1,1,59,0,0.0316717,"\int x^5 \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[x^5*(a + b*ArcTan[c*x]),x]","\frac{1}{6} x^6 \left(a+b \tan ^{-1}(c x)\right)+\frac{b x^3}{18 c^3}-\frac{b x}{6 c^5}+\frac{b \tan ^{-1}(c x)}{6 c^6}-\frac{b x^5}{30 c}","\frac{1}{6} x^6 \left(a+b \tan ^{-1}(c x)\right)+\frac{b x^3}{18 c^3}-\frac{b x}{6 c^5}+\frac{b \tan ^{-1}(c x)}{6 c^6}-\frac{b x^5}{30 c}",1,"-(b*x)/(6*c^5) + (b*x^3)/(18*c^3) - (b*x^5)/(30*c) + (b*ArcTan[c*x])/(6*c^6) + (x^6*(a + b*ArcTan[c*x]))/6","A",4,3,12,0.2500,1,"{4852, 302, 203}"
2,1,56,0,0.0417646,"\int x^4 \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[x^4*(a + b*ArcTan[c*x]),x]","\frac{1}{5} x^5 \left(a+b \tan ^{-1}(c x)\right)+\frac{b x^2}{10 c^3}-\frac{b \log \left(c^2 x^2+1\right)}{10 c^5}-\frac{b x^4}{20 c}","\frac{1}{5} x^5 \left(a+b \tan ^{-1}(c x)\right)+\frac{b x^2}{10 c^3}-\frac{b \log \left(c^2 x^2+1\right)}{10 c^5}-\frac{b x^4}{20 c}",1,"(b*x^2)/(10*c^3) - (b*x^4)/(20*c) + (x^5*(a + b*ArcTan[c*x]))/5 - (b*Log[1 + c^2*x^2])/(10*c^5)","A",4,3,12,0.2500,1,"{4852, 266, 43}"
3,1,48,0,0.0271138,"\int x^3 \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[x^3*(a + b*ArcTan[c*x]),x]","\frac{1}{4} x^4 \left(a+b \tan ^{-1}(c x)\right)+\frac{b x}{4 c^3}-\frac{b \tan ^{-1}(c x)}{4 c^4}-\frac{b x^3}{12 c}","\frac{1}{4} x^4 \left(a+b \tan ^{-1}(c x)\right)+\frac{b x}{4 c^3}-\frac{b \tan ^{-1}(c x)}{4 c^4}-\frac{b x^3}{12 c}",1,"(b*x)/(4*c^3) - (b*x^3)/(12*c) - (b*ArcTan[c*x])/(4*c^4) + (x^4*(a + b*ArcTan[c*x]))/4","A",4,3,12,0.2500,1,"{4852, 302, 203}"
4,1,45,0,0.0318549,"\int x^2 \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[x^2*(a + b*ArcTan[c*x]),x]","\frac{1}{3} x^3 \left(a+b \tan ^{-1}(c x)\right)+\frac{b \log \left(c^2 x^2+1\right)}{6 c^3}-\frac{b x^2}{6 c}","\frac{1}{3} x^3 \left(a+b \tan ^{-1}(c x)\right)+\frac{b \log \left(c^2 x^2+1\right)}{6 c^3}-\frac{b x^2}{6 c}",1,"-(b*x^2)/(6*c) + (x^3*(a + b*ArcTan[c*x]))/3 + (b*Log[1 + c^2*x^2])/(6*c^3)","A",4,3,12,0.2500,1,"{4852, 266, 43}"
5,1,37,0,0.0156177,"\int x \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[x*(a + b*ArcTan[c*x]),x]","\frac{1}{2} x^2 \left(a+b \tan ^{-1}(c x)\right)+\frac{b \tan ^{-1}(c x)}{2 c^2}-\frac{b x}{2 c}","\frac{1}{2} x^2 \left(a+b \tan ^{-1}(c x)\right)+\frac{b \tan ^{-1}(c x)}{2 c^2}-\frac{b x}{2 c}",1,"-(b*x)/(2*c) + (b*ArcTan[c*x])/(2*c^2) + (x^2*(a + b*ArcTan[c*x]))/2","A",3,3,10,0.3000,1,"{4852, 321, 203}"
6,1,29,0,0.0113169,"\int \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[a + b*ArcTan[c*x],x]","a x-\frac{b \log \left(c^2 x^2+1\right)}{2 c}+b x \tan ^{-1}(c x)","a x-\frac{b \log \left(c^2 x^2+1\right)}{2 c}+b x \tan ^{-1}(c x)",1,"a*x + b*x*ArcTan[c*x] - (b*Log[1 + c^2*x^2])/(2*c)","A",3,2,8,0.2500,1,"{4846, 260}"
7,1,35,0,0.028752,"\int \frac{a+b \tan ^{-1}(c x)}{x} \, dx","Int[(a + b*ArcTan[c*x])/x,x]","\frac{1}{2} i b \text{PolyLog}(2,-i c x)-\frac{1}{2} i b \text{PolyLog}(2,i c x)+a \log (x)","\frac{1}{2} i b \text{PolyLog}(2,-i c x)-\frac{1}{2} i b \text{PolyLog}(2,i c x)+a \log (x)",1,"a*Log[x] + (I/2)*b*PolyLog[2, (-I)*c*x] - (I/2)*b*PolyLog[2, I*c*x]","A",3,2,12,0.1667,1,"{4848, 2391}"
8,1,35,0,0.0230129,"\int \frac{a+b \tan ^{-1}(c x)}{x^2} \, dx","Int[(a + b*ArcTan[c*x])/x^2,x]","-\frac{a+b \tan ^{-1}(c x)}{x}-\frac{1}{2} b c \log \left(c^2 x^2+1\right)+b c \log (x)","-\frac{a+b \tan ^{-1}(c x)}{x}-\frac{1}{2} b c \log \left(c^2 x^2+1\right)+b c \log (x)",1,"-((a + b*ArcTan[c*x])/x) + b*c*Log[x] - (b*c*Log[1 + c^2*x^2])/2","A",5,5,12,0.4167,1,"{4852, 266, 36, 29, 31}"
9,1,37,0,0.0195559,"\int \frac{a+b \tan ^{-1}(c x)}{x^3} \, dx","Int[(a + b*ArcTan[c*x])/x^3,x]","-\frac{a+b \tan ^{-1}(c x)}{2 x^2}-\frac{1}{2} b c^2 \tan ^{-1}(c x)-\frac{b c}{2 x}","-\frac{a+b \tan ^{-1}(c x)}{2 x^2}-\frac{1}{2} b c^2 \tan ^{-1}(c x)-\frac{b c}{2 x}",1,"-(b*c)/(2*x) - (b*c^2*ArcTan[c*x])/2 - (a + b*ArcTan[c*x])/(2*x^2)","A",3,3,12,0.2500,1,"{4852, 325, 203}"
10,1,53,0,0.033227,"\int \frac{a+b \tan ^{-1}(c x)}{x^4} \, dx","Int[(a + b*ArcTan[c*x])/x^4,x]","-\frac{a+b \tan ^{-1}(c x)}{3 x^3}+\frac{1}{6} b c^3 \log \left(c^2 x^2+1\right)-\frac{1}{3} b c^3 \log (x)-\frac{b c}{6 x^2}","-\frac{a+b \tan ^{-1}(c x)}{3 x^3}+\frac{1}{6} b c^3 \log \left(c^2 x^2+1\right)-\frac{1}{3} b c^3 \log (x)-\frac{b c}{6 x^2}",1,"-(b*c)/(6*x^2) - (a + b*ArcTan[c*x])/(3*x^3) - (b*c^3*Log[x])/3 + (b*c^3*Log[1 + c^2*x^2])/6","A",4,3,12,0.2500,1,"{4852, 266, 44}"
11,1,48,0,0.0250794,"\int \frac{a+b \tan ^{-1}(c x)}{x^5} \, dx","Int[(a + b*ArcTan[c*x])/x^5,x]","-\frac{a+b \tan ^{-1}(c x)}{4 x^4}+\frac{b c^3}{4 x}+\frac{1}{4} b c^4 \tan ^{-1}(c x)-\frac{b c}{12 x^3}","-\frac{a+b \tan ^{-1}(c x)}{4 x^4}+\frac{b c^3}{4 x}+\frac{1}{4} b c^4 \tan ^{-1}(c x)-\frac{b c}{12 x^3}",1,"-(b*c)/(12*x^3) + (b*c^3)/(4*x) + (b*c^4*ArcTan[c*x])/4 - (a + b*ArcTan[c*x])/(4*x^4)","A",4,3,12,0.2500,1,"{4852, 325, 203}"
12,1,64,0,0.0382962,"\int \frac{a+b \tan ^{-1}(c x)}{x^6} \, dx","Int[(a + b*ArcTan[c*x])/x^6,x]","-\frac{a+b \tan ^{-1}(c x)}{5 x^5}+\frac{b c^3}{10 x^2}-\frac{1}{10} b c^5 \log \left(c^2 x^2+1\right)+\frac{1}{5} b c^5 \log (x)-\frac{b c}{20 x^4}","-\frac{a+b \tan ^{-1}(c x)}{5 x^5}+\frac{b c^3}{10 x^2}-\frac{1}{10} b c^5 \log \left(c^2 x^2+1\right)+\frac{1}{5} b c^5 \log (x)-\frac{b c}{20 x^4}",1,"-(b*c)/(20*x^4) + (b*c^3)/(10*x^2) - (a + b*ArcTan[c*x])/(5*x^5) + (b*c^5*Log[x])/5 - (b*c^5*Log[1 + c^2*x^2])/10","A",4,3,12,0.2500,1,"{4852, 266, 44}"
13,1,144,0,0.3101749,"\int x^5 \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","Int[x^5*(a + b*ArcTan[c*x])^2,x]","\frac{b x^3 \left(a+b \tan ^{-1}(c x)\right)}{9 c^3}-\frac{a b x}{3 c^5}+\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{6 c^6}+\frac{1}{6} x^6 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{b x^5 \left(a+b \tan ^{-1}(c x)\right)}{15 c}+\frac{b^2 x^4}{60 c^2}-\frac{4 b^2 x^2}{45 c^4}+\frac{23 b^2 \log \left(c^2 x^2+1\right)}{90 c^6}-\frac{b^2 x \tan ^{-1}(c x)}{3 c^5}","\frac{b x^3 \left(a+b \tan ^{-1}(c x)\right)}{9 c^3}-\frac{a b x}{3 c^5}+\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{6 c^6}+\frac{1}{6} x^6 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{b x^5 \left(a+b \tan ^{-1}(c x)\right)}{15 c}+\frac{b^2 x^4}{60 c^2}-\frac{4 b^2 x^2}{45 c^4}+\frac{23 b^2 \log \left(c^2 x^2+1\right)}{90 c^6}-\frac{b^2 x \tan ^{-1}(c x)}{3 c^5}",1,"-(a*b*x)/(3*c^5) - (4*b^2*x^2)/(45*c^4) + (b^2*x^4)/(60*c^2) - (b^2*x*ArcTan[c*x])/(3*c^5) + (b*x^3*(a + b*ArcTan[c*x]))/(9*c^3) - (b*x^5*(a + b*ArcTan[c*x]))/(15*c) + (a + b*ArcTan[c*x])^2/(6*c^6) + (x^6*(a + b*ArcTan[c*x])^2)/6 + (23*b^2*Log[1 + c^2*x^2])/(90*c^6)","A",16,7,14,0.5000,1,"{4852, 4916, 266, 43, 4846, 260, 4884}"
14,1,170,0,0.2887369,"\int x^4 \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","Int[x^4*(a + b*ArcTan[c*x])^2,x]","\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{5 c^5}+\frac{b x^2 \left(a+b \tan ^{-1}(c x)\right)}{5 c^3}+\frac{i \left(a+b \tan ^{-1}(c x)\right)^2}{5 c^5}+\frac{2 b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{5 c^5}+\frac{1}{5} x^5 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{b x^4 \left(a+b \tan ^{-1}(c x)\right)}{10 c}+\frac{b^2 x^3}{30 c^2}-\frac{3 b^2 x}{10 c^4}+\frac{3 b^2 \tan ^{-1}(c x)}{10 c^5}","\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{5 c^5}+\frac{b x^2 \left(a+b \tan ^{-1}(c x)\right)}{5 c^3}+\frac{i \left(a+b \tan ^{-1}(c x)\right)^2}{5 c^5}+\frac{2 b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{5 c^5}+\frac{1}{5} x^5 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{b x^4 \left(a+b \tan ^{-1}(c x)\right)}{10 c}+\frac{b^2 x^3}{30 c^2}-\frac{3 b^2 x}{10 c^4}+\frac{3 b^2 \tan ^{-1}(c x)}{10 c^5}",1,"(-3*b^2*x)/(10*c^4) + (b^2*x^3)/(30*c^2) + (3*b^2*ArcTan[c*x])/(10*c^5) + (b*x^2*(a + b*ArcTan[c*x]))/(5*c^3) - (b*x^4*(a + b*ArcTan[c*x]))/(10*c) + ((I/5)*(a + b*ArcTan[c*x])^2)/c^5 + (x^5*(a + b*ArcTan[c*x])^2)/5 + (2*b*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/(5*c^5) + ((I/5)*b^2*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^5","A",14,9,14,0.6429,1,"{4852, 4916, 302, 203, 321, 4920, 4854, 2402, 2315}"
15,1,112,0,0.2087294,"\int x^3 \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","Int[x^3*(a + b*ArcTan[c*x])^2,x]","\frac{a b x}{2 c^3}-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{4 c^4}+\frac{1}{4} x^4 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{b x^3 \left(a+b \tan ^{-1}(c x)\right)}{6 c}+\frac{b^2 x^2}{12 c^2}-\frac{b^2 \log \left(c^2 x^2+1\right)}{3 c^4}+\frac{b^2 x \tan ^{-1}(c x)}{2 c^3}","\frac{a b x}{2 c^3}-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{4 c^4}+\frac{1}{4} x^4 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{b x^3 \left(a+b \tan ^{-1}(c x)\right)}{6 c}+\frac{b^2 x^2}{12 c^2}-\frac{b^2 \log \left(c^2 x^2+1\right)}{3 c^4}+\frac{b^2 x \tan ^{-1}(c x)}{2 c^3}",1,"(a*b*x)/(2*c^3) + (b^2*x^2)/(12*c^2) + (b^2*x*ArcTan[c*x])/(2*c^3) - (b*x^3*(a + b*ArcTan[c*x]))/(6*c) - (a + b*ArcTan[c*x])^2/(4*c^4) + (x^4*(a + b*ArcTan[c*x])^2)/4 - (b^2*Log[1 + c^2*x^2])/(3*c^4)","A",11,7,14,0.5000,1,"{4852, 4916, 266, 43, 4846, 260, 4884}"
16,1,138,0,0.1936607,"\int x^2 \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","Int[x^2*(a + b*ArcTan[c*x])^2,x]","-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{3 c^3}-\frac{i \left(a+b \tan ^{-1}(c x)\right)^2}{3 c^3}-\frac{2 b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{b x^2 \left(a+b \tan ^{-1}(c x)\right)}{3 c}+\frac{b^2 x}{3 c^2}-\frac{b^2 \tan ^{-1}(c x)}{3 c^3}","-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{3 c^3}-\frac{i \left(a+b \tan ^{-1}(c x)\right)^2}{3 c^3}-\frac{2 b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{b x^2 \left(a+b \tan ^{-1}(c x)\right)}{3 c}+\frac{b^2 x}{3 c^2}-\frac{b^2 \tan ^{-1}(c x)}{3 c^3}",1,"(b^2*x)/(3*c^2) - (b^2*ArcTan[c*x])/(3*c^3) - (b*x^2*(a + b*ArcTan[c*x]))/(3*c) - ((I/3)*(a + b*ArcTan[c*x])^2)/c^3 + (x^3*(a + b*ArcTan[c*x])^2)/3 - (2*b*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/(3*c^3) - ((I/3)*b^2*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^3","A",9,8,14,0.5714,1,"{4852, 4916, 321, 203, 4920, 4854, 2402, 2315}"
17,1,76,0,0.1062312,"\int x \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","Int[x*(a + b*ArcTan[c*x])^2,x]","\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{a b x}{c}+\frac{b^2 \log \left(c^2 x^2+1\right)}{2 c^2}-\frac{b^2 x \tan ^{-1}(c x)}{c}","\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{a b x}{c}+\frac{b^2 \log \left(c^2 x^2+1\right)}{2 c^2}-\frac{b^2 x \tan ^{-1}(c x)}{c}",1,"-((a*b*x)/c) - (b^2*x*ArcTan[c*x])/c + (a + b*ArcTan[c*x])^2/(2*c^2) + (x^2*(a + b*ArcTan[c*x])^2)/2 + (b^2*Log[1 + c^2*x^2])/(2*c^2)","A",6,5,12,0.4167,1,"{4852, 4916, 4846, 260, 4884}"
18,1,83,0,0.0978475,"\int \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","Int[(a + b*ArcTan[c*x])^2,x]","\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c}+x \left(a+b \tan ^{-1}(c x)\right)^2+\frac{i \left(a+b \tan ^{-1}(c x)\right)^2}{c}+\frac{2 b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c}","\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c}+x \left(a+b \tan ^{-1}(c x)\right)^2+\frac{i \left(a+b \tan ^{-1}(c x)\right)^2}{c}+\frac{2 b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c}",1,"(I*(a + b*ArcTan[c*x])^2)/c + x*(a + b*ArcTan[c*x])^2 + (2*b*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/c + (I*b^2*PolyLog[2, 1 - 2/(1 + I*c*x)])/c","A",5,5,10,0.5000,1,"{4846, 4920, 4854, 2402, 2315}"
19,1,132,0,0.249742,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^2}{x} \, dx","Int[(a + b*ArcTan[c*x])^2/x,x]","-i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)+i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x}\right)+2 \tanh ^{-1}\left(1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2","-i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)+i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x}\right)+2 \tanh ^{-1}\left(1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2",1,"2*(a + b*ArcTan[c*x])^2*ArcTanh[1 - 2/(1 + I*c*x)] - I*b*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 + I*c*x)] + I*b*(a + b*ArcTan[c*x])*PolyLog[2, -1 + 2/(1 + I*c*x)] - (b^2*PolyLog[3, 1 - 2/(1 + I*c*x)])/2 + (b^2*PolyLog[3, -1 + 2/(1 + I*c*x)])/2","A",6,5,14,0.3571,1,"{4850, 4988, 4884, 4994, 6610}"
20,1,82,0,0.1469335,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^2}{x^2} \, dx","Int[(a + b*ArcTan[c*x])^2/x^2,x]","-i b^2 c \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right)-i c \left(a+b \tan ^{-1}(c x)\right)^2-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{x}+2 b c \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)","-i b^2 c \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right)-i c \left(a+b \tan ^{-1}(c x)\right)^2-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{x}+2 b c \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)",1,"(-I)*c*(a + b*ArcTan[c*x])^2 - (a + b*ArcTan[c*x])^2/x + 2*b*c*(a + b*ArcTan[c*x])*Log[2 - 2/(1 - I*c*x)] - I*b^2*c*PolyLog[2, -1 + 2/(1 - I*c*x)]","A",4,4,14,0.2857,1,"{4852, 4924, 4868, 2447}"
21,1,79,0,0.1275182,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^2}{x^3} \, dx","Int[(a + b*ArcTan[c*x])^2/x^3,x]","-\frac{1}{2} c^2 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{2 x^2}-\frac{b c \left(a+b \tan ^{-1}(c x)\right)}{x}-\frac{1}{2} b^2 c^2 \log \left(c^2 x^2+1\right)+b^2 c^2 \log (x)","-\frac{1}{2} c^2 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{2 x^2}-\frac{b c \left(a+b \tan ^{-1}(c x)\right)}{x}-\frac{1}{2} b^2 c^2 \log \left(c^2 x^2+1\right)+b^2 c^2 \log (x)",1,"-((b*c*(a + b*ArcTan[c*x]))/x) - (c^2*(a + b*ArcTan[c*x])^2)/2 - (a + b*ArcTan[c*x])^2/(2*x^2) + b^2*c^2*Log[x] - (b^2*c^2*Log[1 + c^2*x^2])/2","A",8,7,14,0.5000,1,"{4852, 4918, 266, 36, 29, 31, 4884}"
22,1,140,0,0.2299906,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^2}{x^4} \, dx","Int[(a + b*ArcTan[c*x])^2/x^4,x]","\frac{1}{3} i b^2 c^3 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right)+\frac{1}{3} i c^3 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{2}{3} b c^3 \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)-\frac{b c \left(a+b \tan ^{-1}(c x)\right)}{3 x^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{3 x^3}-\frac{b^2 c^2}{3 x}-\frac{1}{3} b^2 c^3 \tan ^{-1}(c x)","\frac{1}{3} i b^2 c^3 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right)+\frac{1}{3} i c^3 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{2}{3} b c^3 \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)-\frac{b c \left(a+b \tan ^{-1}(c x)\right)}{3 x^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{3 x^3}-\frac{b^2 c^2}{3 x}-\frac{1}{3} b^2 c^3 \tan ^{-1}(c x)",1,"-(b^2*c^2)/(3*x) - (b^2*c^3*ArcTan[c*x])/3 - (b*c*(a + b*ArcTan[c*x]))/(3*x^2) + (I/3)*c^3*(a + b*ArcTan[c*x])^2 - (a + b*ArcTan[c*x])^2/(3*x^3) - (2*b*c^3*(a + b*ArcTan[c*x])*Log[2 - 2/(1 - I*c*x)])/3 + (I/3)*b^2*c^3*PolyLog[2, -1 + 2/(1 - I*c*x)]","A",8,7,14,0.5000,1,"{4852, 4918, 325, 203, 4924, 4868, 2447}"
23,1,116,0,0.2189437,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^2}{x^5} \, dx","Int[(a + b*ArcTan[c*x])^2/x^5,x]","\frac{1}{4} c^4 \left(a+b \tan ^{-1}(c x)\right)^2+\frac{b c^3 \left(a+b \tan ^{-1}(c x)\right)}{2 x}-\frac{b c \left(a+b \tan ^{-1}(c x)\right)}{6 x^3}-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{4 x^4}-\frac{b^2 c^2}{12 x^2}+\frac{1}{3} b^2 c^4 \log \left(c^2 x^2+1\right)-\frac{2}{3} b^2 c^4 \log (x)","\frac{1}{4} c^4 \left(a+b \tan ^{-1}(c x)\right)^2+\frac{b c^3 \left(a+b \tan ^{-1}(c x)\right)}{2 x}-\frac{b c \left(a+b \tan ^{-1}(c x)\right)}{6 x^3}-\frac{\left(a+b \tan ^{-1}(c x)\right)^2}{4 x^4}-\frac{b^2 c^2}{12 x^2}+\frac{1}{3} b^2 c^4 \log \left(c^2 x^2+1\right)-\frac{2}{3} b^2 c^4 \log (x)",1,"-(b^2*c^2)/(12*x^2) - (b*c*(a + b*ArcTan[c*x]))/(6*x^3) + (b*c^3*(a + b*ArcTan[c*x]))/(2*x) + (c^4*(a + b*ArcTan[c*x])^2)/4 - (a + b*ArcTan[c*x])^2/(4*x^4) - (2*b^2*c^4*Log[x])/3 + (b^2*c^4*Log[1 + c^2*x^2])/3","A",13,8,14,0.5714,1,"{4852, 4918, 266, 44, 36, 29, 31, 4884}"
24,1,255,0,0.9476596,"\int x^5 \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","Int[x^5*(a + b*ArcTan[c*x])^3,x]","-\frac{23 i b^3 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{30 c^6}+\frac{b^2 x^4 \left(a+b \tan ^{-1}(c x)\right)}{20 c^2}-\frac{4 b^2 x^2 \left(a+b \tan ^{-1}(c x)\right)}{15 c^4}-\frac{23 b^2 \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{15 c^6}+\frac{b x^3 \left(a+b \tan ^{-1}(c x)\right)^2}{6 c^3}-\frac{b x \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^5}+\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{6 c^6}-\frac{23 i b \left(a+b \tan ^{-1}(c x)\right)^2}{30 c^6}+\frac{1}{6} x^6 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{b x^5 \left(a+b \tan ^{-1}(c x)\right)^2}{10 c}-\frac{b^3 x^3}{60 c^3}+\frac{19 b^3 x}{60 c^5}-\frac{19 b^3 \tan ^{-1}(c x)}{60 c^6}","-\frac{23 i b^3 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{30 c^6}+\frac{b^2 x^4 \left(a+b \tan ^{-1}(c x)\right)}{20 c^2}-\frac{4 b^2 x^2 \left(a+b \tan ^{-1}(c x)\right)}{15 c^4}-\frac{23 b^2 \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{15 c^6}+\frac{b x^3 \left(a+b \tan ^{-1}(c x)\right)^2}{6 c^3}-\frac{b x \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^5}+\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{6 c^6}-\frac{23 i b \left(a+b \tan ^{-1}(c x)\right)^2}{30 c^6}+\frac{1}{6} x^6 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{b x^5 \left(a+b \tan ^{-1}(c x)\right)^2}{10 c}-\frac{b^3 x^3}{60 c^3}+\frac{19 b^3 x}{60 c^5}-\frac{19 b^3 \tan ^{-1}(c x)}{60 c^6}",1,"(19*b^3*x)/(60*c^5) - (b^3*x^3)/(60*c^3) - (19*b^3*ArcTan[c*x])/(60*c^6) - (4*b^2*x^2*(a + b*ArcTan[c*x]))/(15*c^4) + (b^2*x^4*(a + b*ArcTan[c*x]))/(20*c^2) - (((23*I)/30)*b*(a + b*ArcTan[c*x])^2)/c^6 - (b*x*(a + b*ArcTan[c*x])^2)/(2*c^5) + (b*x^3*(a + b*ArcTan[c*x])^2)/(6*c^3) - (b*x^5*(a + b*ArcTan[c*x])^2)/(10*c) + (a + b*ArcTan[c*x])^3/(6*c^6) + (x^6*(a + b*ArcTan[c*x])^3)/6 - (23*b^2*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/(15*c^6) - (((23*I)/30)*b^3*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^6","A",33,11,14,0.7857,1,"{4852, 4916, 302, 203, 321, 4920, 4854, 2402, 2315, 4846, 4884}"
25,1,271,0,0.7558952,"\int x^4 \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","Int[x^4*(a + b*ArcTan[c*x])^3,x]","\frac{3 i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{5 c^5}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{10 c^5}+\frac{b^2 x^3 \left(a+b \tan ^{-1}(c x)\right)}{10 c^2}-\frac{9 a b^2 x}{10 c^4}+\frac{3 b x^2 \left(a+b \tan ^{-1}(c x)\right)^2}{10 c^3}+\frac{i \left(a+b \tan ^{-1}(c x)\right)^3}{5 c^5}+\frac{9 b \left(a+b \tan ^{-1}(c x)\right)^2}{20 c^5}+\frac{3 b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{5 c^5}+\frac{1}{5} x^5 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{3 b x^4 \left(a+b \tan ^{-1}(c x)\right)^2}{20 c}-\frac{b^3 x^2}{20 c^3}+\frac{b^3 \log \left(c^2 x^2+1\right)}{2 c^5}-\frac{9 b^3 x \tan ^{-1}(c x)}{10 c^4}","\frac{3 i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{5 c^5}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{10 c^5}+\frac{b^2 x^3 \left(a+b \tan ^{-1}(c x)\right)}{10 c^2}-\frac{9 a b^2 x}{10 c^4}+\frac{3 b x^2 \left(a+b \tan ^{-1}(c x)\right)^2}{10 c^3}+\frac{i \left(a+b \tan ^{-1}(c x)\right)^3}{5 c^5}+\frac{9 b \left(a+b \tan ^{-1}(c x)\right)^2}{20 c^5}+\frac{3 b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{5 c^5}+\frac{1}{5} x^5 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{3 b x^4 \left(a+b \tan ^{-1}(c x)\right)^2}{20 c}-\frac{b^3 x^2}{20 c^3}+\frac{b^3 \log \left(c^2 x^2+1\right)}{2 c^5}-\frac{9 b^3 x \tan ^{-1}(c x)}{10 c^4}",1,"(-9*a*b^2*x)/(10*c^4) - (b^3*x^2)/(20*c^3) - (9*b^3*x*ArcTan[c*x])/(10*c^4) + (b^2*x^3*(a + b*ArcTan[c*x]))/(10*c^2) + (9*b*(a + b*ArcTan[c*x])^2)/(20*c^5) + (3*b*x^2*(a + b*ArcTan[c*x])^2)/(10*c^3) - (3*b*x^4*(a + b*ArcTan[c*x])^2)/(20*c) + ((I/5)*(a + b*ArcTan[c*x])^3)/c^5 + (x^5*(a + b*ArcTan[c*x])^3)/5 + (3*b*(a + b*ArcTan[c*x])^2*Log[2/(1 + I*c*x)])/(5*c^5) + (b^3*Log[1 + c^2*x^2])/(2*c^5) + (((3*I)/5)*b^2*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^5 + (3*b^3*PolyLog[3, 1 - 2/(1 + I*c*x)])/(10*c^5)","A",24,11,14,0.7857,1,"{4852, 4916, 266, 43, 4846, 260, 4884, 4920, 4854, 4994, 6610}"
26,1,194,0,0.5453852,"\int x^3 \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","Int[x^3*(a + b*ArcTan[c*x])^3,x]","\frac{i b^3 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c^4}+\frac{b^2 x^2 \left(a+b \tan ^{-1}(c x)\right)}{4 c^2}+\frac{2 b^2 \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^4}+\frac{3 b x \left(a+b \tan ^{-1}(c x)\right)^2}{4 c^3}-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{4 c^4}+\frac{i b \left(a+b \tan ^{-1}(c x)\right)^2}{c^4}+\frac{1}{4} x^4 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{b x^3 \left(a+b \tan ^{-1}(c x)\right)^2}{4 c}-\frac{b^3 x}{4 c^3}+\frac{b^3 \tan ^{-1}(c x)}{4 c^4}","\frac{i b^3 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{c^4}+\frac{b^2 x^2 \left(a+b \tan ^{-1}(c x)\right)}{4 c^2}+\frac{2 b^2 \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^4}+\frac{3 b x \left(a+b \tan ^{-1}(c x)\right)^2}{4 c^3}-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{4 c^4}+\frac{i b \left(a+b \tan ^{-1}(c x)\right)^2}{c^4}+\frac{1}{4} x^4 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{b x^3 \left(a+b \tan ^{-1}(c x)\right)^2}{4 c}-\frac{b^3 x}{4 c^3}+\frac{b^3 \tan ^{-1}(c x)}{4 c^4}",1,"-(b^3*x)/(4*c^3) + (b^3*ArcTan[c*x])/(4*c^4) + (b^2*x^2*(a + b*ArcTan[c*x]))/(4*c^2) + (I*b*(a + b*ArcTan[c*x])^2)/c^4 + (3*b*x*(a + b*ArcTan[c*x])^2)/(4*c^3) - (b*x^3*(a + b*ArcTan[c*x])^2)/(4*c) - (a + b*ArcTan[c*x])^3/(4*c^4) + (x^4*(a + b*ArcTan[c*x])^3)/4 + (2*b^2*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/c^4 + (I*b^3*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^4","A",18,10,14,0.7143,1,"{4852, 4916, 321, 203, 4920, 4854, 2402, 2315, 4846, 4884}"
27,1,206,0,0.43386,"\int x^2 \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","Int[x^2*(a + b*ArcTan[c*x])^3,x]","-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^3}-\frac{b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 c^3}+\frac{a b^2 x}{c^2}-\frac{b \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^3}-\frac{i \left(a+b \tan ^{-1}(c x)\right)^3}{3 c^3}-\frac{b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c^3}-\frac{b x^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 c}+\frac{1}{3} x^3 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{b^3 \log \left(c^2 x^2+1\right)}{2 c^3}+\frac{b^3 x \tan ^{-1}(c x)}{c^2}","-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^3}-\frac{b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 c^3}+\frac{a b^2 x}{c^2}-\frac{b \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^3}-\frac{i \left(a+b \tan ^{-1}(c x)\right)^3}{3 c^3}-\frac{b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c^3}-\frac{b x^2 \left(a+b \tan ^{-1}(c x)\right)^2}{2 c}+\frac{1}{3} x^3 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{b^3 \log \left(c^2 x^2+1\right)}{2 c^3}+\frac{b^3 x \tan ^{-1}(c x)}{c^2}",1,"(a*b^2*x)/c^2 + (b^3*x*ArcTan[c*x])/c^2 - (b*(a + b*ArcTan[c*x])^2)/(2*c^3) - (b*x^2*(a + b*ArcTan[c*x])^2)/(2*c) - ((I/3)*(a + b*ArcTan[c*x])^3)/c^3 + (x^3*(a + b*ArcTan[c*x])^3)/3 - (b*(a + b*ArcTan[c*x])^2*Log[2/(1 + I*c*x)])/c^3 - (b^3*Log[1 + c^2*x^2])/(2*c^3) - (I*b^2*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^3 - (b^3*PolyLog[3, 1 - 2/(1 + I*c*x)])/(2*c^3)","A",12,9,14,0.6429,1,"{4852, 4916, 4846, 260, 4884, 4920, 4854, 4994, 6610}"
28,1,131,0,0.2388228,"\int x \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","Int[x*(a + b*ArcTan[c*x])^3,x]","-\frac{3 i b^3 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{2 c^2}-\frac{3 b^2 \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2}-\frac{3 i b \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^2}+\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{2 c^2}+\frac{1}{2} x^2 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{3 b x \left(a+b \tan ^{-1}(c x)\right)^2}{2 c}","-\frac{3 i b^3 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right)}{2 c^2}-\frac{3 b^2 \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c^2}-\frac{3 i b \left(a+b \tan ^{-1}(c x)\right)^2}{2 c^2}+\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{2 c^2}+\frac{1}{2} x^2 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{3 b x \left(a+b \tan ^{-1}(c x)\right)^2}{2 c}",1,"(((-3*I)/2)*b*(a + b*ArcTan[c*x])^2)/c^2 - (3*b*x*(a + b*ArcTan[c*x])^2)/(2*c) + (a + b*ArcTan[c*x])^3/(2*c^2) + (x^2*(a + b*ArcTan[c*x])^3)/2 - (3*b^2*(a + b*ArcTan[c*x])*Log[2/(1 + I*c*x)])/c^2 - (((3*I)/2)*b^3*PolyLog[2, 1 - 2/(1 + I*c*x)])/c^2","A",8,8,12,0.6667,1,"{4852, 4916, 4846, 4920, 4854, 2402, 2315, 4884}"
29,1,119,0,0.2092677,"\int \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","Int[(a + b*ArcTan[c*x])^3,x]","\frac{3 i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 c}+x \left(a+b \tan ^{-1}(c x)\right)^3+\frac{i \left(a+b \tan ^{-1}(c x)\right)^3}{c}+\frac{3 b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c}","\frac{3 i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)}{c}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right)}{2 c}+x \left(a+b \tan ^{-1}(c x)\right)^3+\frac{i \left(a+b \tan ^{-1}(c x)\right)^3}{c}+\frac{3 b \log \left(\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2}{c}",1,"(I*(a + b*ArcTan[c*x])^3)/c + x*(a + b*ArcTan[c*x])^3 + (3*b*(a + b*ArcTan[c*x])^2*Log[2/(1 + I*c*x)])/c + ((3*I)*b^2*(a + b*ArcTan[c*x])*PolyLog[2, 1 - 2/(1 + I*c*x)])/c + (3*b^3*PolyLog[3, 1 - 2/(1 + I*c*x)])/(2*c)","A",5,6,10,0.6000,1,"{4846, 4920, 4854, 4884, 4994, 6610}"
30,1,206,0,0.4270192,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^3}{x} \, dx","Int[(a + b*ArcTan[c*x])^3/x,x]","-\frac{3}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)+\frac{3}{2} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)-\frac{3}{2} i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2+\frac{3}{2} i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2+\frac{3}{4} i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+i c x}\right)-\frac{3}{4} i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+i c x}\right)+2 \tanh ^{-1}\left(1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^3","-\frac{3}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)+\frac{3}{2} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)-\frac{3}{2} i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2+\frac{3}{2} i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2+\frac{3}{4} i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+i c x}\right)-\frac{3}{4} i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+i c x}\right)+2 \tanh ^{-1}\left(1-\frac{2}{1+i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^3",1,"2*(a + b*ArcTan[c*x])^3*ArcTanh[1 - 2/(1 + I*c*x)] - ((3*I)/2)*b*(a + b*ArcTan[c*x])^2*PolyLog[2, 1 - 2/(1 + I*c*x)] + ((3*I)/2)*b*(a + b*ArcTan[c*x])^2*PolyLog[2, -1 + 2/(1 + I*c*x)] - (3*b^2*(a + b*ArcTan[c*x])*PolyLog[3, 1 - 2/(1 + I*c*x)])/2 + (3*b^2*(a + b*ArcTan[c*x])*PolyLog[3, -1 + 2/(1 + I*c*x)])/2 + ((3*I)/4)*b^3*PolyLog[4, 1 - 2/(1 + I*c*x)] - ((3*I)/4)*b^3*PolyLog[4, -1 + 2/(1 + I*c*x)]","A",8,6,14,0.4286,1,"{4850, 4988, 4884, 4994, 4998, 6610}"
