1,1,57,0,0.431039," ","integrate(x^5*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{90} \, {\left(15 \, x^{6} \arctan\left(c x\right) - c {\left(\frac{3 \, c^{4} x^{5} - 5 \, c^{2} x^{3} + 15 \, x}{c^{6}} - \frac{15 \, \arctan\left(c x\right)}{c^{7}}\right)}\right)} b"," ",0,"1/6*a*x^6 + 1/90*(15*x^6*arctan(c*x) - c*((3*c^4*x^5 - 5*c^2*x^3 + 15*x)/c^6 - 15*arctan(c*x)/c^7))*b","A",0
2,1,56,0,0.330243," ","integrate(x^4*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{20} \, {\left(4 \, x^{5} \arctan\left(c x\right) - c {\left(\frac{c^{2} x^{4} - 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{6}}\right)}\right)} b"," ",0,"1/5*a*x^5 + 1/20*(4*x^5*arctan(c*x) - c*((c^2*x^4 - 2*x^2)/c^4 + 2*log(c^2*x^2 + 1)/c^6))*b","A",0
3,1,48,0,0.469502," ","integrate(x^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{12} \, {\left(3 \, x^{4} \arctan\left(c x\right) - c {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4}} + \frac{3 \, \arctan\left(c x\right)}{c^{5}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/12*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b","A",0
4,1,46,0,0.320510," ","integrate(x^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \arctan\left(c x\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)}\right)} b"," ",0,"1/3*a*x^3 + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b","A",0
5,1,37,0,0.469007," ","integrate(x*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{2} \, {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} b"," ",0,"1/2*a*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b","A",0
6,1,31,0,0.323672," ","integrate(a+b*arctan(c*x),x, algorithm=""maxima"")","a x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b}{2 \, c}"," ",0,"a*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b/c","A",0
7,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x,x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"b*integrate(arctan(c*x)/x, x) + a*log(x)","F",0
8,1,39,0,0.326645," ","integrate((a+b*arctan(c*x))/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} + 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \arctan\left(c x\right)}{x}\right)} b - \frac{a}{x}"," ",0,"-1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b - a/x","A",0
9,1,31,0,0.435200," ","integrate((a+b*arctan(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"-1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b - 1/2*a/x^2","A",0
10,1,51,0,0.340019," ","integrate((a+b*arctan(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} + 1\right) - c^{2} \log\left(x^{2}\right) - \frac{1}{x^{2}}\right)} c - \frac{2 \, \arctan\left(c x\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"1/6*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b - 1/3*a/x^3","A",0
11,1,46,0,0.426519," ","integrate((a+b*arctan(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{12} \, {\left({\left(3 \, c^{3} \arctan\left(c x\right) + \frac{3 \, c^{2} x^{2} - 1}{x^{3}}\right)} c - \frac{3 \, \arctan\left(c x\right)}{x^{4}}\right)} b - \frac{a}{4 \, x^{4}}"," ",0,"1/12*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b - 1/4*a/x^4","A",0
12,1,62,0,0.334559," ","integrate((a+b*arctan(c*x))/x^6,x, algorithm=""maxima"")","-\frac{1}{20} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} + 1\right) - 2 \, c^{4} \log\left(x^{2}\right) - \frac{2 \, c^{2} x^{2} - 1}{x^{4}}\right)} c + \frac{4 \, \arctan\left(c x\right)}{x^{5}}\right)} b - \frac{a}{5 \, x^{5}}"," ",0,"-1/20*((2*c^4*log(c^2*x^2 + 1) - 2*c^4*log(x^2) - (2*c^2*x^2 - 1)/x^4)*c + 4*arctan(c*x)/x^5)*b - 1/5*a/x^5","A",0
13,1,163,0,0.457819," ","integrate(x^5*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} x^{6} \arctan\left(c x\right)^{2} + \frac{1}{6} \, a^{2} x^{6} + \frac{1}{45} \, {\left(15 \, x^{6} \arctan\left(c x\right) - c {\left(\frac{3 \, c^{4} x^{5} - 5 \, c^{2} x^{3} + 15 \, x}{c^{6}} - \frac{15 \, \arctan\left(c x\right)}{c^{7}}\right)}\right)} a b - \frac{1}{180} \, {\left(4 \, c {\left(\frac{3 \, c^{4} x^{5} - 5 \, c^{2} x^{3} + 15 \, x}{c^{6}} - \frac{15 \, \arctan\left(c x\right)}{c^{7}}\right)} \arctan\left(c x\right) - \frac{3 \, c^{4} x^{4} - 16 \, c^{2} x^{2} - 30 \, \arctan\left(c x\right)^{2} + 46 \, \log\left(c^{2} x^{2} + 1\right)}{c^{6}}\right)} b^{2}"," ",0,"1/6*b^2*x^6*arctan(c*x)^2 + 1/6*a^2*x^6 + 1/45*(15*x^6*arctan(c*x) - c*((3*c^4*x^5 - 5*c^2*x^3 + 15*x)/c^6 - 15*arctan(c*x)/c^7))*a*b - 1/180*(4*c*((3*c^4*x^5 - 5*c^2*x^3 + 15*x)/c^6 - 15*arctan(c*x)/c^7)*arctan(c*x) - (3*c^4*x^4 - 16*c^2*x^2 - 30*arctan(c*x)^2 + 46*log(c^2*x^2 + 1))/c^6)*b^2","A",0
14,0,0,0,0.000000," ","integrate(x^4*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} x^{5} + \frac{1}{10} \, {\left(4 \, x^{5} \arctan\left(c x\right) - c {\left(\frac{c^{2} x^{4} - 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{6}}\right)}\right)} a b + \frac{1}{80} \, {\left(4 \, x^{5} \arctan\left(c x\right)^{2} - x^{5} \log\left(c^{2} x^{2} + 1\right)^{2} + 80 \, \int \frac{4 \, c^{2} x^{6} \log\left(c^{2} x^{2} + 1\right) - 8 \, c x^{5} \arctan\left(c x\right) + 60 \, {\left(c^{2} x^{6} + x^{4}\right)} \arctan\left(c x\right)^{2} + 5 \, {\left(c^{2} x^{6} + x^{4}\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{80 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}\right)} b^{2}"," ",0,"1/5*a^2*x^5 + 1/10*(4*x^5*arctan(c*x) - c*((c^2*x^4 - 2*x^2)/c^4 + 2*log(c^2*x^2 + 1)/c^6))*a*b + 1/80*(4*x^5*arctan(c*x)^2 - x^5*log(c^2*x^2 + 1)^2 + 80*integrate(1/80*(4*c^2*x^6*log(c^2*x^2 + 1) - 8*c*x^5*arctan(c*x) + 60*(c^2*x^6 + x^4)*arctan(c*x)^2 + 5*(c^2*x^6 + x^4)*log(c^2*x^2 + 1)^2)/(c^2*x^2 + 1), x))*b^2","F",0
15,1,136,0,0.432166," ","integrate(x^3*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x^{4} \arctan\left(c x\right)^{2} + \frac{1}{4} \, a^{2} x^{4} + \frac{1}{6} \, {\left(3 \, x^{4} \arctan\left(c x\right) - c {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4}} + \frac{3 \, \arctan\left(c x\right)}{c^{5}}\right)}\right)} a b - \frac{1}{12} \, {\left(2 \, c {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4}} + \frac{3 \, \arctan\left(c x\right)}{c^{5}}\right)} \arctan\left(c x\right) - \frac{c^{2} x^{2} + 3 \, \arctan\left(c x\right)^{2} - 4 \, \log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)} b^{2}"," ",0,"1/4*b^2*x^4*arctan(c*x)^2 + 1/4*a^2*x^4 + 1/6*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a*b - 1/12*(2*c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5)*arctan(c*x) - (c^2*x^2 + 3*arctan(c*x)^2 - 4*log(c^2*x^2 + 1))/c^4)*b^2","A",0
16,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \arctan\left(c x\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)}\right)} a b + \frac{1}{48} \, {\left(4 \, x^{3} \arctan\left(c x\right)^{2} - x^{3} \log\left(c^{2} x^{2} + 1\right)^{2} + 48 \, \int \frac{4 \, c^{2} x^{4} \log\left(c^{2} x^{2} + 1\right) - 8 \, c x^{3} \arctan\left(c x\right) + 36 \, {\left(c^{2} x^{4} + x^{2}\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(c^{2} x^{4} + x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}\right)} b^{2}"," ",0,"1/3*a^2*x^3 + 1/3*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b + 1/48*(4*x^3*arctan(c*x)^2 - x^3*log(c^2*x^2 + 1)^2 + 48*integrate(1/48*(4*c^2*x^4*log(c^2*x^2 + 1) - 8*c*x^3*arctan(c*x) + 36*(c^2*x^4 + x^2)*arctan(c*x)^2 + 3*(c^2*x^4 + x^2)*log(c^2*x^2 + 1)^2)/(c^2*x^2 + 1), x))*b^2","F",0
17,1,104,0,0.474459," ","integrate(x*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \arctan\left(c x\right)^{2} + \frac{1}{2} \, a^{2} x^{2} + {\left(x^{2} \arctan\left(c x\right) - c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)}\right)} a b - \frac{1}{2} \, {\left(2 \, c {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)} \arctan\left(c x\right) + \frac{\arctan\left(c x\right)^{2} - \log\left(c^{2} x^{2} + 1\right)}{c^{2}}\right)} b^{2}"," ",0,"1/2*b^2*x^2*arctan(c*x)^2 + 1/2*a^2*x^2 + (x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b - 1/2*(2*c*(x/c^2 - arctan(c*x)/c^3)*arctan(c*x) + (arctan(c*x)^2 - log(c^2*x^2 + 1))/c^2)*b^2","A",0
18,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(4 \, x \arctan\left(c x\right)^{2} + 192 \, c^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 16 \, c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 64 \, c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - x \log\left(c^{2} x^{2} + 1\right)^{2} + \frac{4 \, \arctan\left(c x\right)^{3}}{c} - 128 \, c \int \frac{x \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 16 \, \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}\right)} b^{2} + a^{2} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b}{c}"," ",0,"1/16*(4*x*arctan(c*x)^2 + 192*c^2*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 16*c^2*integrate(1/16*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 64*c^2*integrate(1/16*x^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - x*log(c^2*x^2 + 1)^2 + 4*arctan(c*x)^3/c - 128*c*integrate(1/16*x*arctan(c*x)/(c^2*x^2 + 1), x) + 16*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x))*b^2 + a^2*x + (2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b/c","F",0
19,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \frac{1}{16} \, \int \frac{12 \, b^{2} \arctan\left(c x\right)^{2} + b^{2} \log\left(c^{2} x^{2} + 1\right)^{2} + 32 \, a b \arctan\left(c x\right)}{x}\,{d x}"," ",0,"a^2*log(x) + 1/16*integrate((12*b^2*arctan(c*x)^2 + b^2*log(c^2*x^2 + 1)^2 + 32*a*b*arctan(c*x))/x, x)","F",0
20,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,1,98,0,0.442464," ","integrate((a+b*arctan(c*x))^2/x^3,x, algorithm=""maxima"")","-{\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} a b + \frac{1}{2} \, {\left({\left(\arctan\left(c x\right)^{2} - \log\left(c^{2} x^{2} + 1\right) + 2 \, \log\left(x\right)\right)} c^{2} - 2 \, {\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c \arctan\left(c x\right)\right)} b^{2} - \frac{b^{2} \arctan\left(c x\right)^{2}}{2 \, x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"-((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*a*b + 1/2*((arctan(c*x)^2 - log(c^2*x^2 + 1) + 2*log(x))*c^2 - 2*(c*arctan(c*x) + 1/x)*c*arctan(c*x))*b^2 - 1/2*b^2*arctan(c*x)^2/x^2 - 1/2*a^2/x^2","A",0
22,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} + 1\right) - c^{2} \log\left(x^{2}\right) - \frac{1}{x^{2}}\right)} c - \frac{2 \, \arctan\left(c x\right)}{x^{3}}\right)} a b + \frac{\frac{1}{4} \, {\left(4 \, x^{3} \int -\frac{12 \, c^{2} x^{2} \log\left(c^{2} x^{2} + 1\right) - 56 \, c x \arctan\left(c x\right) - 108 \, {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} - 9 \, {\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{4 \, {\left(c^{2} x^{6} + x^{4}\right)}}\,{d x} - 28 \, \arctan\left(c x\right)^{2} + 3 \, \log\left(c^{2} x^{2} + 1\right)^{2}\right)} b^{2}}{48 \, x^{3}} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"1/3*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*a*b + 1/48*(48*x^3*integrate(-1/48*(4*c^2*x^2*log(c^2*x^2 + 1) - 8*c*x*arctan(c*x) - 36*(c^2*x^2 + 1)*arctan(c*x)^2 - 3*(c^2*x^2 + 1)*log(c^2*x^2 + 1)^2)/(c^2*x^6 + x^4), x) - 4*arctan(c*x)^2 + log(c^2*x^2 + 1)^2)*b^2/x^3 - 1/3*a^2/x^3","F",0
23,1,152,0,0.418703," ","integrate((a+b*arctan(c*x))^2/x^5,x, algorithm=""maxima"")","\frac{1}{6} \, {\left({\left(3 \, c^{3} \arctan\left(c x\right) + \frac{3 \, c^{2} x^{2} - 1}{x^{3}}\right)} c - \frac{3 \, \arctan\left(c x\right)}{x^{4}}\right)} a b + \frac{1}{12} \, {\left(2 \, {\left(3 \, c^{3} \arctan\left(c x\right) + \frac{3 \, c^{2} x^{2} - 1}{x^{3}}\right)} c \arctan\left(c x\right) - \frac{{\left(3 \, c^{2} x^{2} \arctan\left(c x\right)^{2} - 4 \, c^{2} x^{2} \log\left(c^{2} x^{2} + 1\right) + 8 \, c^{2} x^{2} \log\left(x\right) + 1\right)} c^{2}}{x^{2}}\right)} b^{2} - \frac{b^{2} \arctan\left(c x\right)^{2}}{4 \, x^{4}} - \frac{a^{2}}{4 \, x^{4}}"," ",0,"1/6*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*a*b + 1/12*(2*(3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c*arctan(c*x) - (3*c^2*x^2*arctan(c*x)^2 - 4*c^2*x^2*log(c^2*x^2 + 1) + 8*c^2*x^2*log(x) + 1)*c^2/x^2)*b^2 - 1/4*b^2*arctan(c*x)^2/x^4 - 1/4*a^2/x^4","A",0
24,-1,0,0,0.000000," ","integrate(x^5*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,0,0,0,0.000000," ","integrate(x^4*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","\frac{1}{40} \, b^{3} x^{5} \arctan\left(c x\right)^{3} - \frac{3}{160} \, b^{3} x^{5} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} + \frac{1}{5} \, a^{3} x^{5} + \frac{3}{20} \, {\left(4 \, x^{5} \arctan\left(c x\right) - c {\left(\frac{c^{2} x^{4} - 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{6}}\right)}\right)} a^{2} b + \int \frac{12 \, b^{3} c^{2} x^{6} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + 140 \, {\left(b^{3} c^{2} x^{6} + b^{3} x^{4}\right)} \arctan\left(c x\right)^{3} + 12 \, {\left(40 \, a b^{2} c^{2} x^{6} - b^{3} c x^{5} + 40 \, a b^{2} x^{4}\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(b^{3} c x^{5} + 5 \, {\left(b^{3} c^{2} x^{6} + b^{3} x^{4}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{160 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/40*b^3*x^5*arctan(c*x)^3 - 3/160*b^3*x^5*arctan(c*x)*log(c^2*x^2 + 1)^2 + 1/5*a^3*x^5 + 3/20*(4*x^5*arctan(c*x) - c*((c^2*x^4 - 2*x^2)/c^4 + 2*log(c^2*x^2 + 1)/c^6))*a^2*b + integrate(1/160*(12*b^3*c^2*x^6*arctan(c*x)*log(c^2*x^2 + 1) + 140*(b^3*c^2*x^6 + b^3*x^4)*arctan(c*x)^3 + 12*(40*a*b^2*c^2*x^6 - b^3*c*x^5 + 40*a*b^2*x^4)*arctan(c*x)^2 + 3*(b^3*c*x^5 + 5*(b^3*c^2*x^6 + b^3*x^4)*arctan(c*x))*log(c^2*x^2 + 1)^2)/(c^2*x^2 + 1), x)","F",0
