1,1,109,0,0.406582," ","integrate(x^3*(d+I*c*d*x)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{5} i \, a c d x^{5} + \frac{1}{4} \, a d x^{4} + \frac{1}{20} i \, {\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 c d + \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 d"," ",0,"1/5*I*a*c*d*x^5 + 1/4*a*d*x^4 + 1/20*I*(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*c*d + 1/12*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*d","A",0
2,1,99,0,0.406548," ","integrate(x^2*(d+I*c*d*x)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{4} i \, a c d x^{4} + \frac{1}{3} \, a d x^{3} + \frac{1}{12} i \, {\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 c d + \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 d"," ",0,"1/4*I*a*c*d*x^4 + 1/3*a*d*x^3 + 1/12*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*c*d + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d","A",0
3,1,88,0,0.409744," ","integrate(x*(d+I*c*d*x)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{3} i \, a c d x^{3} + \frac{1}{6} i \, {\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 c d + \frac{1}{2} \, a d 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 d"," ",0,"1/3*I*a*c*d*x^3 + 1/6*I*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*c*d + 1/2*a*d*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d","A",0
4,1,73,0,0.404084," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{2} i \, a c d x^{2} + \frac{1}{2} i \, {\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 c d + a d x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d}{2 \, c}"," ",0,"1/2*I*a*c*d*x^2 + 1/2*I*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*c*d + a*d*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d/c","A",0
5,0,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))/x,x, algorithm=""maxima"")","i \, a c d x + \frac{1}{2} i \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d + b d \int \frac{\arctan\left(c x\right)}{x}\,{d x} + a d \log\left(x\right)"," ",0,"I*a*c*d*x + 1/2*I*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d + b*d*integrate(arctan(c*x)/x, x) + a*d*log(x)","F",0
6,0,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))/x^2,x, algorithm=""maxima"")","i \, b c d \int \frac{\arctan\left(c x\right)}{x}\,{d x} + i \, a c d \log\left(x\right) - \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 d - \frac{a d}{x}"," ",0,"I*b*c*d*integrate(arctan(c*x)/x, x) + I*a*c*d*log(x) - 1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d - a*d/x","F",0
7,1,75,0,0.410448," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{2} i \, {\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 c d - \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 d - \frac{i \, a c d}{x} - \frac{a d}{2 \, x^{2}}"," ",0,"-1/2*I*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*c*d - 1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d - I*a*c*d/x - 1/2*a*d/x^2","A",0
8,1,87,0,0.408935," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{2} i \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b c d + \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 d - \frac{i \, a c d}{2 \, x^{2}} - \frac{a d}{3 \, x^{3}}"," ",0,"-1/2*I*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*c*d + 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*d - 1/2*I*a*c*d/x^2 - 1/3*a*d/x^3","A",0
9,1,102,0,0.409837," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{6} i \, {\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 c d + \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 d - \frac{i \, a c d}{3 \, x^{3}} - \frac{a d}{4 \, x^{4}}"," ",0,"1/6*I*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b*c*d + 1/12*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*d - 1/3*I*a*c*d/x^3 - 1/4*a*d/x^4","A",0
10,1,185,0,0.415529," ","integrate(x^3*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","-\frac{1}{6} \, a c^{2} d^{2} x^{6} + \frac{2}{5} i \, a c d^{2} x^{5} + \frac{1}{4} \, a d^{2} x^{4} - \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 c^{2} d^{2} + \frac{1}{10} i \, {\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 c d^{2} + \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 d^{2}"," ",0,"-1/6*a*c^2*d^2*x^6 + 2/5*I*a*c*d^2*x^5 + 1/4*a*d^2*x^4 - 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*c^2*d^2 + 1/10*I*(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*c*d^2 + 1/12*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*d^2","A",0
11,1,174,0,0.409673," ","integrate(x^2*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","-\frac{1}{5} \, a c^{2} d^{2} x^{5} + \frac{1}{2} i \, a c d^{2} x^{4} - \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 c^{2} d^{2} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{6} i \, {\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 c d^{2} + \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 d^{2}"," ",0,"-1/5*a*c^2*d^2*x^5 + 1/2*I*a*c*d^2*x^4 - 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*c^2*d^2 + 1/3*a*d^2*x^3 + 1/6*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*c*d^2 + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d^2","A",0
12,1,155,0,0.411241," ","integrate(x*(d+I*c*d*x)^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","-\frac{1}{4} \, a c^{2} d^{2} x^{4} + \frac{2}{3} i \, a c d^{2} x^{3} - \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 c^{2} d^{2} + \frac{1}{3} i \, {\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 c d^{2} + \frac{1}{2} \, a d^{2} 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 d^{2}"," ",0,"-1/4*a*c^2*d^2*x^4 + 2/3*I*a*c*d^2*x^3 - 1/12*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*c^2*d^2 + 1/3*I*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*c*d^2 + 1/2*a*d^2*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d^2","A",0
13,1,138,0,0.412263," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","-\frac{1}{3} \, a c^{2} d^{2} 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 c^{2} d^{2} + i \, a c d^{2} x^{2} + i \, {\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 c d^{2} + a d^{2} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{2}}{2 \, c}"," ",0,"-1/3*a*c^2*d^2*x^3 - 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*c^2*d^2 + I*a*c*d^2*x^2 + I*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*c*d^2 + a*d^2*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^2/c","B",0
14,1,142,0,0.614377," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a c^{2} d^{2} x^{2} + 2 i \, a c d^{2} x + \frac{1}{2} \, b c d^{2} x - \frac{1}{4} \, \pi b d^{2} \log\left(c^{2} x^{2} + 1\right) + b d^{2} \arctan\left(c x\right) \log\left(c x\right) + i \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{2} - \frac{1}{2} i \, b d^{2} {\rm Li}_2\left(i \, c x + 1\right) + \frac{1}{2} i \, b d^{2} {\rm Li}_2\left(-i \, c x + 1\right) + a d^{2} \log\left(x\right) - \frac{1}{2} \, {\left(b c^{2} d^{2} x^{2} + b d^{2}\right)} \arctan\left(c x\right)"," ",0,"-1/2*a*c^2*d^2*x^2 + 2*I*a*c*d^2*x + 1/2*b*c*d^2*x - 1/4*pi*b*d^2*log(c^2*x^2 + 1) + b*d^2*arctan(c*x)*log(c*x) + I*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^2 - 1/2*I*b*d^2*dilog(I*c*x + 1) + 1/2*I*b*d^2*dilog(-I*c*x + 1) + a*d^2*log(x) - 1/2*(b*c^2*d^2*x^2 + b*d^2)*arctan(c*x)","A",0
15,0,0,0,0.000000," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^2,x, algorithm=""maxima"")","-a c^{2} d^{2} x - \frac{1}{2} \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b c d^{2} + 2 i \, b c d^{2} \int \frac{\arctan\left(c x\right)}{x}\,{d x} + 2 i \, a c d^{2} \log\left(x\right) - \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 d^{2} - \frac{a d^{2}}{x}"," ",0,"-a*c^2*d^2*x - 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*c*d^2 + 2*I*b*c*d^2*integrate(arctan(c*x)/x, x) + 2*I*a*c*d^2*log(x) - 1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d^2 - a*d^2/x","F",0
16,0,0,0,0.000000," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^3,x, algorithm=""maxima"")","-b c^{2} d^{2} \int \frac{\arctan\left(c x\right)}{x}\,{d x} - a c^{2} d^{2} \log\left(x\right) - i \, {\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 c d^{2} - \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 d^{2} - \frac{2 i \, a c d^{2}}{x} - \frac{a d^{2}}{2 \, x^{2}}"," ",0,"-b*c^2*d^2*integrate(arctan(c*x)/x, x) - a*c^2*d^2*log(x) - I*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*c*d^2 - 1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d^2 - 2*I*a*c*d^2/x - 1/2*a*d^2/x^2","F",0
17,1,144,0,0.411550," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^4,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 c^{2} d^{2} - i \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b c d^{2} + \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 d^{2} + \frac{a c^{2} d^{2}}{x} - \frac{i \, a c d^{2}}{x^{2}} - \frac{a d^{2}}{3 \, x^{3}}"," ",0,"1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*c^2*d^2 - I*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*c*d^2 + 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*d^2 + a*c^2*d^2/x - I*a*c*d^2/x^2 - 1/3*a*d^2/x^3","A",0
18,1,152,0,0.410046," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^5,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 c^{2} d^{2} + \frac{1}{3} i \, {\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 c d^{2} + \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 d^{2} + \frac{a c^{2} d^{2}}{2 \, x^{2}} - \frac{2 i \, a c d^{2}}{3 \, x^{3}} - \frac{a d^{2}}{4 \, x^{4}}"," ",0,"1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*c^2*d^2 + 1/3*I*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b*c*d^2 + 1/12*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*d^2 + 1/2*a*c^2*d^2/x^2 - 2/3*I*a*c*d^2/x^3 - 1/4*a*d^2/x^4","A",0
19,1,183,0,0.415230," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))/x^6,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 c^{2} d^{2} + \frac{1}{6} i \, {\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 c d^{2} - \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 d^{2} + \frac{a c^{2} d^{2}}{3 \, x^{3}} - \frac{i \, a c d^{2}}{2 \, x^{4}} - \frac{a d^{2}}{5 \, x^{5}}"," ",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*c^2*d^2 + 1/6*I*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*c*d^2 - 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*d^2 + 1/3*a*c^2*d^2/x^3 - 1/2*I*a*c*d^2/x^4 - 1/5*a*d^2/x^5","A",0
20,1,261,0,0.411525," ","integrate(x^3*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","-\frac{1}{7} i \, a c^{3} d^{3} x^{7} - \frac{1}{2} \, a c^{2} d^{3} x^{6} + \frac{3}{5} i \, a c d^{3} x^{5} - \frac{1}{84} i \, {\left(12 \, x^{7} \arctan\left(c x\right) - c {\left(\frac{2 \, c^{4} x^{6} - 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} - \frac{6 \, \log\left(c^{2} x^{2} + 1\right)}{c^{8}}\right)}\right)} b c^{3} d^{3} + \frac{1}{4} \, a d^{3} x^{4} - \frac{1}{30} \, {\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 c^{2} d^{3} + \frac{3}{20} i \, {\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 c d^{3} + \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 d^{3}"," ",0,"-1/7*I*a*c^3*d^3*x^7 - 1/2*a*c^2*d^3*x^6 + 3/5*I*a*c*d^3*x^5 - 1/84*I*(12*x^7*arctan(c*x) - c*((2*c^4*x^6 - 3*c^2*x^4 + 6*x^2)/c^6 - 6*log(c^2*x^2 + 1)/c^8))*b*c^3*d^3 + 1/4*a*d^3*x^4 - 1/30*(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*c^2*d^3 + 3/20*I*(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*c*d^3 + 1/12*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*d^3","A",0
21,1,242,0,0.415627," ","integrate(x^2*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","-\frac{1}{6} i \, a c^{3} d^{3} x^{6} - \frac{3}{5} \, a c^{2} d^{3} x^{5} + \frac{3}{4} i \, a c d^{3} x^{4} - \frac{1}{90} i \, {\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 c^{3} d^{3} - \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)} b c^{2} d^{3} + \frac{1}{3} \, a d^{3} x^{3} + \frac{1}{4} i \, {\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 c d^{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 d^{3}"," ",0,"-1/6*I*a*c^3*d^3*x^6 - 3/5*a*c^2*d^3*x^5 + 3/4*I*a*c*d^3*x^4 - 1/90*I*(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*c^3*d^3 - 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))*b*c^2*d^3 + 1/3*a*d^3*x^3 + 1/4*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*c*d^3 + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d^3","A",0
22,1,222,0,0.421566," ","integrate(x*(d+I*c*d*x)^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","-\frac{1}{5} i \, a c^{3} d^{3} x^{5} - \frac{3}{4} \, a c^{2} d^{3} x^{4} - \frac{1}{20} i \, {\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 c^{3} d^{3} + i \, a c d^{3} x^{3} - \frac{1}{4} \, {\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 c^{2} d^{3} + \frac{1}{2} i \, {\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 c d^{3} + \frac{1}{2} \, a d^{3} 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 d^{3}"," ",0,"-1/5*I*a*c^3*d^3*x^5 - 3/4*a*c^2*d^3*x^4 - 1/20*I*(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*c^3*d^3 + I*a*c*d^3*x^3 - 1/4*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*c^2*d^3 + 1/2*I*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*c*d^3 + 1/2*a*d^3*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d^3","A",0
23,1,197,0,0.416943," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","-\frac{1}{4} i \, a c^{3} d^{3} x^{4} - a c^{2} d^{3} x^{3} - \frac{1}{12} i \, {\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 c^{3} d^{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)} b c^{2} d^{3} + \frac{3}{2} i \, a c d^{3} x^{2} + \frac{3}{2} i \, {\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 c d^{3} + a d^{3} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{3}}{2 \, c}"," ",0,"-1/4*I*a*c^3*d^3*x^4 - a*c^2*d^3*x^3 - 1/12*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*c^3*d^3 - 1/2*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*c^2*d^3 + 3/2*I*a*c*d^3*x^2 + 3/2*I*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*c*d^3 + a*d^3*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^3/c","B",0
24,1,184,0,0.618661," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{3} i \, a c^{3} d^{3} x^{3} - \frac{3}{2} \, a c^{2} d^{3} x^{2} + \frac{1}{6} i \, b c^{2} d^{3} x^{2} + 3 i \, a c d^{3} x + \frac{3}{2} \, b c d^{3} x - \frac{1}{12} \, {\left(3 \, \pi + 2 i\right)} b d^{3} \log\left(c^{2} x^{2} + 1\right) + b d^{3} \arctan\left(c x\right) \log\left(c x\right) + \frac{3}{2} i \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{3} - \frac{1}{2} i \, b d^{3} {\rm Li}_2\left(i \, c x + 1\right) + \frac{1}{2} i \, b d^{3} {\rm Li}_2\left(-i \, c x + 1\right) + a d^{3} \log\left(x\right) - \frac{1}{12} \, {\left(4 i \, b c^{3} d^{3} x^{3} + 18 \, b c^{2} d^{3} x^{2} + 18 \, b d^{3}\right)} \arctan\left(c x\right)"," ",0,"-1/3*I*a*c^3*d^3*x^3 - 3/2*a*c^2*d^3*x^2 + 1/6*I*b*c^2*d^3*x^2 + 3*I*a*c*d^3*x + 3/2*b*c*d^3*x - 1/12*(3*pi + 2*I)*b*d^3*log(c^2*x^2 + 1) + b*d^3*arctan(c*x)*log(c*x) + 3/2*I*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^3 - 1/2*I*b*d^3*dilog(I*c*x + 1) + 1/2*I*b*d^3*dilog(-I*c*x + 1) + a*d^3*log(x) - 1/12*(4*I*b*c^3*d^3*x^3 + 18*b*c^2*d^3*x^2 + 18*b*d^3)*arctan(c*x)","A",0
25,1,201,0,0.611780," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^2,x, algorithm=""maxima"")","-\frac{1}{2} i \, a c^{3} d^{3} x^{2} - 3 \, a c^{2} d^{3} x + \frac{1}{2} i \, b c^{2} d^{3} x - \frac{3}{4} i \, \pi b c d^{3} \log\left(c^{2} x^{2} + 1\right) + 3 i \, b c d^{3} \arctan\left(c x\right) \log\left(c x\right) - \frac{3}{2} \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b c d^{3} + \frac{3}{2} \, b c d^{3} {\rm Li}_2\left(i \, c x + 1\right) - \frac{3}{2} \, b c d^{3} {\rm Li}_2\left(-i \, c x + 1\right) + 3 i \, a c d^{3} \log\left(x\right) - \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 d^{3} - \frac{a d^{3}}{x} - \frac{1}{4} \, {\left(2 i \, b c^{3} d^{3} x^{2} + 2 i \, b c d^{3}\right)} \arctan\left(c x\right)"," ",0,"-1/2*I*a*c^3*d^3*x^2 - 3*a*c^2*d^3*x + 1/2*I*b*c^2*d^3*x - 3/4*I*pi*b*c*d^3*log(c^2*x^2 + 1) + 3*I*b*c*d^3*arctan(c*x)*log(c*x) - 3/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*c*d^3 + 3/2*b*c*d^3*dilog(I*c*x + 1) - 3/2*b*c*d^3*dilog(-I*c*x + 1) + 3*I*a*c*d^3*log(x) - 1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d^3 - a*d^3/x - 1/4*(2*I*b*c^3*d^3*x^2 + 2*I*b*c*d^3)*arctan(c*x)","A",0
26,0,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^3,x, algorithm=""maxima"")","-i \, a c^{3} d^{3} x - \frac{1}{2} i \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b c^{2} d^{3} - 3 \, b c^{2} d^{3} \int \frac{\arctan\left(c x\right)}{x}\,{d x} - 3 \, a c^{2} d^{3} \log\left(x\right) - \frac{3}{2} i \, {\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 c d^{3} - \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 d^{3} - \frac{3 i \, a c d^{3}}{x} - \frac{a d^{3}}{2 \, x^{2}}"," ",0,"-I*a*c^3*d^3*x - 1/2*I*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*c^2*d^3 - 3*b*c^2*d^3*integrate(arctan(c*x)/x, x) - 3*a*c^2*d^3*log(x) - 3/2*I*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*c*d^3 - 1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d^3 - 3*I*a*c*d^3/x - 1/2*a*d^3/x^2","F",0
27,0,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^4,x, algorithm=""maxima"")","-i \, b c^{3} d^{3} \int \frac{\arctan\left(c x\right)}{x}\,{d x} - i \, a c^{3} d^{3} \log\left(x\right) + \frac{3}{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 c^{2} d^{3} - \frac{3}{2} i \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b c d^{3} + \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 d^{3} + \frac{3 \, a c^{2} d^{3}}{x} - \frac{3 i \, a c d^{3}}{2 \, x^{2}} - \frac{a d^{3}}{3 \, x^{3}}"," ",0,"-I*b*c^3*d^3*integrate(arctan(c*x)/x, x) - I*a*c^3*d^3*log(x) + 3/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*c^2*d^3 - 3/2*I*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*c*d^3 + 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*d^3 + 3*a*c^2*d^3/x - 3/2*I*a*c*d^3/x^2 - 1/3*a*d^3/x^3","F",0
28,1,202,0,0.423375," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{2} i \, {\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 c^{3} d^{3} + \frac{3}{2} \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b c^{2} d^{3} + \frac{1}{2} i \, {\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 c d^{3} + \frac{i \, a c^{3} d^{3}}{x} + \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 d^{3} + \frac{3 \, a c^{2} d^{3}}{2 \, x^{2}} - \frac{i \, a c d^{3}}{x^{3}} - \frac{a d^{3}}{4 \, x^{4}}"," ",0,"1/2*I*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*c^3*d^3 + 3/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*c^2*d^3 + 1/2*I*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b*c*d^3 + I*a*c^3*d^3/x + 1/12*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*d^3 + 3/2*a*c^2*d^3/x^2 - I*a*c*d^3/x^3 - 1/4*a*d^3/x^4","B",0
29,1,224,0,0.418259," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^6,x, algorithm=""maxima"")","\frac{1}{2} i \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b c^{3} d^{3} - \frac{1}{2} \, {\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 c^{2} d^{3} + \frac{1}{4} i \, {\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 c d^{3} - \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 d^{3} + \frac{i \, a c^{3} d^{3}}{2 \, x^{2}} + \frac{a c^{2} d^{3}}{x^{3}} - \frac{3 i \, a c d^{3}}{4 \, x^{4}} - \frac{a d^{3}}{5 \, x^{5}}"," ",0,"1/2*I*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*c^3*d^3 - 1/2*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b*c^2*d^3 + 1/4*I*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*c*d^3 - 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*d^3 + 1/2*I*a*c^3*d^3/x^2 + a*c^2*d^3/x^3 - 3/4*I*a*c*d^3/x^4 - 1/5*a*d^3/x^5","A",0
30,1,248,0,0.413284," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))/x^7,x, algorithm=""maxima"")","-\frac{1}{6} i \, {\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 c^{3} d^{3} - \frac{1}{4} \, {\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 c^{2} d^{3} - \frac{3}{20} i \, {\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 c d^{3} - \frac{1}{90} \, {\left({\left(15 \, c^{5} \arctan\left(c x\right) + \frac{15 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 3}{x^{5}}\right)} c + \frac{15 \, \arctan\left(c x\right)}{x^{6}}\right)} b d^{3} + \frac{i \, a c^{3} d^{3}}{3 \, x^{3}} + \frac{3 \, a c^{2} d^{3}}{4 \, x^{4}} - \frac{3 i \, a c d^{3}}{5 \, x^{5}} - \frac{a d^{3}}{6 \, x^{6}}"," ",0,"-1/6*I*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b*c^3*d^3 - 1/4*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*c^2*d^3 - 3/20*I*((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*c*d^3 - 1/90*((15*c^5*arctan(c*x) + (15*c^4*x^4 - 5*c^2*x^2 + 3)/x^5)*c + 15*arctan(c*x)/x^6)*b*d^3 + 1/3*I*a*c^3*d^3/x^3 + 3/4*a*c^2*d^3/x^4 - 3/5*I*a*c*d^3/x^5 - 1/6*a*d^3/x^6","A",0
31,1,337,0,0.413783," ","integrate(x^3*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a c^{4} d^{4} x^{8} - \frac{4}{7} i \, a c^{3} d^{4} x^{7} - a c^{2} d^{4} x^{6} + \frac{4}{5} i \, a c d^{4} x^{5} + \frac{1}{840} \, {\left(105 \, x^{8} \arctan\left(c x\right) - c {\left(\frac{15 \, c^{6} x^{7} - 21 \, c^{4} x^{5} + 35 \, c^{2} x^{3} - 105 \, x}{c^{8}} + \frac{105 \, \arctan\left(c x\right)}{c^{9}}\right)}\right)} b c^{4} d^{4} - \frac{1}{21} i \, {\left(12 \, x^{7} \arctan\left(c x\right) - c {\left(\frac{2 \, c^{4} x^{6} - 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} - \frac{6 \, \log\left(c^{2} x^{2} + 1\right)}{c^{8}}\right)}\right)} b c^{3} d^{4} + \frac{1}{4} \, a d^{4} x^{4} - \frac{1}{15} \, {\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 c^{2} d^{4} + \frac{1}{5} i \, {\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 c d^{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 d^{4}"," ",0,"1/8*a*c^4*d^4*x^8 - 4/7*I*a*c^3*d^4*x^7 - a*c^2*d^4*x^6 + 4/5*I*a*c*d^4*x^5 + 1/840*(105*x^8*arctan(c*x) - c*((15*c^6*x^7 - 21*c^4*x^5 + 35*c^2*x^3 - 105*x)/c^8 + 105*arctan(c*x)/c^9))*b*c^4*d^4 - 1/21*I*(12*x^7*arctan(c*x) - c*((2*c^4*x^6 - 3*c^2*x^4 + 6*x^2)/c^6 - 6*log(c^2*x^2 + 1)/c^8))*b*c^3*d^4 + 1/4*a*d^4*x^4 - 1/15*(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*c^2*d^4 + 1/5*I*(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*c*d^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*d^4","A",0
32,1,318,0,0.414338," ","integrate(x^2*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a c^{4} d^{4} x^{7} - \frac{2}{3} i \, a c^{3} d^{4} x^{6} - \frac{6}{5} \, a c^{2} d^{4} x^{5} + \frac{1}{84} \, {\left(12 \, x^{7} \arctan\left(c x\right) - c {\left(\frac{2 \, c^{4} x^{6} - 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} - \frac{6 \, \log\left(c^{2} x^{2} + 1\right)}{c^{8}}\right)}\right)} b c^{4} d^{4} + i \, a c d^{4} x^{4} - \frac{2}{45} i \, {\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 c^{3} d^{4} - \frac{3}{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)} b c^{2} d^{4} + \frac{1}{3} \, a d^{4} x^{3} + \frac{1}{3} i \, {\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 c d^{4} + \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 d^{4}"," ",0,"1/7*a*c^4*d^4*x^7 - 2/3*I*a*c^3*d^4*x^6 - 6/5*a*c^2*d^4*x^5 + 1/84*(12*x^7*arctan(c*x) - c*((2*c^4*x^6 - 3*c^2*x^4 + 6*x^2)/c^6 - 6*log(c^2*x^2 + 1)/c^8))*b*c^4*d^4 + I*a*c*d^4*x^4 - 2/45*I*(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*c^3*d^4 - 3/10*(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))*b*c^2*d^4 + 1/3*a*d^4*x^3 + 1/3*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*c*d^4 + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d^4","B",0
33,1,290,0,0.414198," ","integrate(x*(d+I*c*d*x)^4*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a c^{4} d^{4} x^{6} - \frac{4}{5} i \, a c^{3} d^{4} x^{5} - \frac{3}{2} \, a c^{2} d^{4} x^{4} + \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 c^{4} d^{4} - \frac{1}{5} i \, {\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 c^{3} d^{4} + \frac{4}{3} i \, a c d^{4} x^{3} - \frac{1}{2} \, {\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 c^{2} d^{4} + \frac{2}{3} i \, {\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 c d^{4} + \frac{1}{2} \, a d^{4} 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 d^{4}"," ",0,"1/6*a*c^4*d^4*x^6 - 4/5*I*a*c^3*d^4*x^5 - 3/2*a*c^2*d^4*x^4 + 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*c^4*d^4 - 1/5*I*(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*c^3*d^4 + 4/3*I*a*c*d^4*x^3 - 1/2*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*c^2*d^4 + 2/3*I*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*c*d^4 + 1/2*a*d^4*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d^4","B",0
34,1,264,0,0.413048," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a c^{4} d^{4} x^{5} - i \, a c^{3} d^{4} x^{4} + \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 c^{4} d^{4} - 2 \, a c^{2} d^{4} x^{3} - \frac{1}{3} i \, {\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 c^{3} d^{4} - {\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 c^{2} d^{4} + 2 i \, a c d^{4} x^{2} + 2 i \, {\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 c d^{4} + a d^{4} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{4}}{2 \, c}"," ",0,"1/5*a*c^4*d^4*x^5 - I*a*c^3*d^4*x^4 + 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*c^4*d^4 - 2*a*c^2*d^4*x^3 - 1/3*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*c^3*d^4 - (2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*c^2*d^4 + 2*I*a*c*d^4*x^2 + 2*I*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*c*d^4 + a*d^4*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^4/c","B",0
35,1,220,0,0.625211," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, a c^{4} d^{4} x^{4} - \frac{4}{3} i \, a c^{3} d^{4} x^{3} - \frac{1}{12} \, b c^{3} d^{4} x^{3} - 3 \, a c^{2} d^{4} x^{2} + \frac{2}{3} i \, b c^{2} d^{4} x^{2} + 4 i \, a c d^{4} x + \frac{13}{4} \, b c d^{4} x - \frac{1}{12} \, {\left(3 \, \pi + 8 i\right)} b d^{4} \log\left(c^{2} x^{2} + 1\right) + b d^{4} \arctan\left(c x\right) \log\left(c x\right) + 2 i \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{4} - \frac{1}{2} i \, b d^{4} {\rm Li}_2\left(i \, c x + 1\right) + \frac{1}{2} i \, b d^{4} {\rm Li}_2\left(-i \, c x + 1\right) + a d^{4} \log\left(x\right) + \frac{1}{12} \, {\left(3 \, b c^{4} d^{4} x^{4} - 16 i \, b c^{3} d^{4} x^{3} - 36 \, b c^{2} d^{4} x^{2} - 39 \, b d^{4}\right)} \arctan\left(c x\right)"," ",0,"1/4*a*c^4*d^4*x^4 - 4/3*I*a*c^3*d^4*x^3 - 1/12*b*c^3*d^4*x^3 - 3*a*c^2*d^4*x^2 + 2/3*I*b*c^2*d^4*x^2 + 4*I*a*c*d^4*x + 13/4*b*c*d^4*x - 1/12*(3*pi + 8*I)*b*d^4*log(c^2*x^2 + 1) + b*d^4*arctan(c*x)*log(c*x) + 2*I*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^4 - 1/2*I*b*d^4*dilog(I*c*x + 1) + 1/2*I*b*d^4*dilog(-I*c*x + 1) + a*d^4*log(x) + 1/12*(3*b*c^4*d^4*x^4 - 16*I*b*c^3*d^4*x^3 - 36*b*c^2*d^4*x^2 - 39*b*d^4)*arctan(c*x)","A",0
36,1,241,0,0.636328," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a c^{4} d^{4} x^{3} - 2 i \, a c^{3} d^{4} x^{2} - \frac{1}{6} \, b c^{3} d^{4} x^{2} - 6 \, a c^{2} d^{4} x + 2 i \, b c^{2} d^{4} x - \frac{1}{6} \, {\left(6 i \, \pi - 1\right)} b c d^{4} \log\left(c^{2} x^{2} + 1\right) + 4 i \, b c d^{4} \arctan\left(c x\right) \log\left(c x\right) - 3 \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b c d^{4} + 2 \, b c d^{4} {\rm Li}_2\left(i \, c x + 1\right) - 2 \, b c d^{4} {\rm Li}_2\left(-i \, c x + 1\right) + 4 i \, a c d^{4} \log\left(x\right) - \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 d^{4} - \frac{a d^{4}}{x} + \frac{1}{6} \, {\left(2 \, b c^{4} d^{4} x^{3} - 12 i \, b c^{3} d^{4} x^{2} - 12 i \, b c d^{4}\right)} \arctan\left(c x\right)"," ",0,"1/3*a*c^4*d^4*x^3 - 2*I*a*c^3*d^4*x^2 - 1/6*b*c^3*d^4*x^2 - 6*a*c^2*d^4*x + 2*I*b*c^2*d^4*x - 1/6*(6*I*pi - 1)*b*c*d^4*log(c^2*x^2 + 1) + 4*I*b*c*d^4*arctan(c*x)*log(c*x) - 3*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*c*d^4 + 2*b*c*d^4*dilog(I*c*x + 1) - 2*b*c*d^4*dilog(-I*c*x + 1) + 4*I*a*c*d^4*log(x) - 1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d^4 - a*d^4/x + 1/6*(2*b*c^4*d^4*x^3 - 12*I*b*c^3*d^4*x^2 - 12*I*b*c*d^4)*arctan(c*x)","A",0
37,1,251,0,0.616202," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a c^{4} d^{4} x^{2} - 4 i \, a c^{3} d^{4} x - \frac{1}{2} \, b c^{3} d^{4} x + \frac{3}{2} \, \pi b c^{2} d^{4} \log\left(c^{2} x^{2} + 1\right) - 6 \, b c^{2} d^{4} \arctan\left(c x\right) \log\left(c x\right) - 2 i \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b c^{2} d^{4} + 3 i \, b c^{2} d^{4} {\rm Li}_2\left(i \, c x + 1\right) - 3 i \, b c^{2} d^{4} {\rm Li}_2\left(-i \, c x + 1\right) - 6 \, a c^{2} d^{4} \log\left(x\right) - 2 i \, {\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 c d^{4} - \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 d^{4} - \frac{4 i \, a c d^{4}}{x} - \frac{a d^{4}}{2 \, x^{2}} + \frac{1}{2} \, {\left(b c^{4} d^{4} x^{2} + b c^{2} d^{4}\right)} \arctan\left(c x\right)"," ",0,"1/2*a*c^4*d^4*x^2 - 4*I*a*c^3*d^4*x - 1/2*b*c^3*d^4*x + 3/2*pi*b*c^2*d^4*log(c^2*x^2 + 1) - 6*b*c^2*d^4*arctan(c*x)*log(c*x) - 2*I*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*c^2*d^4 + 3*I*b*c^2*d^4*dilog(I*c*x + 1) - 3*I*b*c^2*d^4*dilog(-I*c*x + 1) - 6*a*c^2*d^4*log(x) - 2*I*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*c*d^4 - 1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d^4 - 4*I*a*c*d^4/x - 1/2*a*d^4/x^2 + 1/2*(b*c^4*d^4*x^2 + b*c^2*d^4)*arctan(c*x)","A",0
38,0,0,0,0.000000," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^4,x, algorithm=""maxima"")","a c^{4} d^{4} x + \frac{1}{2} \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b c^{3} d^{4} - 4 i \, b c^{3} d^{4} \int \frac{\arctan\left(c x\right)}{x}\,{d x} - 4 i \, a c^{3} d^{4} \log\left(x\right) + 3 \, {\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 c^{2} d^{4} - 2 i \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b c d^{4} + \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 d^{4} + \frac{6 \, a c^{2} d^{4}}{x} - \frac{2 i \, a c d^{4}}{x^{2}} - \frac{a d^{4}}{3 \, x^{3}}"," ",0,"a*c^4*d^4*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*c^3*d^4 - 4*I*b*c^3*d^4*integrate(arctan(c*x)/x, x) - 4*I*a*c^3*d^4*log(x) + 3*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*c^2*d^4 - 2*I*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*c*d^4 + 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*d^4 + 6*a*c^2*d^4/x - 2*I*a*c*d^4/x^2 - 1/3*a*d^4/x^3","F",0
39,0,0,0,0.000000," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^5,x, algorithm=""maxima"")","b c^{4} d^{4} \int \frac{\arctan\left(c x\right)}{x}\,{d x} + a c^{4} d^{4} \log\left(x\right) + 2 i \, {\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 c^{3} d^{4} + 3 \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b c^{2} d^{4} + \frac{2}{3} i \, {\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 c d^{4} + \frac{4 i \, a c^{3} d^{4}}{x} + \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 d^{4} + \frac{3 \, a c^{2} d^{4}}{x^{2}} - \frac{4 i \, a c d^{4}}{3 \, x^{3}} - \frac{a d^{4}}{4 \, x^{4}}"," ",0,"b*c^4*d^4*integrate(arctan(c*x)/x, x) + a*c^4*d^4*log(x) + 2*I*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*c^3*d^4 + 3*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*c^2*d^4 + 2/3*I*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b*c*d^4 + 4*I*a*c^3*d^4/x + 1/12*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*d^4 + 3*a*c^2*d^4/x^2 - 4/3*I*a*c*d^4/x^3 - 1/4*a*d^4/x^4","F",0
40,1,275,0,0.426790," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^6,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 c^{4} d^{4} + 2 i \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b c^{3} d^{4} - {\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 c^{2} d^{4} - \frac{a c^{4} d^{4}}{x} + \frac{1}{3} i \, {\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 c d^{4} - \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 d^{4} + \frac{2 i \, a c^{3} d^{4}}{x^{2}} + \frac{2 \, a c^{2} d^{4}}{x^{3}} - \frac{i \, a c d^{4}}{x^{4}} - \frac{a d^{4}}{5 \, x^{5}}"," ",0,"-1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*c^4*d^4 + 2*I*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*c^3*d^4 - ((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b*c^2*d^4 - a*c^4*d^4/x + 1/3*I*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*c*d^4 - 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*d^4 + 2*I*a*c^3*d^4/x^2 + 2*a*c^2*d^4/x^3 - I*a*c*d^4/x^4 - 1/5*a*d^4/x^5","B",0
41,1,290,0,0.418241," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^7,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 c^{4} d^{4} - \frac{2}{3} i \, {\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 c^{3} d^{4} - \frac{1}{2} \, {\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 c^{2} d^{4} - \frac{1}{5} i \, {\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 c d^{4} - \frac{a c^{4} d^{4}}{2 \, x^{2}} - \frac{1}{90} \, {\left({\left(15 \, c^{5} \arctan\left(c x\right) + \frac{15 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 3}{x^{5}}\right)} c + \frac{15 \, \arctan\left(c x\right)}{x^{6}}\right)} b d^{4} + \frac{4 i \, a c^{3} d^{4}}{3 \, x^{3}} + \frac{3 \, a c^{2} d^{4}}{2 \, x^{4}} - \frac{4 i \, a c d^{4}}{5 \, x^{5}} - \frac{a d^{4}}{6 \, x^{6}}"," ",0,"-1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*c^4*d^4 - 2/3*I*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b*c^3*d^4 - 1/2*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*c^2*d^4 - 1/5*I*((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*c*d^4 - 1/2*a*c^4*d^4/x^2 - 1/90*((15*c^5*arctan(c*x) + (15*c^4*x^4 - 5*c^2*x^2 + 3)/x^5)*c + 15*arctan(c*x)/x^6)*b*d^4 + 4/3*I*a*c^3*d^4/x^3 + 3/2*a*c^2*d^4/x^4 - 4/5*I*a*c*d^4/x^5 - 1/6*a*d^4/x^6","B",0
42,1,329,0,0.411971," ","integrate((d+I*c*d*x)^4*(a+b*arctan(c*x))/x^8,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 c^{4} d^{4} - \frac{1}{3} i \, {\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 c^{3} d^{4} + \frac{3}{10} \, {\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 c^{2} d^{4} - \frac{2}{45} i \, {\left({\left(15 \, c^{5} \arctan\left(c x\right) + \frac{15 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 3}{x^{5}}\right)} c + \frac{15 \, \arctan\left(c x\right)}{x^{6}}\right)} b c d^{4} + \frac{1}{84} \, {\left({\left(6 \, c^{6} \log\left(c^{2} x^{2} + 1\right) - 6 \, c^{6} \log\left(x^{2}\right) - \frac{6 \, c^{4} x^{4} - 3 \, c^{2} x^{2} + 2}{x^{6}}\right)} c - \frac{12 \, \arctan\left(c x\right)}{x^{7}}\right)} b d^{4} - \frac{a c^{4} d^{4}}{3 \, x^{3}} + \frac{i \, a c^{3} d^{4}}{x^{4}} + \frac{6 \, a c^{2} d^{4}}{5 \, x^{5}} - \frac{2 i \, a c d^{4}}{3 \, x^{6}} - \frac{a d^{4}}{7 \, x^{7}}"," ",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*c^4*d^4 - 1/3*I*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*c^3*d^4 + 3/10*((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*c^2*d^4 - 2/45*I*((15*c^5*arctan(c*x) + (15*c^4*x^4 - 5*c^2*x^2 + 3)/x^5)*c + 15*arctan(c*x)/x^6)*b*c*d^4 + 1/84*((6*c^6*log(c^2*x^2 + 1) - 6*c^6*log(x^2) - (6*c^4*x^4 - 3*c^2*x^2 + 2)/x^6)*c - 12*arctan(c*x)/x^7)*b*d^4 - 1/3*a*c^4*d^4/x^3 + I*a*c^3*d^4/x^4 + 6/5*a*c^2*d^4/x^5 - 2/3*I*a*c*d^4/x^6 - 1/7*a*d^4/x^7","A",0
43,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))/(d+I*c*d*x),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{i \, {\left(2 \, c^{2} x^{3} + 3 i \, c x^{2} - 6 \, x\right)}}{c^{3} d} + \frac{6 \, \log\left(i \, c x + 1\right)}{c^{4} d}\right)} - \frac{-\frac{1}{2} \, {\left(-12 i \, {\left(2 \, {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{7} d} + \frac{3 \, \arctan\left(c x\right)}{c^{8} d}\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^{8} d}\right)} c^{8} d - 36 \, c^{8} d \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{c^{5} d x^{2} + c^{3} d}\,{d x} - 9 i \, {\left(2 \, {\left(\frac{x^{2}}{c^{5} d} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{7} d}\right)} \log\left(c^{2} x^{2} + 1\right) - \frac{2 \, c^{2} x^{2} - \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{7} d}\right)} c^{7} d + 72 \, c^{7} d \int \frac{x^{3} \arctan\left(c x\right)}{c^{5} d x^{2} + c^{3} d}\,{d x} - 72 \, c^{5} d \int \frac{x \arctan\left(c x\right)}{c^{5} d x^{2} + c^{3} d}\,{d x} - 8 \, c^{3} x^{3} + 36 \, c^{4} d \int \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{5} d x^{2} + c^{3} d}\,{d x} - 6 i \, c^{2} x^{2} + 60 \, c x - 2 \, {\left(12 i \, c^{3} x^{3} - 18 \, c^{2} x^{2} - 36 i \, c x + 30\right)} \arctan\left(c x\right) - 36 i \, \arctan\left(c x\right)^{2} + 2 \, {\left(6 \, c^{3} x^{3} + 9 i \, c^{2} x^{2} - 18 \, c x + 3 i\right)} \log\left(c^{2} x^{2} + 1\right) - 9 i \, \log\left(c^{2} x^{2} + 1\right)^{2} - 36 i \, \log\left(12 \, c^{5} d x^{2} + 12 \, c^{3} d\right)\right)} b}{72 \, c^{4} d}"," ",0,"-1/6*a*(I*(2*c^2*x^3 + 3*I*c*x^2 - 6*x)/(c^3*d) + 6*log(I*c*x + 1)/(c^4*d)) - 1/72*(432*I*c^8*d*integrate(1/12*x^4*arctan(c*x)/(c^5*d*x^2 + c^3*d), x) + 216*c^8*d*integrate(1/12*x^4*log(c^2*x^2 + 1)/(c^5*d*x^2 + c^3*d), x) - 432*c^7*d*integrate(1/12*x^3*arctan(c*x)/(c^5*d*x^2 + c^3*d), x) + 216*I*c^7*d*integrate(1/12*x^3*log(c^2*x^2 + 1)/(c^5*d*x^2 + c^3*d), x) + 432*c^5*d*integrate(1/12*x*arctan(c*x)/(c^5*d*x^2 + c^3*d), x) - 216*I*c^5*d*integrate(1/12*x*log(c^2*x^2 + 1)/(c^5*d*x^2 + c^3*d), x) + 4*c^3*x^3 - 216*c^4*d*integrate(1/12*log(c^2*x^2 + 1)/(c^5*d*x^2 + c^3*d), x) + 3*I*c^2*x^2 - 30*c*x + (12*I*c^3*x^3 - 18*c^2*x^2 - 36*I*c*x + 30)*arctan(c*x) + 18*I*arctan(c*x)^2 - (6*c^3*x^3 + 9*I*c^2*x^2 - 18*c*x + 3*I)*log(c^2*x^2 + 1) + 9*I*log(c^2*x^2 + 1)^2 + 18*I*log(12*c^5*d*x^2 + 12*c^3*d))*b/(c^4*d)","F",0
44,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))/(d+I*c*d*x),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{i \, c x^{2} - 2 \, x}{c^{2} d} - \frac{2 i \, \log\left(i \, c x + 1\right)}{c^{3} d}\right)} - \frac{\frac{1}{2} \, {\left({\left(2 \, {\left(\frac{x^{2}}{c^{4} d} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{6} d}\right)} \log\left(c^{2} x^{2} + 1\right) - \frac{2 \, c^{2} x^{2} - \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{6} d}\right)} c^{6} d + 8 i \, c^{6} d \int \frac{x^{3} \arctan\left(c x\right)}{c^{4} d x^{2} + c^{2} d}\,{d x} - 4 \, {\left(2 \, {\left(\frac{x}{c^{4} d} - \frac{\arctan\left(c x\right)}{c^{5} d}\right)} \arctan\left(c x\right) + \frac{\arctan\left(c x\right)^{2} - \log\left(c^{2} x^{2} + 1\right)}{c^{5} d}\right)} c^{5} d + 4 i \, c^{5} d \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{c^{4} d x^{2} + c^{2} d}\,{d x} - 8 i \, c^{4} d \int \frac{x \arctan\left(c x\right)}{c^{4} d x^{2} + c^{2} d}\,{d x} + 4 i \, c^{3} d \int \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4} d x^{2} + c^{2} d}\,{d x} + 2 \, c^{2} x^{2} + 4 i \, c x + 2 \, {\left(2 i \, c^{2} x^{2} - 4 \, c x - 2 i\right)} \arctan\left(c x\right) + 4 \, \arctan\left(c x\right)^{2} - 2 \, {\left(c^{2} x^{2} + 2 i \, c x + 1\right)} \log\left(c^{2} x^{2} + 1\right) + \log\left(c^{2} x^{2} + 1\right)^{2} + 4 \, \log\left(8 \, c^{4} d x^{2} + 8 \, c^{2} d\right)\right)} b}{8 \, c^{3} d}"," ",0,"-1/2*a*((I*c*x^2 - 2*x)/(c^2*d) - 2*I*log(I*c*x + 1)/(c^3*d)) - 1/8*(32*I*c^6*d*integrate(1/8*x^3*arctan(c*x)/(c^4*d*x^2 + c^2*d), x) + 16*c^6*d*integrate(1/8*x^3*log(c^2*x^2 + 1)/(c^4*d*x^2 + c^2*d), x) - 32*c^5*d*integrate(1/8*x^2*arctan(c*x)/(c^4*d*x^2 + c^2*d), x) + 16*I*c^5*d*integrate(1/8*x^2*log(c^2*x^2 + 1)/(c^4*d*x^2 + c^2*d), x) - 32*I*c^4*d*integrate(1/8*x*arctan(c*x)/(c^4*d*x^2 + c^2*d), x) - 16*c^4*d*integrate(1/8*x*log(c^2*x^2 + 1)/(c^4*d*x^2 + c^2*d), x) + 16*I*c^3*d*integrate(1/8*log(c^2*x^2 + 1)/(c^4*d*x^2 + c^2*d), x) + c^2*x^2 + 2*I*c*x + (2*I*c^2*x^2 - 4*c*x - 2*I)*arctan(c*x) + 2*arctan(c*x)^2 - (c^2*x^2 + 2*I*c*x + 1)*log(c^2*x^2 + 1) + log(c^2*x^2 + 1)^2 + 2*log(8*c^4*d*x^2 + 8*c^2*d))*b/(c^3*d)","F",0
45,0,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))/(d+I*c*d*x),x, algorithm=""maxima"")","a {\left(-\frac{i \, x}{c d} + \frac{\log\left(i \, c x + 1\right)}{c^{2} d}\right)} - \frac{{\left(2 i \, {\left(2 \, {\left(\frac{x}{c^{3} d} - \frac{\arctan\left(c x\right)}{c^{4} d}\right)} \arctan\left(c x\right) + \frac{\arctan\left(c x\right)^{2} - \log\left(c^{2} x^{2} + 1\right)}{c^{4} d}\right)} c^{4} d + 2 \, c^{4} d \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{c^{3} d x^{2} + c d}\,{d x} - 8 \, c^{3} d \int \frac{x \arctan\left(c x\right)}{c^{3} d x^{2} + c d}\,{d x} + 2 \, c^{2} d \int \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{3} d x^{2} + c d}\,{d x} - 2 \, c x \log\left(c^{2} x^{2} + 1\right) + 4 \, c x - 4 \, {\left(-i \, c x + 1\right)} \arctan\left(c x\right) - 2 i \, \arctan\left(c x\right)^{2} - 2 i \, \log\left(2 \, c^{3} d x^{2} + 2 \, c d\right)\right)} b}{8 \, c^{2} d}"," ",0,"a*(-I*x/(c*d) + log(I*c*x + 1)/(c^2*d)) - 1/8*(8*I*c^4*d*integrate(1/2*x^2*arctan(c*x)/(c^3*d*x^2 + c*d), x) + 4*c^4*d*integrate(1/2*x^2*log(c^2*x^2 + 1)/(c^3*d*x^2 + c*d), x) - 16*c^3*d*integrate(1/2*x*arctan(c*x)/(c^3*d*x^2 + c*d), x) + 8*I*c^3*d*integrate(1/2*x*log(c^2*x^2 + 1)/(c^3*d*x^2 + c*d), x) + 4*c^2*d*integrate(1/2*log(c^2*x^2 + 1)/(c^3*d*x^2 + c*d), x) - 2*c*x*log(c^2*x^2 + 1) + 4*c*x - 4*(-I*c*x + 1)*arctan(c*x) - 2*I*arctan(c*x)^2 - I*log(c^2*x^2 + 1)^2 - 2*I*log(2*c^3*d*x^2 + 2*c*d))*b/(c^2*d)","F",0
46,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/(d+I*c*d*x),x, algorithm=""maxima"")","-\frac{{\left(8 i \, c^{2} d \mathit{sage}_{0} x - 4 \, \arctan\left(c x\right)^{2}\right)} b}{8 \, c d} - \frac{i \, a \log\left(i \, c d x + d\right)}{c d}"," ",0,"-1/8*(8*I*c^2*d*integrate(x*arctan(c*x)/(c^2*d*x^2 + d), x) + 4*c^2*d*integrate(x*log(c^2*x^2 + 1)/(c^2*d*x^2 + d), x) - 4*arctan(c*x)^2 - log(c^2*x^2 + 1)^2)*b/(c*d) - I*a*log(I*c*d*x + d)/(c*d)","F",0
47,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x/(d+I*c*d*x),x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{i \, \arctan\left(c x\right)^{2}}{d} - 2 \, \int \frac{\arctan\left(c x\right)}{c^{2} d x^{3} + d x}\,{d x}\right)} - a {\left(\frac{\log\left(i \, c x + 1\right)}{d} - \frac{\log\left(x\right)}{d}\right)}"," ",0,"-1/2*b*(I*arctan(c*x)^2/d - 2*integrate(arctan(c*x)/(c^2*d*x^3 + d*x), x)) - a*(log(I*c*x + 1)/d - log(x)/d)","F",0
48,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^2/(d+I*c*d*x),x, algorithm=""maxima"")","{\left(-i \, c \int \frac{\arctan\left(c x\right)}{c^{2} d x^{3} + d x}\,{d x} + \int \frac{\arctan\left(c x\right)}{c^{2} d x^{4} + d x^{2}}\,{d x}\right)} b + a {\left(\frac{i \, c \log\left(i \, c x + 1\right)}{d} - \frac{i \, c \log\left(x\right)}{d} - \frac{1}{d x}\right)}"," ",0,"(-I*c*integrate(arctan(c*x)/(c^2*d*x^3 + d*x), x) + integrate(arctan(c*x)/(c^2*d*x^4 + d*x^2), x))*b + a*(I*c*log(I*c*x + 1)/d - I*c*log(x)/d - 1/(d*x))","F",0
49,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^3/(d+I*c*d*x),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{2 \, c^{2} \log\left(i \, c x + 1\right)}{d} - \frac{2 \, c^{2} \log\left(x\right)}{d} + \frac{2 i \, c x - 1}{d x^{2}}\right)} a + {\left(-i \, c \int \frac{\arctan\left(c x\right)}{c^{2} d x^{4} + d x^{2}}\,{d x} + \int \frac{\arctan\left(c x\right)}{c^{2} d x^{5} + d x^{3}}\,{d x}\right)} b"," ",0,"1/2*(2*c^2*log(I*c*x + 1)/d - 2*c^2*log(x)/d + (2*I*c*x - 1)/(d*x^2))*a + (-I*c*integrate(arctan(c*x)/(c^2*d*x^4 + d*x^2), x) + integrate(arctan(c*x)/(c^2*d*x^5 + d*x^3), x))*b","F",0
50,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^4/(d+I*c*d*x),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{6 i \, c^{3} \log\left(i \, c x + 1\right)}{d} - \frac{6 i \, c^{3} \log\left(x\right)}{d} - \frac{6 \, c^{2} x^{2} + 3 i \, c x - 2}{d x^{3}}\right)} a + {\left(-i \, c \int \frac{\arctan\left(c x\right)}{c^{2} d x^{5} + d x^{3}}\,{d x} + \int \frac{\arctan\left(c x\right)}{c^{2} d x^{6} + d x^{4}}\,{d x}\right)} b"," ",0,"-1/6*(6*I*c^3*log(I*c*x + 1)/d - 6*I*c^3*log(x)/d - (6*c^2*x^2 + 3*I*c*x - 2)/(d*x^3))*a + (-I*c*integrate(arctan(c*x)/(c^2*d*x^5 + d*x^3), x) + integrate(arctan(c*x)/(c^2*d*x^6 + d*x^4), x))*b","F",0
51,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 i}{c^{5} d^{2} x - i \, c^{4} d^{2}} + \frac{c x^{2} + 4 i \, x}{c^{3} d^{2}} - \frac{6 \, \log\left(c x - i\right)}{c^{4} d^{2}}\right)} - \frac{-\frac{1}{2} \, {\left(32 i \, c^{3} x^{3} - 160 \, c^{2} x^{2} - 32 \, c x {\left(2 \, \arctan\left(1, c x\right) - 6 i\right)} - 384 \, {\left(-i \, c x - 1\right)} \arctan\left(c x\right)^{2} - 96 \, {\left(-i \, c x - 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, {\left(16 i \, c^{9} d^{2} x + 16 \, c^{8} d^{2}\right)} {\left(\frac{{\left(c^{4} x^{4} + c^{2} x^{2} - {\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - {\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right) + 1\right)} c^{3}}{c^{13} d^{2} x^{2} + c^{11} d^{2}} + c {\left(\frac{1}{c^{11} d^{2} x^{2} + c^{9} d^{2}} - \frac{x^{2}}{c^{7} d^{2}} + \frac{2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{9} d^{2}}\right)} \log\left(c^{2} x^{2} + 1\right) + 2 \, {\left(\frac{x}{c^{9} d^{2} x^{2} + c^{7} d^{2}} + \frac{2 \, x}{c^{7} d^{2}} - \frac{3 \, \arctan\left(c x\right)}{c^{8} d^{2}}\right)} \arctan\left(c x\right) + \frac{{\left(3 \, {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} - 2 \, {\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right) + 1\right)} c}{c^{11} d^{2} x^{2} + c^{9} d^{2}}\right)} - {\left(-48 i \, c^{7} d^{2} x - 48 \, c^{6} d^{2}\right)} {\left(\frac{{\left({\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 2\right)} c^{3}}{c^{11} d^{2} x^{2} + c^{9} d^{2}} - 2 \, c {\left(\frac{1}{c^{9} d^{2} x^{2} + c^{7} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{7} d^{2}}\right)} \log\left(c^{2} x^{2} + 1\right) - 4 \, {\left(\frac{x}{c^{7} d^{2} x^{2} + c^{5} d^{2}} - \frac{\arctan\left(c x\right)}{c^{6} d^{2}}\right)} \arctan\left(c x\right) - \frac{2 \, {\left({\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} + 1\right)} c}{c^{9} d^{2} x^{2} + c^{7} d^{2}}\right)} + {\left(-16 i \, c^{8} d^{2} x - 16 \, c^{7} d^{2}\right)} {\left(4 \, c {\left(\frac{x}{c^{9} d^{2} x^{2} + c^{7} d^{2}} + \frac{2 \, x}{c^{7} d^{2}} - \frac{3 \, \arctan\left(c x\right)}{c^{8} d^{2}}\right)} \arctan\left(c x\right) + \frac{2 \, {\left(3 \, {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} - 2 \, {\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right) + 1\right)} c^{2}}{c^{11} d^{2} x^{2} + c^{9} d^{2}} - \frac{{\left({\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 2\right)} c^{2}}{c^{11} d^{2} x^{2} + c^{9} d^{2}} + 2 \, {\left(\frac{1}{c^{9} d^{2} x^{2} + c^{7} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{7} d^{2}}\right)} \log\left(c^{2} x^{2} + 1\right)\right)} - 96 \, {\left(c^{5} d^{2} x - i \, c^{4} d^{2}\right)} {\left({\left(c {\left(\frac{x}{c^{7} d^{2} x^{2} + c^{5} d^{2}} + \frac{\arctan\left(c x\right)}{c^{6} d^{2}}\right)} - \frac{2 \, \arctan\left(c x\right)}{c^{7} d^{2} x^{2} + c^{5} d^{2}}\right)} c + 2 \, \int \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{7} d^{2} x^{4} + 2 \, c^{5} d^{2} x^{2} + c^{3} d^{2}}\,{d x}\right)} - 2 \, {\left(-96 i \, c^{6} d^{2} x - 96 \, c^{5} d^{2}\right)} {\left({\left(2 \, {\left(\frac{x}{c^{7} d^{2} x^{2} + c^{5} d^{2}} - \frac{\arctan\left(c x\right)}{c^{6} d^{2}}\right)} \arctan\left(c x\right) + \frac{{\left({\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} + 1\right)} c}{c^{9} d^{2} x^{2} + c^{7} d^{2}}\right)} c + \frac{c^{2}}{c^{9} d^{2} x^{2} + c^{7} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{7} d^{2} x^{2} + c^{5} d^{2}}\right)} - 2 \, {\left(48 i \, c^{5} d^{2} x + 48 \, c^{4} d^{2}\right)} {\left(c {\left(\frac{c^{2}}{c^{9} d^{2} x^{2} + c^{7} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{7} d^{2} x^{2} + c^{5} d^{2}}\right)} + 2 \, {\left(\frac{x}{c^{5} d^{2} x^{2} + c^{3} d^{2}} + \frac{\arctan\left(c x\right)}{c^{4} d^{2}}\right)} \arctan\left(c x\right) - \frac{{\left({\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} - 1\right)} c}{c^{7} d^{2} x^{2} + c^{5} d^{2}}\right)} + 192 \, {\left(c^{6} d^{2} x - i \, c^{5} d^{2}\right)} {\left(c {\left(\frac{x}{c^{7} d^{2} x^{2} + c^{5} d^{2}} + \frac{\arctan\left(c x\right)}{c^{6} d^{2}}\right)} - 2 \, c \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{c^{7} d^{2} x^{4} + 2 \, c^{5} d^{2} x^{2} + c^{3} d^{2}}\,{d x} - \frac{2 \, \arctan\left(c x\right)}{c^{7} d^{2} x^{2} + c^{5} d^{2}}\right)} - 32 \, {\left(2 \, c^{3} x^{3} + 6 i \, c^{2} x^{2} + 8 \, c x + 4 i\right)} \arctan\left(c x\right) + 32 \, {\left(-i \, c^{3} x^{3} + 3 \, c^{2} x^{2} - i \, c x + 5\right)} \log\left(c^{2} x^{2} + 1\right) + \frac{4 \, {\left(c^{9} d^{2} x - i \, c^{8} d^{2}\right)} {\left(32 \, c^{3} x^{3} + 6 \, c^{2} x^{2} \arctan\left(1, c x\right) + 12 \, c x - 3 \, {\left(9 \, c^{2} x^{2} + 1\right)} \arctan\left(c x\right) + 3 \, {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x, -1\right) - 32 \, {\left(c^{14} d^{2} x^{2} + c^{12} d^{2}\right)} \int \frac{x^{5} \arctan\left(c x\right)}{c^{10} d^{2} x^{4} + 2 \, c^{8} d^{2} x^{2} + c^{6} d^{2}}\,{d x} - 48 \, {\left(c^{12} d^{2} x^{2} + c^{10} d^{2}\right)} \int \frac{x^{3} \arctan\left(c x\right)}{c^{10} d^{2} x^{4} + 2 \, c^{8} d^{2} x^{2} + c^{6} d^{2}}\,{d x} - 8 \, {\left(2 \, c^{3} x^{3} + 3 \, c x - 3 \, {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right) + 6 \, \arctan\left(1, c x\right)\right)}}{c^{10} d^{2} x^{2} + c^{8} d^{2}} + \frac{4 \, {\left(c^{8} d^{2} x - i \, c^{7} d^{2}\right)} {\left(32 \, c^{3} x^{3} + 6 \, c^{2} x^{2} \arctan\left(1, c x\right) + 12 \, c x - 3 \, {\left(9 \, c^{2} x^{2} + 1\right)} \arctan\left(c x\right) + 3 \, {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x, -1\right) - 16 \, {\left(c^{11} d^{2} x^{2} + c^{9} d^{2}\right)} \int \frac{x^{3} \arctan\left(c x\right)}{c^{9} d^{2} x^{4} + 2 \, c^{7} d^{2} x^{2} + c^{5} d^{2}}\,{d x} - 8 \, {\left(2 \, c^{3} x^{3} + 3 \, c x - 3 \, {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right) + 6 \, \arctan\left(1, c x\right)\right)}}{c^{9} d^{2} x^{2} + c^{7} d^{2}} + \frac{12 \, {\left(c^{7} d^{2} x - i \, c^{6} d^{2}\right)} {\left(2 \, c^{2} x^{2} \arctan\left(1, c x\right) - 12 \, c x + {\left(7 \, c^{2} x^{2} + 15\right)} \arctan\left(c x\right) + {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x, -1\right) + 16 \, {\left(c^{10} d^{2} x^{2} + c^{8} d^{2}\right)} \int \frac{x^{3} \arctan\left(c x\right)}{c^{8} d^{2} x^{4} + 2 \, c^{6} d^{2} x^{2} + c^{4} d^{2}}\,{d x} - 8 \, {\left(c x - {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right) + 2 \, \arctan\left(1, c x\right)\right)}}{c^{8} d^{2} x^{2} + c^{6} d^{2}} + 64 i \, \arctan\left(1, c x\right)\right)} b}{128 \, {\left(c^{5} d^{2} x - i \, c^{4} d^{2}\right)}}"," ",0,"-1/2*a*(2*I/(c^5*d^2*x - I*c^4*d^2) + (c*x^2 + 4*I*x)/(c^3*d^2) - 6*log(c*x - I)/(c^4*d^2)) - 1/128*(-16*I*c^3*x^3 + 80*c^2*x^2 + 16*c*x*(2*arctan2(1, c*x) - 6*I) + 192*(-I*c*x - 1)*arctan(c*x)^2 + 48*(-I*c*x - 1)*log(c^2*x^2 + 1)^2 + 48*(c^5*d^2*x - I*c^4*d^2)*((c*(x/(c^7*d^2*x^2 + c^5*d^2) + arctan(c*x)/(c^6*d^2)) - 2*arctan(c*x)/(c^7*d^2*x^2 + c^5*d^2))*c + 16*integrate(1/8*log(c^2*x^2 + 1)/(c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2), x)) + (48*I*c^5*d^2*x + 48*c^4*d^2)*(c*(c^2/(c^9*d^2*x^2 + c^7*d^2) + log(c^2*x^2 + 1)/(c^7*d^2*x^2 + c^5*d^2)) + 32*integrate(1/8*arctan(c*x)/(c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2), x)) - 96*(c^6*d^2*x - I*c^5*d^2)*(c*(x/(c^7*d^2*x^2 + c^5*d^2) + arctan(c*x)/(c^6*d^2)) - 16*c*integrate(1/8*x^2*log(c^2*x^2 + 1)/(c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2), x) - 2*arctan(c*x)/(c^7*d^2*x^2 + c^5*d^2)) - (-96*I*c^6*d^2*x - 96*c^5*d^2)*(32*c*integrate(1/8*x^2*arctan(c*x)/(c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2), x) - c^2/(c^9*d^2*x^2 + c^7*d^2) - log(c^2*x^2 + 1)/(c^7*d^2*x^2 + c^5*d^2)) + 16*(2*c^3*x^3 + 6*I*c^2*x^2 + 8*c*x + 4*I)*arctan(c*x) + 256*(c^9*d^2*x - I*c^8*d^2)*integrate(1/8*(2*c*x^5*arctan(c*x) + x^4*log(c^2*x^2 + 1))/(c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2), x) - 16*(16*I*c^9*d^2*x + 16*c^8*d^2)*integrate(1/8*(c*x^5*log(c^2*x^2 + 1) - 2*x^4*arctan(c*x))/(c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2), x) - 16*(-16*I*c^8*d^2*x - 16*c^7*d^2)*integrate(1/8*(2*c*x^4*arctan(c*x) + x^3*log(c^2*x^2 + 1))/(c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2), x) + 256*(c^8*d^2*x - I*c^7*d^2)*integrate(1/8*(c*x^4*log(c^2*x^2 + 1) - 2*x^3*arctan(c*x))/(c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2), x) - 768*(c^7*d^2*x - I*c^6*d^2)*integrate(1/8*(2*c*x^3*arctan(c*x) + x^2*log(c^2*x^2 + 1))/(c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2), x) - 16*(-48*I*c^7*d^2*x - 48*c^6*d^2)*integrate(1/8*(c*x^3*log(c^2*x^2 + 1) - 2*x^2*arctan(c*x))/(c^7*d^2*x^4 + 2*c^5*d^2*x^2 + c^3*d^2), x) - 16*(-I*c^3*x^3 + 3*c^2*x^2 - I*c*x + 5)*log(c^2*x^2 + 1) - 32*I*arctan2(1, c*x))*b/(c^5*d^2*x - I*c^4*d^2)","F",0
52,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x, algorithm=""maxima"")","-a {\left(\frac{1}{c^{4} d^{2} x - i \, c^{3} d^{2}} + \frac{x}{c^{2} d^{2}} + \frac{2 i \, \log\left(c x - i\right)}{c^{3} d^{2}}\right)} - \frac{-\frac{1}{8} \, {\left(128 i \, c^{2} x^{2} + 64 \, {\left(4 \, c x - 4 i\right)} \arctan\left(c x\right)^{2} + 64 \, {\left(c x - i\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 48 \, {\left(c^{6} d^{2} x - i \, c^{5} d^{2}\right)} {\left(\frac{{\left({\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 2\right)} c^{3}}{c^{10} d^{2} x^{2} + c^{8} d^{2}} - 2 \, c {\left(\frac{1}{c^{8} d^{2} x^{2} + c^{6} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{6} d^{2}}\right)} \log\left(c^{2} x^{2} + 1\right) - 4 \, {\left(\frac{x}{c^{6} d^{2} x^{2} + c^{4} d^{2}} - \frac{\arctan\left(c x\right)}{c^{5} d^{2}}\right)} \arctan\left(c x\right) - \frac{2 \, {\left({\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} + 1\right)} c}{c^{8} d^{2} x^{2} + c^{6} d^{2}}\right)} - 16 \, {\left(c^{7} d^{2} x - i \, c^{6} d^{2}\right)} {\left(4 \, c {\left(\frac{x}{c^{8} d^{2} x^{2} + c^{6} d^{2}} + \frac{2 \, x}{c^{6} d^{2}} - \frac{3 \, \arctan\left(c x\right)}{c^{7} d^{2}}\right)} \arctan\left(c x\right) + \frac{2 \, {\left(3 \, {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} - 2 \, {\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right) + 1\right)} c^{2}}{c^{10} d^{2} x^{2} + c^{8} d^{2}} - \frac{{\left({\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 2\right)} c^{2}}{c^{10} d^{2} x^{2} + c^{8} d^{2}} + 2 \, {\left(\frac{1}{c^{8} d^{2} x^{2} + c^{6} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{6} d^{2}}\right)} \log\left(c^{2} x^{2} + 1\right)\right)} + 8 \, {\left(8 i \, c^{4} d^{2} x + 8 \, c^{3} d^{2}\right)} {\left({\left(c {\left(\frac{x}{c^{6} d^{2} x^{2} + c^{4} d^{2}} + \frac{\arctan\left(c x\right)}{c^{5} d^{2}}\right)} - \frac{2 \, \arctan\left(c x\right)}{c^{6} d^{2} x^{2} + c^{4} d^{2}}\right)} c + 2 \, \int \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{6} d^{2} x^{4} + 2 \, c^{4} d^{2} x^{2} + c^{2} d^{2}}\,{d x}\right)} + 128 \, {\left(c^{5} d^{2} x - i \, c^{4} d^{2}\right)} {\left({\left(2 \, {\left(\frac{x}{c^{6} d^{2} x^{2} + c^{4} d^{2}} - \frac{\arctan\left(c x\right)}{c^{5} d^{2}}\right)} \arctan\left(c x\right) + \frac{{\left({\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} + 1\right)} c}{c^{8} d^{2} x^{2} + c^{6} d^{2}}\right)} c + \frac{c^{2}}{c^{8} d^{2} x^{2} + c^{6} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{6} d^{2} x^{2} + c^{4} d^{2}}\right)} - 64 \, {\left(c^{4} d^{2} x - i \, c^{3} d^{2}\right)} {\left(c {\left(\frac{c^{2}}{c^{8} d^{2} x^{2} + c^{6} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{6} d^{2} x^{2} + c^{4} d^{2}}\right)} + 2 \, {\left(\frac{x}{c^{4} d^{2} x^{2} + c^{2} d^{2}} + \frac{\arctan\left(c x\right)}{c^{3} d^{2}}\right)} \arctan\left(c x\right) - \frac{{\left({\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} - 1\right)} c}{c^{6} d^{2} x^{2} + c^{4} d^{2}}\right)} - 8 \, {\left(16 i \, c^{5} d^{2} x + 16 \, c^{4} d^{2}\right)} {\left(c {\left(\frac{x}{c^{6} d^{2} x^{2} + c^{4} d^{2}} + \frac{\arctan\left(c x\right)}{c^{5} d^{2}}\right)} - 2 \, c \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{c^{6} d^{2} x^{4} + 2 \, c^{4} d^{2} x^{2} + c^{2} d^{2}}\,{d x} - \frac{2 \, \arctan\left(c x\right)}{c^{6} d^{2} x^{2} + c^{4} d^{2}}\right)} + 128 \, c x - 128 \, {\left(c^{2} x^{2} - i \, c x + 1\right)} \arctan\left(c x\right) + 64 \, {\left(-i \, c^{2} x^{2} - 2 i\right)} \log\left(c^{2} x^{2} + 1\right) - \frac{{\left(4 i \, c^{7} d^{2} x + 4 \, c^{6} d^{2}\right)} {\left(32 \, c^{3} x^{3} + 6 \, c^{2} x^{2} \arctan\left(1, c x\right) + 12 \, c x - 3 \, {\left(9 \, c^{2} x^{2} + 1\right)} \arctan\left(c x\right) + 3 \, {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x, -1\right) - 16 \, {\left(c^{10} d^{2} x^{2} + c^{8} d^{2}\right)} \int \frac{x^{3} \arctan\left(c x\right)}{c^{8} d^{2} x^{4} + 2 \, c^{6} d^{2} x^{2} + c^{4} d^{2}}\,{d x} - 8 \, {\left(2 \, c^{3} x^{3} + 3 \, c x - 3 \, {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right) + 6 \, \arctan\left(1, c x\right)\right)}}{c^{8} d^{2} x^{2} + c^{6} d^{2}} + \frac{{\left(-12 i \, c^{6} d^{2} x - 12 \, c^{5} d^{2}\right)} {\left(2 \, c^{2} x^{2} \arctan\left(1, c x\right) - 12 \, c x + {\left(7 \, c^{2} x^{2} + 15\right)} \arctan\left(c x\right) + {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x, -1\right) + 16 \, {\left(c^{9} d^{2} x^{2} + c^{7} d^{2}\right)} \int \frac{x^{3} \arctan\left(c x\right)}{c^{7} d^{2} x^{4} + 2 \, c^{5} d^{2} x^{2} + c^{3} d^{2}}\,{d x} - 8 \, {\left(c x - {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right) + 2 \, \arctan\left(1, c x\right)\right)}}{c^{7} d^{2} x^{2} + c^{5} d^{2}}\right)} b}{32 \, {\left(c^{4} d^{2} x - i \, c^{3} d^{2}\right)}}"," ",0,"-a*(1/(c^4*d^2*x - I*c^3*d^2) + x/(c^2*d^2) + 2*I*log(c*x - I)/(c^3*d^2)) - 1/32*(-16*I*c^2*x^2 - 8*(4*c*x - 4*I)*arctan(c*x)^2 - 8*(c*x - I)*log(c^2*x^2 + 1)^2 - (8*I*c^4*d^2*x + 8*c^3*d^2)*((c*(x/(c^6*d^2*x^2 + c^4*d^2) + arctan(c*x)/(c^5*d^2)) - 2*arctan(c*x)/(c^6*d^2*x^2 + c^4*d^2))*c + 8*integrate(1/4*log(c^2*x^2 + 1)/(c^6*d^2*x^4 + 2*c^4*d^2*x^2 + c^2*d^2), x)) + 8*(c^4*d^2*x - I*c^3*d^2)*(c*(c^2/(c^8*d^2*x^2 + c^6*d^2) + log(c^2*x^2 + 1)/(c^6*d^2*x^2 + c^4*d^2)) + 16*integrate(1/4*arctan(c*x)/(c^6*d^2*x^4 + 2*c^4*d^2*x^2 + c^2*d^2), x)) + (16*I*c^5*d^2*x + 16*c^4*d^2)*(c*(x/(c^6*d^2*x^2 + c^4*d^2) + arctan(c*x)/(c^5*d^2)) - 8*c*integrate(1/4*x^2*log(c^2*x^2 + 1)/(c^6*d^2*x^4 + 2*c^4*d^2*x^2 + c^2*d^2), x) - 2*arctan(c*x)/(c^6*d^2*x^2 + c^4*d^2)) + 16*(c^5*d^2*x - I*c^4*d^2)*(16*c*integrate(1/4*x^2*arctan(c*x)/(c^6*d^2*x^4 + 2*c^4*d^2*x^2 + c^2*d^2), x) - c^2/(c^8*d^2*x^2 + c^6*d^2) - log(c^2*x^2 + 1)/(c^6*d^2*x^2 + c^4*d^2)) - 16*c*x + 16*(c^2*x^2 - I*c*x + 1)*arctan(c*x) + 32*(c^7*d^2*x - I*c^6*d^2)*integrate(1/4*(2*c*x^4*arctan(c*x) + x^3*log(c^2*x^2 + 1))/(c^6*d^2*x^4 + 2*c^4*d^2*x^2 + c^2*d^2), x) - 8*(4*I*c^7*d^2*x + 4*c^6*d^2)*integrate(1/4*(c*x^4*log(c^2*x^2 + 1) - 2*x^3*arctan(c*x))/(c^6*d^2*x^4 + 2*c^4*d^2*x^2 + c^2*d^2), x) - 8*(-12*I*c^6*d^2*x - 12*c^5*d^2)*integrate(1/4*(2*c*x^3*arctan(c*x) + x^2*log(c^2*x^2 + 1))/(c^6*d^2*x^4 + 2*c^4*d^2*x^2 + c^2*d^2), x) + 96*(c^6*d^2*x - I*c^5*d^2)*integrate(1/4*(c*x^3*log(c^2*x^2 + 1) - 2*x^2*arctan(c*x))/(c^6*d^2*x^4 + 2*c^4*d^2*x^2 + c^2*d^2), x) - 8*(-I*c^2*x^2 - 2*I)*log(c^2*x^2 + 1))*b/(c^4*d^2*x - I*c^3*d^2)","F",0
53,0,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))/(d+I*c*d*x)^2,x, algorithm=""maxima"")","a {\left(\frac{i}{c^{3} d^{2} x - i \, c^{2} d^{2}} - \frac{\log\left(c x - i\right)}{c^{2} d^{2}}\right)} - \frac{\frac{1}{2} \, {\left(64 \, {\left(i \, c x + 1\right)} \arctan\left(c x\right)^{2} + 64 \, c x \arctan\left(1, c x\right) - 16 \, {\left(-i \, c x - 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + {\left(16 i \, c^{5} d^{2} x + 16 \, c^{4} d^{2}\right)} {\left(\frac{{\left({\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 2\right)} c^{3}}{c^{9} d^{2} x^{2} + c^{7} d^{2}} - 2 \, c {\left(\frac{1}{c^{7} d^{2} x^{2} + c^{5} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{5} d^{2}}\right)} \log\left(c^{2} x^{2} + 1\right) - 4 \, {\left(\frac{x}{c^{5} d^{2} x^{2} + c^{3} d^{2}} - \frac{\arctan\left(c x\right)}{c^{4} d^{2}}\right)} \arctan\left(c x\right) - \frac{2 \, {\left({\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} + 1\right)} c}{c^{7} d^{2} x^{2} + c^{5} d^{2}}\right)} - 16 \, {\left(c^{3} d^{2} x - i \, c^{2} d^{2}\right)} {\left({\left(c {\left(\frac{x}{c^{5} d^{2} x^{2} + c^{3} d^{2}} + \frac{\arctan\left(c x\right)}{c^{4} d^{2}}\right)} - \frac{2 \, \arctan\left(c x\right)}{c^{5} d^{2} x^{2} + c^{3} d^{2}}\right)} c + 2 \, \int \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{5} d^{2} x^{4} + 2 \, c^{3} d^{2} x^{2} + c d^{2}}\,{d x}\right)} + 2 \, {\left(8 i \, c^{4} d^{2} x + 8 \, c^{3} d^{2}\right)} {\left({\left(2 \, {\left(\frac{x}{c^{5} d^{2} x^{2} + c^{3} d^{2}} - \frac{\arctan\left(c x\right)}{c^{4} d^{2}}\right)} \arctan\left(c x\right) + \frac{{\left({\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} + 1\right)} c}{c^{7} d^{2} x^{2} + c^{5} d^{2}}\right)} c + \frac{c^{2}}{c^{7} d^{2} x^{2} + c^{5} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{5} d^{2} x^{2} + c^{3} d^{2}}\right)} + 2 \, {\left(-8 i \, c^{3} d^{2} x - 8 \, c^{2} d^{2}\right)} {\left(c {\left(\frac{c^{2}}{c^{7} d^{2} x^{2} + c^{5} d^{2}} + \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{5} d^{2} x^{2} + c^{3} d^{2}}\right)} + 2 \, {\left(\frac{x}{c^{3} d^{2} x^{2} + c d^{2}} + \frac{\arctan\left(c x\right)}{c^{2} d^{2}}\right)} \arctan\left(c x\right) - \frac{{\left({\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)^{2} - 1\right)} c}{c^{5} d^{2} x^{2} + c^{3} d^{2}}\right)} + 16 \, {\left(c^{4} d^{2} x - i \, c^{3} d^{2}\right)} {\left(c {\left(\frac{x}{c^{5} d^{2} x^{2} + c^{3} d^{2}} + \frac{\arctan\left(c x\right)}{c^{4} d^{2}}\right)} - 2 \, c \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{c^{5} d^{2} x^{4} + 2 \, c^{3} d^{2} x^{2} + c d^{2}}\,{d x} - \frac{2 \, \arctan\left(c x\right)}{c^{5} d^{2} x^{2} + c^{3} d^{2}}\right)} + \frac{4 \, {\left(c^{5} d^{2} x - i \, c^{4} d^{2}\right)} {\left(2 \, c^{2} x^{2} \arctan\left(1, c x\right) - 12 \, c x + {\left(7 \, c^{2} x^{2} + 15\right)} \arctan\left(c x\right) + {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x, -1\right) + 16 \, {\left(c^{8} d^{2} x^{2} + c^{6} d^{2}\right)} \int \frac{x^{3} \arctan\left(c x\right)}{c^{6} d^{2} x^{4} + 2 \, c^{4} d^{2} x^{2} + c^{2} d^{2}}\,{d x} - 8 \, {\left(c x - {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right) + 2 \, \arctan\left(1, c x\right)\right)}}{c^{6} d^{2} x^{2} + c^{4} d^{2}} - 64 i \, \arctan\left(c x\right) - 64 i \, \arctan\left(1, c x\right) + 32 \, \log\left(c^{2} x^{2} + 1\right)\right)} b}{64 \, {\left(c^{3} d^{2} x - i \, c^{2} d^{2}\right)}}"," ",0,"a*(I/(c^3*d^2*x - I*c^2*d^2) - log(c*x - I)/(c^2*d^2)) - 1/64*(32*(I*c*x + 1)*arctan(c*x)^2 + 32*c*x*arctan2(1, c*x) - 8*(-I*c*x - 1)*log(c^2*x^2 + 1)^2 - 8*(c^3*d^2*x - I*c^2*d^2)*((c*(x/(c^5*d^2*x^2 + c^3*d^2) + arctan(c*x)/(c^4*d^2)) - 2*arctan(c*x)/(c^5*d^2*x^2 + c^3*d^2))*c + 8*integrate(1/4*log(c^2*x^2 + 1)/(c^5*d^2*x^4 + 2*c^3*d^2*x^2 + c*d^2), x)) + (-8*I*c^3*d^2*x - 8*c^2*d^2)*(c*(c^2/(c^7*d^2*x^2 + c^5*d^2) + log(c^2*x^2 + 1)/(c^5*d^2*x^2 + c^3*d^2)) + 16*integrate(1/4*arctan(c*x)/(c^5*d^2*x^4 + 2*c^3*d^2*x^2 + c*d^2), x)) + 8*(c^4*d^2*x - I*c^3*d^2)*(c*(x/(c^5*d^2*x^2 + c^3*d^2) + arctan(c*x)/(c^4*d^2)) - 8*c*integrate(1/4*x^2*log(c^2*x^2 + 1)/(c^5*d^2*x^4 + 2*c^3*d^2*x^2 + c*d^2), x) - 2*arctan(c*x)/(c^5*d^2*x^2 + c^3*d^2)) - (8*I*c^4*d^2*x + 8*c^3*d^2)*(16*c*integrate(1/4*x^2*arctan(c*x)/(c^5*d^2*x^4 + 2*c^3*d^2*x^2 + c*d^2), x) - c^2/(c^7*d^2*x^2 + c^5*d^2) - log(c^2*x^2 + 1)/(c^5*d^2*x^2 + c^3*d^2)) + 128*(c^5*d^2*x - I*c^4*d^2)*integrate(1/4*(2*c*x^3*arctan(c*x) + x^2*log(c^2*x^2 + 1))/(c^5*d^2*x^4 + 2*c^3*d^2*x^2 + c*d^2), x) - 8*(16*I*c^5*d^2*x + 16*c^4*d^2)*integrate(1/4*(c*x^3*log(c^2*x^2 + 1) - 2*x^2*arctan(c*x))/(c^5*d^2*x^4 + 2*c^3*d^2*x^2 + c*d^2), x) - 32*I*arctan(c*x) - 32*I*arctan2(1, c*x) + 16*log(c^2*x^2 + 1))*b/(c^3*d^2*x - I*c^2*d^2)","F",0
54,-2,0,0,0.000000," ","integrate((a+b*arctan(c*x))/(d+I*c*d*x)^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
55,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x/(d+I*c*d*x)^2,x, algorithm=""maxima"")","{\left(-2 i \, c \int \frac{\arctan\left(c x\right)}{c^{4} d^{2} x^{4} + 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x} - \int \frac{{\left(c^{2} x^{2} - 1\right)} \arctan\left(c x\right)}{c^{4} d^{2} x^{5} + 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x}\right)} b + a {\left(-\frac{i}{c d^{2} x - i \, d^{2}} - \frac{\log\left(c x - i\right)}{d^{2}} + \frac{\log\left(x\right)}{d^{2}}\right)}"," ",0,"(-2*I*c*integrate(arctan(c*x)/(c^4*d^2*x^4 + 2*c^2*d^2*x^2 + d^2), x) - integrate((c^2*x^2 - 1)*arctan(c*x)/(c^4*d^2*x^5 + 2*c^2*d^2*x^3 + d^2*x), x))*b + a*(-I/(c*d^2*x - I*d^2) - log(c*x - I)/d^2 + log(x)/d^2)","F",0
56,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^2/(d+I*c*d*x)^2,x, algorithm=""maxima"")","{\left(-2 i \, c \int \frac{\arctan\left(c x\right)}{c^{4} d^{2} x^{5} + 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x} - \int \frac{{\left(c^{2} x^{2} - 1\right)} \arctan\left(c x\right)}{c^{4} d^{2} x^{6} + 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}}\,{d x}\right)} b - a {\left(\frac{c}{c d^{2} x - i \, d^{2}} - \frac{2 i \, c \log\left(c x - i\right)}{d^{2}} + \frac{2 i \, c \log\left(x\right)}{d^{2}} + \frac{1}{d^{2} x}\right)}"," ",0,"(-2*I*c*integrate(arctan(c*x)/(c^4*d^2*x^5 + 2*c^2*d^2*x^3 + d^2*x), x) - integrate((c^2*x^2 - 1)*arctan(c*x)/(c^4*d^2*x^6 + 2*c^2*d^2*x^4 + d^2*x^2), x))*b - a*(c/(c*d^2*x - I*d^2) - 2*I*c*log(c*x - I)/d^2 + 2*I*c*log(x)/d^2 + 1/(d^2*x))","F",0
57,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^3/(d+I*c*d*x)^2,x, algorithm=""maxima"")","{\left(-2 i \, c \int \frac{\arctan\left(c x\right)}{c^{4} d^{2} x^{6} + 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}}\,{d x} - \int \frac{{\left(c^{2} x^{2} - 1\right)} \arctan\left(c x\right)}{c^{4} d^{2} x^{7} + 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}\,{d x}\right)} b - \frac{1}{2} \, a {\left(-\frac{2 i \, c^{2}}{c d^{2} x - i \, d^{2}} - \frac{6 \, c^{2} \log\left(c x - i\right)}{d^{2}} + \frac{6 \, c^{2} \log\left(x\right)}{d^{2}} - \frac{4 i \, c x - 1}{d^{2} x^{2}}\right)}"," ",0,"(-2*I*c*integrate(arctan(c*x)/(c^4*d^2*x^6 + 2*c^2*d^2*x^4 + d^2*x^2), x) - integrate((c^2*x^2 - 1)*arctan(c*x)/(c^4*d^2*x^7 + 2*c^2*d^2*x^5 + d^2*x^3), x))*b - 1/2*a*(-2*I*c^2/(c*d^2*x - I*d^2) - 6*c^2*log(c*x - I)/d^2 + 6*c^2*log(x)/d^2 - (4*I*c*x - 1)/(d^2*x^2))","F",0
58,1,356,0,0.445638," ","integrate(x^4*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x, algorithm=""maxima"")","\frac{8 i \, a c^{4} x^{4} - 8 \, {\left(4 \, a + i \, b\right)} c^{3} x^{3} + {\left(b {\left(5 i \, \arctan\left(1, c x\right) - 16\right)} + 88 i \, a\right)} c^{2} x^{2} + {\left(b {\left(10 \, \arctan\left(1, c x\right) + 38 i\right)} - 16 \, a\right)} c x + {\left(24 \, b c^{2} x^{2} - 48 i \, b c x - 24 \, b\right)} \arctan\left(c x\right)^{2} + {\left(6 \, b c^{2} x^{2} - 12 i \, b c x - 6 \, b\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + {\left(-24 i \, b c^{2} x^{2} - 48 \, b c x + 24 i \, b\right)} \arctan\left(c x\right) \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right) + b {\left(-5 i \, \arctan\left(1, c x\right) + 28\right)} + {\left(8 i \, b c^{4} x^{4} - 32 \, b c^{3} x^{3} + {\left(96 \, a + 131 i \, b\right)} c^{2} x^{2} + {\left(-192 i \, a + 70 \, b\right)} c x - 96 \, a + 13 i \, b\right)} \arctan\left(c x\right) - {\left(48 \, b c^{2} x^{2} - 96 i \, b c x - 48 \, b\right)} {\rm Li}_2\left(\frac{1}{2} i \, c x + \frac{1}{2}\right) + {\left({\left(-48 i \, a + 24 \, b\right)} c^{2} x^{2} - 48 \, {\left(2 \, a + i \, b\right)} c x - {\left(12 \, b c^{2} x^{2} - 24 i \, b c x - 12 \, b\right)} \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right) + 48 i \, a - 24 \, b\right)} \log\left(c^{2} x^{2} + 1\right) + 56 i \, a}{16 \, c^{7} d^{3} x^{2} - 32 i \, c^{6} d^{3} x - 16 \, c^{5} d^{3}}"," ",0,"(8*I*a*c^4*x^4 - 8*(4*a + I*b)*c^3*x^3 + (b*(5*I*arctan2(1, c*x) - 16) + 88*I*a)*c^2*x^2 + (b*(10*arctan2(1, c*x) + 38*I) - 16*a)*c*x + (24*b*c^2*x^2 - 48*I*b*c*x - 24*b)*arctan(c*x)^2 + (6*b*c^2*x^2 - 12*I*b*c*x - 6*b)*log(c^2*x^2 + 1)^2 + (-24*I*b*c^2*x^2 - 48*b*c*x + 24*I*b)*arctan(c*x)*log(1/4*c^2*x^2 + 1/4) + b*(-5*I*arctan2(1, c*x) + 28) + (8*I*b*c^4*x^4 - 32*b*c^3*x^3 + (96*a + 131*I*b)*c^2*x^2 + (-192*I*a + 70*b)*c*x - 96*a + 13*I*b)*arctan(c*x) - (48*b*c^2*x^2 - 96*I*b*c*x - 48*b)*dilog(1/2*I*c*x + 1/2) + ((-48*I*a + 24*b)*c^2*x^2 - 48*(2*a + I*b)*c*x - (12*b*c^2*x^2 - 24*I*b*c*x - 12*b)*log(1/4*c^2*x^2 + 1/4) + 48*I*a - 24*b)*log(c^2*x^2 + 1) + 56*I*a)/(16*c^7*d^3*x^2 - 32*I*c^6*d^3*x - 16*c^5*d^3)","A",0
59,1,327,0,0.426837," ","integrate(x^3*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x, algorithm=""maxima"")","-\frac{-16 i \, a c^{3} x^{3} - 32 \, a c^{2} x^{2} + {\left(-32 i \, a - 22 \, b\right)} c x + {\left(12 i \, b c^{2} x^{2} + 24 \, b c x - 12 i \, b\right)} \arctan\left(c x\right)^{2} + {\left(3 i \, b c^{2} x^{2} + 6 \, b c x - 3 i \, b\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + {\left(12 \, b c^{2} x^{2} - 24 i \, b c x - 12 \, b\right)} \arctan\left(c x\right) \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right) + {\left(-16 i \, b c^{3} x^{3} + {\left(48 i \, a - 51 \, b\right)} c^{2} x^{2} + 6 \, {\left(16 \, a + i \, b\right)} c x - 48 i \, a - 21 \, b\right)} \arctan\left(c x\right) + {\left(3 \, b c^{2} x^{2} - 6 i \, b c x - 3 \, b\right)} \arctan\left(c x, -1\right) + {\left(-24 i \, b c^{2} x^{2} - 48 \, b c x + 24 i \, b\right)} {\rm Li}_2\left(\frac{1}{2} i \, c x + \frac{1}{2}\right) + {\left(8 \, {\left(3 \, a + i \, b\right)} c^{2} x^{2} + {\left(-48 i \, a + 16 \, b\right)} c x + {\left(-6 i \, b c^{2} x^{2} - 12 \, b c x + 6 i \, b\right)} \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right) - 24 \, a - 8 i \, b\right)} \log\left(c^{2} x^{2} + 1\right) - 40 \, a + 20 i \, b}{16 \, c^{6} d^{3} x^{2} - 32 i \, c^{5} d^{3} x - 16 \, c^{4} d^{3}}"," ",0,"-(-16*I*a*c^3*x^3 - 32*a*c^2*x^2 + (-32*I*a - 22*b)*c*x + (12*I*b*c^2*x^2 + 24*b*c*x - 12*I*b)*arctan(c*x)^2 + (3*I*b*c^2*x^2 + 6*b*c*x - 3*I*b)*log(c^2*x^2 + 1)^2 + (12*b*c^2*x^2 - 24*I*b*c*x - 12*b)*arctan(c*x)*log(1/4*c^2*x^2 + 1/4) + (-16*I*b*c^3*x^3 + (48*I*a - 51*b)*c^2*x^2 + 6*(16*a + I*b)*c*x - 48*I*a - 21*b)*arctan(c*x) + (3*b*c^2*x^2 - 6*I*b*c*x - 3*b)*arctan2(c*x, -1) + (-24*I*b*c^2*x^2 - 48*b*c*x + 24*I*b)*dilog(1/2*I*c*x + 1/2) + (8*(3*a + I*b)*c^2*x^2 + (-48*I*a + 16*b)*c*x + (-6*I*b*c^2*x^2 - 12*b*c*x + 6*I*b)*log(1/4*c^2*x^2 + 1/4) - 24*a - 8*I*b)*log(c^2*x^2 + 1) - 40*a + 20*I*b)/(16*c^6*d^3*x^2 - 32*I*c^5*d^3*x - 16*c^4*d^3)","A",0
