1,1,54,0,0.455398," ","integrate(x^5*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{15 \, a c^{6} x^{6} - 3 \, b c^{5} x^{5} + 5 \, b c^{3} x^{3} - 15 \, b c x + 15 \, {\left(b c^{6} x^{6} + b\right)} \arctan\left(c x\right)}{90 \, c^{6}}"," ",0,"1/90*(15*a*c^6*x^6 - 3*b*c^5*x^5 + 5*b*c^3*x^3 - 15*b*c*x + 15*(b*c^6*x^6 + b)*arctan(c*x))/c^6","A",0
2,1,59,0,0.448013," ","integrate(x^4*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{4 \, b c^{5} x^{5} \arctan\left(c x\right) + 4 \, a c^{5} x^{5} - b c^{4} x^{4} + 2 \, b c^{2} x^{2} - 2 \, b \log\left(c^{2} x^{2} + 1\right)}{20 \, c^{5}}"," ",0,"1/20*(4*b*c^5*x^5*arctan(c*x) + 4*a*c^5*x^5 - b*c^4*x^4 + 2*b*c^2*x^2 - 2*b*log(c^2*x^2 + 1))/c^5","A",0
3,1,47,0,0.466908," ","integrate(x^3*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{3 \, a c^{4} x^{4} - b c^{3} x^{3} + 3 \, b c x + 3 \, {\left(b c^{4} x^{4} - b\right)} \arctan\left(c x\right)}{12 \, c^{4}}"," ",0,"1/12*(3*a*c^4*x^4 - b*c^3*x^3 + 3*b*c*x + 3*(b*c^4*x^4 - b)*arctan(c*x))/c^4","A",0
4,1,49,0,0.435394," ","integrate(x^2*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{2 \, b c^{3} x^{3} \arctan\left(c x\right) + 2 \, a c^{3} x^{3} - b c^{2} x^{2} + b \log\left(c^{2} x^{2} + 1\right)}{6 \, c^{3}}"," ",0,"1/6*(2*b*c^3*x^3*arctan(c*x) + 2*a*c^3*x^3 - b*c^2*x^2 + b*log(c^2*x^2 + 1))/c^3","A",0
5,1,34,0,0.419606," ","integrate(x*(a+b*arctan(c*x)),x, algorithm=""fricas"")","\frac{a c^{2} x^{2} - b c x + {\left(b c^{2} x^{2} + b\right)} \arctan\left(c x\right)}{2 \, c^{2}}"," ",0,"1/2*(a*c^2*x^2 - b*c*x + (b*c^2*x^2 + b)*arctan(c*x))/c^2","A",0
6,1,33,0,0.421553," ","integrate(a+b*arctan(c*x),x, algorithm=""fricas"")","\frac{2 \, b c x \arctan\left(c x\right) + 2 \, a c x - b \log\left(c^{2} x^{2} + 1\right)}{2 \, c}"," ",0,"1/2*(2*b*c*x*arctan(c*x) + 2*a*c*x - b*log(c^2*x^2 + 1))/c","A",0
7,0,0,0,0.414305," ","integrate((a+b*arctan(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x\right) + a}{x}, x\right)"," ",0,"integral((b*arctan(c*x) + a)/x, x)","F",0
8,1,37,0,0.425488," ","integrate((a+b*arctan(c*x))/x^2,x, algorithm=""fricas"")","-\frac{b c x \log\left(c^{2} x^{2} + 1\right) - 2 \, b c x \log\left(x\right) + 2 \, b \arctan\left(c x\right) + 2 \, a}{2 \, x}"," ",0,"-1/2*(b*c*x*log(c^2*x^2 + 1) - 2*b*c*x*log(x) + 2*b*arctan(c*x) + 2*a)/x","A",0
9,1,26,0,0.441354," ","integrate((a+b*arctan(c*x))/x^3,x, algorithm=""fricas"")","-\frac{b c x + {\left(b c^{2} x^{2} + b\right)} \arctan\left(c x\right) + a}{2 \, x^{2}}"," ",0,"-1/2*(b*c*x + (b*c^2*x^2 + b)*arctan(c*x) + a)/x^2","A",0
10,1,50,0,0.434188," ","integrate((a+b*arctan(c*x))/x^4,x, algorithm=""fricas"")","\frac{b c^{3} x^{3} \log\left(c^{2} x^{2} + 1\right) - 2 \, b c^{3} x^{3} \log\left(x\right) - b c x - 2 \, b \arctan\left(c x\right) - 2 \, a}{6 \, x^{3}}"," ",0,"1/6*(b*c^3*x^3*log(c^2*x^2 + 1) - 2*b*c^3*x^3*log(x) - b*c*x - 2*b*arctan(c*x) - 2*a)/x^3","A",0
11,1,41,0,0.422933," ","integrate((a+b*arctan(c*x))/x^5,x, algorithm=""fricas"")","\frac{3 \, b c^{3} x^{3} - b c x + 3 \, {\left(b c^{4} x^{4} - b\right)} \arctan\left(c x\right) - 3 \, a}{12 \, x^{4}}"," ",0,"1/12*(3*b*c^3*x^3 - b*c*x + 3*(b*c^4*x^4 - b)*arctan(c*x) - 3*a)/x^4","A",0
12,1,59,0,0.425660," ","integrate((a+b*arctan(c*x))/x^6,x, algorithm=""fricas"")","-\frac{2 \, b c^{5} x^{5} \log\left(c^{2} x^{2} + 1\right) - 4 \, b c^{5} x^{5} \log\left(x\right) - 2 \, b c^{3} x^{3} + b c x + 4 \, b \arctan\left(c x\right) + 4 \, a}{20 \, x^{5}}"," ",0,"-1/20*(2*b*c^5*x^5*log(c^2*x^2 + 1) - 4*b*c^5*x^5*log(x) - 2*b*c^3*x^3 + b*c*x + 4*b*arctan(c*x) + 4*a)/x^5","A",0
13,1,152,0,0.427853," ","integrate(x^5*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{30 \, a^{2} c^{6} x^{6} - 12 \, a b c^{5} x^{5} + 3 \, b^{2} c^{4} x^{4} + 20 \, a b c^{3} x^{3} - 16 \, b^{2} c^{2} x^{2} - 60 \, a b c x + 30 \, {\left(b^{2} c^{6} x^{6} + b^{2}\right)} \arctan\left(c x\right)^{2} + 46 \, b^{2} \log\left(c^{2} x^{2} + 1\right) + 4 \, {\left(15 \, a b c^{6} x^{6} - 3 \, b^{2} c^{5} x^{5} + 5 \, b^{2} c^{3} x^{3} - 15 \, b^{2} c x + 15 \, a b\right)} \arctan\left(c x\right)}{180 \, c^{6}}"," ",0,"1/180*(30*a^2*c^6*x^6 - 12*a*b*c^5*x^5 + 3*b^2*c^4*x^4 + 20*a*b*c^3*x^3 - 16*b^2*c^2*x^2 - 60*a*b*c*x + 30*(b^2*c^6*x^6 + b^2)*arctan(c*x)^2 + 46*b^2*log(c^2*x^2 + 1) + 4*(15*a*b*c^6*x^6 - 3*b^2*c^5*x^5 + 5*b^2*c^3*x^3 - 15*b^2*c*x + 15*a*b)*arctan(c*x))/c^6","A",0
14,0,0,0,0.422022," ","integrate(x^4*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{4} \arctan\left(c x\right)^{2} + 2 \, a b x^{4} \arctan\left(c x\right) + a^{2} x^{4}, x\right)"," ",0,"integral(b^2*x^4*arctan(c*x)^2 + 2*a*b*x^4*arctan(c*x) + a^2*x^4, x)","F",0
15,1,121,0,0.431894," ","integrate(x^3*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} c^{4} x^{4} - 2 \, a b c^{3} x^{3} + b^{2} c^{2} x^{2} + 6 \, a b c x + 3 \, {\left(b^{2} c^{4} x^{4} - b^{2}\right)} \arctan\left(c x\right)^{2} - 4 \, b^{2} \log\left(c^{2} x^{2} + 1\right) + 2 \, {\left(3 \, a b c^{4} x^{4} - b^{2} c^{3} x^{3} + 3 \, b^{2} c x - 3 \, a b\right)} \arctan\left(c x\right)}{12 \, c^{4}}"," ",0,"1/12*(3*a^2*c^4*x^4 - 2*a*b*c^3*x^3 + b^2*c^2*x^2 + 6*a*b*c*x + 3*(b^2*c^4*x^4 - b^2)*arctan(c*x)^2 - 4*b^2*log(c^2*x^2 + 1) + 2*(3*a*b*c^4*x^4 - b^2*c^3*x^3 + 3*b^2*c*x - 3*a*b)*arctan(c*x))/c^4","A",0
16,0,0,0,0.436751," ","integrate(x^2*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \arctan\left(c x\right)^{2} + 2 \, a b x^{2} \arctan\left(c x\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*arctan(c*x)^2 + 2*a*b*x^2*arctan(c*x) + a^2*x^2, x)","F",0
17,1,83,0,0.429717," ","integrate(x*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","\frac{a^{2} c^{2} x^{2} - 2 \, a b c x + {\left(b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x\right)^{2} + b^{2} \log\left(c^{2} x^{2} + 1\right) + 2 \, {\left(a b c^{2} x^{2} - b^{2} c x + a b\right)} \arctan\left(c x\right)}{2 \, c^{2}}"," ",0,"1/2*(a^2*c^2*x^2 - 2*a*b*c*x + (b^2*c^2*x^2 + b^2)*arctan(c*x)^2 + b^2*log(c^2*x^2 + 1) + 2*(a*b*c^2*x^2 - b^2*c*x + a*b)*arctan(c*x))/c^2","A",0
18,0,0,0,0.428919," ","integrate((a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}, x\right)"," ",0,"integral(b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2, x)","F",0
19,0,0,0,0.436080," ","integrate((a+b*arctan(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/x, x)","F",0
20,0,0,0,0.451605," ","integrate((a+b*arctan(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/x^2, x)","F",0
21,1,94,0,0.511284," ","integrate((a+b*arctan(c*x))^2/x^3,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} x^{2} \log\left(c^{2} x^{2} + 1\right) - 2 \, b^{2} c^{2} x^{2} \log\left(x\right) + 2 \, a b c x + {\left(b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x\right)^{2} + a^{2} + 2 \, {\left(a b c^{2} x^{2} + b^{2} c x + a b\right)} \arctan\left(c x\right)}{2 \, x^{2}}"," ",0,"-1/2*(b^2*c^2*x^2*log(c^2*x^2 + 1) - 2*b^2*c^2*x^2*log(x) + 2*a*b*c*x + (b^2*c^2*x^2 + b^2)*arctan(c*x)^2 + a^2 + 2*(a*b*c^2*x^2 + b^2*c*x + a*b)*arctan(c*x))/x^2","A",0
22,0,0,0,0.458620," ","integrate((a+b*arctan(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}}{x^{4}}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)/x^4, x)","F",0
23,1,135,0,0.453078," ","integrate((a+b*arctan(c*x))^2/x^5,x, algorithm=""fricas"")","\frac{4 \, b^{2} c^{4} x^{4} \log\left(c^{2} x^{2} + 1\right) - 8 \, b^{2} c^{4} x^{4} \log\left(x\right) + 6 \, a b c^{3} x^{3} - b^{2} c^{2} x^{2} - 2 \, a b c x + 3 \, {\left(b^{2} c^{4} x^{4} - b^{2}\right)} \arctan\left(c x\right)^{2} - 3 \, a^{2} + 2 \, {\left(3 \, a b c^{4} x^{4} + 3 \, b^{2} c^{3} x^{3} - b^{2} c x - 3 \, a b\right)} \arctan\left(c x\right)}{12 \, x^{4}}"," ",0,"1/12*(4*b^2*c^4*x^4*log(c^2*x^2 + 1) - 8*b^2*c^4*x^4*log(x) + 6*a*b*c^3*x^3 - b^2*c^2*x^2 - 2*a*b*c*x + 3*(b^2*c^4*x^4 - b^2)*arctan(c*x)^2 - 3*a^2 + 2*(3*a*b*c^4*x^4 + 3*b^2*c^3*x^3 - b^2*c*x - 3*a*b)*arctan(c*x))/x^4","A",0
24,0,0,0,0.427192," ","integrate(x^5*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{5} \arctan\left(c x\right)^{3} + 3 \, a b^{2} x^{5} \arctan\left(c x\right)^{2} + 3 \, a^{2} b x^{5} \arctan\left(c x\right) + a^{3} x^{5}, x\right)"," ",0,"integral(b^3*x^5*arctan(c*x)^3 + 3*a*b^2*x^5*arctan(c*x)^2 + 3*a^2*b*x^5*arctan(c*x) + a^3*x^5, x)","F",0
25,0,0,0,0.424913," ","integrate(x^4*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{4} \arctan\left(c x\right)^{3} + 3 \, a b^{2} x^{4} \arctan\left(c x\right)^{2} + 3 \, a^{2} b x^{4} \arctan\left(c x\right) + a^{3} x^{4}, x\right)"," ",0,"integral(b^3*x^4*arctan(c*x)^3 + 3*a*b^2*x^4*arctan(c*x)^2 + 3*a^2*b*x^4*arctan(c*x) + a^3*x^4, x)","F",0
26,0,0,0,0.469194," ","integrate(x^3*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} x^{3} \arctan\left(c x\right)^{2} + 3 \, a^{2} b x^{3} \arctan\left(c x\right) + a^{3} x^{3}, x\right)"," ",0,"integral(b^3*x^3*arctan(c*x)^3 + 3*a*b^2*x^3*arctan(c*x)^2 + 3*a^2*b*x^3*arctan(c*x) + a^3*x^3, x)","F",0
27,0,0,0,0.416114," ","integrate(x^2*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \arctan\left(c x\right)^{3} + 3 \, a b^{2} x^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b x^{2} \arctan\left(c x\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*arctan(c*x)^3 + 3*a*b^2*x^2*arctan(c*x)^2 + 3*a^2*b*x^2*arctan(c*x) + a^3*x^2, x)","F",0