26,-1,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","\frac{1}{24} \, b^{3} x^{3} \arctan\left(c x\right)^{3} - \frac{1}{32} \, b^{3} x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} + \frac{1}{3} \, a^{3} x^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \arctan\left(c x\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)}\right)} a^{2} b + \int \frac{4 \, b^{3} c^{2} x^{4} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + 28 \, {\left(b^{3} c^{2} x^{4} + b^{3} x^{2}\right)} \arctan\left(c x\right)^{3} + 4 \, {\left(24 \, a b^{2} c^{2} x^{4} - b^{3} c x^{3} + 24 \, a b^{2} x^{2}\right)} \arctan\left(c x\right)^{2} + {\left(b^{3} c x^{3} + 3 \, {\left(b^{3} c^{2} x^{4} + b^{3} x^{2}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/24*b^3*x^3*arctan(c*x)^3 - 1/32*b^3*x^3*arctan(c*x)*log(c^2*x^2 + 1)^2 + 1/3*a^3*x^3 + 1/2*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a^2*b + integrate(1/32*(4*b^3*c^2*x^4*arctan(c*x)*log(c^2*x^2 + 1) + 28*(b^3*c^2*x^4 + b^3*x^2)*arctan(c*x)^3 + 4*(24*a*b^2*c^2*x^4 - b^3*c*x^3 + 24*a*b^2*x^2)*arctan(c*x)^2 + (b^3*c*x^3 + 3*(b^3*c^2*x^4 + b^3*x^2)*arctan(c*x))*log(c^2*x^2 + 1)^2)/(c^2*x^2 + 1), x)","F",0
28,-1,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3,x, algorithm=""maxima"")","\frac{1}{8} \, b^{3} x \arctan\left(c x\right)^{3} - \frac{3}{32} \, b^{3} x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} + \frac{7 \, b^{3} \arctan\left(c x\right)^{4}}{32 \, c} + 28 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(c x\right)^{3}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} c^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{a b^{2} \arctan\left(c x\right)^{3}}{c} - 12 \, b^{3} c \int \frac{x \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + a^{3} x + 3 \, b^{3} \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{3 \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a^{2} b}{2 \, c}"," ",0,"1/8*b^3*x*arctan(c*x)^3 - 3/32*b^3*x*arctan(c*x)*log(c^2*x^2 + 1)^2 + 7/32*b^3*arctan(c*x)^4/c + 28*b^3*c^2*integrate(1/32*x^2*arctan(c*x)^3/(c^2*x^2 + 1), x) + 3*b^3*c^2*integrate(1/32*x^2*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 96*a*b^2*c^2*integrate(1/32*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 12*b^3*c^2*integrate(1/32*x^2*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + a*b^2*arctan(c*x)^3/c - 12*b^3*c*integrate(1/32*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^3*c*integrate(1/32*x*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + a^3*x + 3*b^3*integrate(1/32*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 3/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a^2*b/c","F",0
30,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/x,x, algorithm=""maxima"")","a^{3} \log\left(x\right) + \frac{1}{32} \, \int \frac{28 \, b^{3} \arctan\left(c x\right)^{3} + 3 \, b^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} + 96 \, a b^{2} \arctan\left(c x\right)^{2} + 96 \, a^{2} b \arctan\left(c x\right)}{x}\,{d x}"," ",0,"a^3*log(x) + 1/32*integrate((28*b^3*arctan(c*x)^3 + 3*b^3*arctan(c*x)*log(c^2*x^2 + 1)^2 + 96*a*b^2*arctan(c*x)^2 + 96*a^2*b*arctan(c*x))/x, x)","F",0
31,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/x^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/x^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,0,0,0,0.000000," ","integrate(x/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x/arctan(a*x), x)","F",0
36,0,0,0,0.000000," ","integrate(1/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/arctan(a*x), x)","F",0
37,0,0,0,0.000000," ","integrate(1/x/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/(x*arctan(a*x)), x)","F",0
38,0,0,0,0.000000," ","integrate(x/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{2} x^{3} - \mathit{sage}_{0} x \arctan\left(a x\right) + x}{a \arctan\left(a x\right)}"," ",0,"-(a^2*x^3 - arctan(a*x)*integrate((3*a^2*x^2 + 1)/arctan(a*x), x) + x)/(a*arctan(a*x))","F",0
39,0,0,0,0.000000," ","integrate(1/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{-2 \, a^{2} \mathit{sage}_{0} x \arctan\left(a x\right) + a^{2} x^{2} + 1}{a \arctan\left(a x\right)}"," ",0,"-(a^2*x^2 - 2*a^2*arctan(a*x)*integrate(x/arctan(a*x), x) + 1)/(a*arctan(a*x))","F",0
40,0,0,0,0.000000," ","integrate(1/x/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{2} x^{2} - \mathit{sage}_{0} x^{2} \arctan\left(a x\right) + 1}{a x \arctan\left(a x\right)}"," ",0,"-(a^2*x^2 - x*arctan(a*x)*integrate((a^2*x^2 - 1)/(x^2*arctan(a*x)), x) + 1)/(a*x*arctan(a*x))","F",0
41,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
42,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
43,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
44,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
45,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
46,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
47,-2,0,0,0.000000," ","integrate(x/arctan(a*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
48,-2,0,0,0.000000," ","integrate(1/arctan(a*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
49,-2,0,0,0.000000," ","integrate(1/x/arctan(a*x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
50,-2,0,0,0.000000," ","integrate(x/arctan(a*x)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
51,-2,0,0,0.000000," ","integrate(1/arctan(a*x)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
52,-2,0,0,0.000000," ","integrate(1/x/arctan(a*x)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
53,1,86,0,0.410972," ","integrate(arctan(x)*x^(1/2),x, algorithm=""maxima"")","\frac{2}{3} \, x^{\frac{3}{2}} \arctan\left(x\right) + \frac{1}{3} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{x}\right)}\right) + \frac{1}{3} \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{x}\right)}\right) + \frac{1}{6} \, \sqrt{2} \log\left(\sqrt{2} \sqrt{x} + x + 1\right) - \frac{1}{6} \, \sqrt{2} \log\left(-\sqrt{2} \sqrt{x} + x + 1\right) - \frac{4}{3} \, \sqrt{x}"," ",0,"2/3*x^(3/2)*arctan(x) + 1/3*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(x))) + 1/3*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(x))) + 1/6*sqrt(2)*log(sqrt(2)*sqrt(x) + x + 1) - 1/6*sqrt(2)*log(-sqrt(2)*sqrt(x) + x + 1) - 4/3*sqrt(x)","A",0
54,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","\frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \frac{\frac{15}{2} \, b^{3} d^{m} x x^{m} \arctan\left(c x\right)^{3} - \frac{21}{8} \, b^{3} d^{m} x x^{m} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} + {\left(m + 1\right)} \int \frac{84 \, b^{3} c^{2} d^{m} x^{2} x^{m} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + 196 \, {\left(b^{3} d^{m} m + b^{3} d^{m} + {\left(b^{3} c^{2} d^{m} m + b^{3} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \arctan\left(c x\right)^{3} - 12 \, {\left(15 \, b^{3} c d^{m} x - 64 \, a b^{2} d^{m} m - 64 \, a b^{2} d^{m} - 64 \, {\left(a b^{2} c^{2} d^{m} m + a b^{2} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \arctan\left(c x\right)^{2} + 768 \, {\left(a^{2} b d^{m} m + a^{2} b d^{m} + {\left(a^{2} b c^{2} d^{m} m + a^{2} b c^{2} d^{m}\right)} x^{2}\right)} x^{m} \arctan\left(c x\right) + 21 \, {\left(b^{3} c d^{m} x x^{m} + {\left(b^{3} d^{m} m + b^{3} d^{m} + {\left(b^{3} c^{2} d^{m} m + b^{3} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{8 \, {\left({\left(c^{2} m + c^{2}\right)} x^{2} + m + 1\right)}}\,{d x}}{32 \, {\left(m + 1\right)}}"," ",0,"(d*x)^(m + 1)*a^3/(d*(m + 1)) + 1/32*(4*b^3*d^m*x*x^m*arctan(c*x)^3 - 3*b^3*d^m*x*x^m*arctan(c*x)*log(c^2*x^2 + 1)^2 + 32*(m + 1)*integrate(1/32*(12*b^3*c^2*d^m*x^2*x^m*arctan(c*x)*log(c^2*x^2 + 1) + 28*(b^3*d^m*m + b^3*d^m + (b^3*c^2*d^m*m + b^3*c^2*d^m)*x^2)*x^m*arctan(c*x)^3 - 12*(b^3*c*d^m*x - 8*a*b^2*d^m*m - 8*a*b^2*d^m - 8*(a*b^2*c^2*d^m*m + a*b^2*c^2*d^m)*x^2)*x^m*arctan(c*x)^2 + 96*(a^2*b*d^m*m + a^2*b*d^m + (a^2*b*c^2*d^m*m + a^2*b*c^2*d^m)*x^2)*x^m*arctan(c*x) + 3*(b^3*c*d^m*x*x^m + (b^3*d^m*m + b^3*d^m + (b^3*c^2*d^m*m + b^3*c^2*d^m)*x^2)*x^m*arctan(c*x))*log(c^2*x^2 + 1)^2)/((c^2*m + c^2)*x^2 + m + 1), x))/(m + 1)","F",0
55,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}} + \frac{7 \, b^{2} d^{m} x x^{m} \arctan\left(c x\right)^{2} - \frac{3}{4} \, b^{2} d^{m} x x^{m} \log\left(c^{2} x^{2} + 1\right)^{2} + {\left(m + 1\right)} \int \frac{12 \, b^{2} c^{2} d^{m} x^{2} x^{m} \log\left(c^{2} x^{2} + 1\right) + 36 \, {\left(b^{2} d^{m} m + b^{2} d^{m} + {\left(b^{2} c^{2} d^{m} m + b^{2} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \arctan\left(c x\right)^{2} + 3 \, {\left(b^{2} d^{m} m + b^{2} d^{m} + {\left(b^{2} c^{2} d^{m} m + b^{2} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \log\left(c^{2} x^{2} + 1\right)^{2} - 8 \, {\left(7 \, b^{2} c d^{m} x - 16 \, a b d^{m} m - 16 \, a b d^{m} - 16 \, {\left(a b c^{2} d^{m} m + a b c^{2} d^{m}\right)} x^{2}\right)} x^{m} \arctan\left(c x\right)}{4 \, {\left({\left(c^{2} m + c^{2}\right)} x^{2} + m + 1\right)}}\,{d x}}{16 \, {\left(m + 1\right)}}"," ",0,"(d*x)^(m + 1)*a^2/(d*(m + 1)) + 1/16*(4*b^2*d^m*x*x^m*arctan(c*x)^2 - b^2*d^m*x*x^m*log(c^2*x^2 + 1)^2 + 16*(m + 1)*integrate(1/16*(4*b^2*c^2*d^m*x^2*x^m*log(c^2*x^2 + 1) + 12*(b^2*d^m*m + b^2*d^m + (b^2*c^2*d^m*m + b^2*c^2*d^m)*x^2)*x^m*arctan(c*x)^2 + (b^2*d^m*m + b^2*d^m + (b^2*c^2*d^m*m + b^2*c^2*d^m)*x^2)*x^m*log(c^2*x^2 + 1)^2 - 8*(b^2*c*d^m*x - 4*a*b*d^m*m - 4*a*b*d^m - 4*(a*b*c^2*d^m*m + a*b*c^2*d^m)*x^2)*x^m*arctan(c*x))/((c^2*m + c^2)*x^2 + m + 1), x))/(m + 1)","F",0
56,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{{\left(d^{m} x x^{m} \arctan\left(c x\right) - {\left(c d^{m} m + c d^{m}\right)} \int \frac{x x^{m}}{{\left(c^{2} m + c^{2}\right)} x^{2} + m + 1}\,{d x}\right)} b}{m + 1} + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"(d^m*x*x^m*arctan(c*x) - (c*d^m*m + c*d^m)*integrate(x*x^m/((c^2*m + c^2)*x^2 + m + 1), x))*b/(m + 1) + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
57,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \arctan\left(c x\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctan(c*x) + a), x)","F",0
58,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^p,x, algorithm=""maxima"")","\int {\left(b \arctan\left(c x\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)^p, x)","F",0
59,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctan(c*x))^p,x, algorithm=""maxima"")","\int \left(d x\right)^{m} {\left(b \arctan\left(c x\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x)^m*(b*arctan(c*x) + a)^p, x)","F",0
60,1,54,0,0.413016," ","integrate(x^7*(a+b*arctan(c*x^2)),x, algorithm=""maxima"")","\frac{1}{8} \, a x^{8} + \frac{1}{24} \, {\left(3 \, x^{8} \arctan\left(c x^{2}\right) - c {\left(\frac{c^{2} x^{6} - 3 \, x^{2}}{c^{4}} + \frac{3 \, \arctan\left(c x^{2}\right)}{c^{5}}\right)}\right)} b"," ",0,"1/8*a*x^8 + 1/24*(3*x^8*arctan(c*x^2) - c*((c^2*x^6 - 3*x^2)/c^4 + 3*arctan(c*x^2)/c^5))*b","A",0
61,1,48,0,0.307466," ","integrate(x^5*(a+b*arctan(c*x^2)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{12} \, {\left(2 \, x^{6} \arctan\left(c x^{2}\right) - {\left(\frac{x^{4}}{c^{2}} - \frac{\log\left(c^{2} x^{4} + 1\right)}{c^{4}}\right)} c\right)} b"," ",0,"1/6*a*x^6 + 1/12*(2*x^6*arctan(c*x^2) - (x^4/c^2 - log(c^2*x^4 + 1)/c^4)*c)*b","A",0
62,1,43,0,0.410801," ","integrate(x^3*(a+b*arctan(c*x^2)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{4} \, {\left(x^{4} \arctan\left(c x^{2}\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\arctan\left(c x^{2}\right)}{c^{3}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/4*(x^4*arctan(c*x^2) - c*(x^2/c^2 - arctan(c*x^2)/c^3))*b","A",0
63,1,38,0,0.308465," ","integrate(x*(a+b*arctan(c*x^2)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{{\left(2 \, c x^{2} \arctan\left(c x^{2}\right) - \log\left(c^{2} x^{4} + 1\right)\right)} b}{4 \, c}"," ",0,"1/2*a*x^2 + 1/4*(2*c*x^2*arctan(c*x^2) - log(c^2*x^4 + 1))*b/c","A",0
64,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))/x,x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x^{2}\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"b*integrate(arctan(c*x^2)/x, x) + a*log(x)","F",0
65,1,41,0,0.317380," ","integrate((a+b*arctan(c*x^2))/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(c {\left(\log\left(c^{2} x^{4} + 1\right) - \log\left(x^{4}\right)\right)} + \frac{2 \, \arctan\left(c x^{2}\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"-1/4*(c*(log(c^2*x^4 + 1) - log(x^4)) + 2*arctan(c*x^2)/x^2)*b - 1/2*a/x^2","A",0
66,1,35,0,0.417659," ","integrate((a+b*arctan(c*x^2))/x^5,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left({\left(c \arctan\left(c x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{\arctan\left(c x^{2}\right)}{x^{4}}\right)} b - \frac{a}{4 \, x^{4}}"," ",0,"-1/4*((c*arctan(c*x^2) + 1/x^2)*c + arctan(c*x^2)/x^4)*b - 1/4*a/x^4","A",0
67,1,53,0,0.324297," ","integrate((a+b*arctan(c*x^2))/x^7,x, algorithm=""maxima"")","\frac{1}{12} \, {\left({\left(c^{2} \log\left(c^{2} x^{4} + 1\right) - c^{2} \log\left(x^{4}\right) - \frac{1}{x^{4}}\right)} c - \frac{2 \, \arctan\left(c x^{2}\right)}{x^{6}}\right)} b - \frac{a}{6 \, x^{6}}"," ",0,"1/12*((c^2*log(c^2*x^4 + 1) - c^2*log(x^4) - 1/x^4)*c - 2*arctan(c*x^2)/x^6)*b - 1/6*a/x^6","A",0
68,1,147,0,0.445456," ","integrate(x^4*(a+b*arctan(c*x^2)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{60} \, {\left(12 \, x^{5} \arctan\left(c x^{2}\right) - c {\left(\frac{8 \, x^{3}}{c^{2}} - \frac{3 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}}\right)}}{c^{2}}\right)}\right)} b"," ",0,"1/5*a*x^5 + 1/60*(12*x^5*arctan(c*x^2) - c*(8*x^3/c^2 - 3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) - sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/c^(3/2) + sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/c^(3/2))/c^2))*b","A",0