60,1,293,0,0.394862," ","integrate(x^2*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x, algorithm=""maxima"")","-\frac{-7 i \, b c^{2} x^{2} \arctan\left(1, c x\right) - {\left(b {\left(14 \, \arctan\left(1, c x\right) - 14 i\right)} + 32 \, a\right)} c x + {\left(4 \, b c^{2} x^{2} - 8 i \, b c x - 4 \, b\right)} \arctan\left(c x\right)^{2} + {\left(b c^{2} x^{2} - 2 i \, b c x - b\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + {\left(-4 i \, b c^{2} x^{2} - 8 \, b c x + 4 i \, b\right)} \arctan\left(c x\right) \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right) + b {\left(7 i \, \arctan\left(1, c x\right) + 12\right)} + {\left({\left(16 \, a + 7 i \, b\right)} c^{2} x^{2} + {\left(-32 i \, a - 18 \, b\right)} c x - 16 \, a + 17 i \, b\right)} \arctan\left(c x\right) - {\left(8 \, b c^{2} x^{2} - 16 i \, b c x - 8 \, b\right)} {\rm Li}_2\left(\frac{1}{2} i \, c x + \frac{1}{2}\right) + {\left(-8 i \, a c^{2} x^{2} - 16 \, a c x - {\left(2 \, b c^{2} x^{2} - 4 i \, b c x - 2 \, b\right)} \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right) + 8 i \, a\right)} \log\left(c^{2} x^{2} + 1\right) + 24 i \, a}{16 \, c^{5} d^{3} x^{2} - 32 i \, c^{4} d^{3} x - 16 \, c^{3} d^{3}}"," ",0,"-(-7*I*b*c^2*x^2*arctan2(1, c*x) - (b*(14*arctan2(1, c*x) - 14*I) + 32*a)*c*x + (4*b*c^2*x^2 - 8*I*b*c*x - 4*b)*arctan(c*x)^2 + (b*c^2*x^2 - 2*I*b*c*x - b)*log(c^2*x^2 + 1)^2 + (-4*I*b*c^2*x^2 - 8*b*c*x + 4*I*b)*arctan(c*x)*log(1/4*c^2*x^2 + 1/4) + b*(7*I*arctan2(1, c*x) + 12) + ((16*a + 7*I*b)*c^2*x^2 + (-32*I*a - 18*b)*c*x - 16*a + 17*I*b)*arctan(c*x) - (8*b*c^2*x^2 - 16*I*b*c*x - 8*b)*dilog(1/2*I*c*x + 1/2) + (-8*I*a*c^2*x^2 - 16*a*c*x - (2*b*c^2*x^2 - 4*I*b*c*x - 2*b)*log(1/4*c^2*x^2 + 1/4) + 8*I*a)*log(c^2*x^2 + 1) + 24*I*a)/(16*c^5*d^3*x^2 - 32*I*c^4*d^3*x - 16*c^3*d^3)","A",0
61,1,71,0,0.340984," ","integrate(x*(a+b*arctan(c*x))/(d+I*c*d*x)^3,x, algorithm=""maxima"")","-\frac{{\left(8 i \, a + 3 \, b\right)} c x + {\left(3 \, b c^{2} x^{2} + 2 i \, b c x + b\right)} \arctan\left(c x\right) + 4 \, a - 2 i \, b}{8 \, c^{4} d^{3} x^{2} - 16 i \, c^{3} d^{3} x - 8 \, c^{2} d^{3}}"," ",0,"-((8*I*a + 3*b)*c*x + (3*b*c^2*x^2 + 2*I*b*c*x + b)*arctan(c*x) + 4*a - 2*I*b)/(8*c^4*d^3*x^2 - 16*I*c^3*d^3*x - 8*c^2*d^3)","A",0
62,1,66,0,0.345502," ","integrate((a+b*arctan(c*x))/(d+I*c*d*x)^3,x, algorithm=""maxima"")","-\frac{i \, b c x + {\left(i \, b c^{2} x^{2} + 2 \, b c x + 3 i \, b\right)} \arctan\left(c x\right) + 4 i \, a + 2 \, b}{8 \, c^{3} d^{3} x^{2} - 16 i \, c^{2} d^{3} x - 8 \, c d^{3}}"," ",0,"-(I*b*c*x + (I*b*c^2*x^2 + 2*b*c*x + 3*I*b)*arctan(c*x) + 4*I*a + 2*b)/(8*c^3*d^3*x^2 - 16*I*c^2*d^3*x - 8*c*d^3)","A",0
63,1,399,0,0.422000," ","integrate((a+b*arctan(c*x))/x/(d+I*c*d*x)^3,x, algorithm=""maxima"")","-\frac{{\left(16 i \, a + 10 \, b\right)} c x + {\left(4 i \, b c^{2} x^{2} + 8 \, b c x - 4 i \, b\right)} \arctan\left(c x\right)^{2} + {\left(i \, b c^{2} x^{2} + 2 \, b c x - i \, b\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + {\left(4 \, b c^{2} x^{2} - 8 i \, b c x - 4 \, b\right)} \arctan\left(c x\right) \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right) - {\left(16 \, b c^{2} x^{2} - 32 i \, b c x - 16 \, b\right)} \arctan\left(c x\right) \log\left(c x\right) + {\left({\left(16 i \, a + 5 \, b\right)} c^{2} x^{2} + 2 \, {\left(16 \, a + 3 i \, b\right)} c x - 16 i \, a + 19 \, b\right)} \arctan\left(c x\right) - {\left(5 \, b c^{2} x^{2} - 10 i \, b c x - 5 \, b\right)} \arctan\left(c x, -1\right) + {\left(8 i \, b c^{2} x^{2} + 16 \, b c x - 8 i \, b\right)} {\rm Li}_2\left(i \, c x + 1\right) + {\left(-8 i \, b c^{2} x^{2} - 16 \, b c x + 8 i \, b\right)} {\rm Li}_2\left(\frac{1}{2} i \, c x + \frac{1}{2}\right) + {\left(-8 i \, b c^{2} x^{2} - 16 \, b c x + 8 i \, b\right)} {\rm Li}_2\left(-i \, c x + 1\right) + {\left(4 \, {\left(\pi b + 2 \, a\right)} c^{2} x^{2} + {\left(-8 i \, \pi b - 16 i \, a\right)} c x - 4 \, \pi b + {\left(-2 i \, b c^{2} x^{2} - 4 \, b c x + 2 i \, b\right)} \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right) - 8 \, a\right)} \log\left(c^{2} x^{2} + 1\right) - 16 \, {\left(a c^{2} x^{2} - 2 i \, a c x - a\right)} \log\left(x\right) + 24 \, a - 12 i \, b}{16 \, c^{2} d^{3} x^{2} - 32 i \, c d^{3} x - 16 \, d^{3}}"," ",0,"-((16*I*a + 10*b)*c*x + (4*I*b*c^2*x^2 + 8*b*c*x - 4*I*b)*arctan(c*x)^2 + (I*b*c^2*x^2 + 2*b*c*x - I*b)*log(c^2*x^2 + 1)^2 + (4*b*c^2*x^2 - 8*I*b*c*x - 4*b)*arctan(c*x)*log(1/4*c^2*x^2 + 1/4) - (16*b*c^2*x^2 - 32*I*b*c*x - 16*b)*arctan(c*x)*log(c*x) + ((16*I*a + 5*b)*c^2*x^2 + 2*(16*a + 3*I*b)*c*x - 16*I*a + 19*b)*arctan(c*x) - (5*b*c^2*x^2 - 10*I*b*c*x - 5*b)*arctan2(c*x, -1) + (8*I*b*c^2*x^2 + 16*b*c*x - 8*I*b)*dilog(I*c*x + 1) + (-8*I*b*c^2*x^2 - 16*b*c*x + 8*I*b)*dilog(1/2*I*c*x + 1/2) + (-8*I*b*c^2*x^2 - 16*b*c*x + 8*I*b)*dilog(-I*c*x + 1) + (4*(pi*b + 2*a)*c^2*x^2 + (-8*I*pi*b - 16*I*a)*c*x - 4*pi*b + (-2*I*b*c^2*x^2 - 4*b*c*x + 2*I*b)*log(1/4*c^2*x^2 + 1/4) - 8*a)*log(c^2*x^2 + 1) - 16*(a*c^2*x^2 - 2*I*a*c*x - a)*log(x) + 24*a - 12*I*b)/(16*c^2*d^3*x^2 - 32*I*c*d^3*x - 16*d^3)","B",0
64,1,519,0,0.427772," ","integrate((a+b*arctan(c*x))/x^2/(d+I*c*d*x)^3,x, algorithm=""maxima"")","-\frac{17 i \, b c^{3} x^{3} \arctan\left(1, c x\right) + {\left(b {\left(34 \, \arctan\left(1, c x\right) - 18 i\right)} + 48 \, a\right)} c^{2} x^{2} + {\left(b {\left(-17 i \, \arctan\left(1, c x\right) - 20\right)} - 72 i \, a\right)} c x + {\left(12 \, b c^{3} x^{3} - 24 i \, b c^{2} x^{2} - 12 \, b c x\right)} \arctan\left(c x\right)^{2} + {\left(3 \, b c^{3} x^{3} - 6 i \, b c^{2} x^{2} - 3 \, b c x\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + {\left(-12 i \, b c^{3} x^{3} - 24 \, b c^{2} x^{2} + 12 i \, b c x\right)} \arctan\left(c x\right) \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right) + {\left(48 i \, b c^{3} x^{3} + 96 \, b c^{2} x^{2} - 48 i \, b c x\right)} \arctan\left(c x\right) \log\left(c x\right) + {\left({\left(48 \, a - i \, b\right)} c^{3} x^{3} + {\left(-96 i \, a + 46 \, b\right)} c^{2} x^{2} - {\left(48 \, a + 71 i \, b\right)} c x - 16 \, b\right)} \arctan\left(c x\right) + {\left(24 \, b c^{3} x^{3} - 48 i \, b c^{2} x^{2} - 24 \, b c x\right)} {\rm Li}_2\left(i \, c x + 1\right) - {\left(24 \, b c^{3} x^{3} - 48 i \, b c^{2} x^{2} - 24 \, b c x\right)} {\rm Li}_2\left(\frac{1}{2} i \, c x + \frac{1}{2}\right) - {\left(24 \, b c^{3} x^{3} - 48 i \, b c^{2} x^{2} - 24 \, b c x\right)} {\rm Li}_2\left(-i \, c x + 1\right) - {\left(4 \, {\left({\left(3 i \, \pi - 2\right)} b + 6 i \, a\right)} c^{3} x^{3} + {\left({\left(24 \, \pi + 16 i\right)} b + 48 \, a\right)} c^{2} x^{2} + 4 \, {\left({\left(-3 i \, \pi + 2\right)} b - 6 i \, a\right)} c x + {\left(6 \, b c^{3} x^{3} - 12 i \, b c^{2} x^{2} - 6 \, b c x\right)} \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right)\right)} \log\left(c^{2} x^{2} + 1\right) + {\left({\left(48 i \, a - 16 \, b\right)} c^{3} x^{3} + 32 \, {\left(3 \, a + i \, b\right)} c^{2} x^{2} + {\left(-48 i \, a + 16 \, b\right)} c x\right)} \log\left(x\right) - 16 \, a}{16 \, {\left(c^{2} d^{3} x^{3} - 2 i \, c d^{3} x^{2} - d^{3} x\right)}}"," ",0,"-1/16*(17*I*b*c^3*x^3*arctan2(1, c*x) + (b*(34*arctan2(1, c*x) - 18*I) + 48*a)*c^2*x^2 + (b*(-17*I*arctan2(1, c*x) - 20) - 72*I*a)*c*x + (12*b*c^3*x^3 - 24*I*b*c^2*x^2 - 12*b*c*x)*arctan(c*x)^2 + (3*b*c^3*x^3 - 6*I*b*c^2*x^2 - 3*b*c*x)*log(c^2*x^2 + 1)^2 + (-12*I*b*c^3*x^3 - 24*b*c^2*x^2 + 12*I*b*c*x)*arctan(c*x)*log(1/4*c^2*x^2 + 1/4) + (48*I*b*c^3*x^3 + 96*b*c^2*x^2 - 48*I*b*c*x)*arctan(c*x)*log(c*x) + ((48*a - I*b)*c^3*x^3 + (-96*I*a + 46*b)*c^2*x^2 - (48*a + 71*I*b)*c*x - 16*b)*arctan(c*x) + (24*b*c^3*x^3 - 48*I*b*c^2*x^2 - 24*b*c*x)*dilog(I*c*x + 1) - (24*b*c^3*x^3 - 48*I*b*c^2*x^2 - 24*b*c*x)*dilog(1/2*I*c*x + 1/2) - (24*b*c^3*x^3 - 48*I*b*c^2*x^2 - 24*b*c*x)*dilog(-I*c*x + 1) - (4*((3*I*pi - 2)*b + 6*I*a)*c^3*x^3 + ((24*pi + 16*I)*b + 48*a)*c^2*x^2 + 4*((-3*I*pi + 2)*b - 6*I*a)*c*x + (6*b*c^3*x^3 - 12*I*b*c^2*x^2 - 6*b*c*x)*log(1/4*c^2*x^2 + 1/4))*log(c^2*x^2 + 1) + ((48*I*a - 16*b)*c^3*x^3 + 32*(3*a + I*b)*c^2*x^2 + (-48*I*a + 16*b)*c*x)*log(x) - 16*a)/(c^2*d^3*x^3 - 2*I*c*d^3*x^2 - d^3*x)","B",0
65,1,594,0,0.441777," ","integrate((a+b*arctan(c*x))/x^3/(d+I*c*d*x)^3,x, algorithm=""maxima"")","-\frac{33 \, b c^{4} x^{4} \arctan\left(1, c x\right) + 6 \, {\left(b {\left(-11 i \, \arctan\left(1, c x\right) - 3\right)} - 16 i \, a\right)} c^{3} x^{3} - {\left(b {\left(33 \, \arctan\left(1, c x\right) - 12 i\right)} + 144 \, a\right)} c^{2} x^{2} - {\left(-32 i \, a + 8 \, b\right)} c x - {\left(24 i \, b c^{4} x^{4} + 48 \, b c^{3} x^{3} - 24 i \, b c^{2} x^{2}\right)} \arctan\left(c x\right)^{2} - {\left(6 i \, b c^{4} x^{4} + 12 \, b c^{3} x^{3} - 6 i \, b c^{2} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - {\left(24 \, b c^{4} x^{4} - 48 i \, b c^{3} x^{3} - 24 \, b c^{2} x^{2}\right)} \arctan\left(c x\right) \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right) + {\left(96 \, b c^{4} x^{4} - 192 i \, b c^{3} x^{3} - 96 \, b c^{2} x^{2}\right)} \arctan\left(c x\right) \log\left(c x\right) - {\left({\left(96 i \, a - 15 \, b\right)} c^{4} x^{4} + 6 \, {\left(32 \, a + 21 i \, b\right)} c^{3} x^{3} + {\left(-96 i \, a + 159 \, b\right)} c^{2} x^{2} - 32 i \, b c x + 8 \, b\right)} \arctan\left(c x\right) - {\left(48 i \, b c^{4} x^{4} + 96 \, b c^{3} x^{3} - 48 i \, b c^{2} x^{2}\right)} {\rm Li}_2\left(i \, c x + 1\right) - {\left(-48 i \, b c^{4} x^{4} - 96 \, b c^{3} x^{3} + 48 i \, b c^{2} x^{2}\right)} {\rm Li}_2\left(\frac{1}{2} i \, c x + \frac{1}{2}\right) - {\left(-48 i \, b c^{4} x^{4} - 96 \, b c^{3} x^{3} + 48 i \, b c^{2} x^{2}\right)} {\rm Li}_2\left(-i \, c x + 1\right) - {\left({\left({\left(24 \, \pi + 24 i\right)} b + 48 \, a\right)} c^{4} x^{4} - 48 \, {\left({\left(i \, \pi - 1\right)} b + 2 i \, a\right)} c^{3} x^{3} - {\left({\left(24 \, \pi + 24 i\right)} b + 48 \, a\right)} c^{2} x^{2} + {\left(-12 i \, b c^{4} x^{4} - 24 \, b c^{3} x^{3} + 12 i \, b c^{2} x^{2}\right)} \log\left(\frac{1}{4} \, c^{2} x^{2} + \frac{1}{4}\right)\right)} \log\left(c^{2} x^{2} + 1\right) + {\left(48 \, {\left(2 \, a + i \, b\right)} c^{4} x^{4} - {\left(192 i \, a - 96 \, b\right)} c^{3} x^{3} - 48 \, {\left(2 \, a + i \, b\right)} c^{2} x^{2}\right)} \log\left(x\right) - 8 \, a}{16 \, {\left(c^{2} d^{3} x^{4} - 2 i \, c d^{3} x^{3} - d^{3} x^{2}\right)}}"," ",0,"-1/16*(33*b*c^4*x^4*arctan2(1, c*x) + 6*(b*(-11*I*arctan2(1, c*x) - 3) - 16*I*a)*c^3*x^3 - (b*(33*arctan2(1, c*x) - 12*I) + 144*a)*c^2*x^2 - (-32*I*a + 8*b)*c*x - (24*I*b*c^4*x^4 + 48*b*c^3*x^3 - 24*I*b*c^2*x^2)*arctan(c*x)^2 - (6*I*b*c^4*x^4 + 12*b*c^3*x^3 - 6*I*b*c^2*x^2)*log(c^2*x^2 + 1)^2 - (24*b*c^4*x^4 - 48*I*b*c^3*x^3 - 24*b*c^2*x^2)*arctan(c*x)*log(1/4*c^2*x^2 + 1/4) + (96*b*c^4*x^4 - 192*I*b*c^3*x^3 - 96*b*c^2*x^2)*arctan(c*x)*log(c*x) - ((96*I*a - 15*b)*c^4*x^4 + 6*(32*a + 21*I*b)*c^3*x^3 + (-96*I*a + 159*b)*c^2*x^2 - 32*I*b*c*x + 8*b)*arctan(c*x) - (48*I*b*c^4*x^4 + 96*b*c^3*x^3 - 48*I*b*c^2*x^2)*dilog(I*c*x + 1) - (-48*I*b*c^4*x^4 - 96*b*c^3*x^3 + 48*I*b*c^2*x^2)*dilog(1/2*I*c*x + 1/2) - (-48*I*b*c^4*x^4 - 96*b*c^3*x^3 + 48*I*b*c^2*x^2)*dilog(-I*c*x + 1) - (((24*pi + 24*I)*b + 48*a)*c^4*x^4 - 48*((I*pi - 1)*b + 2*I*a)*c^3*x^3 - ((24*pi + 24*I)*b + 48*a)*c^2*x^2 + (-12*I*b*c^4*x^4 - 24*b*c^3*x^3 + 12*I*b*c^2*x^2)*log(1/4*c^2*x^2 + 1/4))*log(c^2*x^2 + 1) + (48*(2*a + I*b)*c^4*x^4 - (192*I*a - 96*b)*c^3*x^3 - 48*(2*a + I*b)*c^2*x^2)*log(x) - 8*a)/(c^2*d^3*x^4 - 2*I*c*d^3*x^3 - d^3*x^2)","B",0
66,1,83,0,0.334251," ","integrate((a+b*arctan(c*x))/(1+I*c*x)^4,x, algorithm=""maxima"")","-\frac{3 i \, b c^{2} x^{2} + 9 \, b c x + {\left(3 i \, b c^{3} x^{3} + 9 \, b c^{2} x^{2} - 9 i \, b c x + 21 \, b\right)} \arctan\left(c x\right) + 24 \, a - 10 i \, b}{72 \, c^{4} x^{3} - 216 i \, c^{3} x^{2} - 216 \, c^{2} x + 72 i \, c}"," ",0,"-(3*I*b*c^2*x^2 + 9*b*c*x + (3*I*b*c^3*x^3 + 9*b*c^2*x^2 - 9*I*b*c*x + 21*b)*arctan(c*x) + 24*a - 10*I*b)/(72*c^4*x^3 - 216*I*c^3*x^2 - 216*c^2*x + 72*I*c)","A",0
67,1,126,0,0.412802," ","integrate(arctan(a*x)/(c*x+I*a*c*x^2),x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(-\frac{i \, \log\left(i \, a x + 1\right)^{2}}{a c} + \frac{2 i \, {\left(\log\left(i \, a x + 1\right) \log\left(-\frac{1}{2} i \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} i \, a x + \frac{1}{2}\right)\right)}}{a c} + \frac{2 i \, {\left(\log\left(i \, a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-i \, a x\right)\right)}}{a c} - \frac{2 i \, {\left(\log\left(-i \, a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(i \, a x\right)\right)}}{a c}\right)} - {\left(\frac{\log\left(i \, a x + 1\right)}{c} - \frac{\log\left(x\right)}{c}\right)} \arctan\left(a x\right)"," ",0,"1/4*a*(-I*log(I*a*x + 1)^2/(a*c) + 2*I*(log(I*a*x + 1)*log(-1/2*I*a*x + 1/2) + dilog(1/2*I*a*x + 1/2))/(a*c) + 2*I*(log(I*a*x + 1)*log(x) + dilog(-I*a*x))/(a*c) - 2*I*(log(-I*a*x + 1)*log(x) + dilog(I*a*x))/(a*c)) - (log(I*a*x + 1)/c - log(x)/c)*arctan(a*x)","B",0
68,0,0,0,0.000000," ","integrate(x^3*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} i \, a^{2} c d x^{5} + \frac{1}{4} \, b^{2} d x^{4} \arctan\left(c x\right)^{2} + \frac{1}{4} \, a^{2} d x^{4} + \frac{1}{10} i \, {\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 c d + \frac{1}{80} i \, {\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} c d + \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 d - \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} d"," ",0,"1/5*I*a^2*c*d*x^5 + 1/4*b^2*d*x^4*arctan(c*x)^2 + 1/4*a^2*d*x^4 + 1/10*I*(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*c*d + 1/80*I*(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*c*d + 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*d - 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*d","F",0
69,0,0,0,0.000000," ","integrate(x^2*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} i \, a^{2} c d x^{4} + \frac{1}{3} \, a^{2} d x^{3} + \frac{1}{6} i \, {\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 c d + \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 d + \frac{1}{192} \, {\left(12 i \, b^{2} c d x^{4} + 16 \, b^{2} d x^{3}\right)} \arctan\left(c x\right)^{2} - \frac{1}{48} \, {\left(3 \, b^{2} c d x^{4} - 4 i \, b^{2} d x^{3}\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + \frac{1}{192} \, {\left(-3 i \, b^{2} c d x^{4} - 4 \, b^{2} d x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + i \, \int -\frac{14 \, b^{2} c^{2} d x^{4} \arctan\left(c x\right) - 36 \, {\left(b^{2} c^{3} d x^{5} + b^{2} c d x^{3}\right)} \arctan\left(c x\right)^{2} - 3 \, {\left(b^{2} c^{3} d x^{5} + b^{2} c d x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - {\left(3 \, b^{2} c^{3} d x^{5} - 4 \, b^{2} c d x^{3} - 12 \, {\left(b^{2} c^{2} d x^{4} + b^{2} d x^{2}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \int \frac{36 \, {\left(b^{2} c^{2} d x^{4} + b^{2} d x^{2}\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(b^{2} c^{2} d x^{4} + b^{2} d x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 2 \, {\left(3 \, b^{2} c^{3} d x^{5} - 4 \, b^{2} c d x^{3}\right)} \arctan\left(c x\right) + {\left(7 \, b^{2} c^{2} d x^{4} + 12 \, {\left(b^{2} c^{3} d x^{5} + b^{2} c d x^{3}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/4*I*a^2*c*d*x^4 + 1/3*a^2*d*x^3 + 1/6*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a*b*c*d + 1/3*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*d + 1/192*(12*I*b^2*c*d*x^4 + 16*b^2*d*x^3)*arctan(c*x)^2 - 1/48*(3*b^2*c*d*x^4 - 4*I*b^2*d*x^3)*arctan(c*x)*log(c^2*x^2 + 1) + 1/192*(-3*I*b^2*c*d*x^4 - 4*b^2*d*x^3)*log(c^2*x^2 + 1)^2 + I*integrate(-1/48*(14*b^2*c^2*d*x^4*arctan(c*x) - 36*(b^2*c^3*d*x^5 + b^2*c*d*x^3)*arctan(c*x)^2 - 3*(b^2*c^3*d*x^5 + b^2*c*d*x^3)*log(c^2*x^2 + 1)^2 - (3*b^2*c^3*d*x^5 - 4*b^2*c*d*x^3 - 12*(b^2*c^2*d*x^4 + b^2*d*x^2)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x) + integrate(1/48*(36*(b^2*c^2*d*x^4 + b^2*d*x^2)*arctan(c*x)^2 + 3*(b^2*c^2*d*x^4 + b^2*d*x^2)*log(c^2*x^2 + 1)^2 + 2*(3*b^2*c^3*d*x^5 - 4*b^2*c*d*x^3)*arctan(c*x) + (7*b^2*c^2*d*x^4 + 12*(b^2*c^3*d*x^5 + b^2*c*d*x^3)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
70,0,0,0,0.000000," ","integrate(x*(d+I*c*d*x)*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} i \, a^{2} c d x^{3} + \frac{1}{2} \, b^{2} d x^{2} \arctan\left(c x\right)^{2} + \frac{1}{3} i \, {\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 c d + \frac{1}{48} i \, {\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} c d + \frac{1}{2} \, a^{2} d 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 d - \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} d"," ",0,"1/3*I*a^2*c*d*x^3 + 1/2*b^2*d*x^2*arctan(c*x)^2 + 1/3*I*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*c*d + 1/48*I*(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*c*d + 1/2*a^2*d*x^2 + (x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*d - 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*d","F",0
71,0,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","4 \, b^{2} c^{3} d \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 4 \, b^{2} c^{3} d \int \frac{x^{3} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{1}{2} i \, a^{2} c d x^{2} + 12 \, b^{2} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + b^{2} c^{2} d \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{2} c^{2} d \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + i \, {\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 c d + \frac{b^{2} d \arctan\left(c x\right)^{3}}{4 \, c} + 4 \, b^{2} c d \int \frac{x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 8 \, b^{2} c d \int \frac{x \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + a^{2} d x + b^{2} d \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d}{c} + \frac{1}{32} \, {\left(4 i \, b^{2} c d x^{2} + 8 \, b^{2} d x\right)} \arctan\left(c x\right)^{2} - \frac{1}{8} \, {\left(b^{2} c d x^{2} - 2 i \, b^{2} d x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + \frac{1}{32} \, {\left(-i \, b^{2} c d x^{2} - 2 \, b^{2} d x\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + i \, \int -\frac{12 \, b^{2} c^{2} d x^{2} \arctan\left(c x\right) - 12 \, {\left(b^{2} c^{3} d x^{3} + b^{2} c d x\right)} \arctan\left(c x\right)^{2} - {\left(b^{2} c^{3} d x^{3} + b^{2} c d x\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, {\left(b^{2} c^{3} d x^{3} - 2 \, b^{2} c d x - 2 \, {\left(b^{2} c^{2} d x^{2} + b^{2} d\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"4*b^2*c^3*d*integrate(1/16*x^3*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 4*b^2*c^3*d*integrate(1/16*x^3*arctan(c*x)/(c^2*x^2 + 1), x) + 1/2*I*a^2*c*d*x^2 + 12*b^2*c^2*d*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + b^2*c^2*d*integrate(1/16*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 6*b^2*c^2*d*integrate(1/16*x^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + I*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*c*d + 1/4*b^2*d*arctan(c*x)^3/c + 4*b^2*c*d*integrate(1/16*x*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - 8*b^2*c*d*integrate(1/16*x*arctan(c*x)/(c^2*x^2 + 1), x) + a^2*d*x + b^2*d*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + (2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d/c + 1/32*(4*I*b^2*c*d*x^2 + 8*b^2*d*x)*arctan(c*x)^2 - 1/8*(b^2*c*d*x^2 - 2*I*b^2*d*x)*arctan(c*x)*log(c^2*x^2 + 1) + 1/32*(-I*b^2*c*d*x^2 - 2*b^2*d*x)*log(c^2*x^2 + 1)^2 + I*integrate(-1/16*(12*b^2*c^2*d*x^2*arctan(c*x) - 12*(b^2*c^3*d*x^3 + b^2*c*d*x)*arctan(c*x)^2 - (b^2*c^3*d*x^3 + b^2*c*d*x)*log(c^2*x^2 + 1)^2 - 2*(b^2*c^3*d*x^3 - 2*b^2*c*d*x - 2*(b^2*c^2*d*x^2 + b^2*d)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
72,0,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^2/x,x, algorithm=""maxima"")","\frac{1}{4} i \, b^{2} c d x \arctan\left(c x\right)^{2} + 12 i \, b^{2} c^{3} d \int \frac{x^{3} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 4 \, b^{2} c^{3} d \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + i \, b^{2} c^{3} d \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 8 \, b^{2} c^{3} d \int \frac{x^{3} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 4 i \, b^{2} c^{3} d \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - \frac{1}{4} \, b^{2} c d x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - \frac{1}{16} i \, b^{2} c d x \log\left(c^{2} x^{2} + 1\right)^{2} + \frac{1}{4} i \, b^{2} d \arctan\left(c x\right)^{3} + 12 \, b^{2} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 4 i \, b^{2} c^{2} d \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b c^{2} d \int \frac{x^{2} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 8 i \, b^{2} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + \frac{1}{96} \, b^{2} d \log\left(c^{2} x^{2} + 1\right)^{3} + i \, a^{2} c d x + 4 \, b^{2} c d \int \frac{x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + i \, b^{2} c d \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + \frac{1}{16} \, b^{2} d \log\left(c^{2} x^{2} + 1\right)^{2} + i \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d + 12 \, b^{2} d \int \frac{\arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 4 i \, b^{2} d \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + b^{2} d \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b d \int \frac{\arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + a^{2} d \log\left(x\right)"," ",0,"1/4*I*b^2*c*d*x*arctan(c*x)^2 + 12*I*b^2*c^3*d*integrate(1/16*x^3*arctan(c*x)^2/(c^2*x^3 + x), x) + 4*b^2*c^3*d*integrate(1/16*x^3*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + I*b^2*c^3*d*integrate(1/16*x^3*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 8*b^2*c^3*d*integrate(1/16*x^3*arctan(c*x)/(c^2*x^3 + x), x) + 4*I*b^2*c^3*d*integrate(1/16*x^3*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) - 1/4*b^2*c*d*x*arctan(c*x)*log(c^2*x^2 + 1) - 1/16*I*b^2*c*d*x*log(c^2*x^2 + 1)^2 + 1/4*I*b^2*d*arctan(c*x)^3 + 12*b^2*c^2*d*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^3 + x), x) - 4*I*b^2*c^2*d*integrate(1/16*x^2*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + 32*a*b*c^2*d*integrate(1/16*x^2*arctan(c*x)/(c^2*x^3 + x), x) - 8*I*b^2*c^2*d*integrate(1/16*x^2*arctan(c*x)/(c^2*x^3 + x), x) + 1/96*b^2*d*log(c^2*x^2 + 1)^3 + I*a^2*c*d*x + 4*b^2*c*d*integrate(1/16*x*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + I*b^2*c*d*integrate(1/16*x*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 1/16*b^2*d*log(c^2*x^2 + 1)^2 + I*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d + 12*b^2*d*integrate(1/16*arctan(c*x)^2/(c^2*x^3 + x), x) - 4*I*b^2*d*integrate(1/16*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + b^2*d*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 32*a*b*d*integrate(1/16*arctan(c*x)/(c^2*x^3 + x), x) + a^2*d*log(x)","F",0
73,-1,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^2/x^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,0,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^2/x^4,x, algorithm=""maxima"")","-i \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} a b c d + \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 d - \frac{i \, a^{2} c d}{2 \, x^{2}} - \frac{a^{2} d}{3 \, x^{3}} + \frac{-12 \, b^{2} c d x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - 6 \, b^{2} d \arctan\left(c x\right)^{2} - \frac{1}{2} \, b^{2} d \log\left(c^{2} x^{2} + 1\right)^{2} + i \, {\left(20 \, {\left(\arctan\left(c x\right)^{2} - \log\left(c^{2} x^{2} + 1\right) + 2 \, \log\left(x\right)\right)} b^{2} c^{3} d - 40 \, {\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} b^{2} c^{2} d \arctan\left(c x\right) + \frac{56 \, b^{2} c^{3} d x^{3} \log\left(x\right) - 56 \, b^{2} c^{2} d x^{2} \arctan\left(c x\right) - 3 \, b^{2} c d x \log\left(c^{2} x^{2} + 1\right)^{2} - 4 \, {\left(7 \, b^{2} c^{3} d x^{3} + 9 \, b^{2} c d x\right)} \arctan\left(c x\right)^{2} - 4 \, {\left(7 \, b^{2} c^{3} d x^{3} - 2 \, b^{2} d \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{x^{3}}\right)} x^{3} + 2 \, x^{3} \int -\frac{12 \, b^{2} c^{2} d x^{2} \log\left(c^{2} x^{2} + 1\right) - 56 \, b^{2} c d x \arctan\left(c x\right) - 108 \, {\left(b^{2} c^{2} d x^{2} + b^{2} d\right)} \arctan\left(c x\right)^{2} - 9 \, {\left(b^{2} c^{2} d x^{2} + b^{2} d\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{4 \, {\left(c^{2} x^{6} + x^{4}\right)}}\,{d x} + {\left(-12 i \, b^{2} c d x - 8 \, b^{2} d\right)} \arctan\left(c x\right)^{2} + 4 \, {\left(3 \, b^{2} c d x - 2 i \, b^{2} d\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + {\left(3 i \, b^{2} c d x + 2 \, b^{2} d\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{96 \, x^{3}}"," ",0,"-I*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*a*b*c*d + 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*d - 1/2*I*a^2*c*d/x^2 - 1/3*a^2*d/x^3 + 1/96*(96*I*x^3*integrate(1/48*(20*b^2*c^2*d*x^2*arctan(c*x) + 36*(b^2*c^3*d*x^3 + b^2*c*d*x)*arctan(c*x)^2 + 3*(b^2*c^3*d*x^3 + b^2*c*d*x)*log(c^2*x^2 + 1)^2 - 2*(3*b^2*c^3*d*x^3 - 2*b^2*c*d*x + 6*(b^2*c^2*d*x^2 + b^2*d)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^6 + x^4), x) + 96*x^3*integrate(1/48*(36*(b^2*c^2*d*x^2 + b^2*d)*arctan(c*x)^2 + 3*(b^2*c^2*d*x^2 + b^2*d)*log(c^2*x^2 + 1)^2 - 4*(3*b^2*c^3*d*x^3 - 2*b^2*c*d*x)*arctan(c*x) - 2*(5*b^2*c^2*d*x^2 - 6*(b^2*c^3*d*x^3 + b^2*c*d*x)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^6 + x^4), x) + (-12*I*b^2*c*d*x - 8*b^2*d)*arctan(c*x)^2 + 4*(3*b^2*c*d*x - 2*I*b^2*d)*arctan(c*x)*log(c^2*x^2 + 1) + (3*I*b^2*c*d*x + 2*b^2*d)*log(c^2*x^2 + 1)^2)/x^3","F",0
76,0,0,0,0.000000," ","integrate(x^3*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{6} \, a^{2} c^{2} d^{2} x^{6} + \frac{2}{5} i \, a^{2} c d^{2} x^{5} + \frac{1}{4} \, b^{2} d^{2} x^{4} \arctan\left(c x\right)^{2} + \frac{1}{4} \, a^{2} d^{2} x^{4} - \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 c^{2} d^{2} + \frac{1}{5} i \, {\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 c d^{2} + \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 d^{2} - \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} d^{2} - \frac{1}{480} \, {\left(20 \, b^{2} c^{2} d^{2} x^{6} - 48 i \, b^{2} c d^{2} x^{5}\right)} \arctan\left(c x\right)^{2} + \frac{1}{120} \, {\left(-5 i \, b^{2} c^{2} d^{2} x^{6} - 12 \, b^{2} c d^{2} x^{5}\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + \frac{1}{480} \, {\left(5 \, b^{2} c^{2} d^{2} x^{6} - 12 i \, b^{2} c d^{2} x^{5}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - \int -\frac{68 \, b^{2} c^{3} d^{2} x^{6} \arctan\left(c x\right) - 180 \, {\left(b^{2} c^{4} d^{2} x^{7} + b^{2} c^{2} d^{2} x^{5}\right)} \arctan\left(c x\right)^{2} - 15 \, {\left(b^{2} c^{4} d^{2} x^{7} + b^{2} c^{2} d^{2} x^{5}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, {\left(5 \, b^{2} c^{4} d^{2} x^{7} - 12 \, b^{2} c^{2} d^{2} x^{5} - 60 \, {\left(b^{2} c^{3} d^{2} x^{6} + b^{2} c d^{2} x^{4}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + i \, \int \frac{180 \, {\left(b^{2} c^{3} d^{2} x^{6} + b^{2} c d^{2} x^{4}\right)} \arctan\left(c x\right)^{2} + 15 \, {\left(b^{2} c^{3} d^{2} x^{6} + b^{2} c d^{2} x^{4}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 2 \, {\left(5 \, b^{2} c^{4} d^{2} x^{7} - 12 \, b^{2} c^{2} d^{2} x^{5}\right)} \arctan\left(c x\right) + {\left(17 \, b^{2} c^{3} d^{2} x^{6} + 30 \, {\left(b^{2} c^{4} d^{2} x^{7} + b^{2} c^{2} d^{2} x^{5}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{120 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"-1/6*a^2*c^2*d^2*x^6 + 2/5*I*a^2*c*d^2*x^5 + 1/4*b^2*d^2*x^4*arctan(c*x)^2 + 1/4*a^2*d^2*x^4 - 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*c^2*d^2 + 1/5*I*(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*c*d^2 + 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*d^2 - 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*d^2 - 1/480*(20*b^2*c^2*d^2*x^6 - 48*I*b^2*c*d^2*x^5)*arctan(c*x)^2 + 1/120*(-5*I*b^2*c^2*d^2*x^6 - 12*b^2*c*d^2*x^5)*arctan(c*x)*log(c^2*x^2 + 1) + 1/480*(5*b^2*c^2*d^2*x^6 - 12*I*b^2*c*d^2*x^5)*log(c^2*x^2 + 1)^2 - integrate(-1/240*(68*b^2*c^3*d^2*x^6*arctan(c*x) - 180*(b^2*c^4*d^2*x^7 + b^2*c^2*d^2*x^5)*arctan(c*x)^2 - 15*(b^2*c^4*d^2*x^7 + b^2*c^2*d^2*x^5)*log(c^2*x^2 + 1)^2 - 2*(5*b^2*c^4*d^2*x^7 - 12*b^2*c^2*d^2*x^5 - 60*(b^2*c^3*d^2*x^6 + b^2*c*d^2*x^4)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x) + I*integrate(1/120*(180*(b^2*c^3*d^2*x^6 + b^2*c*d^2*x^4)*arctan(c*x)^2 + 15*(b^2*c^3*d^2*x^6 + b^2*c*d^2*x^4)*log(c^2*x^2 + 1)^2 + 2*(5*b^2*c^4*d^2*x^7 - 12*b^2*c^2*d^2*x^5)*arctan(c*x) + (17*b^2*c^3*d^2*x^6 + 30*(b^2*c^4*d^2*x^7 + b^2*c^2*d^2*x^5)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
77,0,0,0,0.000000," ","integrate(x^2*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{5} \, a^{2} c^{2} d^{2} x^{5} + \frac{1}{2} i \, a^{2} c d^{2} x^{4} - \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 c^{2} d^{2} + \frac{1}{3} \, a^{2} d^{2} x^{3} + \frac{1}{3} i \, {\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 c d^{2} + \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 d^{2} - \frac{1}{480} \, {\left(24 \, b^{2} c^{2} d^{2} x^{5} - 60 i \, b^{2} c d^{2} x^{4} - 40 \, b^{2} d^{2} x^{3}\right)} \arctan\left(c x\right)^{2} - \frac{1}{480} \, {\left(24 i \, b^{2} c^{2} d^{2} x^{5} + 60 \, b^{2} c d^{2} x^{4} - 40 i \, b^{2} d^{2} x^{3}\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + \frac{1}{480} \, {\left(6 \, b^{2} c^{2} d^{2} x^{5} - 15 i \, b^{2} c d^{2} x^{4} - 10 \, b^{2} d^{2} x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - \int \frac{180 \, {\left(b^{2} c^{4} d^{2} x^{6} - b^{2} d^{2} x^{2}\right)} \arctan\left(c x\right)^{2} + 15 \, {\left(b^{2} c^{4} d^{2} x^{6} - b^{2} d^{2} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 4 \, {\left(21 \, b^{2} c^{3} d^{2} x^{5} - 10 \, b^{2} c d^{2} x^{3}\right)} \arctan\left(c x\right) + 2 \, {\left(6 \, b^{2} c^{4} d^{2} x^{6} - 25 \, b^{2} c^{2} d^{2} x^{4} - 60 \, {\left(b^{2} c^{3} d^{2} x^{5} + b^{2} c d^{2} x^{3}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + i \, \int \frac{180 \, {\left(b^{2} c^{3} d^{2} x^{5} + b^{2} c d^{2} x^{3}\right)} \arctan\left(c x\right)^{2} + 15 \, {\left(b^{2} c^{3} d^{2} x^{5} + b^{2} c d^{2} x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 2 \, {\left(6 \, b^{2} c^{4} d^{2} x^{6} - 25 \, b^{2} c^{2} d^{2} x^{4}\right)} \arctan\left(c x\right) + {\left(21 \, b^{2} c^{3} d^{2} x^{5} - 10 \, b^{2} c d^{2} x^{3} + 30 \, {\left(b^{2} c^{4} d^{2} x^{6} - b^{2} d^{2} x^{2}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{120 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"-1/5*a^2*c^2*d^2*x^5 + 1/2*I*a^2*c*d^2*x^4 - 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*c^2*d^2 + 1/3*a^2*d^2*x^3 + 1/3*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a*b*c*d^2 + 1/3*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*d^2 - 1/480*(24*b^2*c^2*d^2*x^5 - 60*I*b^2*c*d^2*x^4 - 40*b^2*d^2*x^3)*arctan(c*x)^2 - 1/480*(24*I*b^2*c^2*d^2*x^5 + 60*b^2*c*d^2*x^4 - 40*I*b^2*d^2*x^3)*arctan(c*x)*log(c^2*x^2 + 1) + 1/480*(6*b^2*c^2*d^2*x^5 - 15*I*b^2*c*d^2*x^4 - 10*b^2*d^2*x^3)*log(c^2*x^2 + 1)^2 - integrate(1/240*(180*(b^2*c^4*d^2*x^6 - b^2*d^2*x^2)*arctan(c*x)^2 + 15*(b^2*c^4*d^2*x^6 - b^2*d^2*x^2)*log(c^2*x^2 + 1)^2 - 4*(21*b^2*c^3*d^2*x^5 - 10*b^2*c*d^2*x^3)*arctan(c*x) + 2*(6*b^2*c^4*d^2*x^6 - 25*b^2*c^2*d^2*x^4 - 60*(b^2*c^3*d^2*x^5 + b^2*c*d^2*x^3)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x) + I*integrate(1/120*(180*(b^2*c^3*d^2*x^5 + b^2*c*d^2*x^3)*arctan(c*x)^2 + 15*(b^2*c^3*d^2*x^5 + b^2*c*d^2*x^3)*log(c^2*x^2 + 1)^2 + 2*(6*b^2*c^4*d^2*x^6 - 25*b^2*c^2*d^2*x^4)*arctan(c*x) + (21*b^2*c^3*d^2*x^5 - 10*b^2*c*d^2*x^3 + 30*(b^2*c^4*d^2*x^6 - b^2*d^2*x^2)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
78,0,0,0,0.000000," ","integrate(x*(d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} c^{2} d^{2} x^{4} + \frac{2}{3} i \, a^{2} c d^{2} x^{3} + \frac{1}{2} \, b^{2} d^{2} x^{2} \arctan\left(c x\right)^{2} - \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 c^{2} d^{2} + \frac{2}{3} i \, {\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 c d^{2} + \frac{1}{2} \, a^{2} d^{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 d^{2} - \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} d^{2} - \frac{1}{192} \, {\left(12 \, b^{2} c^{2} d^{2} x^{4} - 32 i \, b^{2} c d^{2} x^{3}\right)} \arctan\left(c x\right)^{2} + \frac{1}{48} \, {\left(-3 i \, b^{2} c^{2} d^{2} x^{4} - 8 \, b^{2} c d^{2} x^{3}\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + \frac{1}{192} \, {\left(3 \, b^{2} c^{2} d^{2} x^{4} - 8 i \, b^{2} c d^{2} x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - \int -\frac{22 \, b^{2} c^{3} d^{2} x^{4} \arctan\left(c x\right) - 36 \, {\left(b^{2} c^{4} d^{2} x^{5} + b^{2} c^{2} d^{2} x^{3}\right)} \arctan\left(c x\right)^{2} - 3 \, {\left(b^{2} c^{4} d^{2} x^{5} + b^{2} c^{2} d^{2} x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - {\left(3 \, b^{2} c^{4} d^{2} x^{5} - 8 \, b^{2} c^{2} d^{2} x^{3} - 24 \, {\left(b^{2} c^{3} d^{2} x^{4} + b^{2} c d^{2} x^{2}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + i \, \int \frac{72 \, {\left(b^{2} c^{3} d^{2} x^{4} + b^{2} c d^{2} x^{2}\right)} \arctan\left(c x\right)^{2} + 6 \, {\left(b^{2} c^{3} d^{2} x^{4} + b^{2} c d^{2} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 2 \, {\left(3 \, b^{2} c^{4} d^{2} x^{5} - 8 \, b^{2} c^{2} d^{2} x^{3}\right)} \arctan\left(c x\right) + {\left(11 \, b^{2} c^{3} d^{2} x^{4} + 12 \, {\left(b^{2} c^{4} d^{2} x^{5} + b^{2} c^{2} d^{2} x^{3}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"-1/4*a^2*c^2*d^2*x^4 + 2/3*I*a^2*c*d^2*x^3 + 1/2*b^2*d^2*x^2*arctan(c*x)^2 - 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*c^2*d^2 + 2/3*I*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*c*d^2 + 1/2*a^2*d^2*x^2 + (x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*d^2 - 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*d^2 - 1/192*(12*b^2*c^2*d^2*x^4 - 32*I*b^2*c*d^2*x^3)*arctan(c*x)^2 + 1/48*(-3*I*b^2*c^2*d^2*x^4 - 8*b^2*c*d^2*x^3)*arctan(c*x)*log(c^2*x^2 + 1) + 1/192*(3*b^2*c^2*d^2*x^4 - 8*I*b^2*c*d^2*x^3)*log(c^2*x^2 + 1)^2 - integrate(-1/48*(22*b^2*c^3*d^2*x^4*arctan(c*x) - 36*(b^2*c^4*d^2*x^5 + b^2*c^2*d^2*x^3)*arctan(c*x)^2 - 3*(b^2*c^4*d^2*x^5 + b^2*c^2*d^2*x^3)*log(c^2*x^2 + 1)^2 - (3*b^2*c^4*d^2*x^5 - 8*b^2*c^2*d^2*x^3 - 24*(b^2*c^3*d^2*x^4 + b^2*c*d^2*x^2)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x) + I*integrate(1/48*(72*(b^2*c^3*d^2*x^4 + b^2*c*d^2*x^2)*arctan(c*x)^2 + 6*(b^2*c^3*d^2*x^4 + b^2*c*d^2*x^2)*log(c^2*x^2 + 1)^2 + 2*(3*b^2*c^4*d^2*x^5 - 8*b^2*c^2*d^2*x^3)*arctan(c*x) + (11*b^2*c^3*d^2*x^4 + 12*(b^2*c^4*d^2*x^5 + b^2*c^2*d^2*x^3)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
79,0,0,0,0.000000," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} c^{2} d^{2} x^{3} - 36 \, b^{2} c^{4} d^{2} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 3 \, b^{2} c^{4} d^{2} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 4 \, b^{2} c^{4} d^{2} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 24 \, b^{2} c^{3} d^{2} \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 32 \, b^{2} c^{3} d^{2} \int \frac{x^{3} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - \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 c^{2} d^{2} + i \, a^{2} c d^{2} x^{2} + 24 \, b^{2} c^{2} d^{2} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 2 i \, {\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 c d^{2} + \frac{b^{2} d^{2} \arctan\left(c x\right)^{3}}{4 \, c} + 24 \, b^{2} c d^{2} \int \frac{x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 24 \, b^{2} c d^{2} \int \frac{x \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + a^{2} d^{2} x + 3 \, b^{2} d^{2} \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d^{2}}{c} - \frac{1}{48} \, {\left(4 \, b^{2} c^{2} d^{2} x^{3} - 12 i \, b^{2} c d^{2} x^{2} - 12 \, b^{2} d^{2} x\right)} \arctan\left(c x\right)^{2} - \frac{1}{48} \, {\left(4 i \, b^{2} c^{2} d^{2} x^{3} + 12 \, b^{2} c d^{2} x^{2} - 12 i \, b^{2} d^{2} x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + \frac{1}{48} \, {\left(b^{2} c^{2} d^{2} x^{3} - 3 i \, b^{2} c d^{2} x^{2} - 3 \, b^{2} d^{2} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + i \, \int \frac{36 \, {\left(b^{2} c^{3} d^{2} x^{3} + b^{2} c d^{2} x\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(b^{2} c^{3} d^{2} x^{3} + b^{2} c d^{2} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 4 \, {\left(b^{2} c^{4} d^{2} x^{4} - 6 \, b^{2} c^{2} d^{2} x^{2}\right)} \arctan\left(c x\right) + 2 \, {\left(4 \, b^{2} c^{3} d^{2} x^{3} - 3 \, b^{2} c d^{2} x + 3 \, {\left(b^{2} c^{4} d^{2} x^{4} - b^{2} d^{2}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{24 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"-1/3*a^2*c^2*d^2*x^3 - 36*b^2*c^4*d^2*integrate(1/48*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) - 3*b^2*c^4*d^2*integrate(1/48*x^4*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 4*b^2*c^4*d^2*integrate(1/48*x^4*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 24*b^2*c^3*d^2*integrate(1/48*x^3*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 32*b^2*c^3*d^2*integrate(1/48*x^3*arctan(c*x)/(c^2*x^2 + 1), x) - 1/3*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*c^2*d^2 + I*a^2*c*d^2*x^2 + 24*b^2*c^2*d^2*integrate(1/48*x^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 2*I*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*c*d^2 + 1/4*b^2*d^2*arctan(c*x)^3/c + 24*b^2*c*d^2*integrate(1/48*x*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - 24*b^2*c*d^2*integrate(1/48*x*arctan(c*x)/(c^2*x^2 + 1), x) + a^2*d^2*x + 3*b^2*d^2*integrate(1/48*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + (2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d^2/c - 1/48*(4*b^2*c^2*d^2*x^3 - 12*I*b^2*c*d^2*x^2 - 12*b^2*d^2*x)*arctan(c*x)^2 - 1/48*(4*I*b^2*c^2*d^2*x^3 + 12*b^2*c*d^2*x^2 - 12*I*b^2*d^2*x)*arctan(c*x)*log(c^2*x^2 + 1) + 1/48*(b^2*c^2*d^2*x^3 - 3*I*b^2*c*d^2*x^2 - 3*b^2*d^2*x)*log(c^2*x^2 + 1)^2 + I*integrate(1/24*(36*(b^2*c^3*d^2*x^3 + b^2*c*d^2*x)*arctan(c*x)^2 + 3*(b^2*c^3*d^2*x^3 + b^2*c*d^2*x)*log(c^2*x^2 + 1)^2 + 4*(b^2*c^4*d^2*x^4 - 6*b^2*c^2*d^2*x^2)*arctan(c*x) + 2*(4*b^2*c^3*d^2*x^3 - 3*b^2*c*d^2*x + 3*(b^2*c^4*d^2*x^4 - b^2*d^2)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
80,0,0,0,0.000000," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x,x, algorithm=""maxima"")","-12 \, b^{2} c^{4} d^{2} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 2 i \, b^{2} c^{4} d^{2} \int \frac{x^{4} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{8 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - b^{2} c^{4} d^{2} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 2 i \, b^{2} c^{4} d^{2} \int \frac{x^{4} \arctan\left(c x\right)}{8 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 32 \, a b c^{4} d^{2} \int \frac{x^{4} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 2 \, b^{2} c^{4} d^{2} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - \frac{1}{2} \, a^{2} c^{2} d^{2} x^{2} + 12 i \, b^{2} c^{3} d^{2} \int \frac{x^{3} \arctan\left(c x\right)^{2}}{8 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 8 \, b^{2} c^{3} d^{2} \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + i \, b^{2} c^{3} d^{2} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{8 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 20 \, b^{2} c^{3} d^{2} \int \frac{x^{3} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 5 i \, b^{2} c^{3} d^{2} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)}{8 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + \frac{1}{2} i \, b^{2} d^{2} \arctan\left(c x\right)^{3} - 8 i \, b^{2} c^{2} d^{2} \int \frac{x^{2} \arctan\left(c x\right)}{8 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 2 i \, a^{2} c d^{2} x + 8 \, b^{2} c d^{2} \int \frac{x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + i \, b^{2} c d^{2} \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{8 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + \frac{1}{8} \, b^{2} d^{2} \log\left(c^{2} x^{2} + 1\right)^{2} + 2 i \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d^{2} + 12 \, b^{2} d^{2} \int \frac{\arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 2 i \, b^{2} d^{2} \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{8 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + b^{2} d^{2} \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b d^{2} \int \frac{\arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + a^{2} d^{2} \log\left(x\right) - \frac{1}{32} \, {\left(4 \, b^{2} c^{2} d^{2} x^{2} - 16 i \, b^{2} c d^{2} x\right)} \arctan\left(c x\right)^{2} + \frac{1}{8} \, {\left(-i \, b^{2} c^{2} d^{2} x^{2} - 4 \, b^{2} c d^{2} x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + \frac{1}{32} \, {\left(b^{2} c^{2} d^{2} x^{2} - 4 i \, b^{2} c d^{2} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"-12*b^2*c^4*d^2*integrate(1/16*x^4*arctan(c*x)^2/(c^2*x^3 + x), x) + 2*I*b^2*c^4*d^2*integrate(1/8*x^4*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) - b^2*c^4*d^2*integrate(1/16*x^4*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 2*I*b^2*c^4*d^2*integrate(1/8*x^4*arctan(c*x)/(c^2*x^3 + x), x) - 32*a*b*c^4*d^2*integrate(1/16*x^4*arctan(c*x)/(c^2*x^3 + x), x) - 2*b^2*c^4*d^2*integrate(1/16*x^4*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) - 1/2*a^2*c^2*d^2*x^2 + 12*I*b^2*c^3*d^2*integrate(1/8*x^3*arctan(c*x)^2/(c^2*x^3 + x), x) + 8*b^2*c^3*d^2*integrate(1/16*x^3*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + I*b^2*c^3*d^2*integrate(1/8*x^3*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 20*b^2*c^3*d^2*integrate(1/16*x^3*arctan(c*x)/(c^2*x^3 + x), x) + 5*I*b^2*c^3*d^2*integrate(1/8*x^3*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + 1/2*I*b^2*d^2*arctan(c*x)^3 - 8*I*b^2*c^2*d^2*integrate(1/8*x^2*arctan(c*x)/(c^2*x^3 + x), x) + 2*I*a^2*c*d^2*x + 8*b^2*c*d^2*integrate(1/16*x*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + I*b^2*c*d^2*integrate(1/8*x*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 1/8*b^2*d^2*log(c^2*x^2 + 1)^2 + 2*I*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d^2 + 12*b^2*d^2*integrate(1/16*arctan(c*x)^2/(c^2*x^3 + x), x) - 2*I*b^2*d^2*integrate(1/8*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + b^2*d^2*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 32*a*b*d^2*integrate(1/16*arctan(c*x)/(c^2*x^3 + x), x) + a^2*d^2*log(x) - 1/32*(4*b^2*c^2*d^2*x^2 - 16*I*b^2*c*d^2*x)*arctan(c*x)^2 + 1/8*(-I*b^2*c^2*d^2*x^2 - 4*b^2*c*d^2*x)*arctan(c*x)*log(c^2*x^2 + 1) + 1/32*(b^2*c^2*d^2*x^2 - 4*I*b^2*c*d^2*x)*log(c^2*x^2 + 1)^2","F",0
81,-1,0,0,0.000000," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^2/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,0,0,0,0.000000," ","integrate(x^3*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{7} i \, a^{2} c^{3} d^{3} x^{7} - \frac{1}{2} \, a^{2} c^{2} d^{3} x^{6} + \frac{3}{5} i \, a^{2} c d^{3} x^{5} + \frac{1}{4} \, b^{2} d^{3} x^{4} \arctan\left(c x\right)^{2} - \frac{1}{42} i \, {\left(12 \, x^{7} \arctan\left(c x\right) - c {\left(\frac{2 \, c^{4} x^{6} - 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} - \frac{6 \, \log\left(c^{2} x^{2} + 1\right)}{c^{8}}\right)}\right)} a b c^{3} d^{3} + \frac{1}{4} \, a^{2} d^{3} x^{4} - \frac{1}{15} \, {\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 c^{2} d^{3} + \frac{3}{10} i \, {\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 c d^{3} + \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 d^{3} - \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} d^{3} - \frac{1}{1120} \, {\left(40 i \, b^{2} c^{3} d^{3} x^{7} + 140 \, b^{2} c^{2} d^{3} x^{6} - 168 i \, b^{2} c d^{3} x^{5}\right)} \arctan\left(c x\right)^{2} + \frac{1}{1120} \, {\left(40 \, b^{2} c^{3} d^{3} x^{7} - 140 i \, b^{2} c^{2} d^{3} x^{6} - 168 \, b^{2} c d^{3} x^{5}\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - \frac{1}{1120} \, {\left(-10 i \, b^{2} c^{3} d^{3} x^{7} - 35 \, b^{2} c^{2} d^{3} x^{6} + 42 i \, b^{2} c d^{3} x^{5}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - i \, \int \frac{420 \, {\left(b^{2} c^{5} d^{3} x^{8} - 2 \, b^{2} c^{3} d^{3} x^{6} - 3 \, b^{2} c d^{3} x^{4}\right)} \arctan\left(c x\right)^{2} + 35 \, {\left(b^{2} c^{5} d^{3} x^{8} - 2 \, b^{2} c^{3} d^{3} x^{6} - 3 \, b^{2} c d^{3} x^{4}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 12 \, {\left(15 \, b^{2} c^{4} d^{3} x^{7} - 14 \, b^{2} c^{2} d^{3} x^{5}\right)} \arctan\left(c x\right) + 2 \, {\left(10 \, b^{2} c^{5} d^{3} x^{8} - 77 \, b^{2} c^{3} d^{3} x^{6} - 210 \, {\left(b^{2} c^{4} d^{3} x^{7} + b^{2} c^{2} d^{3} x^{5}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{560 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - \int \frac{1260 \, {\left(b^{2} c^{4} d^{3} x^{7} + b^{2} c^{2} d^{3} x^{5}\right)} \arctan\left(c x\right)^{2} + 105 \, {\left(b^{2} c^{4} d^{3} x^{7} + b^{2} c^{2} d^{3} x^{5}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 4 \, {\left(10 \, b^{2} c^{5} d^{3} x^{8} - 77 \, b^{2} c^{3} d^{3} x^{6}\right)} \arctan\left(c x\right) + 2 \, {\left(45 \, b^{2} c^{4} d^{3} x^{7} - 42 \, b^{2} c^{2} d^{3} x^{5} + 70 \, {\left(b^{2} c^{5} d^{3} x^{8} - 2 \, b^{2} c^{3} d^{3} x^{6} - 3 \, b^{2} c d^{3} x^{4}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{560 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"-1/7*I*a^2*c^3*d^3*x^7 - 1/2*a^2*c^2*d^3*x^6 + 3/5*I*a^2*c*d^3*x^5 + 1/4*b^2*d^3*x^4*arctan(c*x)^2 - 1/42*I*(12*x^7*arctan(c*x) - c*((2*c^4*x^6 - 3*c^2*x^4 + 6*x^2)/c^6 - 6*log(c^2*x^2 + 1)/c^8))*a*b*c^3*d^3 + 1/4*a^2*d^3*x^4 - 1/15*(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*c^2*d^3 + 3/10*I*(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*c*d^3 + 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*d^3 - 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*d^3 - 1/1120*(40*I*b^2*c^3*d^3*x^7 + 140*b^2*c^2*d^3*x^6 - 168*I*b^2*c*d^3*x^5)*arctan(c*x)^2 + 1/1120*(40*b^2*c^3*d^3*x^7 - 140*I*b^2*c^2*d^3*x^6 - 168*b^2*c*d^3*x^5)*arctan(c*x)*log(c^2*x^2 + 1) - 1/1120*(-10*I*b^2*c^3*d^3*x^7 - 35*b^2*c^2*d^3*x^6 + 42*I*b^2*c*d^3*x^5)*log(c^2*x^2 + 1)^2 - I*integrate(1/560*(420*(b^2*c^5*d^3*x^8 - 2*b^2*c^3*d^3*x^6 - 3*b^2*c*d^3*x^4)*arctan(c*x)^2 + 35*(b^2*c^5*d^3*x^8 - 2*b^2*c^3*d^3*x^6 - 3*b^2*c*d^3*x^4)*log(c^2*x^2 + 1)^2 - 12*(15*b^2*c^4*d^3*x^7 - 14*b^2*c^2*d^3*x^5)*arctan(c*x) + 2*(10*b^2*c^5*d^3*x^8 - 77*b^2*c^3*d^3*x^6 - 210*(b^2*c^4*d^3*x^7 + b^2*c^2*d^3*x^5)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x) - integrate(1/560*(1260*(b^2*c^4*d^3*x^7 + b^2*c^2*d^3*x^5)*arctan(c*x)^2 + 105*(b^2*c^4*d^3*x^7 + b^2*c^2*d^3*x^5)*log(c^2*x^2 + 1)^2 + 4*(10*b^2*c^5*d^3*x^8 - 77*b^2*c^3*d^3*x^6)*arctan(c*x) + 2*(45*b^2*c^4*d^3*x^7 - 42*b^2*c^2*d^3*x^5 + 70*(b^2*c^5*d^3*x^8 - 2*b^2*c^3*d^3*x^6 - 3*b^2*c*d^3*x^4)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
85,0,0,0,0.000000," ","integrate(x^2*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{6} i \, a^{2} c^{3} d^{3} x^{6} - \frac{3}{5} \, a^{2} c^{2} d^{3} x^{5} + \frac{3}{4} i \, a^{2} c d^{3} x^{4} - \frac{1}{45} i \, {\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 c^{3} d^{3} - \frac{3}{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 c^{2} d^{3} + \frac{1}{3} \, a^{2} d^{3} x^{3} + \frac{1}{2} i \, {\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 c d^{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 d^{3} - \frac{1}{960} \, {\left(40 i \, b^{2} c^{3} d^{3} x^{6} + 144 \, b^{2} c^{2} d^{3} x^{5} - 180 i \, b^{2} c d^{3} x^{4} - 80 \, b^{2} d^{3} x^{3}\right)} \arctan\left(c x\right)^{2} + \frac{1}{960} \, {\left(40 \, b^{2} c^{3} d^{3} x^{6} - 144 i \, b^{2} c^{2} d^{3} x^{5} - 180 \, b^{2} c d^{3} x^{4} + 80 i \, b^{2} d^{3} x^{3}\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - \frac{1}{960} \, {\left(-10 i \, b^{2} c^{3} d^{3} x^{6} - 36 \, b^{2} c^{2} d^{3} x^{5} + 45 i \, b^{2} c d^{3} x^{4} + 20 \, b^{2} d^{3} x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - i \, \int \frac{180 \, {\left(b^{2} c^{5} d^{3} x^{7} - 2 \, b^{2} c^{3} d^{3} x^{5} - 3 \, b^{2} c d^{3} x^{3}\right)} \arctan\left(c x\right)^{2} + 15 \, {\left(b^{2} c^{5} d^{3} x^{7} - 2 \, b^{2} c^{3} d^{3} x^{5} - 3 \, b^{2} c d^{3} x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, {\left(46 \, b^{2} c^{4} d^{3} x^{6} - 65 \, b^{2} c^{2} d^{3} x^{4}\right)} \arctan\left(c x\right) + {\left(10 \, b^{2} c^{5} d^{3} x^{7} - 81 \, b^{2} c^{3} d^{3} x^{5} + 20 \, b^{2} c d^{3} x^{3} - 60 \, {\left(3 \, b^{2} c^{4} d^{3} x^{6} + 2 \, b^{2} c^{2} d^{3} x^{4} - b^{2} d^{3} x^{2}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - \int \frac{180 \, {\left(3 \, b^{2} c^{4} d^{3} x^{6} + 2 \, b^{2} c^{2} d^{3} x^{4} - b^{2} d^{3} x^{2}\right)} \arctan\left(c x\right)^{2} + 15 \, {\left(3 \, b^{2} c^{4} d^{3} x^{6} + 2 \, b^{2} c^{2} d^{3} x^{4} - b^{2} d^{3} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 2 \, {\left(10 \, b^{2} c^{5} d^{3} x^{7} - 81 \, b^{2} c^{3} d^{3} x^{5} + 20 \, b^{2} c d^{3} x^{3}\right)} \arctan\left(c x\right) + {\left(46 \, b^{2} c^{4} d^{3} x^{6} - 65 \, b^{2} c^{2} d^{3} x^{4} + 60 \, {\left(b^{2} c^{5} d^{3} x^{7} - 2 \, b^{2} c^{3} d^{3} x^{5} - 3 \, b^{2} c d^{3} x^{3}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"-1/6*I*a^2*c^3*d^3*x^6 - 3/5*a^2*c^2*d^3*x^5 + 3/4*I*a^2*c*d^3*x^4 - 1/45*I*(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*c^3*d^3 - 3/10*(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*c^2*d^3 + 1/3*a^2*d^3*x^3 + 1/2*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a*b*c*d^3 + 1/3*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*d^3 - 1/960*(40*I*b^2*c^3*d^3*x^6 + 144*b^2*c^2*d^3*x^5 - 180*I*b^2*c*d^3*x^4 - 80*b^2*d^3*x^3)*arctan(c*x)^2 + 1/960*(40*b^2*c^3*d^3*x^6 - 144*I*b^2*c^2*d^3*x^5 - 180*b^2*c*d^3*x^4 + 80*I*b^2*d^3*x^3)*arctan(c*x)*log(c^2*x^2 + 1) - 1/960*(-10*I*b^2*c^3*d^3*x^6 - 36*b^2*c^2*d^3*x^5 + 45*I*b^2*c*d^3*x^4 + 20*b^2*d^3*x^3)*log(c^2*x^2 + 1)^2 - I*integrate(1/240*(180*(b^2*c^5*d^3*x^7 - 2*b^2*c^3*d^3*x^5 - 3*b^2*c*d^3*x^3)*arctan(c*x)^2 + 15*(b^2*c^5*d^3*x^7 - 2*b^2*c^3*d^3*x^5 - 3*b^2*c*d^3*x^3)*log(c^2*x^2 + 1)^2 - 2*(46*b^2*c^4*d^3*x^6 - 65*b^2*c^2*d^3*x^4)*arctan(c*x) + (10*b^2*c^5*d^3*x^7 - 81*b^2*c^3*d^3*x^5 + 20*b^2*c*d^3*x^3 - 60*(3*b^2*c^4*d^3*x^6 + 2*b^2*c^2*d^3*x^4 - b^2*d^3*x^2)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x) - integrate(1/240*(180*(3*b^2*c^4*d^3*x^6 + 2*b^2*c^2*d^3*x^4 - b^2*d^3*x^2)*arctan(c*x)^2 + 15*(3*b^2*c^4*d^3*x^6 + 2*b^2*c^2*d^3*x^4 - b^2*d^3*x^2)*log(c^2*x^2 + 1)^2 + 2*(10*b^2*c^5*d^3*x^7 - 81*b^2*c^3*d^3*x^5 + 20*b^2*c*d^3*x^3)*arctan(c*x) + (46*b^2*c^4*d^3*x^6 - 65*b^2*c^2*d^3*x^4 + 60*(b^2*c^5*d^3*x^7 - 2*b^2*c^3*d^3*x^5 - 3*b^2*c*d^3*x^3)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
86,0,0,0,0.000000," ","integrate(x*(d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{5} i \, a^{2} c^{3} d^{3} x^{5} - \frac{3}{4} \, a^{2} c^{2} d^{3} x^{4} - \frac{1}{10} i \, {\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 c^{3} d^{3} + i \, a^{2} c d^{3} x^{3} + \frac{1}{2} \, b^{2} d^{3} x^{2} \arctan\left(c x\right)^{2} - \frac{1}{2} \, {\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 c^{2} d^{3} + i \, {\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 c d^{3} + \frac{1}{2} \, a^{2} d^{3} 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 d^{3} - \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} d^{3} - \frac{1}{320} \, {\left(16 i \, b^{2} c^{3} d^{3} x^{5} + 60 \, b^{2} c^{2} d^{3} x^{4} - 80 i \, b^{2} c d^{3} x^{3}\right)} \arctan\left(c x\right)^{2} + \frac{1}{320} \, {\left(16 \, b^{2} c^{3} d^{3} x^{5} - 60 i \, b^{2} c^{2} d^{3} x^{4} - 80 \, b^{2} c d^{3} x^{3}\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - \frac{1}{320} \, {\left(-4 i \, b^{2} c^{3} d^{3} x^{5} - 15 \, b^{2} c^{2} d^{3} x^{4} + 20 i \, b^{2} c d^{3} x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - i \, \int \frac{60 \, {\left(b^{2} c^{5} d^{3} x^{6} - 2 \, b^{2} c^{3} d^{3} x^{4} - 3 \, b^{2} c d^{3} x^{2}\right)} \arctan\left(c x\right)^{2} + 5 \, {\left(b^{2} c^{5} d^{3} x^{6} - 2 \, b^{2} c^{3} d^{3} x^{4} - 3 \, b^{2} c d^{3} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, {\left(19 \, b^{2} c^{4} d^{3} x^{5} - 20 \, b^{2} c^{2} d^{3} x^{3}\right)} \arctan\left(c x\right) + {\left(4 \, b^{2} c^{5} d^{3} x^{6} - 35 \, b^{2} c^{3} d^{3} x^{4} - 60 \, {\left(b^{2} c^{4} d^{3} x^{5} + b^{2} c^{2} d^{3} x^{3}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{80 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - \int \frac{180 \, {\left(b^{2} c^{4} d^{3} x^{5} + b^{2} c^{2} d^{3} x^{3}\right)} \arctan\left(c x\right)^{2} + 15 \, {\left(b^{2} c^{4} d^{3} x^{5} + b^{2} c^{2} d^{3} x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 2 \, {\left(4 \, b^{2} c^{5} d^{3} x^{6} - 35 \, b^{2} c^{3} d^{3} x^{4}\right)} \arctan\left(c x\right) + {\left(19 \, b^{2} c^{4} d^{3} x^{5} - 20 \, b^{2} c^{2} d^{3} x^{3} + 20 \, {\left(b^{2} c^{5} d^{3} x^{6} - 2 \, b^{2} c^{3} d^{3} x^{4} - 3 \, b^{2} c d^{3} x^{2}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{80 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"-1/5*I*a^2*c^3*d^3*x^5 - 3/4*a^2*c^2*d^3*x^4 - 1/10*I*(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*c^3*d^3 + I*a^2*c*d^3*x^3 + 1/2*b^2*d^3*x^2*arctan(c*x)^2 - 1/2*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a*b*c^2*d^3 + I*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*c*d^3 + 1/2*a^2*d^3*x^2 + (x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*d^3 - 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*d^3 - 1/320*(16*I*b^2*c^3*d^3*x^5 + 60*b^2*c^2*d^3*x^4 - 80*I*b^2*c*d^3*x^3)*arctan(c*x)^2 + 1/320*(16*b^2*c^3*d^3*x^5 - 60*I*b^2*c^2*d^3*x^4 - 80*b^2*c*d^3*x^3)*arctan(c*x)*log(c^2*x^2 + 1) - 1/320*(-4*I*b^2*c^3*d^3*x^5 - 15*b^2*c^2*d^3*x^4 + 20*I*b^2*c*d^3*x^3)*log(c^2*x^2 + 1)^2 - I*integrate(1/80*(60*(b^2*c^5*d^3*x^6 - 2*b^2*c^3*d^3*x^4 - 3*b^2*c*d^3*x^2)*arctan(c*x)^2 + 5*(b^2*c^5*d^3*x^6 - 2*b^2*c^3*d^3*x^4 - 3*b^2*c*d^3*x^2)*log(c^2*x^2 + 1)^2 - 2*(19*b^2*c^4*d^3*x^5 - 20*b^2*c^2*d^3*x^3)*arctan(c*x) + (4*b^2*c^5*d^3*x^6 - 35*b^2*c^3*d^3*x^4 - 60*(b^2*c^4*d^3*x^5 + b^2*c^2*d^3*x^3)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x) - integrate(1/80*(180*(b^2*c^4*d^3*x^5 + b^2*c^2*d^3*x^3)*arctan(c*x)^2 + 15*(b^2*c^4*d^3*x^5 + b^2*c^2*d^3*x^3)*log(c^2*x^2 + 1)^2 + 2*(4*b^2*c^5*d^3*x^6 - 35*b^2*c^3*d^3*x^4)*arctan(c*x) + (19*b^2*c^4*d^3*x^5 - 20*b^2*c^2*d^3*x^3 + 20*(b^2*c^5*d^3*x^6 - 2*b^2*c^3*d^3*x^4 - 3*b^2*c*d^3*x^2)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
87,0,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{4} i \, a^{2} c^{3} d^{3} x^{4} - 4 \, b^{2} c^{5} d^{3} \int \frac{x^{5} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 2 \, b^{2} c^{5} d^{3} \int \frac{x^{5} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - a^{2} c^{2} d^{3} x^{3} - 36 \, b^{2} c^{4} d^{3} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 3 \, b^{2} c^{4} d^{3} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 5 \, b^{2} c^{4} d^{3} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - \frac{1}{6} i \, {\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 c^{3} d^{3} + 8 \, b^{2} c^{3} d^{3} \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 20 \, b^{2} c^{3} d^{3} \int \frac{x^{3} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - {\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 c^{2} d^{3} + \frac{3}{2} i \, a^{2} c d^{3} x^{2} - 24 \, b^{2} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 2 \, b^{2} c^{2} d^{3} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 10 \, b^{2} c^{2} d^{3} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 i \, {\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 c d^{3} + \frac{b^{2} d^{3} \arctan\left(c x\right)^{3}}{4 \, c} + 12 \, b^{2} c d^{3} \int \frac{x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 8 \, b^{2} c d^{3} \int \frac{x \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + a^{2} d^{3} x + b^{2} d^{3} \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d^{3}}{c} - \frac{1}{64} \, {\left(4 i \, b^{2} c^{3} d^{3} x^{4} + 16 \, b^{2} c^{2} d^{3} x^{3} - 24 i \, b^{2} c d^{3} x^{2} - 16 \, b^{2} d^{3} x\right)} \arctan\left(c x\right)^{2} + \frac{1}{64} \, {\left(4 \, b^{2} c^{3} d^{3} x^{4} - 16 i \, b^{2} c^{2} d^{3} x^{3} - 24 \, b^{2} c d^{3} x^{2} + 16 i \, b^{2} d^{3} x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - \frac{1}{64} \, {\left(-i \, b^{2} c^{3} d^{3} x^{4} - 4 \, b^{2} c^{2} d^{3} x^{3} + 6 i \, b^{2} c d^{3} x^{2} + 4 \, b^{2} d^{3} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - i \, \int \frac{12 \, {\left(b^{2} c^{5} d^{3} x^{5} - 2 \, b^{2} c^{3} d^{3} x^{3} - 3 \, b^{2} c d^{3} x\right)} \arctan\left(c x\right)^{2} + {\left(b^{2} c^{5} d^{3} x^{5} - 2 \, b^{2} c^{3} d^{3} x^{3} - 3 \, b^{2} c d^{3} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 10 \, {\left(b^{2} c^{4} d^{3} x^{4} - 2 \, b^{2} c^{2} d^{3} x^{2}\right)} \arctan\left(c x\right) + {\left(b^{2} c^{5} d^{3} x^{5} - 10 \, b^{2} c^{3} d^{3} x^{3} + 4 \, b^{2} c d^{3} x - 4 \, {\left(3 \, b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"-1/4*I*a^2*c^3*d^3*x^4 - 4*b^2*c^5*d^3*integrate(1/16*x^5*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - 2*b^2*c^5*d^3*integrate(1/16*x^5*arctan(c*x)/(c^2*x^2 + 1), x) - a^2*c^2*d^3*x^3 - 36*b^2*c^4*d^3*integrate(1/16*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) - 3*b^2*c^4*d^3*integrate(1/16*x^4*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 5*b^2*c^4*d^3*integrate(1/16*x^4*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - 1/6*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a*b*c^3*d^3 + 8*b^2*c^3*d^3*integrate(1/16*x^3*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 20*b^2*c^3*d^3*integrate(1/16*x^3*arctan(c*x)/(c^2*x^2 + 1), x) - (2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*c^2*d^3 + 3/2*I*a^2*c*d^3*x^2 - 24*b^2*c^2*d^3*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) - 2*b^2*c^2*d^3*integrate(1/16*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 10*b^2*c^2*d^3*integrate(1/16*x^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 3*I*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*c*d^3 + 1/4*b^2*d^3*arctan(c*x)^3/c + 12*b^2*c*d^3*integrate(1/16*x*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - 8*b^2*c*d^3*integrate(1/16*x*arctan(c*x)/(c^2*x^2 + 1), x) + a^2*d^3*x + b^2*d^3*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + (2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d^3/c - 1/64*(4*I*b^2*c^3*d^3*x^4 + 16*b^2*c^2*d^3*x^3 - 24*I*b^2*c*d^3*x^2 - 16*b^2*d^3*x)*arctan(c*x)^2 + 1/64*(4*b^2*c^3*d^3*x^4 - 16*I*b^2*c^2*d^3*x^3 - 24*b^2*c*d^3*x^2 + 16*I*b^2*d^3*x)*arctan(c*x)*log(c^2*x^2 + 1) - 1/64*(-I*b^2*c^3*d^3*x^4 - 4*b^2*c^2*d^3*x^3 + 6*I*b^2*c*d^3*x^2 + 4*b^2*d^3*x)*log(c^2*x^2 + 1)^2 - I*integrate(1/16*(12*(b^2*c^5*d^3*x^5 - 2*b^2*c^3*d^3*x^3 - 3*b^2*c*d^3*x)*arctan(c*x)^2 + (b^2*c^5*d^3*x^5 - 2*b^2*c^3*d^3*x^3 - 3*b^2*c*d^3*x)*log(c^2*x^2 + 1)^2 - 10*(b^2*c^4*d^3*x^4 - 2*b^2*c^2*d^3*x^2)*arctan(c*x) + (b^2*c^5*d^3*x^5 - 10*b^2*c^3*d^3*x^3 + 4*b^2*c*d^3*x - 4*(3*b^2*c^4*d^3*x^4 + 2*b^2*c^2*d^3*x^2 - b^2*d^3)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
88,0,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{3} i \, a^{2} c^{3} d^{3} x^{3} - 36 i \, b^{2} c^{5} d^{3} \int \frac{x^{5} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 12 \, b^{2} c^{5} d^{3} \int \frac{x^{5} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 3 i \, b^{2} c^{5} d^{3} \int \frac{x^{5} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 96 i \, a b c^{5} d^{3} \int \frac{x^{5} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 8 \, b^{2} c^{5} d^{3} \int \frac{x^{5} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 4 i \, b^{2} c^{5} d^{3} \int \frac{x^{5} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 108 \, b^{2} c^{4} d^{3} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 36 i \, b^{2} c^{4} d^{3} \int \frac{x^{4} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 9 \, b^{2} c^{4} d^{3} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 288 \, a b c^{4} d^{3} \int \frac{x^{4} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 44 i \, b^{2} c^{4} d^{3} \int \frac{x^{4} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 22 \, b^{2} c^{4} d^{3} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - \frac{3}{2} \, a^{2} c^{2} d^{3} x^{2} + 72 i \, b^{2} c^{3} d^{3} \int \frac{x^{3} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 24 \, b^{2} c^{3} d^{3} \int \frac{x^{3} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 6 i \, b^{2} c^{3} d^{3} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 96 i \, a b c^{3} d^{3} \int \frac{x^{3} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 108 \, b^{2} c^{3} d^{3} \int \frac{x^{3} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 54 i \, b^{2} c^{3} d^{3} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + \frac{3}{4} i \, b^{2} d^{3} \arctan\left(c x\right)^{3} - 72 \, b^{2} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 24 i \, b^{2} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 192 \, a b c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 72 i \, b^{2} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - \frac{1}{48} \, b^{2} d^{3} \log\left(c^{2} x^{2} + 1\right)^{3} + 3 i \, a^{2} c d^{3} x + 36 \, b^{2} c d^{3} \int \frac{x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 9 i \, b^{2} c d^{3} \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + \frac{3}{16} \, b^{2} d^{3} \log\left(c^{2} x^{2} + 1\right)^{2} + 3 i \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d^{3} + 36 \, b^{2} d^{3} \int \frac{\arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 12 i \, b^{2} d^{3} \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 3 \, b^{2} d^{3} \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 96 \, a b d^{3} \int \frac{\arctan\left(c x\right)}{48 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + a^{2} d^{3} \log\left(x\right) - \frac{1}{96} \, {\left(8 i \, b^{2} c^{3} d^{3} x^{3} + 36 \, b^{2} c^{2} d^{3} x^{2} - 72 i \, b^{2} c d^{3} x\right)} \arctan\left(c x\right)^{2} + \frac{1}{96} \, {\left(8 \, b^{2} c^{3} d^{3} x^{3} - 36 i \, b^{2} c^{2} d^{3} x^{2} - 72 \, b^{2} c d^{3} x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - \frac{1}{96} \, {\left(-2 i \, b^{2} c^{3} d^{3} x^{3} - 9 \, b^{2} c^{2} d^{3} x^{2} + 18 i \, b^{2} c d^{3} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"-1/3*I*a^2*c^3*d^3*x^3 - 36*I*b^2*c^5*d^3*integrate(1/48*x^5*arctan(c*x)^2/(c^2*x^3 + x), x) - 12*b^2*c^5*d^3*integrate(1/48*x^5*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) - 3*I*b^2*c^5*d^3*integrate(1/48*x^5*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) - 96*I*a*b*c^5*d^3*integrate(1/48*x^5*arctan(c*x)/(c^2*x^3 + x), x) - 8*b^2*c^5*d^3*integrate(1/48*x^5*arctan(c*x)/(c^2*x^3 + x), x) - 4*I*b^2*c^5*d^3*integrate(1/48*x^5*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) - 108*b^2*c^4*d^3*integrate(1/48*x^4*arctan(c*x)^2/(c^2*x^3 + x), x) + 36*I*b^2*c^4*d^3*integrate(1/48*x^4*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) - 9*b^2*c^4*d^3*integrate(1/48*x^4*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) - 288*a*b*c^4*d^3*integrate(1/48*x^4*arctan(c*x)/(c^2*x^3 + x), x) + 44*I*b^2*c^4*d^3*integrate(1/48*x^4*arctan(c*x)/(c^2*x^3 + x), x) - 22*b^2*c^4*d^3*integrate(1/48*x^4*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) - 3/2*a^2*c^2*d^3*x^2 + 72*I*b^2*c^3*d^3*integrate(1/48*x^3*arctan(c*x)^2/(c^2*x^3 + x), x) + 24*b^2*c^3*d^3*integrate(1/48*x^3*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + 6*I*b^2*c^3*d^3*integrate(1/48*x^3*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) - 96*I*a*b*c^3*d^3*integrate(1/48*x^3*arctan(c*x)/(c^2*x^3 + x), x) + 108*b^2*c^3*d^3*integrate(1/48*x^3*arctan(c*x)/(c^2*x^3 + x), x) + 54*I*b^2*c^3*d^3*integrate(1/48*x^3*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + 3/4*I*b^2*d^3*arctan(c*x)^3 - 72*b^2*c^2*d^3*integrate(1/48*x^2*arctan(c*x)^2/(c^2*x^3 + x), x) + 24*I*b^2*c^2*d^3*integrate(1/48*x^2*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) - 192*a*b*c^2*d^3*integrate(1/48*x^2*arctan(c*x)/(c^2*x^3 + x), x) - 72*I*b^2*c^2*d^3*integrate(1/48*x^2*arctan(c*x)/(c^2*x^3 + x), x) - 1/48*b^2*d^3*log(c^2*x^2 + 1)^3 + 3*I*a^2*c*d^3*x + 36*b^2*c*d^3*integrate(1/48*x*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + 9*I*b^2*c*d^3*integrate(1/48*x*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 3/16*b^2*d^3*log(c^2*x^2 + 1)^2 + 3*I*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d^3 + 36*b^2*d^3*integrate(1/48*arctan(c*x)^2/(c^2*x^3 + x), x) - 12*I*b^2*d^3*integrate(1/48*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + 3*b^2*d^3*integrate(1/48*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 96*a*b*d^3*integrate(1/48*arctan(c*x)/(c^2*x^3 + x), x) + a^2*d^3*log(x) - 1/96*(8*I*b^2*c^3*d^3*x^3 + 36*b^2*c^2*d^3*x^2 - 72*I*b^2*c*d^3*x)*arctan(c*x)^2 + 1/96*(8*b^2*c^3*d^3*x^3 - 36*I*b^2*c^2*d^3*x^2 - 72*b^2*c*d^3*x)*arctan(c*x)*log(c^2*x^2 + 1) - 1/96*(-2*I*b^2*c^3*d^3*x^3 - 9*b^2*c^2*d^3*x^2 + 18*I*b^2*c*d^3*x)*log(c^2*x^2 + 1)^2","F",0
89,-1,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,0,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^6,x, algorithm=""maxima"")","i \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} a b c^{3} d^{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 c^{2} d^{3} + \frac{1}{2} i \, {\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 c d^{3} - \frac{1}{10} \, {\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)} a b d^{3} + \frac{i \, a^{2} c^{3} d^{3}}{2 \, x^{2}} + \frac{a^{2} c^{2} d^{3}}{x^{3}} - \frac{3 i \, a^{2} c d^{3}}{4 \, x^{4}} - \frac{a^{2} d^{3}}{5 \, x^{5}} - \frac{\frac{1}{3} i \, {\left(360 \, {\left(\arctan\left(c x\right)^{2} - \log\left(c^{2} x^{2} + 1\right) + 2 \, \log\left(x\right)\right)} b^{2} c^{5} d^{3} - 720 \, {\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} b^{2} c^{4} d^{3} \arctan\left(c x\right) - 152 \, {\left(3 \, c^{3} \arctan\left(c x\right) + \frac{3 \, c^{2} x^{2} - 1}{x^{3}}\right)} b^{2} c^{2} d^{3} \arctan\left(c x\right) + \frac{76 \, {\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)} b^{2} c^{3} d^{3}}{x^{2}} + \frac{1552 \, b^{2} c^{5} d^{3} x^{5} \log\left(x\right) + 164 \, b^{2} c^{3} d^{3} x^{3} - 36 \, {\left(17 \, b^{2} c^{5} d^{3} x^{5} + 10 \, b^{2} c^{3} d^{3} x^{3} - 15 \, b^{2} c d^{3} x\right)} \arctan\left(c x\right)^{2} - 15 \, {\left(2 \, b^{2} c^{3} d^{3} x^{3} - 3 \, b^{2} c d^{3} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 8 \, {\left(153 \, b^{2} c^{4} d^{3} x^{4} - 41 \, b^{2} c^{2} d^{3} x^{2}\right)} \arctan\left(c x\right) - 8 \, {\left(97 \, b^{2} c^{5} d^{3} x^{5} - 6 \, {\left(5 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{x^{5}}\right)} x^{5} + 4 \, x^{5} \int \frac{180 \, {\left(3 \, b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \arctan\left(c x\right)^{2} + 15 \, {\left(3 \, b^{2} c^{4} d^{3} x^{4} + 2 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 56 \, {\left(5 \, b^{2} c^{3} d^{3} x^{3} - b^{2} c d^{3} x\right)} \arctan\left(c x\right) - 12 \, {\left(5 \, b^{2} c^{4} d^{3} x^{4} - b^{2} c^{2} d^{3} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{4 \, {\left(c^{2} x^{8} + x^{6}\right)}}\,{d x} + {\left(-40 i \, b^{2} c^{3} d^{3} x^{3} - 80 \, b^{2} c^{2} d^{3} x^{2} + 60 i \, b^{2} c d^{3} x + 16 \, b^{2} d^{3}\right)} \arctan\left(c x\right)^{2} - 12 \, {\left(5 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \arctan\left(c x\right)^{2} + {\left(40 \, b^{2} c^{3} d^{3} x^{3} - 80 i \, b^{2} c^{2} d^{3} x^{2} - 60 \, b^{2} c d^{3} x + 16 i \, b^{2} d^{3}\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - 20 \, {\left(2 \, b^{2} c^{3} d^{3} x^{3} - 3 \, b^{2} c d^{3} x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) + {\left(10 i \, b^{2} c^{3} d^{3} x^{3} + 20 \, b^{2} c^{2} d^{3} x^{2} - 15 i \, b^{2} c d^{3} x - 4 \, b^{2} d^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - {\left(5 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{320 \, x^{5}}"," ",0,"I*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*a*b*c^3*d^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*c^2*d^3 + 1/2*I*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*a*b*c*d^3 - 1/10*((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)*a*b*d^3 + 1/2*I*a^2*c^3*d^3/x^2 + a^2*c^2*d^3/x^3 - 3/4*I*a^2*c*d^3/x^4 - 1/5*a^2*d^3/x^5 - 1/320*(320*I*x^5*integrate(1/80*(60*(b^2*c^5*d^3*x^5 - 2*b^2*c^3*d^3*x^3 - 3*b^2*c*d^3*x)*arctan(c*x)^2 + 5*(b^2*c^5*d^3*x^5 - 2*b^2*c^3*d^3*x^3 - 3*b^2*c*d^3*x)*log(c^2*x^2 + 1)^2 + 2*(30*b^2*c^4*d^3*x^4 - 19*b^2*c^2*d^3*x^2)*arctan(c*x) - (10*b^2*c^5*d^3*x^5 - 35*b^2*c^3*d^3*x^3 + 4*b^2*c*d^3*x + 20*(3*b^2*c^4*d^3*x^4 + 2*b^2*c^2*d^3*x^2 - b^2*d^3)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^8 + x^6), x) + 320*x^5*integrate(1/80*(60*(3*b^2*c^4*d^3*x^4 + 2*b^2*c^2*d^3*x^2 - b^2*d^3)*arctan(c*x)^2 + 5*(3*b^2*c^4*d^3*x^4 + 2*b^2*c^2*d^3*x^2 - b^2*d^3)*log(c^2*x^2 + 1)^2 - 2*(10*b^2*c^5*d^3*x^5 - 35*b^2*c^3*d^3*x^3 + 4*b^2*c*d^3*x)*arctan(c*x) - (30*b^2*c^4*d^3*x^4 - 19*b^2*c^2*d^3*x^2 - 20*(b^2*c^5*d^3*x^5 - 2*b^2*c^3*d^3*x^3 - 3*b^2*c*d^3*x)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^8 + x^6), x) + (-40*I*b^2*c^3*d^3*x^3 - 80*b^2*c^2*d^3*x^2 + 60*I*b^2*c*d^3*x + 16*b^2*d^3)*arctan(c*x)^2 + (40*b^2*c^3*d^3*x^3 - 80*I*b^2*c^2*d^3*x^2 - 60*b^2*c*d^3*x + 16*I*b^2*d^3)*arctan(c*x)*log(c^2*x^2 + 1) + (10*I*b^2*c^3*d^3*x^3 + 20*b^2*c^2*d^3*x^2 - 15*I*b^2*c*d^3*x - 4*b^2*d^3)*log(c^2*x^2 + 1)^2)/x^5","F",0
