1,1,53,49,0.008000," ","int(x^5*(a+b*arctan(c*x)),x)","\frac{x^{6} a}{6}+\frac{b \,x^{6} \arctan \left(c x \right)}{6}-\frac{b \,x^{5}}{30 c}+\frac{b \,x^{3}}{18 c^{3}}-\frac{b x}{6 c^{5}}+\frac{b \arctan \left(c x \right)}{6 c^{6}}"," ",0,"1/6*x^6*a+1/6*b*x^6*arctan(c*x)-1/30*b*x^5/c+1/18*b*x^3/c^3-1/6*b*x/c^5+1/6*b*arctan(c*x)/c^6","A"
2,1,52,48,0.007000," ","int(x^4*(a+b*arctan(c*x)),x)","\frac{a \,x^{5}}{5}+\frac{x^{5} b \arctan \left(c x \right)}{5}-\frac{b \,x^{4}}{20 c}+\frac{b \,x^{2}}{10 c^{3}}-\frac{b \ln \left(c^{2} x^{2}+1\right)}{10 c^{5}}"," ",0,"1/5*a*x^5+1/5*x^5*b*arctan(c*x)-1/20*b*x^4/c+1/10*b*x^2/c^3-1/10*b*ln(c^2*x^2+1)/c^5","A"
3,1,44,40,0.006000," ","int(x^3*(a+b*arctan(c*x)),x)","\frac{x^{4} a}{4}+\frac{x^{4} b \arctan \left(c x \right)}{4}-\frac{b \,x^{3}}{12 c}+\frac{b x}{4 c^{3}}-\frac{b \arctan \left(c x \right)}{4 c^{4}}"," ",0,"1/4*x^4*a+1/4*x^4*b*arctan(c*x)-1/12*b*x^3/c+1/4*b*x/c^3-1/4*b*arctan(c*x)/c^4","A"
4,1,43,39,0.006000," ","int(x^2*(a+b*arctan(c*x)),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctan \left(c x \right)}{3}-\frac{b \,x^{2}}{6 c}+\frac{b \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctan(c*x)-1/6*b*x^2/c+1/6*b*ln(c^2*x^2+1)/c^3","A"
5,1,35,31,0.006000," ","int(x*(a+b*arctan(c*x)),x)","\frac{a \,x^{2}}{2}+\frac{b \,x^{2} \arctan \left(c x \right)}{2}-\frac{b x}{2 c}+\frac{b \arctan \left(c x \right)}{2 c^{2}}"," ",0,"1/2*a*x^2+1/2*b*x^2*arctan(c*x)-1/2*b*x/c+1/2*b*arctan(c*x)/c^2","A"
6,1,28,27,0.004000," ","int(a+b*arctan(c*x),x)","a x +b x \arctan \left(c x \right)-\frac{b \ln \left(c^{2} x^{2}+1\right)}{2 c}"," ",0,"a*x+b*x*arctan(c*x)-1/2*b*ln(c^2*x^2+1)/c","A"
7,1,74,27,0.029000," ","int((a+b*arctan(c*x))/x,x)","a \ln \left(c x \right)+b \ln \left(c x \right) \arctan \left(c x \right)+\frac{i b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{i b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}+\frac{i b \dilog \left(i c x +1\right)}{2}-\frac{i b \dilog \left(-i c x +1\right)}{2}"," ",0,"a*ln(c*x)+b*ln(c*x)*arctan(c*x)+1/2*I*b*ln(c*x)*ln(1+I*c*x)-1/2*I*b*ln(c*x)*ln(1-I*c*x)+1/2*I*b*dilog(1+I*c*x)-1/2*I*b*dilog(1-I*c*x)","B"
8,1,39,35,0.011000," ","int((a+b*arctan(c*x))/x^2,x)","-\frac{a}{x}-\frac{b \arctan \left(c x \right)}{x}+c b \ln \left(c x \right)-\frac{b c \ln \left(c^{2} x^{2}+1\right)}{2}"," ",0,"-a/x-b/x*arctan(c*x)+c*b*ln(c*x)-1/2*b*c*ln(c^2*x^2+1)","A"
9,1,35,34,0.009000," ","int((a+b*arctan(c*x))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctan \left(c x \right)}{2 x^{2}}-\frac{b c}{2 x}-\frac{b \,c^{2} \arctan \left(c x \right)}{2}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctan(c*x)-1/2*b*c/x-1/2*b*c^2*arctan(c*x)","A"
10,1,51,48,0.013000," ","int((a+b*arctan(c*x))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctan \left(c x \right)}{3 x^{3}}-\frac{b c}{6 x^{2}}-\frac{c^{3} b \ln \left(c x \right)}{3}+\frac{b \,c^{3} \ln \left(c^{2} x^{2}+1\right)}{6}"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctan(c*x)-1/6*b*c/x^2-1/3*c^3*b*ln(c*x)+1/6*b*c^3*ln(c^2*x^2+1)","A"
11,1,44,43,0.009000," ","int((a+b*arctan(c*x))/x^5,x)","-\frac{a}{4 x^{4}}-\frac{b \arctan \left(c x \right)}{4 x^{4}}-\frac{b c}{12 x^{3}}+\frac{b \,c^{3}}{4 x}+\frac{b \,c^{4} \arctan \left(c x \right)}{4}"," ",0,"-1/4*a/x^4-1/4*b/x^4*arctan(c*x)-1/12*b*c/x^3+1/4*b*c^3/x+1/4*b*c^4*arctan(c*x)","A"
12,1,60,57,0.011000," ","int((a+b*arctan(c*x))/x^6,x)","-\frac{a}{5 x^{5}}-\frac{b \arctan \left(c x \right)}{5 x^{5}}-\frac{b c}{20 x^{4}}+\frac{c^{5} b \ln \left(c x \right)}{5}+\frac{b \,c^{3}}{10 x^{2}}-\frac{b \,c^{5} \ln \left(c^{2} x^{2}+1\right)}{10}"," ",0,"-1/5*a/x^5-1/5*b/x^5*arctan(c*x)-1/20*b*c/x^4+1/5*c^5*b*ln(c*x)+1/10*b*c^3/x^2-1/10*b*c^5*ln(c^2*x^2+1)","A"
13,1,171,126,0.015000," ","int(x^5*(a+b*arctan(c*x))^2,x)","\frac{x^{6} a^{2}}{6}+\frac{b^{2} x^{6} \arctan \left(c x \right)^{2}}{6}-\frac{b^{2} \arctan \left(c x \right) x^{5}}{15 c}+\frac{b^{2} \arctan \left(c x \right) x^{3}}{9 c^{3}}-\frac{b^{2} x \arctan \left(c x \right)}{3 c^{5}}+\frac{b^{2} \arctan \left(c x \right)^{2}}{6 c^{6}}+\frac{b^{2} x^{4}}{60 c^{2}}-\frac{4 b^{2} x^{2}}{45 c^{4}}+\frac{23 b^{2} \ln \left(c^{2} x^{2}+1\right)}{90 c^{6}}+\frac{a b \,x^{6} \arctan \left(c x \right)}{3}-\frac{x^{5} a b}{15 c}+\frac{a b \,x^{3}}{9 c^{3}}-\frac{a b x}{3 c^{5}}+\frac{a b \arctan \left(c x \right)}{3 c^{6}}"," ",0,"1/6*x^6*a^2+1/6*b^2*x^6*arctan(c*x)^2-1/15/c*b^2*arctan(c*x)*x^5+1/9/c^3*b^2*arctan(c*x)*x^3-1/3*b^2*x*arctan(c*x)/c^5+1/6/c^6*b^2*arctan(c*x)^2+1/60*b^2*x^4/c^2-4/45*b^2*x^2/c^4+23/90*b^2*ln(c^2*x^2+1)/c^6+1/3*a*b*x^6*arctan(c*x)-1/15/c*x^5*a*b+1/9*a*b*x^3/c^3-1/3*a*b*x/c^5+1/3/c^6*a*b*arctan(c*x)","A"
14,1,334,148,0.095000," ","int(x^4*(a+b*arctan(c*x))^2,x)","\frac{x^{5} a^{2}}{5}+\frac{x^{5} b^{2} \arctan \left(c x \right)^{2}}{5}-\frac{b^{2} \arctan \left(c x \right) x^{4}}{10 c}+\frac{b^{2} \arctan \left(c x \right) x^{2}}{5 c^{3}}-\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{5 c^{5}}+\frac{b^{2} x^{3}}{30 c^{2}}-\frac{3 b^{2} x}{10 c^{4}}+\frac{3 b^{2} \arctan \left(c x \right)}{10 c^{5}}+\frac{i b^{2} \ln \left(c x -i\right)^{2}}{20 c^{5}}-\frac{i b^{2} \ln \left(c x +i\right)^{2}}{20 c^{5}}+\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{10 c^{5}}-\frac{i b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{10 c^{5}}+\frac{i b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{10 c^{5}}-\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{10 c^{5}}+\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{10 c^{5}}-\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{10 c^{5}}+\frac{2 x^{5} a b \arctan \left(c x \right)}{5}-\frac{x^{4} a b}{10 c}+\frac{a b \,x^{2}}{5 c^{3}}-\frac{a b \ln \left(c^{2} x^{2}+1\right)}{5 c^{5}}"," ",0,"1/5*x^5*a^2+1/5*x^5*b^2*arctan(c*x)^2-1/10/c*b^2*arctan(c*x)*x^4+1/5/c^3*b^2*arctan(c*x)*x^2-1/5/c^5*b^2*arctan(c*x)*ln(c^2*x^2+1)+1/30*b^2*x^3/c^2-3/10*b^2*x/c^4+3/10*b^2*arctan(c*x)/c^5+1/20*I/c^5*b^2*ln(c*x-I)^2-1/10*I/c^5*b^2*dilog(1/2*I*(c*x-I))-1/20*I/c^5*b^2*ln(I+c*x)^2+1/10*I/c^5*b^2*dilog(-1/2*I*(I+c*x))+1/10*I/c^5*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/10*I/c^5*b^2*ln(c*x-I)*ln(c^2*x^2+1)+1/10*I/c^5*b^2*ln(I+c*x)*ln(c^2*x^2+1)-1/10*I/c^5*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+2/5*x^5*a*b*arctan(c*x)-1/10/c*x^4*a*b+1/5*a*b*x^2/c^3-1/5/c^5*a*b*ln(c^2*x^2+1)","B"
15,1,135,98,0.014000," ","int(x^3*(a+b*arctan(c*x))^2,x)","\frac{a^{2} x^{4}}{4}+\frac{b^{2} x^{4} \arctan \left(c x \right)^{2}}{4}-\frac{b^{2} \arctan \left(c x \right) x^{3}}{6 c}+\frac{b^{2} x \arctan \left(c x \right)}{2 c^{3}}-\frac{b^{2} \arctan \left(c x \right)^{2}}{4 c^{4}}+\frac{b^{2} x^{2}}{12 c^{2}}-\frac{b^{2} \ln \left(c^{2} x^{2}+1\right)}{3 c^{4}}+\frac{x^{4} a b \arctan \left(c x \right)}{2}-\frac{a b \,x^{3}}{6 c}+\frac{a b x}{2 c^{3}}-\frac{a b \arctan \left(c x \right)}{2 c^{4}}"," ",0,"1/4*a^2*x^4+1/4*b^2*x^4*arctan(c*x)^2-1/6/c*b^2*arctan(c*x)*x^3+1/2*b^2*x*arctan(c*x)/c^3-1/4/c^4*b^2*arctan(c*x)^2+1/12*b^2*x^2/c^2-1/3*b^2*ln(c^2*x^2+1)/c^4+1/2*x^4*a*b*arctan(c*x)-1/6*a*b*x^3/c+1/2*a*b*x/c^3-1/2/c^4*a*b*arctan(c*x)","A"
16,1,298,120,0.016000," ","int(x^2*(a+b*arctan(c*x))^2,x)","\frac{x^{3} a^{2}}{3}+\frac{b^{2} x^{3} \arctan \left(c x \right)^{2}}{3}-\frac{b^{2} \arctan \left(c x \right) x^{2}}{3 c}+\frac{b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{3 c^{3}}+\frac{b^{2} x}{3 c^{2}}-\frac{b^{2} \arctan \left(c x \right)}{3 c^{3}}+\frac{i b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}-\frac{i b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{6 c^{3}}+\frac{i b^{2} \ln \left(c x +i\right)^{2}}{12 c^{3}}+\frac{i b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{6 c^{3}}-\frac{i b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{6 c^{3}}-\frac{i b^{2} \ln \left(c x -i\right)^{2}}{12 c^{3}}+\frac{i b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{6 c^{3}}-\frac{i b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{6 c^{3}}+\frac{2 a b \,x^{3} \arctan \left(c x \right)}{3}-\frac{a b \,x^{2}}{3 c}+\frac{a b \ln \left(c^{2} x^{2}+1\right)}{3 c^{3}}"," ",0,"1/3*x^3*a^2+1/3*b^2*x^3*arctan(c*x)^2-1/3/c*b^2*arctan(c*x)*x^2+1/3/c^3*b^2*arctan(c*x)*ln(c^2*x^2+1)+1/3*b^2*x/c^2-1/3*b^2*arctan(c*x)/c^3+1/6*I/c^3*b^2*ln(c*x-I)*ln(c^2*x^2+1)+1/12*I/c^3*b^2*ln(I+c*x)^2+1/6*I/c^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-1/6*I/c^3*b^2*dilog(-1/2*I*(I+c*x))-1/6*I/c^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/12*I/c^3*b^2*ln(c*x-I)^2+1/6*I/c^3*b^2*dilog(1/2*I*(c*x-I))-1/6*I/c^3*b^2*ln(I+c*x)*ln(c^2*x^2+1)+2/3*a*b*x^3*arctan(c*x)-1/3*a*b*x^2/c+1/3/c^3*a*b*ln(c^2*x^2+1)","B"
17,1,97,70,0.022000," ","int(x*(a+b*arctan(c*x))^2,x)","\frac{a^{2} x^{2}}{2}+\frac{x^{2} b^{2} \arctan \left(c x \right)^{2}}{2}+\frac{b^{2} \arctan \left(c x \right)^{2}}{2 c^{2}}-\frac{b^{2} x \arctan \left(c x \right)}{c}+\frac{b^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{2}}+a b \,x^{2} \arctan \left(c x \right)+\frac{a b \arctan \left(c x \right)}{c^{2}}-\frac{a b x}{c}"," ",0,"1/2*a^2*x^2+1/2*x^2*b^2*arctan(c*x)^2+1/2/c^2*b^2*arctan(c*x)^2-b^2*x*arctan(c*x)/c+1/2*b^2*ln(c^2*x^2+1)/c^2+a*b*x^2*arctan(c*x)+1/c^2*a*b*arctan(c*x)-a*b*x/c","A"
18,1,128,79,0.192000," ","int((a+b*arctan(c*x))^2,x)","x \,b^{2} \arctan \left(c x \right)^{2}-\frac{i \arctan \left(c x \right)^{2} b^{2}}{c}+2 x a b \arctan \left(c x \right)+\frac{2 \arctan \left(c x \right) \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right) b^{2}}{c}-\frac{i \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) b^{2}}{c}+a^{2} x -\frac{a b \ln \left(c^{2} x^{2}+1\right)}{c}"," ",0,"x*b^2*arctan(c*x)^2-I/c*arctan(c*x)^2*b^2+2*x*a*b*arctan(c*x)+2/c*arctan(c*x)*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*b^2-I/c*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))*b^2+a^2*x-1/c*a*b*ln(c^2*x^2+1)","A"
19,1,1128,121,0.513000," ","int((a+b*arctan(c*x))^2/x,x)","b^{2} \ln \left(c x \right) \arctan \left(c x \right)^{2}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+i a b \ln \left(c x \right) \ln \left(i c x +1\right)-i a b \ln \left(c x \right) \ln \left(-i c x +1\right)-b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)+b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-i a b \dilog \left(-i c x +1\right)+i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)-2 i b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-2 i b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+i a b \dilog \left(i c x +1\right)+\frac{i b^{2} \pi  \arctan \left(c x \right)^{2}}{2}+2 a b \ln \left(c x \right) \arctan \left(c x \right)+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+a^{2} \ln \left(c x \right)-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}+2 b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+2 b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}"," ",0,"b^2*ln(c*x)*arctan(c*x)^2-b^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+b^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+I*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-2*I*b^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-2*I*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I*b^2*Pi*arctan(c*x)^2+I*a*b*dilog(1+I*c*x)+2*a*b*ln(c*x)*arctan(c*x)-I*a*b*dilog(1-I*c*x)-1/2*I*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2*I*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*b^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+2*b^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+2*b^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+a^2*ln(c*x)-1/2*I*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-1/2*I*b^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+1/2*I*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+I*a*b*ln(c*x)*ln(1+I*c*x)-I*a*b*ln(c*x)*ln(1-I*c*x)+1/2*I*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-1/2*I*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2","C"
20,1,323,78,0.018000," ","int((a+b*arctan(c*x))^2/x^2,x)","-\frac{a^{2}}{x}-\frac{b^{2} \arctan \left(c x \right)^{2}}{x}+2 c \,b^{2} \ln \left(c x \right) \arctan \left(c x \right)-c \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)-i c \,b^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)-i c \,b^{2} \dilog \left(-i c x +1\right)+\frac{i c \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2}+i c \,b^{2} \ln \left(c x \right) \ln \left(i c x +1\right)-\frac{i c \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{2}+\frac{i c \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{2}+\frac{i c \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2}-\frac{i c \,b^{2} \ln \left(c x +i\right)^{2}}{4}-\frac{i c \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{2}+\frac{i c \,b^{2} \ln \left(c x -i\right)^{2}}{4}-\frac{i c \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2}+i c \,b^{2} \dilog \left(i c x +1\right)-\frac{2 a b \arctan \left(c x \right)}{x}+2 c a b \ln \left(c x \right)-c a b \ln \left(c^{2} x^{2}+1\right)"," ",0,"-a^2/x-b^2/x*arctan(c*x)^2+2*c*b^2*ln(c*x)*arctan(c*x)-c*b^2*arctan(c*x)*ln(c^2*x^2+1)-I*c*b^2*ln(c*x)*ln(1-I*c*x)+1/2*I*c*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+I*c*b^2*dilog(1+I*c*x)+I*c*b^2*ln(c*x)*ln(1+I*c*x)-1/2*I*c*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+1/2*I*c*b^2*ln(I+c*x)*ln(c^2*x^2+1)-I*c*b^2*dilog(1-I*c*x)-1/4*I*c*b^2*ln(I+c*x)^2-1/2*I*c*b^2*ln(c*x-I)*ln(c^2*x^2+1)-1/2*I*c*b^2*dilog(1/2*I*(c*x-I))+1/4*I*c*b^2*ln(c*x-I)^2+1/2*I*c*b^2*dilog(-1/2*I*(I+c*x))-2*a*b/x*arctan(c*x)+2*c*a*b*ln(c*x)-c*a*b*ln(c^2*x^2+1)","B"
21,1,110,73,0.013000," ","int((a+b*arctan(c*x))^2/x^3,x)","-\frac{a^{2}}{2 x^{2}}-\frac{b^{2} \arctan \left(c x \right)^{2}}{2 x^{2}}-\frac{c \,b^{2} \arctan \left(c x \right)}{x}-\frac{c^{2} b^{2} \arctan \left(c x \right)^{2}}{2}+c^{2} b^{2} \ln \left(c x \right)-\frac{b^{2} c^{2} \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{a b \arctan \left(c x \right)}{x^{2}}-\frac{a b c}{x}-c^{2} a b \arctan \left(c x \right)"," ",0,"-1/2*a^2/x^2-1/2*b^2/x^2*arctan(c*x)^2-c*b^2*arctan(c*x)/x-1/2*c^2*b^2*arctan(c*x)^2+c^2*b^2*ln(c*x)-1/2*b^2*c^2*ln(c^2*x^2+1)-a*b/x^2*arctan(c*x)-a*b*c/x-c^2*a*b*arctan(c*x)","A"
22,1,399,122,0.019000," ","int((a+b*arctan(c*x))^2/x^4,x)","-\frac{a^{2}}{3 x^{3}}-\frac{b^{2} \arctan \left(c x \right)^{2}}{3 x^{3}}-\frac{c \,b^{2} \arctan \left(c x \right)}{3 x^{2}}-\frac{2 c^{3} b^{2} \ln \left(c x \right) \arctan \left(c x \right)}{3}+\frac{c^{3} b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{3}+\frac{i c^{3} b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{6}-\frac{i c^{3} b^{2} \dilog \left(i c x +1\right)}{3}-\frac{i c^{3} b^{2} \ln \left(c x -i\right)^{2}}{12}-\frac{i c^{3} b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{6}-\frac{i c^{3} b^{2} \ln \left(c x \right) \ln \left(i c x +1\right)}{3}+\frac{i c^{3} b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{6}+\frac{i c^{3} b^{2} \dilog \left(-i c x +1\right)}{3}-\frac{i c^{3} b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{6}-\frac{b^{2} c^{2}}{3 x}-\frac{b^{2} c^{3} \arctan \left(c x \right)}{3}+\frac{i c^{3} b^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)}{3}+\frac{i c^{3} b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{6}+\frac{i c^{3} b^{2} \ln \left(c x +i\right)^{2}}{12}-\frac{i c^{3} b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{6}-\frac{2 a b \arctan \left(c x \right)}{3 x^{3}}-\frac{c a b}{3 x^{2}}-\frac{2 c^{3} a b \ln \left(c x \right)}{3}+\frac{c^{3} a b \ln \left(c^{2} x^{2}+1\right)}{3}"," ",0,"-1/3*a^2/x^3-1/3*b^2/x^3*arctan(c*x)^2-1/3*c*b^2*arctan(c*x)/x^2-2/3*c^3*b^2*ln(c*x)*arctan(c*x)+1/3*c^3*b^2*arctan(c*x)*ln(c^2*x^2+1)+1/6*I*c^3*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-1/12*I*c^3*b^2*ln(c*x-I)^2-1/6*I*c^3*b^2*ln(I+c*x)*ln(c^2*x^2+1)-1/3*I*c^3*b^2*dilog(1+I*c*x)-1/3*I*c^3*b^2*ln(c*x)*ln(1+I*c*x)+1/6*I*c^3*b^2*ln(c*x-I)*ln(c^2*x^2+1)-1/6*I*c^3*b^2*dilog(-1/2*I*(I+c*x))+1/3*I*c^3*b^2*dilog(1-I*c*x)-1/3*b^2*c^2/x-1/3*b^2*c^3*arctan(c*x)+1/3*I*c^3*b^2*ln(c*x)*ln(1-I*c*x)+1/6*I*c^3*b^2*dilog(1/2*I*(c*x-I))+1/12*I*c^3*b^2*ln(I+c*x)^2-1/6*I*c^3*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-2/3*a*b/x^3*arctan(c*x)-1/3*c*a*b/x^2-2/3*c^3*a*b*ln(c*x)+1/3*c^3*a*b*ln(c^2*x^2+1)","B"
