^2 - b^2*c^2*e^6*n^2)*a^6 + (48*c^5*d^4*e^2*n^2 - 96*b*c^4*d^3*e^3*n^2 + 24*b^2*c^3*d^2*e^4*n^2 + 24*b^3*c^2*d*e^5*n^2 + b^4*c*e^6*n^2)*a^5 + (16*c^6*d^6*n^2 - 48*b*c^5*d^5*e*n^2 + 24*b^2*c^4*d^4*e^2*n^2 + 32*b^3*c^3*d^3*e^3*n^2 - 21*b^4*c^2*d^2*e^4*n^2 - 3*b^5*c*d*e^5*n^2)*a^4 - (8*b^2*c^5*d^6*n^2 - 24*b^3*c^4*d^5*e*n^2 + 21*b^4*c^3*d^4*e^2*n^2 - 2*b^5*c^2*d^3*e^3*n^2 - 3*b^6*c*d^2*e^4*n^2)*a^3 + (b^4*c^4*d^6*n^2 - 3*b^5*c^3*d^5*e*n^2 + 3*b^6*c^2*d^4*e^2*n^2 - b^7*c*d^3*e^3*n^2)*a^2)*x^(2*n) + (16*a^7*b*c^2*e^6*n^2 + 8*(6*b*c^3*d^2*e^4*n^2 - 6*b^2*c^2*d*e^5*n^2 - b^3*c*e^6*n^2)*a^6 + (48*b*c^4*d^4*e^2*n^2 - 96*b^2*c^3*d^3*e^3*n^2 + 24*b^3*c^2*d^2*e^4*n^2 + 24*b^4*c*d*e^5*n^2 + b^5*e^6*n^2)*a^5 + (16*b*c^5*d^6*n^2 - 48*b^2*c^4*d^5*e*n^2 + 24*b^3*c^3*d^4*e^2*n^2 + 32*b^4*c^2*d^3*e^3*n^2 - 21*b^5*c*d^2*e^4*n^2 - 3*b^6*d*e^5*n^2)*a^4 - (8*b^3*c^4*d^6*n^2 - 24*b^4*c^3*d^5*e*n^2 + 21*b^5*c^2*d^4*e^2*n^2 - 2*b^6*c*d^3*e^3*n^2 - 3*b^7*d^2*e^4*n^2)*a^3 + (b^5*c^3*d^6*n^2 - 3*b^6*c^2*d^5*e*n^2 + 3*b^7*c*d^4*e^2*n^2 - b^8*d^3*e^3*n^2)*a^2)*x^n), x)","F",0
84,0,0,0,0.000000," ","integrate(1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""maxima"")","{\left(c d^{2} e^{6} {\left(7 \, n - 1\right)} - b d e^{7} {\left(4 \, n - 1\right)} + a e^{8} {\left(n - 1\right)}\right)} \int \frac{1}{c^{4} d^{10} n - 4 \, b c^{3} d^{9} e n + 6 \, b^{2} c^{2} d^{8} e^{2} n - 4 \, b^{3} c d^{7} e^{3} n + b^{4} d^{6} e^{4} n + a^{4} d^{2} e^{8} n + 4 \, {\left(c d^{4} e^{6} n - b d^{3} e^{7} n\right)} a^{3} + 6 \, {\left(c^{2} d^{6} e^{4} n - 2 \, b c d^{5} e^{5} n + b^{2} d^{4} e^{6} n\right)} a^{2} + 4 \, {\left(c^{3} d^{8} e^{2} n - 3 \, b c^{2} d^{7} e^{3} n + 3 \, b^{2} c d^{6} e^{4} n - b^{3} d^{5} e^{5} n\right)} a + {\left(c^{4} d^{9} e n - 4 \, b c^{3} d^{8} e^{2} n + 6 \, b^{2} c^{2} d^{7} e^{3} n - 4 \, b^{3} c d^{6} e^{4} n + b^{4} d^{5} e^{5} n + a^{4} d e^{9} n + 4 \, {\left(c d^{3} e^{7} n - b d^{2} e^{8} n\right)} a^{3} + 6 \, {\left(c^{2} d^{5} e^{5} n - 2 \, b c d^{4} e^{6} n + b^{2} d^{3} e^{7} n\right)} a^{2} + 4 \, {\left(c^{3} d^{7} e^{3} n - 3 \, b c^{2} d^{6} e^{4} n + 3 \, b^{2} c d^{5} e^{5} n - b^{3} d^{4} e^{6} n\right)} a\right)} x^{n}}\,{d x} + \frac{{\left(b^{3} c^{5} d^{5} e {\left(2 \, n - 1\right)} - 3 \, b^{4} c^{4} d^{4} e^{2} {\left(2 \, n - 1\right)} + 3 \, b^{5} c^{3} d^{3} e^{3} {\left(2 \, n - 1\right)} - b^{6} c^{2} d^{2} e^{4} {\left(2 \, n - 1\right)} + 32 \, a^{4} c^{4} e^{6} n + 2 \, {\left(b c^{4} d e^{5} {\left(33 \, n - 4\right)} - 4 \, c^{5} d^{2} e^{4} {\left(11 \, n - 1\right)} - 8 \, b^{2} c^{3} e^{6} n\right)} a^{3} + 2 \, {\left(b^{2} c^{4} d^{2} e^{4} {\left(29 \, n - 1\right)} - 3 \, b^{3} c^{3} d e^{5} {\left(7 \, n - 1\right)} - 4 \, c^{6} d^{4} e^{2} {\left(3 \, n - 1\right)} + 6 \, b c^{5} d^{3} e^{3} {\left(n - 1\right)} + b^{4} c^{2} e^{6} n\right)} a^{2} - {\left(3 \, b^{3} c^{4} d^{3} e^{3} {\left(12 \, n - 5\right)} + 2 \, b c^{6} d^{5} e {\left(7 \, n - 2\right)} - b^{5} c^{2} d e^{5} {\left(6 \, n - 1\right)} - 14 \, b^{2} c^{5} d^{4} e^{2} {\left(3 \, n - 1\right)} - 2 \, b^{4} c^{3} d^{2} e^{4} {\left(n - 2\right)}\right)} a\right)} x x^{4 \, n} + {\left(b^{3} c^{5} d^{6} {\left(2 \, n - 1\right)} - b^{4} c^{4} d^{5} e {\left(2 \, n - 1\right)} - 3 \, b^{5} c^{3} d^{4} e^{2} {\left(2 \, n - 1\right)} + 5 \, b^{6} c^{2} d^{3} e^{3} {\left(2 \, n - 1\right)} - 2 \, b^{7} c d^{2} e^{4} {\left(2 \, n - 1\right)} - 4 \, {\left(c^{4} d e^{5} {\left(8 \, n - 1\right)} - 16 \, b c^{3} e^{6} n\right)} a^{4} + {\left(b^{2} c^{3} d e^{5} {\left(163 \, n - 21\right)} - 6 \, b c^{4} d^{2} e^{4} {\left(27 \, n - 2\right)} - 8 \, c^{5} d^{3} e^{3} {\left(5 \, n - 1\right)} - 32 \, b^{3} c^{2} e^{6} n\right)} a^{3} - {\left(b^{4} c^{2} d e^{5} {\left(89 \, n - 13\right)} - b^{3} c^{3} d^{2} e^{4} {\left(77 \, n + 5\right)} - 2 \, b^{2} c^{4} d^{3} e^{3} {\left(50 \, n - 19\right)} + 8 \, b c^{5} d^{4} e^{2} {\left(9 \, n - 2\right)} + 4 \, c^{6} d^{5} e {\left(2 \, n - 1\right)} - 4 \, b^{5} c e^{6} n\right)} a^{2} - {\left(b^{4} c^{3} d^{3} e^{3} {\left(73 \, n - 29\right)} - b^{3} c^{4} d^{4} e^{2} {\left(51 \, n - 16\right)} - b^{2} c^{5} d^{5} e {\left(13 \, n - 5\right)} - b^{5} c^{2} d^{2} e^{4} {\left(11 \, n - 10\right)} + 2 \, b c^{6} d^{6} {\left(7 \, n - 2\right)} - 2 \, b^{6} c d e^{5} {\left(6 \, n - 1\right)}\right)} a\right)} x x^{3 \, n} + {\left(2 \, b^{4} c^{4} d^{6} {\left(2 \, n - 1\right)} - 5 \, b^{5} c^{3} d^{5} e {\left(2 \, n - 1\right)} + 3 \, b^{6} c^{2} d^{4} e^{2} {\left(2 \, n - 1\right)} + b^{7} c d^{3} e^{3} {\left(2 \, n - 