94,0,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^2/x^7,x, algorithm=""maxima"")","-\frac{1}{3} i \, {\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 c^{3} d^{3} - \frac{1}{2} \, {\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 c^{2} d^{3} - \frac{3}{10} i \, {\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)} a b c d^{3} - \frac{1}{45} \, {\left({\left(15 \, c^{5} \arctan\left(c x\right) + \frac{15 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 3}{x^{5}}\right)} c + \frac{15 \, \arctan\left(c x\right)}{x^{6}}\right)} a b d^{3} - \frac{1}{180} \, {\left(4 \, {\left(15 \, c^{5} \arctan\left(c x\right) + \frac{15 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 3}{x^{5}}\right)} c \arctan\left(c x\right) - \frac{{\left(30 \, c^{4} x^{4} \arctan\left(c x\right)^{2} - 46 \, c^{4} x^{4} \log\left(c^{2} x^{2} + 1\right) + 92 \, c^{4} x^{4} \log\left(x\right) + 16 \, c^{2} x^{2} - 3\right)} c^{2}}{x^{4}}\right)} b^{2} d^{3} + \frac{i \, a^{2} c^{3} d^{3}}{3 \, x^{3}} + \frac{3 \, a^{2} c^{2} d^{3}}{4 \, x^{4}} - \frac{3 i \, a^{2} c d^{3}}{5 \, x^{5}} - \frac{b^{2} d^{3} \arctan\left(c x\right)^{2}}{6 \, x^{6}} - \frac{a^{2} d^{3}}{6 \, x^{6}} - \frac{180 i \, b^{2} c^{2} d^{3} x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - {\left(80 \, {\left(\arctan\left(c x\right)^{2} - \log\left(c^{2} x^{2} + 1\right) + 2 \, \log\left(x\right)\right)} b^{2} c^{6} d^{3} - 160 \, {\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} b^{2} c^{5} d^{3} \arctan\left(c x\right) - 216 \, {\left(3 \, c^{3} \arctan\left(c x\right) + \frac{3 \, c^{2} x^{2} - 1}{x^{3}}\right)} b^{2} c^{3} d^{3} \arctan\left(c x\right) + \frac{108 \, {\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)} b^{2} c^{4} d^{3}}{x^{2}} + \frac{896 \, b^{2} c^{6} d^{3} x^{5} \log\left(x\right) + 132 \, b^{2} c^{4} d^{3} x^{3} + 45 \, b^{2} c^{2} d^{3} x \log\left(c^{2} x^{2} + 1\right)^{2} - 4 \, {\left(79 \, b^{2} c^{6} d^{3} x^{5} - 135 \, b^{2} c^{2} d^{3} x\right)} \arctan\left(c x\right)^{2} - 8 \, {\left(79 \, b^{2} c^{5} d^{3} x^{4} - 33 \, b^{2} c^{3} d^{3} x^{2}\right)} \arctan\left(c x\right) - 16 \, {\left(28 \, b^{2} c^{6} d^{3} x^{5} - {\left(5 \, b^{2} c^{3} d^{3} x^{2} - 9 \, b^{2} c d^{3}\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{x^{5}}\right)} x^{5} + 4 i \, x^{5} \int \frac{540 \, {\left(b^{2} c^{5} d^{3} x^{4} - 2 \, b^{2} c^{3} d^{3} x^{2} - 3 \, b^{2} c d^{3}\right)} \arctan\left(c x\right)^{2} + 45 \, {\left(b^{2} c^{5} d^{3} x^{4} - 2 \, b^{2} c^{3} d^{3} x^{2} - 3 \, b^{2} c d^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 56 \, {\left(5 \, b^{2} c^{4} d^{3} x^{3} - 9 \, b^{2} c^{2} d^{3} x\right)} \arctan\left(c x\right) - 12 \, {\left(5 \, b^{2} c^{5} d^{3} x^{4} - 9 \, b^{2} c^{3} d^{3} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{4 \, {\left(c^{2} x^{8} + x^{6}\right)}}\,{d x} - 12 i \, {\left(5 \, b^{2} c^{3} d^{3} x^{2} - 9 \, b^{2} c d^{3}\right)} \arctan\left(c x\right)^{2} + {\left(-80 i \, b^{2} c^{3} d^{3} x^{2} - 180 \, b^{2} c^{2} d^{3} x + 144 i \, b^{2} c d^{3}\right)} \arctan\left(c x\right)^{2} + {\left(80 \, b^{2} c^{3} d^{3} x^{2} - 180 i \, b^{2} c^{2} d^{3} x - 144 \, b^{2} c d^{3}\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right) - i \, {\left(5 \, b^{2} c^{3} d^{3} x^{2} - 9 \, b^{2} c d^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + {\left(20 i \, b^{2} c^{3} d^{3} x^{2} + 45 \, b^{2} c^{2} d^{3} x - 36 i \, b^{2} c d^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{960 \, x^{5}}"," ",0,"-1/3*I*((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*c^3*d^3 - 1/2*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*a*b*c^2*d^3 - 3/10*I*((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)*a*b*c*d^3 - 1/45*((15*c^5*arctan(c*x) + (15*c^4*x^4 - 5*c^2*x^2 + 3)/x^5)*c + 15*arctan(c*x)/x^6)*a*b*d^3 - 1/180*(4*(15*c^5*arctan(c*x) + (15*c^4*x^4 - 5*c^2*x^2 + 3)/x^5)*c*arctan(c*x) - (30*c^4*x^4*arctan(c*x)^2 - 46*c^4*x^4*log(c^2*x^2 + 1) + 92*c^4*x^4*log(x) + 16*c^2*x^2 - 3)*c^2/x^4)*b^2*d^3 + 1/3*I*a^2*c^3*d^3/x^3 + 3/4*a^2*c^2*d^3/x^4 - 3/5*I*a^2*c*d^3/x^5 - 1/6*b^2*d^3*arctan(c*x)^2/x^6 - 1/6*a^2*d^3/x^6 - 1/960*(960*I*x^5*integrate(1/240*(180*(b^2*c^5*d^3*x^4 - 2*b^2*c^3*d^3*x^2 - 3*b^2*c*d^3)*arctan(c*x)^2 + 15*(b^2*c^5*d^3*x^4 - 2*b^2*c^3*d^3*x^2 - 3*b^2*c*d^3)*log(c^2*x^2 + 1)^2 + 2*(65*b^2*c^4*d^3*x^3 - 36*b^2*c^2*d^3*x)*arctan(c*x) - (20*b^2*c^5*d^3*x^4 - 81*b^2*c^3*d^3*x^2 + 180*(b^2*c^4*d^3*x^3 + b^2*c^2*d^3*x)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^8 + x^6), x) + 960*x^5*integrate(1/240*(540*(b^2*c^4*d^3*x^3 + b^2*c^2*d^3*x)*arctan(c*x)^2 + 45*(b^2*c^4*d^3*x^3 + b^2*c^2*d^3*x)*log(c^2*x^2 + 1)^2 - 2*(20*b^2*c^5*d^3*x^4 - 81*b^2*c^3*d^3*x^2)*arctan(c*x) - (65*b^2*c^4*d^3*x^3 - 36*b^2*c^2*d^3*x - 60*(b^2*c^5*d^3*x^4 - 2*b^2*c^3*d^3*x^2 - 3*b^2*c*d^3)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^8 + x^6), x) + (-80*I*b^2*c^3*d^3*x^2 - 180*b^2*c^2*d^3*x + 144*I*b^2*c*d^3)*arctan(c*x)^2 + (80*b^2*c^3*d^3*x^2 - 180*I*b^2*c^2*d^3*x - 144*b^2*c*d^3)*arctan(c*x)*log(c^2*x^2 + 1) + (20*I*b^2*c^3*d^3*x^2 + 45*b^2*c^2*d^3*x - 36*I*b^2*c*d^3)*log(c^2*x^2 + 1)^2)/x^5","F",0
95,-1,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))^2/(d+I*c*d*x),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/(d+I*c*d*x),x, algorithm=""maxima"")","-\frac{i \, a^{2} \log\left(i \, c d x + d\right)}{c d} + \frac{24 \, b^{2} \arctan\left(c x\right)^{3} + 6 \, b^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, {\left(12 \, b^{2} c \int \frac{x \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{c^{2} d x^{2} + d}\,{d x} - \frac{4 \, b^{2} \arctan\left(c x\right)^{3}}{c d} + 3 \, b^{2} \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{c^{2} d x^{2} + d}\,{d x} - \frac{48 \, a b \arctan\left(c x\right)^{2}}{c d}\right)} c d - 6 i \, c d \int \frac{16 \, {\left(b^{2} c x \arctan\left(c x\right)^{2} + 2 \, a b c x \arctan\left(c x\right)\right)}}{c^{2} d x^{2} + d}\,{d x}}{96 \, c d}"," ",0,"-I*a^2*log(I*c*d*x + d)/(c*d) + 1/96*(24*b^2*arctan(c*x)^3 + 12*I*b^2*arctan(c*x)^2*log(c^2*x^2 + 1) + 6*b^2*arctan(c*x)*log(c^2*x^2 + 1)^2 + 3*I*b^2*log(c^2*x^2 + 1)^3 - 8*(48*b^2*c*integrate(1/16*x*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*d*x^2 + d), x) - b^2*arctan(c*x)^3/(c*d) + 12*b^2*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*d*x^2 + d), x) - 12*a*b*arctan(c*x)^2/(c*d))*c*d - 96*I*c*d*integrate(1/16*(20*b^2*c*x*arctan(c*x)^2 + 3*b^2*c*x*log(c^2*x^2 + 1)^2 + 32*a*b*c*x*arctan(c*x) + 4*b^2*arctan(c*x)*log(c^2*x^2 + 1))/(c^2*d*x^2 + d), x))/(c*d)","F",0
99,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x/(d+I*c*d*x),x, algorithm=""maxima"")","-a^{2} {\left(\frac{\log\left(i \, c x + 1\right)}{d} - \frac{\log\left(x\right)}{d}\right)} + \frac{-24 i \, b^{2} \arctan\left(c x\right)^{3} + 12 \, b^{2} \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right) - 6 i \, b^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} + 3 \, b^{2} \log\left(c^{2} x^{2} + 1\right)^{3} - {\left(48 \, b^{2} c^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{c^{2} d x^{3} + d x}\,{d x} + \frac{2 \, b^{2} \log\left(c^{2} x^{2} + 1\right)^{3}}{d} + {\left(\frac{\log\left(c^{2} x^{2} + 1\right)^{3}}{d} - \frac{3 \, {\left(\log\left(c^{2} x^{2} + 1\right)^{2} \log\left(-c^{2} x^{2}\right) + 2 \, {\rm Li}_2\left(c^{2} x^{2} + 1\right) \log\left(c^{2} x^{2} + 1\right) - 2 \, {\rm Li}_{3}(c^{2} x^{2} + 1)\right)}}{d}\right)} b^{2} - 72 \, b^{2} \int \frac{\arctan\left(c x\right)^{2}}{c^{2} d x^{3} + d x}\,{d x} - 192 \, a b \int \frac{\arctan\left(c x\right)}{c^{2} d x^{3} + d x}\,{d x} - \frac{12 \, {\left(2 \, c^{2} d \mathit{sage}_{0} x - \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right)\right)} b^{2}}{d}\right)} d - 2 i \, {\left(\frac{4 \, b^{2} \arctan\left(c x\right)^{3}}{d} - 3 \, b^{2} c \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{c^{2} d x^{3} + d x}\,{d x} + \frac{48 \, a b \arctan\left(c x\right)^{2}}{d} + 12 \, b^{2} \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{c^{2} d x^{3} + d x}\,{d x}\right)} d}{96 \, d}"," ",0,"-a^2*(log(I*c*x + 1)/d - log(x)/d) + 1/96*(-24*I*b^2*arctan(c*x)^3 + 12*b^2*arctan(c*x)^2*log(c^2*x^2 + 1) - 6*I*b^2*arctan(c*x)*log(c^2*x^2 + 1)^2 + 3*b^2*log(c^2*x^2 + 1)^3 - 2*(384*b^2*c^2*integrate(1/16*x^2*arctan(c*x)^2/(c^2*d*x^3 + d*x), x) + 192*b^2*c*integrate(1/16*x*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*d*x^3 + d*x), x) + b^2*log(c^2*x^2 + 1)^3/d - 576*b^2*integrate(1/16*arctan(c*x)^2/(c^2*d*x^3 + d*x), x) - 48*b^2*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*d*x^3 + d*x), x) - 1536*a*b*integrate(1/16*arctan(c*x)/(c^2*d*x^3 + d*x), x))*d - 8*I*(b^2*arctan(c*x)^3/d - 12*b^2*c*integrate(1/16*x*log(c^2*x^2 + 1)^2/(c^2*d*x^3 + d*x), x) + 12*a*b*arctan(c*x)^2/d + 48*b^2*integrate(1/16*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*d*x^3 + d*x), x))*d)/d","F",0
100,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^2/(d+I*c*d*x),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^3/(d+I*c*d*x),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^4/(d+I*c*d*x),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate(x^4*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))^2/(d+I*c*d*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-2,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/(d+I*c*d*x)^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
108,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x/(d+I*c*d*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^2/(d+I*c*d*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^3/(d+I*c*d*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(x^4*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,1,142,0,0.476897," ","integrate(x*(a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x, algorithm=""maxima"")","-\frac{{\left(16 i \, a^{2} + 12 \, a b - 5 i \, b^{2}\right)} c x + {\left(6 \, b^{2} c^{2} x^{2} + 4 i \, b^{2} c x + 2 \, b^{2}\right)} \arctan\left(c x\right)^{2} + 8 \, a^{2} - 8 i \, a b - 4 \, b^{2} + {\left({\left(12 \, a b - 5 i \, b^{2}\right)} c^{2} x^{2} + {\left(8 i \, a b + 2 \, b^{2}\right)} c x + 4 \, a b - 3 i \, b^{2}\right)} \arctan\left(c x\right)}{16 \, c^{4} d^{3} x^{2} - 32 i \, c^{3} d^{3} x - 16 \, c^{2} d^{3}}"," ",0,"-((16*I*a^2 + 12*a*b - 5*I*b^2)*c*x + (6*b^2*c^2*x^2 + 4*I*b^2*c*x + 2*b^2)*arctan(c*x)^2 + 8*a^2 - 8*I*a*b - 4*b^2 + ((12*a*b - 5*I*b^2)*c^2*x^2 + (8*I*a*b + 2*b^2)*c*x + 4*a*b - 3*I*b^2)*arctan(c*x))/(16*c^4*d^3*x^2 - 32*I*c^3*d^3*x - 16*c^2*d^3)","A",0
115,1,136,0,0.673833," ","integrate((a+b*arctan(c*x))^2/(d+I*c*d*x)^3,x, algorithm=""maxima"")","-\frac{{\left(4 i \, a b + 3 \, b^{2}\right)} c x + {\left(2 i \, b^{2} c^{2} x^{2} + 4 \, b^{2} c x + 6 i \, b^{2}\right)} \arctan\left(c x\right)^{2} + 8 i \, a^{2} + 8 \, a b - 4 i \, b^{2} + {\left({\left(4 i \, a b + 3 \, b^{2}\right)} c^{2} x^{2} + 2 \, {\left(4 \, a b - i \, b^{2}\right)} c x + 12 i \, a b + 5 \, b^{2}\right)} \arctan\left(c x\right)}{16 \, c^{3} d^{3} x^{2} - 32 i \, c^{2} d^{3} x - 16 \, c d^{3}}"," ",0,"-((4*I*a*b + 3*b^2)*c*x + (2*I*b^2*c^2*x^2 + 4*b^2*c*x + 6*I*b^2)*arctan(c*x)^2 + 8*I*a^2 + 8*a*b - 4*I*b^2 + ((4*I*a*b + 3*b^2)*c^2*x^2 + 2*(4*a*b - I*b^2)*c*x + 12*I*a*b + 5*b^2)*arctan(c*x))/(16*c^3*d^3*x^2 - 32*I*c^2*d^3*x - 16*c*d^3)","A",0
116,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x/(d+I*c*d*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^2/(d+I*c*d*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,1,181,0,0.428364," ","integrate((a+b*arctan(c*x))^2/(1+I*c*x)^4,x, algorithm=""maxima"")","-\frac{{\left(36 i \, a b + 33 \, b^{2}\right)} c^{2} x^{2} + 27 \, {\left(4 \, a b - 3 i \, b^{2}\right)} c x + {\left(18 i \, b^{2} c^{3} x^{3} + 54 \, b^{2} c^{2} x^{2} - 54 i \, b^{2} c x + 126 \, b^{2}\right)} \arctan\left(c x\right)^{2} + 144 \, a^{2} - 120 i \, a b - 56 \, b^{2} + {\left({\left(36 i \, a b + 33 \, b^{2}\right)} c^{3} x^{3} + 9 \, {\left(12 \, a b - 7 i \, b^{2}\right)} c^{2} x^{2} + {\left(-108 i \, a b + 9 \, b^{2}\right)} c x + 252 \, a b - 87 i \, b^{2}\right)} \arctan\left(c x\right)}{432 \, c^{4} x^{3} - 1296 i \, c^{3} x^{2} - 1296 \, c^{2} x + 432 i \, c}"," ",0,"-((36*I*a*b + 33*b^2)*c^2*x^2 + 27*(4*a*b - 3*I*b^2)*c*x + (18*I*b^2*c^3*x^3 + 54*b^2*c^2*x^2 - 54*I*b^2*c*x + 126*b^2)*arctan(c*x)^2 + 144*a^2 - 120*I*a*b - 56*b^2 + ((36*I*a*b + 33*b^2)*c^3*x^3 + 9*(12*a*b - 7*I*b^2)*c^2*x^2 + (-108*I*a*b + 9*b^2)*c*x + 252*a*b - 87*I*b^2)*arctan(c*x))/(432*c^4*x^3 - 1296*I*c^3*x^2 - 1296*c^2*x + 432*I*c)","A",0
119,0,0,0,0.000000," ","integrate(arctan(a*x)^2/(c*x-I*a*c*x^2),x, algorithm=""maxima"")","\frac{8 i \, \arctan\left(a x\right)^{3} - 12 \, \arctan\left(a x\right)^{2} \log\left(a^{2} x^{2} + 1\right) - 6 i \, \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + 3 \, \log\left(a^{2} x^{2} + 1\right)^{2} \log\left(-a^{2} x^{2}\right) + 6 i \, {\left(\frac{4 \, \arctan\left(a x\right)^{3}}{c} + a \int \frac{x \log\left(a^{2} x^{2} + 1\right)^{2}}{a^{2} c x^{3} + c x}\,{d x} - 4 \, \int \frac{\arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)}{a^{2} c x^{3} + c x}\,{d x}\right)} c - 6 \, c \int \frac{4 \, {\left(a^{2} x^{2} - 3\right)} \arctan\left(a x\right)^{2}}{a^{2} c x^{3} + c x}\,{d x} + 6 \, {\left(2 \, \arctan\left(a x\right)^{2} + {\rm Li}_2\left(a^{2} x^{2} + 1\right)\right)} \log\left(a^{2} x^{2} + 1\right) - 6 \, {\rm Li}_{3}(a^{2} x^{2} + 1)}{96 \, c}"," ",0,"1/96*(8*I*arctan(a*x)^3 - 12*arctan(a*x)^2*log(a^2*x^2 + 1) - 6*I*arctan(a*x)*log(a^2*x^2 + 1)^2 + log(a^2*x^2 + 1)^3 + 24*I*(arctan(a*x)^3/c + 4*a*integrate(1/16*x*log(a^2*x^2 + 1)^2/(a^2*c*x^3 + c*x), x) - 16*integrate(1/16*arctan(a*x)*log(a^2*x^2 + 1)/(a^2*c*x^3 + c*x), x))*c + 96*c*integrate(1/16*(4*a*x*arctan(a*x)*log(a^2*x^2 + 1) + 12*arctan(a*x)^2 + log(a^2*x^2 + 1)^2)/(a^2*c*x^3 + c*x), x))/c","F",0
120,0,0,0,0.000000," ","integrate((d+I*c*d*x)^3*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","-\frac{1}{4} i \, a^{3} c^{3} d^{3} x^{4} - 24 \, b^{3} c^{5} d^{3} \int \frac{x^{5} \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right)}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 2 \, b^{3} c^{5} d^{3} \int \frac{x^{5} \log\left(c^{2} x^{2} + 1\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 12 \, b^{3} c^{5} d^{3} \int \frac{x^{5} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c^{5} d^{3} \int \frac{x^{5} \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - a^{3} c^{2} d^{3} x^{3} - 336 \, b^{3} c^{4} d^{3} \int \frac{x^{4} \arctan\left(c x\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 36 \, b^{3} c^{4} d^{3} \int \frac{x^{4} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 1152 \, a b^{2} c^{4} d^{3} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 60 \, b^{3} c^{4} d^{3} \int \frac{x^{4} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - \frac{1}{4} i \, {\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^{2} b c^{3} d^{3} + 48 \, b^{3} c^{3} d^{3} \int \frac{x^{3} \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right)}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 4 \, b^{3} c^{3} d^{3} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 120 \, b^{3} c^{3} d^{3} \int \frac{x^{3} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 30 \, b^{3} c^{3} d^{3} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - \frac{3}{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 c^{2} d^{3} + \frac{3}{2} i \, a^{3} c d^{3} x^{2} + \frac{7 \, b^{3} d^{3} \arctan\left(c x\right)^{4}}{32 \, c} - 224 \, b^{3} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 24 \, b^{3} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 768 \, a b^{2} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 120 \, b^{3} c^{2} d^{3} \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{9}{2} i \, {\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^{2} b c d^{3} + \frac{a b^{2} d^{3} \arctan\left(c x\right)^{3}}{c} + 72 \, b^{3} c d^{3} \int \frac{x \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right)}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 6 \, b^{3} c d^{3} \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{3}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 48 \, b^{3} c d^{3} \int \frac{x \arctan\left(c x\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d^{3} \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + a^{3} d^{3} x + 12 \, b^{3} d^{3} \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{128 \, {\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 d^{3}}{2 \, c} + \frac{1}{256} \, {\left(-8 i \, b^{3} c^{3} d^{3} x^{4} - 32 \, b^{3} c^{2} d^{3} x^{3} + 48 i \, b^{3} c d^{3} x^{2} + 32 \, b^{3} d^{3} x\right)} \arctan\left(c x\right)^{3} + \frac{1}{256} \, {\left(12 \, b^{3} c^{3} d^{3} x^{4} - 48 i \, b^{3} c^{2} d^{3} x^{3} - 72 \, b^{3} c d^{3} x^{2} + 48 i \, b^{3} d^{3} x\right)} \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right) + \frac{1}{256} \, {\left(6 i \, b^{3} c^{3} d^{3} x^{4} + 24 \, b^{3} c^{2} d^{3} x^{3} - 36 i \, b^{3} c d^{3} x^{2} - 24 \, b^{3} d^{3} x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} - \frac{1}{256} \, {\left(b^{3} c^{3} d^{3} x^{4} - 4 i \, b^{3} c^{2} d^{3} x^{3} - 6 \, b^{3} c d^{3} x^{2} + 4 i \, b^{3} d^{3} x\right)} \log\left(c^{2} x^{2} + 1\right)^{3} - i \, \int \frac{112 \, {\left(b^{3} c^{5} d^{3} x^{5} - 2 \, b^{3} c^{3} d^{3} x^{3} - 3 \, b^{3} c d^{3} x\right)} \arctan\left(c x\right)^{3} + 2 \, {\left(3 \, b^{3} c^{4} d^{3} x^{4} + 2 \, b^{3} c^{2} d^{3} x^{2} - b^{3} d^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{3} + 12 \, {\left(32 \, a b^{2} c^{5} d^{3} x^{5} - 5 \, b^{3} c^{4} d^{3} x^{4} - 64 \, a b^{2} c^{3} d^{3} x^{3} + 10 \, b^{3} c^{2} d^{3} x^{2} - 96 \, a b^{2} c d^{3} x\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(5 \, b^{3} c^{4} d^{3} x^{4} - 10 \, b^{3} c^{2} d^{3} x^{2} + 4 \, {\left(b^{3} c^{5} d^{3} x^{5} - 2 \, b^{3} c^{3} d^{3} x^{3} - 3 \, b^{3} c d^{3} x\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 12 \, {\left(2 \, {\left(3 \, b^{3} c^{4} d^{3} x^{4} + 2 \, b^{3} c^{2} d^{3} x^{2} - b^{3} d^{3}\right)} \arctan\left(c x\right)^{2} - {\left(b^{3} c^{5} d^{3} x^{5} - 10 \, b^{3} c^{3} d^{3} x^{3} + 4 \, b^{3} c d^{3} x\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{128 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"-1/4*I*a^3*c^3*d^3*x^4 - 24*b^3*c^5*d^3*integrate(1/128*x^5*arctan(c*x)^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 2*b^3*c^5*d^3*integrate(1/128*x^5*log(c^2*x^2 + 1)^3/(c^2*x^2 + 1), x) - 12*b^3*c^5*d^3*integrate(1/128*x^5*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^3*c^5*d^3*integrate(1/128*x^5*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - a^3*c^2*d^3*x^3 - 336*b^3*c^4*d^3*integrate(1/128*x^4*arctan(c*x)^3/(c^2*x^2 + 1), x) - 36*b^3*c^4*d^3*integrate(1/128*x^4*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 1152*a*b^2*c^4*d^3*integrate(1/128*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) - 60*b^3*c^4*d^3*integrate(1/128*x^4*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - 1/4*I*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a^2*b*c^3*d^3 + 48*b^3*c^3*d^3*integrate(1/128*x^3*arctan(c*x)^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - 4*b^3*c^3*d^3*integrate(1/128*x^3*log(c^2*x^2 + 1)^3/(c^2*x^2 + 1), x) + 120*b^3*c^3*d^3*integrate(1/128*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) - 30*b^3*c^3*d^3*integrate(1/128*x^3*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 3/2*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a^2*b*c^2*d^3 + 3/2*I*a^3*c*d^3*x^2 + 7/32*b^3*d^3*arctan(c*x)^4/c - 224*b^3*c^2*d^3*integrate(1/128*x^2*arctan(c*x)^3/(c^2*x^2 + 1), x) - 24*b^3*c^2*d^3*integrate(1/128*x^2*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 768*a*b^2*c^2*d^3*integrate(1/128*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 120*b^3*c^2*d^3*integrate(1/128*x^2*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 9/2*I*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a^2*b*c*d^3 + a*b^2*d^3*arctan(c*x)^3/c + 72*b^3*c*d^3*integrate(1/128*x*arctan(c*x)^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - 6*b^3*c*d^3*integrate(1/128*x*log(c^2*x^2 + 1)^3/(c^2*x^2 + 1), x) - 48*b^3*c*d^3*integrate(1/128*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 12*b^3*c*d^3*integrate(1/128*x*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + a^3*d^3*x + 12*b^3*d^3*integrate(1/128*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*d^3/c + 1/256*(-8*I*b^3*c^3*d^3*x^4 - 32*b^3*c^2*d^3*x^3 + 48*I*b^3*c*d^3*x^2 + 32*b^3*d^3*x)*arctan(c*x)^3 + 1/256*(12*b^3*c^3*d^3*x^4 - 48*I*b^3*c^2*d^3*x^3 - 72*b^3*c*d^3*x^2 + 48*I*b^3*d^3*x)*arctan(c*x)^2*log(c^2*x^2 + 1) + 1/256*(6*I*b^3*c^3*d^3*x^4 + 24*b^3*c^2*d^3*x^3 - 36*I*b^3*c*d^3*x^2 - 24*b^3*d^3*x)*arctan(c*x)*log(c^2*x^2 + 1)^2 - 1/256*(b^3*c^3*d^3*x^4 - 4*I*b^3*c^2*d^3*x^3 - 6*b^3*c*d^3*x^2 + 4*I*b^3*d^3*x)*log(c^2*x^2 + 1)^3 - I*integrate(1/128*(112*(b^3*c^5*d^3*x^5 - 2*b^3*c^3*d^3*x^3 - 3*b^3*c*d^3*x)*arctan(c*x)^3 + 2*(3*b^3*c^4*d^3*x^4 + 2*b^3*c^2*d^3*x^2 - b^3*d^3)*log(c^2*x^2 + 1)^3 + 12*(32*a*b^2*c^5*d^3*x^5 - 5*b^3*c^4*d^3*x^4 - 64*a*b^2*c^3*d^3*x^3 + 10*b^3*c^2*d^3*x^2 - 96*a*b^2*c*d^3*x)*arctan(c*x)^2 + 3*(5*b^3*c^4*d^3*x^4 - 10*b^3*c^2*d^3*x^2 + 4*(b^3*c^5*d^3*x^5 - 2*b^3*c^3*d^3*x^3 - 3*b^3*c*d^3*x)*arctan(c*x))*log(c^2*x^2 + 1)^2 - 12*(2*(3*b^3*c^4*d^3*x^4 + 2*b^3*c^2*d^3*x^2 - b^3*d^3)*arctan(c*x)^2 - (b^3*c^5*d^3*x^5 - 10*b^3*c^3*d^3*x^3 + 4*b^3*c*d^3*x)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
121,0,0,0,0.000000," ","integrate((d+I*c*d*x)^2*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","-\frac{1}{3} \, a^{3} c^{2} d^{2} x^{3} - 28 \, b^{3} c^{4} d^{2} \int \frac{x^{4} \arctan\left(c x\right)^{3}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 3 \, b^{3} c^{4} d^{2} \int \frac{x^{4} \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^{4} d^{2} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 4 \, b^{3} c^{4} d^{2} \int \frac{x^{4} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{3} d^{2} \int \frac{x^{3} \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right)}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - b^{3} c^{3} d^{2} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{3}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 16 \, b^{3} c^{3} d^{2} \int \frac{x^{3} \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 4 \, b^{3} c^{3} d^{2} \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - \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 c^{2} d^{2} + i \, a^{3} c d^{2} x^{2} + \frac{7 \, b^{3} d^{2} \arctan\left(c x\right)^{4}}{32 \, c} + 24 \, b^{3} c^{2} d^{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} + 3 i \, {\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^{2} b c d^{2} + \frac{a b^{2} d^{2} \arctan\left(c x\right)^{3}}{c} + 12 \, b^{3} c d^{2} \int \frac{x \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right)}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - b^{3} c d^{2} \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{3}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 12 \, b^{3} c d^{2} \int \frac{x \arctan\left(c x\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c d^{2} \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + a^{3} d^{2} x + 3 \, b^{3} d^{2} \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 d^{2}}{2 \, c} - \frac{1}{192} \, {\left(8 \, b^{3} c^{2} d^{2} x^{3} - 24 i \, b^{3} c d^{2} x^{2} - 24 \, b^{3} d^{2} x\right)} \arctan\left(c x\right)^{3} - \frac{1}{192} \, {\left(12 i \, b^{3} c^{2} d^{2} x^{3} + 36 \, b^{3} c d^{2} x^{2} - 36 i \, b^{3} d^{2} x\right)} \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right) + \frac{1}{192} \, {\left(6 \, b^{3} c^{2} d^{2} x^{3} - 18 i \, b^{3} c d^{2} x^{2} - 18 \, b^{3} d^{2} x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} - \frac{1}{192} \, {\left(-i \, b^{3} c^{2} d^{2} x^{3} - 3 \, b^{3} c d^{2} x^{2} + 3 i \, b^{3} d^{2} x\right)} \log\left(c^{2} x^{2} + 1\right)^{3} - i \, \int -\frac{112 \, {\left(b^{3} c^{3} d^{2} x^{3} + b^{3} c d^{2} x\right)} \arctan\left(c x\right)^{3} - {\left(b^{3} c^{4} d^{2} x^{4} - b^{3} d^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{3} + 8 \, {\left(b^{3} c^{4} d^{2} x^{4} + 48 \, a b^{2} c^{3} d^{2} x^{3} - 6 \, b^{3} c^{2} d^{2} x^{2} + 48 \, a b^{2} c d^{2} x\right)} \arctan\left(c x\right)^{2} - 2 \, {\left(b^{3} c^{4} d^{2} x^{4} - 6 \, b^{3} c^{2} d^{2} x^{2} - 6 \, {\left(b^{3} c^{3} d^{2} x^{3} + b^{3} c d^{2} x\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 4 \, {\left(3 \, {\left(b^{3} c^{4} d^{2} x^{4} - b^{3} d^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(4 \, b^{3} c^{3} d^{2} x^{3} - 3 \, b^{3} c d^{2} x\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"-1/3*a^3*c^2*d^2*x^3 - 28*b^3*c^4*d^2*integrate(1/32*x^4*arctan(c*x)^3/(c^2*x^2 + 1), x) - 3*b^3*c^4*d^2*integrate(1/32*x^4*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 96*a*b^2*c^4*d^2*integrate(1/32*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) - 4*b^3*c^4*d^2*integrate(1/32*x^4*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 12*b^3*c^3*d^2*integrate(1/32*x^3*arctan(c*x)^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - b^3*c^3*d^2*integrate(1/32*x^3*log(c^2*x^2 + 1)^3/(c^2*x^2 + 1), x) + 16*b^3*c^3*d^2*integrate(1/32*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) - 4*b^3*c^3*d^2*integrate(1/32*x^3*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) - 1/2*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a^2*b*c^2*d^2 + I*a^3*c*d^2*x^2 + 7/32*b^3*d^2*arctan(c*x)^4/c + 24*b^3*c^2*d^2*integrate(1/32*x^2*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 3*I*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a^2*b*c*d^2 + a*b^2*d^2*arctan(c*x)^3/c + 12*b^3*c*d^2*integrate(1/32*x*arctan(c*x)^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - b^3*c*d^2*integrate(1/32*x*log(c^2*x^2 + 1)^3/(c^2*x^2 + 1), x) - 12*b^3*c*d^2*integrate(1/32*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^3*c*d^2*integrate(1/32*x*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + a^3*d^2*x + 3*b^3*d^2*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*d^2/c - 1/192*(8*b^3*c^2*d^2*x^3 - 24*I*b^3*c*d^2*x^2 - 24*b^3*d^2*x)*arctan(c*x)^3 - 1/192*(12*I*b^3*c^2*d^2*x^3 + 36*b^3*c*d^2*x^2 - 36*I*b^3*d^2*x)*arctan(c*x)^2*log(c^2*x^2 + 1) + 1/192*(6*b^3*c^2*d^2*x^3 - 18*I*b^3*c*d^2*x^2 - 18*b^3*d^2*x)*arctan(c*x)*log(c^2*x^2 + 1)^2 - 1/192*(-I*b^3*c^2*d^2*x^3 - 3*b^3*c*d^2*x^2 + 3*I*b^3*d^2*x)*log(c^2*x^2 + 1)^3 - I*integrate(-1/64*(112*(b^3*c^3*d^2*x^3 + b^3*c*d^2*x)*arctan(c*x)^3 - (b^3*c^4*d^2*x^4 - b^3*d^2)*log(c^2*x^2 + 1)^3 + 8*(b^3*c^4*d^2*x^4 + 48*a*b^2*c^3*d^2*x^3 - 6*b^3*c^2*d^2*x^2 + 48*a*b^2*c*d^2*x)*arctan(c*x)^2 - 2*(b^3*c^4*d^2*x^4 - 6*b^3*c^2*d^2*x^2 - 6*(b^3*c^3*d^2*x^3 + b^3*c*d^2*x)*arctan(c*x))*log(c^2*x^2 + 1)^2 + 4*(3*(b^3*c^4*d^2*x^4 - b^3*d^2)*arctan(c*x)^2 + 2*(4*b^3*c^3*d^2*x^3 - 3*b^3*c*d^2*x)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
122,0,0,0,0.000000," ","integrate((d+I*c*d*x)*(a+b*arctan(c*x))^3,x, algorithm=""maxima"")","12 \, b^{3} c^{3} d \int \frac{x^{3} \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right)}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - b^{3} c^{3} d \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{3}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{3} d \int \frac{x^{3} \arctan\left(c x\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 3 \, b^{3} c^{3} d \int \frac{x^{3} \log\left(c^{2} x^{2} + 1\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{1}{2} i \, a^{3} c d x^{2} + \frac{7 \, b^{3} d \arctan\left(c x\right)^{4}}{32 \, c} + 56 \, b^{3} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)^{3}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c^{2} d \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{3} c^{2} d \int \frac{x^{2} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{3}{2} i \, {\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^{2} b c d + \frac{a b^{2} d \arctan\left(c x\right)^{3}}{c} + 12 \, b^{3} c d \int \frac{x \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right)}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - b^{3} c d \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{3}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 24 \, b^{3} c d \int \frac{x \arctan\left(c x\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c d \int \frac{x \log\left(c^{2} x^{2} + 1\right)^{2}}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + a^{3} d x + 6 \, b^{3} d \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{64 \, {\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 d}{2 \, c} - \frac{1}{128} \, {\left(-8 i \, b^{3} c d x^{2} - 16 \, b^{3} d x\right)} \arctan\left(c x\right)^{3} - \frac{3}{32} \, {\left(b^{3} c d x^{2} - 2 i \, b^{3} d x\right)} \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right) - \frac{1}{128} \, {\left(6 i \, b^{3} c d x^{2} + 12 \, b^{3} d x\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2} + \frac{1}{128} \, {\left(b^{3} c d x^{2} - 2 i \, b^{3} d x\right)} \log\left(c^{2} x^{2} + 1\right)^{3} + i \, \int \frac{56 \, {\left(b^{3} c^{3} d x^{3} + b^{3} c d x\right)} \arctan\left(c x\right)^{3} + {\left(b^{3} c^{2} d x^{2} + b^{3} d\right)} \log\left(c^{2} x^{2} + 1\right)^{3} + 12 \, {\left(16 \, a b^{2} c^{3} d x^{3} - 3 \, b^{3} c^{2} d x^{2} + 16 \, a b^{2} c d x\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(3 \, b^{3} c^{2} d x^{2} + 2 \, {\left(b^{3} c^{3} d x^{3} + b^{3} c d x\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 12 \, {\left({\left(b^{3} c^{2} d x^{2} + b^{3} d\right)} \arctan\left(c x\right)^{2} - {\left(b^{3} c^{3} d x^{3} - 2 \, b^{3} c d x\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{64 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"12*b^3*c^3*d*integrate(1/64*x^3*arctan(c*x)^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - b^3*c^3*d*integrate(1/64*x^3*log(c^2*x^2 + 1)^3/(c^2*x^2 + 1), x) + 12*b^3*c^3*d*integrate(1/64*x^3*arctan(c*x)^2/(c^2*x^2 + 1), x) - 3*b^3*c^3*d*integrate(1/64*x^3*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 1/2*I*a^3*c*d*x^2 + 7/32*b^3*d*arctan(c*x)^4/c + 56*b^3*c^2*d*integrate(1/64*x^2*arctan(c*x)^3/(c^2*x^2 + 1), x) + 6*b^3*c^2*d*integrate(1/64*x^2*arctan(c*x)*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 192*a*b^2*c^2*d*integrate(1/64*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 36*b^3*c^2*d*integrate(1/64*x^2*arctan(c*x)*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 3/2*I*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a^2*b*c*d + a*b^2*d*arctan(c*x)^3/c + 12*b^3*c*d*integrate(1/64*x*arctan(c*x)^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) - b^3*c*d*integrate(1/64*x*log(c^2*x^2 + 1)^3/(c^2*x^2 + 1), x) - 24*b^3*c*d*integrate(1/64*x*arctan(c*x)^2/(c^2*x^2 + 1), x) + 6*b^3*c*d*integrate(1/64*x*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + a^3*d*x + 6*b^3*d*integrate(1/64*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*d/c - 1/128*(-8*I*b^3*c*d*x^2 - 16*b^3*d*x)*arctan(c*x)^3 - 3/32*(b^3*c*d*x^2 - 2*I*b^3*d*x)*arctan(c*x)^2*log(c^2*x^2 + 1) - 1/128*(6*I*b^3*c*d*x^2 + 12*b^3*d*x)*arctan(c*x)*log(c^2*x^2 + 1)^2 + 1/128*(b^3*c*d*x^2 - 2*I*b^3*d*x)*log(c^2*x^2 + 1)^3 + I*integrate(1/64*(56*(b^3*c^3*d*x^3 + b^3*c*d*x)*arctan(c*x)^3 + (b^3*c^2*d*x^2 + b^3*d)*log(c^2*x^2 + 1)^3 + 12*(16*a*b^2*c^3*d*x^3 - 3*b^3*c^2*d*x^2 + 16*a*b^2*c*d*x)*arctan(c*x)^2 + 3*(3*b^3*c^2*d*x^2 + 2*(b^3*c^3*d*x^3 + b^3*c*d*x)*arctan(c*x))*log(c^2*x^2 + 1)^2 - 12*((b^3*c^2*d*x^2 + b^3*d)*arctan(c*x)^2 - (b^3*c^3*d*x^3 - 2*b^3*c*d*x)*arctan(c*x))*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
123,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/(d+I*c*d*x),x, algorithm=""maxima"")","-\frac{i \, a^{3} \log\left(i \, c d x + d\right)}{c d} + \frac{16 \, b^{3} \arctan\left(c x\right)^{4} - b^{3} \log\left(c^{2} x^{2} + 1\right)^{4} + {\left(b^{3} c {\left(\frac{4 \, \log\left(c^{2} d x^{2} + d\right) \log\left(c^{2} x^{2} + 1\right)^{3}}{c^{2} d} + \frac{\frac{4 \, {\left(\log\left(c^{2} x^{2} + 1\right)^{3} + 3 \, \log\left(c^{2} x^{2} + 1\right)^{2} \log\left(d\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)^{4} + 4 \, \log\left(c^{2} x^{2} + 1\right)^{3} \log\left(d\right)}{c^{2}}}{d} - \frac{6 \, {\left(\log\left(c^{2} x^{2} + 1\right)^{2} + 2 \, \log\left(c^{2} x^{2} + 1\right) \log\left(d\right)\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{c^{2} d}\right)} + \frac{16 \, b^{3} \arctan\left(c x\right)^{4}}{c d} + \frac{128 \, a b^{2} \arctan\left(c x\right)^{3}}{c d} + \frac{192 \, a^{2} b \arctan\left(c x\right)^{2}}{c d}\right)} c d - 4 i \, c d \int \frac{32 \, {\left(b^{3} c x \arctan\left(c x\right)^{3} + 3 \, a b^{2} c x \arctan\left(c x\right)^{2} + 3 \, a^{2} b c x \arctan\left(c x\right)\right)}}{c^{2} d x^{2} + d}\,{d x}}{128 \, c d}"," ",0,"-I*a^3*log(I*c*d*x + d)/(c*d) + 1/128*(16*b^3*arctan(c*x)^4 + 16*I*b^3*arctan(c*x)^3*log(c^2*x^2 + 1) + 4*I*b^3*arctan(c*x)*log(c^2*x^2 + 1)^3 - b^3*log(c^2*x^2 + 1)^4 + 16*(b^3*arctan(c*x)^4/(c*d) + 8*b^3*c*integrate(1/16*x*log(c^2*x^2 + 1)^3/(c^2*d*x^2 + d), x) + 8*a*b^2*arctan(c*x)^3/(c*d) + 12*a^2*b*arctan(c*x)^2/(c*d))*c*d - 128*I*c*d*integrate(1/32*(40*b^3*c*x*arctan(c*x)^3 + 6*b^3*c*x*arctan(c*x)*log(c^2*x^2 + 1)^2 + 96*a*b^2*c*x*arctan(c*x)^2 + 96*a^2*b*c*x*arctan(c*x) + 12*b^3*arctan(c*x)^2*log(c^2*x^2 + 1) + b^3*log(c^2*x^2 + 1)^3)/(c^2*d*x^2 + d), x))/(c*d)","F",0
124,-2,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/(d+I*c*d*x)^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
125,1,229,0,0.476254," ","integrate((a+b*arctan(c*x))^3/(d+I*c*d*x)^3,x, algorithm=""maxima"")","-\frac{{\left(8 i \, b^{3} c^{2} x^{2} + 16 \, b^{3} c x + 24 i \, b^{3}\right)} \arctan\left(c x\right)^{3} + 32 i \, a^{3} + 48 \, a^{2} b - 48 i \, a b^{2} - 24 \, b^{3} + {\left(24 i \, a^{2} b + 36 \, a b^{2} - 21 i \, b^{3}\right)} c x + {\left({\left(24 i \, a b^{2} + 18 \, b^{3}\right)} c^{2} x^{2} + 72 i \, a b^{2} + 30 \, b^{3} + 12 \, {\left(4 \, a b^{2} - i \, b^{3}\right)} c x\right)} \arctan\left(c x\right)^{2} + {\left({\left(24 i \, a^{2} b + 36 \, a b^{2} - 21 i \, b^{3}\right)} c^{2} x^{2} + 72 i \, a^{2} b + 60 \, a b^{2} - 27 i \, b^{3} + {\left(48 \, a^{2} b - 24 i \, a b^{2} - 6 \, b^{3}\right)} c x\right)} \arctan\left(c x\right)}{64 \, c^{3} d^{3} x^{2} - 128 i \, c^{2} d^{3} x - 64 \, c d^{3}}"," ",0,"-((8*I*b^3*c^2*x^2 + 16*b^3*c*x + 24*I*b^3)*arctan(c*x)^3 + 32*I*a^3 + 48*a^2*b - 48*I*a*b^2 - 24*b^3 + (24*I*a^2*b + 36*a*b^2 - 21*I*b^3)*c*x + ((24*I*a*b^2 + 18*b^3)*c^2*x^2 + 72*I*a*b^2 + 30*b^3 + 12*(4*a*b^2 - I*b^3)*c*x)*arctan(c*x)^2 + ((24*I*a^2*b + 36*a*b^2 - 21*I*b^3)*c^2*x^2 + 72*I*a^2*b + 60*a*b^2 - 27*I*b^3 + (48*a^2*b - 24*I*a*b^2 - 6*b^3)*c*x)*arctan(c*x))/(64*c^3*d^3*x^2 - 128*I*c^2*d^3*x - 64*c*d^3)","A",0
126,1,320,0,0.568061," ","integrate((a+b*arctan(c*x))^3/(d+I*c*d*x)^4,x, algorithm=""maxima"")","-\frac{{\left(216 i \, a^{2} b + 396 \, a b^{2} - 255 i \, b^{3}\right)} c^{2} x^{2} + {\left(72 i \, b^{3} c^{3} x^{3} + 216 \, b^{3} c^{2} x^{2} - 216 i \, b^{3} c x + 504 \, b^{3}\right)} \arctan\left(c x\right)^{3} + 576 \, a^{3} - 720 i \, a^{2} b - 672 \, a b^{2} + 328 i \, b^{3} + {\left(648 \, a^{2} b - 972 i \, a b^{2} - 567 \, b^{3}\right)} c x + {\left({\left(216 i \, a b^{2} + 198 \, b^{3}\right)} c^{3} x^{3} + 54 \, {\left(12 \, a b^{2} - 7 i \, b^{3}\right)} c^{2} x^{2} + 1512 \, a b^{2} - 522 i \, b^{3} + {\left(-648 i \, a b^{2} + 54 \, b^{3}\right)} c x\right)} \arctan\left(c x\right)^{2} + {\left({\left(216 i \, a^{2} b + 396 \, a b^{2} - 255 i \, b^{3}\right)} c^{3} x^{3} + {\left(648 \, a^{2} b - 756 i \, a b^{2} - 369 \, b^{3}\right)} c^{2} x^{2} + 1512 \, a^{2} b - 1044 i \, a b^{2} - 417 \, b^{3} + {\left(-648 i \, a^{2} b + 108 \, a b^{2} - 207 i \, b^{3}\right)} c x\right)} \arctan\left(c x\right)}{1728 \, c^{4} d^{4} x^{3} - 5184 i \, c^{3} d^{4} x^{2} - 5184 \, c^{2} d^{4} x + 1728 i \, c d^{4}}"," ",0,"-((216*I*a^2*b + 396*a*b^2 - 255*I*b^3)*c^2*x^2 + (72*I*b^3*c^3*x^3 + 216*b^3*c^2*x^2 - 216*I*b^3*c*x + 504*b^3)*arctan(c*x)^3 + 576*a^3 - 720*I*a^2*b - 672*a*b^2 + 328*I*b^3 + (648*a^2*b - 972*I*a*b^2 - 567*b^3)*c*x + ((216*I*a*b^2 + 198*b^3)*c^3*x^3 + 54*(12*a*b^2 - 7*I*b^3)*c^2*x^2 + 1512*a*b^2 - 522*I*b^3 + (-648*I*a*b^2 + 54*b^3)*c*x)*arctan(c*x)^2 + ((216*I*a^2*b + 396*a*b^2 - 255*I*b^3)*c^3*x^3 + (648*a^2*b - 756*I*a*b^2 - 369*b^3)*c^2*x^2 + 1512*a^2*b - 1044*I*a*b^2 - 417*b^3 + (-648*I*a^2*b + 108*a*b^2 - 207*I*b^3)*c*x)*arctan(c*x))/(1728*c^4*d^4*x^3 - 5184*I*c^3*d^4*x^2 - 5184*c^2*d^4*x + 1728*I*c*d^4)","A",0
127,-1,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))^3/(d+I*c*d*x),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))^3/(d+I*c*d*x),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/(d+I*c*d*x),x, algorithm=""maxima"")","-\frac{i \, a^{3} \log\left(i \, c d x + d\right)}{c d} + \frac{16 \, b^{3} \arctan\left(c x\right)^{4} - b^{3} \log\left(c^{2} x^{2} + 1\right)^{4} + {\left(b^{3} c {\left(\frac{4 \, \log\left(c^{2} d x^{2} + d\right) \log\left(c^{2} x^{2} + 1\right)^{3}}{c^{2} d} + \frac{\frac{4 \, {\left(\log\left(c^{2} x^{2} + 1\right)^{3} + 3 \, \log\left(c^{2} x^{2} + 1\right)^{2} \log\left(d\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)^{4} + 4 \, \log\left(c^{2} x^{2} + 1\right)^{3} \log\left(d\right)}{c^{2}}}{d} - \frac{6 \, {\left(\log\left(c^{2} x^{2} + 1\right)^{2} + 2 \, \log\left(c^{2} x^{2} + 1\right) \log\left(d\right)\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{c^{2} d}\right)} + \frac{16 \, b^{3} \arctan\left(c x\right)^{4}}{c d} + \frac{128 \, a b^{2} \arctan\left(c x\right)^{3}}{c d} + \frac{192 \, a^{2} b \arctan\left(c x\right)^{2}}{c d}\right)} c d - 4 i \, c d \int \frac{32 \, {\left(b^{3} c x \arctan\left(c x\right)^{3} + 3 \, a b^{2} c x \arctan\left(c x\right)^{2} + 3 \, a^{2} b c x \arctan\left(c x\right)\right)}}{c^{2} d x^{2} + d}\,{d x}}{128 \, c d}"," ",0,"-I*a^3*log(I*c*d*x + d)/(c*d) + 1/128*(16*b^3*arctan(c*x)^4 + 16*I*b^3*arctan(c*x)^3*log(c^2*x^2 + 1) + 4*I*b^3*arctan(c*x)*log(c^2*x^2 + 1)^3 - b^3*log(c^2*x^2 + 1)^4 + 16*(b^3*arctan(c*x)^4/(c*d) + 8*b^3*c*integrate(1/16*x*log(c^2*x^2 + 1)^3/(c^2*d*x^2 + d), x) + 8*a*b^2*arctan(c*x)^3/(c*d) + 12*a^2*b*arctan(c*x)^2/(c*d))*c*d - 128*I*c*d*integrate(1/32*(40*b^3*c*x*arctan(c*x)^3 + 6*b^3*c*x*arctan(c*x)*log(c^2*x^2 + 1)^2 + 96*a*b^2*c*x*arctan(c*x)^2 + 96*a^2*b*c*x*arctan(c*x) + 12*b^3*arctan(c*x)^2*log(c^2*x^2 + 1) + b^3*log(c^2*x^2 + 1)^3)/(c^2*d*x^2 + d), x))/(c*d)","F",0
130,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/x/(d+I*c*d*x),x, algorithm=""maxima"")","-a^{3} {\left(\frac{\log\left(i \, c x + 1\right)}{d} - \frac{\log\left(x\right)}{d}\right)} + \frac{-64 i \, b^{3} \arctan\left(c x\right)^{4} + 64 \, b^{3} \arctan\left(c x\right)^{3} \log\left(c^{2} x^{2} + 1\right) + 4 i \, b^{3} \log\left(c^{2} x^{2} + 1\right)^{4} - i \, {\left(\frac{64 \, b^{3} \arctan\left(c x\right)^{4}}{d} + 96 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right)}{c^{2} d x^{3} + d x}\,{d x} + \frac{3 \, b^{3} \log\left(c^{2} x^{2} + 1\right)^{4}}{d} + \frac{512 \, a b^{2} \arctan\left(c x\right)^{3}}{d} + {\left(\frac{\log\left(c^{2} x^{2} + 1\right)^{4}}{d} - \frac{4 \, {\left(\log\left(c^{2} x^{2} + 1\right)^{3} \log\left(-c^{2} x^{2}\right) + 3 \, {\rm Li}_2\left(c^{2} x^{2} + 1\right) \log\left(c^{2} x^{2} + 1\right)^{2} - 6 \, \log\left(c^{2} x^{2} + 1\right) {\rm Li}_{3}(c^{2} x^{2} + 1) + 6 \, {\rm Li}_{4}(c^{2} x^{2} + 1)\right)}}{d}\right)} b^{3} + \frac{768 \, a^{2} b \arctan\left(c x\right)^{2}}{d} + 96 \, b^{3} \int \frac{\arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right)}{c^{2} d x^{3} + d x}\,{d x}\right)} d + 16 \, d \int -\frac{12 \, b^{3} c x \arctan\left(c x\right)^{2} \log\left(c^{2} x^{2} + 1\right) - 96 \, a b^{2} \arctan\left(c x\right)^{2} - 96 \, a^{2} b \arctan\left(c x\right) + 4 \, {\left(3 \, b^{3} c^{2} x^{2} - 7 \, b^{3}\right)} \arctan\left(c x\right)^{3} - 3 \, {\left(b^{3} c^{2} x^{2} + b^{3}\right)} \arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)^{2}}{c^{2} d x^{3} + d x}\,{d x}}{512 \, d}"," ",0,"-a^3*(log(I*c*x + 1)/d - log(x)/d) + 1/512*(-64*I*b^3*arctan(c*x)^4 + 64*b^3*arctan(c*x)^3*log(c^2*x^2 + 1) + 16*b^3*arctan(c*x)*log(c^2*x^2 + 1)^3 + 4*I*b^3*log(c^2*x^2 + 1)^4 - I*(64*b^3*arctan(c*x)^4/d + 6144*b^3*c^2*integrate(1/64*x^2*arctan(c*x)^2*log(c^2*x^2 + 1)/(c^2*d*x^3 + d*x), x) + 3*b^3*log(c^2*x^2 + 1)^4/d + 512*a*b^2*arctan(c*x)^3/d + 768*a^2*b*arctan(c*x)^2/d + 6144*b^3*integrate(1/64*arctan(c*x)^2*log(c^2*x^2 + 1)/(c^2*d*x^3 + d*x), x) - 512*b^3*integrate(1/64*log(c^2*x^2 + 1)^3/(c^2*d*x^3 + d*x), x))*d - 512*d*integrate(1/32*(12*b^3*c*x*arctan(c*x)^2*log(c^2*x^2 + 1) + b^3*c*x*log(c^2*x^2 + 1)^3 - 96*a*b^2*arctan(c*x)^2 - 96*a^2*b*arctan(c*x) + 4*(3*b^3*c^2*x^2 - 7*b^3)*arctan(c*x)^3 + 3*(b^3*c^2*x^2 - b^3)*arctan(c*x)*log(c^2*x^2 + 1)^2)/(c^2*d*x^3 + d*x), x))/d","F",0
131,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/x^2/(d+I*c*d*x),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^3/x^3/(d+I*c*d*x),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,0,0,0,0.000000," ","integrate(1/(d+I*c*d*x)/(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(i \, c d x + d\right)} {\left(b \arctan\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((I*c*d*x + d)*(b*arctan(c*x) + a)), x)","F",0
134,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))/(e*x+d),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{6 \, d^{3} \log\left(e x + d\right)}{e^{4}} - \frac{2 \, e^{2} x^{3} - 3 \, d e x^{2} + 6 \, d^{2} x}{e^{3}}\right)} + 2 \, b \int \frac{x^{3} \arctan\left(c x\right)}{2 \, {\left(e x + d\right)}}\,{d x}"," ",0,"-1/6*a*(6*d^3*log(e*x + d)/e^4 - (2*e^2*x^3 - 3*d*e*x^2 + 6*d^2*x)/e^3) + 2*b*integrate(1/2*x^3*arctan(c*x)/(e*x + d), x)","F",0
135,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{2 \, d^{2} \log\left(e x + d\right)}{e^{3}} + \frac{e x^{2} - 2 \, d x}{e^{2}}\right)} + 2 \, b \int \frac{x^{2} \arctan\left(c x\right)}{2 \, {\left(e x + d\right)}}\,{d x}"," ",0,"1/2*a*(2*d^2*log(e*x + d)/e^3 + (e*x^2 - 2*d*x)/e^2) + 2*b*integrate(1/2*x^2*arctan(c*x)/(e*x + d), x)","F",0
136,0,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))/(e*x+d),x, algorithm=""maxima"")","a {\left(\frac{x}{e} - \frac{d \log\left(e x + d\right)}{e^{2}}\right)} + 2 \, b \int \frac{x \arctan\left(c x\right)}{2 \, {\left(e x + d\right)}}\,{d x}"," ",0,"a*(x/e - d*log(e*x + d)/e^2) + 2*b*integrate(1/2*x*arctan(c*x)/(e*x + d), x)","F",0
137,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/(e*x+d),x, algorithm=""maxima"")","2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x + d\right)}}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"2*b*integrate(1/2*arctan(c*x)/(e*x + d), x) + a*log(e*x + d)/e","F",0
138,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x/(e*x+d),x, algorithm=""maxima"")","-a {\left(\frac{\log\left(e x + d\right)}{d} - \frac{\log\left(x\right)}{d}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{2} + d x\right)}}\,{d x}"," ",0,"-a*(log(e*x + d)/d - log(x)/d) + 2*b*integrate(1/2*arctan(c*x)/(e*x^2 + d*x), x)","F",0
139,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^2/(e*x+d),x, algorithm=""maxima"")","a {\left(\frac{e \log\left(e x + d\right)}{d^{2}} - \frac{e \log\left(x\right)}{d^{2}} - \frac{1}{d x}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{3} + d x^{2}\right)}}\,{d x}"," ",0,"a*(e*log(e*x + d)/d^2 - e*log(x)/d^2 - 1/(d*x)) + 2*b*integrate(1/2*arctan(c*x)/(e*x^3 + d*x^2), x)","F",0
140,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^3/(e*x+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, e^{2} \log\left(e x + d\right)}{d^{3}} - \frac{2 \, e^{2} \log\left(x\right)}{d^{3}} - \frac{2 \, e x - d}{d^{2} x^{2}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{4} + d x^{3}\right)}}\,{d x}"," ",0,"-1/2*a*(2*e^2*log(e*x + d)/d^3 - 2*e^2*log(x)/d^3 - (2*e*x - d)/(d^2*x^2)) + 2*b*integrate(1/2*arctan(c*x)/(e*x^4 + d*x^3), x)","F",0
141,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))^2/(e*x+d),x, algorithm=""maxima"")","-\frac{1}{6} \, a^{2} {\left(\frac{6 \, d^{3} \log\left(e x + d\right)}{e^{4}} - \frac{2 \, e^{2} x^{3} - 3 \, d e x^{2} + 6 \, d^{2} x}{e^{3}}\right)} + \frac{2 \, e^{3} \int \frac{36 \, {\left(b^{2} c^{2} e^{3} x^{5} + b^{2} e^{3} x^{3}\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(b^{2} c^{2} e^{3} x^{5} + b^{2} e^{3} x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 4 \, {\left(24 \, a b c^{2} e^{3} x^{5} - 2 \, b^{2} c e^{3} x^{4} - 3 \, b^{2} c d^{2} e x^{2} - 6 \, b^{2} c d^{3} x + {\left(b^{2} c d e^{2} + 24 \, a b e^{3}\right)} x^{3}\right)} \arctan\left(c x\right) + 2 \, {\left(2 \, b^{2} c^{2} e^{3} x^{5} - b^{2} c^{2} d e^{2} x^{4} + 3 \, b^{2} c^{2} d^{2} e x^{3} + 6 \, b^{2} c^{2} d^{3} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{2} e^{4} x^{3} + c^{2} d e^{3} x^{2} + e^{4} x + d e^{3}}\,{d x} + 4 \, {\left(2 \, b^{2} e^{2} x^{3} - 3 \, b^{2} d e x^{2} + 6 \, b^{2} d^{2} x\right)} \arctan\left(c x\right)^{2} - {\left(2 \, b^{2} e^{2} x^{3} - 3 \, b^{2} d e x^{2} + 6 \, b^{2} d^{2} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{96 \, e^{3}}"," ",0,"-1/6*a^2*(6*d^3*log(e*x + d)/e^4 - (2*e^2*x^3 - 3*d*e*x^2 + 6*d^2*x)/e^3) + 1/96*(96*e^3*integrate(1/48*(36*(b^2*c^2*e^3*x^5 + b^2*e^3*x^3)*arctan(c*x)^2 + 3*(b^2*c^2*e^3*x^5 + b^2*e^3*x^3)*log(c^2*x^2 + 1)^2 + 4*(24*a*b*c^2*e^3*x^5 - 2*b^2*c*e^3*x^4 - 3*b^2*c*d^2*e*x^2 - 6*b^2*c*d^3*x + (b^2*c*d*e^2 + 24*a*b*e^3)*x^3)*arctan(c*x) + 2*(2*b^2*c^2*e^3*x^5 - b^2*c^2*d*e^2*x^4 + 3*b^2*c^2*d^2*e*x^3 + 6*b^2*c^2*d^3*x^2)*log(c^2*x^2 + 1))/(c^2*e^4*x^3 + c^2*d*e^3*x^2 + e^4*x + d*e^3), x) + 4*(2*b^2*e^2*x^3 - 3*b^2*d*e*x^2 + 6*b^2*d^2*x)*arctan(c*x)^2 - (2*b^2*e^2*x^3 - 3*b^2*d*e*x^2 + 6*b^2*d^2*x)*log(c^2*x^2 + 1)^2)/e^3","F",0
142,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))^2/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{2 \, d^{2} \log\left(e x + d\right)}{e^{3}} + \frac{e x^{2} - 2 \, d x}{e^{2}}\right)} + \frac{4 \, {\left(b^{2} e x^{2} - 2 \, b^{2} d x\right)} \arctan\left(c x\right)^{2} + 2 \, e^{2} \int \frac{12 \, {\left(b^{2} c^{2} e^{2} x^{4} + b^{2} e^{2} x^{2}\right)} \arctan\left(c x\right)^{2} + {\left(b^{2} c^{2} e^{2} x^{4} + b^{2} e^{2} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 4 \, {\left(8 \, a b c^{2} e^{2} x^{4} - b^{2} c e^{2} x^{3} + 2 \, b^{2} c d^{2} x + {\left(b^{2} c d e + 8 \, a b e^{2}\right)} x^{2}\right)} \arctan\left(c x\right) + 2 \, {\left(b^{2} c^{2} e^{2} x^{4} - b^{2} c^{2} d e x^{3} - 2 \, b^{2} c^{2} d^{2} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{2} e^{3} x^{3} + c^{2} d e^{2} x^{2} + e^{3} x + d e^{2}}\,{d x} - {\left(b^{2} e x^{2} - 2 \, b^{2} d x\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, e^{2}}"," ",0,"1/2*a^2*(2*d^2*log(e*x + d)/e^3 + (e*x^2 - 2*d*x)/e^2) + 1/32*(4*(b^2*e*x^2 - 2*b^2*d*x)*arctan(c*x)^2 + 32*e^2*integrate(1/16*(12*(b^2*c^2*e^2*x^4 + b^2*e^2*x^2)*arctan(c*x)^2 + (b^2*c^2*e^2*x^4 + b^2*e^2*x^2)*log(c^2*x^2 + 1)^2 + 4*(8*a*b*c^2*e^2*x^4 - b^2*c*e^2*x^3 + 2*b^2*c*d^2*x + (b^2*c*d*e + 8*a*b*e^2)*x^2)*arctan(c*x) + 2*(b^2*c^2*e^2*x^4 - b^2*c^2*d*e*x^3 - 2*b^2*c^2*d^2*x^2)*log(c^2*x^2 + 1))/(c^2*e^3*x^3 + c^2*d*e^2*x^2 + e^3*x + d*e^2), x) - (b^2*e*x^2 - 2*b^2*d*x)*log(c^2*x^2 + 1)^2)/e^2","F",0
143,0,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))^2/(e*x+d),x, algorithm=""maxima"")","a^{2} {\left(\frac{x}{e} - \frac{d \log\left(e x + d\right)}{e^{2}}\right)} + \frac{4 \, b^{2} x \arctan\left(c x\right)^{2} - b^{2} x \log\left(c^{2} x^{2} + 1\right)^{2} + e \int \frac{12 \, {\left(b^{2} c^{2} e x^{3} + b^{2} e x\right)} \arctan\left(c x\right)^{2} + {\left(b^{2} c^{2} e x^{3} + b^{2} e x\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 8 \, {\left(4 \, a b c^{2} e x^{3} - b^{2} c e x^{2} - {\left(b^{2} c d - 4 \, a b e\right)} x\right)} \arctan\left(c x\right) + 4 \, {\left(b^{2} c^{2} e x^{3} + b^{2} c^{2} d x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{2} e^{2} x^{3} + c^{2} d e x^{2} + e^{2} x + d e}\,{d x}}{16 \, e}"," ",0,"a^2*(x/e - d*log(e*x + d)/e^2) + 1/16*(4*b^2*x*arctan(c*x)^2 - b^2*x*log(c^2*x^2 + 1)^2 + 16*e*integrate(1/16*(12*(b^2*c^2*e*x^3 + b^2*e*x)*arctan(c*x)^2 + (b^2*c^2*e*x^3 + b^2*e*x)*log(c^2*x^2 + 1)^2 + 8*(4*a*b*c^2*e*x^3 - b^2*c*e*x^2 - (b^2*c*d - 4*a*b*e)*x)*arctan(c*x) + 4*(b^2*c^2*e*x^3 + b^2*c^2*d*x^2)*log(c^2*x^2 + 1))/(c^2*e^2*x^3 + c^2*d*e*x^2 + e^2*x + d*e), x))/e","F",0
144,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/(e*x+d),x, algorithm=""maxima"")","\frac{a^{2} \log\left(e x + d\right)}{e} + \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)}{16 \, {\left(e x + d\right)}}\,{d x}"," ",0,"a^2*log(e*x + d)/e + integrate(1/16*(12*b^2*arctan(c*x)^2 + b^2*log(c^2*x^2 + 1)^2 + 32*a*b*arctan(c*x))/(e*x + d), x)","F",0
145,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x/(e*x+d),x, algorithm=""maxima"")","-a^{2} {\left(\frac{\log\left(e x + d\right)}{d} - \frac{\log\left(x\right)}{d}\right)} + \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)}{16 \, {\left(e x^{2} + d x\right)}}\,{d x}"," ",0,"-a^2*(log(e*x + d)/d - log(x)/d) + integrate(1/16*(12*b^2*arctan(c*x)^2 + b^2*log(c^2*x^2 + 1)^2 + 32*a*b*arctan(c*x))/(e*x^2 + d*x), x)","F",0
146,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^2/(e*x+d),x, algorithm=""maxima"")","a^{2} {\left(\frac{e \log\left(e x + d\right)}{d^{2}} - \frac{e \log\left(x\right)}{d^{2}} - \frac{1}{d x}\right)} - \frac{4 \, b^{2} \arctan\left(c x\right)^{2} - b^{2} \log\left(c^{2} x^{2} + 1\right)^{2} - d x \int \frac{12 \, {\left(b^{2} c^{2} d x^{2} + b^{2} d\right)} \arctan\left(c x\right)^{2} + {\left(b^{2} c^{2} d x^{2} + b^{2} d\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 8 \, {\left(b^{2} c d x + 4 \, a b d + {\left(4 \, a b c^{2} d + b^{2} c e\right)} x^{2}\right)} \arctan\left(c x\right) - 4 \, {\left(b^{2} c^{2} e x^{3} + b^{2} c^{2} d x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{2} d e x^{5} + c^{2} d^{2} x^{4} + d e x^{3} + d^{2} x^{2}}\,{d x}}{16 \, d x}"," ",0,"a^2*(e*log(e*x + d)/d^2 - e*log(x)/d^2 - 1/(d*x)) - 1/16*(4*b^2*arctan(c*x)^2 - b^2*log(c^2*x^2 + 1)^2 - 16*d*x*integrate(1/16*(12*(b^2*c^2*d*x^2 + b^2*d)*arctan(c*x)^2 + (b^2*c^2*d*x^2 + b^2*d)*log(c^2*x^2 + 1)^2 + 8*(b^2*c*d*x + 4*a*b*d + (4*a*b*c^2*d + b^2*c*e)*x^2)*arctan(c*x) - 4*(b^2*c^2*e*x^3 + b^2*c^2*d*x^2)*log(c^2*x^2 + 1))/(c^2*d*e*x^5 + c^2*d^2*x^4 + d*e*x^3 + d^2*x^2), x))/(d*x)","F",0
147,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^3/(e*x+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{2 \, e^{2} \log\left(e x + d\right)}{d^{3}} - \frac{2 \, e^{2} \log\left(x\right)}{d^{3}} - \frac{2 \, e x - d}{d^{2} x^{2}}\right)} + \frac{2 \, d^{2} x^{2} \int \frac{12 \, {\left(b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 4 \, {\left(2 \, b^{2} c e^{2} x^{3} - b^{2} c d^{2} x - 8 \, a b d^{2} - {\left(8 \, a b c^{2} d^{2} - b^{2} c d e\right)} x^{2}\right)} \arctan\left(c x\right) + 2 \, {\left(2 \, b^{2} c^{2} e^{2} x^{4} + b^{2} c^{2} d e x^{3} - b^{2} c^{2} d^{2} x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{2} d^{2} e x^{6} + c^{2} d^{3} x^{5} + d^{2} e x^{4} + d^{3} x^{3}}\,{d x} + 4 \, {\left(2 \, b^{2} e x - b^{2} d\right)} \arctan\left(c x\right)^{2} - {\left(2 \, b^{2} e x - b^{2} d\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{32 \, d^{2} x^{2}}"," ",0,"-1/2*a^2*(2*e^2*log(e*x + d)/d^3 - 2*e^2*log(x)/d^3 - (2*e*x - d)/(d^2*x^2)) + 1/32*(32*d^2*x^2*integrate(1/16*(12*(b^2*c^2*d^2*x^2 + b^2*d^2)*arctan(c*x)^2 + (b^2*c^2*d^2*x^2 + b^2*d^2)*log(c^2*x^2 + 1)^2 - 4*(2*b^2*c*e^2*x^3 - b^2*c*d^2*x - 8*a*b*d^2 - (8*a*b*c^2*d^2 - b^2*c*d*e)*x^2)*arctan(c*x) + 2*(2*b^2*c^2*e^2*x^4 + b^2*c^2*d*e*x^3 - b^2*c^2*d^2*x^2)*log(c^2*x^2 + 1))/(c^2*d^2*e*x^6 + c^2*d^3*x^5 + d^2*e*x^4 + d^3*x^3), x) + 4*(2*b^2*e*x - b^2*d)*arctan(c*x)^2 - (2*b^2*e*x - b^2*d)*log(c^2*x^2 + 1)^2)/(d^2*x^2)","F",0
148,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x + d\right)} {\left(b \arctan\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x + d)*(b*arctan(c*x) + a)), x)","F",0
149,1,64,0,0.427724," ","integrate(x^3*(a^2*c*x^2+c)*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{180} \, a {\left(\frac{6 \, a^{4} c x^{5} + 5 \, a^{2} c x^{3} - 15 \, c x}{a^{4}} + \frac{15 \, c \arctan\left(a x\right)}{a^{5}}\right)} + \frac{1}{12} \, {\left(2 \, a^{2} c x^{6} + 3 \, c x^{4}\right)} \arctan\left(a x\right)"," ",0,"-1/180*a*((6*a^4*c*x^5 + 5*a^2*c*x^3 - 15*c*x)/a^4 + 15*c*arctan(a*x)/a^5) + 1/12*(2*a^2*c*x^6 + 3*c*x^4)*arctan(a*x)","A",0
150,1,63,0,0.323555," ","integrate(x^2*(a^2*c*x^2+c)*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{60} \, a {\left(\frac{3 \, a^{2} c x^{4} + 4 \, c x^{2}}{a^{2}} - \frac{4 \, c \log\left(a^{2} x^{2} + 1\right)}{a^{4}}\right)} + \frac{1}{15} \, {\left(3 \, a^{2} c x^{5} + 5 \, c x^{3}\right)} \arctan\left(a x\right)"," ",0,"-1/60*a*((3*a^2*c*x^4 + 4*c*x^2)/a^2 - 4*c*log(a^2*x^2 + 1)/a^4) + 1/15*(3*a^2*c*x^5 + 5*c*x^3)*arctan(a*x)","A",0
151,1,50,0,0.326931," ","integrate(x*(a^2*c*x^2+c)*arctan(a*x),x, algorithm=""maxima"")","\frac{{\left(a^{2} c x^{2} + c\right)}^{2} \arctan\left(a x\right)}{4 \, a^{2} c} - \frac{a^{2} c^{2} x^{3} + 3 \, c^{2} x}{12 \, a c}"," ",0,"1/4*(a^2*c*x^2 + c)^2*arctan(a*x)/(a^2*c) - 1/12*(a^2*c^2*x^3 + 3*c^2*x)/(a*c)","A",0
152,1,45,0,0.327064," ","integrate((a^2*c*x^2+c)*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(c x^{2} + \frac{2 \, c \log\left(a^{2} x^{2} + 1\right)}{a^{2}}\right)} a + \frac{1}{3} \, {\left(a^{2} c x^{3} + 3 \, c x\right)} \arctan\left(a x\right)"," ",0,"-1/6*(c*x^2 + 2*c*log(a^2*x^2 + 1)/a^2)*a + 1/3*(a^2*c*x^3 + 3*c*x)*arctan(a*x)","A",0
153,1,66,0,0.493528," ","integrate((a^2*c*x^2+c)*arctan(a*x)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a c x - \frac{1}{4} \, \pi c \log\left(a^{2} x^{2} + 1\right) + c \arctan\left(a x\right) \log\left(a x\right) + \frac{1}{2} \, {\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right) - \frac{1}{2} i \, c {\rm Li}_2\left(i \, a x + 1\right) + \frac{1}{2} i \, c {\rm Li}_2\left(-i \, a x + 1\right)"," ",0,"-1/2*a*c*x - 1/4*pi*c*log(a^2*x^2 + 1) + c*arctan(a*x)*log(a*x) + 1/2*(a^2*c*x^2 + c)*arctan(a*x) - 1/2*I*c*dilog(I*a*x + 1) + 1/2*I*c*dilog(-I*a*x + 1)","A",0
154,1,40,0,0.330886," ","integrate((a^2*c*x^2+c)*arctan(a*x)/x^2,x, algorithm=""maxima"")","-{\left(c \log\left(a^{2} x^{2} + 1\right) - c \log\left(x\right)\right)} a + {\left(a^{2} c x - \frac{c}{x}\right)} \arctan\left(a x\right)"," ",0,"-(c*log(a^2*x^2 + 1) - c*log(x))*a + (a^2*c*x - c/x)*arctan(a*x)","A",0
155,1,95,0,0.498962," ","integrate((a^2*c*x^2+c)*arctan(a*x)/x^3,x, algorithm=""maxima"")","-\frac{\pi a^{2} c x^{2} \log\left(a^{2} x^{2} + 1\right) - 4 \, a^{2} c x^{2} \arctan\left(a x\right) \log\left(a x\right) + 2 i \, a^{2} c x^{2} {\rm Li}_2\left(i \, a x + 1\right) - 2 i \, a^{2} c x^{2} {\rm Li}_2\left(-i \, a x + 1\right) + 2 \, a c x + 2 \, {\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}{4 \, x^{2}}"," ",0,"-1/4*(pi*a^2*c*x^2*log(a^2*x^2 + 1) - 4*a^2*c*x^2*arctan(a*x)*log(a*x) + 2*I*a^2*c*x^2*dilog(I*a*x + 1) - 2*I*a^2*c*x^2*dilog(-I*a*x + 1) + 2*a*c*x + 2*(a^2*c*x^2 + c)*arctan(a*x))/x^2","A",0
156,1,56,0,0.321137," ","integrate((a^2*c*x^2+c)*arctan(a*x)/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(2 \, a^{2} c \log\left(a^{2} x^{2} + 1\right) - 2 \, a^{2} c \log\left(x^{2}\right) + \frac{c}{x^{2}}\right)} a - \frac{{\left(3 \, a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}{3 \, x^{3}}"," ",0,"-1/6*(2*a^2*c*log(a^2*x^2 + 1) - 2*a^2*c*log(x^2) + c/x^2)*a - 1/3*(3*a^2*c*x^2 + c)*arctan(a*x)/x^3","A",0
157,1,98,0,0.436786," ","integrate(x^3*(a^2*c*x^2+c)^2*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{504} \, a {\left(\frac{21 \, c^{2} \arctan\left(a x\right)}{a^{5}} + \frac{9 \, a^{6} c^{2} x^{7} + 21 \, a^{4} c^{2} x^{5} + 7 \, a^{2} c^{2} x^{3} - 21 \, c^{2} x}{a^{4}}\right)} + \frac{1}{24} \, {\left(3 \, a^{4} c^{2} x^{8} + 8 \, a^{2} c^{2} x^{6} + 6 \, c^{2} x^{4}\right)} \arctan\left(a x\right)"," ",0,"-1/504*a*(21*c^2*arctan(a*x)/a^5 + (9*a^6*c^2*x^7 + 21*a^4*c^2*x^5 + 7*a^2*c^2*x^3 - 21*c^2*x)/a^4) + 1/24*(3*a^4*c^2*x^8 + 8*a^2*c^2*x^6 + 6*c^2*x^4)*arctan(a*x)","A",0
158,1,95,0,0.330699," ","integrate(x^2*(a^2*c*x^2+c)^2*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{420} \, a {\left(\frac{10 \, a^{4} c^{2} x^{6} + 27 \, a^{2} c^{2} x^{4} + 16 \, c^{2} x^{2}}{a^{2}} - \frac{16 \, c^{2} \log\left(a^{2} x^{2} + 1\right)}{a^{4}}\right)} + \frac{1}{105} \, {\left(15 \, a^{4} c^{2} x^{7} + 42 \, a^{2} c^{2} x^{5} + 35 \, c^{2} x^{3}\right)} \arctan\left(a x\right)"," ",0,"-1/420*a*((10*a^4*c^2*x^6 + 27*a^2*c^2*x^4 + 16*c^2*x^2)/a^2 - 16*c^2*log(a^2*x^2 + 1)/a^4) + 1/105*(15*a^4*c^2*x^7 + 42*a^2*c^2*x^5 + 35*c^2*x^3)*arctan(a*x)","A",0
159,1,62,0,0.320564," ","integrate(x*(a^2*c*x^2+c)^2*arctan(a*x),x, algorithm=""maxima"")","\frac{{\left(a^{2} c x^{2} + c\right)}^{3} \arctan\left(a x\right)}{6 \, a^{2} c} - \frac{3 \, a^{4} c^{3} x^{5} + 10 \, a^{2} c^{3} x^{3} + 15 \, c^{3} x}{90 \, a c}"," ",0,"1/6*(a^2*c*x^2 + c)^3*arctan(a*x)/(a^2*c) - 1/90*(3*a^4*c^3*x^5 + 10*a^2*c^3*x^3 + 15*c^3*x)/(a*c)","A",0
160,1,77,0,0.323236," ","integrate((a^2*c*x^2+c)^2*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{60} \, {\left(3 \, a^{2} c^{2} x^{4} + 14 \, c^{2} x^{2} + \frac{16 \, c^{2} \log\left(a^{2} x^{2} + 1\right)}{a^{2}}\right)} a + \frac{1}{15} \, {\left(3 \, a^{4} c^{2} x^{5} + 10 \, a^{2} c^{2} x^{3} + 15 \, c^{2} x\right)} \arctan\left(a x\right)"," ",0,"-1/60*(3*a^2*c^2*x^4 + 14*c^2*x^2 + 16*c^2*log(a^2*x^2 + 1)/a^2)*a + 1/15*(3*a^4*c^2*x^5 + 10*a^2*c^2*x^3 + 15*c^2*x)*arctan(a*x)","A",0
161,1,104,0,0.508167," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)/x,x, algorithm=""maxima"")","-\frac{1}{12} \, a^{3} c^{2} x^{3} - \frac{3}{4} \, a c^{2} x - \frac{1}{4} \, \pi c^{2} \log\left(a^{2} x^{2} + 1\right) + c^{2} \arctan\left(a x\right) \log\left(a x\right) - \frac{1}{2} i \, c^{2} {\rm Li}_2\left(i \, a x + 1\right) + \frac{1}{2} i \, c^{2} {\rm Li}_2\left(-i \, a x + 1\right) + \frac{1}{4} \, {\left(a^{4} c^{2} x^{4} + 4 \, a^{2} c^{2} x^{2} + 3 \, c^{2}\right)} \arctan\left(a x\right)"," ",0,"-1/12*a^3*c^2*x^3 - 3/4*a*c^2*x - 1/4*pi*c^2*log(a^2*x^2 + 1) + c^2*arctan(a*x)*log(a*x) - 1/2*I*c^2*dilog(I*a*x + 1) + 1/2*I*c^2*dilog(-I*a*x + 1) + 1/4*(a^4*c^2*x^4 + 4*a^2*c^2*x^2 + 3*c^2)*arctan(a*x)","A",0
162,1,71,0,0.318384," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)/x^2,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(a^{2} c^{2} x^{2} + 8 \, c^{2} \log\left(a^{2} x^{2} + 1\right) - 6 \, c^{2} \log\left(x\right)\right)} a + \frac{1}{3} \, {\left(a^{4} c^{2} x^{3} + 6 \, a^{2} c^{2} x - \frac{3 \, c^{2}}{x}\right)} \arctan\left(a x\right)"," ",0,"-1/6*(a^2*c^2*x^2 + 8*c^2*log(a^2*x^2 + 1) - 6*c^2*log(x))*a + 1/3*(a^4*c^2*x^3 + 6*a^2*c^2*x - 3*c^2/x)*arctan(a*x)","A",0
163,1,120,0,0.485059," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)/x^3,x, algorithm=""maxima"")","-\frac{a^{3} c^{2} x^{3} + \pi a^{2} c^{2} x^{2} \log\left(a^{2} x^{2} + 1\right) - 4 \, a^{2} c^{2} x^{2} \arctan\left(a x\right) \log\left(a x\right) + 2 i \, a^{2} c^{2} x^{2} {\rm Li}_2\left(i \, a x + 1\right) - 2 i \, a^{2} c^{2} x^{2} {\rm Li}_2\left(-i \, a x + 1\right) + a c^{2} x - {\left(a^{4} c^{2} x^{4} - c^{2}\right)} \arctan\left(a x\right)}{2 \, x^{2}}"," ",0,"-1/2*(a^3*c^2*x^3 + pi*a^2*c^2*x^2*log(a^2*x^2 + 1) - 4*a^2*c^2*x^2*arctan(a*x)*log(a*x) + 2*I*a^2*c^2*x^2*dilog(I*a*x + 1) - 2*I*a^2*c^2*x^2*dilog(-I*a*x + 1) + a*c^2*x - (a^4*c^2*x^4 - c^2)*arctan(a*x))/x^2","A",0
164,1,76,0,0.329009," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(8 \, a^{2} c^{2} \log\left(a^{2} x^{2} + 1\right) - 10 \, a^{2} c^{2} \log\left(x\right) + \frac{c^{2}}{x^{2}}\right)} a + \frac{1}{3} \, {\left(3 \, a^{4} c^{2} x - \frac{6 \, a^{2} c^{2} x^{2} + c^{2}}{x^{3}}\right)} \arctan\left(a x\right)"," ",0,"-1/6*(8*a^2*c^2*log(a^2*x^2 + 1) - 10*a^2*c^2*log(x) + c^2/x^2)*a + 1/3*(3*a^4*c^2*x - (6*a^2*c^2*x^2 + c^2)/x^3)*arctan(a*x)","A",0
165,1,120,0,0.421456," ","integrate(x^3*(a^2*c*x^2+c)^3*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{12600} \, a {\left(\frac{315 \, c^{3} \arctan\left(a x\right)}{a^{5}} + \frac{140 \, a^{8} c^{3} x^{9} + 495 \, a^{6} c^{3} x^{7} + 567 \, a^{4} c^{3} x^{5} + 105 \, a^{2} c^{3} x^{3} - 315 \, c^{3} x}{a^{4}}\right)} + \frac{1}{40} \, {\left(4 \, a^{6} c^{3} x^{10} + 15 \, a^{4} c^{3} x^{8} + 20 \, a^{2} c^{3} x^{6} + 10 \, c^{3} x^{4}\right)} \arctan\left(a x\right)"," ",0,"-1/12600*a*(315*c^3*arctan(a*x)/a^5 + (140*a^8*c^3*x^9 + 495*a^6*c^3*x^7 + 567*a^4*c^3*x^5 + 105*a^2*c^3*x^3 - 315*c^3*x)/a^4) + 1/40*(4*a^6*c^3*x^10 + 15*a^4*c^3*x^8 + 20*a^2*c^3*x^6 + 10*c^3*x^4)*arctan(a*x)","A",0
166,1,118,0,0.318465," ","integrate(x^2*(a^2*c*x^2+c)^3*arctan(a*x),x, algorithm=""maxima"")","\frac{1}{7560} \, a {\left(\frac{192 \, c^{3} \log\left(a^{2} x^{2} + 1\right)}{a^{4}} - \frac{105 \, a^{6} c^{3} x^{8} + 400 \, a^{4} c^{3} x^{6} + 534 \, a^{2} c^{3} x^{4} + 192 \, c^{3} x^{2}}{a^{2}}\right)} + \frac{1}{315} \, {\left(35 \, a^{6} c^{3} x^{9} + 135 \, a^{4} c^{3} x^{7} + 189 \, a^{2} c^{3} x^{5} + 105 \, c^{3} x^{3}\right)} \arctan\left(a x\right)"," ",0,"1/7560*a*(192*c^3*log(a^2*x^2 + 1)/a^4 - (105*a^6*c^3*x^8 + 400*a^4*c^3*x^6 + 534*a^2*c^3*x^4 + 192*c^3*x^2)/a^2) + 1/315*(35*a^6*c^3*x^9 + 135*a^4*c^3*x^7 + 189*a^2*c^3*x^5 + 105*c^3*x^3)*arctan(a*x)","A",0
167,1,73,0,0.317937," ","integrate(x*(a^2*c*x^2+c)^3*arctan(a*x),x, algorithm=""maxima"")","\frac{{\left(a^{2} c x^{2} + c\right)}^{4} \arctan\left(a x\right)}{8 \, a^{2} c} - \frac{5 \, a^{6} c^{4} x^{7} + 21 \, a^{4} c^{4} x^{5} + 35 \, a^{2} c^{4} x^{3} + 35 \, c^{4} x}{280 \, a c}"," ",0,"1/8*(a^2*c*x^2 + c)^4*arctan(a*x)/(a^2*c) - 1/280*(5*a^6*c^4*x^7 + 21*a^4*c^4*x^5 + 35*a^2*c^4*x^3 + 35*c^4*x)/(a*c)","A",0
168,1,99,0,0.317540," ","integrate((a^2*c*x^2+c)^3*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{210} \, {\left(5 \, a^{4} c^{3} x^{6} + 24 \, a^{2} c^{3} x^{4} + 57 \, c^{3} x^{2} + \frac{48 \, c^{3} \log\left(a^{2} x^{2} + 1\right)}{a^{2}}\right)} a + \frac{1}{35} \, {\left(5 \, a^{6} c^{3} x^{7} + 21 \, a^{4} c^{3} x^{5} + 35 \, a^{2} c^{3} x^{3} + 35 \, c^{3} x\right)} \arctan\left(a x\right)"," ",0,"-1/210*(5*a^4*c^3*x^6 + 24*a^2*c^3*x^4 + 57*c^3*x^2 + 48*c^3*log(a^2*x^2 + 1)/a^2)*a + 1/35*(5*a^6*c^3*x^7 + 21*a^4*c^3*x^5 + 35*a^2*c^3*x^3 + 35*c^3*x)*arctan(a*x)","A",0
169,1,127,0,0.471951," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)/x,x, algorithm=""maxima"")","-\frac{1}{30} \, a^{5} c^{3} x^{5} - \frac{7}{36} \, a^{3} c^{3} x^{3} - \frac{11}{12} \, a c^{3} x - \frac{1}{4} \, \pi c^{3} \log\left(a^{2} x^{2} + 1\right) + c^{3} \arctan\left(a x\right) \log\left(a x\right) - \frac{1}{2} i \, c^{3} {\rm Li}_2\left(i \, a x + 1\right) + \frac{1}{2} i \, c^{3} {\rm Li}_2\left(-i \, a x + 1\right) + \frac{1}{12} \, {\left(2 \, a^{6} c^{3} x^{6} + 9 \, a^{4} c^{3} x^{4} + 18 \, a^{2} c^{3} x^{2} + 11 \, c^{3}\right)} \arctan\left(a x\right)"," ",0,"-1/30*a^5*c^3*x^5 - 7/36*a^3*c^3*x^3 - 11/12*a*c^3*x - 1/4*pi*c^3*log(a^2*x^2 + 1) + c^3*arctan(a*x)*log(a*x) - 1/2*I*c^3*dilog(I*a*x + 1) + 1/2*I*c^3*dilog(-I*a*x + 1) + 1/12*(2*a^6*c^3*x^6 + 9*a^4*c^3*x^4 + 18*a^2*c^3*x^2 + 11*c^3)*arctan(a*x)","A",0
170,1,93,0,0.328212," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)/x^2,x, algorithm=""maxima"")","-\frac{1}{20} \, {\left(a^{4} c^{3} x^{4} + 8 \, a^{2} c^{3} x^{2} + 32 \, c^{3} \log\left(a^{2} x^{2} + 1\right) - 20 \, c^{3} \log\left(x\right)\right)} a + \frac{1}{5} \, {\left(a^{6} c^{3} x^{5} + 5 \, a^{4} c^{3} x^{3} + 15 \, a^{2} c^{3} x - \frac{5 \, c^{3}}{x}\right)} \arctan\left(a x\right)"," ",0,"-1/20*(a^4*c^3*x^4 + 8*a^2*c^3*x^2 + 32*c^3*log(a^2*x^2 + 1) - 20*c^3*log(x))*a + 1/5*(a^6*c^3*x^5 + 5*a^4*c^3*x^3 + 15*a^2*c^3*x - 5*c^3/x)*arctan(a*x)","A",0
171,1,155,0,0.489064," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)/x^3,x, algorithm=""maxima"")","-\frac{a^{5} c^{3} x^{5} + 15 \, a^{3} c^{3} x^{3} + 9 \, \pi a^{2} c^{3} x^{2} \log\left(a^{2} x^{2} + 1\right) - 36 \, a^{2} c^{3} x^{2} \arctan\left(a x\right) \log\left(a x\right) + 18 i \, a^{2} c^{3} x^{2} {\rm Li}_2\left(i \, a x + 1\right) - 18 i \, a^{2} c^{3} x^{2} {\rm Li}_2\left(-i \, a x + 1\right) + 6 \, a c^{3} x - 3 \, {\left(a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - 2 \, c^{3}\right)} \arctan\left(a x\right)}{12 \, x^{2}}"," ",0,"-1/12*(a^5*c^3*x^5 + 15*a^3*c^3*x^3 + 9*pi*a^2*c^3*x^2*log(a^2*x^2 + 1) - 36*a^2*c^3*x^2*arctan(a*x)*log(a*x) + 18*I*a^2*c^3*x^2*dilog(I*a*x + 1) - 18*I*a^2*c^3*x^2*dilog(-I*a*x + 1) + 6*a*c^3*x - 3*(a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - 2*c^3)*arctan(a*x))/x^2","A",0
172,1,96,0,0.330997," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(a^{4} c^{3} x^{2} + 16 \, a^{2} c^{3} \log\left(a^{2} x^{2} + 1\right) - 16 \, a^{2} c^{3} \log\left(x\right) + \frac{c^{3}}{x^{2}}\right)} a + \frac{1}{3} \, {\left(a^{6} c^{3} x^{3} + 9 \, a^{4} c^{3} x - \frac{9 \, a^{2} c^{3} x^{2} + c^{3}}{x^{3}}\right)} \arctan\left(a x\right)"," ",0,"-1/6*(a^4*c^3*x^2 + 16*a^2*c^3*log(a^2*x^2 + 1) - 16*a^2*c^3*log(x) + c^3/x^2)*a + 1/3*(a^6*c^3*x^3 + 9*a^4*c^3*x - (9*a^2*c^3*x^2 + c^3)/x^3)*arctan(a*x)","A",0
173,1,74,0,0.431997," ","integrate(x^4*arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{a^{2} x^{3} - 3 \, x}{a^{4} c} + \frac{3 \, \arctan\left(a x\right)}{a^{5} c}\right)} \arctan\left(a x\right) - \frac{a^{2} x^{2} + 3 \, \arctan\left(a x\right)^{2} - 4 \, \log\left(a^{2} x^{2} + 1\right)}{6 \, a^{5} c}"," ",0,"1/3*((a^2*x^3 - 3*x)/(a^4*c) + 3*arctan(a*x)/(a^5*c))*arctan(a*x) - 1/6*(a^2*x^2 + 3*arctan(a*x)^2 - 4*log(a^2*x^2 + 1))/(a^5*c)","A",0
174,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)/(a^2*c*x^2 + c), x)","F",0
175,1,54,0,0.424991," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""maxima"")","{\left(\frac{x}{a^{2} c} - \frac{\arctan\left(a x\right)}{a^{3} c}\right)} \arctan\left(a x\right) + \frac{\arctan\left(a x\right)^{2} - \log\left(a^{2} x^{2} + 1\right)}{2 \, a^{3} c}"," ",0,"(x/(a^2*c) - arctan(a*x)/(a^3*c))*arctan(a*x) + 1/2*(arctan(a*x)^2 - log(a^2*x^2 + 1))/(a^3*c)","A",0
176,0,0,0,0.000000," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x \arctan\left(a x\right)}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x*arctan(a*x)/(a^2*c*x^2 + c), x)","F",0
177,1,14,0,0.419691," ","integrate(arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{\arctan\left(a x\right)^{2}}{2 \, a c}"," ",0,"1/2*arctan(a*x)^2/(a*c)","A",0
178,0,0,0,0.000000," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)} x}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)*x), x)","F",0
179,1,53,0,0.441631," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","-{\left(\frac{a \arctan\left(a x\right)}{c} + \frac{1}{c x}\right)} \arctan\left(a x\right) + \frac{{\left(\arctan\left(a x\right)^{2} - \log\left(a^{2} x^{2} + 1\right) + 2 \, \log\left(x\right)\right)} a}{2 \, c}"," ",0,"-(a*arctan(a*x)/c + 1/(c*x))*arctan(a*x) + 1/2*(arctan(a*x)^2 - log(a^2*x^2 + 1) + 2*log(x))*a/c","A",0
180,0,0,0,0.000000," ","integrate(arctan(a*x)/x^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)*x^3), x)","F",0
181,1,90,0,0.429762," ","integrate(arctan(a*x)/x^4/(a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{3 \, a^{3} \arctan\left(a x\right)}{c} + \frac{3 \, a^{2} x^{2} - 1}{c x^{3}}\right)} \arctan\left(a x\right) - \frac{{\left(3 \, a^{2} x^{2} \arctan\left(a x\right)^{2} - 4 \, a^{2} x^{2} \log\left(a^{2} x^{2} + 1\right) + 8 \, a^{2} x^{2} \log\left(x\right) + 1\right)} a}{6 \, c x^{2}}"," ",0,"1/3*(3*a^3*arctan(a*x)/c + (3*a^2*x^2 - 1)/(c*x^3))*arctan(a*x) - 1/6*(3*a^2*x^2*arctan(a*x)^2 - 4*a^2*x^2*log(a^2*x^2 + 1) + 8*a^2*x^2*log(x) + 1)*a/(c*x^2)","A",0
182,0,0,0,0.000000," ","integrate(x^5*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{5} \arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(x^5*arctan(a*x)/(a^2*c*x^2 + c)^2, x)","F",0
183,1,114,0,0.434232," ","integrate(x^4*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x}{a^{6} c^{2} x^{2} + a^{4} c^{2}} + \frac{2 \, x}{a^{4} c^{2}} - \frac{3 \, \arctan\left(a x\right)}{a^{5} c^{2}}\right)} \arctan\left(a x\right) + \frac{{\left(3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} - 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a^{2} x^{2} + 1\right) + 1\right)} a}{4 \, {\left(a^{8} c^{2} x^{2} + a^{6} c^{2}\right)}}"," ",0,"1/2*(x/(a^6*c^2*x^2 + a^4*c^2) + 2*x/(a^4*c^2) - 3*arctan(a*x)/(a^5*c^2))*arctan(a*x) + 1/4*(3*(a^2*x^2 + 1)*arctan(a*x)^2 - 2*(a^2*x^2 + 1)*log(a^2*x^2 + 1) + 1)*a/(a^8*c^2*x^2 + a^6*c^2)","A",0
184,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)/(a^2*c*x^2 + c)^2, x)","F",0
185,1,83,0,0.439110," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{x}{a^{4} c^{2} x^{2} + a^{2} c^{2}} - \frac{\arctan\left(a x\right)}{a^{3} c^{2}}\right)} \arctan\left(a x\right) - \frac{{\left({\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 1\right)} a}{4 \, {\left(a^{6} c^{2} x^{2} + a^{4} c^{2}\right)}}"," ",0,"-1/2*(x/(a^4*c^2*x^2 + a^2*c^2) - arctan(a*x)/(a^3*c^2))*arctan(a*x) - 1/4*((a^2*x^2 + 1)*arctan(a*x)^2 + 1)*a/(a^6*c^2*x^2 + a^4*c^2)","A",0
186,1,59,0,0.428550," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{\frac{x}{a^{2} c x^{2} + c} + \frac{\arctan\left(a x\right)}{a c}}{4 \, a c} - \frac{\arctan\left(a x\right)}{2 \, {\left(a^{2} c x^{2} + c\right)} a^{2} c}"," ",0,"1/4*(x/(a^2*c*x^2 + c) + arctan(a*x)/(a*c))/(a*c) - 1/2*arctan(a*x)/((a^2*c*x^2 + c)*a^2*c)","A",0
187,1,78,0,0.432150," ","integrate(arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x}{a^{2} c^{2} x^{2} + c^{2}} + \frac{\arctan\left(a x\right)}{a c^{2}}\right)} \arctan\left(a x\right) - \frac{{\left({\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} - 1\right)} a}{4 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)}}"," ",0,"1/2*(x/(a^2*c^2*x^2 + c^2) + arctan(a*x)/(a*c^2))*arctan(a*x) - 1/4*((a^2*x^2 + 1)*arctan(a*x)^2 - 1)*a/(a^4*c^2*x^2 + a^2*c^2)","A",0
188,0,0,0,0.000000," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{2} x}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)^2*x), x)","F",0
189,1,119,0,0.436901," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{3 \, a^{2} x^{2} + 2}{a^{2} c^{2} x^{3} + c^{2} x} + \frac{3 \, a \arctan\left(a x\right)}{c^{2}}\right)} \arctan\left(a x\right) + \frac{{\left(3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} - 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a^{2} x^{2} + 1\right) + 4 \, {\left(a^{2} x^{2} + 1\right)} \log\left(x\right) - 1\right)} a}{4 \, {\left(a^{2} c^{2} x^{2} + c^{2}\right)}}"," ",0,"-1/2*((3*a^2*x^2 + 2)/(a^2*c^2*x^3 + c^2*x) + 3*a*arctan(a*x)/c^2)*arctan(a*x) + 1/4*(3*(a^2*x^2 + 1)*arctan(a*x)^2 - 2*(a^2*x^2 + 1)*log(a^2*x^2 + 1) + 4*(a^2*x^2 + 1)*log(x) - 1)*a/(a^2*c^2*x^2 + c^2)","A",0
190,0,0,0,0.000000," ","integrate(arctan(a*x)/x^3/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)^2*x^3), x)","F",0
191,1,160,0,0.448433," ","integrate(arctan(a*x)/x^4/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{15 \, a^{3} \arctan\left(a x\right)}{c^{2}} + \frac{15 \, a^{4} x^{4} + 10 \, a^{2} x^{2} - 2}{a^{2} c^{2} x^{5} + c^{2} x^{3}}\right)} \arctan\left(a x\right) + \frac{{\left(a^{2} x^{2} - 15 \, {\left(a^{4} x^{4} + a^{2} x^{2}\right)} \arctan\left(a x\right)^{2} + 14 \, {\left(a^{4} x^{4} + a^{2} x^{2}\right)} \log\left(a^{2} x^{2} + 1\right) - 28 \, {\left(a^{4} x^{4} + a^{2} x^{2}\right)} \log\left(x\right) - 2\right)} a}{12 \, {\left(a^{2} c^{2} x^{4} + c^{2} x^{2}\right)}}"," ",0,"1/6*(15*a^3*arctan(a*x)/c^2 + (15*a^4*x^4 + 10*a^2*x^2 - 2)/(a^2*c^2*x^5 + c^2*x^3))*arctan(a*x) + 1/12*(a^2*x^2 - 15*(a^4*x^4 + a^2*x^2)*arctan(a*x)^2 + 14*(a^4*x^4 + a^2*x^2)*log(a^2*x^2 + 1) - 28*(a^4*x^4 + a^2*x^2)*log(x) - 2)*a/(a^2*c^2*x^4 + c^2*x^2)","A",0
192,1,108,0,0.423561," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{32} \, a {\left(\frac{5 \, a^{2} x^{3} + 3 \, x}{a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}} + \frac{5 \, \arctan\left(a x\right)}{a^{5} c^{3}}\right)} - \frac{{\left(2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{4 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}}"," ",0,"1/32*a*((5*a^2*x^3 + 3*x)/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3) + 5*arctan(a*x)/(a^5*c^3)) - 1/4*(2*a^2*x^2 + 1)*arctan(a*x)/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)","A",0
193,1,129,0,0.439194," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{a^{2} x^{3} - x}{a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}} + \frac{\arctan\left(a x\right)}{a^{3} c^{3}}\right)} \arctan\left(a x\right) + \frac{{\left(a^{2} x^{2} - {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2}\right)} a}{16 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}}"," ",0,"1/8*((a^2*x^3 - x)/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3) + arctan(a*x)/(a^3*c^3))*arctan(a*x) + 1/16*(a^2*x^2 - (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2)*a/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)","A",0
194,1,86,0,0.415791," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{\frac{3 \, a^{2} x^{3} + 5 \, x}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}} + \frac{3 \, \arctan\left(a x\right)}{a c^{2}}}{32 \, a c} - \frac{\arctan\left(a x\right)}{4 \, {\left(a^{2} c x^{2} + c\right)}^{2} a^{2} c}"," ",0,"1/32*((3*a^2*x^3 + 5*x)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2) + 3*arctan(a*x)/(a*c^2))/(a*c) - 1/4*arctan(a*x)/((a^2*c*x^2 + c)^2*a^2*c)","A",0