23,1,147,102,0.018000," ","int((a+b*arctan(c*x))^2/x^5,x)","-\frac{a^{2}}{4 x^{4}}-\frac{b^{2} \arctan \left(c x \right)^{2}}{4 x^{4}}-\frac{c \,b^{2} \arctan \left(c x \right)}{6 x^{3}}+\frac{c^{3} b^{2} \arctan \left(c x \right)}{2 x}+\frac{c^{4} b^{2} \arctan \left(c x \right)^{2}}{4}-\frac{b^{2} c^{2}}{12 x^{2}}-\frac{2 c^{4} b^{2} \ln \left(c x \right)}{3}+\frac{b^{2} c^{4} \ln \left(c^{2} x^{2}+1\right)}{3}-\frac{a b \arctan \left(c x \right)}{2 x^{4}}-\frac{a b c}{6 x^{3}}+\frac{c^{3} a b}{2 x}+\frac{c^{4} a b \arctan \left(c x \right)}{2}"," ",0,"-1/4*a^2/x^4-1/4*b^2/x^4*arctan(c*x)^2-1/6*c*b^2*arctan(c*x)/x^3+1/2*c^3*b^2*arctan(c*x)/x+1/4*c^4*b^2*arctan(c*x)^2-1/12*b^2*c^2/x^2-2/3*c^4*b^2*ln(c*x)+1/3*b^2*c^4*ln(c^2*x^2+1)-1/2*a*b/x^4*arctan(c*x)-1/6*a*b*c/x^3+1/2*c^3*a*b/x+1/2*c^4*a*b*arctan(c*x)","A"
24,1,528,225,0.023000," ","int(x^5*(a+b*arctan(c*x))^3,x)","-\frac{23 i b^{3} \ln \left(c x -i\right)^{2}}{120 c^{6}}+\frac{23 i b^{3} \ln \left(c x +i\right)^{2}}{120 c^{6}}-\frac{23 i b^{3} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{60 c^{6}}+\frac{23 i b^{3} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{60 c^{6}}-\frac{b^{3} \arctan \left(c x \right)^{2} x^{5}}{10 c}+\frac{b^{3} \arctan \left(c x \right)^{2} x^{3}}{6 c^{3}}+\frac{b^{3} \arctan \left(c x \right) x^{4}}{20 c^{2}}-\frac{4 b^{3} \arctan \left(c x \right) x^{2}}{15 c^{4}}-\frac{b^{3} \arctan \left(c x \right)^{2} x}{2 c^{5}}+\frac{a \,b^{2} x^{6} \arctan \left(c x \right)^{2}}{2}+\frac{a^{2} b \,x^{6} \arctan \left(c x \right)}{2}+\frac{a^{2} b \arctan \left(c x \right)}{2 c^{6}}+\frac{a \,b^{2} \arctan \left(c x \right)^{2}}{2 c^{6}}+\frac{23 a \,b^{2} \ln \left(c^{2} x^{2}+1\right)}{30 c^{6}}+\frac{23 b^{3} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{30 c^{6}}-\frac{x \,a^{2} b}{2 c^{5}}+\frac{a \,b^{2} x^{4}}{20 c^{2}}-\frac{x^{5} a^{2} b}{10 c}+\frac{a^{2} b \,x^{3}}{6 c^{3}}-\frac{4 x^{2} a \,b^{2}}{15 c^{4}}+\frac{19 b^{3} x}{60 c^{5}}-\frac{b^{3} x^{3}}{60 c^{3}}-\frac{19 b^{3} \arctan \left(c x \right)}{60 c^{6}}+\frac{x^{6} a^{3}}{6}+\frac{b^{3} x^{6} \arctan \left(c x \right)^{3}}{6}+\frac{b^{3} \arctan \left(c x \right)^{3}}{6 c^{6}}+\frac{23 i b^{3} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{60 c^{6}}-\frac{23 i b^{3} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{60 c^{6}}+\frac{23 i b^{3} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{60 c^{6}}-\frac{23 i b^{3} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{60 c^{6}}+\frac{a \,b^{2} x^{3} \arctan \left(c x \right)}{3 c^{3}}-\frac{a \,b^{2} x \arctan \left(c x \right)}{c^{5}}-\frac{a \,b^{2} x^{5} \arctan \left(c x \right)}{5 c}"," ",0,"-23/60*I/c^6*b^3*dilog(-1/2*I*(I+c*x))-23/120*I/c^6*b^3*ln(c*x-I)^2-1/10/c*b^3*arctan(c*x)^2*x^5+1/6/c^3*b^3*arctan(c*x)^2*x^3+1/20/c^2*b^3*arctan(c*x)*x^4-4/15/c^4*b^3*arctan(c*x)*x^2-1/2/c^5*b^3*arctan(c*x)^2*x+1/2*a*b^2*x^6*arctan(c*x)^2+1/2*a^2*b*x^6*arctan(c*x)+23/60*I/c^6*b^3*dilog(1/2*I*(c*x-I))+23/120*I/c^6*b^3*ln(I+c*x)^2+1/2/c^6*a^2*b*arctan(c*x)+1/2/c^6*a*b^2*arctan(c*x)^2+23/30/c^6*a*b^2*ln(c^2*x^2+1)+23/30/c^6*b^3*arctan(c*x)*ln(c^2*x^2+1)-1/2/c^5*x*a^2*b+1/20/c^2*a*b^2*x^4-1/10/c*x^5*a^2*b+1/6/c^3*a^2*b*x^3-4/15/c^4*x^2*a*b^2+19/60*b^3*x/c^5-1/60*b^3*x^3/c^3-19/60*b^3*arctan(c*x)/c^6+1/6*x^6*a^3+1/6*b^3*x^6*arctan(c*x)^3+1/6/c^6*b^3*arctan(c*x)^3+1/3/c^3*a*b^2*x^3*arctan(c*x)-1/c^5*a*b^2*x*arctan(c*x)-23/60*I/c^6*b^3*ln(I+c*x)*ln(c^2*x^2+1)-23/60*I/c^6*b^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))+23/60*I/c^6*b^3*ln(c*x-I)*ln(c^2*x^2+1)+23/60*I/c^6*b^3*ln(I+c*x)*ln(1/2*I*(c*x-I))-1/5/c*a*b^2*x^5*arctan(c*x)","B"
25,1,3053,240,5.524000," ","int(x^4*(a+b*arctan(c*x))^3,x)","\text{output too large to display}"," ",0,"-3/160/c^2*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2*x^3-9/80/c^4*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2*x+3/80/c^2*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2*x^3+9/80/c^4*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)*arctan(c*x)^2*x+9/160*I/c^3*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^3*arctan(c*x)^2*x^2-1/20*b^3*x^2/c^3-3/80/c^2*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)*arctan(c*x)^2*x^3+3/160/c^2*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*arctan(c*x)^2*x^3+3/10*I/c^5*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*arctan(c*x)^2+1/5*x^5*a^3-1/20/c^5*b^3-3/10*I/c^5*a*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-3/20*I/c^5*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*arctan(c*x)^2-3/20*I/c^5*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+21/160*I/c^5*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^3*arctan(c*x)^2+3/160*I/c^5*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2+3/160/c^2*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^3*arctan(c*x)^2*x^3+9/160/c^4*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2*x-3/160/c^2*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2*x^3-9/160/c^4*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^3*arctan(c*x)^2*x-3/10*I/c^5*a*b^2*ln(c*x-I)*ln(c^2*x^2+1)+3/10*I/c^5*a*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+3/10*I/c^5*a*b^2*ln(I+c*x)*ln(c^2*x^2+1)-9/160/c^4*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*arctan(c*x)^2*x-3/20*I/c^5*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*arctan(c*x)^2+3/20*I/c^5*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+3/20*I/c^5*b^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2-9/80*I/c^3*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)*arctan(c*x)^2*x^2+9/160*I/c^3*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*arctan(c*x)^2*x^2-9/160*I/c^3*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2*x^2+9/80*I/c^3*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2*x^2-3/20*I/c^5*b^3*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2-9/160*I/c^3*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2*x^2-3/80*I/c^5*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2+21/160*I/c^5*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*arctan(c*x)^2+9/20/c^5*b^3*arctan(c*x)^2-1/c^5*b^3*ln((1+I*c*x)^2/(c^2*x^2+1)+1)+3/10/c^5*b^3*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+1/5*x^5*b^3*arctan(c*x)^3-3/10/c*a*b^2*x^4*arctan(c*x)+3/5/c^5*b^3*ln(2)*arctan(c*x)^2+I/c^5*b^3*arctan(c*x)-3/10/c^5*a^2*b*ln(c^2*x^2+1)+9/10/c^5*a*b^2*arctan(c*x)+1/10/c^2*b^3*arctan(c*x)*x^3+3/10/c^3*b^3*arctan(c*x)^2*x^2-3/20/c*b^3*x^4*arctan(c*x)^2-1/5*I/c^5*b^3*arctan(c*x)^3+9/160/c^4*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2*x-21/80*I/c^5*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)*arctan(c*x)^2+3/160*I/c^5*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2+1/10*a*b^2*x^3/c^2-9/10*b^3*x*arctan(c*x)/c^4-9/10*a*b^2*x/c^4+3/5/c^3*a*b^2*x^2*arctan(c*x)-3/5/c^5*a*b^2*arctan(c*x)*ln(c^2*x^2+1)+3/20*I/c^5*a*b^2*ln(c*x-I)^2+3/10*I/c^5*a*b^2*dilog(-1/2*I*(I+c*x))-3/20*I/c^5*a*b^2*ln(I+c*x)^2-3/10*I/c^5*a*b^2*dilog(1/2*I*(c*x-I))-3/5*I/c^5*b^3*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-3/20/c*a^2*b*x^4+3/10/c^3*b*x^2*a^2+3/5*x^5*a^2*b*arctan(c*x)+3/5*x^5*a*b^2*arctan(c*x)^2+3/5/c^5*b^3*arctan(c*x)^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-3/10/c^5*b^3*arctan(c*x)^2*ln(c^2*x^2+1)","C"
26,1,445,176,0.019000," ","int(x^3*(a+b*arctan(c*x))^3,x)","\frac{i b^{3} \ln \left(c x -i\right)^{2}}{4 c^{4}}-\frac{i b^{3} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2 c^{4}}+\frac{i b^{3} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{4}}-\frac{i b^{3} \ln \left(c x +i\right)^{2}}{4 c^{4}}-\frac{b^{3} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{c^{4}}-\frac{b^{3} \arctan \left(c x \right)^{2} x^{3}}{4 c}+\frac{3 b^{3} \arctan \left(c x \right)^{2} x}{4 c^{3}}+\frac{b^{3} \arctan \left(c x \right) x^{2}}{4 c^{2}}-\frac{a^{2} b \,x^{3}}{4 c}+\frac{x^{2} a \,b^{2}}{4 c^{2}}+\frac{3 x \,a^{2} b}{4 c^{3}}-\frac{a \,b^{2} \ln \left(c^{2} x^{2}+1\right)}{c^{4}}-\frac{3 a^{2} b \arctan \left(c x \right)}{4 c^{4}}+\frac{3 x^{4} a^{2} b \arctan \left(c x \right)}{4}+\frac{3 a \,b^{2} x^{4} \arctan \left(c x \right)^{2}}{4}-\frac{3 a \,b^{2} \arctan \left(c x \right)^{2}}{4 c^{4}}-\frac{b^{3} x}{4 c^{3}}+\frac{b^{3} \arctan \left(c x \right)}{4 c^{4}}+\frac{x^{4} a^{3}}{4}+\frac{b^{3} x^{4} \arctan \left(c x \right)^{3}}{4}-\frac{b^{3} \arctan \left(c x \right)^{3}}{4 c^{4}}-\frac{i b^{3} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{2 c^{4}}+\frac{i b^{3} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{2 c^{4}}-\frac{i b^{3} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{2 c^{4}}+\frac{i b^{3} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{4}}-\frac{a \,b^{2} x^{3} \arctan \left(c x \right)}{2 c}+\frac{3 a \,b^{2} x \arctan \left(c x \right)}{2 c^{3}}"," ",0,"-1/c^4*b^3*arctan(c*x)*ln(c^2*x^2+1)-1/4/c*b^3*arctan(c*x)^2*x^3+3/4/c^3*b^3*arctan(c*x)^2*x+1/4/c^2*b^3*arctan(c*x)*x^2-1/4/c*a^2*b*x^3+1/4/c^2*x^2*a*b^2+3/4/c^3*x*a^2*b-1/2*I/c^4*b^3*dilog(1/2*I*(c*x-I))-1/4*I/c^4*b^3*ln(I+c*x)^2+1/4*I/c^4*b^3*ln(c*x-I)^2-1/c^4*a*b^2*ln(c^2*x^2+1)-3/4/c^4*a^2*b*arctan(c*x)+3/4*x^4*a^2*b*arctan(c*x)+3/4*a*b^2*x^4*arctan(c*x)^2+1/2*I/c^4*b^3*dilog(-1/2*I*(I+c*x))-3/4/c^4*a*b^2*arctan(c*x)^2-1/4*b^3*x/c^3+1/4*b^3*arctan(c*x)/c^4+1/4*x^4*a^3+1/4*b^3*x^4*arctan(c*x)^3-1/4/c^4*b^3*arctan(c*x)^3+1/2*I/c^4*b^3*ln(I+c*x)*ln(c^2*x^2+1)-1/2*I/c^4*b^3*ln(I+c*x)*ln(1/2*I*(c*x-I))+1/2*I/c^4*b^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2/c*a*b^2*x^3*arctan(c*x)+3/2/c^3*a*b^2*x*arctan(c*x)-1/2*I/c^4*b^3*ln(c*x-I)*ln(c^2*x^2+1)","B"
27,1,2020,189,2.526000," ","int(x^2*(a+b*arctan(c*x))^3,x)","\frac{b^{3} x \arctan \left(c x \right)}{c^{2}}+\frac{a \,b^{2} x}{c^{2}}+\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(c x \right)^{2} \pi}{4 c^{3}}-\frac{i b^{3} \arctan \left(c x \right)}{c^{3}}+\frac{i b^{3} \arctan \left(c x \right)^{3}}{3 c^{3}}-\frac{b^{3} \arctan \left(c x \right)^{2} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)}{c^{3}}-\frac{b^{3} \arctan \left(c x \right)^{2}}{2 c^{3}}+\frac{x^{3} b^{3} \arctan \left(c x \right)^{3}}{3}-\frac{b^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(c x \right)^{2} x}{8 c^{2}}+\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{4}}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i\right)^{3} \arctan \left(c x \right)^{2} x}{8 c^{2}}+\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{3} \arctan \left(c x \right)^{2} \pi}{4 c^{3}}+\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)^{3} \arctan \left(c x \right)^{2} \pi}{4 c^{3}}-\frac{i b^{3} \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)^{3} \arctan \left(c x \right)^{2} \pi}{8 c^{3}}-\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{4}}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i\right)^{3} \arctan \left(c x \right)^{2} \pi}{8 c^{3}}+\frac{i a \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{2 c^{3}}-\frac{i a \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{3}}-\frac{i a \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{2 c^{3}}+\frac{i a \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{2 c^{3}}-\frac{a \,b^{2} x^{2} \arctan \left(c x \right)}{c}+\frac{a \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{c^{3}}-\frac{i a \,b^{2} \ln \left(c x -i\right)^{2}}{4 c^{3}}+\frac{i a \,b^{2} \ln \left(c x +i\right)^{2}}{4 c^{3}}+\frac{i b^{3} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c^{3}}-\frac{i a \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2 c^{3}}+\frac{i a \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2 c^{3}}-\frac{b^{3} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right) \arctan \left(c x \right)^{2} x}{8 c^{2}}+\frac{b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)^{2} \arctan \left(c x \right)^{2} x}{4 c^{2}}-\frac{b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{4}}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i\right)^{2} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i\right) \arctan \left(c x \right)^{2} x}{4 c^{2}}+\frac{b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{4}}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i\right)^{2} \arctan \left(c x \right)^{2} x}{8 c^{2}}-\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \arctan \left(c x \right)^{2} \pi}{4 c^{3}}-\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{2} \mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \arctan \left(c x \right)^{2} \pi}{4 c^{3}}+\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \arctan \left(c x \right)^{2} \pi}{4 c^{3}}-\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)^{2} \arctan \left(c x \right)^{2} \pi}{2 c^{3}}+\frac{i b^{3} \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)\right) \arctan \left(c x \right)^{2} \pi}{4 c^{3}}-\frac{i b^{3} \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right) \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)\right)^{2} \arctan \left(c x \right)^{2} \pi}{8 c^{3}}+\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{4}}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i\right)^{2} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i\right) \arctan \left(c x \right)^{2} \pi}{4 c^{3}}-\frac{i b^{3} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{4}}{\left(c^{2} x^{2}+1\right)^{2}}+\frac{2 i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+i\right)^{2} \arctan \left(c x \right)^{2} \pi}{8 c^{3}}-\frac{b \,x^{2} a^{2}}{2 c}+b^{2} x^{3} a \arctan \left(c x \right)^{2}+a^{2} b \,x^{3} \arctan \left(c x \right)+\frac{b^{3} \arctan \left(c x \right)^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{3}}-\frac{a \,b^{2} \arctan \left(c x \right)}{c^{3}}+\frac{a^{2} b \ln \left(c^{2} x^{2}+1\right)}{2 c^{3}}-\frac{b^{3} \ln \left(2\right) \arctan \left(c x \right)^{2}}{c^{3}}-\frac{b^{3} \arctan \left(c x \right)^{2} x^{2}}{2 c}-\frac{b^{3} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c^{3}}+\frac{b^{3} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c^{3}}+\frac{a^{3} x^{3}}{3}"," ",0,"b^3*x*arctan(c*x)/c^2+a*b^2*x/c^2+1/4*I/c^3*b^3*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2*Pi-1/2/c^3*b^3*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-1/2/c^3*b^3*arctan(c*x)^2+1/3*x^3*b^3*arctan(c*x)^3+1/c^3*b^3*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-1/8/c^2*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2*x+1/8/c^2*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^3*arctan(c*x)^2*x+1/4*I/c^3*b^3*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2*Pi+1/4*I/c^3*b^3*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3*arctan(c*x)^2*Pi-1/8*I/c^3*b^3*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3*arctan(c*x)^2*Pi-1/8*I/c^3*b^3*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^3*arctan(c*x)^2*Pi+1/2*I/c^3*a*b^2*ln(c*x-I)*ln(c^2*x^2+1)-1/2*I/c^3*a*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))-1/2*I/c^3*a*b^2*ln(I+c*x)*ln(c^2*x^2+1)+1/2*I/c^3*a*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))-1/c*a*b^2*x^2*arctan(c*x)+I/c^3*b^3*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+1/c^3*a*b^2*arctan(c*x)*ln(c^2*x^2+1)-1/4*I/c^3*a*b^2*ln(c*x-I)^2-1/2*I/c^3*a*b^2*dilog(-1/2*I*(I+c*x))+1/4*I/c^3*a*b^2*ln(I+c*x)^2+1/2*I/c^3*a*b^2*dilog(1/2*I*(c*x-I))-1/8/c^2*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2*x+1/4/c^2*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*arctan(c*x)^2*x-1/4/c^2*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)*arctan(c*x)^2*x+1/8/c^2*b^3*Pi*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*arctan(c*x)^2*x-1/4*I/c^3*b^3*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^2*Pi-1/4*I/c^3*b^3*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*arctan(c*x)^2*Pi+1/4*I/c^3*b^3*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*arctan(c*x)^2*Pi-1/2*I/c^3*b^3*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2*arctan(c*x)^2*Pi+1/4*I/c^3*b^3*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2*Pi-1/8*I/c^3*b^3*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2*Pi+1/4*I/c^3*b^3*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)*arctan(c*x)^2*Pi-1/8*I/c^3*b^3*csgn(I*(1+I*c*x)^4/(c^2*x^2+1)^2+2*I*(1+I*c*x)^2/(c^2*x^2+1)+I)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)+I)^2*arctan(c*x)^2*Pi-I/c^3*b^3*arctan(c*x)+1/3*I/c^3*b^3*arctan(c*x)^3-1/2/c*b*x^2*a^2+b^2*x^3*a*arctan(c*x)^2+a^2*b*x^3*arctan(c*x)-1/c^3*b^3*arctan(c*x)^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2/c^3*b^3*arctan(c*x)^2*ln(c^2*x^2+1)-1/c^3*a*b^2*arctan(c*x)+1/2/c^3*a^2*b*ln(c^2*x^2+1)-1/c^3*b^3*ln(2)*arctan(c*x)^2-1/2/c*b^3*arctan(c*x)^2*x^2+1/3*a^3*x^3","C"