1\right)} - b^{8} d^{2} e^{4} {\left(2 \, n - 1\right)} + 64 \, a^{5} c^{3} e^{6} n - 2 \, {\left(2 \, c^{4} d^{2} e^{4} {\left(34 \, n - 3\right)} - b c^{3} d e^{5} {\left(23 \, n - 2\right)}\right)} a^{4} + {\left(b^{2} c^{3} d^{2} e^{4} {\left(81 \, n - 11\right)} + b^{3} c^{2} d e^{5} {\left(48 \, n - 7\right)} - 8 \, b c^{4} d^{3} e^{3} {\left(18 \, n - 1\right)} + 8 \, c^{5} d^{4} e^{2} {\left(n + 1\right)} - 12 \, b^{4} c e^{6} n\right)} a^{3} - {\left(2 \, b c^{5} d^{5} e {\left(43 \, n - 14\right)} + b^{4} c^{2} d^{2} e^{4} {\left(21 \, n - 10\right)} + 2 \, b^{5} c d e^{5} {\left(20 \, n - 3\right)} - 5 \, b^{3} c^{3} d^{3} e^{3} {\left(19 \, n - 2\right)} - 4 \, c^{6} d^{6} {\left(4 \, n - 1\right)} - 10 \, b^{2} c^{4} d^{4} e^{2} {\left(4 \, n - 3\right)} - 2 \, b^{6} e^{6} n\right)} a^{2} - {\left(b^{4} c^{3} d^{4} e^{2} {\left(39 \, n - 19\right)} + b^{2} c^{5} d^{6} {\left(29 \, n - 9\right)} + b^{5} c^{2} d^{3} e^{3} {\left(25 \, n - 6\right)} - 3 \, b^{3} c^{4} d^{5} e {\left(25 \, n - 9\right)} - b^{7} d e^{5} {\left(6 \, n - 1\right)} - 6 \, b^{6} c d^{2} e^{4} {\left(2 \, n - 1\right)}\right)} a\right)} x x^{2 \, n} + {\left(b^{5} c^{3} d^{6} {\left(2 \, n - 1\right)} - 3 \, b^{6} c^{2} d^{5} e {\left(2 \, n - 1\right)} + 3 \, b^{7} c d^{4} e^{2} {\left(2 \, n - 1\right)} - b^{8} d^{3} e^{3} {\left(2 \, n - 1\right)} - 4 \, {\left(c^{3} d e^{5} {\left(10 \, n - 1\right)} - 16 \, b c^{2} e^{6} n\right)} a^{5} + {\left(b^{2} c^{2} d e^{5} {\left(115 \, n - 13\right)} - 2 \, b c^{3} d^{2} e^{4} {\left(55 \, n - 4\right)} - 8 \, c^{4} d^{3} e^{3} {\left(7 \, n - 1\right)} - 32 \, b^{3} c e^{6} n\right)} a^{4} - {\left(b^{4} c d e^{5} {\left(55 \, n - 7\right)} - 3 \, b^{3} c^{2} d^{2} e^{4} {\left(35 \, n - 2\right)} + 2 \, b^{2} c^{3} d^{3} e^{3} {\left(8 \, n + 7\right)} + 4 \, c^{5} d^{5} e {\left(4 \, n - 1\right)} + 8 \, b c^{4} d^{4} e^{2} {\left(n - 1\right)} - 4 \, b^{5} e^{6} n\right)} a^{3} + {\left(b^{3} c^{3} d^{4} e^{2} {\left(41 \, n - 26\right)} - b^{5} c d^{2} e^{4} {\left(31 \, n - 1\right)} - b^{2} c^{4} d^{5} e {\left(23 \, n - 11\right)} + b^{4} c^{2} d^{3} e^{3} {\left(8 \, n + 15\right)} + b^{6} d e^{5} {\left(7 \, n - 1\right)} - 2 \, b c^{5} d^{6} n\right)} a^{2} + {\left(3 \, b^{4} c^{3} d^{5} e {\left(13 \, n - 5\right)} - 3 \, b^{5} c^{2} d^{4} e^{2} {\left(13 \, n - 6\right)} + b^{6} c d^{3} e^{3} {\left(9 \, n - 7\right)} - 4 \, b^{3} c^{4} d^{6} {\left(3 \, n - 1\right)} + 3 \, b^{7} d^{2} e^{4} n\right)} a\right)} x x^{n} + {\left(32 \, a^{6} c^{2} e^{6} n - 4 \, {\left(c^{3} d^{2} e^{4} {\left(10 \, n - 1\right)} + 4 \, b^{2} c e^{6} n\right)} a^{5} + {\left(b^{2} c^{2} d^{2} e^{4} {\left(115 \, n - 13\right)} - 12 \, b c^{3} d^{3} e^{3} {\left(13 \, n - 1\right)} + 48 \, c^{4} d^{4} e^{2} n + 2 \, b^{4} e^{6} n\right)} a^{4} + {\left(b^{3} c^{2} d^{3} e^{3} {\left(57 \, n + 1\right)} - b^{4} c d^{2} e^{4} {\left(55 \, n - 7\right)} - 4 \, b c^{4} d^{5} e {\left(23 \, n - 5\right)} + 6 \, b^{2} c^{3} d^{4} e^{2} {\left(11 \, n - 4\right)} + 4 \, c^{5} d^{6} {\left(6 \, n - 1\right)}\right)} a^{3} + {\left(b^{3} c^{3} d^{5} e {\left(65 \, n - 17\right)} - b^{2} c^{4} d^{6} {\left(21 \, n - 5\right)} - 6 \, b^{4} c^{2} d^{4} e^{2} {\left(10 \, n - 3\right)} + b^{5} c d^{3} e^{3} {\left(9 \, n - 5\right)} + b^{6} d^{2} e^{4} {\left(7 \, n - 1\right)}\right)} a^{2} + {\left(b^{4} c^{3} d^{6} {\left(3 \, n - 1\right)} - 3 \, b^{5} c^{2} d^{5} e {\left(3 \, n - 1\right)} + 3 \, b^{6} c d^{4} e^{2} {\left(3 \, n - 1\right)} - b^{7} d^{3} e^{3} {\left(3 \, n - 1\right)}\right)} a\right)} x}{2 \, {\left(16 \, a^{9} c^{2} d^{2} e^{6} n^{2} + 8 \, {\left(6 \, c^{3} d^{4} e^{4} n^{2} - 6 \, b c^{2} d^{3} e^{5} n^{2} - b^{2} c d^{2} e^{6} n^{2}\right)} a^{8} + {\left(48 \, c^{4} d^{6} e^{2} n^{2} - 96 \, b c^{3} d^{5} e^{3} n^{2} + 24 \, b^{2} c^{2} d^{4} e^{4} n^{2} + 24 \, b^{3} c d^{3} e^{5} n^{2} + b^{4} d^{2} e^{6} n^{2}\right)} a^{7} + {\left(16 \, c^{5} d^{8} n^{2} - 48 \, b c^{4} d^{7} e n^{2} + 24 \, b^{2} c^{3} d^{6} e^{2} n^{2} + 32 \, b^{3} c^{2} d^{5} e^{3} n^{2} - 21 \, b^{4} c d^{4} e^{4} n^{2} - 3 \, b^{5} d^{3} e^{5} n^{2}\right)} a^{6} - {\left(8 \, b^{2} c^{4} d^{8} n^{2} - 24 \, b^{3} c^{3} d^{7} e n^{2} + 21 \, b^{4} c^{2} d^{6} e^{2} n^{2} - 2 \, b^{5} c d^{5} e^{3} n^{2} - 3 \, b^{6} d^{4} e^{4} n^{2}\right)} a^{5} + {\left(b^{4} c^{3} d^{8} n^{2} - 3 \, b^{5} c^{2} d^{7} e n^{2} + 3 \, b^{6} c d^{6} e^{2} n^{2} - b^{7} d^{5} e^{3} n^{2}\right)} a^{4} + {\left(16 \, a^{7} c^{4} d e^{7} n^{2} + 8 \, {\left(6 \, c^{5} d^{3} e^{5} n^{2} - 6 \, b