195,1,129,0,0.432529," ","integrate(arctan(a*x)/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{3 \, a^{2} x^{3} + 5 \, x}{a^{4} c^{3} x^{4} + 2 \, a^{2} c^{3} x^{2} + c^{3}} + \frac{3 \, \arctan\left(a x\right)}{a c^{3}}\right)} \arctan\left(a x\right) + \frac{{\left(3 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 4\right)} a}{16 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)}}"," ",0,"1/8*((3*a^2*x^3 + 5*x)/(a^4*c^3*x^4 + 2*a^2*c^3*x^2 + c^3) + 3*arctan(a*x)/(a*c^3))*arctan(a*x) + 1/16*(3*a^2*x^2 - 3*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 4)*a/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)","A",0
196,0,0,0,0.000000," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{3} x}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)^3*x), x)","F",0
197,1,181,0,0.444498," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(\frac{15 \, a^{4} x^{4} + 25 \, a^{2} x^{2} + 8}{a^{4} c^{3} x^{5} + 2 \, a^{2} c^{3} x^{3} + c^{3} x} + \frac{15 \, a \arctan\left(a x\right)}{c^{3}}\right)} \arctan\left(a x\right) - \frac{{\left(7 \, a^{2} x^{2} - 15 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 8 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \log\left(a^{2} x^{2} + 1\right) - 16 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \log\left(x\right) + 8\right)} a}{16 \, {\left(a^{4} c^{3} x^{4} + 2 \, a^{2} c^{3} x^{2} + c^{3}\right)}}"," ",0,"-1/8*((15*a^4*x^4 + 25*a^2*x^2 + 8)/(a^4*c^3*x^5 + 2*a^2*c^3*x^3 + c^3*x) + 15*a*arctan(a*x)/c^3)*arctan(a*x) - 1/16*(7*a^2*x^2 - 15*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 8*(a^4*x^4 + 2*a^2*x^2 + 1)*log(a^2*x^2 + 1) - 16*(a^4*x^4 + 2*a^2*x^2 + 1)*log(x) + 8)*a/(a^4*c^3*x^4 + 2*a^2*c^3*x^2 + c^3)","A",0
198,0,0,0,0.000000," ","integrate(arctan(a*x)/x^3/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)^3*x^3), x)","F",0
199,1,223,0,0.462720," ","integrate(arctan(a*x)/x^4/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{24} \, {\left(\frac{105 \, a^{3} \arctan\left(a x\right)}{c^{3}} + \frac{105 \, a^{6} x^{6} + 175 \, a^{4} x^{4} + 56 \, a^{2} x^{2} - 8}{a^{4} c^{3} x^{7} + 2 \, a^{2} c^{3} x^{5} + c^{3} x^{3}}\right)} \arctan\left(a x\right) + \frac{{\left(25 \, a^{4} x^{4} + 20 \, a^{2} x^{2} - 105 \, {\left(a^{6} x^{6} + 2 \, a^{4} x^{4} + a^{2} x^{2}\right)} \arctan\left(a x\right)^{2} + 80 \, {\left(a^{6} x^{6} + 2 \, a^{4} x^{4} + a^{2} x^{2}\right)} \log\left(a^{2} x^{2} + 1\right) - 160 \, {\left(a^{6} x^{6} + 2 \, a^{4} x^{4} + a^{2} x^{2}\right)} \log\left(x\right) - 8\right)} a}{48 \, {\left(a^{4} c^{3} x^{6} + 2 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)}}"," ",0,"1/24*(105*a^3*arctan(a*x)/c^3 + (105*a^6*x^6 + 175*a^4*x^4 + 56*a^2*x^2 - 8)/(a^4*c^3*x^7 + 2*a^2*c^3*x^5 + c^3*x^3))*arctan(a*x) + 1/48*(25*a^4*x^4 + 20*a^2*x^2 - 105*(a^6*x^6 + 2*a^4*x^4 + a^2*x^2)*arctan(a*x)^2 + 80*(a^6*x^6 + 2*a^4*x^4 + a^2*x^2)*log(a^2*x^2 + 1) - 160*(a^6*x^6 + 2*a^4*x^4 + a^2*x^2)*log(x) - 8)*a/(a^4*c^3*x^6 + 2*a^2*c^3*x^4 + c^3*x^2)","A",0
200,1,127,0,0.454984," ","integrate(x^3*arctan(a*x)*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{1}{120} \, {\left(a {\left(\frac{3 \, {\left(\frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{2}} - \frac{\sqrt{a^{2} x^{2} + 1} x}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{a^{3}}\right)}}{a^{2}} - \frac{8 \, {\left(\sqrt{a^{2} x^{2} + 1} x + \frac{\operatorname{arsinh}\left(a x\right)}{a}\right)}}{a^{4}}\right)} - 8 \, {\left(\frac{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{a^{2}} - \frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{4}}\right)} \arctan\left(a x\right)\right)} \sqrt{c}"," ",0,"-1/120*(a*(3*(2*(a^2*x^2 + 1)^(3/2)*x/a^2 - sqrt(a^2*x^2 + 1)*x/a^2 - arcsinh(a*x)/a^3)/a^2 - 8*(sqrt(a^2*x^2 + 1)*x + arcsinh(a*x)/a)/a^4) - 8*(3*(a^2*x^2 + 1)^(3/2)*x^2/a^2 - 2*(a^2*x^2 + 1)^(3/2)/a^4)*arctan(a*x))*sqrt(c)","A",0
201,0,0,0,0.000000," ","integrate(x^2*arctan(a*x)*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x^{2} \arctan\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^2*arctan(a*x), x)","F",0
202,1,260,0,0.529369," ","integrate(x*arctan(a*x)*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{4 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \sqrt{c} \arctan\left(a x\right) - 2 \, {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} {\left(a x \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right) + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right)\right)} \sqrt{c} + \sqrt{c} {\left(\arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) + 2, a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right) + \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) - 2, -a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right)\right)}}{12 \, a^{2}}"," ",0,"1/12*(4*(a^2*x^2 + 1)^(3/2)*sqrt(c)*arctan(a*x) - 2*(a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*(a*x*cos(1/2*arctan2(4*a*x, -a^2*x^2 + 3)) + 2*sin(1/2*arctan2(4*a*x, -a^2*x^2 + 3)))*sqrt(c) + sqrt(c)*(arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) + 2, a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))) + arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) - 2, -a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3)))))/a^2","B",0
203,0,0,0,0.000000," ","integrate(arctan(a*x)*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x), x)","F",0
204,0,0,0,0.000000," ","integrate(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{x}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)/x, x)","F",0
205,0,0,0,0.000000," ","integrate(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)/x^2, x)","F",0
206,0,0,0,0.000000," ","integrate(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)/x^3, x)","F",0
207,1,73,0,0.458428," ","integrate(arctan(a*x)*(a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(a^{2} \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right) - \sqrt{a^{2} x^{2} + 1} a^{2} + \frac{{\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{x^{2}}\right)} a + \frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} \arctan\left(a x\right)}{x^{3}}\right)} \sqrt{c}"," ",0,"-1/6*((a^2*arcsinh(1/(a*abs(x))) - sqrt(a^2*x^2 + 1)*a^2 + (a^2*x^2 + 1)^(3/2)/x^2)*a + 2*(a^2*x^2 + 1)^(3/2)*arctan(a*x)/x^3)*sqrt(c)","A",0
208,1,214,0,0.522806," ","integrate(x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{1680} \, {\left({\left(5 \, {\left(\frac{8 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}{a^{2}} - \frac{6 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{4}} + \frac{3 \, \sqrt{a^{2} x^{2} + 1} x}{a^{4}} + \frac{3 \, \operatorname{arsinh}\left(a x\right)}{a^{5}}\right)} c + \frac{18 \, c {\left(\frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{2}} - \frac{\sqrt{a^{2} x^{2} + 1} x}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{a^{3}}\right)}}{a^{2}} - \frac{48 \, {\left(\sqrt{a^{2} x^{2} + 1} x + \frac{\operatorname{arsinh}\left(a x\right)}{a}\right)} c}{a^{4}}\right)} a - 48 \, {\left(5 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c x^{4} + \frac{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c x^{2}}{a^{2}} - \frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c}{a^{4}}\right)} \arctan\left(a x\right)\right)} \sqrt{c}"," ",0,"-1/1680*((5*(8*(a^2*x^2 + 1)^(3/2)*x^3/a^2 - 6*(a^2*x^2 + 1)^(3/2)*x/a^4 + 3*sqrt(a^2*x^2 + 1)*x/a^4 + 3*arcsinh(a*x)/a^5)*c + 18*c*(2*(a^2*x^2 + 1)^(3/2)*x/a^2 - sqrt(a^2*x^2 + 1)*x/a^2 - arcsinh(a*x)/a^3)/a^2 - 48*(sqrt(a^2*x^2 + 1)*x + arcsinh(a*x)/a)*c/a^4)*a - 48*(5*(a^2*x^2 + 1)^(3/2)*c*x^4 + 3*(a^2*x^2 + 1)^(3/2)*c*x^2/a^2 - 2*(a^2*x^2 + 1)^(3/2)*c/a^4)*arctan(a*x))*sqrt(c)","A",0
209,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2} \arctan\left(a x\right)\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^2*arctan(a*x), x)","F",0
210,1,406,0,0.603669," ","integrate(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x, algorithm=""maxima"")","\frac{40 \, {\left(a^{2} c x^{2} + c\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{c} \arctan\left(a x\right) - 20 \, {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} {\left(a c x \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right) + 2 \, c \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right)\right)} \sqrt{c} - {\left({\left(a {\left(\frac{3 \, {\left(\frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{2}} - \frac{\sqrt{a^{2} x^{2} + 1} x}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{a^{3}}\right)}}{a^{2}} - \frac{8 \, {\left(\sqrt{a^{2} x^{2} + 1} x + \frac{\operatorname{arsinh}\left(a x\right)}{a}\right)}}{a^{4}}\right)} - 8 \, {\left(\frac{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{a^{2}} - \frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{4}}\right)} \arctan\left(a x\right)\right)} a^{4} c - 10 \, c \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) + 2, a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right) - 10 \, c \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) - 2, -a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right)\right)} \sqrt{c}}{120 \, a^{2}}"," ",0,"1/120*(40*(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*sqrt(c)*arctan(a*x) - 20*(a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*(a*c*x*cos(1/2*arctan2(4*a*x, -a^2*x^2 + 3)) + 2*c*sin(1/2*arctan2(4*a*x, -a^2*x^2 + 3)))*sqrt(c) - ((a*(3*(2*(a^2*x^2 + 1)^(3/2)*x/a^2 - sqrt(a^2*x^2 + 1)*x/a^2 - arcsinh(a*x)/a^3)/a^2 - 8*(sqrt(a^2*x^2 + 1)*x + arcsinh(a*x)/a)/a^4) - 8*(3*(a^2*x^2 + 1)^(3/2)*x^2/a^2 - 2*(a^2*x^2 + 1)^(3/2)/a^4)*arctan(a*x))*a^4*c - 10*c*arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) + 2, a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))) - 10*c*arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) - 2, -a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))))*sqrt(c))/a^2","B",0
211,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x), x)","F",0
212,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(a^{2} c x^{2} + c\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{c} \arctan\left(a x\right) - \frac{1}{6} \, {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} {\left(a c x \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right) + 2 \, c \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right)\right)} \sqrt{c} + \frac{1}{12} \, {\left(c \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) + 2, a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right) + c \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) - 2, -a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right) + 12 \, c \int \frac{\sqrt{a^{2} x^{2} + 1} \arctan\left(a x\right)}{x}\,{d x}\right)} \sqrt{c}"," ",0,"1/3*(a^2*c*x^2 + c)*sqrt(a^2*x^2 + 1)*sqrt(c)*arctan(a*x) - 1/6*(a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*(a*c*x*cos(1/2*arctan2(4*a*x, -a^2*x^2 + 3)) + 2*c*sin(1/2*arctan2(4*a*x, -a^2*x^2 + 3)))*sqrt(c) + 1/12*(c*arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) + 2, a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))) + c*arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) - 2, -a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))) + 12*c*integrate(sqrt(a^2*x^2 + 1)*arctan(a*x)/x, x))*sqrt(c)","F",0
213,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}{x^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)/x^2, x)","F",0
214,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}{x^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)/x^3, x)","F",0
215,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}{x^{4}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)/x^4, x)","F",0
216,1,338,0,0.601101," ","integrate(x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{24192} \, {\left({\left(7 \, {\left(\frac{48 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{5}}{a^{2}} - \frac{40 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}{a^{4}} + \frac{30 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{6}} - \frac{15 \, \sqrt{a^{2} x^{2} + 1} x}{a^{6}} - \frac{15 \, \operatorname{arsinh}\left(a x\right)}{a^{7}}\right)} a^{2} c^{2} + 96 \, {\left(\frac{8 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}{a^{2}} - \frac{6 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{4}} + \frac{3 \, \sqrt{a^{2} x^{2} + 1} x}{a^{4}} + \frac{3 \, \operatorname{arsinh}\left(a x\right)}{a^{5}}\right)} c^{2} + \frac{144 \, c^{2} {\left(\frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{2}} - \frac{\sqrt{a^{2} x^{2} + 1} x}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{a^{3}}\right)}}{a^{2}} - \frac{384 \, {\left(\sqrt{a^{2} x^{2} + 1} x + \frac{\operatorname{arsinh}\left(a x\right)}{a}\right)} c^{2}}{a^{4}}\right)} a - 384 \, {\left(7 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2} c^{2} x^{6} + 12 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2} x^{4} + \frac{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2} x^{2}}{a^{2}} - \frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} c^{2}}{a^{4}}\right)} \arctan\left(a x\right)\right)} \sqrt{c}"," ",0,"-1/24192*((7*(48*(a^2*x^2 + 1)^(3/2)*x^5/a^2 - 40*(a^2*x^2 + 1)^(3/2)*x^3/a^4 + 30*(a^2*x^2 + 1)^(3/2)*x/a^6 - 15*sqrt(a^2*x^2 + 1)*x/a^6 - 15*arcsinh(a*x)/a^7)*a^2*c^2 + 96*(8*(a^2*x^2 + 1)^(3/2)*x^3/a^2 - 6*(a^2*x^2 + 1)^(3/2)*x/a^4 + 3*sqrt(a^2*x^2 + 1)*x/a^4 + 3*arcsinh(a*x)/a^5)*c^2 + 144*c^2*(2*(a^2*x^2 + 1)^(3/2)*x/a^2 - sqrt(a^2*x^2 + 1)*x/a^2 - arcsinh(a*x)/a^3)/a^2 - 384*(sqrt(a^2*x^2 + 1)*x + arcsinh(a*x)/a)*c^2/a^4)*a - 384*(7*(a^2*x^2 + 1)^(3/2)*a^2*c^2*x^6 + 12*(a^2*x^2 + 1)^(3/2)*c^2*x^4 + 3*(a^2*x^2 + 1)^(3/2)*c^2*x^2/a^2 - 2*(a^2*x^2 + 1)^(3/2)*c^2/a^4)*arctan(a*x))*sqrt(c)","A",0
217,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2} \arctan\left(a x\right)\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x^2*arctan(a*x), x)","F",0
218,1,637,0,0.685336," ","integrate(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x, algorithm=""maxima"")","\frac{560 \, {\left(a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{c} \arctan\left(a x\right) - 280 \, {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} {\left(a c^{2} x \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right) + 2 \, c^{2} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right)\right)} \sqrt{c} - {\left({\left(a {\left(\frac{5 \, {\left(\frac{8 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}{a^{2}} - \frac{6 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{4}} + \frac{3 \, \sqrt{a^{2} x^{2} + 1} x}{a^{4}} + \frac{3 \, \operatorname{arsinh}\left(a x\right)}{a^{5}}\right)}}{a^{2}} - \frac{24 \, {\left(\frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{2}} - \frac{\sqrt{a^{2} x^{2} + 1} x}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{a^{3}}\right)}}{a^{4}} + \frac{64 \, {\left(\sqrt{a^{2} x^{2} + 1} x + \frac{\operatorname{arsinh}\left(a x\right)}{a}\right)}}{a^{6}}\right)} - 16 \, {\left(\frac{15 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{4}}{a^{2}} - \frac{12 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{a^{4}} + \frac{8 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{6}}\right)} \arctan\left(a x\right)\right)} a^{6} c^{2} + 28 \, {\left(a {\left(\frac{3 \, {\left(\frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{2}} - \frac{\sqrt{a^{2} x^{2} + 1} x}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{a^{3}}\right)}}{a^{2}} - \frac{8 \, {\left(\sqrt{a^{2} x^{2} + 1} x + \frac{\operatorname{arsinh}\left(a x\right)}{a}\right)}}{a^{4}}\right)} - 8 \, {\left(\frac{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{a^{2}} - \frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{4}}\right)} \arctan\left(a x\right)\right)} a^{4} c^{2} - 140 \, c^{2} \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) + 2, a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right) - 140 \, c^{2} \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) - 2, -a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right)\right)} \sqrt{c}}{1680 \, a^{2}}"," ",0,"1/1680*(560*(a^2*c^2*x^2 + c^2)*sqrt(a^2*x^2 + 1)*sqrt(c)*arctan(a*x) - 280*(a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*(a*c^2*x*cos(1/2*arctan2(4*a*x, -a^2*x^2 + 3)) + 2*c^2*sin(1/2*arctan2(4*a*x, -a^2*x^2 + 3)))*sqrt(c) - ((a*(5*(8*(a^2*x^2 + 1)^(3/2)*x^3/a^2 - 6*(a^2*x^2 + 1)^(3/2)*x/a^4 + 3*sqrt(a^2*x^2 + 1)*x/a^4 + 3*arcsinh(a*x)/a^5)/a^2 - 24*(2*(a^2*x^2 + 1)^(3/2)*x/a^2 - sqrt(a^2*x^2 + 1)*x/a^2 - arcsinh(a*x)/a^3)/a^4 + 64*(sqrt(a^2*x^2 + 1)*x + arcsinh(a*x)/a)/a^6) - 16*(15*(a^2*x^2 + 1)^(3/2)*x^4/a^2 - 12*(a^2*x^2 + 1)^(3/2)*x^2/a^4 + 8*(a^2*x^2 + 1)^(3/2)/a^6)*arctan(a*x))*a^6*c^2 + 28*(a*(3*(2*(a^2*x^2 + 1)^(3/2)*x/a^2 - sqrt(a^2*x^2 + 1)*x/a^2 - arcsinh(a*x)/a^3)/a^2 - 8*(sqrt(a^2*x^2 + 1)*x + arcsinh(a*x)/a)/a^4) - 8*(3*(a^2*x^2 + 1)^(3/2)*x^2/a^2 - 2*(a^2*x^2 + 1)^(3/2)/a^4)*arctan(a*x))*a^4*c^2 - 140*c^2*arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) + 2, a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))) - 140*c^2*arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) - 2, -a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))))*sqrt(c))/a^2","B",0
219,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x), x)","F",0
220,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x,x, algorithm=""maxima"")","\frac{2}{3} \, {\left(a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{c} \arctan\left(a x\right) - \frac{1}{3} \, {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} {\left(a c^{2} x \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right) + 2 \, c^{2} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right)\right)} \sqrt{c} - \frac{1}{120} \, {\left({\left(a {\left(\frac{3 \, {\left(\frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{a^{2}} - \frac{\sqrt{a^{2} x^{2} + 1} x}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{a^{3}}\right)}}{a^{2}} - \frac{8 \, {\left(\sqrt{a^{2} x^{2} + 1} x + \frac{\operatorname{arsinh}\left(a x\right)}{a}\right)}}{a^{4}}\right)} - 8 \, {\left(\frac{3 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{a^{2}} - \frac{2 \, {\left(a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{a^{4}}\right)} \arctan\left(a x\right)\right)} a^{4} c^{2} - 20 \, c^{2} \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) + 2, a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right) - 20 \, c^{2} \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) - 2, -a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right) - 120 \, c^{2} \int \frac{\sqrt{a^{2} x^{2} + 1} \arctan\left(a x\right)}{x}\,{d x}\right)} \sqrt{c}"," ",0,"2/3*(a^2*c^2*x^2 + c^2)*sqrt(a^2*x^2 + 1)*sqrt(c)*arctan(a*x) - 1/3*(a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*(a*c^2*x*cos(1/2*arctan2(4*a*x, -a^2*x^2 + 3)) + 2*c^2*sin(1/2*arctan2(4*a*x, -a^2*x^2 + 3)))*sqrt(c) - 1/120*((a*(3*(2*(a^2*x^2 + 1)^(3/2)*x/a^2 - sqrt(a^2*x^2 + 1)*x/a^2 - arcsinh(a*x)/a^3)/a^2 - 8*(sqrt(a^2*x^2 + 1)*x + arcsinh(a*x)/a)/a^4) - 8*(3*(a^2*x^2 + 1)^(3/2)*x^2/a^2 - 2*(a^2*x^2 + 1)^(3/2)/a^4)*arctan(a*x))*a^4*c^2 - 20*c^2*arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) + 2, a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))) - 20*c^2*arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) - 2, -a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))) - 120*c^2*integrate(sqrt(a^2*x^2 + 1)*arctan(a*x)/x, x))*sqrt(c)","F",0
221,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)}{x^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)/x^2, x)","F",0
222,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^3,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{c} \arctan\left(a x\right) - \frac{1}{6} \, {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} {\left(a^{3} c^{2} x \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right) + 2 \, a^{2} c^{2} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, -a^{2} x^{2} + 3\right)\right)\right)} \sqrt{c} + \frac{1}{12} \, {\left(a^{2} c^{2} \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) + 2, a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right) + a^{2} c^{2} \arctan\left({\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right) - 2, -a x + {\left(a^{4} x^{4} + 10 \, a^{2} x^{2} + 9\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(4 \, a x, a^{2} x^{2} - 3\right)\right)\right) + 24 \, a^{2} c^{2} \int \frac{\sqrt{a^{2} x^{2} + 1} \arctan\left(a x\right)}{x}\,{d x} + 12 \, c^{2} \int \frac{\sqrt{a^{2} x^{2} + 1} \arctan\left(a x\right)}{x^{3}}\,{d x}\right)} \sqrt{c}"," ",0,"1/3*(a^4*c^2*x^2 + a^2*c^2)*sqrt(a^2*x^2 + 1)*sqrt(c)*arctan(a*x) - 1/6*(a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*(a^3*c^2*x*cos(1/2*arctan2(4*a*x, -a^2*x^2 + 3)) + 2*a^2*c^2*sin(1/2*arctan2(4*a*x, -a^2*x^2 + 3)))*sqrt(c) + 1/12*(a^2*c^2*arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) + 2, a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))) + a^2*c^2*arctan2((a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*sin(1/2*arctan2(4*a*x, a^2*x^2 - 3)) - 2, -a*x + (a^4*x^4 + 10*a^2*x^2 + 9)^(1/4)*cos(1/2*arctan2(4*a*x, a^2*x^2 - 3))) + 24*a^2*c^2*integrate(sqrt(a^2*x^2 + 1)*arctan(a*x)/x, x) + 12*c^2*integrate(sqrt(a^2*x^2 + 1)*arctan(a*x)/x^3, x))*sqrt(c)","F",0
223,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)}{x^{4}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)/x^4, x)","F",0
224,1,89,0,0.468651," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{a {\left(\frac{\frac{\sqrt{a^{2} x^{2} + 1} x}{a^{2}} - \frac{\operatorname{arsinh}\left(a x\right)}{a^{3}}}{a^{2}} - \frac{4 \, \operatorname{arsinh}\left(a x\right)}{a^{5}}\right)} - 2 \, {\left(\frac{\sqrt{a^{2} x^{2} + 1} x^{2}}{a^{2}} - \frac{2 \, \sqrt{a^{2} x^{2} + 1}}{a^{4}}\right)} \arctan\left(a x\right)}{6 \, \sqrt{c}}"," ",0,"-1/6*(a*((sqrt(a^2*x^2 + 1)*x/a^2 - arcsinh(a*x)/a^3)/a^2 - 4*arcsinh(a*x)/a^5) - 2*(sqrt(a^2*x^2 + 1)*x^2/a^2 - 2*sqrt(a^2*x^2 + 1)/a^4)*arctan(a*x))/sqrt(c)","A",0
225,0,0,0,0.000000," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \arctan\left(a x\right)}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^2*arctan(a*x)/sqrt(a^2*c*x^2 + c), x)","F",0
226,1,61,0,0.489288," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{a^{2} x^{2} + 1} \arctan\left(a x\right) - \log\left(a x + \sqrt{a^{2} x^{2} + 1}\right) + \log\left(-a x + \sqrt{a^{2} x^{2} + 1}\right)}{2 \, a^{2} \sqrt{c}}"," ",0,"1/2*(2*sqrt(a^2*x^2 + 1)*arctan(a*x) - log(a*x + sqrt(a^2*x^2 + 1)) + log(-a*x + sqrt(a^2*x^2 + 1)))/(a^2*sqrt(c))","A",0
227,0,0,0,0.000000," ","integrate(arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(arctan(a*x)/sqrt(a^2*c*x^2 + c), x)","F",0
228,0,0,0,0.000000," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{\sqrt{a^{2} c x^{2} + c} x}\,{d x}"," ",0,"integrate(arctan(a*x)/(sqrt(a^2*c*x^2 + c)*x), x)","F",0
229,1,36,0,0.476878," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","-\frac{a \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right) + \frac{\sqrt{a^{2} x^{2} + 1} \arctan\left(a x\right)}{x}}{\sqrt{c}}"," ",0,"-(a*arcsinh(1/(a*abs(x))) + sqrt(a^2*x^2 + 1)*arctan(a*x)/x)/sqrt(c)","A",0
230,0,0,0,0.000000," ","integrate(arctan(a*x)/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{\sqrt{a^{2} c x^{2} + c} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)/(sqrt(a^2*c*x^2 + c)*x^3), x)","F",0
231,1,81,0,0.498768," ","integrate(arctan(a*x)/x^4/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left(5 \, a^{2} \operatorname{arsinh}\left(\frac{1}{a {\left| x \right|}}\right) - \frac{\sqrt{a^{2} x^{2} + 1}}{x^{2}}\right)} a + 2 \, {\left(\frac{2 \, \sqrt{a^{2} x^{2} + 1} a^{2}}{x} - \frac{\sqrt{a^{2} x^{2} + 1}}{x^{3}}\right)} \arctan\left(a x\right)}{6 \, \sqrt{c}}"," ",0,"1/6*((5*a^2*arcsinh(1/(a*abs(x))) - sqrt(a^2*x^2 + 1)/x^2)*a + 2*(2*sqrt(a^2*x^2 + 1)*a^2/x - sqrt(a^2*x^2 + 1)/x^3)*arctan(a*x))/sqrt(c)","A",0
232,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)/(a^2*c*x^2 + c)^(3/2), x)","F",0
233,0,0,0,0.000000," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2} \arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*arctan(a*x)/(a^2*c*x^2 + c)^(3/2), x)","F",0
234,1,28,0,0.501636," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{a x - \arctan\left(a x\right)}{\sqrt{a^{2} x^{2} + 1} a^{2} c^{\frac{3}{2}}}"," ",0,"(a*x - arctan(a*x))/(sqrt(a^2*x^2 + 1)*a^2*c^(3/2))","A",0
235,1,41,0,0.336817," ","integrate(arctan(a*x)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{x \arctan\left(a x\right)}{\sqrt{a^{2} c x^{2} + c} c} + \frac{1}{\sqrt{a^{2} c x^{2} + c} a c}"," ",0,"x*arctan(a*x)/(sqrt(a^2*c*x^2 + c)*c) + 1/(sqrt(a^2*c*x^2 + c)*a*c)","A",0
236,0,0,0,0.000000," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)^(3/2)*x), x)","F",0
237,0,0,0,0.000000," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)^(3/2)*x^2), x)","F",0
238,0,0,0,0.000000," ","integrate(arctan(a*x)/x^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)^(3/2)*x^3), x)","F",0
239,0,0,0,0.000000," ","integrate(arctan(a*x)/x^4/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)^(3/2)*x^4), x)","F",0
240,0,0,0,0.000000," ","integrate(x^5*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{5} \arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^5*arctan(a*x)/(a^2*c*x^2 + c)^(5/2), x)","F",0
241,0,0,0,0.000000," ","integrate(x^4*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{4} \arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^4*arctan(a*x)/(a^2*c*x^2 + c)^(5/2), x)","F",0
242,1,65,0,0.463234," ","integrate(x^3*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{7 \, a^{3} x^{3} + 6 \, a x - 3 \, {\left(3 \, a^{2} x^{2} + 2\right)} \arctan\left(a x\right)}{9 \, {\left(a^{6} c^{2} x^{2} + a^{4} c^{2}\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{c}}"," ",0,"1/9*(7*a^3*x^3 + 6*a*x - 3*(3*a^2*x^2 + 2)*arctan(a*x))/((a^6*c^2*x^2 + a^4*c^2)*sqrt(a^2*x^2 + 1)*sqrt(c))","A",0
243,1,93,0,0.358104," ","integrate(x^2*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{9} \, a {\left(\frac{3}{\sqrt{a^{2} c x^{2} + c} a^{4} c^{2}} - \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{4} c}\right)} + \frac{1}{3} \, {\left(\frac{x}{\sqrt{a^{2} c x^{2} + c} a^{2} c^{2}} - \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{2} c}\right)} \arctan\left(a x\right)"," ",0,"1/9*a*(3/(sqrt(a^2*c*x^2 + c)*a^4*c^2) - 1/((a^2*c*x^2 + c)^(3/2)*a^4*c)) + 1/3*(x/(sqrt(a^2*c*x^2 + c)*a^2*c^2) - x/((a^2*c*x^2 + c)^(3/2)*a^2*c))*arctan(a*x)","A",0
244,1,66,0,0.441561," ","integrate(x*arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{{\left(2 \, a^{3} x^{3} + 3 \, a x - 3 \, \arctan\left(a x\right)\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{c}}{9 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)}}"," ",0,"1/9*(2*a^3*x^3 + 3*a*x - 3*arctan(a*x))*sqrt(a^2*x^2 + 1)*sqrt(c)/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)","A",0
245,1,86,0,0.336746," ","integrate(arctan(a*x)/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{9} \, a {\left(\frac{6}{\sqrt{a^{2} c x^{2} + c} a^{2} c^{2}} + \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{2} c}\right)} + \frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{a^{2} c x^{2} + c} c^{2}} + \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c}\right)} \arctan\left(a x\right)"," ",0,"1/9*a*(6/(sqrt(a^2*c*x^2 + c)*a^2*c^2) + 1/((a^2*c*x^2 + c)^(3/2)*a^2*c)) + 1/3*(2*x/(sqrt(a^2*c*x^2 + c)*c^2) + x/((a^2*c*x^2 + c)^(3/2)*c))*arctan(a*x)","A",0
246,0,0,0,0.000000," ","integrate(arctan(a*x)/x/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)^(5/2)*x), x)","F",0
247,0,0,0,0.000000," ","integrate(arctan(a*x)/x^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate(arctan(a*x)/((a^2*c*x^2 + c)^(5/2)*x^2), x)","F",0
248,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^3*arctan(a*x),x, algorithm=""maxima"")","\frac{{\left({\left(a^{6} c^{3} m^{3} + 9 \, a^{6} c^{3} m^{2} + 23 \, a^{6} c^{3} m + 15 \, a^{6} c^{3}\right)} x^{7} + 3 \, {\left(a^{4} c^{3} m^{3} + 11 \, a^{4} c^{3} m^{2} + 31 \, a^{4} c^{3} m + 21 \, a^{4} c^{3}\right)} x^{5} + 3 \, {\left(a^{2} c^{3} m^{3} + 13 \, a^{2} c^{3} m^{2} + 47 \, a^{2} c^{3} m + 35 \, a^{2} c^{3}\right)} x^{3} + {\left(c^{3} m^{3} + 15 \, c^{3} m^{2} + 71 \, c^{3} m + 105 \, c^{3}\right)} x\right)} x^{m} \arctan\left(a x\right) - {\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} \int \frac{{\left({\left(a^{7} c^{3} m^{3} + 9 \, a^{7} c^{3} m^{2} + 23 \, a^{7} c^{3} m + 15 \, a^{7} c^{3}\right)} x^{7} + 3 \, {\left(a^{5} c^{3} m^{3} + 11 \, a^{5} c^{3} m^{2} + 31 \, a^{5} c^{3} m + 21 \, a^{5} c^{3}\right)} x^{5} + 3 \, {\left(a^{3} c^{3} m^{3} + 13 \, a^{3} c^{3} m^{2} + 47 \, a^{3} c^{3} m + 35 \, a^{3} c^{3}\right)} x^{3} + {\left(a c^{3} m^{3} + 15 \, a c^{3} m^{2} + 71 \, a c^{3} m + 105 \, a c^{3}\right)} x\right)} x^{m}}{m^{4} + 16 \, m^{3} + {\left(a^{2} m^{4} + 16 \, a^{2} m^{3} + 86 \, a^{2} m^{2} + 176 \, a^{2} m + 105 \, a^{2}\right)} x^{2} + 86 \, m^{2} + 176 \, m + 105}\,{d x}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"(((a^6*c^3*m^3 + 9*a^6*c^3*m^2 + 23*a^6*c^3*m + 15*a^6*c^3)*x^7 + 3*(a^4*c^3*m^3 + 11*a^4*c^3*m^2 + 31*a^4*c^3*m + 21*a^4*c^3)*x^5 + 3*(a^2*c^3*m^3 + 13*a^2*c^3*m^2 + 47*a^2*c^3*m + 35*a^2*c^3)*x^3 + (c^3*m^3 + 15*c^3*m^2 + 71*c^3*m + 105*c^3)*x)*x^m*arctan(a*x) - (m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*integrate(((a^7*c^3*m^3 + 9*a^7*c^3*m^2 + 23*a^7*c^3*m + 15*a^7*c^3)*x^7 + 3*(a^5*c^3*m^3 + 11*a^5*c^3*m^2 + 31*a^5*c^3*m + 21*a^5*c^3)*x^5 + 3*(a^3*c^3*m^3 + 13*a^3*c^3*m^2 + 47*a^3*c^3*m + 35*a^3*c^3)*x^3 + (a*c^3*m^3 + 15*a*c^3*m^2 + 71*a*c^3*m + 105*a*c^3)*x)*x^m/(m^4 + 16*m^3 + (a^2*m^4 + 16*a^2*m^3 + 86*a^2*m^2 + 176*a^2*m + 105*a^2)*x^2 + 86*m^2 + 176*m + 105), x))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","F",0
249,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2*arctan(a*x),x, algorithm=""maxima"")","\frac{{\left({\left(a^{4} c^{2} m^{2} + 4 \, a^{4} c^{2} m + 3 \, a^{4} c^{2}\right)} x^{5} + 2 \, {\left(a^{2} c^{2} m^{2} + 6 \, a^{2} c^{2} m + 5 \, a^{2} c^{2}\right)} x^{3} + {\left(c^{2} m^{2} + 8 \, c^{2} m + 15 \, c^{2}\right)} x\right)} x^{m} \arctan\left(a x\right) - {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} \int \frac{{\left({\left(a^{5} c^{2} m^{2} + 4 \, a^{5} c^{2} m + 3 \, a^{5} c^{2}\right)} x^{5} + 2 \, {\left(a^{3} c^{2} m^{2} + 6 \, a^{3} c^{2} m + 5 \, a^{3} c^{2}\right)} x^{3} + {\left(a c^{2} m^{2} + 8 \, a c^{2} m + 15 \, a c^{2}\right)} x\right)} x^{m}}{m^{3} + {\left(a^{2} m^{3} + 9 \, a^{2} m^{2} + 23 \, a^{2} m + 15 \, a^{2}\right)} x^{2} + 9 \, m^{2} + 23 \, m + 15}\,{d x}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"(((a^4*c^2*m^2 + 4*a^4*c^2*m + 3*a^4*c^2)*x^5 + 2*(a^2*c^2*m^2 + 6*a^2*c^2*m + 5*a^2*c^2)*x^3 + (c^2*m^2 + 8*c^2*m + 15*c^2)*x)*x^m*arctan(a*x) - (m^3 + 9*m^2 + 23*m + 15)*integrate(((a^5*c^2*m^2 + 4*a^5*c^2*m + 3*a^5*c^2)*x^5 + 2*(a^3*c^2*m^2 + 6*a^3*c^2*m + 5*a^3*c^2)*x^3 + (a*c^2*m^2 + 8*a*c^2*m + 15*a*c^2)*x)*x^m/(m^3 + (a^2*m^3 + 9*a^2*m^2 + 23*a^2*m + 15*a^2)*x^2 + 9*m^2 + 23*m + 15), x))/(m^3 + 9*m^2 + 23*m + 15)","F",0
250,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)*arctan(a*x),x, algorithm=""maxima"")","\frac{{\left({\left(a^{2} c m + a^{2} c\right)} x^{3} + {\left(c m + 3 \, c\right)} x\right)} x^{m} \arctan\left(a x\right) - {\left(m^{2} + 4 \, m + 3\right)} \int \frac{{\left({\left(a^{3} c m + a^{3} c\right)} x^{3} + {\left(a c m + 3 \, a c\right)} x\right)} x^{m}}{{\left(a^{2} m^{2} + 4 \, a^{2} m + 3 \, a^{2}\right)} x^{2} + m^{2} + 4 \, m + 3}\,{d x}}{m^{2} + 4 \, m + 3}"," ",0,"(((a^2*c*m + a^2*c)*x^3 + (c*m + 3*c)*x)*x^m*arctan(a*x) - (m^2 + 4*m + 3)*integrate(((a^3*c*m + a^3*c)*x^3 + (a*c*m + 3*a*c)*x)*x^m/((a^2*m^2 + 4*a^2*m + 3*a^2)*x^2 + m^2 + 4*m + 3), x))/(m^2 + 4*m + 3)","F",0
251,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)/(a^2*c*x^2 + c), x)","F",0
252,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)/(a^2*c*x^2 + c)^2, x)","F",0
253,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{m} \arctan\left(a x\right)\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x^m*arctan(a*x), x)","F",0
254,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x),x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m} \arctan\left(a x\right)\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^m*arctan(a*x), x)","F",0
255,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x), x)","F",0
256,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)/sqrt(a^2*c*x^2 + c), x)","F",0
257,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)/(a^2*c*x^2 + c)^(3/2), x)","F",0
258,1,116,0,0.444521," ","integrate(x^3*(a^2*c*x^2+c)*arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{1}{90} \, a {\left(\frac{6 \, a^{4} c x^{5} + 5 \, a^{2} c x^{3} - 15 \, c x}{a^{4}} + \frac{15 \, c \arctan\left(a x\right)}{a^{5}}\right)} \arctan\left(a x\right) + \frac{1}{12} \, {\left(2 \, a^{2} c x^{6} + 3 \, c x^{4}\right)} \arctan\left(a x\right)^{2} + \frac{3 \, a^{4} c x^{4} - a^{2} c x^{2} + 15 \, c \arctan\left(a x\right)^{2} - 14 \, c \log\left(a^{2} x^{2} + 1\right)}{180 \, a^{4}}"," ",0,"-1/90*a*((6*a^4*c*x^5 + 5*a^2*c*x^3 - 15*c*x)/a^4 + 15*c*arctan(a*x)/a^5)*arctan(a*x) + 1/12*(2*a^2*c*x^6 + 3*c*x^4)*arctan(a*x)^2 + 1/180*(3*a^4*c*x^4 - a^2*c*x^2 + 15*c*arctan(a*x)^2 - 14*c*log(a^2*x^2 + 1))/a^4","A",0
259,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)*arctan(a*x)^2,x, algorithm=""maxima"")","\frac{1}{60} \, {\left(3 \, a^{2} c x^{5} + 5 \, c x^{3}\right)} \arctan\left(a x\right)^{2} - \frac{1}{240} \, {\left(3 \, a^{2} c x^{5} + 5 \, c x^{3}\right)} \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{180 \, {\left(a^{4} c x^{6} + 2 \, a^{2} c x^{4} + c x^{2}\right)} \arctan\left(a x\right)^{2} + 15 \, {\left(a^{4} c x^{6} + 2 \, a^{2} c x^{4} + c x^{2}\right)} \log\left(a^{2} x^{2} + 1\right)^{2} - 8 \, {\left(3 \, a^{3} c x^{5} + 5 \, a c x^{3}\right)} \arctan\left(a x\right) + 4 \, {\left(3 \, a^{4} c x^{6} + 5 \, a^{2} c x^{4}\right)} \log\left(a^{2} x^{2} + 1\right)}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/60*(3*a^2*c*x^5 + 5*c*x^3)*arctan(a*x)^2 - 1/240*(3*a^2*c*x^5 + 5*c*x^3)*log(a^2*x^2 + 1)^2 + integrate(1/240*(180*(a^4*c*x^6 + 2*a^2*c*x^4 + c*x^2)*arctan(a*x)^2 + 15*(a^4*c*x^6 + 2*a^2*c*x^4 + c*x^2)*log(a^2*x^2 + 1)^2 - 8*(3*a^3*c*x^5 + 5*a*c*x^3)*arctan(a*x) + 4*(3*a^4*c*x^6 + 5*a^2*c*x^4)*log(a^2*x^2 + 1))/(a^2*x^2 + 1), x)","F",0
260,1,87,0,0.320238," ","integrate(x*(a^2*c*x^2+c)*arctan(a*x)^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} c x^{2} + c\right)}^{2} \arctan\left(a x\right)^{2}}{4 \, a^{2} c} + \frac{{\left(c^{2} x^{2} + \frac{2 \, c^{2} \log\left(a^{2} x^{2} + 1\right)}{a^{2}}\right)} a - 2 \, {\left(a^{2} c^{2} x^{3} + 3 \, c^{2} x\right)} \arctan\left(a x\right)}{12 \, a c}"," ",0,"1/4*(a^2*c*x^2 + c)^2*arctan(a*x)^2/(a^2*c) + 1/12*((c^2*x^2 + 2*c^2*log(a^2*x^2 + 1)/a^2)*a - 2*(a^2*c^2*x^3 + 3*c^2*x)*arctan(a*x))/(a*c)","A",0
261,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^2,x, algorithm=""maxima"")","36 \, a^{4} c \int \frac{x^{4} \arctan\left(a x\right)^{2}}{48 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 3 \, a^{4} c \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)^{2}}{48 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 4 \, a^{4} c \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)}{48 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 8 \, a^{3} c \int \frac{x^{3} \arctan\left(a x\right)}{48 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 72 \, a^{2} c \int \frac{x^{2} \arctan\left(a x\right)^{2}}{48 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 6 \, a^{2} c \int \frac{x^{2} \log\left(a^{2} x^{2} + 1\right)^{2}}{48 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 12 \, a^{2} c \int \frac{x^{2} \log\left(a^{2} x^{2} + 1\right)}{48 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{1}{12} \, {\left(a^{2} c x^{3} + 3 \, c x\right)} \arctan\left(a x\right)^{2} + \frac{c \arctan\left(a x\right)^{3}}{4 \, a} - 24 \, a c \int \frac{x \arctan\left(a x\right)}{48 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - \frac{1}{48} \, {\left(a^{2} c x^{3} + 3 \, c x\right)} \log\left(a^{2} x^{2} + 1\right)^{2} + 3 \, c \int \frac{\log\left(a^{2} x^{2} + 1\right)^{2}}{48 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"36*a^4*c*integrate(1/48*x^4*arctan(a*x)^2/(a^2*x^2 + 1), x) + 3*a^4*c*integrate(1/48*x^4*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 4*a^4*c*integrate(1/48*x^4*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 8*a^3*c*integrate(1/48*x^3*arctan(a*x)/(a^2*x^2 + 1), x) + 72*a^2*c*integrate(1/48*x^2*arctan(a*x)^2/(a^2*x^2 + 1), x) + 6*a^2*c*integrate(1/48*x^2*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 12*a^2*c*integrate(1/48*x^2*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) + 1/12*(a^2*c*x^3 + 3*c*x)*arctan(a*x)^2 + 1/4*c*arctan(a*x)^3/a - 24*a*c*integrate(1/48*x*arctan(a*x)/(a^2*x^2 + 1), x) - 1/48*(a^2*c*x^3 + 3*c*x)*log(a^2*x^2 + 1)^2 + 3*c*integrate(1/48*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x)","F",0
262,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^2/x,x, algorithm=""maxima"")","\frac{1}{8} \, a^{2} c x^{2} \arctan\left(a x\right)^{2} - \frac{1}{32} \, a^{2} c x^{2} \log\left(a^{2} x^{2} + 1\right)^{2} + 12 \, a^{4} c \int \frac{x^{4} \arctan\left(a x\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + a^{4} c \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 2 \, a^{4} c \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} - 4 \, a^{3} c \int \frac{x^{3} \arctan\left(a x\right)}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 24 \, a^{2} c \int \frac{x^{2} \arctan\left(a x\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + \frac{1}{48} \, c \log\left(a^{2} x^{2} + 1\right)^{3} + 12 \, c \int \frac{\arctan\left(a x\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + c \int \frac{\log\left(a^{2} x^{2} + 1\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x}"," ",0,"1/8*a^2*c*x^2*arctan(a*x)^2 - 1/32*a^2*c*x^2*log(a^2*x^2 + 1)^2 + 12*a^4*c*integrate(1/16*x^4*arctan(a*x)^2/(a^2*x^3 + x), x) + a^4*c*integrate(1/16*x^4*log(a^2*x^2 + 1)^2/(a^2*x^3 + x), x) + 2*a^4*c*integrate(1/16*x^4*log(a^2*x^2 + 1)/(a^2*x^3 + x), x) - 4*a^3*c*integrate(1/16*x^3*arctan(a*x)/(a^2*x^3 + x), x) + 24*a^2*c*integrate(1/16*x^2*arctan(a*x)^2/(a^2*x^3 + x), x) + 1/48*c*log(a^2*x^2 + 1)^3 + 12*c*integrate(1/16*arctan(a*x)^2/(a^2*x^3 + x), x) + c*integrate(1/16*log(a^2*x^2 + 1)^2/(a^2*x^3 + x), x)","F",0
263,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^2/x^3,x, algorithm=""maxima"")","\frac{{\left(72 \, a^{4} c \int \frac{x^{4} \arctan\left(a x\right)^{2}}{a^{2} x^{5} + x^{3}}\,{d x} + a^{2} c \log\left(a^{2} x^{2} + 1\right)^{3} - 3 \, {\left(a^{2} {\left(\frac{\log\left(a^{2} x^{2} + 1\right)^{2}}{a^{2}} - \frac{2 \, {\left(2 \, \log\left(a^{2} x^{2} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a^{2} x^{2}\right)\right)}}{a^{2}}\right)} - 2 \, {\left(\log\left(a^{2} x^{2} + 1\right) - 2 \, \log\left(x\right)\right)} \log\left(a^{2} x^{2} + 1\right)\right)} a^{2} c - 2 \, {\left(\log\left(a^{2} x^{2} + 1\right)^{3} - 3 \, \log\left(a^{2} x^{2} + 1\right)^{2} \log\left(-a^{2} x^{2}\right) - 6 \, {\rm Li}_2\left(a^{2} x^{2} + 1\right) \log\left(a^{2} x^{2} + 1\right) + 6 \, {\rm Li}_{3}(a^{2} x^{2} + 1)\right)} a^{2} c + 144 \, a^{2} c \int \frac{x^{2} \arctan\left(a x\right)^{2}}{a^{2} x^{5} + x^{3}}\,{d x} + 12 \, {\left({\left(\arctan\left(a x\right)^{2} - \log\left(a^{2} x^{2} + 1\right) + 2 \, \log\left(x\right)\right)} a - 2 \, {\left(a \arctan\left(a x\right) + \frac{1}{x}\right)} \arctan\left(a x\right)\right)} a c - {\left(3 \, {\left(\log\left(a^{2} x^{2} + 1\right)^{2} \log\left(-a^{2} x^{2}\right) + 2 \, {\rm Li}_2\left(a^{2} x^{2} + 1\right) \log\left(a^{2} x^{2} + 1\right) - 2 \, {\rm Li}_{3}(a^{2} x^{2} + 1)\right)} a^{2} - 6 \, {\left(\log\left(a^{2} x^{2} + 1\right) \log\left(-a^{2} x^{2}\right) + {\rm Li}_2\left(a^{2} x^{2} + 1\right)\right)} a^{2} - \frac{a^{2} x^{2} \log\left(a^{2} x^{2} + 1\right)^{3} - 3 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{x^{2}}\right)} c + 72 \, c \int \frac{\arctan\left(a x\right)^{2}}{a^{2} x^{5} + x^{3}}\,{d x}\right)} x^{2} - 12 \, c \arctan\left(a x\right)^{2} + 3 \, c \log\left(a^{2} x^{2} + 1\right)^{2}}{96 \, x^{2}}"," ",0,"1/96*((1152*a^4*c*integrate(1/16*x^4*arctan(a*x)^2/(a^2*x^5 + x^3), x) + a^2*c*log(a^2*x^2 + 1)^3 + 2304*a^2*c*integrate(1/16*x^2*arctan(a*x)^2/(a^2*x^5 + x^3), x) + 192*a^2*c*integrate(1/16*x^2*log(a^2*x^2 + 1)^2/(a^2*x^5 + x^3), x) - 192*a^2*c*integrate(1/16*x^2*log(a^2*x^2 + 1)/(a^2*x^5 + x^3), x) + 384*a*c*integrate(1/16*x*arctan(a*x)/(a^2*x^5 + x^3), x) + 1152*c*integrate(1/16*arctan(a*x)^2/(a^2*x^5 + x^3), x) + 96*c*integrate(1/16*log(a^2*x^2 + 1)^2/(a^2*x^5 + x^3), x))*x^2 - 12*c*arctan(a*x)^2 + 3*c*log(a^2*x^2 + 1)^2)/x^2","F",0
265,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^2/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,1,169,0,0.428549," ","integrate(x^3*(a^2*c*x^2+c)^2*arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{1}{252} \, a {\left(\frac{21 \, c^{2} \arctan\left(a x\right)}{a^{5}} + \frac{9 \, a^{6} c^{2} x^{7} + 21 \, a^{4} c^{2} x^{5} + 7 \, a^{2} c^{2} x^{3} - 21 \, c^{2} x}{a^{4}}\right)} \arctan\left(a x\right) + \frac{1}{24} \, {\left(3 \, a^{4} c^{2} x^{8} + 8 \, a^{2} c^{2} x^{6} + 6 \, c^{2} x^{4}\right)} \arctan\left(a x\right)^{2} + \frac{3 \, a^{6} c^{2} x^{6} + 6 \, a^{4} c^{2} x^{4} - 5 \, a^{2} c^{2} x^{2} + 21 \, c^{2} \arctan\left(a x\right)^{2} - 16 \, c^{2} \log\left(a^{2} x^{2} + 1\right)}{504 \, a^{4}}"," ",0,"-1/252*a*(21*c^2*arctan(a*x)/a^5 + (9*a^6*c^2*x^7 + 21*a^4*c^2*x^5 + 7*a^2*c^2*x^3 - 21*c^2*x)/a^4)*arctan(a*x) + 1/24*(3*a^4*c^2*x^8 + 8*a^2*c^2*x^6 + 6*c^2*x^4)*arctan(a*x)^2 + 1/504*(3*a^6*c^2*x^6 + 6*a^4*c^2*x^4 - 5*a^2*c^2*x^2 + 21*c^2*arctan(a*x)^2 - 16*c^2*log(a^2*x^2 + 1))/a^4","A",0
267,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^2,x, algorithm=""maxima"")","\frac{1}{420} \, {\left(15 \, a^{4} c^{2} x^{7} + 42 \, a^{2} c^{2} x^{5} + 35 \, c^{2} x^{3}\right)} \arctan\left(a x\right)^{2} - \frac{1}{1680} \, {\left(15 \, a^{4} c^{2} x^{7} + 42 \, a^{2} c^{2} x^{5} + 35 \, c^{2} x^{3}\right)} \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{1260 \, {\left(a^{6} c^{2} x^{8} + 3 \, a^{4} c^{2} x^{6} + 3 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)^{2} + 105 \, {\left(a^{6} c^{2} x^{8} + 3 \, a^{4} c^{2} x^{6} + 3 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \log\left(a^{2} x^{2} + 1\right)^{2} - 8 \, {\left(15 \, a^{5} c^{2} x^{7} + 42 \, a^{3} c^{2} x^{5} + 35 \, a c^{2} x^{3}\right)} \arctan\left(a x\right) + 4 \, {\left(15 \, a^{6} c^{2} x^{8} + 42 \, a^{4} c^{2} x^{6} + 35 \, a^{2} c^{2} x^{4}\right)} \log\left(a^{2} x^{2} + 1\right)}{1680 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/420*(15*a^4*c^2*x^7 + 42*a^2*c^2*x^5 + 35*c^2*x^3)*arctan(a*x)^2 - 1/1680*(15*a^4*c^2*x^7 + 42*a^2*c^2*x^5 + 35*c^2*x^3)*log(a^2*x^2 + 1)^2 + integrate(1/1680*(1260*(a^6*c^2*x^8 + 3*a^4*c^2*x^6 + 3*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x)^2 + 105*(a^6*c^2*x^8 + 3*a^4*c^2*x^6 + 3*a^2*c^2*x^4 + c^2*x^2)*log(a^2*x^2 + 1)^2 - 8*(15*a^5*c^2*x^7 + 42*a^3*c^2*x^5 + 35*a*c^2*x^3)*arctan(a*x) + 4*(15*a^6*c^2*x^8 + 42*a^4*c^2*x^6 + 35*a^2*c^2*x^4)*log(a^2*x^2 + 1))/(a^2*x^2 + 1), x)","F",0
268,1,111,0,0.311006," ","integrate(x*(a^2*c*x^2+c)^2*arctan(a*x)^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} c x^{2} + c\right)}^{3} \arctan\left(a x\right)^{2}}{6 \, a^{2} c} + \frac{{\left(3 \, a^{2} c^{3} x^{4} + 14 \, c^{3} x^{2} + \frac{16 \, c^{3} \log\left(a^{2} x^{2} + 1\right)}{a^{2}}\right)} a - 4 \, {\left(3 \, a^{4} c^{3} x^{5} + 10 \, a^{2} c^{3} x^{3} + 15 \, c^{3} x\right)} \arctan\left(a x\right)}{180 \, a c}"," ",0,"1/6*(a^2*c*x^2 + c)^3*arctan(a*x)^2/(a^2*c) + 1/180*((3*a^2*c^3*x^4 + 14*c^3*x^2 + 16*c^3*log(a^2*x^2 + 1)/a^2)*a - 4*(3*a^4*c^3*x^5 + 10*a^2*c^3*x^3 + 15*c^3*x)*arctan(a*x))/(a*c)","A",0
269,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^2,x, algorithm=""maxima"")","180 \, a^{6} c^{2} \int \frac{x^{6} \arctan\left(a x\right)^{2}}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 15 \, a^{6} c^{2} \int \frac{x^{6} \log\left(a^{2} x^{2} + 1\right)^{2}}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 12 \, a^{6} c^{2} \int \frac{x^{6} \log\left(a^{2} x^{2} + 1\right)}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 24 \, a^{5} c^{2} \int \frac{x^{5} \arctan\left(a x\right)}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 540 \, a^{4} c^{2} \int \frac{x^{4} \arctan\left(a x\right)^{2}}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 45 \, a^{4} c^{2} \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)^{2}}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 40 \, a^{4} c^{2} \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 80 \, a^{3} c^{2} \int \frac{x^{3} \arctan\left(a x\right)}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 540 \, a^{2} c^{2} \int \frac{x^{2} \arctan\left(a x\right)^{2}}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 45 \, a^{2} c^{2} \int \frac{x^{2} \log\left(a^{2} x^{2} + 1\right)^{2}}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 60 \, a^{2} c^{2} \int \frac{x^{2} \log\left(a^{2} x^{2} + 1\right)}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{c^{2} \arctan\left(a x\right)^{3}}{4 \, a} - 120 \, a c^{2} \int \frac{x \arctan\left(a x\right)}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{1}{60} \, {\left(3 \, a^{4} c^{2} x^{5} + 10 \, a^{2} c^{2} x^{3} + 15 \, c^{2} x\right)} \arctan\left(a x\right)^{2} + 15 \, c^{2} \int \frac{\log\left(a^{2} x^{2} + 1\right)^{2}}{240 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - \frac{1}{240} \, {\left(3 \, a^{4} c^{2} x^{5} + 10 \, a^{2} c^{2} x^{3} + 15 \, c^{2} x\right)} \log\left(a^{2} x^{2} + 1\right)^{2}"," ",0,"180*a^6*c^2*integrate(1/240*x^6*arctan(a*x)^2/(a^2*x^2 + 1), x) + 15*a^6*c^2*integrate(1/240*x^6*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 12*a^6*c^2*integrate(1/240*x^6*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 24*a^5*c^2*integrate(1/240*x^5*arctan(a*x)/(a^2*x^2 + 1), x) + 540*a^4*c^2*integrate(1/240*x^4*arctan(a*x)^2/(a^2*x^2 + 1), x) + 45*a^4*c^2*integrate(1/240*x^4*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 40*a^4*c^2*integrate(1/240*x^4*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 80*a^3*c^2*integrate(1/240*x^3*arctan(a*x)/(a^2*x^2 + 1), x) + 540*a^2*c^2*integrate(1/240*x^2*arctan(a*x)^2/(a^2*x^2 + 1), x) + 45*a^2*c^2*integrate(1/240*x^2*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 60*a^2*c^2*integrate(1/240*x^2*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) + 1/4*c^2*arctan(a*x)^3/a - 120*a*c^2*integrate(1/240*x*arctan(a*x)/(a^2*x^2 + 1), x) + 1/60*(3*a^4*c^2*x^5 + 10*a^2*c^2*x^3 + 15*c^2*x)*arctan(a*x)^2 + 15*c^2*integrate(1/240*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) - 1/240*(3*a^4*c^2*x^5 + 10*a^2*c^2*x^3 + 15*c^2*x)*log(a^2*x^2 + 1)^2","F",0
270,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^2/x,x, algorithm=""maxima"")","12 \, a^{6} c^{2} \int \frac{x^{6} \arctan\left(a x\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + a^{6} c^{2} \int \frac{x^{6} \log\left(a^{2} x^{2} + 1\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + a^{6} c^{2} \int \frac{x^{6} \log\left(a^{2} x^{2} + 1\right)}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} - 2 \, a^{5} c^{2} \int \frac{x^{5} \arctan\left(a x\right)}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 36 \, a^{4} c^{2} \int \frac{x^{4} \arctan\left(a x\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 3 \, a^{4} c^{2} \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 4 \, a^{4} c^{2} \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} - 8 \, a^{3} c^{2} \int \frac{x^{3} \arctan\left(a x\right)}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 36 \, a^{2} c^{2} \int \frac{x^{2} \arctan\left(a x\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + \frac{1}{32} \, c^{2} \log\left(a^{2} x^{2} + 1\right)^{3} + \frac{1}{16} \, {\left(a^{4} c^{2} x^{4} + 4 \, a^{2} c^{2} x^{2}\right)} \arctan\left(a x\right)^{2} + 12 \, c^{2} \int \frac{\arctan\left(a x\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + c^{2} \int \frac{\log\left(a^{2} x^{2} + 1\right)^{2}}{16 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} - \frac{1}{64} \, {\left(a^{4} c^{2} x^{4} + 4 \, a^{2} c^{2} x^{2}\right)} \log\left(a^{2} x^{2} + 1\right)^{2}"," ",0,"12*a^6*c^2*integrate(1/16*x^6*arctan(a*x)^2/(a^2*x^3 + x), x) + a^6*c^2*integrate(1/16*x^6*log(a^2*x^2 + 1)^2/(a^2*x^3 + x), x) + a^6*c^2*integrate(1/16*x^6*log(a^2*x^2 + 1)/(a^2*x^3 + x), x) - 2*a^5*c^2*integrate(1/16*x^5*arctan(a*x)/(a^2*x^3 + x), x) + 36*a^4*c^2*integrate(1/16*x^4*arctan(a*x)^2/(a^2*x^3 + x), x) + 3*a^4*c^2*integrate(1/16*x^4*log(a^2*x^2 + 1)^2/(a^2*x^3 + x), x) + 4*a^4*c^2*integrate(1/16*x^4*log(a^2*x^2 + 1)/(a^2*x^3 + x), x) - 8*a^3*c^2*integrate(1/16*x^3*arctan(a*x)/(a^2*x^3 + x), x) + 36*a^2*c^2*integrate(1/16*x^2*arctan(a*x)^2/(a^2*x^3 + x), x) + 1/32*c^2*log(a^2*x^2 + 1)^3 + 1/16*(a^4*c^2*x^4 + 4*a^2*c^2*x^2)*arctan(a*x)^2 + 12*c^2*integrate(1/16*arctan(a*x)^2/(a^2*x^3 + x), x) + c^2*integrate(1/16*log(a^2*x^2 + 1)^2/(a^2*x^3 + x), x) - 1/64*(a^4*c^2*x^4 + 4*a^2*c^2*x^2)*log(a^2*x^2 + 1)^2","F",0
271,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^2/x^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^2/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,1,202,0,0.417769," ","integrate(x^3*(a^2*c*x^2+c)^3*arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{1}{6300} \, a {\left(\frac{315 \, c^{3} \arctan\left(a x\right)}{a^{5}} + \frac{140 \, a^{8} c^{3} x^{9} + 495 \, a^{6} c^{3} x^{7} + 567 \, a^{4} c^{3} x^{5} + 105 \, a^{2} c^{3} x^{3} - 315 \, c^{3} x}{a^{4}}\right)} \arctan\left(a x\right) + \frac{1}{40} \, {\left(4 \, a^{6} c^{3} x^{10} + 15 \, a^{4} c^{3} x^{8} + 20 \, a^{2} c^{3} x^{6} + 10 \, c^{3} x^{4}\right)} \arctan\left(a x\right)^{2} + \frac{105 \, a^{8} c^{3} x^{8} + 355 \, a^{6} c^{3} x^{6} + 318 \, a^{4} c^{3} x^{4} - 321 \, a^{2} c^{3} x^{2} + 945 \, c^{3} \arctan\left(a x\right)^{2} - 624 \, c^{3} \log\left(a^{2} x^{2} + 1\right)}{37800 \, a^{4}}"," ",0,"-1/6300*a*(315*c^3*arctan(a*x)/a^5 + (140*a^8*c^3*x^9 + 495*a^6*c^3*x^7 + 567*a^4*c^3*x^5 + 105*a^2*c^3*x^3 - 315*c^3*x)/a^4)*arctan(a*x) + 1/40*(4*a^6*c^3*x^10 + 15*a^4*c^3*x^8 + 20*a^2*c^3*x^6 + 10*c^3*x^4)*arctan(a*x)^2 + 1/37800*(105*a^8*c^3*x^8 + 355*a^6*c^3*x^6 + 318*a^4*c^3*x^4 - 321*a^2*c^3*x^2 + 945*c^3*arctan(a*x)^2 - 624*c^3*log(a^2*x^2 + 1))/a^4","A",0
275,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^2,x, algorithm=""maxima"")","\frac{1}{1260} \, {\left(35 \, a^{6} c^{3} x^{9} + 135 \, a^{4} c^{3} x^{7} + 189 \, a^{2} c^{3} x^{5} + 105 \, c^{3} x^{3}\right)} \arctan\left(a x\right)^{2} - \frac{1}{5040} \, {\left(35 \, a^{6} c^{3} x^{9} + 135 \, a^{4} c^{3} x^{7} + 189 \, a^{2} c^{3} x^{5} + 105 \, c^{3} x^{3}\right)} \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{3780 \, {\left(a^{8} c^{3} x^{10} + 4 \, a^{6} c^{3} x^{8} + 6 \, a^{4} c^{3} x^{6} + 4 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)^{2} + 315 \, {\left(a^{8} c^{3} x^{10} + 4 \, a^{6} c^{3} x^{8} + 6 \, a^{4} c^{3} x^{6} + 4 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \log\left(a^{2} x^{2} + 1\right)^{2} - 8 \, {\left(35 \, a^{7} c^{3} x^{9} + 135 \, a^{5} c^{3} x^{7} + 189 \, a^{3} c^{3} x^{5} + 105 \, a c^{3} x^{3}\right)} \arctan\left(a x\right) + 4 \, {\left(35 \, a^{8} c^{3} x^{10} + 135 \, a^{6} c^{3} x^{8} + 189 \, a^{4} c^{3} x^{6} + 105 \, a^{2} c^{3} x^{4}\right)} \log\left(a^{2} x^{2} + 1\right)}{5040 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/1260*(35*a^6*c^3*x^9 + 135*a^4*c^3*x^7 + 189*a^2*c^3*x^5 + 105*c^3*x^3)*arctan(a*x)^2 - 1/5040*(35*a^6*c^3*x^9 + 135*a^4*c^3*x^7 + 189*a^2*c^3*x^5 + 105*c^3*x^3)*log(a^2*x^2 + 1)^2 + integrate(1/5040*(3780*(a^8*c^3*x^10 + 4*a^6*c^3*x^8 + 6*a^4*c^3*x^6 + 4*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x)^2 + 315*(a^8*c^3*x^10 + 4*a^6*c^3*x^8 + 6*a^4*c^3*x^6 + 4*a^2*c^3*x^4 + c^3*x^2)*log(a^2*x^2 + 1)^2 - 8*(35*a^7*c^3*x^9 + 135*a^5*c^3*x^7 + 189*a^3*c^3*x^5 + 105*a*c^3*x^3)*arctan(a*x) + 4*(35*a^8*c^3*x^10 + 135*a^6*c^3*x^8 + 189*a^4*c^3*x^6 + 105*a^2*c^3*x^4)*log(a^2*x^2 + 1))/(a^2*x^2 + 1), x)","F",0
276,1,133,0,0.317915," ","integrate(x*(a^2*c*x^2+c)^3*arctan(a*x)^2,x, algorithm=""maxima"")","\frac{{\left(a^{2} c x^{2} + c\right)}^{4} \arctan\left(a x\right)^{2}}{8 \, a^{2} c} + \frac{{\left(5 \, a^{4} c^{4} x^{6} + 24 \, a^{2} c^{4} x^{4} + 57 \, c^{4} x^{2} + \frac{48 \, c^{4} \log\left(a^{2} x^{2} + 1\right)}{a^{2}}\right)} a - 6 \, {\left(5 \, a^{6} c^{4} x^{7} + 21 \, a^{4} c^{4} x^{5} + 35 \, a^{2} c^{4} x^{3} + 35 \, c^{4} x\right)} \arctan\left(a x\right)}{840 \, a c}"," ",0,"1/8*(a^2*c*x^2 + c)^4*arctan(a*x)^2/(a^2*c) + 1/840*((5*a^4*c^4*x^6 + 24*a^2*c^4*x^4 + 57*c^4*x^2 + 48*c^4*log(a^2*x^2 + 1)/a^2)*a - 6*(5*a^6*c^4*x^7 + 21*a^4*c^4*x^5 + 35*a^2*c^4*x^3 + 35*c^4*x)*arctan(a*x))/(a*c)","A",0
277,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^2,x, algorithm=""maxima"")","420 \, a^{8} c^{3} \int \frac{x^{8} \arctan\left(a x\right)^{2}}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 35 \, a^{8} c^{3} \int \frac{x^{8} \log\left(a^{2} x^{2} + 1\right)^{2}}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 20 \, a^{8} c^{3} \int \frac{x^{8} \log\left(a^{2} x^{2} + 1\right)}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 40 \, a^{7} c^{3} \int \frac{x^{7} \arctan\left(a x\right)}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 1680 \, a^{6} c^{3} \int \frac{x^{6} \arctan\left(a x\right)^{2}}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 140 \, a^{6} c^{3} \int \frac{x^{6} \log\left(a^{2} x^{2} + 1\right)^{2}}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 84 \, a^{6} c^{3} \int \frac{x^{6} \log\left(a^{2} x^{2} + 1\right)}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 168 \, a^{5} c^{3} \int \frac{x^{5} \arctan\left(a x\right)}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 2520 \, a^{4} c^{3} \int \frac{x^{4} \arctan\left(a x\right)^{2}}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 210 \, a^{4} c^{3} \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)^{2}}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 140 \, a^{4} c^{3} \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 280 \, a^{3} c^{3} \int \frac{x^{3} \arctan\left(a x\right)}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 1680 \, a^{2} c^{3} \int \frac{x^{2} \arctan\left(a x\right)^{2}}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 140 \, a^{2} c^{3} \int \frac{x^{2} \log\left(a^{2} x^{2} + 1\right)^{2}}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 140 \, a^{2} c^{3} \int \frac{x^{2} \log\left(a^{2} x^{2} + 1\right)}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{c^{3} \arctan\left(a x\right)^{3}}{4 \, a} - 280 \, a c^{3} \int \frac{x \arctan\left(a x\right)}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 35 \, c^{3} \int \frac{\log\left(a^{2} x^{2} + 1\right)^{2}}{560 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{1}{140} \, {\left(5 \, a^{6} c^{3} x^{7} + 21 \, a^{4} c^{3} x^{5} + 35 \, a^{2} c^{3} x^{3} + 35 \, c^{3} x\right)} \arctan\left(a x\right)^{2} - \frac{1}{560} \, {\left(5 \, a^{6} c^{3} x^{7} + 21 \, a^{4} c^{3} x^{5} + 35 \, a^{2} c^{3} x^{3} + 35 \, c^{3} x\right)} \log\left(a^{2} x^{2} + 1\right)^{2}"," ",0,"420*a^8*c^3*integrate(1/560*x^8*arctan(a*x)^2/(a^2*x^2 + 1), x) + 35*a^8*c^3*integrate(1/560*x^8*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 20*a^8*c^3*integrate(1/560*x^8*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 40*a^7*c^3*integrate(1/560*x^7*arctan(a*x)/(a^2*x^2 + 1), x) + 1680*a^6*c^3*integrate(1/560*x^6*arctan(a*x)^2/(a^2*x^2 + 1), x) + 140*a^6*c^3*integrate(1/560*x^6*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 84*a^6*c^3*integrate(1/560*x^6*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 168*a^5*c^3*integrate(1/560*x^5*arctan(a*x)/(a^2*x^2 + 1), x) + 2520*a^4*c^3*integrate(1/560*x^4*arctan(a*x)^2/(a^2*x^2 + 1), x) + 210*a^4*c^3*integrate(1/560*x^4*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 140*a^4*c^3*integrate(1/560*x^4*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 280*a^3*c^3*integrate(1/560*x^3*arctan(a*x)/(a^2*x^2 + 1), x) + 1680*a^2*c^3*integrate(1/560*x^2*arctan(a*x)^2/(a^2*x^2 + 1), x) + 140*a^2*c^3*integrate(1/560*x^2*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 140*a^2*c^3*integrate(1/560*x^2*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) + 1/4*c^3*arctan(a*x)^3/a - 280*a*c^3*integrate(1/560*x*arctan(a*x)/(a^2*x^2 + 1), x) + 35*c^3*integrate(1/560*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 1/140*(5*a^6*c^3*x^7 + 21*a^4*c^3*x^5 + 35*a^2*c^3*x^3 + 35*c^3*x)*arctan(a*x)^2 - 1/560*(5*a^6*c^3*x^7 + 21*a^4*c^3*x^5 + 35*a^2*c^3*x^3 + 35*c^3*x)*log(a^2*x^2 + 1)^2","F",0
278,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^2/x,x, algorithm=""maxima"")","36 \, a^{8} c^{3} \int \frac{x^{8} \arctan\left(a x\right)^{2}}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 3 \, a^{8} c^{3} \int \frac{x^{8} \log\left(a^{2} x^{2} + 1\right)^{2}}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 2 \, a^{8} c^{3} \int \frac{x^{8} \log\left(a^{2} x^{2} + 1\right)}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} - 4 \, a^{7} c^{3} \int \frac{x^{7} \arctan\left(a x\right)}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 144 \, a^{6} c^{3} \int \frac{x^{6} \arctan\left(a x\right)^{2}}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 12 \, a^{6} c^{3} \int \frac{x^{6} \log\left(a^{2} x^{2} + 1\right)^{2}}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 9 \, a^{6} c^{3} \int \frac{x^{6} \log\left(a^{2} x^{2} + 1\right)}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} - 18 \, a^{5} c^{3} \int \frac{x^{5} \arctan\left(a x\right)}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 216 \, a^{4} c^{3} \int \frac{x^{4} \arctan\left(a x\right)^{2}}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 18 \, a^{4} c^{3} \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)^{2}}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 18 \, a^{4} c^{3} \int \frac{x^{4} \log\left(a^{2} x^{2} + 1\right)}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} - 36 \, a^{3} c^{3} \int \frac{x^{3} \arctan\left(a x\right)}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 144 \, a^{2} c^{3} \int \frac{x^{2} \arctan\left(a x\right)^{2}}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + \frac{1}{24} \, c^{3} \log\left(a^{2} x^{2} + 1\right)^{3} + 36 \, c^{3} \int \frac{\arctan\left(a x\right)^{2}}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + 3 \, c^{3} \int \frac{\log\left(a^{2} x^{2} + 1\right)^{2}}{48 \, {\left(a^{2} x^{3} + x\right)}}\,{d x} + \frac{1}{48} \, {\left(2 \, a^{6} c^{3} x^{6} + 9 \, a^{4} c^{3} x^{4} + 18 \, a^{2} c^{3} x^{2}\right)} \arctan\left(a x\right)^{2} - \frac{1}{192} \, {\left(2 \, a^{6} c^{3} x^{6} + 9 \, a^{4} c^{3} x^{4} + 18 \, a^{2} c^{3} x^{2}\right)} \log\left(a^{2} x^{2} + 1\right)^{2}"," ",0,"36*a^8*c^3*integrate(1/48*x^8*arctan(a*x)^2/(a^2*x^3 + x), x) + 3*a^8*c^3*integrate(1/48*x^8*log(a^2*x^2 + 1)^2/(a^2*x^3 + x), x) + 2*a^8*c^3*integrate(1/48*x^8*log(a^2*x^2 + 1)/(a^2*x^3 + x), x) - 4*a^7*c^3*integrate(1/48*x^7*arctan(a*x)/(a^2*x^3 + x), x) + 144*a^6*c^3*integrate(1/48*x^6*arctan(a*x)^2/(a^2*x^3 + x), x) + 12*a^6*c^3*integrate(1/48*x^6*log(a^2*x^2 + 1)^2/(a^2*x^3 + x), x) + 9*a^6*c^3*integrate(1/48*x^6*log(a^2*x^2 + 1)/(a^2*x^3 + x), x) - 18*a^5*c^3*integrate(1/48*x^5*arctan(a*x)/(a^2*x^3 + x), x) + 216*a^4*c^3*integrate(1/48*x^4*arctan(a*x)^2/(a^2*x^3 + x), x) + 18*a^4*c^3*integrate(1/48*x^4*log(a^2*x^2 + 1)^2/(a^2*x^3 + x), x) + 18*a^4*c^3*integrate(1/48*x^4*log(a^2*x^2 + 1)/(a^2*x^3 + x), x) - 36*a^3*c^3*integrate(1/48*x^3*arctan(a*x)/(a^2*x^3 + x), x) + 144*a^2*c^3*integrate(1/48*x^2*arctan(a*x)^2/(a^2*x^3 + x), x) + 1/24*c^3*log(a^2*x^2 + 1)^3 + 36*c^3*integrate(1/48*arctan(a*x)^2/(a^2*x^3 + x), x) + 3*c^3*integrate(1/48*log(a^2*x^2 + 1)^2/(a^2*x^3 + x), x) + 1/48*(2*a^6*c^3*x^6 + 9*a^4*c^3*x^4 + 18*a^2*c^3*x^2)*arctan(a*x)^2 - 1/192*(2*a^6*c^3*x^6 + 9*a^4*c^3*x^4 + 18*a^2*c^3*x^2)*log(a^2*x^2 + 1)^2","F",0
279,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^2/x^3,x, algorithm=""maxima"")","\frac{\frac{1}{6} \, {\left({\left(6 \, {\left(\frac{a^{2} x^{4} - 2 \, x^{2}}{a^{4}} + \frac{2 \, \log\left(a^{2} x^{2} + 1\right)}{a^{6}}\right)} \log\left(a^{2} x^{2} + 1\right)^{2} - \frac{6 \, {\left(a^{4} x^{4} - 6 \, a^{2} x^{2} + 2 \, \log\left(a^{2} x^{2} + 1\right)^{2} + 6 \, \log\left(a^{2} x^{2} + 1\right)\right)} \log\left(a^{2} x^{2} + 1\right)}{a^{6}} + \frac{3 \, a^{4} x^{4} - 42 \, a^{2} x^{2} + 4 \, \log\left(a^{2} x^{2} + 1\right)^{3} + 18 \, \log\left(a^{2} x^{2} + 1\right)^{2} + 42 \, \log\left(a^{2} x^{2} + 1\right)}{a^{6}}\right)} a^{8} c^{3} + 3 \, {\left(2 \, {\left(\frac{a^{2} x^{4} - 2 \, x^{2}}{a^{4}} + \frac{2 \, \log\left(a^{2} x^{2} + 1\right)}{a^{6}}\right)} \log\left(a^{2} x^{2} + 1\right) - \frac{a^{4} x^{4} - 6 \, a^{2} x^{2} + 2 \, \log\left(a^{2} x^{2} + 1\right)^{2} + 6 \, \log\left(a^{2} x^{2} + 1\right)}{a^{6}}\right)} a^{8} c^{3} + 288 \, a^{8} c^{3} \int \frac{x^{8} \arctan\left(a x\right)^{2}}{a^{2} x^{5} + x^{3}}\,{d x} - 8 \, {\left(2 \, {\left(\frac{a^{2} x^{3} - 3 \, x}{a^{4}} + \frac{3 \, \arctan\left(a x\right)}{a^{5}}\right)} \arctan\left(a x\right) - \frac{a^{2} x^{2} + 3 \, \arctan\left(a x\right)^{2} - 4 \, \log\left(a^{2} x^{2} + 1\right)}{a^{5}}\right)} a^{7} c^{3} + 16 \, {\left(3 \, {\left(\frac{x^{2}}{a^{2}} - \frac{\log\left(a^{2} x^{2} + 1\right)}{a^{4}}\right)} \log\left(a^{2} x^{2} + 1\right)^{2} - \frac{3 \, {\left(2 \, a^{2} x^{2} - \log\left(a^{2} x^{2} + 1\right)^{2} - 2 \, \log\left(a^{2} x^{2} + 1\right)\right)} \log\left(a^{2} x^{2} + 1\right)}{a^{4}} + \frac{6 \, a^{2} x^{2} - \log\left(a^{2} x^{2} + 1\right)^{3} - 3 \, \log\left(a^{2} x^{2} + 1\right)^{2} - 6 \, \log\left(a^{2} x^{2} + 1\right)}{a^{4}}\right)} a^{6} c^{3} + 36 \, {\left(2 \, {\left(\frac{x^{2}}{a^{2}} - \frac{\log\left(a^{2} x^{2} + 1\right)}{a^{4}}\right)} \log\left(a^{2} x^{2} + 1\right) - \frac{2 \, a^{2} x^{2} - \log\left(a^{2} x^{2} + 1\right)^{2} - 2 \, \log\left(a^{2} x^{2} + 1\right)}{a^{4}}\right)} a^{6} c^{3} + 1152 \, a^{6} c^{3} \int \frac{x^{6} \arctan\left(a x\right)^{2}}{a^{2} x^{5} + x^{3}}\,{d x} - 144 \, {\left(2 \, {\left(\frac{x}{a^{2}} - \frac{\arctan\left(a x\right)}{a^{3}}\right)} \arctan\left(a x\right) + \frac{\arctan\left(a x\right)^{2} - \log\left(a^{2} x^{2} + 1\right)}{a^{3}}\right)} a^{5} c^{3} + 1728 \, a^{4} c^{3} \int \frac{x^{4} \arctan\left(a x\right)^{2}}{a^{2} x^{5} + x^{3}}\,{d x} + 24 \, a^{2} c^{3} \log\left(a^{2} x^{2} + 1\right)^{3} - 12 \, {\left(a^{2} {\left(\frac{\log\left(a^{2} x^{2} + 1\right)^{2}}{a^{2}} - \frac{2 \, {\left(2 \, \log\left(a^{2} x^{2} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a^{2} x^{2}\right)\right)}}{a^{2}}\right)} - 2 \, {\left(\log\left(a^{2} x^{2} + 1\right) - 2 \, \log\left(x\right)\right)} \log\left(a^{2} x^{2} + 1\right)\right)} a^{2} c^{3} - 16 \, {\left(\log\left(a^{2} x^{2} + 1\right)^{3} - 3 \, \log\left(a^{2} x^{2} + 1\right)^{2} \log\left(-a^{2} x^{2}\right) - 6 \, {\rm Li}_2\left(a^{2} x^{2} + 1\right) \log\left(a^{2} x^{2} + 1\right) + 6 \, {\rm Li}_{3}(a^{2} x^{2} + 1)\right)} a^{2} c^{3} + 1152 \, a^{2} c^{3} \int \frac{x^{2} \arctan\left(a x\right)^{2}}{a^{2} x^{5} + x^{3}}\,{d x} + 48 \, {\left({\left(\arctan\left(a x\right)^{2} - \log\left(a^{2} x^{2} + 1\right) + 2 \, \log\left(x\right)\right)} a - 2 \, {\left(a \arctan\left(a x\right) + \frac{1}{x}\right)} \arctan\left(a x\right)\right)} a c^{3} - 4 \, {\left(3 \, {\left(\log\left(a^{2} x^{2} + 1\right)^{2} \log\left(-a^{2} x^{2}\right) + 2 \, {\rm Li}_2\left(a^{2} x^{2} + 1\right) \log\left(a^{2} x^{2} + 1\right) - 2 \, {\rm Li}_{3}(a^{2} x^{2} + 1)\right)} a^{2} - 6 \, {\left(\log\left(a^{2} x^{2} + 1\right) \log\left(-a^{2} x^{2}\right) + {\rm Li}_2\left(a^{2} x^{2} + 1\right)\right)} a^{2} - \frac{a^{2} x^{2} \log\left(a^{2} x^{2} + 1\right)^{3} - 3 \, {\left(a^{2} x^{2} + 1\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{x^{2}}\right)} c^{3} + 288 \, c^{3} \int \frac{\arctan\left(a x\right)^{2}}{a^{2} x^{5} + x^{3}}\,{d x}\right)} x^{2} + 4 \, {\left(a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} - 2 \, c^{3}\right)} \arctan\left(a x\right)^{2} - {\left(a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} - 2 \, c^{3}\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{64 \, x^{2}}"," ",0,"1/64*(4*(192*a^8*c^3*integrate(1/16*x^8*arctan(a*x)^2/(a^2*x^5 + x^3), x) + 16*a^8*c^3*integrate(1/16*x^8*log(a^2*x^2 + 1)^2/(a^2*x^5 + x^3), x) + 16*a^8*c^3*integrate(1/16*x^8*log(a^2*x^2 + 1)/(a^2*x^5 + x^3), x) - 32*a^7*c^3*integrate(1/16*x^7*arctan(a*x)/(a^2*x^5 + x^3), x) + 768*a^6*c^3*integrate(1/16*x^6*arctan(a*x)^2/(a^2*x^5 + x^3), x) + 64*a^6*c^3*integrate(1/16*x^6*log(a^2*x^2 + 1)^2/(a^2*x^5 + x^3), x) + 96*a^6*c^3*integrate(1/16*x^6*log(a^2*x^2 + 1)/(a^2*x^5 + x^3), x) - 192*a^5*c^3*integrate(1/16*x^5*arctan(a*x)/(a^2*x^5 + x^3), x) + 1152*a^4*c^3*integrate(1/16*x^4*arctan(a*x)^2/(a^2*x^5 + x^3), x) + a^2*c^3*log(a^2*x^2 + 1)^3 + 768*a^2*c^3*integrate(1/16*x^2*arctan(a*x)^2/(a^2*x^5 + x^3), x) + 64*a^2*c^3*integrate(1/16*x^2*log(a^2*x^2 + 1)^2/(a^2*x^5 + x^3), x) - 32*a^2*c^3*integrate(1/16*x^2*log(a^2*x^2 + 1)/(a^2*x^5 + x^3), x) + 64*a*c^3*integrate(1/16*x*arctan(a*x)/(a^2*x^5 + x^3), x) + 192*c^3*integrate(1/16*arctan(a*x)^2/(a^2*x^5 + x^3), x) + 16*c^3*integrate(1/16*log(a^2*x^2 + 1)^2/(a^2*x^5 + x^3), x))*x^2 + 4*(a^6*c^3*x^6 + 6*a^4*c^3*x^4 - 2*c^3)*arctan(a*x)^2 - (a^6*c^3*x^6 + 6*a^4*c^3*x^4 - 2*c^3)*log(a^2*x^2 + 1)^2)/x^2","F",0
281,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^2/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate(x^4*arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)^{2}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)^2/(a^2*c*x^2 + c), x)","F",0
284,-1,0,0,0.000000," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,0,0,0,0.000000," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x \arctan\left(a x\right)^{2}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x*arctan(a*x)^2/(a^2*c*x^2 + c), x)","F",0
286,1,14,0,0.414910," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{\arctan\left(a x\right)^{3}}{3 \, a c}"," ",0,"1/3*arctan(a*x)^3/(a*c)","A",0
287,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)} x}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)*x), x)","F",0
288,-1,0,0,0.000000," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)*x^3), x)","F",0
290,-1,0,0,0.000000," ","integrate(arctan(a*x)^2/x^4/(a^2*c*x^2+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)^2/(a^2*c*x^2 + c)^2, x)","F",0
292,1,151,0,0.448598," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{x}{a^{4} c^{2} x^{2} + a^{2} c^{2}} - \frac{\arctan\left(a x\right)}{a^{3} c^{2}}\right)} \arctan\left(a x\right)^{2} + \frac{{\left(2 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} + 3 \, a x + 3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a^{2}}{12 \, {\left(a^{7} c^{2} x^{2} + a^{5} c^{2}\right)}} - \frac{{\left({\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 1\right)} a \arctan\left(a x\right)}{2 \, {\left(a^{6} c^{2} x^{2} + a^{4} c^{2}\right)}}"," ",0,"-1/2*(x/(a^4*c^2*x^2 + a^2*c^2) - arctan(a*x)/(a^3*c^2))*arctan(a*x)^2 + 1/12*(2*(a^2*x^2 + 1)*arctan(a*x)^3 + 3*a*x + 3*(a^2*x^2 + 1)*arctan(a*x))*a^2/(a^7*c^2*x^2 + a^5*c^2) - 1/2*((a^2*x^2 + 1)*arctan(a*x)^2 + 1)*a*arctan(a*x)/(a^6*c^2*x^2 + a^4*c^2)","A",0
293,1,104,0,0.415176," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{{\left(\frac{x}{a^{2} c x^{2} + c} + \frac{\arctan\left(a x\right)}{a c}\right)} \arctan\left(a x\right)}{2 \, a c} - \frac{{\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} - 1}{4 \, {\left(a^{4} c x^{2} + a^{2} c\right)} c} - \frac{\arctan\left(a x\right)^{2}}{2 \, {\left(a^{2} c x^{2} + c\right)} a^{2} c}"," ",0,"1/2*(x/(a^2*c*x^2 + c) + arctan(a*x)/(a*c))*arctan(a*x)/(a*c) - 1/4*((a^2*x^2 + 1)*arctan(a*x)^2 - 1)/((a^4*c*x^2 + a^2*c)*c) - 1/2*arctan(a*x)^2/((a^2*c*x^2 + c)*a^2*c)","A",0
294,1,146,0,0.453347," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x}{a^{2} c^{2} x^{2} + c^{2}} + \frac{\arctan\left(a x\right)}{a c^{2}}\right)} \arctan\left(a x\right)^{2} + \frac{{\left(2 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} - 3 \, a x - 3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a^{2}}{12 \, {\left(a^{5} c^{2} x^{2} + a^{3} c^{2}\right)}} - \frac{{\left({\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} - 1\right)} a \arctan\left(a x\right)}{2 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)}}"," ",0,"1/2*(x/(a^2*c^2*x^2 + c^2) + arctan(a*x)/(a*c^2))*arctan(a*x)^2 + 1/12*(2*(a^2*x^2 + 1)*arctan(a*x)^3 - 3*a*x - 3*(a^2*x^2 + 1)*arctan(a*x))*a^2/(a^5*c^2*x^2 + a^3*c^2) - 1/2*((a^2*x^2 + 1)*arctan(a*x)^2 - 1)*a*arctan(a*x)/(a^4*c^2*x^2 + a^2*c^2)","A",0
295,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{2} x}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)^2*x), x)","F",0
296,-1,0,0,0.000000," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)^2*x^3), x)","F",0
298,-1,0,0,0.000000," ","integrate(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,1,185,0,0.429619," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{16} \, a {\left(\frac{5 \, a^{2} x^{3} + 3 \, x}{a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}} + \frac{5 \, \arctan\left(a x\right)}{a^{5} c^{3}}\right)} \arctan\left(a x\right) + \frac{{\left(5 \, a^{2} x^{2} - 5 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 4\right)} a^{2}}{32 \, {\left(a^{10} c^{3} x^{4} + 2 \, a^{8} c^{3} x^{2} + a^{6} c^{3}\right)}} - \frac{{\left(2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2}}{4 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}}"," ",0,"1/16*a*((5*a^2*x^3 + 3*x)/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3) + 5*arctan(a*x)/(a^5*c^3))*arctan(a*x) + 1/32*(5*a^2*x^2 - 5*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 4)*a^2/(a^10*c^3*x^4 + 2*a^8*c^3*x^2 + a^6*c^3) - 1/4*(2*a^2*x^2 + 1)*arctan(a*x)^2/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)","A",0
300,1,232,0,0.472703," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{a^{2} x^{3} - x}{a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}} + \frac{\arctan\left(a x\right)}{a^{3} c^{3}}\right)} \arctan\left(a x\right)^{2} - \frac{{\left(3 \, a^{3} x^{3} - 8 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} - 3 \, a x + 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a^{2}}{192 \, {\left(a^{9} c^{3} x^{4} + 2 \, a^{7} c^{3} x^{2} + a^{5} c^{3}\right)}} + \frac{{\left(a^{2} x^{2} - {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2}\right)} a \arctan\left(a x\right)}{8 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}}"," ",0,"1/8*((a^2*x^3 - x)/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3) + arctan(a*x)/(a^3*c^3))*arctan(a*x)^2 - 1/192*(3*a^3*x^3 - 8*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^3 - 3*a*x + 3*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x))*a^2/(a^9*c^3*x^4 + 2*a^7*c^3*x^2 + a^5*c^3) + 1/8*(a^2*x^2 - (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2)*a*arctan(a*x)/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3)","A",0