28,1,352,117,0.018000," ","int(x*(a+b*arctan(c*x))^3,x)","\frac{x^{2} a^{3}}{2}+\frac{x^{2} b^{3} \arctan \left(c x \right)^{3}}{2}+\frac{b^{3} \arctan \left(c x \right)^{3}}{2 c^{2}}-\frac{3 b^{3} \arctan \left(c x \right)^{2} x}{2 c}+\frac{3 b^{3} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{2 c^{2}}-\frac{3 i b^{3} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{4 c^{2}}+\frac{3 i b^{3} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{4 c^{2}}-\frac{3 i b^{3} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{4 c^{2}}-\frac{3 i b^{3} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{4 c^{2}}-\frac{3 i b^{3} \ln \left(c x -i\right)^{2}}{8 c^{2}}+\frac{3 i b^{3} \ln \left(c x +i\right)^{2}}{8 c^{2}}+\frac{3 i b^{3} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{4 c^{2}}+\frac{3 i b^{3} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{4 c^{2}}+\frac{3 x^{2} a \,b^{2} \arctan \left(c x \right)^{2}}{2}+\frac{3 a \,b^{2} \arctan \left(c x \right)^{2}}{2 c^{2}}-\frac{3 a \,b^{2} x \arctan \left(c x \right)}{c}+\frac{3 a \,b^{2} \ln \left(c^{2} x^{2}+1\right)}{2 c^{2}}+\frac{3 b \,x^{2} a^{2} \arctan \left(c x \right)}{2}-\frac{3 x \,a^{2} b}{2 c}+\frac{3 a^{2} b \arctan \left(c x \right)}{2 c^{2}}"," ",0,"1/2*x^2*a^3+1/2*x^2*b^3*arctan(c*x)^3+1/2/c^2*b^3*arctan(c*x)^3-3/2/c*b^3*arctan(c*x)^2*x+3/2/c^2*b^3*arctan(c*x)*ln(c^2*x^2+1)-3/4*I/c^2*b^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))+3/4*I/c^2*b^3*dilog(1/2*I*(c*x-I))+3/4*I/c^2*b^3*ln(c*x-I)*ln(c^2*x^2+1)-3/4*I/c^2*b^3*ln(I+c*x)*ln(c^2*x^2+1)-3/8*I/c^2*b^3*ln(c*x-I)^2+3/8*I/c^2*b^3*ln(I+c*x)^2-3/4*I/c^2*b^3*dilog(-1/2*I*(I+c*x))+3/4*I/c^2*b^3*ln(I+c*x)*ln(1/2*I*(c*x-I))+3/2*x^2*a*b^2*arctan(c*x)^2+3/2/c^2*a*b^2*arctan(c*x)^2-3/c*a*b^2*x*arctan(c*x)+3/2/c^2*a*b^2*ln(c^2*x^2+1)+3/2*b*x^2*a^2*arctan(c*x)-3/2/c*x*a^2*b+3/2/c^2*a^2*b*arctan(c*x)","B"
29,1,270,112,0.227000," ","int((a+b*arctan(c*x))^3,x)","x \,a^{3}-\frac{i b^{3} \arctan \left(c x \right)^{3}}{c}+b^{3} x \arctan \left(c x \right)^{3}+\frac{3 b^{3} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)}{c}-\frac{3 i b^{3} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{c}+\frac{3 b^{3} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2 c}-\frac{3 i \arctan \left(c x \right)^{2} a \,b^{2}}{c}+3 x a \,b^{2} \arctan \left(c x \right)^{2}+\frac{6 \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right) \arctan \left(c x \right) a \,b^{2}}{c}-\frac{3 i \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) a \,b^{2}}{c}+3 x \,a^{2} b \arctan \left(c x \right)-\frac{3 a^{2} b \ln \left(c^{2} x^{2}+1\right)}{2 c}"," ",0,"x*a^3-I/c*b^3*arctan(c*x)^3+b^3*x*arctan(c*x)^3+3/c*b^3*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)+1)-3*I/c*b^3*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+3/2/c*b^3*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))-3*I/c*arctan(c*x)^2*a*b^2+3*x*a*b^2*arctan(c*x)^2+6/c*ln((1+I*c*x)^2/(c^2*x^2+1)+1)*arctan(c*x)*a*b^2-3*I/c*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))*a*b^2+3*x*a^2*b*arctan(c*x)-3/2/c*a^2*b*ln(c^2*x^2+1)","B"
30,1,2309,183,0.243000," ","int((a+b*arctan(c*x))^3/x,x)","-3 a \,b^{2} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)+3 a \,b^{2} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+3 a \,b^{2} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{i b^{3} \pi  \arctan \left(c x \right)^{3}}{2}+\frac{3 i b^{3} \arctan \left(c x \right)^{2} \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}-3 i b^{3} \arctan \left(c x \right)^{2} \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{3 i a^{2} b \dilog \left(i c x +1\right)}{2}-\frac{3 i a^{2} b \dilog \left(-i c x +1\right)}{2}-3 i b^{3} \arctan \left(c x \right)^{2} \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{3 i a \,b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{3 i a \,b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{3}}{2}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{3}}{2}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{3}}{2}-\frac{i b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{3}}{2}-\frac{3 i a \,b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+a^{3} \ln \left(c x \right)+\frac{i b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{3}}{2}-\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+3 a \,b^{2} \ln \left(c x \right) \arctan \left(c x \right)^{2}+3 a^{2} b \ln \left(c x \right) \arctan \left(c x \right)+3 i a \,b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)+\frac{3 i a^{2} b \ln \left(c x \right) \ln \left(i c x +1\right)}{2}-\frac{3 i a^{2} b \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}-\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{3}}{2}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{3}}{2}+\frac{i b^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{3}}{2}+\frac{3 i a \,b^{2} \pi  \arctan \left(c x \right)^{2}}{2}-6 i a \,b^{2} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}+6 i b^{3} \polylog \left(4, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{3 a \,b^{2} \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}+6 a \,b^{2} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+6 a \,b^{2} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+6 b^{3} \arctan \left(c x \right) \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+6 b^{3} \arctan \left(c x \right) \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{3 b^{3} \arctan \left(c x \right) \polylog \left(3, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{2}+6 i b^{3} \polylog \left(4, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-\frac{3 i b^{3} \polylog \left(4, -\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{4}-b^{3} \arctan \left(c x \right)^{3} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)+b^{3} \arctan \left(c x \right)^{3} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+b^{3} \arctan \left(c x \right)^{3} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+\frac{3 i a \,b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}-6 i a \,b^{2} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+b^{3} \ln \left(c x \right) \arctan \left(c x \right)^{3}"," ",0,"3/2*I*a*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+3/2*I*a*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+1/2*I*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^3-1/2*I*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3-1/2*I*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3-1/2*I*b^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3-3/2*I*a*b^2*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*a^2*b*ln(c*x)*ln(1+I*c*x)-3/2*I*a^2*b*ln(c*x)*ln(1-I*c*x)-1/2*I*b^3*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^3+1/2*I*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^3+a^3*ln(c*x)+1/2*I*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^3-3/2*I*a*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*a*b^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*a*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*a*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+3*a*b^2*ln(c*x)*arctan(c*x)^2-3*a*b^2*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+3*a*b^2*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*a*b^2*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*a^2*b*ln(c*x)*arctan(c*x)+3/2*I*a^2*b*dilog(1+I*c*x)-3/2*I*a^2*b*dilog(1-I*c*x)+1/2*I*b^3*Pi*arctan(c*x)^3-3*I*b^3*arctan(c*x)^2*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+1/2*I*b^3*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^3-6*I*a*b^2*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*I*a*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I*a*b^2*Pi*arctan(c*x)^2+3*I*a*b^2*arctan(c*x)*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))+6*I*b^3*polylog(4,(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*a*b^2*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+3/2*I*b^3*arctan(c*x)^2*polylog(2,-(1+I*c*x)^2/(c^2*x^2+1))-3*I*b^3*arctan(c*x)^2*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I*a*b^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2+6*a*b^2*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*a*b^2*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^3*ln(c*x)*arctan(c*x)^3-b^3*arctan(c*x)^3*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+b^3*arctan(c*x)^3*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*b^3*arctan(c*x)*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+b^3*arctan(c*x)^3*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*b^3*arctan(c*x)*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*b^3*arctan(c*x)*polylog(3,-(1+I*c*x)^2/(c^2*x^2+1))+6*I*b^3*polylog(4,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/4*I*b^3*polylog(4,-(1+I*c*x)^2/(c^2*x^2+1))","C"
31,1,2159,109,0.291000," ","int((a+b*arctan(c*x))^3/x^2,x)","\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}+\frac{3 i c \,b^{3} \arctan \left(c x \right)^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)^{3}}{4}-\frac{3 i c a \,b^{2} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{2}+\frac{3 i c a \,b^{2} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2}+\frac{3 i c a \,b^{2} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{3 i c a \,b^{2} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{2}+3 i c a \,b^{2} \ln \left(c x \right) \ln \left(i c x +1\right)-3 i c a \,b^{2} \ln \left(c x \right) \ln \left(-i c x +1\right)-3 c \,b^{3} \arctan \left(c x \right)^{2} \ln \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)-i c \,b^{3} \arctan \left(c x \right)^{3}+3 c \,b^{3} \arctan \left(c x \right)^{2} \ln \left(1-\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+3 c \,b^{3} \arctan \left(c x \right)^{2} \ln \left(1+\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+3 c \,b^{3} \arctan \left(c x \right)^{2} \ln \left(\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+3 c \,b^{3} \ln \left(c x \right) \arctan \left(c x \right)^{2}-\frac{3 a \,b^{2} \arctan \left(c x \right)^{2}}{x}-\frac{3 a^{2} b \arctan \left(c x \right)}{x}+3 c \,a^{2} b \ln \left(c x \right)+3 c \,b^{3} \ln \left(2\right) \arctan \left(c x \right)^{2}-\frac{3 c \,a^{2} b \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{3 c \,b^{3} \arctan \left(c x \right)^{2} \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{b^{3} \arctan \left(c x \right)^{3}}{x}-\frac{3 i c a \,b^{2} \ln \left(c x +i\right)^{2}}{4}+\frac{3 i c \,b^{3} \pi  \arctan \left(c x \right)^{2}}{2}+\frac{3 i c a \,b^{2} \ln \left(c x -i\right)^{2}}{4}+\frac{3 i c a \,b^{2} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2}-\frac{3 i c a \,b^{2} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2}+3 i c a \,b^{2} \dilog \left(i c x +1\right)-3 i c a \,b^{2} \dilog \left(-i c x +1\right)-6 i c \,b^{3} \arctan \left(c x \right) \polylog \left(2, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+6 c \,b^{3} \polylog \left(3, \frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)+6 c \,b^{3} \polylog \left(3, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-6 i c \,b^{3} \arctan \left(c x \right) \polylog \left(2, -\frac{i c x +1}{\sqrt{c^{2} x^{2}+1}}\right)-3 c a \,b^{2} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)+6 c a \,b^{2} \ln \left(c x \right) \arctan \left(c x \right)-\frac{3 i c \,b^{3} \arctan \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{3}}{4}-\frac{3 i c \,b^{3} \arctan \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)^{3}}{4}+\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{3} \arctan \left(c x \right)^{2}}{2}-\frac{3 i c \,b^{3} \pi  \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{3 i c \,b^{3} \arctan \left(c x \right)^{2} \pi  \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)\right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)}{4}-\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}-\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{3 i c \,b^{3} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)^{2}}{2}-\frac{3 i c \,b^{3} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)\right) \mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}\right)^{2}}{2}+\frac{3 i c \,b^{3} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4}+\frac{3 i c \,b^{3} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)^{2}}{4}+\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}-\frac{3 i c \,b^{3} \arctan \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(i c x +1\right)}{\sqrt{c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right)}{4}-\frac{a^{3}}{x}-\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right)^{2} \arctan \left(c x \right)^{2}}{2}+\frac{3 i c \,b^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}-1\right)}{\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1}\right) \arctan \left(c x \right)^{2}}{2}-\frac{3 i c \,b^{3} \arctan \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{c^{2} x^{2}+1}\right) \mathrm{csgn}\left(\frac{i \left(i c x +1\right)^{2}}{\left(c^{2} x^{2}+1\right) \left(\frac{\left(i c x +1\right)^{2}}{c^{2} x^{2}+1}+1\right)^{2}}\right)}{4}"," ",0,"3/2*I*c*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-3/4*I*c*b^3*arctan(c*x)^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)-3/2*I*c*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/4*I*c*b^3*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))^2*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)-3/2*I*c*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2-3/2*I*c*b^3*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*c*b^3*arctan(c*x)^2*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^2-3/2*I*c*b^3*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2+3/4*I*c*b^3*arctan(c*x)^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2+3/4*I*c*b^3*arctan(c*x)^2*Pi*csgn(I/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^2-3*c*b^3*arctan(c*x)^2*ln((1+I*c*x)^2/(c^2*x^2+1)-1)+3*c*b^3*ln(c*x)*arctan(c*x)^2-3*a*b^2/x*arctan(c*x)^2-3*a^2*b/x*arctan(c*x)-I*c*b^3*arctan(c*x)^3+3*c*a^2*b*ln(c*x)+3*c*b^3*ln(2)*arctan(c*x)^2-3/2*c*a^2*b*ln(c^2*x^2+1)+3*c*b^3*arctan(c*x)^2*ln(1-(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*c*b^3*arctan(c*x)^2*ln(1+(1+I*c*x)/(c^2*x^2+1)^(1/2))+3*c*b^3*arctan(c*x)^2*ln((1+I*c*x)/(c^2*x^2+1)^(1/2))-3/2*c*b^3*arctan(c*x)^2*ln(c^2*x^2+1)-b^3/x*arctan(c*x)^3+6*c*b^3*polylog(3,(1+I*c*x)/(c^2*x^2+1)^(1/2))+6*c*b^3*polylog(3,-(1+I*c*x)/(c^2*x^2+1)^(1/2))-3/4*I*c*b^3*arctan(c*x)^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1)/((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-3/4*I*c*b^3*arctan(c*x)^2*Pi*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))^3+3/2*I*c*b^3*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2-3/2*I*c*b^3*Pi*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^2*arctan(c*x)^2+3/2*I*c*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))^3*arctan(c*x)^2+3/4*I*c*b^3*arctan(c*x)^2*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)+1)^2)^3-3/2*I*c*a*b^2*ln(c*x-I)*ln(c^2*x^2+1)+3/2*I*c*a*b^2*ln(c*x-I)*ln(-1/2*I*(I+c*x))+3/2*I*c*a*b^2*ln(I+c*x)*ln(c^2*x^2+1)-3/2*I*c*a*b^2*ln(I+c*x)*ln(1/2*I*(c*x-I))+3*I*c*a*b^2*ln(c*x)*ln(1+I*c*x)-3*I*c*a*b^2*ln(c*x)*ln(1-I*c*x)-3*c*a*b^2*arctan(c*x)*ln(c^2*x^2+1)+6*c*a*b^2*ln(c*x)*arctan(c*x)+3/2*I*c*a*b^2*dilog(-1/2*I*(I+c*x))-3/4*I*c*a*b^2*ln(I+c*x)^2-3/2*I*c*a*b^2*dilog(1/2*I*(c*x-I))+3*I*c*a*b^2*dilog(1+I*c*x)-3*I*c*a*b^2*dilog(1-I*c*x)-6*I*c*b^3*arctan(c*x)*polylog(2,(1+I*c*x)/(c^2*x^2+1)^(1/2))-6*I*c*b^3*arctan(c*x)*polylog(2,-(1+I*c*x)/(c^2*x^2+1)^(1/2))+3/2*I*c*b^3*Pi*arctan(c*x)^2+3/4*I*c*a*b^2*ln(c*x-I)^2-a^3/x+3/2*I*c*b^3*Pi*csgn(I*((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*csgn(((1+I*c*x)^2/(c^2*x^2+1)-1)/((1+I*c*x)^2/(c^2*x^2+1)+1))*arctan(c*x)^2-3/4*I*c*b^3*arctan(c*x)^2*Pi*csgn(I*(1+I*c*x)/(c^2*x^2+1)^(1/2))^2*csgn(I*(1+I*c*x)^2/(c^2*x^2+1))","C"