28,0,0,0,0.425367," ","integrate(x*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \arctan\left(c x\right)^{3} + 3 \, a b^{2} x \arctan\left(c x\right)^{2} + 3 \, a^{2} b x \arctan\left(c x\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*arctan(c*x)^3 + 3*a*b^2*x*arctan(c*x)^2 + 3*a^2*b*x*arctan(c*x) + a^3*x, x)","F",0
29,0,0,0,0.428319," ","integrate((a+b*arctan(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b \arctan\left(c x\right) + a^{3}, x\right)"," ",0,"integral(b^3*arctan(c*x)^3 + 3*a*b^2*arctan(c*x)^2 + 3*a^2*b*arctan(c*x) + a^3, x)","F",0
30,0,0,0,0.420007," ","integrate((a+b*arctan(c*x))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b \arctan\left(c x\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*arctan(c*x)^3 + 3*a*b^2*arctan(c*x)^2 + 3*a^2*b*arctan(c*x) + a^3)/x, x)","F",0
31,0,0,0,0.422499," ","integrate((a+b*arctan(c*x))^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b \arctan\left(c x\right) + a^{3}}{x^{2}}, x\right)"," ",0,"integral((b^3*arctan(c*x)^3 + 3*a*b^2*arctan(c*x)^2 + 3*a^2*b*arctan(c*x) + a^3)/x^2, x)","F",0
32,0,0,0,0.443605," ","integrate((a+b*arctan(c*x))^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b \arctan\left(c x\right) + a^{3}}{x^{3}}, x\right)"," ",0,"integral((b^3*arctan(c*x)^3 + 3*a*b^2*arctan(c*x)^2 + 3*a^2*b*arctan(c*x) + a^3)/x^3, x)","F",0
33,0,0,0,0.420686," ","integrate((a+b*arctan(c*x))^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b \arctan\left(c x\right) + a^{3}}{x^{4}}, x\right)"," ",0,"integral((b^3*arctan(c*x)^3 + 3*a*b^2*arctan(c*x)^2 + 3*a^2*b*arctan(c*x) + a^3)/x^4, x)","F",0
34,0,0,0,0.428639," ","integrate((a+b*arctan(c*x))^3/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b \arctan\left(c x\right) + a^{3}}{x^{5}}, x\right)"," ",0,"integral((b^3*arctan(c*x)^3 + 3*a*b^2*arctan(c*x)^2 + 3*a^2*b*arctan(c*x) + a^3)/x^5, x)","F",0
35,0,0,0,0.417965," ","integrate(x/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\arctan\left(a x\right)}, x\right)"," ",0,"integral(x/arctan(a*x), x)","F",0
36,0,0,0,0.416286," ","integrate(1/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\arctan\left(a x\right)}, x\right)"," ",0,"integral(1/arctan(a*x), x)","F",0
37,0,0,0,0.420383," ","integrate(1/x/arctan(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \arctan\left(a x\right)}, x\right)"," ",0,"integral(1/(x*arctan(a*x)), x)","F",0
38,0,0,0,0.403089," ","integrate(x/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(x/arctan(a*x)^2, x)","F",0
39,0,0,0,0.417087," ","integrate(1/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(arctan(a*x)^(-2), x)","F",0
40,0,0,0,0.403515," ","integrate(1/x/arctan(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \arctan\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/(x*arctan(a*x)^2), x)","F",0
41,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
42,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
43,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
44,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
45,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
46,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
47,-2,0,0,0.000000," ","integrate(x/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
48,-2,0,0,0.000000," ","integrate(1/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
49,-2,0,0,0.000000," ","integrate(1/x/arctan(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
50,-2,0,0,0.000000," ","integrate(x/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
51,-2,0,0,0.000000," ","integrate(1/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
52,-2,0,0,0.000000," ","integrate(1/x/arctan(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
53,1,118,0,0.476396," ","integrate(arctan(x)*x^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(x \arctan\left(x\right) - 2\right)} \sqrt{x} - \frac{2}{3} \, \sqrt{2} \arctan\left(\sqrt{2} \sqrt{\sqrt{2} \sqrt{x} + x + 1} - \sqrt{2} \sqrt{x} - 1\right) - \frac{2}{3} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{-4 \, \sqrt{2} \sqrt{x} + 4 \, x + 4} - \sqrt{2} \sqrt{x} + 1\right) + \frac{1}{6} \, \sqrt{2} \log\left(4 \, \sqrt{2} \sqrt{x} + 4 \, x + 4\right) - \frac{1}{6} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{x} + 4 \, x + 4\right)"," ",0,"2/3*(x*arctan(x) - 2)*sqrt(x) - 2/3*sqrt(2)*arctan(sqrt(2)*sqrt(sqrt(2)*sqrt(x) + x + 1) - sqrt(2)*sqrt(x) - 1) - 2/3*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-4*sqrt(2)*sqrt(x) + 4*x + 4) - sqrt(2)*sqrt(x) + 1) + 1/6*sqrt(2)*log(4*sqrt(2)*sqrt(x) + 4*x + 4) - 1/6*sqrt(2)*log(-4*sqrt(2)*sqrt(x) + 4*x + 4)","A",0
54,0,0,0,0.450640," ","integrate((d*x)^m*(a+b*arctan(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \arctan\left(c x\right)^{3} + 3 \, a b^{2} \arctan\left(c x\right)^{2} + 3 \, a^{2} b \arctan\left(c x\right) + a^{3}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^3*arctan(c*x)^3 + 3*a*b^2*arctan(c*x)^2 + 3*a^2*b*arctan(c*x) + a^3)*(d*x)^m, x)","F",0
55,0,0,0,0.430266," ","integrate((d*x)^m*(a+b*arctan(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right) + a^{2}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x) + a^2)*(d*x)^m, x)","F",0
56,0,0,0,0.426319," ","integrate((d*x)^m*(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x\right) + a\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b*arctan(c*x) + a)*(d*x)^m, x)","F",0
57,0,0,0,0.429666," ","integrate((d*x)^m/(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b \arctan\left(c x\right) + a}, x\right)"," ",0,"integral((d*x)^m/(b*arctan(c*x) + a), x)","F",0
58,0,0,0,0.435391," ","integrate((a+b*arctan(c*x))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*arctan(c*x) + a)^p, x)","F",0
59,0,0,0,0.444372," ","integrate((d*x)^m*(a+b*arctan(c*x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(d x\right)^{m} {\left(b \arctan\left(c x\right) + a\right)}^{p}, x\right)"," ",0,"integral((d*x)^m*(b*arctan(c*x) + a)^p, x)","F",0
60,1,51,0,0.425502," ","integrate(x^7*(a+b*arctan(c*x^2)),x, algorithm=""fricas"")","\frac{3 \, a c^{4} x^{8} - b c^{3} x^{6} + 3 \, b c x^{2} + 3 \, {\left(b c^{4} x^{8} - b\right)} \arctan\left(c x^{2}\right)}{24 \, c^{4}}"," ",0,"1/24*(3*a*c^4*x^8 - b*c^3*x^6 + 3*b*c*x^2 + 3*(b*c^4*x^8 - b)*arctan(c*x^2))/c^4","A",0
61,1,51,0,0.433957," ","integrate(x^5*(a+b*arctan(c*x^2)),x, algorithm=""fricas"")","\frac{2 \, b c^{3} x^{6} \arctan\left(c x^{2}\right) + 2 \, a c^{3} x^{6} - b c^{2} x^{4} + b \log\left(c^{2} x^{4} + 1\right)}{12 \, c^{3}}"," ",0,"1/12*(2*b*c^3*x^6*arctan(c*x^2) + 2*a*c^3*x^6 - b*c^2*x^4 + b*log(c^2*x^4 + 1))/c^3","A",0
62,1,38,0,0.429006," ","integrate(x^3*(a+b*arctan(c*x^2)),x, algorithm=""fricas"")","\frac{a c^{2} x^{4} - b c x^{2} + {\left(b c^{2} x^{4} + b\right)} \arctan\left(c x^{2}\right)}{4 \, c^{2}}"," ",0,"1/4*(a*c^2*x^4 - b*c*x^2 + (b*c^2*x^4 + b)*arctan(c*x^2))/c^2","A",0
63,1,39,0,0.416738," ","integrate(x*(a+b*arctan(c*x^2)),x, algorithm=""fricas"")","\frac{2 \, b c x^{2} \arctan\left(c x^{2}\right) + 2 \, a c x^{2} - b \log\left(c^{2} x^{4} + 1\right)}{4 \, c}"," ",0,"1/4*(2*b*c*x^2*arctan(c*x^2) + 2*a*c*x^2 - b*log(c^2*x^4 + 1))/c","A",0
64,0,0,0,0.409278," ","integrate((a+b*arctan(c*x^2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x^{2}\right) + a}{x}, x\right)"," ",0,"integral((b*arctan(c*x^2) + a)/x, x)","F",0
65,1,43,0,0.436944," ","integrate((a+b*arctan(c*x^2))/x^3,x, algorithm=""fricas"")","-\frac{b c x^{2} \log\left(c^{2} x^{4} + 1\right) - 4 \, b c x^{2} \log\left(x\right) + 2 \, b \arctan\left(c x^{2}\right) + 2 \, a}{4 \, x^{2}}"," ",0,"-1/4*(b*c*x^2*log(c^2*x^4 + 1) - 4*b*c*x^2*log(x) + 2*b*arctan(c*x^2) + 2*a)/x^2","A",0
66,1,30,0,0.402946," ","integrate((a+b*arctan(c*x^2))/x^5,x, algorithm=""fricas"")","-\frac{b c x^{2} + {\left(b c^{2} x^{4} + b\right)} \arctan\left(c x^{2}\right) + a}{4 \, x^{4}}"," ",0,"-1/4*(b*c*x^2 + (b*c^2*x^4 + b)*arctan(c*x^2) + a)/x^4","A",0
67,1,54,0,0.437926," ","integrate((a+b*arctan(c*x^2))/x^7,x, algorithm=""fricas"")","\frac{b c^{3} x^{6} \log\left(c^{2} x^{4} + 1\right) - 4 \, b c^{3} x^{6} \log\left(x\right) - b c x^{2} - 2 \, b \arctan\left(c x^{2}\right) - 2 \, a}{12 \, x^{6}}"," ",0,"1/12*(b*c^3*x^6*log(c^2*x^4 + 1) - 4*b*c^3*x^6*log(x) - b*c*x^2 - 2*b*arctan(c*x^2) - 2*a)/x^6","A",0
68,1,372,0,0.462437," ","integrate(x^4*(a+b*arctan(c*x^2)),x, algorithm=""fricas"")","\frac{12 \, b c x^{5} \arctan\left(c x^{2}\right) + 12 \, a c x^{5} - 8 \, b x^{3} - 12 \, \sqrt{2} c \left(\frac{b^{4}}{c^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} b^{3} c^{3} x \left(\frac{b^{4}}{c^{10}}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{\sqrt{2} b^{3} c^{7} x \left(\frac{b^{4}}{c^{10}}\right)^{\frac{3}{4}} + b^{4} c^{4} \sqrt{\frac{b^{4}}{c^{10}}} + b^{6} x^{2}} c^{3} \left(\frac{b^{4}}{c^{10}}\right)^{\frac{1}{4}} + b^{4}}{b^{4}}\right) - 12 \, \sqrt{2} c \left(\frac{b^{4}}{c^{10}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} b^{3} c^{3} x \left(\frac{b^{4}}{c^{10}}\right)^{\frac{1}{4}} - \sqrt{2} \sqrt{-\sqrt{2} b^{3} c^{7} x \left(\frac{b^{4}}{c^{10}}\right)^{\frac{3}{4}} + b^{4} c^{4} \sqrt{\frac{b^{4}}{c^{10}}} + b^{6} x^{2}} c^{3} \left(\frac{b^{4}}{c^{10}}\right)^{\frac{1}{4}} - b^{4}}{b^{4}}\right) - 3 \, \sqrt{2} c \left(\frac{b^{4}}{c^{10}}\right)^{\frac{1}{4}} \log\left(\sqrt{2} b^{3} c^{7} x \left(\frac{b^{4}}{c^{10}}\right)^{\frac{3}{4}} + b^{4} c^{4} \sqrt{\frac{b^{4}}{c^{10}}} + b^{6} x^{2}\right) + 3 \, \sqrt{2} c \left(\frac{b^{4}}{c^{10}}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} b^{3} c^{7} x \left(\frac{b^{4}}{c^{10}}\right)^{\frac{3}{4}} + b^{4} c^{4} \sqrt{\frac{b^{4}}{c^{10}}} + b^{6} x^{2}\right)}{60 \, c}"," ",0,"1/60*(12*b*c*x^5*arctan(c*x^2) + 12*a*c*x^5 - 8*b*x^3 - 12*sqrt(2)*c*(b^4/c^10)^(1/4)*arctan(-(sqrt(2)*b^3*c^3*x*(b^4/c^10)^(1/4) - sqrt(2)*sqrt(sqrt(2)*b^3*c^7*x*(b^4/c^10)^(3/4) + b^4*c^4*sqrt(b^4/c^10) + b^6*x^2)*c^3*(b^4/c^10)^(1/4) + b^4)/b^4) - 12*sqrt(2)*c*(b^4/c^10)^(1/4)*arctan(-(sqrt(2)*b^3*c^3*x*(b^4/c^10)^(1/4) - sqrt(2)*sqrt(-sqrt(2)*b^3*c^7*x*(b^4/c^10)^(3/4) + b^4*c^4*sqrt(b^4/c^10) + b^6*x^2)*c^3*(b^4/c^10)^(1/4) - b^4)/b^4) - 3*sqrt(2)*c*(b^4/c^10)^(1/4)*log(sqrt(2)*b^3*c^7*x*(b^4/c^10)^(3/4) + b^4*c^4*sqrt(b^4/c^10) + b^6*x^2) + 3*sqrt(2)*c*(b^4/c^10)^(1/4)*log(-sqrt(2)*b^3*c^7*x*(b^4/c^10)^(3/4) + b^4*c^4*sqrt(b^4/c^10) + b^6*x^2))/c","B",0