301,1,163,0,0.425924," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{3 \, a^{2} x^{3} + 5 \, x}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}} + \frac{3 \, \arctan\left(a x\right)}{a c^{2}}\right)} \arctan\left(a x\right)}{16 \, a c} + \frac{3 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 4}{32 \, {\left(a^{6} c^{2} x^{4} + 2 \, a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} c} - \frac{\arctan\left(a x\right)^{2}}{4 \, {\left(a^{2} c x^{2} + c\right)}^{2} a^{2} c}"," ",0,"1/16*((3*a^2*x^3 + 5*x)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2) + 3*arctan(a*x)/(a*c^2))*arctan(a*x)/(a*c) + 1/32*(3*a^2*x^2 - 3*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 4)/((a^6*c^2*x^4 + 2*a^4*c^2*x^2 + a^2*c^2)*c) - 1/4*arctan(a*x)^2/((a^2*c*x^2 + c)^2*a^2*c)","A",0
302,1,232,0,0.470883," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{3 \, a^{2} x^{3} + 5 \, x}{a^{4} c^{3} x^{4} + 2 \, a^{2} c^{3} x^{2} + c^{3}} + \frac{3 \, \arctan\left(a x\right)}{a c^{3}}\right)} \arctan\left(a x\right)^{2} - \frac{{\left(15 \, a^{3} x^{3} - 8 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} + 17 \, a x + 15 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a^{2}}{64 \, {\left(a^{7} c^{3} x^{4} + 2 \, a^{5} c^{3} x^{2} + a^{3} c^{3}\right)}} + \frac{{\left(3 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 4\right)} a \arctan\left(a x\right)}{8 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)}}"," ",0,"1/8*((3*a^2*x^3 + 5*x)/(a^4*c^3*x^4 + 2*a^2*c^3*x^2 + c^3) + 3*arctan(a*x)/(a*c^3))*arctan(a*x)^2 - 1/64*(15*a^3*x^3 - 8*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^3 + 17*a*x + 15*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x))*a^2/(a^7*c^3*x^4 + 2*a^5*c^3*x^2 + a^3*c^3) + 1/8*(3*a^2*x^2 - 3*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 4)*a*arctan(a*x)/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)","A",0
303,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{3} x}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)^3*x), x)","F",0
304,-1,0,0,0.000000," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)^3*x^3), x)","F",0
306,-1,0,0,0.000000," ","integrate(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x^{3} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^3*arctan(a*x)^2, x)","F",0
308,0,0,0,0.000000," ","integrate(x^2*arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x^{2} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^2*arctan(a*x)^2, x)","F",0
309,0,0,0,0.000000," ","integrate(x*arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x*arctan(a*x)^2, x)","F",0
310,0,0,0,0.000000," ","integrate(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2, x)","F",0
311,0,0,0,0.000000," ","integrate(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x, x)","F",0
312,0,0,0,0.000000," ","integrate(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x^2, x)","F",0
313,0,0,0,0.000000," ","integrate(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x^3, x)","F",0
314,0,0,0,0.000000," ","integrate(arctan(a*x)^2*(a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2/x^4, x)","F",0
315,0,0,0,0.000000," ","integrate(x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{3} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^3*arctan(a*x)^2, x)","F",0
316,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^2*arctan(a*x)^2, x)","F",0
317,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x*arctan(a*x)^2, x)","F",0
318,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2, x)","F",0
319,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2/x, x)","F",0
320,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2/x^2, x)","F",0
321,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}{x^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2/x^3, x)","F",0
322,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^2/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}{x^{4}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2/x^4, x)","F",0
323,0,0,0,0.000000," ","integrate(x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{3} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x^3*arctan(a*x)^2, x)","F",0
324,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x^2*arctan(a*x)^2, x)","F",0
325,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x*arctan(a*x)^2, x)","F",0
326,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2, x)","F",0
327,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2/x, x)","F",0
328,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2/x^2, x)","F",0
329,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}{x^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2/x^3, x)","F",0
330,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^2/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}{x^{4}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2/x^4, x)","F",0
331,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)^2/sqrt(a^2*c*x^2 + c), x)","F",0
332,0,0,0,0.000000," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^2*arctan(a*x)^2/sqrt(a^2*c*x^2 + c), x)","F",0
333,0,0,0,0.000000," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x \arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x*arctan(a*x)^2/sqrt(a^2*c*x^2 + c), x)","F",0
334,0,0,0,0.000000," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/sqrt(a^2*c*x^2 + c), x)","F",0
335,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c} x}\,{d x}"," ",0,"integrate(arctan(a*x)^2/(sqrt(a^2*c*x^2 + c)*x), x)","F",0
336,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/(sqrt(a^2*c*x^2 + c)*x^2), x)","F",0
337,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/(sqrt(a^2*c*x^2 + c)*x^3), x)","F",0
338,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c} x^{4}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/(sqrt(a^2*c*x^2 + c)*x^4), x)","F",0
339,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)^2/(a^2*c*x^2 + c)^(3/2), x)","F",0
340,0,0,0,0.000000," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2} \arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*arctan(a*x)^2/(a^2*c*x^2 + c)^(3/2), x)","F",0
341,1,73,0,0.716633," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\sqrt{c} {\left(\frac{2 \, x \arctan\left(a x\right)}{\sqrt{a^{2} x^{2} + 1} a c^{2}} - \frac{\arctan\left(a x\right)^{2}}{\sqrt{a^{2} x^{2} + 1} a^{2} c^{2}} + \frac{2}{\sqrt{a^{2} x^{2} + 1} a^{2} c^{2}}\right)}"," ",0,"sqrt(c)*(2*x*arctan(a*x)/(sqrt(a^2*x^2 + 1)*a*c^2) - arctan(a*x)^2/(sqrt(a^2*x^2 + 1)*a^2*c^2) + 2/(sqrt(a^2*x^2 + 1)*a^2*c^2))","A",0
342,1,53,0,0.485713," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{x \arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c} c} - \frac{2 \, {\left(a x - \arctan\left(a x\right)\right)}}{\sqrt{a^{2} x^{2} + 1} a c^{\frac{3}{2}}}"," ",0,"x*arctan(a*x)^2/(sqrt(a^2*c*x^2 + c)*c) - 2*(a*x - arctan(a*x))/(sqrt(a^2*x^2 + 1)*a*c^(3/2))","A",0
343,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)^(3/2)*x), x)","F",0
344,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)^(3/2)*x^2), x)","F",0
345,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)^(3/2)*x^3), x)","F",0
346,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x^4/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)^(3/2)*x^4), x)","F",0
347,0,0,0,0.000000," ","integrate(x^5*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{5} \arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^5*arctan(a*x)^2/(a^2*c*x^2 + c)^(5/2), x)","F",0
348,0,0,0,0.000000," ","integrate(x^4*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{4} \arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^4*arctan(a*x)^2/(a^2*c*x^2 + c)^(5/2), x)","F",0
349,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)^2/(a^2*c*x^2 + c)^(5/2), x)","F",0
350,1,117,0,0.428641," ","integrate(x^2*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{x}{\sqrt{a^{2} c x^{2} + c} a^{2} c^{2}} - \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} a^{2} c}\right)} \arctan\left(a x\right)^{2} - \frac{2 \, {\left(7 \, a^{3} x^{3} + 6 \, a x - 3 \, {\left(3 \, a^{2} x^{2} + 2\right)} \arctan\left(a x\right)\right)} a}{27 \, {\left(a^{6} c^{2} x^{2} + a^{4} c^{2}\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{c}}"," ",0,"1/3*(x/(sqrt(a^2*c*x^2 + c)*a^2*c^2) - x/((a^2*c*x^2 + c)^(3/2)*a^2*c))*arctan(a*x)^2 - 2/27*(7*a^3*x^3 + 6*a*x - 3*(3*a^2*x^2 + 2)*arctan(a*x))*a/((a^6*c^2*x^2 + a^4*c^2)*sqrt(a^2*x^2 + 1)*sqrt(c))","A",0
351,0,0,0,0.000000," ","integrate(x*arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x \arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x*arctan(a*x)^2/(a^2*c*x^2 + c)^(5/2), x)","F",0
352,1,111,0,0.434750," ","integrate(arctan(a*x)^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{a^{2} c x^{2} + c} c^{2}} + \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c}\right)} \arctan\left(a x\right)^{2} - \frac{2 \, {\left(20 \, a^{3} x^{3} + 21 \, a x - 3 \, {\left(6 \, a^{2} x^{2} + 7\right)} \arctan\left(a x\right)\right)} a}{27 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \sqrt{a^{2} x^{2} + 1} \sqrt{c}}"," ",0,"1/3*(2*x/(sqrt(a^2*c*x^2 + c)*c^2) + x/((a^2*c*x^2 + c)^(3/2)*c))*arctan(a*x)^2 - 2/27*(20*a^3*x^3 + 21*a*x - 3*(6*a^2*x^2 + 7)*arctan(a*x))*a/((a^4*c^2*x^2 + a^2*c^2)*sqrt(a^2*x^2 + 1)*sqrt(c))","A",0
353,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)^(5/2)*x), x)","F",0
354,0,0,0,0.000000," ","integrate(arctan(a*x)^2/x^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate(arctan(a*x)^2/((a^2*c*x^2 + c)^(5/2)*x^2), x)","F",0
355,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^2,x, algorithm=""maxima"")","\frac{7 \, {\left({\left(a^{4} c^{2} m^{2} + 4 \, a^{4} c^{2} m + 3 \, a^{4} c^{2}\right)} x^{5} + 2 \, {\left(a^{2} c^{2} m^{2} + 6 \, a^{2} c^{2} m + 5 \, a^{2} c^{2}\right)} x^{3} + {\left(c^{2} m^{2} + 8 \, c^{2} m + 15 \, c^{2}\right)} x\right)} x^{m} \arctan\left(a x\right)^{2} - \frac{3}{4} \, {\left({\left(a^{4} c^{2} m^{2} + 4 \, a^{4} c^{2} m + 3 \, a^{4} c^{2}\right)} x^{5} + 2 \, {\left(a^{2} c^{2} m^{2} + 6 \, a^{2} c^{2} m + 5 \, a^{2} c^{2}\right)} x^{3} + {\left(c^{2} m^{2} + 8 \, c^{2} m + 15 \, c^{2}\right)} x\right)} x^{m} \log\left(a^{2} x^{2} + 1\right)^{2} + {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} \int \frac{36 \, {\left({\left(a^{6} c^{2} m^{3} + 9 \, a^{6} c^{2} m^{2} + 23 \, a^{6} c^{2} m + 15 \, a^{6} c^{2}\right)} x^{6} + c^{2} m^{3} + 3 \, {\left(a^{4} c^{2} m^{3} + 9 \, a^{4} c^{2} m^{2} + 23 \, a^{4} c^{2} m + 15 \, a^{4} c^{2}\right)} x^{4} + 9 \, c^{2} m^{2} + 23 \, c^{2} m + 3 \, {\left(a^{2} c^{2} m^{3} + 9 \, a^{2} c^{2} m^{2} + 23 \, a^{2} c^{2} m + 15 \, a^{2} c^{2}\right)} x^{2} + 15 \, c^{2}\right)} x^{m} \arctan\left(a x\right)^{2} + 3 \, {\left({\left(a^{6} c^{2} m^{3} + 9 \, a^{6} c^{2} m^{2} + 23 \, a^{6} c^{2} m + 15 \, a^{6} c^{2}\right)} x^{6} + c^{2} m^{3} + 3 \, {\left(a^{4} c^{2} m^{3} + 9 \, a^{4} c^{2} m^{2} + 23 \, a^{4} c^{2} m + 15 \, a^{4} c^{2}\right)} x^{4} + 9 \, c^{2} m^{2} + 23 \, c^{2} m + 3 \, {\left(a^{2} c^{2} m^{3} + 9 \, a^{2} c^{2} m^{2} + 23 \, a^{2} c^{2} m + 15 \, a^{2} c^{2}\right)} x^{2} + 15 \, c^{2}\right)} x^{m} \log\left(a^{2} x^{2} + 1\right)^{2} - 56 \, {\left({\left(a^{5} c^{2} m^{2} + 4 \, a^{5} c^{2} m + 3 \, a^{5} c^{2}\right)} x^{5} + 2 \, {\left(a^{3} c^{2} m^{2} + 6 \, a^{3} c^{2} m + 5 \, a^{3} c^{2}\right)} x^{3} + {\left(a c^{2} m^{2} + 8 \, a c^{2} m + 15 \, a c^{2}\right)} x\right)} x^{m} \arctan\left(a x\right) + 12 \, {\left({\left(a^{6} c^{2} m^{2} + 4 \, a^{6} c^{2} m + 3 \, a^{6} c^{2}\right)} x^{6} + 2 \, {\left(a^{4} c^{2} m^{2} + 6 \, a^{4} c^{2} m + 5 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{2} c^{2} m^{2} + 8 \, a^{2} c^{2} m + 15 \, a^{2} c^{2}\right)} x^{2}\right)} x^{m} \log\left(a^{2} x^{2} + 1\right)}{4 \, {\left(m^{3} + {\left(a^{2} m^{3} + 9 \, a^{2} m^{2} + 23 \, a^{2} m + 15 \, a^{2}\right)} x^{2} + 9 \, m^{2} + 23 \, m + 15\right)}}\,{d x}}{16 \, {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)}}"," ",0,"1/16*(4*((a^4*c^2*m^2 + 4*a^4*c^2*m + 3*a^4*c^2)*x^5 + 2*(a^2*c^2*m^2 + 6*a^2*c^2*m + 5*a^2*c^2)*x^3 + (c^2*m^2 + 8*c^2*m + 15*c^2)*x)*x^m*arctan(a*x)^2 - ((a^4*c^2*m^2 + 4*a^4*c^2*m + 3*a^4*c^2)*x^5 + 2*(a^2*c^2*m^2 + 6*a^2*c^2*m + 5*a^2*c^2)*x^3 + (c^2*m^2 + 8*c^2*m + 15*c^2)*x)*x^m*log(a^2*x^2 + 1)^2 + 16*(m^3 + 9*m^2 + 23*m + 15)*integrate(1/16*(12*((a^6*c^2*m^3 + 9*a^6*c^2*m^2 + 23*a^6*c^2*m + 15*a^6*c^2)*x^6 + c^2*m^3 + 3*(a^4*c^2*m^3 + 9*a^4*c^2*m^2 + 23*a^4*c^2*m + 15*a^4*c^2)*x^4 + 9*c^2*m^2 + 23*c^2*m + 3*(a^2*c^2*m^3 + 9*a^2*c^2*m^2 + 23*a^2*c^2*m + 15*a^2*c^2)*x^2 + 15*c^2)*x^m*arctan(a*x)^2 + ((a^6*c^2*m^3 + 9*a^6*c^2*m^2 + 23*a^6*c^2*m + 15*a^6*c^2)*x^6 + c^2*m^3 + 3*(a^4*c^2*m^3 + 9*a^4*c^2*m^2 + 23*a^4*c^2*m + 15*a^4*c^2)*x^4 + 9*c^2*m^2 + 23*c^2*m + 3*(a^2*c^2*m^3 + 9*a^2*c^2*m^2 + 23*a^2*c^2*m + 15*a^2*c^2)*x^2 + 15*c^2)*x^m*log(a^2*x^2 + 1)^2 - 8*((a^5*c^2*m^2 + 4*a^5*c^2*m + 3*a^5*c^2)*x^5 + 2*(a^3*c^2*m^2 + 6*a^3*c^2*m + 5*a^3*c^2)*x^3 + (a*c^2*m^2 + 8*a*c^2*m + 15*a*c^2)*x)*x^m*arctan(a*x) + 4*((a^6*c^2*m^2 + 4*a^6*c^2*m + 3*a^6*c^2)*x^6 + 2*(a^4*c^2*m^2 + 6*a^4*c^2*m + 5*a^4*c^2)*x^4 + (a^2*c^2*m^2 + 8*a^2*c^2*m + 15*a^2*c^2)*x^2)*x^m*log(a^2*x^2 + 1))/(m^3 + (a^2*m^3 + 9*a^2*m^2 + 23*a^2*m + 15*a^2)*x^2 + 9*m^2 + 23*m + 15), x))/(m^3 + 9*m^2 + 23*m + 15)","F",0
356,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)*arctan(a*x)^2,x, algorithm=""maxima"")","\frac{7 \, {\left({\left(a^{2} c m + a^{2} c\right)} x^{3} + {\left(c m + 3 \, c\right)} x\right)} x^{m} \arctan\left(a x\right)^{2} - \frac{3}{4} \, {\left({\left(a^{2} c m + a^{2} c\right)} x^{3} + {\left(c m + 3 \, c\right)} x\right)} x^{m} \log\left(a^{2} x^{2} + 1\right)^{2} + {\left(m^{2} + 4 \, m + 3\right)} \int \frac{36 \, {\left({\left(a^{4} c m^{2} + 4 \, a^{4} c m + 3 \, a^{4} c\right)} x^{4} + c m^{2} + 2 \, {\left(a^{2} c m^{2} + 4 \, a^{2} c m + 3 \, a^{2} c\right)} x^{2} + 4 \, c m + 3 \, c\right)} x^{m} \arctan\left(a x\right)^{2} + 3 \, {\left({\left(a^{4} c m^{2} + 4 \, a^{4} c m + 3 \, a^{4} c\right)} x^{4} + c m^{2} + 2 \, {\left(a^{2} c m^{2} + 4 \, a^{2} c m + 3 \, a^{2} c\right)} x^{2} + 4 \, c m + 3 \, c\right)} x^{m} \log\left(a^{2} x^{2} + 1\right)^{2} - 56 \, {\left({\left(a^{3} c m + a^{3} c\right)} x^{3} + {\left(a c m + 3 \, a c\right)} x\right)} x^{m} \arctan\left(a x\right) + 12 \, {\left({\left(a^{4} c m + a^{4} c\right)} x^{4} + {\left(a^{2} c m + 3 \, a^{2} c\right)} x^{2}\right)} x^{m} \log\left(a^{2} x^{2} + 1\right)}{4 \, {\left({\left(a^{2} m^{2} + 4 \, a^{2} m + 3 \, a^{2}\right)} x^{2} + m^{2} + 4 \, m + 3\right)}}\,{d x}}{16 \, {\left(m^{2} + 4 \, m + 3\right)}}"," ",0,"1/16*(4*((a^2*c*m + a^2*c)*x^3 + (c*m + 3*c)*x)*x^m*arctan(a*x)^2 - ((a^2*c*m + a^2*c)*x^3 + (c*m + 3*c)*x)*x^m*log(a^2*x^2 + 1)^2 + 16*(m^2 + 4*m + 3)*integrate(1/16*(12*((a^4*c*m^2 + 4*a^4*c*m + 3*a^4*c)*x^4 + c*m^2 + 2*(a^2*c*m^2 + 4*a^2*c*m + 3*a^2*c)*x^2 + 4*c*m + 3*c)*x^m*arctan(a*x)^2 + ((a^4*c*m^2 + 4*a^4*c*m + 3*a^4*c)*x^4 + c*m^2 + 2*(a^2*c*m^2 + 4*a^2*c*m + 3*a^2*c)*x^2 + 4*c*m + 3*c)*x^m*log(a^2*x^2 + 1)^2 - 8*((a^3*c*m + a^3*c)*x^3 + (a*c*m + 3*a*c)*x)*x^m*arctan(a*x) + 4*((a^4*c*m + a^4*c)*x^4 + (a^2*c*m + 3*a^2*c)*x^2)*x^m*log(a^2*x^2 + 1))/((a^2*m^2 + 4*a^2*m + 3*a^2)*x^2 + m^2 + 4*m + 3), x))/(m^2 + 4*m + 3)","F",0
357,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)^{2}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)^2/(a^2*c*x^2 + c), x)","F",0
358,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)^2/(a^2*c*x^2 + c)^2, x)","F",0
359,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^2,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^m*arctan(a*x)^2, x)","F",0
360,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)*arctan(a*x)^2,x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^2, x)","F",0
361,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)^{2}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)^2/sqrt(a^2*c*x^2 + c), x)","F",0
362,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)^2/(a^2*c*x^2 + c)^(3/2), x)","F",0
363,-1,0,0,0.000000," ","integrate(x^3*(a^2*c*x^2+c)*arctan(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)*arctan(a*x)^3,x, algorithm=""maxima"")","\frac{1}{120} \, {\left(3 \, a^{2} c x^{5} + 5 \, c x^{3}\right)} \arctan\left(a x\right)^{3} - \frac{1}{160} \, {\left(3 \, a^{2} c x^{5} + 5 \, c x^{3}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{140 \, {\left(a^{4} c x^{6} + 2 \, a^{2} c x^{4} + c x^{2}\right)} \arctan\left(a x\right)^{3} - 4 \, {\left(3 \, a^{3} c x^{5} + 5 \, a c x^{3}\right)} \arctan\left(a x\right)^{2} + 4 \, {\left(3 \, a^{4} c x^{6} + 5 \, a^{2} c x^{4}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right) + {\left(3 \, a^{3} c x^{5} + 5 \, a c x^{3} + 15 \, {\left(a^{4} c x^{6} + 2 \, a^{2} c x^{4} + c x^{2}\right)} \arctan\left(a x\right)\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/120*(3*a^2*c*x^5 + 5*c*x^3)*arctan(a*x)^3 - 1/160*(3*a^2*c*x^5 + 5*c*x^3)*arctan(a*x)*log(a^2*x^2 + 1)^2 + integrate(1/160*(140*(a^4*c*x^6 + 2*a^2*c*x^4 + c*x^2)*arctan(a*x)^3 - 4*(3*a^3*c*x^5 + 5*a*c*x^3)*arctan(a*x)^2 + 4*(3*a^4*c*x^6 + 5*a^2*c*x^4)*arctan(a*x)*log(a^2*x^2 + 1) + (3*a^3*c*x^5 + 5*a*c*x^3 + 15*(a^4*c*x^6 + 2*a^2*c*x^4 + c*x^2)*arctan(a*x))*log(a^2*x^2 + 1)^2)/(a^2*x^2 + 1), x)","F",0
365,-1,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)*arctan(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^3,x, algorithm=""maxima"")","28 \, a^{4} c \int \frac{x^{4} \arctan\left(a x\right)^{3}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 3 \, a^{4} c \int \frac{x^{4} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 4 \, a^{4} c \int \frac{x^{4} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 4 \, a^{3} c \int \frac{x^{3} \arctan\left(a x\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + a^{3} c \int \frac{x^{3} \log\left(a^{2} x^{2} + 1\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{1}{24} \, {\left(a^{2} c x^{3} + 3 \, c x\right)} \arctan\left(a x\right)^{3} + \frac{7 \, c \arctan\left(a x\right)^{4}}{32 \, a} + 56 \, a^{2} c \int \frac{x^{2} \arctan\left(a x\right)^{3}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 6 \, a^{2} c \int \frac{x^{2} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 12 \, a^{2} c \int \frac{x^{2} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - \frac{1}{32} \, {\left(a^{2} c x^{3} + 3 \, c x\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} - 12 \, a c \int \frac{x \arctan\left(a x\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 3 \, a c \int \frac{x \log\left(a^{2} x^{2} + 1\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 3 \, c \int \frac{\arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"28*a^4*c*integrate(1/32*x^4*arctan(a*x)^3/(a^2*x^2 + 1), x) + 3*a^4*c*integrate(1/32*x^4*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 4*a^4*c*integrate(1/32*x^4*arctan(a*x)*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 4*a^3*c*integrate(1/32*x^3*arctan(a*x)^2/(a^2*x^2 + 1), x) + a^3*c*integrate(1/32*x^3*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 1/24*(a^2*c*x^3 + 3*c*x)*arctan(a*x)^3 + 7/32*c*arctan(a*x)^4/a + 56*a^2*c*integrate(1/32*x^2*arctan(a*x)^3/(a^2*x^2 + 1), x) + 6*a^2*c*integrate(1/32*x^2*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 12*a^2*c*integrate(1/32*x^2*arctan(a*x)*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 1/32*(a^2*c*x^3 + 3*c*x)*arctan(a*x)*log(a^2*x^2 + 1)^2 - 12*a*c*integrate(1/32*x*arctan(a*x)^2/(a^2*x^2 + 1), x) + 3*a*c*integrate(1/32*x*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 3*c*integrate(1/32*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x)","F",0
367,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^3/x,x, algorithm=""maxima"")","\frac{1}{16} \, a^{2} c x^{2} \arctan\left(a x\right)^{3} - \frac{3}{64} \, a^{2} c x^{2} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{12 \, a^{4} c x^{4} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right) - 12 \, a^{3} c x^{3} \arctan\left(a x\right)^{2} + 56 \, {\left(a^{4} c x^{4} + 2 \, a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3} + 3 \, {\left(a^{3} c x^{3} + 2 \, {\left(a^{4} c x^{4} + 2 \, a^{2} c x^{2} + c\right)} \arctan\left(a x\right)\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{64 \, {\left(a^{2} x^{3} + x\right)}}\,{d x}"," ",0,"1/16*a^2*c*x^2*arctan(a*x)^3 - 3/64*a^2*c*x^2*arctan(a*x)*log(a^2*x^2 + 1)^2 + integrate(1/64*(12*a^4*c*x^4*arctan(a*x)*log(a^2*x^2 + 1) - 12*a^3*c*x^3*arctan(a*x)^2 + 56*(a^4*c*x^4 + 2*a^2*c*x^2 + c)*arctan(a*x)^3 + 3*(a^3*c*x^3 + 2*(a^4*c*x^4 + 2*a^2*c*x^2 + c)*arctan(a*x))*log(a^2*x^2 + 1)^2)/(a^2*x^3 + x), x)","F",0
368,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^3/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^3/x^3,x, algorithm=""maxima"")","-\frac{4 \, c \arctan\left(a x\right)^{3} - 3 \, c \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + x^{2} \int \frac{12 \, a^{2} c x^{2} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right) - 12 \, a c x \arctan\left(a x\right)^{2} - 56 \, {\left(a^{4} c x^{4} + 2 \, a^{2} c x^{2} + c\right)} \arctan\left(a x\right)^{3} + 3 \, {\left(a c x - 2 \, {\left(a^{4} c x^{4} + 2 \, a^{2} c x^{2} + c\right)} \arctan\left(a x\right)\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{a^{2} x^{5} + x^{3}}\,{d x}}{64 \, x^{2}}"," ",0,"-1/64*(4*c*arctan(a*x)^3 - 3*c*arctan(a*x)*log(a^2*x^2 + 1)^2 - 64*x^2*integrate(-1/64*(12*a^2*c*x^2*arctan(a*x)*log(a^2*x^2 + 1) - 12*a*c*x*arctan(a*x)^2 - 56*(a^4*c*x^4 + 2*a^2*c*x^2 + c)*arctan(a*x)^3 + 3*(a*c*x - 2*(a^4*c*x^4 + 2*a^2*c*x^2 + c)*arctan(a*x))*log(a^2*x^2 + 1)^2)/(a^2*x^5 + x^3), x))/x^2","F",0
370,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^3/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate(x^3*(a^2*c*x^2+c)^2*arctan(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^3,x, algorithm=""maxima"")","\frac{1}{840} \, {\left(15 \, a^{4} c^{2} x^{7} + 42 \, a^{2} c^{2} x^{5} + 35 \, c^{2} x^{3}\right)} \arctan\left(a x\right)^{3} - \frac{1}{1120} \, {\left(15 \, a^{4} c^{2} x^{7} + 42 \, a^{2} c^{2} x^{5} + 35 \, c^{2} x^{3}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{980 \, {\left(a^{6} c^{2} x^{8} + 3 \, a^{4} c^{2} x^{6} + 3 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)^{3} - 4 \, {\left(15 \, a^{5} c^{2} x^{7} + 42 \, a^{3} c^{2} x^{5} + 35 \, a c^{2} x^{3}\right)} \arctan\left(a x\right)^{2} + 4 \, {\left(15 \, a^{6} c^{2} x^{8} + 42 \, a^{4} c^{2} x^{6} + 35 \, a^{2} c^{2} x^{4}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right) + {\left(15 \, a^{5} c^{2} x^{7} + 42 \, a^{3} c^{2} x^{5} + 35 \, a c^{2} x^{3} + 105 \, {\left(a^{6} c^{2} x^{8} + 3 \, a^{4} c^{2} x^{6} + 3 \, a^{2} c^{2} x^{4} + c^{2} x^{2}\right)} \arctan\left(a x\right)\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/840*(15*a^4*c^2*x^7 + 42*a^2*c^2*x^5 + 35*c^2*x^3)*arctan(a*x)^3 - 1/1120*(15*a^4*c^2*x^7 + 42*a^2*c^2*x^5 + 35*c^2*x^3)*arctan(a*x)*log(a^2*x^2 + 1)^2 + integrate(1/1120*(980*(a^6*c^2*x^8 + 3*a^4*c^2*x^6 + 3*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x)^3 - 4*(15*a^5*c^2*x^7 + 42*a^3*c^2*x^5 + 35*a*c^2*x^3)*arctan(a*x)^2 + 4*(15*a^6*c^2*x^8 + 42*a^4*c^2*x^6 + 35*a^2*c^2*x^4)*arctan(a*x)*log(a^2*x^2 + 1) + (15*a^5*c^2*x^7 + 42*a^3*c^2*x^5 + 35*a*c^2*x^3 + 105*(a^6*c^2*x^8 + 3*a^4*c^2*x^6 + 3*a^2*c^2*x^4 + c^2*x^2)*arctan(a*x))*log(a^2*x^2 + 1)^2)/(a^2*x^2 + 1), x)","F",0
373,-1,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2*arctan(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^3,x, algorithm=""maxima"")","140 \, a^{6} c^{2} \int \frac{x^{6} \arctan\left(a x\right)^{3}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 15 \, a^{6} c^{2} \int \frac{x^{6} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 12 \, a^{6} c^{2} \int \frac{x^{6} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 12 \, a^{5} c^{2} \int \frac{x^{5} \arctan\left(a x\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 3 \, a^{5} c^{2} \int \frac{x^{5} \log\left(a^{2} x^{2} + 1\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 420 \, a^{4} c^{2} \int \frac{x^{4} \arctan\left(a x\right)^{3}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 45 \, a^{4} c^{2} \int \frac{x^{4} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 40 \, a^{4} c^{2} \int \frac{x^{4} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 40 \, a^{3} c^{2} \int \frac{x^{3} \arctan\left(a x\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 10 \, a^{3} c^{2} \int \frac{x^{3} \log\left(a^{2} x^{2} + 1\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{7 \, c^{2} \arctan\left(a x\right)^{4}}{32 \, a} + 420 \, a^{2} c^{2} \int \frac{x^{2} \arctan\left(a x\right)^{3}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 45 \, a^{2} c^{2} \int \frac{x^{2} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 60 \, a^{2} c^{2} \int \frac{x^{2} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{1}{120} \, {\left(3 \, a^{4} c^{2} x^{5} + 10 \, a^{2} c^{2} x^{3} + 15 \, c^{2} x\right)} \arctan\left(a x\right)^{3} - 60 \, a c^{2} \int \frac{x \arctan\left(a x\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 15 \, a c^{2} \int \frac{x \log\left(a^{2} x^{2} + 1\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - \frac{1}{160} \, {\left(3 \, a^{4} c^{2} x^{5} + 10 \, a^{2} c^{2} x^{3} + 15 \, c^{2} x\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + 15 \, c^{2} \int \frac{\arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"140*a^6*c^2*integrate(1/160*x^6*arctan(a*x)^3/(a^2*x^2 + 1), x) + 15*a^6*c^2*integrate(1/160*x^6*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 12*a^6*c^2*integrate(1/160*x^6*arctan(a*x)*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 12*a^5*c^2*integrate(1/160*x^5*arctan(a*x)^2/(a^2*x^2 + 1), x) + 3*a^5*c^2*integrate(1/160*x^5*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 420*a^4*c^2*integrate(1/160*x^4*arctan(a*x)^3/(a^2*x^2 + 1), x) + 45*a^4*c^2*integrate(1/160*x^4*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 40*a^4*c^2*integrate(1/160*x^4*arctan(a*x)*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 40*a^3*c^2*integrate(1/160*x^3*arctan(a*x)^2/(a^2*x^2 + 1), x) + 10*a^3*c^2*integrate(1/160*x^3*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 7/32*c^2*arctan(a*x)^4/a + 420*a^2*c^2*integrate(1/160*x^2*arctan(a*x)^3/(a^2*x^2 + 1), x) + 45*a^2*c^2*integrate(1/160*x^2*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 60*a^2*c^2*integrate(1/160*x^2*arctan(a*x)*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) + 1/120*(3*a^4*c^2*x^5 + 10*a^2*c^2*x^3 + 15*c^2*x)*arctan(a*x)^3 - 60*a*c^2*integrate(1/160*x*arctan(a*x)^2/(a^2*x^2 + 1), x) + 15*a*c^2*integrate(1/160*x*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) - 1/160*(3*a^4*c^2*x^5 + 10*a^2*c^2*x^3 + 15*c^2*x)*arctan(a*x)*log(a^2*x^2 + 1)^2 + 15*c^2*integrate(1/160*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x)","F",0
375,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^3/x,x, algorithm=""maxima"")","\frac{1}{32} \, {\left(a^{4} c^{2} x^{4} + 4 \, a^{2} c^{2} x^{2}\right)} \arctan\left(a x\right)^{3} - \frac{3}{128} \, {\left(a^{4} c^{2} x^{4} + 4 \, a^{2} c^{2} x^{2}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{112 \, {\left(a^{6} c^{2} x^{6} + 3 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)^{3} - 12 \, {\left(a^{5} c^{2} x^{5} + 4 \, a^{3} c^{2} x^{3}\right)} \arctan\left(a x\right)^{2} + 12 \, {\left(a^{6} c^{2} x^{6} + 4 \, a^{4} c^{2} x^{4}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right) + 3 \, {\left(a^{5} c^{2} x^{5} + 4 \, a^{3} c^{2} x^{3} + 4 \, {\left(a^{6} c^{2} x^{6} + 3 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{128 \, {\left(a^{2} x^{3} + x\right)}}\,{d x}"," ",0,"1/32*(a^4*c^2*x^4 + 4*a^2*c^2*x^2)*arctan(a*x)^3 - 3/128*(a^4*c^2*x^4 + 4*a^2*c^2*x^2)*arctan(a*x)*log(a^2*x^2 + 1)^2 + integrate(1/128*(112*(a^6*c^2*x^6 + 3*a^4*c^2*x^4 + 3*a^2*c^2*x^2 + c^2)*arctan(a*x)^3 - 12*(a^5*c^2*x^5 + 4*a^3*c^2*x^3)*arctan(a*x)^2 + 12*(a^6*c^2*x^6 + 4*a^4*c^2*x^4)*arctan(a*x)*log(a^2*x^2 + 1) + 3*(a^5*c^2*x^5 + 4*a^3*c^2*x^3 + 4*(a^6*c^2*x^6 + 3*a^4*c^2*x^4 + 3*a^2*c^2*x^2 + c^2)*arctan(a*x))*log(a^2*x^2 + 1)^2)/(a^2*x^3 + x), x)","F",0
376,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^3/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^3/x^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^3/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate(x^3*(a^2*c*x^2+c)^3*arctan(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^3,x, algorithm=""maxima"")","\frac{1}{2520} \, {\left(35 \, a^{6} c^{3} x^{9} + 135 \, a^{4} c^{3} x^{7} + 189 \, a^{2} c^{3} x^{5} + 105 \, c^{3} x^{3}\right)} \arctan\left(a x\right)^{3} - \frac{1}{3360} \, {\left(35 \, a^{6} c^{3} x^{9} + 135 \, a^{4} c^{3} x^{7} + 189 \, a^{2} c^{3} x^{5} + 105 \, c^{3} x^{3}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{2940 \, {\left(a^{8} c^{3} x^{10} + 4 \, a^{6} c^{3} x^{8} + 6 \, a^{4} c^{3} x^{6} + 4 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)^{3} - 4 \, {\left(35 \, a^{7} c^{3} x^{9} + 135 \, a^{5} c^{3} x^{7} + 189 \, a^{3} c^{3} x^{5} + 105 \, a c^{3} x^{3}\right)} \arctan\left(a x\right)^{2} + 4 \, {\left(35 \, a^{8} c^{3} x^{10} + 135 \, a^{6} c^{3} x^{8} + 189 \, a^{4} c^{3} x^{6} + 105 \, a^{2} c^{3} x^{4}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right) + {\left(35 \, a^{7} c^{3} x^{9} + 135 \, a^{5} c^{3} x^{7} + 189 \, a^{3} c^{3} x^{5} + 105 \, a c^{3} x^{3} + 315 \, {\left(a^{8} c^{3} x^{10} + 4 \, a^{6} c^{3} x^{8} + 6 \, a^{4} c^{3} x^{6} + 4 \, a^{2} c^{3} x^{4} + c^{3} x^{2}\right)} \arctan\left(a x\right)\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{3360 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/2520*(35*a^6*c^3*x^9 + 135*a^4*c^3*x^7 + 189*a^2*c^3*x^5 + 105*c^3*x^3)*arctan(a*x)^3 - 1/3360*(35*a^6*c^3*x^9 + 135*a^4*c^3*x^7 + 189*a^2*c^3*x^5 + 105*c^3*x^3)*arctan(a*x)*log(a^2*x^2 + 1)^2 + integrate(1/3360*(2940*(a^8*c^3*x^10 + 4*a^6*c^3*x^8 + 6*a^4*c^3*x^6 + 4*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x)^3 - 4*(35*a^7*c^3*x^9 + 135*a^5*c^3*x^7 + 189*a^3*c^3*x^5 + 105*a*c^3*x^3)*arctan(a*x)^2 + 4*(35*a^8*c^3*x^10 + 135*a^6*c^3*x^8 + 189*a^4*c^3*x^6 + 105*a^2*c^3*x^4)*arctan(a*x)*log(a^2*x^2 + 1) + (35*a^7*c^3*x^9 + 135*a^5*c^3*x^7 + 189*a^3*c^3*x^5 + 105*a*c^3*x^3 + 315*(a^8*c^3*x^10 + 4*a^6*c^3*x^8 + 6*a^4*c^3*x^6 + 4*a^2*c^3*x^4 + c^3*x^2)*arctan(a*x))*log(a^2*x^2 + 1)^2)/(a^2*x^2 + 1), x)","F",0
381,-1,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3*arctan(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^3,x, algorithm=""maxima"")","980 \, a^{8} c^{3} \int \frac{x^{8} \arctan\left(a x\right)^{3}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 105 \, a^{8} c^{3} \int \frac{x^{8} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 60 \, a^{8} c^{3} \int \frac{x^{8} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 60 \, a^{7} c^{3} \int \frac{x^{7} \arctan\left(a x\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 15 \, a^{7} c^{3} \int \frac{x^{7} \log\left(a^{2} x^{2} + 1\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 3920 \, a^{6} c^{3} \int \frac{x^{6} \arctan\left(a x\right)^{3}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 420 \, a^{6} c^{3} \int \frac{x^{6} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 252 \, a^{6} c^{3} \int \frac{x^{6} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 252 \, a^{5} c^{3} \int \frac{x^{5} \arctan\left(a x\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 63 \, a^{5} c^{3} \int \frac{x^{5} \log\left(a^{2} x^{2} + 1\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 5880 \, a^{4} c^{3} \int \frac{x^{4} \arctan\left(a x\right)^{3}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 630 \, a^{4} c^{3} \int \frac{x^{4} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 420 \, a^{4} c^{3} \int \frac{x^{4} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 420 \, a^{3} c^{3} \int \frac{x^{3} \arctan\left(a x\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 105 \, a^{3} c^{3} \int \frac{x^{3} \log\left(a^{2} x^{2} + 1\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{7 \, c^{3} \arctan\left(a x\right)^{4}}{32 \, a} + 3920 \, a^{2} c^{3} \int \frac{x^{2} \arctan\left(a x\right)^{3}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 420 \, a^{2} c^{3} \int \frac{x^{2} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 420 \, a^{2} c^{3} \int \frac{x^{2} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 420 \, a c^{3} \int \frac{x \arctan\left(a x\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 105 \, a c^{3} \int \frac{x \log\left(a^{2} x^{2} + 1\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{1}{280} \, {\left(5 \, a^{6} c^{3} x^{7} + 21 \, a^{4} c^{3} x^{5} + 35 \, a^{2} c^{3} x^{3} + 35 \, c^{3} x\right)} \arctan\left(a x\right)^{3} + 105 \, c^{3} \int \frac{\arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{1120 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - \frac{3}{1120} \, {\left(5 \, a^{6} c^{3} x^{7} + 21 \, a^{4} c^{3} x^{5} + 35 \, a^{2} c^{3} x^{3} + 35 \, c^{3} x\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2}"," ",0,"980*a^8*c^3*integrate(1/1120*x^8*arctan(a*x)^3/(a^2*x^2 + 1), x) + 105*a^8*c^3*integrate(1/1120*x^8*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 60*a^8*c^3*integrate(1/1120*x^8*arctan(a*x)*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 60*a^7*c^3*integrate(1/1120*x^7*arctan(a*x)^2/(a^2*x^2 + 1), x) + 15*a^7*c^3*integrate(1/1120*x^7*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 3920*a^6*c^3*integrate(1/1120*x^6*arctan(a*x)^3/(a^2*x^2 + 1), x) + 420*a^6*c^3*integrate(1/1120*x^6*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 252*a^6*c^3*integrate(1/1120*x^6*arctan(a*x)*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 252*a^5*c^3*integrate(1/1120*x^5*arctan(a*x)^2/(a^2*x^2 + 1), x) + 63*a^5*c^3*integrate(1/1120*x^5*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 5880*a^4*c^3*integrate(1/1120*x^4*arctan(a*x)^3/(a^2*x^2 + 1), x) + 630*a^4*c^3*integrate(1/1120*x^4*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 420*a^4*c^3*integrate(1/1120*x^4*arctan(a*x)*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 420*a^3*c^3*integrate(1/1120*x^3*arctan(a*x)^2/(a^2*x^2 + 1), x) + 105*a^3*c^3*integrate(1/1120*x^3*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 7/32*c^3*arctan(a*x)^4/a + 3920*a^2*c^3*integrate(1/1120*x^2*arctan(a*x)^3/(a^2*x^2 + 1), x) + 420*a^2*c^3*integrate(1/1120*x^2*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 420*a^2*c^3*integrate(1/1120*x^2*arctan(a*x)*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 420*a*c^3*integrate(1/1120*x*arctan(a*x)^2/(a^2*x^2 + 1), x) + 105*a*c^3*integrate(1/1120*x*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 1/280*(5*a^6*c^3*x^7 + 21*a^4*c^3*x^5 + 35*a^2*c^3*x^3 + 35*c^3*x)*arctan(a*x)^3 + 105*c^3*integrate(1/1120*arctan(a*x)*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) - 3/1120*(5*a^6*c^3*x^7 + 21*a^4*c^3*x^5 + 35*a^2*c^3*x^3 + 35*c^3*x)*arctan(a*x)*log(a^2*x^2 + 1)^2","F",0
383,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^3/x,x, algorithm=""maxima"")","\frac{1}{96} \, {\left(2 \, a^{6} c^{3} x^{6} + 9 \, a^{4} c^{3} x^{4} + 18 \, a^{2} c^{3} x^{2}\right)} \arctan\left(a x\right)^{3} - \frac{1}{128} \, {\left(2 \, a^{6} c^{3} x^{6} + 9 \, a^{4} c^{3} x^{4} + 18 \, a^{2} c^{3} x^{2}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{112 \, {\left(a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3} - 4 \, {\left(2 \, a^{7} c^{3} x^{7} + 9 \, a^{5} c^{3} x^{5} + 18 \, a^{3} c^{3} x^{3}\right)} \arctan\left(a x\right)^{2} + 4 \, {\left(2 \, a^{8} c^{3} x^{8} + 9 \, a^{6} c^{3} x^{6} + 18 \, a^{4} c^{3} x^{4}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right) + {\left(2 \, a^{7} c^{3} x^{7} + 9 \, a^{5} c^{3} x^{5} + 18 \, a^{3} c^{3} x^{3} + 12 \, {\left(a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{128 \, {\left(a^{2} x^{3} + x\right)}}\,{d x}"," ",0,"1/96*(2*a^6*c^3*x^6 + 9*a^4*c^3*x^4 + 18*a^2*c^3*x^2)*arctan(a*x)^3 - 1/128*(2*a^6*c^3*x^6 + 9*a^4*c^3*x^4 + 18*a^2*c^3*x^2)*arctan(a*x)*log(a^2*x^2 + 1)^2 + integrate(1/128*(112*(a^8*c^3*x^8 + 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 4*a^2*c^3*x^2 + c^3)*arctan(a*x)^3 - 4*(2*a^7*c^3*x^7 + 9*a^5*c^3*x^5 + 18*a^3*c^3*x^3)*arctan(a*x)^2 + 4*(2*a^8*c^3*x^8 + 9*a^6*c^3*x^6 + 18*a^4*c^3*x^4)*arctan(a*x)*log(a^2*x^2 + 1) + (2*a^7*c^3*x^7 + 9*a^5*c^3*x^5 + 18*a^3*c^3*x^3 + 12*(a^8*c^3*x^8 + 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 4*a^2*c^3*x^2 + c^3)*arctan(a*x))*log(a^2*x^2 + 1)^2)/(a^2*x^3 + x), x)","F",0
384,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^3/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^3/x^3,x, algorithm=""maxima"")","\frac{4 \, {\left(a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} - 2 \, c^{3}\right)} \arctan\left(a x\right)^{3} - 3 \, {\left(a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} - 2 \, c^{3}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + x^{2} \int \frac{112 \, {\left(a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)^{3} - 12 \, {\left(a^{7} c^{3} x^{7} + 6 \, a^{5} c^{3} x^{5} - 2 \, a c^{3} x\right)} \arctan\left(a x\right)^{2} + 12 \, {\left(a^{8} c^{3} x^{8} + 6 \, a^{6} c^{3} x^{6} - 2 \, a^{2} c^{3} x^{2}\right)} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right) + 3 \, {\left(a^{7} c^{3} x^{7} + 6 \, a^{5} c^{3} x^{5} - 2 \, a c^{3} x + 4 \, {\left(a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{a^{2} x^{5} + x^{3}}\,{d x}}{128 \, x^{2}}"," ",0,"1/128*(4*(a^6*c^3*x^6 + 6*a^4*c^3*x^4 - 2*c^3)*arctan(a*x)^3 - 3*(a^6*c^3*x^6 + 6*a^4*c^3*x^4 - 2*c^3)*arctan(a*x)*log(a^2*x^2 + 1)^2 + 128*x^2*integrate(1/128*(112*(a^8*c^3*x^8 + 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 4*a^2*c^3*x^2 + c^3)*arctan(a*x)^3 - 12*(a^7*c^3*x^7 + 6*a^5*c^3*x^5 - 2*a*c^3*x)*arctan(a*x)^2 + 12*(a^8*c^3*x^8 + 6*a^6*c^3*x^6 - 2*a^2*c^3*x^2)*arctan(a*x)*log(a^2*x^2 + 1) + 3*(a^7*c^3*x^7 + 6*a^5*c^3*x^5 - 2*a*c^3*x + 4*(a^8*c^3*x^8 + 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 4*a^2*c^3*x^2 + c^3)*arctan(a*x))*log(a^2*x^2 + 1)^2)/(a^2*x^5 + x^3), x))/x^2","F",0
386,-1,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^3/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate(x^4*arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)^{3}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)^3/(a^2*c*x^2 + c), x)","F",0
389,-1,0,0,0.000000," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,0,0,0,0.000000," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x \arctan\left(a x\right)^{3}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x*arctan(a*x)^3/(a^2*c*x^2 + c), x)","F",0
391,1,14,0,0.613825," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{\arctan\left(a x\right)^{4}}{4 \, a c}"," ",0,"1/4*arctan(a*x)^4/(a*c)","A",0
392,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)} x}\,{d x}"," ",0,"integrate(arctan(a*x)^3/((a^2*c*x^2 + c)*x), x)","F",0
393,-1,0,0,0.000000," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)^3/((a^2*c*x^2 + c)*x^3), x)","F",0
395,-1,0,0,0.000000," ","integrate(arctan(a*x)^3/x^4/(a^2*c*x^2+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)^3/(a^2*c*x^2 + c)^2, x)","F",0
397,1,218,0,0.474620," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{x}{a^{4} c^{2} x^{2} + a^{2} c^{2}} - \frac{\arctan\left(a x\right)}{a^{3} c^{2}}\right)} \arctan\left(a x\right)^{3} - \frac{3 \, {\left({\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 1\right)} a \arctan\left(a x\right)^{2}}{4 \, {\left(a^{6} c^{2} x^{2} + a^{4} c^{2}\right)}} - \frac{1}{8} \, {\left(\frac{{\left({\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{4} + 3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} - 3\right)} a^{2}}{a^{8} c^{2} x^{2} + a^{6} c^{2}} - \frac{2 \, {\left(2 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} + 3 \, a x + 3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a \arctan\left(a x\right)}{a^{7} c^{2} x^{2} + a^{5} c^{2}}\right)} a"," ",0,"-1/2*(x/(a^4*c^2*x^2 + a^2*c^2) - arctan(a*x)/(a^3*c^2))*arctan(a*x)^3 - 3/4*((a^2*x^2 + 1)*arctan(a*x)^2 + 1)*a*arctan(a*x)^2/(a^6*c^2*x^2 + a^4*c^2) - 1/8*(((a^2*x^2 + 1)*arctan(a*x)^4 + 3*(a^2*x^2 + 1)*arctan(a*x)^2 - 3)*a^2/(a^8*c^2*x^2 + a^6*c^2) - 2*(2*(a^2*x^2 + 1)*arctan(a*x)^3 + 3*a*x + 3*(a^2*x^2 + 1)*arctan(a*x))*a*arctan(a*x)/(a^7*c^2*x^2 + a^5*c^2))*a","A",0
398,1,174,0,0.445977," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{3 \, {\left(\frac{x}{a^{2} c x^{2} + c} + \frac{\arctan\left(a x\right)}{a c}\right)} \arctan\left(a x\right)^{2}}{4 \, a c} + \frac{\frac{{\left(2 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} - 3 \, a x - 3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a^{2}}{a^{5} c x^{2} + a^{3} c} - \frac{6 \, {\left({\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} - 1\right)} a \arctan\left(a x\right)}{a^{4} c x^{2} + a^{2} c}}{8 \, a c} - \frac{\arctan\left(a x\right)^{3}}{2 \, {\left(a^{2} c x^{2} + c\right)} a^{2} c}"," ",0,"3/4*(x/(a^2*c*x^2 + c) + arctan(a*x)/(a*c))*arctan(a*x)^2/(a*c) + 1/8*((2*(a^2*x^2 + 1)*arctan(a*x)^3 - 3*a*x - 3*(a^2*x^2 + 1)*arctan(a*x))*a^2/(a^5*c*x^2 + a^3*c) - 6*((a^2*x^2 + 1)*arctan(a*x)^2 - 1)*a*arctan(a*x)/(a^4*c*x^2 + a^2*c))/(a*c) - 1/2*arctan(a*x)^3/((a^2*c*x^2 + c)*a^2*c)","A",0
399,1,213,0,0.473727," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x}{a^{2} c^{2} x^{2} + c^{2}} + \frac{\arctan\left(a x\right)}{a c^{2}}\right)} \arctan\left(a x\right)^{3} - \frac{3 \, {\left({\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} - 1\right)} a \arctan\left(a x\right)^{2}}{4 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)}} - \frac{1}{8} \, {\left(\frac{{\left({\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{4} - 3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 3\right)} a^{2}}{a^{6} c^{2} x^{2} + a^{4} c^{2}} - \frac{2 \, {\left(2 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} - 3 \, a x - 3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a \arctan\left(a x\right)}{a^{5} c^{2} x^{2} + a^{3} c^{2}}\right)} a"," ",0,"1/2*(x/(a^2*c^2*x^2 + c^2) + arctan(a*x)/(a*c^2))*arctan(a*x)^3 - 3/4*((a^2*x^2 + 1)*arctan(a*x)^2 - 1)*a*arctan(a*x)^2/(a^4*c^2*x^2 + a^2*c^2) - 1/8*(((a^2*x^2 + 1)*arctan(a*x)^4 - 3*(a^2*x^2 + 1)*arctan(a*x)^2 + 3)*a^2/(a^6*c^2*x^2 + a^4*c^2) - 2*(2*(a^2*x^2 + 1)*arctan(a*x)^3 - 3*a*x - 3*(a^2*x^2 + 1)*arctan(a*x))*a*arctan(a*x)/(a^5*c^2*x^2 + a^3*c^2))*a","A",0
400,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{2} x}\,{d x}"," ",0,"integrate(arctan(a*x)^3/((a^2*c*x^2 + c)^2*x), x)","F",0
401,-1,0,0,0.000000," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x^3/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)^3/((a^2*c*x^2 + c)^2*x^3), x)","F",0
403,-1,0,0,0.000000," ","integrate(arctan(a*x)^3/x^4/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,1,289,0,0.477129," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{3}{32} \, a {\left(\frac{5 \, a^{2} x^{3} + 3 \, x}{a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}} + \frac{5 \, \arctan\left(a x\right)}{a^{5} c^{3}}\right)} \arctan\left(a x\right)^{2} - \frac{{\left(2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3}}{4 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}} - \frac{1}{256} \, {\left(\frac{{\left(51 \, a^{3} x^{3} - 40 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} + 45 \, a x + 51 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a^{2}}{a^{11} c^{3} x^{4} + 2 \, a^{9} c^{3} x^{2} + a^{7} c^{3}} - \frac{24 \, {\left(5 \, a^{2} x^{2} - 5 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 4\right)} a \arctan\left(a x\right)}{a^{10} c^{3} x^{4} + 2 \, a^{8} c^{3} x^{2} + a^{6} c^{3}}\right)} a"," ",0,"3/32*a*((5*a^2*x^3 + 3*x)/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3) + 5*arctan(a*x)/(a^5*c^3))*arctan(a*x)^2 - 1/4*(2*a^2*x^2 + 1)*arctan(a*x)^3/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3) - 1/256*((51*a^3*x^3 - 40*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^3 + 45*a*x + 51*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x))*a^2/(a^11*c^3*x^4 + 2*a^9*c^3*x^2 + a^7*c^3) - 24*(5*a^2*x^2 - 5*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 4)*a*arctan(a*x)/(a^10*c^3*x^4 + 2*a^8*c^3*x^2 + a^6*c^3))*a","A",0
405,1,334,0,0.520164," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{a^{2} x^{3} - x}{a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}} + \frac{\arctan\left(a x\right)}{a^{3} c^{3}}\right)} \arctan\left(a x\right)^{3} + \frac{3 \, {\left(a^{2} x^{2} - {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2}\right)} a \arctan\left(a x\right)^{2}}{16 \, {\left(a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}\right)}} - \frac{1}{128} \, {\left(\frac{{\left(4 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{4} + 3 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2}\right)} a^{2}}{a^{10} c^{3} x^{4} + 2 \, a^{8} c^{3} x^{2} + a^{6} c^{3}} + \frac{2 \, {\left(3 \, a^{3} x^{3} - 8 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} - 3 \, a x + 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a \arctan\left(a x\right)}{a^{9} c^{3} x^{4} + 2 \, a^{7} c^{3} x^{2} + a^{5} c^{3}}\right)} a"," ",0,"1/8*((a^2*x^3 - x)/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3) + arctan(a*x)/(a^3*c^3))*arctan(a*x)^3 + 3/16*(a^2*x^2 - (a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2)*a*arctan(a*x)^2/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3) - 1/128*((4*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^4 + 3*a^2*x^2 - 3*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2)*a^2/(a^10*c^3*x^4 + 2*a^8*c^3*x^2 + a^6*c^3) + 2*(3*a^3*x^3 - 8*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^3 - 3*a*x + 3*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x))*a*arctan(a*x)/(a^9*c^3*x^4 + 2*a^7*c^3*x^2 + a^5*c^3))*a","A",0
406,1,272,0,0.466632," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{3 \, {\left(\frac{3 \, a^{2} x^{3} + 5 \, x}{a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}} + \frac{3 \, \arctan\left(a x\right)}{a c^{2}}\right)} \arctan\left(a x\right)^{2}}{32 \, a c} - \frac{3 \, {\left(\frac{{\left(15 \, a^{3} x^{3} - 8 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} + 17 \, a x + 15 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a^{2}}{a^{7} c^{2} x^{4} + 2 \, a^{5} c^{2} x^{2} + a^{3} c^{2}} - \frac{8 \, {\left(3 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 4\right)} a \arctan\left(a x\right)}{a^{6} c^{2} x^{4} + 2 \, a^{4} c^{2} x^{2} + a^{2} c^{2}}\right)}}{256 \, a c} - \frac{\arctan\left(a x\right)^{3}}{4 \, {\left(a^{2} c x^{2} + c\right)}^{2} a^{2} c}"," ",0,"3/32*((3*a^2*x^3 + 5*x)/(a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2) + 3*arctan(a*x)/(a*c^2))*arctan(a*x)^2/(a*c) - 3/256*((15*a^3*x^3 - 8*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^3 + 17*a*x + 15*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x))*a^2/(a^7*c^2*x^4 + 2*a^5*c^2*x^2 + a^3*c^2) - 8*(3*a^2*x^2 - 3*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 4)*a*arctan(a*x)/(a^6*c^2*x^4 + 2*a^4*c^2*x^2 + a^2*c^2))/(a*c) - 1/4*arctan(a*x)^3/((a^2*c*x^2 + c)^2*a^2*c)","A",0
407,1,335,0,0.522380," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{3 \, a^{2} x^{3} + 5 \, x}{a^{4} c^{3} x^{4} + 2 \, a^{2} c^{3} x^{2} + c^{3}} + \frac{3 \, \arctan\left(a x\right)}{a c^{3}}\right)} \arctan\left(a x\right)^{3} + \frac{3 \, {\left(3 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 4\right)} a \arctan\left(a x\right)^{2}}{16 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)}} - \frac{3}{128} \, {\left(\frac{{\left(4 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{4} + 15 \, a^{2} x^{2} - 15 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{2} + 16\right)} a^{2}}{a^{8} c^{3} x^{4} + 2 \, a^{6} c^{3} x^{2} + a^{4} c^{3}} + \frac{2 \, {\left(15 \, a^{3} x^{3} - 8 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)^{3} + 17 \, a x + 15 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)\right)} a \arctan\left(a x\right)}{a^{7} c^{3} x^{4} + 2 \, a^{5} c^{3} x^{2} + a^{3} c^{3}}\right)} a"," ",0,"1/8*((3*a^2*x^3 + 5*x)/(a^4*c^3*x^4 + 2*a^2*c^3*x^2 + c^3) + 3*arctan(a*x)/(a*c^3))*arctan(a*x)^3 + 3/16*(3*a^2*x^2 - 3*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 4)*a*arctan(a*x)^2/(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3) - 3/128*((4*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^4 + 15*a^2*x^2 - 15*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^2 + 16)*a^2/(a^8*c^3*x^4 + 2*a^6*c^3*x^2 + a^4*c^3) + 2*(15*a^3*x^3 - 8*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x)^3 + 17*a*x + 15*(a^4*x^4 + 2*a^2*x^2 + 1)*arctan(a*x))*a*arctan(a*x)/(a^7*c^3*x^4 + 2*a^5*c^3*x^2 + a^3*c^3))*a","A",0
408,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{3} x}\,{d x}"," ",0,"integrate(arctan(a*x)^3/((a^2*c*x^2 + c)^3*x), x)","F",0
409,-1,0,0,0.000000," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x^3/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)^3/((a^2*c*x^2 + c)^3*x^3), x)","F",0
411,-1,0,0,0.000000," ","integrate(arctan(a*x)^3/x^4/(a^2*c*x^2+c)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x^{3} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^3*arctan(a*x)^3, x)","F",0
413,0,0,0,0.000000," ","integrate(x^2*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x^{2} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^2*arctan(a*x)^3, x)","F",0
414,0,0,0,0.000000," ","integrate(x*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x*arctan(a*x)^3, x)","F",0
415,0,0,0,0.000000," ","integrate(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3, x)","F",0
416,0,0,0,0.000000," ","integrate(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x, x)","F",0
417,0,0,0,0.000000," ","integrate(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x^2, x)","F",0
418,0,0,0,0.000000," ","integrate(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x^3, x)","F",0
419,0,0,0,0.000000," ","integrate(arctan(a*x)^3*(a^2*c*x^2+c)^(1/2)/x^4,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3/x^4, x)","F",0
420,0,0,0,0.000000," ","integrate(x^3*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{3} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^3*arctan(a*x)^3, x)","F",0
421,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^2*arctan(a*x)^3, x)","F",0
422,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x*arctan(a*x)^3, x)","F",0
423,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3, x)","F",0
424,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}{x}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3/x, x)","F",0
425,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}{x^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3/x^2, x)","F",0
426,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}{x^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3/x^3, x)","F",0
427,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^3/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}{x^{4}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3/x^4, x)","F",0
428,0,0,0,0.000000," ","integrate(x^3*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{3} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x^3*arctan(a*x)^3, x)","F",0
429,0,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x^2*arctan(a*x)^3, x)","F",0
430,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x*arctan(a*x)^3, x)","F",0
431,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3, x)","F",0
432,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}{x}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3/x, x)","F",0
433,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}{x^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3/x^2, x)","F",0
434,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}{x^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3/x^3, x)","F",0
435,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^3/x^4,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}{x^{4}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3/x^4, x)","F",0
436,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)^3/sqrt(a^2*c*x^2 + c), x)","F",0
437,0,0,0,0.000000," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^2*arctan(a*x)^3/sqrt(a^2*c*x^2 + c), x)","F",0
438,0,0,0,0.000000," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x \arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x*arctan(a*x)^3/sqrt(a^2*c*x^2 + c), x)","F",0
439,0,0,0,0.000000," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(arctan(a*x)^3/sqrt(a^2*c*x^2 + c), x)","F",0
440,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c} x}\,{d x}"," ",0,"integrate(arctan(a*x)^3/(sqrt(a^2*c*x^2 + c)*x), x)","F",0
441,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c} x^{2}}\,{d x}"," ",0,"integrate(arctan(a*x)^3/(sqrt(a^2*c*x^2 + c)*x^2), x)","F",0
442,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c} x^{3}}\,{d x}"," ",0,"integrate(arctan(a*x)^3/(sqrt(a^2*c*x^2 + c)*x^3), x)","F",0
443,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x^4/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c} x^{4}}\,{d x}"," ",0,"integrate(arctan(a*x)^3/(sqrt(a^2*c*x^2 + c)*x^4), x)","F",0
444,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)^3/(a^2*c*x^2 + c)^(3/2), x)","F",0
445,0,0,0,0.000000," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2} \arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*arctan(a*x)^3/(a^2*c*x^2 + c)^(3/2), x)","F",0
446,1,98,0,0.891439," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\sqrt{c} {\left(\frac{3 \, x \arctan\left(a x\right)^{2}}{\sqrt{a^{2} x^{2} + 1} a c^{2}} - \frac{\arctan\left(a x\right)^{3}}{\sqrt{a^{2} x^{2} + 1} a^{2} c^{2}} - \frac{6 \, {\left(\frac{x}{\sqrt{a^{2} x^{2} + 1}} - \frac{\arctan\left(a x\right)}{\sqrt{a^{2} x^{2} + 1} a}\right)}}{a c^{2}}\right)}"," ",0,"sqrt(c)*(3*x*arctan(a*x)^2/(sqrt(a^2*x^2 + 1)*a*c^2) - arctan(a*x)^3/(sqrt(a^2*x^2 + 1)*a^2*c^2) - 6*(x/sqrt(a^2*x^2 + 1) - arctan(a*x)/(sqrt(a^2*x^2 + 1)*a))/(a*c^2))","A",0
447,1,99,0,0.723007," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{x \arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c} c} - \frac{3 \, a {\left(\frac{2 \, x \arctan\left(a x\right)}{\sqrt{a^{2} x^{2} + 1} a c} - \frac{\arctan\left(a x\right)^{2}}{\sqrt{a^{2} x^{2} + 1} a^{2} c} + \frac{2}{\sqrt{a^{2} x^{2} + 1} a^{2} c}\right)}}{\sqrt{c}}"," ",0,"x*arctan(a*x)^3/(sqrt(a^2*c*x^2 + c)*c) - 3*a*(2*x*arctan(a*x)/(sqrt(a^2*x^2 + 1)*a*c) - arctan(a*x)^2/(sqrt(a^2*x^2 + 1)*a^2*c) + 2/(sqrt(a^2*x^2 + 1)*a^2*c))/sqrt(c)","A",0
448,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(arctan(a*x)^3/((a^2*c*x^2 + c)^(3/2)*x), x)","F",0
449,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(arctan(a*x)^3/((a^2*c*x^2 + c)^(3/2)*x^2), x)","F",0
450,0,0,0,0.000000," ","integrate(x^5*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{5} \arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^5*arctan(a*x)^3/(a^2*c*x^2 + c)^(5/2), x)","F",0
451,0,0,0,0.000000," ","integrate(x^4*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{4} \arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^4*arctan(a*x)^3/(a^2*c*x^2 + c)^(5/2), x)","F",0
452,0,0,0,0.000000," ","integrate(x^3*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{3} \arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^3*arctan(a*x)^3/(a^2*c*x^2 + c)^(5/2), x)","F",0
453,0,0,0,0.000000," ","integrate(x^2*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x^{2} \arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x^2*arctan(a*x)^3/(a^2*c*x^2 + c)^(5/2), x)","F",0
454,0,0,0,0.000000," ","integrate(x*arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{x \arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x*arctan(a*x)^3/(a^2*c*x^2 + c)^(5/2), x)","F",0
455,0,0,0,0.000000," ","integrate(arctan(a*x)^3/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(arctan(a*x)^3/(a^2*c*x^2 + c)^(5/2), x)","F",0
456,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate(arctan(a*x)^3/((a^2*c*x^2 + c)^(5/2)*x), x)","F",0
457,0,0,0,0.000000," ","integrate(arctan(a*x)^3/x^2/(a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate(arctan(a*x)^3/((a^2*c*x^2 + c)^(5/2)*x^2), x)","F",0
458,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^3,x, algorithm=""maxima"")","\frac{\frac{15}{2} \, {\left({\left(a^{4} c^{2} m^{2} + 4 \, a^{4} c^{2} m + 3 \, a^{4} c^{2}\right)} x^{5} + 2 \, {\left(a^{2} c^{2} m^{2} + 6 \, a^{2} c^{2} m + 5 \, a^{2} c^{2}\right)} x^{3} + {\left(c^{2} m^{2} + 8 \, c^{2} m + 15 \, c^{2}\right)} x\right)} x^{m} \arctan\left(a x\right)^{3} - \frac{21}{8} \, {\left({\left(a^{4} c^{2} m^{2} + 4 \, a^{4} c^{2} m + 3 \, a^{4} c^{2}\right)} x^{5} + 2 \, {\left(a^{2} c^{2} m^{2} + 6 \, a^{2} c^{2} m + 5 \, a^{2} c^{2}\right)} x^{3} + {\left(c^{2} m^{2} + 8 \, c^{2} m + 15 \, c^{2}\right)} x\right)} x^{m} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} \int \frac{196 \, {\left({\left(a^{6} c^{2} m^{3} + 9 \, a^{6} c^{2} m^{2} + 23 \, a^{6} c^{2} m + 15 \, a^{6} c^{2}\right)} x^{6} + c^{2} m^{3} + 3 \, {\left(a^{4} c^{2} m^{3} + 9 \, a^{4} c^{2} m^{2} + 23 \, a^{4} c^{2} m + 15 \, a^{4} c^{2}\right)} x^{4} + 9 \, c^{2} m^{2} + 23 \, c^{2} m + 3 \, {\left(a^{2} c^{2} m^{3} + 9 \, a^{2} c^{2} m^{2} + 23 \, a^{2} c^{2} m + 15 \, a^{2} c^{2}\right)} x^{2} + 15 \, c^{2}\right)} x^{m} \arctan\left(a x\right)^{3} - 180 \, {\left({\left(a^{5} c^{2} m^{2} + 4 \, a^{5} c^{2} m + 3 \, a^{5} c^{2}\right)} x^{5} + 2 \, {\left(a^{3} c^{2} m^{2} + 6 \, a^{3} c^{2} m + 5 \, a^{3} c^{2}\right)} x^{3} + {\left(a c^{2} m^{2} + 8 \, a c^{2} m + 15 \, a c^{2}\right)} x\right)} x^{m} \arctan\left(a x\right)^{2} + 84 \, {\left({\left(a^{6} c^{2} m^{2} + 4 \, a^{6} c^{2} m + 3 \, a^{6} c^{2}\right)} x^{6} + 2 \, {\left(a^{4} c^{2} m^{2} + 6 \, a^{4} c^{2} m + 5 \, a^{4} c^{2}\right)} x^{4} + {\left(a^{2} c^{2} m^{2} + 8 \, a^{2} c^{2} m + 15 \, a^{2} c^{2}\right)} x^{2}\right)} x^{m} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right) + 21 \, {\left({\left({\left(a^{6} c^{2} m^{3} + 9 \, a^{6} c^{2} m^{2} + 23 \, a^{6} c^{2} m + 15 \, a^{6} c^{2}\right)} x^{6} + c^{2} m^{3} + 3 \, {\left(a^{4} c^{2} m^{3} + 9 \, a^{4} c^{2} m^{2} + 23 \, a^{4} c^{2} m + 15 \, a^{4} c^{2}\right)} x^{4} + 9 \, c^{2} m^{2} + 23 \, c^{2} m + 3 \, {\left(a^{2} c^{2} m^{3} + 9 \, a^{2} c^{2} m^{2} + 23 \, a^{2} c^{2} m + 15 \, a^{2} c^{2}\right)} x^{2} + 15 \, c^{2}\right)} x^{m} \arctan\left(a x\right) + {\left({\left(a^{5} c^{2} m^{2} + 4 \, a^{5} c^{2} m + 3 \, a^{5} c^{2}\right)} x^{5} + 2 \, {\left(a^{3} c^{2} m^{2} + 6 \, a^{3} c^{2} m + 5 \, a^{3} c^{2}\right)} x^{3} + {\left(a c^{2} m^{2} + 8 \, a c^{2} m + 15 \, a c^{2}\right)} x\right)} x^{m}\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{8 \, {\left(m^{3} + {\left(a^{2} m^{3} + 9 \, a^{2} m^{2} + 23 \, a^{2} m + 15 \, a^{2}\right)} x^{2} + 9 \, m^{2} + 23 \, m + 15\right)}}\,{d x}}{32 \, {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)}}"," ",0,"1/32*(4*((a^4*c^2*m^2 + 4*a^4*c^2*m + 3*a^4*c^2)*x^5 + 2*(a^2*c^2*m^2 + 6*a^2*c^2*m + 5*a^2*c^2)*x^3 + (c^2*m^2 + 8*c^2*m + 15*c^2)*x)*x^m*arctan(a*x)^3 - 3*((a^4*c^2*m^2 + 4*a^4*c^2*m + 3*a^4*c^2)*x^5 + 2*(a^2*c^2*m^2 + 6*a^2*c^2*m + 5*a^2*c^2)*x^3 + (c^2*m^2 + 8*c^2*m + 15*c^2)*x)*x^m*arctan(a*x)*log(a^2*x^2 + 1)^2 + 32*(m^3 + 9*m^2 + 23*m + 15)*integrate(1/32*(28*((a^6*c^2*m^3 + 9*a^6*c^2*m^2 + 23*a^6*c^2*m + 15*a^6*c^2)*x^6 + c^2*m^3 + 3*(a^4*c^2*m^3 + 9*a^4*c^2*m^2 + 23*a^4*c^2*m + 15*a^4*c^2)*x^4 + 9*c^2*m^2 + 23*c^2*m + 3*(a^2*c^2*m^3 + 9*a^2*c^2*m^2 + 23*a^2*c^2*m + 15*a^2*c^2)*x^2 + 15*c^2)*x^m*arctan(a*x)^3 - 12*((a^5*c^2*m^2 + 4*a^5*c^2*m + 3*a^5*c^2)*x^5 + 2*(a^3*c^2*m^2 + 6*a^3*c^2*m + 5*a^3*c^2)*x^3 + (a*c^2*m^2 + 8*a*c^2*m + 15*a*c^2)*x)*x^m*arctan(a*x)^2 + 12*((a^6*c^2*m^2 + 4*a^6*c^2*m + 3*a^6*c^2)*x^6 + 2*(a^4*c^2*m^2 + 6*a^4*c^2*m + 5*a^4*c^2)*x^4 + (a^2*c^2*m^2 + 8*a^2*c^2*m + 15*a^2*c^2)*x^2)*x^m*arctan(a*x)*log(a^2*x^2 + 1) + 3*(((a^6*c^2*m^3 + 9*a^6*c^2*m^2 + 23*a^6*c^2*m + 15*a^6*c^2)*x^6 + c^2*m^3 + 3*(a^4*c^2*m^3 + 9*a^4*c^2*m^2 + 23*a^4*c^2*m + 15*a^4*c^2)*x^4 + 9*c^2*m^2 + 23*c^2*m + 3*(a^2*c^2*m^3 + 9*a^2*c^2*m^2 + 23*a^2*c^2*m + 15*a^2*c^2)*x^2 + 15*c^2)*x^m*arctan(a*x) + ((a^5*c^2*m^2 + 4*a^5*c^2*m + 3*a^5*c^2)*x^5 + 2*(a^3*c^2*m^2 + 6*a^3*c^2*m + 5*a^3*c^2)*x^3 + (a*c^2*m^2 + 8*a*c^2*m + 15*a*c^2)*x)*x^m)*log(a^2*x^2 + 1)^2)/(m^3 + (a^2*m^3 + 9*a^2*m^2 + 23*a^2*m + 15*a^2)*x^2 + 9*m^2 + 23*m + 15), x))/(m^3 + 9*m^2 + 23*m + 15)","F",0
459,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)*arctan(a*x)^3,x, algorithm=""maxima"")","\frac{\frac{15}{2} \, {\left({\left(a^{2} c m + a^{2} c\right)} x^{3} + {\left(c m + 3 \, c\right)} x\right)} x^{m} \arctan\left(a x\right)^{3} - \frac{21}{8} \, {\left({\left(a^{2} c m + a^{2} c\right)} x^{3} + {\left(c m + 3 \, c\right)} x\right)} x^{m} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + {\left(m^{2} + 4 \, m + 3\right)} \int \frac{196 \, {\left({\left(a^{4} c m^{2} + 4 \, a^{4} c m + 3 \, a^{4} c\right)} x^{4} + c m^{2} + 2 \, {\left(a^{2} c m^{2} + 4 \, a^{2} c m + 3 \, a^{2} c\right)} x^{2} + 4 \, c m + 3 \, c\right)} x^{m} \arctan\left(a x\right)^{3} - 180 \, {\left({\left(a^{3} c m + a^{3} c\right)} x^{3} + {\left(a c m + 3 \, a c\right)} x\right)} x^{m} \arctan\left(a x\right)^{2} + 84 \, {\left({\left(a^{4} c m + a^{4} c\right)} x^{4} + {\left(a^{2} c m + 3 \, a^{2} c\right)} x^{2}\right)} x^{m} \arctan\left(a x\right) \log\left(a^{2} x^{2} + 1\right) + 21 \, {\left({\left({\left(a^{4} c m^{2} + 4 \, a^{4} c m + 3 \, a^{4} c\right)} x^{4} + c m^{2} + 2 \, {\left(a^{2} c m^{2} + 4 \, a^{2} c m + 3 \, a^{2} c\right)} x^{2} + 4 \, c m + 3 \, c\right)} x^{m} \arctan\left(a x\right) + {\left({\left(a^{3} c m + a^{3} c\right)} x^{3} + {\left(a c m + 3 \, a c\right)} x\right)} x^{m}\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{8 \, {\left({\left(a^{2} m^{2} + 4 \, a^{2} m + 3 \, a^{2}\right)} x^{2} + m^{2} + 4 \, m + 3\right)}}\,{d x}}{32 \, {\left(m^{2} + 4 \, m + 3\right)}}"," ",0,"1/32*(4*((a^2*c*m + a^2*c)*x^3 + (c*m + 3*c)*x)*x^m*arctan(a*x)^3 - 3*((a^2*c*m + a^2*c)*x^3 + (c*m + 3*c)*x)*x^m*arctan(a*x)*log(a^2*x^2 + 1)^2 + 32*(m^2 + 4*m + 3)*integrate(1/32*(28*((a^4*c*m^2 + 4*a^4*c*m + 3*a^4*c)*x^4 + c*m^2 + 2*(a^2*c*m^2 + 4*a^2*c*m + 3*a^2*c)*x^2 + 4*c*m + 3*c)*x^m*arctan(a*x)^3 - 12*((a^3*c*m + a^3*c)*x^3 + (a*c*m + 3*a*c)*x)*x^m*arctan(a*x)^2 + 12*((a^4*c*m + a^4*c)*x^4 + (a^2*c*m + 3*a^2*c)*x^2)*x^m*arctan(a*x)*log(a^2*x^2 + 1) + 3*(((a^4*c*m^2 + 4*a^4*c*m + 3*a^4*c)*x^4 + c*m^2 + 2*(a^2*c*m^2 + 4*a^2*c*m + 3*a^2*c)*x^2 + 4*c*m + 3*c)*x^m*arctan(a*x) + ((a^3*c*m + a^3*c)*x^3 + (a*c*m + 3*a*c)*x)*x^m)*log(a^2*x^2 + 1)^2)/((a^2*m^2 + 4*a^2*m + 3*a^2)*x^2 + m^2 + 4*m + 3), x))/(m^2 + 4*m + 3)","F",0
460,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)^3/(a^2*c*x^2+c),x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)^{3}}{a^{2} c x^{2} + c}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)^3/(a^2*c*x^2 + c), x)","F",0
461,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)^3/(a^2*c*x^2 + c)^2, x)","F",0
462,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^3,x, algorithm=""maxima"")","\int {\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^m*arctan(a*x)^3, x)","F",0
463,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)^3*(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} c x^{2} + c} x^{m} \arctan\left(a x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^m*arctan(a*x)^3, x)","F",0
464,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)^{3}}{\sqrt{a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)^3/sqrt(a^2*c*x^2 + c), x)","F",0
465,0,0,0,0.000000," ","integrate(x^m*arctan(a*x)^3/(a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{x^{m} \arctan\left(a x\right)^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^m*arctan(a*x)^3/(a^2*c*x^2 + c)^(3/2), x)","F",0
466,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)} x}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)*x/arctan(a*x), x)","F",0
467,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{a^{2} c x^{2} + c}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)/arctan(a*x), x)","F",0
468,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)/x/arctan(a*x),x, algorithm=""maxima"")","\int \frac{a^{2} c x^{2} + c}{x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)/(x*arctan(a*x)), x)","F",0
469,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{2} x}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^2*x/arctan(a*x), x)","F",0
470,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{2}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^2/arctan(a*x), x)","F",0
471,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/x/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{2}}{x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^2/(x*arctan(a*x)), x)","F",0
472,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{3} x}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^3*x/arctan(a*x), x)","F",0
473,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{3}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^3/arctan(a*x), x)","F",0
474,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/x/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{3}}{x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^3/(x*arctan(a*x)), x)","F",0
475,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/((a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
476,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x/((a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
477,1,15,0,0.321194," ","integrate(1/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""maxima"")","\frac{\log\left(2 \, {\left| \arctan\left(a x\right) \right|}\right)}{a c}"," ",0,"log(2*abs(arctan(a*x)))/(a*c)","A",0
478,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)} x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)*x*arctan(a*x)), x)","F",0
479,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)} x^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)*x^2*arctan(a*x)), x)","F",0
480,0,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(a^{2} c x^{2} + c\right)}^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^4/((a^2*c*x^2 + c)^2*arctan(a*x)), x)","F",0
481,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a^{2} c x^{2} + c\right)}^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^3/((a^2*c*x^2 + c)^2*arctan(a*x)), x)","F",0
482,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)}^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/((a^2*c*x^2 + c)^2*arctan(a*x)), x)","F",0
483,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x/((a^2*c*x^2 + c)^2*arctan(a*x)), x)","F",0
484,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^2*arctan(a*x)), x)","F",0
485,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{2} x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^2*x*arctan(a*x)), x)","F",0
486,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{2} x^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^2*x^2*arctan(a*x)), x)","F",0
487,0,0,0,0.000000," ","integrate(x^6/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{6}}{{\left(a^{2} c x^{2} + c\right)}^{3} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^6/((a^2*c*x^2 + c)^3*arctan(a*x)), x)","F",0
488,0,0,0,0.000000," ","integrate(x^5/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{5}}{{\left(a^{2} c x^{2} + c\right)}^{3} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^5/((a^2*c*x^2 + c)^3*arctan(a*x)), x)","F",0
489,0,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(a^{2} c x^{2} + c\right)}^{3} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^4/((a^2*c*x^2 + c)^3*arctan(a*x)), x)","F",0
490,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a^{2} c x^{2} + c\right)}^{3} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^3/((a^2*c*x^2 + c)^3*arctan(a*x)), x)","F",0
491,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)}^{3} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/((a^2*c*x^2 + c)^3*arctan(a*x)), x)","F",0
492,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{3} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x/((a^2*c*x^2 + c)^3*arctan(a*x)), x)","F",0
493,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{3} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^3*arctan(a*x)), x)","F",0
494,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{3} x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^3*x*arctan(a*x)), x)","F",0
495,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{3} x^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^3*x^2*arctan(a*x)), x)","F",0
496,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} x}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x/arctan(a*x), x)","F",0
497,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)/arctan(a*x), x)","F",0
498,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/x/arctan(a*x),x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c}}{x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)/(x*arctan(a*x)), x)","F",0
499,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x/arctan(a*x), x)","F",0
500,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)/arctan(a*x), x)","F",0
501,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/x/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)/(x*arctan(a*x)), x)","F",0
502,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x/arctan(a*x), x)","F",0
503,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)/arctan(a*x), x)","F",0
504,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/x/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)/(x*arctan(a*x)), x)","F",0
505,0,0,0,0.000000," ","integrate(x/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x/(sqrt(a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
506,0,0,0,0.000000," ","integrate(1/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
507,0,0,0,0.000000," ","integrate(1/x/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*x*arctan(a*x)), x)","F",0
508,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^3/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)), x)","F",0
509,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)), x)","F",0
510,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)), x)","F",0
511,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)), x)","F",0
512,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*x*arctan(a*x)), x)","F",0
513,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*x^2*arctan(a*x)), x)","F",0
514,0,0,0,0.000000," ","integrate(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{5}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^5/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)), x)","F",0
515,0,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^4/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)), x)","F",0
516,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^3/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)), x)","F",0
517,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)), x)","F",0
518,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)), x)","F",0
519,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)), x)","F",0