69,1,145,0,0.432966," ","integrate(x^2*(a+b*arctan(c*x^2)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{12} \, {\left(4 \, x^{3} \arctan\left(c x^{2}\right) - c {\left(\frac{8 \, x}{c^{2}} - \frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}} - \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}}}{c^{2}}\right)}\right)} b"," ",0,"1/3*a*x^3 + 1/12*(4*x^3*arctan(c*x^2) - c*(8*x/c^2 - (2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/sqrt(c) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/sqrt(c) + sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/sqrt(c) - sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/sqrt(c))/c^2))*b","A",0
70,1,127,0,0.427509," ","integrate(a+b*arctan(c*x^2),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}}\right)} - 4 \, x \arctan\left(c x^{2}\right)\right)} b + a x"," ",0,"-1/4*(c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) - sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/c^(3/2) + sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/c^(3/2)) - 4*x*arctan(c*x^2))*b + a*x","A",0
71,1,132,0,0.420800," ","integrate((a+b*arctan(c*x^2))/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}} - \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}}\right)} - \frac{4 \, \arctan\left(c x^{2}\right)}{x}\right)} b - \frac{a}{x}"," ",0,"1/4*(c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/sqrt(c) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/sqrt(c) + sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/sqrt(c) - sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/sqrt(c)) - 4*arctan(c*x^2)/x)*b - a/x","A",0
72,1,142,0,0.413223," ","integrate((a+b*arctan(c*x^2))/x^4,x, algorithm=""maxima"")","-\frac{1}{12} \, {\left({\left(c^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}}\right)} + \frac{8}{x}\right)} c + \frac{4 \, \arctan\left(c x^{2}\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"-1/12*((c^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) - sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/c^(3/2) + sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/c^(3/2)) + 8/x)*c + 4*arctan(c*x^2)/x^3)*b - 1/3*a/x^3","A",0
73,1,138,0,0.413790," ","integrate((a+b*arctan(c*x^2))/x^6,x, algorithm=""maxima"")","-\frac{1}{60} \, {\left({\left(6 \, \sqrt{2} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right) + 6 \, \sqrt{2} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right) + 3 \, \sqrt{2} c^{\frac{3}{2}} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right) - 3 \, \sqrt{2} c^{\frac{3}{2}} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right) + \frac{8}{x^{3}}\right)} c + \frac{12 \, \arctan\left(c x^{2}\right)}{x^{5}}\right)} b - \frac{a}{5 \, x^{5}}"," ",0,"-1/60*((6*sqrt(2)*c^(3/2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c)) + 6*sqrt(2)*c^(3/2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c)) + 3*sqrt(2)*c^(3/2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1) - 3*sqrt(2)*c^(3/2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1) + 8/x^3)*c + 12*arctan(c*x^2)/x^5)*b - 1/5*a/x^5","A",0
74,1,169,0,0.490189," ","integrate(x^7*(a+b*arctan(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} x^{8} \arctan\left(c x^{2}\right)^{2} + \frac{1}{8} \, a^{2} x^{8} + \frac{1}{12} \, {\left(3 \, x^{8} \arctan\left(c x^{2}\right) - c {\left(\frac{c^{2} x^{6} - 3 \, x^{2}}{c^{4}} + \frac{3 \, \arctan\left(c x^{2}\right)}{c^{5}}\right)}\right)} a b - \frac{1}{24} \, {\left(2 \, c {\left(\frac{c^{2} x^{6} - 3 \, x^{2}}{c^{4}} + \frac{3 \, \arctan\left(c x^{2}\right)}{c^{5}}\right)} \arctan\left(c x^{2}\right) - \frac{c^{2} x^{4} + 3 \, \arctan\left(c x^{2}\right)^{2} - 3 \, \log\left(12 \, c^{7} x^{4} + 12 \, c^{5}\right) - \log\left(c^{2} x^{4} + 1\right)}{c^{4}}\right)} b^{2}"," ",0,"1/8*b^2*x^8*arctan(c*x^2)^2 + 1/8*a^2*x^8 + 1/12*(3*x^8*arctan(c*x^2) - c*((c^2*x^6 - 3*x^2)/c^4 + 3*arctan(c*x^2)/c^5))*a*b - 1/24*(2*c*((c^2*x^6 - 3*x^2)/c^4 + 3*arctan(c*x^2)/c^5)*arctan(c*x^2) - (c^2*x^4 + 3*arctan(c*x^2)^2 - 3*log(12*c^7*x^4 + 12*c^5) - log(c^2*x^4 + 1))/c^4)*b^2","A",0
75,0,0,0,0.000000," ","integrate(x^5*(a+b*arctan(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} x^{6} + \frac{1}{6} \, {\left(2 \, x^{6} \arctan\left(c x^{2}\right) - {\left(\frac{x^{4}}{c^{2}} - \frac{\log\left(c^{2} x^{4} + 1\right)}{c^{4}}\right)} c\right)} a b + \frac{1}{96} \, {\left(4 \, x^{6} \arctan\left(c x^{2}\right)^{2} - x^{6} \log\left(c^{2} x^{4} + 1\right)^{2} + 96 \, \int \frac{4 \, c^{2} x^{9} \log\left(c^{2} x^{4} + 1\right) - 8 \, c x^{7} \arctan\left(c x^{2}\right) + 36 \, {\left(c^{2} x^{9} + x^{5}\right)} \arctan\left(c x^{2}\right)^{2} + 3 \, {\left(c^{2} x^{9} + x^{5}\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{48 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x}\right)} b^{2}"," ",0,"1/6*a^2*x^6 + 1/6*(2*x^6*arctan(c*x^2) - (x^4/c^2 - log(c^2*x^4 + 1)/c^4)*c)*a*b + 1/96*(4*x^6*arctan(c*x^2)^2 - x^6*log(c^2*x^4 + 1)^2 + 96*integrate(1/48*(4*c^2*x^9*log(c^2*x^4 + 1) - 8*c*x^7*arctan(c*x^2) + 36*(c^2*x^9 + x^5)*arctan(c*x^2)^2 + 3*(c^2*x^9 + x^5)*log(c^2*x^4 + 1)^2)/(c^2*x^4 + 1), x))*b^2","F",0
76,1,126,0,0.488350," ","integrate(x^3*(a+b*arctan(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x^{4} \arctan\left(c x^{2}\right)^{2} + \frac{1}{4} \, a^{2} x^{4} + \frac{1}{2} \, {\left(x^{4} \arctan\left(c x^{2}\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\arctan\left(c x^{2}\right)}{c^{3}}\right)}\right)} a b - \frac{1}{4} \, {\left(2 \, c {\left(\frac{x^{2}}{c^{2}} - \frac{\arctan\left(c x^{2}\right)}{c^{3}}\right)} \arctan\left(c x^{2}\right) + \frac{\arctan\left(c x^{2}\right)^{2} - \log\left(4 \, c^{5} x^{4} + 4 \, c^{3}\right)}{c^{2}}\right)} b^{2}"," ",0,"1/4*b^2*x^4*arctan(c*x^2)^2 + 1/4*a^2*x^4 + 1/2*(x^4*arctan(c*x^2) - c*(x^2/c^2 - arctan(c*x^2)/c^3))*a*b - 1/4*(2*c*(x^2/c^2 - arctan(c*x^2)/c^3)*arctan(c*x^2) + (arctan(c*x^2)^2 - log(4*c^5*x^4 + 4*c^3))/c^2)*b^2","A",0
77,0,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} x^{2} + \frac{1}{32} \, {\left(4 \, x^{2} \arctan\left(c x^{2}\right)^{2} - x^{2} \log\left(c^{2} x^{4} + 1\right)^{2} + 384 \, c^{2} \int \frac{x^{5} \arctan\left(c x^{2}\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 32 \, c^{2} \int \frac{x^{5} \log\left(c^{2} x^{4} + 1\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 128 \, c^{2} \int \frac{x^{5} \log\left(c^{2} x^{4} + 1\right)}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + \frac{4 \, \arctan\left(c x^{2}\right)^{3}}{c} - 256 \, c \int \frac{x^{3} \arctan\left(c x^{2}\right)}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 32 \, \int \frac{x \log\left(c^{2} x^{4} + 1\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x}\right)} b^{2} + \frac{{\left(2 \, c x^{2} \arctan\left(c x^{2}\right) - \log\left(c^{2} x^{4} + 1\right)\right)} a b}{2 \, c}"," ",0,"1/2*a^2*x^2 + 1/32*(4*x^2*arctan(c*x^2)^2 - x^2*log(c^2*x^4 + 1)^2 + 384*c^2*integrate(1/16*x^5*arctan(c*x^2)^2/(c^2*x^4 + 1), x) + 32*c^2*integrate(1/16*x^5*log(c^2*x^4 + 1)^2/(c^2*x^4 + 1), x) + 128*c^2*integrate(1/16*x^5*log(c^2*x^4 + 1)/(c^2*x^4 + 1), x) + 4*arctan(c*x^2)^3/c - 256*c*integrate(1/16*x^3*arctan(c*x^2)/(c^2*x^4 + 1), x) + 32*integrate(1/16*x*log(c^2*x^4 + 1)^2/(c^2*x^4 + 1), x))*b^2 + 1/2*(2*c*x^2*arctan(c*x^2) - log(c^2*x^4 + 1))*a*b/c","F",0
78,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \frac{1}{16} \, \int \frac{12 \, b^{2} \arctan\left(c x^{2}\right)^{2} + b^{2} \log\left(c^{2} x^{4} + 1\right)^{2} + 32 \, a b \arctan\left(c x^{2}\right)}{x}\,{d x}"," ",0,"a^2*log(x) + 1/16*integrate((12*b^2*arctan(c*x^2)^2 + b^2*log(c^2*x^4 + 1)^2 + 32*a*b*arctan(c*x^2))/x, x)","F",0
79,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^2/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{4} + 1\right) - \log\left(x^{4}\right)\right)} + \frac{2 \, \arctan\left(c x^{2}\right)}{x^{2}}\right)} a b + \frac{\frac{1}{4} \, {\left(8 \, x^{2} \int -\frac{12 \, c^{2} x^{4} \log\left(c^{2} x^{4} + 1\right) - 56 \, c x^{2} \arctan\left(c x^{2}\right) - 36 \, {\left(c^{2} x^{4} + 1\right)} \arctan\left(c x^{2}\right)^{2} - 3 \, {\left(c^{2} x^{4} + 1\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{4 \, {\left(c^{2} x^{7} + x^{3}\right)}}\,{d x} - 28 \, \arctan\left(c x^{2}\right)^{2} + 3 \, \log\left(c^{2} x^{4} + 1\right)^{2}\right)} b^{2}}{32 \, x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"-1/2*(c*(log(c^2*x^4 + 1) - log(x^4)) + 2*arctan(c*x^2)/x^2)*a*b + 1/32*(32*x^2*integrate(-1/16*(4*c^2*x^4*log(c^2*x^4 + 1) - 8*c*x^2*arctan(c*x^2) - 12*(c^2*x^4 + 1)*arctan(c*x^2)^2 - (c^2*x^4 + 1)*log(c^2*x^4 + 1)^2)/(c^2*x^7 + x^3), x) - 4*arctan(c*x^2)^2 + log(c^2*x^4 + 1)^2)*b^2/x^2 - 1/2*a^2/x^2","F",0
80,1,110,0,0.519483," ","integrate((a+b*arctan(c*x^2))^2/x^5,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left(c \arctan\left(c x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{\arctan\left(c x^{2}\right)}{x^{4}}\right)} a b + \frac{1}{4} \, {\left({\left(\arctan\left(c x^{2}\right)^{2} - \log\left(c^{2} x^{4} + 1\right) + 4 \, \log\left(x\right)\right)} c^{2} - 2 \, {\left(c \arctan\left(c x^{2}\right) + \frac{1}{x^{2}}\right)} c \arctan\left(c x^{2}\right)\right)} b^{2} - \frac{b^{2} \arctan\left(c x^{2}\right)^{2}}{4 \, x^{4}} - \frac{a^{2}}{4 \, x^{4}}"," ",0,"-1/2*((c*arctan(c*x^2) + 1/x^2)*c + arctan(c*x^2)/x^4)*a*b + 1/4*((arctan(c*x^2)^2 - log(c^2*x^4 + 1) + 4*log(x))*c^2 - 2*(c*arctan(c*x^2) + 1/x^2)*c*arctan(c*x^2))*b^2 - 1/4*b^2*arctan(c*x^2)^2/x^4 - 1/4*a^2/x^4","A",0
81,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{6} \, {\left(4 \, x^{3} \arctan\left(c x^{2}\right) - c {\left(\frac{8 \, x}{c^{2}} - \frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}} - \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}}}{c^{2}}\right)}\right)} a b + \frac{1}{48} \, {\left(4 \, x^{3} \arctan\left(c x^{2}\right)^{2} - x^{3} \log\left(c^{2} x^{4} + 1\right)^{2} + 48 \, \int \frac{8 \, c^{2} x^{6} \log\left(c^{2} x^{4} + 1\right) - 16 \, c x^{4} \arctan\left(c x^{2}\right) + 36 \, {\left(c^{2} x^{6} + x^{2}\right)} \arctan\left(c x^{2}\right)^{2} + 3 \, {\left(c^{2} x^{6} + x^{2}\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{48 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x}\right)} b^{2}"," ",0,"1/3*a^2*x^3 + 1/6*(4*x^3*arctan(c*x^2) - c*(8*x/c^2 - (2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/sqrt(c) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/sqrt(c) + sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/sqrt(c) - sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/sqrt(c))/c^2))*a*b + 1/48*(4*x^3*arctan(c*x^2)^2 - x^3*log(c^2*x^4 + 1)^2 + 48*integrate(1/48*(8*c^2*x^6*log(c^2*x^4 + 1) - 16*c*x^4*arctan(c*x^2) + 36*(c^2*x^6 + x^2)*arctan(c*x^2)^2 + 3*(c^2*x^6 + x^2)*log(c^2*x^4 + 1)^2)/(c^2*x^4 + 1), x))*b^2","F",0
82,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}}\right)} - 4 \, x \arctan\left(c x^{2}\right)\right)} a b + \frac{1}{16} \, {\left(4 \, x \arctan\left(c x^{2}\right)^{2} - x \log\left(c^{2} x^{4} + 1\right)^{2} + 16 \, \int \frac{8 \, c^{2} x^{4} \log\left(c^{2} x^{4} + 1\right) - 16 \, c x^{2} \arctan\left(c x^{2}\right) + 12 \, {\left(c^{2} x^{4} + 1\right)} \arctan\left(c x^{2}\right)^{2} + {\left(c^{2} x^{4} + 1\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{16 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"-1/2*(c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) - sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/c^(3/2) + sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/c^(3/2)) - 4*x*arctan(c*x^2))*a*b + 1/16*(4*x*arctan(c*x^2)^2 - x*log(c^2*x^4 + 1)^2 + 16*integrate(1/16*(8*c^2*x^4*log(c^2*x^4 + 1) - 16*c*x^2*arctan(c*x^2) + 12*(c^2*x^4 + 1)*arctan(c*x^2)^2 + (c^2*x^4 + 1)*log(c^2*x^4 + 1)^2)/(c^2*x^4 + 1), x))*b^2 + a^2*x","F",0
83,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^2/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}} - \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{\sqrt{c}}\right)} - \frac{4 \, \arctan\left(c x^{2}\right)}{x}\right)} a b - \frac{\frac{1}{4} \, {\left(28 \, \arctan\left(c x^{2}\right)^{2} - 4 \, x \int -\frac{24 \, c^{2} x^{4} \log\left(c^{2} x^{4} + 1\right) - 112 \, c x^{2} \arctan\left(c x^{2}\right) - 36 \, {\left(c^{2} x^{4} + 1\right)} \arctan\left(c x^{2}\right)^{2} - 3 \, {\left(c^{2} x^{4} + 1\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{4 \, {\left(c^{2} x^{6} + x^{2}\right)}}\,{d x} - 3 \, \log\left(c^{2} x^{4} + 1\right)^{2}\right)} b^{2}}{16 \, x} - \frac{a^{2}}{x}"," ",0,"1/2*(c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/sqrt(c) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/sqrt(c) + sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/sqrt(c) - sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/sqrt(c)) - 4*arctan(c*x^2)/x)*a*b - 1/16*(4*arctan(c*x^2)^2 - 16*x*integrate(-1/16*(8*c^2*x^4*log(c^2*x^4 + 1) - 16*c*x^2*arctan(c*x^2) - 12*(c^2*x^4 + 1)*arctan(c*x^2)^2 - (c^2*x^4 + 1)*log(c^2*x^4 + 1)^2)/(c^2*x^6 + x^2), x) - log(c^2*x^4 + 1)^2)*b^2/x - a^2/x","F",0
84,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^2/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right)}{c^{\frac{3}{2}}}\right)} + \frac{8}{x}\right)} c + \frac{4 \, \arctan\left(c x^{2}\right)}{x^{3}}\right)} a b + \frac{\frac{1}{4} \, {\left(4 \, x^{3} \int -\frac{24 \, c^{2} x^{4} \log\left(c^{2} x^{4} + 1\right) - 112 \, c x^{2} \arctan\left(c x^{2}\right) - 108 \, {\left(c^{2} x^{4} + 1\right)} \arctan\left(c x^{2}\right)^{2} - 9 \, {\left(c^{2} x^{4} + 1\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{4 \, {\left(c^{2} x^{8} + x^{4}\right)}}\,{d x} - 28 \, \arctan\left(c x^{2}\right)^{2} + 3 \, \log\left(c^{2} x^{4} + 1\right)^{2}\right)} b^{2}}{48 \, x^{3}} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"-1/6*((c^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c))/c^(3/2) - sqrt(2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1)/c^(3/2) + sqrt(2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1)/c^(3/2)) + 8/x)*c + 4*arctan(c*x^2)/x^3)*a*b + 1/48*(48*x^3*integrate(-1/48*(8*c^2*x^4*log(c^2*x^4 + 1) - 16*c*x^2*arctan(c*x^2) - 36*(c^2*x^4 + 1)*arctan(c*x^2)^2 - 3*(c^2*x^4 + 1)*log(c^2*x^4 + 1)^2)/(c^2*x^8 + x^4), x) - 4*arctan(c*x^2)^2 + log(c^2*x^4 + 1)^2)*b^2/x^3 - 1/3*a^2/x^3","F",0