32,1,457,119,0.021000," ","int((a+b*arctan(c*x))^3/x^3,x)","-\frac{3 i c^{2} b^{3} \ln \left(c x +i\right)^{2}}{8}+\frac{3 i c^{2} b^{3} \ln \left(c x -i\right)^{2}}{8}-\frac{3 i c^{2} b^{3} \dilog \left(-i c x +1\right)}{2}+\frac{3 i c^{2} b^{3} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{4}-\frac{3 i c^{2} b^{3} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{4}+\frac{3 i c^{2} b^{3} \dilog \left(i c x +1\right)}{2}+3 c^{2} a \,b^{2} \ln \left(c x \right)-\frac{3 c^{2} a \,b^{2} \arctan \left(c x \right)^{2}}{2}-\frac{3 c \,a^{2} b}{2 x}-\frac{3 c^{2} b^{3} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)}{2}+3 c^{2} b^{3} \arctan \left(c x \right) \ln \left(c x \right)-\frac{3 c^{2} a^{2} b \arctan \left(c x \right)}{2}-\frac{3 c^{2} a \,b^{2} \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{3 a \,b^{2} \arctan \left(c x \right)^{2}}{2 x^{2}}-\frac{3 a^{2} b \arctan \left(c x \right)}{2 x^{2}}-\frac{3 c \,b^{3} \arctan \left(c x \right)^{2}}{2 x}-\frac{a^{3}}{2 x^{2}}+\frac{3 i c^{2} b^{3} \ln \left(c x \right) \ln \left(i c x +1\right)}{2}+\frac{3 i c^{2} b^{3} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{4}-\frac{3 i c^{2} b^{3} \ln \left(c x \right) \ln \left(-i c x +1\right)}{2}-\frac{3 i c^{2} b^{3} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{4}-\frac{3 i c^{2} b^{3} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{4}+\frac{3 i c^{2} b^{3} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{4}-\frac{b^{3} \arctan \left(c x \right)^{3}}{2 x^{2}}-\frac{c^{2} b^{3} \arctan \left(c x \right)^{3}}{2}-\frac{3 c a \,b^{2} \arctan \left(c x \right)}{x}"," ",0,"3*c^2*a*b^2*ln(c*x)-3/2*c^2*a*b^2*arctan(c*x)^2-3/2*c*a^2*b/x+3/2*I*c^2*b^3*dilog(1+I*c*x)+3/4*I*c^2*b^3*dilog(-1/2*I*(I+c*x))-3/8*I*c^2*b^3*ln(I+c*x)^2-3/4*I*c^2*b^3*dilog(1/2*I*(c*x-I))-3/2*c^2*b^3*arctan(c*x)*ln(c^2*x^2+1)+3*c^2*b^3*arctan(c*x)*ln(c*x)-3/2*c^2*a^2*b*arctan(c*x)-3/2*c^2*a*b^2*ln(c^2*x^2+1)-3/2*a*b^2/x^2*arctan(c*x)^2-3/2*a^2*b/x^2*arctan(c*x)-3/2*c*b^3*arctan(c*x)^2/x+3/8*I*c^2*b^3*ln(c*x-I)^2-3/2*I*c^2*b^3*dilog(1-I*c*x)-1/2*a^3/x^2-1/2*b^3/x^2*arctan(c*x)^3-1/2*c^2*b^3*arctan(c*x)^3-3/2*I*c^2*b^3*ln(c*x)*ln(1-I*c*x)-3/4*I*c^2*b^3*ln(c*x-I)*ln(c^2*x^2+1)-3/4*I*c^2*b^3*ln(I+c*x)*ln(1/2*I*(c*x-I))+3/4*I*c^2*b^3*ln(I+c*x)*ln(c^2*x^2+1)+3/2*I*c^2*b^3*ln(c*x)*ln(1+I*c*x)+3/4*I*c^2*b^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))-3*c*a*b^2/x*arctan(c*x)","B"
33,1,5974,196,3.190000," ","int((a+b*arctan(c*x))^3/x^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
34,1,550,180,0.024000," ","int((a+b*arctan(c*x))^3/x^5,x)","i c^{4} b^{3} \dilog \left(-i c x +1\right)-\frac{i c^{4} b^{3} \dilog \left(-\frac{i \left(c x +i\right)}{2}\right)}{2}-i c^{4} b^{3} \dilog \left(i c x +1\right)+\frac{i c^{4} b^{3} \dilog \left(\frac{i \left(c x -i\right)}{2}\right)}{2}+\frac{i c^{4} b^{3} \ln \left(c x +i\right)^{2}}{4}-\frac{i c^{4} b^{3} \ln \left(c x -i\right)^{2}}{4}-\frac{c \,a^{2} b}{4 x^{3}}-\frac{c^{2} a \,b^{2}}{4 x^{2}}+\frac{3 c^{3} a^{2} b}{4 x}+c^{4} a \,b^{2} \ln \left(c^{2} x^{2}+1\right)+\frac{3 c^{4} a^{2} b \arctan \left(c x \right)}{4}+\frac{3 c^{4} a \,b^{2} \arctan \left(c x \right)^{2}}{4}-\frac{3 a^{2} b \arctan \left(c x \right)}{4 x^{4}}-\frac{3 a \,b^{2} \arctan \left(c x \right)^{2}}{4 x^{4}}-\frac{c^{2} b^{3} \arctan \left(c x \right)}{4 x^{2}}-\frac{c \,b^{3} \arctan \left(c x \right)^{2}}{4 x^{3}}+\frac{3 c^{3} b^{3} \arctan \left(c x \right)^{2}}{4 x}+c^{4} b^{3} \arctan \left(c x \right) \ln \left(c^{2} x^{2}+1\right)-2 c^{4} b^{3} \arctan \left(c x \right) \ln \left(c x \right)-2 c^{4} a \,b^{2} \ln \left(c x \right)-\frac{b^{3} c^{3}}{4 x}-\frac{b^{3} c^{4} \arctan \left(c x \right)}{4}-\frac{c a \,b^{2} \arctan \left(c x \right)}{2 x^{3}}+\frac{3 c^{3} a \,b^{2} \arctan \left(c x \right)}{2 x}-\frac{a^{3}}{4 x^{4}}+\frac{i c^{4} b^{3} \ln \left(c x -i\right) \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{i c^{4} b^{3} \ln \left(c x +i\right) \ln \left(c^{2} x^{2}+1\right)}{2}-\frac{i c^{4} b^{3} \ln \left(c x -i\right) \ln \left(-\frac{i \left(c x +i\right)}{2}\right)}{2}-i c^{4} b^{3} \ln \left(c x \right) \ln \left(i c x +1\right)+\frac{i c^{4} b^{3} \ln \left(c x +i\right) \ln \left(\frac{i \left(c x -i\right)}{2}\right)}{2}+i c^{4} b^{3} \ln \left(c x \right) \ln \left(-i c x +1\right)-\frac{b^{3} \arctan \left(c x \right)^{3}}{4 x^{4}}+\frac{c^{4} b^{3} \arctan \left(c x \right)^{3}}{4}"," ",0,"-1/4*c*a^2*b/x^3-1/4*c^2*a*b^2/x^2+3/4*c^3*a^2*b/x+c^4*a*b^2*ln(c^2*x^2+1)+3/4*c^4*a^2*b*arctan(c*x)+3/4*c^4*a*b^2*arctan(c*x)^2+I*c^4*b^3*dilog(1-I*c*x)-3/4*a^2*b/x^4*arctan(c*x)-3/4*a*b^2/x^4*arctan(c*x)^2-1/2*I*c^4*b^3*dilog(-1/2*I*(I+c*x))+1/4*I*c^4*b^3*ln(I+c*x)^2-I*c^4*b^3*dilog(1+I*c*x)-1/4*I*c^4*b^3*ln(c*x-I)^2+1/2*I*c^4*b^3*dilog(1/2*I*(c*x-I))-1/4*c^2*b^3*arctan(c*x)/x^2-1/4*c*b^3*arctan(c*x)^2/x^3+3/4*c^3*b^3*arctan(c*x)^2/x+c^4*b^3*arctan(c*x)*ln(c^2*x^2+1)-2*c^4*b^3*arctan(c*x)*ln(c*x)-2*c^4*a*b^2*ln(c*x)-1/4*b^3*c^3/x-1/4*b^3*c^4*arctan(c*x)-1/2*c*a*b^2/x^3*arctan(c*x)+3/2*c^3*a*b^2/x*arctan(c*x)+1/2*I*c^4*b^3*ln(c*x-I)*ln(c^2*x^2+1)-1/2*I*c^4*b^3*ln(I+c*x)*ln(c^2*x^2+1)-1/2*I*c^4*b^3*ln(c*x-I)*ln(-1/2*I*(I+c*x))-I*c^4*b^3*ln(c*x)*ln(1+I*c*x)+1/2*I*c^4*b^3*ln(I+c*x)*ln(1/2*I*(c*x-I))+I*c^4*b^3*ln(c*x)*ln(1-I*c*x)-1/4*a^3/x^4-1/4*b^3/x^4*arctan(c*x)^3+1/4*c^4*b^3*arctan(c*x)^3","B"
35,0,0,10,0.466000," ","int(x/arctan(a*x),x)","\int \frac{x}{\arctan \left(a x \right)}\, dx"," ",0,"int(x/arctan(a*x),x)","F"
36,0,0,8,0.269000," ","int(1/arctan(a*x),x)","\int \frac{1}{\arctan \left(a x \right)}\, dx"," ",0,"int(1/arctan(a*x),x)","F"
37,0,0,12,0.321000," ","int(1/x/arctan(a*x),x)","\int \frac{1}{x \arctan \left(a x \right)}\, dx"," ",0,"int(1/x/arctan(a*x),x)","F"
38,0,0,10,0.708000," ","int(x/arctan(a*x)^2,x)","\int \frac{x}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(x/arctan(a*x)^2,x)","F"
39,0,0,8,0.264000," ","int(1/arctan(a*x)^2,x)","\int \frac{1}{\arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/arctan(a*x)^2,x)","F"
40,0,0,12,0.382000," ","int(1/x/arctan(a*x)^2,x)","\int \frac{1}{x \arctan \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/arctan(a*x)^2,x)","F"
41,0,0,10,0.966000," ","int(x*arctan(a*x)^(1/2),x)","\int x \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(x*arctan(a*x)^(1/2),x)","F"
42,0,0,8,0.488000," ","int(arctan(a*x)^(1/2),x)","\int \sqrt{\arctan \left(a x \right)}\, dx"," ",0,"int(arctan(a*x)^(1/2),x)","F"
43,0,0,12,0.999000," ","int(arctan(a*x)^(1/2)/x,x)","\int \frac{\sqrt{\arctan \left(a x \right)}}{x}\, dx"," ",0,"int(arctan(a*x)^(1/2)/x,x)","F"
44,0,0,10,0.952000," ","int(x*arctan(a*x)^(3/2),x)","\int x \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(x*arctan(a*x)^(3/2),x)","F"
45,0,0,8,0.448000," ","int(arctan(a*x)^(3/2),x)","\int \arctan \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int(arctan(a*x)^(3/2),x)","F"
46,0,0,12,1.136000," ","int(arctan(a*x)^(3/2)/x,x)","\int \frac{\arctan \left(a x \right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int(arctan(a*x)^(3/2)/x,x)","F"
47,0,0,10,0.977000," ","int(x/arctan(a*x)^(1/2),x)","\int \frac{x}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(x/arctan(a*x)^(1/2),x)","F"
48,0,0,8,0.452000," ","int(1/arctan(a*x)^(1/2),x)","\int \frac{1}{\sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/arctan(a*x)^(1/2),x)","F"
49,0,0,12,0.716000," ","int(1/x/arctan(a*x)^(1/2),x)","\int \frac{1}{x \sqrt{\arctan \left(a x \right)}}\, dx"," ",0,"int(1/x/arctan(a*x)^(1/2),x)","F"
50,0,0,10,0.977000," ","int(x/arctan(a*x)^(3/2),x)","\int \frac{x}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/arctan(a*x)^(3/2),x)","F"
51,0,0,8,0.508000," ","int(1/arctan(a*x)^(3/2),x)","\int \frac{1}{\arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/arctan(a*x)^(3/2),x)","F"
52,0,0,12,1.138000," ","int(1/x/arctan(a*x)^(3/2),x)","\int \frac{1}{x \arctan \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/x/arctan(a*x)^(3/2),x)","F"
53,1,74,76,0.025000," ","int(arctan(x)*x^(1/2),x)","\frac{2 x^{\frac{3}{2}} \arctan \left(x \right)}{3}-\frac{4 \sqrt{x}}{3}+\frac{\arctan \left(1+\sqrt{2}\, \sqrt{x}\right) \sqrt{2}}{3}+\frac{\arctan \left(-1+\sqrt{2}\, \sqrt{x}\right) \sqrt{2}}{3}+\frac{\sqrt{2}\, \ln \left(\frac{1+x +\sqrt{2}\, \sqrt{x}}{1+x -\sqrt{2}\, \sqrt{x}}\right)}{6}"," ",0,"2/3*x^(3/2)*arctan(x)-4/3*x^(1/2)+1/3*arctan(1+2^(1/2)*x^(1/2))*2^(1/2)+1/3*arctan(-1+2^(1/2)*x^(1/2))*2^(1/2)+1/6*2^(1/2)*ln((1+x+2^(1/2)*x^(1/2))/(1+x-2^(1/2)*x^(1/2)))","A"
54,0,0,18,3.371000," ","int((d*x)^m*(a+b*arctan(c*x))^3,x)","\int \left(d x \right)^{m} \left(a +b \arctan \left(c x \right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arctan(c*x))^3,x)","F"
55,0,0,18,2.928000," ","int((d*x)^m*(a+b*arctan(c*x))^2,x)","\int \left(d x \right)^{m} \left(a +b \arctan \left(c x \right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arctan(c*x))^2,x)","F"
56,0,0,71,2.771000," ","int((d*x)^m*(a+b*arctan(c*x)),x)","\int \left(d x \right)^{m} \left(a +b \arctan \left(c x \right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arctan(c*x)),x)","F"
57,0,0,18,1.127000," ","int((d*x)^m/(a+b*arctan(c*x)),x)","\int \frac{\left(d x \right)^{m}}{a +b \arctan \left(c x \right)}\, dx"," ",0,"int((d*x)^m/(a+b*arctan(c*x)),x)","F"
58,0,0,12,0.696000," ","int((a+b*arctan(c*x))^p,x)","\int \left(a +b \arctan \left(c x \right)\right)^{p}\, dx"," ",0,"int((a+b*arctan(c*x))^p,x)","F"
59,0,0,18,1.359000," ","int((d*x)^m*(a+b*arctan(c*x))^p,x)","\int \left(d x \right)^{m} \left(a +b \arctan \left(c x \right)\right)^{p}\, dx"," ",0,"int((d*x)^m*(a+b*arctan(c*x))^p,x)","F"
60,1,50,46,0.031000," ","int(x^7*(a+b*arctan(c*x^2)),x)","\frac{x^{8} a}{8}+\frac{b \,x^{8} \arctan \left(c \,x^{2}\right)}{8}-\frac{b \,x^{6}}{24 c}+\frac{b \,x^{2}}{8 c^{3}}-\frac{b \arctan \left(c \,x^{2}\right)}{8 c^{4}}"," ",0,"1/8*x^8*a+1/8*b*x^8*arctan(c*x^2)-1/24*b*x^6/c+1/8*b*x^2/c^3-1/8*b*arctan(c*x^2)/c^4","A"
61,1,45,41,0.035000," ","int(x^5*(a+b*arctan(c*x^2)),x)","\frac{x^{6} a}{6}+\frac{b \,x^{6} \arctan \left(c \,x^{2}\right)}{6}-\frac{b \,x^{4}}{12 c}+\frac{b \ln \left(c^{2} x^{4}+1\right)}{12 c^{3}}"," ",0,"1/6*x^6*a+1/6*b*x^6*arctan(c*x^2)-1/12*b*x^4/c+1/12*b*ln(c^2*x^4+1)/c^3","A"
62,1,41,37,0.029000," ","int(x^3*(a+b*arctan(c*x^2)),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arctan \left(c \,x^{2}\right)}{4}-\frac{b \,x^{2}}{4 c}+\frac{b \arctan \left(c \,x^{2}\right)}{4 c^{2}}"," ",0,"1/4*x^4*a+1/4*b*x^4*arctan(c*x^2)-1/4*b*x^2/c+1/4*b*arctan(c*x^2)/c^2","A"
63,1,36,32,0.023000," ","int(x*(a+b*arctan(c*x^2)),x)","\frac{a \,x^{2}}{2}+\frac{b \,x^{2} \arctan \left(c \,x^{2}\right)}{2}-\frac{b \ln \left(c^{2} x^{4}+1\right)}{4 c}"," ",0,"1/2*a*x^2+1/2*b*x^2*arctan(c*x^2)-1/4*b*ln(c^2*x^4+1)/c","A"
64,1,63,31,0.109000," ","int((a+b*arctan(c*x^2))/x,x)","a \ln \left(x \right)+b \ln \left(x \right) \arctan \left(c \,x^{2}\right)-\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} \textit{\_Z}^{4}+1\right)}{\sum}\frac{\ln \left(x \right) \ln \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)}{\textit{\_R1}^{2}}\right)}{2 c}"," ",0,"a*ln(x)+b*ln(x)*arctan(c*x^2)-1/2*b/c*sum(1/_R1^2*(ln(x)*ln((_R1-x)/_R1)+dilog((_R1-x)/_R1)),_R1=RootOf(_Z^4*c^2+1))","C"
65,1,39,38,0.030000," ","int((a+b*arctan(c*x^2))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctan \left(c \,x^{2}\right)}{2 x^{2}}+b c \ln \left(x \right)-\frac{b c \ln \left(c^{2} x^{4}+1\right)}{4}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctan(c*x^2)+b*c*ln(x)-1/4*b*c*ln(c^2*x^4+1)","A"
66,1,39,38,0.032000," ","int((a+b*arctan(c*x^2))/x^5,x)","-\frac{a}{4 x^{4}}-\frac{b \arctan \left(c \,x^{2}\right)}{4 x^{4}}-\frac{b \,c^{2} \arctan \left(c \,x^{2}\right)}{4}-\frac{b c}{4 x^{2}}"," ",0,"-1/4*a/x^4-1/4*b/x^4*arctan(c*x^2)-1/4*b*c^2*arctan(c*x^2)-1/4*b*c/x^2","A"
67,1,51,50,0.033000," ","int((a+b*arctan(c*x^2))/x^7,x)","-\frac{a}{6 x^{6}}-\frac{b \arctan \left(c \,x^{2}\right)}{6 x^{6}}-\frac{b c}{12 x^{4}}-\frac{b \,c^{3} \ln \left(x \right)}{3}+\frac{b \,c^{3} \ln \left(c^{2} x^{4}+1\right)}{12}"," ",0,"-1/6*a/x^6-1/6*b/x^6*arctan(c*x^2)-1/12*b*c/x^4-1/3*b*c^3*ln(x)+1/12*b*c^3*ln(c^2*x^4+1)","A"
68,1,140,116,0.039000," ","int(x^4*(a+b*arctan(c*x^2)),x)","\frac{a \,x^{5}}{5}+\frac{b \,x^{5} \arctan \left(c \,x^{2}\right)}{5}-\frac{2 b \,x^{3}}{15 c}+\frac{b \sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{20 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{10 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{10 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}"," ",0,"1/5*a*x^5+1/5*b*x^5*arctan(c*x^2)-2/15*b*x^3/c+1/20*b/c^3/(1/c^2)^(1/4)*2^(1/2)*ln((x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))+1/10*b/c^3/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)+1/10*b/c^3/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)","A"
69,1,138,114,0.027000," ","int(x^2*(a+b*arctan(c*x^2)),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctan \left(c \,x^{2}\right)}{3}-\frac{2 b x}{3 c}+\frac{b \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{12 c}+\frac{b \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{6 c}+\frac{b \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{6 c}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctan(c*x^2)-2/3*b*x/c+1/12*b/c*(1/c^2)^(1/4)*2^(1/2)*ln((x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))+1/6*b/c*(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)+1/6*b/c*(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)","A"
70,1,125,104,0.029000," ","int(a+b*arctan(c*x^2),x)","a x +b x \arctan \left(c \,x^{2}\right)-\frac{b \sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}"," ",0,"a*x+b*x*arctan(c*x^2)-1/4*b/c/(1/c^2)^(1/4)*2^(1/2)*ln((x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))-1/2*b/c/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)-1/2*b/c/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)","A"
71,1,125,109,0.026000," ","int((a+b*arctan(c*x^2))/x^2,x)","-\frac{a}{x}-\frac{b \arctan \left(c \,x^{2}\right)}{x}+\frac{b c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{2}+\frac{b c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{4}+\frac{b c \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{2}"," ",0,"-a/x-b/x*arctan(c*x^2)+1/2*b*c*(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)+1/4*b*c*(1/c^2)^(1/4)*2^(1/2)*ln((x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))+1/2*b*c*(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)","A"
72,1,132,117,0.033000," ","int((a+b*arctan(c*x^2))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctan \left(c \,x^{2}\right)}{3 x^{3}}-\frac{2 b c}{3 x}-\frac{b c \sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{12 \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b c \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{6 \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-\frac{b c \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{6 \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctan(c*x^2)-2/3*b*c/x-1/12*b*c/(1/c^2)^(1/4)*2^(1/2)*ln((x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))-1/6*b*c/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)-1/6*b*c/(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)","A"
73,1,138,117,0.032000," ","int((a+b*arctan(c*x^2))/x^6,x)","-\frac{a}{5 x^{5}}-\frac{b \arctan \left(c \,x^{2}\right)}{5 x^{5}}-\frac{2 b c}{15 x^{3}}-\frac{b \,c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}-1\right)}{10}-\frac{b \,c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}{x^{2}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{\frac{1}{c^{2}}}}\right)}{20}-\frac{b \,c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{4}}}+1\right)}{10}"," ",0,"-1/5*a/x^5-1/5*b/x^5*arctan(c*x^2)-2/15*b*c/x^3-1/10*b*c^3*(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x-1)-1/20*b*c^3*(1/c^2)^(1/4)*2^(1/2)*ln((x^2+(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2))/(x^2-(1/c^2)^(1/4)*x*2^(1/2)+(1/c^2)^(1/2)))-1/10*b*c^3*(1/c^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(1/c^2)^(1/4)*x+1)","A"
74,1,151,110,0.051000," ","int(x^7*(a+b*arctan(c*x^2))^2,x)","\frac{x^{8} a^{2}}{8}+\frac{b^{2} x^{8} \arctan \left(c \,x^{2}\right)^{2}}{8}-\frac{b^{2} \arctan \left(c \,x^{2}\right) x^{6}}{12 c}+\frac{b^{2} x^{2} \arctan \left(c \,x^{2}\right)}{4 c^{3}}-\frac{b^{2} \arctan \left(c \,x^{2}\right)^{2}}{8 c^{4}}+\frac{b^{2} x^{4}}{24 c^{2}}-\frac{b^{2} \ln \left(c^{2} x^{4}+1\right)}{6 c^{4}}+\frac{a b \,x^{8} \arctan \left(c \,x^{2}\right)}{4}-\frac{a b \,x^{6}}{12 c}+\frac{a b \,x^{2}}{4 c^{3}}-\frac{a b \arctan \left(c \,x^{2}\right)}{4 c^{4}}"," ",0,"1/8*x^8*a^2+1/8*b^2*x^8*arctan(c*x^2)^2-1/12*b^2*arctan(c*x^2)/c*x^6+1/4*b^2*x^2*arctan(c*x^2)/c^3-1/8*b^2/c^4*arctan(c*x^2)^2+1/24*b^2*x^4/c^2-1/6*b^2*ln(c^2*x^4+1)/c^4+1/4*a*b*x^8*arctan(c*x^2)-1/12*a*b/c*x^6+1/4*a*b*x^2/c^3-1/4*a*b/c^4*arctan(c*x^2)","A"