69,1,337,0,0.442050," ","integrate(x^2*(a+b*arctan(c*x^2)),x, algorithm=""fricas"")","\frac{4 \, b c x^{3} \arctan\left(c x^{2}\right) + 4 \, a c x^{3} - 4 \, \sqrt{2} c \left(\frac{b^{4}}{c^{6}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} b c^{5} x \left(\frac{b^{4}}{c^{6}}\right)^{\frac{3}{4}} - \sqrt{2} \sqrt{b^{2} x^{2} + \sqrt{2} b c x \left(\frac{b^{4}}{c^{6}}\right)^{\frac{1}{4}} + c^{2} \sqrt{\frac{b^{4}}{c^{6}}}} c^{5} \left(\frac{b^{4}}{c^{6}}\right)^{\frac{3}{4}} + b^{4}}{b^{4}}\right) - 4 \, \sqrt{2} c \left(\frac{b^{4}}{c^{6}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} b c^{5} x \left(\frac{b^{4}}{c^{6}}\right)^{\frac{3}{4}} - \sqrt{2} \sqrt{b^{2} x^{2} - \sqrt{2} b c x \left(\frac{b^{4}}{c^{6}}\right)^{\frac{1}{4}} + c^{2} \sqrt{\frac{b^{4}}{c^{6}}}} c^{5} \left(\frac{b^{4}}{c^{6}}\right)^{\frac{3}{4}} - b^{4}}{b^{4}}\right) + \sqrt{2} c \left(\frac{b^{4}}{c^{6}}\right)^{\frac{1}{4}} \log\left(b^{2} x^{2} + \sqrt{2} b c x \left(\frac{b^{4}}{c^{6}}\right)^{\frac{1}{4}} + c^{2} \sqrt{\frac{b^{4}}{c^{6}}}\right) - \sqrt{2} c \left(\frac{b^{4}}{c^{6}}\right)^{\frac{1}{4}} \log\left(b^{2} x^{2} - \sqrt{2} b c x \left(\frac{b^{4}}{c^{6}}\right)^{\frac{1}{4}} + c^{2} \sqrt{\frac{b^{4}}{c^{6}}}\right) - 8 \, b x}{12 \, c}"," ",0,"1/12*(4*b*c*x^3*arctan(c*x^2) + 4*a*c*x^3 - 4*sqrt(2)*c*(b^4/c^6)^(1/4)*arctan(-(sqrt(2)*b*c^5*x*(b^4/c^6)^(3/4) - sqrt(2)*sqrt(b^2*x^2 + sqrt(2)*b*c*x*(b^4/c^6)^(1/4) + c^2*sqrt(b^4/c^6))*c^5*(b^4/c^6)^(3/4) + b^4)/b^4) - 4*sqrt(2)*c*(b^4/c^6)^(1/4)*arctan(-(sqrt(2)*b*c^5*x*(b^4/c^6)^(3/4) - sqrt(2)*sqrt(b^2*x^2 - sqrt(2)*b*c*x*(b^4/c^6)^(1/4) + c^2*sqrt(b^4/c^6))*c^5*(b^4/c^6)^(3/4) - b^4)/b^4) + sqrt(2)*c*(b^4/c^6)^(1/4)*log(b^2*x^2 + sqrt(2)*b*c*x*(b^4/c^6)^(1/4) + c^2*sqrt(b^4/c^6)) - sqrt(2)*c*(b^4/c^6)^(1/4)*log(b^2*x^2 - sqrt(2)*b*c*x*(b^4/c^6)^(1/4) + c^2*sqrt(b^4/c^6)) - 8*b*x)/c","B",0
70,1,319,0,0.442700," ","integrate(a+b*arctan(c*x^2),x, algorithm=""fricas"")","b x \arctan\left(c x^{2}\right) + a x + \sqrt{2} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{1}{4}} b^{3} c x + b^{4} - \sqrt{2} \sqrt{b^{6} x^{2} + \sqrt{2} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{3}{4}} b^{3} c x + \sqrt{\frac{b^{4}}{c^{2}}} b^{4}} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{1}{4}} c}{b^{4}}\right) + \sqrt{2} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{1}{4}} b^{3} c x - b^{4} - \sqrt{2} \sqrt{b^{6} x^{2} - \sqrt{2} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{3}{4}} b^{3} c x + \sqrt{\frac{b^{4}}{c^{2}}} b^{4}} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{1}{4}} c}{b^{4}}\right) + \frac{1}{4} \, \sqrt{2} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{1}{4}} \log\left(b^{6} x^{2} + \sqrt{2} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{3}{4}} b^{3} c x + \sqrt{\frac{b^{4}}{c^{2}}} b^{4}\right) - \frac{1}{4} \, \sqrt{2} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{1}{4}} \log\left(b^{6} x^{2} - \sqrt{2} \left(\frac{b^{4}}{c^{2}}\right)^{\frac{3}{4}} b^{3} c x + \sqrt{\frac{b^{4}}{c^{2}}} b^{4}\right)"," ",0,"b*x*arctan(c*x^2) + a*x + sqrt(2)*(b^4/c^2)^(1/4)*arctan(-(sqrt(2)*(b^4/c^2)^(1/4)*b^3*c*x + b^4 - sqrt(2)*sqrt(b^6*x^2 + sqrt(2)*(b^4/c^2)^(3/4)*b^3*c*x + sqrt(b^4/c^2)*b^4)*(b^4/c^2)^(1/4)*c)/b^4) + sqrt(2)*(b^4/c^2)^(1/4)*arctan(-(sqrt(2)*(b^4/c^2)^(1/4)*b^3*c*x - b^4 - sqrt(2)*sqrt(b^6*x^2 - sqrt(2)*(b^4/c^2)^(3/4)*b^3*c*x + sqrt(b^4/c^2)*b^4)*(b^4/c^2)^(1/4)*c)/b^4) + 1/4*sqrt(2)*(b^4/c^2)^(1/4)*log(b^6*x^2 + sqrt(2)*(b^4/c^2)^(3/4)*b^3*c*x + sqrt(b^4/c^2)*b^4) - 1/4*sqrt(2)*(b^4/c^2)^(1/4)*log(b^6*x^2 - sqrt(2)*(b^4/c^2)^(3/4)*b^3*c*x + sqrt(b^4/c^2)*b^4)","B",0
71,1,322,0,0.448496," ","integrate((a+b*arctan(c*x^2))/x^2,x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{1}{4}} x \arctan\left(-\frac{b^{4} c^{2} + \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{3}{4}} b c x - \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{3}{4}} \sqrt{b^{2} c^{2} x^{2} + \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{1}{4}} b c x + \sqrt{b^{4} c^{2}}}}{b^{4} c^{2}}\right) + 4 \, \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{1}{4}} x \arctan\left(\frac{b^{4} c^{2} - \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{3}{4}} b c x + \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{3}{4}} \sqrt{b^{2} c^{2} x^{2} - \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{1}{4}} b c x + \sqrt{b^{4} c^{2}}}}{b^{4} c^{2}}\right) - \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{1}{4}} x \log\left(b^{2} c^{2} x^{2} + \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{1}{4}} b c x + \sqrt{b^{4} c^{2}}\right) + \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{1}{4}} x \log\left(b^{2} c^{2} x^{2} - \sqrt{2} \left(b^{4} c^{2}\right)^{\frac{1}{4}} b c x + \sqrt{b^{4} c^{2}}\right) + 4 \, b \arctan\left(c x^{2}\right) + 4 \, a}{4 \, x}"," ",0,"-1/4*(4*sqrt(2)*(b^4*c^2)^(1/4)*x*arctan(-(b^4*c^2 + sqrt(2)*(b^4*c^2)^(3/4)*b*c*x - sqrt(2)*(b^4*c^2)^(3/4)*sqrt(b^2*c^2*x^2 + sqrt(2)*(b^4*c^2)^(1/4)*b*c*x + sqrt(b^4*c^2)))/(b^4*c^2)) + 4*sqrt(2)*(b^4*c^2)^(1/4)*x*arctan((b^4*c^2 - sqrt(2)*(b^4*c^2)^(3/4)*b*c*x + sqrt(2)*(b^4*c^2)^(3/4)*sqrt(b^2*c^2*x^2 - sqrt(2)*(b^4*c^2)^(1/4)*b*c*x + sqrt(b^4*c^2)))/(b^4*c^2)) - sqrt(2)*(b^4*c^2)^(1/4)*x*log(b^2*c^2*x^2 + sqrt(2)*(b^4*c^2)^(1/4)*b*c*x + sqrt(b^4*c^2)) + sqrt(2)*(b^4*c^2)^(1/4)*x*log(b^2*c^2*x^2 - sqrt(2)*(b^4*c^2)^(1/4)*b*c*x + sqrt(b^4*c^2)) + 4*b*arctan(c*x^2) + 4*a)/x","B",0
72,1,389,0,0.449177," ","integrate((a+b*arctan(c*x^2))/x^4,x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} \left(b^{4} c^{6}\right)^{\frac{1}{4}} x^{3} \arctan\left(-\frac{b^{4} c^{6} + \sqrt{2} \left(b^{4} c^{6}\right)^{\frac{1}{4}} b^{3} c^{5} x - \sqrt{2} \sqrt{b^{6} c^{10} x^{2} + \sqrt{b^{4} c^{6}} b^{4} c^{6} + \sqrt{2} \left(b^{4} c^{6}\right)^{\frac{3}{4}} b^{3} c^{5} x} \left(b^{4} c^{6}\right)^{\frac{1}{4}}}{b^{4} c^{6}}\right) + 4 \, \sqrt{2} \left(b^{4} c^{6}\right)^{\frac{1}{4}} x^{3} \arctan\left(\frac{b^{4} c^{6} - \sqrt{2} \left(b^{4} c^{6}\right)^{\frac{1}{4}} b^{3} c^{5} x + \sqrt{2} \sqrt{b^{6} c^{10} x^{2} + \sqrt{b^{4} c^{6}} b^{4} c^{6} - \sqrt{2} \left(b^{4} c^{6}\right)^{\frac{3}{4}} b^{3} c^{5} x} \left(b^{4} c^{6}\right)^{\frac{1}{4}}}{b^{4} c^{6}}\right) + \sqrt{2} \left(b^{4} c^{6}\right)^{\frac{1}{4}} x^{3} \log\left(b^{6} c^{10} x^{2} + \sqrt{b^{4} c^{6}} b^{4} c^{6} + \sqrt{2} \left(b^{4} c^{6}\right)^{\frac{3}{4}} b^{3} c^{5} x\right) - \sqrt{2} \left(b^{4} c^{6}\right)^{\frac{1}{4}} x^{3} \log\left(b^{6} c^{10} x^{2} + \sqrt{b^{4} c^{6}} b^{4} c^{6} - \sqrt{2} \left(b^{4} c^{6}\right)^{\frac{3}{4}} b^{3} c^{5} x\right) - 8 \, b c x^{2} - 4 \, b \arctan\left(c x^{2}\right) - 4 \, a}{12 \, x^{3}}"," ",0,"1/12*(4*sqrt(2)*(b^4*c^6)^(1/4)*x^3*arctan(-(b^4*c^6 + sqrt(2)*(b^4*c^6)^(1/4)*b^3*c^5*x - sqrt(2)*sqrt(b^6*c^10*x^2 + sqrt(b^4*c^6)*b^4*c^6 + sqrt(2)*(b^4*c^6)^(3/4)*b^3*c^5*x)*(b^4*c^6)^(1/4))/(b^4*c^6)) + 4*sqrt(2)*(b^4*c^6)^(1/4)*x^3*arctan((b^4*c^6 - sqrt(2)*(b^4*c^6)^(1/4)*b^3*c^5*x + sqrt(2)*sqrt(b^6*c^10*x^2 + sqrt(b^4*c^6)*b^4*c^6 - sqrt(2)*(b^4*c^6)^(3/4)*b^3*c^5*x)*(b^4*c^6)^(1/4))/(b^4*c^6)) + sqrt(2)*(b^4*c^6)^(1/4)*x^3*log(b^6*c^10*x^2 + sqrt(b^4*c^6)*b^4*c^6 + sqrt(2)*(b^4*c^6)^(3/4)*b^3*c^5*x) - sqrt(2)*(b^4*c^6)^(1/4)*x^3*log(b^6*c^10*x^2 + sqrt(b^4*c^6)*b^4*c^6 - sqrt(2)*(b^4*c^6)^(3/4)*b^3*c^5*x) - 8*b*c*x^2 - 4*b*arctan(c*x^2) - 4*a)/x^3","B",0