31,1,116,0,0.2671365,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^3}{x^2} \, dx","Int[(a + b*ArcTan[c*x])^3/x^2,x]","-3 i b^2 c \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)+\frac{3}{2} b^3 c \text{PolyLog}\left(3,-1+\frac{2}{1-i c x}\right)-i c \left(a+b \tan ^{-1}(c x)\right)^3-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{x}+3 b c \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2","-3 i b^2 c \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)+\frac{3}{2} b^3 c \text{PolyLog}\left(3,-1+\frac{2}{1-i c x}\right)-i c \left(a+b \tan ^{-1}(c x)\right)^3-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{x}+3 b c \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2",1,"(-I)*c*(a + b*ArcTan[c*x])^3 - (a + b*ArcTan[c*x])^3/x + 3*b*c*(a + b*ArcTan[c*x])^2*Log[2 - 2/(1 - I*c*x)] - (3*I)*b^2*c*(a + b*ArcTan[c*x])*PolyLog[2, -1 + 2/(1 - I*c*x)] + (3*b^3*c*PolyLog[3, -1 + 2/(1 - I*c*x)])/2","A",5,6,14,0.4286,1,"{4852, 4924, 4868, 4884, 4992, 6610}"
32,1,133,0,0.2847301,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^3}{x^3} \, dx","Int[(a + b*ArcTan[c*x])^3/x^3,x]","-\frac{3}{2} i b^3 c^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right)+3 b^2 c^2 \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)-\frac{3}{2} i b c^2 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{1}{2} c^2 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{2 x^2}-\frac{3 b c \left(a+b \tan ^{-1}(c x)\right)^2}{2 x}","-\frac{3}{2} i b^3 c^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right)+3 b^2 c^2 \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)-\frac{3}{2} i b c^2 \left(a+b \tan ^{-1}(c x)\right)^2-\frac{1}{2} c^2 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{2 x^2}-\frac{3 b c \left(a+b \tan ^{-1}(c x)\right)^2}{2 x}",1,"((-3*I)/2)*b*c^2*(a + b*ArcTan[c*x])^2 - (3*b*c*(a + b*ArcTan[c*x])^2)/(2*x) - (c^2*(a + b*ArcTan[c*x])^3)/2 - (a + b*ArcTan[c*x])^3/(2*x^2) + 3*b^2*c^2*(a + b*ArcTan[c*x])*Log[2 - 2/(1 - I*c*x)] - ((3*I)/2)*b^3*c^2*PolyLog[2, -1 + 2/(1 - I*c*x)]","A",7,6,14,0.4286,1,"{4852, 4918, 4924, 4868, 2447, 4884}"
33,1,213,0,0.4763348,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^3}{x^4} \, dx","Int[(a + b*ArcTan[c*x])^3/x^4,x]","i b^2 c^3 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)-\frac{1}{2} b^3 c^3 \text{PolyLog}\left(3,-1+\frac{2}{1-i c x}\right)-\frac{b^2 c^2 \left(a+b \tan ^{-1}(c x)\right)}{x}+\frac{1}{3} i c^3 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{1}{2} b c^3 \left(a+b \tan ^{-1}(c x)\right)^2-b c^3 \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2-\frac{b c \left(a+b \tan ^{-1}(c x)\right)^2}{2 x^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{3 x^3}-\frac{1}{2} b^3 c^3 \log \left(c^2 x^2+1\right)+b^3 c^3 \log (x)","i b^2 c^3 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)-\frac{1}{2} b^3 c^3 \text{PolyLog}\left(3,-1+\frac{2}{1-i c x}\right)-\frac{b^2 c^2 \left(a+b \tan ^{-1}(c x)\right)}{x}+\frac{1}{3} i c^3 \left(a+b \tan ^{-1}(c x)\right)^3-\frac{1}{2} b c^3 \left(a+b \tan ^{-1}(c x)\right)^2-b c^3 \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)^2-\frac{b c \left(a+b \tan ^{-1}(c x)\right)^2}{2 x^2}-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{3 x^3}-\frac{1}{2} b^3 c^3 \log \left(c^2 x^2+1\right)+b^3 c^3 \log (x)",1,"-((b^2*c^2*(a + b*ArcTan[c*x]))/x) - (b*c^3*(a + b*ArcTan[c*x])^2)/2 - (b*c*(a + b*ArcTan[c*x])^2)/(2*x^2) + (I/3)*c^3*(a + b*ArcTan[c*x])^3 - (a + b*ArcTan[c*x])^3/(3*x^3) + b^3*c^3*Log[x] - (b^3*c^3*Log[1 + c^2*x^2])/2 - b*c^3*(a + b*ArcTan[c*x])^2*Log[2 - 2/(1 - I*c*x)] + I*b^2*c^3*(a + b*ArcTan[c*x])*PolyLog[2, -1 + 2/(1 - I*c*x)] - (b^3*c^3*PolyLog[3, -1 + 2/(1 - I*c*x)])/2","A",14,11,14,0.7857,1,"{4852, 4918, 266, 36, 29, 31, 4884, 4924, 4868, 4992, 6610}"
34,1,198,0,0.6005759,"\int \frac{\left(a+b \tan ^{-1}(c x)\right)^3}{x^5} \, dx","Int[(a + b*ArcTan[c*x])^3/x^5,x]","i b^3 c^4 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right)-\frac{b^2 c^2 \left(a+b \tan ^{-1}(c x)\right)}{4 x^2}-2 b^2 c^4 \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)+\frac{1}{4} c^4 \left(a+b \tan ^{-1}(c x)\right)^3+i b c^4 \left(a+b \tan ^{-1}(c x)\right)^2+\frac{3 b c^3 \left(a+b \tan ^{-1}(c x)\right)^2}{4 x}-\frac{b c \left(a+b \tan ^{-1}(c x)\right)^2}{4 x^3}-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{4 x^4}-\frac{b^3 c^3}{4 x}-\frac{1}{4} b^3 c^4 \tan ^{-1}(c x)","i b^3 c^4 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x}\right)-\frac{b^2 c^2 \left(a+b \tan ^{-1}(c x)\right)}{4 x^2}-2 b^2 c^4 \log \left(2-\frac{2}{1-i c x}\right) \left(a+b \tan ^{-1}(c x)\right)+\frac{1}{4} c^4 \left(a+b \tan ^{-1}(c x)\right)^3+i b c^4 \left(a+b \tan ^{-1}(c x)\right)^2+\frac{3 b c^3 \left(a+b \tan ^{-1}(c x)\right)^2}{4 x}-\frac{b c \left(a+b \tan ^{-1}(c x)\right)^2}{4 x^3}-\frac{\left(a+b \tan ^{-1}(c x)\right)^3}{4 x^4}-\frac{b^3 c^3}{4 x}-\frac{1}{4} b^3 c^4 \tan ^{-1}(c x)",1,"-(b^3*c^3)/(4*x) - (b^3*c^4*ArcTan[c*x])/4 - (b^2*c^2*(a + b*ArcTan[c*x]))/(4*x^2) + I*b*c^4*(a + b*ArcTan[c*x])^2 - (b*c*(a + b*ArcTan[c*x])^2)/(4*x^3) + (3*b*c^3*(a + b*ArcTan[c*x])^2)/(4*x) + (c^4*(a + b*ArcTan[c*x])^3)/4 - (a + b*ArcTan[c*x])^3/(4*x^4) - 2*b^2*c^4*(a + b*ArcTan[c*x])*Log[2 - 2/(1 - I*c*x)] + I*b^3*c^4*PolyLog[2, -1 + 2/(1 - I*c*x)]","A",16,8,14,0.5714,1,"{4852, 4918, 325, 203, 4924, 4868, 2447, 4884}"
35,0,0,0,0.0084395,"\int \frac{x}{\tan ^{-1}(a x)} \, dx","Int[x/ArcTan[a*x],x]","\int \frac{x}{\tan ^{-1}(a x)} \, dx","\text{Int}\left(\frac{x}{\tan ^{-1}(a x)},x\right)",0,"Defer[Int][x/ArcTan[a*x], x]","A",0,0,0,0,-1,"{}"
36,0,0,0,0.0032902,"\int \frac{1}{\tan ^{-1}(a x)} \, dx","Int[ArcTan[a*x]^(-1),x]","\int \frac{1}{\tan ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{\tan ^{-1}(a x)},x\right)",0,"Defer[Int][ArcTan[a*x]^(-1), x]","A",0,0,0,0,-1,"{}"
37,0,0,0,0.0145322,"\int \frac{1}{x \tan ^{-1}(a x)} \, dx","Int[1/(x*ArcTan[a*x]),x]","\int \frac{1}{x \tan ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \tan ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x*ArcTan[a*x]), x]","A",0,0,0,0,-1,"{}"
38,0,0,0,0.0075483,"\int \frac{x}{\tan ^{-1}(a x)^2} \, dx","Int[x/ArcTan[a*x]^2,x]","\int \frac{x}{\tan ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{x}{\tan ^{-1}(a x)^2},x\right)",0,"Defer[Int][x/ArcTan[a*x]^2, x]","A",0,0,0,0,-1,"{}"
39,0,0,0,0.0032723,"\int \frac{1}{\tan ^{-1}(a x)^2} \, dx","Int[ArcTan[a*x]^(-2),x]","\int \frac{1}{\tan ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{\tan ^{-1}(a x)^2},x\right)",0,"Defer[Int][ArcTan[a*x]^(-2), x]","A",0,0,0,0,-1,"{}"
40,0,0,0,0.0130932,"\int \frac{1}{x \tan ^{-1}(a x)^2} \, dx","Int[1/(x*ArcTan[a*x]^2),x]","\int \frac{1}{x \tan ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{x \tan ^{-1}(a x)^2},x\right)",0,"Defer[Int][1/(x*ArcTan[a*x]^2), x]","A",0,0,0,0,-1,"{}"
41,0,0,0,0.0073851,"\int x \sqrt{\tan ^{-1}(a x)} \, dx","Int[x*Sqrt[ArcTan[a*x]],x]","\int x \sqrt{\tan ^{-1}(a x)} \, dx","\text{Int}\left(x \sqrt{\tan ^{-1}(a x)},x\right)",0,"Defer[Int][x*Sqrt[ArcTan[a*x]], x]","A",0,0,0,0,-1,"{}"
42,0,0,0,0.003199,"\int \sqrt{\tan ^{-1}(a x)} \, dx","Int[Sqrt[ArcTan[a*x]],x]","\int \sqrt{\tan ^{-1}(a x)} \, dx","\text{Int}\left(\sqrt{\tan ^{-1}(a x)},x\right)",0,"Defer[Int][Sqrt[ArcTan[a*x]], x]","A",0,0,0,0,-1,"{}"
43,0,0,0,0.0131621,"\int \frac{\sqrt{\tan ^{-1}(a x)}}{x} \, dx","Int[Sqrt[ArcTan[a*x]]/x,x]","\int \frac{\sqrt{\tan ^{-1}(a x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt{\tan ^{-1}(a x)}}{x},x\right)",0,"Defer[Int][Sqrt[ArcTan[a*x]]/x, x]","A",0,0,0,0,-1,"{}"
44,0,0,0,0.0071999,"\int x \tan ^{-1}(a x)^{3/2} \, dx","Int[x*ArcTan[a*x]^(3/2),x]","\int x \tan ^{-1}(a x)^{3/2} \, dx","\text{Int}\left(x \tan ^{-1}(a x)^{3/2},x\right)",0,"Defer[Int][x*ArcTan[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
45,0,0,0,0.0030674,"\int \tan ^{-1}(a x)^{3/2} \, dx","Int[ArcTan[a*x]^(3/2),x]","\int \tan ^{-1}(a x)^{3/2} \, dx","\text{Int}\left(\tan ^{-1}(a x)^{3/2},x\right)",0,"Defer[Int][ArcTan[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
46,0,0,0,0.0125215,"\int \frac{\tan ^{-1}(a x)^{3/2}}{x} \, dx","Int[ArcTan[a*x]^(3/2)/x,x]","\int \frac{\tan ^{-1}(a x)^{3/2}}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(a x)^{3/2}}{x},x\right)",0,"Defer[Int][ArcTan[a*x]^(3/2)/x, x]","A",0,0,0,0,-1,"{}"
47,0,0,0,0.0074883,"\int \frac{x}{\sqrt{\tan ^{-1}(a x)}} \, dx","Int[x/Sqrt[ArcTan[a*x]],x]","\int \frac{x}{\sqrt{\tan ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{x}{\sqrt{\tan ^{-1}(a x)}},x\right)",0,"Defer[Int][x/Sqrt[ArcTan[a*x]], x]","A",0,0,0,0,-1,"{}"
48,0,0,0,0.0031163,"\int \frac{1}{\sqrt{\tan ^{-1}(a x)}} \, dx","Int[1/Sqrt[ArcTan[a*x]],x]","\int \frac{1}{\sqrt{\tan ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{\sqrt{\tan ^{-1}(a x)}},x\right)",0,"Defer[Int][1/Sqrt[ArcTan[a*x]], x]","A",0,0,0,0,-1,"{}"
49,0,0,0,0.0138701,"\int \frac{1}{x \sqrt{\tan ^{-1}(a x)}} \, dx","Int[1/(x*Sqrt[ArcTan[a*x]]),x]","\int \frac{1}{x \sqrt{\tan ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{\tan ^{-1}(a x)}},x\right)",0,"Defer[Int][1/(x*Sqrt[ArcTan[a*x]]), x]","A",0,0,0,0,-1,"{}"
50,0,0,0,0.0073448,"\int \frac{x}{\tan ^{-1}(a x)^{3/2}} \, dx","Int[x/ArcTan[a*x]^(3/2),x]","\int \frac{x}{\tan ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{x}{\tan ^{-1}(a x)^{3/2}},x\right)",0,"Defer[Int][x/ArcTan[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
51,0,0,0,0.0030854,"\int \frac{1}{\tan ^{-1}(a x)^{3/2}} \, dx","Int[ArcTan[a*x]^(-3/2),x]","\int \frac{1}{\tan ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{1}{\tan ^{-1}(a x)^{3/2}},x\right)",0,"Defer[Int][ArcTan[a*x]^(-3/2), x]","A",0,0,0,0,-1,"{}"
52,0,0,0,0.0128075,"\int \frac{1}{x \tan ^{-1}(a x)^{3/2}} \, dx","Int[1/(x*ArcTan[a*x]^(3/2)),x]","\int \frac{1}{x \tan ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{1}{x \tan ^{-1}(a x)^{3/2}},x\right)",0,"Defer[Int][1/(x*ArcTan[a*x]^(3/2)), x]","A",0,0,0,0,-1,"{}"
53,1,117,0,0.0674999,"\int \sqrt{x} \tan ^{-1}(x) \, dx","Int[Sqrt[x]*ArcTan[x],x]","\frac{2}{3} x^{3/2} \tan ^{-1}(x)-\frac{4 \sqrt{x}}{3}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{3 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{3 \sqrt{2}}-\frac{1}{3} \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)+\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)","\frac{2}{3} x^{3/2} \tan ^{-1}(x)-\frac{4 \sqrt{x}}{3}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{3 \sqrt{2}}+\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{3 \sqrt{2}}-\frac{1}{3} \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)+\frac{1}{3} \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)",1,"(-4*Sqrt[x])/3 - (Sqrt[2]*ArcTan[1 - Sqrt[2]*Sqrt[x]])/3 + (Sqrt[2]*ArcTan[1 + Sqrt[2]*Sqrt[x]])/3 + (2*x^(3/2)*ArcTan[x])/3 - Log[1 - Sqrt[2]*Sqrt[x] + x]/(3*Sqrt[2]) + Log[1 + Sqrt[2]*Sqrt[x] + x]/(3*Sqrt[2])","A",12,9,8,1.125,1,"{4852, 321, 329, 211, 1165, 628, 1162, 617, 204}"
54,0,0,0,0.0216028,"\int (d x)^m \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcTan[c*x])^3,x]","\int (d x)^m \left(a+b \tan ^{-1}(c x)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \tan ^{-1}(c x)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTan[c*x])^3, x]","A",0,0,0,0,-1,"{}"
55,0,0,0,0.0212714,"\int (d x)^m \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcTan[c*x])^2,x]","\int (d x)^m \left(a+b \tan ^{-1}(c x)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \tan ^{-1}(c x)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTan[c*x])^2, x]","A",0,0,0,0,-1,"{}"
56,1,73,0,0.0311376,"\int (d x)^m \left(a+b \tan ^{-1}(c x)\right) \, dx","Int[(d*x)^m*(a + b*ArcTan[c*x]),x]","\frac{(d x)^{m+1} \left(a+b \tan ^{-1}(c x)\right)}{d (m+1)}-\frac{b c (d x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{d^2 (m+1) (m+2)}","\frac{(d x)^{m+1} \left(a+b \tan ^{-1}(c x)\right)}{d (m+1)}-\frac{b c (d x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{d^2 (m+1) (m+2)}",1,"((d*x)^(1 + m)*(a + b*ArcTan[c*x]))/(d*(1 + m)) - (b*c*(d*x)^(2 + m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -(c^2*x^2)])/(d^2*(1 + m)*(2 + m))","A",2,2,14,0.1429,1,"{4852, 364}"
57,0,0,0,0.0244613,"\int \frac{(d x)^m}{a+b \tan ^{-1}(c x)} \, dx","Int[(d*x)^m/(a + b*ArcTan[c*x]),x]","\int \frac{(d x)^m}{a+b \tan ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \tan ^{-1}(c x)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTan[c*x]), x]","A",0,0,0,0,-1,"{}"
58,0,0,0,0.0049583,"\int \left(a+b \tan ^{-1}(c x)\right)^p \, dx","Int[(a + b*ArcTan[c*x])^p,x]","\int \left(a+b \tan ^{-1}(c x)\right)^p \, dx","\text{Int}\left(\left(a+b \tan ^{-1}(c x)\right)^p,x\right)",0,"Defer[Int][(a + b*ArcTan[c*x])^p, x]","A",0,0,0,0,-1,"{}"
59,0,0,0,0.0213625,"\int (d x)^m \left(a+b \tan ^{-1}(c x)\right)^p \, dx","Int[(d*x)^m*(a + b*ArcTan[c*x])^p,x]","\int (d x)^m \left(a+b \tan ^{-1}(c x)\right)^p \, dx","\text{Int}\left((d x)^m \left(a+b \tan ^{-1}(c x)\right)^p,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTan[c*x])^p, x]","A",0,0,0,0,-1,"{}"
60,1,54,0,0.0351121,"\int x^7 \left(a+b \tan ^{-1}\left(c x^2\right)\right) \, dx","Int[x^7*(a + b*ArcTan[c*x^2]),x]","\frac{1}{8} x^8 \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{b x^2}{8 c^3}-\frac{b \tan ^{-1}\left(c x^2\right)}{8 c^4}-\frac{b x^6}{24 c}","\frac{1}{8} x^8 \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{b x^2}{8 c^3}-\frac{b \tan ^{-1}\left(c x^2\right)}{8 c^4}-\frac{b x^6}{24 c}",1,"(b*x^2)/(8*c^3) - (b*x^6)/(24*c) - (b*ArcTan[c*x^2])/(8*c^4) + (x^8*(a + b*ArcTan[c*x^2]))/8","A",5,4,14,0.2857,1,"{5033, 275, 302, 203}"
61,1,47,0,0.0308981,"\int x^5 \left(a+b \tan ^{-1}\left(c x^2\right)\right) \, dx","Int[x^5*(a + b*ArcTan[c*x^2]),x]","\frac{1}{6} x^6 \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{b \log \left(c^2 x^4+1\right)}{12 c^3}-\frac{b x^4}{12 c}","\frac{1}{6} x^6 \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{b \log \left(c^2 x^4+1\right)}{12 c^3}-\frac{b x^4}{12 c}",1,"-(b*x^4)/(12*c) + (x^6*(a + b*ArcTan[c*x^2]))/6 + (b*Log[1 + c^2*x^4])/(12*c^3)","A",4,3,14,0.2143,1,"{5033, 266, 43}"
62,1,43,0,0.026978,"\int x^3 \left(a+b \tan ^{-1}\left(c x^2\right)\right) \, dx","Int[x^3*(a + b*ArcTan[c*x^2]),x]","\frac{1}{4} x^4 \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{b \tan ^{-1}\left(c x^2\right)}{4 c^2}-\frac{b x^2}{4 c}","\frac{1}{4} x^4 \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{b \tan ^{-1}\left(c x^2\right)}{4 c^2}-\frac{b x^2}{4 c}",1,"-(b*x^2)/(4*c) + (b*ArcTan[c*x^2])/(4*c^2) + (x^4*(a + b*ArcTan[c*x^2]))/4","A",4,4,14,0.2857,1,"{5033, 275, 321, 203}"
63,1,36,0,0.01395,"\int x \left(a+b \tan ^{-1}\left(c x^2\right)\right) \, dx","Int[x*(a + b*ArcTan[c*x^2]),x]","\frac{1}{2} x^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)-\frac{b \log \left(c^2 x^4+1\right)}{4 c}","\frac{1}{2} x^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)-\frac{b \log \left(c^2 x^4+1\right)}{4 c}",1,"(x^2*(a + b*ArcTan[c*x^2]))/2 - (b*Log[1 + c^2*x^4])/(4*c)","A",2,2,12,0.1667,1,"{5033, 260}"
64,1,39,0,0.0454425,"\int \frac{a+b \tan ^{-1}\left(c x^2\right)}{x} \, dx","Int[(a + b*ArcTan[c*x^2])/x,x]","\frac{1}{4} i b \text{PolyLog}\left(2,-i c x^2\right)-\frac{1}{4} i b \text{PolyLog}\left(2,i c x^2\right)+a \log (x)","\frac{1}{4} i b \text{PolyLog}\left(2,-i c x^2\right)-\frac{1}{4} i b \text{PolyLog}\left(2,i c x^2\right)+a \log (x)",1,"a*Log[x] + (I/4)*b*PolyLog[2, (-I)*c*x^2] - (I/4)*b*PolyLog[2, I*c*x^2]","A",4,3,14,0.2143,1,"{5031, 4848, 2391}"
65,1,39,0,0.0236941,"\int \frac{a+b \tan ^{-1}\left(c x^2\right)}{x^3} \, dx","Int[(a + b*ArcTan[c*x^2])/x^3,x]","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{2 x^2}-\frac{1}{4} b c \log \left(c^2 x^4+1\right)+b c \log (x)","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{2 x^2}-\frac{1}{4} b c \log \left(c^2 x^4+1\right)+b c \log (x)",1,"-(a + b*ArcTan[c*x^2])/(2*x^2) + b*c*Log[x] - (b*c*Log[1 + c^2*x^4])/4","A",5,5,14,0.3571,1,"{5033, 266, 36, 29, 31}"
66,1,41,0,0.0247925,"\int \frac{a+b \tan ^{-1}\left(c x^2\right)}{x^5} \, dx","Int[(a + b*ArcTan[c*x^2])/x^5,x]","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{4 x^4}-\frac{1}{4} b c^2 \tan ^{-1}\left(c x^2\right)-\frac{b c}{4 x^2}","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{4 x^4}-\frac{1}{4} b c^2 \tan ^{-1}\left(c x^2\right)-\frac{b c}{4 x^2}",1,"-(b*c)/(4*x^2) - (b*c^2*ArcTan[c*x^2])/4 - (a + b*ArcTan[c*x^2])/(4*x^4)","A",4,4,14,0.2857,1,"{5033, 275, 325, 203}"
67,1,55,0,0.0322249,"\int \frac{a+b \tan ^{-1}\left(c x^2\right)}{x^7} \, dx","Int[(a + b*ArcTan[c*x^2])/x^7,x]","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{6 x^6}+\frac{1}{12} b c^3 \log \left(c^2 x^4+1\right)-\frac{1}{3} b c^3 \log (x)-\frac{b c}{12 x^4}","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{6 x^6}+\frac{1}{12} b c^3 \log \left(c^2 x^4+1\right)-\frac{1}{3} b c^3 \log (x)-\frac{b c}{12 x^4}",1,"-(b*c)/(12*x^4) - (a + b*ArcTan[c*x^2])/(6*x^6) - (b*c^3*Log[x])/3 + (b*c^3*Log[1 + c^2*x^4])/12","A",4,3,14,0.2143,1,"{5033, 266, 44}"
68,1,161,0,0.1125583,"\int x^4 \left(a+b \tan ^{-1}\left(c x^2\right)\right) \, dx","Int[x^4*(a + b*ArcTan[c*x^2]),x]","\frac{1}{5} x^5 \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{b \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{10 \sqrt{2} c^{5/2}}-\frac{b \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{10 \sqrt{2} c^{5/2}}-\frac{b \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{5 \sqrt{2} c^{5/2}}+\frac{b \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{5 \sqrt{2} c^{5/2}}-\frac{2 b x^3}{15 c}","\frac{1}{5} x^5 \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{b \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{10 \sqrt{2} c^{5/2}}-\frac{b \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{10 \sqrt{2} c^{5/2}}-\frac{b \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{5 \sqrt{2} c^{5/2}}+\frac{b \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{5 \sqrt{2} c^{5/2}}-\frac{2 b x^3}{15 c}",1,"(-2*b*x^3)/(15*c) + (x^5*(a + b*ArcTan[c*x^2]))/5 - (b*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/(5*Sqrt[2]*c^(5/2)) + (b*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/(5*Sqrt[2]*c^(5/2)) + (b*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(10*Sqrt[2]*c^(5/2)) - (b*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(10*Sqrt[2]*c^(5/2))","A",11,8,14,0.5714,1,"{5033, 321, 297, 1162, 617, 204, 1165, 628}"
69,1,159,0,0.1014703,"\int x^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right) \, dx","Int[x^2*(a + b*ArcTan[c*x^2]),x]","\frac{1}{3} x^3 \left(a+b \tan ^{-1}\left(c x^2\right)\right)-\frac{b \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2} c^{3/2}}+\frac{b \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2} c^{3/2}}-\frac{b \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{3 \sqrt{2} c^{3/2}}+\frac{b \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{3 \sqrt{2} c^{3/2}}-\frac{2 b x}{3 c}","\frac{1}{3} x^3 \left(a+b \tan ^{-1}\left(c x^2\right)\right)-\frac{b \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2} c^{3/2}}+\frac{b \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2} c^{3/2}}-\frac{b \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{3 \sqrt{2} c^{3/2}}+\frac{b \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{3 \sqrt{2} c^{3/2}}-\frac{2 b x}{3 c}",1,"(-2*b*x)/(3*c) + (x^3*(a + b*ArcTan[c*x^2]))/3 - (b*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/(3*Sqrt[2]*c^(3/2)) + (b*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/(3*Sqrt[2]*c^(3/2)) - (b*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(6*Sqrt[2]*c^(3/2)) + (b*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(6*Sqrt[2]*c^(3/2))","A",11,8,14,0.5714,1,"{5033, 321, 211, 1165, 628, 1162, 617, 204}"
70,1,140,0,0.1046429,"\int \left(a+b \tan ^{-1}\left(c x^2\right)\right) \, dx","Int[a + b*ArcTan[c*x^2],x]","a x-\frac{b \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \sqrt{c}}+\frac{b \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \sqrt{c}}+b x \tan ^{-1}\left(c x^2\right)+\frac{b \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{\sqrt{2} \sqrt{c}}-\frac{b \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{\sqrt{2} \sqrt{c}}","a x-\frac{b \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \sqrt{c}}+\frac{b \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2} \sqrt{c}}+b x \tan ^{-1}\left(c x^2\right)+\frac{b \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{\sqrt{2} \sqrt{c}}-\frac{b \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{\sqrt{2} \sqrt{c}}",1,"a*x + b*x*ArcTan[c*x^2] + (b*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/(Sqrt[2]*Sqrt[c]) - (b*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/(Sqrt[2]*Sqrt[c]) - (b*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(2*Sqrt[2]*Sqrt[c]) + (b*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(2*Sqrt[2]*Sqrt[c])","A",11,7,10,0.7000,1,"{5027, 297, 1162, 617, 204, 1165, 628}"
71,1,143,0,0.0861341,"\int \frac{a+b \tan ^{-1}\left(c x^2\right)}{x^2} \, dx","Int[(a + b*ArcTan[c*x^2])/x^2,x]","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{x}-\frac{b \sqrt{c} \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2}}+\frac{b \sqrt{c} \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2}}-\frac{b \sqrt{c} \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{\sqrt{2}}+\frac{b \sqrt{c} \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{\sqrt{2}}","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{x}-\frac{b \sqrt{c} \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2}}+\frac{b \sqrt{c} \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{2 \sqrt{2}}-\frac{b \sqrt{c} \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{\sqrt{2}}+\frac{b \sqrt{c} \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{\sqrt{2}}",1,"-((a + b*ArcTan[c*x^2])/x) - (b*Sqrt[c]*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/Sqrt[2] + (b*Sqrt[c]*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/Sqrt[2] - (b*Sqrt[c]*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(2*Sqrt[2]) + (b*Sqrt[c]*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(2*Sqrt[2])","A",10,7,14,0.5000,1,"{5033, 211, 1165, 628, 1162, 617, 204}"
72,1,159,0,0.1041422,"\int \frac{a+b \tan ^{-1}\left(c x^2\right)}{x^4} \, dx","Int[(a + b*ArcTan[c*x^2])/x^4,x]","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{3 x^3}-\frac{b c^{3/2} \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2}}+\frac{b c^{3/2} \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2}}+\frac{b c^{3/2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{3 \sqrt{2}}-\frac{b c^{3/2} \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{3 \sqrt{2}}-\frac{2 b c}{3 x}","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{3 x^3}-\frac{b c^{3/2} \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2}}+\frac{b c^{3/2} \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{6 \sqrt{2}}+\frac{b c^{3/2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{3 \sqrt{2}}-\frac{b c^{3/2} \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{3 \sqrt{2}}-\frac{2 b c}{3 x}",1,"(-2*b*c)/(3*x) - (a + b*ArcTan[c*x^2])/(3*x^3) + (b*c^(3/2)*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/(3*Sqrt[2]) - (b*c^(3/2)*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/(3*Sqrt[2]) - (b*c^(3/2)*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(6*Sqrt[2]) + (b*c^(3/2)*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(6*Sqrt[2])","A",11,8,14,0.5714,1,"{5033, 325, 297, 1162, 617, 204, 1165, 628}"
73,1,159,0,0.1027186,"\int \frac{a+b \tan ^{-1}\left(c x^2\right)}{x^6} \, dx","Int[(a + b*ArcTan[c*x^2])/x^6,x]","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{5 x^5}+\frac{b c^{5/2} \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{10 \sqrt{2}}-\frac{b c^{5/2} \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{10 \sqrt{2}}+\frac{b c^{5/2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{5 \sqrt{2}}-\frac{b c^{5/2} \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{5 \sqrt{2}}-\frac{2 b c}{15 x^3}","-\frac{a+b \tan ^{-1}\left(c x^2\right)}{5 x^5}+\frac{b c^{5/2} \log \left(c x^2-\sqrt{2} \sqrt{c} x+1\right)}{10 \sqrt{2}}-\frac{b c^{5/2} \log \left(c x^2+\sqrt{2} \sqrt{c} x+1\right)}{10 \sqrt{2}}+\frac{b c^{5/2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{c} x\right)}{5 \sqrt{2}}-\frac{b c^{5/2} \tan ^{-1}\left(\sqrt{2} \sqrt{c} x+1\right)}{5 \sqrt{2}}-\frac{2 b c}{15 x^3}",1,"(-2*b*c)/(15*x^3) - (a + b*ArcTan[c*x^2])/(5*x^5) + (b*c^(5/2)*ArcTan[1 - Sqrt[2]*Sqrt[c]*x])/(5*Sqrt[2]) - (b*c^(5/2)*ArcTan[1 + Sqrt[2]*Sqrt[c]*x])/(5*Sqrt[2]) + (b*c^(5/2)*Log[1 - Sqrt[2]*Sqrt[c]*x + c*x^2])/(10*Sqrt[2]) - (b*c^(5/2)*Log[1 + Sqrt[2]*Sqrt[c]*x + c*x^2])/(10*Sqrt[2])","A",11,8,14,0.5714,1,"{5033, 325, 211, 1165, 628, 1162, 617, 204}"
74,1,731,0,1.6269763,"\int x^7 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x^7*(a + b*ArcTan[c*x^2])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right)}{16 c^4}-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^2\right)\right)}{16 c^4}+\frac{a b x^2}{8 c^3}-\frac{b x^4 \left(2 i a-b \log \left(1-i c x^2\right)\right)}{32 c^2}+\frac{1}{192} i b \left(-\frac{3 \left(1-i c x^2\right)^4}{c^4}+\frac{16 \left(1-i c x^2\right)^3}{c^4}-\frac{36 \left(1-i c x^2\right)^2}{c^4}+\frac{48 \left(1-i c x^2\right)}{c^4}-\frac{12 \log \left(1-i c x^2\right)}{c^4}\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)+\frac{b \log \left(\frac{1}{2} \left(1+i c x^2\right)\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)}{16 c^4}+\frac{1}{32} x^8 \left(2 a+i b \log \left(1-i c x^2\right)\right)^2+\frac{1}{64} b x^8 \left(2 i a-b \log \left(1-i c x^2\right)\right)-\frac{1}{16} b x^8 \log \left(1+i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)+\frac{i b x^6 \left(2 i a-b \log \left(1-i c x^2\right)\right)}{48 c}+\frac{b^2 x^4}{128 c^2}-\frac{23 i b^2 x^2}{192 c^3}-\frac{b^2 \left(1-i c x^2\right)^4}{256 c^4}+\frac{b^2 \left(1-i c x^2\right)^3}{36 c^4}-\frac{3 b^2 \left(1-i c x^2\right)^2}{32 c^4}-\frac{b^2 \log ^2\left(1-i c x^2\right)}{32 c^4}+\frac{b^2 \log ^2\left(1+i c x^2\right)}{32 c^4}-\frac{b^2 \log \left(-c x^2+i\right)}{24 c^4}-\frac{b^2 \left(1-i c x^2\right) \log \left(1-i c x^2\right)}{16 c^4}-\frac{b^2 \left(1+i c x^2\right) \log \left(1+i c x^2\right)}{8 c^4}-\frac{b^2 \log \left(\frac{1}{2} \left(1-i c x^2\right)\right) \log \left(1+i c x^2\right)}{16 c^4}+\frac{5 b^2 \log \left(c x^2+i\right)}{192 c^4}-\frac{7 i b^2 x^6}{576 c}-\frac{1}{32} b^2 x^8 \log ^2\left(1+i c x^2\right)+\frac{i b^2 x^6 \log \left(1+i c x^2\right)}{24 c}+\frac{b^2 x^8}{256}","\frac{a b x^2}{4 c^3}-\frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{8 c^4}+\frac{1}{8} x^8 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2-\frac{b x^6 \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{12 c}+\frac{b^2 x^4}{24 c^2}-\frac{b^2 \log \left(c^2 x^4+1\right)}{6 c^4}+\frac{b^2 x^2 \tan ^{-1}\left(c x^2\right)}{4 c^3}",1,"(a*b*x^2)/(8*c^3) - (((23*I)/192)*b^2*x^2)/c^3 + (b^2*x^4)/(128*c^2) - (((7*I)/576)*b^2*x^6)/c + (b^2*x^8)/256 - (3*b^2*(1 - I*c*x^2)^2)/(32*c^4) + (b^2*(1 - I*c*x^2)^3)/(36*c^4) - (b^2*(1 - I*c*x^2)^4)/(256*c^4) - (b^2*Log[I - c*x^2])/(24*c^4) - (b^2*(1 - I*c*x^2)*Log[1 - I*c*x^2])/(16*c^4) - (b^2*Log[1 - I*c*x^2]^2)/(32*c^4) - (b*x^4*((2*I)*a - b*Log[1 - I*c*x^2]))/(32*c^2) + ((I/48)*b*x^6*((2*I)*a - b*Log[1 - I*c*x^2]))/c + (b*x^8*((2*I)*a - b*Log[1 - I*c*x^2]))/64 + (x^8*(2*a + I*b*Log[1 - I*c*x^2])^2)/32 + (I/192)*b*(2*a + I*b*Log[1 - I*c*x^2])*((48*(1 - I*c*x^2))/c^4 - (36*(1 - I*c*x^2)^2)/c^4 + (16*(1 - I*c*x^2)^3)/c^4 - (3*(1 - I*c*x^2)^4)/c^4 - (12*Log[1 - I*c*x^2])/c^4) + (b*((2*I)*a - b*Log[1 - I*c*x^2])*Log[(1 + I*c*x^2)/2])/(16*c^4) + ((I/24)*b^2*x^6*Log[1 + I*c*x^2])/c - (b^2*(1 + I*c*x^2)*Log[1 + I*c*x^2])/(8*c^4) - (b^2*Log[(1 - I*c*x^2)/2]*Log[1 + I*c*x^2])/(16*c^4) - (b*x^8*((2*I)*a - b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2])/16 + (b^2*Log[1 + I*c*x^2]^2)/(32*c^4) - (b^2*x^8*Log[1 + I*c*x^2]^2)/32 + (5*b^2*Log[I + c*x^2])/(192*c^4) - (b^2*PolyLog[2, (1 - I*c*x^2)/2])/(16*c^4) - (b^2*PolyLog[2, (1 + I*c*x^2)/2])/(16*c^4)","C",62,19,16,1.187,0,"{5035, 2454, 2398, 2411, 43, 2334, 12, 14, 2301, 2395, 2439, 2416, 2389, 2295, 2394, 2393, 2391, 2410, 2390}"