75,-2,0,136,180.000000," ","int(x^5*(a+b*arctan(c*x^2))^2,x)","\int x^{5} \left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int(x^5*(a+b*arctan(c*x^2))^2,x)","F"
76,1,113,80,0.035000," ","int(x^3*(a+b*arctan(c*x^2))^2,x)","\frac{a^{2} x^{4}}{4}+\frac{b^{2} x^{4} \arctan \left(c \,x^{2}\right)^{2}}{4}-\frac{b^{2} x^{2} \arctan \left(c \,x^{2}\right)}{2 c}+\frac{b^{2} \arctan \left(c \,x^{2}\right)^{2}}{4 c^{2}}+\frac{b^{2} \ln \left(c^{2} x^{4}+1\right)}{4 c^{2}}+\frac{a b \,x^{4} \arctan \left(c \,x^{2}\right)}{2}-\frac{a b \,x^{2}}{2 c}+\frac{a b \arctan \left(c \,x^{2}\right)}{2 c^{2}}"," ",0,"1/4*a^2*x^4+1/4*b^2*x^4*arctan(c*x^2)^2-1/2*b^2*x^2*arctan(c*x^2)/c+1/4*b^2/c^2*arctan(c*x^2)^2+1/4*b^2*ln(c^2*x^4+1)/c^2+1/2*a*b*x^4*arctan(c*x^2)-1/2*a*b*x^2/c+1/2*a*b/c^2*arctan(c*x^2)","A"
77,1,146,91,0.206000," ","int(x*(a+b*arctan(c*x^2))^2,x)","\frac{\arctan \left(c \,x^{2}\right)^{2} x^{2} b^{2}}{2}+x^{2} a b \arctan \left(c \,x^{2}\right)-\frac{i \arctan \left(c \,x^{2}\right)^{2} b^{2}}{2 c}+\frac{a^{2} x^{2}}{2}-\frac{i \polylog \left(2, -\frac{\left(i c \,x^{2}+1\right)^{2}}{c^{2} x^{4}+1}\right) b^{2}}{2 c}+\frac{\arctan \left(c \,x^{2}\right) \ln \left(\frac{\left(i c \,x^{2}+1\right)^{2}}{c^{2} x^{4}+1}+1\right) b^{2}}{c}-\frac{a b \ln \left(c^{2} x^{4}+1\right)}{2 c}"," ",0,"1/2*arctan(c*x^2)^2*x^2*b^2+x^2*a*b*arctan(c*x^2)-1/2*I/c*arctan(c*x^2)^2*b^2+1/2*a^2*x^2-1/2*I/c*polylog(2,-(1+I*c*x^2)^2/(c^2*x^4+1))*b^2+1/c*arctan(c*x^2)*ln((1+I*c*x^2)^2/(c^2*x^4+1)+1)*b^2-1/2/c*a*b*ln(c^2*x^4+1)","A"
78,0,0,137,0.356000," ","int((a+b*arctan(c*x^2))^2/x,x)","\int \frac{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}}{x}\, dx"," ",0,"int((a+b*arctan(c*x^2))^2/x,x)","F"
79,0,0,87,0.595000," ","int((a+b*arctan(c*x^2))^2/x^3,x)","\int \frac{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}}{x^{3}}\, dx"," ",0,"int((a+b*arctan(c*x^2))^2/x^3,x)","F"
80,1,118,79,0.056000," ","int((a+b*arctan(c*x^2))^2/x^5,x)","-\frac{a^{2}}{4 x^{4}}-\frac{b^{2} \arctan \left(c \,x^{2}\right)^{2}}{4 x^{4}}-\frac{b^{2} c^{2} \arctan \left(c \,x^{2}\right)^{2}}{4}-\frac{b^{2} c \arctan \left(c \,x^{2}\right)}{2 x^{2}}+b^{2} c^{2} \ln \left(x \right)-\frac{b^{2} c^{2} \ln \left(c^{2} x^{4}+1\right)}{4}-\frac{a b \arctan \left(c \,x^{2}\right)}{2 x^{4}}-\frac{a b \,c^{2} \arctan \left(c \,x^{2}\right)}{2}-\frac{c a b}{2 x^{2}}"," ",0,"-1/4*a^2/x^4-1/4*b^2/x^4*arctan(c*x^2)^2-1/4*b^2*c^2*arctan(c*x^2)^2-1/2*b^2*c*arctan(c*x^2)/x^2+b^2*c^2*ln(x)-1/4*b^2*c^2*ln(c^2*x^4+1)-1/2*a*b/x^4*arctan(c*x^2)-1/2*a*b*c^2*arctan(c*x^2)-1/2*c*a*b/x^2","A"
81,0,0,1030,0.357000," ","int(x^2*(a+b*arctan(c*x^2))^2,x)","\int x^{2} \left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int(x^2*(a+b*arctan(c*x^2))^2,x)","F"
82,0,0,901,0.307000," ","int((a+b*arctan(c*x^2))^2,x)","\int \left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int((a+b*arctan(c*x^2))^2,x)","F"
83,0,0,882,0.326000," ","int((a+b*arctan(c*x^2))^2/x^2,x)","\int \frac{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}}{x^{2}}\, dx"," ",0,"int((a+b*arctan(c*x^2))^2/x^2,x)","F"
84,0,0,1004,0.333000," ","int((a+b*arctan(c*x^2))^2/x^4,x)","\int \frac{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}}{x^{4}}\, dx"," ",0,"int((a+b*arctan(c*x^2))^2/x^4,x)","F"
85,0,0,1075,0.346000," ","int((a+b*arctan(c*x^2))^2/x^6,x)","\int \frac{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}}{x^{6}}\, dx"," ",0,"int((a+b*arctan(c*x^2))^2/x^6,x)","F"
86,1,690,133,1.560000," ","int(x^3*(a+b*arctan(c*x^2))^3,x)","-\frac{3 a \,b^{2} x^{4} \ln \left(-i c \,x^{2}+1\right)^{2}}{16}+\frac{3 a \,b^{2} \ln \left(c^{2} x^{4}+1\right)}{4 c^{2}}-\frac{3 a \,b^{2} \ln \left(-i c \,x^{2}+1\right)^{2}}{16 c^{2}}-\frac{3 b^{2} \left(i x^{4} b \ln \left(-i c \,x^{2}+1\right) c^{2}+2 a \,c^{2} x^{4}-2 b c \,x^{2}+i b \ln \left(-i c \,x^{2}+1\right)+2 i b +2 a \right) \ln \left(i c \,x^{2}+1\right)^{2}}{32 c^{2}}+\frac{3 i a^{2} b \,x^{4} \ln \left(-i c \,x^{2}+1\right)}{8}-\frac{i b^{3} x^{4} \ln \left(-i c \,x^{2}+1\right)^{3}}{32}+\frac{i b^{3} \left(c^{2} x^{4}+1\right) \ln \left(i c \,x^{2}+1\right)^{3}}{32 c^{2}}-\frac{3 i a \,b^{2} x^{2} \ln \left(-i c \,x^{2}+1\right)}{4 c}+\frac{3 a^{2} b \arctan \left(c \,x^{2}\right)}{4 c^{2}}+\frac{3 b^{3} x^{2} \ln \left(-i c \,x^{2}+1\right)^{2}}{16 c}-\frac{i b^{3} \ln \left(-i c \,x^{2}+1\right)^{3}}{32 c^{2}}+\frac{3 i b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{2}-\RootOf \left(\textit{\_Z}^{2}+1, \mathit{index} =1\right)\right)}{\sum}\frac{\left(\ln \left(x -\underline{\hspace{1.25 ex}}\alpha  \right) \ln \left(-i c \,x^{2}+1\right)+2 c \left(-\frac{\ln \left(x -\underline{\hspace{1.25 ex}}\alpha  \right) \left(\ln \left(\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \left(i \sqrt{\frac{i}{c}}+\sqrt{\frac{i}{c}}+x -\underline{\hspace{1.25 ex}}\alpha  \right)}{\sqrt{\frac{i}{c}}}\right)+\ln \left(\frac{\left(-\frac{1}{2}-\frac{i}{2}\right) \left(i \sqrt{\frac{i}{c}}-\sqrt{\frac{i}{c}}-x +\underline{\hspace{1.25 ex}}\alpha  \right)}{\sqrt{\frac{i}{c}}}\right)\right)}{2 c}-\frac{\dilog \left(\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \left(i \sqrt{\frac{i}{c}}+\sqrt{\frac{i}{c}}+x -\underline{\hspace{1.25 ex}}\alpha  \right)}{\sqrt{\frac{i}{c}}}\right)+\dilog \left(\frac{\left(-\frac{1}{2}-\frac{i}{2}\right) \left(i \sqrt{\frac{i}{c}}-\sqrt{\frac{i}{c}}-x +\underline{\hspace{1.25 ex}}\alpha  \right)}{\sqrt{\frac{i}{c}}}\right)}{2 c}\right)\right) b}{c}\right)}{4 c}+\left(\frac{3 i b^{3} \left(c^{2} x^{4}+1\right) \ln \left(-i c \,x^{2}+1\right)^{2}}{32 c^{2}}+\frac{3 b^{2} x^{2} \left(a \,x^{2} c -b \right) \ln \left(-i c \,x^{2}+1\right)}{8 c}-\frac{3 i b \left(a^{2} c^{2} x^{4}-2 a b c \,x^{2}+b^{2} \ln \left(-i c \,x^{2}+1\right)+i \ln \left(-i c \,x^{2}+1\right) a b \right)}{8 c^{2}}\right) \ln \left(i c \,x^{2}+1\right)-\frac{3 b \,x^{2} a^{2}}{4 c}+\frac{x^{4} a^{3}}{4}+\frac{3 i b^{3} \ln \left(-i c \,x^{2}+1\right)^{2}}{16 c^{2}}"," ",0,"-3/16*a*b^2*x^4*ln(1-I*c*x^2)^2+3/4/c^2*a*b^2*ln(c^2*x^4+1)-3/16/c^2*a*b^2*ln(1-I*c*x^2)^2-3/32*b^2*(I*x^4*b*ln(1-I*c*x^2)*c^2+2*a*c^2*x^4-2*b*c*x^2+I*b*ln(1-I*c*x^2)+2*I*b+2*a)/c^2*ln(1+I*c*x^2)^2-1/32*I*b^3*x^4*ln(1-I*c*x^2)^3-3/4*I/c*a*b^2*x^2*ln(1-I*c*x^2)+3/8*I*a^2*b*x^4*ln(1-I*c*x^2)+1/32*I*b^3*(c^2*x^4+1)/c^2*ln(1+I*c*x^2)^3+3/4*a^2*b/c^2*arctan(c*x^2)+3/16*b^3/c*x^2*ln(1-I*c*x^2)^2+3/4*I/c*b^2*Sum((ln(x-_alpha)*ln(1-I*c*x^2)+2*c*(-1/2*ln(x-_alpha)*(ln((1/2-1/2*I)*(I*(I/c)^(1/2)+(I/c)^(1/2)+x-_alpha)/(I/c)^(1/2))+ln((-1/2-1/2*I)*(I*(I/c)^(1/2)-(I/c)^(1/2)-x+_alpha)/(I/c)^(1/2)))/c-1/2*(dilog((1/2-1/2*I)*(I*(I/c)^(1/2)+(I/c)^(1/2)+x-_alpha)/(I/c)^(1/2))+dilog((-1/2-1/2*I)*(I*(I/c)^(1/2)-(I/c)^(1/2)-x+_alpha)/(I/c)^(1/2)))/c))*b/c,_alpha=RootOf(c*_Z^2-RootOf(_Z^2+1,index=1)))-1/32*I*b^3/c^2*ln(1-I*c*x^2)^3+(3/32*I*b^3*(c^2*x^4+1)/c^2*ln(1-I*c*x^2)^2+3/8*b^2*x^2*(a*c*x^2-b)/c*ln(1-I*c*x^2)-3/8*I*b*(a^2*c^2*x^4-2*a*b*c*x^2+b^2*ln(1-I*c*x^2)+I*ln(1-I*c*x^2)*a*b)/c^2)*ln(1+I*c*x^2)-3/4/c*b*x^2*a^2+1/4*x^4*a^3+3/16*I/c^2*b^3*ln(1-I*c*x^2)^2","C"
87,1,306,129,0.243000," ","int(x*(a+b*arctan(c*x^2))^3,x)","\frac{x^{2} a^{3}}{2}-\frac{i b^{3} \arctan \left(c \,x^{2}\right)^{3}}{2 c}+\frac{b^{3} x^{2} \arctan \left(c \,x^{2}\right)^{3}}{2}+\frac{3 b^{3} \arctan \left(c \,x^{2}\right)^{2} \ln \left(\frac{\left(i c \,x^{2}+1\right)^{2}}{c^{2} x^{4}+1}+1\right)}{2 c}-\frac{3 i b^{3} \arctan \left(c \,x^{2}\right) \polylog \left(2, -\frac{\left(i c \,x^{2}+1\right)^{2}}{c^{2} x^{4}+1}\right)}{2 c}+\frac{3 b^{3} \polylog \left(3, -\frac{\left(i c \,x^{2}+1\right)^{2}}{c^{2} x^{4}+1}\right)}{4 c}-\frac{3 i \arctan \left(c \,x^{2}\right)^{2} a \,b^{2}}{2 c}+\frac{3 x^{2} a \,b^{2} \arctan \left(c \,x^{2}\right)^{2}}{2}+\frac{3 \ln \left(\frac{\left(i c \,x^{2}+1\right)^{2}}{c^{2} x^{4}+1}+1\right) \arctan \left(c \,x^{2}\right) a \,b^{2}}{c}-\frac{3 i \polylog \left(2, -\frac{\left(i c \,x^{2}+1\right)^{2}}{c^{2} x^{4}+1}\right) a \,b^{2}}{2 c}+\frac{3 x^{2} a^{2} b \arctan \left(c \,x^{2}\right)}{2}-\frac{3 a^{2} b \ln \left(c^{2} x^{4}+1\right)}{4 c}"," ",0,"1/2*x^2*a^3-1/2*I/c*b^3*arctan(c*x^2)^3+1/2*b^3*x^2*arctan(c*x^2)^3+3/2/c*b^3*arctan(c*x^2)^2*ln((1+I*c*x^2)^2/(c^2*x^4+1)+1)-3/2*I/c*b^3*arctan(c*x^2)*polylog(2,-(1+I*c*x^2)^2/(c^2*x^4+1))+3/4/c*b^3*polylog(3,-(1+I*c*x^2)^2/(c^2*x^4+1))-3/2*I/c*arctan(c*x^2)^2*a*b^2+3/2*x^2*a*b^2*arctan(c*x^2)^2+3/c*ln((1+I*c*x^2)^2/(c^2*x^4+1)+1)*arctan(c*x^2)*a*b^2-3/2*I/c*polylog(2,-(1+I*c*x^2)^2/(c^2*x^4+1))*a*b^2+3/2*x^2*a^2*b*arctan(c*x^2)-3/4/c*a^2*b*ln(c^2*x^4+1)","B"
88,0,0,207,0.403000," ","int((a+b*arctan(c*x^2))^3/x,x)","\int \frac{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{3}}{x}\, dx"," ",0,"int((a+b*arctan(c*x^2))^3/x,x)","F"
89,0,0,123,0.559000," ","int((a+b*arctan(c*x^2))^3/x^3,x)","\int \frac{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{3}}{x^{3}}\, dx"," ",0,"int((a+b*arctan(c*x^2))^3/x^3,x)","F"
90,0,0,133,1.182000," ","int((a+b*arctan(c*x^2))^3/x^5,x)","\int \frac{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{3}}{x^{5}}\, dx"," ",0,"int((a+b*arctan(c*x^2))^3/x^5,x)","F"
91,0,0,20,0.265000," ","int((d*x)^m*(a+b*arctan(c*x^2))^3,x)","\int \left(d x \right)^{m} \left(a +b \arctan \left(c \,x^{2}\right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arctan(c*x^2))^3,x)","F"
92,0,0,20,0.250000," ","int((d*x)^m*(a+b*arctan(c*x^2))^2,x)","\int \left(d x \right)^{m} \left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arctan(c*x^2))^2,x)","F"
93,0,0,73,0.241000," ","int((d*x)^m*(a+b*arctan(c*x^2)),x)","\int \left(d x \right)^{m} \left(a +b \arctan \left(c \,x^{2}\right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arctan(c*x^2)),x)","F"
94,0,0,20,0.145000," ","int((d*x)^m/(a+b*arctan(c*x^2)),x)","\int \frac{\left(d x \right)^{m}}{a +b \arctan \left(c \,x^{2}\right)}\, dx"," ",0,"int((d*x)^m/(a+b*arctan(c*x^2)),x)","F"
95,0,0,20,0.189000," ","int((d*x)^m/(a+b*arctan(c*x^2))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \arctan \left(c \,x^{2}\right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arctan(c*x^2))^2,x)","F"
96,1,50,46,0.031000," ","int(x^11*(a+b*arctan(c*x^3)),x)","\frac{x^{12} a}{12}+\frac{b \,x^{12} \arctan \left(c \,x^{3}\right)}{12}-\frac{b \,x^{9}}{36 c}+\frac{b \,x^{3}}{12 c^{3}}-\frac{b \arctan \left(c \,x^{3}\right)}{12 c^{4}}"," ",0,"1/12*x^12*a+1/12*b*x^12*arctan(c*x^3)-1/36*b*x^9/c+1/12*b*x^3/c^3-1/12*b*arctan(c*x^3)/c^4","A"
97,1,45,41,0.033000," ","int(x^8*(a+b*arctan(c*x^3)),x)","\frac{x^{9} a}{9}+\frac{b \,x^{9} \arctan \left(c \,x^{3}\right)}{9}-\frac{b \,x^{6}}{18 c}+\frac{b \ln \left(c^{2} x^{6}+1\right)}{18 c^{3}}"," ",0,"1/9*x^9*a+1/9*b*x^9*arctan(c*x^3)-1/18*b*x^6/c+1/18*b*ln(c^2*x^6+1)/c^3","A"
98,1,41,37,0.028000," ","int(x^5*(a+b*arctan(c*x^3)),x)","\frac{x^{6} a}{6}+\frac{b \,x^{6} \arctan \left(c \,x^{3}\right)}{6}-\frac{b \,x^{3}}{6 c}+\frac{b \arctan \left(c \,x^{3}\right)}{6 c^{2}}"," ",0,"1/6*x^6*a+1/6*b*x^6*arctan(c*x^3)-1/6*b*x^3/c+1/6*b*arctan(c*x^3)/c^2","A"
99,1,36,32,0.026000," ","int(x^2*(a+b*arctan(c*x^3)),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctan \left(c \,x^{3}\right)}{3}-\frac{b \ln \left(c^{2} x^{6}+1\right)}{6 c}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctan(c*x^3)-1/6*b*ln(c^2*x^6+1)/c","A"
100,1,63,31,0.103000," ","int((a+b*arctan(c*x^3))/x,x)","a \ln \left(x \right)+b \ln \left(x \right) \arctan \left(c \,x^{3}\right)-\frac{b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} \textit{\_Z}^{6}+1\right)}{\sum}\frac{\ln \left(x \right) \ln \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)}{\textit{\_R1}^{3}}\right)}{2 c}"," ",0,"a*ln(x)+b*ln(x)*arctan(c*x^3)-1/2*b/c*sum(1/_R1^3*(ln(x)*ln((_R1-x)/_R1)+dilog((_R1-x)/_R1)),_R1=RootOf(_Z^6*c^2+1))","C"
101,1,39,38,0.031000," ","int((a+b*arctan(c*x^3))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctan \left(c \,x^{3}\right)}{3 x^{3}}-\frac{b c \ln \left(c^{2} x^{6}+1\right)}{6}+b c \ln \left(x \right)"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctan(c*x^3)-1/6*b*c*ln(c^2*x^6+1)+b*c*ln(x)","A"
102,1,39,38,0.037000," ","int((a+b*arctan(c*x^3))/x^7,x)","-\frac{a}{6 x^{6}}-\frac{b \arctan \left(c \,x^{3}\right)}{6 x^{6}}-\frac{b \,c^{2} \arctan \left(c \,x^{3}\right)}{6}-\frac{b c}{6 x^{3}}"," ",0,"-1/6*a/x^6-1/6*b/x^6*arctan(c*x^3)-1/6*b*c^2*arctan(c*x^3)-1/6*b*c/x^3","A"
103,1,51,50,0.034000," ","int((a+b*arctan(c*x^3))/x^10,x)","-\frac{a}{9 x^{9}}-\frac{b \arctan \left(c \,x^{3}\right)}{9 x^{9}}+\frac{b \,c^{3} \ln \left(c^{2} x^{6}+1\right)}{18}-\frac{b c}{18 x^{6}}-\frac{b \,c^{3} \ln \left(x \right)}{3}"," ",0,"-1/9*a/x^9-1/9*b/x^9*arctan(c*x^3)+1/18*b*c^3*ln(c^2*x^6+1)-1/18*b*c/x^6-1/3*b*c^3*ln(x)","A"
104,1,165,126,0.156000," ","int(x^3*(a+b*arctan(c*x^3)),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arctan \left(c \,x^{3}\right)}{4}-\frac{3 b x}{4 c}+\frac{b \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right)}{4 c}-\frac{b \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{16 c}+\frac{b \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{8 c}+\frac{b \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{16 c}+\frac{b \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{8 c}"," ",0,"1/4*x^4*a+1/4*b*x^4*arctan(c*x^3)-3/4*b*x/c+1/4*b/c*(1/c^2)^(1/6)*arctan(x/(1/c^2)^(1/6))-1/16*b/c*3^(1/2)*(1/c^2)^(1/6)*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))+1/8*b/c*(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))+1/16*b/c*3^(1/2)*(1/c^2)^(1/6)*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))+1/8*b/c*(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))","A"
105,1,98,78,0.026000," ","int(a+b*arctan(c*x^3),x)","a x +b x \arctan \left(c \,x^{3}\right)+\frac{b \ln \left(x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}-\frac{b \ln \left(x^{4}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}} x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}-\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x^{2}}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}"," ",0,"a*x+b*x*arctan(c*x^3)+1/2*b/c/(1/c^2)^(1/3)*ln(x^2+(1/c^2)^(1/3))-1/4*b/c/(1/c^2)^(1/3)*ln(x^4-(1/c^2)^(1/3)*x^2+(1/c^2)^(2/3))-1/2*b*3^(1/2)/c/(1/c^2)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c^2)^(1/3)*x^2-1))","A"
106,1,148,122,0.108000," ","int((a+b*arctan(c*x^3))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctan \left(c \,x^{3}\right)}{2 x^{2}}+\frac{b c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right)}{2}-\frac{b c \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{8}+\frac{b c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{4}+\frac{b c \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{8}+\frac{b c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{4}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctan(c*x^3)+1/2*b*c*(1/c^2)^(1/6)*arctan(x/(1/c^2)^(1/6))-1/8*b*c*3^(1/2)*(1/c^2)^(1/6)*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))+1/4*b*c*(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))+1/8*b*c*3^(1/2)*(1/c^2)^(1/6)*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))+1/4*b*c*(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))","A"
107,1,105,91,0.038000," ","int((a+b*arctan(c*x^3))/x^6,x)","-\frac{a}{5 x^{5}}-\frac{b \arctan \left(c \,x^{3}\right)}{5 x^{5}}+\frac{b c \ln \left(x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{10 \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}-\frac{b c \ln \left(x^{4}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}} x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}\right)}{20 \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}-\frac{b c \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x^{2}}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{10 \left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}-\frac{3 b c}{10 x^{2}}"," ",0,"-1/5*a/x^5-1/5*b/x^5*arctan(c*x^3)+1/10*b*c/(1/c^2)^(1/3)*ln(x^2+(1/c^2)^(1/3))-1/20*b*c/(1/c^2)^(1/3)*ln(x^4-(1/c^2)^(1/3)*x^2+(1/c^2)^(2/3))-1/10*b*c*3^(1/2)/(1/c^2)^(1/3)*arctan(1/3*3^(1/2)*(2/(1/c^2)^(1/3)*x^2-1))-3/10*b*c/x^2","A"