520,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*x*arctan(a*x)), x)","F",0
521,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*x^2*arctan(a*x)), x)","F",0
522,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{3} x^{m}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^3*x^m/arctan(a*x), x)","F",0
523,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{2} x^{m}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^2*x^m/arctan(a*x), x)","F",0
524,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)} x^{m}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)*x^m/arctan(a*x), x)","F",0
525,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^m/((a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
526,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^2/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)}^{2} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^m/((a^2*c*x^2 + c)^2*arctan(a*x)), x)","F",0
527,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^3/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)}^{3} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^m/((a^2*c*x^2 + c)^3*arctan(a*x)), x)","F",0
528,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{m}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x^m/arctan(a*x), x)","F",0
529,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^m/arctan(a*x), x)","F",0
530,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x), x)","F",0
531,0,0,0,0.000000," ","integrate(x^m/arctan(a*x)/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^m/(sqrt(a^2*c*x^2 + c)*arctan(a*x)), x)","F",0
532,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^m/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)), x)","F",0
533,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)}\,{d x}"," ",0,"integrate(x^m/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)), x)","F",0
534,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{4} c x^{5} + 2 \, a^{2} c x^{3} - \mathit{sage}_{0} x \arctan\left(a x\right) + c x}{a \arctan\left(a x\right)}"," ",0,"-(a^4*c*x^5 + 2*a^2*c*x^3 + c*x - arctan(a*x)*integrate((5*a^4*c*x^4 + 6*a^2*c*x^2 + c)/arctan(a*x), x))/(a*arctan(a*x))","F",0
535,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{4} c x^{4} + 2 \, a^{2} c x^{2} - 4 \, a \arctan\left(a x\right) \int \frac{a^{3} c x^{3} + a c x}{\arctan\left(a x\right)}\,{d x} + c}{a \arctan\left(a x\right)}"," ",0,"-(a^4*c*x^4 + 2*a^2*c*x^2 - a*arctan(a*x)*integrate(4*(a^3*c*x^3 + a*c*x)/arctan(a*x), x) + c)/(a*arctan(a*x))","F",0
536,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)/x/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{4} c x^{4} + 2 \, a^{2} c x^{2} - \mathit{sage}_{0} x^{2} \arctan\left(a x\right) + c}{a x \arctan\left(a x\right)}"," ",0,"-(a^4*c*x^4 + 2*a^2*c*x^2 - x*arctan(a*x)*integrate((3*a^4*c*x^4 + 2*a^2*c*x^2 - c)/(x^2*arctan(a*x)), x) + c)/(a*x*arctan(a*x))","F",0
537,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{6} c^{2} x^{7} + 3 \, a^{4} c^{2} x^{5} + 3 \, a^{2} c^{2} x^{3} + c^{2} x - \mathit{sage}_{0} x \arctan\left(a x\right)}{a \arctan\left(a x\right)}"," ",0,"-(a^6*c^2*x^7 + 3*a^4*c^2*x^5 + 3*a^2*c^2*x^3 + c^2*x - arctan(a*x)*integrate((7*a^6*c^2*x^6 + 15*a^4*c^2*x^4 + 9*a^2*c^2*x^2 + c^2)/arctan(a*x), x))/(a*arctan(a*x))","F",0
538,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{6} c^{2} x^{6} + 3 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} - 6 \, a \arctan\left(a x\right) \int \frac{a^{5} c^{2} x^{5} + 2 \, a^{3} c^{2} x^{3} + a c^{2} x}{\arctan\left(a x\right)}\,{d x} + c^{2}}{a \arctan\left(a x\right)}"," ",0,"-(a^6*c^2*x^6 + 3*a^4*c^2*x^4 + 3*a^2*c^2*x^2 - a*arctan(a*x)*integrate(6*(a^5*c^2*x^5 + 2*a^3*c^2*x^3 + a*c^2*x)/arctan(a*x), x) + c^2)/(a*arctan(a*x))","F",0
539,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/x/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{6} c^{2} x^{6} + 3 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} - \mathit{sage}_{0} x^{2} \arctan\left(a x\right) + c^{2}}{a x \arctan\left(a x\right)}"," ",0,"-(a^6*c^2*x^6 + 3*a^4*c^2*x^4 + 3*a^2*c^2*x^2 - x*arctan(a*x)*integrate((5*a^6*c^2*x^6 + 9*a^4*c^2*x^4 + 3*a^2*c^2*x^2 - c^2)/(x^2*arctan(a*x)), x) + c^2)/(a*x*arctan(a*x))","F",0
540,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{8} c^{3} x^{9} + 4 \, a^{6} c^{3} x^{7} + 6 \, a^{4} c^{3} x^{5} + 4 \, a^{2} c^{3} x^{3} + c^{3} x - \mathit{sage}_{0} x \arctan\left(a x\right)}{a \arctan\left(a x\right)}"," ",0,"-(a^8*c^3*x^9 + 4*a^6*c^3*x^7 + 6*a^4*c^3*x^5 + 4*a^2*c^3*x^3 + c^3*x - arctan(a*x)*integrate((9*a^8*c^3*x^8 + 28*a^6*c^3*x^6 + 30*a^4*c^3*x^4 + 12*a^2*c^3*x^2 + c^3)/arctan(a*x), x))/(a*arctan(a*x))","F",0
541,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} + c^{3} - 8 \, a \arctan\left(a x\right) \int \frac{a^{7} c^{3} x^{7} + 3 \, a^{5} c^{3} x^{5} + 3 \, a^{3} c^{3} x^{3} + a c^{3} x}{\arctan\left(a x\right)}\,{d x}}{a \arctan\left(a x\right)}"," ",0,"-(a^8*c^3*x^8 + 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 4*a^2*c^3*x^2 + c^3 - a*arctan(a*x)*integrate(8*(a^7*c^3*x^7 + 3*a^5*c^3*x^5 + 3*a^3*c^3*x^3 + a*c^3*x)/arctan(a*x), x))/(a*arctan(a*x))","F",0
542,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/x/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} - \mathit{sage}_{0} x^{2} \arctan\left(a x\right) + c^{3}}{a x \arctan\left(a x\right)}"," ",0,"-(a^8*c^3*x^8 + 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 4*a^2*c^3*x^2 + c^3 - x*arctan(a*x)*integrate((7*a^8*c^3*x^8 + 20*a^6*c^3*x^6 + 18*a^4*c^3*x^4 + 4*a^2*c^3*x^2 - c^3)/(x^2*arctan(a*x)), x))/(a*x*arctan(a*x))","F",0
543,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{x^{3} - 3 \, \mathit{sage}_{0} x \arctan\left(a x\right)}{a c \arctan\left(a x\right)}"," ",0,"-(x^3 - 3*arctan(a*x)*integrate(x^2/arctan(a*x), x))/(a*c*arctan(a*x))","F",0
544,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{-2 \, \mathit{sage}_{0} x \arctan\left(a x\right) + x^{2}}{a c \arctan\left(a x\right)}"," ",0,"-(x^2 - 2*arctan(a*x)*integrate(x/arctan(a*x), x))/(a*c*arctan(a*x))","F",0
545,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","\frac{\mathit{sage}_{0} x \arctan\left(a x\right) - x}{a c \arctan\left(a x\right)}"," ",0,"(arctan(a*x)*integrate(1/arctan(a*x), x) - x)/(a*c*arctan(a*x))","F",0
546,1,14,0,0.330781," ","integrate(1/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{1}{a c \arctan\left(a x\right)}"," ",0,"-1/(a*c*arctan(a*x))","A",0
547,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{\mathit{sage}_{0} x^{2} \arctan\left(a x\right) + 1}{a c x \arctan\left(a x\right)}"," ",0,"-(x*arctan(a*x)*integrate(1/(x^2*arctan(a*x)), x) + 1)/(a*c*x*arctan(a*x))","F",0
548,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, \mathit{sage}_{0} x^{3} \arctan\left(a x\right) + 1}{a c x^{2} \arctan\left(a x\right)}"," ",0,"-(2*x^2*arctan(a*x)*integrate(1/(x^3*arctan(a*x)), x) + 1)/(a*c*x^2*arctan(a*x))","F",0
549,0,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{3 \, \mathit{sage}_{0} x^{4} \arctan\left(a x\right) + 1}{a c x^{3} \arctan\left(a x\right)}"," ",0,"-(3*x^3*arctan(a*x)*integrate(1/(x^4*arctan(a*x)), x) + 1)/(a*c*x^3*arctan(a*x))","F",0
550,0,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{4 \, \mathit{sage}_{0} x^{5} \arctan\left(a x\right) + 1}{a c x^{4} \arctan\left(a x\right)}"," ",0,"-(4*x^4*arctan(a*x)*integrate(1/(x^5*arctan(a*x)), x) + 1)/(a*c*x^4*arctan(a*x))","F",0
551,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{-{\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \mathit{sage}_{0} x \arctan\left(a x\right) + x^{3}}{{\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \arctan\left(a x\right)}"," ",0,"-(x^3 - (a^3*c^2*x^2 + a*c^2)*arctan(a*x)*integrate((a^2*x^4 + 3*x^2)/((a^5*c^2*x^4 + 2*a^3*c^2*x^2 + a*c^2)*arctan(a*x)), x))/((a^3*c^2*x^2 + a*c^2)*arctan(a*x))","F",0
552,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \arctan\left(a x\right) \int \frac{x}{{\left(a^{5} c^{2} x^{4} + 2 \, a^{3} c^{2} x^{2} + a c^{2}\right)} \arctan\left(a x\right)}\,{d x} - x^{2}}{{\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \arctan\left(a x\right)}"," ",0,"(4*(a^3*c^2*x^2 + a*c^2)*arctan(a*x)*integrate(1/2*x/((a^5*c^2*x^4 + 2*a^3*c^2*x^2 + a*c^2)*arctan(a*x)), x) - x^2)/((a^3*c^2*x^2 + a*c^2)*arctan(a*x))","F",0
553,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \mathit{sage}_{0} x \arctan\left(a x\right) + x}{{\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \arctan\left(a x\right)}"," ",0,"-((a^3*c^2*x^2 + a*c^2)*arctan(a*x)*integrate((a^2*x^2 - 1)/((a^5*c^2*x^4 + 2*a^3*c^2*x^2 + a*c^2)*arctan(a*x)), x) + x)/((a^3*c^2*x^2 + a*c^2)*arctan(a*x))","F",0
554,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \arctan\left(a x\right) \int \frac{x}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}\,{d x} + 1}{{\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \arctan\left(a x\right)}"," ",0,"-(4*(a^4*c^2*x^2 + a^2*c^2)*arctan(a*x)*integrate(1/2*x/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x) + 1)/((a^3*c^2*x^2 + a*c^2)*arctan(a*x))","F",0
555,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{3} c^{2} x^{3} + a c^{2} x\right)} \mathit{sage}_{0} x \arctan\left(a x\right) + 1}{{\left(a^{3} c^{2} x^{3} + a c^{2} x\right)} \arctan\left(a x\right)}"," ",0,"-((a^3*c^2*x^3 + a*c^2*x)*arctan(a*x)*integrate((3*a^2*x^2 + 1)/((a^5*c^2*x^6 + 2*a^3*c^2*x^4 + a*c^2*x^2)*arctan(a*x)), x) + 1)/((a^3*c^2*x^3 + a*c^2*x)*arctan(a*x))","F",0
556,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{3} c^{2} x^{4} + a c^{2} x^{2}\right)} \arctan\left(a x\right) \int \frac{2 \, a^{2} x^{2} + 1}{{\left(a^{5} c^{2} x^{7} + 2 \, a^{3} c^{2} x^{5} + a c^{2} x^{3}\right)} \arctan\left(a x\right)}\,{d x} + 1}{{\left(a^{3} c^{2} x^{4} + a c^{2} x^{2}\right)} \arctan\left(a x\right)}"," ",0,"-((a^3*c^2*x^4 + a*c^2*x^2)*arctan(a*x)*integrate(2*(2*a^2*x^2 + 1)/((a^5*c^2*x^7 + 2*a^3*c^2*x^5 + a*c^2*x^3)*arctan(a*x)), x) + 1)/((a^3*c^2*x^4 + a*c^2*x^2)*arctan(a*x))","F",0
557,0,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{3} c^{2} x^{5} + a c^{2} x^{3}\right)} \mathit{sage}_{0} x \arctan\left(a x\right) + 1}{{\left(a^{3} c^{2} x^{5} + a c^{2} x^{3}\right)} \arctan\left(a x\right)}"," ",0,"-((a^3*c^2*x^5 + a*c^2*x^3)*arctan(a*x)*integrate((5*a^2*x^2 + 3)/((a^5*c^2*x^8 + 2*a^3*c^2*x^6 + a*c^2*x^4)*arctan(a*x)), x) + 1)/((a^3*c^2*x^5 + a*c^2*x^3)*arctan(a*x))","F",0
558,0,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{3} c^{2} x^{6} + a c^{2} x^{4}\right)} \arctan\left(a x\right) \int \frac{3 \, a^{2} x^{2} + 2}{{\left(a^{5} c^{2} x^{9} + 2 \, a^{3} c^{2} x^{7} + a c^{2} x^{5}\right)} \arctan\left(a x\right)}\,{d x} + 1}{{\left(a^{3} c^{2} x^{6} + a c^{2} x^{4}\right)} \arctan\left(a x\right)}"," ",0,"-((a^3*c^2*x^6 + a*c^2*x^4)*arctan(a*x)*integrate(2*(3*a^2*x^2 + 2)/((a^5*c^2*x^9 + 2*a^3*c^2*x^7 + a*c^2*x^5)*arctan(a*x)), x) + 1)/((a^3*c^2*x^6 + a*c^2*x^4)*arctan(a*x))","F",0
559,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \mathit{sage}_{0} x \arctan\left(a x\right) + x^{3}}{{\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \arctan\left(a x\right)}"," ",0,"-(x^3 + (a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x)*integrate((a^2*x^4 - 3*x^2)/((a^7*c^3*x^6 + 3*a^5*c^3*x^4 + 3*a^3*c^3*x^2 + a*c^3)*arctan(a*x)), x))/((a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x))","F",0
560,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \arctan\left(a x\right) \int \frac{a^{2} x^{3} - x}{{\left(a^{7} c^{3} x^{6} + 3 \, a^{5} c^{3} x^{4} + 3 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \arctan\left(a x\right)}\,{d x} + x^{2}}{{\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \arctan\left(a x\right)}"," ",0,"-((a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x)*integrate(2*(a^2*x^3 - x)/((a^7*c^3*x^6 + 3*a^5*c^3*x^4 + 3*a^3*c^3*x^2 + a*c^3)*arctan(a*x)), x) + x^2)/((a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x))","F",0
561,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \mathit{sage}_{0} x \arctan\left(a x\right) + x}{{\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \arctan\left(a x\right)}"," ",0,"-((a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x)*integrate((3*a^2*x^2 - 1)/((a^7*c^3*x^6 + 3*a^5*c^3*x^4 + 3*a^3*c^3*x^2 + a*c^3)*arctan(a*x)), x) + x)/((a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x))","F",0
562,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)} \arctan\left(a x\right) \int \frac{x}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}\,{d x} + 1}{{\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \arctan\left(a x\right)}"," ",0,"-(8*(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x)*integrate(1/2*x/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x) + 1)/((a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x))","F",0
563,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{5} c^{3} x^{5} + 2 \, a^{3} c^{3} x^{3} + a c^{3} x\right)} \mathit{sage}_{0} x \arctan\left(a x\right) + 1}{{\left(a^{5} c^{3} x^{5} + 2 \, a^{3} c^{3} x^{3} + a c^{3} x\right)} \arctan\left(a x\right)}"," ",0,"-((a^5*c^3*x^5 + 2*a^3*c^3*x^3 + a*c^3*x)*arctan(a*x)*integrate((5*a^2*x^2 + 1)/((a^7*c^3*x^8 + 3*a^5*c^3*x^6 + 3*a^3*c^3*x^4 + a*c^3*x^2)*arctan(a*x)), x) + 1)/((a^5*c^3*x^5 + 2*a^3*c^3*x^3 + a*c^3*x)*arctan(a*x))","F",0
564,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{5} c^{3} x^{6} + 2 \, a^{3} c^{3} x^{4} + a c^{3} x^{2}\right)} \arctan\left(a x\right) \int \frac{3 \, a^{2} x^{2} + 1}{{\left(a^{7} c^{3} x^{9} + 3 \, a^{5} c^{3} x^{7} + 3 \, a^{3} c^{3} x^{5} + a c^{3} x^{3}\right)} \arctan\left(a x\right)}\,{d x} + 1}{{\left(a^{5} c^{3} x^{6} + 2 \, a^{3} c^{3} x^{4} + a c^{3} x^{2}\right)} \arctan\left(a x\right)}"," ",0,"-((a^5*c^3*x^6 + 2*a^3*c^3*x^4 + a*c^3*x^2)*arctan(a*x)*integrate(2*(3*a^2*x^2 + 1)/((a^7*c^3*x^9 + 3*a^5*c^3*x^7 + 3*a^3*c^3*x^5 + a*c^3*x^3)*arctan(a*x)), x) + 1)/((a^5*c^3*x^6 + 2*a^3*c^3*x^4 + a*c^3*x^2)*arctan(a*x))","F",0
565,0,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{5} c^{3} x^{7} + 2 \, a^{3} c^{3} x^{5} + a c^{3} x^{3}\right)} \mathit{sage}_{0} x \arctan\left(a x\right) + 1}{{\left(a^{5} c^{3} x^{7} + 2 \, a^{3} c^{3} x^{5} + a c^{3} x^{3}\right)} \arctan\left(a x\right)}"," ",0,"-((a^5*c^3*x^7 + 2*a^3*c^3*x^5 + a*c^3*x^3)*arctan(a*x)*integrate((7*a^2*x^2 + 3)/((a^7*c^3*x^10 + 3*a^5*c^3*x^8 + 3*a^3*c^3*x^6 + a*c^3*x^4)*arctan(a*x)), x) + 1)/((a^5*c^3*x^7 + 2*a^3*c^3*x^5 + a*c^3*x^3)*arctan(a*x))","F",0
566,0,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(a^{5} c^{3} x^{8} + 2 \, a^{3} c^{3} x^{6} + a c^{3} x^{4}\right)} \arctan\left(a x\right) \int \frac{2 \, a^{2} x^{2} + 1}{{\left(a^{7} c^{3} x^{11} + 3 \, a^{5} c^{3} x^{9} + 3 \, a^{3} c^{3} x^{7} + a c^{3} x^{5}\right)} \arctan\left(a x\right)}\,{d x} + 1}{{\left(a^{5} c^{3} x^{8} + 2 \, a^{3} c^{3} x^{6} + a c^{3} x^{4}\right)} \arctan\left(a x\right)}"," ",0,"-((a^5*c^3*x^8 + 2*a^3*c^3*x^6 + a*c^3*x^4)*arctan(a*x)*integrate(4*(2*a^2*x^2 + 1)/((a^7*c^3*x^11 + 3*a^5*c^3*x^9 + 3*a^3*c^3*x^7 + a*c^3*x^5)*arctan(a*x)), x) + 1)/((a^5*c^3*x^8 + 2*a^3*c^3*x^6 + a*c^3*x^4)*arctan(a*x))","F",0
567,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} x}{\arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x/arctan(a*x)^2, x)","F",0
568,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)/arctan(a*x)^2, x)","F",0
569,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c}}{x \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)/(x*arctan(a*x)^2), x)","F",0
570,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{\arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x/arctan(a*x)^2, x)","F",0
571,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)/arctan(a*x)^2, x)","F",0
572,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{x \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)/(x*arctan(a*x)^2), x)","F",0
573,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}{\arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x/arctan(a*x)^2, x)","F",0
574,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{\arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)/arctan(a*x)^2, x)","F",0
575,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{x \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)/(x*arctan(a*x)^2), x)","F",0
576,0,0,0,0.000000," ","integrate(x/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2), x)","F",0
577,0,0,0,0.000000," ","integrate(1/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2), x)","F",0
578,0,0,0,0.000000," ","integrate(1/x/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} x \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*x*arctan(a*x)^2), x)","F",0
579,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^3/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2), x)","F",0
580,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^2/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2), x)","F",0
581,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2), x)","F",0
582,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2), x)","F",0
583,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*x*arctan(a*x)^2), x)","F",0
584,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*x^2*arctan(a*x)^2), x)","F",0
585,0,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{3} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*x^3*arctan(a*x)^2), x)","F",0
586,0,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{4} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*x^4*arctan(a*x)^2), x)","F",0
587,0,0,0,0.000000," ","integrate(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{x^{5}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^5/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2), x)","F",0
588,0,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^4/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2), x)","F",0
589,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^3/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2), x)","F",0
590,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^2/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2), x)","F",0
591,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2), x)","F",0
592,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2), x)","F",0
593,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*x*arctan(a*x)^2), x)","F",0
594,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*x^2*arctan(a*x)^2), x)","F",0
595,0,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{3} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*x^3*arctan(a*x)^2), x)","F",0
596,0,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{4} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*x^4*arctan(a*x)^2), x)","F",0
597,0,0,0,0.000000," ","integrate((f*x)^(1/2)/(c^2*d*x^2+d)^2/(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{\frac{1}{2} \, {\left(a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arctan\left(c x\right)\right)} \sqrt{f} \int \frac{{\left(a c^{2} x^{2} + 4 \, b c x + {\left(b c^{2} x^{2} + b\right)} \arctan\left(c x\right) + a\right)} \sqrt{x}}{a^{3} c^{4} d^{2} x^{4} + 2 \, a^{3} c^{2} d^{2} x^{2} + a^{3} d^{2} + {\left(b^{3} c^{4} d^{2} x^{4} + 2 \, b^{3} c^{2} d^{2} x^{2} + b^{3} d^{2}\right)} \arctan\left(c x\right)^{3} + 3 \, {\left(a b^{2} c^{4} d^{2} x^{4} + 2 \, a b^{2} c^{2} d^{2} x^{2} + a b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + 3 \, {\left(a^{2} b c^{4} d^{2} x^{4} + 2 \, a^{2} b c^{2} d^{2} x^{2} + a^{2} b d^{2}\right)} \arctan\left(c x\right)}\,{d x} + \sqrt{f} x^{\frac{3}{2}}}{2 \, {\left(a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arctan\left(c x\right)\right)}}"," ",0,"1/2*(2*(a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^2*d^2*x^2 + b^2*d^2)*arctan(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + a*b*d^2)*arctan(c*x))*sqrt(f)*integrate(1/4*(a*c^2*x^2 + 4*b*c*x + (b*c^2*x^2 + b)*arctan(c*x) + a)*sqrt(x)/(a^3*c^4*d^2*x^4 + 2*a^3*c^2*d^2*x^2 + a^3*d^2 + (b^3*c^4*d^2*x^4 + 2*b^3*c^2*d^2*x^2 + b^3*d^2)*arctan(c*x)^3 + 3*(a*b^2*c^4*d^2*x^4 + 2*a*b^2*c^2*d^2*x^2 + a*b^2*d^2)*arctan(c*x)^2 + 3*(a^2*b*c^4*d^2*x^4 + 2*a^2*b*c^2*d^2*x^2 + a^2*b*d^2)*arctan(c*x)), x) + sqrt(f)*x^(3/2))/(a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^2*d^2*x^2 + b^2*d^2)*arctan(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + a*b*d^2)*arctan(c*x))","F",0
598,-1,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)/arctan(a*x)^2,x, algorithm=""maxima"")","\frac{m \mathit{sage}_{0} x \arctan\left(a x\right) - x^{m}}{a c \arctan\left(a x\right)}"," ",0,"(m*arctan(a*x)*integrate(x^m/(x*arctan(a*x)), x) - x^m)/(a*c*arctan(a*x))","F",0
602,-1,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{m}}{\arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x^m/arctan(a*x)^2, x)","F",0
605,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m}}{\arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^m/arctan(a*x)^2, x)","F",0
606,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x)^2, x)","F",0
607,0,0,0,0.000000," ","integrate(x^m/arctan(a*x)^2/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^m/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^2), x)","F",0
608,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^m/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^2), x)","F",0
609,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^2,x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{2}}\,{d x}"," ",0,"integrate(x^m/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^2), x)","F",0
610,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{5} c x^{5} + 2 \, a^{3} c x^{3} - 2 \, a^{2} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} + a c x + {\left(5 \, a^{6} c x^{6} + 11 \, a^{4} c x^{4} + 7 \, a^{2} c x^{2} + c\right)} \arctan\left(a x\right)}{2 \, a^{2} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^5*c*x^5 + 2*a^3*c*x^3 - 2*a^2*arctan(a*x)^2*integrate((15*a^4*c*x^5 + 22*a^2*c*x^3 + 7*c*x)/arctan(a*x), x) + a*c*x + (5*a^6*c*x^6 + 11*a^4*c*x^4 + 7*a^2*c*x^2 + c)*arctan(a*x))/(a^2*arctan(a*x)^2)","F",0
611,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{4} c x^{4} + 2 \, a^{2} c x^{2} - 4 \, a \arctan\left(a x\right)^{2} \int \frac{5 \, a^{4} c x^{4} + 6 \, a^{2} c x^{2} + c}{\arctan\left(a x\right)}\,{d x} + 4 \, {\left(a^{5} c x^{5} + 2 \, a^{3} c x^{3} + a c x\right)} \arctan\left(a x\right) + c}{2 \, a \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^4*c*x^4 + 2*a^2*c*x^2 - 2*a*arctan(a*x)^2*integrate(2*(5*a^4*c*x^4 + 6*a^2*c*x^2 + c)/arctan(a*x), x) + 4*(a^5*c*x^5 + 2*a^3*c*x^3 + a*c*x)*arctan(a*x) + c)/(a*arctan(a*x)^2)","F",0
612,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)/x/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{5} c x^{5} + 2 \, a^{3} c x^{3} - 2 \, \mathit{sage}_{0} x^{3} \arctan\left(a x\right)^{2} + a c x + {\left(3 \, a^{6} c x^{6} + 5 \, a^{4} c x^{4} + a^{2} c x^{2} - c\right)} \arctan\left(a x\right)}{2 \, a^{2} x^{2} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^5*c*x^5 + 2*a^3*c*x^3 - 2*x^2*arctan(a*x)^2*integrate((6*a^6*c*x^6 + 5*a^4*c*x^4 + c)/(x^3*arctan(a*x)), x) + a*c*x + (3*a^6*c*x^6 + 5*a^4*c*x^4 + a^2*c*x^2 - c)*arctan(a*x))/(a^2*x^2*arctan(a*x)^2)","F",0
613,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{7} c^{2} x^{7} + 3 \, a^{5} c^{2} x^{5} + 3 \, a^{3} c^{2} x^{3} - 4 \, a^{2} \arctan\left(a x\right)^{2} \int \frac{14 \, a^{6} c^{2} x^{7} + 33 \, a^{4} c^{2} x^{5} + 24 \, a^{2} c^{2} x^{3} + 5 \, c^{2} x}{\arctan\left(a x\right)}\,{d x} + a c^{2} x + {\left(7 \, a^{8} c^{2} x^{8} + 22 \, a^{6} c^{2} x^{6} + 24 \, a^{4} c^{2} x^{4} + 10 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}{2 \, a^{2} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^7*c^2*x^7 + 3*a^5*c^2*x^5 + 3*a^3*c^2*x^3 - 2*a^2*arctan(a*x)^2*integrate(2*(14*a^6*c^2*x^7 + 33*a^4*c^2*x^5 + 24*a^2*c^2*x^3 + 5*c^2*x)/arctan(a*x), x) + a*c^2*x + (7*a^8*c^2*x^8 + 22*a^6*c^2*x^6 + 24*a^4*c^2*x^4 + 10*a^2*c^2*x^2 + c^2)*arctan(a*x))/(a^2*arctan(a*x)^2)","F",0
614,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{6} c^{2} x^{6} + 3 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} - 6 \, a \arctan\left(a x\right)^{2} \int \frac{7 \, a^{6} c^{2} x^{6} + 15 \, a^{4} c^{2} x^{4} + 9 \, a^{2} c^{2} x^{2} + c^{2}}{\arctan\left(a x\right)}\,{d x} + c^{2} + 6 \, {\left(a^{7} c^{2} x^{7} + 3 \, a^{5} c^{2} x^{5} + 3 \, a^{3} c^{2} x^{3} + a c^{2} x\right)} \arctan\left(a x\right)}{2 \, a \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^6*c^2*x^6 + 3*a^4*c^2*x^4 + 3*a^2*c^2*x^2 - 2*a*arctan(a*x)^2*integrate(3*(7*a^6*c^2*x^6 + 15*a^4*c^2*x^4 + 9*a^2*c^2*x^2 + c^2)/arctan(a*x), x) + c^2 + 6*(a^7*c^2*x^7 + 3*a^5*c^2*x^5 + 3*a^3*c^2*x^3 + a*c^2*x)*arctan(a*x))/(a*arctan(a*x)^2)","F",0
615,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/x/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{7} c^{2} x^{7} + 3 \, a^{5} c^{2} x^{5} + 3 \, a^{3} c^{2} x^{3} - 2 \, \mathit{sage}_{0} x^{3} \arctan\left(a x\right)^{2} + a c^{2} x + {\left(5 \, a^{8} c^{2} x^{8} + 14 \, a^{6} c^{2} x^{6} + 12 \, a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} - c^{2}\right)} \arctan\left(a x\right)}{2 \, a^{2} x^{2} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^7*c^2*x^7 + 3*a^5*c^2*x^5 + 3*a^3*c^2*x^3 - 2*x^2*arctan(a*x)^2*integrate((15*a^8*c^2*x^8 + 28*a^6*c^2*x^6 + 12*a^4*c^2*x^4 + c^2)/(x^3*arctan(a*x)), x) + a*c^2*x + (5*a^8*c^2*x^8 + 14*a^6*c^2*x^6 + 12*a^4*c^2*x^4 + 2*a^2*c^2*x^2 - c^2)*arctan(a*x))/(a^2*x^2*arctan(a*x)^2)","F",0
616,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{9} c^{3} x^{9} + 4 \, a^{7} c^{3} x^{7} + 6 \, a^{5} c^{3} x^{5} + 4 \, a^{3} c^{3} x^{3} - 2 \, a^{2} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} + a c^{3} x + {\left(9 \, a^{10} c^{3} x^{10} + 37 \, a^{8} c^{3} x^{8} + 58 \, a^{6} c^{3} x^{6} + 42 \, a^{4} c^{3} x^{4} + 13 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}{2 \, a^{2} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^9*c^3*x^9 + 4*a^7*c^3*x^7 + 6*a^5*c^3*x^5 + 4*a^3*c^3*x^3 + a*c^3*x - 2*a^2*arctan(a*x)^2*integrate((45*a^8*c^3*x^9 + 148*a^6*c^3*x^7 + 174*a^4*c^3*x^5 + 84*a^2*c^3*x^3 + 13*c^3*x)/arctan(a*x), x) + (9*a^10*c^3*x^10 + 37*a^8*c^3*x^8 + 58*a^6*c^3*x^6 + 42*a^4*c^3*x^4 + 13*a^2*c^3*x^2 + c^3)*arctan(a*x))/(a^2*arctan(a*x)^2)","F",0
617,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{8} c^{3} x^{8} + 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} + 4 \, a^{2} c^{3} x^{2} - 8 \, a \arctan\left(a x\right)^{2} \int \frac{9 \, a^{8} c^{3} x^{8} + 28 \, a^{6} c^{3} x^{6} + 30 \, a^{4} c^{3} x^{4} + 12 \, a^{2} c^{3} x^{2} + c^{3}}{\arctan\left(a x\right)}\,{d x} + c^{3} + 8 \, {\left(a^{9} c^{3} x^{9} + 4 \, a^{7} c^{3} x^{7} + 6 \, a^{5} c^{3} x^{5} + 4 \, a^{3} c^{3} x^{3} + a c^{3} x\right)} \arctan\left(a x\right)}{2 \, a \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^8*c^3*x^8 + 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 + 4*a^2*c^3*x^2 - 2*a*arctan(a*x)^2*integrate(4*(9*a^8*c^3*x^8 + 28*a^6*c^3*x^6 + 30*a^4*c^3*x^4 + 12*a^2*c^3*x^2 + c^3)/arctan(a*x), x) + c^3 + 8*(a^9*c^3*x^9 + 4*a^7*c^3*x^7 + 6*a^5*c^3*x^5 + 4*a^3*c^3*x^3 + a*c^3*x)*arctan(a*x))/(a*arctan(a*x)^2)","F",0
618,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/x/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{a^{9} c^{3} x^{9} + 4 \, a^{7} c^{3} x^{7} + 6 \, a^{5} c^{3} x^{5} + 4 \, a^{3} c^{3} x^{3} - 2 \, \mathit{sage}_{0} x^{3} \arctan\left(a x\right)^{2} + a c^{3} x + {\left(7 \, a^{10} c^{3} x^{10} + 27 \, a^{8} c^{3} x^{8} + 38 \, a^{6} c^{3} x^{6} + 22 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}\right)} \arctan\left(a x\right)}{2 \, a^{2} x^{2} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a^9*c^3*x^9 + 4*a^7*c^3*x^7 + 6*a^5*c^3*x^5 + 4*a^3*c^3*x^3 + a*c^3*x - 2*x^2*arctan(a*x)^2*integrate((28*a^10*c^3*x^10 + 81*a^8*c^3*x^8 + 76*a^6*c^3*x^6 + 22*a^4*c^3*x^4 + c^3)/(x^3*arctan(a*x)), x) + (7*a^10*c^3*x^10 + 27*a^8*c^3*x^8 + 38*a^6*c^3*x^6 + 22*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)*arctan(a*x))/(a^2*x^2*arctan(a*x)^2)","F",0
619,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{a x^{3} - 6 \, \arctan\left(a x\right)^{2} \int \frac{2 \, a^{2} x^{3} + x}{\arctan\left(a x\right)}\,{d x} + 3 \, {\left(a^{2} x^{4} + x^{2}\right)} \arctan\left(a x\right)}{2 \, a^{2} c \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a*x^3 - 2*arctan(a*x)^2*integrate(3*(2*a^2*x^3 + x)/arctan(a*x), x) + 3*(a^2*x^4 + x^2)*arctan(a*x))/(a^2*c*arctan(a*x)^2)","F",0
620,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{-2 \, \mathit{sage}_{0} x \arctan\left(a x\right)^{2} + a x^{2} + 2 \, {\left(a^{2} x^{3} + x\right)} \arctan\left(a x\right)}{2 \, a^{2} c \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a*x^2 - 2*arctan(a*x)^2*integrate((3*a^2*x^2 + 1)/arctan(a*x), x) + 2*(a^2*x^3 + x)*arctan(a*x))/(a^2*c*arctan(a*x)^2)","F",0
621,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, a^{2} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} - a x - {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{2 \, a^{2} c \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*a^2*arctan(a*x)^2*integrate(x/arctan(a*x), x) - a*x - (a^2*x^2 + 1)*arctan(a*x))/(a^2*c*arctan(a*x)^2)","F",0
622,1,14,0,0.433202," ","integrate(1/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{1}{2 \, a c \arctan\left(a x\right)^{2}}"," ",0,"-1/2/(a*c*arctan(a*x)^2)","A",0
623,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, \mathit{sage}_{0} x^{3} \arctan\left(a x\right)^{2} - a x + {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{2 \, a^{2} c x^{2} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*x^2*arctan(a*x)^2*integrate(1/(x^3*arctan(a*x)), x) - a*x + (a^2*x^2 + 1)*arctan(a*x))/(a^2*c*x^2*arctan(a*x)^2)","F",0
624,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, \mathit{sage}_{0} x^{4} \arctan\left(a x\right)^{2} - a x + 2 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{2 \, a^{2} c x^{3} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*x^3*arctan(a*x)^2*integrate((a^2*x^2 + 3)/(x^4*arctan(a*x)), x) - a*x + 2*(a^2*x^2 + 1)*arctan(a*x))/(a^2*c*x^3*arctan(a*x)^2)","F",0
625,0,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{6 \, x^{4} \arctan\left(a x\right)^{2} \int \frac{a^{2} x^{2} + 2}{x^{5} \arctan\left(a x\right)}\,{d x} - a x + 3 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{2 \, a^{2} c x^{4} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*x^4*arctan(a*x)^2*integrate(3*(a^2*x^2 + 2)/(x^5*arctan(a*x)), x) - a*x + 3*(a^2*x^2 + 1)*arctan(a*x))/(a^2*c*x^4*arctan(a*x)^2)","F",0
626,0,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{4 \, x^{5} \arctan\left(a x\right)^{2} \int \frac{3 \, a^{2} x^{2} + 5}{x^{6} \arctan\left(a x\right)}\,{d x} - a x + 4 \, {\left(a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{2 \, a^{2} c x^{5} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*x^5*arctan(a*x)^2*integrate(2*(3*a^2*x^2 + 5)/(x^6*arctan(a*x)), x) - a*x + 4*(a^2*x^2 + 1)*arctan(a*x))/(a^2*c*x^5*arctan(a*x)^2)","F",0
627,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{-2 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} + a x^{3} + {\left(a^{2} x^{4} + 3 \, x^{2}\right)} \arctan\left(a x\right)}{2 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a*x^3 - 2*(a^4*c^2*x^2 + a^2*c^2)*arctan(a*x)^2*integrate((a^4*x^5 + 2*a^2*x^3 + 3*x)/((a^6*c^2*x^4 + 2*a^4*c^2*x^2 + a^2*c^2)*arctan(a*x)), x) + (a^2*x^4 + 3*x^2)*arctan(a*x))/((a^4*c^2*x^2 + a^2*c^2)*arctan(a*x)^2)","F",0
628,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} + a x^{2} + 2 \, x \arctan\left(a x\right)}{2 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(2*(a^4*c^2*x^2 + a^2*c^2)*arctan(a*x)^2*integrate((a^2*x^2 - 1)/((a^6*c^2*x^4 + 2*a^4*c^2*x^2 + a^2*c^2)*arctan(a*x)), x) + a*x^2 + 2*x*arctan(a*x))/((a^4*c^2*x^2 + a^2*c^2)*arctan(a*x)^2)","F",0
629,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \arctan\left(a x\right)^{2} \int \frac{x}{{\left(a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arctan\left(a x\right)}\,{d x} + a x - {\left(a^{2} x^{2} - 1\right)} \arctan\left(a x\right)}{2 \, {\left(a^{4} c^{2} x^{2} + a^{2} c^{2}\right)} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(8*(a^4*c^2*x^2 + a^2*c^2)*arctan(a*x)^2*integrate(1/2*x/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x) + a*x - (a^2*x^2 - 1)*arctan(a*x))/((a^4*c^2*x^2 + a^2*c^2)*arctan(a*x)^2)","F",0
630,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} + 2 \, a x \arctan\left(a x\right) - 1}{2 \, {\left(a^{3} c^{2} x^{2} + a c^{2}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^3*c^2*x^2 + a*c^2)*arctan(a*x)^2*integrate((a^2*x^2 - 1)/((a^4*c^2*x^4 + 2*a^2*c^2*x^2 + c^2)*arctan(a*x)), x) + 2*a*x*arctan(a*x) - 1)/((a^3*c^2*x^2 + a*c^2)*arctan(a*x)^2)","F",0
631,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{4} c^{2} x^{4} + a^{2} c^{2} x^{2}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} - a x + {\left(3 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{2 \, {\left(a^{4} c^{2} x^{4} + a^{2} c^{2} x^{2}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^4*c^2*x^4 + a^2*c^2*x^2)*arctan(a*x)^2*integrate((3*a^4*x^4 + 2*a^2*x^2 + 1)/((a^6*c^2*x^7 + 2*a^4*c^2*x^5 + a^2*c^2*x^3)*arctan(a*x)), x) - a*x + (3*a^2*x^2 + 1)*arctan(a*x))/((a^4*c^2*x^4 + a^2*c^2*x^2)*arctan(a*x)^2)","F",0
632,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{4} c^{2} x^{5} + a^{2} c^{2} x^{3}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} - a x + 2 \, {\left(2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{2 \, {\left(a^{4} c^{2} x^{5} + a^{2} c^{2} x^{3}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^4*c^2*x^5 + a^2*c^2*x^3)*arctan(a*x)^2*integrate((6*a^4*x^4 + 7*a^2*x^2 + 3)/((a^6*c^2*x^8 + 2*a^4*c^2*x^6 + a^2*c^2*x^4)*arctan(a*x)), x) - a*x + 2*(2*a^2*x^2 + 1)*arctan(a*x))/((a^4*c^2*x^5 + a^2*c^2*x^3)*arctan(a*x)^2)","F",0
633,0,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(a^{4} c^{2} x^{6} + a^{2} c^{2} x^{4}\right)} \arctan\left(a x\right)^{2} \int \frac{5 \, a^{4} x^{4} + 7 \, a^{2} x^{2} + 3}{{\left(a^{6} c^{2} x^{9} + 2 \, a^{4} c^{2} x^{7} + a^{2} c^{2} x^{5}\right)} \arctan\left(a x\right)}\,{d x} - a x + {\left(5 \, a^{2} x^{2} + 3\right)} \arctan\left(a x\right)}{2 \, {\left(a^{4} c^{2} x^{6} + a^{2} c^{2} x^{4}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^4*c^2*x^6 + a^2*c^2*x^4)*arctan(a*x)^2*integrate(2*(5*a^4*x^4 + 7*a^2*x^2 + 3)/((a^6*c^2*x^9 + 2*a^4*c^2*x^7 + a^2*c^2*x^5)*arctan(a*x)), x) - a*x + (5*a^2*x^2 + 3)*arctan(a*x))/((a^4*c^2*x^6 + a^2*c^2*x^4)*arctan(a*x)^2)","F",0
634,0,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{4} c^{2} x^{7} + a^{2} c^{2} x^{5}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} - a x + 2 \, {\left(3 \, a^{2} x^{2} + 2\right)} \arctan\left(a x\right)}{2 \, {\left(a^{4} c^{2} x^{7} + a^{2} c^{2} x^{5}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^4*c^2*x^7 + a^2*c^2*x^5)*arctan(a*x)^2*integrate((15*a^4*x^4 + 23*a^2*x^2 + 10)/((a^6*c^2*x^10 + 2*a^4*c^2*x^8 + a^2*c^2*x^6)*arctan(a*x)), x) - a*x + 2*(3*a^2*x^2 + 2)*arctan(a*x))/((a^4*c^2*x^7 + a^2*c^2*x^5)*arctan(a*x)^2)","F",0
635,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} + a x^{3} - {\left(a^{2} x^{4} - 3 \, x^{2}\right)} \arctan\left(a x\right)}{2 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)} \arctan\left(a x\right)^{2}}"," ",0,"-1/2*(a*x^3 + 2*(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x)^2*integrate((5*a^2*x^3 - 3*x)/((a^8*c^3*x^6 + 3*a^6*c^3*x^4 + 3*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x)), x) - (a^2*x^4 - 3*x^2)*arctan(a*x))/((a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x)^2)","F",0
636,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} - a x^{2} + 2 \, {\left(a^{2} x^{3} - x\right)} \arctan\left(a x\right)}{2 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x)^2*integrate((a^4*x^4 - 6*a^2*x^2 + 1)/((a^8*c^3*x^6 + 3*a^6*c^3*x^4 + 3*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x)), x) - a*x^2 + 2*(a^2*x^3 - x)*arctan(a*x))/((a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x)^2)","F",0
637,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} - a x + {\left(3 \, a^{2} x^{2} - 1\right)} \arctan\left(a x\right)}{2 \, {\left(a^{6} c^{3} x^{4} + 2 \, a^{4} c^{3} x^{2} + a^{2} c^{3}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x)^2*integrate((3*a^2*x^3 - 5*x)/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x) - a*x + (3*a^2*x^2 - 1)*arctan(a*x))/((a^6*c^3*x^4 + 2*a^4*c^3*x^2 + a^2*c^3)*arctan(a*x)^2)","F",0
638,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \arctan\left(a x\right)^{2} \int \frac{3 \, a^{2} x^{2} - 1}{{\left(a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} + c^{3}\right)} \arctan\left(a x\right)}\,{d x} + 4 \, a x \arctan\left(a x\right) - 1}{2 \, {\left(a^{5} c^{3} x^{4} + 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x)^2*integrate(2*(3*a^2*x^2 - 1)/((a^6*c^3*x^6 + 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 + c^3)*arctan(a*x)), x) + 4*a*x*arctan(a*x) - 1)/((a^5*c^3*x^4 + 2*a^3*c^3*x^2 + a*c^3)*arctan(a*x)^2)","F",0
639,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{6} c^{3} x^{6} + 2 \, a^{4} c^{3} x^{4} + a^{2} c^{3} x^{2}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} - a x + {\left(5 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{2 \, {\left(a^{6} c^{3} x^{6} + 2 \, a^{4} c^{3} x^{4} + a^{2} c^{3} x^{2}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^6*c^3*x^6 + 2*a^4*c^3*x^4 + a^2*c^3*x^2)*arctan(a*x)^2*integrate((10*a^4*x^4 + 3*a^2*x^2 + 1)/((a^8*c^3*x^9 + 3*a^6*c^3*x^7 + 3*a^4*c^3*x^5 + a^2*c^3*x^3)*arctan(a*x)), x) - a*x + (5*a^2*x^2 + 1)*arctan(a*x))/((a^6*c^3*x^6 + 2*a^4*c^3*x^4 + a^2*c^3*x^2)*arctan(a*x)^2)","F",0
640,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{6} c^{3} x^{7} + 2 \, a^{4} c^{3} x^{5} + a^{2} c^{3} x^{3}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} - a x + 2 \, {\left(3 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{2 \, {\left(a^{6} c^{3} x^{7} + 2 \, a^{4} c^{3} x^{5} + a^{2} c^{3} x^{3}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^6*c^3*x^7 + 2*a^4*c^3*x^5 + a^2*c^3*x^3)*arctan(a*x)^2*integrate((15*a^4*x^4 + 10*a^2*x^2 + 3)/((a^8*c^3*x^10 + 3*a^6*c^3*x^8 + 3*a^4*c^3*x^6 + a^2*c^3*x^4)*arctan(a*x)), x) - a*x + 2*(3*a^2*x^2 + 1)*arctan(a*x))/((a^6*c^3*x^7 + 2*a^4*c^3*x^5 + a^2*c^3*x^3)*arctan(a*x)^2)","F",0
641,0,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{6} c^{3} x^{8} + 2 \, a^{4} c^{3} x^{6} + a^{2} c^{3} x^{4}\right)} \mathit{sage}_{0} x \arctan\left(a x\right)^{2} - a x + {\left(7 \, a^{2} x^{2} + 3\right)} \arctan\left(a x\right)}{2 \, {\left(a^{6} c^{3} x^{8} + 2 \, a^{4} c^{3} x^{6} + a^{2} c^{3} x^{4}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^6*c^3*x^8 + 2*a^4*c^3*x^6 + a^2*c^3*x^4)*arctan(a*x)^2*integrate((21*a^4*x^4 + 19*a^2*x^2 + 6)/((a^8*c^3*x^11 + 3*a^6*c^3*x^9 + 3*a^4*c^3*x^7 + a^2*c^3*x^5)*arctan(a*x)), x) - a*x + (7*a^2*x^2 + 3)*arctan(a*x))/((a^6*c^3*x^8 + 2*a^4*c^3*x^6 + a^2*c^3*x^4)*arctan(a*x)^2)","F",0
642,0,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{4 \, {\left(a^{6} c^{3} x^{9} + 2 \, a^{4} c^{3} x^{7} + a^{2} c^{3} x^{5}\right)} \arctan\left(a x\right)^{2} \int \frac{14 \, a^{4} x^{4} + 15 \, a^{2} x^{2} + 5}{{\left(a^{8} c^{3} x^{12} + 3 \, a^{6} c^{3} x^{10} + 3 \, a^{4} c^{3} x^{8} + a^{2} c^{3} x^{6}\right)} \arctan\left(a x\right)}\,{d x} - a x + 4 \, {\left(2 \, a^{2} x^{2} + 1\right)} \arctan\left(a x\right)}{2 \, {\left(a^{6} c^{3} x^{9} + 2 \, a^{4} c^{3} x^{7} + a^{2} c^{3} x^{5}\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^6*c^3*x^9 + 2*a^4*c^3*x^7 + a^2*c^3*x^5)*arctan(a*x)^2*integrate(2*(14*a^4*x^4 + 15*a^2*x^2 + 5)/((a^8*c^3*x^12 + 3*a^6*c^3*x^10 + 3*a^4*c^3*x^8 + a^2*c^3*x^6)*arctan(a*x)), x) - a*x + 4*(2*a^2*x^2 + 1)*arctan(a*x))/((a^6*c^3*x^9 + 2*a^4*c^3*x^7 + a^2*c^3*x^5)*arctan(a*x)^2)","F",0
643,1,14,0,0.478558," ","integrate(x^3/(a^2*x^2+1)/arctan(a*x)^3-3/2*x^2/a/arctan(a*x)^2,x, algorithm=""maxima"")","-\frac{x^{3}}{2 \, a \arctan\left(a x\right)^{2}}"," ",0,"-1/2*x^3/(a*arctan(a*x)^2)","A",0
644,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} x}{\arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x/arctan(a*x)^3, x)","F",0
645,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c}}{\arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)/arctan(a*x)^3, x)","F",0
646,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c}}{x \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)/(x*arctan(a*x)^3), x)","F",0
647,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x}{\arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x/arctan(a*x)^3, x)","F",0
648,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)/arctan(a*x)^3, x)","F",0
649,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{x \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)/(x*arctan(a*x)^3), x)","F",0
650,0,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x}{\arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x/arctan(a*x)^3, x)","F",0
651,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{\arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)/arctan(a*x)^3, x)","F",0
652,0,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{x \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)/(x*arctan(a*x)^3), x)","F",0
653,0,0,0,0.000000," ","integrate(x/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3), x)","F",0
654,0,0,0,0.000000," ","integrate(1/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3), x)","F",0
655,0,0,0,0.000000," ","integrate(1/x/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} x \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*x*arctan(a*x)^3), x)","F",0
656,0,0,0,0.000000," ","integrate(1/x^2/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} x^{2} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*x^2*arctan(a*x)^3), x)","F",0
657,0,0,0,0.000000," ","integrate(1/x^3/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a^{2} c x^{2} + c} x^{3} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/(sqrt(a^2*c*x^2 + c)*x^3*arctan(a*x)^3), x)","F",0
658,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^3/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3), x)","F",0
659,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^2/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3), x)","F",0
660,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3), x)","F",0
661,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3), x)","F",0
662,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*x*arctan(a*x)^3), x)","F",0
663,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{2} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*x^2*arctan(a*x)^3), x)","F",0
664,0,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{3} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*x^3*arctan(a*x)^3), x)","F",0
665,0,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{4} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(3/2)*x^4*arctan(a*x)^3), x)","F",0
666,0,0,0,0.000000," ","integrate(x^5/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{x^{5}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^5/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3), x)","F",0
667,0,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{x^{4}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^4/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3), x)","F",0
668,0,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^3/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3), x)","F",0
669,0,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^2/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3), x)","F",0
670,0,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{x}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3), x)","F",0
671,0,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3), x)","F",0
672,0,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*x*arctan(a*x)^3), x)","F",0
673,0,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{2} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 + c)^(5/2)*x^2*arctan(a*x)^3), x)","F",0
674,-1,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
675,-1,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
676,-1,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
677,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{\mathit{sage}_{0} x^{2} \arctan\left(a x\right)^{2} - a x x^{m} - {\left(a^{2} m x^{2} + m\right)} x^{m} \arctan\left(a x\right)}{2 \, a^{2} c x \arctan\left(a x\right)^{2}}"," ",0,"1/2*(x*arctan(a*x)^2*integrate(((a^2*m^2 + a^2*m)*x^2 + m^2 - m)*x^m/(x^2*arctan(a*x)), x) - a*x*x^m - (a^2*m*x^2 + m)*x^m*arctan(a*x))/(a^2*c*x*arctan(a*x)^2)","F",0
678,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{{\left(a^{4} c^{2} x^{3} + a^{2} c^{2} x\right)} \arctan\left(a x\right)^{2} \int \frac{{\left({\left(a^{4} m^{2} - 3 \, a^{4} m + 2 \, a^{4}\right)} x^{4} + 2 \, {\left(a^{2} m^{2} - 2 \, a^{2} m - a^{2}\right)} x^{2} + m^{2} - m\right)} x^{m}}{{\left(a^{6} c^{2} x^{6} + 2 \, a^{4} c^{2} x^{4} + a^{2} c^{2} x^{2}\right)} \arctan\left(a x\right)}\,{d x} - a x x^{m} - {\left({\left(a^{2} m - 2 \, a^{2}\right)} x^{2} + m\right)} x^{m} \arctan\left(a x\right)}{2 \, {\left(a^{4} c^{2} x^{3} + a^{2} c^{2} x\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^4*c^2*x^3 + a^2*c^2*x)*arctan(a*x)^2*integrate(1/2*((a^4*m^2 - 3*a^4*m + 2*a^4)*x^4 + 2*(a^2*m^2 - 2*a^2*m - a^2)*x^2 + m^2 - m)*x^m/((a^6*c^2*x^6 + 2*a^4*c^2*x^4 + a^2*c^2*x^2)*arctan(a*x)), x) - a*x*x^m - ((a^2*m - 2*a^2)*x^2 + m)*x^m*arctan(a*x))/((a^4*c^2*x^3 + a^2*c^2*x)*arctan(a*x)^2)","F",0
679,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^3,x, algorithm=""maxima"")","\frac{{\left(a^{6} c^{3} x^{5} + 2 \, a^{4} c^{3} x^{3} + a^{2} c^{3} x\right)} \arctan\left(a x\right)^{2} \int \frac{{\left({\left(a^{4} m^{2} - 7 \, a^{4} m + 12 \, a^{4}\right)} x^{4} + 2 \, {\left(a^{2} m^{2} - 4 \, a^{2} m - 2 \, a^{2}\right)} x^{2} + m^{2} - m\right)} x^{m}}{{\left(a^{8} c^{3} x^{8} + 3 \, a^{6} c^{3} x^{6} + 3 \, a^{4} c^{3} x^{4} + a^{2} c^{3} x^{2}\right)} \arctan\left(a x\right)}\,{d x} - a x x^{m} - {\left({\left(a^{2} m - 4 \, a^{2}\right)} x^{2} + m\right)} x^{m} \arctan\left(a x\right)}{2 \, {\left(a^{6} c^{3} x^{5} + 2 \, a^{4} c^{3} x^{3} + a^{2} c^{3} x\right)} \arctan\left(a x\right)^{2}}"," ",0,"1/2*(2*(a^6*c^3*x^5 + 2*a^4*c^3*x^3 + a^2*c^3*x)*arctan(a*x)^2*integrate(1/2*((a^4*m^2 - 7*a^4*m + 12*a^4)*x^4 + 2*(a^2*m^2 - 4*a^2*m - 2*a^2)*x^2 + m^2 - m)*x^m/((a^8*c^3*x^8 + 3*a^6*c^3*x^6 + 3*a^4*c^3*x^4 + a^2*c^3*x^2)*arctan(a*x)), x) - a*x*x^m - ((a^2*m - 4*a^2)*x^2 + m)*x^m*arctan(a*x))/((a^6*c^3*x^5 + 2*a^4*c^3*x^3 + a^2*c^3*x)*arctan(a*x)^2)","F",0
680,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} x^{m}}{\arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(5/2)*x^m/arctan(a*x)^3, x)","F",0
681,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} x^{m}}{\arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate((a^2*c*x^2 + c)^(3/2)*x^m/arctan(a*x)^3, x)","F",0
682,0,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a^{2} c x^{2} + c} x^{m}}{\arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(sqrt(a^2*c*x^2 + c)*x^m/arctan(a*x)^3, x)","F",0
683,0,0,0,0.000000," ","integrate(x^m/arctan(a*x)^3/(a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{a^{2} c x^{2} + c} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^m/(sqrt(a^2*c*x^2 + c)*arctan(a*x)^3), x)","F",0
684,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^m/((a^2*c*x^2 + c)^(3/2)*arctan(a*x)^3), x)","F",0
685,0,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^3,x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arctan\left(a x\right)^{3}}\,{d x}"," ",0,"integrate(x^m/((a^2*c*x^2 + c)^(5/2)*arctan(a*x)^3), x)","F",0
686,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)*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
687,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)*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
688,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*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
689,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*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
690,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2*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
691,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2*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
692,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*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
693,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*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
694,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^3*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
695,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3*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
696,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*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
697,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*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
698,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c),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
699,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c),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
700,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c),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
701,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c),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
702,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c),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
703,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c),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
704,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c),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
705,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^3/(a^2*c*x^2+c),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
706,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^4/(a^2*c*x^2+c),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
707,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^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
708,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^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
709,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^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
710,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^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
711,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^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
712,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^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
713,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,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
714,-2,0,0,0.000000," ","integrate(x^5*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,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
715,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,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
716,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,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
717,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,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
718,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,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
719,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^3,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
720,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^3,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
721,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)*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
722,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(1/2)*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
723,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)*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
724,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)*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
725,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*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
726,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*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
727,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)*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
728,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*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
729,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)*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
730,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*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
731,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)*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
732,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*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
733,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(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
734,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(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
735,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(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
736,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(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
737,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(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
738,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(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
739,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c)^(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
740,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^3/(a^2*c*x^2+c)^(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
741,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^4/(a^2*c*x^2+c)^(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
742,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(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
743,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(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
744,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(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
745,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(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
746,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(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
747,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(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
748,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x^2/(a^2*c*x^2+c)^(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
749,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),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
750,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),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
751,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),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
752,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),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
753,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),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
754,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/(a^2*c*x^2+c)^(5/2),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
755,-2,0,0,0.000000," ","integrate(arctan(a*x)^(1/2)/x/(a^2*c*x^2+c)^(5/2),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
756,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)*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
757,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)*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
758,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)*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
759,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*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
760,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*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
761,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(3/2)/x^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
762,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2*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
763,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^2*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
764,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2*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
765,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*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
766,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*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
767,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(3/2)/x^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
768,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^3*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
769,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^3*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
770,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3*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
771,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*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
772,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*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
773,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(3/2)/x^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
774,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c),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
775,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c),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
776,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c),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
777,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c),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
778,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c),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
779,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c),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
780,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c),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
781,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^3/(a^2*c*x^2+c),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
782,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^4/(a^2*c*x^2+c),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
783,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^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
784,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^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
785,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^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
786,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^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
787,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^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
788,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^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
789,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,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
790,-2,0,0,0.000000," ","integrate(x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,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
791,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,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
792,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,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
793,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,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
794,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,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
795,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^3,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
796,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^3,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
797,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(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
798,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(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
799,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(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
800,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(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
801,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)*(a^2*c*x^2+c)^(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
802,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*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
803,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*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
804,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)*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
805,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*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
806,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*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
807,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)*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
808,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*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
809,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)*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
810,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*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
811,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*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
812,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
813,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
814,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
815,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
816,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
817,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(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
818,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(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
819,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^3/(a^2*c*x^2+c)^(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
820,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^4/(a^2*c*x^2+c)^(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
821,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
822,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
823,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
824,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
825,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
826,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(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
827,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(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
828,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),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
829,-2,0,0,0.000000," ","integrate(x^5*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),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
830,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),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
831,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),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
832,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),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
833,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),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
834,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(5/2),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
835,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x/(a^2*c*x^2+c)^(5/2),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
836,-2,0,0,0.000000," ","integrate(arctan(a*x)^(3/2)/x^2/(a^2*c*x^2+c)^(5/2),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
837,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)*arctan(a*x)^(5/2),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
838,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)*arctan(a*x)^(5/2),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
839,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)*arctan(a*x)^(5/2),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
840,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(5/2),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
841,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(5/2)/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
842,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)*arctan(a*x)^(5/2)/x^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
843,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),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
844,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),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
845,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2*arctan(a*x)^(5/2),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
846,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(5/2),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
847,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/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
848,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2*arctan(a*x)^(5/2)/x^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
849,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),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
850,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),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
851,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3*arctan(a*x)^(5/2),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
852,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(5/2),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
853,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/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
854,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3*arctan(a*x)^(5/2)/x^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
855,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c),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
856,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c),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
857,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c),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
858,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c),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
859,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c),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
860,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c),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
861,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^2/(a^2*c*x^2+c),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
862,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^3/(a^2*c*x^2+c),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
863,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^4/(a^2*c*x^2+c),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
864,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^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
865,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^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
866,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^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
867,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^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
868,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^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
869,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^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
870,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,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
871,-2,0,0,0.000000," ","integrate(x^5*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,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
872,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,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
873,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,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
874,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,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
875,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,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
876,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^3,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
877,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^3,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
878,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(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
879,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(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
880,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(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
881,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(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
882,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)*(a^2*c*x^2+c)^(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
883,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),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
884,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),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
885,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),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
886,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2),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
887,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)*arctan(a*x)^(5/2)/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
888,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),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
889,-2,0,0,0.000000," ","integrate(x^2*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),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
890,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),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
891,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2),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
892,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)*arctan(a*x)^(5/2)/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
893,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
894,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
895,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
896,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
897,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