75,1,647,0,1.3656819,"\int x^5 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x^5*(a + b*ArcTan[c*x^2])^2,x]","\frac{i b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right)}{12 c^3}-\frac{i b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^2\right)\right)}{12 c^3}-\frac{i a b x^2}{6 c^2}+\frac{1}{72} i b \left(\frac{2 i \left(1-i c x^2\right)^3}{c^3}-\frac{9 i \left(1-i c x^2\right)^2}{c^3}+\frac{18 i \left(1-i c x^2\right)}{c^3}-\frac{6 i \log \left(1-i c x^2\right)}{c^3}\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)-\frac{i b \log \left(\frac{1}{2} \left(1+i c x^2\right)\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)}{12 c^3}+\frac{1}{24} x^6 \left(2 a+i b \log \left(1-i c x^2\right)\right)^2+\frac{1}{36} b x^6 \left(2 i a-b \log \left(1-i c x^2\right)\right)-\frac{1}{12} b x^6 \log \left(1+i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)+\frac{i b x^4 \left(2 i a-b \log \left(1-i c x^2\right)\right)}{24 c}+\frac{19 b^2 x^2}{72 c^2}+\frac{i b^2 \left(1-i c x^2\right)^3}{108 c^3}-\frac{i b^2 \left(1-i c x^2\right)^2}{16 c^3}-\frac{i b^2 \log ^2\left(1-i c x^2\right)}{24 c^3}-\frac{i b^2 \log ^2\left(1+i c x^2\right)}{24 c^3}+\frac{i b^2 \log \left(-c x^2+i\right)}{12 c^3}+\frac{i b^2 \left(1-i c x^2\right) \log \left(1-i c x^2\right)}{12 c^3}-\frac{i b^2 \log \left(\frac{1}{2} \left(1-i c x^2\right)\right) \log \left(1+i c x^2\right)}{12 c^3}-\frac{i b^2 \log \left(c x^2+i\right)}{72 c^3}-\frac{5 i b^2 x^4}{144 c}-\frac{1}{24} b^2 x^6 \log ^2\left(1+i c x^2\right)+\frac{i b^2 x^4 \log \left(1+i c x^2\right)}{12 c}+\frac{b^2 x^6}{108}","-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x^2}\right)}{6 c^3}-\frac{i \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{6 c^3}-\frac{b \log \left(\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{3 c^3}+\frac{1}{6} x^6 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2-\frac{b x^4 \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{6 c}+\frac{b^2 x^2}{6 c^2}-\frac{b^2 \tan ^{-1}\left(c x^2\right)}{6 c^3}",1,"((-I/6)*a*b*x^2)/c^2 + (19*b^2*x^2)/(72*c^2) - (((5*I)/144)*b^2*x^4)/c + (b^2*x^6)/108 - ((I/16)*b^2*(1 - I*c*x^2)^2)/c^3 + ((I/108)*b^2*(1 - I*c*x^2)^3)/c^3 + ((I/12)*b^2*Log[I - c*x^2])/c^3 + ((I/12)*b^2*(1 - I*c*x^2)*Log[1 - I*c*x^2])/c^3 - ((I/24)*b^2*Log[1 - I*c*x^2]^2)/c^3 + ((I/24)*b*x^4*((2*I)*a - b*Log[1 - I*c*x^2]))/c + (b*x^6*((2*I)*a - b*Log[1 - I*c*x^2]))/36 + (x^6*(2*a + I*b*Log[1 - I*c*x^2])^2)/24 + (I/72)*b*(2*a + I*b*Log[1 - I*c*x^2])*(((18*I)*(1 - I*c*x^2))/c^3 - ((9*I)*(1 - I*c*x^2)^2)/c^3 + ((2*I)*(1 - I*c*x^2)^3)/c^3 - ((6*I)*Log[1 - I*c*x^2])/c^3) - ((I/12)*b*((2*I)*a - b*Log[1 - I*c*x^2])*Log[(1 + I*c*x^2)/2])/c^3 + ((I/12)*b^2*x^4*Log[1 + I*c*x^2])/c - ((I/12)*b^2*Log[(1 - I*c*x^2)/2]*Log[1 + I*c*x^2])/c^3 - (b*x^6*((2*I)*a - b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2])/12 - ((I/24)*b^2*Log[1 + I*c*x^2]^2)/c^3 - (b^2*x^6*Log[1 + I*c*x^2]^2)/24 - ((I/72)*b^2*Log[I + c*x^2])/c^3 + ((I/12)*b^2*PolyLog[2, (1 - I*c*x^2)/2])/c^3 - ((I/12)*b^2*PolyLog[2, (1 + I*c*x^2)/2])/c^3","B",53,19,16,1.187,0,"{5035, 2454, 2398, 2411, 43, 2334, 12, 14, 2301, 2395, 2439, 2416, 2389, 2295, 2394, 2393, 2391, 2410, 2390}"
76,1,612,0,1.0417284,"\int x^3 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x^3*(a + b*ArcTan[c*x^2])^2,x]","\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right)}{8 c^2}+\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^2\right)\right)}{8 c^2}-\frac{\left(1-i c x^2\right)^2 \left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{16 c^2}+\frac{\left(1-i c x^2\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{8 c^2}+\frac{i b \left(1-i c x^2\right)^2 \left(2 a+i b \log \left(1-i c x^2\right)\right)}{16 c^2}-\frac{b \log \left(\frac{1}{2} \left(1+i c x^2\right)\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)}{8 c^2}-\frac{3 a b x^2}{4 c}+\frac{1}{16} b x^4 \left(2 i a-b \log \left(1-i c x^2\right)\right)-\frac{1}{8} b x^4 \log \left(1+i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)+\frac{b^2 \left(1-i c x^2\right)^2}{32 c^2}+\frac{b^2 \left(1+i c x^2\right)^2}{32 c^2}+\frac{b^2 \left(1+i c x^2\right)^2 \log ^2\left(1+i c x^2\right)}{16 c^2}-\frac{b^2 \left(1+i c x^2\right) \log ^2\left(1+i c x^2\right)}{8 c^2}-\frac{b^2 \log \left(-c x^2+i\right)}{16 c^2}+\frac{3 b^2 \left(1-i c x^2\right) \log \left(1-i c x^2\right)}{8 c^2}-\frac{b^2 \left(1+i c x^2\right)^2 \log \left(1+i c x^2\right)}{16 c^2}+\frac{3 b^2 \left(1+i c x^2\right) \log \left(1+i c x^2\right)}{8 c^2}+\frac{b^2 \log \left(\frac{1}{2} \left(1-i c x^2\right)\right) \log \left(1+i c x^2\right)}{8 c^2}-\frac{b^2 \log \left(c x^2+i\right)}{16 c^2}-\frac{1}{16} b^2 x^4 \log \left(1+i c x^2\right)+\frac{b^2 x^4}{16}","\frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{4 c^2}-\frac{a b x^2}{2 c}+\frac{1}{4} x^4 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2+\frac{b^2 \log \left(c^2 x^4+1\right)}{4 c^2}-\frac{b^2 x^2 \tan ^{-1}\left(c x^2\right)}{2 c}",1,"(-3*a*b*x^2)/(4*c) + (b^2*x^4)/16 + (b^2*(1 - I*c*x^2)^2)/(32*c^2) + (b^2*(1 + I*c*x^2)^2)/(32*c^2) - (b^2*Log[I - c*x^2])/(16*c^2) + (3*b^2*(1 - I*c*x^2)*Log[1 - I*c*x^2])/(8*c^2) + (b*x^4*((2*I)*a - b*Log[1 - I*c*x^2]))/16 + ((I/16)*b*(1 - I*c*x^2)^2*(2*a + I*b*Log[1 - I*c*x^2]))/c^2 + ((1 - I*c*x^2)*(2*a + I*b*Log[1 - I*c*x^2])^2)/(8*c^2) - ((1 - I*c*x^2)^2*(2*a + I*b*Log[1 - I*c*x^2])^2)/(16*c^2) - (b*((2*I)*a - b*Log[1 - I*c*x^2])*Log[(1 + I*c*x^2)/2])/(8*c^2) - (b^2*x^4*Log[1 + I*c*x^2])/16 + (3*b^2*(1 + I*c*x^2)*Log[1 + I*c*x^2])/(8*c^2) - (b^2*(1 + I*c*x^2)^2*Log[1 + I*c*x^2])/(16*c^2) + (b^2*Log[(1 - I*c*x^2)/2]*Log[1 + I*c*x^2])/(8*c^2) - (b*x^4*((2*I)*a - b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2])/8 - (b^2*(1 + I*c*x^2)*Log[1 + I*c*x^2]^2)/(8*c^2) + (b^2*(1 + I*c*x^2)^2*Log[1 + I*c*x^2]^2)/(16*c^2) - (b^2*Log[I + c*x^2])/(16*c^2) + (b^2*PolyLog[2, (1 - I*c*x^2)/2])/(8*c^2) + (b^2*PolyLog[2, (1 + I*c*x^2)/2])/(8*c^2)","C",44,16,16,1.000,0,"{5035, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2395, 43, 2439, 2416, 2394, 2393, 2391}"
77,1,255,0,0.5535973,"\int x \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x*(a + b*ArcTan[c*x^2])^2,x]","-\frac{i b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right)}{4 c}+\frac{i b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^2\right)\right)}{4 c}+\frac{i b \log \left(\frac{1}{2} \left(1+i c x^2\right)\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)}{4 c}-\frac{1}{4} b x^2 \log \left(1+i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)+\frac{i \left(1-i c x^2\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{8 c}+\frac{i b^2 \left(1+i c x^2\right) \log ^2\left(1+i c x^2\right)}{8 c}+\frac{i b^2 \log \left(\frac{1}{2} \left(1-i c x^2\right)\right) \log \left(1+i c x^2\right)}{4 c}","\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x^2}\right)}{2 c}+\frac{1}{2} x^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2+\frac{i \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{2 c}+\frac{b \log \left(\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{c}",1,"((I/8)*(1 - I*c*x^2)*(2*a + I*b*Log[1 - I*c*x^2])^2)/c + ((I/4)*b*((2*I)*a - b*Log[1 - I*c*x^2])*Log[(1 + I*c*x^2)/2])/c + ((I/4)*b^2*Log[(1 - I*c*x^2)/2]*Log[1 + I*c*x^2])/c - (b*x^2*((2*I)*a - b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2])/4 + ((I/8)*b^2*(1 + I*c*x^2)*Log[1 + I*c*x^2]^2)/c - ((I/4)*b^2*PolyLog[2, (1 - I*c*x^2)/2])/c + ((I/4)*b^2*PolyLog[2, (1 + I*c*x^2)/2])/c","B",28,12,14,0.8571,0,"{5035, 2454, 2389, 2296, 2295, 6715, 2430, 43, 2416, 2394, 2393, 2391}"
78,1,151,0,0.3209274,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{x} \, dx","Int[(a + b*ArcTan[c*x^2])^2/x,x]","-\frac{1}{2} i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{1}{2} i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)-\frac{1}{4} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^2}\right)+\frac{1}{4} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x^2}\right)+\tanh ^{-1}\left(1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2","-\frac{1}{2} i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{1}{2} i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)-\frac{1}{4} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^2}\right)+\frac{1}{4} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x^2}\right)+\tanh ^{-1}\left(1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2",1,"(a + b*ArcTan[c*x^2])^2*ArcTanh[1 - 2/(1 + I*c*x^2)] - (I/2)*b*(a + b*ArcTan[c*x^2])*PolyLog[2, 1 - 2/(1 + I*c*x^2)] + (I/2)*b*(a + b*ArcTan[c*x^2])*PolyLog[2, -1 + 2/(1 + I*c*x^2)] - (b^2*PolyLog[3, 1 - 2/(1 + I*c*x^2)])/4 + (b^2*PolyLog[3, -1 + 2/(1 + I*c*x^2)])/4","A",7,6,16,0.3750,1,"{5031, 4850, 4988, 4884, 4994, 6610}"
79,1,290,0,0.6534604,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{x^3} \, dx","Int[(a + b*ArcTan[c*x^2])^2/x^3,x]","\frac{1}{2} i b^2 c \text{PolyLog}\left(2,-i c x^2\right)-\frac{1}{2} i b^2 c \text{PolyLog}\left(2,i c x^2\right)-\frac{1}{4} i b^2 c \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right)+\frac{1}{4} i b^2 c \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^2\right)\right)+\frac{1}{4} i b c \log \left(\frac{1}{2} \left(1+i c x^2\right)\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)+\frac{b \log \left(1+i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)}{4 x^2}-\frac{\left(1-i c x^2\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{8 x^2}+2 a b c \log (x)+\frac{b^2 \left(1+i c x^2\right) \log ^2\left(1+i c x^2\right)}{8 x^2}+\frac{1}{4} i b^2 c \log \left(\frac{1}{2} \left(1-i c x^2\right)\right) \log \left(1+i c x^2\right)","-\frac{1}{2} i b^2 c \text{PolyLog}\left(2,-1+\frac{2}{1-i c x^2}\right)-\frac{1}{2} i c \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2-\frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{2 x^2}+b c \log \left(2-\frac{2}{1-i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)",1,"2*a*b*c*Log[x] - ((1 - I*c*x^2)*(2*a + I*b*Log[1 - I*c*x^2])^2)/(8*x^2) + (I/4)*b*c*((2*I)*a - b*Log[1 - I*c*x^2])*Log[(1 + I*c*x^2)/2] + (I/4)*b^2*c*Log[(1 - I*c*x^2)/2]*Log[1 + I*c*x^2] + (b*((2*I)*a - b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2])/(4*x^2) + (b^2*(1 + I*c*x^2)*Log[1 + I*c*x^2]^2)/(8*x^2) + (I/2)*b^2*c*PolyLog[2, (-I)*c*x^2] - (I/2)*b^2*c*PolyLog[2, I*c*x^2] - (I/4)*b^2*c*PolyLog[2, (1 - I*c*x^2)/2] + (I/4)*b^2*c*PolyLog[2, (1 + I*c*x^2)/2]","B",24,13,16,0.8125,0,"{5035, 2454, 2397, 2392, 2391, 2395, 36, 29, 31, 2439, 2416, 2394, 2393}"
80,1,419,0,1.1362311,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{x^5} \, dx","Int[(a + b*ArcTan[c*x^2])^2/x^5,x]","-\frac{1}{8} b^2 c^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right)-\frac{1}{8} b^2 c^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^2\right)\right)+\frac{1}{8} b c^2 \log \left(\frac{1}{2} \left(1+i c x^2\right)\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)-\frac{1}{16} c^2 \left(2 a+i b \log \left(1-i c x^2\right)\right)^2+\frac{i b c \left(2 i a-b \log \left(1-i c x^2\right)\right)}{8 x^2}-\frac{b c \left(1-i c x^2\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)}{8 x^2}+\frac{b \log \left(1+i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)}{8 x^4}-\frac{\left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{16 x^4}+\frac{1}{16} b^2 c^2 \log ^2\left(1+i c x^2\right)-\frac{1}{4} b^2 c^2 \log \left(-c x^2+i\right)-\frac{1}{8} b^2 c^2 \log \left(\frac{1}{2} \left(1-i c x^2\right)\right) \log \left(1+i c x^2\right)-\frac{1}{8} b^2 c^2 \log \left(c x^2+i\right)+b^2 c^2 \log (x)+\frac{b^2 \log ^2\left(1+i c x^2\right)}{16 x^4}+\frac{i b^2 c \log \left(1+i c x^2\right)}{4 x^2}","-\frac{1}{4} c^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2-\frac{b c \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{2 x^2}-\frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{4 x^4}-\frac{1}{4} b^2 c^2 \log \left(c^2 x^4+1\right)+b^2 c^2 \log (x)",1,"b^2*c^2*Log[x] - (b^2*c^2*Log[I - c*x^2])/4 + ((I/8)*b*c*((2*I)*a - b*Log[1 - I*c*x^2]))/x^2 - (b*c*(1 - I*c*x^2)*(2*a + I*b*Log[1 - I*c*x^2]))/(8*x^2) - (c^2*(2*a + I*b*Log[1 - I*c*x^2])^2)/16 - (2*a + I*b*Log[1 - I*c*x^2])^2/(16*x^4) + (b*c^2*((2*I)*a - b*Log[1 - I*c*x^2])*Log[(1 + I*c*x^2)/2])/8 + ((I/4)*b^2*c*Log[1 + I*c*x^2])/x^2 - (b^2*c^2*Log[(1 - I*c*x^2)/2]*Log[1 + I*c*x^2])/8 + (b*((2*I)*a - b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2])/(8*x^4) + (b^2*c^2*Log[1 + I*c*x^2]^2)/16 + (b^2*Log[1 + I*c*x^2]^2)/(16*x^4) - (b^2*c^2*Log[I + c*x^2])/8 - (b^2*c^2*PolyLog[2, (1 - I*c*x^2)/2])/8 - (b^2*c^2*PolyLog[2, (1 + I*c*x^2)/2])/8","C",46,23,16,1.438,0,"{5035, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2395, 44, 2439, 2416, 36, 29, 2392, 2391, 2394, 2393, 2410, 2390}"
81,1,1393,0,2.6020553,"\int x^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[x^2*(a + b*ArcTan[c*x^2])^2,x]","\frac{1}{12} \left(2 a+i b \log \left(1-i c x^2\right)\right)^2 x^3-\frac{1}{12} b^2 \log ^2\left(i c x^2+1\right) x^3+\frac{2}{9} i a b x^3-\frac{1}{9} b^2 \log \left(1-i c x^2\right) x^3-\frac{1}{9} i b \left(2 a+i b \log \left(1-i c x^2\right)\right) x^3-\frac{1}{3} i a b \log \left(i c x^2+1\right) x^3+\frac{1}{6} b^2 \log \left(1-i c x^2\right) \log \left(i c x^2+1\right) x^3-\frac{2 i b^2 \log \left(1-i c x^2\right) x}{3 c}+\frac{2 i b^2 \log \left(i c x^2+1\right) x}{3 c}-\frac{4 a b x}{3 c}+\frac{\sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2}{3 c^{3/2}}-\frac{(-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2}{3 c^{3/2}}+\frac{4 (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)}{3 c^{3/2}}-\frac{4 (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)}{3 c^{3/2}}-\frac{2 \sqrt[4]{-1} a b \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)}{3 c^{3/2}}-\frac{2 (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right)}{3 c^{3/2}}+\frac{2 (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{(-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{3 c^{3/2}}+\frac{2 (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right)}{3 c^{3/2}}-\frac{2 (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right)}{3 c^{3/2}}+\frac{(-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{3 c^{3/2}}+\frac{(-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{(-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{(-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right)}{3 c^{3/2}}-\frac{\sqrt[4]{-1} b \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)}{3 c^{3/2}}+\frac{(-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right)}{3 c^{3/2}}+\frac{(-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right)}{3 c^{3/2}}+\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right)}{3 c^{3/2}}+\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{6 c^{3/2}}+\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right)}{3 c^{3/2}}+\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right)}{6 c^{3/2}}-\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{6 c^{3/2}}-\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{6 c^{3/2}}","\frac{1}{12} \left(2 a+i b \log \left(1-i c x^2\right)\right)^2 x^3-\frac{1}{12} b^2 \log ^2\left(i c x^2+1\right) x^3+\frac{2}{9} i a b x^3-\frac{1}{9} b^2 \log \left(1-i c x^2\right) x^3-\frac{1}{9} i b \left(2 a+i b \log \left(1-i c x^2\right)\right) x^3-\frac{1}{3} i a b \log \left(i c x^2+1\right) x^3+\frac{1}{6} b^2 \log \left(1-i c x^2\right) \log \left(i c x^2+1\right) x^3-\frac{2 i b^2 \log \left(1-i c x^2\right) x}{3 c}+\frac{2 i b^2 \log \left(i c x^2+1\right) x}{3 c}-\frac{4 a b x}{3 c}+\frac{\sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2}{3 c^{3/2}}-\frac{(-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2}{3 c^{3/2}}+\frac{4 (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)}{3 c^{3/2}}-\frac{4 (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)}{3 c^{3/2}}-\frac{2 \sqrt[4]{-1} a b \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)}{3 c^{3/2}}-\frac{2 (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right)}{3 c^{3/2}}+\frac{2 (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{(-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{3 c^{3/2}}+\frac{2 (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right)}{3 c^{3/2}}-\frac{2 (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right)}{3 c^{3/2}}+\frac{(-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{3 c^{3/2}}+\frac{(-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{(-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{(-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right)}{3 c^{3/2}}-\frac{\sqrt[4]{-1} b \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)}{3 c^{3/2}}+\frac{(-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right)}{3 c^{3/2}}+\frac{(-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right)}{3 c^{3/2}}+\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right)}{3 c^{3/2}}+\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{6 c^{3/2}}+\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right)}{3 c^{3/2}}+\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right)}{3 c^{3/2}}-\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right)}{6 c^{3/2}}-\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{6 c^{3/2}}-\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{6 c^{3/2}}",1,"(-4*a*b*x)/(3*c) + ((2*I)/9)*a*b*x^3 + (4*(-1)^(3/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x])/(3*c^(3/2)) + ((-1)^(1/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]^2)/(3*c^(3/2)) - (2*(-1)^(1/4)*a*b*ArcTanh[(-1)^(3/4)*Sqrt[c]*x])/(3*c^(3/2)) - (4*(-1)^(3/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x])/(3*c^(3/2)) - ((-1)^(3/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]^2)/(3*c^(3/2)) - (2*(-1)^(3/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) + (2*(-1)^(3/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) - ((-1)^(3/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[(Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) + (2*(-1)^(3/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/(3*c^(3/2)) - (2*(-1)^(3/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(3*c^(3/2)) + ((-1)^(3/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[-((Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x))])/(3*c^(3/2)) + ((-1)^(3/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(3*c^(3/2)) - ((-1)^(3/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) - (((2*I)/3)*b^2*x*Log[1 - I*c*x^2])/c - (b^2*x^3*Log[1 - I*c*x^2])/9 - ((-1)^(3/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2])/(3*c^(3/2)) - (I/9)*b*x^3*(2*a + I*b*Log[1 - I*c*x^2]) - ((-1)^(1/4)*b*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*(2*a + I*b*Log[1 - I*c*x^2]))/(3*c^(3/2)) + (x^3*(2*a + I*b*Log[1 - I*c*x^2])^2)/12 + (((2*I)/3)*b^2*x*Log[1 + I*c*x^2])/c - (I/3)*a*b*x^3*Log[1 + I*c*x^2] + ((-1)^(3/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/(3*c^(3/2)) + ((-1)^(3/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/(3*c^(3/2)) + (b^2*x^3*Log[1 - I*c*x^2]*Log[1 + I*c*x^2])/6 - (b^2*x^3*Log[1 + I*c*x^2]^2)/12 + ((-1)^(1/4)*b^2*PolyLog[2, 1 - 2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) + ((-1)^(1/4)*b^2*PolyLog[2, 1 - 2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(3*c^(3/2)) - ((-1)^(1/4)*b^2*PolyLog[2, 1 - (Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(6*c^(3/2)) + ((-1)^(3/4)*b^2*PolyLog[2, 1 - 2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/(3*c^(3/2)) + ((-1)^(3/4)*b^2*PolyLog[2, 1 - 2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(3*c^(3/2)) - ((-1)^(3/4)*b^2*PolyLog[2, 1 + (Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(6*c^(3/2)) - ((-1)^(3/4)*b^2*PolyLog[2, 1 - ((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(6*c^(3/2)) - ((-1)^(1/4)*b^2*PolyLog[2, 1 - ((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(6*c^(3/2))","A",86,27,16,1.687,1,"{5035, 2457, 2476, 2448, 321, 203, 2455, 302, 2470, 12, 4920, 4854, 2402, 2315, 6742, 206, 30, 2557, 205, 4928, 4856, 2447, 208, 5992, 5920, 5984, 5918}"
82,1,1191,0,1.7778519,"\int \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[(a + b*ArcTan[c*x^2])^2,x]","x a^2-\frac{2 (-1)^{3/4} b \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) a}{\sqrt{c}}+\frac{2 (-1)^{3/4} b \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) a}{\sqrt{c}}+i b x \log \left(1-i c x^2\right) a-i b x \log \left(i c x^2+1\right) a+\frac{(-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2}{\sqrt{c}}-\frac{\sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2}{\sqrt{c}}-\frac{1}{4} b^2 x \log ^2\left(1-i c x^2\right)-\frac{1}{4} b^2 x \log ^2\left(i c x^2+1\right)+\frac{2 \sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right)}{\sqrt{c}}-\frac{2 \sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{2 \sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right)}{\sqrt{c}}-\frac{2 \sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right)}{\sqrt{c}}-\frac{\sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right)}{\sqrt{c}}-\frac{\sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right)}{\sqrt{c}}+\frac{1}{2} b^2 x \log \left(1-i c x^2\right) \log \left(i c x^2+1\right)+\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right)}{\sqrt{c}}+\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{2 \sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right)}{2 \sqrt{c}}-\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{2 \sqrt{c}}-\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{2 \sqrt{c}}","x a^2-\frac{2 (-1)^{3/4} b \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) a}{\sqrt{c}}+\frac{2 (-1)^{3/4} b \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) a}{\sqrt{c}}+i b x \log \left(1-i c x^2\right) a-i b x \log \left(i c x^2+1\right) a+\frac{(-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2}{\sqrt{c}}-\frac{\sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2}{\sqrt{c}}-\frac{1}{4} b^2 x \log ^2\left(1-i c x^2\right)-\frac{1}{4} b^2 x \log ^2\left(i c x^2+1\right)+\frac{2 \sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right)}{\sqrt{c}}-\frac{2 \sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{2 \sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right)}{\sqrt{c}}-\frac{2 \sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right)}{\sqrt{c}}-\frac{\sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right)}{\sqrt{c}}-\frac{\sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right)}{\sqrt{c}}+\frac{1}{2} b^2 x \log \left(1-i c x^2\right) \log \left(i c x^2+1\right)+\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right)}{\sqrt{c}}+\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{2 \sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right)}{\sqrt{c}}+\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right)}{\sqrt{c}}-\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right)}{2 \sqrt{c}}-\frac{\sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right)}{2 \sqrt{c}}-\frac{(-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right)}{2 \sqrt{c}}",1,"a^2*x - (2*(-1)^(3/4)*a*b*ArcTan[(-1)^(3/4)*Sqrt[c]*x])/Sqrt[c] + ((-1)^(3/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]^2)/Sqrt[c] + (2*(-1)^(3/4)*a*b*ArcTanh[(-1)^(3/4)*Sqrt[c]*x])/Sqrt[c] - ((-1)^(1/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]^2)/Sqrt[c] + (2*(-1)^(1/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] - (2*(-1)^(1/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[(Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + (2*(-1)^(1/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] - (2*(-1)^(1/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[-((Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x))])/Sqrt[c] + ((-1)^(1/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + I*a*b*x*Log[1 - I*c*x^2] + ((-1)^(1/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2])/Sqrt[c] - ((-1)^(1/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2])/Sqrt[c] - (b^2*x*Log[1 - I*c*x^2]^2)/4 - I*a*b*x*Log[1 + I*c*x^2] - ((-1)^(1/4)*b^2*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/Sqrt[c] + ((-1)^(1/4)*b^2*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/Sqrt[c] + (b^2*x*Log[1 - I*c*x^2]*Log[1 + I*c*x^2])/2 - (b^2*x*Log[1 + I*c*x^2]^2)/4 + ((-1)^(3/4)*b^2*PolyLog[2, 1 - 2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(3/4)*b^2*PolyLog[2, 1 - 2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/Sqrt[c] - ((-1)^(3/4)*b^2*PolyLog[2, 1 - (Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(2*Sqrt[c]) + ((-1)^(1/4)*b^2*PolyLog[2, 1 - 2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] + ((-1)^(1/4)*b^2*PolyLog[2, 1 - 2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/Sqrt[c] - ((-1)^(1/4)*b^2*PolyLog[2, 1 + (Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(2*Sqrt[c]) - ((-1)^(1/4)*b^2*PolyLog[2, 1 - ((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/(2*Sqrt[c]) - ((-1)^(3/4)*b^2*PolyLog[2, 1 - ((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/(2*Sqrt[c])","A",69,23,12,1.917,1,"{5029, 2448, 321, 203, 2450, 2476, 2470, 12, 4920, 4854, 2402, 2315, 206, 2556, 205, 4928, 4856, 2447, 208, 5992, 5920, 5984, 5918}"