73,1,350,0,0.467129," ","integrate((a+b*arctan(c*x^2))/x^6,x, algorithm=""fricas"")","\frac{12 \, \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{1}{4}} x^{5} \arctan\left(-\frac{b^{4} c^{10} + \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{3}{4}} b c^{3} x - \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{3}{4}} \sqrt{b^{2} c^{6} x^{2} + \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{1}{4}} b c^{3} x + \sqrt{b^{4} c^{10}}}}{b^{4} c^{10}}\right) + 12 \, \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{1}{4}} x^{5} \arctan\left(\frac{b^{4} c^{10} - \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{3}{4}} b c^{3} x + \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{3}{4}} \sqrt{b^{2} c^{6} x^{2} - \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{1}{4}} b c^{3} x + \sqrt{b^{4} c^{10}}}}{b^{4} c^{10}}\right) - 3 \, \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{1}{4}} x^{5} \log\left(b^{2} c^{6} x^{2} + \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{1}{4}} b c^{3} x + \sqrt{b^{4} c^{10}}\right) + 3 \, \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{1}{4}} x^{5} \log\left(b^{2} c^{6} x^{2} - \sqrt{2} \left(b^{4} c^{10}\right)^{\frac{1}{4}} b c^{3} x + \sqrt{b^{4} c^{10}}\right) - 8 \, b c x^{2} - 12 \, b \arctan\left(c x^{2}\right) - 12 \, a}{60 \, x^{5}}"," ",0,"1/60*(12*sqrt(2)*(b^4*c^10)^(1/4)*x^5*arctan(-(b^4*c^10 + sqrt(2)*(b^4*c^10)^(3/4)*b*c^3*x - sqrt(2)*(b^4*c^10)^(3/4)*sqrt(b^2*c^6*x^2 + sqrt(2)*(b^4*c^10)^(1/4)*b*c^3*x + sqrt(b^4*c^10)))/(b^4*c^10)) + 12*sqrt(2)*(b^4*c^10)^(1/4)*x^5*arctan((b^4*c^10 - sqrt(2)*(b^4*c^10)^(3/4)*b*c^3*x + sqrt(2)*(b^4*c^10)^(3/4)*sqrt(b^2*c^6*x^2 - sqrt(2)*(b^4*c^10)^(1/4)*b*c^3*x + sqrt(b^4*c^10)))/(b^4*c^10)) - 3*sqrt(2)*(b^4*c^10)^(1/4)*x^5*log(b^2*c^6*x^2 + sqrt(2)*(b^4*c^10)^(1/4)*b*c^3*x + sqrt(b^4*c^10)) + 3*sqrt(2)*(b^4*c^10)^(1/4)*x^5*log(b^2*c^6*x^2 - sqrt(2)*(b^4*c^10)^(1/4)*b*c^3*x + sqrt(b^4*c^10)) - 8*b*c*x^2 - 12*b*arctan(c*x^2) - 12*a)/x^5","B",0
74,1,137,0,0.448535," ","integrate(x^7*(a+b*arctan(c*x^2))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} c^{4} x^{8} - 2 \, a b c^{3} x^{6} + b^{2} c^{2} x^{4} + 6 \, a b c x^{2} + 3 \, {\left(b^{2} c^{4} x^{8} - b^{2}\right)} \arctan\left(c x^{2}\right)^{2} + 6 \, a b \arctan\left(\frac{1}{c x^{2}}\right) - 4 \, b^{2} \log\left(c^{2} x^{4} + 1\right) + 2 \, {\left(3 \, a b c^{4} x^{8} - b^{2} c^{3} x^{6} + 3 \, b^{2} c x^{2}\right)} \arctan\left(c x^{2}\right)}{24 \, c^{4}}"," ",0,"1/24*(3*a^2*c^4*x^8 - 2*a*b*c^3*x^6 + b^2*c^2*x^4 + 6*a*b*c*x^2 + 3*(b^2*c^4*x^8 - b^2)*arctan(c*x^2)^2 + 6*a*b*arctan(1/(c*x^2)) - 4*b^2*log(c^2*x^4 + 1) + 2*(3*a*b*c^4*x^8 - b^2*c^3*x^6 + 3*b^2*c*x^2)*arctan(c*x^2))/c^4","A",0
75,0,0,0,0.421737," ","integrate(x^5*(a+b*arctan(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{5} \arctan\left(c x^{2}\right)^{2} + 2 \, a b x^{5} \arctan\left(c x^{2}\right) + a^{2} x^{5}, x\right)"," ",0,"integral(b^2*x^5*arctan(c*x^2)^2 + 2*a*b*x^5*arctan(c*x^2) + a^2*x^5, x)","F",0
76,1,100,0,0.445412," ","integrate(x^3*(a+b*arctan(c*x^2))^2,x, algorithm=""fricas"")","\frac{a^{2} c^{2} x^{4} - 2 \, a b c x^{2} + {\left(b^{2} c^{2} x^{4} + b^{2}\right)} \arctan\left(c x^{2}\right)^{2} - 2 \, a b \arctan\left(\frac{1}{c x^{2}}\right) + b^{2} \log\left(c^{2} x^{4} + 1\right) + 2 \, {\left(a b c^{2} x^{4} - b^{2} c x^{2}\right)} \arctan\left(c x^{2}\right)}{4 \, c^{2}}"," ",0,"1/4*(a^2*c^2*x^4 - 2*a*b*c*x^2 + (b^2*c^2*x^4 + b^2)*arctan(c*x^2)^2 - 2*a*b*arctan(1/(c*x^2)) + b^2*log(c^2*x^4 + 1) + 2*(a*b*c^2*x^4 - b^2*c*x^2)*arctan(c*x^2))/c^2","A",0
77,0,0,0,0.428834," ","integrate(x*(a+b*arctan(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \arctan\left(c x^{2}\right)^{2} + 2 \, a b x \arctan\left(c x^{2}\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*arctan(c*x^2)^2 + 2*a*b*x*arctan(c*x^2) + a^2*x, x)","F",0
78,0,0,0,0.424089," ","integrate((a+b*arctan(c*x^2))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2) + a^2)/x, x)","F",0
79,0,0,0,0.427369," ","integrate((a+b*arctan(c*x^2))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right) + a^{2}}{x^{3}}, x\right)"," ",0,"integral((b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2) + a^2)/x^3, x)","F",0
80,1,115,0,0.440037," ","integrate((a+b*arctan(c*x^2))^2/x^5,x, algorithm=""fricas"")","\frac{2 \, a b c^{2} x^{4} \arctan\left(\frac{1}{c x^{2}}\right) - b^{2} c^{2} x^{4} \log\left(c^{2} x^{4} + 1\right) + 4 \, b^{2} c^{2} x^{4} \log\left(x\right) - 2 \, a b c x^{2} - {\left(b^{2} c^{2} x^{4} + b^{2}\right)} \arctan\left(c x^{2}\right)^{2} - a^{2} - 2 \, {\left(b^{2} c x^{2} + a b\right)} \arctan\left(c x^{2}\right)}{4 \, x^{4}}"," ",0,"1/4*(2*a*b*c^2*x^4*arctan(1/(c*x^2)) - b^2*c^2*x^4*log(c^2*x^4 + 1) + 4*b^2*c^2*x^4*log(x) - 2*a*b*c*x^2 - (b^2*c^2*x^4 + b^2)*arctan(c*x^2)^2 - a^2 - 2*(b^2*c*x^2 + a*b)*arctan(c*x^2))/x^4","A",0
81,0,0,0,0.438465," ","integrate(x^2*(a+b*arctan(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b x^{2} \arctan\left(c x^{2}\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*arctan(c*x^2)^2 + 2*a*b*x^2*arctan(c*x^2) + a^2*x^2, x)","F",0
82,0,0,0,0.425107," ","integrate((a+b*arctan(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right) + a^{2}, x\right)"," ",0,"integral(b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2) + a^2, x)","F",0
83,0,0,0,0.439473," ","integrate((a+b*arctan(c*x^2))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2) + a^2)/x^2, x)","F",0
84,0,0,0,0.416703," ","integrate((a+b*arctan(c*x^2))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right) + a^{2}}{x^{4}}, x\right)"," ",0,"integral((b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2) + a^2)/x^4, x)","F",0
85,0,0,0,0.430117," ","integrate((a+b*arctan(c*x^2))^2/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right) + a^{2}}{x^{6}}, x\right)"," ",0,"integral((b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2) + a^2)/x^6, x)","F",0
86,0,0,0,0.416292," ","integrate(x^3*(a+b*arctan(c*x^2))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{3} \arctan\left(c x^{2}\right)^{3} + 3 \, a b^{2} x^{3} \arctan\left(c x^{2}\right)^{2} + 3 \, a^{2} b x^{3} \arctan\left(c x^{2}\right) + a^{3} x^{3}, x\right)"," ",0,"integral(b^3*x^3*arctan(c*x^2)^3 + 3*a*b^2*x^3*arctan(c*x^2)^2 + 3*a^2*b*x^3*arctan(c*x^2) + a^3*x^3, x)","F",0
87,0,0,0,0.420715," ","integrate(x*(a+b*arctan(c*x^2))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \arctan\left(c x^{2}\right)^{3} + 3 \, a b^{2} x \arctan\left(c x^{2}\right)^{2} + 3 \, a^{2} b x \arctan\left(c x^{2}\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*arctan(c*x^2)^3 + 3*a*b^2*x*arctan(c*x^2)^2 + 3*a^2*b*x*arctan(c*x^2) + a^3*x, x)","F",0
88,0,0,0,0.417116," ","integrate((a+b*arctan(c*x^2))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x^{2}\right)^{3} + 3 \, a b^{2} \arctan\left(c x^{2}\right)^{2} + 3 \, a^{2} b \arctan\left(c x^{2}\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*arctan(c*x^2)^3 + 3*a*b^2*arctan(c*x^2)^2 + 3*a^2*b*arctan(c*x^2) + a^3)/x, x)","F",0
89,0,0,0,0.430728," ","integrate((a+b*arctan(c*x^2))^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x^{2}\right)^{3} + 3 \, a b^{2} \arctan\left(c x^{2}\right)^{2} + 3 \, a^{2} b \arctan\left(c x^{2}\right) + a^{3}}{x^{3}}, x\right)"," ",0,"integral((b^3*arctan(c*x^2)^3 + 3*a*b^2*arctan(c*x^2)^2 + 3*a^2*b*arctan(c*x^2) + a^3)/x^3, x)","F",0
90,0,0,0,0.422953," ","integrate((a+b*arctan(c*x^2))^3/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x^{2}\right)^{3} + 3 \, a b^{2} \arctan\left(c x^{2}\right)^{2} + 3 \, a^{2} b \arctan\left(c x^{2}\right) + a^{3}}{x^{5}}, x\right)"," ",0,"integral((b^3*arctan(c*x^2)^3 + 3*a*b^2*arctan(c*x^2)^2 + 3*a^2*b*arctan(c*x^2) + a^3)/x^5, x)","F",0
91,0,0,0,0.434280," ","integrate((d*x)^m*(a+b*arctan(c*x^2))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \arctan\left(c x^{2}\right)^{3} + 3 \, a b^{2} \arctan\left(c x^{2}\right)^{2} + 3 \, a^{2} b \arctan\left(c x^{2}\right) + a^{3}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^3*arctan(c*x^2)^3 + 3*a*b^2*arctan(c*x^2)^2 + 3*a^2*b*arctan(c*x^2) + a^3)*(d*x)^m, x)","F",0
92,0,0,0,0.424361," ","integrate((d*x)^m*(a+b*arctan(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right) + a^{2}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2) + a^2)*(d*x)^m, x)","F",0
93,0,0,0,0.434821," ","integrate((d*x)^m*(a+b*arctan(c*x^2)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x^{2}\right) + a\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b*arctan(c*x^2) + a)*(d*x)^m, x)","F",0
94,0,0,0,0.408168," ","integrate((d*x)^m/(a+b*arctan(c*x^2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b \arctan\left(c x^{2}\right) + a}, x\right)"," ",0,"integral((d*x)^m/(b*arctan(c*x^2) + a), x)","F",0
95,0,0,0,0.430068," ","integrate((d*x)^m/(a+b*arctan(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{2} \arctan\left(c x^{2}\right)^{2} + 2 \, a b \arctan\left(c x^{2}\right) + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(b^2*arctan(c*x^2)^2 + 2*a*b*arctan(c*x^2) + a^2), x)","F",0
96,1,51,0,0.413560," ","integrate(x^11*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","\frac{3 \, a c^{4} x^{12} - b c^{3} x^{9} + 3 \, b c x^{3} + 3 \, {\left(b c^{4} x^{12} - b\right)} \arctan\left(c x^{3}\right)}{36 \, c^{4}}"," ",0,"1/36*(3*a*c^4*x^12 - b*c^3*x^9 + 3*b*c*x^3 + 3*(b*c^4*x^12 - b)*arctan(c*x^3))/c^4","A",0
97,1,51,0,0.416614," ","integrate(x^8*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","\frac{2 \, b c^{3} x^{9} \arctan\left(c x^{3}\right) + 2 \, a c^{3} x^{9} - b c^{2} x^{6} + b \log\left(c^{2} x^{6} + 1\right)}{18 \, c^{3}}"," ",0,"1/18*(2*b*c^3*x^9*arctan(c*x^3) + 2*a*c^3*x^9 - b*c^2*x^6 + b*log(c^2*x^6 + 1))/c^3","A",0
98,1,38,0,0.423564," ","integrate(x^5*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","\frac{a c^{2} x^{6} - b c x^{3} + {\left(b c^{2} x^{6} + b\right)} \arctan\left(c x^{3}\right)}{6 \, c^{2}}"," ",0,"1/6*(a*c^2*x^6 - b*c*x^3 + (b*c^2*x^6 + b)*arctan(c*x^3))/c^2","A",0