c^{4} d^{2} e^{6} n^{2} - b^{2} c^{3} d e^{7} n^{2}\right)} a^{6} + {\left(48 \, c^{6} d^{5} e^{3} n^{2} - 96 \, b c^{5} d^{4} e^{4} n^{2} + 24 \, b^{2} c^{4} d^{3} e^{5} n^{2} + 24 \, b^{3} c^{3} d^{2} e^{6} n^{2} + b^{4} c^{2} d e^{7} n^{2}\right)} a^{5} + {\left(16 \, c^{7} d^{7} e n^{2} - 48 \, b c^{6} d^{6} e^{2} n^{2} + 24 \, b^{2} c^{5} d^{5} e^{3} n^{2} + 32 \, b^{3} c^{4} d^{4} e^{4} n^{2} - 21 \, b^{4} c^{3} d^{3} e^{5} n^{2} - 3 \, b^{5} c^{2} d^{2} e^{6} n^{2}\right)} a^{4} - {\left(8 \, b^{2} c^{6} d^{7} e n^{2} - 24 \, b^{3} c^{5} d^{6} e^{2} n^{2} + 21 \, b^{4} c^{4} d^{5} e^{3} n^{2} - 2 \, b^{5} c^{3} d^{4} e^{4} n^{2} - 3 \, b^{6} c^{2} d^{3} e^{5} n^{2}\right)} a^{3} + {\left(b^{4} c^{5} d^{7} e n^{2} - 3 \, b^{5} c^{4} d^{6} e^{2} n^{2} + 3 \, b^{6} c^{3} d^{5} e^{3} n^{2} - b^{7} c^{2} d^{4} e^{4} n^{2}\right)} a^{2}\right)} x^{5 \, n} + {\left(16 \, {\left(c^{4} d^{2} e^{6} n^{2} + 2 \, b c^{3} d e^{7} n^{2}\right)} a^{7} + 8 \, {\left(6 \, c^{5} d^{4} e^{4} n^{2} + 6 \, b c^{4} d^{3} e^{5} n^{2} - 13 \, b^{2} c^{3} d^{2} e^{6} n^{2} - 2 \, b^{3} c^{2} d e^{7} n^{2}\right)} a^{6} + {\left(48 \, c^{6} d^{6} e^{2} n^{2} - 168 \, b^{2} c^{4} d^{4} e^{4} n^{2} + 72 \, b^{3} c^{3} d^{3} e^{5} n^{2} + 49 \, b^{4} c^{2} d^{2} e^{6} n^{2} + 2 \, b^{5} c d e^{7} n^{2}\right)} a^{5} + {\left(16 \, c^{7} d^{8} n^{2} - 16 \, b c^{6} d^{7} e n^{2} - 72 \, b^{2} c^{5} d^{6} e^{2} n^{2} + 80 \, b^{3} c^{4} d^{5} e^{3} n^{2} + 43 \, b^{4} c^{3} d^{4} e^{4} n^{2} - 45 \, b^{5} c^{2} d^{3} e^{5} n^{2} - 6 \, b^{6} c d^{2} e^{6} n^{2}\right)} a^{4} - {\left(8 \, b^{2} c^{6} d^{8} n^{2} - 8 \, b^{3} c^{5} d^{7} e n^{2} - 27 \, b^{4} c^{4} d^{6} e^{2} n^{2} + 40 \, b^{5} c^{3} d^{5} e^{3} n^{2} - 7 \, b^{6} c^{2} d^{4} e^{4} n^{2} - 6 \, b^{7} c d^{3} e^{5} n^{2}\right)} a^{3} + {\left(b^{4} c^{5} d^{8} n^{2} - b^{5} c^{4} d^{7} e n^{2} - 3 \, b^{6} c^{3} d^{6} e^{2} n^{2} + 5 \, b^{7} c^{2} d^{5} e^{3} n^{2} - 2 \, b^{8} c d^{4} e^{4} n^{2}\right)} a^{2}\right)} x^{4 \, n} + {\left(32 \, a^{8} c^{3} d e^{7} n^{2} + 32 \, {\left(3 \, c^{4} d^{3} e^{5} n^{2} - 2 \, b c^{3} d^{2} e^{6} n^{2}\right)} a^{7} + 2 \, {\left(48 \, c^{5} d^{5} e^{3} n^{2} - 48 \, b c^{4} d^{4} e^{4} n^{2} - 8 \, b^{3} c^{2} d^{2} e^{6} n^{2} - 3 \, b^{4} c d e^{7} n^{2}\right)} a^{6} + {\left(32 \, c^{6} d^{7} e n^{2} - 96 \, b^{2} c^{4} d^{5} e^{3} n^{2} + 16 \, b^{3} c^{3} d^{4} e^{4} n^{2} + 30 \, b^{4} c^{2} d^{3} e^{5} n^{2} + 20 \, b^{5} c d^{2} e^{6} n^{2} + b^{6} d e^{7} n^{2}\right)} a^{5} + {\left(32 \, b c^{6} d^{8} n^{2} - 96 \, b^{2} c^{5} d^{7} e n^{2} + 48 \, b^{3} c^{4} d^{6} e^{2} n^{2} + 46 \, b^{4} c^{3} d^{5} e^{3} n^{2} - 6 \, b^{5} c^{2} d^{4} e^{4} n^{2} - 21 \, b^{6} c d^{3} e^{5} n^{2} - 3 \, b^{7} d^{2} e^{6} n^{2}\right)} a^{4} - {\left(16 \, b^{3} c^{5} d^{8} n^{2} - 42 \, b^{4} c^{4} d^{7} e n^{2} + 24 \, b^{5} c^{3} d^{6} e^{2} n^{2} + 11 \, b^{6} c^{2} d^{5} e^{3} n^{2} - 6 \, b^{7} c d^{4} e^{4} n^{2} - 3 \, b^{8} d^{3} e^{5} n^{2}\right)} a^{3} + {\left(2 \, b^{5} c^{4} d^{8} n^{2} - 5 \, b^{6} c^{3} d^{7} e n^{2} + 3 \, b^{7} c^{2} d^{6} e^{2} n^{2} + b^{8} c d^{5} e^{3} n^{2} - b^{9} d^{4} e^{4} n^{2}\right)} a^{2}\right)} x^{3 \, n} + {\left(32 \, {\left(c^{3} d^{2} e^{6} n^{2} + b c^{2} d e^{7} n^{2}\right)} a^{8} + 16 \, {\left(6 \, c^{4} d^{4} e^{4} n^{2} - 6 \, b^{2} c^{2} d^{2} e^{6} n^{2} - b^{3} c d e^{7} n^{2}\right)} a^{7} + 2 \, {\left(48 \, c^{5} d^{6} e^{2} n^{2} - 48 \, b c^{4} d^{5} e^{3} n^{2} - 48 \, b^{2} c^{3} d^{4} e^{4} n^{2} + 24 \, b^{3} c^{2} d^{3} e^{5} n^{2} + 21 \, b^{4} c d^{2} e^{6} n^{2} + b^{5} d e^{7} n^{2}\right)} a^{6} + {\left(32 \, c^{6} d^{8} n^{2} - 64 \, b c^{5} d^{7} e n^{2} + 16 \, b^{3} c^{3} d^{5} e^{3} n^{2} + 46 \, b^{4} c^{2} d^{4} e^{4} n^{2} - 24 \, b^{5} c d^{3} e^{5} n^{2} - 5 \, b^{6} d^{2} e^{6} n^{2}\right)} a^{5} - {\left(16 \, b^{3} c^{4} d^{7} e n^{2} - 30 \, b^{4} c^{3} d^{6} e^{2} n^{2} + 6 \, b^{5} c^{2} d^{5} e^{3} n^{2} + 11 \, b^{6} c d^{4} e^{4} n^{2} - 3 \, b^{7} d^{3} e^{5} n^{2}\right)} a^{4} - {\left(6 \, b^{4} c^{4} d^{8} n^{2} - 20 \, b^{5} c^{3} d^{7} e n^{2} + 21 \, b^{6} c^{2} d^{6} e^{2} n^{2} - 6 \, b^{7} c d^{5} e^{3} n^{2} - b^{8} d^{4} e^{4} n^{2}\right)} a^{3} + {\left(b^{6} c^{3} d^{8} n^{2} - 3 \, b^{7} c^{2} d^{7} e n^{2} + 3 \, b^{8} c d^{6} e^{2} n^{2} - b^{9} d^{5} e^{3} n^{2}\right)} a^{2}\right)} x^{2 \, n} + {\left(16 \, a^{9} c^{2} d e^{7} n^{2} + 8 \, {\left(6 \, c^{3} d^{3} e^{5} n^{2} - 2 \, b c^{2} d^{2} e^{6} n^{2} - b^{2} c d e^{7} n^{2}\right)} a^{8} + {\left(48 \, c^{4} d^{5} e^{3} n^{2} - 72 \, b^{2} c^{2} d^{3} e^{5} n^{2} + 8 \, b^{3} c d^{2} e^{6} n^{2} + b^{4} d e^{7} n^{2}\right)} a^{7} + {\left(16 \, c^{5} d^{7} e n^{2} + 48 \, b c^{4} d^{6} e^{2} n^{2} - 168 \, b^{2} c^{3} d^{5} e^{3} n^{2} + 80 \, b^{3} c^{2} d^{4} e^{4} n^{2} + 27 \, b^{4} c d^{3} e^{5} n^{2} - b^{5} d^{2} e^{6} n^{2}\right)} a^{6} + {\left(32 \, b c^{5} d^{8} n^{2} - 104 \, b^{2} c^{4} d^{7} e n^{2} + 72 \, b^{3} c^{3} d^{6} e^{2} n^{2} + 43 \, b^{4} c^{2} d^{5} e^{3} n^{2} - 40 \, b^{5} c d^{4} e^{4} n^{2} - 3 \, b^{6} d^{3} e^{5} n^{2}\right)} a^{5} - {\left(16 \, b^{3} c^{4} d^{8} n^{2} - 49 \, b^{4} c^{3} d^{7} e n^{2} + 45 \, b^{5} c^{2} d^{6} e^{2} n^{2} - 7 \, b^{6} c d^{5} e^{3} n^{2} - 5 \, b^{7} d^{4} e^{4} n^{2}\right)} a^{4} + 2 \, {\left(b^{5} c^{3} d^{8} n^{2} - 3 \, b^{6} c^{2} d^{7} e n^{2} + 3 \, b^{7} c d^{6} e^{2} n^{2} - b^{8} d^{5} e^{3} n^{2}\right)} a^{3}\right)} x^{n}\right)}} + \int \frac{{\left(2 \, n^{2} - 3 \, n + 1\right)} b^{4} c^{4} d^{6} - 4 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{5} c^{3} d^{5} e + 6 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{6} c^{2} d^{4} e^{2} - 4 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{7} c d^{3} e^{3} + {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{8} d^{2} e^{4} - 4 \, {\left(24 \, n^{2} - 10 \, n + 1\right)} a^{5} c^{3} e^{6} + {\left(4 \, {\left(48 \, n^{2} - 2 \, n - 1\right)} c^{4} d^{2} e^{4} - 4 \, {\left(96 \, n^{2} - 29 \, n + 2\right)} b c^{3} d e^{5} + {\left(240 \, n^{2} - 115 \, n + 13\right)} b^{2} c^{2} e^{6}\right)} a^{4} + {\left(4 \, {\left(32 \, n^{2} - 18 \, n + 1\right)} c^{5} d^{4} e^{2} - 8 \, {\left(48 \, n^{2} - 37 \, n + 4\right)} b c^{4} d^{3} e^{3} + {\left(288 \, n^{2} - 337 \, n + 49\right)} b^{2} c^{3} d^{2} e^{4} + 2 \, {\left(32 \, n^{2} + 29 \, n - 7\right)} b^{3} c^{2} d e^{5} - {\left(102 \, n^{2} - 55 \, n + 7\right)} b^{4} c e^{6}\right)} a^{3} + {\left(4 \, {\left(8 \, n^{2} - 6 \, n + 1\right)} c^{6} d^{6} - 4 \, {\left(32 \, n^{2} - 29 \, n + 6\right)} b c^{5} d^{5} e + {\left(128 \, n^{2} - 137 \, n + 39\right)} b^{2} c^{4} d^{4} e^{2} + 8 \, {\left(8 \, n^{2} - 7 \, n - 1\right)} b^{3} c^{3} d^{3} e^{3} - 4 \, {\left(37 \, n^{2} - 43 \, n + 6\right)} b^{4} c^{2} d^{2} e^{4} + 4 \, {\left(10 \, n^{2} - 16 \, n + 3\right)} b^{5} c d e^{5} + {\left(12 \, n^{2} - 7 \, n + 1\right)} b^{6} e^{6}\right)} a^{2} - {\left({\left(16 \, n^{2} - 21 \, n + 5\right)} b^{2} c^{5} d^{6} - 2 \, {\left(32 \, n^{2} - 43 \, n + 11\right)} b^{3} c^{4} d^{5} e + 2 \, {\left(44 \, n^{2} - 61 \, n + 17\right)} b^{4} c^{3} d^{4} e^{2} - 20 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{5} c^{2} d^{3} e^{3} - {\left(8 \, n^{2} - 7 \, n - 1\right)} b^{6} c d^{2} e^{4} + 2 \, {\left(4 \, n^{2} - 5 \, n + 1\right)} b^{7} d e^{5}\right)} a + {\left({\left(2 \, n^{2} - 3 \, n + 1\right)} b^{3} c^{5} d^{6} - 4 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{4} c^{4} d^{5} e + 6 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{5} c^{3} d^{4} e^{2} - 4 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{6} c^{2} d^{3} e^{3} + {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{7} c d^{2} e^{4} - 2 \, {\left(4 \, {\left(35 \, n^{2} - 12 \, n + 1\right)} c^{4} d e^{5} - {\left(81 \, n^{2} - 37 \, n + 4\right)} b c^{3} e^{6}\right)} a^{4} - 2 \, {\left(8 \, {\left(7 \, n^{2} - 8 \, n + 1\right)} c^{5} d^{3} e^{3} - {\left(83 \, n^{2} - 97 \, n + 14\right)} b c^{4} d^{2} e^{4} - {\left(44 \, n^{2} + 7 \, n - 3\right)} b^{2} c^{3} d e^{5} + 3 \, {\left(15 \, n^{2} - 8 \, n + 1\right)} b^{3} c^{2} e^{6}\right)} a^{3} - {\left(8 \, {\left(3 \, n^{2} - 4 \, n + 1\right)} c^{6} d^{5} e - 2 \, {\left(11 \, n^{2} - 19 \, n + 8\right)} b c^{5} d^{4} e^{2} - 4 \, {\left(22 \, n^{2} - 23 \, n + 1\right)} b^{2} c^{4} d^{3} e^{3} + {\left(136 \, n^{2} - 159 \, n + 23\right)} b^{3} c^{3} d^{2} e^{4} - 2 \, {\left(16 \, n^{2} - 27 \, n + 5\right)} b^{4} c^{2} d e^{5} - {\left(12 \, n^{2} - 7 \, n + 1\right)} b^{5} c e^{6}\right)} a^{2} - 2 \, {\left({\left(7 \, n^{2} - 9 \, n + 2\right)} b c^{6} d^{6} - {\left(28 \, n^{2} - 37 \, n + 9\right)} b^{2} c^{5} d^{5} e + 2 \, {\left(19 \, n^{2} - 26 \, n + 7\right)} b^{3} c^{4} d^{4} e^{2} - 8 \, {\left(2 \, n^{2} - 3 \, n + 1\right)} b^{4} c^{3} d^{3} e^{3} - 5 \, {\left(n^{2} - n\right)} b^{5} c^{2} d^{2} e^{4} + {\left(4 \, n^{2} - 5 \, n + 1\right)} b^{6} c d e^{5}\right)} a\right)} x^{n}}{2 \, {\left(16 \, a^{9} c^{2} e^{8} n^{2} + 8 \, {\left(8 \, c^{3} d^{2} e^{6} n^{2} - 8 \, b c^{2} d e^{7} n^{2} - b^{2} c e^{8} n^{2}\right)} a^{8} + {\left(96 \, c^{4} d^{4} e^{4} n^{2} - 