83,1,1164,0,1.621682,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{x^2} \, dx","Int[(a + b*ArcTan[c*x^2])^2/x^2,x]","\sqrt[4]{-1} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 b^2-(-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 b^2+\frac{\log ^2\left(i c x^2+1\right) b^2}{4 x}-2 (-1)^{3/4} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) b^2+2 (-1)^{3/4} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-(-1)^{3/4} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+2 (-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) b^2-2 (-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2+(-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2+(-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2-(-1)^{3/4} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-(-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right) b^2+(-1)^{3/4} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) b^2+(-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) b^2-\frac{\log \left(1-i c x^2\right) \log \left(i c x^2+1\right) b^2}{2 x}+\sqrt[4]{-1} \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) b^2+\sqrt[4]{-1} \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-\frac{1}{2} \sqrt[4]{-1} \sqrt{c} \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+(-1)^{3/4} \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) b^2+(-1)^{3/4} \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2-\frac{1}{2} (-1)^{3/4} \sqrt{c} \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right) b^2-\frac{1}{2} (-1)^{3/4} \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2-\frac{1}{2} \sqrt[4]{-1} \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-2 \sqrt[4]{-1} a \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) b-\sqrt[4]{-1} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \left(2 a+i b \log \left(1-i c x^2\right)\right) b+\frac{i a \log \left(i c x^2+1\right) b}{x}-\frac{\left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{4 x}","\sqrt[4]{-1} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 b^2-(-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 b^2+\frac{\log ^2\left(i c x^2+1\right) b^2}{4 x}-2 (-1)^{3/4} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) b^2+2 (-1)^{3/4} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-(-1)^{3/4} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+2 (-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) b^2-2 (-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2+(-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2+(-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2-(-1)^{3/4} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-(-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right) b^2+(-1)^{3/4} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) b^2+(-1)^{3/4} \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) b^2-\frac{\log \left(1-i c x^2\right) \log \left(i c x^2+1\right) b^2}{2 x}+\sqrt[4]{-1} \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) b^2+\sqrt[4]{-1} \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-\frac{1}{2} \sqrt[4]{-1} \sqrt{c} \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+(-1)^{3/4} \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) b^2+(-1)^{3/4} \sqrt{c} \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2-\frac{1}{2} (-1)^{3/4} \sqrt{c} \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right) b^2-\frac{1}{2} (-1)^{3/4} \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2-\frac{1}{2} \sqrt[4]{-1} \sqrt{c} \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-2 \sqrt[4]{-1} a \sqrt{c} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) b-\sqrt[4]{-1} \sqrt{c} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \left(2 a+i b \log \left(1-i c x^2\right)\right) b+\frac{i a \log \left(i c x^2+1\right) b}{x}-\frac{\left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{4 x}",1,"(-1)^(1/4)*b^2*Sqrt[c]*ArcTan[(-1)^(3/4)*Sqrt[c]*x]^2 - 2*(-1)^(1/4)*a*b*Sqrt[c]*ArcTanh[(-1)^(3/4)*Sqrt[c]*x] - (-1)^(3/4)*b^2*Sqrt[c]*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]^2 - 2*(-1)^(3/4)*b^2*Sqrt[c]*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(1/4)*Sqrt[c]*x)] + 2*(-1)^(3/4)*b^2*Sqrt[c]*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(1/4)*Sqrt[c]*x)] - (-1)^(3/4)*b^2*Sqrt[c]*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[(Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)] + 2*(-1)^(3/4)*b^2*Sqrt[c]*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(3/4)*Sqrt[c]*x)] - 2*(-1)^(3/4)*b^2*Sqrt[c]*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(3/4)*Sqrt[c]*x)] + (-1)^(3/4)*b^2*Sqrt[c]*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[-((Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x))] + (-1)^(3/4)*b^2*Sqrt[c]*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)] - (-1)^(3/4)*b^2*Sqrt[c]*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)] - (-1)^(3/4)*b^2*Sqrt[c]*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2] - (-1)^(1/4)*b*Sqrt[c]*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*(2*a + I*b*Log[1 - I*c*x^2]) - (2*a + I*b*Log[1 - I*c*x^2])^2/(4*x) + (I*a*b*Log[1 + I*c*x^2])/x + (-1)^(3/4)*b^2*Sqrt[c]*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2] + (-1)^(3/4)*b^2*Sqrt[c]*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2] - (b^2*Log[1 - I*c*x^2]*Log[1 + I*c*x^2])/(2*x) + (b^2*Log[1 + I*c*x^2]^2)/(4*x) + (-1)^(1/4)*b^2*Sqrt[c]*PolyLog[2, 1 - 2/(1 - (-1)^(1/4)*Sqrt[c]*x)] + (-1)^(1/4)*b^2*Sqrt[c]*PolyLog[2, 1 - 2/(1 + (-1)^(1/4)*Sqrt[c]*x)] - ((-1)^(1/4)*b^2*Sqrt[c]*PolyLog[2, 1 - (Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/2 + (-1)^(3/4)*b^2*Sqrt[c]*PolyLog[2, 1 - 2/(1 - (-1)^(3/4)*Sqrt[c]*x)] + (-1)^(3/4)*b^2*Sqrt[c]*PolyLog[2, 1 - 2/(1 + (-1)^(3/4)*Sqrt[c]*x)] - ((-1)^(3/4)*b^2*Sqrt[c]*PolyLog[2, 1 + (Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/2 - ((-1)^(3/4)*b^2*Sqrt[c]*PolyLog[2, 1 - ((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/2 - ((-1)^(1/4)*b^2*Sqrt[c]*PolyLog[2, 1 - ((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/2","A",47,23,16,1.438,1,"{5035, 2457, 203, 2470, 12, 4920, 4854, 2402, 2315, 2455, 6742, 206, 30, 2557, 205, 4928, 4856, 2447, 208, 5992, 5920, 5984, 5918}"
84,1,1360,0,2.2273179,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{x^4} \, dx","Int[(a + b*ArcTan[c*x^2])^2/x^4,x]","\frac{1}{3} (-1)^{3/4} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 b^2-\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 b^2+\frac{\log ^2\left(i c x^2+1\right) b^2}{12 x^3}-\frac{4}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) b^2-\frac{4}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) b^2+\frac{2}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) b^2-\frac{2}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+\frac{2}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) b^2-\frac{2}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right) b^2-\frac{i c \log \left(1-i c x^2\right) b^2}{3 x}-\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) b^2-\frac{\log \left(1-i c x^2\right) \log \left(i c x^2+1\right) b^2}{6 x^3}+\frac{2 i c \log \left(i c x^2+1\right) b^2}{3 x}+\frac{1}{3} (-1)^{3/4} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) b^2+\frac{1}{3} (-1)^{3/4} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-\frac{1}{6} (-1)^{3/4} c^{3/2} \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2-\frac{1}{6} \sqrt[4]{-1} c^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right) b^2-\frac{1}{6} \sqrt[4]{-1} c^{3/2} \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2-\frac{1}{6} (-1)^{3/4} c^{3/2} \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+\frac{2}{3} (-1)^{3/4} a c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) b-\frac{1}{3} (-1)^{3/4} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \left(2 a+i b \log \left(1-i c x^2\right)\right) b-\frac{c \left(2 a+i b \log \left(1-i c x^2\right)\right) b}{3 x}+\frac{i a \log \left(i c x^2+1\right) b}{3 x^3}-\frac{2 a c b}{3 x}-\frac{\left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{12 x^3}","\frac{1}{3} (-1)^{3/4} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 b^2-\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 b^2+\frac{\log ^2\left(i c x^2+1\right) b^2}{12 x^3}-\frac{4}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) b^2-\frac{4}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) b^2+\frac{2}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) b^2-\frac{2}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+\frac{2}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) b^2-\frac{2}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right) b^2-\frac{i c \log \left(1-i c x^2\right) b^2}{3 x}-\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) b^2-\frac{\log \left(1-i c x^2\right) \log \left(i c x^2+1\right) b^2}{6 x^3}+\frac{2 i c \log \left(i c x^2+1\right) b^2}{3 x}+\frac{1}{3} (-1)^{3/4} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) b^2+\frac{1}{3} (-1)^{3/4} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2-\frac{1}{6} (-1)^{3/4} c^{3/2} \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) b^2+\frac{1}{3} \sqrt[4]{-1} c^{3/2} \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2-\frac{1}{6} \sqrt[4]{-1} c^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right) b^2-\frac{1}{6} \sqrt[4]{-1} c^{3/2} \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) b^2-\frac{1}{6} (-1)^{3/4} c^{3/2} \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) b^2+\frac{2}{3} (-1)^{3/4} a c^{3/2} \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) b-\frac{1}{3} (-1)^{3/4} c^{3/2} \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \left(2 a+i b \log \left(1-i c x^2\right)\right) b-\frac{c \left(2 a+i b \log \left(1-i c x^2\right)\right) b}{3 x}+\frac{i a \log \left(i c x^2+1\right) b}{3 x^3}-\frac{2 a c b}{3 x}-\frac{\left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{12 x^3}",1,"(-2*a*b*c)/(3*x) - (4*(-1)^(1/4)*b^2*c^(3/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x])/3 + ((-1)^(3/4)*b^2*c^(3/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]^2)/3 + (2*(-1)^(3/4)*a*b*c^(3/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x])/3 - (4*(-1)^(1/4)*b^2*c^(3/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x])/3 - ((-1)^(1/4)*b^2*c^(3/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]^2)/3 + (2*(-1)^(1/4)*b^2*c^(3/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/3 - (2*(-1)^(1/4)*b^2*c^(3/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/3 + ((-1)^(1/4)*b^2*c^(3/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[(Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/3 + (2*(-1)^(1/4)*b^2*c^(3/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/3 - (2*(-1)^(1/4)*b^2*c^(3/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/3 + ((-1)^(1/4)*b^2*c^(3/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[-((Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x))])/3 + ((-1)^(1/4)*b^2*c^(3/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/3 + ((-1)^(1/4)*b^2*c^(3/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/3 - ((I/3)*b^2*c*Log[1 - I*c*x^2])/x - ((-1)^(1/4)*b^2*c^(3/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2])/3 - (b*c*(2*a + I*b*Log[1 - I*c*x^2]))/(3*x) - ((-1)^(3/4)*b*c^(3/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*(2*a + I*b*Log[1 - I*c*x^2]))/3 - (2*a + I*b*Log[1 - I*c*x^2])^2/(12*x^3) + ((I/3)*a*b*Log[1 + I*c*x^2])/x^3 + (((2*I)/3)*b^2*c*Log[1 + I*c*x^2])/x - ((-1)^(1/4)*b^2*c^(3/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/3 + ((-1)^(1/4)*b^2*c^(3/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/3 - (b^2*Log[1 - I*c*x^2]*Log[1 + I*c*x^2])/(6*x^3) + (b^2*Log[1 + I*c*x^2]^2)/(12*x^3) + ((-1)^(3/4)*b^2*c^(3/2)*PolyLog[2, 1 - 2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/3 + ((-1)^(3/4)*b^2*c^(3/2)*PolyLog[2, 1 - 2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/3 - ((-1)^(3/4)*b^2*c^(3/2)*PolyLog[2, 1 - (Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/6 + ((-1)^(1/4)*b^2*c^(3/2)*PolyLog[2, 1 - 2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/3 + ((-1)^(1/4)*b^2*c^(3/2)*PolyLog[2, 1 - 2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/3 - ((-1)^(1/4)*b^2*c^(3/2)*PolyLog[2, 1 + (Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/6 - ((-1)^(1/4)*b^2*c^(3/2)*PolyLog[2, 1 - ((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/6 - ((-1)^(3/4)*b^2*c^(3/2)*PolyLog[2, 1 - ((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/6","A",64,25,16,1.562,1,"{5035, 2457, 2476, 2455, 203, 205, 2470, 12, 4920, 4854, 2402, 2315, 325, 6742, 206, 30, 2557, 4928, 4856, 2447, 208, 5992, 5920, 5984, 5918}"
85,1,1444,0,2.4265725,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{x^6} \, dx","Int[(a + b*ArcTan[c*x^2])^2/x^6,x]","-\frac{1}{5} \sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 c^{5/2}+\frac{1}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 c^{5/2}-\frac{4}{15} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) c^{5/2}+\frac{4}{15} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) c^{5/2}+\frac{2}{5} \sqrt[4]{-1} a b \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) c^{5/2}+\frac{2}{5} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) c^{5/2}-\frac{2}{5} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{5} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}-\frac{2}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) c^{5/2}+\frac{2}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{5} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right) c^{5/2}+\frac{1}{5} \sqrt[4]{-1} b \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \left(2 a+i b \log \left(1-i c x^2\right)\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) c^{5/2}-\frac{1}{5} \sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) c^{5/2}-\frac{1}{5} \sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{10} \sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{10} (-1)^{3/4} b^2 \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right) c^{5/2}+\frac{1}{10} (-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{10} \sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}-\frac{b^2 \log \left(1-i c x^2\right) c^2}{5 x}-\frac{i b \left(2 a+i b \log \left(1-i c x^2\right)\right) c^2}{5 x}-\frac{8 b^2 c^2}{15 x}+\frac{2 i a b c^2}{5 x}-\frac{i b^2 \log \left(1-i c x^2\right) c}{15 x^3}-\frac{b \left(2 a+i b \log \left(1-i c x^2\right)\right) c}{15 x^3}+\frac{2 i b^2 \log \left(i c x^2+1\right) c}{15 x^3}-\frac{2 a b c}{15 x^3}-\frac{\left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{20 x^5}+\frac{b^2 \log ^2\left(i c x^2+1\right)}{20 x^5}-\frac{b^2 \log \left(1-i c x^2\right) \log \left(i c x^2+1\right)}{10 x^5}+\frac{i a b \log \left(i c x^2+1\right)}{5 x^5}","-\frac{1}{5} \sqrt[4]{-1} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 c^{5/2}+\frac{1}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right)^2 c^{5/2}-\frac{4}{15} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) c^{5/2}+\frac{4}{15} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) c^{5/2}+\frac{2}{5} \sqrt[4]{-1} a b \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) c^{5/2}+\frac{2}{5} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) c^{5/2}-\frac{2}{5} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{5} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}-\frac{2}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) c^{5/2}+\frac{2}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(-\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{5} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(1-i c x^2\right) c^{5/2}+\frac{1}{5} \sqrt[4]{-1} b \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \left(2 a+i b \log \left(1-i c x^2\right)\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \tan ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{c} x\right) \log \left(i c x^2+1\right) c^{5/2}-\frac{1}{5} \sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-\sqrt[4]{-1} \sqrt{c} x}\right) c^{5/2}-\frac{1}{5} \sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{2}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{10} \sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{\sqrt{2} \left(\sqrt{c} x+\sqrt[4]{-1}\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{1-(-1)^{3/4} \sqrt{c} x}\right) c^{5/2}-\frac{1}{5} (-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{2}{(-1)^{3/4} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{10} (-1)^{3/4} b^2 \text{PolyLog}\left(2,\frac{\sqrt{2} \left(\sqrt{c} x+(-1)^{3/4}\right)}{(-1)^{3/4} \sqrt{c} x+1}+1\right) c^{5/2}+\frac{1}{10} (-1)^{3/4} b^2 \text{PolyLog}\left(2,1-\frac{(1+i) \left(\sqrt[4]{-1} \sqrt{c} x+1\right)}{(-1)^{3/4} \sqrt{c} x+1}\right) c^{5/2}+\frac{1}{10} \sqrt[4]{-1} b^2 \text{PolyLog}\left(2,1-\frac{(1-i) \left((-1)^{3/4} \sqrt{c} x+1\right)}{\sqrt[4]{-1} \sqrt{c} x+1}\right) c^{5/2}-\frac{b^2 \log \left(1-i c x^2\right) c^2}{5 x}-\frac{i b \left(2 a+i b \log \left(1-i c x^2\right)\right) c^2}{5 x}-\frac{8 b^2 c^2}{15 x}+\frac{2 i a b c^2}{5 x}-\frac{i b^2 \log \left(1-i c x^2\right) c}{15 x^3}-\frac{b \left(2 a+i b \log \left(1-i c x^2\right)\right) c}{15 x^3}+\frac{2 i b^2 \log \left(i c x^2+1\right) c}{15 x^3}-\frac{2 a b c}{15 x^3}-\frac{\left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{20 x^5}+\frac{b^2 \log ^2\left(i c x^2+1\right)}{20 x^5}-\frac{b^2 \log \left(1-i c x^2\right) \log \left(i c x^2+1\right)}{10 x^5}+\frac{i a b \log \left(i c x^2+1\right)}{5 x^5}",1,"(-2*a*b*c)/(15*x^3) + (((2*I)/5)*a*b*c^2)/x - (8*b^2*c^2)/(15*x) - (4*(-1)^(3/4)*b^2*c^(5/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x])/15 - ((-1)^(1/4)*b^2*c^(5/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]^2)/5 + (2*(-1)^(1/4)*a*b*c^(5/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x])/5 + (4*(-1)^(3/4)*b^2*c^(5/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x])/15 + ((-1)^(3/4)*b^2*c^(5/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]^2)/5 + (2*(-1)^(3/4)*b^2*c^(5/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/5 - (2*(-1)^(3/4)*b^2*c^(5/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/5 + ((-1)^(3/4)*b^2*c^(5/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[(Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/5 - (2*(-1)^(3/4)*b^2*c^(5/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/5 + (2*(-1)^(3/4)*b^2*c^(5/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/5 - ((-1)^(3/4)*b^2*c^(5/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[-((Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x))])/5 - ((-1)^(3/4)*b^2*c^(5/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/5 + ((-1)^(3/4)*b^2*c^(5/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/5 - ((I/15)*b^2*c*Log[1 - I*c*x^2])/x^3 - (b^2*c^2*Log[1 - I*c*x^2])/(5*x) + ((-1)^(3/4)*b^2*c^(5/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 - I*c*x^2])/5 - (b*c*(2*a + I*b*Log[1 - I*c*x^2]))/(15*x^3) - ((I/5)*b*c^2*(2*a + I*b*Log[1 - I*c*x^2]))/x + ((-1)^(1/4)*b*c^(5/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*(2*a + I*b*Log[1 - I*c*x^2]))/5 - (2*a + I*b*Log[1 - I*c*x^2])^2/(20*x^5) + ((I/5)*a*b*Log[1 + I*c*x^2])/x^5 + (((2*I)/15)*b^2*c*Log[1 + I*c*x^2])/x^3 - ((-1)^(3/4)*b^2*c^(5/2)*ArcTan[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/5 - ((-1)^(3/4)*b^2*c^(5/2)*ArcTanh[(-1)^(3/4)*Sqrt[c]*x]*Log[1 + I*c*x^2])/5 - (b^2*Log[1 - I*c*x^2]*Log[1 + I*c*x^2])/(10*x^5) + (b^2*Log[1 + I*c*x^2]^2)/(20*x^5) - ((-1)^(1/4)*b^2*c^(5/2)*PolyLog[2, 1 - 2/(1 - (-1)^(1/4)*Sqrt[c]*x)])/5 - ((-1)^(1/4)*b^2*c^(5/2)*PolyLog[2, 1 - 2/(1 + (-1)^(1/4)*Sqrt[c]*x)])/5 + ((-1)^(1/4)*b^2*c^(5/2)*PolyLog[2, 1 - (Sqrt[2]*((-1)^(1/4) + Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/10 - ((-1)^(3/4)*b^2*c^(5/2)*PolyLog[2, 1 - 2/(1 - (-1)^(3/4)*Sqrt[c]*x)])/5 - ((-1)^(3/4)*b^2*c^(5/2)*PolyLog[2, 1 - 2/(1 + (-1)^(3/4)*Sqrt[c]*x)])/5 + ((-1)^(3/4)*b^2*c^(5/2)*PolyLog[2, 1 + (Sqrt[2]*((-1)^(3/4) + Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/10 + ((-1)^(3/4)*b^2*c^(5/2)*PolyLog[2, 1 - ((1 + I)*(1 + (-1)^(1/4)*Sqrt[c]*x))/(1 + (-1)^(3/4)*Sqrt[c]*x)])/10 + ((-1)^(1/4)*b^2*c^(5/2)*PolyLog[2, 1 - ((1 - I)*(1 + (-1)^(3/4)*Sqrt[c]*x))/(1 + (-1)^(1/4)*Sqrt[c]*x)])/10","A",77,25,16,1.562,1,"{5035, 2457, 2476, 2455, 325, 203, 205, 2470, 12, 4920, 4854, 2402, 2315, 6742, 206, 30, 2557, 4928, 4856, 2447, 208, 5992, 5920, 5984, 5918}"
86,1,951,0,4.7359543,"\int x^3 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3 \, dx","Int[x^3*(a + b*ArcTan[c*x^2])^3,x]","\frac{3}{32} i b^2 \left(2 i a-b \log \left(1-i c x^2\right)\right) \log ^2\left(i c x^2+1\right) x^4+\frac{3}{32} i b \left(2 i a-b \log \left(1-i c x^2\right)\right)^2 \log \left(i c x^2+1\right) x^4+\frac{3 b^2 \left(2 i a-b \log \left(1-i c x^2\right)\right) \log \left(i c x^2+1\right) x^2}{8 c}-\frac{\left(1-i c x^2\right)^2 \left(2 a+i b \log \left(1-i c x^2\right)\right)^3}{32 c^2}+\frac{\left(1-i c x^2\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)^3}{16 c^2}-\frac{i b^3 \left(i c x^2+1\right)^2 \log ^3\left(i c x^2+1\right)}{32 c^2}+\frac{i b^3 \left(i c x^2+1\right) \log ^3\left(i c x^2+1\right)}{16 c^2}+\frac{3 i b \left(1-i c x^2\right)^2 \left(2 i a-b \log \left(1-i c x^2\right)\right)^2}{64 c^2}+\frac{3 i b \left(1-i c x^2\right)^2 \left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{64 c^2}-\frac{3 i b \left(1-i c x^2\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{16 c^2}-\frac{3 i b^3 \left(i c x^2+1\right) \log ^2\left(i c x^2+1\right)}{16 c^2}-\frac{3 b^2 \left(2 a+i b \log \left(1-i c x^2\right)\right) \log ^2\left(i c x^2+1\right)}{32 c^2}+\frac{3 i b^2 \left(1-i c x^2\right)^2 \left(2 i a-b \log \left(1-i c x^2\right)\right)}{64 c^2}+\frac{3 b^2 \left(1-i c x^2\right)^2 \left(2 a+i b \log \left(1-i c x^2\right)\right)}{64 c^2}+\frac{3 i b \left(2 i a-b \log \left(1-i c x^2\right)\right)^2 \log \left(\frac{1}{2} \left(i c x^2+1\right)\right)}{32 c^2}+\frac{3 i b \left(2 a+i b \log \left(1-i c x^2\right)\right)^2 \log \left(\frac{1}{2} \left(i c x^2+1\right)\right)}{32 c^2}-\frac{3 i b^2 \left(2 i a-b \log \left(1-i c x^2\right)\right) \log \left(\frac{1}{2} \left(i c x^2+1\right)\right)}{8 c^2}-\frac{3 i b \left(2 a+i b \log \left(1-i c x^2\right)\right)^2 \log \left(i c x^2+1\right)}{32 c^2}-\frac{3 i b^3 \log \left(\frac{1}{2} \left(1-i c x^2\right)\right) \log \left(i c x^2+1\right)}{8 c^2}-\frac{3 i b^2 \left(2 i a-b \log \left(1-i c x^2\right)\right) \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right)}{16 c^2}-\frac{3 b^2 \left(2 a+i b \log \left(1-i c x^2\right)\right) \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right)}{16 c^2}+\frac{3 i b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right)}{8 c^2}-\frac{3 i b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(i c x^2+1\right)\right)}{8 c^2}","-\frac{3 i b^3 \text{PolyLog}\left(2,1-\frac{2}{1+i c x^2}\right)}{4 c^2}-\frac{3 b^2 \log \left(\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{2 c^2}+\frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^3}{4 c^2}-\frac{3 i b \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{4 c^2}+\frac{1}{4} x^4 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3-\frac{3 b x^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{4 c}",1,"(((3*I)/64)*b^2*(1 - I*c*x^2)^2*((2*I)*a - b*Log[1 - I*c*x^2]))/c^2 + (((3*I)/64)*b*(1 - I*c*x^2)^2*((2*I)*a - b*Log[1 - I*c*x^2])^2)/c^2 + (3*b^2*(1 - I*c*x^2)^2*(2*a + I*b*Log[1 - I*c*x^2]))/(64*c^2) - (((3*I)/16)*b*(1 - I*c*x^2)*(2*a + I*b*Log[1 - I*c*x^2])^2)/c^2 + (((3*I)/64)*b*(1 - I*c*x^2)^2*(2*a + I*b*Log[1 - I*c*x^2])^2)/c^2 + ((1 - I*c*x^2)*(2*a + I*b*Log[1 - I*c*x^2])^3)/(16*c^2) - ((1 - I*c*x^2)^2*(2*a + I*b*Log[1 - I*c*x^2])^3)/(32*c^2) - (((3*I)/8)*b^2*((2*I)*a - b*Log[1 - I*c*x^2])*Log[(1 + I*c*x^2)/2])/c^2 + (((3*I)/32)*b*((2*I)*a - b*Log[1 - I*c*x^2])^2*Log[(1 + I*c*x^2)/2])/c^2 + (((3*I)/32)*b*(2*a + I*b*Log[1 - I*c*x^2])^2*Log[(1 + I*c*x^2)/2])/c^2 - (((3*I)/8)*b^3*Log[(1 - I*c*x^2)/2]*Log[1 + I*c*x^2])/c^2 + (3*b^2*x^2*((2*I)*a - b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2])/(8*c) + ((3*I)/32)*b*x^4*((2*I)*a - b*Log[1 - I*c*x^2])^2*Log[1 + I*c*x^2] - (((3*I)/32)*b*(2*a + I*b*Log[1 - I*c*x^2])^2*Log[1 + I*c*x^2])/c^2 - (((3*I)/16)*b^3*(1 + I*c*x^2)*Log[1 + I*c*x^2]^2)/c^2 + ((3*I)/32)*b^2*x^4*((2*I)*a - b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2]^2 - (3*b^2*(2*a + I*b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2]^2)/(32*c^2) + ((I/16)*b^3*(1 + I*c*x^2)*Log[1 + I*c*x^2]^3)/c^2 - ((I/32)*b^3*(1 + I*c*x^2)^2*Log[1 + I*c*x^2]^3)/c^2 + (((3*I)/8)*b^3*PolyLog[2, (1 - I*c*x^2)/2])/c^2 - (((3*I)/16)*b^2*((2*I)*a - b*Log[1 - I*c*x^2])*PolyLog[2, (1 - I*c*x^2)/2])/c^2 - (3*b^2*(2*a + I*b*Log[1 - I*c*x^2])*PolyLog[2, (1 - I*c*x^2)/2])/(16*c^2) - (((3*I)/8)*b^3*PolyLog[2, (1 + I*c*x^2)/2])/c^2","B",155,30,16,1.875,0,"{5035, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2439, 2416, 2396, 2433, 2374, 6589, 2411, 43, 2334, 12, 14, 2301, 6742, 2395, 2394, 2393, 2391, 2375, 2317, 2430, 2425}"
87,1,545,0,2.5449973,"\int x \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3 \, dx","Int[x*(a + b*ArcTan[c*x^2])^3,x]","-\frac{3 b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^2\right)\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)}{4 c}-\frac{3 b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(1-i c x^2\right)\right)}{4 c}-\frac{3 b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(1+i c x^2\right)\right)}{4 c}+\frac{3 b^3 \log \left(1+i c x^2\right) \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^2\right)\right)}{4 c}+\frac{3}{16} i b^2 x^2 \log ^2\left(1+i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)+\frac{3 b^2 \log ^2\left(1+i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)}{16 c}+\frac{3 b \left(1-i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)^2}{16 c}+\frac{3 b \left(1-i c x^2\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)^2}{16 c}+\frac{3 b \log \left(\frac{1}{2} \left(1+i c x^2\right)\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)^2}{8 c}+\frac{3}{16} i b x^2 \log \left(1+i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)^2-\frac{3 b \log \left(1+i c x^2\right) \left(2 i a-b \log \left(1-i c x^2\right)\right)^2}{16 c}+\frac{i \left(1-i c x^2\right) \left(2 a+i b \log \left(1-i c x^2\right)\right)^3}{16 c}+\frac{b^3 \left(1+i c x^2\right) \log ^3\left(1+i c x^2\right)}{16 c}+\frac{3 b^3 \log \left(\frac{1}{2} \left(1-i c x^2\right)\right) \log ^2\left(1+i c x^2\right)}{8 c}","\frac{3 i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{2 c}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^2}\right)}{4 c}+\frac{1}{2} x^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3+\frac{i \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3}{2 c}+\frac{3 b \log \left(\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{2 c}",1,"(3*b*(1 - I*c*x^2)*((2*I)*a - b*Log[1 - I*c*x^2])^2)/(16*c) + (3*b*(1 - I*c*x^2)*(2*a + I*b*Log[1 - I*c*x^2])^2)/(16*c) + ((I/16)*(1 - I*c*x^2)*(2*a + I*b*Log[1 - I*c*x^2])^3)/c + (3*b*((2*I)*a - b*Log[1 - I*c*x^2])^2*Log[(1 + I*c*x^2)/2])/(8*c) - (3*b*((2*I)*a - b*Log[1 - I*c*x^2])^2*Log[1 + I*c*x^2])/(16*c) + ((3*I)/16)*b*x^2*((2*I)*a - b*Log[1 - I*c*x^2])^2*Log[1 + I*c*x^2] + (3*b^3*Log[(1 - I*c*x^2)/2]*Log[1 + I*c*x^2]^2)/(8*c) + (3*b^2*((2*I)*a - b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2]^2)/(16*c) + ((3*I)/16)*b^2*x^2*((2*I)*a - b*Log[1 - I*c*x^2])*Log[1 + I*c*x^2]^2 + (b^3*(1 + I*c*x^2)*Log[1 + I*c*x^2]^3)/(16*c) - (3*b^2*((2*I)*a - b*Log[1 - I*c*x^2])*PolyLog[2, (1 - I*c*x^2)/2])/(4*c) + (3*b^3*Log[1 + I*c*x^2]*PolyLog[2, (1 + I*c*x^2)/2])/(4*c) - (3*b^3*PolyLog[3, (1 - I*c*x^2)/2])/(4*c) - (3*b^3*PolyLog[3, (1 + I*c*x^2)/2])/(4*c)","B",82,23,14,1.643,0,"{5035, 2454, 2389, 2296, 2295, 6715, 2430, 2416, 2396, 2433, 2374, 6589, 2411, 2346, 2301, 6742, 43, 2394, 2393, 2391, 2375, 2317, 2425}"