99,1,39,0,0.416417," ","integrate(x^2*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","\frac{2 \, b c x^{3} \arctan\left(c x^{3}\right) + 2 \, a c x^{3} - b \log\left(c^{2} x^{6} + 1\right)}{6 \, c}"," ",0,"1/6*(2*b*c*x^3*arctan(c*x^3) + 2*a*c*x^3 - b*log(c^2*x^6 + 1))/c","A",0
100,0,0,0,0.426398," ","integrate((a+b*arctan(c*x^3))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(c x^{3}\right) + a}{x}, x\right)"," ",0,"integral((b*arctan(c*x^3) + a)/x, x)","F",0
101,1,43,0,0.469283," ","integrate((a+b*arctan(c*x^3))/x^4,x, algorithm=""fricas"")","-\frac{b c x^{3} \log\left(c^{2} x^{6} + 1\right) - 6 \, b c x^{3} \log\left(x\right) + 2 \, b \arctan\left(c x^{3}\right) + 2 \, a}{6 \, x^{3}}"," ",0,"-1/6*(b*c*x^3*log(c^2*x^6 + 1) - 6*b*c*x^3*log(x) + 2*b*arctan(c*x^3) + 2*a)/x^3","A",0
102,1,30,0,0.409828," ","integrate((a+b*arctan(c*x^3))/x^7,x, algorithm=""fricas"")","-\frac{b c x^{3} + {\left(b c^{2} x^{6} + b\right)} \arctan\left(c x^{3}\right) + a}{6 \, x^{6}}"," ",0,"-1/6*(b*c*x^3 + (b*c^2*x^6 + b)*arctan(c*x^3) + a)/x^6","A",0
103,1,54,0,0.444093," ","integrate((a+b*arctan(c*x^3))/x^10,x, algorithm=""fricas"")","\frac{b c^{3} x^{9} \log\left(c^{2} x^{6} + 1\right) - 6 \, b c^{3} x^{9} \log\left(x\right) - b c x^{3} - 2 \, b \arctan\left(c x^{3}\right) - 2 \, a}{18 \, x^{9}}"," ",0,"1/18*(b*c^3*x^9*log(c^2*x^6 + 1) - 6*b*c^3*x^9*log(x) - b*c*x^3 - 2*b*arctan(c*x^3) - 2*a)/x^9","A",0
104,1,399,0,0.459078," ","integrate(x^3*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","\frac{4 \, b c x^{4} \arctan\left(c x^{3}\right) + 4 \, a c x^{4} + \sqrt{3} c \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{6}} \log\left(b^{2} x^{2} + \sqrt{3} b c x \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{6}} + c^{2} \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{3}}\right) - \sqrt{3} c \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{6}} \log\left(b^{2} x^{2} - \sqrt{3} b c x \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{6}} + c^{2} \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{3}}\right) - 4 \, c \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2 \, b c^{7} x \left(\frac{b^{6}}{c^{8}}\right)^{\frac{5}{6}} - 2 \, \sqrt{b^{2} x^{2} + \sqrt{3} b c x \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{6}} + c^{2} \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{3}}} c^{7} \left(\frac{b^{6}}{c^{8}}\right)^{\frac{5}{6}} + \sqrt{3} b^{6}}{b^{6}}\right) - 4 \, c \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2 \, b c^{7} x \left(\frac{b^{6}}{c^{8}}\right)^{\frac{5}{6}} - 2 \, \sqrt{b^{2} x^{2} - \sqrt{3} b c x \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{6}} + c^{2} \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{3}}} c^{7} \left(\frac{b^{6}}{c^{8}}\right)^{\frac{5}{6}} - \sqrt{3} b^{6}}{b^{6}}\right) - 8 \, c \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{6}} \arctan\left(-\frac{b c^{7} x \left(\frac{b^{6}}{c^{8}}\right)^{\frac{5}{6}} - \sqrt{b^{2} x^{2} + c^{2} \left(\frac{b^{6}}{c^{8}}\right)^{\frac{1}{3}}} c^{7} \left(\frac{b^{6}}{c^{8}}\right)^{\frac{5}{6}}}{b^{6}}\right) - 12 \, b x}{16 \, c}"," ",0,"1/16*(4*b*c*x^4*arctan(c*x^3) + 4*a*c*x^4 + sqrt(3)*c*(b^6/c^8)^(1/6)*log(b^2*x^2 + sqrt(3)*b*c*x*(b^6/c^8)^(1/6) + c^2*(b^6/c^8)^(1/3)) - sqrt(3)*c*(b^6/c^8)^(1/6)*log(b^2*x^2 - sqrt(3)*b*c*x*(b^6/c^8)^(1/6) + c^2*(b^6/c^8)^(1/3)) - 4*c*(b^6/c^8)^(1/6)*arctan(-(2*b*c^7*x*(b^6/c^8)^(5/6) - 2*sqrt(b^2*x^2 + sqrt(3)*b*c*x*(b^6/c^8)^(1/6) + c^2*(b^6/c^8)^(1/3))*c^7*(b^6/c^8)^(5/6) + sqrt(3)*b^6)/b^6) - 4*c*(b^6/c^8)^(1/6)*arctan(-(2*b*c^7*x*(b^6/c^8)^(5/6) - 2*sqrt(b^2*x^2 - sqrt(3)*b*c*x*(b^6/c^8)^(1/6) + c^2*(b^6/c^8)^(1/3))*c^7*(b^6/c^8)^(5/6) - sqrt(3)*b^6)/b^6) - 8*c*(b^6/c^8)^(1/6)*arctan(-(b*c^7*x*(b^6/c^8)^(5/6) - sqrt(b^2*x^2 + c^2*(b^6/c^8)^(1/3))*c^7*(b^6/c^8)^(5/6))/b^6) - 12*b*x)/c","B",0
105,1,234,0,0.459456," ","integrate(a+b*arctan(c*x^3),x, algorithm=""fricas"")","\left[\frac{4 \, b c x \arctan\left(c x^{3}\right) + \sqrt{3} b c \sqrt{-\frac{1}{c^{\frac{2}{3}}}} \log\left(\frac{2 \, c^{2} x^{6} - 3 \, c^{\frac{2}{3}} x^{2} - \sqrt{3} {\left(2 \, c^{\frac{5}{3}} x^{4} + c x^{2} - c^{\frac{1}{3}}\right)} \sqrt{-\frac{1}{c^{\frac{2}{3}}}} - 1}{c^{2} x^{6} + 1}\right) + 4 \, a c x - b c^{\frac{2}{3}} \log\left(c^{2} x^{4} - c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right) + 2 \, b c^{\frac{2}{3}} \log\left(c x^{2} + c^{\frac{1}{3}}\right)}{4 \, c}, \frac{4 \, b c x \arctan\left(c x^{3}\right) + 2 \, \sqrt{3} b c^{\frac{2}{3}} \arctan\left(-\frac{\sqrt{3} {\left(2 \, c x^{2} - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right) + 4 \, a c x - b c^{\frac{2}{3}} \log\left(c^{2} x^{4} - c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right) + 2 \, b c^{\frac{2}{3}} \log\left(c x^{2} + c^{\frac{1}{3}}\right)}{4 \, c}\right]"," ",0,"[1/4*(4*b*c*x*arctan(c*x^3) + sqrt(3)*b*c*sqrt(-1/c^(2/3))*log((2*c^2*x^6 - 3*c^(2/3)*x^2 - sqrt(3)*(2*c^(5/3)*x^4 + c*x^2 - c^(1/3))*sqrt(-1/c^(2/3)) - 1)/(c^2*x^6 + 1)) + 4*a*c*x - b*c^(2/3)*log(c^2*x^4 - c^(4/3)*x^2 + c^(2/3)) + 2*b*c^(2/3)*log(c*x^2 + c^(1/3)))/c, 1/4*(4*b*c*x*arctan(c*x^3) + 2*sqrt(3)*b*c^(2/3)*arctan(-1/3*sqrt(3)*(2*c*x^2 - c^(1/3))/c^(1/3)) + 4*a*c*x - b*c^(2/3)*log(c^2*x^4 - c^(4/3)*x^2 + c^(2/3)) + 2*b*c^(2/3)*log(c*x^2 + c^(1/3)))/c]","A",0
106,1,505,0,0.480131," ","integrate((a+b*arctan(c*x^3))/x^3,x, algorithm=""fricas"")","\frac{\sqrt{3} \left(b^{6} c^{4}\right)^{\frac{1}{6}} x^{2} \log\left(4 \, b^{2} c^{2} x^{2} + 4 \, \sqrt{3} \left(b^{6} c^{4}\right)^{\frac{1}{6}} b c x + 4 \, \left(b^{6} c^{4}\right)^{\frac{1}{3}}\right) - \sqrt{3} \left(b^{6} c^{4}\right)^{\frac{1}{6}} x^{2} \log\left(4 \, b^{2} c^{2} x^{2} - 4 \, \sqrt{3} \left(b^{6} c^{4}\right)^{\frac{1}{6}} b c x + 4 \, \left(b^{6} c^{4}\right)^{\frac{1}{3}}\right) + \sqrt{3} \left(b^{6} c^{4}\right)^{\frac{1}{6}} x^{2} \log\left(b^{2} c^{2} x^{2} + \sqrt{3} \left(b^{6} c^{4}\right)^{\frac{1}{6}} b c x + \left(b^{6} c^{4}\right)^{\frac{1}{3}}\right) - \sqrt{3} \left(b^{6} c^{4}\right)^{\frac{1}{6}} x^{2} \log\left(b^{2} c^{2} x^{2} - \sqrt{3} \left(b^{6} c^{4}\right)^{\frac{1}{6}} b c x + \left(b^{6} c^{4}\right)^{\frac{1}{3}}\right) - 8 \, \left(b^{6} c^{4}\right)^{\frac{1}{6}} x^{2} \arctan\left(-\frac{\sqrt{3} b^{6} c^{4} + 2 \, \left(b^{6} c^{4}\right)^{\frac{5}{6}} b c x - 2 \, \left(b^{6} c^{4}\right)^{\frac{5}{6}} \sqrt{b^{2} c^{2} x^{2} + \sqrt{3} \left(b^{6} c^{4}\right)^{\frac{1}{6}} b c x + \left(b^{6} c^{4}\right)^{\frac{1}{3}}}}{b^{6} c^{4}}\right) - 8 \, \left(b^{6} c^{4}\right)^{\frac{1}{6}} x^{2} \arctan\left(\frac{\sqrt{3} b^{6} c^{4} - 2 \, \left(b^{6} c^{4}\right)^{\frac{5}{6}} b c x + 2 \, \left(b^{6} c^{4}\right)^{\frac{5}{6}} \sqrt{b^{2} c^{2} x^{2} - \sqrt{3} \left(b^{6} c^{4}\right)^{\frac{1}{6}} b c x + \left(b^{6} c^{4}\right)^{\frac{1}{3}}}}{b^{6} c^{4}}\right) - 16 \, \left(b^{6} c^{4}\right)^{\frac{1}{6}} x^{2} \arctan\left(-\frac{\left(b^{6} c^{4}\right)^{\frac{5}{6}} b c x - \left(b^{6} c^{4}\right)^{\frac{5}{6}} \sqrt{b^{2} c^{2} x^{2} + \left(b^{6} c^{4}\right)^{\frac{1}{3}}}}{b^{6} c^{4}}\right) - 8 \, b \arctan\left(c x^{3}\right) - 8 \, a}{16 \, x^{2}}"," ",0,"1/16*(sqrt(3)*(b^6*c^4)^(1/6)*x^2*log(4*b^2*c^2*x^2 + 4*sqrt(3)*(b^6*c^4)^(1/6)*b*c*x + 4*(b^6*c^4)^(1/3)) - sqrt(3)*(b^6*c^4)^(1/6)*x^2*log(4*b^2*c^2*x^2 - 4*sqrt(3)*(b^6*c^4)^(1/6)*b*c*x + 4*(b^6*c^4)^(1/3)) + sqrt(3)*(b^6*c^4)^(1/6)*x^2*log(b^2*c^2*x^2 + sqrt(3)*(b^6*c^4)^(1/6)*b*c*x + (b^6*c^4)^(1/3)) - sqrt(3)*(b^6*c^4)^(1/6)*x^2*log(b^2*c^2*x^2 - sqrt(3)*(b^6*c^4)^(1/6)*b*c*x + (b^6*c^4)^(1/3)) - 8*(b^6*c^4)^(1/6)*x^2*arctan(-(sqrt(3)*b^6*c^4 + 2*(b^6*c^4)^(5/6)*b*c*x - 2*(b^6*c^4)^(5/6)*sqrt(b^2*c^2*x^2 + sqrt(3)*(b^6*c^4)^(1/6)*b*c*x + (b^6*c^4)^(1/3)))/(b^6*c^4)) - 8*(b^6*c^4)^(1/6)*x^2*arctan((sqrt(3)*b^6*c^4 - 2*(b^6*c^4)^(5/6)*b*c*x + 2*(b^6*c^4)^(5/6)*sqrt(b^2*c^2*x^2 - sqrt(3)*(b^6*c^4)^(1/6)*b*c*x + (b^6*c^4)^(1/3)))/(b^6*c^4)) - 16*(b^6*c^4)^(1/6)*x^2*arctan(-((b^6*c^4)^(5/6)*b*c*x - (b^6*c^4)^(5/6)*sqrt(b^2*c^2*x^2 + (b^6*c^4)^(1/3)))/(b^6*c^4)) - 8*b*arctan(c*x^3) - 8*a)/x^2","B",0
107,1,121,0,0.430276," ","integrate((a+b*arctan(c*x^3))/x^6,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} b {\left(c^{2}\right)}^{\frac{1}{3}} c x^{5} \arctan\left(\frac{2}{3} \, \sqrt{3} {\left(c^{2}\right)}^{\frac{1}{3}} x^{2} - \frac{1}{3} \, \sqrt{3}\right) + b {\left(c^{2}\right)}^{\frac{1}{3}} c x^{5} \log\left(c^{2} x^{4} - {\left(c^{2}\right)}^{\frac{2}{3}} x^{2} + {\left(c^{2}\right)}^{\frac{1}{3}}\right) - 2 \, b {\left(c^{2}\right)}^{\frac{1}{3}} c x^{5} \log\left(c^{2} x^{2} + {\left(c^{2}\right)}^{\frac{2}{3}}\right) + 6 \, b c x^{3} + 4 \, b \arctan\left(c x^{3}\right) + 4 \, a}{20 \, x^{5}}"," ",0,"-1/20*(2*sqrt(3)*b*(c^2)^(1/3)*c*x^5*arctan(2/3*sqrt(3)*(c^2)^(1/3)*x^2 - 1/3*sqrt(3)) + b*(c^2)^(1/3)*c*x^5*log(c^2*x^4 - (c^2)^(2/3)*x^2 + (c^2)^(1/3)) - 2*b*(c^2)^(1/3)*c*x^5*log(c^2*x^2 + (c^2)^(2/3)) + 6*b*c*x^3 + 4*b*arctan(c*x^3) + 4*a)/x^5","A",0