85,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^2/x^6,x, algorithm=""maxima"")","-\frac{1}{30} \, {\left({\left(6 \, \sqrt{2} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x + \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right) + 6 \, \sqrt{2} c^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(2 \, c x - \sqrt{2} \sqrt{c}\right)}}{2 \, \sqrt{c}}\right) + 3 \, \sqrt{2} c^{\frac{3}{2}} \log\left(c x^{2} + \sqrt{2} \sqrt{c} x + 1\right) - 3 \, \sqrt{2} c^{\frac{3}{2}} \log\left(c x^{2} - \sqrt{2} \sqrt{c} x + 1\right) + \frac{8}{x^{3}}\right)} c + \frac{12 \, \arctan\left(c x^{2}\right)}{x^{5}}\right)} a b + \frac{\frac{1}{4} \, {\left(4 \, x^{5} \int -\frac{24 \, c^{2} x^{4} \log\left(c^{2} x^{4} + 1\right) - 112 \, c x^{2} \arctan\left(c x^{2}\right) - 180 \, {\left(c^{2} x^{4} + 1\right)} \arctan\left(c x^{2}\right)^{2} - 15 \, {\left(c^{2} x^{4} + 1\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{4 \, {\left(c^{2} x^{10} + x^{6}\right)}}\,{d x} - 28 \, \arctan\left(c x^{2}\right)^{2} + 3 \, \log\left(c^{2} x^{4} + 1\right)^{2}\right)} b^{2}}{80 \, x^{5}} - \frac{a^{2}}{5 \, x^{5}}"," ",0,"-1/30*((6*sqrt(2)*c^(3/2)*arctan(1/2*sqrt(2)*(2*c*x + sqrt(2)*sqrt(c))/sqrt(c)) + 6*sqrt(2)*c^(3/2)*arctan(1/2*sqrt(2)*(2*c*x - sqrt(2)*sqrt(c))/sqrt(c)) + 3*sqrt(2)*c^(3/2)*log(c*x^2 + sqrt(2)*sqrt(c)*x + 1) - 3*sqrt(2)*c^(3/2)*log(c*x^2 - sqrt(2)*sqrt(c)*x + 1) + 8/x^3)*c + 12*arctan(c*x^2)/x^5)*a*b + 1/80*(80*x^5*integrate(-1/80*(8*c^2*x^4*log(c^2*x^4 + 1) - 16*c*x^2*arctan(c*x^2) - 60*(c^2*x^4 + 1)*arctan(c*x^2)^2 - 5*(c^2*x^4 + 1)*log(c^2*x^4 + 1)^2)/(c^2*x^10 + x^6), x) - 4*arctan(c*x^2)^2 + log(c^2*x^4 + 1)^2)*b^2/x^5 - 1/5*a^2/x^5","F",0
86,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x^2))^3,x, algorithm=""maxima"")","\frac{3}{4} \, a b^{2} x^{4} \arctan\left(c x^{2}\right)^{2} + \frac{1}{4} \, a^{3} x^{4} + \frac{3}{4} \, {\left(x^{4} \arctan\left(c x^{2}\right) - c {\left(\frac{x^{2}}{c^{2}} - \frac{\arctan\left(c x^{2}\right)}{c^{3}}\right)}\right)} a^{2} b - \frac{3}{4} \, {\left(2 \, c {\left(\frac{x^{2}}{c^{2}} - \frac{\arctan\left(c x^{2}\right)}{c^{3}}\right)} \arctan\left(c x^{2}\right) + \frac{\arctan\left(c x^{2}\right)^{2} - \log\left(4 \, c^{5} x^{4} + 4 \, c^{3}\right)}{c^{2}}\right)} a b^{2} + \frac{1}{128} \, {\left(4 \, x^{4} \arctan\left(c x^{2}\right)^{3} - 3 \, x^{4} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right)^{2} + 128 \, \int \frac{12 \, c^{2} x^{7} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right) - 12 \, c x^{5} \arctan\left(c x^{2}\right)^{2} + 56 \, {\left(c^{2} x^{7} + x^{3}\right)} \arctan\left(c x^{2}\right)^{3} + 3 \, {\left(c x^{5} + 2 \, {\left(c^{2} x^{7} + x^{3}\right)} \arctan\left(c x^{2}\right)\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{64 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x}\right)} b^{3}"," ",0,"3/4*a*b^2*x^4*arctan(c*x^2)^2 + 1/4*a^3*x^4 + 3/4*(x^4*arctan(c*x^2) - c*(x^2/c^2 - arctan(c*x^2)/c^3))*a^2*b - 3/4*(2*c*(x^2/c^2 - arctan(c*x^2)/c^3)*arctan(c*x^2) + (arctan(c*x^2)^2 - log(4*c^5*x^4 + 4*c^3))/c^2)*a*b^2 + 1/128*(4*x^4*arctan(c*x^2)^3 - 3*x^4*arctan(c*x^2)*log(c^2*x^4 + 1)^2 + 128*integrate(1/64*(12*c^2*x^7*arctan(c*x^2)*log(c^2*x^4 + 1) - 12*c*x^5*arctan(c*x^2)^2 + 56*(c^2*x^7 + x^3)*arctan(c*x^2)^3 + 3*(c*x^5 + 2*(c^2*x^7 + x^3)*arctan(c*x^2))*log(c^2*x^4 + 1)^2)/(c^2*x^4 + 1), x))*b^3","F",0
87,0,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x^2))^3,x, algorithm=""maxima"")","\frac{1}{16} \, b^{3} x^{2} \arctan\left(c x^{2}\right)^{3} - \frac{3}{64} \, b^{3} x^{2} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right)^{2} + \frac{7 \, b^{3} \arctan\left(c x^{2}\right)^{4}}{64 \, c} + 28 \, b^{3} c^{2} \int \frac{x^{5} \arctan\left(c x^{2}\right)^{3}}{32 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 3 \, b^{3} c^{2} \int \frac{x^{5} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right)^{2}}{32 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 96 \, a b^{2} c^{2} \int \frac{x^{5} \arctan\left(c x^{2}\right)^{2}}{32 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 12 \, b^{3} c^{2} \int \frac{x^{5} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right)}{32 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + \frac{1}{2} \, a^{3} x^{2} + \frac{a b^{2} \arctan\left(c x^{2}\right)^{3}}{2 \, c} - 12 \, b^{3} c \int \frac{x^{3} \arctan\left(c x^{2}\right)^{2}}{32 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 3 \, b^{3} c \int \frac{x^{3} \log\left(c^{2} x^{4} + 1\right)^{2}}{32 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + 3 \, b^{3} \int \frac{x \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right)^{2}}{32 \, {\left(c^{2} x^{4} + 1\right)}}\,{d x} + \frac{3 \, {\left(2 \, c x^{2} \arctan\left(c x^{2}\right) - \log\left(c^{2} x^{4} + 1\right)\right)} a^{2} b}{4 \, c}"," ",0,"1/16*b^3*x^2*arctan(c*x^2)^3 - 3/64*b^3*x^2*arctan(c*x^2)*log(c^2*x^4 + 1)^2 + 7/64*b^3*arctan(c*x^2)^4/c + 28*b^3*c^2*integrate(1/32*x^5*arctan(c*x^2)^3/(c^2*x^4 + 1), x) + 3*b^3*c^2*integrate(1/32*x^5*arctan(c*x^2)*log(c^2*x^4 + 1)^2/(c^2*x^4 + 1), x) + 96*a*b^2*c^2*integrate(1/32*x^5*arctan(c*x^2)^2/(c^2*x^4 + 1), x) + 12*b^3*c^2*integrate(1/32*x^5*arctan(c*x^2)*log(c^2*x^4 + 1)/(c^2*x^4 + 1), x) + 1/2*a^3*x^2 + 1/2*a*b^2*arctan(c*x^2)^3/c - 12*b^3*c*integrate(1/32*x^3*arctan(c*x^2)^2/(c^2*x^4 + 1), x) + 3*b^3*c*integrate(1/32*x^3*log(c^2*x^4 + 1)^2/(c^2*x^4 + 1), x) + 3*b^3*integrate(1/32*x*arctan(c*x^2)*log(c^2*x^4 + 1)^2/(c^2*x^4 + 1), x) + 3/4*(2*c*x^2*arctan(c*x^2) - log(c^2*x^4 + 1))*a^2*b/c","F",0
88,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^3/x,x, algorithm=""maxima"")","a^{3} \log\left(x\right) + \frac{1}{32} \, \int \frac{28 \, b^{3} \arctan\left(c x^{2}\right)^{3} + 3 \, b^{3} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right)^{2} + 96 \, a b^{2} \arctan\left(c x^{2}\right)^{2} + 96 \, a^{2} b \arctan\left(c x^{2}\right)}{x}\,{d x}"," ",0,"a^3*log(x) + 1/32*integrate((28*b^3*arctan(c*x^2)^3 + 3*b^3*arctan(c*x^2)*log(c^2*x^4 + 1)^2 + 96*a*b^2*arctan(c*x^2)^2 + 96*a^2*b*arctan(c*x^2))/x, x)","F",0
89,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^3/x^3,x, algorithm=""maxima"")","-\frac{3}{4} \, {\left(c {\left(\log\left(c^{2} x^{4} + 1\right) - \log\left(x^{4}\right)\right)} + \frac{2 \, \arctan\left(c x^{2}\right)}{x^{2}}\right)} a^{2} b - \frac{a^{3}}{2 \, x^{2}} - \frac{\frac{15}{2} \, b^{3} \arctan\left(c x^{2}\right)^{3} - \frac{21}{8} \, b^{3} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right)^{2} - 2 \, x^{2} \int -\frac{84 \, b^{3} c^{2} x^{4} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right) - 196 \, {\left(b^{3} c^{2} x^{4} + b^{3}\right)} \arctan\left(c x^{2}\right)^{3} - 12 \, {\left(64 \, a b^{2} c^{2} x^{4} + 15 \, b^{3} c x^{2} + 64 \, a b^{2}\right)} \arctan\left(c x^{2}\right)^{2} + 21 \, {\left(b^{3} c x^{2} - {\left(b^{3} c^{2} x^{4} + b^{3}\right)} \arctan\left(c x^{2}\right)\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{8 \, {\left(c^{2} x^{7} + x^{3}\right)}}\,{d x}}{64 \, x^{2}}"," ",0,"-3/4*(c*(log(c^2*x^4 + 1) - log(x^4)) + 2*arctan(c*x^2)/x^2)*a^2*b - 1/2*a^3/x^2 - 1/64*(4*b^3*arctan(c*x^2)^3 - 3*b^3*arctan(c*x^2)*log(c^2*x^4 + 1)^2 - 64*x^2*integrate(-1/32*(12*b^3*c^2*x^4*arctan(c*x^2)*log(c^2*x^4 + 1) - 28*(b^3*c^2*x^4 + b^3)*arctan(c*x^2)^3 - 12*(8*a*b^2*c^2*x^4 + b^3*c*x^2 + 8*a*b^2)*arctan(c*x^2)^2 + 3*(b^3*c*x^2 - (b^3*c^2*x^4 + b^3)*arctan(c*x^2))*log(c^2*x^4 + 1)^2)/(c^2*x^7 + x^3), x))/x^2","F",0
90,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^2))^3/x^5,x, algorithm=""maxima"")","-\frac{3}{4} \, {\left({\left(c \arctan\left(c x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{\arctan\left(c x^{2}\right)}{x^{4}}\right)} a^{2} b + \frac{3}{4} \, {\left({\left(\arctan\left(c x^{2}\right)^{2} - \log\left(c^{2} x^{4} + 1\right) + 4 \, \log\left(x\right)\right)} c^{2} - 2 \, {\left(c \arctan\left(c x^{2}\right) + \frac{1}{x^{2}}\right)} c \arctan\left(c x^{2}\right)\right)} a b^{2} - \frac{3 \, a b^{2} \arctan\left(c x^{2}\right)^{2}}{4 \, x^{4}} + \frac{\frac{1}{8} \, {\left(16 \, x^{4} \int -\frac{84 \, c^{2} x^{4} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right) - 180 \, c x^{2} \arctan\left(c x^{2}\right)^{2} - 392 \, {\left(c^{2} x^{4} + 1\right)} \arctan\left(c x^{2}\right)^{3} + 21 \, {\left(c x^{2} - 2 \, {\left(c^{2} x^{4} + 1\right)} \arctan\left(c x^{2}\right)\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{8 \, {\left(c^{2} x^{9} + x^{5}\right)}}\,{d x} - 60 \, \arctan\left(c x^{2}\right)^{3} + 21 \, \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right)^{2}\right)} b^{3}}{128 \, x^{4}} - \frac{a^{3}}{4 \, x^{4}}"," ",0,"-3/4*((c*arctan(c*x^2) + 1/x^2)*c + arctan(c*x^2)/x^4)*a^2*b + 3/4*((arctan(c*x^2)^2 - log(c^2*x^4 + 1) + 4*log(x))*c^2 - 2*(c*arctan(c*x^2) + 1/x^2)*c*arctan(c*x^2))*a*b^2 - 3/4*a*b^2*arctan(c*x^2)^2/x^4 + 1/128*(128*x^4*integrate(-1/64*(12*c^2*x^4*arctan(c*x^2)*log(c^2*x^4 + 1) - 12*c*x^2*arctan(c*x^2)^2 - 56*(c^2*x^4 + 1)*arctan(c*x^2)^3 + 3*(c*x^2 - 2*(c^2*x^4 + 1)*arctan(c*x^2))*log(c^2*x^4 + 1)^2)/(c^2*x^9 + x^5), x) - 4*arctan(c*x^2)^3 + 3*arctan(c*x^2)*log(c^2*x^4 + 1)^2)*b^3/x^4 - 1/4*a^3/x^4","F",0
91,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctan(c*x^2))^3,x, algorithm=""maxima"")","\frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \frac{\frac{15}{2} \, b^{3} d^{m} x x^{m} \arctan\left(c x^{2}\right)^{3} - \frac{21}{8} \, b^{3} d^{m} x x^{m} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right)^{2} + {\left(m + 1\right)} \int \frac{168 \, b^{3} c^{2} d^{m} x^{4} x^{m} \arctan\left(c x^{2}\right) \log\left(c^{2} x^{4} + 1\right) + 196 \, {\left(b^{3} d^{m} m + {\left(b^{3} c^{2} d^{m} m + b^{3} c^{2} d^{m}\right)} x^{4} + b^{3} d^{m}\right)} x^{m} \arctan\left(c x^{2}\right)^{3} - 24 \, {\left(15 \, b^{3} c d^{m} x^{2} - 32 \, a b^{2} d^{m} m - 32 \, {\left(a b^{2} c^{2} d^{m} m + a b^{2} c^{2} d^{m}\right)} x^{4} - 32 \, a b^{2} d^{m}\right)} x^{m} \arctan\left(c x^{2}\right)^{2} + 768 \, {\left(a^{2} b d^{m} m + {\left(a^{2} b c^{2} d^{m} m + a^{2} b c^{2} d^{m}\right)} x^{4} + a^{2} b d^{m}\right)} x^{m} \arctan\left(c x^{2}\right) + 21 \, {\left(2 \, b^{3} c d^{m} x^{2} x^{m} + {\left(b^{3} d^{m} m + {\left(b^{3} c^{2} d^{m} m + b^{3} c^{2} d^{m}\right)} x^{4} + b^{3} d^{m}\right)} x^{m} \arctan\left(c x^{2}\right)\right)} \log\left(c^{2} x^{4} + 1\right)^{2}}{8 \, {\left({\left(c^{2} m + c^{2}\right)} x^{4} + m + 1\right)}}\,{d x}}{32 \, {\left(m + 1\right)}}"," ",0,"(d*x)^(m + 1)*a^3/(d*(m + 1)) + 1/32*(4*b^3*d^m*x*x^m*arctan(c*x^2)^3 - 3*b^3*d^m*x*x^m*arctan(c*x^2)*log(c^2*x^4 + 1)^2 + 32*(m + 1)*integrate(1/32*(24*b^3*c^2*d^m*x^4*x^m*arctan(c*x^2)*log(c^2*x^4 + 1) + 28*(b^3*d^m*m + (b^3*c^2*d^m*m + b^3*c^2*d^m)*x^4 + b^3*d^m)*x^m*arctan(c*x^2)^3 - 24*(b^3*c*d^m*x^2 - 4*a*b^2*d^m*m - 4*(a*b^2*c^2*d^m*m + a*b^2*c^2*d^m)*x^4 - 4*a*b^2*d^m)*x^m*arctan(c*x^2)^2 + 96*(a^2*b*d^m*m + (a^2*b*c^2*d^m*m + a^2*b*c^2*d^m)*x^4 + a^2*b*d^m)*x^m*arctan(c*x^2) + 3*(2*b^3*c*d^m*x^2*x^m + (b^3*d^m*m + (b^3*c^2*d^m*m + b^3*c^2*d^m)*x^4 + b^3*d^m)*x^m*arctan(c*x^2))*log(c^2*x^4 + 1)^2)/((c^2*m + c^2)*x^4 + m + 1), x))/(m + 1)","F",0
92,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctan(c*x^2))^2,x, algorithm=""maxima"")","\frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}} + \frac{7 \, b^{2} d^{m} x x^{m} \arctan\left(c x^{2}\right)^{2} - \frac{3}{4} \, b^{2} d^{m} x x^{m} \log\left(c^{2} x^{4} + 1\right)^{2} + {\left(m + 1\right)} \int \frac{24 \, b^{2} c^{2} d^{m} x^{4} x^{m} \log\left(c^{2} x^{4} + 1\right) + 36 \, {\left({\left(b^{2} c^{2} d^{m} m + b^{2} c^{2} d^{m}\right)} x^{4} + b^{2} d^{m} m + b^{2} d^{m}\right)} x^{m} \arctan\left(c x^{2}\right)^{2} + 3 \, {\left({\left(b^{2} c^{2} d^{m} m + b^{2} c^{2} d^{m}\right)} x^{4} + b^{2} d^{m} m + b^{2} d^{m}\right)} x^{m} \log\left(c^{2} x^{4} + 1\right)^{2} - 16 \, {\left(7 \, b^{2} c d^{m} x^{2} - 8 \, {\left(a b c^{2} d^{m} m + a b c^{2} d^{m}\right)} x^{4} - 8 \, a b d^{m} m - 8 \, a b d^{m}\right)} x^{m} \arctan\left(c x^{2}\right)}{4 \, {\left({\left(c^{2} m + c^{2}\right)} x^{4} + m + 1\right)}}\,{d x}}{16 \, {\left(m + 1\right)}}"," ",0,"(d*x)^(m + 1)*a^2/(d*(m + 1)) + 1/16*(4*b^2*d^m*x*x^m*arctan(c*x^2)^2 - b^2*d^m*x*x^m*log(c^2*x^4 + 1)^2 + 16*(m + 1)*integrate(1/16*(8*b^2*c^2*d^m*x^4*x^m*log(c^2*x^4 + 1) + 12*((b^2*c^2*d^m*m + b^2*c^2*d^m)*x^4 + b^2*d^m*m + b^2*d^m)*x^m*arctan(c*x^2)^2 + ((b^2*c^2*d^m*m + b^2*c^2*d^m)*x^4 + b^2*d^m*m + b^2*d^m)*x^m*log(c^2*x^4 + 1)^2 - 16*(b^2*c*d^m*x^2 - 2*(a*b*c^2*d^m*m + a*b*c^2*d^m)*x^4 - 2*a*b*d^m*m - 2*a*b*d^m)*x^m*arctan(c*x^2))/((c^2*m + c^2)*x^4 + m + 1), x))/(m + 1)","F",0
93,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctan(c*x^2)),x, algorithm=""maxima"")","\frac{{\left(d^{m} x x^{m} \arctan\left(c x^{2}\right) - 2 \, {\left(c d^{m} m + c d^{m}\right)} \int \frac{x^{2} x^{m}}{{\left(c^{2} m + c^{2}\right)} x^{4} + m + 1}\,{d x}\right)} b}{m + 1} + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"(d^m*x*x^m*arctan(c*x^2) - 2*(c*d^m*m + c*d^m)*integrate(x^2*x^m/((c^2*m + c^2)*x^4 + m + 1), x))*b/(m + 1) + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
94,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctan(c*x^2)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \arctan\left(c x^{2}\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctan(c*x^2) + a), x)","F",0