192 \, b c^{3} d^{3} e^{5} n^{2} + 64 \, b^{2} c^{2} d^{2} e^{6} n^{2} + 32 \, b^{3} c d e^{7} n^{2} + b^{4} e^{8} n^{2}\right)} a^{7} + 4 \, {\left(16 \, c^{5} d^{6} e^{2} n^{2} - 48 \, b c^{4} d^{5} e^{3} n^{2} + 36 \, b^{2} c^{3} d^{4} e^{4} n^{2} + 8 \, b^{3} c^{2} d^{3} e^{5} n^{2} - 11 \, b^{4} c d^{2} e^{6} n^{2} - b^{5} d e^{7} n^{2}\right)} a^{6} + 2 \, {\left(8 \, c^{6} d^{8} n^{2} - 32 \, b c^{5} d^{7} e n^{2} + 32 \, b^{2} c^{4} d^{6} e^{2} n^{2} + 16 \, b^{3} c^{3} d^{5} e^{3} n^{2} - 37 \, b^{4} c^{2} d^{4} e^{4} n^{2} + 10 \, b^{5} c d^{3} e^{5} n^{2} + 3 \, b^{6} d^{2} e^{6} n^{2}\right)} a^{5} - 4 \, {\left(2 \, b^{2} c^{5} d^{8} n^{2} - 8 \, b^{3} c^{4} d^{7} e n^{2} + 11 \, b^{4} c^{3} d^{6} e^{2} n^{2} - 5 \, b^{5} c^{2} d^{5} e^{3} n^{2} - b^{6} c d^{4} e^{4} n^{2} + b^{7} d^{3} e^{5} n^{2}\right)} a^{4} + {\left(b^{4} c^{4} d^{8} n^{2} - 4 \, b^{5} c^{3} d^{7} e n^{2} + 6 \, b^{6} c^{2} d^{6} e^{2} n^{2} - 4 \, b^{7} c d^{5} e^{3} n^{2} + b^{8} d^{4} e^{4} n^{2}\right)} a^{3} + {\left(16 \, a^{8} c^{3} e^{8} n^{2} + 8 \, {\left(8 \, c^{4} d^{2} e^{6} n^{2} - 8 \, b c^{3} d e^{7} n^{2} - b^{2} c^{2} e^{8} n^{2}\right)} a^{7} + {\left(96 \, c^{5} d^{4} e^{4} n^{2} - 192 \, b c^{4} d^{3} e^{5} n^{2} + 64 \, b^{2} c^{3} d^{2} e^{6} n^{2} + 32 \, b^{3} c^{2} d e^{7} n^{2} + b^{4} c e^{8} n^{2}\right)} a^{6} + 4 \, {\left(16 \, c^{6} d^{6} e^{2} n^{2} - 48 \, b c^{5} d^{5} e^{3} n^{2} + 36 \, b^{2} c^{4} d^{4} e^{4} n^{2} + 8 \, b^{3} c^{3} d^{3} e^{5} n^{2} - 11 \, b^{4} c^{2} d^{2} e^{6} n^{2} - b^{5} c d e^{7} n^{2}\right)} a^{5} + 2 \, {\left(8 \, c^{7} d^{8} n^{2} - 32 \, b c^{6} d^{7} e n^{2} + 32 \, b^{2} c^{5} d^{6} e^{2} n^{2} + 16 \, b^{3} c^{4} d^{5} e^{3} n^{2} - 37 \, b^{4} c^{3} d^{4} e^{4} n^{2} + 10 \, b^{5} c^{2} d^{3} e^{5} n^{2} + 3 \, b^{6} c d^{2} e^{6} n^{2}\right)} a^{4} - 4 \, {\left(2 \, b^{2} c^{6} d^{8} n^{2} - 8 \, b^{3} c^{5} d^{7} e n^{2} + 11 \, b^{4} c^{4} d^{6} e^{2} n^{2} - 5 \, b^{5} c^{3} d^{5} e^{3} n^{2} - b^{6} c^{2} d^{4} e^{4} n^{2} + b^{7} c d^{3} e^{5} n^{2}\right)} a^{3} + {\left(b^{4} c^{5} d^{8} n^{2} - 4 \, b^{5} c^{4} d^{7} e n^{2} + 6 \, b^{6} c^{3} d^{6} e^{2} n^{2} - 4 \, b^{7} c^{2} d^{5} e^{3} n^{2} + b^{8} c d^{4} e^{4} n^{2}\right)} a^{2}\right)} x^{2 \, n} + {\left(16 \, a^{8} b c^{2} e^{8} n^{2} + 8 \, {\left(8 \, b c^{3} d^{2} e^{6} n^{2} - 8 \, b^{2} c^{2} d e^{7} n^{2} - b^{3} c e^{8} n^{2}\right)} a^{7} + {\left(96 \, b c^{4} d^{4} e^{4} n^{2} - 192 \, b^{2} c^{3} d^{3} e^{5} n^{2} + 64 \, b^{3} c^{2} d^{2} e^{6} n^{2} + 32 \, b^{4} c d e^{7} n^{2} + b^{5} e^{8} n^{2}\right)} a^{6} + 4 \, {\left(16 \, b c^{5} d^{6} e^{2} n^{2} - 48 \, b^{2} c^{4} d^{5} e^{3} n^{2} + 36 \, b^{3} c^{3} d^{4} e^{4} n^{2} + 8 \, b^{4} c^{2} d^{3} e^{5} n^{2} - 11 \, b^{5} c d^{2} e^{6} n^{2} - b^{6} d e^{7} n^{2}\right)} a^{5} + 2 \, {\left(8 \, b c^{6} d^{8} n^{2} - 32 \, b^{2} c^{5} d^{7} e n^{2} + 32 \, b^{3} c^{4} d^{6} e^{2} n^{2} + 16 \, b^{4} c^{3} d^{5} e^{3} n^{2} - 37 \, b^{5} c^{2} d^{4} e^{4} n^{2} + 10 \, b^{6} c d^{3} e^{5} n^{2} + 3 \, b^{7} d^{2} e^{6} n^{2}\right)} a^{4} - 4 \, {\left(2 \, b^{3} c^{5} d^{8} n^{2} - 8 \, b^{4} c^{4} d^{7} e n^{2} + 11 \, b^{5} c^{3} d^{6} e^{2} n^{2} - 5 \, b^{6} c^{2} d^{5} e^{3} n^{2} - b^{7} c d^{4} e^{4} n^{2} + b^{8} d^{3} e^{5} n^{2}\right)} a^{3} + {\left(b^{5} c^{4} d^{8} n^{2} - 4 \, b^{6} c^{3} d^{7} e n^{2} + 6 \, b^{7} c^{2} d^{6} e^{2} n^{2} - 4 \, b^{8} c d^{5} e^{3} n^{2} + b^{9} d^{4} e^{4} n^{2}\right)} a^{2}\right)} x^{n}\right)}}\,{d x}"," ",0,"(c*d^2*e^6*(7*n - 1) - b*d*e^7*(4*n - 1) + a*e^8*(n - 1))*integrate(1/(c^4*d^10*n - 4*b*c^3*d^9*e*n + 6*b^2*c^2*d^8*e^2*n - 4*b^3*c*d^7*e^3*n + b^4*d^6*e^4*n + a^4*d^2*e^8*n + 4*(c*d^4*e^6*n - b*d^3*e^7*n)*a^3 + 6*(c^2*d^6*e^4*n - 2*b*c*d^5*e^5*n + b^2*d^4*e^6*n)*a^2 + 4*(c^3*d^8*e^2*n - 3*b*c^2*d^7*e^3*n + 3*b^2*c*d^6*e^4*n - b^3*d^5*e^5*n)*a + (c^4*d^9*e*n - 4*b*c^3*d^8*e^2*n + 6*b^2*c^2*d^7*e^3*n - 4*b^3*c*d^6*e^4*n + b^4*d^5*e^5*n + a^4*d*e^9*n + 4*(c*d^3*e^7*n - b*d^2*e^8*n)*a^3 + 6*(c^2*d^5*e^5*n - 2*b*c*d^4*e^6*n + b^2*d^3*e^7*n)*a^2 + 4*(c^3*d^7*e^3*n - 3*b*c^2*d^6*e^4*n + 3*b^2*c*d^5*e^5*n - b^3*d^4*e^6*n)*a)*x^n), x) + 1/2*((b^3*c^5*d^5*e*(2*n - 1) - 3*b^4*c^4*d^4*e^2*(2*n - 1) + 3*b^5*c^3*d^3*e^3*(2*n - 1) - b^6*c^2*d^2*e^4*(2*n - 1) + 32*a^4*c^4*e^6*n + 2*(b*c^4*d*e^5*(33*n - 4) - 4*c^5*d^2*e^4*(11*n - 1) - 8*b^2*c^3*e^6*n)*a^3 + 2*(b^2*c^4*d^2*e^4*(29*n - 1) - 3*b^3*c^3*d*e^5*(7*n - 1) - 4*c^6*d^4*e^2*(3*n - 1) + 6*b*c^5*d^3*e^3*(n - 1) + b^4*c^2*e^6*n)*a^2 - (3*b^3*c^4*d^3*e^3*(12*n - 5) + 2*b*c^6*d^5*e*(7*n - 