108,1,439,0,0.454637," ","integrate(x^7*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","\frac{20 \, b c x^{8} \arctan\left(c x^{3}\right) + 20 \, a c x^{8} - 12 \, b x^{5} - 5 \, \sqrt{3} c \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}} \log\left(\sqrt{3} b^{5} c^{13} x \left(\frac{b^{6}}{c^{16}}\right)^{\frac{5}{6}} + b^{6} c^{10} \left(\frac{b^{6}}{c^{16}}\right)^{\frac{2}{3}} + b^{10} x^{2}\right) + 5 \, \sqrt{3} c \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}} \log\left(-\sqrt{3} b^{5} c^{13} x \left(\frac{b^{6}}{c^{16}}\right)^{\frac{5}{6}} + b^{6} c^{10} \left(\frac{b^{6}}{c^{16}}\right)^{\frac{2}{3}} + b^{10} x^{2}\right) - 20 \, c \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2 \, b^{5} c^{3} x \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}} + \sqrt{3} b^{6} - 2 \, \sqrt{\sqrt{3} b^{5} c^{13} x \left(\frac{b^{6}}{c^{16}}\right)^{\frac{5}{6}} + b^{6} c^{10} \left(\frac{b^{6}}{c^{16}}\right)^{\frac{2}{3}} + b^{10} x^{2}} c^{3} \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}}}{b^{6}}\right) - 20 \, c \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2 \, b^{5} c^{3} x \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}} - \sqrt{3} b^{6} - 2 \, \sqrt{-\sqrt{3} b^{5} c^{13} x \left(\frac{b^{6}}{c^{16}}\right)^{\frac{5}{6}} + b^{6} c^{10} \left(\frac{b^{6}}{c^{16}}\right)^{\frac{2}{3}} + b^{10} x^{2}} c^{3} \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}}}{b^{6}}\right) - 40 \, c \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}} \arctan\left(-\frac{b^{5} c^{3} x \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}} - \sqrt{b^{6} c^{10} \left(\frac{b^{6}}{c^{16}}\right)^{\frac{2}{3}} + b^{10} x^{2}} c^{3} \left(\frac{b^{6}}{c^{16}}\right)^{\frac{1}{6}}}{b^{6}}\right)}{160 \, c}"," ",0,"1/160*(20*b*c*x^8*arctan(c*x^3) + 20*a*c*x^8 - 12*b*x^5 - 5*sqrt(3)*c*(b^6/c^16)^(1/6)*log(sqrt(3)*b^5*c^13*x*(b^6/c^16)^(5/6) + b^6*c^10*(b^6/c^16)^(2/3) + b^10*x^2) + 5*sqrt(3)*c*(b^6/c^16)^(1/6)*log(-sqrt(3)*b^5*c^13*x*(b^6/c^16)^(5/6) + b^6*c^10*(b^6/c^16)^(2/3) + b^10*x^2) - 20*c*(b^6/c^16)^(1/6)*arctan(-(2*b^5*c^3*x*(b^6/c^16)^(1/6) + sqrt(3)*b^6 - 2*sqrt(sqrt(3)*b^5*c^13*x*(b^6/c^16)^(5/6) + b^6*c^10*(b^6/c^16)^(2/3) + b^10*x^2)*c^3*(b^6/c^16)^(1/6))/b^6) - 20*c*(b^6/c^16)^(1/6)*arctan(-(2*b^5*c^3*x*(b^6/c^16)^(1/6) - sqrt(3)*b^6 - 2*sqrt(-sqrt(3)*b^5*c^13*x*(b^6/c^16)^(5/6) + b^6*c^10*(b^6/c^16)^(2/3) + b^10*x^2)*c^3*(b^6/c^16)^(1/6))/b^6) - 40*c*(b^6/c^16)^(1/6)*arctan(-(b^5*c^3*x*(b^6/c^16)^(1/6) - sqrt(b^6*c^10*(b^6/c^16)^(2/3) + b^10*x^2)*c^3*(b^6/c^16)^(1/6))/b^6))/c","B",0
109,1,137,0,0.447942," ","integrate(x^4*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","\frac{4 \, b c^{3} x^{5} \arctan\left(c x^{3}\right) + 4 \, a c^{3} x^{5} - 6 \, b c^{2} x^{2} + 2 \, \sqrt{3} b {\left(c^{2}\right)}^{\frac{1}{6}} c \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(c^{2}\right)}^{\frac{2}{3}} x^{2} - {\left(c^{2}\right)}^{\frac{1}{3}}\right)} {\left(c^{2}\right)}^{\frac{1}{6}}}{3 \, c}\right) - b {\left(c^{2}\right)}^{\frac{2}{3}} \log\left(c^{2} x^{4} - {\left(c^{2}\right)}^{\frac{2}{3}} x^{2} + {\left(c^{2}\right)}^{\frac{1}{3}}\right) + 2 \, b {\left(c^{2}\right)}^{\frac{2}{3}} \log\left(c^{2} x^{2} + {\left(c^{2}\right)}^{\frac{2}{3}}\right)}{20 \, c^{3}}"," ",0,"1/20*(4*b*c^3*x^5*arctan(c*x^3) + 4*a*c^3*x^5 - 6*b*c^2*x^2 + 2*sqrt(3)*b*(c^2)^(1/6)*c*arctan(1/3*sqrt(3)*(2*(c^2)^(2/3)*x^2 - (c^2)^(1/3))*(c^2)^(1/6)/c) - b*(c^2)^(2/3)*log(c^2*x^4 - (c^2)^(2/3)*x^2 + (c^2)^(1/3)) + 2*b*(c^2)^(2/3)*log(c^2*x^2 + (c^2)^(2/3)))/c^3","A",0
110,1,408,0,0.466540," ","integrate(x*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","\frac{1}{2} \, b x^{2} \arctan\left(c x^{3}\right) + \frac{1}{2} \, a x^{2} + \frac{1}{8} \, \sqrt{3} \left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} \log\left(b^{10} x^{2} + \sqrt{3} \left(\frac{b^{6}}{c^{4}}\right)^{\frac{5}{6}} b^{5} c^{3} x + \left(\frac{b^{6}}{c^{4}}\right)^{\frac{2}{3}} b^{6} c^{2}\right) - \frac{1}{8} \, \sqrt{3} \left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} \log\left(b^{10} x^{2} - \sqrt{3} \left(\frac{b^{6}}{c^{4}}\right)^{\frac{5}{6}} b^{5} c^{3} x + \left(\frac{b^{6}}{c^{4}}\right)^{\frac{2}{3}} b^{6} c^{2}\right) + \frac{1}{2} \, \left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2 \, \left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} b^{5} c x + \sqrt{3} b^{6} - 2 \, \sqrt{b^{10} x^{2} + \sqrt{3} \left(\frac{b^{6}}{c^{4}}\right)^{\frac{5}{6}} b^{5} c^{3} x + \left(\frac{b^{6}}{c^{4}}\right)^{\frac{2}{3}} b^{6} c^{2}} \left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} c}{b^{6}}\right) + \frac{1}{2} \, \left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} \arctan\left(-\frac{2 \, \left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} b^{5} c x - \sqrt{3} b^{6} - 2 \, \sqrt{b^{10} x^{2} - \sqrt{3} \left(\frac{b^{6}}{c^{4}}\right)^{\frac{5}{6}} b^{5} c^{3} x + \left(\frac{b^{6}}{c^{4}}\right)^{\frac{2}{3}} b^{6} c^{2}} \left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} c}{b^{6}}\right) + \left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} \arctan\left(-\frac{\left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} b^{5} c x - \sqrt{b^{10} x^{2} + \left(\frac{b^{6}}{c^{4}}\right)^{\frac{2}{3}} b^{6} c^{2}} \left(\frac{b^{6}}{c^{4}}\right)^{\frac{1}{6}} c}{b^{6}}\right)"," ",0,"1/2*b*x^2*arctan(c*x^3) + 1/2*a*x^2 + 1/8*sqrt(3)*(b^6/c^4)^(1/6)*log(b^10*x^2 + sqrt(3)*(b^6/c^4)^(5/6)*b^5*c^3*x + (b^6/c^4)^(2/3)*b^6*c^2) - 1/8*sqrt(3)*(b^6/c^4)^(1/6)*log(b^10*x^2 - sqrt(3)*(b^6/c^4)^(5/6)*b^5*c^3*x + (b^6/c^4)^(2/3)*b^6*c^2) + 1/2*(b^6/c^4)^(1/6)*arctan(-(2*(b^6/c^4)^(1/6)*b^5*c*x + sqrt(3)*b^6 - 2*sqrt(b^10*x^2 + sqrt(3)*(b^6/c^4)^(5/6)*b^5*c^3*x + (b^6/c^4)^(2/3)*b^6*c^2)*(b^6/c^4)^(1/6)*c)/b^6) + 1/2*(b^6/c^4)^(1/6)*arctan(-(2*(b^6/c^4)^(1/6)*b^5*c*x - sqrt(3)*b^6 - 2*sqrt(b^10*x^2 - sqrt(3)*(b^6/c^4)^(5/6)*b^5*c^3*x + (b^6/c^4)^(2/3)*b^6*c^2)*(b^6/c^4)^(1/6)*c)/b^6) + (b^6/c^4)^(1/6)*arctan(-((b^6/c^4)^(1/6)*b^5*c*x - sqrt(b^10*x^2 + (b^6/c^4)^(2/3)*b^6*c^2)*(b^6/c^4)^(1/6)*c)/b^6)","B",0
111,1,90,0,0.438728," ","integrate((a+b*arctan(c*x^3))/x^2,x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} b c^{\frac{1}{3}} x \arctan\left(\frac{2}{3} \, \sqrt{3} c^{\frac{2}{3}} x^{2} - \frac{1}{3} \, \sqrt{3}\right) - b c^{\frac{1}{3}} x \log\left(c^{2} x^{4} - c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right) + 2 \, b c^{\frac{1}{3}} x \log\left(c x^{2} + c^{\frac{1}{3}}\right) - 4 \, b \arctan\left(c x^{3}\right) - 4 \, a}{4 \, x}"," ",0,"1/4*(2*sqrt(3)*b*c^(1/3)*x*arctan(2/3*sqrt(3)*c^(2/3)*x^2 - 1/3*sqrt(3)) - b*c^(1/3)*x*log(c^2*x^4 - c^(4/3)*x^2 + c^(2/3)) + 2*b*c^(1/3)*x*log(c*x^2 + c^(1/3)) - 4*b*arctan(c*x^3) - 4*a)/x","A",0
112,1,595,0,0.515519," ","integrate((a+b*arctan(c*x^3))/x^5,x, algorithm=""fricas"")","\frac{\sqrt{3} \left(b^{6} c^{8}\right)^{\frac{1}{6}} x^{4} \log\left(4 \, b^{10} c^{14} x^{2} + 4 \, \left(b^{6} c^{8}\right)^{\frac{2}{3}} b^{6} c^{8} + 4 \, \sqrt{3} \left(b^{6} c^{8}\right)^{\frac{5}{6}} b^{5} c^{7} x\right) - \sqrt{3} \left(b^{6} c^{8}\right)^{\frac{1}{6}} x^{4} \log\left(4 \, b^{10} c^{14} x^{2} + 4 \, \left(b^{6} c^{8}\right)^{\frac{2}{3}} b^{6} c^{8} - 4 \, \sqrt{3} \left(b^{6} c^{8}\right)^{\frac{5}{6}} b^{5} c^{7} x\right) + \sqrt{3} \left(b^{6} c^{8}\right)^{\frac{1}{6}} x^{4} \log\left(b^{10} c^{14} x^{2} + \left(b^{6} c^{8}\right)^{\frac{2}{3}} b^{6} c^{8} + \sqrt{3} \left(b^{6} c^{8}\right)^{\frac{5}{6}} b^{5} c^{7} x\right) - \sqrt{3} \left(b^{6} c^{8}\right)^{\frac{1}{6}} x^{4} \log\left(b^{10} c^{14} x^{2} + \left(b^{6} c^{8}\right)^{\frac{2}{3}} b^{6} c^{8} - \sqrt{3} \left(b^{6} c^{8}\right)^{\frac{5}{6}} b^{5} c^{7} x\right) + 8 \, \left(b^{6} c^{8}\right)^{\frac{1}{6}} x^{4} \arctan\left(-\frac{\sqrt{3} b^{6} c^{8} + 2 \, \left(b^{6} c^{8}\right)^{\frac{1}{6}} b^{5} c^{7} x - 2 \, \sqrt{b^{10} c^{14} x^{2} + \left(b^{6} c^{8}\right)^{\frac{2}{3}} b^{6} c^{8} + \sqrt{3} \left(b^{6} c^{8}\right)^{\frac{5}{6}} b^{5} c^{7} x} \left(b^{6} c^{8}\right)^{\frac{1}{6}}}{b^{6} c^{8}}\right) + 8 \, \left(b^{6} c^{8}\right)^{\frac{1}{6}} x^{4} \arctan\left(\frac{\sqrt{3} b^{6} c^{8} - 2 \, \left(b^{6} c^{8}\right)^{\frac{1}{6}} b^{5} c^{7} x + 2 \, \sqrt{b^{10} c^{14} x^{2} + \left(b^{6} c^{8}\right)^{\frac{2}{3}} b^{6} c^{8} - \sqrt{3} \left(b^{6} c^{8}\right)^{\frac{5}{6}} b^{5} c^{7} x} \left(b^{6} c^{8}\right)^{\frac{1}{6}}}{b^{6} c^{8}}\right) + 16 \, \left(b^{6} c^{8}\right)^{\frac{1}{6}} x^{4} \arctan\left(-\frac{\left(b^{6} c^{8}\right)^{\frac{1}{6}} b^{5} c^{7} x - \sqrt{b^{10} c^{14} x^{2} + \left(b^{6} c^{8}\right)^{\frac{2}{3}} b^{6} c^{8}} \left(b^{6} c^{8}\right)^{\frac{1}{6}}}{b^{6} c^{8}}\right) - 24 \, b c x^{3} - 8 \, b \arctan\left(c x^{3}\right) - 8 \, a}{32 \, x^{4}}"," ",0,"1/32*(sqrt(3)*(b^6*c^8)^(1/6)*x^4*log(4*b^10*c^14*x^2 + 4*(b^6*c^8)^(2/3)*b^6*c^8 + 4*sqrt(3)*(b^6*c^8)^(5/6)*b^5*c^7*x) - sqrt(3)*(b^6*c^8)^(1/6)*x^4*log(4*b^10*c^14*x^2 + 4*(b^6*c^8)^(2/3)*b^6*c^8 - 4*sqrt(3)*(b^6*c^8)^(5/6)*b^5*c^7*x) + sqrt(3)*(b^6*c^8)^(1/6)*x^4*log(b^10*c^14*x^2 + (b^6*c^8)^(2/3)*b^6*c^8 + sqrt(3)*(b^6*c^8)^(5/6)*b^5*c^7*x) - sqrt(3)*(b^6*c^8)^(1/6)*x^4*log(b^10*c^14*x^2 + (b^6*c^8)^(2/3)*b^6*c^8 - sqrt(3)*(b^6*c^8)^(5/6)*b^5*c^7*x) + 8*(b^6*c^8)^(1/6)*x^4*arctan(-(sqrt(3)*b^6*c^8 + 2*(b^6*c^8)^(1/6)*b^5*c^7*x - 2*sqrt(b^10*c^14*x^2 + (b^6*c^8)^(2/3)*b^6*c^8 + sqrt(3)*(b^6*c^8)^(5/6)*b^5*c^7*x)*(b^6*c^8)^(1/6))/(b^6*c^8)) + 8*(b^6*c^8)^(1/6)*x^4*arctan((sqrt(3)*b^6*c^8 - 2*(b^6*c^8)^(1/6)*b^5*c^7*x + 2*sqrt(b^10*c^14*x^2 + (b^6*c^8)^(2/3)*b^6*c^8 - sqrt(3)*(b^6*c^8)^(5/6)*b^5*c^7*x)*(b^6*c^8)^(1/6))/(b^6*c^8)) + 16*(b^6*c^8)^(1/6)*x^4*arctan(-((b^6*c^8)^(1/6)*b^5*c^7*x - sqrt(b^10*c^14*x^2 + (b^6*c^8)^(2/3)*b^6*c^8)*(b^6*c^8)^(1/6))/(b^6*c^8)) - 24*b*c*x^3 - 8*b*arctan(c*x^3) - 8*a)/x^4","B",0