898,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(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
899,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^2/(a^2*c*x^2+c)^(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
900,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^3/(a^2*c*x^2+c)^(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
901,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x^4/(a^2*c*x^2+c)^(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
902,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
903,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
904,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
905,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
906,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(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
907,-2,0,0,0.000000," ","integrate(x^m*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),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
908,-2,0,0,0.000000," ","integrate(x^4*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),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
909,-2,0,0,0.000000," ","integrate(x^3*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),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
910,-2,0,0,0.000000," ","integrate(x^2*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),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
911,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),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
912,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(5/2),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
913,-2,0,0,0.000000," ","integrate(arctan(a*x)^(5/2)/x/(a^2*c*x^2+c)^(5/2),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
914,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)/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
915,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)/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
916,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/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
917,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/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
918,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2/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
919,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2/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
920,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/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
921,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/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
922,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^3/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
923,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3/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
924,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/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
925,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/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
926,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)/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
927,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)/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
928,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)/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
929,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)/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
930,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^2/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
931,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^2/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
932,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^2/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
933,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^2/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
934,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/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
935,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^2/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
936,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^3/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
937,-2,0,0,0.000000," ","integrate(x^5/(a^2*c*x^2+c)^3/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
938,-2,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^3/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
939,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^3/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
940,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^3/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
941,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^3/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
942,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^3/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
943,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^3/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
944,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/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
945,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)/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
946,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/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
947,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/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
948,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/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
949,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)/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
950,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/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
951,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/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
952,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/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
953,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)/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
954,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/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
955,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/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
956,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(1/2)/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
957,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(1/2)/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
958,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(1/2)/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
959,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(1/2)/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
960,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/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
961,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/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
962,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(3/2)/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
963,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/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
964,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/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
965,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/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
966,-2,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^(5/2)/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
967,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/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
968,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/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
969,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(5/2)/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
970,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/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
971,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/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
972,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)/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
973,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)/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
974,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/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
975,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/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
976,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2/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
977,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2/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
978,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/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
979,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/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
980,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^3/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
981,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3/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
982,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/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
983,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/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
984,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)/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
985,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)/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
986,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)/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
987,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)/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
988,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^2/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
989,-2,0,0,0.000000," ","integrate(x^4/(a^2*c*x^2+c)^2/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
990,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^2/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
991,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^2/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
992,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^2/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
993,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/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
994,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^2/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
995,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^2/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
996,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^2/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
997,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^2/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
998,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^3/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
999,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^3/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
1000,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^3/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
1001,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^3/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
1002,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^3/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
1003,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^3/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
1004,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^3/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
1005,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^3/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
1006,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^3/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
1007,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/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
1008,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)/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
1009,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/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
1010,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/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
1011,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/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
1012,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)/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
1013,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/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
1014,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/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
1015,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/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
1016,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)/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
1017,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/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
1018,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/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
1019,-2,0,0,0.000000," ","integrate(x^m/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
1020,-2,0,0,0.000000," ","integrate(x/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
1021,-2,0,0,0.000000," ","integrate(1/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
1022,-2,0,0,0.000000," ","integrate(1/x/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
1023,-2,0,0,0.000000," ","integrate(1/x^2/arctan(a*x)^(3/2)/(a^2*c*x^2+c)^(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
1024,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/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
1025,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(3/2)/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
1026,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/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
1027,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(3/2)/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
1028,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/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
1029,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/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
1030,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(3/2)/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
1031,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(3/2)/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
1032,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(3/2)/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
1033,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/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
1034,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/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
1035,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/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
1036,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(5/2)/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
1037,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/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
1038,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/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
1039,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(5/2)/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
1040,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(5/2)/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
1041,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(5/2)/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
1042,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)/arctan(a*x)^(5/2),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
1043,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)/arctan(a*x)^(5/2),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
1044,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/arctan(a*x)^(5/2),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
1045,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)/x/arctan(a*x)^(5/2),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
1046,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1047,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1048,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1049,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^2/x/arctan(a*x)^(5/2),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
1050,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1051,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1052,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1053,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^3/x/arctan(a*x)^(5/2),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
1054,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)/arctan(a*x)^(5/2),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
1055,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)/arctan(a*x)^(5/2),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
1056,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)/arctan(a*x)^(5/2),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
1057,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)/arctan(a*x)^(5/2),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
1058,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1059,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1060,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1061,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1062,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1063,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1064,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1065,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1066,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^2/arctan(a*x)^(5/2),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
1067,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1068,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1069,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1070,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1071,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1072,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1073,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1074,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1075,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^3/arctan(a*x)^(5/2),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
1076,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),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
1077,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),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
1078,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/arctan(a*x)^(5/2),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
1079,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(1/2)/x/arctan(a*x)^(5/2),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
1080,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1081,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1082,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1083,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(3/2)/x/arctan(a*x)^(5/2),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
1084,-2,0,0,0.000000," ","integrate(x^m*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1085,-2,0,0,0.000000," ","integrate(x*(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1086,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1087,-2,0,0,0.000000," ","integrate((a^2*c*x^2+c)^(5/2)/x/arctan(a*x)^(5/2),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
1088,-2,0,0,0.000000," ","integrate(x^m/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
1089,-2,0,0,0.000000," ","integrate(x/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
1090,-2,0,0,0.000000," ","integrate(1/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
1091,-2,0,0,0.000000," ","integrate(1/x/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
1092,-2,0,0,0.000000," ","integrate(1/x^2/arctan(a*x)^(5/2)/(a^2*c*x^2+c)^(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
1093,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1094,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1095,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1096,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1097,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1098,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1099,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1100,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1101,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(3/2)/arctan(a*x)^(5/2),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
1102,-2,0,0,0.000000," ","integrate(x^m/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1103,-2,0,0,0.000000," ","integrate(x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1104,-2,0,0,0.000000," ","integrate(x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1105,-2,0,0,0.000000," ","integrate(x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1106,-2,0,0,0.000000," ","integrate(1/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1107,-2,0,0,0.000000," ","integrate(1/x/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1108,-2,0,0,0.000000," ","integrate(1/x^2/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1109,-2,0,0,0.000000," ","integrate(1/x^3/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1110,-2,0,0,0.000000," ","integrate(1/x^4/(a^2*c*x^2+c)^(5/2)/arctan(a*x)^(5/2),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
1111,-2,0,0,0.000000," ","integrate(x*arctan(a*x)^n/(a^2*c*x^2+c),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
1112,-2,0,0,0.000000," ","integrate(arctan(a*x)^n/(a^2*c*x^2+c),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
1113,0,0,0,0.000000," ","integrate((f*x)^m*(c^2*d*x^2+d)^q*(a+b*arctan(c*x))^p,x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} + d\right)}^{q} \left(f x\right)^{m} {\left(b \arctan\left(c x\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((c^2*d*x^2 + d)^q*(f*x)^m*(b*arctan(c*x) + a)^p, x)","F",0
1114,1,108,0,0.408592," ","integrate(x^3*(e*x^2+d)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e x^{6} + \frac{1}{4} \, a d 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 d + \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 e"," ",0,"1/6*a*e*x^6 + 1/4*a*d*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*d + 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*e","A",0
1115,1,105,0,0.313767," ","integrate(x^2*(e*x^2+d)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e x^{5} + \frac{1}{3} \, a d 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 d + \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 e"," ",0,"1/5*a*e*x^5 + 1/3*a*d*x^3 + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d + 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*e","A",0
1116,1,88,0,0.415485," ","integrate(x*(e*x^2+d)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e x^{4} + \frac{1}{2} \, a d 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 d + \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 e"," ",0,"1/4*a*e*x^4 + 1/2*a*d*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d + 1/12*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*e","A",0
1117,1,80,0,0.313557," ","integrate((e*x^2+d)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e 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 e + a d x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d}{2 \, c}"," ",0,"1/3*a*e*x^3 + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*e + a*d*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d/c","A",0
1118,1,104,0,0.619871," ","integrate((e*x^2+d)*(a+b*arctan(c*x))/x,x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + a d \log\left(x\right) - \frac{\pi b c^{2} d \log\left(c^{2} x^{2} + 1\right) - 4 \, b c^{2} d \arctan\left(c x\right) \log\left(c x\right) + 2 i \, b c^{2} d {\rm Li}_2\left(i \, c x + 1\right) - 2 i \, b c^{2} d {\rm Li}_2\left(-i \, c x + 1\right) + 2 \, b c e x - 2 \, {\left(b c^{2} e x^{2} + b e\right)} \arctan\left(c x\right)}{4 \, c^{2}}"," ",0,"1/2*a*e*x^2 + a*d*log(x) - 1/4*(pi*b*c^2*d*log(c^2*x^2 + 1) - 4*b*c^2*d*arctan(c*x)*log(c*x) + 2*I*b*c^2*d*dilog(I*c*x + 1) - 2*I*b*c^2*d*dilog(-I*c*x + 1) + 2*b*c*e*x - 2*(b*c^2*e*x^2 + b*e)*arctan(c*x))/c^2","A",0
1119,1,73,0,0.321948," ","integrate((e*x^2+d)*(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 d + a e x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b e}{2 \, c} - \frac{a d}{x}"," ",0,"-1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d + a*e*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*e/c - a*d/x","A",0
1120,0,0,0,0.000000," ","integrate((e*x^2+d)*(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 d + b e \int \frac{\arctan\left(c x\right)}{x}\,{d x} + a e \log\left(x\right) - \frac{a d}{2 \, x^{2}}"," ",0,"-1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d + b*e*integrate(arctan(c*x)/x, x) + a*e*log(x) - 1/2*a*d/x^2","F",0
1121,1,93,0,0.319470," ","integrate((e*x^2+d)*(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 d - \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 e - \frac{a e}{x} - \frac{a d}{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*d - 1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*e - a*e/x - 1/3*a*d/x^3","A",0
1122,1,80,0,0.409879," ","integrate((e*x^2+d)*(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 d - \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 e - \frac{a e}{2 \, x^{2}} - \frac{a d}{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*d - 1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*e - 1/2*a*e/x^2 - 1/4*a*d/x^4","A",0
1123,1,116,0,0.312511," ","integrate((e*x^2+d)*(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 d + \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 e - \frac{a e}{3 \, x^{3}} - \frac{a d}{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*d + 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*e - 1/3*a*e/x^3 - 1/5*a*d/x^5","A",0
1124,1,103,0,0.421638," ","integrate((e*x^2+d)*(a+b*arctan(c*x))/x^7,x, algorithm=""maxima"")","-\frac{1}{90} \, {\left({\left(15 \, c^{5} \arctan\left(c x\right) + \frac{15 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 3}{x^{5}}\right)} c + \frac{15 \, \arctan\left(c x\right)}{x^{6}}\right)} b d + \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 e - \frac{a e}{4 \, x^{4}} - \frac{a d}{6 \, x^{6}}"," ",0,"-1/90*((15*c^5*arctan(c*x) + (15*c^4*x^4 - 5*c^2*x^2 + 3)/x^5)*c + 15*arctan(c*x)/x^6)*b*d + 1/12*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*e - 1/4*a*e/x^4 - 1/6*a*d/x^6","A",0
1125,1,184,0,0.410721," ","integrate(x^3*(e*x^2+d)^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a e^{2} x^{8} + \frac{1}{3} \, a d e x^{6} + \frac{1}{4} \, a d^{2} 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 d^{2} + \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)} b d e + \frac{1}{840} \, {\left(105 \, x^{8} \arctan\left(c x\right) - c {\left(\frac{15 \, c^{6} x^{7} - 21 \, c^{4} x^{5} + 35 \, c^{2} x^{3} - 105 \, x}{c^{8}} + \frac{105 \, \arctan\left(c x\right)}{c^{9}}\right)}\right)} b e^{2}"," ",0,"1/8*a*e^2*x^8 + 1/3*a*d*e*x^6 + 1/4*a*d^2*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*d^2 + 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))*b*d*e + 1/840*(105*x^8*arctan(c*x) - c*((15*c^6*x^7 - 21*c^4*x^5 + 35*c^2*x^3 - 105*x)/c^8 + 105*arctan(c*x)/c^9))*b*e^2","A",0
1126,1,181,0,0.317727," ","integrate(x^2*(e*x^2+d)^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e^{2} x^{7} + \frac{2}{5} \, a d e x^{5} + \frac{1}{3} \, a d^{2} 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 d^{2} + \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)} b d e + \frac{1}{84} \, {\left(12 \, x^{7} \arctan\left(c x\right) - c {\left(\frac{2 \, c^{4} x^{6} - 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} - \frac{6 \, \log\left(c^{2} x^{2} + 1\right)}{c^{8}}\right)}\right)} b e^{2}"," ",0,"1/7*a*e^2*x^7 + 2/5*a*d*e*x^5 + 1/3*a*d^2*x^3 + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d^2 + 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))*b*d*e + 1/84*(12*x^7*arctan(c*x) - c*((2*c^4*x^6 - 3*c^2*x^4 + 6*x^2)/c^6 - 6*log(c^2*x^2 + 1)/c^8))*b*e^2","A",0
1127,1,156,0,0.433170," ","integrate(x*(e*x^2+d)^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e^{2} x^{6} + \frac{1}{2} \, a d e x^{4} + \frac{1}{2} \, a d^{2} 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 d^{2} + \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)} b d e + \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 e^{2}"," ",0,"1/6*a*e^2*x^6 + 1/2*a*d*e*x^4 + 1/2*a*d^2*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d^2 + 1/6*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*d*e + 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*e^2","A",0
1128,1,147,0,0.399192," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e^{2} x^{5} + \frac{2}{3} \, a d e 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)} b d e + \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 e^{2} + a d^{2} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{2}}{2 \, c}"," ",0,"1/5*a*e^2*x^5 + 2/3*a*d*e*x^3 + 1/3*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d*e + 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*e^2 + a*d^2*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^2/c","A",0
1129,1,172,0,0.638983," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, a e^{2} x^{4} + a d e x^{2} + a d^{2} \log\left(x\right) - \frac{b c^{3} e^{2} x^{3} + 3 \, \pi b c^{4} d^{2} \log\left(c^{2} x^{2} + 1\right) - 12 \, b c^{4} d^{2} \arctan\left(c x\right) \log\left(c x\right) + 6 i \, b c^{4} d^{2} {\rm Li}_2\left(i \, c x + 1\right) - 6 i \, b c^{4} d^{2} {\rm Li}_2\left(-i \, c x + 1\right) + 3 \, {\left(4 \, b c^{3} d e - b c e^{2}\right)} x - 3 \, {\left(b c^{4} e^{2} x^{4} + 4 \, b c^{4} d e x^{2} + 4 \, b c^{2} d e - b e^{2}\right)} \arctan\left(c x\right)}{12 \, c^{4}}"," ",0,"1/4*a*e^2*x^4 + a*d*e*x^2 + a*d^2*log(x) - 1/12*(b*c^3*e^2*x^3 + 3*pi*b*c^4*d^2*log(c^2*x^2 + 1) - 12*b*c^4*d^2*arctan(c*x)*log(c*x) + 6*I*b*c^4*d^2*dilog(I*c*x + 1) - 6*I*b*c^4*d^2*dilog(-I*c*x + 1) + 3*(4*b*c^3*d*e - b*c*e^2)*x - 3*(b*c^4*e^2*x^4 + 4*b*c^4*d*e*x^2 + 4*b*c^2*d*e - b*e^2)*arctan(c*x))/c^4","A",0
1130,1,130,0,0.331143," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} - \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 d^{2} + \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 e^{2} + 2 \, a d e x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d e}{c} - \frac{a d^{2}}{x}"," ",0,"1/3*a*e^2*x^3 - 1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d^2 + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*e^2 + 2*a*d*e*x + (2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d*e/c - a*d^2/x","A",0
1131,1,153,0,0.624377," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a e^{2} x^{2} - \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 d^{2} + 2 \, a d e \log\left(x\right) - \frac{a d^{2}}{2 \, x^{2}} - \frac{\pi b c^{2} d e \log\left(c^{2} x^{2} + 1\right) - 4 \, b c^{2} d e \arctan\left(c x\right) \log\left(c x\right) + 2 i \, b c^{2} d e {\rm Li}_2\left(i \, c x + 1\right) - 2 i \, b c^{2} d e {\rm Li}_2\left(-i \, c x + 1\right) + b c e^{2} x - {\left(b c^{2} e^{2} x^{2} + b e^{2}\right)} \arctan\left(c x\right)}{2 \, c^{2}}"," ",0,"1/2*a*e^2*x^2 - 1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d^2 + 2*a*d*e*log(x) - 1/2*a*d^2/x^2 - 1/2*(pi*b*c^2*d*e*log(c^2*x^2 + 1) - 4*b*c^2*d*e*arctan(c*x)*log(c*x) + 2*I*b*c^2*d*e*dilog(I*c*x + 1) - 2*I*b*c^2*d*e*dilog(-I*c*x + 1) + b*c*e^2*x - (b*c^2*e^2*x^2 + b*e^2)*arctan(c*x))/c^2","A",0
1132,1,135,0,0.318791," ","integrate((e*x^2+d)^2*(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 d^{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 d e + a e^{2} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b e^{2}}{2 \, c} - \frac{2 \, a d e}{x} - \frac{a d^{2}}{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*d^2 - (c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d*e + a*e^2*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*e^2/c - 2*a*d*e/x - 1/3*a*d^2/x^3","A",0
1133,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(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 d^{2} - {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b d e + b e^{2} \int \frac{\arctan\left(c x\right)}{x}\,{d x} + a e^{2} \log\left(x\right) - \frac{a d e}{x^{2}} - \frac{a d^{2}}{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*d^2 - ((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d*e + b*e^2*integrate(arctan(c*x)/x, x) + a*e^2*log(x) - a*d*e/x^2 - 1/4*a*d^2/x^4","F",0
1134,1,166,0,0.315333," ","integrate((e*x^2+d)^2*(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 d^{2} + \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)} b d e - \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 e^{2} - \frac{a e^{2}}{x} - \frac{2 \, a d e}{3 \, x^{3}} - \frac{a d^{2}}{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*d^2 + 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)*b*d*e - 1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*e^2 - a*e^2/x - 2/3*a*d*e/x^3 - 1/5*a*d^2/x^5","A",0
1135,1,145,0,0.415610," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^7,x, algorithm=""maxima"")","-\frac{1}{90} \, {\left({\left(15 \, c^{5} \arctan\left(c x\right) + \frac{15 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 3}{x^{5}}\right)} c + \frac{15 \, \arctan\left(c x\right)}{x^{6}}\right)} b d^{2} + \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)} b d e - \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 e^{2} - \frac{a e^{2}}{2 \, x^{2}} - \frac{a d e}{2 \, x^{4}} - \frac{a d^{2}}{6 \, x^{6}}"," ",0,"-1/90*((15*c^5*arctan(c*x) + (15*c^4*x^4 - 5*c^2*x^2 + 3)/x^5)*c + 15*arctan(c*x)/x^6)*b*d^2 + 1/6*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*d*e - 1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*e^2 - 1/2*a*e^2/x^2 - 1/2*a*d*e/x^4 - 1/6*a*d^2/x^6","A",0
1136,1,197,0,0.322232," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))/x^8,x, algorithm=""maxima"")","\frac{1}{84} \, {\left({\left(6 \, c^{6} \log\left(c^{2} x^{2} + 1\right) - 6 \, c^{6} \log\left(x^{2}\right) - \frac{6 \, c^{4} x^{4} - 3 \, c^{2} x^{2} + 2}{x^{6}}\right)} c - \frac{12 \, \arctan\left(c x\right)}{x^{7}}\right)} b d^{2} - \frac{1}{10} \, {\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 d e + \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 e^{2} - \frac{a e^{2}}{3 \, x^{3}} - \frac{2 \, a d e}{5 \, x^{5}} - \frac{a d^{2}}{7 \, x^{7}}"," ",0,"1/84*((6*c^6*log(c^2*x^2 + 1) - 6*c^6*log(x^2) - (6*c^4*x^4 - 3*c^2*x^2 + 2)/x^6)*c - 12*arctan(c*x)/x^7)*b*d^2 - 1/10*((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*d*e + 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*e^2 - 1/3*a*e^2/x^3 - 2/5*a*d*e/x^5 - 1/7*a*d^2/x^7","A",0
1137,1,268,0,0.427040," ","integrate(x^3*(e*x^2+d)^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{10} \, a e^{3} x^{10} + \frac{3}{8} \, a d e^{2} x^{8} + \frac{1}{2} \, a d^{2} e x^{6} + \frac{1}{4} \, a d^{3} 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 d^{3} + \frac{1}{30} \, {\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 d^{2} e + \frac{1}{280} \, {\left(105 \, x^{8} \arctan\left(c x\right) - c {\left(\frac{15 \, c^{6} x^{7} - 21 \, c^{4} x^{5} + 35 \, c^{2} x^{3} - 105 \, x}{c^{8}} + \frac{105 \, \arctan\left(c x\right)}{c^{9}}\right)}\right)} b d e^{2} + \frac{1}{3150} \, {\left(315 \, x^{10} \arctan\left(c x\right) - c {\left(\frac{35 \, c^{8} x^{9} - 45 \, c^{6} x^{7} + 63 \, c^{4} x^{5} - 105 \, c^{2} x^{3} + 315 \, x}{c^{10}} - \frac{315 \, \arctan\left(c x\right)}{c^{11}}\right)}\right)} b e^{3}"," ",0,"1/10*a*e^3*x^10 + 3/8*a*d*e^2*x^8 + 1/2*a*d^2*e*x^6 + 1/4*a*d^3*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*d^3 + 1/30*(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*d^2*e + 1/280*(105*x^8*arctan(c*x) - c*((15*c^6*x^7 - 21*c^4*x^5 + 35*c^2*x^3 - 105*x)/c^8 + 105*arctan(c*x)/c^9))*b*d*e^2 + 1/3150*(315*x^10*arctan(c*x) - c*((35*c^8*x^9 - 45*c^6*x^7 + 63*c^4*x^5 - 105*c^2*x^3 + 315*x)/c^10 - 315*arctan(c*x)/c^11))*b*e^3","A",0
1138,1,265,0,0.341387," ","integrate(x^2*(e*x^2+d)^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a e^{3} x^{9} + \frac{3}{7} \, a d e^{2} x^{7} + \frac{3}{5} \, a d^{2} e x^{5} + \frac{1}{3} \, a d^{3} 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 d^{3} + \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)} b d^{2} e + \frac{1}{28} \, {\left(12 \, x^{7} \arctan\left(c x\right) - c {\left(\frac{2 \, c^{4} x^{6} - 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} - \frac{6 \, \log\left(c^{2} x^{2} + 1\right)}{c^{8}}\right)}\right)} b d e^{2} + \frac{1}{216} \, {\left(24 \, x^{9} \arctan\left(c x\right) - c {\left(\frac{3 \, c^{6} x^{8} - 4 \, c^{4} x^{6} + 6 \, c^{2} x^{4} - 12 \, x^{2}}{c^{8}} + \frac{12 \, \log\left(c^{2} x^{2} + 1\right)}{c^{10}}\right)}\right)} b e^{3}"," ",0,"1/9*a*e^3*x^9 + 3/7*a*d*e^2*x^7 + 3/5*a*d^2*e*x^5 + 1/3*a*d^3*x^3 + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d^3 + 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))*b*d^2*e + 1/28*(12*x^7*arctan(c*x) - c*((2*c^4*x^6 - 3*c^2*x^4 + 6*x^2)/c^6 - 6*log(c^2*x^2 + 1)/c^8))*b*d*e^2 + 1/216*(24*x^9*arctan(c*x) - c*((3*c^6*x^8 - 4*c^4*x^6 + 6*c^2*x^4 - 12*x^2)/c^8 + 12*log(c^2*x^2 + 1)/c^10))*b*e^3","A",0
1139,1,232,0,0.429381," ","integrate(x*(e*x^2+d)^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a e^{3} x^{8} + \frac{1}{2} \, a d e^{2} x^{6} + \frac{3}{4} \, a d^{2} e x^{4} + \frac{1}{2} \, a d^{3} 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 d^{3} + \frac{1}{4} \, {\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 d^{2} e + \frac{1}{30} \, {\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 d e^{2} + \frac{1}{840} \, {\left(105 \, x^{8} \arctan\left(c x\right) - c {\left(\frac{15 \, c^{6} x^{7} - 21 \, c^{4} x^{5} + 35 \, c^{2} x^{3} - 105 \, x}{c^{8}} + \frac{105 \, \arctan\left(c x\right)}{c^{9}}\right)}\right)} b e^{3}"," ",0,"1/8*a*e^3*x^8 + 1/2*a*d*e^2*x^6 + 3/4*a*d^2*e*x^4 + 1/2*a*d^3*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d^3 + 1/4*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*d^2*e + 1/30*(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*d*e^2 + 1/840*(105*x^8*arctan(c*x) - c*((15*c^6*x^7 - 21*c^4*x^5 + 35*c^2*x^3 - 105*x)/c^8 + 105*arctan(c*x)/c^9))*b*e^3","A",0
1140,1,222,0,0.327313," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e^{3} x^{7} + \frac{3}{5} \, a d e^{2} x^{5} + a d^{2} e 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)} b d^{2} e + \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)} b d e^{2} + \frac{1}{84} \, {\left(12 \, x^{7} \arctan\left(c x\right) - c {\left(\frac{2 \, c^{4} x^{6} - 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} - \frac{6 \, \log\left(c^{2} x^{2} + 1\right)}{c^{8}}\right)}\right)} b e^{3} + a d^{3} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{3}}{2 \, c}"," ",0,"1/7*a*e^3*x^7 + 3/5*a*d*e^2*x^5 + a*d^2*e*x^3 + 1/2*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d^2*e + 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))*b*d*e^2 + 1/84*(12*x^7*arctan(c*x) - c*((2*c^4*x^6 - 3*c^2*x^4 + 6*x^2)/c^6 - 6*log(c^2*x^2 + 1)/c^8))*b*e^3 + a*d^3*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^3/c","A",0
1141,1,251,0,0.656410," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x,x, algorithm=""maxima"")","\frac{1}{6} \, a e^{3} x^{6} + \frac{3}{4} \, a d e^{2} x^{4} + \frac{3}{2} \, a d^{2} e x^{2} + a d^{3} \log\left(x\right) - \frac{6 \, b c^{5} e^{3} x^{5} + 45 \, \pi b c^{6} d^{3} \log\left(c^{2} x^{2} + 1\right) - 180 \, b c^{6} d^{3} \arctan\left(c x\right) \log\left(c x\right) + 90 i \, b c^{6} d^{3} {\rm Li}_2\left(i \, c x + 1\right) - 90 i \, b c^{6} d^{3} {\rm Li}_2\left(-i \, c x + 1\right) + 5 \, {\left(9 \, b c^{5} d e^{2} - 2 \, b c^{3} e^{3}\right)} x^{3} + 15 \, {\left(18 \, b c^{5} d^{2} e - 9 \, b c^{3} d e^{2} + 2 \, b c e^{3}\right)} x - 15 \, {\left(2 \, b c^{6} e^{3} x^{6} + 9 \, b c^{6} d e^{2} x^{4} + 18 \, b c^{6} d^{2} e x^{2} + 18 \, b c^{4} d^{2} e - 9 \, b c^{2} d e^{2} + 2 \, b e^{3}\right)} \arctan\left(c x\right)}{180 \, c^{6}}"," ",0,"1/6*a*e^3*x^6 + 3/4*a*d*e^2*x^4 + 3/2*a*d^2*e*x^2 + a*d^3*log(x) - 1/180*(6*b*c^5*e^3*x^5 + 45*pi*b*c^6*d^3*log(c^2*x^2 + 1) - 180*b*c^6*d^3*arctan(c*x)*log(c*x) + 90*I*b*c^6*d^3*dilog(I*c*x + 1) - 90*I*b*c^6*d^3*dilog(-I*c*x + 1) + 5*(9*b*c^5*d*e^2 - 2*b*c^3*e^3)*x^3 + 15*(18*b*c^5*d^2*e - 9*b*c^3*d*e^2 + 2*b*c*e^3)*x - 15*(2*b*c^6*e^3*x^6 + 9*b*c^6*d*e^2*x^4 + 18*b*c^6*d^2*e*x^2 + 18*b*c^4*d^2*e - 9*b*c^2*d*e^2 + 2*b*e^3)*arctan(c*x))/c^6","A",0
1142,1,197,0,0.328555," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{5} \, a e^{3} x^{5} + a d e^{2} x^{3} - \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 d^{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)} b d e^{2} + \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 e^{3} + 3 \, a d^{2} e x + \frac{3 \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d^{2} e}{2 \, c} - \frac{a d^{3}}{x}"," ",0,"1/5*a*e^3*x^5 + a*d*e^2*x^3 - 1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d^3 + 1/2*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d*e^2 + 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*e^3 + 3*a*d^2*e*x + 3/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d^2*e/c - a*d^3/x","A",0
1143,1,223,0,1.657894," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, a e^{3} x^{4} + \frac{3}{2} \, a d e^{2} x^{2} - \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 d^{3} + 3 \, a d^{2} e \log\left(x\right) - \frac{a d^{3}}{2 \, x^{2}} - \frac{b c^{3} e^{3} x^{3} + 9 \, \pi b c^{4} d^{2} e \log\left(c^{2} x^{2} + 1\right) - 36 \, b c^{4} d^{2} e \arctan\left(c x\right) \log\left(c x\right) + 18 i \, b c^{4} d^{2} e {\rm Li}_2\left(i \, c x + 1\right) - 18 i \, b c^{4} d^{2} e {\rm Li}_2\left(-i \, c x + 1\right) + 3 \, {\left(6 \, b c^{3} d e^{2} - b c e^{3}\right)} x - 3 \, {\left(b c^{4} e^{3} x^{4} + 6 \, b c^{4} d e^{2} x^{2} + 6 \, b c^{2} d e^{2} - b e^{3}\right)} \arctan\left(c x\right)}{12 \, c^{4}}"," ",0,"1/4*a*e^3*x^4 + 3/2*a*d*e^2*x^2 - 1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d^3 + 3*a*d^2*e*log(x) - 1/2*a*d^3/x^2 - 1/12*(b*c^3*e^3*x^3 + 9*pi*b*c^4*d^2*e*log(c^2*x^2 + 1) - 36*b*c^4*d^2*e*arctan(c*x)*log(c*x) + 18*I*b*c^4*d^2*e*dilog(I*c*x + 1) - 18*I*b*c^4*d^2*e*dilog(-I*c*x + 1) + 3*(6*b*c^3*d*e^2 - b*c*e^3)*x - 3*(b*c^4*e^3*x^4 + 6*b*c^4*d*e^2*x^2 + 6*b*c^2*d*e^2 - b*e^3)*arctan(c*x))/c^4","A",0
1144,1,193,0,0.339209," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, a e^{3} x^{3} + \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 d^{3} - \frac{3}{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 d^{2} e + \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 e^{3} + 3 \, a d e^{2} x + \frac{3 \, {\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d e^{2}}{2 \, c} - \frac{3 \, a d^{2} e}{x} - \frac{a d^{3}}{3 \, x^{3}}"," ",0,"1/3*a*e^3*x^3 + 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*d^3 - 3/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d^2*e + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*e^3 + 3*a*d*e^2*x + 3/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d*e^2/c - 3*a*d^2*e/x - 1/3*a*d^3/x^3","A",0
1145,1,218,0,0.639209," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, a e^{3} x^{2} + \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 d^{3} - \frac{3}{2} \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b d^{2} e + 3 \, a d e^{2} \log\left(x\right) - \frac{3 \, a d^{2} e}{2 \, x^{2}} - \frac{a d^{3}}{4 \, x^{4}} - \frac{3 \, \pi b c^{2} d e^{2} \log\left(c^{2} x^{2} + 1\right) - 12 \, b c^{2} d e^{2} \arctan\left(c x\right) \log\left(c x\right) + 6 i \, b c^{2} d e^{2} {\rm Li}_2\left(i \, c x + 1\right) - 6 i \, b c^{2} d e^{2} {\rm Li}_2\left(-i \, c x + 1\right) + 2 \, b c e^{3} x - 2 \, {\left(b c^{2} e^{3} x^{2} + b e^{3}\right)} \arctan\left(c x\right)}{4 \, c^{2}}"," ",0,"1/2*a*e^3*x^2 + 1/12*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*d^3 - 3/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d^2*e + 3*a*d*e^2*log(x) - 3/2*a*d^2*e/x^2 - 1/4*a*d^3/x^4 - 1/4*(3*pi*b*c^2*d*e^2*log(c^2*x^2 + 1) - 12*b*c^2*d*e^2*arctan(c*x)*log(c*x) + 6*I*b*c^2*d*e^2*dilog(I*c*x + 1) - 6*I*b*c^2*d*e^2*dilog(-I*c*x + 1) + 2*b*c*e^3*x - 2*(b*c^2*e^3*x^2 + b*e^3)*arctan(c*x))/c^2","A",0
1146,1,208,0,0.327418," ","integrate((e*x^2+d)^3*(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 d^{3} + \frac{1}{2} \, {\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 d^{2} e - \frac{3}{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 d e^{2} + a e^{3} x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b e^{3}}{2 \, c} - \frac{3 \, a d e^{2}}{x} - \frac{a d^{2} e}{x^{3}} - \frac{a d^{3}}{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*d^3 + 1/2*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b*d^2*e - 3/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d*e^2 + a*e^3*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*e^3/c - 3*a*d*e^2/x - a*d^2*e/x^3 - 1/5*a*d^3/x^5","A",0
1147,0,0,0,0.000000," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^7,x, algorithm=""maxima"")","-\frac{1}{90} \, {\left({\left(15 \, c^{5} \arctan\left(c x\right) + \frac{15 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 3}{x^{5}}\right)} c + \frac{15 \, \arctan\left(c x\right)}{x^{6}}\right)} b d^{3} + \frac{1}{4} \, {\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 d^{2} e - \frac{3}{2} \, {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} b d e^{2} + b e^{3} \int \frac{\arctan\left(c x\right)}{x}\,{d x} + a e^{3} \log\left(x\right) - \frac{3 \, a d e^{2}}{2 \, x^{2}} - \frac{3 \, a d^{2} e}{4 \, x^{4}} - \frac{a d^{3}}{6 \, x^{6}}"," ",0,"-1/90*((15*c^5*arctan(c*x) + (15*c^4*x^4 - 5*c^2*x^2 + 3)/x^5)*c + 15*arctan(c*x)/x^6)*b*d^3 + 1/4*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*d^2*e - 3/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d*e^2 + b*e^3*integrate(arctan(c*x)/x, x) + a*e^3*log(x) - 3/2*a*d*e^2/x^2 - 3/4*a*d^2*e/x^4 - 1/6*a*d^3/x^6","F",0
1148,1,247,0,0.338596," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^8,x, algorithm=""maxima"")","\frac{1}{84} \, {\left({\left(6 \, c^{6} \log\left(c^{2} x^{2} + 1\right) - 6 \, c^{6} \log\left(x^{2}\right) - \frac{6 \, c^{4} x^{4} - 3 \, c^{2} x^{2} + 2}{x^{6}}\right)} c - \frac{12 \, \arctan\left(c x\right)}{x^{7}}\right)} b d^{3} - \frac{3}{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 d^{2} e + \frac{1}{2} \, {\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 d e^{2} - \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 e^{3} - \frac{a e^{3}}{x} - \frac{a d e^{2}}{x^{3}} - \frac{3 \, a d^{2} e}{5 \, x^{5}} - \frac{a d^{3}}{7 \, x^{7}}"," ",0,"1/84*((6*c^6*log(c^2*x^2 + 1) - 6*c^6*log(x^2) - (6*c^4*x^4 - 3*c^2*x^2 + 2)/x^6)*c - 12*arctan(c*x)/x^7)*b*d^3 - 3/20*((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*d^2*e + 1/2*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c - 2*arctan(c*x)/x^3)*b*d*e^2 - 1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*e^3 - a*e^3/x - a*d*e^2/x^3 - 3/5*a*d^2*e/x^5 - 1/7*a*d^3/x^7","A",0
1149,1,218,0,0.428868," ","integrate((e*x^2+d)^3*(a+b*arctan(c*x))/x^9,x, algorithm=""maxima"")","\frac{1}{840} \, {\left({\left(105 \, c^{7} \arctan\left(c x\right) + \frac{105 \, c^{6} x^{6} - 35 \, c^{4} x^{4} + 21 \, c^{2} x^{2} - 15}{x^{7}}\right)} c - \frac{105 \, \arctan\left(c x\right)}{x^{8}}\right)} b d^{3} - \frac{1}{30} \, {\left({\left(15 \, c^{5} \arctan\left(c x\right) + \frac{15 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 3}{x^{5}}\right)} c + \frac{15 \, \arctan\left(c x\right)}{x^{6}}\right)} b d^{2} e + \frac{1}{4} \, {\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 d e^{2} - \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 e^{3} - \frac{a e^{3}}{2 \, x^{2}} - \frac{3 \, a d e^{2}}{4 \, x^{4}} - \frac{a d^{2} e}{2 \, x^{6}} - \frac{a d^{3}}{8 \, x^{8}}"," ",0,"1/840*((105*c^7*arctan(c*x) + (105*c^6*x^6 - 35*c^4*x^4 + 21*c^2*x^2 - 15)/x^7)*c - 105*arctan(c*x)/x^8)*b*d^3 - 1/30*((15*c^5*arctan(c*x) + (15*c^4*x^4 - 5*c^2*x^2 + 3)/x^5)*c + 15*arctan(c*x)/x^6)*b*d^2*e + 1/4*((3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c - 3*arctan(c*x)/x^4)*b*d*e^2 - 1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*e^3 - 1/2*a*e^3/x^2 - 3/4*a*d*e^2/x^4 - 1/2*a*d^2*e/x^6 - 1/8*a*d^3/x^8","A",0
1150,1,226,0,0.321909," ","integrate((d*x^2+c)^4*arctan(a*x),x, algorithm=""maxima"")","-\frac{1}{7560} \, a {\left(\frac{105 \, a^{6} d^{4} x^{8} + 20 \, {\left(36 \, a^{6} c d^{3} - 7 \, a^{4} d^{4}\right)} x^{6} + 6 \, {\left(378 \, a^{6} c^{2} d^{2} - 180 \, a^{4} c d^{3} + 35 \, a^{2} d^{4}\right)} x^{4} + 12 \, {\left(420 \, a^{6} c^{3} d - 378 \, a^{4} c^{2} d^{2} + 180 \, a^{2} c d^{3} - 35 \, d^{4}\right)} x^{2}}{a^{8}} + \frac{12 \, {\left(315 \, a^{8} c^{4} - 420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} - 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} \log\left(a^{2} x^{2} + 1\right)}{a^{10}}\right)} + \frac{1}{315} \, {\left(35 \, d^{4} x^{9} + 180 \, c d^{3} x^{7} + 378 \, c^{2} d^{2} x^{5} + 420 \, c^{3} d x^{3} + 315 \, c^{4} x\right)} \arctan\left(a x\right)"," ",0,"-1/7560*a*((105*a^6*d^4*x^8 + 20*(36*a^6*c*d^3 - 7*a^4*d^4)*x^6 + 6*(378*a^6*c^2*d^2 - 180*a^4*c*d^3 + 35*a^2*d^4)*x^4 + 12*(420*a^6*c^3*d - 378*a^4*c^2*d^2 + 180*a^2*c*d^3 - 35*d^4)*x^2)/a^8 + 12*(315*a^8*c^4 - 420*a^6*c^3*d + 378*a^4*c^2*d^2 - 180*a^2*c*d^3 + 35*d^4)*log(a^2*x^2 + 1)/a^10) + 1/315*(35*d^4*x^9 + 180*c*d^3*x^7 + 378*c^2*d^2*x^5 + 420*c^3*d*x^3 + 315*c^4*x)*arctan(a*x)","A",0
1151,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x^{2}}{e} - \frac{d \log\left(e x^{2} + d\right)}{e^{2}}\right)} + 2 \, b \int \frac{x^{3} \arctan\left(c x\right)}{2 \, {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"1/2*a*(x^2/e - d*log(e*x^2 + d)/e^2) + 2*b*integrate(1/2*x^3*arctan(c*x)/(e*x^2 + d), x)","F",0
1152,0,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d),x, algorithm=""maxima"")","2 \, b \int \frac{x \arctan\left(c x\right)}{2 \, {\left(e x^{2} + d\right)}}\,{d x} + \frac{a \log\left(e x^{2} + d\right)}{2 \, e}"," ",0,"2*b*integrate(1/2*x*arctan(c*x)/(e*x^2 + d), x) + 1/2*a*log(e*x^2 + d)/e","F",0
1153,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(e x^{2} + d\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{3} + d x\right)}}\,{d x}"," ",0,"-1/2*a*(log(e*x^2 + d)/d - 2*log(x)/d) + 2*b*integrate(1/2*arctan(c*x)/(e*x^3 + d*x), x)","F",0
1154,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{e \log\left(e x^{2} + d\right)}{d^{2}} - \frac{2 \, e \log\left(x\right)}{d^{2}} - \frac{1}{d x^{2}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{5} + d x^{3}\right)}}\,{d x}"," ",0,"1/2*a*(e*log(e*x^2 + d)/d^2 - 2*e*log(x)/d^2 - 1/(d*x^2)) + 2*b*integrate(1/2*arctan(c*x)/(e*x^5 + d*x^3), x)","F",0
1155,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{d \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e} - \frac{x}{e}\right)} + 2 \, b \int \frac{x^{2} \arctan\left(c x\right)}{2 \, {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"-a*(d*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e) - x/e) + 2*b*integrate(1/2*x^2*arctan(c*x)/(e*x^2 + d), x)","F",0
1156,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/(e*x^2+d),x, algorithm=""maxima"")","2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{2} + d\right)}}\,{d x} + \frac{a \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}"," ",0,"2*b*integrate(1/2*arctan(c*x)/(e*x^2 + d), x) + a*arctan(e*x/sqrt(d*e))/sqrt(d*e)","F",0
1157,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d} + \frac{1}{d x}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{4} + d x^{2}\right)}}\,{d x}"," ",0,"-a*(e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d) + 1/(d*x)) + 2*b*integrate(1/2*arctan(c*x)/(e*x^4 + d*x^2), x)","F",0
1158,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{d}{e^{3} x^{2} + d e^{2}} + \frac{\log\left(e x^{2} + d\right)}{e^{2}}\right)} + 2 \, b \int \frac{x^{3} \arctan\left(c x\right)}{2 \, {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)}}\,{d x}"," ",0,"1/2*a*(d/(e^3*x^2 + d*e^2) + log(e*x^2 + d)/e^2) + 2*b*integrate(1/2*x^3*arctan(c*x)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1159,1,90,0,0.427295," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\frac{c \arctan\left(c x\right)}{c^{2} d e - e^{2}} - \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{{\left(c^{2} d - e\right)} \sqrt{d e}}\right)} - \frac{\arctan\left(c x\right)}{e^{2} x^{2} + d e}\right)} b - \frac{a}{2 \, {\left(e^{2} x^{2} + d e\right)}}"," ",0,"1/2*(c*(c*arctan(c*x)/(c^2*d*e - e^2) - arctan(e*x/sqrt(d*e))/((c^2*d - e)*sqrt(d*e))) - arctan(c*x)/(e^2*x^2 + d*e))*b - 1/2*a/(e^2*x^2 + d*e)","A",0
1160,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{1}{d e x^{2} + d^{2}} - \frac{\log\left(e x^{2} + d\right)}{d^{2}} + \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x\right)}}\,{d x}"," ",0,"1/2*a*(1/(d*e*x^2 + d^2) - log(e*x^2 + d)/d^2 + 2*log(x)/d^2) + 2*b*integrate(1/2*arctan(c*x)/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
1161,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, e x^{2} + d}{d^{2} e x^{4} + d^{3} x^{2}} - \frac{2 \, e \log\left(e x^{2} + d\right)}{d^{3}} + \frac{4 \, e \log\left(x\right)}{d^{3}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}\right)}}\,{d x}"," ",0,"-1/2*a*((2*e*x^2 + d)/(d^2*e*x^4 + d^3*x^2) - 2*e*log(e*x^2 + d)/d^3 + 4*e*log(x)/d^3) + 2*b*integrate(1/2*arctan(c*x)/(e^2*x^7 + 2*d*e*x^5 + d^2*x^3), x)","F",0
1162,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{x}{e^{2} x^{2} + d e} - \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e}\right)} + 2 \, b \int \frac{x^{2} \arctan\left(c x\right)}{2 \, {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)}}\,{d x}"," ",0,"-1/2*a*(x/(e^2*x^2 + d*e) - arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e)) + 2*b*integrate(1/2*x^2*arctan(c*x)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1163,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x}{d e x^{2} + d^{2}} + \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)}}\,{d x}"," ",0,"1/2*a*(x/(d*e*x^2 + d^2) + arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d)) + 2*b*integrate(1/2*arctan(c*x)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1164,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{3 \, e x^{2} + 2 \, d}{d^{2} e x^{3} + d^{3} x} + \frac{3 \, e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}\right)}}\,{d x}"," ",0,"-1/2*a*((3*e*x^2 + 2*d)/(d^2*e*x^3 + d^3*x) + 3*e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2)) + 2*b*integrate(1/2*arctan(c*x)/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
1165,0,0,0,0.000000," ","integrate(x^5*(a+b*arctan(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{4 \, d e x^{2} + 3 \, d^{2}}{e^{5} x^{4} + 2 \, d e^{4} x^{2} + d^{2} e^{3}} + \frac{2 \, \log\left(e x^{2} + d\right)}{e^{3}}\right)} + 2 \, b \int \frac{x^{5} \arctan\left(c x\right)}{2 \, {\left(e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}\right)}}\,{d x}"," ",0,"1/4*a*((4*d*e*x^2 + 3*d^2)/(e^5*x^4 + 2*d*e^4*x^2 + d^2*e^3) + 2*log(e*x^2 + d)/e^3) + 2*b*integrate(1/2*x^5*arctan(c*x)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
1166,1,216,0,0.423061," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(c {\left(\frac{{\left(c^{2} d - 3 \, e\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{{\left(c^{4} d^{2} e - 2 \, c^{2} d e^{2} + e^{3}\right)} \sqrt{d e}} - \frac{x}{c^{2} d^{2} e - d e^{2} + {\left(c^{2} d e^{2} - e^{3}\right)} x^{2}} - \frac{2 \, {\left(c^{4} d - 2 \, c^{2} e\right)} \arctan\left(c x\right)}{{\left(c^{4} d^{2} e^{2} - 2 \, c^{2} d e^{3} + e^{4}\right)} c}\right)} + \frac{2 \, {\left(2 \, e x^{2} + d\right)} \arctan\left(c x\right)}{e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}}\right)} b - \frac{{\left(2 \, e x^{2} + d\right)} a}{4 \, {\left(e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}\right)}}"," ",0,"-1/8*(c*((c^2*d - 3*e)*arctan(e*x/sqrt(d*e))/((c^4*d^2*e - 2*c^2*d*e^2 + e^3)*sqrt(d*e)) - x/(c^2*d^2*e - d*e^2 + (c^2*d*e^2 - e^3)*x^2) - 2*(c^4*d - 2*c^2*e)*arctan(c*x)/((c^4*d^2*e^2 - 2*c^2*d*e^3 + e^4)*c)) + 2*(2*e*x^2 + d)*arctan(c*x)/(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2))*b - 1/4*(2*e*x^2 + d)*a/(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2)","A",0
1167,1,185,0,0.425602," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left({\left(\frac{2 \, c^{3} \arctan\left(c x\right)}{c^{4} d^{2} e - 2 \, c^{2} d e^{2} + e^{3}} - \frac{{\left(3 \, c^{2} d - e\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{{\left(c^{4} d^{3} - 2 \, c^{2} d^{2} e + d e^{2}\right)} \sqrt{d e}} - \frac{x}{c^{2} d^{3} - d^{2} e + {\left(c^{2} d^{2} e - d e^{2}\right)} x^{2}}\right)} c - \frac{2 \, \arctan\left(c x\right)}{e^{3} x^{4} + 2 \, d e^{2} x^{2} + d^{2} e}\right)} b - \frac{a}{4 \, {\left(e^{3} x^{4} + 2 \, d e^{2} x^{2} + d^{2} e\right)}}"," ",0,"1/8*((2*c^3*arctan(c*x)/(c^4*d^2*e - 2*c^2*d*e^2 + e^3) - (3*c^2*d - e)*arctan(e*x/sqrt(d*e))/((c^4*d^3 - 2*c^2*d^2*e + d*e^2)*sqrt(d*e)) - x/(c^2*d^3 - d^2*e + (c^2*d^2*e - d*e^2)*x^2))*c - 2*arctan(c*x)/(e^3*x^4 + 2*d*e^2*x^2 + d^2*e))*b - 1/4*a/(e^3*x^4 + 2*d*e^2*x^2 + d^2*e)","A",0
1168,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{2 \, e x^{2} + 3 \, d}{d^{2} e^{2} x^{4} + 2 \, d^{3} e x^{2} + d^{4}} - \frac{2 \, \log\left(e x^{2} + d\right)}{d^{3}} + \frac{4 \, \log\left(x\right)}{d^{3}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{3} x^{7} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + d^{3} x\right)}}\,{d x}"," ",0,"1/4*a*((2*e*x^2 + 3*d)/(d^2*e^2*x^4 + 2*d^3*e*x^2 + d^4) - 2*log(e*x^2 + d)/d^3 + 4*log(x)/d^3) + 2*b*integrate(1/2*arctan(c*x)/(e^3*x^7 + 3*d*e^2*x^5 + 3*d^2*e*x^3 + d^3*x), x)","F",0
1169,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{6 \, e^{2} x^{4} + 9 \, d e x^{2} + 2 \, d^{2}}{d^{3} e^{2} x^{6} + 2 \, d^{4} e x^{4} + d^{5} x^{2}} - \frac{6 \, e \log\left(e x^{2} + d\right)}{d^{4}} + \frac{12 \, e \log\left(x\right)}{d^{4}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{3} x^{9} + 3 \, d e^{2} x^{7} + 3 \, d^{2} e x^{5} + d^{3} x^{3}\right)}}\,{d x}"," ",0,"-1/4*a*((6*e^2*x^4 + 9*d*e*x^2 + 2*d^2)/(d^3*e^2*x^6 + 2*d^4*e*x^4 + d^5*x^2) - 6*e*log(e*x^2 + d)/d^4 + 12*e*log(x)/d^4) + 2*b*integrate(1/2*arctan(c*x)/(e^3*x^9 + 3*d*e^2*x^7 + 3*d^2*e*x^5 + d^3*x^3), x)","F",0
1170,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{e x^{3} - d x}{d e^{3} x^{4} + 2 \, d^{2} e^{2} x^{2} + d^{3} e} + \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d e}\right)} + 2 \, b \int \frac{x^{2} \arctan\left(c x\right)}{2 \, {\left(e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}\right)}}\,{d x}"," ",0,"1/8*a*((e*x^3 - d*x)/(d*e^3*x^4 + 2*d^2*e^2*x^2 + d^3*e) + arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d*e)) + 2*b*integrate(1/2*x^2*arctan(c*x)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
1171,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{3 \, e x^{3} + 5 \, d x}{d^{2} e^{2} x^{4} + 2 \, d^{3} e x^{2} + d^{4}} + \frac{3 \, \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}\right)}}\,{d x}"," ",0,"1/8*a*((3*e*x^3 + 5*d*x)/(d^2*e^2*x^4 + 2*d^3*e*x^2 + d^4) + 3*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2)) + 2*b*integrate(1/2*arctan(c*x)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
1172,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{15 \, e^{2} x^{4} + 25 \, d e x^{2} + 8 \, d^{2}}{d^{3} e^{2} x^{5} + 2 \, d^{4} e x^{3} + d^{5} x} + \frac{15 \, e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{3}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{3} x^{8} + 3 \, d e^{2} x^{6} + 3 \, d^{2} e x^{4} + d^{3} x^{2}\right)}}\,{d x}"," ",0,"-1/8*a*((15*e^2*x^4 + 25*d*e*x^2 + 8*d^2)/(d^3*e^2*x^5 + 2*d^4*e*x^3 + d^5*x) + 15*e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^3)) + 2*b*integrate(1/2*arctan(c*x)/(e^3*x^8 + 3*d*e^2*x^6 + 3*d^2*e*x^4 + d^3*x^2), x)","F",0
1173,0,0,0,0.000000," ","integrate(x^3*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{3 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{e} - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d}{e^{2}}\right)} a + b \int \sqrt{e x^{2} + d} x^{3} \arctan\left(c x\right)\,{d x}"," ",0,"1/15*(3*(e*x^2 + d)^(3/2)*x^2/e - 2*(e*x^2 + d)^(3/2)*d/e^2)*a + b*integrate(sqrt(e*x^2 + d)*x^3*arctan(c*x), x)","F",0
1174,-2,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1175,-2,0,0,0.000000," ","integrate(x*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
1176,-2,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1177,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x,x, algorithm=""maxima"")","-{\left(\sqrt{d} \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right) - \sqrt{e x^{2} + d}\right)} a + b \int \frac{\sqrt{e x^{2} + d} \arctan\left(c x\right)}{x}\,{d x}"," ",0,"-(sqrt(d)*arcsinh(d/(sqrt(d*e)*abs(x))) - sqrt(e*x^2 + d))*a + b*integrate(sqrt(e*x^2 + d)*arctan(c*x)/x, x)","F",0
1178,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^2,x, algorithm=""maxima"")","{\left(\sqrt{e} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right) - \frac{\sqrt{e x^{2} + d}}{x}\right)} a + b \int \frac{\sqrt{e x^{2} + d} \arctan\left(c x\right)}{x^{2}}\,{d x}"," ",0,"(sqrt(e)*arcsinh(e*x/sqrt(d*e)) - sqrt(e*x^2 + d)/x)*a + b*integrate(sqrt(e*x^2 + d)*arctan(c*x)/x^2, x)","F",0
1179,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{\sqrt{d}} - \frac{\sqrt{e x^{2} + d} e}{d} + \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}{d x^{2}}\right)} a + b \int \frac{\sqrt{e x^{2} + d} \arctan\left(c x\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(e*arcsinh(d/(sqrt(d*e)*abs(x)))/sqrt(d) - sqrt(e*x^2 + d)*e/d + (e*x^2 + d)^(3/2)/(d*x^2))*a + b*integrate(sqrt(e*x^2 + d)*arctan(c*x)/x^3, x)","F",0
1180,-2,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1181,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{e^{2} \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{\sqrt{e x^{2} + d} e^{2}}{d^{2}} + \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e}{d^{2} x^{2}} - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}}}{d x^{4}}\right)} a + b \int \frac{\sqrt{e x^{2} + d} \arctan\left(c x\right)}{x^{5}}\,{d x}"," ",0,"1/8*(e^2*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(3/2) - sqrt(e*x^2 + d)*e^2/d^2 + (e*x^2 + d)^(3/2)*e/(d^2*x^2) - 2*(e*x^2 + d)^(3/2)/(d*x^4))*a + b*integrate(sqrt(e*x^2 + d)*arctan(c*x)/x^5, x)","F",0
1182,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)*(a+b*arctan(c*x))/x^6,x, algorithm=""maxima"")","\frac{1}{15} \, a {\left(\frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} e}{d^{2} x^{3}} - \frac{3 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}}}{d x^{5}}\right)} + b \int \frac{\sqrt{e x^{2} + d} \arctan\left(c x\right)}{x^{6}}\,{d x}"," ",0,"1/15*a*(2*(e*x^2 + d)^(3/2)*e/(d^2*x^3) - 3*(e*x^2 + d)^(3/2)/(d*x^5)) + b*integrate(sqrt(e*x^2 + d)*arctan(c*x)/x^6, x)","F",0
1183,0,0,0,0.000000," ","integrate(x^3*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{35} \, {\left(\frac{5 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{e} - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} d}{e^{2}}\right)} a + \frac{1}{2} \, b \int 2 \, {\left(e x^{5} + d x^{3}\right)} \sqrt{e x^{2} + d} \arctan\left(c x\right)\,{d x}"," ",0,"1/35*(5*(e*x^2 + d)^(5/2)*x^2/e - 2*(e*x^2 + d)^(5/2)*d/e^2)*a + 1/2*b*integrate(2*(e*x^5 + d*x^3)*sqrt(e*x^2 + d)*arctan(c*x), x)","F",0
1184,-2,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1185,-2,0,0,0.000000," ","integrate(x*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
1186,-2,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1187,-2,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
1188,-2,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1189,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(3 \, \sqrt{d} e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right) - 3 \, \sqrt{e x^{2} + d} e - \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e}{d} + \frac{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}{d x^{2}}\right)} a + \frac{1}{2} \, b \int \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} \arctan\left(c x\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(3*sqrt(d)*e*arcsinh(d/(sqrt(d*e)*abs(x))) - 3*sqrt(e*x^2 + d)*e - (e*x^2 + d)^(3/2)*e/d + (e*x^2 + d)^(5/2)/(d*x^2))*a + 1/2*b*integrate(2*(e*x^2 + d)^(3/2)*arctan(c*x)/x^3, x)","F",0
1190,-2,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1191,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^5,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(\frac{3 \, e^{2} \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{\sqrt{d}} - \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{2}}{d^{2}} - \frac{3 \, \sqrt{e x^{2} + d} e^{2}}{d} + \frac{{\left(e x^{2} + d\right)}^{\frac{5}{2}} e}{d^{2} x^{2}} + \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}}}{d x^{4}}\right)} a + \frac{1}{2} \, b \int \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} \arctan\left(c x\right)}{x^{5}}\,{d x}"," ",0,"-1/8*(3*e^2*arcsinh(d/(sqrt(d*e)*abs(x)))/sqrt(d) - (e*x^2 + d)^(3/2)*e^2/d^2 - 3*sqrt(e*x^2 + d)*e^2/d + (e*x^2 + d)^(5/2)*e/(d^2*x^2) + 2*(e*x^2 + d)^(5/2)/(d*x^4))*a + 1/2*b*integrate(2*(e*x^2 + d)^(3/2)*arctan(c*x)/x^5, x)","F",0
1192,-2,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arctan(c*x))/x^6,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1193,0,0,0,0.000000," ","integrate(x^3*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{1}{63} \, {\left(\frac{7 \, {\left(e x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{e} - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{7}{2}} d}{e^{2}}\right)} a + \frac{1}{2} \, b \int 2 \, {\left(e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}\right)} \sqrt{e x^{2} + d} \arctan\left(c x\right)\,{d x}"," ",0,"1/63*(7*(e*x^2 + d)^(7/2)*x^2/e - 2*(e*x^2 + d)^(7/2)*d/e^2)*a + 1/2*b*integrate(2*(e^2*x^7 + 2*d*e*x^5 + d^2*x^3)*sqrt(e*x^2 + d)*arctan(c*x), x)","F",0
1194,-2,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1195,-2,0,0,0.000000," ","integrate(x*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
1196,-2,0,0,0.000000," ","integrate((e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1197,-2,0,0,0.000000," ","integrate((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
1198,-2,0,0,0.000000," ","integrate((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1199,-2,0,0,0.000000," ","integrate((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
1200,-2,0,0,0.000000," ","integrate((e*x^2+d)^(5/2)*(a+b*arctan(c*x))/x^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1201,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{\sqrt{e x^{2} + d} x^{2}}{e} - \frac{2 \, \sqrt{e x^{2} + d} d}{e^{2}}\right)} a + b \int \frac{x^{3} \arctan\left(c x\right)}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/3*(sqrt(e*x^2 + d)*x^2/e - 2*sqrt(e*x^2 + d)*d/e^2)*a + b*integrate(x^3*arctan(c*x)/sqrt(e*x^2 + d), x)","F",0
1202,-2,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1203,-2,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
1204,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x\right)}{\sqrt{e x^{2} + d}}\,{d x} + \frac{a \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}"," ",0,"b*integrate(arctan(c*x)/sqrt(e*x^2 + d), x) + a*arcsinh(e*x/sqrt(d*e))/sqrt(e)","F",0
1205,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x\right)}{\sqrt{e x^{2} + d} x}\,{d x} - \frac{a \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{\sqrt{d}}"," ",0,"b*integrate(arctan(c*x)/(sqrt(e*x^2 + d)*x), x) - a*arcsinh(d/(sqrt(d*e)*abs(x)))/sqrt(d)","F",0
1206,-2,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1207,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{\sqrt{e x^{2} + d}}{d x^{2}}\right)} + b \int \frac{\arctan\left(c x\right)}{\sqrt{e x^{2} + d} x^{3}}\,{d x}"," ",0,"1/2*a*(e*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(3/2) - sqrt(e*x^2 + d)/(d*x^2)) + b*integrate(arctan(c*x)/(sqrt(e*x^2 + d)*x^3), x)","F",0
1208,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^4/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{d^{2} x} - \frac{\sqrt{e x^{2} + d}}{d x^{3}}\right)} + b \int \frac{\arctan\left(c x\right)}{\sqrt{e x^{2} + d} x^{4}}\,{d x}"," ",0,"1/3*a*(2*sqrt(e*x^2 + d)*e/(d^2*x) - sqrt(e*x^2 + d)/(d*x^3)) + b*integrate(arctan(c*x)/(sqrt(e*x^2 + d)*x^4), x)","F",0
1209,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","a {\left(\frac{x^{2}}{\sqrt{e x^{2} + d} e} + \frac{2 \, d}{\sqrt{e x^{2} + d} e^{2}}\right)} + 2 \, b \int \frac{x^{3} \arctan\left(c x\right)}{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a*(x^2/(sqrt(e*x^2 + d)*e) + 2*d/(sqrt(e*x^2 + d)*e^2)) + 2*b*integrate(1/2*x^3*arctan(c*x)/(e*x^2 + d)^(3/2), x)","F",0
1210,-2,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1211,-2,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive, negative or zero?","F(-2)",0
1212,-2,0,0,0.000000," ","integrate((a+b*arctan(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1213,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{\operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{1}{\sqrt{e x^{2} + d} d}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{3} + d x\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-a*(arcsinh(d/(sqrt(d*e)*abs(x)))/d^(3/2) - 1/(sqrt(e*x^2 + d)*d)) + 2*b*integrate(1/2*arctan(c*x)/((e*x^3 + d*x)*sqrt(e*x^2 + d)), x)","F",0
1214,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, e x}{\sqrt{e x^{2} + d} d^{2}} + \frac{1}{\sqrt{e x^{2} + d} d x}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{4} + d x^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-a*(2*e*x/(sqrt(e*x^2 + d)*d^2) + 1/(sqrt(e*x^2 + d)*d*x)) + 2*b*integrate(1/2*arctan(c*x)/((e*x^4 + d*x^2)*sqrt(e*x^2 + d)), x)","F",0
1215,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{3 \, e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3 \, e}{\sqrt{e x^{2} + d} d^{2}} - \frac{1}{\sqrt{e x^{2} + d} d x^{2}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{5} + d x^{3}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/2*a*(3*e*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(5/2) - 3*e/(sqrt(e*x^2 + d)*d^2) - 1/(sqrt(e*x^2 + d)*d*x^2)) + 2*b*integrate(1/2*arctan(c*x)/((e*x^5 + d*x^3)*sqrt(e*x^2 + d)), x)","F",0