88,1,229,0,0.5285023,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^3}{x} \, dx","Int[(a + b*ArcTan[c*x^2])^3/x,x]","-\frac{3}{4} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{3}{4} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)-\frac{3}{4} i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2+\frac{3}{4} i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2+\frac{3}{8} i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+i c x^2}\right)-\frac{3}{8} i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+i c x^2}\right)+\tanh ^{-1}\left(1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3","-\frac{3}{4} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{3}{4} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)-\frac{3}{4} i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2+\frac{3}{4} i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2+\frac{3}{8} i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+i c x^2}\right)-\frac{3}{8} i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+i c x^2}\right)+\tanh ^{-1}\left(1-\frac{2}{1+i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3",1,"(a + b*ArcTan[c*x^2])^3*ArcTanh[1 - 2/(1 + I*c*x^2)] - ((3*I)/4)*b*(a + b*ArcTan[c*x^2])^2*PolyLog[2, 1 - 2/(1 + I*c*x^2)] + ((3*I)/4)*b*(a + b*ArcTan[c*x^2])^2*PolyLog[2, -1 + 2/(1 + I*c*x^2)] - (3*b^2*(a + b*ArcTan[c*x^2])*PolyLog[3, 1 - 2/(1 + I*c*x^2)])/4 + (3*b^2*(a + b*ArcTan[c*x^2])*PolyLog[3, -1 + 2/(1 + I*c*x^2)])/4 + ((3*I)/8)*b^3*PolyLog[4, 1 - 2/(1 + I*c*x^2)] - ((3*I)/8)*b^3*PolyLog[4, -1 + 2/(1 + I*c*x^2)]","A",9,7,16,0.4375,1,"{5031, 4850, 4988, 4884, 4994, 4998, 6610}"
89,0,0,0,0.8310096,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^3}{x^3} \, dx","Int[(a + b*ArcTan[c*x^2])^3/x^3,x]","\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^3}{x^3} \, dx","-\frac{3}{2} i b^2 c \text{PolyLog}\left(2,-1+\frac{2}{1-i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)+\frac{3}{4} b^3 c \text{PolyLog}\left(3,-1+\frac{2}{1-i c x^2}\right)-\frac{1}{2} i c \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3-\frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^3}{2 x^2}+\frac{3}{2} b c \log \left(2-\frac{2}{1-i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2",1,"(3*b*c*Log[I*c*x^2]*(2*a + I*b*Log[1 - I*c*x^2])^2)/16 - ((1 - I*c*x^2)*(2*a + I*b*Log[1 - I*c*x^2])^3)/(16*x^2) - (3*b^3*c*Log[(-I)*c*x^2]*Log[1 + I*c*x^2]^2)/16 - ((I/16)*b^3*(1 + I*c*x^2)*Log[1 + I*c*x^2]^3)/x^2 + ((3*I)/8)*b^2*c*(2*a + I*b*Log[1 - I*c*x^2])*PolyLog[2, 1 - I*c*x^2] - (3*b^3*c*Log[1 + I*c*x^2]*PolyLog[2, 1 + I*c*x^2])/8 + (3*b^3*c*PolyLog[3, 1 - I*c*x^2])/8 + (3*b^3*c*PolyLog[3, 1 + I*c*x^2])/8 + ((3*I)/16)*b*Defer[Subst][Defer[Int][(((-2*I)*a + b*Log[1 - I*c*x])^2*Log[1 + I*c*x])/x^2, x], x, x^2] - ((3*I)/16)*b^2*Defer[Subst][Defer[Int][(((-2*I)*a + b*Log[1 - I*c*x])*Log[1 + I*c*x]^2)/x^2, x], x, x^2]","F",0,0,0,0,-1,"{}"
90,0,0,0,1.65887,"\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^3}{x^5} \, dx","Int[(a + b*ArcTan[c*x^2])^3/x^5,x]","\int \frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^3}{x^5} \, dx","-\frac{3}{4} i b^3 c^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x^2}\right)+\frac{3}{2} b^2 c^2 \log \left(2-\frac{2}{1-i c x^2}\right) \left(a+b \tan ^{-1}\left(c x^2\right)\right)-\frac{3}{4} i b c^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2-\frac{1}{4} c^2 \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3-\frac{3 b c \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2}{4 x^2}-\frac{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^3}{4 x^4}",1,"(3*a*b^2*c^2*Log[x])/4 - (3*b*c*(1 - I*c*x^2)*(2*a + I*b*Log[1 - I*c*x^2])^2)/(32*x^2) + ((3*I)/32)*b*c^2*Log[I*c*x^2]*(2*a + I*b*Log[1 - I*c*x^2])^2 - (c^2*(2*a + I*b*Log[1 - I*c*x^2])^3)/32 - (2*a + I*b*Log[1 - I*c*x^2])^3/(32*x^4) + (3*b^3*c*(1 + I*c*x^2)*Log[1 + I*c*x^2]^2)/(32*x^2) + ((3*I)/32)*b^3*c^2*Log[(-I)*c*x^2]*Log[1 + I*c*x^2]^2 - (I/32)*b^3*c^2*Log[1 + I*c*x^2]^3 - ((I/32)*b^3*Log[1 + I*c*x^2]^3)/x^4 + ((3*I)/16)*b^3*c^2*PolyLog[2, (-I)*c*x^2] - ((3*I)/16)*b^3*c^2*PolyLog[2, I*c*x^2] - (3*b^2*c^2*(2*a + I*b*Log[1 - I*c*x^2])*PolyLog[2, 1 - I*c*x^2])/16 + ((3*I)/16)*b^3*c^2*Log[1 + I*c*x^2]*PolyLog[2, 1 + I*c*x^2] + ((3*I)/16)*b^3*c^2*PolyLog[3, 1 - I*c*x^2] - ((3*I)/16)*b^3*c^2*PolyLog[3, 1 + I*c*x^2] + ((3*I)/16)*b*Defer[Subst][Defer[Int][(((-2*I)*a + b*Log[1 - I*c*x])^2*Log[1 + I*c*x])/x^3, x], x, x^2] - ((3*I)/16)*b^2*Defer[Subst][Defer[Int][(((-2*I)*a + b*Log[1 - I*c*x])*Log[1 + I*c*x]^2)/x^3, x], x, x^2]","F",0,0,0,0,-1,"{}"
91,0,0,0,0.0233255,"\int (d x)^m \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcTan[c*x^2])^3,x]","\int (d x)^m \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \tan ^{-1}\left(c x^2\right)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTan[c*x^2])^3, x]","A",0,0,0,0,-1,"{}"
92,0,0,0,0.0235031,"\int (d x)^m \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcTan[c*x^2])^2,x]","\int (d x)^m \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \tan ^{-1}\left(c x^2\right)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTan[c*x^2])^2, x]","A",0,0,0,0,-1,"{}"
93,1,75,0,0.0406812,"\int (d x)^m \left(a+b \tan ^{-1}\left(c x^2\right)\right) \, dx","Int[(d*x)^m*(a + b*ArcTan[c*x^2]),x]","\frac{(d x)^{m+1} \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{d (m+1)}-\frac{2 b c (d x)^{m+3} \, _2F_1\left(1,\frac{m+3}{4};\frac{m+7}{4};-c^2 x^4\right)}{d^3 (m+1) (m+3)}","\frac{(d x)^{m+1} \left(a+b \tan ^{-1}\left(c x^2\right)\right)}{d (m+1)}-\frac{2 b c (d x)^{m+3} \, _2F_1\left(1,\frac{m+3}{4};\frac{m+7}{4};-c^2 x^4\right)}{d^3 (m+1) (m+3)}",1,"((d*x)^(1 + m)*(a + b*ArcTan[c*x^2]))/(d*(1 + m)) - (2*b*c*(d*x)^(3 + m)*Hypergeometric2F1[1, (3 + m)/4, (7 + m)/4, -(c^2*x^4)])/(d^3*(1 + m)*(3 + m))","A",3,3,16,0.1875,1,"{5033, 16, 364}"
94,0,0,0,0.0268812,"\int \frac{(d x)^m}{a+b \tan ^{-1}\left(c x^2\right)} \, dx","Int[(d*x)^m/(a + b*ArcTan[c*x^2]),x]","\int \frac{(d x)^m}{a+b \tan ^{-1}\left(c x^2\right)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \tan ^{-1}\left(c x^2\right)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTan[c*x^2]), x]","A",0,0,0,0,-1,"{}"
95,0,0,0,0.0255398,"\int \frac{(d x)^m}{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcTan[c*x^2])^2,x]","\int \frac{(d x)^m}{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \tan ^{-1}\left(c x^2\right)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTan[c*x^2])^2, x]","A",0,0,0,0,-1,"{}"
96,1,54,0,0.0388067,"\int x^{11} \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[x^11*(a + b*ArcTan[c*x^3]),x]","\frac{1}{12} x^{12} \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{b x^3}{12 c^3}-\frac{b \tan ^{-1}\left(c x^3\right)}{12 c^4}-\frac{b x^9}{36 c}","\frac{1}{12} x^{12} \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{b x^3}{12 c^3}-\frac{b \tan ^{-1}\left(c x^3\right)}{12 c^4}-\frac{b x^9}{36 c}",1,"(b*x^3)/(12*c^3) - (b*x^9)/(36*c) - (b*ArcTan[c*x^3])/(12*c^4) + (x^12*(a + b*ArcTan[c*x^3]))/12","A",5,4,14,0.2857,1,"{5033, 275, 302, 203}"
97,1,47,0,0.036474,"\int x^8 \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[x^8*(a + b*ArcTan[c*x^3]),x]","\frac{1}{9} x^9 \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(c^2 x^6+1\right)}{18 c^3}-\frac{b x^6}{18 c}","\frac{1}{9} x^9 \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(c^2 x^6+1\right)}{18 c^3}-\frac{b x^6}{18 c}",1,"-(b*x^6)/(18*c) + (x^9*(a + b*ArcTan[c*x^3]))/9 + (b*Log[1 + c^2*x^6])/(18*c^3)","A",4,3,14,0.2143,1,"{5033, 266, 43}"
98,1,43,0,0.029365,"\int x^5 \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[x^5*(a + b*ArcTan[c*x^3]),x]","\frac{1}{6} x^6 \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{b \tan ^{-1}\left(c x^3\right)}{6 c^2}-\frac{b x^3}{6 c}","\frac{1}{6} x^6 \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{b \tan ^{-1}\left(c x^3\right)}{6 c^2}-\frac{b x^3}{6 c}",1,"-(b*x^3)/(6*c) + (b*ArcTan[c*x^3])/(6*c^2) + (x^6*(a + b*ArcTan[c*x^3]))/6","A",4,4,14,0.2857,1,"{5033, 275, 321, 203}"
99,1,36,0,0.0206472,"\int x^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[x^2*(a + b*ArcTan[c*x^3]),x]","\frac{1}{3} x^3 \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{b \log \left(c^2 x^6+1\right)}{6 c}","\frac{1}{3} x^3 \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{b \log \left(c^2 x^6+1\right)}{6 c}",1,"(x^3*(a + b*ArcTan[c*x^3]))/3 - (b*Log[1 + c^2*x^6])/(6*c)","A",2,2,14,0.1429,1,"{5033, 260}"
100,1,39,0,0.0503424,"\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{x} \, dx","Int[(a + b*ArcTan[c*x^3])/x,x]","\frac{1}{6} i b \text{PolyLog}\left(2,-i c x^3\right)-\frac{1}{6} i b \text{PolyLog}\left(2,i c x^3\right)+a \log (x)","\frac{1}{6} i b \text{PolyLog}\left(2,-i c x^3\right)-\frac{1}{6} i b \text{PolyLog}\left(2,i c x^3\right)+a \log (x)",1,"a*Log[x] + (I/6)*b*PolyLog[2, (-I)*c*x^3] - (I/6)*b*PolyLog[2, I*c*x^3]","A",4,3,14,0.2143,1,"{5031, 4848, 2391}"
101,1,39,0,0.0245742,"\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{x^4} \, dx","Int[(a + b*ArcTan[c*x^3])/x^4,x]","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{3 x^3}-\frac{1}{6} b c \log \left(c^2 x^6+1\right)+b c \log (x)","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{3 x^3}-\frac{1}{6} b c \log \left(c^2 x^6+1\right)+b c \log (x)",1,"-(a + b*ArcTan[c*x^3])/(3*x^3) + b*c*Log[x] - (b*c*Log[1 + c^2*x^6])/6","A",5,5,14,0.3571,1,"{5033, 266, 36, 29, 31}"
102,1,41,0,0.0266583,"\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{x^7} \, dx","Int[(a + b*ArcTan[c*x^3])/x^7,x]","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{6 x^6}-\frac{1}{6} b c^2 \tan ^{-1}\left(c x^3\right)-\frac{b c}{6 x^3}","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{6 x^6}-\frac{1}{6} b c^2 \tan ^{-1}\left(c x^3\right)-\frac{b c}{6 x^3}",1,"-(b*c)/(6*x^3) - (b*c^2*ArcTan[c*x^3])/6 - (a + b*ArcTan[c*x^3])/(6*x^6)","A",4,4,14,0.2857,1,"{5033, 275, 325, 203}"
103,1,55,0,0.0350834,"\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{x^{10}} \, dx","Int[(a + b*ArcTan[c*x^3])/x^10,x]","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{9 x^9}+\frac{1}{18} b c^3 \log \left(c^2 x^6+1\right)-\frac{1}{3} b c^3 \log (x)-\frac{b c}{18 x^6}","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{9 x^9}+\frac{1}{18} b c^3 \log \left(c^2 x^6+1\right)-\frac{1}{3} b c^3 \log (x)-\frac{b c}{18 x^6}",1,"-(b*c)/(18*x^6) - (a + b*ArcTan[c*x^3])/(9*x^9) - (b*c^3*Log[x])/3 + (b*c^3*Log[1 + c^2*x^6])/18","A",4,3,14,0.2143,1,"{5033, 266, 44}"
104,1,174,0,0.3247213,"\int x^3 \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[x^3*(a + b*ArcTan[c*x^3]),x]","\frac{1}{4} x^4 \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{\sqrt{3} b \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)}{16 c^{4/3}}+\frac{\sqrt{3} b \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)}{16 c^{4/3}}+\frac{b \tan ^{-1}\left(\sqrt[3]{c} x\right)}{4 c^{4/3}}-\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)}{8 c^{4/3}}+\frac{b \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)}{8 c^{4/3}}-\frac{3 b x}{4 c}","\frac{1}{4} x^4 \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{\sqrt{3} b \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)}{16 c^{4/3}}+\frac{\sqrt{3} b \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)}{16 c^{4/3}}+\frac{b \tan ^{-1}\left(\sqrt[3]{c} x\right)}{4 c^{4/3}}-\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)}{8 c^{4/3}}+\frac{b \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)}{8 c^{4/3}}-\frac{3 b x}{4 c}",1,"(-3*b*x)/(4*c) + (b*ArcTan[c^(1/3)*x])/(4*c^(4/3)) + (x^4*(a + b*ArcTan[c*x^3]))/4 - (b*ArcTan[Sqrt[3] - 2*c^(1/3)*x])/(8*c^(4/3)) + (b*ArcTan[Sqrt[3] + 2*c^(1/3)*x])/(8*c^(4/3)) - (Sqrt[3]*b*Log[1 - Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(16*c^(4/3)) + (Sqrt[3]*b*Log[1 + Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(16*c^(4/3))","A",12,8,14,0.5714,1,"{5033, 321, 209, 634, 618, 204, 628, 203}"
105,1,101,0,0.0980866,"\int \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[a + b*ArcTan[c*x^3],x]","a x+\frac{b \log \left(c^{2/3} x^2+1\right)}{2 \sqrt[3]{c}}-\frac{b \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}+b x \tan ^{-1}\left(c x^3\right)","a x+\frac{b \log \left(c^{2/3} x^2+1\right)}{2 \sqrt[3]{c}}-\frac{b \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)}{4 \sqrt[3]{c}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)}{2 \sqrt[3]{c}}+b x \tan ^{-1}\left(c x^3\right)",1,"a*x + b*x*ArcTan[c*x^3] + (Sqrt[3]*b*ArcTan[(1 - 2*c^(2/3)*x^2)/Sqrt[3]])/(2*c^(1/3)) + (b*Log[1 + c^(2/3)*x^2])/(2*c^(1/3)) - (b*Log[1 - c^(2/3)*x^2 + c^(4/3)*x^4])/(4*c^(1/3))","A",9,8,10,0.8000,1,"{5027, 275, 292, 31, 634, 617, 204, 628}"
106,1,165,0,0.2944405,"\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{x^3} \, dx","Int[(a + b*ArcTan[c*x^3])/x^3,x]","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{2 x^2}-\frac{1}{8} \sqrt{3} b c^{2/3} \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)+\frac{1}{8} \sqrt{3} b c^{2/3} \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)+\frac{1}{2} b c^{2/3} \tan ^{-1}\left(\sqrt[3]{c} x\right)-\frac{1}{4} b c^{2/3} \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)+\frac{1}{4} b c^{2/3} \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{2 x^2}-\frac{1}{8} \sqrt{3} b c^{2/3} \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)+\frac{1}{8} \sqrt{3} b c^{2/3} \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)+\frac{1}{2} b c^{2/3} \tan ^{-1}\left(\sqrt[3]{c} x\right)-\frac{1}{4} b c^{2/3} \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)+\frac{1}{4} b c^{2/3} \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)",1,"(b*c^(2/3)*ArcTan[c^(1/3)*x])/2 - (a + b*ArcTan[c*x^3])/(2*x^2) - (b*c^(2/3)*ArcTan[Sqrt[3] - 2*c^(1/3)*x])/4 + (b*c^(2/3)*ArcTan[Sqrt[3] + 2*c^(1/3)*x])/4 - (Sqrt[3]*b*c^(2/3)*Log[1 - Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/8 + (Sqrt[3]*b*c^(2/3)*Log[1 + Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/8","A",11,7,14,0.5000,1,"{5033, 209, 634, 618, 204, 628, 203}"
107,1,115,0,0.0913579,"\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{x^6} \, dx","Int[(a + b*ArcTan[c*x^3])/x^6,x]","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{5 x^5}+\frac{1}{10} b c^{5/3} \log \left(c^{2/3} x^2+1\right)-\frac{1}{20} b c^{5/3} \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)+\frac{1}{10} \sqrt{3} b c^{5/3} \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)-\frac{3 b c}{10 x^2}","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{5 x^5}+\frac{1}{10} b c^{5/3} \log \left(c^{2/3} x^2+1\right)-\frac{1}{20} b c^{5/3} \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)+\frac{1}{10} \sqrt{3} b c^{5/3} \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)-\frac{3 b c}{10 x^2}",1,"(-3*b*c)/(10*x^2) - (a + b*ArcTan[c*x^3])/(5*x^5) + (Sqrt[3]*b*c^(5/3)*ArcTan[(1 - 2*c^(2/3)*x^2)/Sqrt[3]])/10 + (b*c^(5/3)*Log[1 + c^(2/3)*x^2])/10 - (b*c^(5/3)*Log[1 - c^(2/3)*x^2 + c^(4/3)*x^4])/20","A",9,9,14,0.6429,1,"{5033, 275, 325, 292, 31, 634, 617, 204, 628}"
108,1,176,0,0.4308765,"\int x^7 \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[x^7*(a + b*ArcTan[c*x^3]),x]","\frac{1}{8} x^8 \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{\sqrt{3} b \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)}{32 c^{8/3}}-\frac{\sqrt{3} b \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)}{32 c^{8/3}}+\frac{b \tan ^{-1}\left(\sqrt[3]{c} x\right)}{8 c^{8/3}}-\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)}{16 c^{8/3}}+\frac{b \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)}{16 c^{8/3}}-\frac{3 b x^5}{40 c}","\frac{1}{8} x^8 \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{\sqrt{3} b \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)}{32 c^{8/3}}-\frac{\sqrt{3} b \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)}{32 c^{8/3}}+\frac{b \tan ^{-1}\left(\sqrt[3]{c} x\right)}{8 c^{8/3}}-\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)}{16 c^{8/3}}+\frac{b \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)}{16 c^{8/3}}-\frac{3 b x^5}{40 c}",1,"(-3*b*x^5)/(40*c) + (b*ArcTan[c^(1/3)*x])/(8*c^(8/3)) + (x^8*(a + b*ArcTan[c*x^3]))/8 - (b*ArcTan[Sqrt[3] - 2*c^(1/3)*x])/(16*c^(8/3)) + (b*ArcTan[Sqrt[3] + 2*c^(1/3)*x])/(16*c^(8/3)) + (Sqrt[3]*b*Log[1 - Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(32*c^(8/3)) - (Sqrt[3]*b*Log[1 + Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(32*c^(8/3))","A",12,8,14,0.5714,1,"{5033, 321, 295, 634, 618, 204, 628, 203}"
109,1,117,0,0.0955969,"\int x^4 \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[x^4*(a + b*ArcTan[c*x^3]),x]","\frac{1}{5} x^5 \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(c^{2/3} x^2+1\right)}{10 c^{5/3}}-\frac{b \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)}{20 c^{5/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)}{10 c^{5/3}}-\frac{3 b x^2}{10 c}","\frac{1}{5} x^5 \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{b \log \left(c^{2/3} x^2+1\right)}{10 c^{5/3}}-\frac{b \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)}{20 c^{5/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)}{10 c^{5/3}}-\frac{3 b x^2}{10 c}",1,"(-3*b*x^2)/(10*c) + (x^5*(a + b*ArcTan[c*x^3]))/5 - (Sqrt[3]*b*ArcTan[(1 - 2*c^(2/3)*x^2)/Sqrt[3]])/(10*c^(5/3)) + (b*Log[1 + c^(2/3)*x^2])/(10*c^(5/3)) - (b*Log[1 - c^(2/3)*x^2 + c^(4/3)*x^4])/(20*c^(5/3))","A",9,9,14,0.6429,1,"{5033, 275, 321, 200, 31, 634, 617, 204, 628}"
110,1,165,0,0.3934887,"\int x \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[x*(a + b*ArcTan[c*x^3]),x]","\frac{1}{2} x^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{\sqrt{3} b \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)}{8 c^{2/3}}+\frac{\sqrt{3} b \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{b \tan ^{-1}\left(\sqrt[3]{c} x\right)}{2 c^{2/3}}+\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)}{4 c^{2/3}}-\frac{b \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)}{4 c^{2/3}}","\frac{1}{2} x^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{\sqrt{3} b \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)}{8 c^{2/3}}+\frac{\sqrt{3} b \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)}{8 c^{2/3}}-\frac{b \tan ^{-1}\left(\sqrt[3]{c} x\right)}{2 c^{2/3}}+\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)}{4 c^{2/3}}-\frac{b \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)}{4 c^{2/3}}",1,"-(b*ArcTan[c^(1/3)*x])/(2*c^(2/3)) + (x^2*(a + b*ArcTan[c*x^3]))/2 + (b*ArcTan[Sqrt[3] - 2*c^(1/3)*x])/(4*c^(2/3)) - (b*ArcTan[Sqrt[3] + 2*c^(1/3)*x])/(4*c^(2/3)) - (Sqrt[3]*b*Log[1 - Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(8*c^(2/3)) + (Sqrt[3]*b*Log[1 + Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/(8*c^(2/3))","A",11,7,12,0.5833,1,"{5033, 295, 634, 618, 204, 628, 203}"
111,1,104,0,0.0851211,"\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{x^2} \, dx","Int[(a + b*ArcTan[c*x^3])/x^2,x]","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{x}+\frac{1}{2} b \sqrt[3]{c} \log \left(c^{2/3} x^2+1\right)-\frac{1}{4} b \sqrt[3]{c} \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)-\frac{1}{2} \sqrt{3} b \sqrt[3]{c} \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{x}+\frac{1}{2} b \sqrt[3]{c} \log \left(c^{2/3} x^2+1\right)-\frac{1}{4} b \sqrt[3]{c} \log \left(c^{4/3} x^4-c^{2/3} x^2+1\right)-\frac{1}{2} \sqrt{3} b \sqrt[3]{c} \tan ^{-1}\left(\frac{1-2 c^{2/3} x^2}{\sqrt{3}}\right)",1,"-((a + b*ArcTan[c*x^3])/x) - (Sqrt[3]*b*c^(1/3)*ArcTan[(1 - 2*c^(2/3)*x^2)/Sqrt[3]])/2 + (b*c^(1/3)*Log[1 + c^(2/3)*x^2])/2 - (b*c^(1/3)*Log[1 - c^(2/3)*x^2 + c^(4/3)*x^4])/4","A",8,8,14,0.5714,1,"{5033, 275, 200, 31, 634, 617, 204, 628}"
112,1,174,0,0.4128655,"\int \frac{a+b \tan ^{-1}\left(c x^3\right)}{x^5} \, dx","Int[(a + b*ArcTan[c*x^3])/x^5,x]","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{4 x^4}-\frac{1}{16} \sqrt{3} b c^{4/3} \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)+\frac{1}{16} \sqrt{3} b c^{4/3} \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)-\frac{1}{4} b c^{4/3} \tan ^{-1}\left(\sqrt[3]{c} x\right)+\frac{1}{8} b c^{4/3} \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)-\frac{1}{8} b c^{4/3} \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)-\frac{3 b c}{4 x}","-\frac{a+b \tan ^{-1}\left(c x^3\right)}{4 x^4}-\frac{1}{16} \sqrt{3} b c^{4/3} \log \left(c^{2/3} x^2-\sqrt{3} \sqrt[3]{c} x+1\right)+\frac{1}{16} \sqrt{3} b c^{4/3} \log \left(c^{2/3} x^2+\sqrt{3} \sqrt[3]{c} x+1\right)-\frac{1}{4} b c^{4/3} \tan ^{-1}\left(\sqrt[3]{c} x\right)+\frac{1}{8} b c^{4/3} \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{c} x\right)-\frac{1}{8} b c^{4/3} \tan ^{-1}\left(2 \sqrt[3]{c} x+\sqrt{3}\right)-\frac{3 b c}{4 x}",1,"(-3*b*c)/(4*x) - (b*c^(4/3)*ArcTan[c^(1/3)*x])/4 - (a + b*ArcTan[c*x^3])/(4*x^4) + (b*c^(4/3)*ArcTan[Sqrt[3] - 2*c^(1/3)*x])/8 - (b*c^(4/3)*ArcTan[Sqrt[3] + 2*c^(1/3)*x])/8 - (Sqrt[3]*b*c^(4/3)*Log[1 - Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/16 + (Sqrt[3]*b*c^(4/3)*Log[1 + Sqrt[3]*c^(1/3)*x + c^(2/3)*x^2])/16","A",12,8,14,0.5714,1,"{5033, 325, 295, 634, 618, 204, 628, 203}"
113,1,731,0,1.6545485,"\int x^{11} \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2 \, dx","Int[x^11*(a + b*ArcTan[c*x^3])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)}{24 c^4}-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^3\right)\right)}{24 c^4}+\frac{a b x^3}{12 c^3}-\frac{b x^6 \left(2 i a-b \log \left(1-i c x^3\right)\right)}{48 c^2}+\frac{1}{288} i b \left(-\frac{3 \left(1-i c x^3\right)^4}{c^4}+\frac{16 \left(1-i c x^3\right)^3}{c^4}-\frac{36 \left(1-i c x^3\right)^2}{c^4}+\frac{48 \left(1-i c x^3\right)}{c^4}-\frac{12 \log \left(1-i c x^3\right)}{c^4}\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)+\frac{b \log \left(\frac{1}{2} \left(1+i c x^3\right)\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)}{24 c^4}+\frac{1}{48} x^{12} \left(2 a+i b \log \left(1-i c x^3\right)\right)^2+\frac{1}{96} b x^{12} \left(2 i a-b \log \left(1-i c x^3\right)\right)-\frac{1}{24} b x^{12} \log \left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)+\frac{i b x^9 \left(2 i a-b \log \left(1-i c x^3\right)\right)}{72 c}+\frac{b^2 x^6}{192 c^2}-\frac{23 i b^2 x^3}{288 c^3}-\frac{b^2 \left(1-i c x^3\right)^4}{384 c^4}+\frac{b^2 \left(1-i c x^3\right)^3}{54 c^4}-\frac{b^2 \left(1-i c x^3\right)^2}{16 c^4}-\frac{b^2 \log ^2\left(1-i c x^3\right)}{48 c^4}+\frac{b^2 \log ^2\left(1+i c x^3\right)}{48 c^4}-\frac{b^2 \log \left(-c x^3+i\right)}{36 c^4}-\frac{b^2 \left(1-i c x^3\right) \log \left(1-i c x^3\right)}{24 c^4}-\frac{b^2 \left(1+i c x^3\right) \log \left(1+i c x^3\right)}{12 c^4}-\frac{b^2 \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log \left(1+i c x^3\right)}{24 c^4}+\frac{5 b^2 \log \left(c x^3+i\right)}{288 c^4}-\frac{7 i b^2 x^9}{864 c}-\frac{1}{48} b^2 x^{12} \log ^2\left(1+i c x^3\right)+\frac{i b^2 x^9 \log \left(1+i c x^3\right)}{36 c}+\frac{b^2 x^{12}}{384}","\frac{a b x^3}{6 c^3}-\frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{12 c^4}+\frac{1}{12} x^{12} \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2-\frac{b x^9 \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{18 c}+\frac{b^2 x^6}{36 c^2}-\frac{b^2 \log \left(c^2 x^6+1\right)}{9 c^4}+\frac{b^2 x^3 \tan ^{-1}\left(c x^3\right)}{6 c^3}",1,"(a*b*x^3)/(12*c^3) - (((23*I)/288)*b^2*x^3)/c^3 + (b^2*x^6)/(192*c^2) - (((7*I)/864)*b^2*x^9)/c + (b^2*x^12)/384 - (b^2*(1 - I*c*x^3)^2)/(16*c^4) + (b^2*(1 - I*c*x^3)^3)/(54*c^4) - (b^2*(1 - I*c*x^3)^4)/(384*c^4) - (b^2*Log[I - c*x^3])/(36*c^4) - (b^2*(1 - I*c*x^3)*Log[1 - I*c*x^3])/(24*c^4) - (b^2*Log[1 - I*c*x^3]^2)/(48*c^4) - (b*x^6*((2*I)*a - b*Log[1 - I*c*x^3]))/(48*c^2) + ((I/72)*b*x^9*((2*I)*a - b*Log[1 - I*c*x^3]))/c + (b*x^12*((2*I)*a - b*Log[1 - I*c*x^3]))/96 + (x^12*(2*a + I*b*Log[1 - I*c*x^3])^2)/48 + (I/288)*b*(2*a + I*b*Log[1 - I*c*x^3])*((48*(1 - I*c*x^3))/c^4 - (36*(1 - I*c*x^3)^2)/c^4 + (16*(1 - I*c*x^3)^3)/c^4 - (3*(1 - I*c*x^3)^4)/c^4 - (12*Log[1 - I*c*x^3])/c^4) + (b*((2*I)*a - b*Log[1 - I*c*x^3])*Log[(1 + I*c*x^3)/2])/(24*c^4) + ((I/36)*b^2*x^9*Log[1 + I*c*x^3])/c - (b^2*(1 + I*c*x^3)*Log[1 + I*c*x^3])/(12*c^4) - (b^2*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3])/(24*c^4) - (b*x^12*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3])/24 + (b^2*Log[1 + I*c*x^3]^2)/(48*c^4) - (b^2*x^12*Log[1 + I*c*x^3]^2)/48 + (5*b^2*Log[I + c*x^3])/(288*c^4) - (b^2*PolyLog[2, (1 - I*c*x^3)/2])/(24*c^4) - (b^2*PolyLog[2, (1 + I*c*x^3)/2])/(24*c^4)","C",62,19,16,1.187,0,"{5035, 2454, 2398, 2411, 43, 2334, 12, 14, 2301, 2395, 2439, 2416, 2389, 2295, 2394, 2393, 2391, 2410, 2390}"
114,1,647,0,1.3935215,"\int x^8 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2 \, dx","Int[x^8*(a + b*ArcTan[c*x^3])^2,x]","\frac{i b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)}{18 c^3}-\frac{i b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^3\right)\right)}{18 c^3}-\frac{i a b x^3}{9 c^2}+\frac{1}{108} i b \left(\frac{2 i \left(1-i c x^3\right)^3}{c^3}-\frac{9 i \left(1-i c x^3\right)^2}{c^3}+\frac{18 i \left(1-i c x^3\right)}{c^3}-\frac{6 i \log \left(1-i c x^3\right)}{c^3}\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)-\frac{i b \log \left(\frac{1}{2} \left(1+i c x^3\right)\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)}{18 c^3}+\frac{1}{36} x^9 \left(2 a+i b \log \left(1-i c x^3\right)\right)^2+\frac{1}{54} b x^9 \left(2 i a-b \log \left(1-i c x^3\right)\right)-\frac{1}{18} b x^9 \log \left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)+\frac{i b x^6 \left(2 i a-b \log \left(1-i c x^3\right)\right)}{36 c}+\frac{19 b^2 x^3}{108 c^2}+\frac{i b^2 \left(1-i c x^3\right)^3}{162 c^3}-\frac{i b^2 \left(1-i c x^3\right)^2}{24 c^3}-\frac{i b^2 \log ^2\left(1-i c x^3\right)}{36 c^3}-\frac{i b^2 \log ^2\left(1+i c x^3\right)}{36 c^3}+\frac{i b^2 \log \left(-c x^3+i\right)}{18 c^3}+\frac{i b^2 \left(1-i c x^3\right) \log \left(1-i c x^3\right)}{18 c^3}-\frac{i b^2 \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log \left(1+i c x^3\right)}{18 c^3}-\frac{i b^2 \log \left(c x^3+i\right)}{108 c^3}-\frac{5 i b^2 x^6}{216 c}-\frac{1}{36} b^2 x^9 \log ^2\left(1+i c x^3\right)+\frac{i b^2 x^6 \log \left(1+i c x^3\right)}{18 c}+\frac{b^2 x^9}{162}","-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x^3}\right)}{9 c^3}-\frac{i \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{9 c^3}-\frac{2 b \log \left(\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{9 c^3}+\frac{1}{9} x^9 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2-\frac{b x^6 \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{9 c}+\frac{b^2 x^3}{9 c^2}-\frac{b^2 \tan ^{-1}\left(c x^3\right)}{9 c^3}",1,"((-I/9)*a*b*x^3)/c^2 + (19*b^2*x^3)/(108*c^2) - (((5*I)/216)*b^2*x^6)/c + (b^2*x^9)/162 - ((I/24)*b^2*(1 - I*c*x^3)^2)/c^3 + ((I/162)*b^2*(1 - I*c*x^3)^3)/c^3 + ((I/18)*b^2*Log[I - c*x^3])/c^3 + ((I/18)*b^2*(1 - I*c*x^3)*Log[1 - I*c*x^3])/c^3 - ((I/36)*b^2*Log[1 - I*c*x^3]^2)/c^3 + ((I/36)*b*x^6*((2*I)*a - b*Log[1 - I*c*x^3]))/c + (b*x^9*((2*I)*a - b*Log[1 - I*c*x^3]))/54 + (x^9*(2*a + I*b*Log[1 - I*c*x^3])^2)/36 + (I/108)*b*(2*a + I*b*Log[1 - I*c*x^3])*(((18*I)*(1 - I*c*x^3))/c^3 - ((9*I)*(1 - I*c*x^3)^2)/c^3 + ((2*I)*(1 - I*c*x^3)^3)/c^3 - ((6*I)*Log[1 - I*c*x^3])/c^3) - ((I/18)*b*((2*I)*a - b*Log[1 - I*c*x^3])*Log[(1 + I*c*x^3)/2])/c^3 + ((I/18)*b^2*x^6*Log[1 + I*c*x^3])/c - ((I/18)*b^2*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3])/c^3 - (b*x^9*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3])/18 - ((I/36)*b^2*Log[1 + I*c*x^3]^2)/c^3 - (b^2*x^9*Log[1 + I*c*x^3]^2)/36 - ((I/108)*b^2*Log[I + c*x^3])/c^3 + ((I/18)*b^2*PolyLog[2, (1 - I*c*x^3)/2])/c^3 - ((I/18)*b^2*PolyLog[2, (1 + I*c*x^3)/2])/c^3","B",53,19,16,1.187,0,"{5035, 2454, 2398, 2411, 43, 2334, 12, 14, 2301, 2395, 2439, 2416, 2389, 2295, 2394, 2393, 2391, 2410, 2390}"