113,1,129,0,0.470661," ","integrate(x^11*(a+b*arctan(c*x^3))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} c^{4} x^{12} - 2 \, a b c^{3} x^{9} + b^{2} c^{2} x^{6} + 6 \, a b c x^{3} + 3 \, {\left(b^{2} c^{4} x^{12} - b^{2}\right)} \arctan\left(c x^{3}\right)^{2} - 4 \, b^{2} \log\left(c^{2} x^{6} + 1\right) + 2 \, {\left(3 \, a b c^{4} x^{12} - b^{2} c^{3} x^{9} + 3 \, b^{2} c x^{3} - 3 \, a b\right)} \arctan\left(c x^{3}\right)}{36 \, c^{4}}"," ",0,"1/36*(3*a^2*c^4*x^12 - 2*a*b*c^3*x^9 + b^2*c^2*x^6 + 6*a*b*c*x^3 + 3*(b^2*c^4*x^12 - b^2)*arctan(c*x^3)^2 - 4*b^2*log(c^2*x^6 + 1) + 2*(3*a*b*c^4*x^12 - b^2*c^3*x^9 + 3*b^2*c*x^3 - 3*a*b)*arctan(c*x^3))/c^4","A",0
114,0,0,0,0.427089," ","integrate(x^8*(a+b*arctan(c*x^3))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{8} \arctan\left(c x^{3}\right)^{2} + 2 \, a b x^{8} \arctan\left(c x^{3}\right) + a^{2} x^{8}, x\right)"," ",0,"integral(b^2*x^8*arctan(c*x^3)^2 + 2*a*b*x^8*arctan(c*x^3) + a^2*x^8, x)","F",0
115,1,91,0,0.445477," ","integrate(x^5*(a+b*arctan(c*x^3))^2,x, algorithm=""fricas"")","\frac{a^{2} c^{2} x^{6} - 2 \, a b c x^{3} + {\left(b^{2} c^{2} x^{6} + b^{2}\right)} \arctan\left(c x^{3}\right)^{2} + b^{2} \log\left(c^{2} x^{6} + 1\right) + 2 \, {\left(a b c^{2} x^{6} - b^{2} c x^{3} + a b\right)} \arctan\left(c x^{3}\right)}{6 \, c^{2}}"," ",0,"1/6*(a^2*c^2*x^6 - 2*a*b*c*x^3 + (b^2*c^2*x^6 + b^2)*arctan(c*x^3)^2 + b^2*log(c^2*x^6 + 1) + 2*(a*b*c^2*x^6 - b^2*c*x^3 + a*b)*arctan(c*x^3))/c^2","A",0
116,0,0,0,0.419382," ","integrate(x^2*(a+b*arctan(c*x^3))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \arctan\left(c x^{3}\right)^{2} + 2 \, a b x^{2} \arctan\left(c x^{3}\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*arctan(c*x^3)^2 + 2*a*b*x^2*arctan(c*x^3) + a^2*x^2, x)","F",0
117,0,0,0,0.415628," ","integrate((a+b*arctan(c*x^3))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x^{3}\right)^{2} + 2 \, a b \arctan\left(c x^{3}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctan(c*x^3)^2 + 2*a*b*arctan(c*x^3) + a^2)/x, x)","F",0
118,0,0,0,0.441562," ","integrate((a+b*arctan(c*x^3))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x^{3}\right)^{2} + 2 \, a b \arctan\left(c x^{3}\right) + a^{2}}{x^{4}}, x\right)"," ",0,"integral((b^2*arctan(c*x^3)^2 + 2*a*b*arctan(c*x^3) + a^2)/x^4, x)","F",0
119,1,102,0,0.460544," ","integrate((a+b*arctan(c*x^3))^2/x^7,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} x^{6} \log\left(c^{2} x^{6} + 1\right) - 6 \, b^{2} c^{2} x^{6} \log\left(x\right) + 2 \, a b c x^{3} + {\left(b^{2} c^{2} x^{6} + b^{2}\right)} \arctan\left(c x^{3}\right)^{2} + a^{2} + 2 \, {\left(a b c^{2} x^{6} + b^{2} c x^{3} + a b\right)} \arctan\left(c x^{3}\right)}{6 \, x^{6}}"," ",0,"-1/6*(b^2*c^2*x^6*log(c^2*x^6 + 1) - 6*b^2*c^2*x^6*log(x) + 2*a*b*c*x^3 + (b^2*c^2*x^6 + b^2)*arctan(c*x^3)^2 + a^2 + 2*(a*b*c^2*x^6 + b^2*c*x^3 + a*b)*arctan(c*x^3))/x^6","A",0
120,0,0,0,0.433082," ","integrate((a+b*arctan(c*x^3))^2/x^10,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(c x^{3}\right)^{2} + 2 \, a b \arctan\left(c x^{3}\right) + a^{2}}{x^{10}}, x\right)"," ",0,"integral((b^2*arctan(c*x^3)^2 + 2*a*b*arctan(c*x^3) + a^2)/x^10, x)","F",0
121,0,0,0,0.426121," ","integrate(x^8*(a+b*arctan(c*x^3))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{8} \arctan\left(c x^{3}\right)^{3} + 3 \, a b^{2} x^{8} \arctan\left(c x^{3}\right)^{2} + 3 \, a^{2} b x^{8} \arctan\left(c x^{3}\right) + a^{3} x^{8}, x\right)"," ",0,"integral(b^3*x^8*arctan(c*x^3)^3 + 3*a*b^2*x^8*arctan(c*x^3)^2 + 3*a^2*b*x^8*arctan(c*x^3) + a^3*x^8, x)","F",0
122,0,0,0,0.445191," ","integrate(x^5*(a+b*arctan(c*x^3))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{5} \arctan\left(c x^{3}\right)^{3} + 3 \, a b^{2} x^{5} \arctan\left(c x^{3}\right)^{2} + 3 \, a^{2} b x^{5} \arctan\left(c x^{3}\right) + a^{3} x^{5}, x\right)"," ",0,"integral(b^3*x^5*arctan(c*x^3)^3 + 3*a*b^2*x^5*arctan(c*x^3)^2 + 3*a^2*b*x^5*arctan(c*x^3) + a^3*x^5, x)","F",0
123,0,0,0,0.427581," ","integrate(x^2*(a+b*arctan(c*x^3))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \arctan\left(c x^{3}\right)^{3} + 3 \, a b^{2} x^{2} \arctan\left(c x^{3}\right)^{2} + 3 \, a^{2} b x^{2} \arctan\left(c x^{3}\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*arctan(c*x^3)^3 + 3*a*b^2*x^2*arctan(c*x^3)^2 + 3*a^2*b*x^2*arctan(c*x^3) + a^3*x^2, x)","F",0
124,0,0,0,0.417535," ","integrate((a+b*arctan(c*x^3))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x^{3}\right)^{3} + 3 \, a b^{2} \arctan\left(c x^{3}\right)^{2} + 3 \, a^{2} b \arctan\left(c x^{3}\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*arctan(c*x^3)^3 + 3*a*b^2*arctan(c*x^3)^2 + 3*a^2*b*arctan(c*x^3) + a^3)/x, x)","F",0
125,0,0,0,0.451293," ","integrate((a+b*arctan(c*x^3))^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x^{3}\right)^{3} + 3 \, a b^{2} \arctan\left(c x^{3}\right)^{2} + 3 \, a^{2} b \arctan\left(c x^{3}\right) + a^{3}}{x^{4}}, x\right)"," ",0,"integral((b^3*arctan(c*x^3)^3 + 3*a*b^2*arctan(c*x^3)^2 + 3*a^2*b*arctan(c*x^3) + a^3)/x^4, x)","F",0
126,0,0,0,0.445238," ","integrate((a+b*arctan(c*x^3))^3/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(c x^{3}\right)^{3} + 3 \, a b^{2} \arctan\left(c x^{3}\right)^{2} + 3 \, a^{2} b \arctan\left(c x^{3}\right) + a^{3}}{x^{7}}, x\right)"," ",0,"integral((b^3*arctan(c*x^3)^3 + 3*a*b^2*arctan(c*x^3)^2 + 3*a^2*b*arctan(c*x^3) + a^3)/x^7, x)","F",0
127,0,0,0,0.436231," ","integrate((d*x)^m*(a+b*arctan(c*x^3))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \arctan\left(c x^{3}\right)^{3} + 3 \, a b^{2} \arctan\left(c x^{3}\right)^{2} + 3 \, a^{2} b \arctan\left(c x^{3}\right) + a^{3}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^3*arctan(c*x^3)^3 + 3*a*b^2*arctan(c*x^3)^2 + 3*a^2*b*arctan(c*x^3) + a^3)*(d*x)^m, x)","F",0
128,0,0,0,0.437689," ","integrate((d*x)^m*(a+b*arctan(c*x^3))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \arctan\left(c x^{3}\right)^{2} + 2 \, a b \arctan\left(c x^{3}\right) + a^{2}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*arctan(c*x^3)^2 + 2*a*b*arctan(c*x^3) + a^2)*(d*x)^m, x)","F",0
129,0,0,0,0.434774," ","integrate((d*x)^m*(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \arctan\left(c x^{3}\right) + a\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b*arctan(c*x^3) + a)*(d*x)^m, x)","F",0
130,0,0,0,0.408317," ","integrate((d*x)^m/(a+b*arctan(c*x^3)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b \arctan\left(c x^{3}\right) + a}, x\right)"," ",0,"integral((d*x)^m/(b*arctan(c*x^3) + a), x)","F",0
131,0,0,0,0.420091," ","integrate((d*x)^m/(a+b*arctan(c*x^3))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{2} \arctan\left(c x^{3}\right)^{2} + 2 \, a b \arctan\left(c x^{3}\right) + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(b^2*arctan(c*x^3)^2 + 2*a*b*arctan(c*x^3) + a^2), x)","F",0
132,1,41,0,0.401054," ","integrate(x^3*(a+b*arctan(c/x)),x, algorithm=""fricas"")","-\frac{1}{4} \, b c^{3} x + \frac{1}{12} \, b c x^{3} + \frac{1}{4} \, a x^{4} - \frac{1}{4} \, {\left(b c^{4} - b x^{4}\right)} \arctan\left(\frac{c}{x}\right)"," ",0,"-1/4*b*c^3*x + 1/12*b*c*x^3 + 1/4*a*x^4 - 1/4*(b*c^4 - b*x^4)*arctan(c/x)","A",0
133,1,40,0,0.416448," ","integrate(x^2*(a+b*arctan(c/x)),x, algorithm=""fricas"")","\frac{1}{3} \, b x^{3} \arctan\left(\frac{c}{x}\right) - \frac{1}{6} \, b c^{3} \log\left(c^{2} + x^{2}\right) + \frac{1}{6} \, b c x^{2} + \frac{1}{3} \, a x^{3}"," ",0,"1/3*b*x^3*arctan(c/x) - 1/6*b*c^3*log(c^2 + x^2) + 1/6*b*c*x^2 + 1/3*a*x^3","A",0
134,1,31,0,0.415854," ","integrate(x*(a+b*arctan(c/x)),x, algorithm=""fricas"")","\frac{1}{2} \, b c x + \frac{1}{2} \, a x^{2} + \frac{1}{2} \, {\left(b c^{2} + b x^{2}\right)} \arctan\left(\frac{c}{x}\right)"," ",0,"1/2*b*c*x + 1/2*a*x^2 + 1/2*(b*c^2 + b*x^2)*arctan(c/x)","A",0
135,1,25,0,0.419876," ","integrate(a+b*arctan(c/x),x, algorithm=""fricas"")","b x \arctan\left(\frac{c}{x}\right) + \frac{1}{2} \, b c \log\left(c^{2} + x^{2}\right) + a x"," ",0,"b*x*arctan(c/x) + 1/2*b*c*log(c^2 + x^2) + a*x","A",0
136,0,0,0,0.433159," ","integrate((a+b*arctan(c/x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arctan\left(\frac{c}{x}\right) + a}{x}, x\right)"," ",0,"integral((b*arctan(c/x) + a)/x, x)","F",0
137,1,41,0,0.429170," ","integrate((a+b*arctan(c/x))/x^2,x, algorithm=""fricas"")","-\frac{2 \, b c \arctan\left(\frac{c}{x}\right) - b x \log\left(c^{2} + x^{2}\right) + 2 \, b x \log\left(x\right) + 2 \, a c}{2 \, c x}"," ",0,"-1/2*(2*b*c*arctan(c/x) - b*x*log(c^2 + x^2) + 2*b*x*log(x) + 2*a*c)/(c*x)","A",0
138,1,37,0,0.439825," ","integrate((a+b*arctan(c/x))/x^3,x, algorithm=""fricas"")","-\frac{a c^{2} - b c x + {\left(b c^{2} + b x^{2}\right)} \arctan\left(\frac{c}{x}\right)}{2 \, c^{2} x^{2}}"," ",0,"-1/2*(a*c^2 - b*c*x + (b*c^2 + b*x^2)*arctan(c/x))/(c^2*x^2)","A",0
139,1,55,0,0.432988," ","integrate((a+b*arctan(c/x))/x^4,x, algorithm=""fricas"")","-\frac{2 \, b c^{3} \arctan\left(\frac{c}{x}\right) + b x^{3} \log\left(c^{2} + x^{2}\right) - 2 \, b x^{3} \log\left(x\right) + 2 \, a c^{3} - b c^{2} x}{6 \, c^{3} x^{3}}"," ",0,"-1/6*(2*b*c^3*arctan(c/x) + b*x^3*log(c^2 + x^2) - 2*b*x^3*log(x) + 2*a*c^3 - b*c^2*x)/(c^3*x^3)","A",0