1216,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^4/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{8 \, e^{2} x}{\sqrt{e x^{2} + d} d^{3}} + \frac{4 \, e}{\sqrt{e x^{2} + d} d^{2} x} - \frac{1}{\sqrt{e x^{2} + d} d x^{3}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e x^{6} + d x^{4}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/3*a*(8*e^2*x/(sqrt(e*x^2 + d)*d^3) + 4*e/(sqrt(e*x^2 + d)*d^2*x) - 1/(sqrt(e*x^2 + d)*d*x^3)) + 2*b*integrate(1/2*arctan(c*x)/((e*x^6 + d*x^4)*sqrt(e*x^2 + d)), x)","F",0
1217,-2,0,0,0.000000," ","integrate(x^4*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive or negative?","F(-2)",0
1218,-2,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive, negative or zero?","F(-2)",0
1219,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} - \frac{x}{\sqrt{e x^{2} + d} d e}\right)} + 2 \, b \int \frac{x^{2} \arctan\left(c x\right)}{2 \, {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-1/3*a*(x/((e*x^2 + d)^(3/2)*e) - x/(sqrt(e*x^2 + d)*d*e)) + 2*b*integrate(1/2*x^2*arctan(c*x)/((e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)), x)","F",0
1220,-2,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d positive, negative or zero?","F(-2)",0
1221,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{2 \, x}{\sqrt{e x^{2} + d} d^{2}} + \frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/3*a*(2*x/(sqrt(e*x^2 + d)*d^2) + x/((e*x^2 + d)^(3/2)*d)) + 2*b*integrate(1/2*arctan(c*x)/((e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)), x)","F",0
1222,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3}{\sqrt{e x^{2} + d} d^{2}} - \frac{1}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-1/3*a*(3*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(5/2) - 3/(sqrt(e*x^2 + d)*d^2) - 1/((e*x^2 + d)^(3/2)*d)) + 2*b*integrate(1/2*arctan(c*x)/((e^2*x^5 + 2*d*e*x^3 + d^2*x)*sqrt(e*x^2 + d)), x)","F",0
1223,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^2/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{8 \, e x}{\sqrt{e x^{2} + d} d^{3}} + \frac{4 \, e x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}} + \frac{3}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d x}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-1/3*a*(8*e*x/(sqrt(e*x^2 + d)*d^3) + 4*e*x/((e*x^2 + d)^(3/2)*d^2) + 3/((e*x^2 + d)^(3/2)*d*x)) + 2*b*integrate(1/2*arctan(c*x)/((e^2*x^6 + 2*d*e*x^4 + d^2*x^2)*sqrt(e*x^2 + d)), x)","F",0
1224,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^3/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{15 \, e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{7}{2}}} - \frac{15 \, e}{\sqrt{e x^{2} + d} d^{3}} - \frac{5 \, e}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}} - \frac{3}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d x^{2}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/6*a*(15*e*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(7/2) - 15*e/(sqrt(e*x^2 + d)*d^3) - 5*e/((e*x^2 + d)^(3/2)*d^2) - 3/((e*x^2 + d)^(3/2)*d*x^2)) + 2*b*integrate(1/2*arctan(c*x)/((e^2*x^7 + 2*d*e*x^5 + d^2*x^3)*sqrt(e*x^2 + d)), x)","F",0
1225,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))/x^4/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{16 \, e^{2} x}{\sqrt{e x^{2} + d} d^{4}} + \frac{8 \, e^{2} x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{3}} + \frac{6 \, e}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2} x} - \frac{1}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} + 2 \, b \int \frac{\arctan\left(c x\right)}{2 \, {\left(e^{2} x^{8} + 2 \, d e x^{6} + d^{2} x^{4}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/3*a*(16*e^2*x/(sqrt(e*x^2 + d)*d^4) + 8*e^2*x/((e*x^2 + d)^(3/2)*d^3) + 6*e/((e*x^2 + d)^(3/2)*d^2*x) - 1/((e*x^2 + d)^(3/2)*d*x^3)) + 2*b*integrate(1/2*arctan(c*x)/((e^2*x^8 + 2*d*e*x^6 + d^2*x^4)*sqrt(e*x^2 + d)), x)","F",0
1226,-2,0,0,0.000000," ","integrate(arctan(a*x)/(d*x^2+c)^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c positive or negative?","F(-2)",0
1227,-2,0,0,0.000000," ","integrate(arctan(a*x)/(d*x^2+c)^(9/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c positive or negative?","F(-2)",0
1228,0,0,0,0.000000," ","integrate(x^m*(e*x^2+d)^3*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{a e^{3} x^{m + 7}}{m + 7} + \frac{3 \, a d e^{2} x^{m + 5}}{m + 5} + \frac{3 \, a d^{2} e x^{m + 3}}{m + 3} + \frac{a d^{3} x^{m + 1}}{m + 1} + \frac{{\left({\left(b e^{3} m^{3} + 9 \, b e^{3} m^{2} + 23 \, b e^{3} m + 15 \, b e^{3}\right)} x^{7} + 3 \, {\left(b d e^{2} m^{3} + 11 \, b d e^{2} m^{2} + 31 \, b d e^{2} m + 21 \, b d e^{2}\right)} x^{5} + 3 \, {\left(b d^{2} e m^{3} + 13 \, b d^{2} e m^{2} + 47 \, b d^{2} e m + 35 \, b d^{2} e\right)} x^{3} + {\left(b d^{3} m^{3} + 15 \, b d^{3} m^{2} + 71 \, b d^{3} m + 105 \, b d^{3}\right)} x\right)} x^{m} \arctan\left(c x\right) - {\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} \int \frac{{\left({\left(b c e^{3} m^{3} + 9 \, b c e^{3} m^{2} + 23 \, b c e^{3} m + 15 \, b c e^{3}\right)} x^{7} + 3 \, {\left(b c d e^{2} m^{3} + 11 \, b c d e^{2} m^{2} + 31 \, b c d e^{2} m + 21 \, b c d e^{2}\right)} x^{5} + 3 \, {\left(b c d^{2} e m^{3} + 13 \, b c d^{2} e m^{2} + 47 \, b c d^{2} e m + 35 \, b c d^{2} e\right)} x^{3} + {\left(b c d^{3} m^{3} + 15 \, b c d^{3} m^{2} + 71 \, b c d^{3} m + 105 \, b c d^{3}\right)} x\right)} x^{m}}{m^{4} + 16 \, m^{3} + {\left(c^{2} m^{4} + 16 \, c^{2} m^{3} + 86 \, c^{2} m^{2} + 176 \, c^{2} m + 105 \, c^{2}\right)} x^{2} + 86 \, m^{2} + 176 \, m + 105}\,{d x}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"a*e^3*x^(m + 7)/(m + 7) + 3*a*d*e^2*x^(m + 5)/(m + 5) + 3*a*d^2*e*x^(m + 3)/(m + 3) + a*d^3*x^(m + 1)/(m + 1) + (((b*e^3*m^3 + 9*b*e^3*m^2 + 23*b*e^3*m + 15*b*e^3)*x^7 + 3*(b*d*e^2*m^3 + 11*b*d*e^2*m^2 + 31*b*d*e^2*m + 21*b*d*e^2)*x^5 + 3*(b*d^2*e*m^3 + 13*b*d^2*e*m^2 + 47*b*d^2*e*m + 35*b*d^2*e)*x^3 + (b*d^3*m^3 + 15*b*d^3*m^2 + 71*b*d^3*m + 105*b*d^3)*x)*x^m*arctan(c*x) - (m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*integrate(((b*c*e^3*m^3 + 9*b*c*e^3*m^2 + 23*b*c*e^3*m + 15*b*c*e^3)*x^7 + 3*(b*c*d*e^2*m^3 + 11*b*c*d*e^2*m^2 + 31*b*c*d*e^2*m + 21*b*c*d*e^2)*x^5 + 3*(b*c*d^2*e*m^3 + 13*b*c*d^2*e*m^2 + 47*b*c*d^2*e*m + 35*b*c*d^2*e)*x^3 + (b*c*d^3*m^3 + 15*b*c*d^3*m^2 + 71*b*c*d^3*m + 105*b*c*d^3)*x)*x^m/(m^4 + 16*m^3 + (c^2*m^4 + 16*c^2*m^3 + 86*c^2*m^2 + 176*c^2*m + 105*c^2)*x^2 + 86*m^2 + 176*m + 105), x))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","F",0
1229,0,0,0,0.000000," ","integrate(x^m*(e*x^2+d)^2*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{a e^{2} x^{m + 5}}{m + 5} + \frac{2 \, a d e x^{m + 3}}{m + 3} + \frac{a d^{2} x^{m + 1}}{m + 1} + \frac{{\left({\left(b e^{2} m^{2} + 4 \, b e^{2} m + 3 \, b e^{2}\right)} x^{5} + 2 \, {\left(b d e m^{2} + 6 \, b d e m + 5 \, b d e\right)} x^{3} + {\left(b d^{2} m^{2} + 8 \, b d^{2} m + 15 \, b d^{2}\right)} x\right)} x^{m} \arctan\left(c x\right) - {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} \int \frac{{\left({\left(b c e^{2} m^{2} + 4 \, b c e^{2} m + 3 \, b c e^{2}\right)} x^{5} + 2 \, {\left(b c d e m^{2} + 6 \, b c d e m + 5 \, b c d e\right)} x^{3} + {\left(b c d^{2} m^{2} + 8 \, b c d^{2} m + 15 \, b c d^{2}\right)} x\right)} x^{m}}{m^{3} + {\left(c^{2} m^{3} + 9 \, c^{2} m^{2} + 23 \, c^{2} m + 15 \, c^{2}\right)} x^{2} + 9 \, m^{2} + 23 \, m + 15}\,{d x}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"a*e^2*x^(m + 5)/(m + 5) + 2*a*d*e*x^(m + 3)/(m + 3) + a*d^2*x^(m + 1)/(m + 1) + (((b*e^2*m^2 + 4*b*e^2*m + 3*b*e^2)*x^5 + 2*(b*d*e*m^2 + 6*b*d*e*m + 5*b*d*e)*x^3 + (b*d^2*m^2 + 8*b*d^2*m + 15*b*d^2)*x)*x^m*arctan(c*x) - (m^3 + 9*m^2 + 23*m + 15)*integrate(((b*c*e^2*m^2 + 4*b*c*e^2*m + 3*b*c*e^2)*x^5 + 2*(b*c*d*e*m^2 + 6*b*c*d*e*m + 5*b*c*d*e)*x^3 + (b*c*d^2*m^2 + 8*b*c*d^2*m + 15*b*c*d^2)*x)*x^m/(m^3 + (c^2*m^3 + 9*c^2*m^2 + 23*c^2*m + 15*c^2)*x^2 + 9*m^2 + 23*m + 15), x))/(m^3 + 9*m^2 + 23*m + 15)","F",0
1230,0,0,0,0.000000," ","integrate(x^m*(e*x^2+d)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\frac{a e x^{m + 3}}{m + 3} + \frac{a d x^{m + 1}}{m + 1} + \frac{{\left({\left(b e m + b e\right)} x^{3} + {\left(b d m + 3 \, b d\right)} x\right)} x^{m} \arctan\left(c x\right) - {\left(m^{2} + 4 \, m + 3\right)} \int \frac{{\left({\left(b c e m + b c e\right)} x^{3} + {\left(b c d m + 3 \, b c d\right)} x\right)} x^{m}}{{\left(c^{2} m^{2} + 4 \, c^{2} m + 3 \, c^{2}\right)} x^{2} + m^{2} + 4 \, m + 3}\,{d x}}{m^{2} + 4 \, m + 3}"," ",0,"a*e*x^(m + 3)/(m + 3) + a*d*x^(m + 1)/(m + 1) + (((b*e*m + b*e)*x^3 + (b*d*m + 3*b*d)*x)*x^m*arctan(c*x) - (m^2 + 4*m + 3)*integrate(((b*c*e*m + b*c*e)*x^3 + (b*c*d*m + 3*b*c*d)*x)*x^m/((c^2*m^2 + 4*c^2*m + 3*c^2)*x^2 + m^2 + 4*m + 3), x))/(m^2 + 4*m + 3)","F",0
1231,0,0,0,0.000000," ","integrate(x^m*(a+b*arctan(c*x))/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{{\left(b \arctan\left(c x\right) + a\right)} x^{m}}{e x^{2} + d}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)*x^m/(e*x^2 + d), x)","F",0
1232,0,0,0,0.000000," ","integrate(x^m*(a+b*arctan(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \arctan\left(c x\right) + a\right)} x^{m}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)*x^m/(e*x^2 + d)^2, x)","F",0
1233,0,0,0,0.000000," ","integrate(x^m*(e*x^2+d)^(5/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)}^{\frac{5}{2}} {\left(b \arctan\left(c x\right) + a\right)} x^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)^(5/2)*(b*arctan(c*x) + a)*x^m, x)","F",0
1234,0,0,0,0.000000," ","integrate(x^m*(e*x^2+d)^(3/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arctan\left(c x\right) + a\right)} x^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arctan(c*x) + a)*x^m, x)","F",0
1235,0,0,0,0.000000," ","integrate(x^m*(e*x^2+d)^(1/2)*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int \sqrt{e x^{2} + d} {\left(b \arctan\left(c x\right) + a\right)} x^{m}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arctan(c*x) + a)*x^m, x)","F",0
1236,0,0,0,0.000000," ","integrate(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arctan\left(c x\right) + a\right)} x^{m}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)*x^m/sqrt(e*x^2 + d), x)","F",0
1237,0,0,0,0.000000," ","integrate(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arctan\left(c x\right) + a\right)} x^{m}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)*x^m/(e*x^2 + d)^(3/2), x)","F",0
1238,0,0,0,0.000000," ","integrate(x^m*(a+b*arctan(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arctan\left(c x\right) + a\right)} x^{m}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)*x^m/(e*x^2 + d)^(5/2), x)","F",0
1239,0,0,0,0.000000," ","integrate(x^m*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int {\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{m}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^m, x)","F",0
1240,0,0,0,0.000000," ","integrate(x^(-2-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int {\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 2}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 2), x)","F",0
1241,0,0,0,0.000000," ","integrate(x^(-3-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x\right) e^{\left(p \log\left(e x^{2} + d\right) - 2 \, p \log\left(x\right)\right)}}{x^{3}}\,{d x} - \frac{{\left(e x^{2} + d\right)} a e^{\left(p \log\left(e x^{2} + d\right) - 2 \, p \log\left(x\right)\right)}}{2 \, d {\left(p + 1\right)} x^{2}}"," ",0,"b*integrate(arctan(c*x)*e^(p*log(e*x^2 + d) - 2*p*log(x))/x^3, x) - 1/2*(e*x^2 + d)*a*e^(p*log(e*x^2 + d) - 2*p*log(x))/(d*(p + 1)*x^2)","F",0
1242,0,0,0,0.000000," ","integrate(x^(-4-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int {\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 4}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 4), x)","F",0
1243,0,0,0,0.000000," ","integrate(x^(-5-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x\right) e^{\left(p \log\left(e x^{2} + d\right) - 2 \, p \log\left(x\right)\right)}}{x^{5}}\,{d x} + \frac{{\left(e^{2} x^{4} - d e p x^{2} - d^{2} {\left(p + 1\right)}\right)} a e^{\left(p \log\left(e x^{2} + d\right) - 2 \, p \log\left(x\right)\right)}}{2 \, {\left(p^{2} + 3 \, p + 2\right)} d^{2} x^{4}}"," ",0,"b*integrate(arctan(c*x)*e^(p*log(e*x^2 + d) - 2*p*log(x))/x^5, x) + 1/2*(e^2*x^4 - d*e*p*x^2 - d^2*(p + 1))*a*e^(p*log(e*x^2 + d) - 2*p*log(x))/((p^2 + 3*p + 2)*d^2*x^4)","F",0
1244,0,0,0,0.000000," ","integrate(x^(-6-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int {\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 6}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 6), x)","F",0
1245,0,0,0,0.000000," ","integrate(x^(-7-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x\right) e^{\left(p \log\left(e x^{2} + d\right) - 2 \, p \log\left(x\right)\right)}}{x^{7}}\,{d x} - \frac{{\left(2 \, e^{3} x^{6} - 2 \, d e^{2} p x^{4} + {\left(p^{2} + p\right)} d^{2} e x^{2} + {\left(p^{2} + 3 \, p + 2\right)} d^{3}\right)} a e^{\left(p \log\left(e x^{2} + d\right) - 2 \, p \log\left(x\right)\right)}}{2 \, {\left(p^{3} + 6 \, p^{2} + 11 \, p + 6\right)} d^{3} x^{6}}"," ",0,"b*integrate(arctan(c*x)*e^(p*log(e*x^2 + d) - 2*p*log(x))/x^7, x) - 1/2*(2*e^3*x^6 - 2*d*e^2*p*x^4 + (p^2 + p)*d^2*e*x^2 + (p^2 + 3*p + 2)*d^3)*a*e^(p*log(e*x^2 + d) - 2*p*log(x))/((p^3 + 6*p^2 + 11*p + 6)*d^3*x^6)","F",0
1246,0,0,0,0.000000," ","integrate(x^(-8-2*p)*(e*x^2+d)^p*(a+b*arctan(c*x)),x, algorithm=""maxima"")","\int {\left(b \arctan\left(c x\right) + a\right)} {\left(e x^{2} + d\right)}^{p} x^{-2 \, p - 8}\,{d x}"," ",0,"integrate((b*arctan(c*x) + a)*(e*x^2 + d)^p*x^(-2*p - 8), x)","F",0
1247,1,306,0,0.444474," ","integrate(x^3*(e*x^2+d)*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} e x^{6} \arctan\left(c x\right)^{2} + \frac{1}{6} \, a^{2} e x^{6} + \frac{1}{4} \, b^{2} d x^{4} \arctan\left(c x\right)^{2} + \frac{1}{4} \, a^{2} d 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 d - \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} d + \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 e - \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} e"," ",0,"1/6*b^2*e*x^6*arctan(c*x)^2 + 1/6*a^2*e*x^6 + 1/4*b^2*d*x^4*arctan(c*x)^2 + 1/4*a^2*d*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*d - 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*d + 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*e - 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*e","A",0
1248,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d)*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} e x^{5} + \frac{1}{3} \, a^{2} d 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 d + \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 e + \frac{1}{60} \, {\left(3 \, b^{2} e x^{5} + 5 \, b^{2} d x^{3}\right)} \arctan\left(c x\right)^{2} - \frac{1}{240} \, {\left(3 \, b^{2} e x^{5} + 5 \, b^{2} d x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + \int \frac{180 \, {\left(b^{2} c^{2} e x^{6} + b^{2} d x^{2} + {\left(b^{2} c^{2} d + b^{2} e\right)} x^{4}\right)} \arctan\left(c x\right)^{2} + 15 \, {\left(b^{2} c^{2} e x^{6} + b^{2} d x^{2} + {\left(b^{2} c^{2} d + b^{2} e\right)} x^{4}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 8 \, {\left(3 \, b^{2} c e x^{5} + 5 \, b^{2} c d x^{3}\right)} \arctan\left(c x\right) + 4 \, {\left(3 \, b^{2} c^{2} e x^{6} + 5 \, b^{2} c^{2} d x^{4}\right)} \log\left(c^{2} x^{2} + 1\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/5*a^2*e*x^5 + 1/3*a^2*d*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*d + 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*e + 1/60*(3*b^2*e*x^5 + 5*b^2*d*x^3)*arctan(c*x)^2 - 1/240*(3*b^2*e*x^5 + 5*b^2*d*x^3)*log(c^2*x^2 + 1)^2 + integrate(1/240*(180*(b^2*c^2*e*x^6 + b^2*d*x^2 + (b^2*c^2*d + b^2*e)*x^4)*arctan(c*x)^2 + 15*(b^2*c^2*e*x^6 + b^2*d*x^2 + (b^2*c^2*d + b^2*e)*x^4)*log(c^2*x^2 + 1)^2 - 8*(3*b^2*c*e*x^5 + 5*b^2*c*d*x^3)*arctan(c*x) + 4*(3*b^2*c^2*e*x^6 + 5*b^2*c^2*d*x^4)*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
1249,1,247,0,0.436110," ","integrate(x*(e*x^2+d)*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} e x^{4} \arctan\left(c x\right)^{2} + \frac{1}{4} \, a^{2} e x^{4} + \frac{1}{2} \, b^{2} d x^{2} \arctan\left(c x\right)^{2} + \frac{1}{2} \, a^{2} d 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 d - \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} d + \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 e - \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} e"," ",0,"1/4*b^2*e*x^4*arctan(c*x)^2 + 1/4*a^2*e*x^4 + 1/2*b^2*d*x^2*arctan(c*x)^2 + 1/2*a^2*d*x^2 + (x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*d - 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*d + 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*e - 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*e","A",0
1250,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} e x^{3} + 36 \, b^{2} c^{2} e \int \frac{x^{4} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} c^{2} e \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 4 \, b^{2} c^{2} e \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 36 \, b^{2} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} c^{2} d \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c^{2} d \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{b^{2} d \arctan\left(c x\right)^{3}}{4 \, c} - 8 \, b^{2} c e \int \frac{x^{3} \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 24 \, b^{2} c d \int \frac{x \arctan\left(c x\right)}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \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 e + a^{2} d x + 36 \, b^{2} e \int \frac{x^{2} \arctan\left(c x\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} e \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 3 \, b^{2} d \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{48 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d}{c} + \frac{1}{12} \, {\left(b^{2} e x^{3} + 3 \, b^{2} d x\right)} \arctan\left(c x\right)^{2} - \frac{1}{48} \, {\left(b^{2} e x^{3} + 3 \, b^{2} d x\right)} \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"1/3*a^2*e*x^3 + 36*b^2*c^2*e*integrate(1/48*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^2*c^2*e*integrate(1/48*x^4*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 4*b^2*c^2*e*integrate(1/48*x^4*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 36*b^2*c^2*d*integrate(1/48*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^2*c^2*d*integrate(1/48*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 12*b^2*c^2*d*integrate(1/48*x^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 1/4*b^2*d*arctan(c*x)^3/c - 8*b^2*c*e*integrate(1/48*x^3*arctan(c*x)/(c^2*x^2 + 1), x) - 24*b^2*c*d*integrate(1/48*x*arctan(c*x)/(c^2*x^2 + 1), x) + 1/3*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*e + a^2*d*x + 36*b^2*e*integrate(1/48*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 3*b^2*e*integrate(1/48*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 3*b^2*d*integrate(1/48*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + (2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d/c + 1/12*(b^2*e*x^3 + 3*b^2*d*x)*arctan(c*x)^2 - 1/48*(b^2*e*x^3 + 3*b^2*d*x)*log(c^2*x^2 + 1)^2","F",0
1251,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arctan(c*x))^2/x,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} e x^{2} \arctan\left(c x\right)^{2} - \frac{1}{32} \, b^{2} e x^{2} \log\left(c^{2} x^{2} + 1\right)^{2} + 12 \, b^{2} c^{2} e \int \frac{x^{4} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + b^{2} c^{2} e \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b c^{2} e \int \frac{x^{4} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 2 \, b^{2} c^{2} e \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 12 \, b^{2} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b c^{2} d \int \frac{x^{2} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + \frac{1}{96} \, b^{2} d \log\left(c^{2} x^{2} + 1\right)^{3} + \frac{1}{2} \, a^{2} e x^{2} - 4 \, b^{2} c e \int \frac{x^{3} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 12 \, b^{2} e \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b e \int \frac{x^{2} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 12 \, b^{2} d \int \frac{\arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + b^{2} d \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b d \int \frac{\arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + \frac{b^{2} e \log\left(c^{2} x^{2} + 1\right)^{3}}{96 \, c^{2}} + a^{2} d \log\left(x\right)"," ",0,"1/8*b^2*e*x^2*arctan(c*x)^2 - 1/32*b^2*e*x^2*log(c^2*x^2 + 1)^2 + 12*b^2*c^2*e*integrate(1/16*x^4*arctan(c*x)^2/(c^2*x^3 + x), x) + b^2*c^2*e*integrate(1/16*x^4*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 32*a*b*c^2*e*integrate(1/16*x^4*arctan(c*x)/(c^2*x^3 + x), x) + 2*b^2*c^2*e*integrate(1/16*x^4*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + 12*b^2*c^2*d*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^3 + x), x) + 32*a*b*c^2*d*integrate(1/16*x^2*arctan(c*x)/(c^2*x^3 + x), x) + 1/96*b^2*d*log(c^2*x^2 + 1)^3 + 1/2*a^2*e*x^2 - 4*b^2*c*e*integrate(1/16*x^3*arctan(c*x)/(c^2*x^3 + x), x) + 12*b^2*e*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^3 + x), x) + 32*a*b*e*integrate(1/16*x^2*arctan(c*x)/(c^2*x^3 + x), x) + 12*b^2*d*integrate(1/16*arctan(c*x)^2/(c^2*x^3 + x), x) + b^2*d*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 32*a*b*d*integrate(1/16*arctan(c*x)/(c^2*x^3 + x), x) + 1/96*b^2*e*log(c^2*x^2 + 1)^3/c^2 + a^2*d*log(x)","F",0
1252,-1,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arctan(c*x))^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1253,0,0,0,0.000000," ","integrate((e*x^2+d)*(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 d + a^{2} e \log\left(x\right) - \frac{a^{2} d}{2 \, x^{2}} - \frac{12 \, b^{2} d \arctan\left(c x\right)^{2} - 3 \, b^{2} d \log\left(c^{2} x^{2} + 1\right)^{2} + {\left(3 \, {\left(c^{2} {\left(\frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{c^{2}} - \frac{2 \, {\left(2 \, \log\left(c^{2} x^{2} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c^{2} x^{2}\right)\right)}}{c^{2}}\right)} - 2 \, {\left(\log\left(c^{2} x^{2} + 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c^{2} x^{2} + 1\right)\right)} b^{2} c^{2} d + {\left(\log\left(c^{2} x^{2} + 1\right)^{3} - 3 \, \log\left(c^{2} x^{2} + 1\right)^{2} \log\left(-c^{2} x^{2}\right) - 6 \, {\rm Li}_2\left(c^{2} x^{2} + 1\right) \log\left(c^{2} x^{2} + 1\right) + 6 \, {\rm Li}_{3}(c^{2} x^{2} + 1)\right)} b^{2} c^{2} d - 72 \, b^{2} c^{2} e \int \frac{x^{4} \arctan\left(c x\right)^{2}}{c^{2} x^{5} + x^{3}}\,{d x} - 192 \, a b c^{2} e \int \frac{x^{4} \arctan\left(c x\right)}{c^{2} x^{5} + x^{3}}\,{d x} - 72 \, b^{2} c^{2} d \int \frac{x^{2} \arctan\left(c x\right)^{2}}{c^{2} x^{5} + x^{3}}\,{d x} - b^{2} e \log\left(c^{2} x^{2} + 1\right)^{3} - 12 \, {\left({\left(\arctan\left(c x\right)^{2} - \log\left(c^{2} x^{2} + 1\right) + 2 \, \log\left(x\right)\right)} c - 2 \, {\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} \arctan\left(c x\right)\right)} b^{2} c d + {\left(3 \, {\left(\log\left(c^{2} x^{2} + 1\right)^{2} \log\left(-c^{2} x^{2}\right) + 2 \, {\rm Li}_2\left(c^{2} x^{2} + 1\right) \log\left(c^{2} x^{2} + 1\right) - 2 \, {\rm Li}_{3}(c^{2} x^{2} + 1)\right)} c^{2} - 6 \, {\left(\log\left(c^{2} x^{2} + 1\right) \log\left(-c^{2} x^{2}\right) + {\rm Li}_2\left(c^{2} x^{2} + 1\right)\right)} c^{2} - \frac{c^{2} x^{2} \log\left(c^{2} x^{2} + 1\right)^{3} - 3 \, {\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{x^{2}}\right)} b^{2} d + {\left(\log\left(c^{2} x^{2} + 1\right)^{3} - 3 \, \log\left(c^{2} x^{2} + 1\right)^{2} \log\left(-c^{2} x^{2}\right) - 6 \, {\rm Li}_2\left(c^{2} x^{2} + 1\right) \log\left(c^{2} x^{2} + 1\right) + 6 \, {\rm Li}_{3}(c^{2} x^{2} + 1)\right)} b^{2} e - 72 \, b^{2} e \int \frac{x^{2} \arctan\left(c x\right)^{2}}{c^{2} x^{5} + x^{3}}\,{d x} - 192 \, a b e \int \frac{x^{2} \arctan\left(c x\right)}{c^{2} x^{5} + x^{3}}\,{d x} - 72 \, b^{2} d \int \frac{\arctan\left(c x\right)^{2}}{c^{2} x^{5} + x^{3}}\,{d x}\right)} x^{2}}{96 \, x^{2}}"," ",0,"-((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*a*b*d + a^2*e*log(x) - 1/2*a^2*d/x^2 - 1/96*(12*b^2*d*arctan(c*x)^2 - 3*b^2*d*log(c^2*x^2 + 1)^2 - (1152*b^2*c^2*e*integrate(1/16*x^4*arctan(c*x)^2/(c^2*x^5 + x^3), x) + 3072*a*b*c^2*e*integrate(1/16*x^4*arctan(c*x)/(c^2*x^5 + x^3), x) + 1152*b^2*c^2*d*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^5 + x^3), x) + 96*b^2*c^2*d*integrate(1/16*x^2*log(c^2*x^2 + 1)^2/(c^2*x^5 + x^3), x) - 192*b^2*c^2*d*integrate(1/16*x^2*log(c^2*x^2 + 1)/(c^2*x^5 + x^3), x) + b^2*e*log(c^2*x^2 + 1)^3 + 384*b^2*c*d*integrate(1/16*x*arctan(c*x)/(c^2*x^5 + x^3), x) + 1152*b^2*e*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^5 + x^3), x) + 96*b^2*e*integrate(1/16*x^2*log(c^2*x^2 + 1)^2/(c^2*x^5 + x^3), x) + 3072*a*b*e*integrate(1/16*x^2*arctan(c*x)/(c^2*x^5 + x^3), x) + 1152*b^2*d*integrate(1/16*arctan(c*x)^2/(c^2*x^5 + x^3), x) + 96*b^2*d*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^5 + x^3), x))*x^2)/x^2","F",0
1254,1,516,0,0.481336," ","integrate(x^3*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} e^{2} x^{8} \arctan\left(c x\right)^{2} + \frac{1}{8} \, a^{2} e^{2} x^{8} + \frac{1}{3} \, b^{2} d e x^{6} \arctan\left(c x\right)^{2} + \frac{1}{3} \, a^{2} d e x^{6} + \frac{1}{4} \, b^{2} d^{2} x^{4} \arctan\left(c x\right)^{2} + \frac{1}{4} \, a^{2} d^{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 d^{2} - \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} d^{2} + \frac{2}{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 d e - \frac{1}{90} \, {\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} d e + \frac{1}{420} \, {\left(105 \, x^{8} \arctan\left(c x\right) - c {\left(\frac{15 \, c^{6} x^{7} - 21 \, c^{4} x^{5} + 35 \, c^{2} x^{3} - 105 \, x}{c^{8}} + \frac{105 \, \arctan\left(c x\right)}{c^{9}}\right)}\right)} a b e^{2} - \frac{1}{840} \, {\left(2 \, c {\left(\frac{15 \, c^{6} x^{7} - 21 \, c^{4} x^{5} + 35 \, c^{2} x^{3} - 105 \, x}{c^{8}} + \frac{105 \, \arctan\left(c x\right)}{c^{9}}\right)} \arctan\left(c x\right) - \frac{5 \, c^{6} x^{6} - 18 \, c^{4} x^{4} + 71 \, c^{2} x^{2} + 105 \, \arctan\left(c x\right)^{2} - 176 \, \log\left(c^{2} x^{2} + 1\right)}{c^{8}}\right)} b^{2} e^{2}"," ",0,"1/8*b^2*e^2*x^8*arctan(c*x)^2 + 1/8*a^2*e^2*x^8 + 1/3*b^2*d*e*x^6*arctan(c*x)^2 + 1/3*a^2*d*e*x^6 + 1/4*b^2*d^2*x^4*arctan(c*x)^2 + 1/4*a^2*d^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*d^2 - 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*d^2 + 2/45*(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*d*e - 1/90*(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*d*e + 1/420*(105*x^8*arctan(c*x) - c*((15*c^6*x^7 - 21*c^4*x^5 + 35*c^2*x^3 - 105*x)/c^8 + 105*arctan(c*x)/c^9))*a*b*e^2 - 1/840*(2*c*((15*c^6*x^7 - 21*c^4*x^5 + 35*c^2*x^3 - 105*x)/c^8 + 105*arctan(c*x)/c^9)*arctan(c*x) - (5*c^6*x^6 - 18*c^4*x^4 + 71*c^2*x^2 + 105*arctan(c*x)^2 - 176*log(c^2*x^2 + 1))/c^8)*b^2*e^2","A",0
1255,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{7} \, a^{2} e^{2} x^{7} + \frac{2}{5} \, a^{2} d e x^{5} + \frac{1}{3} \, a^{2} d^{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 d^{2} + \frac{1}{5} \, {\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 d e + \frac{1}{42} \, {\left(12 \, x^{7} \arctan\left(c x\right) - c {\left(\frac{2 \, c^{4} x^{6} - 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} - \frac{6 \, \log\left(c^{2} x^{2} + 1\right)}{c^{8}}\right)}\right)} a b e^{2} + \frac{1}{420} \, {\left(15 \, b^{2} e^{2} x^{7} + 42 \, b^{2} d e x^{5} + 35 \, b^{2} d^{2} x^{3}\right)} \arctan\left(c x\right)^{2} - \frac{1}{1680} \, {\left(15 \, b^{2} e^{2} x^{7} + 42 \, b^{2} d e x^{5} + 35 \, b^{2} d^{2} x^{3}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + \int \frac{1260 \, {\left(b^{2} c^{2} e^{2} x^{8} + {\left(2 \, b^{2} c^{2} d e + b^{2} e^{2}\right)} x^{6} + b^{2} d^{2} x^{2} + {\left(b^{2} c^{2} d^{2} + 2 \, b^{2} d e\right)} x^{4}\right)} \arctan\left(c x\right)^{2} + 105 \, {\left(b^{2} c^{2} e^{2} x^{8} + {\left(2 \, b^{2} c^{2} d e + b^{2} e^{2}\right)} x^{6} + b^{2} d^{2} x^{2} + {\left(b^{2} c^{2} d^{2} + 2 \, b^{2} d e\right)} x^{4}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - 8 \, {\left(15 \, b^{2} c e^{2} x^{7} + 42 \, b^{2} c d e x^{5} + 35 \, b^{2} c d^{2} x^{3}\right)} \arctan\left(c x\right) + 4 \, {\left(15 \, b^{2} c^{2} e^{2} x^{8} + 42 \, b^{2} c^{2} d e x^{6} + 35 \, b^{2} c^{2} d^{2} x^{4}\right)} \log\left(c^{2} x^{2} + 1\right)}{1680 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/7*a^2*e^2*x^7 + 2/5*a^2*d*e*x^5 + 1/3*a^2*d^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*d^2 + 1/5*(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*d*e + 1/42*(12*x^7*arctan(c*x) - c*((2*c^4*x^6 - 3*c^2*x^4 + 6*x^2)/c^6 - 6*log(c^2*x^2 + 1)/c^8))*a*b*e^2 + 1/420*(15*b^2*e^2*x^7 + 42*b^2*d*e*x^5 + 35*b^2*d^2*x^3)*arctan(c*x)^2 - 1/1680*(15*b^2*e^2*x^7 + 42*b^2*d*e*x^5 + 35*b^2*d^2*x^3)*log(c^2*x^2 + 1)^2 + integrate(1/1680*(1260*(b^2*c^2*e^2*x^8 + (2*b^2*c^2*d*e + b^2*e^2)*x^6 + b^2*d^2*x^2 + (b^2*c^2*d^2 + 2*b^2*d*e)*x^4)*arctan(c*x)^2 + 105*(b^2*c^2*e^2*x^8 + (2*b^2*c^2*d*e + b^2*e^2)*x^6 + b^2*d^2*x^2 + (b^2*c^2*d^2 + 2*b^2*d*e)*x^4)*log(c^2*x^2 + 1)^2 - 8*(15*b^2*c*e^2*x^7 + 42*b^2*c*d*e*x^5 + 35*b^2*c*d^2*x^3)*arctan(c*x) + 4*(15*b^2*c^2*e^2*x^8 + 42*b^2*c^2*d*e*x^6 + 35*b^2*c^2*d^2*x^4)*log(c^2*x^2 + 1))/(c^2*x^2 + 1), x)","F",0
1256,1,433,0,0.480143," ","integrate(x*(e*x^2+d)^2*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} e^{2} x^{6} \arctan\left(c x\right)^{2} + \frac{1}{6} \, a^{2} e^{2} x^{6} + \frac{1}{2} \, b^{2} d e x^{4} \arctan\left(c x\right)^{2} + \frac{1}{2} \, a^{2} d e x^{4} + \frac{1}{2} \, b^{2} d^{2} x^{2} \arctan\left(c x\right)^{2} + \frac{1}{2} \, a^{2} d^{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 d^{2} - \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} d^{2} + \frac{1}{3} \, {\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 d e - \frac{1}{6} \, {\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} d e + \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 e^{2} - \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} e^{2}"," ",0,"1/6*b^2*e^2*x^6*arctan(c*x)^2 + 1/6*a^2*e^2*x^6 + 1/2*b^2*d*e*x^4*arctan(c*x)^2 + 1/2*a^2*d*e*x^4 + 1/2*b^2*d^2*x^2*arctan(c*x)^2 + 1/2*a^2*d^2*x^2 + (x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*a*b*d^2 - 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*d^2 + 1/3*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a*b*d*e - 1/6*(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*d*e + 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*e^2 - 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*e^2","A",0
1257,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} e^{2} x^{5} + \frac{2}{3} \, a^{2} d e x^{3} + 180 \, b^{2} c^{2} e^{2} \int \frac{x^{6} \arctan\left(c x\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 15 \, b^{2} c^{2} e^{2} \int \frac{x^{6} \log\left(c^{2} x^{2} + 1\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c^{2} e^{2} \int \frac{x^{6} \log\left(c^{2} x^{2} + 1\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 360 \, b^{2} c^{2} d e \int \frac{x^{4} \arctan\left(c x\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 30 \, b^{2} c^{2} d e \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 40 \, b^{2} c^{2} d e \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 180 \, b^{2} c^{2} d^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 15 \, b^{2} c^{2} d^{2} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 60 \, b^{2} c^{2} d^{2} \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{b^{2} d^{2} \arctan\left(c x\right)^{3}}{4 \, c} - 24 \, b^{2} c e^{2} \int \frac{x^{5} \arctan\left(c x\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 80 \, b^{2} c d e \int \frac{x^{3} \arctan\left(c x\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} - 120 \, b^{2} c d^{2} \int \frac{x \arctan\left(c x\right)}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{2}{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 d e + \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 e^{2} + a^{2} d^{2} x + 180 \, b^{2} e^{2} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 15 \, b^{2} e^{2} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 360 \, b^{2} d e \int \frac{x^{2} \arctan\left(c x\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 30 \, b^{2} d e \int \frac{x^{2} \log\left(c^{2} x^{2} + 1\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + 15 \, b^{2} d^{2} \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{240 \, {\left(c^{2} x^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} a b d^{2}}{c} + \frac{1}{60} \, {\left(3 \, b^{2} e^{2} x^{5} + 10 \, b^{2} d e x^{3} + 15 \, b^{2} d^{2} x\right)} \arctan\left(c x\right)^{2} - \frac{1}{240} \, {\left(3 \, b^{2} e^{2} x^{5} + 10 \, b^{2} d e x^{3} + 15 \, b^{2} d^{2} x\right)} \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"1/5*a^2*e^2*x^5 + 2/3*a^2*d*e*x^3 + 180*b^2*c^2*e^2*integrate(1/240*x^6*arctan(c*x)^2/(c^2*x^2 + 1), x) + 15*b^2*c^2*e^2*integrate(1/240*x^6*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 12*b^2*c^2*e^2*integrate(1/240*x^6*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 360*b^2*c^2*d*e*integrate(1/240*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) + 30*b^2*c^2*d*e*integrate(1/240*x^4*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 40*b^2*c^2*d*e*integrate(1/240*x^4*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 180*b^2*c^2*d^2*integrate(1/240*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 15*b^2*c^2*d^2*integrate(1/240*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 60*b^2*c^2*d^2*integrate(1/240*x^2*log(c^2*x^2 + 1)/(c^2*x^2 + 1), x) + 1/4*b^2*d^2*arctan(c*x)^3/c - 24*b^2*c*e^2*integrate(1/240*x^5*arctan(c*x)/(c^2*x^2 + 1), x) - 80*b^2*c*d*e*integrate(1/240*x^3*arctan(c*x)/(c^2*x^2 + 1), x) - 120*b^2*c*d^2*integrate(1/240*x*arctan(c*x)/(c^2*x^2 + 1), x) + 2/3*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*a*b*d*e + 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*e^2 + a^2*d^2*x + 180*b^2*e^2*integrate(1/240*x^4*arctan(c*x)^2/(c^2*x^2 + 1), x) + 15*b^2*e^2*integrate(1/240*x^4*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 360*b^2*d*e*integrate(1/240*x^2*arctan(c*x)^2/(c^2*x^2 + 1), x) + 30*b^2*d*e*integrate(1/240*x^2*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + 15*b^2*d^2*integrate(1/240*log(c^2*x^2 + 1)^2/(c^2*x^2 + 1), x) + (2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*a*b*d^2/c + 1/60*(3*b^2*e^2*x^5 + 10*b^2*d*e*x^3 + 15*b^2*d^2*x)*arctan(c*x)^2 - 1/240*(3*b^2*e^2*x^5 + 10*b^2*d*e*x^3 + 15*b^2*d^2*x)*log(c^2*x^2 + 1)^2","F",0
1258,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} e^{2} x^{4} + 12 \, b^{2} c^{2} e^{2} \int \frac{x^{6} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + b^{2} c^{2} e^{2} \int \frac{x^{6} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b c^{2} e^{2} \int \frac{x^{6} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + b^{2} c^{2} e^{2} \int \frac{x^{6} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 24 \, b^{2} c^{2} d e \int \frac{x^{4} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 2 \, b^{2} c^{2} d e \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 64 \, a b c^{2} d e \int \frac{x^{4} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 4 \, b^{2} c^{2} d e \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 12 \, b^{2} c^{2} d^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b c^{2} d^{2} \int \frac{x^{2} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + \frac{1}{96} \, b^{2} d^{2} \log\left(c^{2} x^{2} + 1\right)^{3} + a^{2} d e x^{2} - 2 \, b^{2} c e^{2} \int \frac{x^{5} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} - 8 \, b^{2} c d e \int \frac{x^{3} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 12 \, b^{2} e^{2} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + b^{2} e^{2} \int \frac{x^{4} \log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b e^{2} \int \frac{x^{4} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 24 \, b^{2} d e \int \frac{x^{2} \arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 64 \, a b d e \int \frac{x^{2} \arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 12 \, b^{2} d^{2} \int \frac{\arctan\left(c x\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + b^{2} d^{2} \int \frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + 32 \, a b d^{2} \int \frac{\arctan\left(c x\right)}{16 \, {\left(c^{2} x^{3} + x\right)}}\,{d x} + \frac{b^{2} d e \log\left(c^{2} x^{2} + 1\right)^{3}}{48 \, c^{2}} + a^{2} d^{2} \log\left(x\right) + \frac{1}{16} \, {\left(b^{2} e^{2} x^{4} + 4 \, b^{2} d e x^{2}\right)} \arctan\left(c x\right)^{2} - \frac{1}{64} \, {\left(b^{2} e^{2} x^{4} + 4 \, b^{2} d e x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2}"," ",0,"1/4*a^2*e^2*x^4 + 12*b^2*c^2*e^2*integrate(1/16*x^6*arctan(c*x)^2/(c^2*x^3 + x), x) + b^2*c^2*e^2*integrate(1/16*x^6*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 32*a*b*c^2*e^2*integrate(1/16*x^6*arctan(c*x)/(c^2*x^3 + x), x) + b^2*c^2*e^2*integrate(1/16*x^6*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + 24*b^2*c^2*d*e*integrate(1/16*x^4*arctan(c*x)^2/(c^2*x^3 + x), x) + 2*b^2*c^2*d*e*integrate(1/16*x^4*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 64*a*b*c^2*d*e*integrate(1/16*x^4*arctan(c*x)/(c^2*x^3 + x), x) + 4*b^2*c^2*d*e*integrate(1/16*x^4*log(c^2*x^2 + 1)/(c^2*x^3 + x), x) + 12*b^2*c^2*d^2*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^3 + x), x) + 32*a*b*c^2*d^2*integrate(1/16*x^2*arctan(c*x)/(c^2*x^3 + x), x) + 1/96*b^2*d^2*log(c^2*x^2 + 1)^3 + a^2*d*e*x^2 - 2*b^2*c*e^2*integrate(1/16*x^5*arctan(c*x)/(c^2*x^3 + x), x) - 8*b^2*c*d*e*integrate(1/16*x^3*arctan(c*x)/(c^2*x^3 + x), x) + 12*b^2*e^2*integrate(1/16*x^4*arctan(c*x)^2/(c^2*x^3 + x), x) + b^2*e^2*integrate(1/16*x^4*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 32*a*b*e^2*integrate(1/16*x^4*arctan(c*x)/(c^2*x^3 + x), x) + 24*b^2*d*e*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^3 + x), x) + 64*a*b*d*e*integrate(1/16*x^2*arctan(c*x)/(c^2*x^3 + x), x) + 12*b^2*d^2*integrate(1/16*arctan(c*x)^2/(c^2*x^3 + x), x) + b^2*d^2*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^3 + x), x) + 32*a*b*d^2*integrate(1/16*arctan(c*x)/(c^2*x^3 + x), x) + 1/48*b^2*d*e*log(c^2*x^2 + 1)^3/c^2 + a^2*d^2*log(x) + 1/16*(b^2*e^2*x^4 + 4*b^2*d*e*x^2)*arctan(c*x)^2 - 1/64*(b^2*e^2*x^4 + 4*b^2*d*e*x^2)*log(c^2*x^2 + 1)^2","F",0
1259,-1,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1260,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arctan(c*x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} e^{2} x^{2} - {\left({\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c + \frac{\arctan\left(c x\right)}{x^{2}}\right)} a b d^{2} + 2 \, a^{2} d e \log\left(x\right) - \frac{a^{2} d^{2}}{2 \, x^{2}} + \frac{-{\left(3 \, {\left(c^{2} {\left(\frac{\log\left(c^{2} x^{2} + 1\right)^{2}}{c^{2}} - \frac{2 \, {\left(2 \, \log\left(c^{2} x^{2} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c^{2} x^{2}\right)\right)}}{c^{2}}\right)} - 2 \, {\left(\log\left(c^{2} x^{2} + 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c^{2} x^{2} + 1\right)\right)} b^{2} c^{2} d^{2} + {\left(\log\left(c^{2} x^{2} + 1\right)^{3} - 3 \, \log\left(c^{2} x^{2} + 1\right)^{2} \log\left(-c^{2} x^{2}\right) - 6 \, {\rm Li}_2\left(c^{2} x^{2} + 1\right) \log\left(c^{2} x^{2} + 1\right) + 6 \, {\rm Li}_{3}(c^{2} x^{2} + 1)\right)} b^{2} c^{2} d^{2} - {\left(3 \, {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} - \frac{3 \, {\left(2 \, c^{2} x^{2} - \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, \log\left(c^{2} x^{2} + 1\right)\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{4}} + \frac{6 \, c^{2} x^{2} - \log\left(c^{2} x^{2} + 1\right)^{3} - 3 \, \log\left(c^{2} x^{2} + 1\right)^{2} - 6 \, \log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)} b^{2} c^{2} e^{2} - 3 \, {\left(2 \, {\left(\frac{x^{2}}{c^{2}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)} \log\left(c^{2} x^{2} + 1\right) - \frac{2 \, c^{2} x^{2} - \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, \log\left(c^{2} x^{2} + 1\right)}{c^{4}}\right)} b^{2} c^{2} e^{2} - 72 \, b^{2} c^{2} e^{2} \int \frac{x^{6} \arctan\left(c x\right)^{2}}{c^{2} x^{5} + x^{3}}\,{d x} - 192 \, a b c^{2} e^{2} \int \frac{x^{6} \arctan\left(c x\right)}{c^{2} x^{5} + x^{3}}\,{d x} - 144 \, b^{2} c^{2} d e \int \frac{x^{4} \arctan\left(c x\right)^{2}}{c^{2} x^{5} + x^{3}}\,{d x} - 384 \, a b c^{2} d e \int \frac{x^{4} \arctan\left(c x\right)}{c^{2} x^{5} + x^{3}}\,{d x} - 72 \, b^{2} c^{2} d^{2} \int \frac{x^{2} \arctan\left(c x\right)^{2}}{c^{2} x^{5} + x^{3}}\,{d x} - 2 \, b^{2} d e \log\left(c^{2} x^{2} + 1\right)^{3} - 12 \, {\left({\left(\arctan\left(c x\right)^{2} - \log\left(c^{2} x^{2} + 1\right) + 2 \, \log\left(x\right)\right)} c - 2 \, {\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} \arctan\left(c x\right)\right)} b^{2} c d^{2} + 12 \, {\left(2 \, {\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^{3}}\right)} b^{2} c e^{2} + {\left(3 \, {\left(\log\left(c^{2} x^{2} + 1\right)^{2} \log\left(-c^{2} x^{2}\right) + 2 \, {\rm Li}_2\left(c^{2} x^{2} + 1\right) \log\left(c^{2} x^{2} + 1\right) - 2 \, {\rm Li}_{3}(c^{2} x^{2} + 1)\right)} c^{2} - 6 \, {\left(\log\left(c^{2} x^{2} + 1\right) \log\left(-c^{2} x^{2}\right) + {\rm Li}_2\left(c^{2} x^{2} + 1\right)\right)} c^{2} - \frac{c^{2} x^{2} \log\left(c^{2} x^{2} + 1\right)^{3} - 3 \, {\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{x^{2}}\right)} b^{2} d^{2} + 2 \, {\left(\log\left(c^{2} x^{2} + 1\right)^{3} - 3 \, \log\left(c^{2} x^{2} + 1\right)^{2} \log\left(-c^{2} x^{2}\right) - 6 \, {\rm Li}_2\left(c^{2} x^{2} + 1\right) \log\left(c^{2} x^{2} + 1\right) + 6 \, {\rm Li}_{3}(c^{2} x^{2} + 1)\right)} b^{2} d e - 72 \, b^{2} e^{2} \int \frac{x^{4} \arctan\left(c x\right)^{2}}{c^{2} x^{5} + x^{3}}\,{d x} - 192 \, a b e^{2} \int \frac{x^{4} \arctan\left(c x\right)}{c^{2} x^{5} + x^{3}}\,{d x} - 144 \, b^{2} d e \int \frac{x^{2} \arctan\left(c x\right)^{2}}{c^{2} x^{5} + x^{3}}\,{d x} - 384 \, a b d e \int \frac{x^{2} \arctan\left(c x\right)}{c^{2} x^{5} + x^{3}}\,{d x} - 72 \, b^{2} d^{2} \int \frac{\arctan\left(c x\right)^{2}}{c^{2} x^{5} + x^{3}}\,{d x} - \frac{b^{2} e^{2} \log\left(c^{2} x^{2} + 1\right)^{3}}{c^{2}}\right)} x^{2} + 12 \, {\left(b^{2} e^{2} x^{4} - b^{2} d^{2}\right)} \arctan\left(c x\right)^{2} - 3 \, {\left(b^{2} e^{2} x^{4} - b^{2} d^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2}}{96 \, x^{2}}"," ",0,"1/2*a^2*e^2*x^2 - ((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*a*b*d^2 + 2*a^2*d*e*log(x) - 1/2*a^2*d^2/x^2 + 1/96*((1152*b^2*c^2*e^2*integrate(1/16*x^6*arctan(c*x)^2/(c^2*x^5 + x^3), x) + 96*b^2*c^2*e^2*integrate(1/16*x^6*log(c^2*x^2 + 1)^2/(c^2*x^5 + x^3), x) + 3072*a*b*c^2*e^2*integrate(1/16*x^6*arctan(c*x)/(c^2*x^5 + x^3), x) + 192*b^2*c^2*e^2*integrate(1/16*x^6*log(c^2*x^2 + 1)/(c^2*x^5 + x^3), x) + 2304*b^2*c^2*d*e*integrate(1/16*x^4*arctan(c*x)^2/(c^2*x^5 + x^3), x) + 6144*a*b*c^2*d*e*integrate(1/16*x^4*arctan(c*x)/(c^2*x^5 + x^3), x) + 1152*b^2*c^2*d^2*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^5 + x^3), x) + 96*b^2*c^2*d^2*integrate(1/16*x^2*log(c^2*x^2 + 1)^2/(c^2*x^5 + x^3), x) - 192*b^2*c^2*d^2*integrate(1/16*x^2*log(c^2*x^2 + 1)/(c^2*x^5 + x^3), x) + 2*b^2*d*e*log(c^2*x^2 + 1)^3 - 384*b^2*c*e^2*integrate(1/16*x^5*arctan(c*x)/(c^2*x^5 + x^3), x) + 384*b^2*c*d^2*integrate(1/16*x*arctan(c*x)/(c^2*x^5 + x^3), x) + 1152*b^2*e^2*integrate(1/16*x^4*arctan(c*x)^2/(c^2*x^5 + x^3), x) + 3072*a*b*e^2*integrate(1/16*x^4*arctan(c*x)/(c^2*x^5 + x^3), x) + 2304*b^2*d*e*integrate(1/16*x^2*arctan(c*x)^2/(c^2*x^5 + x^3), x) + 192*b^2*d*e*integrate(1/16*x^2*log(c^2*x^2 + 1)^2/(c^2*x^5 + x^3), x) + 6144*a*b*d*e*integrate(1/16*x^2*arctan(c*x)/(c^2*x^5 + x^3), x) + 1152*b^2*d^2*integrate(1/16*arctan(c*x)^2/(c^2*x^5 + x^3), x) + 96*b^2*d^2*integrate(1/16*log(c^2*x^2 + 1)^2/(c^2*x^5 + x^3), x) + b^2*e^2*log(c^2*x^2 + 1)^3/c^2)*x^2 + 12*(b^2*e^2*x^4 - b^2*d^2)*arctan(c*x)^2 - 3*(b^2*e^2*x^4 - b^2*d^2)*log(c^2*x^2 + 1)^2)/x^2","F",0
1261,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))^2/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{x^{2}}{e} - \frac{d \log\left(e x^{2} + d\right)}{e^{2}}\right)} + \int \frac{b^{2} x^{3} \arctan\left(c x\right)^{2} + 2 \, a b x^{3} \arctan\left(c x\right)}{e x^{2} + d}\,{d x}"," ",0,"1/2*a^2*(x^2/e - d*log(e*x^2 + d)/e^2) + integrate((b^2*x^3*arctan(c*x)^2 + 2*a*b*x^3*arctan(c*x))/(e*x^2 + d), x)","F",0
1262,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))^2/(e*x^2+d),x, algorithm=""maxima"")","-a^{2} {\left(\frac{d \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e} - \frac{x}{e}\right)} + \frac{4 \, b^{2} x \arctan\left(c x\right)^{2} - b^{2} x \log\left(c^{2} x^{2} + 1\right)^{2} + e \int \frac{12 \, {\left(b^{2} c^{2} e x^{4} + b^{2} e x^{2}\right)} \arctan\left(c x\right)^{2} + {\left(b^{2} c^{2} e x^{4} + b^{2} e x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 8 \, {\left(4 \, a b c^{2} e x^{4} - b^{2} c e x^{3} - b^{2} c d x + 4 \, a b e x^{2}\right)} \arctan\left(c x\right) + 4 \, {\left(b^{2} c^{2} e x^{4} + b^{2} c^{2} d x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{2} e^{2} x^{4} + {\left(c^{2} d e + e^{2}\right)} x^{2} + d e}\,{d x}}{16 \, e}"," ",0,"-a^2*(d*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e) - x/e) + 1/16*(4*b^2*x*arctan(c*x)^2 - b^2*x*log(c^2*x^2 + 1)^2 + 16*e*integrate(1/16*(12*(b^2*c^2*e*x^4 + b^2*e*x^2)*arctan(c*x)^2 + (b^2*c^2*e*x^4 + b^2*e*x^2)*log(c^2*x^2 + 1)^2 + 8*(4*a*b*c^2*e*x^4 - b^2*c*e*x^3 - b^2*c*d*x + 4*a*b*e*x^2)*arctan(c*x) + 4*(b^2*c^2*e*x^4 + b^2*c^2*d*x^2)*log(c^2*x^2 + 1))/(c^2*e^2*x^4 + (c^2*d*e + e^2)*x^2 + d*e), x))/e","F",0
1263,0,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))^2/(e*x^2+d),x, algorithm=""maxima"")","\frac{a^{2} \log\left(e x^{2} + d\right)}{2 \, e} + \int \frac{b^{2} x \arctan\left(c x\right)^{2} + 2 \, a b x \arctan\left(c x\right)}{e x^{2} + d}\,{d x}"," ",0,"1/2*a^2*log(e*x^2 + d)/e + integrate((b^2*x*arctan(c*x)^2 + 2*a*b*x*arctan(c*x))/(e*x^2 + d), x)","F",0
1264,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/(e*x^2+d),x, algorithm=""maxima"")","\frac{a^{2} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}} + \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)}{16 \, {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"a^2*arctan(e*x/sqrt(d*e))/sqrt(d*e) + integrate(1/16*(12*b^2*arctan(c*x)^2 + b^2*log(c^2*x^2 + 1)^2 + 32*a*b*arctan(c*x))/(e*x^2 + d), x)","F",0
1265,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x/(e*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{\log\left(e x^{2} + d\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} + \int \frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right)}{e x^{3} + d x}\,{d x}"," ",0,"-1/2*a^2*(log(e*x^2 + d)/d - 2*log(x)/d) + integrate((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x))/(e*x^3 + d*x), x)","F",0
1266,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^2/(e*x^2+d),x, algorithm=""maxima"")","-a^{2} {\left(\frac{e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d} + \frac{1}{d x}\right)} - \frac{4 \, b^{2} \arctan\left(c x\right)^{2} - b^{2} \log\left(c^{2} x^{2} + 1\right)^{2} - d x \int \frac{12 \, {\left(b^{2} c^{2} d x^{2} + b^{2} d\right)} \arctan\left(c x\right)^{2} + {\left(b^{2} c^{2} d x^{2} + b^{2} d\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 8 \, {\left(4 \, a b c^{2} d x^{2} + b^{2} c e x^{3} + b^{2} c d x + 4 \, a b d\right)} \arctan\left(c x\right) - 4 \, {\left(b^{2} c^{2} e x^{4} + b^{2} c^{2} d x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{2} d e x^{6} + {\left(c^{2} d^{2} + d e\right)} x^{4} + d^{2} x^{2}}\,{d x}}{16 \, d x}"," ",0,"-a^2*(e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d) + 1/(d*x)) - 1/16*(4*b^2*arctan(c*x)^2 - b^2*log(c^2*x^2 + 1)^2 - 16*d*x*integrate(1/16*(12*(b^2*c^2*d*x^2 + b^2*d)*arctan(c*x)^2 + (b^2*c^2*d*x^2 + b^2*d)*log(c^2*x^2 + 1)^2 + 8*(4*a*b*c^2*d*x^2 + b^2*c*e*x^3 + b^2*c*d*x + 4*a*b*d)*arctan(c*x) - 4*(b^2*c^2*e*x^4 + b^2*c^2*d*x^2)*log(c^2*x^2 + 1))/(c^2*d*e*x^6 + (c^2*d^2 + d*e)*x^4 + d^2*x^2), x))/(d*x)","F",0
1267,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^3/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{e \log\left(e x^{2} + d\right)}{d^{2}} - \frac{2 \, e \log\left(x\right)}{d^{2}} - \frac{1}{d x^{2}}\right)} + \int \frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right)}{e x^{5} + d x^{3}}\,{d x}"," ",0,"1/2*a^2*(e*log(e*x^2 + d)/d^2 - 2*e*log(x)/d^2 - 1/(d*x^2)) + integrate((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x))/(e*x^5 + d*x^3), x)","F",0
1268,0,0,0,0.000000," ","integrate(x^3*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{d}{e^{3} x^{2} + d e^{2}} + \frac{\log\left(e x^{2} + d\right)}{e^{2}}\right)} + \int \frac{b^{2} x^{3} \arctan\left(c x\right)^{2} + 2 \, a b x^{3} \arctan\left(c x\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a^2*(d/(e^3*x^2 + d*e^2) + log(e*x^2 + d)/e^2) + integrate((b^2*x^3*arctan(c*x)^2 + 2*a*b*x^3*arctan(c*x))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
1269,0,0,0,0.000000," ","integrate(x^2*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{x}{e^{2} x^{2} + d e} - \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e}\right)} - \frac{4 \, b^{2} x \arctan\left(c x\right)^{2} - b^{2} x \log\left(c^{2} x^{2} + 1\right)^{2} - 2 \, {\left(e^{2} x^{2} + d e\right)} \int \frac{12 \, {\left(b^{2} c^{2} e x^{4} + b^{2} e x^{2}\right)} \arctan\left(c x\right)^{2} + {\left(b^{2} c^{2} e x^{4} + b^{2} e x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)^{2} + 4 \, {\left(8 \, a b c^{2} e x^{4} + b^{2} c e x^{3} + b^{2} c d x + 8 \, a b e x^{2}\right)} \arctan\left(c x\right) - 2 \, {\left(b^{2} c^{2} e x^{4} + b^{2} c^{2} d x^{2}\right)} \log\left(c^{2} x^{2} + 1\right)}{c^{2} e^{3} x^{6} + {\left(2 \, c^{2} d e^{2} + e^{3}\right)} x^{4} + d^{2} e + {\left(c^{2} d^{2} e + 2 \, d e^{2}\right)} x^{2}}\,{d x}}{32 \, {\left(e^{2} x^{2} + d e\right)}}"," ",0,"-1/2*a^2*(x/(e^2*x^2 + d*e) - arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e)) - 1/32*(4*b^2*x*arctan(c*x)^2 - b^2*x*log(c^2*x^2 + 1)^2 - 32*(e^2*x^2 + d*e)*integrate(1/16*(12*(b^2*c^2*e*x^4 + b^2*e*x^2)*arctan(c*x)^2 + (b^2*c^2*e*x^4 + b^2*e*x^2)*log(c^2*x^2 + 1)^2 + 4*(8*a*b*c^2*e*x^4 + b^2*c*e*x^3 + b^2*c*d*x + 8*a*b*e*x^2)*arctan(c*x) - 2*(b^2*c^2*e*x^4 + b^2*c^2*d*x^2)*log(c^2*x^2 + 1))/(c^2*e^3*x^6 + (2*c^2*d*e^2 + e^3)*x^4 + d^2*e + (c^2*d^2*e + 2*d*e^2)*x^2), x))/(e^2*x^2 + d*e)","F",0
1270,-1,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))^2/(e*x^2+d)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1271,-1,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/(e*x^2+d)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1272,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{1}{d e x^{2} + d^{2}} - \frac{\log\left(e x^{2} + d\right)}{d^{2}} + \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + \int \frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right)}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}\,{d x}"," ",0,"1/2*a^2*(1/(d*e*x^2 + d^2) - log(e*x^2 + d)/d^2 + 2*log(x)/d^2) + integrate((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x))/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
1273,-2,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^2/(e*x^2+d)^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1274,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))^2/x^3/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{2 \, e x^{2} + d}{d^{2} e x^{4} + d^{3} x^{2}} - \frac{2 \, e \log\left(e x^{2} + d\right)}{d^{3}} + \frac{4 \, e \log\left(x\right)}{d^{3}}\right)} + \int \frac{b^{2} \arctan\left(c x\right)^{2} + 2 \, a b \arctan\left(c x\right)}{e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}}\,{d x}"," ",0,"-1/2*a^2*((2*e*x^2 + d)/(d^2*e*x^4 + d^3*x^2) - 2*e*log(e*x^2 + d)/d^3 + 4*e*log(x)/d^3) + integrate((b^2*arctan(c*x)^2 + 2*a*b*arctan(c*x))/(e^2*x^7 + 2*d*e*x^5 + d^2*x^3), x)","F",0
1275,1,80,0,0.421481," ","integrate(x^4*arctan(x)*log(x^2+1),x, algorithm=""maxima"")","\frac{9}{200} \, x^{4} - \frac{77}{300} \, x^{2} + \frac{1}{75} \, {\left(15 \, x^{5} \log\left(x^{2} + 1\right) - 6 \, x^{5} + 10 \, x^{3} - 30 \, x + 30 \, \arctan\left(x\right)\right)} \arctan\left(x\right) - \frac{1}{5} \, \arctan\left(x\right)^{2} - \frac{1}{300} \, {\left(15 \, x^{4} - 30 \, x^{2} - 137\right)} \log\left(x^{2} + 1\right) - \frac{1}{20} \, \log\left(x^{2} + 1\right)^{2}"," ",0,"9/200*x^4 - 77/300*x^2 + 1/75*(15*x^5*log(x^2 + 1) - 6*x^5 + 10*x^3 - 30*x + 30*arctan(x))*arctan(x) - 1/5*arctan(x)^2 - 1/300*(15*x^4 - 30*x^2 - 137)*log(x^2 + 1) - 1/20*log(x^2 + 1)^2","A",0
1276,1,62,0,0.414862," ","integrate(x^3*arctan(x)*log(x^2+1),x, algorithm=""maxima"")","\frac{7}{72} \, x^{3} + \frac{1}{8} \, {\left(2 \, x^{4} \log\left(x^{2} + 1\right) - x^{4} + 2 \, x^{2} - 2 \, \log\left(x^{2} + 1\right)\right)} \arctan\left(x\right) - \frac{1}{12} \, {\left(x^{3} - 3 \, x\right)} \log\left(x^{2} + 1\right) - \frac{25}{24} \, x + \frac{25}{24} \, \arctan\left(x\right)"," ",0,"7/72*x^3 + 1/8*(2*x^4*log(x^2 + 1) - x^4 + 2*x^2 - 2*log(x^2 + 1))*arctan(x) - 1/12*(x^3 - 3*x)*log(x^2 + 1) - 25/24*x + 25/24*arctan(x)","A",0
1277,1,65,0,0.421392," ","integrate(x^2*arctan(x)*log(x^2+1),x, algorithm=""maxima"")","\frac{5}{18} \, x^{2} + \frac{1}{9} \, {\left(3 \, x^{3} \log\left(x^{2} + 1\right) - 2 \, x^{3} + 6 \, x - 6 \, \arctan\left(x\right)\right)} \arctan\left(x\right) + \frac{1}{3} \, \arctan\left(x\right)^{2} - \frac{1}{18} \, {\left(3 \, x^{2} + 11\right)} \log\left(x^{2} + 1\right) + \frac{1}{12} \, \log\left(x^{2} + 1\right)^{2}"," ",0,"5/18*x^2 + 1/9*(3*x^3*log(x^2 + 1) - 2*x^3 + 6*x - 6*arctan(x))*arctan(x) + 1/3*arctan(x)^2 - 1/18*(3*x^2 + 11)*log(x^2 + 1) + 1/12*log(x^2 + 1)^2","A",0
1278,1,39,0,0.516197," ","integrate(x*arctan(x)*log(x^2+1),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(x^{2} - {\left(x^{2} + 1\right)} \log\left(x^{2} + 1\right) + 1\right)} \arctan\left(x\right) - \frac{1}{2} \, x \log\left(x^{2} + 1\right) + \frac{3}{2} \, x - \arctan\left(x\right)"," ",0,"-1/2*(x^2 - (x^2 + 1)*log(x^2 + 1) + 1)*arctan(x) - 1/2*x*log(x^2 + 1) + 3/2*x - arctan(x)","A",0
1279,1,42,0,0.413860," ","integrate(arctan(x)*log(x^2+1),x, algorithm=""maxima"")","{\left(x \log\left(x^{2} + 1\right) - 2 \, x + 2 \, \arctan\left(x\right)\right)} \arctan\left(x\right) - \arctan\left(x\right)^{2} - \frac{1}{4} \, \log\left(x^{2} + 1\right)^{2} + \log\left(x^{2} + 1\right)"," ",0,"(x*log(x^2 + 1) - 2*x + 2*arctan(x))*arctan(x) - arctan(x)^2 - 1/4*log(x^2 + 1)^2 + log(x^2 + 1)","A",0
1280,0,0,0,0.000000," ","integrate(arctan(x)*log(x^2+1)/x,x, algorithm=""maxima"")","\int \frac{\arctan\left(x\right) \log\left(x^{2} + 1\right)}{x}\,{d x}"," ",0,"integrate(arctan(x)*log(x^2 + 1)/x, x)","F",0
1281,1,58,0,0.423310," ","integrate(arctan(x)*log(x^2+1)/x^2,x, algorithm=""maxima"")","-{\left(\frac{\log\left(x^{2} + 1\right)}{x} - 2 \, \arctan\left(x\right)\right)} \arctan\left(x\right) - \arctan\left(x\right)^{2} + \frac{1}{2} \, \log\left(-x^{2}\right) \log\left(x^{2} + 1\right) - \frac{1}{4} \, \log\left(x^{2} + 1\right)^{2} + \frac{1}{2} \, {\rm Li}_2\left(x^{2} + 1\right)"," ",0,"-(log(x^2 + 1)/x - 2*arctan(x))*arctan(x) - arctan(x)^2 + 1/2*log(-x^2)*log(x^2 + 1) - 1/4*log(x^2 + 1)^2 + 1/2*dilog(x^2 + 1)","A",0
1282,1,70,0,0.471582," ","integrate(arctan(x)*log(x^2+1)/x^3,x, algorithm=""maxima"")","\frac{4 \, x^{2} \arctan\left(x\right) \log\left(x\right) + 4 \, x^{2} \arctan\left(x\right) - 2 i \, x^{2} {\rm Li}_2\left(i \, x + 1\right) + 2 i \, x^{2} {\rm Li}_2\left(-i \, x + 1\right) - {\left(\pi x^{2} + 2 \, {\left(x^{2} + 1\right)} \arctan\left(x\right) + 2 \, x\right)} \log\left(x^{2} + 1\right)}{4 \, x^{2}}"," ",0,"1/4*(4*x^2*arctan(x)*log(x) + 4*x^2*arctan(x) - 2*I*x^2*dilog(I*x + 1) + 2*I*x^2*dilog(-I*x + 1) - (pi*x^2 + 2*(x^2 + 1)*arctan(x) + 2*x)*log(x^2 + 1))/x^2","A",0
1283,1,95,0,0.420412," ","integrate(arctan(x)*log(x^2+1)/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{2}{x} + \frac{\log\left(x^{2} + 1\right)}{x^{3}} + 2 \, \arctan\left(x\right)\right)} \arctan\left(x\right) + \frac{4 \, x^{2} \arctan\left(x\right)^{2} + x^{2} \log\left(x^{2} + 1\right)^{2} - 2 \, x^{2} {\rm Li}_2\left(x^{2} + 1\right) + 12 \, x^{2} \log\left(x\right) - 2 \, {\left(x^{2} \log\left(-x^{2}\right) + 3 \, x^{2} + 1\right)} \log\left(x^{2} + 1\right)}{12 \, x^{2}}"," ",0,"-1/3*(2/x + log(x^2 + 1)/x^3 + 2*arctan(x))*arctan(x) + 1/12*(4*x^2*arctan(x)^2 + x^2*log(x^2 + 1)^2 - 2*x^2*dilog(x^2 + 1) + 12*x^2*log(x) - 2*(x^2*log(-x^2) + 3*x^2 + 1)*log(x^2 + 1))/x^2","A",0
1284,1,89,0,0.489871," ","integrate(arctan(x)*log(x^2+1)/x^5,x, algorithm=""maxima"")","-\frac{12 \, x^{4} \arctan\left(x\right) \log\left(x\right) - 6 i \, x^{4} {\rm Li}_2\left(i \, x + 1\right) + 6 i \, x^{4} {\rm Li}_2\left(-i \, x + 1\right) + 10 \, x^{3} + 2 \, {\left(11 \, x^{4} + 3 \, x^{2}\right)} \arctan\left(x\right) - {\left(3 \, \pi x^{4} + 6 \, x^{3} + 6 \, {\left(x^{4} - 1\right)} \arctan\left(x\right) - 2 \, x\right)} \log\left(x^{2} + 1\right)}{24 \, x^{4}}"," ",0,"-1/24*(12*x^4*arctan(x)*log(x) - 6*I*x^4*dilog(I*x + 1) + 6*I*x^4*dilog(-I*x + 1) + 10*x^3 + 2*(11*x^4 + 3*x^2)*arctan(x) - (3*pi*x^4 + 6*x^3 + 6*(x^4 - 1)*arctan(x) - 2*x)*log(x^2 + 1))/x^4","A",0
1285,1,115,0,0.428566," ","integrate(arctan(x)*log(x^2+1)/x^6,x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{2 \, {\left(3 \, x^{2} - 1\right)}}{x^{3}} - \frac{3 \, \log\left(x^{2} + 1\right)}{x^{5}} + 6 \, \arctan\left(x\right)\right)} \arctan\left(x\right) - \frac{12 \, x^{4} \arctan\left(x\right)^{2} + 3 \, x^{4} \log\left(x^{2} + 1\right)^{2} - 6 \, x^{4} {\rm Li}_2\left(x^{2} + 1\right) + 50 \, x^{4} \log\left(x\right) + 7 \, x^{2} - {\left(6 \, x^{4} \log\left(-x^{2}\right) + 25 \, x^{4} + 6 \, x^{2} - 3\right)} \log\left(x^{2} + 1\right)}{60 \, x^{4}}"," ",0,"1/15*(2*(3*x^2 - 1)/x^3 - 3*log(x^2 + 1)/x^5 + 6*arctan(x))*arctan(x) - 1/60*(12*x^4*arctan(x)^2 + 3*x^4*log(x^2 + 1)^2 - 6*x^4*dilog(x^2 + 1) + 50*x^4*log(x) + 7*x^2 - (6*x^4*log(-x^2) + 25*x^4 + 6*x^2 - 3)*log(x^2 + 1))/x^4","A",0
1286,1,256,0,0.433151," ","integrate(x^4*(a+b*arctan(c*x))*(d+e*log(c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{5} \, a d x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \log\left(c^{2} x^{2} + 1\right) - 2 \, c^{2} {\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 e \arctan\left(c x\right) + \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 d + \frac{1}{75} \, {\left(15 \, x^{5} \log\left(c^{2} x^{2} + 1\right) - 2 \, c^{2} {\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 e + \frac{{\left(27 \, c^{4} x^{4} - 154 \, c^{2} x^{2} - 120 \, \arctan\left(c x\right)^{2} - 2 \, {\left(15 \, c^{4} x^{4} - 30 \, c^{2} x^{2} - 137\right)} \log\left(c^{2} x^{2} + 1\right) - 30 \, \log\left(c^{2} x^{2} + 1\right)^{2}\right)} b e}{600 \, c^{5}}"," ",0,"1/5*a*d*x^5 + 1/75*(15*x^5*log(c^2*x^2 + 1) - 2*c^2*((3*c^4*x^5 - 5*c^2*x^3 + 15*x)/c^6 - 15*arctan(c*x)/c^7))*b*e*arctan(c*x) + 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*d + 1/75*(15*x^5*log(c^2*x^2 + 1) - 2*c^2*((3*c^4*x^5 - 5*c^2*x^3 + 15*x)/c^6 - 15*arctan(c*x)/c^7))*a*e + 1/600*(27*c^4*x^4 - 154*c^2*x^2 - 120*arctan(c*x)^2 - 2*(15*c^4*x^4 - 30*c^2*x^2 - 137)*log(c^2*x^2 + 1) - 30*log(c^2*x^2 + 1)^2)*b*e/c^5","A",0
1287,1,224,0,0.421090," ","integrate(x^3*(a+b*arctan(c*x))*(d+e*log(c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{4} \, a d x^{4} + \frac{1}{72} \, b c e {\left(\frac{7 \, c^{2} x^{3} - 6 \, {\left(c^{2} x^{3} - 3 \, x\right)} \log\left(c^{2} x^{2} + 1\right) - 75 \, x}{c^{4}} + \frac{75 \, \arctan\left(c x\right)}{c^{5}}\right)} + \frac{1}{8} \, {\left(2 \, x^{4} \log\left(c^{2} x^{2} + 1\right) - c^{2} {\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 e \arctan\left(c x\right) + \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 d + \frac{1}{8} \, {\left(2 \, x^{4} \log\left(c^{2} x^{2} + 1\right) - c^{2} {\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 e"," ",0,"1/4*a*d*x^4 + 1/72*b*c*e*((7*c^2*x^3 - 6*(c^2*x^3 - 3*x)*log(c^2*x^2 + 1) - 75*x)/c^4 + 75*arctan(c*x)/c^5) + 1/8*(2*x^4*log(c^2*x^2 + 1) - c^2*((c^2*x^4 - 2*x^2)/c^4 + 2*log(c^2*x^2 + 1)/c^6))*b*e*arctan(c*x) + 1/12*(3*x^4*arctan(c*x) - c*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*d + 1/8*(2*x^4*log(c^2*x^2 + 1) - c^2*((c^2*x^4 - 2*x^2)/c^4 + 2*log(c^2*x^2 + 1)/c^6))*a*e","A",0
1288,1,212,0,0.427096," ","integrate(x^2*(a+b*arctan(c*x))*(d+e*log(c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{3} \, a d x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \log\left(c^{2} x^{2} + 1\right) - 2 \, c^{2} {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4}} + \frac{3 \, \arctan\left(c x\right)}{c^{5}}\right)}\right)} b e \arctan\left(c x\right) + \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 d + \frac{1}{9} \, {\left(3 \, x^{3} \log\left(c^{2} x^{2} + 1\right) - 2 \, c^{2} {\left(\frac{c^{2} x^{3} - 3 \, x}{c^{4}} + \frac{3 \, \arctan\left(c x\right)}{c^{5}}\right)}\right)} a e + \frac{{\left(10 \, c^{2} x^{2} + 12 \, \arctan\left(c x\right)^{2} - 2 \, {\left(3 \, c^{2} x^{2} + 11\right)} \log\left(c^{2} x^{2} + 1\right) + 3 \, \log\left(c^{2} x^{2} + 1\right)^{2}\right)} b e}{36 \, c^{3}}"," ",0,"1/3*a*d*x^3 + 1/9*(3*x^3*log(c^2*x^2 + 1) - 2*c^2*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*b*e*arctan(c*x) + 1/6*(2*x^3*arctan(c*x) - c*(x^2/c^2 - log(c^2*x^2 + 1)/c^4))*b*d + 1/9*(3*x^3*log(c^2*x^2 + 1) - 2*c^2*((c^2*x^3 - 3*x)/c^4 + 3*arctan(c*x)/c^5))*a*e + 1/36*(10*c^2*x^2 + 12*arctan(c*x)^2 - 2*(3*c^2*x^2 + 11)*log(c^2*x^2 + 1) + 3*log(c^2*x^2 + 1)^2)*b*e/c^3","A",0
1289,1,149,0,0.430682," ","integrate(x*(a+b*arctan(c*x))*(d+e*log(c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{2} \, a d 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 d - \frac{{\left(x \log\left(c^{2} x^{2} + 1\right) - 3 \, x + \frac{2 \, \arctan\left(c x\right)}{c}\right)} b e}{2 \, c} - \frac{{\left(c^{2} x^{2} - {\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right) + 1\right)} b e \arctan\left(c x\right)}{2 \, c^{2}} - \frac{{\left(c^{2} x^{2} - {\left(c^{2} x^{2} + 1\right)} \log\left(c^{2} x^{2} + 1\right) + 1\right)} a e}{2 \, c^{2}}"," ",0,"1/2*a*d*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d - 1/2*(x*log(c^2*x^2 + 1) - 3*x + 2*arctan(c*x)/c)*b*e/c - 1/2*(c^2*x^2 - (c^2*x^2 + 1)*log(c^2*x^2 + 1) + 1)*b*e*arctan(c*x)/c^2 - 1/2*(c^2*x^2 - (c^2*x^2 + 1)*log(c^2*x^2 + 1) + 1)*a*e/c^2","A",0
1290,1,153,0,0.439056," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1)),x, algorithm=""maxima"")","-{\left(2 \, c^{2} {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)} - x \log\left(c^{2} x^{2} + 1\right)\right)} b e \arctan\left(c x\right) - {\left(2 \, c^{2} {\left(\frac{x}{c^{2}} - \frac{\arctan\left(c x\right)}{c^{3}}\right)} - x \log\left(c^{2} x^{2} + 1\right)\right)} a e + a d x + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d}{2 \, c} - \frac{{\left(4 \, \arctan\left(c x\right)^{2} + \log\left(c^{2} x^{2} + 1\right)^{2} - 4 \, \log\left(c^{2} x^{2} + 1\right)\right)} b e}{4 \, c}"," ",0,"-(2*c^2*(x/c^2 - arctan(c*x)/c^3) - x*log(c^2*x^2 + 1))*b*e*arctan(c*x) - (2*c^2*(x/c^2 - arctan(c*x)/c^3) - x*log(c^2*x^2 + 1))*a*e + a*d*x + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d/c - 1/4*(4*arctan(c*x)^2 + log(c^2*x^2 + 1)^2 - 4*log(c^2*x^2 + 1))*b*e/c","A",0
1291,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/x,x, algorithm=""maxima"")","a d \log\left(x\right) + \frac{1}{2} \, \int \frac{2 \, {\left(b d \arctan\left(c x\right) + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(c^{2} x^{2} + 1\right)\right)}}{x}\,{d x}"," ",0,"a*d*log(x) + 1/2*integrate(2*(b*d*arctan(c*x) + (b*e*arctan(c*x) + a*e)*log(c^2*x^2 + 1))/x, x)","F",0
1292,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/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 d + {\left(2 \, c \arctan\left(c x\right) - \frac{\log\left(c^{2} x^{2} + 1\right)}{x}\right)} a e + b e \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{x^{2}}\,{d x} - \frac{a d}{x}"," ",0,"-1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d + (2*c*arctan(c*x) - log(c^2*x^2 + 1)/x)*a*e + b*e*integrate(arctan(c*x)*log(c^2*x^2 + 1)/x^2, x) - a*d/x","F",0
1293,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/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 d - \frac{1}{2} \, {\left(c^{2} {\left(\log\left(c^{2} x^{2} + 1\right) - \log\left(x^{2}\right)\right)} + \frac{\log\left(c^{2} x^{2} + 1\right)}{x^{2}}\right)} a e + \frac{{\left(2 \, c^{4} x^{2} \int \frac{x \arctan\left(c x\right)}{c^{2} x^{2} + 1}\,{d x} + 2 \, c^{2} x^{2} \arctan\left(c x\right) + 2 \, c^{2} x^{2} \int \frac{\arctan\left(c x\right)}{c^{2} x^{3} + x}\,{d x} - {\left(c x + {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)\right)} b e}{2 \, x^{2}} - \frac{a d}{2 \, x^{2}}"," ",0,"-1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d - 1/2*(c^2*(log(c^2*x^2 + 1) - log(x^2)) + log(c^2*x^2 + 1)/x^2)*a*e + 1/2*(4*c^4*x^2*integrate(1/2*x*arctan(c*x)/(c^2*x^2 + 1), x) + 2*c^2*x^2*arctan(c*x) + 4*c^2*x^2*integrate(1/2*arctan(c*x)/(c^2*x^3 + x), x) - (c*x + (c^2*x^2 + 1)*arctan(c*x))*log(c^2*x^2 + 1))*b*e/x^2 - 1/2*a*d/x^2","F",0
1294,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/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 d - \frac{1}{3} \, {\left(2 \, {\left(c \arctan\left(c x\right) + \frac{1}{x}\right)} c^{2} + \frac{\log\left(c^{2} x^{2} + 1\right)}{x^{3}}\right)} a e + b e \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{x^{4}}\,{d x} - \frac{a d}{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*d - 1/3*(2*(c*arctan(c*x) + 1/x)*c^2 + log(c^2*x^2 + 1)/x^3)*a*e + b*e*integrate(arctan(c*x)*log(c^2*x^2 + 1)/x^4, x) - 1/3*a*d/x^3","F",0
1295,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/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 d + \frac{1}{4} \, {\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^{2} - \frac{\log\left(c^{2} x^{2} + 1\right)}{x^{4}}\right)} a e - \frac{{\left(6 \, c^{6} x^{4} \int \frac{x \arctan\left(c x\right)}{c^{2} x^{2} + 1}\,{d x} + 8 \, c^{4} x^{4} \arctan\left(c x\right) - 6 \, c^{2} x^{4} \int \frac{\arctan\left(c x\right)}{c^{2} x^{5} + x^{3}}\,{d x} + 2 \, c^{3} x^{3} - {\left(3 \, c^{3} x^{3} - c x + 3 \, {\left(c^{4} x^{4} - 1\right)} \arctan\left(c x\right)\right)} \log\left(c^{2} x^{2} + 1\right)\right)} b e}{12 \, x^{4}} - \frac{a d}{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*d + 1/4*((c^2*log(c^2*x^2 + 1) - c^2*log(x^2) - 1/x^2)*c^2 - log(c^2*x^2 + 1)/x^4)*a*e - 1/12*(72*c^6*x^4*integrate(1/12*x*arctan(c*x)/(c^2*x^2 + 1), x) + 8*c^4*x^4*arctan(c*x) - 72*c^2*x^4*integrate(1/12*arctan(c*x)/(c^2*x^5 + x^3), x) + 2*c^3*x^3 - (3*c^3*x^3 - c*x + 3*(c^4*x^4 - 1)*arctan(c*x))*log(c^2*x^2 + 1))*b*e/x^4 - 1/4*a*d/x^4","F",0
1296,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))*(d+e*log(c^2*x^2+1))/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 d + \frac{1}{15} \, {\left(2 \, {\left(3 \, c^{3} \arctan\left(c x\right) + \frac{3 \, c^{2} x^{2} - 1}{x^{3}}\right)} c^{2} - \frac{3 \, \log\left(c^{2} x^{2} + 1\right)}{x^{5}}\right)} a e + b e \int \frac{\arctan\left(c x\right) \log\left(c^{2} x^{2} + 1\right)}{x^{6}}\,{d x} - \frac{a d}{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*d + 1/15*(2*(3*c^3*arctan(c*x) + (3*c^2*x^2 - 1)/x^3)*c^2 - 3*log(c^2*x^2 + 1)/x^5)*a*e + b*e*integrate(arctan(c*x)*log(c^2*x^2 + 1)/x^6, x) - 1/5*a*d/x^5","F",0
1297,0,0,0,0.000000," ","integrate(x*(a+b*arctan(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""maxima"")","\frac{1}{2} \, a d 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 d - \frac{{\left(g x^{2} - {\left(g x^{2} + f\right)} \log\left(g x^{2} + f\right) + f\right)} a e}{2 \, g} - \frac{{\left(2 \, c f \arctan\left(\frac{g x}{\sqrt{f g}}\right) + {\left(2 \, c^{4} g \int \frac{x^{3} \arctan\left(c x\right)}{c^{2} g x^{2} + c^{2} f}\,{d x} + 2 \, c^{2} g \int \frac{x \arctan\left(c x\right)}{c^{2} g x^{2} + c^{2} f}\,{d x} - 2 \, c x + {\left(c x - {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)\right)} \log\left(g x^{2} + f\right)\right)} \sqrt{f g}\right)} b e}{2 \, \sqrt{f g} c^{2}}"," ",0,"1/2*a*d*x^2 + 1/2*(x^2*arctan(c*x) - c*(x/c^2 - arctan(c*x)/c^3))*b*d - 1/2*(g*x^2 - (g*x^2 + f)*log(g*x^2 + f) + f)*a*e/g - 1/2*(2*c*f*arctan(g*x/sqrt(f*g)) + (4*c^4*g*integrate(1/2*x^3*arctan(c*x)/(c^2*g*x^2 + c^2*f), x) + 4*c^2*g*integrate(1/2*x*arctan(c*x)/(c^2*g*x^2 + c^2*f), x) - 2*c*x + (c*x - (c^2*x^2 + 1)*arctan(c*x))*log(g*x^2 + f))*sqrt(f*g))*b*e/(sqrt(f*g)*c^2)","F",0
1298,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""maxima"")","{\left(2 \, g {\left(\frac{f \arctan\left(\frac{g x}{\sqrt{f g}}\right)}{\sqrt{f g} g} - \frac{x}{g}\right)} + x \log\left(g x^{2} + f\right)\right)} a e + a d x + b e \int \arctan\left(c x\right) \log\left(g x^{2} + f\right)\,{d x} + \frac{{\left(2 \, c x \arctan\left(c x\right) - \log\left(c^{2} x^{2} + 1\right)\right)} b d}{2 \, c}"," ",0,"(2*g*(f*arctan(g*x/sqrt(f*g))/(sqrt(f*g)*g) - x/g) + x*log(g*x^2 + f))*a*e + a*d*x + b*e*integrate(arctan(c*x)*log(g*x^2 + f), x) + 1/2*(2*c*x*arctan(c*x) - log(c^2*x^2 + 1))*b*d/c","F",0
1299,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))*(d+e*log(g*x^2+f))/x,x, algorithm=""maxima"")","a d \log\left(x\right) + \frac{1}{2} \, \int \frac{2 \, {\left(b d \arctan\left(c x\right) + {\left(b e \arctan\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right)\right)}}{x}\,{d x}"," ",0,"a*d*log(x) + 1/2*integrate(2*(b*d*arctan(c*x) + (b*e*arctan(c*x) + a*e)*log(g*x^2 + f))/x, x)","F",0
1300,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))*(d+e*log(g*x^2+f))/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 d + {\left(\frac{2 \, g \arctan\left(\frac{g x}{\sqrt{f g}}\right)}{\sqrt{f g}} - \frac{\log\left(g x^{2} + f\right)}{x}\right)} a e + b e \int \frac{\arctan\left(c x\right) \log\left(g x^{2} + f\right)}{x^{2}}\,{d x} - \frac{a d}{x}"," ",0,"-1/2*(c*(log(c^2*x^2 + 1) - log(x^2)) + 2*arctan(c*x)/x)*b*d + (2*g*arctan(g*x/sqrt(f*g))/sqrt(f*g) - log(g*x^2 + f)/x)*a*e + b*e*integrate(arctan(c*x)*log(g*x^2 + f)/x^2, x) - a*d/x","F",0
1301,0,0,0,0.000000," ","integrate((a+b*arctan(c*x))*(d+e*log(g*x^2+f))/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 d - \frac{1}{2} \, {\left(g {\left(\frac{\log\left(g x^{2} + f\right)}{f} - \frac{\log\left(x^{2}\right)}{f}\right)} + \frac{\log\left(g x^{2} + f\right)}{x^{2}}\right)} a e + \frac{{\left(2 \, c g x^{2} \arctan\left(\frac{g x}{\sqrt{f g}}\right) + {\left(2 \, c^{2} g x^{2} \int \frac{x \arctan\left(c x\right)}{g x^{2} + f}\,{d x} + 2 \, g x^{2} \int \frac{\arctan\left(c x\right)}{g x^{3} + f x}\,{d x} - {\left(c x + {\left(c^{2} x^{2} + 1\right)} \arctan\left(c x\right)\right)} \log\left(g x^{2} + f\right)\right)} \sqrt{f g}\right)} b e}{2 \, \sqrt{f g} x^{2}} - \frac{a d}{2 \, x^{2}}"," ",0,"-1/2*((c*arctan(c*x) + 1/x)*c + arctan(c*x)/x^2)*b*d - 1/2*(g*(log(g*x^2 + f)/f - log(x^2)/f) + log(g*x^2 + f)/x^2)*a*e + 1/2*(2*c*g*x^2*arctan(g*x/sqrt(f*g)) + (4*c^2*g*x^2*integrate(1/2*x*arctan(c*x)/(g*x^2 + f), x) + 4*g*x^2*integrate(1/2*arctan(c*x)/(g*x^3 + f*x), x) - (c*x + (c^2*x^2 + 1)*arctan(c*x))*log(g*x^2 + f))*sqrt(f*g))*b*e/(sqrt(f*g)*x^2) - 1/2*a*d/x^2","F",0