115,1,612,0,1.0517362,"\int x^5 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2 \, dx","Int[x^5*(a + b*ArcTan[c*x^3])^2,x]","\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)}{12 c^2}+\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^3\right)\right)}{12 c^2}-\frac{\left(1-i c x^3\right)^2 \left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{24 c^2}+\frac{\left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{12 c^2}+\frac{i b \left(1-i c x^3\right)^2 \left(2 a+i b \log \left(1-i c x^3\right)\right)}{24 c^2}-\frac{b \log \left(\frac{1}{2} \left(1+i c x^3\right)\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)}{12 c^2}-\frac{a b x^3}{2 c}+\frac{1}{24} b x^6 \left(2 i a-b \log \left(1-i c x^3\right)\right)-\frac{1}{12} b x^6 \log \left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)+\frac{b^2 \left(1-i c x^3\right)^2}{48 c^2}+\frac{b^2 \left(1+i c x^3\right)^2}{48 c^2}+\frac{b^2 \left(1+i c x^3\right)^2 \log ^2\left(1+i c x^3\right)}{24 c^2}-\frac{b^2 \left(1+i c x^3\right) \log ^2\left(1+i c x^3\right)}{12 c^2}-\frac{b^2 \log \left(-c x^3+i\right)}{24 c^2}+\frac{b^2 \left(1-i c x^3\right) \log \left(1-i c x^3\right)}{4 c^2}-\frac{b^2 \left(1+i c x^3\right)^2 \log \left(1+i c x^3\right)}{24 c^2}+\frac{b^2 \left(1+i c x^3\right) \log \left(1+i c x^3\right)}{4 c^2}+\frac{b^2 \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log \left(1+i c x^3\right)}{12 c^2}-\frac{b^2 \log \left(c x^3+i\right)}{24 c^2}-\frac{1}{24} b^2 x^6 \log \left(1+i c x^3\right)+\frac{b^2 x^6}{24}","\frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{6 c^2}-\frac{a b x^3}{3 c}+\frac{1}{6} x^6 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2+\frac{b^2 \log \left(c^2 x^6+1\right)}{6 c^2}-\frac{b^2 x^3 \tan ^{-1}\left(c x^3\right)}{3 c}",1,"-(a*b*x^3)/(2*c) + (b^2*x^6)/24 + (b^2*(1 - I*c*x^3)^2)/(48*c^2) + (b^2*(1 + I*c*x^3)^2)/(48*c^2) - (b^2*Log[I - c*x^3])/(24*c^2) + (b^2*(1 - I*c*x^3)*Log[1 - I*c*x^3])/(4*c^2) + (b*x^6*((2*I)*a - b*Log[1 - I*c*x^3]))/24 + ((I/24)*b*(1 - I*c*x^3)^2*(2*a + I*b*Log[1 - I*c*x^3]))/c^2 + ((1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^2)/(12*c^2) - ((1 - I*c*x^3)^2*(2*a + I*b*Log[1 - I*c*x^3])^2)/(24*c^2) - (b*((2*I)*a - b*Log[1 - I*c*x^3])*Log[(1 + I*c*x^3)/2])/(12*c^2) - (b^2*x^6*Log[1 + I*c*x^3])/24 + (b^2*(1 + I*c*x^3)*Log[1 + I*c*x^3])/(4*c^2) - (b^2*(1 + I*c*x^3)^2*Log[1 + I*c*x^3])/(24*c^2) + (b^2*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3])/(12*c^2) - (b*x^6*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3])/12 - (b^2*(1 + I*c*x^3)*Log[1 + I*c*x^3]^2)/(12*c^2) + (b^2*(1 + I*c*x^3)^2*Log[1 + I*c*x^3]^2)/(24*c^2) - (b^2*Log[I + c*x^3])/(24*c^2) + (b^2*PolyLog[2, (1 - I*c*x^3)/2])/(12*c^2) + (b^2*PolyLog[2, (1 + I*c*x^3)/2])/(12*c^2)","C",44,16,16,1.000,0,"{5035, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2395, 43, 2439, 2416, 2394, 2393, 2391}"
116,1,255,0,0.6441466,"\int x^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2 \, dx","Int[x^2*(a + b*ArcTan[c*x^3])^2,x]","-\frac{i b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)}{6 c}+\frac{i b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^3\right)\right)}{6 c}-\frac{1}{6} b x^3 \log \left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)+\frac{i \left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{12 c}+\frac{i b \log \left(\frac{1}{2} \left(1+i c x^3\right)\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)}{6 c}+\frac{i b^2 \left(1+i c x^3\right) \log ^2\left(1+i c x^3\right)}{12 c}+\frac{i b^2 \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log \left(1+i c x^3\right)}{6 c}","\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x^3}\right)}{3 c}+\frac{1}{3} x^3 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2+\frac{i \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{3 c}+\frac{2 b \log \left(\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{3 c}",1,"((I/12)*(1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^2)/c + ((I/6)*b*((2*I)*a - b*Log[1 - I*c*x^3])*Log[(1 + I*c*x^3)/2])/c + ((I/6)*b^2*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3])/c - (b*x^3*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3])/6 + ((I/12)*b^2*(1 + I*c*x^3)*Log[1 + I*c*x^3]^2)/c - ((I/6)*b^2*PolyLog[2, (1 - I*c*x^3)/2])/c + ((I/6)*b^2*PolyLog[2, (1 + I*c*x^3)/2])/c","B",28,12,16,0.7500,0,"{5035, 2454, 2389, 2296, 2295, 6715, 2430, 43, 2416, 2394, 2393, 2391}"
117,1,154,0,0.3164835,"\int \frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{x} \, dx","Int[(a + b*ArcTan[c*x^3])^2/x,x]","-\frac{1}{3} i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{1}{3} i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{1}{6} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^3}\right)+\frac{1}{6} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x^3}\right)+\frac{2}{3} \tanh ^{-1}\left(1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2","-\frac{1}{3} i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{1}{3} i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{1}{6} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^3}\right)+\frac{1}{6} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x^3}\right)+\frac{2}{3} \tanh ^{-1}\left(1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2",1,"(2*(a + b*ArcTan[c*x^3])^2*ArcTanh[1 - 2/(1 + I*c*x^3)])/3 - (I/3)*b*(a + b*ArcTan[c*x^3])*PolyLog[2, 1 - 2/(1 + I*c*x^3)] + (I/3)*b*(a + b*ArcTan[c*x^3])*PolyLog[2, -1 + 2/(1 + I*c*x^3)] - (b^2*PolyLog[3, 1 - 2/(1 + I*c*x^3)])/6 + (b^2*PolyLog[3, -1 + 2/(1 + I*c*x^3)])/6","A",7,6,16,0.3750,1,"{5031, 4850, 4988, 4884, 4994, 6610}"
118,1,290,0,0.6607951,"\int \frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{x^4} \, dx","Int[(a + b*ArcTan[c*x^3])^2/x^4,x]","\frac{1}{3} i b^2 c \text{PolyLog}\left(2,-i c x^3\right)-\frac{1}{3} i b^2 c \text{PolyLog}\left(2,i c x^3\right)-\frac{1}{6} i b^2 c \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)+\frac{1}{6} i b^2 c \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^3\right)\right)+\frac{1}{6} i b c \log \left(\frac{1}{2} \left(1+i c x^3\right)\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)+\frac{b \log \left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)}{6 x^3}-\frac{\left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{12 x^3}+2 a b c \log (x)+\frac{b^2 \left(1+i c x^3\right) \log ^2\left(1+i c x^3\right)}{12 x^3}+\frac{1}{6} i b^2 c \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log \left(1+i c x^3\right)","-\frac{1}{3} i b^2 c \text{PolyLog}\left(2,-1+\frac{2}{1-i c x^3}\right)-\frac{1}{3} i c \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2-\frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{3 x^3}+\frac{2}{3} b c \log \left(2-\frac{2}{1-i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)",1,"2*a*b*c*Log[x] - ((1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^2)/(12*x^3) + (I/6)*b*c*((2*I)*a - b*Log[1 - I*c*x^3])*Log[(1 + I*c*x^3)/2] + (I/6)*b^2*c*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3] + (b*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3])/(6*x^3) + (b^2*(1 + I*c*x^3)*Log[1 + I*c*x^3]^2)/(12*x^3) + (I/3)*b^2*c*PolyLog[2, (-I)*c*x^3] - (I/3)*b^2*c*PolyLog[2, I*c*x^3] - (I/6)*b^2*c*PolyLog[2, (1 - I*c*x^3)/2] + (I/6)*b^2*c*PolyLog[2, (1 + I*c*x^3)/2]","B",24,13,16,0.8125,0,"{5035, 2454, 2397, 2392, 2391, 2395, 36, 29, 31, 2439, 2416, 2394, 2393}"
119,1,419,0,1.1224518,"\int \frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{x^7} \, dx","Int[(a + b*ArcTan[c*x^3])^2/x^7,x]","-\frac{1}{12} b^2 c^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)-\frac{1}{12} b^2 c^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^3\right)\right)+\frac{1}{12} b c^2 \log \left(\frac{1}{2} \left(1+i c x^3\right)\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)-\frac{1}{24} c^2 \left(2 a+i b \log \left(1-i c x^3\right)\right)^2+\frac{i b c \left(2 i a-b \log \left(1-i c x^3\right)\right)}{12 x^3}-\frac{b c \left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)}{12 x^3}+\frac{b \log \left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)}{12 x^6}-\frac{\left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{24 x^6}+\frac{1}{24} b^2 c^2 \log ^2\left(1+i c x^3\right)-\frac{1}{6} b^2 c^2 \log \left(-c x^3+i\right)-\frac{1}{12} b^2 c^2 \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log \left(1+i c x^3\right)-\frac{1}{12} b^2 c^2 \log \left(c x^3+i\right)+b^2 c^2 \log (x)+\frac{b^2 \log ^2\left(1+i c x^3\right)}{24 x^6}+\frac{i b^2 c \log \left(1+i c x^3\right)}{6 x^3}","-\frac{1}{6} c^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2-\frac{b c \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{3 x^3}-\frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{6 x^6}-\frac{1}{6} b^2 c^2 \log \left(c^2 x^6+1\right)+b^2 c^2 \log (x)",1,"b^2*c^2*Log[x] - (b^2*c^2*Log[I - c*x^3])/6 + ((I/12)*b*c*((2*I)*a - b*Log[1 - I*c*x^3]))/x^3 - (b*c*(1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3]))/(12*x^3) - (c^2*(2*a + I*b*Log[1 - I*c*x^3])^2)/24 - (2*a + I*b*Log[1 - I*c*x^3])^2/(24*x^6) + (b*c^2*((2*I)*a - b*Log[1 - I*c*x^3])*Log[(1 + I*c*x^3)/2])/12 + ((I/6)*b^2*c*Log[1 + I*c*x^3])/x^3 - (b^2*c^2*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3])/12 + (b*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3])/(12*x^6) + (b^2*c^2*Log[1 + I*c*x^3]^2)/24 + (b^2*Log[1 + I*c*x^3]^2)/(24*x^6) - (b^2*c^2*Log[I + c*x^3])/12 - (b^2*c^2*PolyLog[2, (1 - I*c*x^3)/2])/12 - (b^2*c^2*PolyLog[2, (1 + I*c*x^3)/2])/12","C",46,23,16,1.438,0,"{5035, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2395, 44, 2439, 2416, 36, 29, 2392, 2391, 2394, 2393, 2410, 2390}"
120,1,536,0,1.4499553,"\int \frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{x^{10}} \, dx","Int[(a + b*ArcTan[c*x^3])^2/x^10,x]","-\frac{1}{9} i b^2 c^3 \text{PolyLog}\left(2,-i c x^3\right)+\frac{1}{9} i b^2 c^3 \text{PolyLog}\left(2,i c x^3\right)+\frac{1}{18} i b^2 c^3 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)-\frac{1}{18} i b^2 c^3 \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^3\right)\right)-\frac{1}{36} i c^3 \left(2 a+i b \log \left(1-i c x^3\right)\right)^2-\frac{1}{18} i b c^3 \log \left(\frac{1}{2} \left(1+i c x^3\right)\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)+\frac{b c^2 \left(2 i a-b \log \left(1-i c x^3\right)\right)}{18 x^3}-\frac{i b c^2 \left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)}{18 x^3}-\frac{2}{3} a b c^3 \log (x)+\frac{i b c \left(2 i a-b \log \left(1-i c x^3\right)\right)}{36 x^6}-\frac{b c \left(2 a+i b \log \left(1-i c x^3\right)\right)}{36 x^6}-\frac{\left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{36 x^9}+\frac{b \log \left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)}{18 x^9}-\frac{b^2 c^2}{9 x^3}-\frac{1}{36} i b^2 c^3 \log ^2\left(1+i c x^3\right)+\frac{1}{18} i b^2 c^3 \log \left(-c x^3+i\right)-\frac{1}{18} i b^2 c^3 \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log \left(1+i c x^3\right)+\frac{b^2 \log ^2\left(1+i c x^3\right)}{36 x^9}+\frac{i b^2 c \log \left(1+i c x^3\right)}{18 x^6}","\frac{1}{9} i b^2 c^3 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x^3}\right)+\frac{1}{9} i c^3 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2-\frac{2}{9} b c^3 \log \left(2-\frac{2}{1-i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{b c \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{9 x^6}-\frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{9 x^9}-\frac{b^2 c^2}{9 x^3}-\frac{1}{9} b^2 c^3 \tan ^{-1}\left(c x^3\right)",1,"-(b^2*c^2)/(9*x^3) - (2*a*b*c^3*Log[x])/3 + (I/18)*b^2*c^3*Log[I - c*x^3] + ((I/36)*b*c*((2*I)*a - b*Log[1 - I*c*x^3]))/x^6 + (b*c^2*((2*I)*a - b*Log[1 - I*c*x^3]))/(18*x^3) - (b*c*(2*a + I*b*Log[1 - I*c*x^3]))/(36*x^6) - ((I/18)*b*c^2*(1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3]))/x^3 - (I/36)*c^3*(2*a + I*b*Log[1 - I*c*x^3])^2 - (2*a + I*b*Log[1 - I*c*x^3])^2/(36*x^9) - (I/18)*b*c^3*((2*I)*a - b*Log[1 - I*c*x^3])*Log[(1 + I*c*x^3)/2] + ((I/18)*b^2*c*Log[1 + I*c*x^3])/x^6 - (I/18)*b^2*c^3*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3] + (b*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3])/(18*x^9) - (I/36)*b^2*c^3*Log[1 + I*c*x^3]^2 + (b^2*Log[1 + I*c*x^3]^2)/(36*x^9) - (I/9)*b^2*c^3*PolyLog[2, (-I)*c*x^3] + (I/9)*b^2*c^3*PolyLog[2, I*c*x^3] + (I/18)*b^2*c^3*PolyLog[2, (1 - I*c*x^3)/2] - (I/18)*b^2*c^3*PolyLog[2, (1 + I*c*x^3)/2]","B",59,24,16,1.500,0,"{5035, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2319, 44, 2395, 2439, 2416, 36, 29, 2392, 2391, 2394, 2393, 2410, 2390}"
121,1,1867,0,7.0336978,"\int x^8 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3 \, dx","Int[x^8*(a + b*ArcTan[c*x^3])^3,x]","\frac{1}{324} i b^3 x^9-\frac{1}{72} i b \left(2 i a-b \log \left(1-i c x^3\right)\right)^2 x^9+\frac{1}{72} i b^3 \log ^2\left(i c x^3+1\right) x^9+\frac{1}{24} i b^2 \left(2 i a-b \log \left(1-i c x^3\right)\right) \log ^2\left(i c x^3+1\right) x^9-\frac{1}{108} i b^3 \log \left(i c x^3+1\right) x^9+\frac{1}{24} i b \left(2 i a-b \log \left(1-i c x^3\right)\right)^2 \log \left(i c x^3+1\right) x^9-\frac{b^2 \left(2 i a-b \log \left(1-i c x^3\right)\right) x^6}{24 c}+\frac{b^2 \left(2 i a-b \log \left(1-i c x^3\right)\right) \log \left(i c x^3+1\right) x^6}{12 c}+\frac{b^3 \log \left(i c x^3+1\right) x^6}{18 c}-\frac{23 b^3 x^6}{432 c}+\frac{7 i b^3 x^3}{216 c^2}+\frac{2 a b^2 x^3}{3 c^2}+\frac{b^3 \left(i c x^3+1\right)^3}{324 c^3}-\frac{i \left(1-i c x^3\right)^3 \left(2 a+i b \log \left(1-i c x^3\right)\right)^3}{72 c^3}+\frac{i \left(1-i c x^3\right)^2 \left(2 a+i b \log \left(1-i c x^3\right)\right)^3}{24 c^3}-\frac{i \left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)^3}{24 c^3}-\frac{b^3 \left(i c x^3+1\right)^3 \log ^3\left(i c x^3+1\right)}{72 c^3}+\frac{b^3 \left(i c x^3+1\right)^2 \log ^3\left(i c x^3+1\right)}{24 c^3}-\frac{b^3 \left(i c x^3+1\right) \log ^3\left(i c x^3+1\right)}{24 c^3}-\frac{b^3 \left(1-i c x^3\right)^2}{48 c^3}-\frac{b^3 \left(i c x^3+1\right)^2}{24 c^3}+\frac{b^3 \log ^2\left(1-i c x^3\right)}{72 c^3}-\frac{b \left(1-i c x^3\right)^2 \left(2 i a-b \log \left(1-i c x^3\right)\right)^2}{48 c^3}-\frac{b \left(1-i c x^3\right)^3 \left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{72 c^3}+\frac{b \left(1-i c x^3\right)^2 \left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{16 c^3}-\frac{b \left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{8 c^3}+\frac{b^3 \left(i c x^3+1\right)^3 \log ^2\left(i c x^3+1\right)}{72 c^3}-\frac{b^3 \left(i c x^3+1\right)^2 \log ^2\left(i c x^3+1\right)}{12 c^3}+\frac{b^3 \left(i c x^3+1\right) \log ^2\left(i c x^3+1\right)}{8 c^3}-\frac{b^3 \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log ^2\left(i c x^3+1\right)}{12 c^3}-\frac{i b^2 \left(2 a+i b \log \left(1-i c x^3\right)\right) \log ^2\left(i c x^3+1\right)}{24 c^3}-\frac{b^3 \log ^2\left(i c x^3+1\right)}{72 c^3}+\frac{7 b^3 \log \left(i-c x^3\right)}{108 c^3}-\frac{b^3 \left(1-i c x^3\right) \log \left(1-i c x^3\right)}{3 c^3}-\frac{b^2 \left(1-i c x^3\right)^2 \left(2 i a-b \log \left(1-i c x^3\right)\right)}{48 c^3}+\frac{i b^2 \left(1-i c x^3\right)^3 \left(2 a+i b \log \left(1-i c x^3\right)\right)}{108 c^3}-\frac{i b^2 \left(1-i c x^3\right)^2 \left(2 a+i b \log \left(1-i c x^3\right)\right)}{16 c^3}+\frac{1}{216} i b^2 \left(2 i a-b \log \left(1-i c x^3\right)\right) \left(\frac{2 i \left(1-i c x^3\right)^3}{c^3}-\frac{9 i \left(1-i c x^3\right)^2}{c^3}+\frac{18 i \left(1-i c x^3\right)}{c^3}-\frac{6 i \log \left(1-i c x^3\right)}{c^3}\right)-\frac{b \left(2 i a-b \log \left(1-i c x^3\right)\right)^2 \log \left(\frac{1}{2} \left(i c x^3+1\right)\right)}{24 c^3}+\frac{b \left(2 a+i b \log \left(1-i c x^3\right)\right)^2 \log \left(\frac{1}{2} \left(i c x^3+1\right)\right)}{24 c^3}+\frac{b^2 \left(2 i a-b \log \left(1-i c x^3\right)\right) \log \left(\frac{1}{2} \left(i c x^3+1\right)\right)}{12 c^3}-\frac{b^3 \left(i c x^3+1\right)^3 \log \left(i c x^3+1\right)}{108 c^3}+\frac{b^3 \left(i c x^3+1\right)^2 \log \left(i c x^3+1\right)}{12 c^3}-\frac{b \left(2 a+i b \log \left(1-i c x^3\right)\right)^2 \log \left(i c x^3+1\right)}{24 c^3}-\frac{11 b^3 \left(i c x^3+1\right) \log \left(i c x^3+1\right)}{36 c^3}-\frac{b^3 \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log \left(i c x^3+1\right)}{12 c^3}+\frac{b^3 \log \left(c x^3+i\right)}{24 c^3}+\frac{b^2 \left(2 i a-b \log \left(1-i c x^3\right)\right) \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)}{12 c^3}+\frac{i b^2 \left(2 a+i b \log \left(1-i c x^3\right)\right) \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)}{12 c^3}-\frac{b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)}{12 c^3}-\frac{b^3 \log \left(i c x^3+1\right) \text{PolyLog}\left(2,\frac{1}{2} \left(i c x^3+1\right)\right)}{6 c^3}-\frac{b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(i c x^3+1\right)\right)}{12 c^3}+\frac{b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(1-i c x^3\right)\right)}{6 c^3}+\frac{b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(i c x^3+1\right)\right)}{6 c^3}","-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{3 c^3}-\frac{b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^3}\right)}{6 c^3}+\frac{a b^2 x^3}{3 c^2}-\frac{i \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3}{9 c^3}-\frac{b \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{6 c^3}-\frac{b \log \left(\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{3 c^3}+\frac{1}{9} x^9 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3-\frac{b x^6 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{6 c}-\frac{b^3 \log \left(c^2 x^6+1\right)}{6 c^3}+\frac{b^3 x^3 \tan ^{-1}\left(c x^3\right)}{3 c^2}",1,"(2*a*b^2*x^3)/(3*c^2) + (((7*I)/216)*b^3*x^3)/c^2 - (23*b^3*x^6)/(432*c) + (I/324)*b^3*x^9 - (b^3*(1 - I*c*x^3)^2)/(48*c^3) - (b^3*(1 + I*c*x^3)^2)/(24*c^3) + (b^3*(1 + I*c*x^3)^3)/(324*c^3) + (7*b^3*Log[I - c*x^3])/(108*c^3) - (b^3*(1 - I*c*x^3)*Log[1 - I*c*x^3])/(3*c^3) + (b^3*Log[1 - I*c*x^3]^2)/(72*c^3) - (b^2*x^6*((2*I)*a - b*Log[1 - I*c*x^3]))/(24*c) - (b^2*(1 - I*c*x^3)^2*((2*I)*a - b*Log[1 - I*c*x^3]))/(48*c^3) - (I/72)*b*x^9*((2*I)*a - b*Log[1 - I*c*x^3])^2 - (b*(1 - I*c*x^3)^2*((2*I)*a - b*Log[1 - I*c*x^3])^2)/(48*c^3) - ((I/16)*b^2*(1 - I*c*x^3)^2*(2*a + I*b*Log[1 - I*c*x^3]))/c^3 + ((I/108)*b^2*(1 - I*c*x^3)^3*(2*a + I*b*Log[1 - I*c*x^3]))/c^3 - (b*(1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^2)/(8*c^3) + (b*(1 - I*c*x^3)^2*(2*a + I*b*Log[1 - I*c*x^3])^2)/(16*c^3) - (b*(1 - I*c*x^3)^3*(2*a + I*b*Log[1 - I*c*x^3])^2)/(72*c^3) - ((I/24)*(1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^3)/c^3 + ((I/24)*(1 - I*c*x^3)^2*(2*a + I*b*Log[1 - I*c*x^3])^3)/c^3 - ((I/72)*(1 - I*c*x^3)^3*(2*a + I*b*Log[1 - I*c*x^3])^3)/c^3 + (I/216)*b^2*((2*I)*a - b*Log[1 - I*c*x^3])*(((18*I)*(1 - I*c*x^3))/c^3 - ((9*I)*(1 - I*c*x^3)^2)/c^3 + ((2*I)*(1 - I*c*x^3)^3)/c^3 - ((6*I)*Log[1 - I*c*x^3])/c^3) + (b^2*((2*I)*a - b*Log[1 - I*c*x^3])*Log[(1 + I*c*x^3)/2])/(12*c^3) - (b*((2*I)*a - b*Log[1 - I*c*x^3])^2*Log[(1 + I*c*x^3)/2])/(24*c^3) + (b*(2*a + I*b*Log[1 - I*c*x^3])^2*Log[(1 + I*c*x^3)/2])/(24*c^3) + (b^3*x^6*Log[1 + I*c*x^3])/(18*c) - (I/108)*b^3*x^9*Log[1 + I*c*x^3] - (11*b^3*(1 + I*c*x^3)*Log[1 + I*c*x^3])/(36*c^3) + (b^3*(1 + I*c*x^3)^2*Log[1 + I*c*x^3])/(12*c^3) - (b^3*(1 + I*c*x^3)^3*Log[1 + I*c*x^3])/(108*c^3) - (b^3*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3])/(12*c^3) + (b^2*x^6*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3])/(12*c) + (I/24)*b*x^9*((2*I)*a - b*Log[1 - I*c*x^3])^2*Log[1 + I*c*x^3] - (b*(2*a + I*b*Log[1 - I*c*x^3])^2*Log[1 + I*c*x^3])/(24*c^3) - (b^3*Log[1 + I*c*x^3]^2)/(72*c^3) + (I/72)*b^3*x^9*Log[1 + I*c*x^3]^2 + (b^3*(1 + I*c*x^3)*Log[1 + I*c*x^3]^2)/(8*c^3) - (b^3*(1 + I*c*x^3)^2*Log[1 + I*c*x^3]^2)/(12*c^3) + (b^3*(1 + I*c*x^3)^3*Log[1 + I*c*x^3]^2)/(72*c^3) - (b^3*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3]^2)/(12*c^3) + (I/24)*b^2*x^9*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3]^2 - ((I/24)*b^2*(2*a + I*b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3]^2)/c^3 - (b^3*(1 + I*c*x^3)*Log[1 + I*c*x^3]^3)/(24*c^3) + (b^3*(1 + I*c*x^3)^2*Log[1 + I*c*x^3]^3)/(24*c^3) - (b^3*(1 + I*c*x^3)^3*Log[1 + I*c*x^3]^3)/(72*c^3) + (b^3*Log[I + c*x^3])/(24*c^3) - (b^3*PolyLog[2, (1 - I*c*x^3)/2])/(12*c^3) + (b^2*((2*I)*a - b*Log[1 - I*c*x^3])*PolyLog[2, (1 - I*c*x^3)/2])/(12*c^3) + ((I/12)*b^2*(2*a + I*b*Log[1 - I*c*x^3])*PolyLog[2, (1 - I*c*x^3)/2])/c^3 - (b^3*PolyLog[2, (1 + I*c*x^3)/2])/(12*c^3) - (b^3*Log[1 + I*c*x^3]*PolyLog[2, (1 + I*c*x^3)/2])/(6*c^3) + (b^3*PolyLog[3, (1 - I*c*x^3)/2])/(6*c^3) + (b^3*PolyLog[3, (1 + I*c*x^3)/2])/(6*c^3)","B",239,32,16,2.000,0,"{5035, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2398, 2411, 43, 2334, 12, 14, 2301, 2439, 2416, 2396, 2433, 2374, 6589, 6742, 2430, 2394, 2393, 2391, 2395, 2375, 2317, 2410, 2425}"
122,1,951,0,4.7331537,"\int x^5 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3 \, dx","Int[x^5*(a + b*ArcTan[c*x^3])^3,x]","\frac{1}{16} i b^2 \left(2 i a-b \log \left(1-i c x^3\right)\right) \log ^2\left(i c x^3+1\right) x^6+\frac{1}{16} i b \left(2 i a-b \log \left(1-i c x^3\right)\right)^2 \log \left(i c x^3+1\right) x^6+\frac{b^2 \left(2 i a-b \log \left(1-i c x^3\right)\right) \log \left(i c x^3+1\right) x^3}{4 c}-\frac{\left(1-i c x^3\right)^2 \left(2 a+i b \log \left(1-i c x^3\right)\right)^3}{48 c^2}+\frac{\left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)^3}{24 c^2}-\frac{i b^3 \left(i c x^3+1\right)^2 \log ^3\left(i c x^3+1\right)}{48 c^2}+\frac{i b^3 \left(i c x^3+1\right) \log ^3\left(i c x^3+1\right)}{24 c^2}+\frac{i b \left(1-i c x^3\right)^2 \left(2 i a-b \log \left(1-i c x^3\right)\right)^2}{32 c^2}+\frac{i b \left(1-i c x^3\right)^2 \left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{32 c^2}-\frac{i b \left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{8 c^2}-\frac{i b^3 \left(i c x^3+1\right) \log ^2\left(i c x^3+1\right)}{8 c^2}-\frac{b^2 \left(2 a+i b \log \left(1-i c x^3\right)\right) \log ^2\left(i c x^3+1\right)}{16 c^2}+\frac{i b^2 \left(1-i c x^3\right)^2 \left(2 i a-b \log \left(1-i c x^3\right)\right)}{32 c^2}+\frac{b^2 \left(1-i c x^3\right)^2 \left(2 a+i b \log \left(1-i c x^3\right)\right)}{32 c^2}+\frac{i b \left(2 i a-b \log \left(1-i c x^3\right)\right)^2 \log \left(\frac{1}{2} \left(i c x^3+1\right)\right)}{16 c^2}+\frac{i b \left(2 a+i b \log \left(1-i c x^3\right)\right)^2 \log \left(\frac{1}{2} \left(i c x^3+1\right)\right)}{16 c^2}-\frac{i b^2 \left(2 i a-b \log \left(1-i c x^3\right)\right) \log \left(\frac{1}{2} \left(i c x^3+1\right)\right)}{4 c^2}-\frac{i b \left(2 a+i b \log \left(1-i c x^3\right)\right)^2 \log \left(i c x^3+1\right)}{16 c^2}-\frac{i b^3 \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log \left(i c x^3+1\right)}{4 c^2}-\frac{i b^2 \left(2 i a-b \log \left(1-i c x^3\right)\right) \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)}{8 c^2}-\frac{b^2 \left(2 a+i b \log \left(1-i c x^3\right)\right) \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)}{8 c^2}+\frac{i b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right)}{4 c^2}-\frac{i b^3 \text{PolyLog}\left(2,\frac{1}{2} \left(i c x^3+1\right)\right)}{4 c^2}","-\frac{i b^3 \text{PolyLog}\left(2,1-\frac{2}{1+i c x^3}\right)}{2 c^2}-\frac{b^2 \log \left(\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{c^2}+\frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^3}{6 c^2}-\frac{i b \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{2 c^2}+\frac{1}{6} x^6 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3-\frac{b x^3 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{2 c}",1,"((I/32)*b^2*(1 - I*c*x^3)^2*((2*I)*a - b*Log[1 - I*c*x^3]))/c^2 + ((I/32)*b*(1 - I*c*x^3)^2*((2*I)*a - b*Log[1 - I*c*x^3])^2)/c^2 + (b^2*(1 - I*c*x^3)^2*(2*a + I*b*Log[1 - I*c*x^3]))/(32*c^2) - ((I/8)*b*(1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^2)/c^2 + ((I/32)*b*(1 - I*c*x^3)^2*(2*a + I*b*Log[1 - I*c*x^3])^2)/c^2 + ((1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^3)/(24*c^2) - ((1 - I*c*x^3)^2*(2*a + I*b*Log[1 - I*c*x^3])^3)/(48*c^2) - ((I/4)*b^2*((2*I)*a - b*Log[1 - I*c*x^3])*Log[(1 + I*c*x^3)/2])/c^2 + ((I/16)*b*((2*I)*a - b*Log[1 - I*c*x^3])^2*Log[(1 + I*c*x^3)/2])/c^2 + ((I/16)*b*(2*a + I*b*Log[1 - I*c*x^3])^2*Log[(1 + I*c*x^3)/2])/c^2 - ((I/4)*b^3*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3])/c^2 + (b^2*x^3*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3])/(4*c) + (I/16)*b*x^6*((2*I)*a - b*Log[1 - I*c*x^3])^2*Log[1 + I*c*x^3] - ((I/16)*b*(2*a + I*b*Log[1 - I*c*x^3])^2*Log[1 + I*c*x^3])/c^2 - ((I/8)*b^3*(1 + I*c*x^3)*Log[1 + I*c*x^3]^2)/c^2 + (I/16)*b^2*x^6*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3]^2 - (b^2*(2*a + I*b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3]^2)/(16*c^2) + ((I/24)*b^3*(1 + I*c*x^3)*Log[1 + I*c*x^3]^3)/c^2 - ((I/48)*b^3*(1 + I*c*x^3)^2*Log[1 + I*c*x^3]^3)/c^2 + ((I/4)*b^3*PolyLog[2, (1 - I*c*x^3)/2])/c^2 - ((I/8)*b^2*((2*I)*a - b*Log[1 - I*c*x^3])*PolyLog[2, (1 - I*c*x^3)/2])/c^2 - (b^2*(2*a + I*b*Log[1 - I*c*x^3])*PolyLog[2, (1 - I*c*x^3)/2])/(8*c^2) - ((I/4)*b^3*PolyLog[2, (1 + I*c*x^3)/2])/c^2","B",155,30,16,1.875,0,"{5035, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2439, 2416, 2396, 2433, 2374, 6589, 2411, 43, 2334, 12, 14, 2301, 6742, 2395, 2394, 2393, 2391, 2375, 2317, 2430, 2425}"
123,1,545,0,2.7018458,"\int x^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3 \, dx","Int[x^2*(a + b*ArcTan[c*x^3])^3,x]","-\frac{b^2 \text{PolyLog}\left(2,\frac{1}{2} \left(1-i c x^3\right)\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)}{2 c}-\frac{b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(1-i c x^3\right)\right)}{2 c}-\frac{b^3 \text{PolyLog}\left(3,\frac{1}{2} \left(1+i c x^3\right)\right)}{2 c}+\frac{b^3 \log \left(1+i c x^3\right) \text{PolyLog}\left(2,\frac{1}{2} \left(1+i c x^3\right)\right)}{2 c}+\frac{1}{8} i b^2 x^3 \log ^2\left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)+\frac{b^2 \log ^2\left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)}{8 c}+\frac{b \left(1-i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)^2}{8 c}+\frac{b \left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)^2}{8 c}+\frac{b \log \left(\frac{1}{2} \left(1+i c x^3\right)\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)^2}{4 c}+\frac{1}{8} i b x^3 \log \left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)^2-\frac{b \log \left(1+i c x^3\right) \left(2 i a-b \log \left(1-i c x^3\right)\right)^2}{8 c}+\frac{i \left(1-i c x^3\right) \left(2 a+i b \log \left(1-i c x^3\right)\right)^3}{24 c}+\frac{b^3 \left(1+i c x^3\right) \log ^3\left(1+i c x^3\right)}{24 c}+\frac{b^3 \log \left(\frac{1}{2} \left(1-i c x^3\right)\right) \log ^2\left(1+i c x^3\right)}{4 c}","\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{c}+\frac{b^3 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^3}\right)}{2 c}+\frac{1}{3} x^3 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3+\frac{i \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3}{3 c}+\frac{b \log \left(\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{c}",1,"(b*(1 - I*c*x^3)*((2*I)*a - b*Log[1 - I*c*x^3])^2)/(8*c) + (b*(1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^2)/(8*c) + ((I/24)*(1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^3)/c + (b*((2*I)*a - b*Log[1 - I*c*x^3])^2*Log[(1 + I*c*x^3)/2])/(4*c) - (b*((2*I)*a - b*Log[1 - I*c*x^3])^2*Log[1 + I*c*x^3])/(8*c) + (I/8)*b*x^3*((2*I)*a - b*Log[1 - I*c*x^3])^2*Log[1 + I*c*x^3] + (b^3*Log[(1 - I*c*x^3)/2]*Log[1 + I*c*x^3]^2)/(4*c) + (b^2*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3]^2)/(8*c) + (I/8)*b^2*x^3*((2*I)*a - b*Log[1 - I*c*x^3])*Log[1 + I*c*x^3]^2 + (b^3*(1 + I*c*x^3)*Log[1 + I*c*x^3]^3)/(24*c) - (b^2*((2*I)*a - b*Log[1 - I*c*x^3])*PolyLog[2, (1 - I*c*x^3)/2])/(2*c) + (b^3*Log[1 + I*c*x^3]*PolyLog[2, (1 + I*c*x^3)/2])/(2*c) - (b^3*PolyLog[3, (1 - I*c*x^3)/2])/(2*c) - (b^3*PolyLog[3, (1 + I*c*x^3)/2])/(2*c)","B",82,23,16,1.438,0,"{5035, 2454, 2389, 2296, 2295, 6715, 2430, 2416, 2396, 2433, 2374, 6589, 2411, 2346, 2301, 6742, 43, 2394, 2393, 2391, 2375, 2317, 2425}"