95,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctan(c*x^2))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} d^{m} x^{4} + d^{m}\right)} x^{m} - {\left(b^{2} c x \arctan\left(c x^{2}\right) + a b c x\right)} \int \frac{{\left({\left(c^{2} d^{m} m + 3 \, c^{2} d^{m}\right)} x^{4} + d^{m} m - d^{m}\right)} x^{m}}{b^{2} c x^{2} \arctan\left(c x^{2}\right) + a b c x^{2}}\,{d x}}{2 \, {\left(b^{2} c x \arctan\left(c x^{2}\right) + a b c x\right)}}"," ",0,"-1/2*((c^2*d^m*x^4 + d^m)*x^m - 2*(b^2*c*x*arctan(c*x^2) + a*b*c*x)*integrate(1/2*((c^2*d^m*m + 3*c^2*d^m)*x^4 + d^m*m - d^m)*x^m/(b^2*c*x^2*arctan(c*x^2) + a*b*c*x^2), x))/(b^2*c*x*arctan(c*x^2) + a*b*c*x)","F",0
96,1,54,0,0.416972," ","integrate(x^11*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{1}{12} \, a x^{12} + \frac{1}{36} \, {\left(3 \, x^{12} \arctan\left(c x^{3}\right) - c {\left(\frac{c^{2} x^{9} - 3 \, x^{3}}{c^{4}} + \frac{3 \, \arctan\left(c x^{3}\right)}{c^{5}}\right)}\right)} b"," ",0,"1/12*a*x^12 + 1/36*(3*x^12*arctan(c*x^3) - c*((c^2*x^9 - 3*x^3)/c^4 + 3*arctan(c*x^3)/c^5))*b","A",0
97,1,48,0,0.314699," ","integrate(x^8*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{1}{9} \, a x^{9} + \frac{1}{18} \, {\left(2 \, x^{9} \arctan\left(c x^{3}\right) - {\left(\frac{x^{6}}{c^{2}} - \frac{\log\left(c^{2} x^{6} + 1\right)}{c^{4}}\right)} c\right)} b"," ",0,"1/9*a*x^9 + 1/18*(2*x^9*arctan(c*x^3) - (x^6/c^2 - log(c^2*x^6 + 1)/c^4)*c)*b","A",0
98,1,43,0,0.413064," ","integrate(x^5*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{6} \, {\left(x^{6} \arctan\left(c x^{3}\right) - c {\left(\frac{x^{3}}{c^{2}} - \frac{\arctan\left(c x^{3}\right)}{c^{3}}\right)}\right)} b"," ",0,"1/6*a*x^6 + 1/6*(x^6*arctan(c*x^3) - c*(x^3/c^2 - arctan(c*x^3)/c^3))*b","A",0
99,1,38,0,0.313400," ","integrate(x^2*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{{\left(2 \, c x^{3} \arctan\left(c x^{3}\right) - \log\left(c^{2} x^{6} + 1\right)\right)} b}{6 \, c}"," ",0,"1/3*a*x^3 + 1/6*(2*c*x^3*arctan(c*x^3) - log(c^2*x^6 + 1))*b/c","A",0
100,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^3))/x,x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x^{3}\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"b*integrate(arctan(c*x^3)/x, x) + a*log(x)","F",0
101,1,41,0,0.317761," ","integrate((a+b*arctan(c*x^3))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(c {\left(\log\left(c^{2} x^{6} + 1\right) - \log\left(x^{6}\right)\right)} + \frac{2 \, \arctan\left(c x^{3}\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"-1/6*(c*(log(c^2*x^6 + 1) - log(x^6)) + 2*arctan(c*x^3)/x^3)*b - 1/3*a/x^3","A",0
102,1,35,0,0.424376," ","integrate((a+b*arctan(c*x^3))/x^7,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c \arctan\left(c x^{3}\right) + \frac{1}{x^{3}}\right)} c + \frac{\arctan\left(c x^{3}\right)}{x^{6}}\right)} b - \frac{a}{6 \, x^{6}}"," ",0,"-1/6*((c*arctan(c*x^3) + 1/x^3)*c + arctan(c*x^3)/x^6)*b - 1/6*a/x^6","A",0
103,1,53,0,0.325814," ","integrate((a+b*arctan(c*x^3))/x^10,x, algorithm=""maxima"")","\frac{1}{18} \, {\left({\left(c^{2} \log\left(c^{2} x^{6} + 1\right) - c^{2} \log\left(x^{6}\right) - \frac{1}{x^{6}}\right)} c - \frac{2 \, \arctan\left(c x^{3}\right)}{x^{9}}\right)} b - \frac{a}{9 \, x^{9}}"," ",0,"1/18*((c^2*log(c^2*x^6 + 1) - c^2*log(x^6) - 1/x^6)*c - 2*arctan(c*x^3)/x^9)*b - 1/9*a/x^9","A",0
104,1,148,0,0.428389," ","integrate(x^3*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{16} \, {\left(4 \, x^{4} \arctan\left(c x^{3}\right) + c {\left(\frac{\frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} + \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{1}{3}}} - \frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} - \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{1}{3}}} + \frac{4 \, \arctan\left(c^{\frac{1}{3}} x\right)}{c^{\frac{1}{3}}} + \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x + \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} + \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x - \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}}}{c^{2}} - \frac{12 \, x}{c^{2}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/16*(4*x^4*arctan(c*x^3) + c*((sqrt(3)*log(c^(2/3)*x^2 + sqrt(3)*c^(1/3)*x + 1)/c^(1/3) - sqrt(3)*log(c^(2/3)*x^2 - sqrt(3)*c^(1/3)*x + 1)/c^(1/3) + 4*arctan(c^(1/3)*x)/c^(1/3) + 2*arctan((2*c^(2/3)*x + sqrt(3)*c^(1/3))/c^(1/3))/c^(1/3) + 2*arctan((2*c^(2/3)*x - sqrt(3)*c^(1/3))/c^(1/3))/c^(1/3))/c^2 - 12*x/c^2))*b","A",0
105,1,92,0,0.420742," ","integrate(a+b*arctan(c*x^3),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} - c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}} + \frac{\log\left(c^{\frac{4}{3}} x^{4} - c^{\frac{2}{3}} x^{2} + 1\right)}{c^{\frac{4}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{2}{3}} x^{2} + 1}{c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}}\right)} - 4 \, x \arctan\left(c x^{3}\right)\right)} b + a x"," ",0,"-1/4*(c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 - c^(2/3))/c^(2/3))/c^(4/3) + log(c^(4/3)*x^4 - c^(2/3)*x^2 + 1)/c^(4/3) - 2*log((c^(2/3)*x^2 + 1)/c^(2/3))/c^(4/3)) - 4*x*arctan(c*x^3))*b + a*x","A",0
106,1,137,0,0.416330," ","integrate((a+b*arctan(c*x^3))/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left({\left(\frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} + \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{1}{3}}} - \frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} - \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{1}{3}}} + \frac{4 \, \arctan\left(c^{\frac{1}{3}} x\right)}{c^{\frac{1}{3}}} + \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x + \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} + \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x - \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}}\right)} c - \frac{4 \, \arctan\left(c x^{3}\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"1/8*((sqrt(3)*log(c^(2/3)*x^2 + sqrt(3)*c^(1/3)*x + 1)/c^(1/3) - sqrt(3)*log(c^(2/3)*x^2 - sqrt(3)*c^(1/3)*x + 1)/c^(1/3) + 4*arctan(c^(1/3)*x)/c^(1/3) + 2*arctan((2*c^(2/3)*x + sqrt(3)*c^(1/3))/c^(1/3))/c^(1/3) + 2*arctan((2*c^(2/3)*x - sqrt(3)*c^(1/3))/c^(1/3))/c^(1/3))*c - 4*arctan(c*x^3)/x^2)*b - 1/2*a/x^2","A",0
107,1,102,0,0.412778," ","integrate((a+b*arctan(c*x^3))/x^6,x, algorithm=""maxima"")","-\frac{1}{20} \, {\left({\left(2 \, \sqrt{3} c^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} - c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right) + c^{\frac{2}{3}} \log\left(c^{\frac{4}{3}} x^{4} - c^{\frac{2}{3}} x^{2} + 1\right) - 2 \, c^{\frac{2}{3}} \log\left(\frac{c^{\frac{2}{3}} x^{2} + 1}{c^{\frac{2}{3}}}\right) + \frac{6}{x^{2}}\right)} c + \frac{4 \, \arctan\left(c x^{3}\right)}{x^{5}}\right)} b - \frac{a}{5 \, x^{5}}"," ",0,"-1/20*((2*sqrt(3)*c^(2/3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 - c^(2/3))/c^(2/3)) + c^(2/3)*log(c^(4/3)*x^4 - c^(2/3)*x^2 + 1) - 2*c^(2/3)*log((c^(2/3)*x^2 + 1)/c^(2/3)) + 6/x^2)*c + 4*arctan(c*x^3)/x^5)*b - 1/5*a/x^5","A",0
108,1,152,0,0.422709," ","integrate(x^7*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{1}{8} \, a x^{8} + \frac{1}{160} \, {\left(20 \, x^{8} \arctan\left(c x^{3}\right) - {\left(\frac{12 \, x^{5}}{c^{2}} + \frac{5 \, {\left(\frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} + \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} - \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{4 \, \arctan\left(c^{\frac{1}{3}} x\right)}{c^{\frac{5}{3}}} - \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x + \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} - \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x - \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}}\right)}}{c^{2}}\right)} c\right)} b"," ",0,"1/8*a*x^8 + 1/160*(20*x^8*arctan(c*x^3) - (12*x^5/c^2 + 5*(sqrt(3)*log(c^(2/3)*x^2 + sqrt(3)*c^(1/3)*x + 1)/c^(5/3) - sqrt(3)*log(c^(2/3)*x^2 - sqrt(3)*c^(1/3)*x + 1)/c^(5/3) - 4*arctan(c^(1/3)*x)/c^(5/3) - 2*arctan((2*c^(2/3)*x + sqrt(3)*c^(1/3))/c^(1/3))/c^(5/3) - 2*arctan((2*c^(2/3)*x - sqrt(3)*c^(1/3))/c^(1/3))/c^(5/3))/c^2)*c)*b","A",0
109,1,106,0,0.423893," ","integrate(x^4*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{20} \, {\left(4 \, x^{5} \arctan\left(c x^{3}\right) - c {\left(\frac{6 \, x^{2}}{c^{2}} - \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} - c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{8}{3}}} + \frac{\log\left(c^{\frac{4}{3}} x^{4} - c^{\frac{2}{3}} x^{2} + 1\right)}{c^{\frac{8}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{2}{3}} x^{2} + 1}{c^{\frac{2}{3}}}\right)}{c^{\frac{8}{3}}}\right)}\right)} b"," ",0,"1/5*a*x^5 + 1/20*(4*x^5*arctan(c*x^3) - c*(6*x^2/c^2 - 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 - c^(2/3))/c^(2/3))/c^(8/3) + log(c^(4/3)*x^4 - c^(2/3)*x^2 + 1)/c^(8/3) - 2*log((c^(2/3)*x^2 + 1)/c^(2/3))/c^(8/3)))*b","A",0
110,1,137,0,0.431044," ","integrate(x*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{8} \, {\left(4 \, x^{2} \arctan\left(c x^{3}\right) + c {\left(\frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} + \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} - \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{4 \, \arctan\left(c^{\frac{1}{3}} x\right)}{c^{\frac{5}{3}}} - \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x + \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} - \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x - \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}}\right)}\right)} b"," ",0,"1/2*a*x^2 + 1/8*(4*x^2*arctan(c*x^3) + c*(sqrt(3)*log(c^(2/3)*x^2 + sqrt(3)*c^(1/3)*x + 1)/c^(5/3) - sqrt(3)*log(c^(2/3)*x^2 - sqrt(3)*c^(1/3)*x + 1)/c^(5/3) - 4*arctan(c^(1/3)*x)/c^(5/3) - 2*arctan((2*c^(2/3)*x + sqrt(3)*c^(1/3))/c^(1/3))/c^(5/3) - 2*arctan((2*c^(2/3)*x - sqrt(3)*c^(1/3))/c^(1/3))/c^(5/3)))*b","A",0
111,1,98,0,0.421350," ","integrate((a+b*arctan(c*x^3))/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} - c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{2}{3}}} - \frac{\log\left(c^{\frac{4}{3}} x^{4} - c^{\frac{2}{3}} x^{2} + 1\right)}{c^{\frac{2}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{2}{3}} x^{2} + 1}{c^{\frac{2}{3}}}\right)}{c^{\frac{2}{3}}}\right)} - \frac{4 \, \arctan\left(c x^{3}\right)}{x}\right)} b - \frac{a}{x}"," ",0,"1/4*(c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 - c^(2/3))/c^(2/3))/c^(2/3) - log(c^(4/3)*x^4 - c^(2/3)*x^2 + 1)/c^(2/3) + 2*log((c^(2/3)*x^2 + 1)/c^(2/3))/c^(2/3)) - 4*arctan(c*x^3)/x)*b - a/x","A",0
112,1,147,0,0.419859," ","integrate((a+b*arctan(c*x^3))/x^5,x, algorithm=""maxima"")","\frac{1}{16} \, {\left({\left(c^{2} {\left(\frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} + \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{\sqrt{3} \log\left(c^{\frac{2}{3}} x^{2} - \sqrt{3} c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{4 \, \arctan\left(c^{\frac{1}{3}} x\right)}{c^{\frac{5}{3}}} - \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x + \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} - \frac{2 \, \arctan\left(\frac{2 \, c^{\frac{2}{3}} x - \sqrt{3} c^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}}\right)} - \frac{12}{x}\right)} c - \frac{4 \, \arctan\left(c x^{3}\right)}{x^{4}}\right)} b - \frac{a}{4 \, x^{4}}"," ",0,"1/16*((c^2*(sqrt(3)*log(c^(2/3)*x^2 + sqrt(3)*c^(1/3)*x + 1)/c^(5/3) - sqrt(3)*log(c^(2/3)*x^2 - sqrt(3)*c^(1/3)*x + 1)/c^(5/3) - 4*arctan(c^(1/3)*x)/c^(5/3) - 2*arctan((2*c^(2/3)*x + sqrt(3)*c^(1/3))/c^(1/3))/c^(5/3) - 2*arctan((2*c^(2/3)*x - sqrt(3)*c^(1/3))/c^(1/3))/c^(5/3)) - 12/x)*c - 4*arctan(c*x^3)/x^4)*b - 1/4*a/x^4","A",0
113,1,169,0,0.517541," ","integrate(x^11*(a+b*arctan(c*x^3))^2,x, algorithm=""maxima"")","\frac{1}{12} \, b^{2} x^{12} \arctan\left(c x^{3}\right)^{2} + \frac{1}{12} \, a^{2} x^{12} + \frac{1}{18} \, {\left(3 \, x^{12} \arctan\left(c x^{3}\right) - c {\left(\frac{c^{2} x^{9} - 3 \, x^{3}}{c^{4}} + \frac{3 \, \arctan\left(c x^{3}\right)}{c^{5}}\right)}\right)} a b - \frac{1}{36} \, {\left(2 \, c {\left(\frac{c^{2} x^{9} - 3 \, x^{3}}{c^{4}} + \frac{3 \, \arctan\left(c x^{3}\right)}{c^{5}}\right)} \arctan\left(c x^{3}\right) - \frac{c^{2} x^{6} + 3 \, \arctan\left(c x^{3}\right)^{2} - 3 \, \log\left(18 \, c^{7} x^{6} + 18 \, c^{5}\right) - \log\left(c^{2} x^{6} + 1\right)}{c^{4}}\right)} b^{2}"," ",0,"1/12*b^2*x^12*arctan(c*x^3)^2 + 1/12*a^2*x^12 + 1/18*(3*x^12*arctan(c*x^3) - c*((c^2*x^9 - 3*x^3)/c^4 + 3*arctan(c*x^3)/c^5))*a*b - 1/36*(2*c*((c^2*x^9 - 3*x^3)/c^4 + 3*arctan(c*x^3)/c^5)*arctan(c*x^3) - (c^2*x^6 + 3*arctan(c*x^3)^2 - 3*log(18*c^7*x^6 + 18*c^5) - log(c^2*x^6 + 1))/c^4)*b^2","A",0
114,0,0,0,0.000000," ","integrate(x^8*(a+b*arctan(c*x^3))^2,x, algorithm=""maxima"")","\frac{1}{9} \, a^{2} x^{9} + \frac{1}{9} \, {\left(2 \, x^{9} \arctan\left(c x^{3}\right) - {\left(\frac{x^{6}}{c^{2}} - \frac{\log\left(c^{2} x^{6} + 1\right)}{c^{4}}\right)} c\right)} a b + \frac{1}{144} \, {\left(4 \, x^{9} \arctan\left(c x^{3}\right)^{2} - x^{9} \log\left(c^{2} x^{6} + 1\right)^{2} + 144 \, \int \frac{4 \, c^{2} x^{14} \log\left(c^{2} x^{6} + 1\right) - 8 \, c x^{11} \arctan\left(c x^{3}\right) + 36 \, {\left(c^{2} x^{14} + x^{8}\right)} \arctan\left(c x^{3}\right)^{2} + 3 \, {\left(c^{2} x^{14} + x^{8}\right)} \log\left(c^{2} x^{6} + 1\right)^{2}}{48 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x}\right)} b^{2}"," ",0,"1/9*a^2*x^9 + 1/9*(2*x^9*arctan(c*x^3) - (x^6/c^2 - log(c^2*x^6 + 1)/c^4)*c)*a*b + 1/144*(4*x^9*arctan(c*x^3)^2 - x^9*log(c^2*x^6 + 1)^2 + 144*integrate(1/48*(4*c^2*x^14*log(c^2*x^6 + 1) - 8*c*x^11*arctan(c*x^3) + 36*(c^2*x^14 + x^8)*arctan(c*x^3)^2 + 3*(c^2*x^14 + x^8)*log(c^2*x^6 + 1)^2)/(c^2*x^6 + 1), x))*b^2","F",0