108,1,167,128,0.108000," ","int(x^7*(a+b*arctan(c*x^3)),x)","\frac{x^{8} a}{8}+\frac{x^{8} b \arctan \left(c \,x^{3}\right)}{8}-\frac{3 b \,x^{5}}{40 c}+\frac{b \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right)}{8 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\frac{b \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{32 c}+\frac{b \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{16 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\frac{b \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{32 c}+\frac{b \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{16 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}"," ",0,"1/8*x^8*a+1/8*x^8*b*arctan(c*x^3)-3/40*b*x^5/c+1/8*b/c^3/(1/c^2)^(1/6)*arctan(x/(1/c^2)^(1/6))+1/32*b/c*3^(1/2)*(1/c^2)^(5/6)*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))+1/16*b/c^3/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))-1/32*b/c*3^(1/2)*(1/c^2)^(5/6)*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))+1/16*b/c^3/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))","A"
109,1,113,90,0.030000," ","int(x^4*(a+b*arctan(c*x^3)),x)","\frac{a \,x^{5}}{5}+\frac{b \,x^{5} \arctan \left(c \,x^{3}\right)}{5}-\frac{3 b \,x^{2}}{10 c}+\frac{b \ln \left(x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{10 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}-\frac{b \ln \left(x^{4}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}} x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}\right)}{20 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x^{2}}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{10 c^{3} \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}"," ",0,"1/5*a*x^5+1/5*b*x^5*arctan(c*x^3)-3/10*b*x^2/c+1/10*b/c^3/(1/c^2)^(2/3)*ln(x^2+(1/c^2)^(1/3))-1/20*b/c^3/(1/c^2)^(2/3)*ln(x^4-(1/c^2)^(1/3)*x^2+(1/c^2)^(2/3))+1/10*b/c^3/(1/c^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c^2)^(1/3)*x^2-1))","A"
110,1,154,119,0.108000," ","int(x*(a+b*arctan(c*x^3)),x)","\frac{a \,x^{2}}{2}+\frac{b \,x^{2} \arctan \left(c \,x^{3}\right)}{2}-\frac{b \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\frac{b c \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{8}-\frac{b \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\frac{b c \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{8}-\frac{b \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}"," ",0,"1/2*a*x^2+1/2*b*x^2*arctan(c*x^3)-1/2*b/c/(1/c^2)^(1/6)*arctan(x/(1/c^2)^(1/6))-1/8*b*c*3^(1/2)*(1/c^2)^(5/6)*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))-1/4*b/c/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))+1/8*b*c*3^(1/2)*(1/c^2)^(5/6)*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))-1/4*b/c/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))","A"
111,1,104,83,0.026000," ","int((a+b*arctan(c*x^3))/x^2,x)","-\frac{a}{x}-\frac{b \arctan \left(c \,x^{3}\right)}{x}+\frac{b \ln \left(x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}-\frac{b \ln \left(x^{4}-\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}} x^{2}+\left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}\right)}{4 c \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}+\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x^{2}}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{2 c \left(\frac{1}{c^{2}}\right)^{\frac{2}{3}}}"," ",0,"-a/x-b/x*arctan(c*x^3)+1/2*b/c/(1/c^2)^(2/3)*ln(x^2+(1/c^2)^(1/3))-1/4*b/c/(1/c^2)^(2/3)*ln(x^4-(1/c^2)^(1/3)*x^2+(1/c^2)^(2/3))+1/2*b/c/(1/c^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c^2)^(1/3)*x^2-1))","A"
112,1,159,129,0.105000," ","int((a+b*arctan(c*x^3))/x^5,x)","-\frac{a}{4 x^{4}}-\frac{b \arctan \left(c \,x^{3}\right)}{4 x^{4}}-\frac{b c \arctan \left(\frac{x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}\right)}{4 \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\frac{b \,c^{3} \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \ln \left(x^{2}-\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{16}-\frac{b c \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\sqrt{3}\right)}{8 \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\frac{b \,c^{3} \sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{5}{6}} \ln \left(x^{2}+\sqrt{3}\, \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}} x +\left(\frac{1}{c^{2}}\right)^{\frac{1}{3}}\right)}{16}-\frac{b c \arctan \left(\frac{2 x}{\left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}+\sqrt{3}\right)}{8 \left(\frac{1}{c^{2}}\right)^{\frac{1}{6}}}-\frac{3 b c}{4 x}"," ",0,"-1/4*a/x^4-1/4*b/x^4*arctan(c*x^3)-1/4*b*c/(1/c^2)^(1/6)*arctan(x/(1/c^2)^(1/6))-1/16*b*c^3*3^(1/2)*(1/c^2)^(5/6)*ln(x^2-3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))-1/8*b*c/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)-3^(1/2))+1/16*b*c^3*3^(1/2)*(1/c^2)^(5/6)*ln(x^2+3^(1/2)*(1/c^2)^(1/6)*x+(1/c^2)^(1/3))-1/8*b*c/(1/c^2)^(1/6)*arctan(2*x/(1/c^2)^(1/6)+3^(1/2))-3/4*b*c/x","A"
113,1,151,110,0.047000," ","int(x^11*(a+b*arctan(c*x^3))^2,x)","\frac{x^{12} a^{2}}{12}+\frac{b^{2} x^{12} \arctan \left(c \,x^{3}\right)^{2}}{12}-\frac{b^{2} \arctan \left(c \,x^{3}\right) x^{9}}{18 c}+\frac{b^{2} x^{3} \arctan \left(c \,x^{3}\right)}{6 c^{3}}-\frac{b^{2} \arctan \left(c \,x^{3}\right)^{2}}{12 c^{4}}+\frac{b^{2} x^{6}}{36 c^{2}}-\frac{b^{2} \ln \left(c^{2} x^{6}+1\right)}{9 c^{4}}+\frac{a b \,x^{12} \arctan \left(c \,x^{3}\right)}{6}-\frac{a b \,x^{9}}{18 c}+\frac{a b \,x^{3}}{6 c^{3}}-\frac{a b \arctan \left(c \,x^{3}\right)}{6 c^{4}}"," ",0,"1/12*x^12*a^2+1/12*b^2*x^12*arctan(c*x^3)^2-1/18*b^2*arctan(c*x^3)/c*x^9+1/6*b^2*x^3*arctan(c*x^3)/c^3-1/12*b^2/c^4*arctan(c*x^3)^2+1/36*b^2*x^6/c^2-1/9*b^2*ln(c^2*x^6+1)/c^4+1/6*a*b*x^12*arctan(c*x^3)-1/18*a*b/c*x^9+1/6*a*b*x^3/c^3-1/6*a*b/c^4*arctan(c*x^3)","A"
114,-2,0,136,180.000000," ","int(x^8*(a+b*arctan(c*x^3))^2,x)","\int x^{8} \left(a +b \arctan \left(c \,x^{3}\right)\right)^{2}\, dx"," ",0,"int(x^8*(a+b*arctan(c*x^3))^2,x)","F"
115,1,113,80,0.043000," ","int(x^5*(a+b*arctan(c*x^3))^2,x)","\frac{x^{6} a^{2}}{6}+\frac{b^{2} x^{6} \arctan \left(c \,x^{3}\right)^{2}}{6}-\frac{b^{2} x^{3} \arctan \left(c \,x^{3}\right)}{3 c}+\frac{b^{2} \arctan \left(c \,x^{3}\right)^{2}}{6 c^{2}}+\frac{b^{2} \ln \left(c^{2} x^{6}+1\right)}{6 c^{2}}+\frac{a b \,x^{6} \arctan \left(c \,x^{3}\right)}{3}-\frac{a b \,x^{3}}{3 c}+\frac{a b \arctan \left(c \,x^{3}\right)}{3 c^{2}}"," ",0,"1/6*x^6*a^2+1/6*b^2*x^6*arctan(c*x^3)^2-1/3*b^2*x^3*arctan(c*x^3)/c+1/6*b^2/c^2*arctan(c*x^3)^2+1/6*b^2*ln(c^2*x^6+1)/c^2+1/3*a*b*x^6*arctan(c*x^3)-1/3*a*b*x^3/c+1/3*a*b/c^2*arctan(c*x^3)","A"
116,1,148,92,0.234000," ","int(x^2*(a+b*arctan(c*x^3))^2,x)","\frac{\arctan \left(c \,x^{3}\right)^{2} x^{3} b^{2}}{3}+\frac{2 x^{3} a b \arctan \left(c \,x^{3}\right)}{3}+\frac{x^{3} a^{2}}{3}-\frac{i \arctan \left(c \,x^{3}\right)^{2} b^{2}}{3 c}-\frac{i \polylog \left(2, -\frac{\left(i c \,x^{3}+1\right)^{2}}{c^{2} x^{6}+1}\right) b^{2}}{3 c}+\frac{2 \arctan \left(c \,x^{3}\right) \ln \left(\frac{\left(i c \,x^{3}+1\right)^{2}}{c^{2} x^{6}+1}+1\right) b^{2}}{3 c}-\frac{a b \ln \left(c^{2} x^{6}+1\right)}{3 c}"," ",0,"1/3*arctan(c*x^3)^2*x^3*b^2+2/3*x^3*a*b*arctan(c*x^3)+1/3*x^3*a^2-1/3*I/c*arctan(c*x^3)^2*b^2-1/3*I/c*polylog(2,-(1+I*c*x^3)^2/(c^2*x^6+1))*b^2+2/3/c*arctan(c*x^3)*ln((1+I*c*x^3)^2/(c^2*x^6+1)+1)*b^2-1/3/c*a*b*ln(c^2*x^6+1)","A"
117,0,0,137,0.400000," ","int((a+b*arctan(c*x^3))^2/x,x)","\int \frac{\left(a +b \arctan \left(c \,x^{3}\right)\right)^{2}}{x}\, dx"," ",0,"int((a+b*arctan(c*x^3))^2/x,x)","F"
118,0,0,88,0.592000," ","int((a+b*arctan(c*x^3))^2/x^4,x)","\int \frac{\left(a +b \arctan \left(c \,x^{3}\right)\right)^{2}}{x^{4}}\, dx"," ",0,"int((a+b*arctan(c*x^3))^2/x^4,x)","F"
119,1,118,79,0.045000," ","int((a+b*arctan(c*x^3))^2/x^7,x)","-\frac{a^{2}}{6 x^{6}}-\frac{b^{2} \arctan \left(c \,x^{3}\right)^{2}}{6 x^{6}}-\frac{b^{2} c^{2} \arctan \left(c \,x^{3}\right)^{2}}{6}-\frac{b^{2} c \arctan \left(c \,x^{3}\right)}{3 x^{3}}-\frac{b^{2} c^{2} \ln \left(c^{2} x^{6}+1\right)}{6}+b^{2} c^{2} \ln \left(x \right)-\frac{a b \arctan \left(c \,x^{3}\right)}{3 x^{6}}-\frac{a b \,c^{2} \arctan \left(c \,x^{3}\right)}{3}-\frac{a b c}{3 x^{3}}"," ",0,"-1/6*a^2/x^6-1/6*b^2/x^6*arctan(c*x^3)^2-1/6*b^2*c^2*arctan(c*x^3)^2-1/3*b^2*c*arctan(c*x^3)/x^3-1/6*b^2*c^2*ln(c^2*x^6+1)+b^2*c^2*ln(x)-1/3*a*b/x^6*arctan(c*x^3)-1/3*a*b*c^2*arctan(c*x^3)-1/3*a*b*c/x^3","A"
120,0,0,136,0.418000," ","int((a+b*arctan(c*x^3))^2/x^10,x)","\int \frac{\left(a +b \arctan \left(c \,x^{3}\right)\right)^{2}}{x^{10}}\, dx"," ",0,"int((a+b*arctan(c*x^3))^2/x^10,x)","F"
121,0,0,215,0.411000," ","int(x^8*(a+b*arctan(c*x^3))^3,x)","\int x^{8} \left(a +b \arctan \left(c \,x^{3}\right)\right)^{3}\, dx"," ",0,"int(x^8*(a+b*arctan(c*x^3))^3,x)","F"
122,1,867,133,1.776000," ","int(x^5*(a+b*arctan(c*x^3))^3,x)","\frac{a^{2} b \arctan \left(c \,x^{3}\right)}{2 c^{2}}-\frac{a^{2} b \,x^{3}}{2 c}+\frac{x^{6} a^{3}}{6}+\frac{i a^{2} b \,x^{6} \ln \left(-i c \,x^{3}+1\right)}{4}-\frac{i a \,b^{2} x^{3} \ln \left(-i c \,x^{3}+1\right)}{2 c}+\frac{i b^{3} \left(c^{2} x^{6}+1\right) \ln \left(i c \,x^{3}+1\right)^{3}}{48 c^{2}}+\frac{b^{3} x^{3} \ln \left(-i c \,x^{3}+1\right)^{2}}{8 c}+\frac{i b^{3} \ln \left(-i c \,x^{3}+1\right)^{2}}{8 c^{2}}-\frac{i b^{3} \ln \left(-i c \,x^{3}+1\right)^{3}}{48 c^{2}}-\frac{a \,b^{2} x^{6} \ln \left(-i c \,x^{3}+1\right)^{2}}{8}+\frac{a \,b^{2} \ln \left(c^{2} x^{6}+1\right)}{2 c^{2}}-\frac{a \,b^{2} \ln \left(-i c \,x^{3}+1\right)^{2}}{8 c^{2}}-\frac{b^{2} \left(i x^{6} b \ln \left(-i c \,x^{3}+1\right) c^{2}+2 a \,c^{2} x^{6}-2 b c \,x^{3}+i b \ln \left(-i c \,x^{3}+1\right)+2 i b +2 a \right) \ln \left(i c \,x^{3}+1\right)^{2}}{16 c^{2}}+\frac{3 i b^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(c \,\textit{\_Z}^{3}-\RootOf \left(\textit{\_Z}^{2}+1, \mathit{index} =1\right)\right)}{\sum}\frac{2 \left(\ln \left(x -\underline{\hspace{1.25 ex}}\alpha  \right) \ln \left(-i c \,x^{3}+1\right)+3 c \left(-\frac{\ln \left(x -\underline{\hspace{1.25 ex}}\alpha  \right) \left(\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \RootOf \left(c \,\textit{\_Z}^{3}-i\right)+\RootOf \left(c \,\textit{\_Z}^{3}-i\right)^{2}, \mathit{index} =1\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \RootOf \left(c \,\textit{\_Z}^{3}-i\right)+\RootOf \left(c \,\textit{\_Z}^{3}-i\right)^{2}, \mathit{index} =1\right)}\right)+\ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \RootOf \left(c \,\textit{\_Z}^{3}-i\right)+\RootOf \left(c \,\textit{\_Z}^{3}-i\right)^{2}, \mathit{index} =2\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \RootOf \left(c \,\textit{\_Z}^{3}-i\right)+\RootOf \left(c \,\textit{\_Z}^{3}-i\right)^{2}, \mathit{index} =2\right)}\right)+\ln \left(\frac{2 \left(\frac{i}{c}\right)^{\frac{1}{3}}+x -\underline{\hspace{1.25 ex}}\alpha }{2 \left(\frac{i}{c}\right)^{\frac{1}{3}}}\right)\right)}{3 c}-\frac{\dilog \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \RootOf \left(c \,\textit{\_Z}^{3}-i\right)+\RootOf \left(c \,\textit{\_Z}^{3}-i\right)^{2}, \mathit{index} =1\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \RootOf \left(c \,\textit{\_Z}^{3}-i\right)+\RootOf \left(c \,\textit{\_Z}^{3}-i\right)^{2}, \mathit{index} =1\right)}\right)+\dilog \left(\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \RootOf \left(c \,\textit{\_Z}^{3}-i\right)+\RootOf \left(c \,\textit{\_Z}^{3}-i\right)^{2}, \mathit{index} =2\right)-x +\underline{\hspace{1.25 ex}}\alpha }{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} \RootOf \left(c \,\textit{\_Z}^{3}-i\right)+\RootOf \left(c \,\textit{\_Z}^{3}-i\right)^{2}, \mathit{index} =2\right)}\right)+\dilog \left(\frac{2 \left(\frac{i}{c}\right)^{\frac{1}{3}}+x -\underline{\hspace{1.25 ex}}\alpha }{2 \left(\frac{i}{c}\right)^{\frac{1}{3}}}\right)}{3 c}\right)\right) b}{3 c}\right)}{4 c}-\frac{i b^{3} x^{6} \ln \left(-i c \,x^{3}+1\right)^{3}}{48}+\left(\frac{i b^{3} \left(c^{2} x^{6}+1\right) \ln \left(-i c \,x^{3}+1\right)^{2}}{16 c^{2}}+\frac{b^{2} x^{3} \left(a c \,x^{3}-b \right) \ln \left(-i c \,x^{3}+1\right)}{4 c}-\frac{i b \left(a^{2} c^{2} x^{6}-2 a b c \,x^{3}+b^{2} \ln \left(-i c \,x^{3}+1\right)+i \ln \left(-i c \,x^{3}+1\right) a b \right)}{4 c^{2}}\right) \ln \left(i c \,x^{3}+1\right)"," ",0,"1/2/c^2*a^2*b*arctan(c*x^3)-1/2/c*a^2*b*x^3+1/6*x^6*a^3-1/2*I/c*a*b^2*x^3*ln(1-I*c*x^3)+1/48*I*b^3*(c^2*x^6+1)/c^2*ln(1+I*c*x^3)^3-1/48*I*b^3/c^2*ln(1-I*c*x^3)^3+1/8*b^3/c*x^3*ln(1-I*c*x^3)^2+1/4*I*a^2*b*x^6*ln(1-I*c*x^3)+1/8*I/c^2*b^3*ln(1-I*c*x^3)^2-1/8*a*b^2*x^6*ln(1-I*c*x^3)^2+1/2/c^2*a*b^2*ln(c^2*x^6+1)-1/8/c^2*a*b^2*ln(1-I*c*x^3)^2-1/16*b^2*(I*x^6*b*ln(1-I*c*x^3)*c^2+2*a*c^2*x^6-2*b*c*x^3+I*b*ln(1-I*c*x^3)+2*I*b+2*a)/c^2*ln(1+I*c*x^3)^2+3/4*I/c*b^2*Sum(2/3*(ln(x-_alpha)*ln(1-I*c*x^3)+3*c*(-1/3*ln(x-_alpha)*(ln((RootOf(_Z^2+_Z*RootOf(c*_Z^3-I)+RootOf(c*_Z^3-I)^2,index=1)-x+_alpha)/RootOf(_Z^2+_Z*RootOf(c*_Z^3-I)+RootOf(c*_Z^3-I)^2,index=1))+ln((RootOf(_Z^2+_Z*RootOf(c*_Z^3-I)+RootOf(c*_Z^3-I)^2,index=2)-x+_alpha)/RootOf(_Z^2+_Z*RootOf(c*_Z^3-I)+RootOf(c*_Z^3-I)^2,index=2))+ln(1/2*(2*(I/c)^(1/3)+x-_alpha)/(I/c)^(1/3)))/c-1/3*(dilog((RootOf(_Z^2+_Z*RootOf(c*_Z^3-I)+RootOf(c*_Z^3-I)^2,index=1)-x+_alpha)/RootOf(_Z^2+_Z*RootOf(c*_Z^3-I)+RootOf(c*_Z^3-I)^2,index=1))+dilog((RootOf(_Z^2+_Z*RootOf(c*_Z^3-I)+RootOf(c*_Z^3-I)^2,index=2)-x+_alpha)/RootOf(_Z^2+_Z*RootOf(c*_Z^3-I)+RootOf(c*_Z^3-I)^2,index=2))+dilog(1/2*(2*(I/c)^(1/3)+x-_alpha)/(I/c)^(1/3)))/c))*b/c,_alpha=RootOf(c*_Z^3-RootOf(_Z^2+1,index=1)))-1/48*I*b^3*x^6*ln(1-I*c*x^3)^3+(1/16*I*b^3*(c^2*x^6+1)/c^2*ln(1-I*c*x^3)^2+1/4*b^2*x^3*(a*c*x^3-b)/c*ln(1-I*c*x^3)-1/4*I*b*(a^2*c^2*x^6-2*a*b*c*x^3+b^2*ln(1-I*c*x^3)+I*ln(1-I*c*x^3)*a*b)/c^2)*ln(1+I*c*x^3)","C"
123,1,303,128,0.244000," ","int(x^2*(a+b*arctan(c*x^3))^3,x)","\frac{a^{3} x^{3}}{3}-\frac{i b^{3} \arctan \left(c \,x^{3}\right)^{3}}{3 c}+\frac{b^{3} x^{3} \arctan \left(c \,x^{3}\right)^{3}}{3}+\frac{b^{3} \arctan \left(c \,x^{3}\right)^{2} \ln \left(\frac{\left(i c \,x^{3}+1\right)^{2}}{c^{2} x^{6}+1}+1\right)}{c}-\frac{i b^{3} \arctan \left(c \,x^{3}\right) \polylog \left(2, -\frac{\left(i c \,x^{3}+1\right)^{2}}{c^{2} x^{6}+1}\right)}{c}+\frac{b^{3} \polylog \left(3, -\frac{\left(i c \,x^{3}+1\right)^{2}}{c^{2} x^{6}+1}\right)}{2 c}-\frac{i \arctan \left(c \,x^{3}\right)^{2} a \,b^{2}}{c}+x^{3} a \,b^{2} \arctan \left(c \,x^{3}\right)^{2}+\frac{2 \ln \left(\frac{\left(i c \,x^{3}+1\right)^{2}}{c^{2} x^{6}+1}+1\right) \arctan \left(c \,x^{3}\right) a \,b^{2}}{c}-\frac{i \polylog \left(2, -\frac{\left(i c \,x^{3}+1\right)^{2}}{c^{2} x^{6}+1}\right) a \,b^{2}}{c}+x^{3} a^{2} b \arctan \left(c \,x^{3}\right)-\frac{a^{2} b \ln \left(c^{2} x^{6}+1\right)}{2 c}"," ",0,"1/3*a^3*x^3-1/3*I/c*b^3*arctan(c*x^3)^3+1/3*b^3*x^3*arctan(c*x^3)^3+1/c*b^3*arctan(c*x^3)^2*ln((1+I*c*x^3)^2/(c^2*x^6+1)+1)-I/c*b^3*arctan(c*x^3)*polylog(2,-(1+I*c*x^3)^2/(c^2*x^6+1))+1/2/c*b^3*polylog(3,-(1+I*c*x^3)^2/(c^2*x^6+1))-I/c*arctan(c*x^3)^2*a*b^2+x^3*a*b^2*arctan(c*x^3)^2+2/c*ln((1+I*c*x^3)^2/(c^2*x^6+1)+1)*arctan(c*x^3)*a*b^2-I/c*polylog(2,-(1+I*c*x^3)^2/(c^2*x^6+1))*a*b^2+x^3*a^2*b*arctan(c*x^3)-1/2/c*a^2*b*ln(c^2*x^6+1)","B"
124,0,0,207,0.394000," ","int((a+b*arctan(c*x^3))^3/x,x)","\int \frac{\left(a +b \arctan \left(c \,x^{3}\right)\right)^{3}}{x}\, dx"," ",0,"int((a+b*arctan(c*x^3))^3/x,x)","F"
125,0,0,122,0.570000," ","int((a+b*arctan(c*x^3))^3/x^4,x)","\int \frac{\left(a +b \arctan \left(c \,x^{3}\right)\right)^{3}}{x^{4}}\, dx"," ",0,"int((a+b*arctan(c*x^3))^3/x^4,x)","F"
126,0,0,132,0.885000," ","int((a+b*arctan(c*x^3))^3/x^7,x)","\int \frac{\left(a +b \arctan \left(c \,x^{3}\right)\right)^{3}}{x^{7}}\, dx"," ",0,"int((a+b*arctan(c*x^3))^3/x^7,x)","F"
127,0,0,20,0.268000," ","int((d*x)^m*(a+b*arctan(c*x^3))^3,x)","\int \left(d x \right)^{m} \left(a +b \arctan \left(c \,x^{3}\right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arctan(c*x^3))^3,x)","F"
128,0,0,20,0.243000," ","int((d*x)^m*(a+b*arctan(c*x^3))^2,x)","\int \left(d x \right)^{m} \left(a +b \arctan \left(c \,x^{3}\right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arctan(c*x^3))^2,x)","F"
129,0,0,73,0.227000," ","int((d*x)^m*(a+b*arctan(c*x^3)),x)","\int \left(d x \right)^{m} \left(a +b \arctan \left(c \,x^{3}\right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arctan(c*x^3)),x)","F"
130,0,0,20,0.151000," ","int((d*x)^m/(a+b*arctan(c*x^3)),x)","\int \frac{\left(d x \right)^{m}}{a +b \arctan \left(c \,x^{3}\right)}\, dx"," ",0,"int((d*x)^m/(a+b*arctan(c*x^3)),x)","F"
131,0,0,20,0.181000," ","int((d*x)^m/(a+b*arctan(c*x^3))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \arctan \left(c \,x^{3}\right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arctan(c*x^3))^2,x)","F"