124,1,232,0,0.5234766,"\int \frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^3}{x} \, dx","Int[(a + b*ArcTan[c*x^3])^3/x,x]","-\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{1}{2} i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2+\frac{1}{2} i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2+\frac{1}{4} i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+i c x^3}\right)-\frac{1}{4} i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+i c x^3}\right)+\frac{2}{3} \tanh ^{-1}\left(1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3","-\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{1}{2} i b \text{PolyLog}\left(2,1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2+\frac{1}{2} i b \text{PolyLog}\left(2,-1+\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2+\frac{1}{4} i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+i c x^3}\right)-\frac{1}{4} i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+i c x^3}\right)+\frac{2}{3} \tanh ^{-1}\left(1-\frac{2}{1+i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3",1,"(2*(a + b*ArcTan[c*x^3])^3*ArcTanh[1 - 2/(1 + I*c*x^3)])/3 - (I/2)*b*(a + b*ArcTan[c*x^3])^2*PolyLog[2, 1 - 2/(1 + I*c*x^3)] + (I/2)*b*(a + b*ArcTan[c*x^3])^2*PolyLog[2, -1 + 2/(1 + I*c*x^3)] - (b^2*(a + b*ArcTan[c*x^3])*PolyLog[3, 1 - 2/(1 + I*c*x^3)])/2 + (b^2*(a + b*ArcTan[c*x^3])*PolyLog[3, -1 + 2/(1 + I*c*x^3)])/2 + (I/4)*b^3*PolyLog[4, 1 - 2/(1 + I*c*x^3)] - (I/4)*b^3*PolyLog[4, -1 + 2/(1 + I*c*x^3)]","A",9,7,16,0.4375,1,"{5031, 4850, 4988, 4884, 4994, 4998, 6610}"
125,0,0,0,0.8600012,"\int \frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^3}{x^4} \, dx","Int[(a + b*ArcTan[c*x^3])^3/x^4,x]","\int \frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^3}{x^4} \, dx","-i b^2 c \text{PolyLog}\left(2,-1+\frac{2}{1-i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)+\frac{1}{2} b^3 c \text{PolyLog}\left(3,-1+\frac{2}{1-i c x^3}\right)-\frac{1}{3} i c \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3-\frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^3}{3 x^3}+b c \log \left(2-\frac{2}{1-i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2",1,"(b*c*Log[I*c*x^3]*(2*a + I*b*Log[1 - I*c*x^3])^2)/8 - ((1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^3)/(24*x^3) - (b^3*c*Log[(-I)*c*x^3]*Log[1 + I*c*x^3]^2)/8 - ((I/24)*b^3*(1 + I*c*x^3)*Log[1 + I*c*x^3]^3)/x^3 + (I/4)*b^2*c*(2*a + I*b*Log[1 - I*c*x^3])*PolyLog[2, 1 - I*c*x^3] - (b^3*c*Log[1 + I*c*x^3]*PolyLog[2, 1 + I*c*x^3])/4 + (b^3*c*PolyLog[3, 1 - I*c*x^3])/4 + (b^3*c*PolyLog[3, 1 + I*c*x^3])/4 + (I/8)*b*Defer[Subst][Defer[Int][(((-2*I)*a + b*Log[1 - I*c*x])^2*Log[1 + I*c*x])/x^2, x], x, x^3] - (I/8)*b^2*Defer[Subst][Defer[Int][(((-2*I)*a + b*Log[1 - I*c*x])*Log[1 + I*c*x]^2)/x^2, x], x, x^3]","F",0,0,0,0,-1,"{}"
126,0,0,0,1.6699226,"\int \frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^3}{x^7} \, dx","Int[(a + b*ArcTan[c*x^3])^3/x^7,x]","\int \frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^3}{x^7} \, dx","-\frac{1}{2} i b^3 c^2 \text{PolyLog}\left(2,-1+\frac{2}{1-i c x^3}\right)+b^2 c^2 \log \left(2-\frac{2}{1-i c x^3}\right) \left(a+b \tan ^{-1}\left(c x^3\right)\right)-\frac{1}{2} i b c^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2-\frac{1}{6} c^2 \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3-\frac{b c \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2}{2 x^3}-\frac{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^3}{6 x^6}",1,"(3*a*b^2*c^2*Log[x])/4 - (b*c*(1 - I*c*x^3)*(2*a + I*b*Log[1 - I*c*x^3])^2)/(16*x^3) + (I/16)*b*c^2*Log[I*c*x^3]*(2*a + I*b*Log[1 - I*c*x^3])^2 - (c^2*(2*a + I*b*Log[1 - I*c*x^3])^3)/48 - (2*a + I*b*Log[1 - I*c*x^3])^3/(48*x^6) + (b^3*c*(1 + I*c*x^3)*Log[1 + I*c*x^3]^2)/(16*x^3) + (I/16)*b^3*c^2*Log[(-I)*c*x^3]*Log[1 + I*c*x^3]^2 - (I/48)*b^3*c^2*Log[1 + I*c*x^3]^3 - ((I/48)*b^3*Log[1 + I*c*x^3]^3)/x^6 + (I/8)*b^3*c^2*PolyLog[2, (-I)*c*x^3] - (I/8)*b^3*c^2*PolyLog[2, I*c*x^3] - (b^2*c^2*(2*a + I*b*Log[1 - I*c*x^3])*PolyLog[2, 1 - I*c*x^3])/8 + (I/8)*b^3*c^2*Log[1 + I*c*x^3]*PolyLog[2, 1 + I*c*x^3] + (I/8)*b^3*c^2*PolyLog[3, 1 - I*c*x^3] - (I/8)*b^3*c^2*PolyLog[3, 1 + I*c*x^3] + (I/8)*b*Defer[Subst][Defer[Int][(((-2*I)*a + b*Log[1 - I*c*x])^2*Log[1 + I*c*x])/x^3, x], x, x^3] - (I/8)*b^2*Defer[Subst][Defer[Int][(((-2*I)*a + b*Log[1 - I*c*x])*Log[1 + I*c*x]^2)/x^3, x], x, x^3]","F",0,0,0,0,-1,"{}"
127,0,0,0,0.0236325,"\int (d x)^m \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcTan[c*x^3])^3,x]","\int (d x)^m \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \tan ^{-1}\left(c x^3\right)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTan[c*x^3])^3, x]","A",0,0,0,0,-1,"{}"
128,0,0,0,0.0240861,"\int (d x)^m \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcTan[c*x^3])^2,x]","\int (d x)^m \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \tan ^{-1}\left(c x^3\right)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcTan[c*x^3])^2, x]","A",0,0,0,0,-1,"{}"
129,1,75,0,0.0424709,"\int (d x)^m \left(a+b \tan ^{-1}\left(c x^3\right)\right) \, dx","Int[(d*x)^m*(a + b*ArcTan[c*x^3]),x]","\frac{(d x)^{m+1} \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{d (m+1)}-\frac{3 b c (d x)^{m+4} \, _2F_1\left(1,\frac{m+4}{6};\frac{m+10}{6};-c^2 x^6\right)}{d^4 (m+1) (m+4)}","\frac{(d x)^{m+1} \left(a+b \tan ^{-1}\left(c x^3\right)\right)}{d (m+1)}-\frac{3 b c (d x)^{m+4} \, _2F_1\left(1,\frac{m+4}{6};\frac{m+10}{6};-c^2 x^6\right)}{d^4 (m+1) (m+4)}",1,"((d*x)^(1 + m)*(a + b*ArcTan[c*x^3]))/(d*(1 + m)) - (3*b*c*(d*x)^(4 + m)*Hypergeometric2F1[1, (4 + m)/6, (10 + m)/6, -(c^2*x^6)])/(d^4*(1 + m)*(4 + m))","A",3,3,16,0.1875,1,"{5033, 16, 364}"
130,0,0,0,0.0266075,"\int \frac{(d x)^m}{a+b \tan ^{-1}\left(c x^3\right)} \, dx","Int[(d*x)^m/(a + b*ArcTan[c*x^3]),x]","\int \frac{(d x)^m}{a+b \tan ^{-1}\left(c x^3\right)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \tan ^{-1}\left(c x^3\right)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTan[c*x^3]), x]","A",0,0,0,0,-1,"{}"
131,0,0,0,0.0258208,"\int \frac{(d x)^m}{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcTan[c*x^3])^2,x]","\int \frac{(d x)^m}{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \tan ^{-1}\left(c x^3\right)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcTan[c*x^3])^2, x]","A",0,0,0,0,-1,"{}"
132,1,50,0,0.0309079,"\int x^3 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[x^3*(a + b*ArcTan[c/x]),x]","\frac{1}{4} x^4 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)-\frac{1}{4} b c^3 x+\frac{1}{4} b c^4 \tan ^{-1}\left(\frac{x}{c}\right)+\frac{1}{12} b c x^3","\frac{1}{4} x^4 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)-\frac{1}{4} b c^3 x+\frac{1}{4} b c^4 \tan ^{-1}\left(\frac{x}{c}\right)+\frac{1}{12} b c x^3",1,"-(b*c^3*x)/4 + (b*c*x^3)/12 + (x^4*(a + b*ArcTan[c/x]))/4 + (b*c^4*ArcTan[x/c])/4","A",5,4,14,0.2857,1,"{5033, 263, 302, 203}"
133,1,43,0,0.029785,"\int x^2 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[x^2*(a + b*ArcTan[c/x]),x]","\frac{1}{3} x^3 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)-\frac{1}{6} b c^3 \log \left(c^2+x^2\right)+\frac{1}{6} b c x^2","\frac{1}{3} x^3 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)-\frac{1}{6} b c^3 \log \left(c^2+x^2\right)+\frac{1}{6} b c x^2",1,"(b*c*x^2)/6 + (x^3*(a + b*ArcTan[c/x]))/3 - (b*c^3*Log[c^2 + x^2])/6","A",5,4,14,0.2857,1,"{5033, 263, 266, 43}"
134,1,39,0,0.0173373,"\int x \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[x*(a + b*ArcTan[c/x]),x]","\frac{1}{2} x^2 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)-\frac{1}{2} b c^2 \tan ^{-1}\left(\frac{x}{c}\right)+\frac{b c x}{2}","\frac{1}{2} x^2 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)-\frac{1}{2} b c^2 \tan ^{-1}\left(\frac{x}{c}\right)+\frac{b c x}{2}",1,"(b*c*x)/2 + (x^2*(a + b*ArcTan[c/x]))/2 - (b*c^2*ArcTan[x/c])/2","A",4,4,12,0.3333,1,"{5033, 193, 321, 203}"
135,1,27,0,0.0116355,"\int \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right) \, dx","Int[a + b*ArcTan[c/x],x]","a x+\frac{1}{2} b c \log \left(c^2+x^2\right)+b x \tan ^{-1}\left(\frac{c}{x}\right)","a x+\frac{1}{2} b c \log \left(c^2+x^2\right)+b x \tan ^{-1}\left(\frac{c}{x}\right)",1,"a*x + b*x*ArcTan[c/x] + (b*c*Log[c^2 + x^2])/2","A",4,3,10,0.3000,1,"{5027, 263, 260}"
136,1,39,0,0.0448919,"\int \frac{a+b \tan ^{-1}\left(\frac{c}{x}\right)}{x} \, dx","Int[(a + b*ArcTan[c/x])/x,x]","-\frac{1}{2} i b \text{PolyLog}\left(2,-\frac{i c}{x}\right)+\frac{1}{2} i b \text{PolyLog}\left(2,\frac{i c}{x}\right)+a \log (x)","-\frac{1}{2} i b \text{PolyLog}\left(2,-\frac{i c}{x}\right)+\frac{1}{2} i b \text{PolyLog}\left(2,\frac{i c}{x}\right)+a \log (x)",1,"a*Log[x] - (I/2)*b*PolyLog[2, ((-I)*c)/x] + (I/2)*b*PolyLog[2, (I*c)/x]","A",4,3,14,0.2143,1,"{5031, 4848, 2391}"
137,1,34,0,0.0190498,"\int \frac{a+b \tan ^{-1}\left(\frac{c}{x}\right)}{x^2} \, dx","Int[(a + b*ArcTan[c/x])/x^2,x]","\frac{b \log \left(\frac{c^2}{x^2}+1\right)}{2 c}-\frac{a+b \tan ^{-1}\left(\frac{c}{x}\right)}{x}","\frac{b \log \left(\frac{c^2}{x^2}+1\right)}{2 c}-\frac{a+b \tan ^{-1}\left(\frac{c}{x}\right)}{x}",1,"-((a + b*ArcTan[c/x])/x) + (b*Log[1 + c^2/x^2])/(2*c)","A",2,2,14,0.1429,1,"{5033, 260}"
138,1,43,0,0.0238361,"\int \frac{a+b \tan ^{-1}\left(\frac{c}{x}\right)}{x^3} \, dx","Int[(a + b*ArcTan[c/x])/x^3,x]","-\frac{a+b \tan ^{-1}\left(\frac{c}{x}\right)}{2 x^2}+\frac{b \tan ^{-1}\left(\frac{x}{c}\right)}{2 c^2}+\frac{b}{2 c x}","-\frac{a+b \tan ^{-1}\left(\frac{c}{x}\right)}{2 x^2}+\frac{b \tan ^{-1}\left(\frac{x}{c}\right)}{2 c^2}+\frac{b}{2 c x}",1,"b/(2*c*x) - (a + b*ArcTan[c/x])/(2*x^2) + (b*ArcTan[x/c])/(2*c^2)","A",4,4,14,0.2857,1,"{5033, 263, 325, 203}"
139,1,55,0,0.0362819,"\int \frac{a+b \tan ^{-1}\left(\frac{c}{x}\right)}{x^4} \, dx","Int[(a + b*ArcTan[c/x])/x^4,x]","-\frac{a+b \tan ^{-1}\left(\frac{c}{x}\right)}{3 x^3}-\frac{b \log \left(c^2+x^2\right)}{6 c^3}+\frac{b \log (x)}{3 c^3}+\frac{b}{6 c x^2}","-\frac{a+b \tan ^{-1}\left(\frac{c}{x}\right)}{3 x^3}-\frac{b \log \left(c^2+x^2\right)}{6 c^3}+\frac{b \log (x)}{3 c^3}+\frac{b}{6 c x^2}",1,"b/(6*c*x^2) - (a + b*ArcTan[c/x])/(3*x^3) + (b*Log[x])/(3*c^3) - (b*Log[c^2 + x^2])/(6*c^3)","A",5,4,14,0.2857,1,"{5033, 263, 266, 44}"
140,1,862,0,1.7907572,"\int x^3 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^2 \, dx","Int[x^3*(a + b*ArcTan[c/x])^2,x]","-\frac{1}{16} \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^2 c^4+\frac{1}{16} b^2 \log ^2\left(\frac{i c}{x}+1\right) c^4-\frac{11}{48} b^2 \log \left(i-\frac{c}{x}\right) c^4-\frac{5}{48} b^2 \log \left(\frac{c}{x}+i\right) c^4-\frac{5}{48} b^2 \log (c-i x) c^4+\frac{1}{4} i a b \log (c-i x) c^4-\frac{1}{8} b^2 \log \left(1-\frac{i c}{x}\right) \log (c-i x) c^4-\frac{5}{48} b^2 \log (c+i x) c^4-\frac{1}{8} b^2 \log \left(\frac{i c}{x}+1\right) \log (c+i x) c^4+\frac{1}{8} b^2 \log \left(\frac{c-i x}{2 c}\right) \log (c+i x) c^4+\frac{1}{8} b^2 \log (c-i x) \log \left(\frac{c+i x}{2 c}\right) c^4-\frac{11}{24} b^2 \log (x) c^4-\frac{1}{4} i a b \log (x) c^4-\frac{1}{8} b^2 \log (c+i x) \log \left(-\frac{i x}{c}\right) c^4-\frac{1}{8} b^2 \log (c-i x) \log \left(\frac{i x}{c}\right) c^4+\frac{1}{8} b^2 \text{PolyLog}\left(2,\frac{c-i x}{2 c}\right) c^4+\frac{1}{8} b^2 \text{PolyLog}\left(2,\frac{c+i x}{2 c}\right) c^4+\frac{1}{8} b^2 \text{PolyLog}\left(2,-\frac{i c}{x}\right) c^4+\frac{1}{8} b^2 \text{PolyLog}\left(2,\frac{i c}{x}\right) c^4-\frac{1}{8} b^2 \text{PolyLog}\left(2,1-\frac{i x}{c}\right) c^4-\frac{1}{8} b^2 \text{PolyLog}\left(2,\frac{i x}{c}+1\right) c^4-\frac{1}{4} a b x c^3-\frac{1}{8} i b^2 x \log \left(1-\frac{i c}{x}\right) c^3-\frac{1}{8} b \left(1-\frac{i c}{x}\right) x \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right) c^3+\frac{1}{4} i b^2 x \log \left(\frac{i c}{x}+1\right) c^3+\frac{1}{12} b^2 x^2 c^2-\frac{1}{8} i a b x^2 c^2+\frac{1}{16} b^2 x^2 \log \left(1-\frac{i c}{x}\right) c^2+\frac{1}{16} i b x^2 \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right) c^2+\frac{1}{12} a b x^3 c+\frac{1}{24} i b^2 x^3 \log \left(1-\frac{i c}{x}\right) c+\frac{1}{24} b x^3 \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right) c-\frac{1}{12} i b^2 x^3 \log \left(\frac{i c}{x}+1\right) c+\frac{1}{16} x^4 \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^2-\frac{1}{16} b^2 x^4 \log ^2\left(\frac{i c}{x}+1\right)-\frac{1}{4} i a b x^4 \log \left(\frac{i c}{x}+1\right)+\frac{1}{8} b^2 x^4 \log \left(1-\frac{i c}{x}\right) \log \left(\frac{i c}{x}+1\right)","-\frac{1}{4} c^4 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2-\frac{1}{2} b c^3 x \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{6} b c x^3 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{4} x^4 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{12} b^2 c^2 x^2-\frac{1}{3} b^2 c^4 \log \left(\frac{c^2}{x^2}+1\right)-\frac{2}{3} b^2 c^4 \log (x)",1,"-(a*b*c^3*x)/4 - (I/8)*a*b*c^2*x^2 + (b^2*c^2*x^2)/12 + (a*b*c*x^3)/12 - (11*b^2*c^4*Log[I - c/x])/48 - (I/8)*b^2*c^3*x*Log[1 - (I*c)/x] + (b^2*c^2*x^2*Log[1 - (I*c)/x])/16 + (I/24)*b^2*c*x^3*Log[1 - (I*c)/x] - (b*c^3*(1 - (I*c)/x)*x*(2*a + I*b*Log[1 - (I*c)/x]))/8 + (I/16)*b*c^2*x^2*(2*a + I*b*Log[1 - (I*c)/x]) + (b*c*x^3*(2*a + I*b*Log[1 - (I*c)/x]))/24 - (c^4*(2*a + I*b*Log[1 - (I*c)/x])^2)/16 + (x^4*(2*a + I*b*Log[1 - (I*c)/x])^2)/16 + (I/4)*b^2*c^3*x*Log[1 + (I*c)/x] - (I/12)*b^2*c*x^3*Log[1 + (I*c)/x] - (I/4)*a*b*x^4*Log[1 + (I*c)/x] + (b^2*x^4*Log[1 - (I*c)/x]*Log[1 + (I*c)/x])/8 + (b^2*c^4*Log[1 + (I*c)/x]^2)/16 - (b^2*x^4*Log[1 + (I*c)/x]^2)/16 - (5*b^2*c^4*Log[I + c/x])/48 + (I/4)*a*b*c^4*Log[c - I*x] - (5*b^2*c^4*Log[c - I*x])/48 - (b^2*c^4*Log[1 - (I*c)/x]*Log[c - I*x])/8 - (5*b^2*c^4*Log[c + I*x])/48 - (b^2*c^4*Log[1 + (I*c)/x]*Log[c + I*x])/8 + (b^2*c^4*Log[(c - I*x)/(2*c)]*Log[c + I*x])/8 + (b^2*c^4*Log[c - I*x]*Log[(c + I*x)/(2*c)])/8 - (I/4)*a*b*c^4*Log[x] - (11*b^2*c^4*Log[x])/24 - (b^2*c^4*Log[c + I*x]*Log[((-I)*x)/c])/8 - (b^2*c^4*Log[c - I*x]*Log[(I*x)/c])/8 + (b^2*c^4*PolyLog[2, (c - I*x)/(2*c)])/8 + (b^2*c^4*PolyLog[2, (c + I*x)/(2*c)])/8 + (b^2*c^4*PolyLog[2, ((-I)*c)/x])/8 + (b^2*c^4*PolyLog[2, (I*c)/x])/8 - (b^2*c^4*PolyLog[2, 1 - (I*x)/c])/8 - (b^2*c^4*PolyLog[2, 1 + (I*x)/c])/8","C",88,34,16,2.125,0,"{5035, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2319, 44, 2455, 263, 43, 6742, 30, 2557, 12, 2466, 2448, 2462, 260, 2416, 2394, 2393, 2391, 193, 2410, 2395, 36, 29, 2390}"
141,1,787,0,1.4901634,"\int x^2 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^2 \, dx","Int[x^2*(a + b*ArcTan[c/x])^2,x]","\frac{1}{6} i b^2 c^3 \text{PolyLog}\left(2,\frac{c-i x}{2 c}\right)-\frac{1}{6} i b^2 c^3 \text{PolyLog}\left(2,\frac{c+i x}{2 c}\right)+\frac{1}{6} i b^2 c^3 \text{PolyLog}\left(2,-\frac{i c}{x}\right)-\frac{1}{6} i b^2 c^3 \text{PolyLog}\left(2,\frac{i c}{x}\right)-\frac{1}{6} i b^2 c^3 \text{PolyLog}\left(2,1-\frac{i x}{c}\right)+\frac{1}{6} i b^2 c^3 \text{PolyLog}\left(2,1+\frac{i x}{c}\right)-\frac{1}{3} i a b c^2 x+\frac{1}{12} i c^3 \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^2-\frac{1}{3} a b c^3 \log (c-i x)-\frac{1}{3} a b c^3 \log (x)+\frac{1}{6} i b c^2 x \left(1-\frac{i c}{x}\right) \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)+\frac{1}{6} a b c x^2+\frac{1}{12} b c x^2 \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)+\frac{1}{12} x^3 \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^2-\frac{1}{3} i a b x^3 \log \left(1+\frac{i c}{x}\right)+\frac{1}{3} b^2 c^2 x+\frac{1}{12} i b^2 c^3 \log ^2\left(1+\frac{i c}{x}\right)-\frac{1}{4} i b^2 c^3 \log \left(-\frac{c}{x}+i\right)+\frac{1}{12} i b^2 c^3 \log \left(\frac{c}{x}+i\right)+\frac{1}{12} i b^2 c^3 \log (c-i x)-\frac{1}{6} i b^2 c^3 \log \left(1-\frac{i c}{x}\right) \log (c-i x)-\frac{1}{12} i b^2 c^3 \log (c+i x)+\frac{1}{6} i b^2 c^3 \log \left(1+\frac{i c}{x}\right) \log (c+i x)-\frac{1}{6} i b^2 c^3 \log \left(\frac{c-i x}{2 c}\right) \log (c+i x)+\frac{1}{6} i b^2 c^3 \log (c-i x) \log \left(\frac{c+i x}{2 c}\right)+\frac{1}{6} i b^2 c^3 \log (c+i x) \log \left(-\frac{i x}{c}\right)-\frac{1}{6} i b^2 c^3 \log (c-i x) \log \left(\frac{i x}{c}\right)+\frac{1}{6} b^2 c^2 x \log \left(1-\frac{i c}{x}\right)-\frac{1}{12} b^2 x^3 \log ^2\left(1+\frac{i c}{x}\right)+\frac{1}{12} i b^2 c x^2 \log \left(1-\frac{i c}{x}\right)-\frac{1}{6} i b^2 c x^2 \log \left(1+\frac{i c}{x}\right)+\frac{1}{6} b^2 x^3 \log \left(1-\frac{i c}{x}\right) \log \left(1+\frac{i c}{x}\right)","-\frac{1}{3} i b^2 c^3 \text{PolyLog}\left(2,-1+\frac{2}{1-\frac{i c}{x}}\right)-\frac{1}{3} i c^3 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{2}{3} b c^3 \log \left(2-\frac{2}{1-\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{3} b c x^2 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{3} x^3 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{3} b^2 c^2 x+\frac{1}{3} b^2 c^3 \cot ^{-1}\left(\frac{x}{c}\right)",1,"(-I/3)*a*b*c^2*x + (b^2*c^2*x)/3 + (a*b*c*x^2)/6 - (I/4)*b^2*c^3*Log[I - c/x] + (b^2*c^2*x*Log[1 - (I*c)/x])/6 + (I/12)*b^2*c*x^2*Log[1 - (I*c)/x] + (I/6)*b*c^2*(1 - (I*c)/x)*x*(2*a + I*b*Log[1 - (I*c)/x]) + (b*c*x^2*(2*a + I*b*Log[1 - (I*c)/x]))/12 + (I/12)*c^3*(2*a + I*b*Log[1 - (I*c)/x])^2 + (x^3*(2*a + I*b*Log[1 - (I*c)/x])^2)/12 - (I/6)*b^2*c*x^2*Log[1 + (I*c)/x] - (I/3)*a*b*x^3*Log[1 + (I*c)/x] + (b^2*x^3*Log[1 - (I*c)/x]*Log[1 + (I*c)/x])/6 + (I/12)*b^2*c^3*Log[1 + (I*c)/x]^2 - (b^2*x^3*Log[1 + (I*c)/x]^2)/12 + (I/12)*b^2*c^3*Log[I + c/x] - (a*b*c^3*Log[c - I*x])/3 + (I/12)*b^2*c^3*Log[c - I*x] - (I/6)*b^2*c^3*Log[1 - (I*c)/x]*Log[c - I*x] - (I/12)*b^2*c^3*Log[c + I*x] + (I/6)*b^2*c^3*Log[1 + (I*c)/x]*Log[c + I*x] - (I/6)*b^2*c^3*Log[(c - I*x)/(2*c)]*Log[c + I*x] + (I/6)*b^2*c^3*Log[c - I*x]*Log[(c + I*x)/(2*c)] - (a*b*c^3*Log[x])/3 + (I/6)*b^2*c^3*Log[c + I*x]*Log[((-I)*x)/c] - (I/6)*b^2*c^3*Log[c - I*x]*Log[(I*x)/c] + (I/6)*b^2*c^3*PolyLog[2, (c - I*x)/(2*c)] - (I/6)*b^2*c^3*PolyLog[2, (c + I*x)/(2*c)] + (I/6)*b^2*c^3*PolyLog[2, ((-I)*c)/x] - (I/6)*b^2*c^3*PolyLog[2, (I*c)/x] - (I/6)*b^2*c^3*PolyLog[2, 1 - (I*x)/c] + (I/6)*b^2*c^3*PolyLog[2, 1 + (I*x)/c]","B",73,34,16,2.125,0,"{5035, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2319, 44, 2455, 263, 43, 6742, 30, 2557, 12, 2466, 2448, 2462, 260, 2416, 2394, 2393, 2391, 193, 2410, 2395, 36, 29, 2390}"
142,1,663,0,1.1263644,"\int x \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^2 \, dx","Int[x*(a + b*ArcTan[c/x])^2,x]","-\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,\frac{c-i x}{2 c}\right)-\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,\frac{c+i x}{2 c}\right)-\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,-\frac{i c}{x}\right)-\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,\frac{i c}{x}\right)+\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,1-\frac{i x}{c}\right)+\frac{1}{4} b^2 c^2 \text{PolyLog}\left(2,1+\frac{i x}{c}\right)-\frac{1}{2} i a b c^2 \log (c-i x)+\frac{1}{2} i a b c^2 \log (x)+\frac{1}{8} c^2 \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^2-\frac{1}{2} i a b x^2 \log \left(1+\frac{i c}{x}\right)+\frac{1}{8} x^2 \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^2+\frac{1}{2} a b c x+\frac{1}{4} b c x \left(1-\frac{i c}{x}\right) \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)-\frac{1}{8} b^2 c^2 \log ^2\left(1+\frac{i c}{x}\right)+\frac{1}{4} b^2 c^2 \log \left(-\frac{c}{x}+i\right)+\frac{1}{4} b^2 c^2 \log (c-i x)+\frac{1}{4} b^2 c^2 \log \left(1-\frac{i c}{x}\right) \log (c-i x)+\frac{1}{4} b^2 c^2 \log (c+i x)+\frac{1}{4} b^2 c^2 \log \left(1+\frac{i c}{x}\right) \log (c+i x)-\frac{1}{4} b^2 c^2 \log \left(\frac{c-i x}{2 c}\right) \log (c+i x)-\frac{1}{4} b^2 c^2 \log (c-i x) \log \left(\frac{c+i x}{2 c}\right)+\frac{1}{2} b^2 c^2 \log (x)+\frac{1}{4} b^2 c^2 \log (c+i x) \log \left(-\frac{i x}{c}\right)+\frac{1}{4} b^2 c^2 \log (c-i x) \log \left(\frac{i x}{c}\right)-\frac{1}{8} b^2 x^2 \log ^2\left(1+\frac{i c}{x}\right)+\frac{1}{4} b^2 x^2 \log \left(1-\frac{i c}{x}\right) \log \left(1+\frac{i c}{x}\right)+\frac{1}{4} i b^2 c x \log \left(1-\frac{i c}{x}\right)-\frac{1}{2} i b^2 c x \log \left(1+\frac{i c}{x}\right)","\frac{1}{2} c^2 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{2} x^2 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+b c x \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{2} b^2 c^2 \log \left(\frac{c^2}{x^2}+1\right)+b^2 c^2 \log (x)",1,"(a*b*c*x)/2 + (b^2*c^2*Log[I - c/x])/4 + (I/4)*b^2*c*x*Log[1 - (I*c)/x] + (b*c*(1 - (I*c)/x)*x*(2*a + I*b*Log[1 - (I*c)/x]))/4 + (c^2*(2*a + I*b*Log[1 - (I*c)/x])^2)/8 + (x^2*(2*a + I*b*Log[1 - (I*c)/x])^2)/8 - (I/2)*b^2*c*x*Log[1 + (I*c)/x] - (I/2)*a*b*x^2*Log[1 + (I*c)/x] + (b^2*x^2*Log[1 - (I*c)/x]*Log[1 + (I*c)/x])/4 - (b^2*c^2*Log[1 + (I*c)/x]^2)/8 - (b^2*x^2*Log[1 + (I*c)/x]^2)/8 - (I/2)*a*b*c^2*Log[c - I*x] + (b^2*c^2*Log[c - I*x])/4 + (b^2*c^2*Log[1 - (I*c)/x]*Log[c - I*x])/4 + (b^2*c^2*Log[c + I*x])/4 + (b^2*c^2*Log[1 + (I*c)/x]*Log[c + I*x])/4 - (b^2*c^2*Log[(c - I*x)/(2*c)]*Log[c + I*x])/4 - (b^2*c^2*Log[c - I*x]*Log[(c + I*x)/(2*c)])/4 + (I/2)*a*b*c^2*Log[x] + (b^2*c^2*Log[x])/2 + (b^2*c^2*Log[c + I*x]*Log[((-I)*x)/c])/4 + (b^2*c^2*Log[c - I*x]*Log[(I*x)/c])/4 - (b^2*c^2*PolyLog[2, (c - I*x)/(2*c)])/4 - (b^2*c^2*PolyLog[2, (c + I*x)/(2*c)])/4 - (b^2*c^2*PolyLog[2, ((-I)*c)/x])/4 - (b^2*c^2*PolyLog[2, (I*c)/x])/4 + (b^2*c^2*PolyLog[2, 1 - (I*x)/c])/4 + (b^2*c^2*PolyLog[2, 1 + (I*x)/c])/4","C",58,32,14,2.286,0,"{5035, 2454, 2398, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2455, 193, 43, 6742, 30, 2557, 12, 2466, 2448, 263, 2462, 260, 2416, 2394, 2393, 2391, 2410, 2395, 36, 29, 2390}"
143,1,478,0,0.4400429,"\int \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^2 \, dx","Int[(a + b*ArcTan[c/x])^2,x]","-\frac{1}{2} i b^2 c \text{PolyLog}\left(2,\frac{c-i x}{2 c}\right)+\frac{1}{2} i b^2 c \text{PolyLog}\left(2,\frac{c+i x}{2 c}\right)-\frac{1}{2} i b^2 c \text{PolyLog}\left(2,-\frac{i c}{x}\right)+\frac{1}{2} i b^2 c \text{PolyLog}\left(2,\frac{i c}{x}\right)+\frac{1}{2} i b^2 c \text{PolyLog}\left(2,1-\frac{i x}{c}\right)-\frac{1}{2} i b^2 c \text{PolyLog}\left(2,1+\frac{i x}{c}\right)+a^2 x+i a b x \log \left(1-\frac{i c}{x}\right)-i a b x \log \left(1+\frac{i c}{x}\right)+a b c \log (c-i x)+a b c \log (c+i x)+\frac{1}{4} b^2 (-x+i c) \log ^2\left(1-\frac{i c}{x}\right)-\frac{1}{4} b^2 (x+i c) \log ^2\left(1+\frac{i c}{x}\right)+\frac{1}{2} b^2 x \log \left(1-\frac{i c}{x}\right) \log \left(1+\frac{i c}{x}\right)-\frac{1}{2} i b^2 c \log \left(1+\frac{i c}{x}\right) \log (-c-i x)+\frac{1}{2} i b^2 c \log (-c-i x) \log \left(\frac{c-i x}{2 c}\right)+\frac{1}{2} i b^2 c \log \left(1-\frac{i c}{x}\right) \log (-c+i x)-\frac{1}{2} i b^2 c \log (-c+i x) \log \left(\frac{c+i x}{2 c}\right)-\frac{1}{2} i b^2 c \log (-c-i x) \log \left(-\frac{i x}{c}\right)+\frac{1}{2} i b^2 c \log (-c+i x) \log \left(\frac{i x}{c}\right)","i b^2 c \text{PolyLog}\left(2,1-\frac{2 c}{c+i x}\right)+i c \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+x \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2-2 b c \log \left(\frac{2 c}{c+i x}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)",1,"a^2*x + I*a*b*x*Log[1 - (I*c)/x] + (b^2*(I*c - x)*Log[1 - (I*c)/x]^2)/4 - I*a*b*x*Log[1 + (I*c)/x] + (b^2*x*Log[1 - (I*c)/x]*Log[1 + (I*c)/x])/2 - (b^2*(I*c + x)*Log[1 + (I*c)/x]^2)/4 - (I/2)*b^2*c*Log[1 + (I*c)/x]*Log[-c - I*x] + a*b*c*Log[c - I*x] + (I/2)*b^2*c*Log[-c - I*x]*Log[(c - I*x)/(2*c)] + (I/2)*b^2*c*Log[1 - (I*c)/x]*Log[-c + I*x] + a*b*c*Log[c + I*x] - (I/2)*b^2*c*Log[-c + I*x]*Log[(c + I*x)/(2*c)] - (I/2)*b^2*c*Log[-c - I*x]*Log[((-I)*x)/c] + (I/2)*b^2*c*Log[-c + I*x]*Log[(I*x)/c] - (I/2)*b^2*c*PolyLog[2, (c - I*x)/(2*c)] + (I/2)*b^2*c*PolyLog[2, (c + I*x)/(2*c)] - (I/2)*b^2*c*PolyLog[2, ((-I)*c)/x] + (I/2)*b^2*c*PolyLog[2, (I*c)/x] + (I/2)*b^2*c*PolyLog[2, 1 - (I*x)/c] - (I/2)*b^2*c*PolyLog[2, 1 + (I*x)/c]","B",31,14,12,1.167,0,"{5029, 2448, 263, 31, 2449, 2391, 2556, 12, 2462, 260, 2416, 2394, 2393, 2315}"
144,1,148,0,0.2935806,"\int \frac{\left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^2}{x} \, dx","Int[(a + b*ArcTan[c/x])^2/x,x]","i b \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)-i b \text{PolyLog}\left(2,-1+\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+\frac{i c}{x}}\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+\frac{i c}{x}}\right)-2 \tanh ^{-1}\left(1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2","i b \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)-i b \text{PolyLog}\left(2,-1+\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+\frac{i c}{x}}\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+\frac{i c}{x}}\right)-2 \tanh ^{-1}\left(1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2",1,"-2*(a + b*ArcCot[x/c])^2*ArcTanh[1 - 2/(1 + (I*c)/x)] + I*b*(a + b*ArcCot[x/c])*PolyLog[2, 1 - 2/(1 + (I*c)/x)] - I*b*(a + b*ArcCot[x/c])*PolyLog[2, -1 + 2/(1 + (I*c)/x)] + (b^2*PolyLog[3, 1 - 2/(1 + (I*c)/x)])/2 - (b^2*PolyLog[3, -1 + 2/(1 + (I*c)/x)])/2","A",7,6,16,0.3750,1,"{5031, 4850, 4988, 4884, 4994, 6610}"
145,1,259,0,0.5279439,"\int \frac{\left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^2}{x^2} \, dx","Int[(a + b*ArcTan[c/x])^2/x^2,x]","\frac{i b^2 \text{PolyLog}\left(2,-\frac{-x+i c}{2 x}\right)}{2 c}-\frac{i b^2 \text{PolyLog}\left(2,\frac{x+i c}{2 x}\right)}{2 c}+\frac{b \log \left(1+\frac{i c}{x}\right) \left(2 i a-b \log \left(1-\frac{i c}{x}\right)\right)}{2 x}-\frac{i b \log \left(\frac{x+i c}{2 x}\right) \left(2 i a-b \log \left(1-\frac{i c}{x}\right)\right)}{2 c}-\frac{i \left(1-\frac{i c}{x}\right) \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^2}{4 c}-\frac{i b^2 \left(1+\frac{i c}{x}\right) \log ^2\left(1+\frac{i c}{x}\right)}{4 c}-\frac{i b^2 \log \left(1+\frac{i c}{x}\right) \log \left(-\frac{-x+i c}{2 x}\right)}{2 c}","-\frac{i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i c}{x}}\right)}{c}-\frac{i \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2}{c}-\frac{\left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2}{x}-\frac{2 b \log \left(\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)}{c}",1,"((-I/4)*(1 - (I*c)/x)*(2*a + I*b*Log[1 - (I*c)/x])^2)/c + (b*((2*I)*a - b*Log[1 - (I*c)/x])*Log[1 + (I*c)/x])/(2*x) - ((I/4)*b^2*(1 + (I*c)/x)*Log[1 + (I*c)/x]^2)/c - ((I/2)*b^2*Log[1 + (I*c)/x]*Log[-(I*c - x)/(2*x)])/c - ((I/2)*b*((2*I)*a - b*Log[1 - (I*c)/x])*Log[(I*c + x)/(2*x)])/c + ((I/2)*b^2*PolyLog[2, -(I*c - x)/(2*x)])/c - ((I/2)*b^2*PolyLog[2, (I*c + x)/(2*x)])/c","B",28,12,16,0.7500,0,"{5035, 2454, 2389, 2296, 2295, 6715, 2430, 43, 2416, 2394, 2393, 2391}"