140,1,125,0,0.433561," ","integrate(x^3*(a+b*arctan(c/x))^2,x, algorithm=""fricas"")","\frac{1}{2} \, a b c^{4} \arctan\left(\frac{x}{c}\right) - \frac{1}{3} \, b^{2} c^{4} \log\left(c^{2} + x^{2}\right) - \frac{1}{2} \, a b c^{3} x + \frac{1}{12} \, b^{2} c^{2} x^{2} + \frac{1}{6} \, a b c x^{3} + \frac{1}{4} \, a^{2} x^{4} - \frac{1}{4} \, {\left(b^{2} c^{4} - b^{2} x^{4}\right)} \arctan\left(\frac{c}{x}\right)^{2} - \frac{1}{6} \, {\left(3 \, b^{2} c^{3} x - b^{2} c x^{3} - 3 \, a b x^{4}\right)} \arctan\left(\frac{c}{x}\right)"," ",0,"1/2*a*b*c^4*arctan(x/c) - 1/3*b^2*c^4*log(c^2 + x^2) - 1/2*a*b*c^3*x + 1/12*b^2*c^2*x^2 + 1/6*a*b*c*x^3 + 1/4*a^2*x^4 - 1/4*(b^2*c^4 - b^2*x^4)*arctan(c/x)^2 - 1/6*(3*b^2*c^3*x - b^2*c*x^3 - 3*a*b*x^4)*arctan(c/x)","A",0
141,0,0,0,0.426074," ","integrate(x^2*(a+b*arctan(c/x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \arctan\left(\frac{c}{x}\right)^{2} + 2 \, a b x^{2} \arctan\left(\frac{c}{x}\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*arctan(c/x)^2 + 2*a*b*x^2*arctan(c/x) + a^2*x^2, x)","F",0
142,1,88,0,0.422175," ","integrate(x*(a+b*arctan(c/x))^2,x, algorithm=""fricas"")","-a b c^{2} \arctan\left(\frac{x}{c}\right) + \frac{1}{2} \, b^{2} c^{2} \log\left(c^{2} + x^{2}\right) + a b c x + \frac{1}{2} \, a^{2} x^{2} + \frac{1}{2} \, {\left(b^{2} c^{2} + b^{2} x^{2}\right)} \arctan\left(\frac{c}{x}\right)^{2} + {\left(b^{2} c x + a b x^{2}\right)} \arctan\left(\frac{c}{x}\right)"," ",0,"-a*b*c^2*arctan(x/c) + 1/2*b^2*c^2*log(c^2 + x^2) + a*b*c*x + 1/2*a^2*x^2 + 1/2*(b^2*c^2 + b^2*x^2)*arctan(c/x)^2 + (b^2*c*x + a*b*x^2)*arctan(c/x)","A",0
143,0,0,0,1.103240," ","integrate((a+b*arctan(c/x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \arctan\left(\frac{c}{x}\right)^{2} + 2 \, a b \arctan\left(\frac{c}{x}\right) + a^{2}, x\right)"," ",0,"integral(b^2*arctan(c/x)^2 + 2*a*b*arctan(c/x) + a^2, x)","F",0
144,0,0,0,0.559405," ","integrate((a+b*arctan(c/x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(\frac{c}{x}\right)^{2} + 2 \, a b \arctan\left(\frac{c}{x}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctan(c/x)^2 + 2*a*b*arctan(c/x) + a^2)/x, x)","F",0
145,0,0,0,0.434663," ","integrate((a+b*arctan(c/x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arctan\left(\frac{c}{x}\right)^{2} + 2 \, a b \arctan\left(\frac{c}{x}\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*arctan(c/x)^2 + 2*a*b*arctan(c/x) + a^2)/x^2, x)","F",0
146,1,109,0,0.467819," ","integrate((a+b*arctan(c/x))^2/x^3,x, algorithm=""fricas"")","\frac{2 \, a b x^{2} \arctan\left(\frac{x}{c}\right) - b^{2} x^{2} \log\left(c^{2} + x^{2}\right) + 2 \, b^{2} x^{2} \log\left(x\right) - a^{2} c^{2} + 2 \, a b c x - {\left(b^{2} c^{2} + b^{2} x^{2}\right)} \arctan\left(\frac{c}{x}\right)^{2} - 2 \, {\left(a b c^{2} - b^{2} c x\right)} \arctan\left(\frac{c}{x}\right)}{2 \, c^{2} x^{2}}"," ",0,"1/2*(2*a*b*x^2*arctan(x/c) - b^2*x^2*log(c^2 + x^2) + 2*b^2*x^2*log(x) - a^2*c^2 + 2*a*b*c*x - (b^2*c^2 + b^2*x^2)*arctan(c/x)^2 - 2*(a*b*c^2 - b^2*c*x)*arctan(c/x))/(c^2*x^2)","A",0
147,0,0,0,0.433712," ","integrate(x^3*(a+b*arctan(c/x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{3} \arctan\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} x^{3} \arctan\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b x^{3} \arctan\left(\frac{c}{x}\right) + a^{3} x^{3}, x\right)"," ",0,"integral(b^3*x^3*arctan(c/x)^3 + 3*a*b^2*x^3*arctan(c/x)^2 + 3*a^2*b*x^3*arctan(c/x) + a^3*x^3, x)","F",0
148,0,0,0,1.467032," ","integrate(x^2*(a+b*arctan(c/x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \arctan\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} x^{2} \arctan\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b x^{2} \arctan\left(\frac{c}{x}\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*arctan(c/x)^3 + 3*a*b^2*x^2*arctan(c/x)^2 + 3*a^2*b*x^2*arctan(c/x) + a^3*x^2, x)","F",0
149,0,0,0,0.418703," ","integrate(x*(a+b*arctan(c/x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \arctan\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} x \arctan\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b x \arctan\left(\frac{c}{x}\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*arctan(c/x)^3 + 3*a*b^2*x*arctan(c/x)^2 + 3*a^2*b*x*arctan(c/x) + a^3*x, x)","F",0
150,0,0,0,0.408087," ","integrate((a+b*arctan(c/x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \arctan\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} \arctan\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b \arctan\left(\frac{c}{x}\right) + a^{3}, x\right)"," ",0,"integral(b^3*arctan(c/x)^3 + 3*a*b^2*arctan(c/x)^2 + 3*a^2*b*arctan(c/x) + a^3, x)","F",0
151,0,0,0,0.412704," ","integrate((a+b*arctan(c/x))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} \arctan\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b \arctan\left(\frac{c}{x}\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*arctan(c/x)^3 + 3*a*b^2*arctan(c/x)^2 + 3*a^2*b*arctan(c/x) + a^3)/x, x)","F",0
152,0,0,0,0.520897," ","integrate((a+b*arctan(c/x))^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} \arctan\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b \arctan\left(\frac{c}{x}\right) + a^{3}}{x^{2}}, x\right)"," ",0,"integral((b^3*arctan(c/x)^3 + 3*a*b^2*arctan(c/x)^2 + 3*a^2*b*arctan(c/x) + a^3)/x^2, x)","F",0
153,0,0,0,0.469383," ","integrate((a+b*arctan(c/x))^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \arctan\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} \arctan\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b \arctan\left(\frac{c}{x}\right) + a^{3}}{x^{3}}, x\right)"," ",0,"integral((b^3*arctan(c/x)^3 + 3*a*b^2*arctan(c/x)^2 + 3*a^2*b*arctan(c/x) + a^3)/x^3, x)","F",0
154,1,27,0,0.468656," ","integrate(x^2*arctan(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(x^{3} + 1\right)} \arctan\left(\sqrt{x}\right) - \frac{1}{45} \, {\left(3 \, x^{2} - 5 \, x + 15\right)} \sqrt{x}"," ",0,"1/3*(x^3 + 1)*arctan(sqrt(x)) - 1/45*(3*x^2 - 5*x + 15)*sqrt(x)","A",0
155,1,20,0,0.484253," ","integrate(x*arctan(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x^{2} - 1\right)} \arctan\left(\sqrt{x}\right) - \frac{1}{6} \, {\left(x - 3\right)} \sqrt{x}"," ",0,"1/2*(x^2 - 1)*arctan(sqrt(x)) - 1/6*(x - 3)*sqrt(x)","A",0
156,1,14,0,0.412174," ","integrate(arctan(x^(1/2)),x, algorithm=""fricas"")","{\left(x + 1\right)} \arctan\left(\sqrt{x}\right) - \sqrt{x}"," ",0,"(x + 1)*arctan(sqrt(x)) - sqrt(x)","A",0
157,0,0,0,0.528201," ","integrate(arctan(x^(1/2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\sqrt{x}\right)}{x}, x\right)"," ",0,"integral(arctan(sqrt(x))/x, x)","F",0
158,1,17,0,0.434309," ","integrate(arctan(x^(1/2))/x^2,x, algorithm=""fricas"")","-\frac{{\left(x + 1\right)} \arctan\left(\sqrt{x}\right) + \sqrt{x}}{x}"," ",0,"-((x + 1)*arctan(sqrt(x)) + sqrt(x))/x","A",0
159,1,26,0,0.458969," ","integrate(arctan(x^(1/2))/x^3,x, algorithm=""fricas"")","\frac{3 \, {\left(x^{2} - 1\right)} \arctan\left(\sqrt{x}\right) + {\left(3 \, x - 1\right)} \sqrt{x}}{6 \, x^{2}}"," ",0,"1/6*(3*(x^2 - 1)*arctan(sqrt(x)) + (3*x - 1)*sqrt(x))/x^2","A",0
160,1,24,0,0.481401," ","integrate(x^(3/2)*arctan(x^(1/2)),x, algorithm=""fricas"")","\frac{2}{5} \, x^{\frac{5}{2}} \arctan\left(\sqrt{x}\right) - \frac{1}{10} \, x^{2} + \frac{1}{5} \, x - \frac{1}{5} \, \log\left(x + 1\right)"," ",0,"2/5*x^(5/2)*arctan(sqrt(x)) - 1/10*x^2 + 1/5*x - 1/5*log(x + 1)","A",0
161,1,19,0,0.468328," ","integrate(x^(1/2)*arctan(x^(1/2)),x, algorithm=""fricas"")","\frac{2}{3} \, x^{\frac{3}{2}} \arctan\left(\sqrt{x}\right) - \frac{1}{3} \, x + \frac{1}{3} \, \log\left(x + 1\right)"," ",0,"2/3*x^(3/2)*arctan(sqrt(x)) - 1/3*x + 1/3*log(x + 1)","A",0
162,1,16,0,0.437036," ","integrate(arctan(x^(1/2))/x^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{x} \arctan\left(\sqrt{x}\right) - \log\left(x + 1\right)"," ",0,"2*sqrt(x)*arctan(sqrt(x)) - log(x + 1)","A",0
163,1,26,0,0.430604," ","integrate(arctan(x^(1/2))/x^(3/2),x, algorithm=""fricas"")","-\frac{x \log\left(x + 1\right) - x \log\left(x\right) + 2 \, \sqrt{x} \arctan\left(\sqrt{x}\right)}{x}"," ",0,"-(x*log(x + 1) - x*log(x) + 2*sqrt(x)*arctan(sqrt(x)))/x","A",0
164,1,33,0,0.478599," ","integrate(arctan(x^(1/2))/x^(5/2),x, algorithm=""fricas"")","\frac{x^{2} \log\left(x + 1\right) - x^{2} \log\left(x\right) - 2 \, \sqrt{x} \arctan\left(\sqrt{x}\right) - x}{3 \, x^{2}}"," ",0,"1/3*(x^2*log(x + 1) - x^2*log(x) - 2*sqrt(x)*arctan(sqrt(x)) - x)/x^2","A",0
165,0,0,0,0.450599," ","integrate(arctan(a*x^5)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(a x^{5}\right)}{x}, x\right)"," ",0,"integral(arctan(a*x^5)/x, x)","F",0
166,1,63,0,0.472508," ","integrate(arctan(a*x^n)/x,x, algorithm=""fricas"")","\frac{2 \, n \arctan\left(a x^{n}\right) \log\left(x\right) + i \, n \log\left(i \, a x^{n} + 1\right) \log\left(x\right) - i \, n \log\left(-i \, a x^{n} + 1\right) \log\left(x\right) - i \, {\rm Li}_2\left(i \, a x^{n}\right) + i \, {\rm Li}_2\left(-i \, a x^{n}\right)}{2 \, n}"," ",0,"1/2*(2*n*arctan(a*x^n)*log(x) + I*n*log(I*a*x^n + 1)*log(x) - I*n*log(-I*a*x^n + 1)*log(x) - I*dilog(I*a*x^n) + I*dilog(-I*a*x^n))/n","B",0