132,1,46,42,0.042000," ","int(x^3*(a+b*arctan(c/x)),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arctan \left(\frac{c}{x}\right)}{4}+\frac{b c \,x^{3}}{12}-\frac{b \,c^{3} x}{4}+\frac{b \,c^{4} \arctan \left(\frac{x}{c}\right)}{4}"," ",0,"1/4*x^4*a+1/4*b*x^4*arctan(c/x)+1/12*b*c*x^3-1/4*b*c^3*x+1/4*b*c^4*arctan(x/c)","A"
133,1,55,37,0.047000," ","int(x^2*(a+b*arctan(c/x)),x)","\frac{x^{3} a}{3}+\frac{b \,x^{3} \arctan \left(\frac{c}{x}\right)}{3}+\frac{b c \,x^{2}}{6}+\frac{c^{3} b \ln \left(\frac{c}{x}\right)}{3}-\frac{c^{3} b \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{6}"," ",0,"1/3*x^3*a+1/3*b*x^3*arctan(c/x)+1/6*b*c*x^2+1/3*c^3*b*ln(c/x)-1/6*c^3*b*ln(1+c^2/x^2)","A"
134,1,37,33,0.037000," ","int(x*(a+b*arctan(c/x)),x)","\frac{a \,x^{2}}{2}+\frac{\arctan \left(\frac{c}{x}\right) b \,x^{2}}{2}+\frac{x b c}{2}-\frac{b \,c^{2} \arctan \left(\frac{x}{c}\right)}{2}"," ",0,"1/2*a*x^2+1/2*arctan(c/x)*b*x^2+1/2*x*b*c-1/2*b*c^2*arctan(x/c)","A"
135,1,38,25,0.036000," ","int(a+b*arctan(c/x),x)","a x +b x \arctan \left(\frac{c}{x}\right)-b c \ln \left(\frac{c}{x}\right)+\frac{b c \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2}"," ",0,"a*x+b*x*arctan(c/x)-b*c*ln(c/x)+1/2*b*c*ln(1+c^2/x^2)","A"
136,1,94,31,0.052000," ","int((a+b*arctan(c/x))/x,x)","-a \ln \left(\frac{c}{x}\right)-b \ln \left(\frac{c}{x}\right) \arctan \left(\frac{c}{x}\right)-\frac{i b \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{i c}{x}\right)}{2}+\frac{i b \ln \left(\frac{c}{x}\right) \ln \left(1-\frac{i c}{x}\right)}{2}-\frac{i b \dilog \left(1+\frac{i c}{x}\right)}{2}+\frac{i b \dilog \left(1-\frac{i c}{x}\right)}{2}"," ",0,"-a*ln(c/x)-b*ln(c/x)*arctan(c/x)-1/2*I*b*ln(c/x)*ln(1+I*c/x)+1/2*I*b*ln(c/x)*ln(1-I*c/x)-1/2*I*b*dilog(1+I*c/x)+1/2*I*b*dilog(1-I*c/x)","B"
137,1,36,34,0.024000," ","int((a+b*arctan(c/x))/x^2,x)","-\frac{a}{x}-\frac{b \arctan \left(\frac{c}{x}\right)}{x}+\frac{b \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2 c}"," ",0,"-a/x-b/x*arctan(c/x)+1/2*b*ln(1+c^2/x^2)/c","A"
138,1,41,40,0.033000," ","int((a+b*arctan(c/x))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arctan \left(\frac{c}{x}\right)}{2 x^{2}}+\frac{b}{2 c x}+\frac{b \arctan \left(\frac{x}{c}\right)}{2 c^{2}}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arctan(c/x)+1/2*b/c/x+1/2*b*arctan(x/c)/c^2","A"
139,1,45,50,0.033000," ","int((a+b*arctan(c/x))/x^4,x)","-\frac{a}{3 x^{3}}-\frac{b \arctan \left(\frac{c}{x}\right)}{3 x^{3}}+\frac{b}{6 c \,x^{2}}-\frac{b \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{6 c^{3}}"," ",0,"-1/3*a/x^3-1/3*b/x^3*arctan(c/x)+1/6*b/c/x^2-1/6/c^3*b*ln(1+c^2/x^2)","A"
140,1,157,108,0.056000," ","int(x^3*(a+b*arctan(c/x))^2,x)","\frac{a^{2} x^{4}}{4}+\frac{b^{2} x^{4} \arctan \left(\frac{c}{x}\right)^{2}}{4}+\frac{c \,b^{2} \arctan \left(\frac{c}{x}\right) x^{3}}{6}-\frac{c^{3} b^{2} \arctan \left(\frac{c}{x}\right) x}{2}-\frac{c^{4} b^{2} \arctan \left(\frac{c}{x}\right)^{2}}{4}+\frac{b^{2} c^{2} x^{2}}{12}+\frac{2 c^{4} b^{2} \ln \left(\frac{c}{x}\right)}{3}-\frac{b^{2} c^{4} \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{3}+\frac{a b \,x^{4} \arctan \left(\frac{c}{x}\right)}{2}+\frac{a b c \,x^{3}}{6}-\frac{c^{3} a b x}{2}+\frac{c^{4} a b \arctan \left(\frac{x}{c}\right)}{2}"," ",0,"1/4*a^2*x^4+1/4*b^2*x^4*arctan(c/x)^2+1/6*c*b^2*arctan(c/x)*x^3-1/2*c^3*b^2*arctan(c/x)*x-1/4*c^4*b^2*arctan(c/x)^2+1/12*b^2*c^2*x^2+2/3*c^4*b^2*ln(c/x)-1/3*b^2*c^4*ln(1+c^2/x^2)+1/2*a*b*x^4*arctan(c/x)+1/6*a*b*c*x^3-1/2*c^3*a*b*x+1/2*c^4*a*b*arctan(x/c)","A"
141,1,445,134,0.128000," ","int(x^2*(a+b*arctan(c/x))^2,x)","\frac{x^{3} a^{2}}{3}+\frac{b^{2} x^{3} \arctan \left(\frac{c}{x}\right)^{2}}{3}+\frac{c \,b^{2} \arctan \left(\frac{c}{x}\right) x^{2}}{3}+\frac{2 c^{3} b^{2} \ln \left(\frac{c}{x}\right) \arctan \left(\frac{c}{x}\right)}{3}-\frac{c^{3} b^{2} \arctan \left(\frac{c}{x}\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{3}-\frac{i c^{3} b^{2} \ln \left(\frac{c}{x}-i\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{6}+\frac{i c^{3} b^{2} \ln \left(\frac{c}{x}-i\right)^{2}}{12}-\frac{i c^{3} b^{2} \dilog \left(1-\frac{i c}{x}\right)}{3}-\frac{i c^{3} b^{2} \dilog \left(\frac{i \left(\frac{c}{x}-i\right)}{2}\right)}{6}-\frac{i c^{3} b^{2} \ln \left(i+\frac{c}{x}\right)^{2}}{12}-\frac{i c^{3} b^{2} \ln \left(i+\frac{c}{x}\right) \ln \left(\frac{i \left(\frac{c}{x}-i\right)}{2}\right)}{6}+\frac{i c^{3} b^{2} \dilog \left(-\frac{i \left(i+\frac{c}{x}\right)}{2}\right)}{6}+\frac{i c^{3} b^{2} \ln \left(\frac{c}{x}-i\right) \ln \left(-\frac{i \left(i+\frac{c}{x}\right)}{2}\right)}{6}+\frac{b^{2} c^{2} x}{3}-\frac{c^{3} b^{2} \arctan \left(\frac{x}{c}\right)}{3}+\frac{i c^{3} b^{2} \ln \left(i+\frac{c}{x}\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{6}+\frac{i c^{3} b^{2} \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{i c}{x}\right)}{3}+\frac{i c^{3} b^{2} \dilog \left(1+\frac{i c}{x}\right)}{3}-\frac{i c^{3} b^{2} \ln \left(\frac{c}{x}\right) \ln \left(1-\frac{i c}{x}\right)}{3}+\frac{2 a b \,x^{3} \arctan \left(\frac{c}{x}\right)}{3}+\frac{a b c \,x^{2}}{3}+\frac{2 c^{3} a b \ln \left(\frac{c}{x}\right)}{3}-\frac{c^{3} a b \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{3}"," ",0,"1/3*x^3*a^2+1/3*b^2*x^3*arctan(c/x)^2+1/3*c*b^2*arctan(c/x)*x^2+2/3*c^3*b^2*ln(c/x)*arctan(c/x)-1/3*c^3*b^2*arctan(c/x)*ln(1+c^2/x^2)-1/6*I*c^3*b^2*ln(c/x-I)*ln(1+c^2/x^2)+1/12*I*c^3*b^2*ln(c/x-I)^2+1/3*I*c^3*b^2*dilog(1+I*c/x)-1/12*I*c^3*b^2*ln(I+c/x)^2-1/6*I*c^3*b^2*ln(I+c/x)*ln(1/2*I*(c/x-I))-1/3*I*c^3*b^2*dilog(1-I*c/x)-1/6*I*c^3*b^2*dilog(1/2*I*(c/x-I))+1/6*I*c^3*b^2*ln(c/x-I)*ln(-1/2*I*(I+c/x))+1/3*b^2*c^2*x-1/3*c^3*b^2*arctan(x/c)+1/6*I*c^3*b^2*ln(I+c/x)*ln(1+c^2/x^2)+1/3*I*c^3*b^2*ln(c/x)*ln(1+I*c/x)+1/6*I*c^3*b^2*dilog(-1/2*I*(I+c/x))-1/3*I*c^3*b^2*ln(c/x)*ln(1-I*c/x)+2/3*a*b*x^3*arctan(c/x)+1/3*a*b*c*x^2+2/3*c^3*a*b*ln(c/x)-1/3*c^3*a*b*ln(1+c^2/x^2)","B"
142,1,116,76,0.051000," ","int(x*(a+b*arctan(c/x))^2,x)","\frac{a^{2} x^{2}}{2}+\frac{b^{2} x^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2}+c \,b^{2} \arctan \left(\frac{c}{x}\right) x +\frac{c^{2} b^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2}-c^{2} b^{2} \ln \left(\frac{c}{x}\right)+\frac{b^{2} c^{2} \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2}+a b \,x^{2} \arctan \left(\frac{c}{x}\right)+a b c x -c^{2} a b \arctan \left(\frac{x}{c}\right)"," ",0,"1/2*a^2*x^2+1/2*b^2*x^2*arctan(c/x)^2+c*b^2*arctan(c/x)*x+1/2*c^2*b^2*arctan(c/x)^2-c^2*b^2*ln(c/x)+1/2*b^2*c^2*ln(1+c^2/x^2)+a*b*x^2*arctan(c/x)+a*b*c*x-c^2*a*b*arctan(x/c)","A"
143,1,357,79,0.104000," ","int((a+b*arctan(c/x))^2,x)","a^{2} x +b^{2} x \arctan \left(\frac{c}{x}\right)^{2}-2 c \,b^{2} \ln \left(\frac{c}{x}\right) \arctan \left(\frac{c}{x}\right)+c \,b^{2} \arctan \left(\frac{c}{x}\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)+i c \,b^{2} \dilog \left(1-\frac{i c}{x}\right)+i c \,b^{2} \ln \left(\frac{c}{x}\right) \ln \left(1-\frac{i c}{x}\right)+\frac{i c \,b^{2} \ln \left(i+\frac{c}{x}\right) \ln \left(\frac{i \left(\frac{c}{x}-i\right)}{2}\right)}{2}-\frac{i c \,b^{2} \ln \left(\frac{c}{x}-i\right) \ln \left(-\frac{i \left(i+\frac{c}{x}\right)}{2}\right)}{2}-\frac{i c \,b^{2} \ln \left(i+\frac{c}{x}\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2}+\frac{i c \,b^{2} \ln \left(\frac{c}{x}-i\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2}-i c \,b^{2} \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{i c}{x}\right)+\frac{i c \,b^{2} \ln \left(i+\frac{c}{x}\right)^{2}}{4}+\frac{i c \,b^{2} \dilog \left(\frac{i \left(\frac{c}{x}-i\right)}{2}\right)}{2}-i c \,b^{2} \dilog \left(1+\frac{i c}{x}\right)-\frac{i c \,b^{2} \ln \left(\frac{c}{x}-i\right)^{2}}{4}-\frac{i c \,b^{2} \dilog \left(-\frac{i \left(i+\frac{c}{x}\right)}{2}\right)}{2}+2 a b x \arctan \left(\frac{c}{x}\right)-2 c a b \ln \left(\frac{c}{x}\right)+c a b \ln \left(1+\frac{c^{2}}{x^{2}}\right)"," ",0,"a^2*x+b^2*x*arctan(c/x)^2-2*c*b^2*ln(c/x)*arctan(c/x)+c*b^2*arctan(c/x)*ln(1+c^2/x^2)-1/2*I*c*b^2*dilog(-1/2*I*(I+c/x))+I*c*b^2*ln(c/x)*ln(1-I*c/x)+1/2*I*c*b^2*dilog(1/2*I*(c/x-I))+1/2*I*c*b^2*ln(I+c/x)*ln(1/2*I*(c/x-I))-1/2*I*c*b^2*ln(c/x-I)*ln(-1/2*I*(I+c/x))-1/2*I*c*b^2*ln(I+c/x)*ln(1+c^2/x^2)+1/2*I*c*b^2*ln(c/x-I)*ln(1+c^2/x^2)-I*c*b^2*ln(c/x)*ln(1+I*c/x)+1/4*I*c*b^2*ln(I+c/x)^2-I*c*b^2*dilog(1+I*c/x)-1/4*I*c*b^2*ln(c/x-I)^2+I*c*b^2*dilog(1-I*c/x)+2*a*b*x*arctan(c/x)-2*c*a*b*ln(c/x)+c*a*b*ln(1+c^2/x^2)","B"
144,1,1249,137,0.340000," ","int((a+b*arctan(c/x))^2/x,x)","\frac{b^{2} \polylog \left(3, -\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}\right)}{2}-2 b^{2} \polylog \left(3, -\frac{1+\frac{i c}{x}}{\sqrt{1+\frac{c^{2}}{x^{2}}}}\right)-2 b^{2} \polylog \left(3, \frac{1+\frac{i c}{x}}{\sqrt{1+\frac{c^{2}}{x^{2}}}}\right)-i b^{2} \arctan \left(\frac{c}{x}\right) \polylog \left(2, -\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}\right)+2 i b^{2} \arctan \left(\frac{c}{x}\right) \polylog \left(2, \frac{1+\frac{i c}{x}}{\sqrt{1+\frac{c^{2}}{x^{2}}}}\right)+2 i b^{2} \arctan \left(\frac{c}{x}\right) \polylog \left(2, -\frac{1+\frac{i c}{x}}{\sqrt{1+\frac{c^{2}}{x^{2}}}}\right)-i a b \dilog \left(1+\frac{i c}{x}\right)+i a b \dilog \left(1-\frac{i c}{x}\right)-a^{2} \ln \left(\frac{c}{x}\right)+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right)^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1\right)}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right) \arctan \left(\frac{c}{x}\right)^{2}}{2}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1\right)}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right)^{3} \arctan \left(\frac{c}{x}\right)^{2}}{2}-i a b \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{i c}{x}\right)+i a b \ln \left(\frac{c}{x}\right) \ln \left(1-\frac{i c}{x}\right)-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right)^{3} \arctan \left(\frac{c}{x}\right)^{2}}{2}+b^{2} \arctan \left(\frac{c}{x}\right)^{2} \ln \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1\right)-b^{2} \arctan \left(\frac{c}{x}\right)^{2} \ln \left(1+\frac{1+\frac{i c}{x}}{\sqrt{1+\frac{c^{2}}{x^{2}}}}\right)-b^{2} \arctan \left(\frac{c}{x}\right)^{2} \ln \left(1-\frac{1+\frac{i c}{x}}{\sqrt{1+\frac{c^{2}}{x^{2}}}}\right)-b^{2} \ln \left(\frac{c}{x}\right) \arctan \left(\frac{c}{x}\right)^{2}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1\right)}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right)^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1\right)}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right) \arctan \left(\frac{c}{x}\right)^{2}}{2}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1\right)}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right)^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1\right)}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right) \mathrm{csgn}\left(\frac{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}-1}{\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1}\right)^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2}-2 a b \ln \left(\frac{c}{x}\right) \arctan \left(\frac{c}{x}\right)-\frac{i b^{2} \pi  \arctan \left(\frac{c}{x}\right)^{2}}{2}"," ",0,"-1/2*I*b^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^3*arctan(c/x)^2-I*a*b*ln(c/x)*ln(1+I*c/x)+I*a*b*ln(c/x)*ln(1-I*c/x)-1/2*I*b^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1))*csgn(I/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*arctan(c/x)^2+1/2*b^2*polylog(3,-(1+I*c/x)^2/(1+c^2/x^2))-2*b^2*polylog(3,-(1+I*c/x)/(1+c^2/x^2)^(1/2))-2*b^2*polylog(3,(1+I*c/x)/(1+c^2/x^2)^(1/2))-a^2*ln(c/x)-1/2*I*b^2*Pi*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^3*arctan(c/x)^2+1/2*I*b^2*Pi*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2-b^2*ln(c/x)*arctan(c/x)^2+1/2*I*b^2*Pi*csgn(I/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2-1/2*I*b^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*arctan(c/x)^2+1/2*I*b^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2+1/2*I*b^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2-I*b^2*arctan(c/x)*polylog(2,-(1+I*c/x)^2/(1+c^2/x^2))+2*I*b^2*arctan(c/x)*polylog(2,(1+I*c/x)/(1+c^2/x^2)^(1/2))+2*I*b^2*arctan(c/x)*polylog(2,-(1+I*c/x)/(1+c^2/x^2)^(1/2))-1/2*I*b^2*Pi*arctan(c/x)^2-I*a*b*dilog(1+I*c/x)+I*a*b*dilog(1-I*c/x)-2*a*b*ln(c/x)*arctan(c/x)+b^2*arctan(c/x)^2*ln((1+I*c/x)^2/(1+c^2/x^2)-1)-b^2*arctan(c/x)^2*ln(1+(1+I*c/x)/(1+c^2/x^2)^(1/2))-b^2*arctan(c/x)^2*ln(1-(1+I*c/x)/(1+c^2/x^2)^(1/2))","C"
145,1,147,92,0.207000," ","int((a+b*arctan(c/x))^2/x^2,x)","-\frac{a^{2}}{x}+\frac{i \arctan \left(\frac{c}{x}\right)^{2} b^{2}}{c}-\frac{\arctan \left(\frac{c}{x}\right)^{2} b^{2}}{x}+\frac{i \polylog \left(2, -\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}\right) b^{2}}{c}-\frac{2 \arctan \left(\frac{c}{x}\right) \ln \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1\right) b^{2}}{c}-\frac{2 a b \arctan \left(\frac{c}{x}\right)}{x}+\frac{a b \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{c}"," ",0,"-a^2/x+I/c*arctan(c/x)^2*b^2-arctan(c/x)^2/x*b^2+I/c*polylog(2,-(1+I*c/x)^2/(1+c^2/x^2))*b^2-2/c*arctan(c/x)*ln((1+I*c/x)^2/(1+c^2/x^2)+1)*b^2-2/x*a*b*arctan(c/x)+1/c*a*b*ln(1+c^2/x^2)","A"
146,1,110,78,0.046000," ","int((a+b*arctan(c/x))^2/x^3,x)","-\frac{a^{2}}{2 x^{2}}-\frac{b^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2 x^{2}}-\frac{b^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2 c^{2}}+\frac{b^{2} \arctan \left(\frac{c}{x}\right)}{c x}-\frac{b^{2} \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2 c^{2}}-\frac{a b \arctan \left(\frac{c}{x}\right)}{x^{2}}+\frac{a b \arctan \left(\frac{x}{c}\right)}{c^{2}}+\frac{a b}{c x}"," ",0,"-1/2*a^2/x^2-1/2*b^2/x^2*arctan(c/x)^2-1/2/c^2*b^2*arctan(c/x)^2+1/c*b^2*arctan(c/x)/x-1/2*b^2*ln(1+c^2/x^2)/c^2-a*b/x^2*arctan(c/x)+1/c^2*a*b*arctan(x/c)+a*b/c/x","A"
147,1,608,196,0.127000," ","int(x^3*(a+b*arctan(c/x))^3,x)","-\frac{c^{4} b^{3} \arctan \left(\frac{c}{x}\right)^{3}}{4}-\frac{c^{4} b^{3} \arctan \left(\frac{x}{c}\right)}{4}+\frac{b^{3} x^{4} \arctan \left(\frac{c}{x}\right)^{3}}{4}+\frac{b^{3} c^{3} x}{4}+2 c^{4} a \,b^{2} \ln \left(\frac{c}{x}\right)-\frac{3 c^{4} a \,b^{2} \arctan \left(\frac{c}{x}\right)^{2}}{4}+\frac{3 a \,b^{2} x^{4} \arctan \left(\frac{c}{x}\right)^{2}}{4}+\frac{3 a^{2} b \,x^{4} \arctan \left(\frac{c}{x}\right)}{4}-\frac{3 c^{3} x \,a^{2} b}{4}+\frac{c \,b^{3} \arctan \left(\frac{c}{x}\right)^{2} x^{3}}{4}+\frac{c^{2} b^{3} \arctan \left(\frac{c}{x}\right) x^{2}}{4}+\frac{i c^{4} b^{3} \dilog \left(-\frac{i \left(i+\frac{c}{x}\right)}{2}\right)}{2}-i c^{4} b^{3} \dilog \left(1-\frac{i c}{x}\right)+\frac{i c^{4} b^{3} \ln \left(\frac{c}{x}-i\right)^{2}}{4}-\frac{i c^{4} b^{3} \ln \left(i+\frac{c}{x}\right)^{2}}{4}-\frac{i c^{4} b^{3} \dilog \left(\frac{i \left(\frac{c}{x}-i\right)}{2}\right)}{2}+i c^{4} b^{3} \dilog \left(1+\frac{i c}{x}\right)+\frac{c^{2} x^{2} a \,b^{2}}{4}-c^{4} b^{3} \arctan \left(\frac{c}{x}\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)+2 c^{4} b^{3} \arctan \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}\right)+\frac{3 c^{4} a^{2} b \arctan \left(\frac{x}{c}\right)}{4}-\frac{i c^{4} b^{3} \ln \left(i+\frac{c}{x}\right) \ln \left(\frac{i \left(\frac{c}{x}-i\right)}{2}\right)}{2}-i c^{4} b^{3} \ln \left(\frac{c}{x}\right) \ln \left(1-\frac{i c}{x}\right)+\frac{i c^{4} b^{3} \ln \left(i+\frac{c}{x}\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2}+\frac{i c^{4} b^{3} \ln \left(\frac{c}{x}-i\right) \ln \left(-\frac{i \left(i+\frac{c}{x}\right)}{2}\right)}{2}+i c^{4} b^{3} \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{i c}{x}\right)-\frac{i c^{4} b^{3} \ln \left(\frac{c}{x}-i\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2}+\frac{c a \,b^{2} \arctan \left(\frac{c}{x}\right) x^{3}}{2}-\frac{3 c^{3} a \,b^{2} x \arctan \left(\frac{c}{x}\right)}{2}+\frac{x^{4} a^{3}}{4}-c^{4} a \,b^{2} \ln \left(1+\frac{c^{2}}{x^{2}}\right)-\frac{3 c^{3} b^{3} \arctan \left(\frac{c}{x}\right)^{2} x}{4}+\frac{c \,a^{2} b \,x^{3}}{4}"," ",0,"-1/4*c^4*b^3*arctan(c/x)^3-1/4*c^4*b^3*arctan(x/c)+1/4*b^3*x^4*arctan(c/x)^3+1/4*b^3*c^3*x+2*c^4*a*b^2*ln(c/x)-3/4*c^4*a*b^2*arctan(c/x)^2+1/4*I*c^4*b^3*ln(c/x-I)^2-1/2*I*c^4*b^3*dilog(1/2*I*(c/x-I))+3/4*a*b^2*x^4*arctan(c/x)^2+3/4*a^2*b*x^4*arctan(c/x)-3/4*c^3*x*a^2*b+I*c^4*b^3*dilog(1+I*c/x)+1/4*c*b^3*arctan(c/x)^2*x^3+1/4*c^2*b^3*arctan(c/x)*x^2-1/4*I*c^4*b^3*ln(I+c/x)^2+1/2*I*c^4*b^3*dilog(-1/2*I*(I+c/x))+1/4*c^2*x^2*a*b^2-c^4*b^3*arctan(c/x)*ln(1+c^2/x^2)+2*c^4*b^3*arctan(c/x)*ln(c/x)+3/4*c^4*a^2*b*arctan(x/c)-I*c^4*b^3*dilog(1-I*c/x)+1/2*I*c^4*b^3*ln(I+c/x)*ln(1+c^2/x^2)+1/2*I*c^4*b^3*ln(c/x-I)*ln(-1/2*I*(I+c/x))+1/2*c*a*b^2*arctan(c/x)*x^3-3/2*c^3*a*b^2*x*arctan(c/x)+I*c^4*b^3*ln(c/x)*ln(1+I*c/x)-1/2*I*c^4*b^3*ln(c/x-I)*ln(1+c^2/x^2)-1/2*I*c^4*b^3*ln(I+c/x)*ln(1/2*I*(c/x-I))+1/4*x^4*a^3-I*c^4*b^3*ln(c/x)*ln(1-I*c/x)-c^4*a*b^2*ln(1+c^2/x^2)-3/4*c^3*b^3*arctan(c/x)^2*x+1/4*c*a^2*b*x^3","B"