115,1,126,0,0.514511," ","integrate(x^5*(a+b*arctan(c*x^3))^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} x^{6} \arctan\left(c x^{3}\right)^{2} + \frac{1}{6} \, a^{2} x^{6} + \frac{1}{3} \, {\left(x^{6} \arctan\left(c x^{3}\right) - c {\left(\frac{x^{3}}{c^{2}} - \frac{\arctan\left(c x^{3}\right)}{c^{3}}\right)}\right)} a b - \frac{1}{6} \, {\left(2 \, c {\left(\frac{x^{3}}{c^{2}} - \frac{\arctan\left(c x^{3}\right)}{c^{3}}\right)} \arctan\left(c x^{3}\right) + \frac{\arctan\left(c x^{3}\right)^{2} - \log\left(6 \, c^{5} x^{6} + 6 \, c^{3}\right)}{c^{2}}\right)} b^{2}"," ",0,"1/6*b^2*x^6*arctan(c*x^3)^2 + 1/6*a^2*x^6 + 1/3*(x^6*arctan(c*x^3) - c*(x^3/c^2 - arctan(c*x^3)/c^3))*a*b - 1/6*(2*c*(x^3/c^2 - arctan(c*x^3)/c^3)*arctan(c*x^3) + (arctan(c*x^3)^2 - log(6*c^5*x^6 + 6*c^3))/c^2)*b^2","A",0
116,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x^3))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{48} \, {\left(4 \, x^{3} \arctan\left(c x^{3}\right)^{2} - x^{3} \log\left(c^{2} x^{6} + 1\right)^{2} + 576 \, c^{2} \int \frac{x^{8} \arctan\left(c x^{3}\right)^{2}}{16 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + 48 \, c^{2} \int \frac{x^{8} \log\left(c^{2} x^{6} + 1\right)^{2}}{16 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + 192 \, c^{2} \int \frac{x^{8} \log\left(c^{2} x^{6} + 1\right)}{16 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + \frac{4 \, \arctan\left(c x^{3}\right)^{3}}{c} - 384 \, c \int \frac{x^{5} \arctan\left(c x^{3}\right)}{16 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + 48 \, \int \frac{x^{2} \log\left(c^{2} x^{6} + 1\right)^{2}}{16 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x}\right)} b^{2} + \frac{{\left(2 \, c x^{3} \arctan\left(c x^{3}\right) - \log\left(c^{2} x^{6} + 1\right)\right)} a b}{3 \, c}"," ",0,"1/3*a^2*x^3 + 1/48*(4*x^3*arctan(c*x^3)^2 - x^3*log(c^2*x^6 + 1)^2 + 576*c^2*integrate(1/16*x^8*arctan(c*x^3)^2/(c^2*x^6 + 1), x) + 48*c^2*integrate(1/16*x^8*log(c^2*x^6 + 1)^2/(c^2*x^6 + 1), x) + 192*c^2*integrate(1/16*x^8*log(c^2*x^6 + 1)/(c^2*x^6 + 1), x) + 4*arctan(c*x^3)^3/c - 384*c*integrate(1/16*x^5*arctan(c*x^3)/(c^2*x^6 + 1), x) + 48*integrate(1/16*x^2*log(c^2*x^6 + 1)^2/(c^2*x^6 + 1), x))*b^2 + 1/3*(2*c*x^3*arctan(c*x^3) - log(c^2*x^6 + 1))*a*b/c","F",0
117,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^3))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \frac{1}{16} \, \int \frac{12 \, b^{2} \arctan\left(c x^{3}\right)^{2} + b^{2} \log\left(c^{2} x^{6} + 1\right)^{2} + 32 \, a b \arctan\left(c x^{3}\right)}{x}\,{d x}"," ",0,"a^2*log(x) + 1/16*integrate((12*b^2*arctan(c*x^3)^2 + b^2*log(c^2*x^6 + 1)^2 + 32*a*b*arctan(c*x^3))/x, x)","F",0
118,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^3))^2/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(c {\left(\log\left(c^{2} x^{6} + 1\right) - \log\left(x^{6}\right)\right)} + \frac{2 \, \arctan\left(c x^{3}\right)}{x^{3}}\right)} a b + \frac{\frac{1}{4} \, {\left(12 \, x^{3} \int -\frac{12 \, c^{2} x^{6} \log\left(c^{2} x^{6} + 1\right) - 56 \, c x^{3} \arctan\left(c x^{3}\right) - 36 \, {\left(c^{2} x^{6} + 1\right)} \arctan\left(c x^{3}\right)^{2} - 3 \, {\left(c^{2} x^{6} + 1\right)} \log\left(c^{2} x^{6} + 1\right)^{2}}{4 \, {\left(c^{2} x^{10} + x^{4}\right)}}\,{d x} - 28 \, \arctan\left(c x^{3}\right)^{2} + 3 \, \log\left(c^{2} x^{6} + 1\right)^{2}\right)} b^{2}}{48 \, x^{3}} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"-1/3*(c*(log(c^2*x^6 + 1) - log(x^6)) + 2*arctan(c*x^3)/x^3)*a*b + 1/48*(48*x^3*integrate(-1/16*(4*c^2*x^6*log(c^2*x^6 + 1) - 8*c*x^3*arctan(c*x^3) - 12*(c^2*x^6 + 1)*arctan(c*x^3)^2 - (c^2*x^6 + 1)*log(c^2*x^6 + 1)^2)/(c^2*x^10 + x^4), x) - 4*arctan(c*x^3)^2 + log(c^2*x^6 + 1)^2)*b^2/x^3 - 1/3*a^2/x^3","F",0
119,1,110,0,0.540200," ","integrate((a+b*arctan(c*x^3))^2/x^7,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left({\left(c \arctan\left(c x^{3}\right) + \frac{1}{x^{3}}\right)} c + \frac{\arctan\left(c x^{3}\right)}{x^{6}}\right)} a b + \frac{1}{6} \, {\left({\left(\arctan\left(c x^{3}\right)^{2} - \log\left(c^{2} x^{6} + 1\right) + 6 \, \log\left(x\right)\right)} c^{2} - 2 \, {\left(c \arctan\left(c x^{3}\right) + \frac{1}{x^{3}}\right)} c \arctan\left(c x^{3}\right)\right)} b^{2} - \frac{b^{2} \arctan\left(c x^{3}\right)^{2}}{6 \, x^{6}} - \frac{a^{2}}{6 \, x^{6}}"," ",0,"-1/3*((c*arctan(c*x^3) + 1/x^3)*c + arctan(c*x^3)/x^6)*a*b + 1/6*((arctan(c*x^3)^2 - log(c^2*x^6 + 1) + 6*log(x))*c^2 - 2*(c*arctan(c*x^3) + 1/x^3)*c*arctan(c*x^3))*b^2 - 1/6*b^2*arctan(c*x^3)^2/x^6 - 1/6*a^2/x^6","A",0
120,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^3))^2/x^10,x, algorithm=""maxima"")","\frac{1}{9} \, {\left({\left(c^{2} \log\left(c^{2} x^{6} + 1\right) - c^{2} \log\left(x^{6}\right) - \frac{1}{x^{6}}\right)} c - \frac{2 \, \arctan\left(c x^{3}\right)}{x^{9}}\right)} a b + \frac{\frac{1}{4} \, {\left(12 \, x^{9} \int -\frac{12 \, c^{2} x^{6} \log\left(c^{2} x^{6} + 1\right) - 56 \, c x^{3} \arctan\left(c x^{3}\right) - 108 \, {\left(c^{2} x^{6} + 1\right)} \arctan\left(c x^{3}\right)^{2} - 9 \, {\left(c^{2} x^{6} + 1\right)} \log\left(c^{2} x^{6} + 1\right)^{2}}{4 \, {\left(c^{2} x^{16} + x^{10}\right)}}\,{d x} - 28 \, \arctan\left(c x^{3}\right)^{2} + 3 \, \log\left(c^{2} x^{6} + 1\right)^{2}\right)} b^{2}}{144 \, x^{9}} - \frac{a^{2}}{9 \, x^{9}}"," ",0,"1/9*((c^2*log(c^2*x^6 + 1) - c^2*log(x^6) - 1/x^6)*c - 2*arctan(c*x^3)/x^9)*a*b + 1/144*(144*x^9*integrate(-1/48*(4*c^2*x^6*log(c^2*x^6 + 1) - 8*c*x^3*arctan(c*x^3) - 36*(c^2*x^6 + 1)*arctan(c*x^3)^2 - 3*(c^2*x^6 + 1)*log(c^2*x^6 + 1)^2)/(c^2*x^16 + x^10), x) - 4*arctan(c*x^3)^2 + log(c^2*x^6 + 1)^2)*b^2/x^9 - 1/9*a^2/x^9","F",0
121,0,0,0,0.000000," ","integrate(x^8*(a+b*arctan(c*x^3))^3,x, algorithm=""maxima"")","\frac{1}{72} \, b^{3} x^{9} \arctan\left(c x^{3}\right)^{3} - \frac{1}{96} \, b^{3} x^{9} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right)^{2} + \frac{1}{9} \, a^{3} x^{9} + \frac{1}{6} \, {\left(2 \, x^{9} \arctan\left(c x^{3}\right) - {\left(\frac{x^{6}}{c^{2}} - \frac{\log\left(c^{2} x^{6} + 1\right)}{c^{4}}\right)} c\right)} a^{2} b + \int \frac{4 \, b^{3} c^{2} x^{14} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right) + 28 \, {\left(b^{3} c^{2} x^{14} + b^{3} x^{8}\right)} \arctan\left(c x^{3}\right)^{3} + 4 \, {\left(24 \, a b^{2} c^{2} x^{14} - b^{3} c x^{11} + 24 \, a b^{2} x^{8}\right)} \arctan\left(c x^{3}\right)^{2} + {\left(b^{3} c x^{11} + 3 \, {\left(b^{3} c^{2} x^{14} + b^{3} x^{8}\right)} \arctan\left(c x^{3}\right)\right)} \log\left(c^{2} x^{6} + 1\right)^{2}}{32 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x}"," ",0,"1/72*b^3*x^9*arctan(c*x^3)^3 - 1/96*b^3*x^9*arctan(c*x^3)*log(c^2*x^6 + 1)^2 + 1/9*a^3*x^9 + 1/6*(2*x^9*arctan(c*x^3) - (x^6/c^2 - log(c^2*x^6 + 1)/c^4)*c)*a^2*b + integrate(1/32*(4*b^3*c^2*x^14*arctan(c*x^3)*log(c^2*x^6 + 1) + 28*(b^3*c^2*x^14 + b^3*x^8)*arctan(c*x^3)^3 + 4*(24*a*b^2*c^2*x^14 - b^3*c*x^11 + 24*a*b^2*x^8)*arctan(c*x^3)^2 + (b^3*c*x^11 + 3*(b^3*c^2*x^14 + b^3*x^8)*arctan(c*x^3))*log(c^2*x^6 + 1)^2)/(c^2*x^6 + 1), x)","F",0
122,0,0,0,0.000000," ","integrate(x^5*(a+b*arctan(c*x^3))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a b^{2} x^{6} \arctan\left(c x^{3}\right)^{2} + \frac{1}{6} \, a^{3} x^{6} + \frac{1}{2} \, {\left(x^{6} \arctan\left(c x^{3}\right) - c {\left(\frac{x^{3}}{c^{2}} - \frac{\arctan\left(c x^{3}\right)}{c^{3}}\right)}\right)} a^{2} b - \frac{1}{2} \, {\left(2 \, c {\left(\frac{x^{3}}{c^{2}} - \frac{\arctan\left(c x^{3}\right)}{c^{3}}\right)} \arctan\left(c x^{3}\right) + \frac{\arctan\left(c x^{3}\right)^{2} - \log\left(6 \, c^{5} x^{6} + 6 \, c^{3}\right)}{c^{2}}\right)} a b^{2} + \frac{1}{192} \, {\left(4 \, x^{6} \arctan\left(c x^{3}\right)^{3} - 3 \, x^{6} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right)^{2} + 192 \, \int \frac{12 \, c^{2} x^{11} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right) - 12 \, c x^{8} \arctan\left(c x^{3}\right)^{2} + 56 \, {\left(c^{2} x^{11} + x^{5}\right)} \arctan\left(c x^{3}\right)^{3} + 3 \, {\left(c x^{8} + 2 \, {\left(c^{2} x^{11} + x^{5}\right)} \arctan\left(c x^{3}\right)\right)} \log\left(c^{2} x^{6} + 1\right)^{2}}{64 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x}\right)} b^{3}"," ",0,"1/2*a*b^2*x^6*arctan(c*x^3)^2 + 1/6*a^3*x^6 + 1/2*(x^6*arctan(c*x^3) - c*(x^3/c^2 - arctan(c*x^3)/c^3))*a^2*b - 1/2*(2*c*(x^3/c^2 - arctan(c*x^3)/c^3)*arctan(c*x^3) + (arctan(c*x^3)^2 - log(6*c^5*x^6 + 6*c^3))/c^2)*a*b^2 + 1/192*(4*x^6*arctan(c*x^3)^3 - 3*x^6*arctan(c*x^3)*log(c^2*x^6 + 1)^2 + 192*integrate(1/64*(12*c^2*x^11*arctan(c*x^3)*log(c^2*x^6 + 1) - 12*c*x^8*arctan(c*x^3)^2 + 56*(c^2*x^11 + x^5)*arctan(c*x^3)^3 + 3*(c*x^8 + 2*(c^2*x^11 + x^5)*arctan(c*x^3))*log(c^2*x^6 + 1)^2)/(c^2*x^6 + 1), x))*b^3","F",0
123,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x^3))^3,x, algorithm=""maxima"")","\frac{1}{24} \, b^{3} x^{3} \arctan\left(c x^{3}\right)^{3} - \frac{1}{32} \, b^{3} x^{3} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right)^{2} + \frac{1}{3} \, a^{3} x^{3} + \frac{7 \, b^{3} \arctan\left(c x^{3}\right)^{4}}{96 \, c} + 28 \, b^{3} c^{2} \int \frac{x^{8} \arctan\left(c x^{3}\right)^{3}}{32 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + 3 \, b^{3} c^{2} \int \frac{x^{8} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right)^{2}}{32 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + 96 \, a b^{2} c^{2} \int \frac{x^{8} \arctan\left(c x^{3}\right)^{2}}{32 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + 12 \, b^{3} c^{2} \int \frac{x^{8} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right)}{32 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + \frac{a b^{2} \arctan\left(c x^{3}\right)^{3}}{3 \, c} - 12 \, b^{3} c \int \frac{x^{5} \arctan\left(c x^{3}\right)^{2}}{32 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + 3 \, b^{3} c \int \frac{x^{5} \log\left(c^{2} x^{6} + 1\right)^{2}}{32 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + 3 \, b^{3} \int \frac{x^{2} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right)^{2}}{32 \, {\left(c^{2} x^{6} + 1\right)}}\,{d x} + \frac{{\left(2 \, c x^{3} \arctan\left(c x^{3}\right) - \log\left(c^{2} x^{6} + 1\right)\right)} a^{2} b}{2 \, c}"," ",0,"1/24*b^3*x^3*arctan(c*x^3)^3 - 1/32*b^3*x^3*arctan(c*x^3)*log(c^2*x^6 + 1)^2 + 1/3*a^3*x^3 + 7/96*b^3*arctan(c*x^3)^4/c + 28*b^3*c^2*integrate(1/32*x^8*arctan(c*x^3)^3/(c^2*x^6 + 1), x) + 3*b^3*c^2*integrate(1/32*x^8*arctan(c*x^3)*log(c^2*x^6 + 1)^2/(c^2*x^6 + 1), x) + 96*a*b^2*c^2*integrate(1/32*x^8*arctan(c*x^3)^2/(c^2*x^6 + 1), x) + 12*b^3*c^2*integrate(1/32*x^8*arctan(c*x^3)*log(c^2*x^6 + 1)/(c^2*x^6 + 1), x) + 1/3*a*b^2*arctan(c*x^3)^3/c - 12*b^3*c*integrate(1/32*x^5*arctan(c*x^3)^2/(c^2*x^6 + 1), x) + 3*b^3*c*integrate(1/32*x^5*log(c^2*x^6 + 1)^2/(c^2*x^6 + 1), x) + 3*b^3*integrate(1/32*x^2*arctan(c*x^3)*log(c^2*x^6 + 1)^2/(c^2*x^6 + 1), x) + 1/2*(2*c*x^3*arctan(c*x^3) - log(c^2*x^6 + 1))*a^2*b/c","F",0
124,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^3))^3/x,x, algorithm=""maxima"")","a^{3} \log\left(x\right) + \frac{1}{32} \, \int \frac{28 \, b^{3} \arctan\left(c x^{3}\right)^{3} + 3 \, b^{3} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right)^{2} + 96 \, a b^{2} \arctan\left(c x^{3}\right)^{2} + 96 \, a^{2} b \arctan\left(c x^{3}\right)}{x}\,{d x}"," ",0,"a^3*log(x) + 1/32*integrate((28*b^3*arctan(c*x^3)^3 + 3*b^3*arctan(c*x^3)*log(c^2*x^6 + 1)^2 + 96*a*b^2*arctan(c*x^3)^2 + 96*a^2*b*arctan(c*x^3))/x, x)","F",0
125,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^3))^3/x^4,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{6} + 1\right) - \log\left(x^{6}\right)\right)} + \frac{2 \, \arctan\left(c x^{3}\right)}{x^{3}}\right)} a^{2} b - \frac{a^{3}}{3 \, x^{3}} - \frac{\frac{15}{2} \, b^{3} \arctan\left(c x^{3}\right)^{3} - \frac{21}{8} \, b^{3} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right)^{2} - 3 \, x^{3} \int -\frac{84 \, b^{3} c^{2} x^{6} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right) - 196 \, {\left(b^{3} c^{2} x^{6} + b^{3}\right)} \arctan\left(c x^{3}\right)^{3} - 12 \, {\left(64 \, a b^{2} c^{2} x^{6} + 15 \, b^{3} c x^{3} + 64 \, a b^{2}\right)} \arctan\left(c x^{3}\right)^{2} + 21 \, {\left(b^{3} c x^{3} - {\left(b^{3} c^{2} x^{6} + b^{3}\right)} \arctan\left(c x^{3}\right)\right)} \log\left(c^{2} x^{6} + 1\right)^{2}}{8 \, {\left(c^{2} x^{10} + x^{4}\right)}}\,{d x}}{96 \, x^{3}}"," ",0,"-1/2*(c*(log(c^2*x^6 + 1) - log(x^6)) + 2*arctan(c*x^3)/x^3)*a^2*b - 1/3*a^3/x^3 - 1/96*(4*b^3*arctan(c*x^3)^3 - 3*b^3*arctan(c*x^3)*log(c^2*x^6 + 1)^2 - 96*x^3*integrate(-1/32*(12*b^3*c^2*x^6*arctan(c*x^3)*log(c^2*x^6 + 1) - 28*(b^3*c^2*x^6 + b^3)*arctan(c*x^3)^3 - 12*(8*a*b^2*c^2*x^6 + b^3*c*x^3 + 8*a*b^2)*arctan(c*x^3)^2 + 3*(b^3*c*x^3 - (b^3*c^2*x^6 + b^3)*arctan(c*x^3))*log(c^2*x^6 + 1)^2)/(c^2*x^10 + x^4), x))/x^3","F",0
126,0,0,0,0.000000," ","integrate((a+b*arctan(c*x^3))^3/x^7,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left(c \arctan\left(c x^{3}\right) + \frac{1}{x^{3}}\right)} c + \frac{\arctan\left(c x^{3}\right)}{x^{6}}\right)} a^{2} b + \frac{1}{2} \, {\left({\left(\arctan\left(c x^{3}\right)^{2} - \log\left(c^{2} x^{6} + 1\right) + 6 \, \log\left(x\right)\right)} c^{2} - 2 \, {\left(c \arctan\left(c x^{3}\right) + \frac{1}{x^{3}}\right)} c \arctan\left(c x^{3}\right)\right)} a b^{2} - \frac{a b^{2} \arctan\left(c x^{3}\right)^{2}}{2 \, x^{6}} + \frac{\frac{3}{8} \, {\left(8 \, x^{6} \int -\frac{84 \, c^{2} x^{6} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right) - 180 \, c x^{3} \arctan\left(c x^{3}\right)^{2} - 392 \, {\left(c^{2} x^{6} + 1\right)} \arctan\left(c x^{3}\right)^{3} + 21 \, {\left(c x^{3} - 2 \, {\left(c^{2} x^{6} + 1\right)} \arctan\left(c x^{3}\right)\right)} \log\left(c^{2} x^{6} + 1\right)^{2}}{8 \, {\left(c^{2} x^{13} + x^{7}\right)}}\,{d x} - 20 \, \arctan\left(c x^{3}\right)^{3} + 7 \, \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right)^{2}\right)} b^{3}}{192 \, x^{6}} - \frac{a^{3}}{6 \, x^{6}}"," ",0,"-1/2*((c*arctan(c*x^3) + 1/x^3)*c + arctan(c*x^3)/x^6)*a^2*b + 1/2*((arctan(c*x^3)^2 - log(c^2*x^6 + 1) + 6*log(x))*c^2 - 2*(c*arctan(c*x^3) + 1/x^3)*c*arctan(c*x^3))*a*b^2 - 1/2*a*b^2*arctan(c*x^3)^2/x^6 + 1/192*(192*x^6*integrate(-1/64*(12*c^2*x^6*arctan(c*x^3)*log(c^2*x^6 + 1) - 12*c*x^3*arctan(c*x^3)^2 - 56*(c^2*x^6 + 1)*arctan(c*x^3)^3 + 3*(c*x^3 - 2*(c^2*x^6 + 1)*arctan(c*x^3))*log(c^2*x^6 + 1)^2)/(c^2*x^13 + x^7), x) - 4*arctan(c*x^3)^3 + 3*arctan(c*x^3)*log(c^2*x^6 + 1)^2)*b^3/x^6 - 1/6*a^3/x^6","F",0