2) - b^5*c^2*d*e^5*(6*n - 1) - 14*b^2*c^5*d^4*e^2*(3*n - 1) - 2*b^4*c^3*d^2*e^4*(n - 2))*a)*x*x^(4*n) + (b^3*c^5*d^6*(2*n - 1) - b^4*c^4*d^5*e*(2*n - 1) - 3*b^5*c^3*d^4*e^2*(2*n - 1) + 5*b^6*c^2*d^3*e^3*(2*n - 1) - 2*b^7*c*d^2*e^4*(2*n - 1) - 4*(c^4*d*e^5*(8*n - 1) - 16*b*c^3*e^6*n)*a^4 + (b^2*c^3*d*e^5*(163*n - 21) - 6*b*c^4*d^2*e^4*(27*n - 2) - 8*c^5*d^3*e^3*(5*n - 1) - 32*b^3*c^2*e^6*n)*a^3 - (b^4*c^2*d*e^5*(89*n - 13) - b^3*c^3*d^2*e^4*(77*n + 5) - 2*b^2*c^4*d^3*e^3*(50*n - 19) + 8*b*c^5*d^4*e^2*(9*n - 2) + 4*c^6*d^5*e*(2*n - 1) - 4*b^5*c*e^6*n)*a^2 - (b^4*c^3*d^3*e^3*(73*n - 29) - b^3*c^4*d^4*e^2*(51*n - 16) - b^2*c^5*d^5*e*(13*n - 5) - b^5*c^2*d^2*e^4*(11*n - 10) + 2*b*c^6*d^6*(7*n - 2) - 2*b^6*c*d*e^5*(6*n - 1))*a)*x*x^(3*n) + (2*b^4*c^4*d^6*(2*n - 1) - 5*b^5*c^3*d^5*e*(2*n - 1) + 3*b^6*c^2*d^4*e^2*(2*n - 1) + b^7*c*d^3*e^3*(2*n - 1) - b^8*d^2*e^4*(2*n - 1) + 64*a^5*c^3*e^6*n - 2*(2*c^4*d^2*e^4*(34*n - 3) - b*c^3*d*e^5*(23*n - 2))*a^4 + (b^2*c^3*d^2*e^4*(81*n - 11) + b^3*c^2*d*e^5*(48*n - 7) - 8*b*c^4*d^3*e^3*(18*n - 1) + 8*c^5*d^4*e^2*(n + 1) - 12*b^4*c*e^6*n)*a^3 - (2*b*c^5*d^5*e*(43*n - 14) + b^4*c^2*d^2*e^4*(21*n - 10) + 2*b^5*c*d*e^5*(20*n - 3) - 5*b^3*c^3*d^3*e^3*(19*n - 2) - 4*c^6*d^6*(4*n - 1) - 10*b^2*c^4*d^4*e^2*(4*n - 3) - 2*b^6*e^6*n)*a^2 - (b^4*c^3*d^4*e^2*(39*n - 19) + b^2*c^5*d^6*(29*n - 9) + b^5*c^2*d^3*e^3*(25*n - 6) - 3*b^3*c^4*d^5*e*(25*n - 9) - b^7*d*e^5*(6*n - 1) - 6*b^6*c*d^2*e^4*(2*n - 1))*a)*x*x^(2*n) + (b^5*c^3*d^6*(2*n - 1) - 3*b^6*c^2*d^5*e*(2*n - 1) + 3*b^7*c*d^4*e^2*(2*n - 1) - b^8*d^3*e^3*(2*n - 1) - 4*(c^3*d*e^5*(10*n - 1) - 16*b*c^2*e^6*n)*a^5 + (b^2*c^2*d*e^5*(115*n - 13) - 2*b*c^3*d^2*e^4*(55*n - 4) - 8*c^4*d^3*e^3*(7*n - 1) - 32*b^3*c*e^6*n)*a^4 - (b^4*c*d*e^5*(55*n - 7) - 3*b^3*c^2*d^2*e^4*(35*n - 2) + 2*b^2*c^3*d^3*e^3*(8*n + 7) + 4*c^5*d^5*e*(4*n - 1) + 8*b*c^4*d^4*e^2*(n - 1) - 4*b^5*e^6*n)*a^3 + (b^3*c^3*d^4*e^2*(41*n - 26) - b^5*c*d^2*e^4*(31*n - 1) - b^2*c^4*d^5*e*(23*n - 11) + b^4*c^2*d^3*e^3*(8*n + 15) + b^6*d*e^5*(7*n - 1) - 2*b*c^5*d^6*n)*a^2 + (3*b^4*c^3*d^5*e*(13*n - 5) - 3*b^5*c^2*d^4*e^2*(13*n - 6) + b^6*c*d^3*e^3*(9*n - 7) - 4*b^3*c^4*d^6*(3*n - 1) + 3*b^7*d^2*e^4*n)*a)*x*x^n + (32*a^6*c^2*e^6*n - 4*(c^3*d^2*e^4*(10*n - 1) + 4*b^2*c*e^6*n)*a^5 + (b^2*c^2*d^2*e^4*(115*n - 13) - 12*b*c^3*d^3*e^3*(13*n - 1) + 48*c^4*d^4*e^2*n + 2*b^4*e^6*n)*a^4 + (b^3*c^2*d^3*e^3*(57*n + 1) - b^4*c*d^2*e^4*(55*n - 7) - 4*b*c^4*d^5*e*(23*n - 5) + 6*b^2*c^3*d^4*e^2*(11*n - 4) + 4*c^5*d^6*(6*n - 1))*a^3 + (b^3*c^3*d^5*e*(65*n - 17) - b^2*c^4*d^6*(21*n - 5) - 6*b^4*c^2*d^4*e^2*(10*n - 3) + b^5*c*d^3*e^3*(9*n - 5) + b^6*d^2*e^4*(7*n - 1))*a^2 + (b^4*c^3*d^6*(3*n - 1) - 3*b^5*c^2*d^5*e*(3*n - 1) + 3*b^6*c*d^4*e^2*(3*n - 1) - b^7*d^3*e^3*(3*n - 1))*a)*x)/(16*a^9*c^2*d^2*e^6*n^2 + 8*(6*c^3*d^4*e^4*n^2 - 6*b*c^2*d^3*e^5*n^2 - b^2*c*d^2*e^6*n^2)*a^8 + (48*c^4*d^6*e^2*n^2 - 96*b*c^3*d^5*e^3*n^2 + 24*b^2*c^2*d^4*e^4*n^2 + 24*b^3*c*d^3*e^5*n^2 + b^4*d^2*e^6*n^2)*a^7 + (16*c^5*d^8*n^2 - 48*b*c^4*d^7*e*n^2 + 24*b^2*c^3*d^6*e^2*n^2 + 32*b^3*c^2*d^5*e^3*n^2 - 21*b^4*c*d^4*e^4*n^2 - 3*b^5*d^3*e^5*n^2)*a^6 - (8*b^2*c^4*d^8*n^2 - 24*b^3*c^3*d^7*e*n^2 + 21*b^4*c^2*d^6*e^2*n^2 - 2*b^5*c*d^5*e^3*n^2 - 3*b^6*d^4*e^4*n^2)*a^5 + (b^4*c^3*d^8*n^2 - 3*b^5*c^2*d^7*e*n^2 + 3*b^6*c*d^6*e^2*n^2 - b^7*d^5*e^3*n^2)*a^4 + (16*a^7*c^4*d*e^7*n^2 + 8*(6*c^5*d^3*e^5*n^2 - 6*b*c^4*d^2*e^6*n^2 - b^2*c^3*d*e^7*n^2)*a^6 + (48*c^6*d^5*e^3*n^2 - 96*b*c^5*d^4*e^4*n^2 + 24*b^2*c^4*d^3*e^5*n^2 + 24*b^3*c^3*d^2*e^6*n^2 + b^4*c^2*d*e^7*n^2)*a^5 + (16*c^7*d^7*e*n^2 - 48*b*c^6*d^6*e^2*n^2 + 24*b^2*c^5*d^5*e^3*n^2 + 32*b^3*c^4*d^4*e^4*n^2 - 21*b^4*c^3*d^3*e^5*n^2 - 3*b^5*c^2*d^2*e^6*n^2)*a^4 - (8*b^2*c^6*d^7*e*n^2 - 24*b^3*c^5*d^6*e^2*n^2 + 21*b^4*c^4*d^5*e^3*n^2 - 2*b^5*c^3*d^4*e^4*n^2 - 3*b^6*c^2*d^3*e^5*n^2)*a^3 + (b^4*c^5*d^7*e*n^2 - 3*b^5*c^4*d^6*e^2*n^2 + 3*b^6*c^3*d^5*e^3*n^2 - b^7*c^2*d^4*e^4*n^2)*a^2)*x^(5*n) + (16*(c^4*d^2*e^6*n^2 + 2*b*c^3*d*e^7*n^2)*a^7 + 8*(6*c^5*d^4*e^4*n^2 + 6*b*c^4*d^3*e^5*n^2 - 13*b^2*c^3*d^2*e^6*n^2 - 2*b^3*c^2*d*e^7*n^2)*a^6 + (48*c^6*d^6*e^2*n^2 - 168*b^2*c^4*d^4*e^4*n^2 + 72*b^3*c^3*d^3*e^5*n^2 + 49*b^4*c^2*d^2*e^6*n^2 + 2*b^5*c*d*e^7*n^2)*a^5 + (16*c^7*d^8*n^2 - 16*b*c^6*d^7*e*n^2 - 72*b^2*c^5*d^6*e^2*n^2 + 80*b^3*c^4*d^5*e^3*n^2 + 43*b^4*c^3*d^4*e^4*n^2 - 45*b^5*c^2*d^3*e^5*n^2 - 6*b^6*c*d^2*e^6*n^2)*a^4 - (8*b^2*c^6*d^8*n^2 - 8*b^3*c^5*d^7*e*n^2 - 27*b^4*c^4*d^6*e^2*n^2 + 40*b^5*c^3*d^5*e^3*n^2 - 7*b^6*c^2*d^4*e^4*n^2 - 6*b^7*c*d^3*e^5*n^2)*a^3 + (b^4*c^5*d^8*n^2 - b^5*c^4*d^7*e*n^2 - 3*b^6*c^3*d^6*e^2*n^2 + 5*b^7*c^2*d^5*e^3*n^2 - 2*b^8*c*d^4*e^4*n^2)*a^2)*x^(4*n) + (32*a^8*c^3*d*e^7*n^2 + 32*(3*c^4*d^3*e^5*n^2 - 2*b*c^3*d^2*e^6*n^2)*a^7 + 2*(48*c^5*d^5*e^3*n^2 - 48*b*c^4*d^4*e^4*n^2 - 8*b^3*c^2*d^2*e^6*n^2 - 3*b^4*c*d*e^7*n^2)*a^6 + (32*c^6*d^7*e*n^2 - 96*b^2*c^4*d^5*e^3*n^2 + 16*b^3*c^3*d^4*e^4*n^2 + 30*b^4*c^2*d^3*e^5*n^2 + 20*b^5*c*d^2*e^6*n^2 + b^6*d*e^7*n^2)*a^5 + (32*b*c^6*d^8*n^2 - 96*b^2*c^5*d^7*e*n^2 + 48*b^3*c^4*d^6*e^2*n^2 + 46*b^4*c^3*d^5*e^3*n^2 - 6*b^5*c^2*d^4*e^4*n^2 - 21*b^6*c*d^3*e^5*n^2 - 3*b^7*d^2*e^6*n^2)*a^4 - (16*b^3*c^5*d^8*n^2 - 42*b^4*c^4*d^7*e*n^2 + 24*b^5*c^3*d^6*e^2*n^2 + 11*b^6*c^2*d^5*e^3*n^2 - 6*b^7*c*d^4*e^4*n^2 - 3*b^8*d^3*e^5*n^2)*a^3 + (2*b^5*c^4*d^8*n^2 - 5*b^6*c^3*d^7*e*n^2 + 3*b^7*c^2*d^6*e^2*n^2 + b^8*c*d^5*e^3*n^2 - b^9*d^4*e^4*n^2)*a^2)*x^(3*n) + (32*(c^3*d^2*e^6*n^2 + b*c^2*d*e^7*n^2)*a^8 + 16*(6*c^4*d^4*e^4*n^2 - 6*b^2*c^2*d^2*e^6*n^2 - b^3*c*d*e^7*n^2)*a^7 + 2*(48*c^5*d^6*e^2*n^2 - 48*b*c^4*d^5*e^3*n^2 - 48*b^2*c^3*d^4*e^4*n^2 + 24*b^3*c^2*d^3*e^5*n^2 + 21*b^4*c*d^2*e^6*n^2 + b^5*d*e^7*n^2)*a^6 + (32*c^6*d^8*n^2 - 64*b*c^5*d^7*e*n^2 + 16*b^3*c^3*d^5*e^3*n^2 + 46*b^4*c^2*d^4*e^4*n^2 - 24*b^5*c*d^3*e^5*n^2 - 5*b^6*d^2*e^6*n^2)*a^5 - (16*b^3*c^4*d^7*e*n^2 - 30*b^4*c^3*d^6*e^2*n^2 + 6*b^5*c^2*d^5*e^3*n^2 + 11*b^6*c*d^4*e^4*n^2 - 3*b^7*d^3*e^5*n^2)*a^4 - (6*b^4*c^4*d^8*n^2 - 20*b^5*c^3*d^7*e*n^2 + 21*b^6*c^2*d^6*e^2*n^2 - 6*b^7*c*d^5*e^3*n^2 - b^8*d^4*e^4*n^2)*a^3 + (b^6*c^3*d^8*n^2 - 3*b^7*c^2*d^7*e*n^2 + 3*b^8*c*d^6*e^2*n^2 - b^9*d^5*e^3*n^2)*a^2)*x^(2*n) + (16*a^9*c^2*d*e^7*n^2 + 8*(6*c^3*d^3*e^5*n^2 - 2*b*c^2*d^2*e^6*n^2 - b^2*c*d*e^7*n^2)*a^8 + (48*c^4*d^5*e^3*n^2 - 72*b^2*c^2*d^3*e^5*n^2 + 8*b^3*c*d^2*e^6*n^2 + b^4*d*e^7*n^2)*a^7 + (16*c^5*d^7*e*n^2 + 48*b*c^4*d^6*e^2*n^2 - 168*b^2*c^3*d^5*e^3*n^2 + 80*b^3*c^2*d^4*e^4*n^2 + 27*b^4*c*d^3*e^5*n^2 - b^5*d^2*e^6*n^2)*a^6 + (32*b*c^5*d^8*n^2 - 104*b^2*c^4*d^7*e*n^2 + 72*b^3*c^3*d^6*e^2*n^2 + 43*b^4*c^2*d^5*e^3*n^2 - 40*b^5*c*d^4*e^4*n^2 - 3*b^6*d^3*e^5*n^2)*a^5 - (16*b^3*c^4*d^8*n^2 - 49*b^4*c^3*d^7*e*n^2 + 45*b^5*c^2*d^6*e^2*n^2 - 7*b^6*c*d^5*e^3*n^2 - 5*b^7*d^4*e^4*n^2)*a^4 + 2*(b^5*c^3*d^8*n^2 - 3*b^6*c^2*d^7*e*n^2 + 3*b^7*c*d^6*e^2*n^2 - b^8*d^5*e^3*n^2)*a^3)*x^n) + integrate(1/2*((2*n^2 - 3*n + 1)*b^4*c^4*d^6 - 4*(2*n^2 - 3*n + 1)*b^5*c^3*d^5*e + 6*(2*n^2 - 3*n + 1)*b^6*c^2*d^4*e^2 - 4*(2*n^2 - 3*n + 1)*b^7*c*d^3*e^3 + (2*n^2 - 3*n + 1)*b^8*d^2*e^4 - 4*(24*n^2 - 10*n + 1)*a^5*c^3*e^6 + (4*(48*n^2 - 2*n - 1)*c^4*d^2*e^4 - 4*(96*n^2 - 29*n + 2)*b*c^3*d*e^5 + (240*n^2 - 115*n + 13)*b^2*c^2*e^6)*a^4 + (4*(32*n^2 - 18*n + 1)*c^5*d^4*e^2 - 8*(48*n^2 - 37*n + 4)*b*c^4*d^3*e^3 + (288*n^2 - 337*n + 49)*b^2*c^3*d^2*e^4 + 2*(32*n^2 + 29*n - 7)*b^3*c^2*d*e^5 - (102*n^2 - 55*n + 7)*b^4*c*e^6)*a^3 + (4*(8*n^2 - 6*n + 1)*c^6*d^6 - 4*(32*n^2 - 29*n + 6)*b*c^5*d^5*e + (128*n^2 - 137*n + 39)*b^2*c^4*d^4*e^2 + 8*(8*n^2 - 7*n - 1)*b^3*c^3*d^3*e^3 - 4*(37*n^2 - 43*n + 6)*b^4*c^2*d^2*e^4 + 4*(10*n^2 - 16*n + 3)*b^5*c*d*e^5 + (12*n^2 - 7*n + 1)*b^6*e^6)*a^2 - ((16*n^2 - 21*n + 5)*b^2*c^5*d^6 - 2*(32*n^2 - 43*n + 11)*b^3*c^4*d^5*e + 2*(44*n^2 - 61*n + 17)*b^4*c^3*d^4*e^2 - 20*(2*n^2 - 3*n + 1)*b^5*c^2*d^3*e^3 - (8*n^2 - 7*n - 1)*b^6*c*d^2*e^4 + 2*(4*n^2 - 5*n + 1)*b^7*d*e^5)*a + ((2*n^2 - 3*n + 1)*b^3*c^5*d^6 - 4*(2*n^2 - 3*n + 1)*b^4*c^4*d^5*e + 6*(2*n^2 - 3*n + 1)*b^5*c^3*d^4*e^2 - 4*(2*n^2 - 3*n + 1)*b^6*c^2*d^3*e^3 + (2*n^2 - 3*n + 1)*b^7*c*d^2*e^4 - 2*(4*(35*n^2 - 12*n + 1)*c^4*d*e^5 - (81*n^2 - 37*n + 4)*b*c^3*e^6)*a^4 - 2*(8*(7*n^2 - 8*n + 1)*c^5*d^3*e^3 - (83*n^2 - 97*n + 14)*b*c^4*d^2*e^4 - (44*n^2 + 7*n - 3)*b^2*c^3*d*e^5 + 3*(15*n^2 - 8*n + 1)*b^3*c^2*e^6)*a^3 - (8*(3*n^2 - 4*n + 1)*c^6*d^5*e - 2*(11*n^2 - 19*n + 8)*b*c^5*d^4*e^2 - 4*(22*n^2 - 23*n + 1)*b^2*c^4*d^3*e^3 + (136*n^2 - 159*n + 23)*b^3*c^3*d^2*e^4 - 2*(16*n^2 - 27*n + 5)*b^4*c^2*d*e^5 - (12*n^2 - 7*n + 1)*b^5*c*e^6)*a^2 - 2*((7*n^2 - 9*n + 2)*b*c^6*d^6 - (28*n^2 - 37*n + 9)*b^2*c^5*d^5*e + 2*(19*n^2 - 26*n + 7)*b^3*c^4*d^4*e^2 - 8*(2*n^2 - 3*n + 1)*b^4*c^3*d^3*e^3 - 5*(n^2 - n)*b^5*c^2*d^2*e^4 + (4*n^2 - 5*n + 1)*b^6*c*d*e^5)*a)*x^n)/(16*a^9*c^2*e^8*n^2 + 8*(8*c^3*d^2*e^6*n^2 - 8*b*c^2*d*e^7*n^2 - b^2*c*e^8*n^2)*a^8 + (96*c^4*d^4*e^4*n^2 - 192*b*c^3*d^3*e^5*n^2 + 64*b^2*c^2*d^2*e^6*n^2 + 32*b^3*c*d*e^7*n^2 + b^4*e^8*n^2)*a^7 + 4*(16*c^5*d^6*e^2*n^2 - 48*b*c^4*d^5*e^3*n^2 + 36*b^2*c^3*d^4*e^4*n^2 + 8*b^3*c^2*d^3*e^5*n^2 - 11*b^4*c*d^2*e^6*n^2 - b^5*d*e^7*n^2)*a^6 + 2*(8*c^6*d^8*n^2 - 32*b*c^5*d^7*e*n^2 + 32*b^2*c^4*d^6*e^2*n^2 + 16*b^3*c^3*d^5*e^3*n^2 - 37*b^4*c^2*d^4*e^4*n^2 + 10*b^5*c*d^3*e^5*n^2 + 3*b^6*d^2*e^6*n^2)*a^5 - 4*(2*b^2*c^5*d^8*n^2 - 8*b^3*c^4*d^7*e*n^2 + 11*b^4*c^3*d^6*e^2*n^2 - 5*b^5*c^2*d^5*e^3*n^2 - b^6*c*d^4*e^4*n^2 + b^7*d^3*e^5*n^2)*a^4 + (b^4*c^4*d^8*n^2 - 4*b^5*c^3*d^7*e*n^2 + 6*b^6*c^2*d^6*e^2*n^2 - 4*b^7*c*d^5*e^3*n^2 + b^8*d^4*e^4*n^2)*a^3 + (16*a^8*c^3*e^8*n^2 + 8*(8*c^4*d^2*e^6*n^2 - 8*b*c^3*d*e^7*n^2 - b^2*c^2*e^8*n^2)*a^7 + (96*c^5*d^4*e^4*n^2 - 192*b*c^4*d^3*e^5*n^2 + 64*b^2*c^3*d^2*e^6*n^2 + 32*b^3*c^2*d*e^7*n^2 + b^4*c*e^8*n^2)*a^6 + 4*(16*c^6*d^6*e^2*n^2 - 48*b*c^5*d^5*e^3*n^2 + 36*b^2*c^4*d^4*e^4*n^2 + 8*b^3*c^3*d^3*e^5*n^2 - 11*b^4*c^2*d^2*e^6*n^2 - b^5*c*d*e^7*n^2)*a^5 + 2*(8*c^7*d^8*n^2 - 32*b*c^6*d^7*e*n^2 + 32*b^2*c^5*d^6*e^2*n^2 + 16*b^3*c^4*d^5*e^3*n^2 - 37*b^4*c^3*d^4*e^4*n^2 + 10*b^5*c^2*d^3*e^5*n^2 + 3*b^6*c*d^2*e^6*n^2)*a^4 - 4*(2*b^2*c^6*d^8*n^2 - 8*b^3*c^5*d^7*e*n^2 + 11*b^4*c^4*d^6*e^2*n^2 - 5*b^5*c^3*d^5*e^3*n^2 - b^6*c^2*d^4*e^4*n^2 + b^7*c*d^3*e^5*n^2)*a^3 + (b^4*c^5*d^8*n^2 - 4*b^5*c^4*d^7*e*n^2 + 6*b^6*c^3*d^6*e^2*n^2 - 4*b^7*c^2*d^5*e^3*n^2 + b^8*c*d^4*e^4*n^2)*a^2)*x^(2*n) + (16*a^8*b*c^2*e^8*n^2 + 8*(8*b*c^3*d^2*e^6*n^2 - 8*b^2*c^2*d*e^7*n^2 - b^3*c*e^8*n^2)*a^7 + (96*b*c^4*d^4*e^4*n^2 - 192*b^2*c^3*d^3*e^5*n^2 + 64*b^3*c^2*d^2*e^6*n^2 + 32*b^4*c*d*e^7*n^2 + b^5*e^8*n^2)*a^6 + 4*(16*b*c^5*d^6*e^2*n^2 - 48*b^2*c^4*d^5*e^3*n^2 + 36*b^3*c^3*d^4*e^4*n^2 + 8*b^4*c^2*d^3*e^5*n^2 - 11*b^5*c*d^2*e^6*n^2 - b^6*d*e^7*n^2)*a^5 + 2*(8*b*c^6*d^8*n^2 - 32*b^2*c^5*d^7*e*n^2 + 32*b^3*c^4*d^6*e^2*n^2 + 16*b^4*c^3*d^5*e^3*n^2 - 37*b^5*c^2*d^4*e^4*n^2 + 10*b^6*c*d^3*e^5*n^2 + 3*b^7*d^2*e^6*n^2)*a^4 - 4*(2*b^3*c^5*d^8*n^2 - 8*b^4*c^4*d^7*e*n^2 + 11*b^5*c^3*d^6*e^2*n^2 - 5*b^6*c^2*d^5*e^3*n^2 - b^7*c*d^4*e^4*n^2 + b^8*d^3*e^5*n^2)*a^3 + (b^5*c^4*d^8*n^2 - 4*b^6*c^3*d^7*e*n^2 + 6*b^7*c^2*d^6*e^2*n^2 - 4*b^8*c*d^5*e^3*n^2 + b^9*d^4*e^4*n^2)*a^2)*x^n), x)","F",0
85,0,0,0,0.000000," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""maxima"")","\int \sqrt{c x^{2 \, n} + b x^{n} + a} {\left(e x^{n} + d\right)}\,{d x}"," ",0,"integrate(sqrt(c*x^(2*n) + b*x^n + a)*(e*x^n + d), x)","F",0
86,0,0,0,0.000000," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""maxima"")","\int {\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}} {\left(e x^{n} + d\right)}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^(3/2)*(e*x^n + d), x)","F",0
87,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""maxima"")","\int \frac{e x^{n} + d}{\sqrt{c x^{2 \, n} + b x^{n} + a}}\,{d x}"," ",0,"integrate((e*x^n + d)/sqrt(c*x^(2*n) + b*x^n + a), x)","F",0
88,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""maxima"")","\int \frac{e x^{n} + d}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + b*x^n + a)^(3/2), x)","F",0
89,0,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^(5/2),x, algorithm=""maxima"")","\int \frac{e x^{n} + d}{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((e*x^n + d)/(c*x^(2*n) + b*x^n + a)^(5/2), x)","F",0
90,0,0,0,0.000000," ","integrate((d+e*x^n)^q*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""maxima"")","\int {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} {\left(e x^{n} + d\right)}^{q}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p*(e*x^n + d)^q, x)","F",0
91,0,0,0,0.000000," ","integrate((d+e*x^n)^3*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""maxima"")","\int {\left(e x^{n} + d\right)}^{3} {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^n + d)^3*(c*x^(2*n) + b*x^n + a)^p, x)","F",0
92,0,0,0,0.000000," ","integrate((d+e*x^n)^2*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""maxima"")","\int {\left(e x^{n} + d\right)}^{2} {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^n + d)^2*(c*x^(2*n) + b*x^n + a)^p, x)","F",0
93,0,0,0,0.000000," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""maxima"")","\int {\left(e x^{n} + d\right)} {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}\,{d x}"," ",0,"integrate((e*x^n + d)*(c*x^(2*n) + b*x^n + a)^p, x)","F",0
94,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^p/(d+e*x^n),x, algorithm=""maxima"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}}{e x^{n} + d}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p/(e*x^n + d), x)","F",0
95,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^p/(d+e*x^n)^2,x, algorithm=""maxima"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}}{{\left(e x^{n} + d\right)}^{2}}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p/(e*x^n + d)^2, x)","F",0
96,0,0,0,0.000000," ","integrate((a+b*x^n+c*x^(2*n))^p/(d+e*x^n)^3,x, algorithm=""maxima"")","\int \frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}}{{\left(e x^{n} + d\right)}^{3}}\,{d x}"," ",0,"integrate((c*x^(2*n) + b*x^n + a)^p/(e*x^n + d)^3, x)","F",0