148,1,6441,212,1.376000," ","int(x^2*(a+b*arctan(c/x))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
149,1,507,131,0.125000," ","int(x*(a+b*arctan(c/x))^3,x)","\frac{c^{2} b^{3} \arctan \left(\frac{c}{x}\right)^{3}}{2}+\frac{b^{3} x^{2} \arctan \left(\frac{c}{x}\right)^{3}}{2}+\frac{x^{2} a^{3}}{2}-\frac{3 i c^{2} b^{3} \dilog \left(1+\frac{i c}{x}\right)}{2}-\frac{3 i c^{2} b^{3} \ln \left(\frac{c}{x}-i\right)^{2}}{8}+\frac{3 i c^{2} b^{3} \ln \left(i+\frac{c}{x}\right)^{2}}{8}+\frac{3 i c^{2} b^{3} \dilog \left(1-\frac{i c}{x}\right)}{2}+\frac{3 i c^{2} b^{3} \dilog \left(\frac{i \left(\frac{c}{x}-i\right)}{2}\right)}{4}-\frac{3 i c^{2} b^{3} \dilog \left(-\frac{i \left(i+\frac{c}{x}\right)}{2}\right)}{4}-\frac{3 i c^{2} b^{3} \ln \left(\frac{c}{x}\right) \ln \left(1+\frac{i c}{x}\right)}{2}-\frac{3 i c^{2} b^{3} \ln \left(i+\frac{c}{x}\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{4}-\frac{3 i c^{2} b^{3} \ln \left(\frac{c}{x}-i\right) \ln \left(-\frac{i \left(i+\frac{c}{x}\right)}{2}\right)}{4}+\frac{3 i c^{2} b^{3} \ln \left(\frac{c}{x}\right) \ln \left(1-\frac{i c}{x}\right)}{2}+\frac{3 i c^{2} b^{3} \ln \left(\frac{c}{x}-i\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{4}+\frac{3 i c^{2} b^{3} \ln \left(i+\frac{c}{x}\right) \ln \left(\frac{i \left(\frac{c}{x}-i\right)}{2}\right)}{4}+3 c a \,b^{2} x \arctan \left(\frac{c}{x}\right)+\frac{3 c^{2} b^{3} \arctan \left(\frac{c}{x}\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2}-3 c^{2} b^{3} \arctan \left(\frac{c}{x}\right) \ln \left(\frac{c}{x}\right)-3 c^{2} a \,b^{2} \ln \left(\frac{c}{x}\right)+\frac{3 c^{2} a \,b^{2} \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2}+\frac{3 c x \,a^{2} b}{2}+\frac{3 a^{2} b \,x^{2} \arctan \left(\frac{c}{x}\right)}{2}+\frac{3 a \,b^{2} x^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2}-\frac{3 c^{2} a^{2} b \arctan \left(\frac{x}{c}\right)}{2}+\frac{3 c^{2} a \,b^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2}+\frac{3 c \,b^{3} \arctan \left(\frac{c}{x}\right)^{2} x}{2}"," ",0,"1/2*c^2*b^3*arctan(c/x)^3+1/2*b^3*x^2*arctan(c/x)^3+1/2*x^2*a^3-3/4*I*c^2*b^3*ln(c/x-I)*ln(-1/2*I*(I+c/x))+3/2*I*c^2*b^3*ln(c/x)*ln(1-I*c/x)+3/4*I*c^2*b^3*ln(c/x-I)*ln(1+c^2/x^2)+3/4*I*c^2*b^3*ln(I+c/x)*ln(1/2*I*(c/x-I))+3*c*a*b^2*x*arctan(c/x)-3/2*I*c^2*b^3*ln(c/x)*ln(1+I*c/x)-3/4*I*c^2*b^3*ln(I+c/x)*ln(1+c^2/x^2)+3/2*c^2*b^3*arctan(c/x)*ln(1+c^2/x^2)-3*c^2*b^3*arctan(c/x)*ln(c/x)-3*c^2*a*b^2*ln(c/x)+3/2*c^2*a*b^2*ln(1+c^2/x^2)+3/2*I*c^2*b^3*dilog(1-I*c/x)-3/8*I*c^2*b^3*ln(c/x-I)^2+3/4*I*c^2*b^3*dilog(1/2*I*(c/x-I))+3/8*I*c^2*b^3*ln(I+c/x)^2-3/4*I*c^2*b^3*dilog(-1/2*I*(I+c/x))-3/2*I*c^2*b^3*dilog(1+I*c/x)+3/2*c*x*a^2*b+3/2*a^2*b*x^2*arctan(c/x)+3/2*a*b^2*x^2*arctan(c/x)^2-3/2*c^2*a^2*b*arctan(x/c)+3/2*c^2*a*b^2*arctan(c/x)^2+3/2*c*b^3*arctan(c/x)^2*x","B"
150,1,2363,112,0.352000," ","int((a+b*arctan(c/x))^3,x)","\text{Expression too large to display}"," ",0,"3/4*I*c*b^3*arctan(c/x)^2*Pi*csgn(I/((1+I*c/x)^2/(1+c^2/x^2)+1)^2)*csgn(I*(1+I*c/x)^2/(1+c^2/x^2))*csgn(I*(1+I*c/x)^2/(1+c^2/x^2)/((1+I*c/x)^2/(1+c^2/x^2)+1)^2)-3/2*I*c*b^3*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1))*csgn(I/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*arctan(c/x)^2+3*a^2*b*x*arctan(c/x)+3*a*b^2*x*arctan(c/x)^2-3*c*b^3*arctan(c/x)^2*ln((1+I*c/x)/(1+c^2/x^2)^(1/2))+3/2*c*b^3*arctan(c/x)^2*ln(1+c^2/x^2)-3*c*b^3*ln(c/x)*arctan(c/x)^2-3*c*b^3*arctan(c/x)^2*ln(1-(1+I*c/x)/(1+c^2/x^2)^(1/2))-3*c*b^3*arctan(c/x)^2*ln(1+(1+I*c/x)/(1+c^2/x^2)^(1/2))+3*c*b^3*arctan(c/x)^2*ln((1+I*c/x)^2/(1+c^2/x^2)-1)+3/2*c*a^2*b*ln(1+c^2/x^2)-3*c*b^3*ln(2)*arctan(c/x)^2+I*c*b^3*arctan(c/x)^3-3*c*a^2*b*ln(c/x)-3/4*I*c*b^3*arctan(c/x)^2*Pi*csgn(I/((1+I*c/x)^2/(1+c^2/x^2)+1)^2)*csgn(I*(1+I*c/x)^2/(1+c^2/x^2)/((1+I*c/x)^2/(1+c^2/x^2)+1)^2)^2-3/4*I*c*b^3*arctan(c/x)^2*Pi*csgn(I*(1+I*c/x)^2/(1+c^2/x^2))*csgn(I*(1+I*c/x)^2/(1+c^2/x^2)/((1+I*c/x)^2/(1+c^2/x^2)+1)^2)^2-3/2*I*c*b^3*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*arctan(c/x)^2+3/4*I*c*b^3*arctan(c/x)^2*Pi*csgn(I*(1+I*c/x)/(1+c^2/x^2)^(1/2))^2*csgn(I*(1+I*c/x)^2/(1+c^2/x^2))+3/2*I*c*b^3*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2-3/4*I*c*b^3*arctan(c/x)^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)+1))^2*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)+1)^2)+3/2*I*c*b^3*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2+3/2*I*c*b^3*Pi*csgn(I/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2-3/2*I*c*b^3*arctan(c/x)^2*Pi*csgn(I*(1+I*c/x)/(1+c^2/x^2)^(1/2))*csgn(I*(1+I*c/x)^2/(1+c^2/x^2))^2+3/2*I*c*b^3*arctan(c/x)^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)+1)^2)^2+3/2*I*c*a*b^2*dilog(1/2*I*(c/x-I))+6*I*c*b^3*arctan(c/x)*polylog(2,-(1+I*c/x)/(1+c^2/x^2)^(1/2))-3*I*c*a*b^2*dilog(1+I*c/x)+3*I*c*a*b^2*dilog(1-I*c/x)+3*c*a*b^2*arctan(c/x)*ln(1+c^2/x^2)-6*c*a*b^2*ln(c/x)*arctan(c/x)-3/2*I*c*b^3*Pi*arctan(c/x)^2-3/4*I*c*a*b^2*ln(c/x-I)^2-3/2*I*c*a*b^2*dilog(-1/2*I*(I+c/x))+3/4*I*c*a*b^2*ln(I+c/x)^2+6*I*c*b^3*arctan(c/x)*polylog(2,(1+I*c/x)/(1+c^2/x^2)^(1/2))-3/2*I*c*a*b^2*ln(I+c/x)*ln(1+c^2/x^2)-3/2*I*c*b^3*Pi*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^3*arctan(c/x)^2+3/2*I*c*b^3*Pi*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2+3/2*I*c*a*b^2*ln(I+c/x)*ln(1/2*I*(c/x-I))-3*I*c*a*b^2*ln(c/x)*ln(1+I*c/x)+3*I*c*a*b^2*ln(c/x)*ln(1-I*c/x)-3/2*I*c*b^3*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^3*arctan(c/x)^2-3/4*I*c*b^3*arctan(c/x)^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)+1)^2)^3+3/4*I*c*b^3*arctan(c/x)^2*Pi*csgn(I*(1+I*c/x)^2/(1+c^2/x^2)/((1+I*c/x)^2/(1+c^2/x^2)+1)^2)^3+3/4*I*c*b^3*arctan(c/x)^2*Pi*csgn(I*(1+I*c/x)^2/(1+c^2/x^2))^3+3/2*I*c*a*b^2*ln(c/x-I)*ln(1+c^2/x^2)-6*c*b^3*polylog(3,(1+I*c/x)/(1+c^2/x^2)^(1/2))-6*c*b^3*polylog(3,-(1+I*c/x)/(1+c^2/x^2)^(1/2))+b^3*x*arctan(c/x)^3-3/2*I*c*a*b^2*ln(c/x-I)*ln(-1/2*I*(I+c/x))+x*a^3","C"
151,1,2542,207,0.236000," ","int((a+b*arctan(c/x))^3/x,x)","\text{Expression too large to display}"," ",0,"-3/2*I*a*b^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1))*csgn(I/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*arctan(c/x)^2-3/2*I*a^2*b*dilog(1+I*c/x)+3/2*I*a^2*b*dilog(1-I*c/x)-1/2*I*b^3*Pi*arctan(c/x)^3+3*I*b^3*arctan(c/x)^2*polylog(2,-(1+I*c/x)/(1+c^2/x^2)^(1/2))-3/2*I*b^3*arctan(c/x)^2*polylog(2,-(1+I*c/x)^2/(1+c^2/x^2))+3*I*b^3*arctan(c/x)^2*polylog(2,(1+I*c/x)/(1+c^2/x^2)^(1/2))-3*a*b^2*ln(c/x)*arctan(c/x)^2+3*a*b^2*arctan(c/x)^2*ln((1+I*c/x)^2/(1+c^2/x^2)-1)-3*a*b^2*arctan(c/x)^2*ln(1+(1+I*c/x)/(1+c^2/x^2)^(1/2))-3*a*b^2*arctan(c/x)^2*ln(1-(1+I*c/x)/(1+c^2/x^2)^(1/2))-3*a^2*b*ln(c/x)*arctan(c/x)-a^3*ln(c/x)-1/2*I*b^3*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1))*csgn(I/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*arctan(c/x)^3+3/2*I*a*b^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2+3/2*I*a*b^2*Pi*csgn(I/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2+6*I*a*b^2*arctan(c/x)*polylog(2,-(1+I*c/x)/(1+c^2/x^2)^(1/2))-3/2*I*a*b^2*Pi*arctan(c/x)^2-3*I*a*b^2*arctan(c/x)*polylog(2,-(1+I*c/x)^2/(1+c^2/x^2))-3/2*I*a^2*b*ln(c/x)*ln(1+I*c/x)+3/2*I*a^2*b*ln(c/x)*ln(1-I*c/x)+1/2*I*b^3*Pi*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^3-1/2*I*b^3*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^3*arctan(c/x)^3-1/2*I*b^3*Pi*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^3*arctan(c/x)^3+6*I*a*b^2*arctan(c/x)*polylog(2,(1+I*c/x)/(1+c^2/x^2)^(1/2))+3/2*b^3*arctan(c/x)*polylog(3,-(1+I*c/x)^2/(1+c^2/x^2))-3/2*I*a*b^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^3*arctan(c/x)^2-1/2*I*b^3*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*arctan(c/x)^3+1/2*I*b^3*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^3+1/2*I*b^3*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^3+1/2*I*b^3*Pi*csgn(I/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^3+3/2*I*a*b^2*Pi*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2-3/2*I*a*b^2*Pi*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^3*arctan(c/x)^2-6*I*b^3*polylog(4,(1+I*c/x)/(1+c^2/x^2)^(1/2))-6*I*b^3*polylog(4,-(1+I*c/x)/(1+c^2/x^2)^(1/2))+3/4*I*b^3*polylog(4,-(1+I*c/x)^2/(1+c^2/x^2))+3/2*a*b^2*polylog(3,-(1+I*c/x)^2/(1+c^2/x^2))-6*a*b^2*polylog(3,-(1+I*c/x)/(1+c^2/x^2)^(1/2))-6*a*b^2*polylog(3,(1+I*c/x)/(1+c^2/x^2)^(1/2))-b^3*ln(c/x)*arctan(c/x)^3+b^3*arctan(c/x)^3*ln((1+I*c/x)^2/(1+c^2/x^2)-1)-b^3*arctan(c/x)^3*ln(1+(1+I*c/x)/(1+c^2/x^2)^(1/2))-6*b^3*arctan(c/x)*polylog(3,-(1+I*c/x)/(1+c^2/x^2)^(1/2))-b^3*arctan(c/x)^3*ln(1-(1+I*c/x)/(1+c^2/x^2)^(1/2))-6*b^3*arctan(c/x)*polylog(3,(1+I*c/x)/(1+c^2/x^2)^(1/2))+3/2*I*a*b^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))^2*arctan(c/x)^2-3/2*I*a*b^2*Pi*csgn(I*((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*csgn(((1+I*c/x)^2/(1+c^2/x^2)-1)/((1+I*c/x)^2/(1+c^2/x^2)+1))*arctan(c/x)^2","C"
152,1,306,129,0.253000," ","int((a+b*arctan(c/x))^3/x^2,x)","-\frac{a^{3}}{x}+\frac{i b^{3} \arctan \left(\frac{c}{x}\right)^{3}}{c}-\frac{b^{3} \arctan \left(\frac{c}{x}\right)^{3}}{x}-\frac{3 b^{3} \arctan \left(\frac{c}{x}\right)^{2} \ln \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1\right)}{c}+\frac{3 i b^{3} \arctan \left(\frac{c}{x}\right) \polylog \left(2, -\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}\right)}{c}-\frac{3 b^{3} \polylog \left(3, -\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}\right)}{2 c}+\frac{3 i \arctan \left(\frac{c}{x}\right)^{2} a \,b^{2}}{c}-\frac{3 a \,b^{2} \arctan \left(\frac{c}{x}\right)^{2}}{x}-\frac{6 \ln \left(\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}+1\right) \arctan \left(\frac{c}{x}\right) a \,b^{2}}{c}+\frac{3 i \polylog \left(2, -\frac{\left(1+\frac{i c}{x}\right)^{2}}{1+\frac{c^{2}}{x^{2}}}\right) a \,b^{2}}{c}-\frac{3 a^{2} b \arctan \left(\frac{c}{x}\right)}{x}+\frac{3 a^{2} b \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2 c}"," ",0,"-a^3/x+I/c*b^3*arctan(c/x)^3-b^3/x*arctan(c/x)^3-3/c*b^3*arctan(c/x)^2*ln((1+I*c/x)^2/(1+c^2/x^2)+1)+3*I/c*b^3*arctan(c/x)*polylog(2,-(1+I*c/x)^2/(1+c^2/x^2))-3/2/c*b^3*polylog(3,-(1+I*c/x)^2/(1+c^2/x^2))+3*I/c*arctan(c/x)^2*a*b^2-3/x*a*b^2*arctan(c/x)^2-6/c*ln((1+I*c/x)^2/(1+c^2/x^2)+1)*arctan(c/x)*a*b^2+3*I/c*polylog(2,-(1+I*c/x)^2/(1+c^2/x^2))*a*b^2-3/x*a^2*b*arctan(c/x)+3/2/c*a^2*b*ln(1+c^2/x^2)","B"
153,1,396,133,0.102000," ","int((a+b*arctan(c/x))^3/x^3,x)","-\frac{a^{3}}{2 x^{2}}-\frac{b^{3} \arctan \left(\frac{c}{x}\right)^{3}}{2 x^{2}}-\frac{b^{3} \arctan \left(\frac{c}{x}\right)^{3}}{2 c^{2}}+\frac{3 b^{3} \arctan \left(\frac{c}{x}\right)^{2}}{2 c x}-\frac{3 b^{3} \arctan \left(\frac{c}{x}\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2 c^{2}}-\frac{3 i b^{3} \ln \left(\frac{c}{x}-i\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{4 c^{2}}-\frac{3 i b^{3} \ln \left(i+\frac{c}{x}\right) \ln \left(\frac{i \left(\frac{c}{x}-i\right)}{2}\right)}{4 c^{2}}+\frac{3 i b^{3} \dilog \left(-\frac{i \left(i+\frac{c}{x}\right)}{2}\right)}{4 c^{2}}-\frac{3 i b^{3} \ln \left(i+\frac{c}{x}\right)^{2}}{8 c^{2}}-\frac{3 i b^{3} \dilog \left(\frac{i \left(\frac{c}{x}-i\right)}{2}\right)}{4 c^{2}}+\frac{3 i b^{3} \ln \left(\frac{c}{x}-i\right) \ln \left(-\frac{i \left(i+\frac{c}{x}\right)}{2}\right)}{4 c^{2}}+\frac{3 i b^{3} \ln \left(i+\frac{c}{x}\right) \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{4 c^{2}}+\frac{3 i b^{3} \ln \left(\frac{c}{x}-i\right)^{2}}{8 c^{2}}-\frac{3 a \,b^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2 x^{2}}-\frac{3 a \,b^{2} \arctan \left(\frac{c}{x}\right)^{2}}{2 c^{2}}+\frac{3 a \,b^{2} \arctan \left(\frac{c}{x}\right)}{c x}-\frac{3 a \,b^{2} \ln \left(1+\frac{c^{2}}{x^{2}}\right)}{2 c^{2}}-\frac{3 b \,a^{2} \arctan \left(\frac{c}{x}\right)}{2 x^{2}}+\frac{3 a^{2} b}{2 c x}+\frac{3 a^{2} b \arctan \left(\frac{x}{c}\right)}{2 c^{2}}"," ",0,"-1/2*a^3/x^2-1/2/x^2*b^3*arctan(c/x)^3-1/2/c^2*b^3*arctan(c/x)^3+3/2/c*b^3*arctan(c/x)^2/x-3/2/c^2*b^3*arctan(c/x)*ln(1+c^2/x^2)-3/4*I/c^2*b^3*ln(c/x-I)*ln(1+c^2/x^2)-3/4*I/c^2*b^3*ln(I+c/x)*ln(1/2*I*(c/x-I))-3/4*I/c^2*b^3*dilog(1/2*I*(c/x-I))-3/8*I/c^2*b^3*ln(I+c/x)^2+3/4*I/c^2*b^3*ln(c/x-I)*ln(-1/2*I*(I+c/x))+3/4*I/c^2*b^3*ln(I+c/x)*ln(1+c^2/x^2)+3/8*I/c^2*b^3*ln(c/x-I)^2+3/4*I/c^2*b^3*dilog(-1/2*I*(I+c/x))-3/2/x^2*a*b^2*arctan(c/x)^2-3/2/c^2*a*b^2*arctan(c/x)^2+3/c*a*b^2/x*arctan(c/x)-3/2/c^2*a*b^2*ln(1+c^2/x^2)-3/2*b/x^2*a^2*arctan(c/x)+3/2*a^2*b/c/x+3/2/c^2*a^2*b*arctan(x/c)","B"
154,1,32,31,0.029000," ","int(x^2*arctan(x^(1/2)),x)","\frac{x^{\frac{3}{2}}}{9}-\frac{x^{\frac{5}{2}}}{15}+\frac{\arctan \left(\sqrt{x}\right)}{3}+\frac{x^{3} \arctan \left(\sqrt{x}\right)}{3}-\frac{\sqrt{x}}{3}"," ",0,"1/9*x^(3/2)-1/15*x^(5/2)+1/3*arctan(x^(1/2))+1/3*x^3*arctan(x^(1/2))-1/3*x^(1/2)","A"
155,1,27,26,0.025000," ","int(x*arctan(x^(1/2)),x)","-\frac{x^{\frac{3}{2}}}{6}-\frac{\arctan \left(\sqrt{x}\right)}{2}+\frac{x^{2} \arctan \left(\sqrt{x}\right)}{2}+\frac{\sqrt{x}}{2}"," ",0,"-1/6*x^(3/2)-1/2*arctan(x^(1/2))+1/2*x^2*arctan(x^(1/2))+1/2*x^(1/2)","A"
156,1,17,16,0.023000," ","int(arctan(x^(1/2)),x)","\arctan \left(\sqrt{x}\right)+x \arctan \left(\sqrt{x}\right)-\sqrt{x}"," ",0,"arctan(x^(1/2))+x*arctan(x^(1/2))-x^(1/2)","A"
157,1,61,23,0.040000," ","int(arctan(x^(1/2))/x,x)","\ln \left(x \right) \arctan \left(\sqrt{x}\right)+\frac{i \ln \left(x \right) \ln \left(1+i \sqrt{x}\right)}{2}-\frac{i \ln \left(x \right) \ln \left(1-i \sqrt{x}\right)}{2}+i \dilog \left(1+i \sqrt{x}\right)-i \dilog \left(1-i \sqrt{x}\right)"," ",0,"ln(x)*arctan(x^(1/2))+1/2*I*ln(x)*ln(1+I*x^(1/2))-1/2*I*ln(x)*ln(1-I*x^(1/2))+I*dilog(1+I*x^(1/2))-I*dilog(1-I*x^(1/2))","B"
158,1,22,21,0.031000," ","int(arctan(x^(1/2))/x^2,x)","-\arctan \left(\sqrt{x}\right)-\frac{\arctan \left(\sqrt{x}\right)}{x}-\frac{1}{\sqrt{x}}"," ",0,"-arctan(x^(1/2))-arctan(x^(1/2))/x-1/x^(1/2)","A"
159,1,27,26,0.030000," ","int(arctan(x^(1/2))/x^3,x)","-\frac{1}{6 x^{\frac{3}{2}}}+\frac{\arctan \left(\sqrt{x}\right)}{2}-\frac{\arctan \left(\sqrt{x}\right)}{2 x^{2}}+\frac{1}{2 \sqrt{x}}"," ",0,"-1/6/x^(3/2)+1/2*arctan(x^(1/2))-1/2*arctan(x^(1/2))/x^2+1/2/x^(1/2)","A"
160,1,25,24,0.025000," ","int(x^(3/2)*arctan(x^(1/2)),x)","\frac{x}{5}-\frac{x^{2}}{10}+\frac{2 x^{\frac{5}{2}} \arctan \left(\sqrt{x}\right)}{5}-\frac{\ln \left(x +1\right)}{5}"," ",0,"1/5*x-1/10*x^2+2/5*x^(5/2)*arctan(x^(1/2))-1/5*ln(x+1)","A"
161,1,20,19,0.031000," ","int(x^(1/2)*arctan(x^(1/2)),x)","-\frac{x}{3}+\frac{2 x^{\frac{3}{2}} \arctan \left(\sqrt{x}\right)}{3}+\frac{\ln \left(x +1\right)}{3}"," ",0,"-1/3*x+2/3*x^(3/2)*arctan(x^(1/2))+1/3*ln(x+1)","A"
162,1,17,16,0.025000," ","int(arctan(x^(1/2))/x^(1/2),x)","-\ln \left(x +1\right)+2 \sqrt{x}\, \arctan \left(\sqrt{x}\right)"," ",0,"-ln(x+1)+2*x^(1/2)*arctan(x^(1/2))","A"
163,1,19,18,0.036000," ","int(arctan(x^(1/2))/x^(3/2),x)","\ln \left(x \right)-\ln \left(x +1\right)-\frac{2 \arctan \left(\sqrt{x}\right)}{\sqrt{x}}"," ",0,"ln(x)-ln(x+1)-2*arctan(x^(1/2))/x^(1/2)","A"
164,1,26,25,0.033000," ","int(arctan(x^(1/2))/x^(5/2),x)","-\frac{1}{3 x}-\frac{2 \arctan \left(\sqrt{x}\right)}{3 x^{\frac{3}{2}}}-\frac{\ln \left(x \right)}{3}+\frac{\ln \left(x +1\right)}{3}"," ",0,"-1/3/x-2/3*arctan(x^(1/2))/x^(3/2)-1/3*ln(x)+1/3*ln(x+1)","A"
165,1,57,25,0.091000," ","int(arctan(a*x^5)/x,x)","\ln \left(x \right) \arctan \left(a \,x^{5}\right)-\frac{\munderset{\textit{\_R1} =\RootOf \left(a^{2} \textit{\_Z}^{10}+1\right)}{\sum}\frac{\ln \left(x \right) \ln \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -x}{\textit{\_R1}}\right)}{\textit{\_R1}^{5}}}{2 a}"," ",0,"ln(x)*arctan(a*x^5)-1/2/a*sum(1/_R1^5*(ln(x)*ln((_R1-x)/_R1)+dilog((_R1-x)/_R1)),_R1=RootOf(_Z^10*a^2+1))","C"
166,1,94,31,0.046000," ","int(arctan(a*x^n)/x,x)","\frac{\ln \left(a \,x^{n}\right) \arctan \left(a \,x^{n}\right)}{n}+\frac{i \ln \left(a \,x^{n}\right) \ln \left(1+i a \,x^{n}\right)}{2 n}-\frac{i \ln \left(a \,x^{n}\right) \ln \left(1-i a \,x^{n}\right)}{2 n}+\frac{i \dilog \left(1+i a \,x^{n}\right)}{2 n}-\frac{i \dilog \left(1-i a \,x^{n}\right)}{2 n}"," ",0,"1/n*ln(a*x^n)*arctan(a*x^n)+1/2*I/n*ln(a*x^n)*ln(1+I*a*x^n)-1/2*I/n*ln(a*x^n)*ln(1-I*a*x^n)+1/2*I/n*dilog(1+I*a*x^n)-1/2*I/n*dilog(1-I*a*x^n)","B"