127,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctan(c*x^3))^3,x, algorithm=""maxima"")","\frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \frac{\frac{15}{2} \, b^{3} d^{m} x x^{m} \arctan\left(c x^{3}\right)^{3} - \frac{21}{8} \, b^{3} d^{m} x x^{m} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right)^{2} + {\left(m + 1\right)} \int \frac{252 \, b^{3} c^{2} d^{m} x^{6} x^{m} \arctan\left(c x^{3}\right) \log\left(c^{2} x^{6} + 1\right) + 196 \, {\left({\left(b^{3} c^{2} d^{m} m + b^{3} c^{2} d^{m}\right)} x^{6} + b^{3} d^{m} m + b^{3} d^{m}\right)} x^{m} \arctan\left(c x^{3}\right)^{3} - 12 \, {\left(45 \, b^{3} c d^{m} x^{3} - 64 \, {\left(a b^{2} c^{2} d^{m} m + a b^{2} c^{2} d^{m}\right)} x^{6} - 64 \, a b^{2} d^{m} m - 64 \, a b^{2} d^{m}\right)} x^{m} \arctan\left(c x^{3}\right)^{2} + 768 \, {\left({\left(a^{2} b c^{2} d^{m} m + a^{2} b c^{2} d^{m}\right)} x^{6} + a^{2} b d^{m} m + a^{2} b d^{m}\right)} x^{m} \arctan\left(c x^{3}\right) + 21 \, {\left(3 \, b^{3} c d^{m} x^{3} x^{m} + {\left({\left(b^{3} c^{2} d^{m} m + b^{3} c^{2} d^{m}\right)} x^{6} + b^{3} d^{m} m + b^{3} d^{m}\right)} x^{m} \arctan\left(c x^{3}\right)\right)} \log\left(c^{2} x^{6} + 1\right)^{2}}{8 \, {\left({\left(c^{2} m + c^{2}\right)} x^{6} + m + 1\right)}}\,{d x}}{32 \, {\left(m + 1\right)}}"," ",0,"(d*x)^(m + 1)*a^3/(d*(m + 1)) + 1/32*(4*b^3*d^m*x*x^m*arctan(c*x^3)^3 - 3*b^3*d^m*x*x^m*arctan(c*x^3)*log(c^2*x^6 + 1)^2 + 32*(m + 1)*integrate(1/32*(36*b^3*c^2*d^m*x^6*x^m*arctan(c*x^3)*log(c^2*x^6 + 1) + 28*((b^3*c^2*d^m*m + b^3*c^2*d^m)*x^6 + b^3*d^m*m + b^3*d^m)*x^m*arctan(c*x^3)^3 - 12*(3*b^3*c*d^m*x^3 - 8*(a*b^2*c^2*d^m*m + a*b^2*c^2*d^m)*x^6 - 8*a*b^2*d^m*m - 8*a*b^2*d^m)*x^m*arctan(c*x^3)^2 + 96*((a^2*b*c^2*d^m*m + a^2*b*c^2*d^m)*x^6 + a^2*b*d^m*m + a^2*b*d^m)*x^m*arctan(c*x^3) + 3*(3*b^3*c*d^m*x^3*x^m + ((b^3*c^2*d^m*m + b^3*c^2*d^m)*x^6 + b^3*d^m*m + b^3*d^m)*x^m*arctan(c*x^3))*log(c^2*x^6 + 1)^2)/((c^2*m + c^2)*x^6 + m + 1), x))/(m + 1)","F",0
128,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctan(c*x^3))^2,x, algorithm=""maxima"")","\frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}} + \frac{7 \, b^{2} d^{m} x x^{m} \arctan\left(c x^{3}\right)^{2} - \frac{3}{4} \, b^{2} d^{m} x x^{m} \log\left(c^{2} x^{6} + 1\right)^{2} + {\left(m + 1\right)} \int \frac{36 \, b^{2} c^{2} d^{m} x^{6} x^{m} \log\left(c^{2} x^{6} + 1\right) + 36 \, {\left({\left(b^{2} c^{2} d^{m} m + b^{2} c^{2} d^{m}\right)} x^{6} + b^{2} d^{m} m + b^{2} d^{m}\right)} x^{m} \arctan\left(c x^{3}\right)^{2} + 3 \, {\left({\left(b^{2} c^{2} d^{m} m + b^{2} c^{2} d^{m}\right)} x^{6} + b^{2} d^{m} m + b^{2} d^{m}\right)} x^{m} \log\left(c^{2} x^{6} + 1\right)^{2} - 8 \, {\left(21 \, b^{2} c d^{m} x^{3} - 16 \, {\left(a b c^{2} d^{m} m + a b c^{2} d^{m}\right)} x^{6} - 16 \, a b d^{m} m - 16 \, a b d^{m}\right)} x^{m} \arctan\left(c x^{3}\right)}{4 \, {\left({\left(c^{2} m + c^{2}\right)} x^{6} + m + 1\right)}}\,{d x}}{16 \, {\left(m + 1\right)}}"," ",0,"(d*x)^(m + 1)*a^2/(d*(m + 1)) + 1/16*(4*b^2*d^m*x*x^m*arctan(c*x^3)^2 - b^2*d^m*x*x^m*log(c^2*x^6 + 1)^2 + 16*(m + 1)*integrate(1/16*(12*b^2*c^2*d^m*x^6*x^m*log(c^2*x^6 + 1) + 12*((b^2*c^2*d^m*m + b^2*c^2*d^m)*x^6 + b^2*d^m*m + b^2*d^m)*x^m*arctan(c*x^3)^2 + ((b^2*c^2*d^m*m + b^2*c^2*d^m)*x^6 + b^2*d^m*m + b^2*d^m)*x^m*log(c^2*x^6 + 1)^2 - 8*(3*b^2*c*d^m*x^3 - 4*(a*b*c^2*d^m*m + a*b*c^2*d^m)*x^6 - 4*a*b*d^m*m - 4*a*b*d^m)*x^m*arctan(c*x^3))/((c^2*m + c^2)*x^6 + m + 1), x))/(m + 1)","F",0
129,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\frac{{\left(d^{m} x x^{m} \arctan\left(c x^{3}\right) - 3 \, {\left(c d^{m} m + c d^{m}\right)} \int \frac{x^{3} x^{m}}{{\left(c^{2} m + c^{2}\right)} x^{6} + m + 1}\,{d x}\right)} b}{m + 1} + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"(d^m*x*x^m*arctan(c*x^3) - 3*(c*d^m*m + c*d^m)*integrate(x^3*x^m/((c^2*m + c^2)*x^6 + m + 1), x))*b/(m + 1) + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
130,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctan(c*x^3)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \arctan\left(c x^{3}\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctan(c*x^3) + a), x)","F",0
131,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctan(c*x^3))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} d^{m} x^{6} + d^{m}\right)} x^{m} - {\left(b^{2} c x^{2} \arctan\left(c x^{3}\right) + a b c x^{2}\right)} \int \frac{{\left({\left(c^{2} d^{m} m + 4 \, c^{2} d^{m}\right)} x^{6} + d^{m} m - 2 \, d^{m}\right)} x^{m}}{b^{2} c x^{3} \arctan\left(c x^{3}\right) + a b c x^{3}}\,{d x}}{3 \, {\left(b^{2} c x^{2} \arctan\left(c x^{3}\right) + a b c x^{2}\right)}}"," ",0,"-1/3*((c^2*d^m*x^6 + d^m)*x^m - 3*(b^2*c*x^2*arctan(c*x^3) + a*b*c*x^2)*integrate(1/3*((c^2*d^m*m + 4*c^2*d^m)*x^6 + d^m*m - 2*d^m)*x^m/(b^2*c*x^3*arctan(c*x^3) + a*b*c*x^3), x))/(b^2*c*x^2*arctan(c*x^3) + a*b*c*x^2)","F",0
132,1,45,0,0.415561," ","integrate(x^3*(a+b*arctan(c/x)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{12} \, {\left(3 \, x^{4} \arctan\left(\frac{c}{x}\right) + {\left(3 \, c^{3} \arctan\left(\frac{x}{c}\right) - 3 \, c^{2} x + x^{3}\right)} c\right)} b"," ",0,"1/4*a*x^4 + 1/12*(3*x^4*arctan(c/x) + (3*c^3*arctan(x/c) - 3*c^2*x + x^3)*c)*b","A",0
133,1,43,0,0.434765," ","integrate(x^2*(a+b*arctan(c/x)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \arctan\left(\frac{c}{x}\right) - {\left(c^{2} \log\left(c^{2} + x^{2}\right) - x^{2}\right)} c\right)} b"," ",0,"1/3*a*x^3 + 1/6*(2*x^3*arctan(c/x) - (c^2*log(c^2 + x^2) - x^2)*c)*b","A",0
134,1,36,0,0.415940," ","integrate(x*(a+b*arctan(c/x)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{2} \, {\left(x^{2} \arctan\left(\frac{c}{x}\right) - {\left(c \arctan\left(\frac{x}{c}\right) - x\right)} c\right)} b"," ",0,"1/2*a*x^2 + 1/2*(x^2*arctan(c/x) - (c*arctan(x/c) - x)*c)*b","A",0
135,1,27,0,0.318006," ","integrate(a+b*arctan(c/x),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, x \arctan\left(\frac{c}{x}\right) + c \log\left(c^{2} + x^{2}\right)\right)} b + a x"," ",0,"1/2*(2*x*arctan(c/x) + c*log(c^2 + x^2))*b + a*x","A",0
136,0,0,0,0.000000," ","integrate((a+b*arctan(c/x))/x,x, algorithm=""maxima"")","b \int \frac{\arctan\left(c, x\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"b*integrate(arctan2(c, x)/x, x) + a*log(x)","F",0
137,1,38,0,0.321820," ","integrate((a+b*arctan(c/x))/x^2,x, algorithm=""maxima"")","-\frac{b {\left(\frac{2 \, c \arctan\left(\frac{c}{x}\right)}{x} - \log\left(\frac{c^{2}}{x^{2}} + 1\right)\right)}}{2 \, c} - \frac{a}{x}"," ",0,"-1/2*b*(2*c*arctan(c/x)/x - log(c^2/x^2 + 1))/c - a/x","A",0
138,1,42,0,0.415196," ","integrate((a+b*arctan(c/x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\frac{\arctan\left(\frac{x}{c}\right)}{c^{3}} + \frac{1}{c^{2} x}\right)} - \frac{\arctan\left(\frac{c}{x}\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"1/2*(c*(arctan(x/c)/c^3 + 1/(c^2*x)) - arctan(c/x)/x^2)*b - 1/2*a/x^2","A",0
139,1,54,0,0.313941," ","integrate((a+b*arctan(c/x))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(c {\left(\frac{\log\left(c^{2} + x^{2}\right)}{c^{4}} - \frac{\log\left(x^{2}\right)}{c^{4}} - \frac{1}{c^{2} x^{2}}\right)} + \frac{2 \, \arctan\left(\frac{c}{x}\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"-1/6*(c*(log(c^2 + x^2)/c^4 - log(x^2)/c^4 - 1/(c^2*x^2)) + 2*arctan(c/x)/x^3)*b - 1/3*a/x^3","A",0
140,1,134,0,0.431031," ","integrate(x^3*(a+b*arctan(c/x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x^{4} \arctan\left(\frac{c}{x}\right)^{2} + \frac{1}{4} \, a^{2} x^{4} + \frac{1}{6} \, {\left(3 \, x^{4} \arctan\left(\frac{c}{x}\right) + {\left(3 \, c^{3} \arctan\left(\frac{x}{c}\right) - 3 \, c^{2} x + x^{3}\right)} c\right)} a b + \frac{1}{12} \, {\left({\left(3 \, c^{2} \arctan\left(\frac{x}{c}\right)^{2} - 4 \, c^{2} \log\left(c^{2} + x^{2}\right) + x^{2}\right)} c^{2} + 2 \, {\left(3 \, c^{3} \arctan\left(\frac{x}{c}\right) - 3 \, c^{2} x + x^{3}\right)} c \arctan\left(\frac{c}{x}\right)\right)} b^{2}"," ",0,"1/4*b^2*x^4*arctan(c/x)^2 + 1/4*a^2*x^4 + 1/6*(3*x^4*arctan(c/x) + (3*c^3*arctan(x/c) - 3*c^2*x + x^3)*c)*a*b + 1/12*((3*c^2*arctan(x/c)^2 - 4*c^2*log(c^2 + x^2) + x^2)*c^2 + 2*(3*c^3*arctan(x/c) - 3*c^2*x + x^3)*c*arctan(c/x))*b^2","A",0
141,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c/x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \arctan\left(\frac{c}{x}\right) - {\left(c^{2} \log\left(c^{2} + x^{2}\right) - x^{2}\right)} c\right)} a b + \frac{1}{48} \, {\left(4 \, x^{3} \arctan\left(c, x\right)^{2} - x^{3} \log\left(c^{2} + x^{2}\right)^{2} + 48 \, \int \frac{36 \, c^{2} x^{2} \arctan\left(c, x\right)^{2} + 36 \, x^{4} \arctan\left(c, x\right)^{2} + 8 \, c x^{3} \arctan\left(c, x\right) + 4 \, x^{4} \log\left(c^{2} + x^{2}\right) + 3 \, {\left(c^{2} x^{2} + x^{4}\right)} \log\left(c^{2} + x^{2}\right)^{2}}{48 \, {\left(c^{2} + x^{2}\right)}}\,{d x}\right)} b^{2}"," ",0,"1/3*a^2*x^3 + 1/3*(2*x^3*arctan(c/x) - (c^2*log(c^2 + x^2) - x^2)*c)*a*b + 1/48*(4*x^3*arctan2(c, x)^2 - x^3*log(c^2 + x^2)^2 + 48*integrate(1/48*(36*c^2*x^2*arctan2(c, x)^2 + 36*x^4*arctan2(c, x)^2 + 8*c*x^3*arctan2(c, x) + 4*x^4*log(c^2 + x^2) + 3*(c^2*x^2 + x^4)*log(c^2 + x^2)^2)/(c^2 + x^2), x))*b^2","F",0
142,1,104,0,0.425445," ","integrate(x*(a+b*arctan(c/x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \arctan\left(\frac{c}{x}\right)^{2} + \frac{1}{2} \, a^{2} x^{2} + {\left(x^{2} \arctan\left(\frac{c}{x}\right) - {\left(c \arctan\left(\frac{x}{c}\right) - x\right)} c\right)} a b - \frac{1}{2} \, {\left({\left(\arctan\left(\frac{x}{c}\right)^{2} - \log\left(c^{2} + x^{2}\right)\right)} c^{2} + 2 \, {\left(c \arctan\left(\frac{x}{c}\right) - x\right)} c \arctan\left(\frac{c}{x}\right)\right)} b^{2}"," ",0,"1/2*b^2*x^2*arctan(c/x)^2 + 1/2*a^2*x^2 + (x^2*arctan(c/x) - (c*arctan(x/c) - x)*c)*a*b - 1/2*((arctan(x/c)^2 - log(c^2 + x^2))*c^2 + 2*(c*arctan(x/c) - x)*c*arctan(c/x))*b^2","A",0
143,0,0,0,0.000000," ","integrate((a+b*arctan(c/x))^2,x, algorithm=""maxima"")","{\left(2 \, x \arctan\left(\frac{c}{x}\right) + c \log\left(c^{2} + x^{2}\right)\right)} a b + \frac{1}{16} \, {\left(12 \, c \arctan\left(\frac{c}{x}\right)^{2} \arctan\left(\frac{x}{c}\right) + 4 \, {\left(\frac{3 \, \arctan\left(\frac{c}{x}\right) \arctan\left(\frac{x}{c}\right)^{2}}{c} + \frac{\arctan\left(\frac{x}{c}\right)^{3}}{c}\right)} c^{2} + 4 \, x \arctan\left(c, x\right)^{2} + 16 \, c^{2} \int \frac{\log\left(c^{2} + x^{2}\right)^{2}}{16 \, {\left(c^{2} + x^{2}\right)}}\,{d x} - x \log\left(c^{2} + x^{2}\right)^{2} + 128 \, c \int \frac{x \arctan\left(\frac{c}{x}\right)}{16 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 192 \, \int \frac{x^{2} \arctan\left(\frac{c}{x}\right)^{2}}{16 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 16 \, \int \frac{x^{2} \log\left(c^{2} + x^{2}\right)^{2}}{16 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 64 \, \int \frac{x^{2} \log\left(c^{2} + x^{2}\right)}{16 \, {\left(c^{2} + x^{2}\right)}}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"(2*x*arctan(c/x) + c*log(c^2 + x^2))*a*b + 1/16*(12*c*arctan(c/x)^2*arctan(x/c) + 4*(3*arctan(c/x)*arctan(x/c)^2/c + arctan(x/c)^3/c)*c^2 + 4*x*arctan2(c, x)^2 + 16*c^2*integrate(1/16*log(c^2 + x^2)^2/(c^2 + x^2), x) - x*log(c^2 + x^2)^2 + 128*c*integrate(1/16*x*arctan(c/x)/(c^2 + x^2), x) + 192*integrate(1/16*x^2*arctan(c/x)^2/(c^2 + x^2), x) + 16*integrate(1/16*x^2*log(c^2 + x^2)^2/(c^2 + x^2), x) + 64*integrate(1/16*x^2*log(c^2 + x^2)/(c^2 + x^2), x))*b^2 + a^2*x","F",0
144,0,0,0,0.000000," ","integrate((a+b*arctan(c/x))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \frac{1}{16} \, \int \frac{12 \, b^{2} \arctan\left(c, x\right)^{2} + b^{2} \log\left(c^{2} + x^{2}\right)^{2} + 32 \, a b \arctan\left(c, x\right)}{x}\,{d x}"," ",0,"a^2*log(x) + 1/16*integrate((12*b^2*arctan2(c, x)^2 + b^2*log(c^2 + x^2)^2 + 32*a*b*arctan2(c, x))/x, x)","F",0
145,-1,0,0,0.000000," ","integrate((a+b*arctan(c/x))^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,1,120,0,0.428556," ","integrate((a+b*arctan(c/x))^2/x^3,x, algorithm=""maxima"")","{\left(c {\left(\frac{\arctan\left(\frac{x}{c}\right)}{c^{3}} + \frac{1}{c^{2} x}\right)} - \frac{\arctan\left(\frac{c}{x}\right)}{x^{2}}\right)} a b + \frac{1}{2} \, {\left(2 \, c {\left(\frac{\arctan\left(\frac{x}{c}\right)}{c^{3}} + \frac{1}{c^{2} x}\right)} \arctan\left(\frac{c}{x}\right) + \frac{\arctan\left(\frac{x}{c}\right)^{2} - \log\left(c^{2} + x^{2}\right) + 2 \, \log\left(x\right)}{c^{2}}\right)} b^{2} - \frac{b^{2} \arctan\left(\frac{c}{x}\right)^{2}}{2 \, x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"(c*(arctan(x/c)/c^3 + 1/(c^2*x)) - arctan(c/x)/x^2)*a*b + 1/2*(2*c*(arctan(x/c)/c^3 + 1/(c^2*x))*arctan(c/x) + (arctan(x/c)^2 - log(c^2 + x^2) + 2*log(x))/c^2)*b^2 - 1/2*b^2*arctan(c/x)^2/x^2 - 1/2*a^2/x^2","A",0