146,1,836,0,1.2936251,"\int \frac{\left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^2}{x^3} \, dx","Int[(a + b*ArcTan[c/x])^2/x^3,x]","-\frac{\left(1-\frac{i c}{x}\right)^2 b^2}{16 c^2}-\frac{\left(\frac{i c}{x}+1\right)^2 b^2}{16 c^2}-\frac{\left(\frac{i c}{x}+1\right)^2 \log ^2\left(\frac{i c}{x}+1\right) b^2}{8 c^2}+\frac{\left(\frac{i c}{x}+1\right) \log ^2\left(\frac{i c}{x}+1\right) b^2}{4 c^2}+\frac{\log \left(i-\frac{c}{x}\right) b^2}{8 c^2}-\frac{3 \left(1-\frac{i c}{x}\right) \log \left(1-\frac{i c}{x}\right) b^2}{4 c^2}+\frac{\log \left(1-\frac{i c}{x}\right) b^2}{8 x^2}+\frac{\left(\frac{i c}{x}+1\right)^2 \log \left(\frac{i c}{x}+1\right) b^2}{8 c^2}-\frac{3 \left(\frac{i c}{x}+1\right) \log \left(\frac{i c}{x}+1\right) b^2}{4 c^2}-\frac{\log \left(1-\frac{i c}{x}\right) \log \left(\frac{i c}{x}+1\right) b^2}{4 x^2}+\frac{\log \left(\frac{i c}{x}+1\right) b^2}{8 x^2}+\frac{\log \left(\frac{c}{x}+i\right) b^2}{8 c^2}-\frac{\log \left(1-\frac{i c}{x}\right) \log (c-i x) b^2}{4 c^2}-\frac{\log \left(\frac{i c}{x}+1\right) \log (c+i x) b^2}{4 c^2}+\frac{\log \left(\frac{c-i x}{2 c}\right) \log (c+i x) b^2}{4 c^2}+\frac{\log (c-i x) \log \left(\frac{c+i x}{2 c}\right) b^2}{4 c^2}-\frac{\log (c+i x) \log \left(-\frac{i x}{c}\right) b^2}{4 c^2}-\frac{\log (c-i x) \log \left(\frac{i x}{c}\right) b^2}{4 c^2}+\frac{\text{PolyLog}\left(2,\frac{c-i x}{2 c}\right) b^2}{4 c^2}+\frac{\text{PolyLog}\left(2,\frac{c+i x}{2 c}\right) b^2}{4 c^2}+\frac{\text{PolyLog}\left(2,-\frac{i c}{x}\right) b^2}{4 c^2}+\frac{\text{PolyLog}\left(2,\frac{i c}{x}\right) b^2}{4 c^2}-\frac{\text{PolyLog}\left(2,1-\frac{i x}{c}\right) b^2}{4 c^2}-\frac{\text{PolyLog}\left(2,\frac{i x}{c}+1\right) b^2}{4 c^2}-\frac{b^2}{8 x^2}+\frac{i a \log \left(i-\frac{c}{x}\right) b}{2 c^2}-\frac{i \left(1-\frac{i c}{x}\right)^2 \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right) b}{8 c^2}+\frac{i a \log \left(\frac{i c}{x}+1\right) b}{2 x^2}+\frac{3 a b}{2 c x}-\frac{i a b}{4 x^2}+\frac{\left(1-\frac{i c}{x}\right)^2 \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^2}{8 c^2}-\frac{\left(1-\frac{i c}{x}\right) \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^2}{4 c^2}","-\frac{\left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2}{2 c^2}-\frac{\left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2}{2 x^2}+\frac{a b}{c x}-\frac{b^2 \log \left(\frac{c^2}{x^2}+1\right)}{2 c^2}+\frac{b^2 \cot ^{-1}\left(\frac{x}{c}\right)}{c x}",1,"-(b^2*(1 - (I*c)/x)^2)/(16*c^2) - (b^2*(1 + (I*c)/x)^2)/(16*c^2) - ((I/4)*a*b)/x^2 - b^2/(8*x^2) + (3*a*b)/(2*c*x) + ((I/2)*a*b*Log[I - c/x])/c^2 + (b^2*Log[I - c/x])/(8*c^2) - (3*b^2*(1 - (I*c)/x)*Log[1 - (I*c)/x])/(4*c^2) + (b^2*Log[1 - (I*c)/x])/(8*x^2) - ((I/8)*b*(1 - (I*c)/x)^2*(2*a + I*b*Log[1 - (I*c)/x]))/c^2 - ((1 - (I*c)/x)*(2*a + I*b*Log[1 - (I*c)/x])^2)/(4*c^2) + ((1 - (I*c)/x)^2*(2*a + I*b*Log[1 - (I*c)/x])^2)/(8*c^2) - (3*b^2*(1 + (I*c)/x)*Log[1 + (I*c)/x])/(4*c^2) + (b^2*(1 + (I*c)/x)^2*Log[1 + (I*c)/x])/(8*c^2) + ((I/2)*a*b*Log[1 + (I*c)/x])/x^2 + (b^2*Log[1 + (I*c)/x])/(8*x^2) - (b^2*Log[1 - (I*c)/x]*Log[1 + (I*c)/x])/(4*x^2) + (b^2*(1 + (I*c)/x)*Log[1 + (I*c)/x]^2)/(4*c^2) - (b^2*(1 + (I*c)/x)^2*Log[1 + (I*c)/x]^2)/(8*c^2) + (b^2*Log[I + c/x])/(8*c^2) - (b^2*Log[1 - (I*c)/x]*Log[c - I*x])/(4*c^2) - (b^2*Log[1 + (I*c)/x]*Log[c + I*x])/(4*c^2) + (b^2*Log[(c - I*x)/(2*c)]*Log[c + I*x])/(4*c^2) + (b^2*Log[c - I*x]*Log[(c + I*x)/(2*c)])/(4*c^2) - (b^2*Log[c + I*x]*Log[((-I)*x)/c])/(4*c^2) - (b^2*Log[c - I*x]*Log[(I*x)/c])/(4*c^2) + (b^2*PolyLog[2, (c - I*x)/(2*c)])/(4*c^2) + (b^2*PolyLog[2, (c + I*x)/(2*c)])/(4*c^2) + (b^2*PolyLog[2, ((-I)*c)/x])/(4*c^2) + (b^2*PolyLog[2, (I*c)/x])/(4*c^2) - (b^2*PolyLog[2, 1 - (I*x)/c])/(4*c^2) - (b^2*PolyLog[2, 1 + (I*x)/c])/(4*c^2)","C",66,23,16,1.438,0,"{5035, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2395, 43, 6742, 30, 2557, 12, 2466, 2462, 260, 2416, 2394, 2393, 2391, 2315}"
147,0,0,0,4.6285836,"\int x^3 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","Int[x^3*(a + b*ArcTan[c/x])^3,x]","\int x^3 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","-i b^3 c^4 \text{PolyLog}\left(2,-1+\frac{2}{1-\frac{i c}{x}}\right)+\frac{1}{4} b^2 c^2 x^2 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+2 b^2 c^4 \log \left(2-\frac{2}{1-\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)-\frac{1}{4} c^4 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3-i b c^4 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2-\frac{3}{4} b c^3 x \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{4} b c x^3 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{4} x^4 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3+\frac{1}{4} b^3 c^3 x+\frac{1}{4} b^3 c^4 \cot ^{-1}\left(\frac{x}{c}\right)",1,"(-3*a^2*b*c^3*x)/8 - ((5*I)/16)*a*b^2*c^3*x + (b^3*c^3*x)/16 - ((3*I)/16)*a^2*b*c^2*x^2 + (3*a*b^2*c^2*x^2)/16 + (a^2*b*c*x^3)/8 - (11*a*b^2*c^4*Log[I - c/x])/16 - (I/32)*b^3*c^4*Log[I - c/x] - ((3*I)/8)*a*b^2*c^3*x*Log[1 - (I*c)/x] + (3*a*b^2*c^2*x^2*Log[1 - (I*c)/x])/16 + (I/8)*a*b^2*c*x^3*Log[1 - (I*c)/x] + ((5*I)/32)*b^2*c^3*(1 - (I*c)/x)*x*(2*a + I*b*Log[1 - (I*c)/x]) + (b^2*c^2*x^2*(2*a + I*b*Log[1 - (I*c)/x]))/32 + ((5*I)/64)*b*c^4*(2*a + I*b*Log[1 - (I*c)/x])^2 - (3*b*c^3*(1 - (I*c)/x)*x*(2*a + I*b*Log[1 - (I*c)/x])^2)/32 + ((3*I)/64)*b*c^2*x^2*(2*a + I*b*Log[1 - (I*c)/x])^2 + (b*c*x^3*(2*a + I*b*Log[1 - (I*c)/x])^2)/32 - (c^4*(2*a + I*b*Log[1 - (I*c)/x])^3)/32 + (x^4*(2*a + I*b*Log[1 - (I*c)/x])^3)/32 + ((3*I)/4)*a*b^2*c^3*x*Log[1 + (I*c)/x] - (5*b^3*c^3*(1 + (I*c)/x)*x*Log[1 + (I*c)/x])/32 - (I/32)*b^3*c^2*x^2*Log[1 + (I*c)/x] - (I/4)*a*b^2*c*x^3*Log[1 + (I*c)/x] - ((3*I)/8)*a^2*b*x^4*Log[1 + (I*c)/x] + (3*a*b^2*x^4*Log[1 - (I*c)/x]*Log[1 + (I*c)/x])/8 + (3*a*b^2*c^4*Log[1 + (I*c)/x]^2)/16 + ((5*I)/64)*b^3*c^4*Log[1 + (I*c)/x]^2 + (3*b^3*c^3*(1 + (I*c)/x)*x*Log[1 + (I*c)/x]^2)/32 + ((3*I)/64)*b^3*c^2*x^2*Log[1 + (I*c)/x]^2 - (b^3*c*x^3*Log[1 + (I*c)/x]^2)/32 - (3*a*b^2*x^4*Log[1 + (I*c)/x]^2)/16 - (I/32)*b^3*c^4*Log[1 + (I*c)/x]^3 + (I/32)*b^3*x^4*Log[1 + (I*c)/x]^3 + (I/32)*b^3*c^4*Log[I + c/x] + ((3*I)/8)*a^2*b*c^4*Log[c - I*x] - (5*a*b^2*c^4*Log[c - I*x])/16 - (3*a*b^2*c^4*Log[1 - (I*c)/x]*Log[c - I*x])/8 - (5*a*b^2*c^4*Log[c + I*x])/16 - (3*a*b^2*c^4*Log[1 + (I*c)/x]*Log[c + I*x])/8 + (3*a*b^2*c^4*Log[(c - I*x)/(2*c)]*Log[c + I*x])/8 + (3*a*b^2*c^4*Log[c - I*x]*Log[(c + I*x)/(2*c)])/8 + ((3*I)/32)*b^3*c^4*Log[1 + (I*c)/x]^2*Log[((-I)*c)/x] + ((3*I)/32)*b*c^4*(2*a + I*b*Log[1 - (I*c)/x])^2*Log[(I*c)/x] - (11*a*b^2*c^4*Log[x])/8 - (3*a*b^2*c^4*Log[c + I*x]*Log[((-I)*x)/c])/8 - (3*a*b^2*c^4*Log[c - I*x]*Log[(I*x)/c])/8 - (3*b^2*c^4*(2*a + I*b*Log[1 - (I*c)/x])*PolyLog[2, 1 - (I*c)/x])/16 + ((3*I)/16)*b^3*c^4*Log[1 + (I*c)/x]*PolyLog[2, 1 + (I*c)/x] + (3*a*b^2*c^4*PolyLog[2, (c - I*x)/(2*c)])/8 + (3*a*b^2*c^4*PolyLog[2, (c + I*x)/(2*c)])/8 + (3*a*b^2*c^4*PolyLog[2, ((-I)*c)/x])/8 + ((11*I)/32)*b^3*c^4*PolyLog[2, ((-I)*c)/x] - ((11*I)/32)*b^3*c^4*PolyLog[2, (I*c)/x] - (3*a*b^2*c^4*PolyLog[2, 1 - (I*x)/c])/8 - (3*a*b^2*c^4*PolyLog[2, 1 + (I*x)/c])/8 + ((3*I)/16)*b^3*c^4*PolyLog[3, 1 - (I*c)/x] - ((3*I)/16)*b^3*c^4*PolyLog[3, 1 + (I*c)/x] + ((3*I)/8)*b^3*Defer[Int][x^3*Log[1 - (I*c)/x]^2*Log[1 + (I*c)/x], x] - ((3*I)/8)*b^3*Defer[Int][x^3*Log[1 - (I*c)/x]*Log[1 + (I*c)/x]^2, x]","F",0,0,0,0,-1,"{}"
148,0,0,0,3.5202429,"\int x^2 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","Int[x^2*(a + b*ArcTan[c/x])^3,x]","\int x^2 \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","-i b^2 c^3 \text{PolyLog}\left(2,-1+\frac{2}{1-\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{1}{2} b^3 c^3 \text{PolyLog}\left(3,-1+\frac{2}{1-\frac{i c}{x}}\right)+b^2 c^2 x \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)-\frac{1}{3} i c^3 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3+\frac{1}{2} b c^3 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+b c^3 \log \left(2-\frac{2}{1-\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{2} b c x^2 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{3} x^3 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3+\frac{1}{2} b^3 c^3 \log \left(\frac{c^2}{x^2}+1\right)+b^3 c^3 \log (x)",1,"(-I/2)*a^2*b*c^2*x + (3*a*b^2*c^2*x)/4 + (a^2*b*c*x^2)/4 - ((3*I)/4)*a*b^2*c^3*Log[I - c/x] + (a*b^2*c^2*x*Log[1 - (I*c)/x])/2 + (I/4)*a*b^2*c*x^2*Log[1 - (I*c)/x] + (b^2*c^2*(1 - (I*c)/x)*x*(2*a + I*b*Log[1 - (I*c)/x]))/8 + (b*c^3*(2*a + I*b*Log[1 - (I*c)/x])^2)/16 + (I/8)*b*c^2*(1 - (I*c)/x)*x*(2*a + I*b*Log[1 - (I*c)/x])^2 + (b*c*x^2*(2*a + I*b*Log[1 - (I*c)/x])^2)/16 + (I/24)*c^3*(2*a + I*b*Log[1 - (I*c)/x])^3 + (x^3*(2*a + I*b*Log[1 - (I*c)/x])^3)/24 - (I/8)*b^3*c^2*(1 + (I*c)/x)*x*Log[1 + (I*c)/x] - (I/2)*a*b^2*c*x^2*Log[1 + (I*c)/x] - (I/2)*a^2*b*x^3*Log[1 + (I*c)/x] + (a*b^2*x^3*Log[1 - (I*c)/x]*Log[1 + (I*c)/x])/2 + (I/4)*a*b^2*c^3*Log[1 + (I*c)/x]^2 - (b^3*c^3*Log[1 + (I*c)/x]^2)/16 + (I/8)*b^3*c^2*(1 + (I*c)/x)*x*Log[1 + (I*c)/x]^2 - (b^3*c*x^2*Log[1 + (I*c)/x]^2)/16 - (a*b^2*x^3*Log[1 + (I*c)/x]^2)/4 + (b^3*c^3*Log[1 + (I*c)/x]^3)/24 + (I/24)*b^3*x^3*Log[1 + (I*c)/x]^3 - (a^2*b*c^3*Log[c - I*x])/2 + (I/4)*a*b^2*c^3*Log[c - I*x] - (I/2)*a*b^2*c^3*Log[1 - (I*c)/x]*Log[c - I*x] - (I/4)*a*b^2*c^3*Log[c + I*x] + (I/2)*a*b^2*c^3*Log[1 + (I*c)/x]*Log[c + I*x] - (I/2)*a*b^2*c^3*Log[(c - I*x)/(2*c)]*Log[c + I*x] + (I/2)*a*b^2*c^3*Log[c - I*x]*Log[(c + I*x)/(2*c)] - (b^3*c^3*Log[1 + (I*c)/x]^2*Log[((-I)*c)/x])/8 + (b*c^3*(2*a + I*b*Log[1 - (I*c)/x])^2*Log[(I*c)/x])/8 + (b^3*c^3*Log[x])/4 + (I/2)*a*b^2*c^3*Log[c + I*x]*Log[((-I)*x)/c] - (I/2)*a*b^2*c^3*Log[c - I*x]*Log[(I*x)/c] + (I/4)*b^2*c^3*(2*a + I*b*Log[1 - (I*c)/x])*PolyLog[2, 1 - (I*c)/x] - (b^3*c^3*Log[1 + (I*c)/x]*PolyLog[2, 1 + (I*c)/x])/4 + (I/2)*a*b^2*c^3*PolyLog[2, (c - I*x)/(2*c)] - (I/2)*a*b^2*c^3*PolyLog[2, (c + I*x)/(2*c)] + (I/2)*a*b^2*c^3*PolyLog[2, ((-I)*c)/x] - (3*b^3*c^3*PolyLog[2, ((-I)*c)/x])/8 - (3*b^3*c^3*PolyLog[2, (I*c)/x])/8 - (I/2)*a*b^2*c^3*PolyLog[2, 1 - (I*x)/c] + (I/2)*a*b^2*c^3*PolyLog[2, 1 + (I*x)/c] + (b^3*c^3*PolyLog[3, 1 - (I*c)/x])/4 + (b^3*c^3*PolyLog[3, 1 + (I*c)/x])/4 + ((3*I)/8)*b^3*Defer[Int][x^2*Log[1 - (I*c)/x]^2*Log[1 + (I*c)/x], x] - ((3*I)/8)*b^3*Defer[Int][x^2*Log[1 - (I*c)/x]*Log[1 + (I*c)/x]^2, x]","F",0,0,0,0,-1,"{}"
149,0,0,0,2.3519097,"\int x \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","Int[x*(a + b*ArcTan[c/x])^3,x]","\int x \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","\frac{3}{2} i b^3 c^2 \text{PolyLog}\left(2,-1+\frac{2}{1-\frac{i c}{x}}\right)-3 b^2 c^2 \log \left(2-\frac{2}{1-\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{3}{2} i b c^2 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2+\frac{1}{2} c^2 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3+\frac{1}{2} x^2 \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3+\frac{3}{2} b c x \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2",1,"(3*a^2*b*c*x)/4 + (3*a*b^2*c^2*Log[I - c/x])/4 + ((3*I)/4)*a*b^2*c*x*Log[1 - (I*c)/x] + (3*b*c*(1 - (I*c)/x)*x*(2*a + I*b*Log[1 - (I*c)/x])^2)/16 + (c^2*(2*a + I*b*Log[1 - (I*c)/x])^3)/16 + (x^2*(2*a + I*b*Log[1 - (I*c)/x])^3)/16 - ((3*I)/2)*a*b^2*c*x*Log[1 + (I*c)/x] - ((3*I)/4)*a^2*b*x^2*Log[1 + (I*c)/x] + (3*a*b^2*x^2*Log[1 - (I*c)/x]*Log[1 + (I*c)/x])/4 - (3*a*b^2*c^2*Log[1 + (I*c)/x]^2)/8 - (3*b^3*c*(1 + (I*c)/x)*x*Log[1 + (I*c)/x]^2)/16 - (3*a*b^2*x^2*Log[1 + (I*c)/x]^2)/8 + (I/16)*b^3*c^2*Log[1 + (I*c)/x]^3 + (I/16)*b^3*x^2*Log[1 + (I*c)/x]^3 - ((3*I)/4)*a^2*b*c^2*Log[c - I*x] + (3*a*b^2*c^2*Log[c - I*x])/4 + (3*a*b^2*c^2*Log[1 - (I*c)/x]*Log[c - I*x])/4 + (3*a*b^2*c^2*Log[c + I*x])/4 + (3*a*b^2*c^2*Log[1 + (I*c)/x]*Log[c + I*x])/4 - (3*a*b^2*c^2*Log[(c - I*x)/(2*c)]*Log[c + I*x])/4 - (3*a*b^2*c^2*Log[c - I*x]*Log[(c + I*x)/(2*c)])/4 - ((3*I)/16)*b^3*c^2*Log[1 + (I*c)/x]^2*Log[((-I)*c)/x] - ((3*I)/16)*b*c^2*(2*a + I*b*Log[1 - (I*c)/x])^2*Log[(I*c)/x] + (3*a*b^2*c^2*Log[x])/2 + (3*a*b^2*c^2*Log[c + I*x]*Log[((-I)*x)/c])/4 + (3*a*b^2*c^2*Log[c - I*x]*Log[(I*x)/c])/4 + (3*b^2*c^2*(2*a + I*b*Log[1 - (I*c)/x])*PolyLog[2, 1 - (I*c)/x])/8 - ((3*I)/8)*b^3*c^2*Log[1 + (I*c)/x]*PolyLog[2, 1 + (I*c)/x] - (3*a*b^2*c^2*PolyLog[2, (c - I*x)/(2*c)])/4 - (3*a*b^2*c^2*PolyLog[2, (c + I*x)/(2*c)])/4 - (3*a*b^2*c^2*PolyLog[2, ((-I)*c)/x])/4 - ((3*I)/8)*b^3*c^2*PolyLog[2, ((-I)*c)/x] + ((3*I)/8)*b^3*c^2*PolyLog[2, (I*c)/x] + (3*a*b^2*c^2*PolyLog[2, 1 - (I*x)/c])/4 + (3*a*b^2*c^2*PolyLog[2, 1 + (I*x)/c])/4 - ((3*I)/8)*b^3*c^2*PolyLog[3, 1 - (I*c)/x] + ((3*I)/8)*b^3*c^2*PolyLog[3, 1 + (I*c)/x] + ((3*I)/8)*b^3*Defer[Int][x*Log[1 - (I*c)/x]^2*Log[1 + (I*c)/x], x] - ((3*I)/8)*b^3*Defer[Int][x*Log[1 - (I*c)/x]*Log[1 + (I*c)/x]^2, x]","F",0,0,0,0,-1,"{}"
150,0,0,0,0.7386508,"\int \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","Int[(a + b*ArcTan[c/x])^3,x]","\int \left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3 \, dx","3 i b^2 c \text{PolyLog}\left(2,1-\frac{2 c}{c+i x}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)-\frac{3}{2} b^3 c \text{PolyLog}\left(3,1-\frac{2 c}{c+i x}\right)+i c \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3+x \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3-3 b c \log \left(\frac{2 c}{c+i x}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2",1,"a^3*x + ((3*I)/2)*a^2*b*x*Log[1 - (I*c)/x] + (3*a*b^2*(I*c - x)*Log[1 - (I*c)/x]^2)/4 + (I/8)*b^3*(I*c - x)*Log[1 - (I*c)/x]^3 - ((3*I)/2)*a^2*b*x*Log[1 + (I*c)/x] + (3*a*b^2*x*Log[1 - (I*c)/x]*Log[1 + (I*c)/x])/2 - (3*a*b^2*(I*c + x)*Log[1 + (I*c)/x]^2)/4 + (I/8)*b^3*(I*c + x)*Log[1 + (I*c)/x]^3 - ((3*I)/2)*a*b^2*c*Log[1 + (I*c)/x]*Log[-c - I*x] + (3*a^2*b*c*Log[c - I*x])/2 + ((3*I)/2)*a*b^2*c*Log[-c - I*x]*Log[(c - I*x)/(2*c)] + ((3*I)/2)*a*b^2*c*Log[1 - (I*c)/x]*Log[-c + I*x] + (3*a^2*b*c*Log[c + I*x])/2 - ((3*I)/2)*a*b^2*c*Log[-c + I*x]*Log[(c + I*x)/(2*c)] + (3*b^3*c*Log[1 + (I*c)/x]^2*Log[((-I)*c)/x])/8 + (3*b^3*c*Log[1 - (I*c)/x]^2*Log[(I*c)/x])/8 - ((3*I)/2)*a*b^2*c*Log[-c - I*x]*Log[((-I)*x)/c] + ((3*I)/2)*a*b^2*c*Log[-c + I*x]*Log[(I*x)/c] + (3*b^3*c*Log[1 - (I*c)/x]*PolyLog[2, 1 - (I*c)/x])/4 + (3*b^3*c*Log[1 + (I*c)/x]*PolyLog[2, 1 + (I*c)/x])/4 - ((3*I)/2)*a*b^2*c*PolyLog[2, (c - I*x)/(2*c)] + ((3*I)/2)*a*b^2*c*PolyLog[2, (c + I*x)/(2*c)] - ((3*I)/2)*a*b^2*c*PolyLog[2, ((-I)*c)/x] + ((3*I)/2)*a*b^2*c*PolyLog[2, (I*c)/x] + ((3*I)/2)*a*b^2*c*PolyLog[2, 1 - (I*x)/c] - ((3*I)/2)*a*b^2*c*PolyLog[2, 1 + (I*x)/c] - (3*b^3*c*PolyLog[3, 1 - (I*c)/x])/4 - (3*b^3*c*PolyLog[3, 1 + (I*c)/x])/4 + ((3*I)/8)*b^3*Defer[Int][Log[1 - (I*c)/x]^2*Log[1 + (I*c)/x], x] - ((3*I)/8)*b^3*Defer[Int][Log[1 - (I*c)/x]*Log[1 + (I*c)/x]^2, x]","F",0,0,0,0,-1,"{}"
151,1,230,0,0.4944968,"\int \frac{\left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3}{x} \, dx","Int[(a + b*ArcTan[c/x])^3/x,x]","\frac{3}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)-\frac{3}{2} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{3}{2} i b \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2-\frac{3}{2} i b \text{PolyLog}\left(2,-1+\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2-\frac{3}{4} i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+\frac{i c}{x}}\right)+\frac{3}{4} i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+\frac{i c}{x}}\right)-2 \tanh ^{-1}\left(1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3","\frac{3}{2} b^2 \text{PolyLog}\left(3,1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)-\frac{3}{2} b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)+\frac{3}{2} i b \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2-\frac{3}{2} i b \text{PolyLog}\left(2,-1+\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2-\frac{3}{4} i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+\frac{i c}{x}}\right)+\frac{3}{4} i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+\frac{i c}{x}}\right)-2 \tanh ^{-1}\left(1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3",1,"-2*(a + b*ArcCot[x/c])^3*ArcTanh[1 - 2/(1 + (I*c)/x)] + ((3*I)/2)*b*(a + b*ArcCot[x/c])^2*PolyLog[2, 1 - 2/(1 + (I*c)/x)] - ((3*I)/2)*b*(a + b*ArcCot[x/c])^2*PolyLog[2, -1 + 2/(1 + (I*c)/x)] + (3*b^2*(a + b*ArcCot[x/c])*PolyLog[3, 1 - 2/(1 + (I*c)/x)])/2 - (3*b^2*(a + b*ArcCot[x/c])*PolyLog[3, -1 + 2/(1 + (I*c)/x)])/2 - ((3*I)/4)*b^3*PolyLog[4, 1 - 2/(1 + (I*c)/x)] + ((3*I)/4)*b^3*PolyLog[4, -1 + 2/(1 + (I*c)/x)]","A",9,7,16,0.4375,1,"{5031, 4850, 4988, 4884, 4994, 4998, 6610}"
152,1,551,0,2.3587137,"\int \frac{\left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3}{x^2} \, dx","Int[(a + b*ArcTan[c/x])^3/x^2,x]","\frac{3 b^2 \text{PolyLog}\left(2,-\frac{-x+i c}{2 x}\right) \left(2 i a-b \log \left(1-\frac{i c}{x}\right)\right)}{2 c}+\frac{3 b^3 \text{PolyLog}\left(3,-\frac{-x+i c}{2 x}\right)}{2 c}+\frac{3 b^3 \text{PolyLog}\left(3,\frac{x+i c}{2 x}\right)}{2 c}-\frac{3 b^3 \log \left(1+\frac{i c}{x}\right) \text{PolyLog}\left(2,\frac{x+i c}{2 x}\right)}{2 c}-\frac{3 b^2 \log ^2\left(1+\frac{i c}{x}\right) \left(2 i a-b \log \left(1-\frac{i c}{x}\right)\right)}{8 c}-\frac{3 i b^2 \log ^2\left(1+\frac{i c}{x}\right) \left(2 i a-b \log \left(1-\frac{i c}{x}\right)\right)}{8 x}-\frac{3 b \left(1-\frac{i c}{x}\right) \left(2 i a-b \log \left(1-\frac{i c}{x}\right)\right)^2}{8 c}-\frac{3 b \left(1-\frac{i c}{x}\right) \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^2}{8 c}+\frac{3 b \log \left(1+\frac{i c}{x}\right) \left(2 i a-b \log \left(1-\frac{i c}{x}\right)\right)^2}{8 c}-\frac{3 i b \log \left(1+\frac{i c}{x}\right) \left(2 i a-b \log \left(1-\frac{i c}{x}\right)\right)^2}{8 x}-\frac{3 b \log \left(\frac{x+i c}{2 x}\right) \left(2 i a-b \log \left(1-\frac{i c}{x}\right)\right)^2}{4 c}-\frac{i \left(1-\frac{i c}{x}\right) \left(2 a+i b \log \left(1-\frac{i c}{x}\right)\right)^3}{8 c}-\frac{b^3 \left(1+\frac{i c}{x}\right) \log ^3\left(1+\frac{i c}{x}\right)}{8 c}-\frac{3 b^3 \log ^2\left(1+\frac{i c}{x}\right) \log \left(-\frac{-x+i c}{2 x}\right)}{4 c}","-\frac{3 i b^2 \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)}{c}-\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{1+\frac{i c}{x}}\right)}{2 c}-\frac{i \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3}{c}-\frac{\left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3}{x}-\frac{3 b \log \left(\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2}{c}",1,"(-3*b*(1 - (I*c)/x)*((2*I)*a - b*Log[1 - (I*c)/x])^2)/(8*c) - (3*b*(1 - (I*c)/x)*(2*a + I*b*Log[1 - (I*c)/x])^2)/(8*c) - ((I/8)*(1 - (I*c)/x)*(2*a + I*b*Log[1 - (I*c)/x])^3)/c + (3*b*((2*I)*a - b*Log[1 - (I*c)/x])^2*Log[1 + (I*c)/x])/(8*c) - (((3*I)/8)*b*((2*I)*a - b*Log[1 - (I*c)/x])^2*Log[1 + (I*c)/x])/x - (3*b^2*((2*I)*a - b*Log[1 - (I*c)/x])*Log[1 + (I*c)/x]^2)/(8*c) - (((3*I)/8)*b^2*((2*I)*a - b*Log[1 - (I*c)/x])*Log[1 + (I*c)/x]^2)/x - (b^3*(1 + (I*c)/x)*Log[1 + (I*c)/x]^3)/(8*c) - (3*b^3*Log[1 + (I*c)/x]^2*Log[-(I*c - x)/(2*x)])/(4*c) - (3*b*((2*I)*a - b*Log[1 - (I*c)/x])^2*Log[(I*c + x)/(2*x)])/(4*c) + (3*b^2*((2*I)*a - b*Log[1 - (I*c)/x])*PolyLog[2, -(I*c - x)/(2*x)])/(2*c) - (3*b^3*Log[1 + (I*c)/x]*PolyLog[2, (I*c + x)/(2*x)])/(2*c) + (3*b^3*PolyLog[3, -(I*c - x)/(2*x)])/(2*c) + (3*b^3*PolyLog[3, (I*c + x)/(2*x)])/(2*c)","B",82,23,16,1.438,0,"{5035, 2454, 2389, 2296, 2295, 6715, 2430, 2416, 2396, 2433, 2374, 6589, 2411, 2346, 2301, 6742, 43, 2394, 2393, 2391, 2375, 2317, 2425}"
153,0,0,0,2.2545085,"\int \frac{\left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3}{x^3} \, dx","Int[(a + b*ArcTan[c/x])^3/x^3,x]","\int \frac{\left(a+b \tan ^{-1}\left(\frac{c}{x}\right)\right)^3}{x^3} \, dx","\frac{3 i b^3 \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i c}{x}}\right)}{2 c^2}+\frac{3 b^2 \log \left(\frac{2}{1+\frac{i c}{x}}\right) \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)}{c^2}+\frac{3 i b \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2}{2 c^2}-\frac{\left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3}{2 c^2}-\frac{\left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^3}{2 x^2}+\frac{3 b \left(a+b \cot ^{-1}\left(\frac{x}{c}\right)\right)^2}{2 c x}",1,"(((3*I)/64)*b^3*(1 - (I*c)/x)^2)/c^2 - (3*a*b^2*(1 + (I*c)/x)^2)/(16*c^2) - (((3*I)/64)*b^3*(1 + (I*c)/x)^2)/c^2 - (((3*I)/8)*a^2*b)/x^2 - (3*a*b^2)/(8*x^2) + (3*a^2*b)/(4*c*x) - (3*b^3)/(2*c*x) + (((3*I)/4)*a^2*b*Log[I - c/x])/c^2 + (3*a*b^2*Log[I - c/x])/(8*c^2) - (3*a*b^2*(1 - (I*c)/x)*Log[1 - (I*c)/x])/(4*c^2) + (((3*I)/4)*b^3*(1 - (I*c)/x)*Log[1 - (I*c)/x])/c^2 + (3*a*b^2*Log[1 - (I*c)/x])/(8*x^2) - (3*b^2*(1 - (I*c)/x)^2*(2*a + I*b*Log[1 - (I*c)/x]))/(32*c^2) + (((3*I)/8)*b*(1 - (I*c)/x)*(2*a + I*b*Log[1 - (I*c)/x])^2)/c^2 - (((3*I)/32)*b*(1 - (I*c)/x)^2*(2*a + I*b*Log[1 - (I*c)/x])^2)/c^2 - ((1 - (I*c)/x)*(2*a + I*b*Log[1 - (I*c)/x])^3)/(8*c^2) + ((1 - (I*c)/x)^2*(2*a + I*b*Log[1 - (I*c)/x])^3)/(16*c^2) - (9*a*b^2*(1 + (I*c)/x)*Log[1 + (I*c)/x])/(4*c^2) - (((3*I)/4)*b^3*(1 + (I*c)/x)*Log[1 + (I*c)/x])/c^2 + (3*a*b^2*(1 + (I*c)/x)^2*Log[1 + (I*c)/x])/(8*c^2) + (((3*I)/32)*b^3*(1 + (I*c)/x)^2*Log[1 + (I*c)/x])/c^2 + (((3*I)/4)*a^2*b*Log[1 + (I*c)/x])/x^2 + (3*a*b^2*Log[1 + (I*c)/x])/(8*x^2) - (3*a*b^2*Log[1 - (I*c)/x]*Log[1 + (I*c)/x])/(4*x^2) + (3*a*b^2*(1 + (I*c)/x)*Log[1 + (I*c)/x]^2)/(4*c^2) + (((3*I)/8)*b^3*(1 + (I*c)/x)*Log[1 + (I*c)/x]^2)/c^2 - (3*a*b^2*(1 + (I*c)/x)^2*Log[1 + (I*c)/x]^2)/(8*c^2) - (((3*I)/32)*b^3*(1 + (I*c)/x)^2*Log[1 + (I*c)/x]^2)/c^2 - ((I/8)*b^3*(1 + (I*c)/x)*Log[1 + (I*c)/x]^3)/c^2 + ((I/16)*b^3*(1 + (I*c)/x)^2*Log[1 + (I*c)/x]^3)/c^2 + (3*a*b^2*Log[I + c/x])/(8*c^2) - (3*a*b^2*Log[1 - (I*c)/x]*Log[c - I*x])/(4*c^2) - (3*a*b^2*Log[1 + (I*c)/x]*Log[c + I*x])/(4*c^2) + (3*a*b^2*Log[(c - I*x)/(2*c)]*Log[c + I*x])/(4*c^2) + (3*a*b^2*Log[c - I*x]*Log[(c + I*x)/(2*c)])/(4*c^2) - (3*a*b^2*Log[c + I*x]*Log[((-I)*x)/c])/(4*c^2) - (3*a*b^2*Log[c - I*x]*Log[(I*x)/c])/(4*c^2) + (3*a*b^2*PolyLog[2, (c - I*x)/(2*c)])/(4*c^2) + (3*a*b^2*PolyLog[2, (c + I*x)/(2*c)])/(4*c^2) + (3*a*b^2*PolyLog[2, ((-I)*c)/x])/(4*c^2) + (3*a*b^2*PolyLog[2, (I*c)/x])/(4*c^2) - (3*a*b^2*PolyLog[2, 1 - (I*x)/c])/(4*c^2) - (3*a*b^2*PolyLog[2, 1 + (I*x)/c])/(4*c^2) + ((3*I)/8)*b^3*Defer[Int][(Log[1 - (I*c)/x]^2*Log[1 + (I*c)/x])/x^3, x] - ((3*I)/8)*b^3*Defer[Int][(Log[1 - (I*c)/x]*Log[1 + (I*c)/x]^2)/x^3, x]","F",0,0,0,0,-1,"{}"
154,1,51,0,0.0146102,"\int x^2 \tan ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^2*ArcTan[Sqrt[x]],x]","-\frac{x^{5/2}}{15}+\frac{x^{3/2}}{9}+\frac{1}{3} x^3 \tan ^{-1}\left(\sqrt{x}\right)-\frac{\sqrt{x}}{3}+\frac{1}{3} \tan ^{-1}\left(\sqrt{x}\right)","-\frac{x^{5/2}}{15}+\frac{x^{3/2}}{9}+\frac{1}{3} x^3 \tan ^{-1}\left(\sqrt{x}\right)-\frac{\sqrt{x}}{3}+\frac{1}{3} \tan ^{-1}\left(\sqrt{x}\right)",1,"-Sqrt[x]/3 + x^(3/2)/9 - x^(5/2)/15 + ArcTan[Sqrt[x]]/3 + (x^3*ArcTan[Sqrt[x]])/3","A",6,4,10,0.4000,1,"{5033, 50, 63, 203}"
155,1,42,0,0.0098464,"\int x \tan ^{-1}\left(\sqrt{x}\right) \, dx","Int[x*ArcTan[Sqrt[x]],x]","-\frac{x^{3/2}}{6}+\frac{1}{2} x^2 \tan ^{-1}\left(\sqrt{x}\right)+\frac{\sqrt{x}}{2}-\frac{1}{2} \tan ^{-1}\left(\sqrt{x}\right)","-\frac{x^{3/2}}{6}+\frac{1}{2} x^2 \tan ^{-1}\left(\sqrt{x}\right)+\frac{\sqrt{x}}{2}-\frac{1}{2} \tan ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[x]/2 - x^(3/2)/6 - ArcTan[Sqrt[x]]/2 + (x^2*ArcTan[Sqrt[x]])/2","A",5,4,8,0.5000,1,"{5033, 50, 63, 203}"
156,1,22,0,0.0058701,"\int \tan ^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcTan[Sqrt[x]],x]","-\sqrt{x}+x \tan ^{-1}\left(\sqrt{x}\right)+\tan ^{-1}\left(\sqrt{x}\right)","-\sqrt{x}+x \tan ^{-1}\left(\sqrt{x}\right)+\tan ^{-1}\left(\sqrt{x}\right)",1,"-Sqrt[x] + ArcTan[Sqrt[x]] + x*ArcTan[Sqrt[x]]","A",4,4,6,0.6667,1,"{5027, 50, 63, 203}"
157,1,31,0,0.0353228,"\int \frac{\tan ^{-1}\left(\sqrt{x}\right)}{x} \, dx","Int[ArcTan[Sqrt[x]]/x,x]","i \text{PolyLog}\left(2,-i \sqrt{x}\right)-i \text{PolyLog}\left(2,i \sqrt{x}\right)","i \text{PolyLog}\left(2,-i \sqrt{x}\right)-i \text{PolyLog}\left(2,i \sqrt{x}\right)",1,"I*PolyLog[2, (-I)*Sqrt[x]] - I*PolyLog[2, I*Sqrt[x]]","A",4,3,10,0.3000,1,"{5031, 4848, 2391}"
158,1,27,0,0.011758,"\int \frac{\tan ^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Int[ArcTan[Sqrt[x]]/x^2,x]","-\frac{1}{\sqrt{x}}-\frac{\tan ^{-1}\left(\sqrt{x}\right)}{x}-\tan ^{-1}\left(\sqrt{x}\right)","-\frac{1}{\sqrt{x}}-\frac{\tan ^{-1}\left(\sqrt{x}\right)}{x}-\tan ^{-1}\left(\sqrt{x}\right)",1,"-(1/Sqrt[x]) - ArcTan[Sqrt[x]] - ArcTan[Sqrt[x]]/x","A",4,4,10,0.4000,1,"{5033, 51, 63, 203}"
159,1,42,0,0.0138852,"\int \frac{\tan ^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Int[ArcTan[Sqrt[x]]/x^3,x]","-\frac{1}{6 x^{3/2}}-\frac{\tan ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{1}{2 \sqrt{x}}+\frac{1}{2} \tan ^{-1}\left(\sqrt{x}\right)","-\frac{1}{6 x^{3/2}}-\frac{\tan ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{1}{2 \sqrt{x}}+\frac{1}{2} \tan ^{-1}\left(\sqrt{x}\right)",1,"-1/(6*x^(3/2)) + 1/(2*Sqrt[x]) + ArcTan[Sqrt[x]]/2 - ArcTan[Sqrt[x]]/(2*x^2)","A",5,4,10,0.4000,1,"{5033, 51, 63, 203}"
160,1,36,0,0.0150146,"\int x^{3/2} \tan ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^(3/2)*ArcTan[Sqrt[x]],x]","-\frac{x^2}{10}+\frac{2}{5} x^{5/2} \tan ^{-1}\left(\sqrt{x}\right)+\frac{x}{5}-\frac{1}{5} \log (x+1)","-\frac{x^2}{10}+\frac{2}{5} x^{5/2} \tan ^{-1}\left(\sqrt{x}\right)+\frac{x}{5}-\frac{1}{5} \log (x+1)",1,"x/5 - x^2/10 + (2*x^(5/2)*ArcTan[Sqrt[x]])/5 - Log[1 + x]/5","A",3,2,12,0.1667,1,"{5033, 43}"
161,1,29,0,0.012381,"\int \sqrt{x} \tan ^{-1}\left(\sqrt{x}\right) \, dx","Int[Sqrt[x]*ArcTan[Sqrt[x]],x]","\frac{2}{3} x^{3/2} \tan ^{-1}\left(\sqrt{x}\right)-\frac{x}{3}+\frac{1}{3} \log (x+1)","\frac{2}{3} x^{3/2} \tan ^{-1}\left(\sqrt{x}\right)-\frac{x}{3}+\frac{1}{3} \log (x+1)",1,"-x/3 + (2*x^(3/2)*ArcTan[Sqrt[x]])/3 + Log[1 + x]/3","A",3,2,12,0.1667,1,"{5033, 43}"
162,1,20,0,0.0079356,"\int \frac{\tan ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Int[ArcTan[Sqrt[x]]/Sqrt[x],x]","2 \sqrt{x} \tan ^{-1}\left(\sqrt{x}\right)-\log (x+1)","2 \sqrt{x} \tan ^{-1}\left(\sqrt{x}\right)-\log (x+1)",1,"2*Sqrt[x]*ArcTan[Sqrt[x]] - Log[1 + x]","A",2,2,12,0.1667,1,"{5033, 31}"
163,1,22,0,0.0087961,"\int \frac{\tan ^{-1}\left(\sqrt{x}\right)}{x^{3/2}} \, dx","Int[ArcTan[Sqrt[x]]/x^(3/2),x]","\log (x)-\log (x+1)-\frac{2 \tan ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}}","\log (x)-\log (x+1)-\frac{2 \tan ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}}",1,"(-2*ArcTan[Sqrt[x]])/Sqrt[x] + Log[x] - Log[1 + x]","A",4,4,12,0.3333,1,"{5033, 36, 29, 31}"
164,1,37,0,0.0137589,"\int \frac{\tan ^{-1}\left(\sqrt{x}\right)}{x^{5/2}} \, dx","Int[ArcTan[Sqrt[x]]/x^(5/2),x]","-\frac{2 \tan ^{-1}\left(\sqrt{x}\right)}{3 x^{3/2}}-\frac{1}{3 x}-\frac{\log (x)}{3}+\frac{1}{3} \log (x+1)","-\frac{2 \tan ^{-1}\left(\sqrt{x}\right)}{3 x^{3/2}}-\frac{1}{3 x}-\frac{\log (x)}{3}+\frac{1}{3} \log (x+1)",1,"-1/(3*x) - (2*ArcTan[Sqrt[x]])/(3*x^(3/2)) - Log[x]/3 + Log[1 + x]/3","A",3,2,12,0.1667,1,"{5033, 44}"
165,1,33,0,0.036191,"\int \frac{\tan ^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcTan[a*x^5]/x,x]","\frac{1}{10} i \text{PolyLog}\left(2,-i a x^5\right)-\frac{1}{10} i \text{PolyLog}\left(2,i a x^5\right)","\frac{1}{10} i \text{PolyLog}\left(2,-i a x^5\right)-\frac{1}{10} i \text{PolyLog}\left(2,i a x^5\right)",1,"(I/10)*PolyLog[2, (-I)*a*x^5] - (I/10)*PolyLog[2, I*a*x^5]","A",4,3,10,0.3000,1,"{5031, 4848, 2391}"
166,1,39,0,0.0358367,"\int \frac{\tan ^{-1}\left(a x^n\right)}{x} \, dx","Int[ArcTan[a*x^n]/x,x]","\frac{i \text{PolyLog}\left(2,-i a x^n\right)}{2 n}-\frac{i \text{PolyLog}\left(2,i a x^n\right)}{2 n}","\frac{i \text{PolyLog}\left(2,-i a x^n\right)}{2 n}-\frac{i \text{PolyLog}\left(2,i a x^n\right)}{2 n}",1,"((I/2)*PolyLog[2, (-I)*a*x^n])/n - ((I/2)*PolyLog[2, I*a*x^n])/n","A",4,3,10,0.3000,1,"{5031, 4848, 2391}"