147,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c/x))^3,x, algorithm=""maxima"")","\frac{3}{4} \, a b^{2} x^{4} \arctan\left(\frac{c}{x}\right)^{2} + \frac{1}{4} \, a^{3} x^{4} + \frac{1}{4} \, {\left(3 \, x^{4} \arctan\left(\frac{c}{x}\right) + {\left(3 \, c^{3} \arctan\left(\frac{x}{c}\right) - 3 \, c^{2} x + x^{3}\right)} c\right)} a^{2} b + \frac{1}{4} \, {\left({\left(3 \, c^{2} \arctan\left(\frac{x}{c}\right)^{2} - 4 \, c^{2} \log\left(c^{2} + x^{2}\right) + x^{2}\right)} c^{2} + 2 \, {\left(3 \, c^{3} \arctan\left(\frac{x}{c}\right) - 3 \, c^{2} x + x^{3}\right)} c \arctan\left(\frac{c}{x}\right)\right)} a b^{2} - \frac{1}{64} \, {\left(12 \, c^{4} \arctan\left(\frac{c}{x}\right)^{2} \arctan\left(\frac{x}{c}\right) + 8 \, c^{4} \arctan\left(c, x\right)^{3} - 8 \, x^{4} \arctan\left(c, x\right)^{3} + 4 \, {\left(\frac{3 \, \arctan\left(\frac{c}{x}\right) \arctan\left(\frac{x}{c}\right)^{2}}{c} + \frac{\arctan\left(\frac{x}{c}\right)^{3}}{c}\right)} c^{5} + 12 \, c^{3} x \arctan\left(c, x\right)^{2} - 4 \, c x^{3} \arctan\left(c, x\right)^{2} + 192 \, c^{5} \int \frac{\log\left(c^{2} + x^{2}\right)^{2}}{64 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 1536 \, c^{4} \int \frac{x \arctan\left(\frac{c}{x}\right)}{64 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 768 \, c^{3} \int \frac{x^{2} \log\left(c^{2} + x^{2}\right)}{64 \, {\left(c^{2} + x^{2}\right)}}\,{d x} - 2048 \, c^{2} \int \frac{x^{3} \arctan\left(\frac{c}{x}\right)^{3}}{64 \, {\left(c^{2} + x^{2}\right)}}\,{d x} - 512 \, c^{2} \int \frac{x^{3} \arctan\left(\frac{c}{x}\right)}{64 \, {\left(c^{2} + x^{2}\right)}}\,{d x} - {\left(3 \, c^{3} x - c x^{3}\right)} \log\left(c^{2} + x^{2}\right)^{2} - 768 \, c \int \frac{x^{4} \arctan\left(\frac{c}{x}\right)^{2}}{64 \, {\left(c^{2} + x^{2}\right)}}\,{d x} - 192 \, c \int \frac{x^{4} \log\left(c^{2} + x^{2}\right)^{2}}{64 \, {\left(c^{2} + x^{2}\right)}}\,{d x} - 256 \, c \int \frac{x^{4} \log\left(c^{2} + x^{2}\right)}{64 \, {\left(c^{2} + x^{2}\right)}}\,{d x} - 2048 \, \int \frac{x^{5} \arctan\left(\frac{c}{x}\right)^{3}}{64 \, {\left(c^{2} + x^{2}\right)}}\,{d x}\right)} b^{3}"," ",0,"3/4*a*b^2*x^4*arctan(c/x)^2 + 1/4*a^3*x^4 + 1/4*(3*x^4*arctan(c/x) + (3*c^3*arctan(x/c) - 3*c^2*x + x^3)*c)*a^2*b + 1/4*((3*c^2*arctan(x/c)^2 - 4*c^2*log(c^2 + x^2) + x^2)*c^2 + 2*(3*c^3*arctan(x/c) - 3*c^2*x + x^3)*c*arctan(c/x))*a*b^2 - 1/64*(12*c^4*arctan(c/x)^2*arctan(x/c) + 8*c^4*arctan2(c, x)^3 - 8*x^4*arctan2(c, x)^3 + 4*(3*arctan(c/x)*arctan(x/c)^2/c + arctan(x/c)^3/c)*c^5 + 12*c^3*x*arctan2(c, x)^2 - 4*c*x^3*arctan2(c, x)^2 + 192*c^5*integrate(1/64*log(c^2 + x^2)^2/(c^2 + x^2), x) + 1536*c^4*integrate(1/64*x*arctan(c/x)/(c^2 + x^2), x) + 768*c^3*integrate(1/64*x^2*log(c^2 + x^2)/(c^2 + x^2), x) - 2048*c^2*integrate(1/64*x^3*arctan(c/x)^3/(c^2 + x^2), x) - 512*c^2*integrate(1/64*x^3*arctan(c/x)/(c^2 + x^2), x) - (3*c^3*x - c*x^3)*log(c^2 + x^2)^2 - 768*c*integrate(1/64*x^4*arctan(c/x)^2/(c^2 + x^2), x) - 192*c*integrate(1/64*x^4*log(c^2 + x^2)^2/(c^2 + x^2), x) - 256*c*integrate(1/64*x^4*log(c^2 + x^2)/(c^2 + x^2), x) - 2048*integrate(1/64*x^5*arctan(c/x)^3/(c^2 + x^2), x))*b^3","F",0
148,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c/x))^3,x, algorithm=""maxima"")","\frac{1}{24} \, b^{3} x^{3} \arctan\left(c, x\right)^{3} - \frac{1}{32} \, b^{3} x^{3} \arctan\left(c, x\right) \log\left(c^{2} + x^{2}\right)^{2} + \frac{1}{3} \, a^{3} x^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \arctan\left(\frac{c}{x}\right) - {\left(c^{2} \log\left(c^{2} + x^{2}\right) - x^{2}\right)} c\right)} a^{2} b + \int \frac{4 \, b^{3} c x^{3} \arctan\left(c, x\right)^{2} + 4 \, b^{3} x^{4} \arctan\left(c, x\right) \log\left(c^{2} + x^{2}\right) + 4 \, {\left(7 \, b^{3} \arctan\left(c, x\right)^{3} + 24 \, a b^{2} \arctan\left(c, x\right)^{2}\right)} x^{4} + 4 \, {\left(7 \, b^{3} c^{2} \arctan\left(c, x\right)^{3} + 24 \, a b^{2} c^{2} \arctan\left(c, x\right)^{2}\right)} x^{2} + {\left(3 \, b^{3} c^{2} x^{2} \arctan\left(c, x\right) + 3 \, b^{3} x^{4} \arctan\left(c, x\right) - b^{3} c x^{3}\right)} \log\left(c^{2} + x^{2}\right)^{2}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x}"," ",0,"1/24*b^3*x^3*arctan2(c, x)^3 - 1/32*b^3*x^3*arctan2(c, x)*log(c^2 + x^2)^2 + 1/3*a^3*x^3 + 1/2*(2*x^3*arctan(c/x) - (c^2*log(c^2 + x^2) - x^2)*c)*a^2*b + integrate(1/32*(4*b^3*c*x^3*arctan2(c, x)^2 + 4*b^3*x^4*arctan2(c, x)*log(c^2 + x^2) + 4*(7*b^3*arctan2(c, x)^3 + 24*a*b^2*arctan2(c, x)^2)*x^4 + 4*(7*b^3*c^2*arctan2(c, x)^3 + 24*a*b^2*c^2*arctan2(c, x)^2)*x^2 + (3*b^3*c^2*x^2*arctan2(c, x) + 3*b^3*x^4*arctan2(c, x) - b^3*c*x^3)*log(c^2 + x^2)^2)/(c^2 + x^2), x)","F",0
149,0,0,0,0.000000," ","integrate(x*(a+b*arctan(c/x))^3,x, algorithm=""maxima"")","\frac{3}{2} \, a b^{2} x^{2} \arctan\left(\frac{c}{x}\right)^{2} + \frac{1}{2} \, a^{3} x^{2} + \frac{3}{2} \, {\left(x^{2} \arctan\left(\frac{c}{x}\right) - {\left(c \arctan\left(\frac{x}{c}\right) - x\right)} c\right)} a^{2} b - \frac{3}{2} \, {\left({\left(\arctan\left(\frac{x}{c}\right)^{2} - \log\left(c^{2} + x^{2}\right)\right)} c^{2} + 2 \, {\left(c \arctan\left(\frac{x}{c}\right) - x\right)} c \arctan\left(\frac{c}{x}\right)\right)} a b^{2} + \frac{1}{32} \, {\left(12 \, c^{2} \arctan\left(\frac{c}{x}\right)^{2} \arctan\left(\frac{x}{c}\right) + 8 \, c^{2} \arctan\left(c, x\right)^{3} + 8 \, x^{2} \arctan\left(c, x\right)^{3} + 4 \, {\left(\frac{3 \, \arctan\left(\frac{c}{x}\right) \arctan\left(\frac{x}{c}\right)^{2}}{c} + \frac{\arctan\left(\frac{x}{c}\right)^{3}}{c}\right)} c^{3} + 12 \, c x \arctan\left(c, x\right)^{2} + 96 \, c^{3} \int \frac{\log\left(c^{2} + x^{2}\right)^{2}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} - 3 \, c x \log\left(c^{2} + x^{2}\right)^{2} + 512 \, c^{2} \int \frac{x \arctan\left(\frac{c}{x}\right)^{3}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 768 \, c^{2} \int \frac{x \arctan\left(\frac{c}{x}\right)}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 384 \, c \int \frac{x^{2} \arctan\left(\frac{c}{x}\right)^{2}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 96 \, c \int \frac{x^{2} \log\left(c^{2} + x^{2}\right)^{2}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 384 \, c \int \frac{x^{2} \log\left(c^{2} + x^{2}\right)}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 512 \, \int \frac{x^{3} \arctan\left(\frac{c}{x}\right)^{3}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x}\right)} b^{3}"," ",0,"3/2*a*b^2*x^2*arctan(c/x)^2 + 1/2*a^3*x^2 + 3/2*(x^2*arctan(c/x) - (c*arctan(x/c) - x)*c)*a^2*b - 3/2*((arctan(x/c)^2 - log(c^2 + x^2))*c^2 + 2*(c*arctan(x/c) - x)*c*arctan(c/x))*a*b^2 + 1/32*(12*c^2*arctan(c/x)^2*arctan(x/c) + 8*c^2*arctan2(c, x)^3 + 8*x^2*arctan2(c, x)^3 + 4*(3*arctan(c/x)*arctan(x/c)^2/c + arctan(x/c)^3/c)*c^3 + 12*c*x*arctan2(c, x)^2 + 96*c^3*integrate(1/32*log(c^2 + x^2)^2/(c^2 + x^2), x) - 3*c*x*log(c^2 + x^2)^2 + 512*c^2*integrate(1/32*x*arctan(c/x)^3/(c^2 + x^2), x) + 768*c^2*integrate(1/32*x*arctan(c/x)/(c^2 + x^2), x) + 384*c*integrate(1/32*x^2*arctan(c/x)^2/(c^2 + x^2), x) + 96*c*integrate(1/32*x^2*log(c^2 + x^2)^2/(c^2 + x^2), x) + 384*c*integrate(1/32*x^2*log(c^2 + x^2)/(c^2 + x^2), x) + 512*integrate(1/32*x^3*arctan(c/x)^3/(c^2 + x^2), x))*b^3","F",0
150,0,0,0,0.000000," ","integrate((a+b*arctan(c/x))^3,x, algorithm=""maxima"")","\frac{7}{8} \, b^{3} c \arctan\left(\frac{c}{x}\right)^{3} \arctan\left(\frac{x}{c}\right) + 3 \, a b^{2} c \arctan\left(\frac{c}{x}\right)^{2} \arctan\left(\frac{x}{c}\right) + \frac{1}{8} \, b^{3} x \arctan\left(c, x\right)^{3} - \frac{3}{32} \, b^{3} x \arctan\left(c, x\right) \log\left(c^{2} + x^{2}\right)^{2} + {\left(\frac{3 \, \arctan\left(\frac{c}{x}\right) \arctan\left(\frac{x}{c}\right)^{2}}{c} + \frac{\arctan\left(\frac{x}{c}\right)^{3}}{c}\right)} a b^{2} c^{2} + \frac{7}{32} \, {\left(\frac{6 \, \arctan\left(\frac{c}{x}\right)^{2} \arctan\left(\frac{x}{c}\right)^{2}}{c} + \frac{4 \, \arctan\left(\frac{c}{x}\right) \arctan\left(\frac{x}{c}\right)^{3}}{c} + \frac{\arctan\left(\frac{x}{c}\right)^{4}}{c}\right)} b^{3} c^{2} + 3 \, b^{3} c^{2} \int \frac{\arctan\left(\frac{c}{x}\right) \log\left(c^{2} + x^{2}\right)^{2}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 12 \, b^{3} c \int \frac{x \arctan\left(\frac{c}{x}\right)^{2}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} - 3 \, b^{3} c \int \frac{x \log\left(c^{2} + x^{2}\right)^{2}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + \frac{3}{2} \, {\left(2 \, x \arctan\left(\frac{c}{x}\right) + c \log\left(c^{2} + x^{2}\right)\right)} a^{2} b + a^{3} x + 28 \, b^{3} \int \frac{x^{2} \arctan\left(\frac{c}{x}\right)^{3}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 3 \, b^{3} \int \frac{x^{2} \arctan\left(\frac{c}{x}\right) \log\left(c^{2} + x^{2}\right)^{2}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 96 \, a b^{2} \int \frac{x^{2} \arctan\left(\frac{c}{x}\right)^{2}}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x} + 12 \, b^{3} \int \frac{x^{2} \arctan\left(\frac{c}{x}\right) \log\left(c^{2} + x^{2}\right)}{32 \, {\left(c^{2} + x^{2}\right)}}\,{d x}"," ",0,"7/8*b^3*c*arctan(c/x)^3*arctan(x/c) + 3*a*b^2*c*arctan(c/x)^2*arctan(x/c) + 1/8*b^3*x*arctan2(c, x)^3 - 3/32*b^3*x*arctan2(c, x)*log(c^2 + x^2)^2 + (3*arctan(c/x)*arctan(x/c)^2/c + arctan(x/c)^3/c)*a*b^2*c^2 + 7/32*(6*arctan(c/x)^2*arctan(x/c)^2/c + 4*arctan(c/x)*arctan(x/c)^3/c + arctan(x/c)^4/c)*b^3*c^2 + 3*b^3*c^2*integrate(1/32*arctan(c/x)*log(c^2 + x^2)^2/(c^2 + x^2), x) + 12*b^3*c*integrate(1/32*x*arctan(c/x)^2/(c^2 + x^2), x) - 3*b^3*c*integrate(1/32*x*log(c^2 + x^2)^2/(c^2 + x^2), x) + 3/2*(2*x*arctan(c/x) + c*log(c^2 + x^2))*a^2*b + a^3*x + 28*b^3*integrate(1/32*x^2*arctan(c/x)^3/(c^2 + x^2), x) + 3*b^3*integrate(1/32*x^2*arctan(c/x)*log(c^2 + x^2)^2/(c^2 + x^2), x) + 96*a*b^2*integrate(1/32*x^2*arctan(c/x)^2/(c^2 + x^2), x) + 12*b^3*integrate(1/32*x^2*arctan(c/x)*log(c^2 + x^2)/(c^2 + x^2), x)","F",0
151,0,0,0,0.000000," ","integrate((a+b*arctan(c/x))^3/x,x, algorithm=""maxima"")","a^{3} \log\left(x\right) + \frac{1}{32} \, \int \frac{28 \, b^{3} \arctan\left(c, x\right)^{3} + 3 \, b^{3} \arctan\left(c, x\right) \log\left(c^{2} + x^{2}\right)^{2} + 96 \, a b^{2} \arctan\left(c, x\right)^{2} + 96 \, a^{2} b \arctan\left(c, x\right)}{x}\,{d x}"," ",0,"a^3*log(x) + 1/32*integrate((28*b^3*arctan2(c, x)^3 + 3*b^3*arctan2(c, x)*log(c^2 + x^2)^2 + 96*a*b^2*arctan2(c, x)^2 + 96*a^2*b*arctan2(c, x))/x, x)","F",0
152,-1,0,0,0.000000," ","integrate((a+b*arctan(c/x))^3/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate((a+b*arctan(c/x))^3/x^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,1,31,0,0.412567," ","integrate(x^2*arctan(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(\sqrt{x}\right) - \frac{1}{15} \, x^{\frac{5}{2}} + \frac{1}{9} \, x^{\frac{3}{2}} - \frac{1}{3} \, \sqrt{x} + \frac{1}{3} \, \arctan\left(\sqrt{x}\right)"," ",0,"1/3*x^3*arctan(sqrt(x)) - 1/15*x^(5/2) + 1/9*x^(3/2) - 1/3*sqrt(x) + 1/3*arctan(sqrt(x))","A",0
155,1,26,0,0.412862," ","integrate(x*arctan(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(\sqrt{x}\right) - \frac{1}{6} \, x^{\frac{3}{2}} + \frac{1}{2} \, \sqrt{x} - \frac{1}{2} \, \arctan\left(\sqrt{x}\right)"," ",0,"1/2*x^2*arctan(sqrt(x)) - 1/6*x^(3/2) + 1/2*sqrt(x) - 1/2*arctan(sqrt(x))","A",0
156,1,16,0,0.414321," ","integrate(arctan(x^(1/2)),x, algorithm=""maxima"")","x \arctan\left(\sqrt{x}\right) - \sqrt{x} + \arctan\left(\sqrt{x}\right)"," ",0,"x*arctan(sqrt(x)) - sqrt(x) + arctan(sqrt(x))","A",0
157,1,35,0,0.418469," ","integrate(arctan(x^(1/2))/x,x, algorithm=""maxima"")","-\frac{1}{2} \, \pi \log\left(x + 1\right) + \arctan\left(\sqrt{x}\right) \log\left(x\right) - i \, {\rm Li}_2\left(i \, \sqrt{x} + 1\right) + i \, {\rm Li}_2\left(-i \, \sqrt{x} + 1\right)"," ",0,"-1/2*pi*log(x + 1) + arctan(sqrt(x))*log(x) - I*dilog(I*sqrt(x) + 1) + I*dilog(-I*sqrt(x) + 1)","B",0
158,1,21,0,0.411253," ","integrate(arctan(x^(1/2))/x^2,x, algorithm=""maxima"")","-\frac{\arctan\left(\sqrt{x}\right)}{x} - \frac{1}{\sqrt{x}} - \arctan\left(\sqrt{x}\right)"," ",0,"-arctan(sqrt(x))/x - 1/sqrt(x) - arctan(sqrt(x))","A",0
159,1,26,0,0.408187," ","integrate(arctan(x^(1/2))/x^3,x, algorithm=""maxima"")","\frac{3 \, x - 1}{6 \, x^{\frac{3}{2}}} - \frac{\arctan\left(\sqrt{x}\right)}{2 \, x^{2}} + \frac{1}{2} \, \arctan\left(\sqrt{x}\right)"," ",0,"1/6*(3*x - 1)/x^(3/2) - 1/2*arctan(sqrt(x))/x^2 + 1/2*arctan(sqrt(x))","A",0
160,1,24,0,0.306497," ","integrate(x^(3/2)*arctan(x^(1/2)),x, algorithm=""maxima"")","\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
161,1,19,0,0.307673," ","integrate(x^(1/2)*arctan(x^(1/2)),x, algorithm=""maxima"")","\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
162,1,16,0,0.306823," ","integrate(arctan(x^(1/2))/x^(1/2),x, algorithm=""maxima"")","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
163,1,18,0,0.312683," ","integrate(arctan(x^(1/2))/x^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \arctan\left(\sqrt{x}\right)}{\sqrt{x}} - \log\left(x + 1\right) + \log\left(x\right)"," ",0,"-2*arctan(sqrt(x))/sqrt(x) - log(x + 1) + log(x)","A",0
164,1,25,0,0.310376," ","integrate(arctan(x^(1/2))/x^(5/2),x, algorithm=""maxima"")","-\frac{2 \, \arctan\left(\sqrt{x}\right)}{3 \, x^{\frac{3}{2}}} - \frac{1}{3 \, x} + \frac{1}{3} \, \log\left(x + 1\right) - \frac{1}{3} \, \log\left(x\right)"," ",0,"-2/3*arctan(sqrt(x))/x^(3/2) - 1/3/x + 1/3*log(x + 1) - 1/3*log(x)","A",0
165,1,50,0,0.424015," ","integrate(arctan(a*x^5)/x,x, algorithm=""maxima"")","-\frac{1}{20} \, \pi \log\left(a^{2} x^{10} + 1\right) + \frac{1}{5} \, \arctan\left(a x^{5}\right) \log\left(a x^{5}\right) - \frac{1}{10} i \, {\rm Li}_2\left(i \, a x^{5} + 1\right) + \frac{1}{10} i \, {\rm Li}_2\left(-i \, a x^{5} + 1\right)"," ",0,"-1/20*pi*log(a^2*x^10 + 1) + 1/5*arctan(a*x^5)*log(a*x^5) - 1/10*I*dilog(I*a*x^5 + 1) + 1/10*I*dilog(-I*a*x^5 + 1)","B",0
166,0,0,0,0.000000," ","integrate(arctan(a*x^n)/x,x, algorithm=""maxima"")","-a n \int \frac{x^{n} \log\left(x\right)}{a^{2} x x^{2 \, n} + x}\,{d x} + \arctan\left(a x^{n}\right) \log\left(x\right)"," ",0,"-a*n*integrate(x^n*log(x)/(a^2*x*x^(2*n) + x), x) + arctan(a*x^n)*log(x)","F",0
